UNITED STATES 

DEPARTMENT OF THE INThlRIOR 

BUREAU OF RECLAMATION 

BOULDER CANYON PROJECT 

FINAL REPORTS 

PART V-TECHNICAL INVESTIGATIONS 

Bulletin 3 

MODEL TESTS OF BOULDER DAM 
UNITED STATES

DEPARTMENT OF THE INTERIOR

HAROLDL. ICKES, Secretary

BUREAU OF RECLAMATION

J OR:'! C. PAGE,Commissioner

R. F. WALTER, Chief Engineer

BOULDER CANYON PROJECT

FINAL REPORTS

PART V-TECHNICAL INVESTIGATIONS

Bulletin 3

MODEL TESTS OF BOULDER DAM

DENVER, COLORADO

1939
This bulletin is one of a series prepared to record the history of the Boulder Canyon Project, the results of technical

studies and experimental investigations, and the more unusual

features of design and construction. A list of the bulletins

available and tentatively proposed for publication is given at

the back of this report.

ii
FRONTISPIECE-BOULDER DAM

iii
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0::';::;:;~=-;~~~~~~~~~~2:;';;:;~;-:~:~~

SO' DIVERSION TUNNELS"

0, -. ---

NEVADA SPILLWAY---------

Highway

NEVADA /

Temporary outlets-4 pair 6'x7'..6"SJide gates.~ "-'--

EI 1232-.hi ,! 500 .,.

loaDI

Scale of feet

Intake towerSdm .

,--_>,~--ARIZONA SPILLWAY

"''''

''',

,,-Canyon wall

',', POWER

"

outlet works

",\ PLANT,: ,Stoney gate

;~:::::\~,.;;::-;;--i-::-~ U"

"

'

,

,:COFFERDAM

~~W

(Tunnel portal

/.'

~~,:~~,~~~~L~?~~f~~~sand and gravel

Steel

bul~head 30'Steel

\

Q

penstocks_,-

\ (\ "-'~--;;;:,

"'-, I

COFFER DAM ---:-'"

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LONGITUDINAL SECTION

BOULDER DAM AND APPURTENANT WORKS
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BOULDER CANYON PROJECT-LOCATION MAP

v
BOULDER CANYON PROJECT

ENGINEERING ORGANIZATION DURING CONSTRUCTION

ADMINISTRATIVE OFFICE, WASHINGTON, D. C.

Elwood Meacl* Commissioner of Reclamation

ENGINEERING AND EXECUTIVE OFFICE, DENVER, COLORADO

Raymond F. \V alteL_u u_u_u_u uuuuu u--m_uuChief Engineer

Sinclair O. HarpeL m uu_uuuu--- u__uu_--uAssistant Chief Engineer

John L. Savageuu u -

u--u uChief Designing Engineer

Leslie N. McClellan uuuuu-

_u uuu u_Chief Electrical Engineer

\Villiam H. N aldeLuuuu--u _u--uuAssistant Chief Designing Engineer

13yram 'vV. Steele uu _u__u_u u_u u uCivil Engineer-Dams

Erdman B. Dehler_u_u u_u__u- u--u uu_u--_u uuuu H ydraulic Engineer

Charles M. Day*uu u u--uu_u---u__uuu uuu--Mechanical Engineer

I van E. Houk.--uu---uu u_u_uuu uSenior Engineer-Technical Studies

Harry R. McBirneyuu---uu u_u u---u mu Civil Engineer-Canals

Kenneth B. KeeneL u--uu u---Assistant Civil Engineer-Dams

Harvey F. McPhaiL--_uuu u uu u u---u u_Electrical Engineer

Robert A. Monroeu__u--u uu_--uu u_uu---u Structural Engineer

Porter J. PrestOlLu uuuu_u u uu-Senior Engineer-Investigations

Howard C. Stetson__u--_u__u u__u__u- u--_Senior Engineer-Specification s

PROJECT OFFICE, BOULDER CITY, NEVADA

\Valker R. Y ounguu_u u_uu u---uu__u---u_uConstruction Engineer

Ralph Lowry u

u_u__u-_uu

uuuu__uu_-

uu--uu uuuuu

Field Engineer

John C. Pageu--u uuuuuu_u__u uu_uu--uu u u

uu--_Office Engineer

CONSULTANTS

Colorado River Board :u--uuu--u--_u--uu--\Villiam L. Sibert,* Chairman

Charles P. Berkeyuuu--u uu u--u--u--u_--u uuu uu_\V arren J. Mead

Daniel \V. Meadu_--u u_uu_uu--u_u uuu__u u

uRohert Ridgway*

Boulder Dam Board :uuuu--uuuuuu--u---u_--Andrew J. 'vViley,* Chairman

WilJ iam F. Durand_u u u--u uu uu_--uu Arthur P. Davis*

David C. H enny*uu uu--uu uuu u_u

u m

Louis C. Hill *

Concrete Research Board :---uuu--uuu--u--uu_Phaon H. Bates, Chairman

Franklin R. McMiJlan uu--uuuuuuuuu Raymond E. Davis

Herbert J. GilkeY u-_uuuu_uuu--u---uu uu_mu William K. Hatt

Special Consultants:

Harald M. 'vV estergaard u--uu--u u uu uu u

Mechanics

F reclerick L. Ransome* --u- ---u ---u

u

--

u u- --_u uu u --- ---

u Geology

Gordon B. Kaufmann u u uuuu--_u u--u Architectural Features

PRINCIPAL CONTRACTORS

General Contractorsuuuu--u--uuuuu Six Companies, Inc., San Francisco

Penstock & Outlet Pipe--uu--u--uThe Babcock & \ViJcox Co., New York

*

Deceased.

vi
FOI<EWORD

Colorado River, originating in the melting snows of the \Vyoming

and Colorado Rockies and augmented by rapid run-off from spasmodic

rains and cloudbursts over a vast arid region, has menaced life and

property in its descent to the Gulf of California since the days of the

first covered \vagon.

\Vith increased population along the lower reaches of the river

the problem of controlling the Colorado became more important. During recent years millions of dollars have been spent in mitigating the

evils of silt deposition and in protecting the highly cultivated Imperial

Val1ey lands from annual threats of inundation.

The need for a comprehensive plan of development to check the

ravages of Colorado River, to regulate its flow, and to utilize a part

of its enormous energy led, first, to investigations by the Reclamation

Service of all water storage possibilities; next, to the Colorado River

Compact, a mutual agreement for the protection of the seven basin

states; and, finally, to the adoption of the Boulder Canyon Project, as

the initial development.

The Boulder Canyon Project Act, approved December 21, 1928,

authorized a total appropriation of $165,000,000 for the various features

involved. These include Boulder Dam and appurtenant works, the

power plant, the reservoir, and the All-American Canal System. The

purposes of the project are: (1) flood and silt control for protection of

lands along the lower river; (2) improvement of navigation; (3) river

regulation and storage of water for irrigation and municipal use; and

(4) development of electric power for domestic and industrial purposes. The project is self-liquidating, largely through contracts for

disposal of electrical energy. It was constructed and is being operated

under the supervision of the Bureau of Reclamation, United States

Department of the Interior.

Boulder Dam is located on the Nevada-Arizona boundary near

Las Vegas, Nevada, at a place where Colorado River has carved a deep

gorge between towering rock cliffs, known as Black Canyon. The dam

is a concrete arch gravity structure with a maximum height of 726

feet above foundation rock, a maximum base thickness of 660 feet, and

a crest length of 1,244 feet. The dam and appurtenant works contain

4,400,000 cubic yards of concrete, of which 3,250,000 cubic yards were

required in the dam.

V11
During construction the river was diverted through four 50-foot

diameter, concrete-lined tunnels, two on each side of the river. These

tunnels were subsequently plugged near the upstream ends. The spiIlways, each of 200,000 second-feet capacity, are connected through

inclined shafts to the two outer tunnels. A. 30-foot diameter steel

power penstock is instaIled in each of the inner tunnels. Discharge

from the reservoir is controIled by cylinder gates in four intake towers,

founded on the canyon waIls near the upstream face of the dam. Four

30-foot steel penstocks, connected to the bases of the intake towers,

conduct water to the power plant and to the outlet valves for release

of flood, irrigation, and domestic water supply when the power plant

discharge is insufficient for such purposes. The reservoir above the

dam is 115 miles long and has a capacity of 30,500,000 acre-feet, the

equivalent of two years' normal river flow.

The power plant is in a U-shaped, reinforced concrete structure,

over 200 feet high and 1,500 feet long, located immediately downstream from the dam. The plant is designed for an ultimate installation of fifteen 115,000 and two 55,000 horsepower units, making a total

installed capacity of 1,835,000 horsepower.

The All-American Canal, located near the Mexican border, will

carry water to irrigate lands in the Imperial and Coachella VaIleys.

The canal proper, with a diversion capacity of 15,000 second-feet, is

the largest ever constructed for irrigation purposes in America.

The entire Boulder Canyon Project is characterized by the

extraordinary. The height and base thickness of the dam, the size of

the power units, the dimensions of the fusion-welded, plate-steel pipes,

the novel system of artificially cooling the concrete, the speed and

coordination of construction, and other major features of the project

are without precedent. The magnitude of the undertaking introduced

many new problems and intensified many usual ones, requiring investigations of an extensive and diversified character to insure structures

representing the utmost in efficiency, safety, and economy of construction and operation.

The major credit for the conception of the project and the initiation of investigations leading to its adoption must be given to the late

Arthur P. Davis, former Director of the Reclamation Service. Dr.

Elwood Mead, Commissioner of Reclamation during the greater part

of the construction period, passed away January 26, 1936, four months

after the dedication of Boulder Dam. In commemoration of his untiring services on the Boulder Canyon Project, the reservoir created by

the construction of the dam has been officially named "Lake Mead".

viii
CONTENTS

SECTION PAGE

Introductory statement "' 0000."

00 0... ii

Engineering organization during construction u u. vi

Foreword 0000" 00...0.0000.0000

00 00 00 000000...00.00..".00 00"" vii

Contents 0000"""':0000 0.."..00 0000"'.."''''''''' 1

List of figuresu u

"''''0000''.''.00.'''''.'''.'''.'''.''.''' 00.0.."."'00"00".."'."'." 11

List of tables... 0000."0.","'.00000000",.."'."'00...00"'''0000''0.00 00'''''00'''''

17

CHAPTER I-INTRODUCTION

1 General . 0 00 ,,""00,,"".00

2 Scope of Bulletinuun..n nu nn...u n nn...u......

19

19

MODEL THEORY

3 Model requirements .".00.

.",,,,"..000000.."0000 00.00.0000.,,00

"'..

4 Similarity relations 0 '" 00 00.".".

0000 20

000000 21

EARLY MODEL TESTS

5 Stevenson Creek modeLm. nnn n...m n nu n. 22

6 Gibson model testS n..h.nm n h u.nnnn n"'..."'n..u...n. 22

INVESTIGATION OF MATERIALS

7 Preliminary tests 00000000" 00... ".",00...00... umn nu 23

8 Plaster-celite materials .n.nn u m ". 24

9 Rubber and litharge materiaL 25

BOULDER DAM TESTS

10 Plaster model tests nn

00..,,00...00...00 00...00. 26

11 Rubber model testsnu u. 00.".0000 .0000 00. un 27

12 Acknowledgments "'.00 00",,,,."...00,,""..0000

0.00

00"""''''.'''''''''''''

28

Bibliography nn...n...uun...h...'" "'...00."."'.000000 ... 28

CHAPTER II-INVESTIGATION OF MATERIALS

INTRODUCTION

13 Purpose of tests n

0000...00.0000 00." 000000. 00

00""00 m..."'."""'.

31

14 Specimens "'00"'.""."'."

00"..00.0

00.0. 31

15 Testing apparatus 0000 000000.00 "

00..00.0..0 "",,,,,,,,0000.. 00...0.."00 32

16 Scope of investigation...u h h.u.u u n.u n ".h.""U" 34

1
2 MODEL TESTS OF BOULDER DAM

PRELIMINARY EXPERIMENTS

SECTlOX

17 Tar, pitch, and resin.h..h.

18 Sulphur and celite ..h...h........................

19 Linseed oil

mixtures""""'''''h'..''''' ... h. ..hh.

20 Undersanded concrete "h' uh.................

21 Cement-asbestos sheets

""'''''h..

......

22 Rubber-aggregate concrete

"""""..h """''''..h ''''" 23 Hard rubber h ''''''''''''.....

24 Cement and plaster of Paris..

25 Cement or mortar and asbestos..

26 Cement and celite....

27 Cement, asbestos, and celite.....

28 Plaster of Paris and asbestos.

29 Plaster of Paris and celiteuh"""

PAGE

--U'

' "h U

"""""""""

34

34

''''..h.

35

35

35

35

35

... 36

36

m 36

37

... 37

38

-

un---h_----

u..-----

COMMERCIAL BUILDING PLASTERS

30 Characteristics ''''..h.................

31 Certainteed plaster of Paris........

32 Red Top quick-set plaster....

33 Red Top slow-set plaster......

34 Retarders.. ...................

35 Sunflower molding plaster..............

36 Ideal finishing plaster.."h"'"

37 Acme finishing plaster"'h''''''''''''''''''

38 Acme plaster, celite, and lead......

40

41

41

... 41

... 44

... 44

46

50

51

TESTS OF RECOMMENDED MIX

39 Recommended mix ....

40 Shrinkage of recommended mix """"u".....

41 Workability of recommended mix......

42 Bond at metal insertsu ... .h..''''.. ........................

43 Evaporation rates ..

44 Plotting test data......

53

56

56

62

64

67

CHAPTER IU-PLASTER-CELITE MODEL AND

MATERIALS TESTS

45 Design of mode!..... ".. 71

CONSTRUCTION OF SUPPLEMENTAL BASE

46 Method of construction..........

47 Form for casting canyon walls..............

... 74

74
CONTENTS 3

FORMS FOR MODEL

SECTIO:-!

48 Necessity for wooden forms-m m mm49 Anchors for deflection rods m---...--

PAGE

n"" u."-- 75

77

CASTING THE MODEL

50 General procedure _m m_"_-

51 Installation of thermocouplesm52 Completion of the modeL--------- --------------.....

79

---

79

80

PROPERTIES OF MODEL MATERIAL

53 Concrete base m--- 81

54 Special testing apparatus-- _m_mm" 82

55 Compressometers

--

82

56 Lateral extensometers _m_m m 86

57 Testing machines m-

---

_mm m- m m" 86

58 Grips and strain metersm - m m mmm "--"-- 90

59 Apparatus for torsion tests-m- -m m" "'--"--- 90

60 Apparatus for flexural tests m m__-m 93

61 Methods of plotting mm m_--

94

62 Compression tests _--m _m--"m--m--- m 95

63 Tension tests m-- m--m m m "--m"- 97

64 Torsion tests m- m_"--mm "'''---'' ''' -

98

65 Flexural tests

m_-"'--"''' ''''m_''''--_'' -

m__m --- 99

66 Plastic flow testsm mm "-- 102

67 Coefficient of expansion _mm--" "" _mmmmm___mm 105

68 Unit weight m_-

_mm m 108

69 Average results m m__m- 108

70 Effect of age on plaster_-- _--m 108

SUBSEQUENT INVESTIGATIONS

71 General "--"_m----

72 Segregation mm_..m --_"h mm h_--_--

73 Recommended procedure m- m

_m

"_m--m

74 Isotropy m h_mm

m_--h_--m m "-

109

109

109

110

CH/\PTER IV-PRELIMINARY TESTS OF

PLASTER-CELITE MODEL

TESTING PROCEDURE

75 Loading the modeL-------

7t; Conduct of tests_...........--

mmm--m --_m_m_m--"'-- 115

m m""- m m_,__,m_"" 118
4 MODEL TESTS OF BOULDER DAM

SECTION PAGE

77 First deflection measurements..m -"-- 119

78 Movement of unsupported base m m-.. 119

79 Deflection of supported base m m m_--" m "--"

122

ALTERA TIONS TO MODEL

80 New mercury bag m " m81 Revision of instrument standm m h mm---m--------..----..

82 Loading canyon walls _m m_mm-- 124

124

124

ADDITIONAL TE'STS

83 Movement of base m "--"--- 125

84 Tangential deflection measurements---m_m.. m m--" m m 127

85 Measurements of twists and strains m 128

86 Elastic conditions of modeL 129

CHAPTER V--DEFLECTIONS, STRAINS, AND STRESSES

RADIAL DEFLECTIONS

87 Normal load tests _mm "-- 131

88 Partial load and overload tests m

m 137

TANGENTIAL DEFLECTIONS

89 Methods of making tests m m-__m -

90 Results of tests m m_--m..

"

137

m 142

SLOPE DEFLECTIONS

91 Apparatus " - m m_--m

142

92 Principle of operation m m m-

- mm 146

93 Results of testsm ,," ""_m mmm m "' m_- 146

MATHEMATICAL BASIS FOR STRAIN MEASUREMENTS

94 Stress-strain relations 0 " "0.--",,-_0.-

" " "

m--"-m_m mm_--m- 150

95 E<Iuations for principal strains_h---h "---" " h---" hm--m..- 151

96 Stress-strain equations _0._0 0 "--0.-- ..h--h--m m_m" ""_h 151

APPARATUS FOR STRAIN MEASUREMENTS

97 Strain gages 0 .._hm__h m "h m-_m--"h-

"

0.-_0 153

98 Mounting strain gages h--m m_"--"---" h 154

99 Gage lines m---m_--h h h m hm-_h " hm_m h

154
CONTENTS 5

RESULTS OF STRAIN MEASUREMENTS

SECTION PAGE

100 Arch strains _h_h_h

101 Cantilever strains _h_h102 Diagonal strains h_'-

-hh.. 155

_hh, hh_h

,,---h_hh_- 159

159

STRESSES COMPUTED FROM STRAINS

103 Arch stresses .h_hh---hh

h- h hh hh---hh,h_h h h 159

104 Cantilever stresses

h_'h--" hh -

169

105 Horizontal shearing stresses "__" h__hh- hhh h_hh---

__h h 173

106 Principal stresses ---hh_h hh h_.h hh.h_"h- h",,_h h """""---h 173

CHAPTER VI-MISCELLANEOUS TESTS

SPECIAL DEFLECTION TESTS

107 Crown cantilever movementsh..hhh 181

108 Deflection of interiOLh__h-_h h hhhhhhh---h- ---h_" 185

109 Cantilever curvature at downstream facemhh hhhh_h hhh__h h__mh 185

FLOW TEST

110 Plastic flow h,,_h_hhh

h---hh"" hhm h---h_h_hhhhhh--

111 Calibration of instrument stand-_"hhhhh"h'_h

112 Procedure

---

h '__'__h_-"---

---" " "00 '-- ---------- 113 Results of flow tesL hh""h--'_h---h_'h

h_h h_------

114 Condition of modeL_hh h_.h---h__h_-

115 Effect of cracking 'h_hh---'h h_hh_h_h__hhh_h

h'

186

---

187

---

187

190

190

h h"_'h h 191

TEMPERATURE TESTS

116 Purpose of testsh- __h_hh h_h-_,_hhh _-hhhhhhh---h__hh-- "'_h hhh__h- 195

117 Temperature control

- -

_h___h hhh-m_h_"hh__h

00"" 00_"""" 196

118 Construction of jacket

h hh hhhhh hhh' h h_h hhhh

198

119 Equipment hhhh_h h"h"h

00'_" 00--- h 201

120 Cooling test h h__- h'

201

121 Results of cooling test _hh h___h__hh 203

122 Heating test --h.h_h..hhhh

---h hhh"__h--hhhh_,,h 206

123 Results of heating test 213

124 Condition of modeL

h---h---hhhh h---h_, 213

125 Effect of cracking h__-mh--- h--hh__-h_-_hh h_h-h_h..hhhh 213

TENSION AT DOWNSTREAM FACE

126 Slots in tension areahh---h- __hhhhh_h___h h_h_h h" h

--.

218

127 Radial deflections ",,_h hh'_- ___'h 221

128 Slot openings due to load h_h h "h_h_hhhh_,_- 221

123 Slot openings due to tloW.".""'h"_''''''''''''.'' ''...'''''''''''''''''''''''''''''...''''--''''''.'" 222
6 MODFJL TESTS OF BOULDER DAM

CHAPTER VII-TRIAL LOAD ANALYSIS OF MODEL

INTRODUCTION

SECTION PAGE

130 General __-om

131 Data and assumptions _--m_mm_--_----

132 Cantilever elements

-

_m--m h_-- 0000------------------

133 Arch elements _m---

---

225

00 226

m 227

---

229

RADIAL ADJUSTMENT

134 Procedure

-

m_--_--

135 Distribution of load__-----_------

--nuu.--......... 231

--00 234

TANGENTIAL ADJUSTMENT

136 Tangential arch deflections--h---mm m----

137 Tangential shear loads m m----_----

-" n

n_- 234

235

TWIST ADJUSTMENT

138 Twist loads

h m139 Procedure

-----------------

140 Additional adjustments 00 00

__n.."' U'-U-.h_-

-

237

238

--

--'-._n_n..u---.-- 238

RESULTS OF ANALYSES

141 Stresses and deflections---------

142 Comparison with experimental stresses u---------------

]

43 Comparison with measured deflectionsm_hm__m --00 0000-------

-

240

m_-- 240

--00 248

CHAPTER VIII-INVESTIGATIO:NOF RUBBERLITHARGE MATERIAL

144 Introduction -m hh --hh m ..........--------....---........._---- 249

STRESS STRAIN RELATIONS

145 Characteristics of materiaL hh h_m --00_---------------

146 Notation hm m_h--

-----------------

147 Elastic symmetry 00-- m_----

148 Elastic constants 00 _m_m mh--

149 Volume modulus

- mh hhm

150 Axis of symmetry

-- mmhh__hh_h_--____--

151 Isotropic conditions in two directions h_--

249

250

251

253

0000 254

00--

---

254

m 255
CONTENTS 7

ELASTICITY TESTS

SECTION PAGE

152 Specimens 00 00 oOOUOmOmhunuou

0 unununUOhomUOnmomOomuuow 257

153 End conditions mnUOhnu

UOhOOhmomuu numOUnuomoOOUOnmmmOnmwmOUnUu 258

154 Compression tests 000000000000000000

mnmomOOu_hnomUhomnu_nOnommOomomno 259

155 Tension tests nmOhmhoUUhh",uumu

UOnUO_hhomnUUhomu_hWmnooo_u- 262

156 Torsion and flexure testsnuuu oomuonuumouounnOmom_whomhnwmohnUmonnuuom 265

ELASTICITY DATA

157 Elastic constants nnUUOOhhnhnuUh...uomhouuummnnWhmomonmmhmnouunnumu__ou 266

158 Changes in dimensionsommohnmoo_uouomoumonuuhnnmu UhoonU_hmmmOnmOu- 267

159 Plotting test dataohono_nnmum ouunm_mnmomooomhonmUhmmnonmomnnwmo 268

160 Consistency of results U_mo_muo

umnoumnmomUOOUUOhmnnuOh___nUhUumOm- 272

161 Computed volume modulusnohn_mouhnuoho oohmnOUhuuUUouWnmhnumunhumhUU 274

162 Discussion of resultsuhnuon_mou oum_mommommUOU_hmoumoon_hOhOOm- 275

163 Conclusions omn_ouOUhUhho_onwmooomhOOOUhumnoun_nmOW_hUUhom_uno 000000000-276

THERMAL EXPANSION

164 Specimens and apparatuSm_nmUhOOUnmOU_hOUUU___Ohnn_nU-mh_mh_mOU_hUm- mnu 277

165 Determination of coefficient

mmhum_unnm_UOOh_mUU_hnw__mmUh-m_h_uonu

000 277

CHAPTER IX-CONSTRUCTION OF RUBBERLITHARGE MODEL

MODEL BASE

166 Reconstruction of testing piLmuo_onnn_nnmm_uu_hmuw__w_h_uuuuuunn_h_m_hun 279

167 Boundary of supplemental baseuhumuu- nn_nmh__nu n_mOh-u__nnmmonn- 279

168 Reservoir m_--U _0 0

n_U m--_W_n--_U_n

0_- mn-n_UOOm_hu m___h U_nUO_- 279

169 Laying rubber-litharge slabs_m_muuh_mn_m_muuhmnmuuumn_uhnnu_unmmom_un 280

CONSTRUCTION OF MODEL

170 Plans for modeL_h__hnumn_mouhmoh__m__h_h__nn -mmhmm_Uhm_mmh_U-Wuummnuu 283

171 Installation of apparatUShnhnUOm_ou-u U umn- _hm_wmoU_-_Uh_u 284

172 Waterproofing the upstream facehm_n-m-

-

mhnnO-mUh_mnm_UU_-Uh_U 285

173 Reference structure W_WWuOnonUn_omm-nm_Uhmm_o

_mum-mhnUh_UUhO__h_w_u 288

CHAPTER X-DEFLECTION MEASUREMENTS

RADIAL DEFLECTION TESTS

174 Apparatus m_hnu u_mou_n__u -m_m-nnhmu UOhuoum_hmhunWOhUhm_mnun-n__m_mo 291

175 Test procedure m-mO-Uhu-h__nm-__Uh_hmuUhOm_m

-

_mw___mumuumOnm-UUn 291

176 Full load defiectiOllS""""-"""'",,,,,,,,,,,,,_oo,-,,,,ouohu n-O OUhu_-mUh o-m-_oo_ou_- 294
8 MODEL TESTS OF BOULDER DAM

SECTIOX

PAGE

177 Squeezing of modeL 0 ", 294

178 Partial load deflections ",

297

179 Consistency of repeated tests

297

TANGENTIAL DEFLECTION TESTS

180 Installation of micrometers 0.."",.",

00.

"'.

297

181 Procedure 299

182 Full load deflections"""'h"""'."'.". 0..""'."""". 300

183 Partial load deflections ..."",.",..." "",

...0 ""'."".""." 302

SLOPE DEFLECTION TESTS

184 Apparatus ",..

185 Procedure ,.............

186 Full load deflections n.

187 Partial load deflecticns...

"""."".."''''00..''''''' '''.''''''''...'''.

303

, 303

303

305

VERTICAL DEFLECTION TESTS

188 Effect of squeezing..""...""h.""".. 0 '" 305

189 Apparatus "''''''''00''.'''.'''.''''''...'''.'''''.'''''''..0.''''''

305

190 Results , ."'.""''''''''.'''..'''.''''.0.''.''''''''.''''''..'''.''''' 307

CANYON MOVEMENTS

191 Downstream movements ........

192 Spreading of reservoir walls...............

193 Spreading of downstream walls.........

194 Changes in chord lengths.....................

195 Resultant movement of modeL...

196 Changes in shape of modeL......

0 311

..h "'."'."''''''..'''''''''''.'''' 314

...0.. 315

, ". 315

316

h h "..."." 320

CHAPTER XI-STRAINS AND STRESSES

197 General

""",."'00

0 0 ""'. 321

APPARATUS

198 Gages at upstream face 321

199 Gages at downstream face ",

324

200 Directions of measurements",...".".."."""..""".","'.."..."'."."h"."'."'..'" 325
CONTENTS 9

WATER LOAD CONDITIONS

SECTION PAGE

201 Water load strains...u.mhu.u_m- h_u.m_UUh- hm_mh..m-U.h_hm. 326

202 Arch strEsses m m-- 0. __hhhU.h__m h.U_-mm.u--hU..u --h.u.m--_'U'_h. 327

203 Cantilever stresses _h_m-h_m _mh_hhhh_mhhmhhh.hhmhm _mh_UUhmmuu 331

204 Horizontal shear __hh__mmmm_h___mhm_,h__hmh_.hhh_hhhmh_hhU.h_h..-mUhhhmh_mm 331

205 Principal stresses mm_mh_-Uhu m -h..u-mhUUUhh_mhhUUhm_hmmh__,.U 331

DEAD LOAD CONDITIONS

206 Strain measurements 0._0. h_,h,--h.mm

207 Dead load stressesm-_h-

-

u.h'---m_u_mUhhU_hm-

_mhhu..m-.Uhh_mm___h__- 336

hhh_hh_hhmh___Uh- 336

CO:vrBINED LOAD CONDITIONS

208 Combining strains 0.0.0.-0. h_hh_m_mh_'h.mh__h..hh_--hU"h.-hhh_mh 342

209 Arch stresses hhhhm-hm___hmh_h_m__- _hmhmmm.mhhmm__,h 342

210 Cantilever stresses hmhm- h_hhh_._mhh_h_m h...hh-um_._U U.h_u_m 342

211 Horizontal shear _h_m-hhU Uhmh_h_--hh__m-hh-m_h _m_.-um_h"hh_hm_. 346

212 Principal stresses 0.0.--

-

hhum_mh__h h_.u.m-mh_m_m___UUh 346

CHAPTER XII-FLOW AND TEMPERATURE TESTS

FLOW TEST

213 Effect of flow 0.-

hh-_h_-hm_mm_hh h

u--u _h_mhm-mhu_mmhm_"h"''''U 349

214 Method of making flow tesLUh__hhUhhmmh.hh_h_.h _mmmhmh__mhm _m 349

215 Results of tesL-h.__mmmmh _h_.-u.h_m-mmm,_,hh_h_hh.hmhhUUhUhh 350

216 Condition of model

_0..-"'0.

0. Uhhh_,h_mhm_uU.hm_U,hhhhu.hmhmh- hh mh_- 353

TEMPERA TURE TEST

217 Purpose of test--

218 Procedure '__h_m_-uu-

-

219 Initial temperature conditionsm_-

220 Conditions at end of one daYh_mh

221 Conditions at end of two dayshh---

222 Conditions at end of four daysmhhhh

223 Conditions at end of twelve daysm-h--

224 Conclusions Uhmhh_h h_hh_mh_Uhh_mh_m_'hhU

355

___hmm_h.h_m__- -__mmm_um_.-'U_h"'hm_mu 355

-0.0.0.0.0._0 0.0.0.'0.- --h_m_mhm_mh'h 356

-h__hhumh_.h_.UUhhmh.h.u

-h_mh- 356

mh, h_,h- mhh_mh...hhhmu 361

--_, h " m hh h_hh_0. 361

_h-mhhmh_mh_h_mm__,_hU-__, 364

m 'hm__um'hh"__"'hm 364

CHAPTER XIII-TRIAL LOAD ANALYSIS

OF RUBBER-LITHARGE MODEL

225 General ,. - ...

.''' --. u ----.'-."'."""'''..-' '

371
10 MODEL TESTS OF BOULDER DAM

PROCEDURE

SECTIOX PAGE

226 Data and assumptions m- --hmm--m_-- m_mm 371

227 Cantilever elements h m--_m_mh m h--m m__hh m 372

228 Arch elements h m m

h- m--m--mm--_m--m_h--_h_m_h_--"'-- 372

ADJUSTMENTS

229 Radial adjustment h_u_--_----------

230 Tangential adjustment m----_--

231 Twist adjustment m----

232 Vertical adjustment

m_m--m_"'_mm_m

233 Sequence of adjustmentS m m--m

m

375

m__m 375

m--_u _m m_m 378

378

"'hm--m__"'h_--m m--_m-- 381

RESULTS OF ANALYSIS

234 Computed stresses h m h--mm m h

m_h.h--h- m 382

235 Experimental and analytical stresses mm h---mm m h- 385

236 Comparison of deflections _m -m_hm_--m_-m 395

237 Conclusions m m- m "'hm- m__h mm

h- m--- 395
LIST OF FIGURES

FIGURE PAGE

Frontispiece -m h- - Hi

Boulder Dam and appurtenant works h iv

Boulder Canyon Project, location map m

V

1 Plaster specimen ready for testing 32

2 Instruments for measuring deformations of specimens 32

3 Apparatus for flexural tests on beams h 33

4 Stress-strain diagrams, Red Top slow set cylinders--u m-- 42

5 Plaster cYlinders and beams drying in the sunshine 43

6 Stress-strain diagrams, Sunflower plaster cylinders 45

7 Stress-strain diagrams, Ideal plaster cylinders 47

8 Stress-strain diagrams, 2 by 4-inch Acme cylinders 48

9 Stress-strain diagrams, 3 by 6-inch Acme cylinders h- 49

10 Load-deflection diagrams for Acme beams 50

11 Typical shot-loaded cylinders 51

12 Stress-strain diagrams, shot-loaded cylinders 52

13 Stress-strain diagrams, recommended miL 54

14 Load-deflection diagrams, recommended mix--- n 55

15 Stress-strain diagrams, reduced mixing water n -- 57

16 Stress-strain diagrams, reduced mixing water h nh 58

17 Load-deflection diagrams, variable mixing water 59

18 Shrinkage beam and 3-foot cubical block-- 60

19 Keyways in plaster-celite beam-m --nn n- 61

20 Keyways in plaster-celite beams n61

21 Typical failure of plaster-celite beam 0 62

22 Keyways in plaster-celite beams 63

23 Beam showing bond between layersn n h 63

24 Failure of plaster-celite beam u

n 64

25 Testing bond between plaster and inserts n 65

26 Specimens before and after testing bond-- 66

27 Set of evaporation test specimens 66

28 Evaporation rates, plaster-celite specimens 0

nn n

67

29 Method of plotting compression data n 68

30 Method of plotting flexural data h n---n69

31 Boulder Dam, plan and section, study 32-B h_n 0 0 72

32 Model dam and testing piL n n 73

33 Keyways in supplemental base---h --n m n---n 74

34 Form for casting canyon wal!sn u n--m n 75

35 Lowering form for canyon waIls n n-n-n 76

36 Downstream form before excavating abutments-- 77

37 Anchors for deflection measurements 78

38 Forms prior to pouring first layer of modeL--- 79

39 Model poured to elevation 950 m n__-

80

11
12 MODEL TESTS OF' BOULDER DAM

FIGURE PAGE

40 Dimensions of model as constructed..

41 Compressometer for 2 by 4-inch cylinders..

42 Compressometer for 3 by 6-inch cylinders..

43 Lateral extensometers for cylinder tests..

44 Direct load apparatus for materials tests..

45 Compression machine testing a cylinder.

4,6 Tension testing machine in operation..--...

47 Compressive flow testing machine..

48 Tension grips and 8-inch strain meter..

49 Design of torsion machine..

50 Torsion testing machine in operation..

51 Apparatus for beam tests.. ..

52 Flexural flow tests on beams...------......

53 Method of plotting compression tests..

54 Stress-strain diagrams for compression tests..

55 Method of plotting tension tests..

56 Method of plotting torsion tests..

57 Method of plotting flexuraltests..

58 Typical tension, flexure,and torsion tests..

59 Typicalflowin compression

------

60 Comparison of flow data, compressicn tests.

61 Comparison of flow data, tension tests..

62 Comparison of flow data, flexural tests..

63 Typical flow in torsion.

64 Apparatus for measuring thermal expansion...--

65 Thermal expansion test, plaster-celite beam..

66 Test of cylinder taken from modeL.

67 Compressed-air loading machine h--"'h'''--'

68 Results of tests for isotropic properties..

69 Rubber bag for loading modeL--...

70 Mercury supply tank and piping..

71 Details of instrument stand..

72 Gages for radial deflection measurementS h..

73 Deformation of base as originally constructed

74 Gages for measuring movement cf base.........

75 Deflection of base with downstream supports..

76 Model after altering canyon wallsh--'"''

77 Movement of foundation due to mercury load..----.

78 Measuring tangential deflections of top arch..--

79 Measuring tangential deflections at downstream face.

80 Average radial deflections of arch elements------......

81 Average radial deflections of cantilever elements....--..

82 Radial deflections of arch elements, test 85--............

83 Arch deflections, load at elevation 1232"--""--'--""--"'--'''''h..m''''h--

84 Cantileverdeflections, loadatelevation1232 0 0..

'''--''''''''m''--'

85 Arch deflections, load at elevation 1100--h h"""",,' h hmh--

86 Cantilever deflections,load at elevation 1100 0 --"""h...........

87 Arch deflections, load at elevation 1400 0.0."'--"--''' '

""--,,, 0.--.......

88 Cantilever deflections, load at elevation 1400h"'''h--'''''''' hm'''--h''

81

83

84

85

--''''''' ''''

87

88

88

89

91

.0 "" 92

93

0.","0 94

94

95

96

97

99

100

101

n "" """ 103

103

--

104

104

105

106

107

.."" 0.0.. 110

'--'--" '''''""

111

112

--

115

116

117

118

120

121

--. 123

125

126

127

"h... 128

'. 132

133

134

135

136

138

139

140

141

Unun"'

O

----------------
FIGURES 13

FIGURE PAGE

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

Tangential deflections, load at elevation 1400 143

Tangential deflections, load at elevation 1232 144

Tangential deflections, load at elevation 1100 145

Slope deflections, load at elevation 1400 147

Slope deflections, load at elevation 1232 m m m 148

Slope deflections, load at elevation 1100 m 149

Gages set to measure cantilever strains 154

Arch strains, load at elevation 1400 m 156

Arch strains, load at elevation 1232

m

157

Arch strains, load at elevation 1100 m 158

Cantilever strains, load at elevation 1400 160

Cantilever strains, load at elevation 1232 m ""--" 161

Cantilever strains, load at elevation 1100 m

162

Locations of diagonal strain-gage lines m 163

Arch stresses, load at elevation 1400 166

Arch stresses, load at elevation 1232 m m m 167

Arch stresses, load at elevation 1100 168

Cantilever stresses, load at elevation 1400 mm mm 170

Cantilever stresses, load at elevation 1232 mm---171

Cantilever stresses, load at elevation 1100 m--

mm m

172

Shearing stresses, load at elevation 1400 m 174

Shearing stresses, load at elevation 1232 m 175

Shearing stresses, load at elevation 1100 m--- 176

Principal stresses, load at elevation 1400 177

Principal stresses, load at elevation 1232 m--- 178

Principal stresses, load at elevation 110O w 179

Deflection of crown cantilever, load at elevation 1400m 182

Deflection of crown cantilever, load at elevation 1232 m m..m 183

Deflection of crown cantilever, load at elevation 1100 184

Deflection of interior of crown cantilever 186

Arch deflections due to flow m188

Cantilever deflections due to flow 189

Cracks at upstream face--

--- -- 19'1

Arch deflections after cracking, load at elevation 1400 m 192

Arch deflections after cracking, load at elevation 1232 193

Arch deflections after cracking, load at elevation 1100 m mm 194

Upstream part of model jackeL--- 196

Downstream part of model jackeL..m 197

Downstream part of jacket being installed-- 197

Jacket in place over modeL---m m 198

Model ready for temperature test 199

Locations of thermocouples

" m m

200

Temperature measuring apparatus 201

Locations of thermometers

-- -

202

Temperature record during cooling tesL

" m

204

Temperature record during cooling test, continued 205

Arch deflections due to cooling m---m m--- mm 207

Cantilever deflections due to cooling--- m

208

Arch deflections during recoverY__m m" m_--" mm 209
14 MODEL TESTS OF BOULDER DAM

FIGURE PAGE

138 Cantilever deflections during recoverY hm..mh.

'h.'hmm mh mm...m. 210

139 Temperature record during heating tesL m.'hmh...

" '

211

140 Temperature record during heating test, continued 212

141 Arch deflections due to heatingh hmmh...m..h..h .m'''''''''h. 214

142 Cantilever deflections due to heating.m""hm 215

143 Arch deflections during recoverY hmm h...h h..hm..hh h h h... 216

144 Cantilever deflections during recoverY 217

145 Location of slots in tension area "..h...m '.h

'

218

146 Depths of slots in tension area.m.. ".h h",,,,,,,"..h

'

219

147 Opening of slots 1 and 3.h... ,," h mh...h..h .m'.h'''''..h.h' 221

148 Opening of slot 2h hm..m. ..hmm""".. .. ...m 222

149 Change in slot opening due to flowm. m'm..'h "".h."h..m..'",,,,,,,,,' 223

150 Cantilever section K.m... ',' m""h " mm mhm."hmh

226

151 Typical unit cantilever loads..m'''''''h'''' "'h h m..m 228

152 Typical unit arch loads..

"

m "m h...'...h 230

153 Radial adjustment at arch elements.m "..h"""..h h'h 232

154 Contact of arch and cantilever at abutmenL ".h..mh'..h. m...h.' 233

155 Tangential adjustment at arch elements""h m

"'''h..'''''..m.. 236

156 Twist adjustment at arch elements m...m"h"'" ".hm

h h 239

157 Results of trial load analysis...mmmh.m m ,'h'...hm"h",""''''h 241

158 Experimental and computed arch stresses.. ... 242

159 Lines of equal arch stressm

..mm"'m'"'''h''''''''h..'''''''

.m 244

160 Experimental and computed cantilever stresses.

"" '

245

161 Lines of equal cantilever stress...m m...m m'"hh''''' .m'm""'h.m'h'''''''hm.. 246

162 Computed and measured deflectionsh""'h m..m.

'''''''h h

247

163 Test of rubber-litharge prism showing end restraint 258

164 Test of rubber-litharge prism with ends greasedm m m"h""""""''''''' 259

165 Compression test, specimen A loaded in X-direction"'h"'" '...' 260

166 Compression test, specimen A loaded in Y-directionm'h"""" 261

167 Compression test, specimen A loaded in Z-direction'h'" 262

168 Compression test, specimen B loaded in X-direction""h'"'''''h''''''''''''''''''''''' 263

169 Compression test, specimen B loaded in Y-direction m.m 264

170 Compression test, specimen B loaded in Z-direction "h "' 265

171 Compression test, specimen C loaded in X-direction"'h"'h' ..h"...h.."'.h.m..' 266

172 Compression test, specimen C loaded in Y-directionh'''''' ''''.h... 267

173 Compression test, specimen C loaded in Z-directioll.. m...h"...h.h' 268

174 Results of tests on specimen D h...m h..h.h"""' hh..h.. 269

175 Results of tests on specimen E.. ''''''''''''''''''''h.'m'''h'''''''''''h...m'm '""",,,,,, 270

176 Torsion test on specimen D m...

mh.m,,''''..h'''','

272

177 Torsion test on specimen E m"'"'h''''''''''''''''''''' h'''h...hm 273

178 Flexure test on specimen F m "h"""'''.h.

m'm""'h..m'

274

179 Reconstructed testing piL h m"'''''...h..m.h m m h 280

180 Testing pit, model, and supplemental base. ..h"h..mm.' 281

181 Constructing the supplemental base...h h

mh."'''''"

282

182 Supplemental base built to elevation 505h h... m h" h..h'h.m.h.h 283

183 Plan of Boulder Dam, study 37h m hm. m.m''''''''''''''hh''''''h 284

184 Dimensions of model at crown section.h.h h h m m.h...h. "'.h" 285

185 Abutment excavation lines at Boulder Dam.. ".' 286

186 Model and canyon built to elevation 595 h m"h..h""...h..m'..h..,- 287
FIGURES 15

FIGURE PAGE

187 The completed rubber-litharge modeLm-uuu_mumuuum_um-hh---h_-_h 288

188 Reference structure for deflection measurementsu _mm-h__Uhm_hm 289

189 Inserts for deflection measurementsu m_--mU hhUUuu_mm-h_hmh_ummh 292

190 Typical arrangement of gagesm_m_u_uu mum_mUU_UUh- UU-_Um_m- .um- 293

191 Radial arch deflections, load at elevation 1232_hmmmhhmu uhh mummhh 295

192 Radial cantilever deflections, load at elevation 1232m__muu__uhh_uummumh 296

193 Apparatus for measuring tangential deflectionshh"'__-'hmuu Uh_humuhuhh 300

194 Tangential arch deflections, load at elevation 1232uuuu-mu -UU_h_uuhhm-hh 301

195 Slope deflections, load at elevation 1232---humhh mumm_u__umm- 304

196 Micrometers for measuring vertical deflectionsu m__'hm__m h 307

197 Dial gages for measuring vertical deflectionsm.uuuuuu_h-_h- 308

198 Vertical deflections of arch elementsuu_hmhhhu__mmum_hmu 309

199 Resultant deflection of crown cantileverm u_m_mm hhu uu 311

200 Measurement of downstream movements at abutmentsu U- 312

201 Downstream movements at abutments_h hu_m__h---hm--m h_u_hm- 313

202 Spreading of reservoir wallsuhum_hh__m_hm. UhUh_- 314

203 Measuring changes of chord lengthhuuhumu-- _umuu_m_h_UU_mhuUU-- 316

204 Te,sts for changes in chord lengthsmum- -uh_h_m_hmmmu_uum_mumuhm -u_m 317

205 Resultant horizontal movement of modeL _m--u umhhmmuuu --hh 318

2.06 Dimensions of model after testingmumu um_mmuuu-mh_hh um_uu_- 319

207 Strain gages for upstream facem uhm mmhuuu 322

208 Frame details for vertical strain gagehm- u_hmuUhh 323

209 Pin details for vertical strain gagem-m m- _mmmuu 324

210 Strain gages mounted on upstream facemmu_h_mu_h_m__hm uhu _mhhUUm- 325

211 Hand-operated strain gagemmm uum_m_uuuhh 326

212 Strain gage rosettes on downstream face-hm--mmu_m 327

213 Locations of rosettes on downstream face uu

__h 328

214 Locations of rosettes on upstream faceu uuh_humuu U__humu_h__m 329

215 Arch stresses, load at elevation 1232---huuh-- .U_hm_mhuuu-- uu 330

216 Cantilever stresses, load at elevation 1232u --h 332

217 Horizontal shearing strains and stresses- _umu_m u 333

218 Principal stresses due to water loaduuh_- u__m UUhh_m- u- 334

219 Dead load arch stresses__mmhUmm- UUUUh_-hh_u_U_-hmumh 337

220 Dead load cantilever stressesuu

-

m__- 338

221 Dead load shearing strains and stressesu u uu- 340

222 Principal stresses due to dead loadh--umuhu-_um__h__mhm- m-uuhuuuu 341

223 Arch stresses, combined dead and live loadsuuh---h__u -_hu_m-UUhh__m_h-mh 343

224 Cantilever stresses, combined dead and live loadsm u- 344

225 Shearing stresses, combined dead and live loadsmu__h_mu 345

226 Principal stresses, combined dead and live loads --m- 347

227 Radial arch deflections due to flowu U_humm_mm_humm'_mhhUUhmmuumU_h 351

228 Radial arch deflections due to flow and recoverYm_u m 352

2,2.9 Radial arch deflections before and after flow tesLmu m- 354

230 Locations of thermocouplesu

m_um_m_mUUumu m_uuu 357

231 Deflections of arches at end of one daYm_u m _u-u 359

232 Deflections of cantilevers at end of one day- _u 360

233 Deflections of arches at end of two daysummhhu U_huu_mm__mm_h_m-hu_m362

234 Deflections of cantilevers at end of two daysu u--u- 363

235 Deflection of arches at end of four daysmmu m_m__mh h'Uhhh_umhu-U'mh' 365
16 MODEL TESTS OF BOULDER DAM

FIGURE PAGE

236 Deflections of cantilevers at end of four days... 366

237 Deflections of arches at end of twelve days 367

238 Deflections showing recovery from temperature test.. 368

239 Plan of model showing arches and cantilevers 373

240 Unit vertical loads.. ""

.""'''''

374

241 Radial adjustment at arch elements 376

242 Tangential adjustment at arch elements "m."" ""'''''''''''''''''''''''' 377

243 Twist adjustment at arch elements.. ... 379

244 Vertical adjustment at arch elements.. ... 380

245 Results of trial load analysis 383

246 Arch and cantilever stresses u ou 384

247 Comparison of arch stresses at upstream face 386

248 Comparison of arch stresses at downstream faceu 0 387

249 Lines of equal arch stress at upstream face 388

250 Lines of equal arch stress at downstream face 390

251 Comparison of cantilever stresses at upstream face 391

252 Comparison of cantilever stresses at downstream face 392

253 Lines of equal cantilever stress at upstream face.. 393

254 Lines of equal cantilever stress at downstream face 394

255 Computed and measured radial deflections.. 396

256 Computed and measured tangential deflections.. 397

257 Computed and measured angular movements 398

258 Computed and measured vertical deflections.. 399
LIST OF TABLES

TABLE PAGE

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Effect of age on recommended mix..

Diagonal strains at downstream face."."...".."""..""""---h ".

Deflections of model showing effects of cracking..........

Effect of slots on radial deflections.. .---.---.

Elastic constants based on original dimensions

Elastic constants based on actual dimensions......

Consistency of test results ...---.......---...---.........

Volume modulus of elasticity.. ---.

Radial deflections for full and partial loads....

Radial deflections of cantilever K...---.....---..............

Tangential deflections for full and partial loads..

Slope deflections for full and partial loads..

Vertical deflections of arch elements..

Temperatures in model..

56

164

195

220

271

272

"

h 273

275

298

" '---"""""'."

299

302

.."".h...h... 306

310

358

17

CHAPTER I-INTRODUCTION

1. General.-The preparation of plans for Boulder Dam involved

the development of many new methods of theoretical analysis and

masonry dam design, as well as the application of many existing

theories to problems of greater magnitude than those for which they

had been developed. In verifying the fundamental accuracy of new

and existing theories the use of models took an important part, in

both hydraulic and structural problems. In contrast to the hydraulic

models, which provided direct empirical data, the principal function

of the structural models was to furnish a check on analytical methods

of design. Although considerable information which could not be

readily obtained by analytical methods was derived from the arch dam

model tests, this was only incidental to their use in determining the

adequacy of the trial load method of analysis.1 From this viewpoint,

the method of applying results of structural model tests of dams by

the Bureau of Reclamation differs somewhat from the use of other

types of structural models.

2. Scope of Bulletin.- The program of structural model tests

included materials investigations and tests on two complete models,

representing two designs for Boulder Dam, together with comparisons

of results with mathematical analyses. The first model was constructed of a mixture of plaster and diatomaceous earth developed

in the investigations of materials. The second model, incorporating

design changes, was constructed of a rubber-litharge compound. Detailed studies were also made on cross-sectional models of the crown

cantilever and a thick arch, and are described in a separate bulletin on

"Model Tests of Arch and Cantilever Elements."

In this bulletin are described the results of the tests on the two

complete models. Since the materials investigations and tests on

each model were performed in a separate program, the same order is

followed in presenting the results in this bulletin. The materials

'''Trial Load Method of Analyzing Arch Dams," Bull. 1, Part V-Technical

Investigations, Boulder Canyon Project Final Reports, 1938.

19
20 MODEL TESTS OF BOULDER DAM

investigations, leading to the development of the plaster and diatomaceous earth compound, and the plaster model tests are described

in chapters II to VII, inclusive. Descriptions of the rubber-litharge

material and the rubber model tests are presented in chapters VIII

to XIII, inclusive.

MODEL THEORY

3. Model Requirements.--To obtain similarity between a model

and its prototype, there are certain theoretical requirements which

must be fulfilled. Also, there are many physical requirements which

must be met in order that the experiments may be performed by

practical laboratory procedures. The following list presents the more

important requirements.

1. The model must be a true scalar representation of the

prototype.

2. The loading of the model must be proportional to the

loading of the prototype.

3. Upon application of load, resulting strains and deflections

must be susceptible of measurement with available laboratory

equipment. Since the model must necessarily be constructed to

a small scale, it ordinarily requires a higher specific gravity of

loading, or a greatly reduced stiffness compared to the prototype.

4. In a massive structure where the stress distribution is

influenced by volume strains, Poisson's ratio should he the same

for the model and prototype.

5. The model material must be homogeneous, isotropic, and

obey Hooke's law within the working stress limits, since these

are the conditions assumed to exist in a concrete dam.

6. Foundations and abutments must be sufficiently extensive

to allow freedom for the model to deform in a manner similar to

the prototype.

7. If effects of both live load and gravity forces are to be

investigated, the ratio of dead weight to live load should be the

same in both model and prototype. If the effects of live load only

are to be investigated, the results are not affected by the specific

gravity of the model, providing Hooke's law is obeyed and no

cracking occurs.

Requirement 3 largely determines the scale of the model. With
INTRODUCTION 21

the specific gravity of live load and the modulus of elasticity of the

model material determined, magnitudes of strains and deflections

depend upon the size of the model. \Vith measuring apparatus of a

known sensitivity, the necessary size of model can be easily determined.

4. Similarity Relations.--If all similarity requirements are fulfilled, the relations between model and prototype may be expressed

in simple terms. To express these relations mathematically, the following notation is used:

n = scale ratio of prototype to model.

G =

ratio of specillc gravity of live load on model to live

load on prototype.

Em = modulus of elasticity of model material.

Ed = modulus of elasticity of prototype material.

S = stress at a point on the prototype.

s = stress at corresponding point on model.

D = deflection of a point on prototype.

d =deflection of corresponding point on model.

With the model loaded corresponding to the water load on the

dam, the relation between unit pressures at corresponding points, and

also unit stresses is 8 = (n/G) s. The relation of the unit strains is

the unit stresses multiplied by the ratio of the moduli of elasticity,

n Em

or G

X Ji}'d

n times the corresponding lengths on the model. The deformation

of the dam represents the total effect of the unit strains; therefore

n2E

the deflection of the dam, D = (j E

m X d.

d

The foregoing relations apply when all similarity requirements

are fulfilled, which is not always possible in model tests of masonry

dams. However, since the purpose of the tests conducted by the

Bureau of Reclamation was to obtain data for verifying methods of

theoretical analyses, variations from true similarity could be considered. Therefore, such deficiencies in similarity as were unavoidable

did not detract greatly from the value of the tests.

These strains are acting over lengths on the dam
22 MODEL TESTS OF BOULDE'R DAM

EARLY MODEL TESTS

5. Stevenson Creek Model.-Although the relations between prototype and model are simple when proper similarity is obtained, there

is seldom an opportunity to check model measurements against similar

measurements on the prototype. Such an opportunity did exist when

the investigations of the Stevenson Creek Test Dam were completed.2

The Stevenson Creek Test Dam is a thin concrete arch, 60 feet high,

built to permit accurate observations of arch dam action under actual

service conditions.

In cooperation with the Engineering Foundation Arch Dam Committee and the University of Colorado, the Bureau of Reclamation

conducted a series of arch dam model experiments on the Stevenson

Creek and Gibson dams.3 The Stevenson Creek model was constructed

to a one-twelfth scale, making a modelS feet high, 2 inches thick at

the top, 70 inches thick at the bottom, and 11 feet 8 inches long at

the crest. Concrete, mixed from the same aggregate as in the dam,

was used in the model. The model was loaded with a film of mercury,

contained in a rubber bag which fitted the upstream face and was

held in place by a steel plate, rigidly braced against the walls of the

testing pit. Measurements of deflections and strains were made at

the downstream face. These measurements checked closely with

measurements made on the prototype and also with the deflections

calculated by the trial load method.

The principal conclusions from this investigation were:

1. A properly constructed small scale model can be relied

upon to produce strains and deformations similar to its prototype.

2. Mercury is a satisfactory medium for producing modeltesting loads.

3. The trial load method of analysis gives accurate results

for a thin arch dam.

6. Gibson Model Tests.-The next step in the program was to

build a model of an arch dam in which a considerable portion of the

load is carried by gravity action. The Gibson Dam is an excellent

example of this type. The model was built on a scale of 1 to 68 and

2"Arch Dam Investigation, Report by Committee," Vol. I, Engineering Foundation, Nov., 1927; also Procs. Am. Soc. C. E., May, 1928, Part 3.

'''Arch Dam Investigation, Report by Committee," Vol. II, Engineering Foundation, May, 1934.
INTRODUCTION 23

was 2 feet 100 inches high, 2% inches thick at the top, 15;Vs inches

thick at the hase, and 13 feet 6 inches long at the crest. It was constructed of concrete and loaded with mercury in the same manner

as the model of the Stevenson Creek Dam. The procedure of testing

was also the same as in the first model. However, the Gibson model

investigations included a temperature test as well as live load mercury

tests.

In the temperature test of the Gibson model, the temperature of

the model was first raised by running hot water over the faces. \Vhen

a fairly uniform high temperature was obtained the model was allowed

to cool, after which the temperature was further lowered by running

ice water over the faces. Continuous observations of radial deflection

and temperature were taken throughout the temperature cycle.

The behavior of the Gibson model was entirely satisfactory and

the agreement of the measured deflections with those calculated by

the trial load method was excellent. In the analysis of the model, a

number of refinements were introduced to include effects of tangential

shear and twist. The fact that good agreement was obtained gave

further proof of the accuracy of the trial load method of analyzing

arch dams.

INVESTIGATION OF MATERIALS

7. Preliminary Tests.-It was evident from the tests on the Gibson model that a concrete model of Boulder Dam, with its thick cantilevers and relatively short arches, would be much too rigid to provide

measurable deflections under a mercury load. Consequently, it was

necessary to develop a model material with a low modulus of elasticity,

but possessing other qualities necessary to insure similarity with the

prototype.

The first studies were made on a number of plastic materials

mixed with various ingredients. After heing molded into specimens

these materials still remained plastic and were therefore unfit for the

purpose. Various materials were mixed with Portland cement in

order to lower its strength and stiffness; but these proved to be either

too hard or Jacking in strength. PJaster, having an initial strength and

stiffness lower than cement, offered greater possibilities. After testing

specimens of plaster mixed with various inert materials, it was found

that a mixture of commercial building plaster and diatomaceous

earth, "Celite", had most of the required properties.
24 MODEL TESTS OF BOULDER DAM

8. Plaster-Celite Materials.-After the preliminary tests indicated the possibilities of plaster-celite materials, a thorough study

was made of mixtures of various brands of plaster with different proportions of celite, together with various admixtures. Some of the

mixtures set too fast; others were not workable. Some were mixed

with lead shot to increase the weight. Mixtures having satisfactory

workability were tested for elastic properties and physical characteristics such as bond, shrinkage, and rate of drying.

The mixture, as finally developed, had the following desirable

properties:

1. \V orkable consistency, easily poured in any type of form

likely to be used.

2. Set in 20 to 30 minutes at virtually constant volume.

3. Poisson's ratio about the same as concrete.

4. Straight line stress-strain relation and a relatively low

modulus of elasticity.

5. Easily shaped with hand tools after casting.

6. Bonded satisfactorily with previously cast material when

the latter was coated with shellac and varnish.

7. Almost the same ratio of compressive and tensile

strengths as concrete.

8. Ingredients were inexpensive and readily available.

The material also had the following undesirable properties which

increased the difficulties of the work but did not affect the essential

functions of the model:

1. Slow rate of drying, the material remaining plastic until

dry. This necessitated construction of models in thin layers,

allowing each layer to dry before casting the succeeding layer.

The model, when completed, had to be protected from moisture

throughout the tests.

2. Lack of uniformity in commercial plasters. In order to

obtain a certain modulus of elasticity, trial mixes were necessary

for each shipment of material.

3. Subject to damage by moisture. This prevented the use

of water as a live load, or as a temperature control medium in

direct contact with the model.

The preliminary investigation of materials indicated that usual

laboratory equipment vvould not be satisfactory for testing plastercelite specimens, due to the comparatively low stresses used in testing.
INTRODUCTION 25

Special equipment, using direct loads, \vas therefore developed and

used for most of the tests. Also, light-weight apparatus for attaching'

gages to the specimens was developed.

During the construction of the model, specimens were cast from

the material of each layer and used in establishing a complete record

of the elastic properties of the model. The laboratory measurements

on the specimens included tests for modulus of elasticity and ultimate

strength in tension, compression, and shear, and Poisson's ratio in

compression. In addition, auxiliary tests were made to determine the

rate of plastic flow in tension, compression, and torsion, and the coefficient of thermal expansion. At the conclusion of the model tests,

some questions arose concerning the degree of isotropy in a model

built up in layers. Consequently, when the model was dismantled,

several large specimens comprising several layers of the material were

cut out for further laboratory tests. These were shaped into cubes

and loaded in the direction of the three principal axes, in a special

compressed-air testing machine. These tests showed that the built-up

material was satisfactorily isotropic.

9. Rubber and Litharge Material.-During the testing of the

plaster-celite model, the Aluminum Corporation of America developed

a rubber and litharge compound which they used for a model of the

Calderwood Dam.4 Since the tests on the plaster-celite model of

Boulder Darn, together with further analytical studies, indicated that

some changes in design were desirable, it was decided that another

model, incorporating these changes, should be built. The rubber

and litharge material was selected for this purpose.

The rubber-litharge material had certain advantages over plastercelite, principally in having a lower modulus of elasticity and a unit

weight equal to that of concrete. Vvater load could be applied directly,

giving the same proportion of live load and dead load as in the prototype. Furthermore, apparatus made to work under water permitted

measurements to be made on the upstream face.

A shipment of 40,000 pounds of rubber-litharge was obtained

from the Republic Rubber Company, Youngstown, Ohio, for building

the model. Preliminary tests on specimens, made with available

equipment, indicated that the material had pronounced directional

properties and a high Poisson's ratio. Consequently, mathematical

---

'Karpov, A. V., and R. L. Templin, "Model of Calderwood Dam," Trans. Am.

Soc. C. E., 1935, pp. 185-262.
26 MODEL TESTS OF BOL:LDER DAM

studies were made of the stress-strain relations for an anisotropic

material, in order to interpret properly the results of the materials

tests. Also, apparatus, specimen shapes, and testing procedures were

developed to meet the testing requirements of this type of material.

To determine the modulus of elasticity, volume modulus, and

Poisson's ratio, prism-shaped specimens \vere used to facilitate measurements along three axes. From specimens fabricated of squares of

material, cut from a single sheet of rubber and assembled with the

same relative direction of axes, it was found that the modulus of

elasticity was different for each axis, with a different Poisson's ratio

for each of the two axes normal to the loaded axis. Thus the material

had three different moduli of elasticity and six possible Poisson's

ratios. It was found that there was very little total volume change,

although Poisson's ratios in excess of 0.50 on certain axes were observed. It has been found that some compounds show an actual

increase in volume under load.5

Although the rubber-litharge material had a number of advantages, it is evident that the similarity requirements in regard to elastic

properties were violated. The effect of this violation will be further

discussed.

BOULDER DAM TESTS

10. Plaster Model Tests.-Construction of the plaster model of

Boulder Dam was begun in December, 1930, at the University of

Colorado. The model was located in the same testing pit that was

used for the previous models of Stevenson Creek and Gibson dams.

The model, with foundation and abutments, was cast in layers to

form a monolith so that the dam, with foundation and abutments,

formed a con~inuous elastic body, representing the condition in the

prototype with all joints grouted. The scale selected was I to 240,

or one inch on the model represented 20 feet on the prototype.

The program of tests included measurements of radial, tangential,

and slope deflections, and strains on the downstream face, for partial,

normal, and overload conditions. Mercury was used as the loading

medium. Measurements were made of effects of plastic flow under

constant load, and of radial deflections due to temperature changes.

Also a number of tests for special effects were conducted.

'Ariano, R., "The Resistance of Rubber to Compression." The India Rubber

Journal, August 11, 1928, p. 8.
INTRODUCTION 27

\Vith respect to effects of live load, requirements for similarity

were almost completely obeyed in the plaster-celite model. The model

material, having a Poisson's ratio very nearly the same as concrete,

had a similar distribution of strain and stress, and consequently,

similar deflections. Using the elastic constants determined for the

model, a trial load analysis was made. The agreement hetween computed and ohserved data was satisfactory.

In addition to the check on the trial load analysis, the plastercelite model indicated stress concentrations near the top of the dam

at the abutments, where there was a rapid change in the length of the

arches. This effect was remedied in the later design by providing

fillets at the ends of the upper arches, thus increasing the thickness

of the arches near the abutments.

11. Rubber Model Tests.-The rubber-litharge material was furnished in 6-inch, 12-inch, and 24-inch squares, I-inch thick. The

model was built up in layers, using vulcanizing rubber cement at all

joints, applied without heating. This provided joints of ample

strength and facilitated dismantling, since the unvulcanized rubher

cement was readily soluble in henzol. The scale selected for the

model was 1 to 180, or one inch on the model represented 15 feet

on the prototype. A larger proportion of depth and length of canyon

was included in this model than in the previous one, in order to allow

greater foundation deformation.

\Vater, maintained at the same temperature as the rubher, was

used as a loading medium. In general, the same measurements were

made on the ruhher model as on the plaster model, except for measurements of strain on the upstream face and a different manner of conducting temperature tests. Also the type of testing apparatus was

considerably different.

At the conclusion of the investigations of the rubher-litharge

material, it was evident that similarity between the rubber model and

the prototype would not be obtained. The rubber model, deforming

at constant volume under load, had large vertical movements as well

as horizontal movements. Due to this condition there was no direct

mathematical relation between the rubher model and the concrete

dam. In making the analysis of the model, the observed elastic constants were used and additional calculations to consider the vertical

movements were included. The fact that an agreement hetween the

model results and the theoretical analysis for the model was obtained,
28 MODEL TESTS OF BOULDER DAM

ga \'e further proof of the versatility of the trial load method of arch

dam analysis.

12. Acknowledgments.

-- The model investigations were conducted under the immediate supervision of Engineer A. \iV. Simonds.

Other engineers who assisted in the laboratory investigations were

Eldred D. Smith, J. A. Stubbs, E. \iV. Ryland, C. \iV. Fletcher, F. M.

Russel1, George C. Rouse, D. 13. Holford, and F. C. Knoth. A large

part of the office work was done by L. T. French, \iV. E. Green, J. G.

Ross, and N. J. Castellano R. \iV. \iVhinnerah contributed the analyses

of the models by the trial load method.

Acknowledgment is also due the University of Colorado for placing its testing laboratories, equipment, and shops at the disposal of

the Bureau of Reclamation personnel. Much assistance and cooperation were received from members of the Civil Engineering faculty,

particularly from Professor C. L. Eckel, Head of the Department,

from Professors F. R. Dungan and L. B. Sutherland who assisted in

the tests, and from Professor E. O. Bergman who contributed the

mathematical stress-strain relations of anisotropic materials. A large

part of the equipment and special apparatus for testing was built in

the University machine shop by M. M. Eaton.

BIBLIOGRAPHY

The following bibliography includes the principal articles on

structural mode] tests of dams which have been published in engineering literature up to the present time. A few early tests are described

in publication 8, in addition to the one cited.

1. Engineering Foundation.

Report by Committee, Arch Dam Investigation, Vol. I, Nov" 1927; also Proc. Am. Soc. C. E., Part 3, May, 1928.

2. Houk, Ivan E.

Experimental Work on Small Scale Models of Arch Darns, Reclamation Era, Oct., 1927, pp. 152-154.

3. Karpov, A. V., and R. L. TempJin.

Building and Testing an Arch Da1n Model, Civil Engineering, Jan.,

1932.

4. Savage, J. I.., Ivan E. Houk, H. J. Gilkey, and Frederick Vogt.

Arch Dam Investigation, Vol. II, Engineering Foundation, May, If134.

5. Savage, J. I.., and Ivan E. Houk.

Model Tests Confirm Design of Hoover Dam (now Boulder Dam),

Eng. News,Rec., April 7, 1932.
INTRODUCTION 29

6. Savage, J. L.

Dam Stresses and Strains Studied by Slice Models, Eng. News-Rec.,

Dec. 6, 1934.

7. Smith, Eldred D.

Structural Model Testing of Dams, Dams and Control Works, 2nd

Ed. 1938, U. S. Department of the Interior, Bureau of Reclamation.

8. Wilson, John Sigismund, and William Gore.

Stresses in Dams: An Experimental Investigation by Means of

India-Rubber Models, Proc. Inst. C. E., London, Paper No. 3705,

1907-08, pp. 107-129.

CHAPTER II-INVESTIGATION OF MATERIALS

INTRODUCTION

13. Purpose of Tests.- The early tests on concrete models of

arch dams, briefly discussed in chapter I, showed that a model of the

proportions of Boulder Dam could not be successfully investigated if

built of concrete. The tests discussed in this chapter were made in

an effort to discover or develop a material suitable for use in constructing models of thick arch dams. After considering theoretical

and practical requirements, the following tentative specifications for

a suitable material were prepared:

1. The material should be uniformly elastic in all directions,

for all working stresses.

2. It should have a Poisson's ratio about the same as concrete.

3. It should have a modulus of elasticity sufficiently low to

allow measurable deformations under a mercury load, yet have

sufficient strength to resist damage in handling.

4. The ratios of tensile and shearing strengths to compressive strength should be about the same as for concrete.

5. It should not flow excessively under continuous load.

6. There should be very little or no shrinkage after setting.

7. It should possess a workability which would permit it to

be cast easily into shapes suitable for testing, as well as to allow

mixing and placing of large masses in building the model.

8. It should be possible to repair the model in case of accidental damage.

14. Specimens.-In the early tests small beams and cylinders

were used. Flexural tests were made with 7i by 1 by 8-inch beams,

and compression tests with 2 by 4-inch cylinders. It was soon recognized that the small quantities of material used in making such specimens did not offer an opportunity to judge the workability of the

mIxes. Therefore a practice of using ten to forty pounds of dry

31
32 MODEL TESTS OF BOULDER DAM

material and casting larger specimens was adopted. In the adopted

practice, test specimens usually included 3 by 3 by 4O-inch beams, 3 by

6-inch cylinders, and 2 by 4-inch cylinders.

FIGURE 2-INSTRUMENTS FOR MEASURING DEFORMATIONS

OF COMPRESSION SPECIMENS

15. Testing Apparatus.-In all compression tests described in

this chapter, a hand-operated, 20,000-pound testing machine was used.

A 2 by 4-inch plaster specimen in the testing machine is shown in
INVESTIGATION OF MATERIALS 33

figure 1. Longitudinal and lateral deformations were measured with

the compressometers and extensometers shown in figure 2. These

instruments for measuring deformations of cylinders were used in

tests for determining the modulus of elasticity and Poisson's ratio of

all materials studied in the preliminary investigations. The compressometers and extenso meters were designed for testing concrete

cylinders. In using them on other materials, it was soon recognized

that their steel frames were too heavy for making satisfactory measurements on light specimens of plaster compounds. The points of

the set screws which clamped the apparatus to the specimen would

damage the plaster. The compressometer for the 3 by 6-inch cylmders

was excessively heavy; consequently results of tests on cylinders of

this size are not believed to be as reliable as those obtained on the

smaller cylinders.

After construction of the plaster-celite model was started and

extensive tests on the plaster-celite material were begun, machines

for testing low-strength materials were designed and built. Compressometers and extensometers of aluminum were made for measuring deformations of the specimens. Tests made with the redesigned

light-weight equipment yielded satisfactory results in determining the

modulus of elasticity and Poisson's ratio.

Flexural tests were made with an improvised apparatus which

supported the beam at the ends and allowed a concentrated load to be
34 MODEL TESTS OF BOULDER DAM

applied at the center. The concentrated load was imposed by suspending a bucket of sand or shot from the center of the beam. The

apparatus, with a dial gage for measuring center deflections of a 3 by

3 by 40-inch beam, is shown in figure 3. Tensile strength was not

considered an essential property for the model material. Consequently,

no tensile tests were made during the preliminary investigations.

16. Scope of Investigation.- The investigation included a wide

range of combinations of materials which had been considered as

possibilities for fulfilling the requirements set forth in section 13.

Tests on some of the mixtures were rather limited due to early discoveries of failure to meet one or more of the tentative specifications.

Tests of plaster mixes were comprehensive. Plaster was recognized

as possessing the desired qualities and extensive studies were made

to discover the most suitable brand and proportions for the final

product.

PRELIMINARY EXPERIMENTS

17. Tar, Pitch, and Resin.--Several tar, pitch, and resin combinations were tested and found to be unsatisfactory. A product composed

of one part pitch, one part resin, and one part plaster of Paris was

plastic and began to melt at about 90 degrees Fahrenheit. If more

plaster of Paris was added the mixture was stiffer, but still plastic.

A combination of 3 parts linseed oil, 4 parts tar, and 16 parts resin.

was decidedly plastic. These mixes were inclined to be sticky and

could not be removed from the forms without damaging the specimens.

A mixture of 4 parts iron filings, 2 parts loam, 1 part powdered

sandstone, and salt water produced a material similar to adobe. This

material was not suitable for use in a testing pit where there is a

possibility of damage by water.

18. Sulphur and Celite.-Several compositions using sulphur as

the cementing agent were investigated. Commercial powdered sulphur was very thin when melted and required a watertight form to

hold it. It crystallized on cooling and formed a material which was

not uniform. vVhen celite was added to sulphur a very inflammable

mixture resulted. It was imperative to pour the celite into the melted

sulphur as the mixtnre ignited readily when the two substances were

mixed dry and heated. This mixture was rather gummy and not suitable for model construction.
INVESTIGA. TIO"" OF iVIATERIALS ~" i>,j

19. Linseed-Oil Mixtures.-A number of beams were made of

neat cement using linseed oil in the mixing water. Specimens containing more than 3 per cent of oil had insufficient strength to carry

any load whatever, while those containing smaller percentages of oil

had moduli of elasticity higher than the desired value. Mixtures of

plaster of Paris, water, and lubricating oil showed higher moduli of

elasticity at an age of 34 days, than if no oil were used. Therefore,

tests of such combinations of materials were discontinued.

20. Under-Sanded Concrete.-It was thought that a weak, porous

concrete might have a modulus of elasticity low enough for model

purposes. Some pea gravel containing a small amount of sand was

available from the aggregates used in the model of Gibson Dam. This

was mixed with cement in the proportion of 1 to 6% by weight, water

being added to produce a water-cement ratio of 0.67 by volume. The

product was a porous concrete having an ultimate strength in flexure

of 250 pounds per square inch when 21 days old, and a modulus of

elasticity of 1,700,000 and 1,800,000 pounds per square inch, respectively, for wet and dry curing.

In measuring deflections of the model under load, it was proposed

to use small metal inserts, embedded in the downstream face. Due to

the difficulty involved in securing inserts in the porous material, as

well as the relatively high modulus, this mixture was rejected.

21. Cement-Asbestos Sheets.-A beam, cut from sheets made by

compressing cement and asbestos, gave a fairly straight stress-strain

diagram up to stresses of 175 pounds per square inch. However, the

modulus of elasticity of 3,500,000 pounds per square inch was entirely

too high.

22. Rubber-Aggregate Concrete. - Concrete mixed with finely

ground automobile-tire rubber in place of coarse aggregate, to lower

the modulus of elasticity, was investigated and discarded. The resulting mix was unsuitable for testing. Expansion of the rubber particles

when wet by the mixing water cracked the entire mass into small

pIeces.

23. Hard Rubber. - Modulus of elasticity tests on two small

beams of hard rubber showed values of 390,000 and 480,000 pounds per

square inch. The stress-strain diagrams were fairly straight up to

stresses of 140 pounds per square inch, but curved downward in proportion to the load when the stresses were further increased. One
36 . MODEL TESTS OF BOULDER DAM

of the beams was subjected to a flow test by imposing a maXlll1Um

stress of 200 pounds per square inch for a period of 21 hours. The

total flow during this period was 23 per cent of the initial elastic deformation. Upon release of load, a recovery of 71 per cent of the total

deformation took place, increasing to 84 per cent during the succeeding 24 hours. The results of the tests, together with the difficulty of

casting homogeneous thick sections and the lack of a satisfactory hard

rubber cement, showed that the construction and testing of a hard

rubber model of Boulder Dam would not be advisable.

24. Cement and Plaster of Paris.-Both cement and plaster of

Paris have been considered as binding materials for mixes to be used

in model construction. Plaster of Paris has the advantage that its

modulus of elasticity is only one-half that of cement. Therefore,

products having lower moduli of elasticity are more easily made with

plaster as the binding material than with cement. Furthermore, all

plaster products have a workable quality after hardening which is

not found in cement products. For instance, the thickness of the

model can easily be dressed down to the correct amount, joints and

keyways can be cut in the model sections after casting, and slots can

be made to represent cracks in the dam. The disadvantage of plaster

products compared with concrete, is that they must be protected from

water. If such materials are used, the testing pit must be kept dry

and the model protected with shellac or varnish.

25. Cement or Mortar and Asbestos.-Specimens made with a

mix of cement and asbestos, or mortar and asbestos, were so soft and

fragile that they broke before being tested. An undesirable shrinkage

of from three to four per cent was noticed in the cylinders. The tests

showed that, by using asbestos as an admixture with cement, the

modulus of elasticity could be reduced to about 500,000 pounds per

square inch. Adding asbestos in an effort to lower the modulus beyond this value rapidly reduced the strength and the elastic range,

and caused the deformation to become largely plastic.

26. Cement and Celite.-vVith the assumption that an appreciable amount of celite had to be added to cement to cause a substantial

reduction in the modulus of elasticity, a mix was first made from one

part cement and one-half part celite by weight. In order to obtain

satisfactory workability it was necessary to add 1.9 parts of water.

This combination remained decidedly plastic for a long time. Meas-
INVESTIGATION OF ;\IATERIALS 37

urements on 2 by 4-inch cylinders, after hardening, showed a settlement of five per cent.

A mix of 1.0 part cement to 0.25 parts celite to 1.17 parts water

was unsatisfactory. The average settlement of 2 by 4-inch cylinders

was 4.5 per cent. All of the small heams were hroken by early shrinkage.

One 3 by 3 by 4O-inch beam was macle using 1 part cement to 2

parts sand to 0.2 parts celite to 0.57 parts water. Another was made

with the same formula, with the exception that the celite content was

reduced and 1.0 part water used. \Vith the reduced content of celite

a product of better consistency was obtained. However, the modulus

of elasticity at 28 days was 1,800,000 pounds per square inch. These

beams were cured under water. After a two-week period they had

expanded 0.017 per cent. An equal time in air produced a shrinkage

of 0.08 per cent.

The high strength and modulus of elasticity of cement and celite

mixes, having small amounts of celite, suggested adding sugar to the

mixing water. The sugar satisfactorily checked the hardening of the

cement; but after setting had taken place the material crumbled easily.

On becoming wet, it showed a tendency to disintegrate. From the

standpoint of handling and durability it was altogether unsatisfactory.

Mixes were made with hydrated lime and cement, but with little success, as these materials did not combine very well. The combination

hardened slowly, and like the mixtures of cement and celite, it had

a tendency to crack due to excessive shrinkage.

27. Cement, Asbestos, and Celite.-Beams containing both asbestos and celite were made, some with neat cement and some with

mortar. All specimens were hard and strong, but those having low

moduli of elasticity also had low limits within which the stress-strain

curves were straight. \Vhen additional load was applied the deformations of the beams became plastic.

28. Plaster of Paris and Asbestos.-A number of beams were

made using different mixes of plaster, asbestos, and water. Tests

showed that the beams had moduli of elasticity ranging from 300,000

to 590,000 pounds per square inch, at stresses from 40 to 120 pounds

per square inch. Mixes having the lower moduli or elasticity were

those containing the greater amounts of asbestos. The beams, when

stressed beyond 40 pounds per square inch, were definitely plastic in

deformation.
38 MODEL TESTS OF BOULDER DAM

29. Plaster of Paris and Celite.-Early tests with plaster of Paris

as a binding material established its superiority over cement in one

important respect; namely, there was no tendency for shrinkage cracks

to form during setting, and there was very little shrinkage after

setting. The most satisfactory admixtures tested were asbestos and

celite. In using these materials, relatively large proportions of mixing water had to be added to produce workable mixes. \Vhen the

specimens were dried in air the greater part of the mixing water

evaporated, leaving a porous material which had a low strength and

a low modulus of elasticity. The physical properties were largely

dependent upon the amount of moisture retained in the mixture. The

most satisfactory product seemed to be one in which the moisture

content was reduced to a minimum. In order to preserve uniform

physical properties it was necessary to cover the material with a

waterproof coating. Hot paraffin, shellac, varnish, and paints were

tried with varying degrees of success. The most suitable waterproofing consisted of two coats of orange shellac and one coat of ship

varnish. After extended tests with asbestos and celite admixtures, the

latter was considered the better of the two, due to tendencies of asbestos to produce a softer mixture which showed plastic deformations

under relatively low stresses.

By using plaster of Paris as a binder and celite as an admixture,

a material was produced which more closely approached the desired

product than any which had previously been developed. \Vith this

combination it was possible to obtain a material having a modulus of

elasticity as low as 100,000 pounds per square inch without possessing

undesirable shrinkage characteristics. Furthermore, the material was

highly elastic under ordinary stress conditions.

In order to obtain a workable mix, which would completely fill

the forms, it was necessary to use an amount of water equal to the

weight of the dry materials. The most satisfactory proportion of the

plaster of Paris and celite ingredients was 2 to 1, by weight. An

increase in the amount of celite produced a mix which remained plastic

for a long time. Equal parts of plaster and celite produced a product

which remained highly plastic, even after a period of 24 hours. A

plain mix of plaster and water hardened after about one and one-half

hours. Settlement in the form during this period amounted to about

two per cent. U sing a 2 to I mixture of plaster of Paris and

celite, hardening took place within haH an hour. with no appreciable

settlement in the form. After hardening, an increase in temperature

due to the chemical reaction of the plaster and the mixing water was
INVESTIGATION OF MATERIALS 39

noticed. This temperature change caused a slight increase in the

volume of the material.

When removed from the forms, the weight of specimens made of

plain plaster of Paris with 50 per cent water was about 105 pounds per

cubic foot. For a mixture of two parts plaster of Paris, one part celite,

and three parts water, the weight was about 80 pounds per cubic foot.

After exposure to air for several days, the greater part of the water

evaporated, leaving the plaster of Paris with a weight of 92 pounds

per cubic foot and the plaster and celite mix with about 48 pounds

per cubic foot.

Tests were made on plaster of Paris and celite beams to determine the modulus of elasticity in flexure. For plain mixes of plaster

and water, tested at ages of 4 to 30 days, the modulus of elasticity

varied between 1,550,000 and 1,650,000 pounds per square inch. Plaster

of Paris and celite mixes had moduli of elasticity ranging from 140,000

to 840,000 pounds per square inch. The higher values occurred in

mixes low in celite and the lower values occurred in mixes having

1 part celite to 2 parts plaster of Paris. Flexural specimens were

made in both the 0 by 1 by 8-inch and 3 by 3 by 40-inch sizes. They

were tested to maximum stresses of 31 to 37 pounds per square inch

at 28 days. A 3 by 3 by 40-inch beam made from a mix of 1 part

plaster of Paris, 0 part celite, and 10 parts water, tested at an age

of 28 days to a maximum stress of 37 pounds per square inch, had the

lowest modulus of this group of specimens.

A 2 by 4-inch cylinder, made from a mix of 1 part plaster of Paris,

0 part celite, and 2 parts water, was tested at an age of 28 days to

determine the value of Poisson's ratio. The results showed a value of

0.35 which was fairly constant over a wide range of stress. The

modulus of elasticity for the same specimen was 170,000 pounds per

square inch, which checked closely with the values found in the tests

on beams. The ultimate compressive strength of the material was

about 180 pounds per square inch.

A flow test was made on a beam containing 1 part plaster of Paris

to ?4 part celite to 1 part water. A flow of 8 per cent of the initial

deformation was measured after a stress of 50 pounds per square inch

had been imposed on the specimen for a period of 24 hours. Flow

tests of other beams, some of which contained more moisture, showed

considerably more flow. In some cases, flows in excess of 100 per cent

of the initial deformation were observed. These tests again emphasized the necessity for complete control of moisture content if the

material were to be used successfully for model construction.
40 MODEL TESTS OF BOULDER DAM

COMMERCIAL BUILDING PLASTERS

30. Characteristics.-The preliminary experiments showed that

a mixture of plaster of Paris and celite would more nearly meet the

requirements for a model material than any other product tested. It

was believed that some of the commercial building plasters might be

even more satisfactory than plaster of Paris.

The following excerpts from a book by Edwin C. EckelG may

serve to explain the relation between plaster of Paris and commercial

building plasters, known as cement plasters:

"A theoretically pure plaster of Paris, being a definite chemical compound (Ca S04 + 0 H2O), would have the composition:

lime sulphate, 93.8 per cent; water, 6.2 per cent. This composition

is approached quite closely in plasters made from pure rock

gypsum.

"Cement plasters can be made in two different ways which

give two different products as far as composition is concerned.

(1) Cement plasters may be made by adding retarders to a pure

plaster of Paris. As the retarder is organic matter and rarely

amounts to over one per cent of the total mass, the resulting

product will on analysis differ very little from the plaster of Paris

of which it is made. (2) Cement plaster may also be made by

burning an impure gypsum, with or without the addition of a

retarder. In this case analysis would show the presence of a large

per cent of clayey matter, etc., and a cement plaster of this type

will therefore have a composition very different from pure plaster

of Paris."

The term "cement plasters" refers to slow-setting building plasters which are generally used in structural work. It has no relation

to Portland or natural cement.

Investigations were conducted on the following commercial build

ing plasters, which were obtainable at Boulder, Colorado:

Plaster of Paris:

Certainteed plaster of Paris.

Red Top quick-set plaster.

"Eckel, JiJdwin C., "Cements, Limes and Plasters," 2nd Ed., 1922, p. 63, John

Wiley & Sons, Inc.
INVESTIGATION OF MATERIALS 41

Cement plasters:

Red Top slow-set plaster.

Sunflower molding plaster.

Ideal finishing plaster.

Acme finishing plaster.

I t should be noted that the Certainteed and Red Top quick-set

plasters, being commercial products, cannot be considered as chemically pure plaster of Paris materials. Although the four products

listed as cement-plasters are similar in general, they have individual

characteristics, and, when combined with celite, have somewhat different properties. The differences between these plasters and commercial plaster of Paris suggested that they be classified as cementplasters. Chemical analyses of the brands were not available to

serve as a definite basis for classification.

31. Certainteed Plaster of Paris.-Certainteed plaster of Paris.

normally a quick-setting plaster, did not prove satisfactory for mixing

with celite. The addition of celite decreased the time of set to such

an extent that 36 pounds of dry material could not be mixed with

36 pounds of water before hardening took place. Consequently, it

was necessary to mix the plaster and celite together dry. \Vhen \vater

was added, the mixture became sticky; so that tough balls, from one

to three inches in diameter, formed as the material was worked with

a hoe. On account of the poor workability, experimenting was discontinued on this brand of plaster of Paris.

32. Red Top Quick-Set Plaster.-The action of Red Top quickset plaster resembled that of Certainteed plaster of Paris when combined with celite. The resulting product set quickly and was altogether unsatisfactory for building models.

33. Red Top Slow-Set Plaster.-Adding celite to Red Top slowset plaster shortened its normal time of set 10 to 15 minutes. As the

mix was exceedingly gummy and sticky when water was added, it

required some time to work a batch of 35 to 40 pounds of dry material

to a uniform consistency. Consequently there was no time to lose in

pouring the material into the forms. The 3 by 3 by 40-inch beam

forms could be fil1ed easily, but the 2 by 4-inch cylinder molds required more time and the mix was apt to start setting before they

could be filled. Stress-strain diagrams for compression tests on 2 by

4-inch, Red Top ::;low-::;etcylinder::; are shown on figure 4. The clesig-
""""

400

360

'~RTS-21

320

280 ~0

t1

t'i

240 t"

>-3

RTS-IS.' t'i 00 200 >-3

00

0

'60 "'.J

td

0

120 cj

t"tI

t'i

80 ::0

tI

~40

~.0

0.10 0.20 030 0.40

POISSON'S RATIO

400

I

.,

I

""""[""1-

---- ---

360

320

c

z

:::j 280

'"-<

'"

'"

'"

(J)

240

z

"

g

~ 200

'"

"'"

'"(J) 160

0

c

;;

'"Z 120

"

:J:

80

40

0 0,0002 0,0004 0.0006 0.0008 0.0010 0.0012

UNIT DEFORMATION IN INCHES PER INCH

I

RTS-2h,

Cast: August 21,1930.

Composition: 221bs. plaster, 121bs.Celite,

and 331bs. water.

Age attest: 67to90doys.

Average modulus of ~elasticity: 184,oOOlbs.

per square inch.

Average Poisson's ratio: 0.234.

Maximum allowable working stress: 100

Ibs. per square inch.

!

I

~_!

0.00\4 0.0016 0.0018 ODD2Q 0.0022

FIGURE 4-STRESS-STRAIN DIAGRAMS FOR COMPRESSION TESTS

2 by 4-inch Cylinders Made With Red Top Slow-Set Plaster
NVESTIGATION OF MATE,RIALS 43

nations on the curves refer to the specimen numbers selected as representative of the entire group.

The customary procedure in making plaster and celite specimens

was to mix and pour a batch one day, and remove the forms the following day. As soon as the forms were removed the cylinders were

capped with plaster of Paris. The high relative humidity of the concrete laboratory retarded the drying of the specimens. Therefore, on

FTGURE 5-PLASTER CYLINDERS AND BEAMS DRYING

IN THE SUNSHINE

fair days they were placed outside the building to dry in the sunshine.

Figure 5 shows 3 by 6-inch cylinders and 3 by 3 by 46-inch beams

drying out-of-doors. During the late fall and winter m~nths the

specimens were dried over a steam radiator inside the building.

Tests were made on 3 by 3 by 4O-inch beams to determine the

modulus of elasticity in flexure. The beams were supported at the

ends and 2-pound increments of load successively applied at the center.

As each increment of load was added, the deflection was observed by

reading the dial gage mounted at the center of the beam. The apparatus used in these tests is shown in figure 3. The modulus of elasticity was calculated from the formula for the deflection at the center

of a simple beam. Wooden forms for the 3 by 3 by 40-inch beams had

cross-sectional dimensions varying from 2.85 to 3.15 inches. In cal-'

culations for moment of inertia exact dimensions were used. The
44 MODEL TESTS OF BOULDER DAM

modulus of elasticity in flexure was found to be 228,000 to 270,000

pounds per square inch for two beams tested.

Twenty-one 2 by 4-inch cylinders were cast from the batch represented on figure 4, which shows test data for selected typical specimens. Two cylinders were defective. Some shrinkage of the specimens in the forms was noticed. The average modulus of elasticity

in compression was 184,000 pounds per square inch, the average value

of Poisson's ratio was 0.234, and the average ultimate strength was

293 pounds per square inch.

34. Retarders.--As the experiments with mixes of commercial

huilding plaster and celite progressed, two essential requirements became apparent. First, the mix must be of a thin consistency to prevent

formation of honeycombed places in the specimens due to entrapped

air; and, second, a retarder must be added to prevent the mix from

setting too rapidly. At the suggestion of \"AI. G. Banks, chemist for

the Colorado Portland Cement Company, ground bentonite. trade

name "Aquagel," was added to the mix as a retarder, with the result

that the setting time could easily be controlled. Later it was discovered that cold water was also an effective retarder. Both retarders

were used with equally satisfactory results.

35. Sunflower Molding Plaster. - Sunflower molding plaster,

comhined with celite, produced mixtures with satisfactory workability.

In a few specimens small air pockets were found, but the majority

of the specimens were smooth, sound, and wholly satisfactory. The

modulus of elasticity varied from 80,000 to 217,000 pounds per square

inch for different mixes. Poisson's ratio remained about the same as

for concrete, or approximately 0.175. Typical stress-strain relations

for 2 by 4-inch specimens, made from a mix of 22 pounds of Sunflower

molding plaster, 12 pounds of celite, and 41.6 pounds of water, are

shown in figure 6. Specimens were tested at ages of 24 to 111 days.

The results of all tests on this mixture were as follows:

Size,

Specimens inches

Three beams

n.nhm

3 X 3 x 40

Three cylinders 3 x 6

Twelve cylinders um"--- 2 x 4

Average E

lb. per sq. in.

213,000

138,000

134,000

Poisson's

ratio

0.232

0.175

Since considerable time was required to cast a number of 2 by

4-inch cylinders, several 3 by 6-inch cylinders were also made. The

larger molds could be filled more rapidly than the smaller molds.
, 400

POISSON'S RATIO

360

320

2eo H

Z

<

r:J

240 W

>-3 H

Q

200 >

>-3

0

Z

'60 0

"'J

120 ~>

>-3

r:J

eo

~>

t:"'

40 W

0.10 0.20 0.30 0.40

POISSON'S RATIO

400 ! LATERAL

!

I

360

320

~::j

280

'"

~

240

Z

."g

Z

~

200 -

."m

'"~

160

C,.

'"

'"Z 120

0

:J:

'0

40

0.0002 ':>.0004

LONG'ITUDINA~

i

I

!

Cast: Septem ber 2,1930.

Composition: 22Jbs. plaster,12Ibs.CeHte,

and 41.61bs. water.

Age at test: 17 to 93 days.

AV.erage modulu~ of elasticity: 134.000

Ibs. per square inch.

Average Poisson's ratio! 0.175.

Maximum allowable working stress: 100

Ibs. per square inch.

0.0006 0.0006 0.0010 0.0012 0.0014 0.0016 0.0018

UNIT DEFORMATION IN INCHES PER INCH

0.0020 0.0022

FIGURE 6-STRESS-STRAIN DIAGRAMS FOR COMPRESSION TESTS

2 by 4-inch Cylinders Made With Sunflower Molding Plaster ...

""
Size, Average E Poisson's Ult. strength

Specimens inches lb. per sq. in. ratio lb. per sq. in.

3 beams _-----3 x 3 x 40 233,000

3 cylinders-- 3 x 6 144,000 0.182 231

13 cylinders.. 2 x 4 164,000 0.167 304

46 MODEL TESTS OF BOULDER DAM

However, apparatus for measuring lateral and longitudinal deformations of 3 by 6-inch cylinders was not satisfactory, owing to its excessive weight as mentioned previously. Consequently the results of the

tests on the larger cylinders are not believed to be as reliable as those

on the smaller cylinders.

Tests were made to determine the effect of aquagel on the elastic

properties of specimens made with Sunflower molding plaster and

celite. Test specimens were made from a mix having no aquagel as

well as from mixtures of the same proportions containing varying

amounts of aquagel. The average modulus of elasticity in compression for 12 to 14 specimens, cast from a 36-pound batch, was as

follO\vs: no aquagel, 135,000 pounds per square inch; one teaspoon

of aquagel, 129,000 pounds per square inch; two teaspoons of aquagel,

100,000 pounds per square inch; three teaspoons of aquagel, 80,000

pounds per square inch. Although aquagel is an excellent retarder

for this type of work, its water retaining property, which produces

specimens of lower strength and modulus of elasticity, made its use

undesirable.

36. Ideal Finishing Plaster.-Some combinations of Ideal finishing plaster and celite were satisfactory, while others set too quickly.

The first batch set so rapidly that most of the 2 by 4-inch cylinders

were defective. Fairly satisfactory results were obtained with specimens made of 22 pounds of plaster, 10 pounds of celite, and 37 pounds

of water. This mixture had an average modulus of elasticity of 164,-

600 pounds per square inch in compression, an average Poisson's

ratio of 0.167, and an average ultimate strength of 304 pounds per

square inch. Stress-strain curves for typical 2 by 4-inch specimens

are shown in figure 7. Specimens tested at ages of 31 to 120 days

ga vc the following results:

Leaner mixes using Ideal finishing plaster showed results which

were not very uniform, due in part to using excess water. To make

a homogeneous material, free from air pockets, it was customary to

use as much water as possible without causing segregation. However, at times some segregation occurred unintentionally, thereby

producing erratic specimens. Leaner mixes shrank considerably after
LATER!L LONGI~UDINAL P~ISSON:S

I

RATIO

./ ..\.----

35-£: jf;'" /' --- ~-35. '.25

--26 .-33 '6, .'6 ~"'..31

:23" ~-3I "Y> 31-.

~--- /

'III

V

~~::::-~- -33

)30 ~I

If .3. I

~~lj-',/" {.-30

A

Ii'; a

~/'

I

I~ ~Cost:August 25,1930.

Composition:22Ibs.plaster.IOlbs.,Celite,

and 37 Ibs. water.

I~ ~Ageat test: 100 days.

Averagemodulus of elasticity~]64,800

Ibs. per square inch.

Average Poisson'sratio: 0..167.

br4

Maximum allowable working stress:94

Ibs. per square inch.

260 ......

Z

<1

trJ

en

>-3

...... I:;)

200 >

>-3

......

0

Z 160

0

'-:z:J

120

~>

>-3

trJ

60 ::d

>t-<

en

400 400

360 360

320 320

c

z

=< 2.0 CI>

-<

'"'"CI> CI>

-

240

Z

"

g

Z

'0

200

CI>

"

'"'"(f) 169

'"

c,..

'"'"

.40

-2

120

"

'"

60

40 40

0

0

0

0,40 0.0002 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016

UNIT DEFORMATION IN INCHES PER INCH

0.0016 0.0020 0.0022 0 0.10 0.20 0.30

POISSON'S RATIO

0.0004

FIGURE 7-STRESS-STRAIN DIAGRAMS FOR COMPRESSION TESTS

2 by 4-inch Cylinders Made With Ideal Finishing Plaster ....

-,
360

320

280 is:

0

tj

t':J

240 t"

>-3

t':J

200 Ul

>-3

Ul

0

160 ':rJ

to

0

120

,....,

~tj

t':J

80 ::d

tj

>

--- 4a

400

LONGiTUDIN1L PbISSON;S RATIO LAT RAL

360

320

~

=i 280

'";:

'"

'"CJ) 240

40

L,B

/ 15'.11",

,

12 / ./ 19'"

~

,.:5

/ / II';~/ lIy~"" 12", j '"

~llj(l' /~~~3:C:~~~ ..

,,-

f;

II ~P~/

'/~ ~~/

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\

,~;f;, /'9

II' r' Z

'U0

C

~ 200

'"'U

'"'"~

160

c

..

~

Z 120 0

:r

Cast, August 26,1930

Compo,sition 221bs. plaster\,IOlbs. Celite,

and .35.58 Ib.-c;., water.

Age at test ~5? to 84 days,

Average modulus of ,elos'tLcity~161,OOO

Ibs. per square inch.

Average Pojsson~s rati,a :,0.190.

Maximum allowable working stress':90

Ibs. per square inch.

80

0

0 0.0008 0.0014 0.0016 0.0018 0.0020 0.0022 0.10 0.20 0.00'0 0.0002 0.0004 0.0006 0.0012

UNIT DEFORMATION IN INCHES PER INCH POISSON'S RATIO

FIGURE 8-STRESS-STRAIN DIAGRAMS FOR COMPRESSION TESTS

2 by 4-inch Cylinder Made With Acme Finishing Plaster

....

00

400

0_30

a

0.40
LATERAL LONG ITUDI NAL I POISSON'S , RATIO

f

/" .

j

/' I

Acme3

i

Acme 3.

I

jAcme I

/

I I

/

Acme3 ,"

I

ACr -Acme1

I

/

JAcme 2

/

I

/

Acme 2--/. ,

I, /

/

V

/

.Acme 2

/'

/

V ModeAugust 26,1930.

'I /

Composition: 221bs. plaster,_IO Ibs.

Celite and 35.58Ibs. water

Ageattest: 37to 128days.

/ V

Averagemodulus of elasticity:

176.000Ibs.per square inch.

AveragePoisson'sratio: 0.176.

~/

Mo:dmum allowable worKing

stres 5: \10Ibs. per square

inch.

yv

400

360

320

280 .....

Z

-<t:S

240 00

j

1;'1

200 >

~(3

160 Z

0

":J

120 '"'"" >

~t'!

80 :u

:;

t'"

40 00

400

360

320

c

z

=i 280

'"...

;::

'"en 240

z

"

0

c

~ 200

'"

"

'"'"(JJ 160

0

C

~

'"-

120

z

'"'"

80

40

0

0 0.0002 0.0004 0.0006 0.0008 0,0010 0,0012 0.0014 0.0016 0.0018 0.0020 0.0022 0,10 0.20 0.30

UNIT DEFORMATION IN INCHES PER INCH POISSON'S RATIO

FIGURE 9-STRESS-STRAIN DIAGRAMS FOR COMPRESSION TESTS

3 by 6-inch Cylinders Made With Acme Finishing Plaster

0

0.40

....

<0
BEAM DATE

DA TE AGE COMPOSITION MODULUS WT. PER

OF IN PLASTER CELITE WATER Ar~:~)L OF

1~B~l NO. MADE TEST DAYS (LBS.) (LBS.) ILBS.' ELASTICITY

I 8- 20-30 9-24-30 35 22

"

25.86 None 157,000 40-4

2 8- 20-30 12- 5 -

30 106 22

"

25.86 None 122,000 38.'

3 8-26-30 9 -24- 30 29 22 10 35.58 None 216,000 44.9

4 8- 26-30 12- 5 -30 101 22 10 35.58 None 226,000 44.3

5 9- 5 -30 9-24- 30 19 18 12 42.00 4 106,000 38.9

6 9- 5 -30 12- 5 -30 31 18 12 42.00 4 109,000 37.2

7 9- 9 -30 9-25-30 16 8 6 21.00 2 82,000 36.4

8 9- 9 -30 \2- 5 -30 87 8 6 21.00 2 92,000 35.4

9 9- B -30 9 -25- 30 17 12 12 42.00 5 47,000 31.0

10 9- 15-30 12- 6 - 30 82 4 4 14.00 2 64,000 31.7

11 9- 9 -30 9 -25- 30 16 14 12 42.00 4 59,000 33.9

12 9- 9 -30 12- 6 -30 88 14 12 42.00 4 65 000 32.9

50 MODEL TESTS OF BOULDER DAM

hardening. A batch of 16 pounds of plaster, 12 pounds of celite, 42

pounds of water, and 5 teaspoons of aquagel was about as lean as

could be made without excessive shrinkage.

In casting 3 by 3 by 4O-inch beams, the forms were placed on a

sheet of building paper on a concrete floor, filled with the plaster

mixture, and then removed in about 24 hours. After removing the

forms the beams were placed on three 1 by 4-inch cleats to dry, thus

allowing air to circulate underneath them. Frequently, beams of the

leaner mixes sagged between the cleats during the period of plasticity

before they were entirely dry. }\s soon as sagging was noticed aIJ

3 by 3 by 40-inch beams were allowed to dry either on the floor or

on a flat plank.

'"

0

Z 4

:J

Q. 0

;0

0.004 0.006 O.OOB 0.010

TOTAL DEFLECTION IN INCHES

0,014 0.016

0

"

0

-'2

-' ~

g

FIGURE 10-LOAD-DEFLECTION DIAGRAMS FOR ACME BEAMS

37. Acme Finishing P1aster.--i\cme finishing plaster provecl to

be the most satisfactory of all brands of plaster used in combination

with celite. The workability was satisfactory, and very few specimens were defective due to entrapped air or premature setting. In

setting there was a slight swelling, which was preferred to the shrinkage encountered in some of the other brands of plaster. If the mixing

water had a temperature of 60 degrees Fahrenheit, or less, there was
INVESTIGATION OF MATERIALS 51

no danger of too rapid setting; but when warmer water was used

it was necessary to add a small amount of aquagel as a retarder. This

was particularly true in the case of the leaner mixes.

Typical stress-strain diagrams for cylinders cast from a mix of

22 pounds of Acme finishing plaster, 10 pounds of celite, and 35.58

pounds of water are shown in figures 8 and 9. Figure 8 shows data

for 2 by 4-inch cylinders and figure 9 shows data for 3 by 6-inch

cylinders. Results of fle:.!(ural tests on 3 by 3 by 4O-inch beams of

several different mixes are shown in figure 10. The results of tests

of the richer mixes show greater consistency than those of the leaner

mixes, due in part to the difficulty in preventing segregation of material in the leaner mixes. The spread of the curves for a relatively rich

mix is fairly narrow, as shown in figure 8.

FIGURE Il-TYPICAL SHOT-LOADED CYLINDERS

Acme Finishing Plaster, Celite, and Lead Shot

38. Acme Plaster, Celite, and Lead.-The unit weight of plaster

and celite is relatively low compared with that of most building materials. It was thought that an advantage might be derived from constructing the model of Boulder Dam of a material of the same unit

weight as concrete. Therefore, some experimenting was done in an

effort to increase the unit weight of plaster and celite mixes. It was

found that the unit weight of plaster mixes could easily be controlled

by the addition of small lead shot. Typical appearances of 2 by 4-inch

shot-loaded cylinders are shown in figure 11. The cylinder which had

been cut in half showed an apparent nonuniform distribution of shot.
on

""

400

B-7' "r8-8

t

360

,-8-19 !

320

2.0 ;:::

0

tj

trJ

240 t'"

8

trJ

200 rn

8

rn

0

'60 "'J

t:I:I

0

--< '20 L,

t'"t:I

trJ

.0 ::0

t:I

>

40 ;:::

400

360

320

c:

z

=i 280

'"

;;:

...

'"

(,I) 240

%

"

0

c:

~ 200

'""

...

<h'" 160 0

c: ,.

'"

...

Z 120 0

'"

80

40

0

0 0.0008 0.0010

UNIT OEFOftMATION IN INCHES PER INCH

0.0002 0.0004 0.0006

8-j7-'

POISSON'S RATIO

I

Cast: November 1,1930.

Composition: 41bs. plaster, 21bs. Celite

6lbs. water,20lbs, No.8 shot, and

one teaspoon Aquagel.

Age ottest:7to 49 days.

Average modulus of elasticity: 225,000

Ibs., per squore inch.

Average Poisson's ratio: 0.21'5.

Maximum allowable working stress: 120

fbs. per square inch.

0.0012 0.0014 0.0016 0.0018 0.0020 0.0022 0 0.10 0.20 0.30

POISSON'S RATIO

FIGURE 12-STRESS-STRAIN DIAGRAMS FOR SHOT-LOADED SPECIMENS

Compression Tests on 2 by 4-inch Acme Plaster and Celite Cylinders

0

O.4Q
INVESTIGATION OF MATERIALS 53

This was incorrect because many of the shot were torn out by the saw

in cutting the cylinder.

The addition of shot tended to increase the strength of the plaster

product, with a resulting increase in the modulus of elasticity. It was

difficult to secure uniform distribution of shot in the larger mixes,

since the shot had a tendency to segregate at the bottom of the mixing pan. The plaster and celite mixtures were too thin to hold the

shot in suspension. Several sizes of shot were used in the experiments. Number 5 was the largest, and number 10 the smallest. \Vithin this range no effect of differences in size could be detected. Unit

weights of specimens containing shot varied from 130 to 180 pounds

per cubic foot.

The modulus of elasticity of shot-loaded specimens varied from

68,600 to 235,000 pounds per square inch, depending on the proportions of the ingredients. Poisson's ratio was about 0.20, nearly the

same as for concrete. Stress-strain curves for a shot-loaded Acme

plaster and celite mix are shown in figure 12. No flexural tests were

made as there was insufficient shot available for casting 3 by 3 by

40-inch beams.

TESTS OF RECOMMENDED MIX

39. Recommended Mix.-The most satisfactory material found

for models of thick arch dams was a mixture of 24 pounds of Acme

finishing plaster, 12 pounds of celite, and 45 pounds of water. If the

temperature of the water was above 60 degrees Fahrenheit, one to

four teaspoons of aquagel were needed as a retarder, depending on the

water temperature. This amount of material made a batch of convenient size, which could be handled by one or two men.

The recommended mix had a unit weight of 41.5 pounds per cubic

foot, an average modulus of elasticity of 122,000 pounds per square

inch in compression, and 165,000 pounds per square inch in flexure, a

Poisson's ratio of 0.214, and a maximum allowable working stress of

80 pounds per square inch in compression. Typical stress-strain diagrams are shown in figure 13. Load deflection curves for 3 by 3 by

40-inch beams are shown in figure 14. In all tests the modulus of

elasticity in flexure was greater than in compression. This was probably due to the fact that the flexural tests were made with simply

supported beams in which only the outside fibers were stressed to a

maximum. Also, some of the difference may have been caused by the

apparatu5 u5ed in the compre55ion te5t5.
240

'"

AX-22 } Y

/

200

-

AX-41

-

160

;'AX-21

120

80

40

c:

z

::t 280.

en

...

'"

'"en(I)

240

Z

...

0

c:

~ 200

en

~

~'" 160

c:

>

'"

'"Z 120

"

:z:

400

360

320

Cast, October 6,1930.

Composition: 241bs. plaster ,12 Jbs. Celite.

45 Ibs. water. and 4 teaspoons Aquagel.

Age ottest: 7to77 doys.

Average modulus 01 elastic ity: 123,000 tbs.

per square inch.

Average Poisson's ratio: 0.213.

Maximumallowable working stress :80Ibs.

per square inch.

I I

POISSON'S RATIO

/mAX-18 ~2!.

I

I

AX-18'", /

AX-23',y /

AX-2IYAX-41

AX-23""

AX-2I,~i~8 V

~.

/ //7 ~~I~~X-22 AX-23' j

A~-~:

!//;If

~ ~~I:L

80 ;W ~~

},~ ~~ 40

If/~

0

0

LATERA'L

0.0002 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0022 a 0.10. 0.20 0.30

POISSON'S RATIO

0.0018 0.0020

UNIT DEFORMATION IN POUNDS PER SQUARE INCH

FIGURE 13-STRESS-STRAIN DIAGRAMS FOR RECOMMENDED MIX

Compression Tests on 2 by 4-inch Acme Plaster Cylinders

""

....

400

360

320

280 a::

0

tj

trJ

t"

>-3

trJ

Ul

>-3 Ul

0

"'.1

IJ:I

0

q

t"tj

trJ

::0

tj

P>

a::

0

0.40
DATE AGE COMPOSITION MODULUS WT. PER

BEAM DATE OF IN PLASTER CELITE WATER AQUAGEL OF CU. FT.

NO. MADE TEST DAYS (LBsJ (LBS.) (LBsJ (TSP.) ELASTICITY (LB.)

AX I 10-5-30 10-29-30 24 24 12 45 4 160,000 41.7

AX2 10-5-30 10-29 -30 24 24 12 45 4 167,000 41.7

AXI 10-5-30 II

-

4 -30 30 24 12 45 4 173,000 41.4

AX 2 10- 5-30 II

-

4 -30 30 24 12 45 4 169,000 41.4

AXI 10-5-30 12- 4 -30 60 24 12 45 4 168,000 41.3

AX2 10-5-30 12-4-30 60 24 12 45 4 160 00 a 41.6

INVESTIGATION OF MATERIALS 55

It was found that plaster compounds did not increase in strength

with age after they were about seven days old. This fact is brought

out by E. C. Eckel,7 who stated: "Cement plasters and stuccos attain

almost their full strength at the end of one week, showing little further

gain at three months." In investigating this property, several 2 by

4-inch cylinders and some 3 by 3 by 40-inch beams were tested, with

2

NQte:- ''Acme'' finishing plaster used

in all these specimens.

8

6

If)

0

z

:>

0

"-

~ 4

0

c(

0

J

J

c(

....

0

....

0.002 0.004 0.006 0.008 0.010

TOTAL DEFLECTION IN INCHES

Note:-This mix is the some as used in the 3'x3'x 3' block and 6"x e"shrinkoge beam

FIGURE 14-LOAD-DEFLECTION DIAGRAMS FOR RECOMMENDED MIX

Flexural Tests on 3 by 3 by 40-inch Beams

'Eckel, Edwin C., "Cements, Limes and Plasters," 2nd Ed., 1922, p. 67, John

Wiley & Sons, Inc.
.!\umber of Age in Average Average

Specimens Days Modulus of Poisson's

Tested Elasticity *Ratio

----

~--~ --

4 7 129.000 0.213

4 14 120,000 0.175

4 21 115,000 0.203

4 28 130,000 0.249

3 35 116,000 0.202

56 MODEL TESTS OF BOULDER DAM

TABLE I-EFFECT OF AGE ON RECOMMENDED MIX

Composition: 24 lb. plaster, 12 lb. celite, 45 lb. water, and 4 teaspoons aquagel.

*In pounds per square inch.

results as shown in table 1 and figure 14. The conclusion drawn fro111

the tests was that, after the material had set and dried, age did not

affect the strength or elastic properties.

The recommended mix contained as much water as could be used

without segregation occurring in the mixing pan. If less water was

used the strength and modulus of elasticity were materially increased.

This fact can be seen by comparing the compressive tests shown in

figures 13, 15, and 16, and by studying the flexural tests shown in

figure 17. Tests to determine effects' of varying the water content

were made by keeping the proportions of dry materials the same and

using 45, 40, and 35 pounds of water. The resuJts are given below.

Amount of water

per batch, lb.

45

40

35

Modulus of elasticity,

lb. per sq. in.

122,000

136,000

193,000

Maximum working stress,

lb. per sq. in.

SO

SO

102

40. Shrinkage of Recommended Mix.-Some apprehension was

felt over the possibility of shrinkage of the model dam and abutments

which might cause the formation of cracks along the areas of contact.

In order to study the shrinkage of the recommended mix, a 6 by S-inch

beam was cast on two sheets of rubber, with the ends of the beam

terminating in S by 16 by 20-inch blocks which were securely anchored

to concrete. Plugs for making strain-gage observations were set in

the top of the beam and readings were taken regularly for three

months. No cracks developed and no movements were indicated by

the strain gage. The beam is shown in the foreground of figure IS.

41. Workability of Recommended Mix.-The usual batch of the

recommended mix contained 36 pounds of dry materials and 45 pounds
LA ERAL LONciITUDIN'AL P~ISSON~S RATIO

"

40-W-5\

/'" 4o-W-S""', ~if- 4O-W-5

4o-W-II(

-:I:..

~o-W-12 /~:r-- J

4O-W-'7

/'

~/40-W-19- vA

f '-4o-W-'

~~~<-40-~-'2-- ~40-W-3

/ ~~IA. I

..- 4Q-W-19

.-4o-W-1

fj ~,. 40-W-3 ~~~-;::?V 4D-W-II...1 \

./. .....---- ~'-40-W-3 1 1\

~(1/ ~~~y I

/ \

/ /'" I

&/ ~/ V

Cast:November 8,1930. /

40-W-I/

/

Composition: 241bs. plaster, 121bs. Celite,

.dE 4Qlbs. water,and 4teospoons Aquagel.

~:e/

Ageattest: 9 to 42 days.

Averagemodulus of elasticity: 136,000

~Ibs.per square inch.

Average Poisson's ratio ~O.202.

~Maximumallowable working stress: 80

Ibs. per square inch.

I I I I

400

360

320

280 .....

Z

<1t:j

240 rn

t-3

.....

Q

200 II>-

t-3

.....

0

180 Z

0

>:rJ

120

~II>-

t-3

l':1

80

~......

II>-

t"'

40 rn

400

360

320

c

z

::j 280

..

...

:0

'"..

en 240

Z

..0

c

z

a 200

..

..

'"

:0

~ 160

C,.

:0

'"~ 120

'"

80

40

0

0 0.0002 0.0004 00006 0 0.10 0,20 0.30

POISSON'S RATIO

0,0008 0.0010 0.0012 0.0014 0.0016

UNIT DEFORMATION IN INCHES PER INCH

0.0019 0.0020 00022

FIGURE 15-STRESS-STRAIN DIAGRAMS, REDUCED MIXING WATER

Compression Tests on 2 by 4-inch Acme Plaster Cylinders

0

0.40

-1""
<On

00

400

360

320

260 '"0"'"

I:)

i:'J

240 t"'

'--35-\\1-11 f-j

t:1J

200 U1

f-j

U1

0

160

"'J

tC

0

120 c:

t"' I:)

i:'J 80 ::0

I:)

> 40 :s:

400

360

320

c

z

::j 280

'"-I

"'"'"(J) 240

Z

-c0

c

~

200

-c

'"g'" 160

J>

'"'"~

120

'"

'0

40

0

0 o.oooa 0.0010 0.0012

UNIT DEFORMATION IN INCHES PER INCH

00002 00004 0.0006 0.00r6

Cast: November 8,1930.

Composition ~241bs. plasterI 121bs.CeJite,

35 Jbs. water ,and 6teaspoons Aquogel.

Age at test: 9 to 42 days.

Average modulus of elasticity: J92,OOO

Ibs. per square inch.

Average Poisson's ratio: 0.189.

Maximum allowable working sTres5;!02

Jbs. per square inch.

0.0014 0.0018 0.0020 0.0022

35-W-!9--~-'-

OJ(} 0.20 030

POISSON'S RATIO

FIGURE 16-STRESS-STRAIN DIAGRAMS, REDUCED MIXING WATER

Compression Tests on 2 by 4-inch Acme Plaster Cylinders

0

0.40
DATE AGE COMPOSITION MODULUS WT. PER

BEAM DATE OF IN PLASTER ~IELITE ~t;S~IR A?~:~Y

OF NO. MADE TEST DAYS (LBS.) LBS.) ELASTICITY CrY' LBS. F:\

35-W-1 11-8-30 12-4-30 26 24 12 35 6 249,000 48.6

35-W-2 11-8-.30 12- 4 -30 26 24 12 35 6 251,000 47.8

4O-W-1 11-8-30 12-4-30 26 24 12 40 4 211,000 44.1

4o-W-2 11-8-30 12-4 -30 26 24 12 40 4 201,000 44.4

AXI

*

10-5-30 10-29-30 24 24 12 45 4 160,000 417

AX2

*

10-5-30 10-29-30 24 24 12 45 4 167..000 41.7

INVESTIGATION OF MATERIALS 59

8

6

Note:- "Acme" finishing plaster used

in QII these specimens.

(()

CI

z

:::>

0

0..

~4

CI

<

0

..J

..J

<

~

0

~

2

0.002 0.004 0.006 0.008

TOTAL DEFLECTION IN INCHES

*

First test ~

FIGURE 17-LOAD-DEFLECTION DIAGRAMS, VARIABLE MIXING WATER

Flexural Tests on 3 by 3 by 40-inch Acme Plaster Beams

of water. Since all test specimens were relatively small compared to

the proposed model, it was decided to cast a three-foot cube so that

the problems involved in mixing and placing larger masses of the

material could be studied. It was not feasible to mix sufficient quantities of material to pour the block at one time, owing to the possibility

of initial set occurring before the pour was completed. The block

was therefore cast in three-inch layers, a layer being poured each

morning and afternoon until the desired height was reached. The
60 MODEL TESTS OF BOULDER DAM

bond between the layers proved to be satisfactory. The finished block

is shown in the background of figure 18.

The greatest difficulty involved in building and curing the bJock

was the length of time required for the material to dry. As a possible

means of hastening the time of drying of the proposed model, it was

decided to try pouring a layer from three to four inches thick, aIIowing it to dry, then pouring a succeeding layer on top of the dried

material. Experiments were made with 4 by 6 by 38-inch beams,

cast in two stages, to observe whether a fresh layer would bond to

FIGURE 18-SHRINKAGE BEAM AND 3-FOOT CUBICAL BLOCK

a dry on~. ' When the lower half of the beam was poured, greased

wooden pl~,gs were set in the top, to form keyways for bonding the

o

two halves together. However, as the lower half of the beam dried,

cracks appeared at the corners of the keyways.

Another set of beams was made in which keyways were cut with

a saw and chisel as soon as the first layers were sufficiently dry, see

figures 19 and 20. When thoroughly dry the first layers were placed

in the forms aga,in, and second layers cast. Typical results are shown

in figure 21. The dry base drew water out of the upper part by capillary action so rapidly that shrinkage cracks developed. The difference

jh drying conditions between the two halves produced an upper portion which did not bear arty resen'1blahce to the lower portion. .
INVESTIGATION OF MATERIALS 61

FIGURE 19-KEYWAYS IN LOWER HALF OF PLASTER-CELITE BEAM

FIGURE 20-KEYWAYS IN PLASTER-CELITE BEAMS
62 MODEL TESTS OF BOULDER DAM

FIGURE 21-TYPICAL FAILURE OF PLASTERiCELITE BEAM

Upper Layer Poured on Keyed Lower Layer Shown in Figure 20,

Without Shellacking Dried Surface

A third set of beams was made with keyways of about equal

length as shown in figure 22. To prevent moisture being drawn from

the second layer into the first, the first layer of one beam was painted

with two coats of orange shellac before the second layer was poured.

In this beam the bond between the old and new layers was satisfactory, as may be seen in figure 23. In beams wh~re the first layers

were not shellacked, the two halves'failed to bond satisfactorily. One

of these beams is shown in figure 24.

42. Bond at Metal Inserts.-In older to make deflection measurements of the Stevenson Creek and Gibson models, small metal inserts

were embedded in the concrete at the downstream faces of the models.

Rods which actuated measuring dials wer,e attached to the inserts.

As it was desired to use the same system in measuring movements

of the Boulder model, tests were made to determine the bond of plaster

materials to the metal inserts. Several 2 by 4-inch cylinders of the

recommended mix and also of the shot mixes were made with deflection anchors cast in one end. A section through one of the anchors

is shown in figure 37. The method used in testing the specimens is

shown in figure 25, a hook for supporting the load being attached

to the insert as shown in the figure. The specimens were tested by

placing them on a support with a slot under the insert, and gradually

adding shot to a bucket suspended from the hook until failure occurred. Cylinders before and after being. tested are shown in figure 26.
INVESTIGATION OF 1IATEIRIALS 63

FIGURE 22-KEYWAYS IN PLASTER.CELITE BEAMS

Second Series of Tests. Center Beam Painted With

Two Coats of Orange Shellac

FIGURE 23-BEAM SHOWING SATISFACTORY BOND BETWEEN LAYERS

Surface of First Layer Painted with Shellac Before Pouring Second Layer
64 MODI~L TESTS OF BOULDER DAM

FIGURE 24-FAILURE OF PLASTER-CELJTE BEAM

Surface of First Layer Not Painted with Shellac Before Pouring Second Layer

The strength developed in bond to the metal inserts was remarkable.

For shot-loaded cylinders the average load required to pull out the

inserts was 119 pounds. For cylindeys cast from the recommended

mix, an average of 64 pounds was required to pull out inserts with

plain ends, and 94 pounds for inserts with a wire loop around the ends

of the anchor screws.

43. Evaporation Rates.-An investigation was made of the rate

of evaporation of the recommended mix under different storage conditions and using different sizes of specimens. A set of evaporation

test specimens consisted of one 4 by 6 by 38-inch beam, one 3 by 3

by 40-inch beam, one 6 by 8 by 18-inch block, one 6 by 12-inch cylinder,

two 3 by 6-inch cylinders, and seven 2 by 4-inch cylinders. A group

of evaporation specimens is shown in figure 27. Results of evaporation tests, for various storage and drying conditions, are shown on

figure 28.

The specimens were poured and allowed to remain undisturbed

until the end of the second day when the forms were removed. The

specimens were then weighed and placed in storage. At this time

the weights of all specimens, except the 2 by 4-inch cylinders, were

from 150 to 180 per cent of the dry weights.

Curves showing the ratio of evaporation for representative specimens under different storage conditions are given in figure 28. The

larger specimens, such as the 4 by 6 by 38-inch beams and the 6 by 8

by 18-inch blocks, gave an indication of the rate of evaporation to

be expected in the two to three-inch layers to be used in constructing
INVESTIGATION OF MATE,RIALS 65

FIGURE 25-TESTING BOND BETWEEN PLASTER AND INSERTS

the model. U nder ordinary conditions in the model testing pit, such

layers would require from 15 to 20 days to dry; but by blowing warm

air over them, the time could be reduced to about 7 to 10 days. For

the model, evaporation took place almost entirely through the top of

the layer, except near the top of the model where evaporation also

took place at the sides. For such conditions, rates of evaporation

naturally were lower than for specimens which were exposed on at

least three faces.

The 3 by 3 by 3-foot experimental block which was built in the

concrete laboratory near the testing pit was- watched with considerable interest. Although electric fansa:nd heaters were used to increase
66 MODEL TESTS OF BOULDER DAM

FIGURE 26-SPECIMENS BEFORE AND AFTER TESTING

BOND AT INSERTS

Specimen at Left Ready for Test. Specimens at Right

Show Characteristic Failure

evaporation rates, the interior of the block required considerable time

to dry. Borings were made at intervals to determine the moisture

content of the interior. Six months after the block was finished a

moisture content of eight per cent was found in the material removed

from the center of the block. This was still too high to obtain satisfactory elastic conditions.

FIGURE 27-SET OF EVAPORATION TEST SPECIMENS

4 by 6 by 38-inch Beam, 6 by 8 by 18-inch Block, 6 by 12-inch

Cylinder, 3 by 6-inch Cylinder, and 2 by 4-inch Cylinder
\ ~\ ""

I

I

3 by3 by 40m,h BeamE 2 3 by3by40in,hBeamEI 3by3by40in,h Beam-£4 3by3 by40in,h8eam-E3

"

2

\

"'" \""

........ '-- I

4by 6 by38 inchBeam-a 4by6 by38in,h Beam-£I 4 by 6by381nchBeam-£4 4

by 6 by 38 inch Beam- E 3

\

"'\ "

'-. "'-.. I

6byBbylBinch Black-£2 6 byHy IB,nchBlock-£I Na 0010 an 6 by 8 by IBinch B ck 6 byBby 18m,h Block-£ 3

\

"

~"" \

""

'- '- I

6

by 12mch Cylinder-E2 6 by IZinch Cylinder- £1 6 by IZ inch Cylinder-£4 6bylZ loch Cylinder- £J

,tE4

,~ \ \

£2/

I

J by6inchCylinders£J 5£4 3by6inch Cyllllders-El5E2 3by6inch Cylinder-E6 3by6 nchCylinder-E5

\ \ ~\ I

2

bYj

;n,h

CY/'"ler-E8 Zbyrnch CYlinler £5 Z byrChCYlinjer-£ 25 2by inchCyliner-El9

INVESTIGATION OF MATERIALS 67

44. Plotting Test Data.-The compression tests discussed in this

chapter were made with the 20,OOO-pound, hand-operated testing

machine shown in figure 1, using the strain meters shown in figure 2.

The testing was done by the increment method; that is, the poise

200

100

200

00

200 00

100 00

....

-& 200

~

>- is 100

zoo

00

'5

+-C

~ ZOO

L

~

C

-;;; 100

c

.,

E

-[ 200

CJ)

't5

:E /00

'"~

ZOO

200

00

200

00

200

JOO 00

0 0

0

1

10 ZO 0

1

10

A'F

~Ospecimdns in Da~-

20 0

1

10 20 3

1

0

Sf°ro,9tin concreft laboratory Sf?rage in.ex~r:-imenfQI pit

I

S~raqe oversteam radiator Sfo,:aqe if'! hyqrau/;c fa~Qfory

USing fans II heQf~rs. with outs/de windows open. with tempt!raffJre lJOofal/OoE No c/rculafl"9 arr or or/if/Clal htaf

CompOsition: Z41bs. Acme plaster, 12Ibs.

Celite.45 Ibs. wafer, and 4 teaspoons

Aquagel.

FIGURE 28-EV APORA TION RATES OF PLASTER-CELITE SPECIMENS

was set at SOlne predetermined figure on the scale beam and the load

applied until the beam balanced. At this time the dial gages of the

strain meters were reac!. The poise was then moved ahead another

increment and the load applied as before until the beam balanced,

when the dials were again read.
OTAL OBSERVED DATA REDUCED DATA

LOAD LA..DEF. LONG.DEF. UNIT UNIT UNIT POISSON'S

0.0001" 0.001" STRESS LAT. DEF. LONG.DEF. RATIO

0 0.0 Q.O 0.0 0,00000 0.00000 0.107

50 0.4 0.6 16.2 0.0000 I 0.00008 0.107

100 1.0 1.3 32.5 0.00003 0.00018 0.107

150 1.1 2.2 48.7 0.00003 0.00031 0.107

200 I., 3.2 65.0 0.00005 0.00045 0.107

250 2.2 4.2 81.2 0.0000'6 0,00059 0.107

300 3.0 5.2 92.5 0.00008 '0.00073 0.107

350 3.5 6.1 113.7 0.00009 0.00086 0.107

400 4.3 7.0 130.0 0-0001 J 0.00098 0.J08

450 5.6 9.4 146.2 0.00014 0.00131 0-117

500 6.9 9.8 162.5 0.00017 0.00137 0.124

550 fAilED

68 MODEL TESTS OF BOULDER DAM

A table containing observed and reduced data for a typical test

is shown in figure 29. In this test, 50-pound increments were used

in loading the specimen. The columns headed "Lat. Def." and "Long.

Def." give dial readings of the strain meters, the former being for

the lateral extensometer and the latter for the longitudinal compres someter. In reducing the data the unit stress was obtained by

dividing the total load by the area of the cross section of the specimen

tested. The molds for the 2 by 4-inch cylinders had a diameter of

1.98 inches and a cross-sectional area of 3.079 square inches. The

area of the cross section of the 3 by 6-inch cylinders was 7.065 square

inches. The unit lateral deformation was obtained by multiplying

the observed lateral gage reading by the factor 0.000,025,2 for the

2 by 4-inch cylinders, and by 0.000,016,7 for the 3 by 6-inch cylinders.

These factors were computed from the design and dimensions of the

extensometers. The unit longitudinal deformation was obtained by

multiplying the observed longitudinal gage reading by the factor

0.000,140 for the 2 by 4-inch cylinders, and by 0.000,120,7 for the 3 by

6-inch cylinders. These factors were obtained by calibrating the compressometers against a standard dial gage.

Curves for lateral and longitudinal deformation were next plotted.

Since some slack existed in the assembled apparatus, the deformation

curves rarely passed through the origin of coordinates, as may be

..

..

~

~

40

~

Z

:> 0

Poisson's ratio at

-' this point,

~:~g~~j5 =0.107

~

200

~

~160

~

'"~

ID..120

..0

z

:>0

~

'0

~

N

0.0012 0.0014 0.0016 0.0018

UNIT DEFORMATION IN INCHES PER INCH

0.10 0.20 0.30 0.40

This method was used in all tests of the

2Minch by4-inch and 3-inch by6-inch cylinders.

Curves shown above ore for 2-inch by 4-inch

cylinder AX40.

Deformation curves, when plotted, rarely pass

through the origin of coordinates.Therefore,

they are transposed horizontally until they

intersect the origin.

The modulus of elasticity is the tangent modulus

forthe lower stresses where the deformation

curves are straight.

In this example,

Modulus" ~~~~~~

,," O.'~;IO

125,000 Ibs. per square inch. "

LooCJitudinol gage factor" 0.000,140.

Lateral gage factor" 0.000,025,2.

FIGURE 29-METHOD OF PLOTTING COMPRESSION TEST DATA
LOAD

Gaoe readi~aBs Si~ ~:n:~ho~:cinAdths of on. inch

lBS. 'N TEST I 2 3 4

'

Av.OEF.

0 0 0 0 0 0 0

2 24 23 23 24 23 23

4 45 43 44 47 44 44

6 64 64 64 69 64 64

4 46 44 45 49 44 45

2 25 24 23 28 20 23

0 3 2 3 6 0 3

INVESTIGATION OF MATERIALS 69

seen in figure 29. In order to place all stress-strain curves on the same

basis, the curves were transposed parallel to their original positions,

so that they would pass through the origin. This simplified the computations of the modulus of elasticity and Poisson's ratio.

Values of the modulus of elasticity given in this bulletin are

"tangent moduli" for the parts of the curves which lie below the

elastic limit. As the plaster compounds were very elastic, the stressstrain diagrams for the lower unit stresses were found to be straight

in nearly all of the tests. To find the modulus of elasticity it was

only necessary to produce the initial slope of the longitudinal curve

until it intersected the 0.0010 deformation line. By reading the stress

at this point and dividing by 0.0010, the modulus was obtained. Poisson's ratio was found by dividing the abscissa of the lateral curve by

the abscissa of the longitudinal curve.

Flexural tests were made with the apparatus shown in figure 3.

A typical set of test data and resulting curves are shown in figure

30. The beams were tested four or more times and the average results

used in plotting. A little slack in the apparatus was responsible for

the fact that the loading and unloading curves do not coincide.

a

..

3

;;2

~

0

~

0,001 0.002 0.003 0.004

TOTAL DEFLECTION IN INCHES

0.005 0:006 0.001

.,

a

z4

~"

~

0

0.0

Deflection observations for each beam were repeated

several times and the average value of the observed'def!ection was used in plotting.

As the exoct dimensions of the beams varied somewhat from the nominal dimensions, the exact

dimensions were used in calculating the moments

of inertia.

For the above beam, breadth" 3.06"; depth" 3.04";

and moment of inertia" 7.16.

Modulus of elasticity"

...L x £J! :: ...L x

~,, {

149.QOO pounds per

48 ID 48 7.16 X 0.0064 square inch.

FIGURE 30-METHOD OF PLOTTING FLEXURAL TEST DATA

CHAPTER III-PLASTER-CELITE MODEL AND

MATERIALS TESTS

45. Design of Model The plaster-celite model of Boulder Dam

was designed from the plan and section shown on figure 31. This was

a tentative design, based on technical study 32-B, which was revised

before construction. The design finally adopted for the dam is shown

on page iv. The principal change made in preparing final plans was

the straightening of the downstream face near the base of the dam.

The design shown in figure 31 had constant radius arches and variable

cantilever slopes at the downstream face, in the lower portion of the

dam. By use of constant radius arches, each arch element had a constant thickness from abutment to abutment. The scale selected for the

model was 1 to 240, or 1 inch on the model represented 20 feet on

the dam. This gave a model 3671\ inches high, with a top thickness

of 2.% inches and a maximum base thickness of 32 inches.

The same pit that was used for testing the previous models of

arch dams was used for the model of Boulder Dam. The concrete base

and the reference pier which were used for the Gibson model were left

in the pit, but it was necessary to remove a portion of the base to make

room for the new concrete base for the Boulder model. The old

reference pier, however, served as a support for the bracing required

to hold the mercury loading apparatus.

In order to adapt the testing pit to the Boulder model, concrete

abutments containing 20 cubic yards each, and conforming approximately to the shape of the cross section at Boulder Canyon, were constructed in the testing pit. Since the model would have a much lower

strength and stiffness than concrete, it was necessary to provide a

supplemental plaster-celite base to provide for foundation movements.

Such movements could not be obtained with the model cast directly

against concrete. Figure 32 shows the position of the model in the

testing pit with the concrete base, supplemental plaster base, and

reference base for deflection instruments. A minimum thickness of

12 inches, corresponding to a depth of 240 feet in the canyon rock,

was specified for the supplemental plaster base.

71
a

For finol design see page iv.

-~ 45':-<-

~

z

~

900

.

>

ILl 900

--375'

--431,5'-

8.~~'-~ 490'

',' ~-

: '. R. 875'

1""-110'-~.

-

591'

540'

~--

- R ~970'

-n-650'

-

SECTION ON LINE OF CENTERS

'",

'", ",,

SCALE OF FEET

FIGURE 31-BOULDE'R DAM, PLAN AND MAXIMUM SECTION, STUDY 32-B

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73

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74 MODEL TESTS OF BOULDER DAM

CONSTRUCTION OF SUPPLEMENTAL BASE

46. Method of Construction.- The plaster-celite mixture set in

about an hour in cool weather, and more rapidly in warm weather .

The resulting product held water for a considerable time after setting.

In order to dry the base thoroughly it was cast in layers three inches

thick, and warm air blown over each layer from 10 to IS days until

dry. Samples of the material in each layer, obtained by boring with a

carpenter's auger, were accurately weighed and carefully dried at a

temperature not greater than 100 degrees Fahrenheit to determine

FIGURE 33-KEYWAYS BETWEEN LAYERS OF SUPPL;EMENTAL BASE

the moisture content. The drying was carefully controlled, since

exposure of plaster to excessive heat causes dehydration. When the

moisture content was less than 4 per cent by weight, the test holes

were plugged and the surface of each layer painted with two coa,ts

of orange shellac and one coat of waterproof ship varnish. The next

layer was then cast. To insure a good bond between adjacent layers,

it was customary to cut a series of keyways, intersecting perpendicularly across the face of each layer, before the succeeding layer

was cast, as shown in figure 33.

47. Form for Casting Canyon Walls.-Since it was desired to

duplicate the topography of the canyon as closely as possible, the
PLASTE,R-CELITE MODEL AND MATERIAL TESTS 75

final layer of the base required a special form. A topographical

map of the canyon was made on wallboard to a scale of 1 to 240.

Each contour was traced and transferred to another sheet of wallboard. These contours were then sawed out with a scroll saw and

nailed to blocks of wood having the scale height of the contour interval, so that the air space of the canyon was duplicated to scale.

The form was next covered with a one-inch diamond-mesh wire netting

and plastered over smoothly. After the form was thoroughly dry, it

FIGURE 34-FORM FOR CASTING CANYON WALLS

View Taken Before Covering with Wire Netting and Plaster

was sanded smooth, painted with shellac, and carefully greased with

cup grease. The form was then lowered into place and the final layer

of the canyon poured. Figure 34 shows the form under construction,

and figure 35 shows it being lowered into place.

FORMS FOR MODEL

48. Necessity for Wooden Forms.-Since it was not possible to

develop the surfaces of the model of Boulder Dam from flat plates,

steel forms could not be used. The curved portions of both forms were

made of sugar pine which was carefully shaped to exact dimensions.
76 MODEL TESTS OF BOULDER DAM

FIGURE 35-LOWERING FORM FOR CANYON WALLS

View Taken Prior to Pouring Final Layer of Supplemental Base

The upstream form served for casting the model and, later, for supporting the mercury loading bag against the upstream face. This was

the same general arrangement for applying load as was used in the

previous models, mercury being forced into the rubber bag between the

upstream face of the model and the upstream form. It was imperative

that the upstream form be sufficiently rigid to take the reaction

of the mercury load. As the wooden form was not strong enough
PLASTER-CELITE MODEL AND MATERIAL TESTS 77

to support this pressure, it wa~ reinforced with a flat steel plate,

one-quarter of an inch thick, attached with screws to the back of the

form. It was necessary to trim off a few irregulartities of the canyon

topography upstream from the model to allow the upstream form to

be set properly.

The downstream form was made in sections, 2~ inches thick,

which were held together with bolts. The bolts were arranged so that

the form could be assembled one piece at a time in order to allow

space for pouring and drying the model. The upstream form was

assembled complete in one piece. Both forms ",.ere set in position and

lines of contact with the canyon walls marked on the walls. The contact zone was then excavated according to the plans for the construction of Boulder Dam. Figure 36 shows the downstream form in place

before excavating the model abutments.

FIGURE 36-DOWNSTREAM FORM IN PLACE BEFORE

EXCA V A TING ABUTMENTS

49. Anchors for Deflection Rods.-Anchors to which invar steel

rods could be fastened for measuring radial deflections of the model

were attached to the downstream form with small tacks. The arrangement of the anchors is shown in figure 37. In stripping the forms

from the model, the ,tacks pulled out of the wood readily, leaving the

anchors firmlv embedded in the plaster.
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PLASTE)R-CELITE MODEL AND MATERIAL TESTS 79

CASTING THE MODEL

50. General Procedure.-The procedure followed in casting the

model was the same as in casting the supplemental base. The thickness of the layers, however, was reduced to 2% inches, since such

layers could be easily dried in seven to ten days. The entire upstream

form and a few of the lower sections of the downstream form were

fastened in place with quick-setting plaster, and the bottom of the

canyon painted with shellac and varnish. The canyon with the forms

in place, prior to pouring the first layer of the model, is shown in

FIGURE 38-FORMS. IN PLACE PRIOR TO POURING FIRST

LAYER OF MODEL

figure 38. A portion of the roughened abutments and the upstream

cut-off wall can be seen between the forms.

As soon as each layer had set, grooves were cut in the top of

the layer, one-half inch deep and one inch wide, to increase the bond

between layers. The model poured to elevation 950 is shown in figure

39. The bonding grooves can be seen in the top of the last layer cast.

51. Installation 0£ ThermoCOUples.-A temperature test was

included in the proposed testing program; therefore, thermocouples

were embedded in the interior of the model for measuring tempera-
MODEL TESTS OF BOULDER DAM

hermocouples were m

)ther constantan, eacl1

together and one conr

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52.

elevation

both face

Completion of the Model.- When the .

1050, the section was sufficiently thin

s after the forms were stripped. The re

Lode was poured to

y readily from

maindl er of the model

was poured in two parts to prevent undue segregation of materials

The first part was cast and allowed to set for about an hour. Th~

usual grooves were then cut in the upper surface, the surface shellacked, and the second part poured. Four days after the top of the

model was cast, the forms were stripped and drying was begun on

both faces. Three deflection-rod anchors were accidentally loosened

".h;l~ removing the forms. These were grouted in place vv "'11;;

se1 ttmg plaster, so that they could be used during the test program.

The plaster-celite mixture used in making the model swelled

ightly in setting. Although this was expected t was not feasible

allow for the expansion in setting the forms. 'he result was that
PLASTER-CELITE MODEL AND MATERIAL TESTS 81

the model was slightly thicker than originally intended. Dimensions

of the model as constructed are shown in figure 40. The model was

so near the design dimensions that it was not considered necessary

to dress down the excess portions with sandpaper. The model was

built one-half an inch higher than shown in the plans to protect the

top row of anchors. This increase in height did not add enough

material to affect the stiffness of the model appreciably.

From the time the first layer of the plaster base was poured, five

months and ten days were required to complete the casting of the

model. Altogether, 21 layers were cast, taking an average of about

9 days to dry each layer. The drying periods for the base layers were

slightly longer than for the dam layers.

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FIGURE 40-DIMENSIONS OF MODEL AS CONSTRUCTED

PROPERTIES OF MODEL MATERIAL

53. Concrete Base.- The concrete abutments on which the plaster-celite supplemental base rested were made of 1 :20 :4 proportions

by volume. No record was kept of the water-cement ratio, as a

concrete of high strength was unnecessary, the maximum stress due

to load being about 30 pounds per square inch. The average slump

was 6 inches. Considerable care was taken to obtain a concrete of

uniform density which would be free from rock pockets. Several

6 by 12-inch test cylinders were made from the new concrete. The

28-day strength of standard cured specimens averaged 3,450 pounds

per square inch, Average values of the modulus of elasticity and
82 MODEL TESTS OF BOULDER DAM

Poisson's ratio at the same age were 2,290,000 pounds per square inch

and 0.14, respectively.

54. Special Testing Apparatus.-The preliminary investigations

of contemplated model materials, including plaster-celite mixtures,

comprised a large number of tests. In all the preliminary work

standard apparatus for concrete testing was used. Since the plastercelite material, when dry, had about one-twentieth the ultimate

strength and modulus of elasticity of concrete, some difficulty was

encountered in conducting tests with apparatus designed for concrete

specimens. The weight of the apparatus and the sluggish action of

the hand-operated testing machine of 20,000 pounds capacity often

caused erratic results.

It was desired to make a complete record of the physical properties of the plaster-celite material used in the model. In view of the

difficulties encountered in testing plaster specimens with the equipment used in testing concrete specimens, it was decided to design

special machines for applying load to the specimens, and to develop

strain meters which would be sufficiently sensitive to record deformations caused by small increments of load.

55. Compressometers.-The compressometers used by the Materials Testing Laboratory at the University of Colorado were similar

to those developed in the Lewis Institute, Chicago. The design of

the apparatus was modified to make it suitable for testing plastercelite specimens. Compressometers shown in figures 41 and 42 were

made from the new designs. The parts of the new instruments were

made of aluminum whenever possible, the size of the members being

kept to a minimum. The apparatus is essentially the same as that

previously described.s The essential features of the redesigned

compressometers are:

1. The bottom yoke is attached to the cylinder by three set

screws which bear against small blocks. This insures proper

stability and prevents the points of the set screws from damaging

the specimen.

2. The upper yoke is attached to the cylinder by two set

screws which bear against small blocks with the same advantage

as above.

sWalker, Stanton, "The Modulus of Elasticity of Concrete." Proc. Am. Soc.

Test. Mats., Vol. 19, 1919, Part II, p. 520.
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86 MODEL TESTS OF BOULDER DAM

3. To aid in centering the specimen and to aline the bearing

blocks, a flexible tin band is soldered to the faces of the bearing

blocks.

4. The deformation is measured with a dial gage reading

to 0.0001 of an inch.

5. The average deformation of the cylinder is measured on

a single gage.

6. The gage is easily removable from the apparatus.

7. The deformation is transmitted to the gage by a knurledhead steel screw, which allmvs adjustment of the gage reading

when attaching the compressometer.

56. Lateral Extensometers.-- The extensometers used in measuring the lateral deformations are shown in figure 43. They were modified from the type developed by Professor H. ]. Gilkey and Doctor

Fredrik Vogt.D The essential features of these instruments are:

1. The extensometer consists of two aluminum legs, hinged

at the rear and held together with a spring at the front.

2. The legs bear against the specimen through small aluminum blocks in which two small needle points are fastened. The

tension of the spring and the four needle points keep the apparatus

properly alined.

3. The deformation is measured with a light-weight dial

gage reading to 0.0001 of an inch.

4. Final adjustment of the gage can be made with the

knurled-head steel screw which the gage bears against.

In using the lateral extensometers, two objectionable features

were experienced. The first was the uncertainty as to the exact location of the point of revolution of the hinge of the two legs. This caused

relatively small errors, however, as they amounted to only about one

per cent in the 2 by 4-inch extensometer, and less in the 3 by 6-inch

extensometer. The second was that the rlial gage registered negative

movements which caused occasional erratic lateral rleformations due

to slack or improper hearing of the instrument.

57. Testing Machines.-The direct-load apparatus developed for

use in testing the plaster-celite material is shown in figure 44. The

"Proc. Am. Soc. Test. Mats., Vol. 30, 1930, Part I, p. 632.
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Note:- All connections mode with

screws €"Kcepfos shown.

FIGURE 44-DIRECT.LOAD APPARATUS USED IN MATERIALS TESTS 00-.J
88 MODEL TESTS OF BOUI..DER DAM

FIGURE 45-COMPRESSION MACHINE TESTING A 3 BY 6-INCH CYLINDER

Note the Characteristic Cone-shaped Failure of the Broken Cylinders

FIGURE 46- TENSION TESTING MACHINE IN OPERATION
PLASTEfR-CELITE MODEL AND MATERIAL TESTS 8!!

compression-testing machine, shown in figure 45, and the tensiontesting machine, shown in figure 46, were built for making routine

tests of specimens. These machines were designed for testing 2~

by 12-inch cylinders in tension and 2 by 4-inch, 3 by 6-inch, 3 by 12

inch, or 6 by 12-inch cylinders in compression. The design of the

machines was based on the principle of the lever and fulcrum. In the

tension tests, the load was applied to the specimen by placing bags of

lead shot in a bucket suspended on the end of the tension machine. In

the compression tests, the load was applied by placing small bags of

lead shot on the platform suspended from the end of the lever. Test

loads were applied to specimens through spherical blocks, bearing

against a greased steel plate. This prevented the rotation of the lever ,

caused by strain in the specimen, from producing bending or shear in

the specimen.

Six smaller machines of each type shown in figure 44 were built

for making plastic flow tests under sustained loads. The compressiveflow testing machine is shown in figure 47. As the loads applied in

FIGURE 47-COMPRESSIVE-FLOW TESTING MACHINE

the flow tests were much smaller than the maximum for which the

tension and compression machines were designed, the machines for

making the flow tests were of much lighter construction, These machines were designed for testing 2~ by 12-inch specimens in tension

and 3 by 12-inch cylinders in compression.
90 MODEL TESTS OF BOULDER DAM

58. Grips and Strain Meters.-Tensile tests of 3 by 12-inch concrete cylinders had been made in the Materials Testing Laboratory of

the University of Colorado for some time prior to the Boulder model

tests. The apparatus consisted of a pair of grips and a strain meter on

which three dial gages, measuring to 0.0001 of an inch, were mounted.

Since this apparatus was too heavy for making satisfactory tests of

plaster specimens, the grips and strain meter shown in figure 48 were

developed. The essential features of the redesigned grips are:

1. The rubber liner in the tension collar prevents the grip

from bearing directly on the specimen and damaging it.

2. The grips are self-alining so that no bending can occur in

the specimen.

The tension collar was attached to a circular steel plate with three

loosely connected steel straps 120 degrees apart. The test load was

applicd to the circular steel plates through bolts with spherical heads.

These features permitted the grips to automatically aline themselves

with the load, producing uniform stress in the specimen.

The strain meter for tensile tests consisted of two steel collars

attached to the specimen with knurled-head screws. In order to prevent damage to the plaster, a flexible brass band encircled the specimen for the points of the screws to bear against. Fastened to one

collar were three invar steel rods, 120 degrees apart, on which dial

gages were mounted. On the other collar were three flat-head screws

which were used in adjusting dial-gage settings when mounting the

strain meter on the specimen. This type of strain meter was used in

measuring longitudinal deformations in all tension tests and in the

compressive flow tests.

I t was originally planned to use 3 by 12-inch cylinders in testing

the material in tension. The available forms for casting the 3 by

12-inch cylinders were not exactly circular. Consequently, specimens

cast in these forms were placed in a lathe and turned to a diameter

of 20 inches for a distance of 90 inches in the center portion. The

ends were left approximately three inches in diameter but were turned

to a true circle.

59. Apparatus for Torsion Tests.-In making auxiliary tests of

the materials used in the Stevenson Creek and Gibson models, a torsion

machine for testing 3 by 12-inch concrete cylinders was devised.I° This

JO"Arch Dam Investigation, Report by Committee," Vol. II, Engineering F'oundation, May, 1934, pp. 454 and 455.
3-"Lost Word"

DiOls.~::

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FIGURE 48-TENSION GRIPS AND 8.INCH STRAIN METER ~

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FIGURE 49-DESIGN OF TORSION MACHINE

-t.

~ ",

in '1",

~. M~

TROPTOMETER @)

ONE RE~rf~/i"'H ,l"D. ROO

CD

ONE REQ'D.WITHO'CrrH.'D.ROO

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PLASTER-CELITE MODEL AND MATERIAL TESTS 93

machine operated satisfactorily when testing concrete cylinders, but

was too heavy for testing plaster-celite specimens. The apparatus was

redesigned, using lighter members and counterweights, and arranged

for direct loading. Figures 49 and 50 illustrate the design and operation of the torsion machine. Although the machine was of rather

crude appearance, its operation was satisfactory and the results of

the torsion tests were consistent. The essential feature of the machine

was the system of rockers and clamps which supported the specimen.

By applying a load in the bucket a torque was exerted on the specimen.

FIGURE 50-TORSION TESTING MACHINE IN OPERATION

The deformation was measured by the troptometer on which a dial

gage, reading to 0.0001 of an inch, was mounted. The troptometer was

fastened to the specimen by screws, bearing against flexible brass

bands placed around the specimen.

60. Apparatus for Flexural Tests.-Flexural tests were made on

3 by 3 by 4O-inch beams, simply supported over a span of 38 inches.

A concentrated load was applied at the center and the deflection

measured with the apparatus shown in figure 51. The modulus of elasticity was computed from the deflection at the center of the span.

Flexural tests of beams under sustained loads are shown in figure 52.
MODEL TESTS OF BOULDER DAM

, O , , , .

" , , , ,

SCA'E IN INCHES

END ViEW

FIGURE 51-APPARATUS FOR BEAM TESTS

FIGURE 52-FLEXURAL FLOW TESTS ON BEAMS

61. Methods of Plotting.-Figures 29 and 30, chapter II, illustrate the method used in plotting results of compression and flexure

tests. Except for calibration factors and different means of applying

load, the data from the compression and flexure tests on the model

materia:l were recorded and reduc.ed in the same manner as in the pre-
UNIT OBSERVED DATA REDUCED DATA

LOAD LAT.DEF. LONG. DEF. UNIT UNIT POISSON'S

0.0001~ O.OOOI~ LAT.DEF. LONG. DEF. RATIO

0 00 0.0 0.00000 0,00000

"

1.4 5.5' 0.00002 0.00010 0.198

30 3.0 12.0 0.00005 0.00021 O. '98 45 4.5 22.0 0.00007 0.00038 Q. '98 60 63 29,0 0,00010 0.00050 0.198

75 B.5 38.5 0.00014 0,00067 0.198

90 11.0 48.5 0,00018 0-00084 0.191

L05 !3.1 58.5 0.00021 0,0010' 0.193

120 16.0 6'8.5 0.00026 0.Q0118 0.204

135 18.2 78.0 0.00029 0.00135 0,212

150 2\.3 88.5 0.00035 0.00153 0.228

165 25,0 99.5 0 0004 1 0.00172 0.233

LBO 28.2 '10.5 0,00046 0.00191 0.244

190 31.0 123.0 0.00051 0.00212 0.249

190+ fAilED

PLASTEiR-CELITE MODEL AND MATERIAL TESTS 95

liminary investigations. Similar methods of plotting results were followed in the torsion and tension tests, but the original curves usually

passed through the origin, making it unnecessary to transpose the

curve. In all cases, the slope of the tangent to the lower portion of the

curve was used to calculate the modulus of elasticity.

62. Compression Tests.-A typical stress-strain curve for a 3 by

6-inch plaster-celite cylinder, showing the method of plotting results

of compression tests, is given in figure 53. In using the direct-load

200

%

0

Z

~

~160

~

~120

.,

0

z

~

0

~ BO

z

0.0006 0.0010 0.0012 0.0014 0.0016 0.0018 0.0020

-UNIT DEFORMATION- IN INCHES PER tNCH

0.0 0.10 0.20 0.30

.,

.,

~

~

40

0-

Z

~

0

Curves shown above ore for 3"x6"cylinder

NO.90-5.

Deformation curves, when plOlled, rarely

poss through the origin of coordinates.

They are therefore tronsposed horizontally until they intersect the origin

The modulus of elasticily is the tangenl

modulus for the lower stresses where

the deformation curves ore sfraight.

In this example

-

STRESS

-

~

-{

I04,QOO pounds

MOdulus- 5 TRAIN - 0.0010 -

per square inch.

Longitudinal gage foctor

"

0.000,017,3

Lateral gage foctor

"

0.000,016,3

FIGURE 53-METHOD OF PLOTTING RESULTS OF COMPRESSION TESTS

testing machine, sacks of lead shot were prepared to give load increments of 1j pounds per square inch. These loads were recorded in the

column, "Unit Load." Observed data were actual gage readings, and

reduced data were obtained by multiplying observed readings by calibration factors. Calibration factors, for the 3 by 6-inch apparatus,

were 0.000,017,3 for the longitudinal gage and 0.000,016,3 for the lateral

gage. Calibration factors for the 2 by 4-inch apparatus were 0.000,018,8

and 0.000,023,8, respectively. The decimal points in the calibration

factors were placed so that the factors were applicable to gage readings expressed in ten-thousandths of an inch, as recorded in the table

in figure 53. Factors for lateral gages were calculated from the geo-
LAT RAL

I

LON'GITUDINAL POISSON'S RATIO

I I

I

:

Cast Ju~~ 19,1931;Tested July 1,1931.

Composition: 241b. plaster~ 121b.

Celite. and 451b. water.

,I A ~.3

.£-4 "

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400

360

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0 IJ.OOO2 0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018

UNIT DEFORMATION IN INCHES PER INCH

0.0022 0.10 0.20 0.30

POISSON'S RATIO

0.0020

FIGURE 54-STRESS-STRAIN DIAGRAMS FOR COMPRESSION TESTS

0

0.40
/

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/

/

./

yV

./ V

../ <

,/' ,;,

/' ,,;

./" V

UNIT OBSERVED DATA* REDUCED DATA

LOAD DEFORMATION

~~EF~~G~

UNIT

DIAL I DIAL2D1AL3 DEF.-INCHES

0 0.0 0.0 0.0 0.0 0.000000

2 2.0 1.3 2.0 1.8 0.000023

4 4.2 2.2 3.8 3.4 0.000043

6 6.2 3.8 5.3 4.9 0.000061

8 8.5 4.2 7.0 6.6 0.000083

10 11.5 5.4 8.2 8.4 0.000 I05

12 13.8 6.3 10.0 10.0 0.000 125

14 16.0 7.2 11.8 11.7 0.000 J46

16 18.2 8.2 13.2 13.2 0.000165

18 21.0 9.1 15.0 15.0 0.000185

20 23.8 10.5 17.0 17.1 0.000214

22 26.4 11.0 ,8.8 18.7 0.600234

24 29.3 12.0 20.7 20,7 0.000259

26 32.2 12.8 22.8 22.6 0.000282

28 35.7 13.5 24.8 24.7 0.000304

PLASTER-CELITE MODEL AND MATERIAL TESTS 97

metrical relation between the hinge, point of contact on the specimen,

and point of bearing of the gage. The compressometers were calibrated by the universal calibrator used in the tests of the Stevenson

Creek and Gibson models.ll

The typical stress-strain curve in figure 53 shows that the new

equipment gave consistent results. The plotted points follow the

curves closely throughout the entire range of stress. More consistent

results were obtained with the 3 by 6-inch equipment than with the

2 by 4-inch equipment, due to the longer gage lengths, larger gage

readings, and larger areas. The larger quantities, together with the

improved mechanical operation of the light-weight apparatus, reduced

the proportion of errors considerably. Figure 54 shows typical results

of compression tests of 3 by 6-inch cylinders.

63. Tension Tests.- Tension specimens were tested with two

pounds per square inch stress increments, using the direct-load ma28

0.00004 0.00008 0.00012 0.00016 0.00020

UNIT DEFORMATION -INCHES PER INCH

0.00024 0.00028 0.00032

%

"

! 24

...

a:

..

a 20

..

a:

...

... 16

..

0

z

:> 12 0

...

!:

0

..

0

oJ

...

Z

:>

0

0.0

Curve shown above is for 2~"X 12.cylinderNo. 120-2.

The unit deformation is obtained by dividing the

overage observed deformatton by the gage

length of eight inches.

Unit deformation for unit load of 20 pounds per

square inch equals QQQ!l!.: ~O.OOO214 inches

Modulus of elasticity

8

l

per inch.

E'"

STRESS

=

~= {

95000 p.ounds per

STRAIN 0.00010 square tnch.

*Gage reading in teh-thousandths of an inch

FIGURE 55-METHOD OF PLOTTING RESULTS OF TENSION TESTS

"Loc. cit., DD. 470, 471.
98 MODEL TESTS OF BOULDER DAM

chine shown on figure 46. The method of plotting stress-strain diagrams is shown on figure 55. \Vith three dial gages mounted 120

degrees part, the average reading represented the total deformation,

regardless of the distribution of the readings. The gage length of

eight inches made the readings sufficiently large to insure accuracy.

The tension graphs usually passed through the origin and were always

straight lines since failure occurred at the yield point. The average

ultimate strength in tension was 30 pounds per square inch. Figure

58-A shows typical results of tension tests. Numbers on the curves

represent elevations of the model from which the material was cast,

and specimen numbers. For example, 85-2 represents specimen 2, from

material poured between elevations 800 and 850. The same designation was followed for all types of specimens.

64. Torsion Tests.- Torsion test specimens were cast 12 inches

long by 3 inches in diameter. After drying, they were turned in a

lathe to true circular cylinders of 2'0\-inch diameter. The procedure

lfsed in setting up the apparatus for a test was as follows:

1. The troptometer with dial gage was mounted on the

speClmen.

2. The ends of the specimens were inserted in the rubberlined clamps and the assembly placed on a table or other flat surface. The clamps were then tightened and the dial adjusted to

zero reading.

3. The clamp and specimen assembly was connected to the

rocker arms of the testing machine.

4. Counterweights were used to eliminate initial torsion in

the specimen, caused by dead weight. The amount of weight

was adjusted to return the dial reading to zero.

5. Loads were then applied to the loading bar of the machine and dial readings recorded for all increments of load.

From the dimen:,;ions of the machine, it was determined that one

pound of load on the loading bar produced 6 inch-pounds of torque

on the specimen. \Vith 5-pound load increments, a shearing stress of

6.43 pounds per square inch in the extreme fiber was produced for each

load increment. Figure 56 shows the method of plotting results of

torsion tests and the formulas used in calculating unit stresses and

unit strains. The modulus of elasticity was calculated by dividing

the unit stress by the unit strain. Typical stress-strain graphs for torsion are shown on figure 58-C.
A

,/

~~/

.........

'" 0

----t/ //,

./ !

~.~ '

,~~

f>.Q\\'\~~

~,/o..../

~..../

/'

~./ ....""

N

~........

,

...."" j

./

~./

,

..../

/

....""

1

UNIT OBSERV E D REDUCED DATA

LOAD DATA UNIT UNIT

DEFORM. STRESS DEFORM.

a 0.0 0.00 0.000000

5 30.0 6.43 0.000 I 38

10 56.9 12.86 0.000264

15 .85.2 19.29 0.000392

20 114.6 25.72 0.000527

25 146.2 32.1.5 0.000673

20 122.€i 25.72 0.000564

15 98.0 19.29 0.000450

10 67.8 12.86 0.00031 I

5 39.6 6.43 0.000 I83

0 6.0 0.00 0.000028

PLASTEiR"CELITE MODEL AND MATERIAL TESTS 99

35

a

~ 30

W

0<

..

::>

"

<n 25

::i

"-- <nO<

OW

~~20

0'"

"-w

~~

m~ 15 Wx O<w

~-

'"

Z 10

i<

:\

iii

>-

'<::>

0.0(10 000010 0.00020 0,00030 0,00040 0.00050

UNIT TORSIONAL DEFORMATION IN EXTREME FIBER

0.oa060 0.00070

Curve shown above is for 2~ "x 12" cylinder' No, 100-"5.

The measured gO,ge length of the troptometer was 5.84':

Distance from bearing point of "Lost Word" dial to

radius of cylinder was 3.90':

Each 5-pound load increfT1ent applied a torque of 30

inch-pounds on the specimen.

Shearing stress in extreme fiber for a 5-pou"nd load

increment,

T

30xl.4375 [643 d S,,-$!."[314159 fI437514]" . p~un 5 per

J

[. x2 .

square Inch.

Unit deformation for a 20-pound load,

Lls;I.{l..1.4375(~) ;'0.000527. 5.84

Modulus of elasticity.

E" SSTT~~~~ =O.0~~50 : 48,000 pounds per square inch.

F'IGURE 56-METHOD OF PLOTTING RESULTS OF TORSION TESTS

65. Flexural Tests.--Flexural tests were made on 3 by 3 by 40-

inch beams, simply supported on 38-inch spans. The load was applied

at the center and the deflection of the dial gage observed at the center. Three readings were taken with the beam in one position, after

which the beam was inverted and three additional readings taken.

The mean of the six readings was used to calculate the modulus of

elasticity in flexure.

The stress in the outside fiber was calculated by the usual formula,

S =

jlIc

I

.

for deflection of elastic beams at the center,

The modulus of elasticity was obtained from the formula

E = -.!- PL'

48 Iy

,

where y is the observed deflection at the center. In order that results

of the flexural tests might be shown as stress-strain diagrams, unit
?"

/

E

:/ .'')'

d

~/

~//

p.o\~ ......"",~O\~c;; <D

~\,)~\,.o '" /

0~//

/

/

TOTAL OBSERVED DATA* REDUCED DATA

LOAD 00 BEAM NORMAL BEAM INVERTED AVERAG EUNIT UNIT

BEAM 1 2 3 1 2 3 STRESS DEFORM.-INCHES

0 0.0 0.0 0.0 0.0 0.0 0.0. 0.00 0.00 0.0000000

2 33.0 33.0 33.6 33.5 33.2 33.9 33.23 4.02 0.0000405

4 68.0 67.0 70.3 69.0 67.2 67.2 69.15 6.05 0.0000831

6 106.5 99.4 102.0 106.0 102.5 101.5 102.15 12.06 0.0001246

4 70.3 68.2 71.5 73.6 68.6 68.2 69.98 8.05 0.0000853

2 37.1 38.4 39.0 39.6 35.0 34.0 37.02 4.02 0.0000452

0 3.8 4.5 4.2 5.5 0.8 0.5 2.22 0.00 0.0000039

100 MODEL TESTS OF BOULDER DAM

stresses and unit strains at extreme fibers were calculated in the

following manner:

U nit stress 1 P L'

-=E'=--

48

.~81 Y

or unit strain =

P L' X unit stress.

Unit strain ly

For a simply supported beam with a concentrated load at the center,

the unit stress,

8=

111e

=

PL X~.

1 4 1

Combining,

, 481 Y P L e 12 c y

,S = P L-'- X

4

X 1= L-;-'

'I he modulus of elasticity was obtained by dividing the unit stress

by the unit strain. Figure 57 shows an example of calculations for

modulus of elasticity. Figure 58-B shows a typical set of stress-strain

graphs for flexural tests.

14

"

"

z

~

'"..

g:> 12

'"~

..

'" 10 §

0", ..~

~ ~ 6

",'"

"'~~z

"'~0-",

"'0- 6

~x

;:~

:>x

~

...

0.00002 0.00004 0.00006 0.00008 0.00010

UNIT DEFORMATION -INCHES PER INCH -EXTREME FIBER

0.00012 0.00014

"

~

0-

:>

..

Z

"

" 0

0.0

Curve shown above IS for3"x3"x40" beam NO.120-3.

The beam was simply supported on 0 38"span.

concentrated road applied ot center.

For a concentrated rood of 2 pounds on beam,

stress .n extreme t"lber,

.M[-

"

19/~353" 4.02 (Exact depth: 3.06 tn.)

Unit deformation of extreme tiber,

~:y-

=

12x

I.:~; ~8003323 -0.0000405 in.

Modulus of elasticity.

E =_~=~= {

961000 pounds per

STRAIN a.DOOIQ square inch.

*Gage read ings in ten.thausandths of an inch.

FIGURE 57-METHOD OF PLOTTING RESULTS OF FLEXURAL TESTS
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PLASTER-CELITE MODEL AND MATERIAL TESTS 101

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FIGURE 58-TYPICAL RESULTS OF TENSION, FLEXURE, AND

TORSION TESTS
102 MODEL TESTS OF BOULDER DAM

66. Plastic Flow Tests.-In the preliminary investigations of

materials, some plastic flow tests were made on beams. i\lso, flow

tests of concrete specimens under sustained tensile, compressive, and

flexural loads had been made in connection with the auxiliary tests of

materials used in models of the Stevenson Creek and Gibson dams,

previously cited. With the new testing equipment, constructed for

testing light-weight materials, plastic flow tests for plaster-celite specimens were undertaken.

The equipment for conducting plastic flow tests was the same

as the equipment used in the tests for elastic properties, except that

smaller direct load apparatus, shown in figure 44, was used for the

compression and tension tests. Tension specimens were the same as

those used in the elastic properties tests, but the compression specimens were cast 3 by 12 inches in size and turned in a lathe to true

circular cylinders 2:Ys by 12 inches in size. The strain meter with

8-inch gage length, using three dial gages, was used on both tension

and compression specimens, since the longer gage length recorded

small changes due to flow more accurately than the compressometer

used in the compression tests for elastic properties. No change was

made in the equipment for flexural and torsion flow tests.

Flow tests on compression specimens were made with stresses of

20 and 40 pounds per square inch, tension and flexural tests with 20

pounds per square inch, and torsion tests with shear stresses of

approximately 20 pounds per square inch. Variations in dimensions

of beams caused small variations in unit stresses. Loads applied to

the torsion specimens produced stresses slightly below 20 pounds

per square inch. The 20-pound compressive flow tests gave rather

erratic results due to the small amount of plastic flow. The general

trend was evident, but satisfactory curves were not obtained.

Flow tests were conducted during periods of 20 to 24 days. The

specimens were all exposed to fluctuations of temperature in the laboratory, and considerable variations in observed gage readings were expected. However, a sufficient number of observations were made on

each specimen so that an average curve could be drawn. A large part

of the plastic flow occurred within the first few hours of the test,

during which temperature changes were small. The rate of flow

was so slow at the end of 20 days that a longer period of testing was

not considered necessary.

Figure 59 shows a typical plastic flow curve for compression,

and figure 60 shows comparisons of test data for several specimens.
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NUMBER BETW E EN STRESS ELEVATIONS

55 -. 500 and 550 40

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70-4 650 700 40

75 -I 700 750 40

80-2 750 800 40

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PLASTER-CELITE MODEL AND MATERIAL TESTS 103

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FIGURE 59-TYPICAL PLASTIC FLOW IN COMPRESSION

All curves were plotted on a logarithmic time scale and a linear scale

for strain. The amount of plastic flow plotted on all curves indicates

the increase in strain beyond the initial elastic strain. Specimen 75-1,

figure 60, which showed the highest rate of flow of any test, probably

was affected by an air pocket or improper casting. The principal

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Specimens under constont compres-

~ion of 40 pounds per square inch.

.Pounds per square inch.

FIGURE 60--cOMPARISON 01<' PLASTIC FLOW DATA,

COMPRESSION TESTS
SPECIMEN fROM POUR UNIT *

BETWEEN NUMBER ELEVATIONS STRESS

65 -6 600 and 650 20

70-3 650 700 20

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104 MODEL TESTS OF BOULDER DAM

characteristic of the compression tests was that approximately onequarter of the 20-day flow occurred during the first hour, and about

one-half during the first day. The average plastic flow in 20 days at

40 pounds per square inch stress was 0.000,10 inches per inch which

was 25 per cent of the initial elastic deformation. The average 20-day

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Specimens under conslant tension

of 20 pounds per square- inch.

*Pounds per square inch.

FIGURE 61-COMPARISON OF PLASTIC FLOW DATA, TENSION TESTS

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FIGURE 62-COMPARISON OF PLASTIC FLOW DATA, FLEXURAL TESTS
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PLASTER-CELITE MODEL AND MATERIAL TESTS 105

plastic flow for compression specimens loaded to 20 pounds per square

inch was only 5 per cent of the initial elastic deformation.

Figure 61 shows comparisons of plastic now data for specimens

loaded to 20 pounds per square inch in tension. Rates of flow for tension were greater than for similar loads in compression, probably due

to the fact that the applied stress was a greater proportion of the maximum strength in the case of the tension tests. However, the initial

rate of flow was smaller in tension than in compression. Flow in flexural specimens, shown in figure 62, was approximately the average of

the flow in tension and compression.

Figure 63 shows a typical plastic flow curve for torsion. In the

test illustrated, approximately 70 per cent of the 20-day flow occurred

during the first day. Upon removal of load the recovery was rapid

for the first three days, then it slowed down until about 60 per cent

of the 20-day flow remained as permanent set.

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FIGURE 63-TYPICAL PLASTIC FLOW IN TORSION

The results of the flow tests indicated that, in order to reduce such

effects in the model, the mode I tests should be run with as short a

loading time as possible.

67. Coefficient of Expansion.- The proposed program of tests

on the model included a temperature test. Consequently, a test to

determine the thermal coefficient of expansion of plaster-celite was

made. Four 3 by 3 by 40-inch beams were selected for the tests. Figures 64 and 65 show apparatus used for measuring changes in length

and controlling temperatures. Tests were conducted in the following

manner. The beam was allowed to attain the uniform temperature of

the air in the testing room. The mild steel reference l)ar, which had
Apparatus mad'i;;']~:f mild. sfeel bars.

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FIGURE 64-APP ARA TUS FOR MEASURING THERMAL EXPANSION

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been calibrated against the invar steel reference bar for changes in

length due to temperature variation, was placed in the yoke shown in

figure 64 for a reference reading. The plaster-celite beam was next

placed in the yoke and an initial reading made. The beam was then

placed in the smaller of the two galvanized-iron boxes shown in figure

65 and covered tightly. This box was placed in the larger box, and

water having a temperature different from the initial temperature of

the beam was circulated around the inner box until the beam had a

uniform change in temperature. The beam was placed in the yoke

FIGURE 65-THERMAL-EXPANSION TEST OF PLASTER-CELITE BEAM

again and another set of observations made which was compared

with the mild steel reference bar. 'fhe coefficient of expansion was

computed from the change in length and temperature of the beam.

Several tests were made through different ranges of temperature.

During the heating tests the temperature varied from 78 to 130

degrees Fahrenheit. During the cooling tests the temperature varied

from 83 to 25 degrees. The coefficient of expansion was found by

dividing the net change in length of the beam by the product of the

length of the beam and the change in temperature. It was found to

vary from 0.000,010,7 to 0.000,011,6 inches per inch per degree Fahrenheit, for the different beams. The average coefficient of expansion was

0.000,011 inches per inch per degree Fahrenheit. The tests showed

that the expansion of the material was a linear function of the temperature.
108 MODEL TESTS OF BOULDER DAM

68. Unit Weight.--The unit weight of the material used in building the model and the supplemental base was determined from measurements and weights of the 3 by 3 by 40-inch beams used in the

flexural tests. As the other test specimens were usually capped with

quick-setting plaster before their removal from the forms, they could

not be used in determining unit weights. The dimensions of the

beams were carefully measured at a number of sections. The average

breadth, depth, and length of each beam was used in computing the

volume. Twenty-seven beams were used in determining the unit

weight. The average weight per cubic foot of all beams, when thoroughly dry, was 41.8 pounds per cubic foot. The variation in weight

was small, the maximum weight being 43.1 pounds per cubic foot and

the minimum 41.1 pounds per cubic foot.

69. Average Results.--Nearly 400 specimens were made from

the material used in the model. As each layer was poured, the unused

portion of the batch was cast into compression, tension, torsion, and

flexural specimens, so that a complete record of elastic properties of

each layer was obtained. The average results of the tests were:

Modulus of elasticity in compression, 87,000 lbs. per sq. in.

Modulus of elasticity in tension, 102,400 lbs. per sq. in.

Modulus of elasticity in flexure, 107,000 lbs. per sq. in.

Modulus of elasticity in torsion, 45,000 lbs. per sq. in.

Poisson's ratio for 2 by 4-inch cylinders, 0.177.

Poisson's ratio for 3 by 6-inch cylinders, 0.195.

Due to longer gage lengths and larger deflections, 3 by 6-inch

specimens gave more reliable results than 2 by 4-inch specimens.

The values for the 3 by 6-inch specimens are therefore considered

more reliable.

70. Effect of Age on Plaster.- The length of time that plaster

had been in storage affected the strength and modulus of elasticity

of the resulting product when combined with celite. In making the

preliminary tests for a suitable material for the model of Boulder

Dam, a relatively small quantity of plaster was obtained and mixed a

few days later. In building the model, considerable time was taken in

drying each layer. As a result the plaster was held in storage for

some time. As soon as any deterioration was noticed, the supply was

discarded and a fresh supply obtained.
PLASTEH-CELITE MODEL AND MATERIAL TESTS 109

The plaster was usually purchased in lots of five sacks. The total

amount was immediately poured into a large metal pan and stirred

until thoroughly blended. The plaster was then stored in paper-lined,

galvanized-iron cans with tight-fitting tops. Even in such storage the

plaster deteriorated to some extent if kept longer than two months.

SUBSEQUENT INVESTIGATIONS

71. General.-Plaster-celite mixtures were used in a number of

model tests after the completion of tests for Boulder Dam. Considerable additional data on characteristics of plaster-celite mixtures were

obtained in the later tests, and important conClusions derived therefrom are included in this report to complete the discussion. Also,

certain questions arose concerning the degree of isotropy obtained in

a model built up in layers. Consequently, when the Boulder model

was dismantled, specimens were cut out of the interior and tested

for such properties.

72. Segregation.-In later investigations, the same brand of

plaster, mixed with the same proportion of celite used in the Boulder

model, was found to have considerably different characteristics. It

was believed that these differences were due to changes in the constituents of the plaster, probably caused by variations in the material

at its source. Although these variations would have no effect on the

commercial uses of the plaster, they had pronounced effects on the

plaster-celite mixtures. Contrasted to the mixture used on the

Boulder model, which had a time of set of about 20 minutes, and expanded slightly in setting; mixtures of the same brand of materials

and proportions, three years later, had a time of set of about one hour

and a slight shrinkage during setting. Furthermore, segregation occUlTed in the later mixtures, making the bottom of a layer harder

than the top. It was found that the segregation was cansed by the

longer time of set, which allowed the mixing water to rise and the

heavier material to settle. This situation was remedied by blending

Sunflower molding plaster with the Acme finishing plaster, the former

being faster setting. By this process it was possible to obtain a time

of set of 20 minutes which was snfficient to prevent segregation.

73. Recommended Procedure.-Due to the variations which may

occur in commercial building plasters, the following program was

finally adopted in order to obtain uniformity in plaster-celite models.
110 MODEL TESTS OF BOULDER DAM

1. At the beginning of each program of tests, samples of

plasters were obtained; and, using the results of the preliminary

studies as a guide, trial mixes were made to check the modulus

of elasticity, time of set, and shrinkage or expansion.

2. If the original proportions did not give a satisfactory mixture, the proportions were varied or the plaster blended until a

satisfactory product was obtained. This did not involve more than

two or three trial mixes.

3. 'Vith the proper proportions determined, a fairly large

supply of material was obtained, sufficient to last about two

months. A trial mix was made from each shipment of material

to check on variations.

This procedure was followed on a model project using 3,000

pounds of material, and very uniform elastic properties were obtained.

In making up later mixtures, the moisture content of the celite was

measured and proper allowance made in the weight. Moisture content appeared to be the only variable quantity in celite.

74. Isotropy.-When the tests on the Boulder model were completed, the model was removed intact from the testing pit and stored

in the laboratory. Before disposing of the model, a large block of

material was cut out of the interior, for testing to determine isotropic

properties and, incidentally, the effect of age. Cylinder specimens,

3 by 6 inches in size, were cut out in vertical and horizontal planes

with respect to the model. Typical results of the cylinder tests are

shown on figure 66. These results were practically identical with the

tests made while the model was under construction. Also there was

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FIGURE 66-TEST OF CYLINDER TAKEN FROM MODEL
PLASTER-CELITE MODEL AND MATERIAL TESTS 111

very little difference between the tests made in vertical and horizontal

planes, which indicated that the material was isotropic.

A more conclusive test for isotropic properties could be made on

a cube, where the modulus of elasticity could be measured on three

axes. A 6-inch cube, comprising three layers of material, was cut out

and tested in the laboratory hydraulic testing machine. Dial gages

were attached directly to the faces of the cube, and load was applied

through fiat steel plates with a thin sheet of rubber between each

plate and the specimen.

Results of the cube test indicated practically the same deformations

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on each axis; but the end restraint caused bulging of the specimen,

and the gages did not record true deformations. By applying loads

through steel plates, there was no assurance of uniform load distribution over the ends of the specimens. Although various thicknesses of rubber were used to distribute the load, bulging of the

specimen could not be eliminated.

Lack of satisfactory results on the cube test made necessary

development of loading apparatus which would produce uniform

pressures over the ends of the specimen. A machine was built in

which the load was applied by means of compressed air. This machine

is shown on figure 67. The loading head consisted of two steel plates,

separated by spacers, and a rubber bladder connected to a compressed-
UNIT AVERAGE UNIT DE'FORMATION-IN,/lN.XI06 LOAD

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Size of cube Eight inches

Composition. 2 lb. Sunflower molding plasfer,

21b Acme finishing plasfel'",

2 2 Ib, Celite, 8 lib Water.

OF TESTS FOR ISOTROPIC PROPERTIES
PLASTEH-CELITE MODEL AND MATERIAL TESTS 113

air supply. The bottom plate had a square hole in which the end of

the specimen fitted. The reaction plate was identical, except that the

bladder receiving the reaction was filled with water. This machine

gave uniform pressures on the ends of the specimen and did not cause

restraint.

Since the specimen taken from the dam was not suitable for

further testing, three special cubes for additional tests were prepared.

They were built up in three-inch layers, following the same procedure

used in casting the model. Each layer was cast from a separate batch

of material. After each cube was dry, it was dressed down to a perfect cube 8 inches in size. Typical results from the tests are shown

on figure 68. All three specimens had small variations in moduli

along the three axes, similar to those shown, but the variations were

not on the same axes for the different specimens. It was, therefore,

concluded that the variations were caused by experimental errors

rather than by directional properties of the built-up specimens.

CHAPTER IV-PRELIMINARY TESTS OF

PLASTER-CELITE MODEL

TESTING PROCEDURE

75. Loading the Model.- The method of loading the model of

Boulder Dam was the same as the method used in testing previous

models built by the Bureau of Reclamation. A rubber bag, shaped to

fit the upstream face of the model, was made of heavy automobile

inner-tube stock, see figure 69. The bag served as a container for the

water or mercury during the application of triangular pressure loads

at the upstream face of the model. The upstream form which had been

used in casting the model was reshaped so that it would uniformly

support the rubber bag when placed about three-fourths of an inch

upstream from the model. The rubber bag was placed in the space

between the model and the form and clamped to the top and bottom

of the form so that it would not press against the model while empty.

The form was carefully braced against the opposite side of the testing

pit and against the concrete ceiling of the laboratory, so that it could

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ELE:VAT/ON

FIGURE 69-RUBBER BAG FOR LOADING MODEL

115
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SECTION A-A

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MERCURY TANK OUTL.E:T

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FIGURE 70-MERCURY SUPPLY TANK AND PIPING
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Ccmplelewilh Bolfs and Nuls

FIGURE 7l-DETAILS OF INSTRUMEKT STAND

.....

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-.J
!18 MODEL TESTS OF BOUI..DER DAM

not slide from its original position while supporting the reaction of

the load on the model. The rubber bag was connected to the mercury

supply tank by the piping system shown in figure 70. Water from the

city mains could be used in loading the model, when desired. When

mercury was used as the loading agent, water pressure was admitted

to the top of the supply tank, forcing the mercury from the bottom of

the tank into the rubber bag. A gage made of glass tubing served to

show the elevation of the water or mercury surface inside the bag.

76. Conduct of Tests.-Invar steel rods were used for attaching

gages to the model to reduce temperature effects as much as possible.

For radial deflection tests, dial gages, mounted on radial rods, were

rigidly attached to the face of the model. The dials were kept in

alinement by similar rods, mounted on the reference base and held in

flexible guides. The guides prevented lateral movements of the deflection rods but did not interfere with movement in the direction

of the length of the rods. Figure 71 shows details of the instrument

stand which served as a reference base. Figure 72 shows a typical

arrangement of gages for radial deflection measurements. The dial

gages used on the Boulder model were sensitive to 0.0001 of an inch

FIGURE 72-ARRANGEMENT OF GAGES FOR RADIAL DEFLECTION

MEASUREMl'~NTS
PRELIMINARY MODEL TESTS 119

with a range of 0.023 inches. There was very little inertia to the moving parts of the gage, and by lightly tapping the deflection rods, the

pointers of the gages would vibrate and come to rest at the correct

reading. This process eliminated friction and any stress in the rods

which actuated the dials. This was a valuable feature, especially where

it was necessary to bend the deflection rods, or where the rods were

quite long.

For all load-deflection tests, the procedure was as follows:

1. The dial gages were adjusted to an initial deflection, vibrated, and read.

2. The load was applied to the model and the gages vibrated

and read again.

3. The load was removed and recovery readings made.

Differences between no-load readings and load readings gave deflections due to load. Differences between load and recovery readings

gave the recovery of the model during removal of load.

77. First Deflection Measurements.--The first deflection tests

were made on July 7, 1931. The purpose of this series of tests was

to measure radial deflections of the model when loaded to elevation

1232 with water or mercury. The first three tests were made using

water for the loading agent. In bracing the supporting form, insufficient clearance had been allowed between the upstream face of

the model and the rubber bag. \Vhen the water load was applied, it

was doubtful if the rubber bag was completely filled. The measured

deflections were unusually small and the results were considered questionable. A mercury load was next applied. This load was sufficient

to force the supporting form slightly upstream, loosening the wedges

in the bracing. By adjusting the bracing, a film of mercury approximately one-fourth of an inch thick. was obtained in the rubber bag.

The measured radial deflections were fairly satisfactory but contained several erratic readings.

78. Movement of Unsupported Base.--During the preliminary

series of tests, a lack of symmetry was noticed in the deflection curves.

As the model was nearly symmetrical in shape, a symmetrical deflection curve was expected. The deflection of the model at the Arizona

abutment vvas materially greater than at the Nevada abutment.

During the construction of the plaster-celite supplemental base and

the model, cracking developed between the supplemental base and
'232

>-'

""

1232"

-- 0

1100

~'

~900

-"'00 is

2700

000

100Q

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t INDIC.4TE5 LENGTHENING BF"TWEEN INSERTS

-

INDICATES SHORTENING BETWEEN INSERTS

.ERRAT!C

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SECTION A-A RESULTS OF TESTS

MERCURY AT EL 1232 UNIT ~EASUREMENT 0001

THESE ROOS ARE ATTACHED

TO WALL. OF TESTING PIT ."

AL

-

1.6 -1.9

-7.2 -7.2

-,U ~!.

9.6 -97

-17.7 -17.3

-17.9 -17.9

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-2-0 -1.6

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UNSUPPORTED DOWNSTREAM

EDGE OF SUPPLEMENTAl..

BASE I ~

CONCRETE ARM FOR

REFERENCE ' PLATE",-"'- j

'.UNSUPPORTED DOWNSTREA"'1

EDGE OF" .sUPPLEMENTAL

BASE

r

.CONCRETE ARM FOR

REFERENCE PLATE.

MEASURMENTS IS' TO. 23 INCLUSIVE ARE

RADIAL DEFLECTION MEASUREMENTS

AT CANTILEVER E

MERCURY BAG .No. I USED IN THIS TEST

SUPPLEMENTAL BASE UNSUPPORTED AT

3 3 PLAN DOWNSTRE-*M FACE OF DAM.

G O INDICATES TWOINSERTSBETWEENWHICH

MEASUREMENTS WEs:{E MADE

FIGURE 73-DEFORMATION OF BASE AS ORIGINALLY CONSTRUCTED
PRELIMINARY MODEL TESTS 121

the concrete primary base. The positions 0£ the cracks are shown

in figure 73. It was believed that the cracks closed when the load

was applied and opened when the load was removed. Consequently,

an investigation 0£ the action 0£ the supplemental base and the open

cracks was made.

Inserts were attached to the concrete primary base and to the

supplemental base, using quick-setting plaster to fasten them in

place as shown in figure 74. Invar steel rods, on which dial gages

FIGURE 74-GAGES MOUNTED FOR MEASURING MOVEMENT OF BASE

were mounted, were attached to the inserts at the locations shown

in figure 73, so that any movement of the base could be measured.

When the model was loaded, the crack at the N evada side of the

base closed 0.000,59 inches at measurement 3, figure 73. The corresponding movement at the crack on the Arizona side showed a closure

of 0.000,15 inches at measurement 16. The entire base, however,

deflected downstream under load, as may be seen from measurements

4 to 8 and 10 to 14, inclusive. The largest deflections occurred at

measurements 12 and 13 on the Arizona side of the canyon.

In casting the plaster-celite base against the concrete primary

base, no dowels or keyways were used as a mechanical bond between
122 MODEL TESTS OF BOULDER DAM

the two materials. Cracks developed in several places, either due to

the drying of the plaster or to the different rates of expansion of plaster

and concrete caused by temperature changes. The cracks between the

two materials were undoubtedly affecting the deflection of the model

under load. It was therefore decided to add supports of sand and

quick-setting plaster to the supplemental base as shown in figure 75.

The supports filled the small space at the downstream edge of the

plaster-celite base, and transferred the load from the abutments to

the concrete walls of the testing pit.

79. Deflection of Supported Base.-The effect of the addition

of sand-plaster supports to the plaster-celite base is shown in figure

75. Downstream deflections of both the base and the model were

lessened materially. The closing of the cracks was more uniform.

Measurement 3 showed that the crack on the Nevada side closed

0.000.30 inches, and measurement 16 showed that the corresponding

crack on the Arizona side closed 0.000,37 inches.

Measurements 25 to 30, inclusive, indicated that the upstream

face of the supplemental base deflected downstream under load. However, no appreciable movement along the open cracks was discernible.

Any sliding of the supplemental base along the crack would have

been indicated by measurements 35 and 36. Measurement 35 showed

a reading of zero and measurement 36 showed a reading of 0.000,01 of

an inch.

Measurements 24 and 34 were of particular interest because they

showed that the upstream side of the supplemental base was actually

compressed toward the downstream support when the model was

loaded. The downstream face of the supplemental base did not deflect under load as it was in direct contact with the fairly rigid sandplaster support. Measurements 4, 14, 37, and 38 would show any deflection of the downstream edge of the plaster-celite base toward the

sand-plaster support. The movement registered at each of these

!Joints was very small, being less than 0.0001 of an inch.

The addition of sand-plaster supports did not make a great deal

of difference in the change of chord lengths at measurements 31, 32,

and 33. \Vith the sand-plaster supports added, these measurements

were +°.000,73. +0.001,12, and +0.000.62 inches, respectively. The

change in chord length at elevation 1200 should be corrected by the

amount the cracks closed at measurements 3 and 16. After applying

this correction, the change in chord length was +°.000,06 inches for

the supported basco Measurements of the width of the crack opening
!.lEAS NO.Of

'"

MEAS. NO.OF AVE.

ESTS OfF. TESTS OEF

"

0.'

" "

-11.4 , ,

-3,4

" "

-$.9

.

,

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,

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.

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,

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-4.7

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..

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1100

~

1000

~900

~.oo

0

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'00

505

SECTION A-A

(TH~SE RODS ARE ATTACHED

:rO WALL OF TEST,ING PIT

"\

Al-

,

CONCRETE

ARM FOR

REfERENCE

PLATE .07

'CONCRETE

ARM FOR

REFERENCE

PLATE

3 3 PLAN 0 0 INDICAT($ TWO INSERTS BETWEEN WHICH

MEASUREMENTS WERE MADE

REAR ELEVATION

RESULTS OF TESTS

MERCURYAT EL 1232

UNIT MEASUREMENT

=

0001

tA

FIGURE 75-DEFLECTION OF BASE AFTER ADDING DOWNSTREAM SUPPORTS

MEASUREMENTS 35 AND36 SHOW THE

SLIDING OF THE PLASTER CEUTE BASE

ALONG THE CRACK AT THE JUNCT ION

WITH THE CONCRETE SUPPLEMENTAL BASE.

MEASUREMENTS 16 TO 23 INCL.ARE RADIAL

DEFLECTION MEASUREMENTS AT

CANTILEVER E

MERCURY BAG No-2 USED IN THIS TEST.

SUPPLEMENTAL BASE SUPPORTED AT

DOWNSTREAM FACE OF DAM AS SHOWN

+ INDICATES LENGTHENING BETWEEN

INSERTS

'-

INDICATES SHORTENING BETWEEN

INSERTS

1000

~

900 ~5

700 Z

"d::d

I:".J

S

~.....

Z

~

::d

><:

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0

t:I

I:".J

r-

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rn'"'

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~
124 MODEL TESTS OF BOULDEH DAM

could not be made at other elevations where changes in chord lengths

were measured.

After completion of the preliminary tests with the base of the

model supported at the downstream end, it was concluded that the

action of the model and foundation was satisfactory.

AL TERA TIONS TO MODEL

80. New Mercury Bag.-The rubber mercury bag did not fit

the upstream face satisfactorily, owing to shrinkage which took place

during curing. It lacked sufficient height to reach to the top of the

model on one side. By stretching, it could be made high enough; but

in doing so, the width of the bag was decreased, leaving an uncovered

area of about twenty square inches at the upstream face. The scant

fit of the bag might have been a contributing cause of the unsymmetrical deflection. Consequently, a new mercury bag was obtained.

This bag was made slightly higher than the first, so that it would fit

without being stretched. The first loading bag was designated number

1 and the new bag, number 2. These designations are used on various

drawings which appear in subsequent sections of this report.

81. Revision of Instrument Stand.-The instrument stand, which

served as a reference pier for the radial deflection measurements, consisted of two parts; first, a concrete post, and, second, a steel plate

supported by two concrete arms which were anchored to the wall

of the testing pit, as shown in figure 71. The steel plate was a little

too wide at the bottom edge to fit into the canyon. Notches had been

cut in the canyon walls to permit the installation of the steel plate.

It was feared that these notches might affect the deflection of the

model. Accordingly, the steel plate was removed and rebent until

it fit the canyon satisfactorily. Keyways were cut around the notches

and the canyon walls rebuilt to their original form.

82. Loading Canyon Walls.-Up to this time mercury load had

been applied to the upstream face of the model only. In actual conditions reservoir water pressure is exerted against the sides of the

canyon as well as along the upstream face of the dam. It was not

known what effect reservoir pressure on the walls of the canyon

would have on the deflection of the dam. As this could be determined

approximately by applying mercury pressure to the canyon walls,

the loading apparatus was remodeled so as to permit the application

of the desired pressures.
PRELIMINARY MODEL TESTS 125

Two additional mercury bags were obtained which fit between the

ends of the upstream form and the sides of the canyon. These are

designated on the drawings as numbers 3 and 4. The sides of the

canyon were somewhat irregular and did not make satisfactory supports of the mercury bags. Therefore, keyways were cut in the

upstream canyon walls and an additional layer of plaster-celite poured

against them, so as to eliminate warped surfaces. The three mercury

bags were attached to the supply tank by a system of pipes and valves

which permitted the application of pressure to the model or to the

sides of the canyon as desired. The condition of the model, after the

alterations to the canyon walls were completed, is shown in figure 76.

- -- ,

5ANO PLASTER SUPPC:fIT.'"

"

, .

SCALEOFINCMES

FIGURE 76-MODEL AFTER ALTERING CANYON WALLS

ADDITIONAL TESTS

83. Movement of Base.-Deformations of the foundation and

abutments were measured in the first tests after installing the three

mercury bags. The results of the tests are shown in figure 77. They

may be compared with the tests made before and after adding the

sand-plaster supports, see figures 74 and 75. Additional inserts were

installed so that a more complete investigation of the action of the

base could be made. Results of the measurements showed that the

supplemental base was twisted by the pressures applied at the can-
MEAS. NO.OF AVE. MEA,S. NO.OF AVE. MEAS. NO.OF AVE.

TESTS DEF. TESTS DEF. TESTS DEF.

1 6 +0.2 22 6 -6.8 40 ,

-D.9

2 14 -2.6

"

6 -3.2 41 ,

-0.5 ,

6 -2.5 24 6 -0.3 42 ,

-1.3

4 6

-

0.2 25 6 +7.9 43 ,+4.3

5 6

-

D.9

"

6 -5.9 44 ,

,

-0.3

6 -2.2 27 6 +14.9 AS , ~1.1

5 6 +1.2

"

6 + 4.5 46 ,+2:.9

10 6 -2.6

"

6 -17.1 47 ,+0.2:

13 6 -0.8

"

6 t16.6 48 ,

-0.1

14 6 -0.3

"

5 +7.5 49 ,

-0.9

IS 6 -1.2

"

5 tlO.1 SO ,+0.2

16 6 -I 5

"

, +5.5 51 ,

-0.5

17 14 -2.6 34 6 -0. I 52 ,

-7.0

18 6 -56.3

"

6 +0.9

"

3 +0.9

"

6 -40.9 36 6 -0.9

20 6 -31.4 27 5 +0.6

20-A 6 -21.2

"

6 0.0

21 6 -12.5 3S , +3.4

1600

'505

I

SECTION A-A

-

THESE RODS ARE ATTACHED

--

"",'.j.:'LL OF TES;ING PIT

.

\~

-I--T--~----

L

A

':CONCRETE

ARM FOR

REFERENCE

PLATE-n- ."

,';CONCRE,E

ARM FOR

../ REFERENCE

PLATE

, , PLAN

0 0 INDICATES TWO INSERTS BETWEEN

MEASUREMENTS WERE MADE

....

~

0>

""

H

0

Ij

trJ

t-<

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trJ

w

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w

0

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b:I

0

d

t-<Ij

trJ

~

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>

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REAR ELEVATION

MEASUREMENTS 35 ANO 36 SHOW THE

SLIDING OF THE PLASTER CEUTE SASE ALONG THE

CRACK AT THE JUNCTION WITH THE CONCRETE

SUPPLEMENTAL BASE.

MEASUREMENTS 18 TO 23 INCLUSIVE ARE RADIAL

DEFLECTION MEASUREMENTS AT CANTILEVER E.

MERCURY SAGS NO.2,3,AND4 USED.

SUPPLEMENTAL BASE SUPPORTED AT DOWNSTREAM

FACE OF DAM AS SHOWN.

RESULTS OF TESTS

MERCURY AT EL. 1232

UNI r MEASUREMENTo.OODI"

--1 A

+

INDICATES LENGTHENING BETWEEN INSERTS

INDICATES SHORTENING BETWEEN INSERTS

FIGURE 77-MOYEMENT OF FOUNDATION DUE TO MERCURY LOAD ON DAM

AND CANYON WALLS
PRELIMINARY MODEL TESTS

yon walls. The length of the canyon was relatively short. The application of pressure at the upstream end tended to spread the upstream

part of the canyon and close the downstream part. The arch thrust at

the lower elevations tended to spread the downstream part of the

canyon. The result was that the pressure against the upstream canyon walls acted against the thrust of the arch and decreased the

radial deflections at the lower elevations.

84. Tangential Deflection Measurements.-No attempts to meas

ure tangential deflections had heen made in testing the previou~

model dams built by the Bureau of Reclamation. As tangential de.

flection measurements were desired in the Boulder model investigations, considerable experimenting was necessary before suitable in.

FIGURE 78-EQUIPMENT FOR MEASURING TANGENTIAL

DEFLECTION OF TOP ARCH

stallations of measuring equipment could be made. Figures 78 and 79

show the installations finally devised for measuring tangential deflections.

At the top of the model, elevation 1242, invar steel deflection

rods were attached in a tangential direction at the center line of the

arch element and allowed to bear against dial gages mounted on the

concrete abutment. At the lower elevations, dial gages were mounted

on L-shaped invar rods, fastened to anchors on the downstream face

of the model as shown in figure 79. They were set to record movement

of the model in a tang-ential direction.
128 MODEL TESTS OF BOULDER DAM

Theoretically, all tangential deflection measurements should have

been made at the center lines of the arch elements. This could not

be done at elevations below the top without boring holes in the model.

The measurements were therefore made as close to the downstream

face as the gages could be conveniently mounted. Distances from

the downstream face to the gages varied from 1.1 to 1.6 inches. It

was necessary to apply small corrections to the gage readings to obtain deflections at the downstream face.

85. Measurements of Twists and Strains.- While radial deflection measurements were in progress, some experiments in measuring

FIGURE 79-EQUIPMENT FOR MEASURING TANGENTIAL DEFLECTION

AT DOWNSTREAM FACE

twist or slope deflections of the model were conducted. As angular

changes of the slopes of the arch elements were very small, precise

work was necessary to obtain measurements of reasonable accuracy.

It was found that twist deflections could be measured by an optical

lever system. Since difficulty was experienced in obtaining satisfactory images with mirrors available in the laboratory, optical flats to

be used in place of mirrors were obtained.

Preliminary measurements of strain consisted in trying out avail-
PRELIMINARY MODEL TESTS 129

able apparatus to determine its suitability for use in testing the

Boulder model. No systematic measurements of strain were made at

this time as it was felt that special equipment might have to be developed. The equipment finally adopted for measuring strains is discussed in chapter V.

86. Elastic Conditions of Model.-Investigations of materials

had shown that the model material was highly elastic when dry.

Care was exercised in constructing the model to reduce the moisture

content to less than four per cent before applying protective coatings

of shellac and varnish. The shellac and varnish coatings kept the

moisture content constant during the testing period.

Radial deflection tests showed that the model was highly elastic.

Recovery movements were usually about the same as load deflections.

After taking no-load gage readings, ten to fifteen minutes were required to fill the mercury bags. Observations for load deflections

usually required five to ten minutes. About twenty minutes were

allowed for the mercury to drain out, after which recovery readings

were taken. From the materials tests it was found that plastic flow

would occur if the load was allowed to remain on the model for a

considerable length of time. In order to reduce plastic flow to a minimum, dial gages were read as rapidly as possible and the load released

before plastic flow of any consequence occurred. As the test program

advanced, it was found that most consistent results were obtained

after a few tests had been run. A small amount of flow occurred

during the. first few tests, after which fairly stable conditions were

reached. This was shown by the recovery readings which were equal

to the no-load readings after the first two or three tests were run. It

was also observed that if tests were begun each half hour, gradually

increasing deflections were obtained; while, if the tests were begun

each hour, sufficient time for recovery was allowed so that uniform

results were obtained.

Having demonstrated that satisfactory elastic action was obtained in the model, and having established a technique of testing,

the detailed program of tests described in the following chapters was

begun.

CHAPTER V-DEFLECTIONS. STRAINS. AND

STRESSES

RADIAL DEFLECTIONS

87. Normal Load Tests.-As soon as the sand-plaster supports

for the base were completed and the instrument stand remodeled,

radial deflection tests were made, using the new mercury bag and

applying mercury load to elevation 1232. A set of eleven tests, numbers 84 to 95, was found to be very consistent. The purpose of the

tests was to obtain data for comparison with the results of a trial load

analysis. Test number 85, which was virtually identical with the

average for the group, was used for the actual comparison. Figures 80

and 81 show average results for the group of tests, and figure 82 shows

radial arch deflections for test 85. These tests were run before the

shape of the upstream end of the canyon was altered to provide for

loading the canyon walls.

After the model was arranged for loading the canyon walls, the

radial deflection tests were repeated. Observations were made with

load on the model only and with combined loads on the model and

canyon walls. Results of the tests are shown in figures 83 and 84. The

deflection of the arch at elevation 1232 was characteristic of a long

slender arch. At the abutments, the deflections were negative, a

condition also observed on the Stevenson Creek test dam. No

contraflexure was observed in the lower arches of the model, where

the horizontal elements were relatively short and thick. Deflections

observed between elevations 900 and 1100 were greater at the Arizona

abutment than at the Nevada abutment, due to the fact that the

Arizona sections of the horizontal arch elements were considerably

longer at the upstream face than the Nevada sections.

An interesting observation was the effect of canyon wall loads

on arch deflections. The canyon wall loads produced large increases

in the deflections of the top arches and small decreases in the deflections of the lower arches. It is evident that the direct spreading

effect of the canyon walls at the top would increase the downstream

deflections of the upper arches. Apparently, the spreading effect

near the bottom produced a slight rotation of the arch abutments,

131
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INSERT NUMBER

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ELE VATION 1100 ~ELEVATION 700

~ ELEVATION 1000 ~ELEVATION 600

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0 INDICATES POSITION OF DAM AfTER LOADING

x INDICATES RECOVERED POSITION OFDAM AFTER UNLOADING.

MERCURY SURFACE AT ELEV.12J2.

MERCURY SAG NO.2 USED IN THESE TESTS.

SANO-PLASTER SUPPORT ADDED AT DOWNSTREAM EDGE OF

S-UPPLEMENTAL BASE.

ELEVATION 900

FIGURE 80-A VERAGE RADIAL DEFLECTIONS OF ARCH ELEMENTS, TESTS 84 TO 95
1232 0 10 2030 0 10 20 30 40

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SECTION -A SECTION-a

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1232

RADIAL DEFLECTION IN TEN THOUSANDTHS OF AN INCH

1100

1000

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~

000

700

000

,

SECTION-F

0 INDICATES POSITION OF OAM AFTER LOADING

X INDICATES RECOVERED POSITION DFDAM AFTER UNLOADING.

MERCURY SURFACE AT ELEV. 1232.

MERCURY SAG NO.2 USED IN THESE TESTS.

SAND-PLASTER SUPPORT. ADDEO AT DOWNSTREAM EDGE OF

SUPPLEMENTAL BAS£.

FIGURE 81-A VERAGE RADIAL DEFLECTIONS OF CANTILEVER ELEMENTS,

TESTS 84 TO 95

......

"'" "'"
(NEVADA ABUTMENT ARiZONA ABUTMENT

"

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20

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ELEVATION 1232

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ELEVATION 600

MERCURY SURFACE AT ELEV, 1232.

MERCURY 8AG NO.2 USED IN THIS TEST.

SAND-PLASTER SUPPORT ADDED AT DOWNSTREAM EDGE OF SUPPLEMENTALBAS£

FIGURE 82-RADIAL DEFLECTIONS OF ARCH ELEMENTS, TEST 85
NEVADA ". ABUTMENT ARIZONA ABUTMENTfi 0 2 3 . , . "

13

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ELEVATION 600

ELEVATION 1000

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tj

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ELEVATION 1232

~~"m...

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... (;ZZ

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ELEVATION 1100

0

92 . .~. -

100

00

eo

ELEVATION 700

~

~

~

00 TEST 604 USING MERCURY BAGS NO. 2,3,AND 4.

X---X TEST 606 USING MERCURY BAG NO.2.

MERc,URY PRESSURE IS APPLIED TO MODEL WITH 'MERCURY

BAG NO.2, ANp TO CANYON- WALLS WITH BAGS NO. 3AND4.

THESE TESTS WERE MADE AFTER REMODELING INSTRUMENT

STANO AND DOWNSTREAM CANYON WALLS

>Z

tj

lfJ ~~

t<J

lfJ

lfJ

t:"1

lfJ

ELEVATION 900

FIGURE 83-EFFECT OF CANYON WALL LOADS ON ARCH DEFLECTIONS,

LOAD AT ELEVATION ]232

f-' ~

on
""

0 10 2030 0 60 0 10 20 4050 0 20.30 40

II 4

ill

1100

1

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RADIAL DEFLECTION IN TEN-THOUSANDTHS OF AN INCH

40 01020304050

m

r

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:; 1100

~ ':,. 'I

SECTION A

"

I.' SECTION B

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RADIAL DEFLECTION IN TEN-THOUSANDTHS DF AN INCH

rm

<~

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2

I: SECTION f

SECTION 0

if

"

:\

SECTION E

0 0 TEST NO. 604 USING MERCURY BAGS NQ.2,3ANO 4.

X---X TEST NO. 606 USING MERCURY BAG NO.2.

MERCURY PRESSURE IS APPLIED TO MODEL WITH MERCURY SAG

NO.2, AND TO CANYON WALLS WITH BAGS NO. :3 AND 4.

THESE TESTS WERE MADE AFTER REMODELING INSTRUMENT

STAND AND DOWNSTREAM CANYON WALLS.

FIGURE 84-EFFECT OF CANYON WALL LOADS ON CANTILEVER DEFLECTIONS,

LOAD AT ELEVATION 1232

f-'

""0"> 1232

m

<~

~

~

~

0-;:rj '-'

l'

>-3

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w

>-3

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td

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700

600
DEFLECTIONS, STRAINS, AND STRESSES 137

causing reductions in deflection. The cantilever deflection curves show

the stiffening effect of the upper arch elements. The resistance of

the top arch produced negative loads on the cantilever elements,

causing contraflexure in the cantilever deflection curves.

88. Partial Load and Overload Tests.-In conducting tests on the

model, observations were begun with the load at elevation 1100 and

increased by SO-foot increments to an overload at elevation 1400.

Only results of minimum, normal, and maximum loads are presented

in this report. Figures 85 and 86 show radial arch and cantilever def1ections for loads at elevation 1100. Figures 87 and 88 show similar

data for loads at elevation 1400. In all cases deflections are shown

for both conditions of loading; that is, for loads at the upstream face

of the model only, and for loads on the canyon walls as well as on the

upstream face.

It should be noted that the difference between results with load

on the model only, and combined load on the model and canyon

walls, decreases as the depth of load increases. For load at elevation

1100, the canyon wall load doubled the radial deflection due to load

on the model only, whereas, for load at 1400 the effect of canyon wall

load was very slight. For load at elevation 1100 on the model only, it

was observed that the deflection of the cantilever in the center portion of the model was greater at elevation 1100 than at 1232, indicating

vertical tension in the upper portions of the cantilevers. This again

was caused by the resistance of the top arch.

TANGENTIAL DEFLECTIONS

89. Methods of Making Tests.-In making tests for tangential

deflections, dial gages were mounted to measure deflections of the

top arch at the center line and deflections of the downstream face

at elevations 800, 900, 1000, and 1100. The apparatus used in making

tangential deflection measurements, shown in figure 79, required considerable space to adjust and operate. Consequently, it was not

feasible to install gages for measuring tangential deflections below

elevation 800.

The procedure used in making tangential deflection measurements was the same as in the radial deflection tests. It included tests

for overload, normal load, and partial load conditions. Mercury load

was first applied to the model and all gages read. Load was then

applied to the canyon walls and the observations repeated. Overload
l'~"'D'"

INSER"fNUMBERS

BUTMENT

Z 13 ARIZOtII...... TMENT.".. 5 T .

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15

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3

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ELEVATION 1232 msTIi

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0

00

ELEVATION 800

ELEVATION 1000 .

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ELEVATION 600

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.e. miJ 0--0 TEST No. 6J6 USING MERCURY BAGS No. 2,3,ANO 4.

X~-X TEST No.618 USINGMERCURY BAGNo.2.

MERCURY PRESSURE IS APPLIED TO MODELWITH MERCURY

BAG No.2,ANO TO CANYONWALLS WITHBAGS No.3 ANO 4.

THESE TESTS WERE MADE AfTER REMODELING INSTRUMENT

STAND AND DOWNSTREAM CANYON WALLS

ELEVATION 900

FIGURE 85-EFFECT OF CANYON WALL LOADS ON ARCH DEFLECTIONS,

LOAD AT ELEVATION 1100
I'"

0 1 30 40 SO eo 0 020304050 10 20 30

\

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RADIAL DEFlECTIDN IN TEN-THOUSANDTHS OF AN INCH

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SECTION A

,I SECTION B

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RADIAL DEFLECTION IN TEN-THOUSANDTHS OF AN INCH

40 SECTION P

SECTION E

~

~

~

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0

z

0 0 TEST No.616 USING MERCURY BAGS No.2,3,AND 4

X--X TEST No. 618 USING MERCURY BAG ~o. 2

MERClfRY PRESSURE IS APPLIED TO MODEL WITH MERCURY BAG

No. 2,A-N0 TO CANYON WALLS WITH BAGS No.3 AND

THESE TESTS WERE MADE AFTER REMODELING INSTRUMENT '"

STANO AND DOWNSTREAM CANYON WALLS

SECTION

FIGURE 86-EFFECT OF CANYON WALL LOADS ON CANTILEVER DEFLECTIONS,

LOAD AT ELEVATION 1100

1232

~

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00 1 2

INS RT NUMBE:RS

5 9

ARIZONA ABUTMEN1"m

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130

~

140

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ELEVATION 1232

0 '0

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Z 60

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ELEVATION 1100

- ELEVA TION 1000

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ELEVATION 700

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ELEVATION 800

<> <>TEST 587 USING MERCURY BAGS No.2,3,AND 4.

---~

TEST 5BB USING MERCURY BAG No.2

MERCURY PRESSURE IS APPLIED TO MODEL WITH MERCURY

BAG NO 2 AND TO CANYON WALLS WITH SAGS No3 AND4

THESE TESTS WERE MADE AFTER REMODELING INSTRUMENT

STAND AND DOWNSTREAM CAIIJYOIIJWALLS

FIGURE 87-EFFECT OF CANYON WALL LOADS ON ARCH DEFLECTIONS,

LOAD AT ELEVATION 1400
'''

fifE

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SECTION B

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RADIAL DEFLECTION IN TEN-THOUSANDTHS OF AN INCH

60 60 0 20 40 80 80 10D 20 140 0 20 1~~32

7

m

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RADIAL DEFLECTION IN TEN-THOUSANDTHS OF AN INCH

so 80 120 160 .?O

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SECTION H

f

0 0 TEST 567 USlr>;G MERCURY SAGS No 2,3,AND 4

~~--~ TEST588 USING MERCURY BAG No 2

MERCURY PRESSURE IS APPLIED TO MODEL WITH MERCURY

BAG No.2 AND TO CANYON WALLS WITH BAGSNo.3AND4.

THESE TESTS WERE MADE AfTER REMOOELING INSTRUMENT STAND AND DOWNSTREAM CANYON WALLS.

SECTION

f"

FIGURE 88-EFFECT OF CANYON WALL LOADS OF CANTIL,EVER DEFLECTIONS,

LOAD AT ELEVATION 1400

H

.... H
142 MODEL TFJSTS OF BOULDER DAM

tests were made with the surface of the mercury at elevations 1400,

1350, 1300, and 1250. Partial load tests were made with the surface

of the mercury at elevations 1200, 1150, and 1100. When the surface

of the mercury was below elevation 1100, tangential deflections were

too small to measure satisfactorily.

90. Results of Tests.-There was but little difference in the results of tangential deflection tests for the two methods of loading.

Generally, the tangential deflection was slightly greater when load

was applied to the model alone. Results of tests made with the mercury surface at elevation 1400 are shown in figure 89. The maximum

observed tangential deflection occured at elevation 1100 near the

Arizona abutment and amounted to 0.0054 inches. On the Nevada

side of the model, the deflection was somewhat smaller at this elevation, being 0.0048 inches.

The measured deflection curve of the arch element at elevation

1242 was characteristic of thin arches. The deflection was a maximum

near the quarter points, and diminished toward the abutments. At

lower elevations, where the arch elements were thicker, the maximum

deflection occurred nearer the abutments.

Tangential deflections measured in normal load and partial load

tests are shown in figures 90 and 91. The method of loading the

model did not greatly affect the tangential deflection for normal load

conditions. For partial loads some difference was noted, particularly

when the mercury surface was at elevation 1100, see figure 91. The

curves in figure 91 show that below elevation 1100 the tangential deflection was almost zero when the mercury pressure was applied to

the model and to the canyon walls. By applying pressure to the

model on1y, the deflection was increased considerably, the maximum

deflection along the Arizona abutment being 0.0011 inches and

along the Nevada abutment, 0.0008 inches. This observation confirms the previously mentioned conclusion that the canyon wall

pressure caused a slight rotation of the abutments at the lower

elevations.

SLOPE DEFLECTIONS

91. Apparatus.-Before making slope or angular deflection measurements of the model, it was necessary to develop a system for

accurately measuring very small angular changes. After some experimenting, an optical lever system was developed which gave satis-
I 2

,

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DEFLECTIONS, STRAINS, AND STRESSES

-NEVADA ABUTMENT INSERT NUMBERS AA.IZONA ABUTMENT

-50

-40

-20

20

40

50

ELEV.1242

10 -'4 12

-2

ELEV.IIOO

1

-5

-4 "

4

5

-20

ELEV.IOOO

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2 4 . .

-

10 12

20

40

ELEV.900'

-~

ELEV.800

Deflection of arch at elev. 1242 was measured along

center line of element.

Deflections ot other elevations were measured along

downstream surface of elements.

+ Indicates deflection to left when looking upstream.

-

Indicates deflection to right when looking upstream.

--- Test No.663using mercury 'bags Nos.2,3,ond 4.

.-_ux--- Test No.665 using mercury bog No.2.

FIGURE 89-TANGENTIAL DEFLECTIONS OF ARCH ELEMENTS,

LOAD AT ELEVATION 1400

143
-NEVADA ABUTMENT INSERT NUMBERS ARIZONA ABUTMENT-,

0

I 2 3 4 5 6 7 6 . 10

"

12

0

I I

I

~I -- - - - -

-::::-

;.;--

~0

-= ! -~ I

'-. -~ I

0

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0

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144 MODEL TESTS OF BOULDER DAM

ELEV.1242

I

U

~

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. .

'.

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20

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ELEV.IIOO

~

~

0

Z

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z

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ELEV.IOOO

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2 4

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.__'0'2

-""

2

ELEV.900

~

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357. -2 --"

0

2

ELEV.600

Deflection of arch ot Elev.1242 was measured along

center line of element.

DefJecHonsat other elevations were measured along

dOwnstreamsurface of elements.

+ Indicates deflection to left when Itlcking upstream.

-Indicates deflection to right when laoking u~streom.

-- Test No.6S1 using mercury bags Nos.2,3,ond 4.

~---X---II. Test No.684using me'rcury bag NO.2.

FIGURE 90-TANGENTIAL DEFLECTIONS OF ARCH ELEMENTS,

LOAD AT ELEVATION 1232
"NEVADA ABUTMENT IN SERT NUMBERS ARIZONA ABUTMENT--

I 2 3 4 5 . 7 8 9 10

"

12

I I

0 -

I I

0 -

- I

I I

0

I I

0

--.-- ---r----"

---

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DEFLECTIONS, STRAINS, AND STRESSES

-3

-2

ELEVJ242

10 12

r

u

~

z

~

~

a

-30

-20

20

30

~

I

f-a

z

~.

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a

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...

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ELEV.IIOO

-~o'

-2

z

a

;::

u

5

a

-'~

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ti

"

z

"

20

ELE V.IOOO

'1

r

-1-k .~.

J~F..

'O !2

-- . .

20 ..

ELEV. ~OO

'~~

20-

ELEV.800

Deflection of arch at elev. 1242 was meosured along

center line of element.

Deflections at other elevations were measured along

downstream surface of elements.

+ Indicates deflection to left when looking upstream.

-

Indicates detlectioll to right when Ic.oking upstream.

0 0 :>Test No.697usingmercury bags Nos.2,3 and 4

:'

;< JlTest No.695 using ~ercury bog No.2,

FIGURE 91-TANGENTAL DEFLECTIONS OF ARCH ELEMENTS,

LOAD AT ELEVATION 1100

145
146 MODEL TESTS OF BOULDEH DAM

factory results. The apparatus consisted of an engineer's scale, a

transit having a telescope of good quality, and mirrors having very

flat surfaces.

The transit was mounted on a concrete pedestal in one corner of

the testing room. A number 50 engineer's scale, having a white

celluloid face, was clamped to the pedestal in front of the transit

and perpendicular to its line of sight. Optical flats, ground to a

tolerance of 0.000,003 inches, were obtained for use as mirrors.

These were mounted on trunnions supported by a fork which was

attached to inserts at the downstream face of the model.

92. Principle of Operation.--The principle of operation of the

optical lever system used in these tests is based on the fact that the

angle which an incident ray of light makes with the plane of a mirror

is equal to the angle of the reflected ray. The incident ray was the

line of sight from the telescope to the mirror, and the reflected ray

was the reflection of the scale. Therefore, when the mirror rotated

through a certain angle, the reflected ray was rotated through twice

that angle, and the apparent movement of the image of the scale

across the cross-hair of the telescope was equivalent to the tangent

of twice the angle of rotation of the mirror.

Actually, the mirror rotated through an unknown angle about

an unknown axis. The mirror registered only the component

of the rotation about an axis in the plane of the mirror. Rotations

about axes normal to the face of the mirror produced no apparent

movement of the scale. Since the scale was in a horizontal position,

the angle measured was the angle which had an axis within the plane

of the mirror, the direction of the axis being normal to the direction

of the scale. By an extension of the stem of the mirror, it was possible

to mount the mirror so that the actual angle measured was about a

vertical axis through the point of support. Due to the relatively small

readings obtained, it was necessary to apply small corrections to the

computed angles caused by the displacement of the mirror. Using a

50 scale, readings to the nearest 0.01 of an inch were possible. With a

distance of 150 inches from the scale to the mirror, a sensitivity of

0.01j(150X2), or 0.000,033 radians was obtained.

93. Results of Tests Results of slope deflection tests are shown

in figures 92 to 94, inclusive. As in radial and tangential deflection

tests, slope deflection measurements were made for overload, normal

load, and partial load conditions for both methods of load applica-
.. ABUTMENT _w.~BIZONA ABUTMENT..-

INSERT NUMBER

"""",-, iT 1;"-. 80 I 2 3 4 5

700 /

"00 500

/

40 /

2

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10

0

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100

200

300

40 /

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800

700 I 2 4 8 8 10 12 14

800 --

500

400

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500

800

DEFLECTIONS, STRAINS, AND STRESSES

NEVADA

ELEVATION 1242

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I-Z

0

:i

..J

~

~

700

ELEVATION 1100

500'

-400

-3200

-100

0

100

13

<J)

Z

0

f=

u

w

..J

u.

w

0

w

n.

9<J)

ELEVATION 1000

:~ -

"

,"

1012

-200

-100

100

200

300 --

400

ELEVATION 900

'200

~

3

,

-100

0

100 200 -- ELEVATION 800

~~~~

ELEVATION 700

NOTES

ALL MEASUREMENTS MADE AT DOWNSTREAM FACE OF ARCH

ELEMENTS, EXCEPT AT ELEVATION 1242 WHICH IS MEASURED

AT

{

OF ARCH ELEMENT.

+INOICATES CLOCKWISE DEFLECTION WHEN VIEWED FROM ABOVE.

-INDICATES COUNTER-CLOCKWISE DEFLECTION WHEN VIEWED

FROM ABOVE

X II I[ SLOPE DEFLECTIONDUETO MERCURYPRESSUREON MODEL.

SLOPE DEFLECTION DUE TO MERCURY PRESSURE ON MODEL

AND ON CANYON WALLS.

FIGURE 92-SLOPE DEFLECTIONS OF ARCH ELEMENTS,

LOAD AT ELEVATION 1400

147
A NA UTME

I 4 5

INS~"T NU"1)'E" 8 . 10

"

12

~--

-

-

-- -

148 MODEL TESTS OF BOULDER DAM

NEVADA ABUTMENT RIZO AS NT

-800

-700

-1300

-500

-""" -300

-200

-100

0

100

200

300

400

500

800

700

800

ELEVATION 1242

U)

Z

:..;

0

«

a:

IL

0

U)

I

t-Z

~

.J.J

:1

-700

I

-800

-500

-""" -300

-200

-tOO

0

100

200

300

400

500

800

700

ELEVATION I 100

10 12 14

'!': U)

Z

~

t-Uw

'-'

IL

W

0

W

0-SU)

EIIIII .

5 7

'-

"__'3

-1000

100

200 -

300

400

500 .

ELEVATION 1000

~w~ 00

ELEVATION 900

=:~~---4---~ 200

ELEVATION 800

=:~~ 200-+ ELEVATION 700

t

NOTES

ALL MEASUREMENTS MADE AT DOWNSTREAM FACE OF ARCH

ELEMENTS, EXCEPT AT ELEVATION1242, WHICH IS MEASURED

ALONG i OF ARCH ELEMENT.

+

INDICATES CLOCKWISE DEFLECTION WHEN VIEWED FROM

ABOVE.

-INDICATES COUNTER-CLOCKWISE DEFLECTION WHEN VIEWED

FROM ABOVE.

x x x SLOPE DEFLECTION DUE TO MERCURY PRESSURE ON MODEL

:,SLOPE DEFLECTION DUE TO MERCURY PRESSURE ON MODEL

AND ON CANYON WALLS.

FIGURE 93-SLOPE DEFLECTIONS OF ARCH ELEMENTS,

LOAD AT ELEVATION 1232
.-NEVADA ABUTMENT I:RIZON~

I

ABUTMENI:"""")

I 2 3 4 5

INSERT NUMBER

6 7 6 .

-

DEFLECTIONS, STRAINS, AND STRESSES

-600

-700

-600

-500

-400

-300

-200

-

100

0

100

200

300

400

500

600

700

600

ELEVATION 1242

10 14

I/)

Z

~

0

«

0:

IL

0

I/)

I

fZ

0

J

-'

::;:

Z

I/)

zQ

f-U

w

-'

ILW

0

W

a.

0

-' I/)

-700 I

-600

-500

-400

-300

-200

-100

0

100

200

300

400

500

600

700

ELEVATION 1100

5 13

12

---

"

-500'

-400

-300

-200

-100

0

100

200

300

400

500

ELEVATION 1000

_4oo

~

2 4 6 10 12

-300

-200

-100

0

100

200

300

400

ELEVATION 900

.

-2oo~ 7 .

-~~ - ~ ELEVATION 800

:~~---~- ,i r

ELEVATION 700

t

NOTES

ALL MEASUREMENTS MADE AT DOWNSTREAM FACE Of' ARCH

ELEMENTS,EXCEPT AT EI.EVATION 1242,WHICH 1$ MEASUREO

AT t OF ARCH ELEMENT.

+

INDICATESCLOCKWISE DEFL.ECnON WHEN VIEWED FROM

ABOVE.

-

INDICATES COUNTER~CLOCKWISE DEF!.ECTIDN WHEN" VIEWED

FROM ABOVE.

J! X ~X SLOPE DEFLECTION nUETO MERCURY PRESSURE ON MODEL.

t c

-

SL.OPE DEFLECTION DUE TO MERCURY PRESSURE ON MODEL

AND ON CANYON WALLS.

FIGURE 94-SLOPE DEFLECTIONS OF ARCH ELEMENTS,

LOAD AT ELEVATION 1100

149
150 MODEL TESTS OF BOULDER DAM

tion. Overload tests were made with the mercury surface at elevations

1400, 1350, 1300, and 1250; but results for overload at 1400 only are

included in this report. The two methods of loading the model

caused only small differences in deflection curves.

When the surface of the mercury load was at elevation 1232, the

deflection curves were nearly symmertical, as shown in figure 93. The

maximum deflection occurred at elevation 1242, at insert 4 on the

Nevada side. At the corresponding point on the Arizona side, the

deflection was only slightly smaller. The deflection decreased to zero

at the abutments at this elevation. At lower elevations the deflections

decreased, but were still measurable. Slope deflections for load at

elevation 1100, given in figure 94, show the same general characteristics as the normal load tests. Maximum rotations at elevations 1242,

1100, and 1000 were practically the same.

The position of the line of zero slope on the downstream face

of the model varied with the elevation of the mercury surface. For

partial mercury loads, the line of zero slope was at approximately the

center of the canyon. For normal and overload conditions the

line of zero slope shifted slightly toward the Nevada side.

MATHEMATICAL BASIS FOR STRAIN MEASUREMENTS

94. Stress-Strain Relations.-Systematic measurements of strains

were made at the downstream face of the model. Stresses were computed from the strain measurements, using stress-strain relations

developed by the theory of elasticity. A summary of the development

of these relations is presented.

The magnitude and direction of principal strains at a point may

be found by using the relation between principal strains and a given

strain.

€ = €./'Ol/

()

+ €,/in'()

(1)

where

€ is the linear strain in the gi ven direction.

€x is the algebraically maximum principal strain.

€y is the algebraical1y minimum principal strain.

() is the angle between the direction of € and the

direction of €x' TI1easured from €to €x'
DEFLECTIONS, STRAINS, AND STRESSES 151

An alternate form for this equation is:

(= % ((x + (y) + %((x -

(y) ('0828 (72)

The three quantities, (x' (y' and 8 involved in the determination

of principal strains at a point may be found by measuring linear

strains along three or more gage lines of known directions intersecting

at the point. These strain measurements also furnish data for computing arch and cantilever stresses as well as shearing stresses on

horizontal and vertical planes.

95. Equations for Principal Strains.-Take the measured strain

(11 as the reference direction, and the measured strains (n and (v

making angles of 45 and 90 degrees respectively with (JI' Let 0 be

the angle from (JI to (x' t:n

and (v then make angles of (45 - 0)

and (90 -

0) degrees respectively with (x' measured from (x to (n and

(v' Successive substitution of these angles in equation 2 gives:

(JI = % ((x + (y) + %((x - (1)) cos?]8

(n = % ((x + (y) + % ((x-(y) sin BO

(y

= % ((x + (1)) - % ((x

-

(y) cos 28

Equations 3, 4, and 5 reduce to:

(3)

(4)

(5)

(x + (y = (JI + (1

(x - (y = ((JI- (v) see 20

(6)

(7)

0)

i-'(n-(JI-(v

tan gO =

(8)

(11 -

(y

The magnitude and direction of principal strains may be readily

obtained from equations 6, 7, and 8.

96. Stress-Strain Equations .-A stress aJI acting on a vertical

plane is accompanied by a horizontal strain (JI whose magnitude is

aH -p.aJI

-, and also by a vertical strain whose magnitude is -. The factor

E E

p. denotes Poisson's ratio and the minus sign indicates that the sign

of the transverse strain is opposite to that of the stress which produces it. In like manner a stress av on a horizontal plane is accomav

panied by a vertical strain equal to - and a horizontal strain equal

E
152 MODEL TESTS OF BOULDER DAM

-/La V

to--. The linear strains which accompany shear stresses are

E

of the order of intinitesima]s as long as the requirements imposed by

elastic action and Hooke's law are met. If horizontal and vertical

normal stresses and shear stresses occur simultaneously, the accompanying strains, by superposition, are:

aH WTV

f =---- H E E

(9)

a V

/La H

f =------ V E E

The equations for stresses in terms of strains are:

(10)

E

(fH + /LfV) (11) aH=

J --IL"

E

av = (fV + P.fH)

l-/L'

r

rh . E

e expressIOn is often called the plate modulus and

1 - /L'

designated by the symbol E'. The foregoing equations were derived

for stresses in a plane. Assuming that the curvature between adjacent

inserts can be neglected, the equations are also applicable to surface

stresses at the downstream face of the model. The horizontal and

vertical designations for strain measurements were chosen for convenience in the computation of arch and cantilever strains and stresses,

although in the case of the cantilever elements, the strains and stresses

may be along inclined directions instead of vertical.

If reference directions in the foregoing analysis are taken to coincide with the directions of principal strains and stresses, equations

giving principal stresses in terms of principal strains are obtained.

These equations are:

(112)

E

a ---

( f +

.lIf )

x- 1 '

x r1J

-/L

E

ay = -

1

-~

(fy + /Lfx)

--/L

The shear stress T on a horizontal plane may be found by setting

up the equation for equilibrium in the horizontal direction, using the

forces acting on a small triangular wedge of unit thickness, bounded

by a horizontal plane and by planes parallel to the directions of the

(13)

(14-)
DEFLECTIONS, STRAINS, AND STRESSES 153

two principal stresses. If the side parallel to ay be denoted by dy, the

side parallel to ax be denoted by dx, and the angle between the horizontal distances ds and d;J: be denoted by 0, then

Tds =a 1'080 d,l - a sin 0 d.l: :r.

.J JJ

(15)

or

T =

.l. (a

-

a ) sin BO

93 x J}

(lfJ)

E

If the shearing modulus of elasticity, , is denoted by g (1 + /1-) (}, shearing stresses may be calculated directly from strain measurement by the relation:

T = (E€D - €H - €v)O (17)

If a square of unit thickness be placed in the first quadrant with

respect to the lJ and V axes, and the edges subjected to the normal

stresses aH and.".v' respectively. and to a shear stress THV' then positive shear will be that which causes a lengthening of the positive

diagonal of the square.

APPARATUS FOR STRAIN MEASUREMENTS

97. Strain Gages.-In constructing the model, small anchors

had been cast in the downstream face for attaching invar steel rods

required in making deflection measurements. It was desired to use

these anchors in attaching apparatus for making strain measurements

so as to avoid installing additional inserts at the downstream face.

Several types of hand-operated strain gages were available in

the laboratory, but were unsuitable since they required additional

inserts for mounting. Furthermore, the working space in front of

the model \vas limited and it was difficult for an observer to reach

the lower elevations with a strain gage. After some experimenting,

it was found that by mounting dial gages, reading to 0.0001 of an inch,

on short invar rods between pairs of existing anchors, strains at the

downstream face could be readily measured. By this method strains

could be measured in four desired directions over most of the downstream face. Since the upstream face was covered with the rubber

mercury bag, no strain measurements could be made at upstream

locations.
154 MODEL TESTS OF BOULDER DAM

98. Mounting Strain Gages.-- The method of mounting dial gages

between pairs of anchors is shown in figure 95. Invar steel rods were

cut to the proper lengths and threaded so they could be attached to

plates which were fastened to the anchors with small screws. The

dial gage was mounted on a rod attached to one anchor and allowed

to bear against the polished end of the rod attached to the other anchor.

Any deformation occurring between the two anchors was indicated

by the change in the reading of the gage. The average unit strain

could then be computed by dividing the gage reading by the gage

length. Peak strains occurring in small areas were not obtainable with

this system of measurements because of the relatively long gage lines.

FIGURE 95-GAGES SET TO MEASURE CANTILEVER STRAINS

99. Gage Lines.-The usual arrangement for a set of strain

measurements at a particular location included a square with gage

lines forming the boundary and diagonal gage lines crossing at the

center. A more ideal arrangement would have been for all gage lines

to cross at a point, but with the existing arrangement of anchors, this

was possible only in a few locations. However, by plotting smooth,

continuous ~urves for each component of strain, the four components
DEFLECTIONS, STRAINS, AND STRESSES 155

required for computing stresses at a point were readily obtained. Special computations were necessary where gage lines made odd angles.

Due to the curved face of the dam, gage lines were actually skewed at

all locations except the center. Angles were measured with respect to

the developed downstream face. In order to simplify the work, stresses

were also plotted with respect to the developed face. Unit strains,

however, were calculated with respect to actual lengths of gage lines.

Before calculating stresses from unit strains, the relationship

between strain components at points where the gage lines intersected

at 45-degree angles were checked by the equation

€V+€H=€D+€(/ (18)

Any discrepancies found were adjusted to make the strains fulfill

the requirement of equation 18 before stresses were calculated.

RESULTS OF STRAIN MEASUREMENTS

100. Arch Strains.-Measured horizontal or arch strains for

overload, normal, and partial load tests are shown in figures 96, 97,

and 98. Two diagrams are shown in each figure, so that the effect

of reservoir pressure on the canyon walls can be seen. Applying

reservoir pressure to the canyon walls increased the arch strains

slightly for overload conditions, as may be seen by referring to figure

96. At the Arizona abutment, between elevation 1100 and the top

of the model, maximum compressive strains were increased from 400

to 425 millionths of an inch per inch. At cantilever section E, between

elevations 800 and 900, maximum tensile strains were increased from

100 to 125 millionths of an inch per inch. Slight changes in position of

strain contours were noted in other parts of the model, but the magnitudes of the strains were virtually unchanged.

Measured horizontal strains, with the mercury surface at elevation 1232, are shown in figure 97. As in the case of the overload tests

the effect of applying reservoir pressure to the canyon walls was t~

increase maximum strains. \iVith the load applied to the model only,

the maximum compressive strain of 175 millionths of an inch per

inch occurred along the Arizona abutment between elevations 1100

and 1200. Applying reservoir pressure to the canyon walls increased

this strain to 200 millionths of an inch per inch at the same location.

The maximum tensile strain was the same for the two systems of loading, being 75 millionths of an inch per inch. When pressure was

applied to the model only, the maximum tensile strain occurred be-
156 MODEL TESTS OF BOULDER DAM

STRAINS DUE TO PRESSURE APPLIED TO MODEL

STRAINS DUE TO PRESSURE APPLIED TOMODEL

AND TO CANYONWALLS

Plotted strains are in millionths of an inch per inch.

+ Indicotes compression.

-Indicates tension.

700

"

J

1000 Q:

'"J

~

J1

~'-

:J0

~

00 §

'" iJ

0

if!

0

~

~

::: if

[1

90

700

J" 1000 0:

..J

~'-~

"

0

~

g

iiI

0

!"

~

:::

!

900

600

FIGURE 96-ARCH STRAINS AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1400

1242

, 4
DEFLECTIONS, STRAINS. AND STRESSES

CANTILEVER MEASUFtING SECTIONS

C D

[

F G

000

~

1000

;§

/j

Q

900 J

I-

'" 1i:: eoo §

'"

.:

u

700 I

~

i:J

!

"

STRAINS DUE TO PRESSURE APPUED TO MODEL

H

~

1000 0

..J

'"

.. g

'"

aoo §

~

700

]

1

100

...

STRAINS DUE TO PRESSURE APPLIED TO MODEL

AND TO CANYONWALLS

NOTES

Plotted strains ore in millionths of on inch per Inch.

+ Indicates compression.

-

Indicates tension.

FIGURE 97-ARCH STRAINS AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1232

157

1242

1242
158 MODEL TESTS OF BOULDER DAM

CANTILEvER MEASURING SECTIONS

C 0 E F G

STRAINS DUE: TO PRE:SSURE: APPLlE:D TO MODE:L

..

J

:

"

5g

...

~

i:~"

§

"

i;f

I.

!

STRAINS DUE: TO PRESSURE: APPLIE:D TO MODE:L

AND TO CANYON WALLS

NOTES

Plotted strains ore in millionths of on inch per inch.

.. Indicates compression.

-

Indicates tension.

..

J

:

j"

gOO ,.,.

~

1i:

00 §

"

iiJ

~

i

I

§

FIGURE 98-ARCH STRAINS AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1100

12"2
DEFLECTIONS, STRAINS, AND STRESSES 159

tween cantilever sections E and F and extended from elevation 825

to elevation 875. The area of the maximum tensile strain increased

when the reservoir pressure was applied to the canyon walls. The area

was almost symmetrical about cantilever section E. It was about five

inches wide and extended from elevation 760 to elevation 960.

Horizontal strains with the mercury surface at elevation 1100 are

shown in figure 98. The effect of reservoir pressure on the canyon

walls was to increase maximum compressive strains slightly along

the Arizona abutment between elevations 1125 and 1200, and along

the Nevada abutment between elevations 875 and 1100. The distribution and magnitude of tensile strains were virtually unchanged by the

two methods of loading.

101. Cantilever Strains.-Measured cantilever strains are shown

in figures 99, 100, and 101. For the overload condition, shown in

figure 99, effects of reservoir pressure on the canyon walls reduced

the compressive strain from 100 to 75 millionths of an inch per inch

at the base of the model adjacent to the canyon walls. The maximum

compressive strain was 250 millionths of an inch per inch for both

systems of loading. This strain was observed between elevations

1000 and 1100 near both abutments.

Cantilever strains observed with the mercury surface at elevation 1232 are shown in figure 100. Applying reservoir pressure to

the canyon walls decreased the area of tensile strains at the top of

the model slightly, and increased the area of maximum compressive

strains between cantilever sections D and G and elevations 750 and 950.

Strains for load at elevation 1100 were rather small and there was no

great difference in either magnitude or distribution of strains caused

by the two systems of loading.

102. Diagonal Strains.-Results of diagonal strain measurements

are shown in table 2. Tabular values refer to gage lines on figure 102.

These strains were used in the calculation of principal strains and

stresses.

STRESSES COMPUTED FROM STRAINS

103. Arch Stresses.-Arch stresses computed from strain measurements are shown in figures 103, 104, and 105. The maximum compressive stress for load at elevation 1400 was 60 pounds per square
160 MODEL TESTS OF BOULDER DAM

S05

STRAINS DUE TO PRESSURE APPLIED TO MODEL

STRAINS DUE TO PRESSURE APPLIED TO MODEL

AND TO CANYON WALLS

NOTES

Plotted strains are In millionths of on inch per inch.

... Indicates compression.

-I ndicote tension

1242

~

J

1000 ;

:/

!i

...

000 ~.,

"

0

i::

800 l

i;f

f

700 ~0g

..

800 8

1242

/100

~

J

.. 1000}f

:/ 0

..

...

gOO 'Of

I

l! 000

'"

i;f

u

~

700 ~

~

!3

l

800 8

505

FIGURE 99-CANTILEVER STRAINS AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1400
DEFLECTIONS, STRAINS, A?>ID STRESSES

A

CANTILEV(R ME~SURING SECTIONS

C 0 E F G

1100

~

~

~

1000 ;

Ii

...

900 '"..

§

;:

~

ooo!:f

.,

~Q

700 ~

0

.,~

0008 ""

505

STRAINS DUE TO PRESSURE APPLIED TO MODEL

1100

.,

;§

15

1000 ~

"

0

..

...

'"

900 ..

>: B

~

&OOJ

"

>:

700 f

i

:t

&00

g

"

sos

STRAINS DUE TO PRESSURE APPLIED TO MODEL

AND TO CANYON WALLS

NOTES

Plotted strains are inmi1lionths otoo inch per inch.

... Indicates compression.

-

Indicates tension

FIGURE lOO-CANTILEVER STRAINS AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1232

161

1242

1242
162 MODEL TESTS OF BOULDER DAM

A

CANTILEVER MEASURING SECTIONS

C 0 E F G

AR A or LOW TENSION

STRAINS DUE

STRAINS

NOTES

Plotted strains. are in millionths of on inch per inch.

+

Indicates compression.

-

Indicates tension.

H. 1242

<f"

I000 if'"

:10

..

~

900 :

~"

~

800 !J

"

u

~

700 ~

f

ij

..

'"

600 0

U

1242

1100

<f"

/5

1000 ~0

..

~

~

900 ~

~"

~

eoo !J

"

u

~

700 ~

0

.:;

"

Ii eoo 8

.0.

FIGURE 101-CANTILEVER STRAINS AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1100
DEFLECTIONS, STRAINS, AND STRESSES

CANTILEVER MEASURING SECTIONS

C 0 E F

DIAGONAL STRAINS A- GAGE LINES

CANTILEVER MEASURING SECTIONS

C D E F

~!242

~

..

0

1100 ~

0

.J

:>0

1000 OJ

1242

~

..

0

'"

liDO I/J

3

:>0

CD 1000 .....

..

'"z

900 ~..

>...J

BOO ILl

'"Z

C

z

700 0

..

'"

..

'" 600 ~

"

DIAGONAL STRAINS B- GAGE LINES

Load t -applied 10 model only.

Load2-applied to model and canyon walls

FIGURE 102-LOCATIONS OF DIAGONAL STRAIN-GAGE LINES

163

....

..

'"

Z

900 0

~..

j

BOO.....

'"

z

C

700 ~

..

'"..

'"

600 ~

"

505

505
RESERVOIR MERCURY RESERVOIR MERCURY RESERVOIR MERCURY

SURFACE AT EL. 1400 SURFACE AT EL. 1232 SURFACE AT EL. 1100

A-Gage Lines I B-Gage Lines A-Gage Lines I B-Gage Lines A-Gage Lines B-Gage Lines

Gage Line Load Load Load Load Load I Load

I

Load

I

Load Load Load Load i

Load

No. 1 2 1 2 1 I

') 1 2 1 2 1 2

i

1 110.0 97.3 372.0 382.0 73.9 61.3 23.3 48.2 18.8 27.0 10.0 3.3

2 5.1 15.3 388.0 395.0 10.2 27.1 104.6 108.6 40.7 23.7 16.1 20.1

3 -

11.9 6.0 388.0 400.0 -

19.4 1.5 118.8 128.0 45 23.9 21.3 30.6

4 15.1 32.0 410.0 430.0 -

16.8 3.4 132.0 153.8 5.0 -

3.6 30.0 40.0

5 18.2 23.2 235.0 235.0 -

33.2 -

]8.2 48.6 45.8 21.6 0.0 7.0 9.7

6 ]6.8 -

3.0 317.0 312.7 -

62.6 - 48.8 79.7 80.8 -

22.9 -

6.1 6.9 9.2

7 2.9 11.9 405.0 429.0 -

44.8 -28.4 141.8 ]59.0 -

7.5 -

25.4 28.6 39.8

8 -

40.8 -

33.0 257.5 271. 3 -

39.3 -

28.3 117.0 130 0 -

6.3 -18.9 38.6 48.0

9 -

62.9 -

68.7 ]59.0 145.0 -39.5 -

30.7 17.1 7.1 -

]4.6

-

4.4 -

5.7 -

7.1

10 41.5 38.4 204.0 196.0 -

41.6 -41. 5 30.9 30.9 -

8.0 -

14.4 - 11.1 -

11.1

11 43.5 46.3 214.0 210.4 -

46.2 -46.2 57.5 56.4 -

28.9 -17.4 0.0 -

1.2

12 25.6 19.9 220.0 230.0 -

48.3 -51. 2 82.4 93.4 -

31.3 -38.4 9.9 14.3

13 16.6 18.0 212.0 228.0 -

31. 9 -

31. 9 90.7 104.5 -

25.0 -29.1 25.3 39.0

]4

-

25.0 -25.0 209.0 221.2 -

30.6 -

33.4 95.3 113.8 -

20.8 -20.8 36.9 45.1

15 -

34.2 -42.5 176.0 187.5 -

32.9 -

31. 5 96.9 101.0 -

21. 9 -21.9 40.2 50.5

16 -

41.4 -45.5 181.0 182.5 -

33.1 -29.0 99.8 96.6 -

24.8 -

20.7 47.2 53.7

17 -

58.6 -

62.9 186.6 173.0 -

39.1 -37.7 107.5 105.0 -

22.4 -

28.0 62.0 51.4

18 -

39.1 -

40.5 164.2 142.7 -

25.2 -26.6 90.9 87.1 -

]6.8

-

15.4 46.8 45.5

19 -

43.5 - 42.0 97.6 75.0 -

27.6 -

26.1 15.0 12.5 -

13.0 -13.1 -2.5 2.5

20 -

30.1 -

23.6 137.0 125.6 -

22.2 -14.4 -

4.4 -

7.4 -11.8 -

]3.1 - 8.9 - 7.4

21 120.8 114.7 150.3 142.5 -

19.9 -26.0 3.9 -

1.3 -

13.8 -9.2 - 22.1 -22.0

22 120.0 117.0 152.0 141. 2 -

]3.8

-

12.4 19.8 21.0 -

]3.8

-

23.4 -

17.3 -16.1

23 124.5 123.2 126.0 127.0 -

4.0 -

1.3 25.7 26.9 -

23.8 -

26.15 -

]4.0

-

14.0

24 78.0 74.2 12.0 121.3 -

7.5 -

8.8 42.3 43.5 -

277 -

29.0 0.0 4.6

25 21.0 18.6 128.5 131. 8 -

11.1 -

39.6 50.8 58.7 -

19.8 -

21.0 11.3 13.5

26 40.5 42.9 85.2 94.2 1.2 -

2.5 49.8 44.3 -

14.2 -

18.4 15.5 14.4

27 22.2 17.3 35.4 103.0 -

3.7 - 9.9 52.8 59.6 -

14.8 -13.5 21.4 29.2

28 8.6 3.7 87.4 93.1 -

6.]

-

14.7 49.5 51.7 -

12.2 -

9.8 27.6 28.7

29 I

5.0 - 3.8 92.0 87.2 -

3.8 - 8.8 52.6 51.3 -

7.5 -

I ]8.8 28.7 29.9

30

I

6.4 2.5 55.8 48.5 2.5 -

5.1 I

291 29.1 -

1.3 -6.4 18.2 3.6

TABLE 2-DIAGONAL STRAINS AT DOWNSTREAM FACE ....

~

~

is:

0

t:1

t:rJ

t-<

8

t:rJ

w

8

w

0

"'J

to

0q

t-<

t:1

t:rJ

::d

t:1

>

is:
RESERVOIR MERCURY RESERVOIR MERCURY RESERVOIR MERCURY

SURFACE AT EL. 1400 SURFACE AT EL. 1232 SURFACE AT EL. llOO

A-Gage Lines B-Gage Lines A-Gage Lines B-Gage Lines A-Gage Lines B-Gage Lines

Gage Line Load Load Load Load Load Load Load Load Load Load Load Load

No. 1 2 1 2 1 2 1 2 1 2 1 2

31 -

10.8 -10.8 154.0 141. 4 -

10.8 -

12.1 -7.6 - 10.7 -6.0 -

7.2 -9.1 - 10.7

32 12.9 9.4 86.0 79.2 5.9 2.3 -

18.8 -

20.1 0.0 4.7 -

18.8 -18.8

33 194.0 186.5 72.5 67.3 9.0 6.0 -

19.8 -22.4 - 12.0 -

10.5 -30.4 - 34.3

34 167.5 170.0 56.3 53.7 10.4 10.4 -

12.8 - 10.2 -13.0 -

15.6 -26.8 -28.2

35 172.0 168.3 7.6 25.3 20.9 23.4 -

15.2 -17.7 -13.5 -

18.4 -20.3 -

16.5

36 162.0 164.4 23.5 28.4 30.7 33.5 2.5 3.7 -

ll.8 - 14.2 - 13.6 -

9.9

37 154.0 157.8 17.2 8.6 49.0 50.2 -

1.2 1.2 1.2 0.0 - 3.7 -

7.4

38 120.0 126.8 15.9 8.6 45.7 45.7 - 1.2 1.2 8.0 8.0 -

4.9 -2.5

39 112.5 ll9.4 26.4 12.6 47.3 54.0 13.8 16.4 12.4 14.6 -

1.3 8.8

40 llO.O lll.0 20.5 19.2 55.0 49.4 10.3 ll.5 21.4 23.6 0.0 2.6

41 75.7 72.5 0.0 0.0 41.8 38.4 -

1.3 0.0 17.0 12.5 -

4.0 0.0

42 70.4 64.6 19.8 16.5 38.6 34.1 ll.O ll.O 20.4 15.9 9 9 6.6

43 41.0 36.2 88.0 78.4 21. 7 18.1 -

16.0 -20.8 9.6 12.1 - 1.6 -

3.2

44 57.4 40.3 35.8 24.3 36.6 28.1 -

51.4 -

54.3 13.4 18.3 -

24.3 -25.7

45 205.3 212.5 31.0 33.6 18.8 18.8 - 31.0 -

31.0 -

7.2 -4.3 -

23.9 -.25.4

46 236.0 241. 5 -

49.7 - 56.6 32.7 35.1 -

48.4 -

58.0 -

6.1 -9.7 -29.0 -

29.0

47 259.0 267.0 -

24.9 -

29.1 69.3 68.2 -

33.2 -

30.4 -

1.1 -1.1 -24.9 -

22.1

48 242.7 254.5 -

46.8 -46.7 86.0 90.4 -

41.3 -

41. 3 ll.O 9.9 -

27.5 -

26.1

49 234.0 249.0 -

37.3 -

42.9 94.5 104.5 -

27.7 -31.8 28.3 30.4 -

18.0 -

19.4

50 204.0 215.5 -

40.0 -

35.9 95.8 101. 0 -

24.8 -23.5 38.2 35.0 -

16.6 -

13.8

51 173.3 177.5 -

31. 3 - 31.4 91.3 92.4 -

18.5 -18.5 40.0 40.0 -

14.3 -

12.8

52 161.4 159.5 -

32.1 -

33.4 89.3 85.3 -

20.9 -19.5 39.6 38.6 -

15.3 -

11.1

53 146.0 137.0 -

54.0 -

46.7 82.0 73.8 -

35.0 -

24.8 45.5 38.5 - 21.9 -

14.6

54 ll9.3 110.6 49.5 42.8 69.6 60.7 3.3 -

1.6 38.7 29.8 9.9 4.9

55 97.1 81.0 -

11.9 -16.4 61.4 48.5 -

28.4 -29.9 21.0 32.4 -

3.0 -

10.4

56 291.0 282.5 -

50.6 -

59.6 54.5 53.2 -

44.6 -44.6 4.2 5.6 -

19.4 -

19.4

57 369.5 380.0 -

95.4 -

97.8 96.5 102.1 -

54.8 -51. 9 10.2 14.8 -

22.2 -

22.2

58 372.3 377.0 -

67.4 -65.8 123.2 135.0 - 44.3 -

39.8 24.6 28.2 -

19.9 -19.9

59 242.0 256.7 85.5 86.4 107.2 1136 50.8 55.9 34.6 39.5 22.0 23.8

60 456.5 467.0 79.0 79.0 98.6 95 8 4.2 43.7 21.1 17.3 15.0 11.8

TABLE 2-DlAGONAL STRAINS AT DOWNSTREAM FACE-Continued

t:I

l'J

"'J r

()l'J

j

0

Z

[fJ

rn

,

::0

>

Z

r;n

>

Z

t:I

rn

...,

::0

l'JtJ2

rn

l'Jrn

......

~

0.
0

.0 , . . c . . . . .. IT

~:::::......

.

~-

'0 ~~;::::"'"

-......;

~20

'0

166 MODEL TESTS OF BOULDER DAM

NlVADA AlUTatlJlT ,A..TIUVIR MUIU.f.. 'ICTIOII' ARI%OU aIUTIIE'"

ELEVATION IZ5t

'"

"

!

+20

+'0

TOO

+'0

!

it

~

i

2

+'0

0

ELEVATION 1100

!

+to

+'0

+20

..

..

i

..0

~

:

I

r

t;

'".

8

0

-to

ELEVATION 1000

~

c

i

t;

+'O

~

+20

+to

0

-to

T Compression

- Tension.

..

"

c

i

EL£VATION 900

T20

~

T'O

0

-to

- Load on model only

- ~- Load on mod el and canyon walls.

ELEV.1'10N 800

"O

~

"0

0

-'0 El[VATION 700

+':~

-IO~

ELEVATION 600

FIGURE 103-ARCH STRESSES AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1400
- --....

- - -';;;

.:::::::::.- ,:::::::-

0

0

~/-.0

'0 --- ~'

---- ....... 0

~~~~-

= -~

DEFLECTIONS, STRAINS, AND STRESSES 167

.'0

,.

ARIZONA ABUTMENT

'7

NEVADA ABUTMENT CANTILEVER MEASURING SECTIONS

0

"0

.30

"0

.'0

ELEVATION 1232

..

'3

x

u

z

'"

~

i

~

'"

~

~

~

z

~O

ELEVATION 1100

.

'0

.30

- ..1 .0

'"

0

0

~

..0

'"

u

..

..

I

g

~

..

-'0

ELEVATION 1000

~

~

'"

~

~

~

'"

u

..

~

~

~

"O

~

"0

0

-'0

ELEVATION 900

"O

~

.'0

0

-10

.. Compression.

- Tension.

EL'[VATION 800

HO

~

tlO

0 "'.

-10

- Load on model only

--~ Load on model and canyon walls.

ELEVAnON 700

":crr=r::=J

-IO~

ELEVATION 600

FIGURE 104-ARCH STRESSES AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1232
00 1 . 8 C F H

"

11

0

0

0

10

0

0

10

>----

0 -lI

.30

'20

.,0 f--.

0

-10

}68

NEVADA ABUTMENT

..

'3

'2

MODEL TESTS OF BOULDER DAM

C.uTIL[VER MEASURING SECTIONS ""HZONA ABUTMENT

ELEVATION 1232

..

%0%

'3

'2

E

C

~

'"

w

.~~

W

'"

Z

~

'"

~

Z

ELEVATION 1100

--=

~

~

'"'"~

0

~

0

~

ELEVATION 1000

i

g

~

c

w

~

~

E

~W

W

0

~

..

..

~

..

'10

-'0

+ Compression

-

Tension.

ELEVATION 900

t'O

~

.'0

0

--

-10

- Loadonmodelonly

--- Load on model andcon-yonwoHs,

ELEVATION 800

+20

~

.'0

0 -

-10

ELEvATION 700

.':o=rIJ

-JO~

ELEVATION 600

FIGURE 105-ARCH STRESSES AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1100
DEFLECTIONS, STRAINS, AND STRESSES 1,69

inch at elevation 1232, at the Nevada abutment, when pressure was

applied to the model only. Applying reservoir pressure to the canyon

walls reduced this stress slightly. The maximum tensile stress of ten

pounds per square inch occurred at cantilever section E, between elevations 775 and 900, when reservoir pressure was applied to the canyon walls. vVhen pressure was applied to the model only, this stress

was reduced to eight pounds per square inch.

For load at elevation 1232, maximum compressive and tensile

stresses occurred when the reservoir pressure was applied to the

model and canyon walls. For this loading condition, a maximum

com pression of 20 pounds per square inch occurred along the Nevada

abutment between elevations 1050 and 1150. A maximum tension,

slightly greater than five pounds per square inch, occurred in an area

about four inches wide between cantilever sections D and F and

elevations 725 and 975. vVhen load was applied to the model only,

the stresses were slightly smaller.

With mercury surface at elevation 1100, there was very little

difference between stresses resulting from the two methods of loading,

see figure 105. By applying reservoir pressure to the canyon walls

and the model, stresses along the Nevada abutment between elevations

825 and 1150 were increased slightly over those obtained by loading

the model only.

104. Cantilever Stresses.-Cantilever stresses determined from

strain measurements are shown in figures 106, 107, and 108. When

loaded to elevation 1400, maximum compressive stresses of 30 pounds

per square inch occurred at the abutments, at elevation 1100, with

pressure applied to the model only. \Vhen reservoir pressure was

applied to the canyon walls the maximum stress was reduced to 27.5

pounds per square inch at each abutment. When loaded to elevation

1232, the reservoir pressure on the canyon walls did not affect the

stresses materially. Maximum compressive stresses for both methods

of loading were nearly eight pounds per square inch. The maximum

tensile stress was two pounds per square inch when pressure was

applied to the model only, and about one pound per square inch when

reservoir pressure was applied to the canyon walls.

When the mercury surface was at elevation 1100, cantilever

stresses were relatively small. Reservoir pressure on the canyon walls

had very little effect on the stress distribution. The maximum compressive stress was 2.5 pounds per square inch in the lower part of
0'

~ 10 ~20 +30

r~

SECTION 0

0 ~ 10 +20 -30

1232

~ 900

0 800

SURFACE STRESS AT DOWNSTREAM FACE OF MODEL IN POUNDS PER SQUARE INCH

ljj=J

SECTION! tmSECTION A

ffil SECTION B

a -10 +20 -3D

SURfACE STRESS AT DOWNSTREAM FACE OF YODEL IN POUNDS PER SQUARE INCH

SECTION C

SECTION F

0 +10 -20 +30

-,-- T

SECTION G

~SECTION H

t!TI SECTION 16

+ Compression

-

Tension

~ Lood on model only

---

Load on model and canyon wolls.

FIGURE 106-CANTILEVER STRESSES AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1400

°-

+10 +20 +301232

,....

""" 0

1000

900 :;;

aoo ~

~

0

tj

t".1

r

...,

t".1 U2

...,

U2

0

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tJj

0

f2

tj

l':1 ;Jj

tj

>

~

--

600

SECTION D

0 -10 -20 +30

r '<-p ,

SECTION 17
-I~.~O

SECTION 0

-10 0 +10 1232 "'20

1100

1000

"

~

900

<;

Z 800

SECTION E

SURFACE STRESS AT DOWNSTREAM FACE-OF NODEL IN POUNDS PEA $QUARE INr.H

IW"

-1D:Jj

SECTION I 1mSECTION ...

SEcnON B

0 +10 .20

\

I

I

SECTION C

-10 0 +10 +<20

SURFACE STRESS AT DOWNSTREAM FAcE OF NODEL IN POUNDS PER SQUp,f,fE INCH

I

,

_I~

SEcn ON F

-10 0 +10 "'20

\

,

SECT;QN G

UySEcnON H

lrDSECTION 16

+

Compression

:...Tension

- -

Load on model only.

---

Load on mode!and canyon wa!!:.

FIGURE 107-CANTILEVER STRESSES AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1232

10 a +10 "2012~t

SECTION D

-to 0 "1"10-+20

~ r---1

SECTION 17

1\ 1000

"

900 <

~

~

tJt:r:J >,;J

r

t:r:J

n

j

0

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.00

00

>-3

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800

'00

600

>

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00

>-3

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00

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......

"""

"" -'0 0 +10 t201232

j

II 1100

!

1000

900

~r:::

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t:!

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100 t-<

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00

SECTION0

00""

.'0 0 t'O +20

,.-~----. 0

SECTION 17 "'j

td

0

e

t-<

t:!

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t:!

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900

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z 800,

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I ~ I I

SECTION 0

";i

~

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10

1100

1000

tlO +20

100

~

600

SECTION E

-']

SURFACE STRESS AT OOWNSTREAM FACE OF MODEL IN POUNDS PER SQUARE INCH

r

.'0

T

SE:CTIONI

illJSECTION A

ffil SECTION B

-\~O

I

SECTION C

-10 0 +!O tZO

SURFACE STRESS AT DOWNSTREAM FACE

Of' MODEL IN POUNDS PER SQUARE INCH

\

fh

SECTION F

.'Oif

,

"10 +20

-g;g

SECTION H

.'[ll~J

SECTION 16

+ Compression

... Tension

-

Load on model anI y

--- Load on mod-elond canyon walls.

FIGURE 108-CANTILEVER STRES'SES AT DOWNSTREAM FACE.

LOAD AT ELEVATION 1100

I

I

rH.JJ

SECTION G
DEFLECTIONS, STRAINS, AND STRESSES 173

the model. At elevation 1100 in the central part of the model, a maximum tensile stress of 2.5 pounds per square inch was found.

105. Horizontal Shearing Stresses.-Horizontal shearing stresses

computed from strain measurements are shown in figures 109, 110,

and 111. There was little difference in shearing stresses resulting

from the two methods of loading. With reservoir load at elevation

1400, a maximum shearing stress of 23 pounds per square inch occurred at the Arizona abutment, at elevation 1100, when reservoir

pressure was applied to the canyon walls. The reversal of shearing

stresses at the abutments at elevation 1232, for load at elevation

1232, was due to contraflexure in the deflection of the model for that

loading condition. The radial deflection of the arch element at elevation 1232 was upstream near the abutments, as shown in figure 82.

At lower elevations this reversal of shearing stresses did not occur.

\Vith the mercury surface at elevation 1100, shearing stresses

were rather small, as shown in figure 111. Some reversal of stress

occurred at the abutments at elevations 1232 and 1100.

106. Principal Stresses.-Principal stresses computed from strain

measurements are shown in figures 112, 113, and 114. In figure 112,

principal stresses for the overload condition are shown for the two

methods of loading. Magnitudes of principal stresses were changed

slightly due to the two methods of loading, but directions of stresses

were virtually unchanged. A maximum compressive stress of 64.0

pounds per square inch occurred at elevation 1232 at the Nevada

abutment. This stress was the same for both systems of loading.

A maximum tensile stress of 10.3 pounds per square inch occurred

at cantilever section E, elevation 800, when reservoir pressure was

applied at the canyon walls. At the same location the maximum tension was 8.3 pounds per square inch when load was applied on the

model only.

For load at elevation 1232, compressive stresses were largest

along the abutments above elevation 800. The largest compressive

stress along the Nevada abutment was 21.9 pounds per square inch. It

occurred between elevations 900 and 1000 when pressure was applied

at the canyon walls. The largest compressive stress along the Arizona

abutment was 24.8 pounds per square inch at elevation 1100. The

maximum tensile stresses occurred along cantilever section E. When

pressure was applied at the canyon walls, a tensile stress of 6.5 pounds

per square inch occurred at elevation 800. When pressure was applied
~--=""'-

"""':::--

'30

+20

"0

%u

Z -10

I

-20

~~~Q

Z

~0

~~~-10

~QQ

,.

0

~u

<

~.

g

0- <

~~~Z

0- ~Z

<~%

......

~--:::;:/' -' :.---

174

NEVADA ABUTMENT

+300 I

MODEL TESTS OF BOULDER DAM

CANTILE.VER MEASURING SECTIONS

0 E F G

ARIZONA ABUTMENT

16 17

FIGURE

.00

"0

-10

-20

ELEVATION 1232

ELEVATION II 00

+20

"0

-20

ELEVATION IQOD

.2°

mD. "0 _C?' 0

.:;..---

-10

-20

ELEVATION 900

Positive shear ~s caused by

shear forces acting thus ~

":

-10~~

-20

ELEVATION 800

-Load on model only

---Load on model and canyon walls.

"O

~

0 -

-10

ELEVATION 700

+10

~

0

-

-

-10

ELEVATION 600

109-HORIZONTAL SHEARING STRESSES AT

FACE, LOAD AT ELEVATION 1400

DOWNSTREAM
-t'O

+20

+10

Xu

z

~~~0

0

~~~"

z

f

=

~~" 0

~0

~u

Ii.

i

g

.-? -

-

-_ .-/'

I

- ===

--::.0-

-

NEVADA ABUTMENT

FIGURE

+:'00

+20

+'0

0

-'0

-20

DEFLECTIONS, STRAINS, AND STRESSES 175

CANTILEVER MEASURING SECTIONS ARIZONA ABUTMENT

A

"

17

-

- -

ELEVATION 1232

-10

-20

ELEVATION 1100

+20

+10

-10

-20

ELEVATION 1000

+20

~

+10

-

0

-

-10

-20

Positive shear is caused by shear

forces acting thus ~

ELEVATION 900

+I:

-20

-10~

-

Load on model only.

--- Load on model and canyon walls.

ELEVATION BOO

.'O

~

0 -

-10

ELEVATION 700

+I:~

-IO~

ELEVATION 600

nO-HORIZONTAL SHEARING STRESSES AT

FACE, LOAD AT ELEVATION 1232

DOWNSTREAM
176

NEYAI)A .aUT.",-

+'JOO

+20

"0

-'0

-20

MODFL TESTS OF BOULDER DAM

CANtlLEVEIt IIIASU'U.' SEotIO"S

,

AII%ONA A8UTMENT

EL.£VATION 1232

+'0

'20

+10

%

"

%

0

w

«

;!

g

«w

..

.

"

z

"

"

..

z

-'0

-20

ELEVATION 1100

+20

+10

~

w

"

0

'"~

"

w

"

~

~

i

g

..~

.

'"

w«

'"«..w%..

-10

-20 ELEVATION 1000

'20

~

+10

°

-'°

-20

ELEVATION 900

Positive shear is Caused by

shear forces octing thus :::;:=

"°

°Rm-

-1O

-20

ELEVATION 800

- Loadon modet only.

--. Load Onmodel and canyon walls.

":c:r:::::r:::r::

"IO~

ELEVATION 100

":u==r=o

-IO~

El.EVATION 600

FIGURE Ill-HORIZONTAL SHEARING STRESSES AT DOWNSTREAM

FACE, LOAD AT ELEVATION 1100
DEFLECTIONS, STRAINS, AND STRESSES 177

CANTILEVER MEASURING SECTIONS

r. D F- F 16

APPROXIMATE DEVELOPED DOWNSTREAM FACE

lOAD ON MODEL ONLY

CANTILEVER MEASURING SECTIONS

c 0 E F G 16

0 00

I

,

I

,

I I TENSION

>-- COMPRESStON SCALE'OF STRESS IN POUNDS

PER SQUA~E INCH

APPROXIMATE DEVELOPED DOWNSTREAM FACE

lOAD ON MODEL AND CANYON WALLS

FIGURE 112-PRINCIPAL STRESSES AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1400
178 MODEL. TESTS OF BOUL.DER DAM

CANTILEVER MEASURING SECTIONS

C 0 E F 16

-£1.1242

APPROXIMATE DEVELOPED DOWNSTREAM FACE

LOAD ON MODEL ONLY

CANTILEVER MEASURING SECTIONS

Co 0 E F G 16

-£1.1242

"

,

"

, ~o 40 50

I I I TENSION

COMPRESSION

SCALE OF STRESSES IN POUNDS

PER SQUARE INCH

APPROXIMATE DEVELOPED DOWNSTREAM FACE

LOAD ON MODEL AND CANYON WALLS

FIGURE 113-PRINCIPAL STRESSES AT DOWNSTREAM FACE,

L.OAD AT ELEVATION 1232
DEFLECTIONS, STRAINS, AND STRESSES

CANTILEVER MEASURING SECTIONS

C D E F

APPROXIMATE DEVELOPED DOWNSTREAM FACE

LOAD ON MODEL ONLY

CANTILEVER MEASURING SECTIONS

C D E F

10 20 30 040 50

I I I I I

SCAl& OF STRESSES IN POUNDS

PER SQUARE INCH

APPROXIMATE DEVELOPED DOWNSTREAM FACE

LOAD ON MODEL AND CANYON WALLS

179

16

,-EI.I242

J'.::~_I.IOOO

16

,,-EI,1242

J:~~~.IOOO

TENSION

. II

COMPRESSION

FIGURE 114-PRINCIPAL STRESSES AT DOWNSTREAM FACE,

LOAD AT ELEVATION 1100
180 MODEL TESTS OF BOULDER DAM

to the model only, a maximum tension of 5.3 pounds per square inch

occurred at elevation 900.

The largest compressive stresses were nearly perpendicular to

the abutments and occurred between elevations 900 and 1100. In the

lower portion of the model, the directions were much steeper than in

the upper portion, owing to the distribution of load by tangential

shear. At elevation 1232, stresses near the abutments were inclined

in directions more nearly horizontal than those occurring at lower

elevations. For load at elevation 1100, stresses were negligible except

along the abutments below elevation 1100.
CHAPTER VI-.-MISCELLANEOUS TESTS

SPECIAL DEFLECTION TESTS

107. Crown Cantilever Movements. --- Radial and tangential

measurements indicated that deformations occurred at the foundation

and abutments. Such movements, combined with deformations of

the model, caused vertical as well as horizontal movements at the

cantilever elements. Tests were run to determine resultant movements at the crown cantilever, designated on the drawings as cantilever E.

The first tests were made with gages set to register movements

in a vertical direction. The results of these tests are shown in figures

115, 116, and 117. Points above elevation 1000 rose above their original

position while points below elevation 1000 deflected below their original position. The point at elevation 1100 showed a very small deflection in all tests. Deflections were plotted to an exaggerated scale

from a section on the center line of the model.

By plotting vertical deflections and horizontal radial deflections

from the same point, the position of the downstream face could be

determined. The deflected position of each of the points fell on a

smooth curve. The vertical deflection of the point at the top of the

model was about one-sixth of the radial horizontal deflection when

the mercury surface was at elevation 1400. When the mercury surface

was at elevation 1232, the vertical deflection of the same point was

about one-third the radial horizontal deflection, as shown in figure

116. For partial loads this ratio was still about one-third.

Deflection measurements normal to the face of the cantilever,

also shown on figures 115. 116, and 117, were not as consistent nor

as accurate as the vertical deflection measurements. The difficulty

encountered in normal deflection tests was in setting gage rods in

directions normal to the downstream face. If the directions of the

invar rods deviated from the normal, the plotted points were in error

and did not fall along a smooth curve. This accounts for the difference

in the position of the downstream face as determined by vertical and

normal measurements.

181
182 MODEL TESTS OF BOULDER DAM

-------

POSITION t)F DOWNSTREAM FACE AS DETERMINED BY

VERTICAL AND HORIZONTAL MEASUREMENTS-~~

~,

'

"\\0":'

/////

~

~G

/

""p-\.-Q /

,'<A°'<- /

I--

.

_///~

_,m

-._-

k:'''~VERTICAL DEFLECTION

/':;~SITION OF DOWNSTREAM FACE

AS DETERMINED BY HORIZONTAL

RADIAL MEASUREMENTS

75,- -

RADIAL

7NTAL DEF~,ECTIDN

SECTION ON ~ OF MODEL

20 30 40 50

SCALE OF DEFLECTIONS IN TEN

THOUSANDTHS OF AN INCH

}l DUL[CTIDN MEASURED IN HORIZONTAL RADIAL DIRECTION.

D DEFLECTION MEASURED IN VERTICAL DIRECTION.

/> DEFLECTION MEASURED IN NORMAL RADIAL DIRECTION

0 POSITION DETERMINED BY VERTICAL AND HORIZONTAL MEASUREMENTS

. POSITIONDETERMINEDBY VERTICALAND NORMAL MEASUREMENTS

1232

1100

1000 ~

~

C

~g

"

c

900

0,1}

l

~

~

800 ~

~

750 ~

c

u

700

650

600

520

505

FIGURE 115-RESULTANT DEFLECTION OF CROWN CANTILEVER,

LOAD AT ELEVATION 1400
MISCELLANEOUS TESTS

..-POSITLON OF DOWNSTREAM FAtE AS DETERMINEO BY

'-:ERTICAl AND HORIZONTAL. MEASUREMENTS

:::~_::-_~.~./RA.D[AL

HORIZONTAL. DEFLECTION

.--POSITION OF DOWNSTREAM FACE

AS DETERMINED BY HORIZONTAL

RADIAL MEASUREMENTS

SECTION ON ~ OF MODEL

,. .

It'

10 20 30

"0

, ~o I,

I .

183

1232

1100

~

1000 ~

~

~

'0

"

~

Ii:

~

0

900 ~

a

F

~

0

z

800 0

z

0

iv

700

600

505

FIGURE 116-RESULTANT DEFLECTION OF CROWN CANTILEVER,

LOAD AT ELEVATION 1232

SCALE OF DEFLECTIONS IN TEN

THOUSANDTHS OF AN INCH

.II DEFLECTION MEASURED IN HORIZONTAL RADIAL DIRECTION.

EI DEfLECTION MEASURED IN VERTICAL DIRECTION.

A.OEFl.ECTION MEASURED IN NORMAL RADIAL DIRECTION.

0 po.smON DETERMINED BY.VERTICAL AND HORIZONTAL MEASUREMENTS. .POSITION DETERMINED BYVERTICALANDNORMALMEASUREMENTS.
184 MODEL TESTS OF BOULDER DAM

POS!TION OF DOWNSTRE.A.M FACE AS DETERMIt\ED BY

VERTICAL AND HORIZONTAL MEASUREMENTS

-},''''~

-

..-RAOIAL HORIZONTAL DEFLE.CTION

~

~-~,,--~P~~~~~E~~~N~~N~~~~~~Z6~~;1..

RADIAL MEASUREMENTS

SECTION ON It OF MODEL

00,

I

to 20, 30 40 50 I t l

1232

1100

.

IOOO~

oc

w

c

~

~

c

m

~

c

900~

0

;=

~

~

Z

800~

~

75°3

700

650

600

520

505

FIGURE 117-RESULTANT DEFLECTION OF CROWN CANTILEVER,

LOAD AT ELEVATION 1100

SCALE OF DEFLECTIONS IN TEN

THOUSANDTHS OF AN INCH

J. DEFLECTION MEASURED IN HORIZONTAL RADIAL DIRECTION.

0 DEFLECTION MEASURED IN VERTICAL DIRECTION.

.&. DEfLECTION MEASURED IN NORMAL RADIAL DIRECTION.

0 POSITION DETERMINED BY VERTICAL AND HORIZONTAL MEASUREMENTS.

. POSITION DETERMINED BY VERTICAL AND NORMAL MEASUREMENTS.
MISCELLANEOUS TESTS 185

At first appearance the tests might indicate that, because the upper

points moved upward and the lower points downward, there must

have been a lengthening of the face. Actual1y, the movement represents a rotation about some point within the model. In fact, the strain

measurements showed that there was a slight shortening of the face.

108. Deflection of Interior.--In analyzing the model of Boulder

Dam by the trial load method, radial deflections of the arch elements

were calculated for center-line locations. In testing the model, radial

deflections at the downstream face were measured. Since there were

strains in the interior of the model, particularly at the lower elevations,

it was decided to measure the radial deflections of the arch center

lines.

Horizontal holes were dril1ed in the model to center-line locations,

and invar rods with expansion ends anchored in place. The outer ends

of the rods were supported by flexible couplings at the downstream

face and were al10wed to hear against dial gages reading to 0.0001 of

an inch. The dial gages were attached to anchors on the downstream

face of the model along cantilever section E. Any movement of the

interior of the model at the point of anchorage with respect to the

downstream face was registered on the gage. Locations of the measurements and results obtained are shown in figure 118.

l\t elevations 1100 and 1000 the squeezing of the model between

the center line and the downstream face was smal1, even for overload

conditions. At lower elevations the squeezing was as much as 0.0009

inches for overload conditions, and 0.0005 inches for normal load

conditions. Applying mercury load to the canyon wal1s had very

little effect on the squeezing of the model.

109. Cantilever Curvature at Downstream Face.-In preliminary

designs for Boulder Dam the downstream face had considerable vertical curvature below elevation 700. This curvature evoked considerable discussion about its effect on the cantilever stress distribution.

The objection to the curvature was that it tended to create tensile

stresses in a direction normal to the curved downstream face. Consequently, tests were made to determine the magnitude of the tension.

The hole at F, figure 118, was driUed radial1y from elevation

600 at the downstream face of the crown cantilever. An invar rod, with

an expansion end, was anchored in the hole. The end of the rod at

the downstream face was supported with a flexible coupling and bore

against a dial gage which was rigidly attached to the face of the

model. No movement was registered on the gage, except when the
ELEV.OF M EASUREMENTS

MERCURY WITH MERCURY BAG NO.2 WITH MERCURY BAGS NOS.2-3-4

SURFACE A 8 C D E F A 8 C D E F

140'0 -I.! 2.9 4.9 9.2 9.0 +0.2 0.5 3.' ..-5.4 9.' 7.8

1350 -0.7 -2.3 -4.3 -e.1 -S.2 0.0 -0.6 -2,7 -5.4 -6.2 .-7.2

1300 -0.4 -2.0 -3.8 -7.0 -7.3 0.0 -0.4 -2.0 -3,8 -7.3 -6.7

1250 0.0 -1.2 -3.2 -6.2 -6.8 0.0 -0.2 -, 5 -3.4 -6.0 -S.7

1232 +0.1 -1.0 -2.8 -5.2 -5.8 0.0 0.0 -1.2 -3.3 -5.4 -5.2

1200 +0.1 -0.9 -2.3 -5.2 -5.8 0.0 0.0

-

1.0 -2.8 -5.0 -4.8

1150 +0.2 -0.3 -

1.8 -4.1 -4.9 0.0 0.0 -0.7 -2.1 -4.1 -4.1

1100 +0.1 0.0 -1.1 -3.3 -4.0 0.0 0.0 -0.3 -1.6

-

3.3 -3.4

186 MODEL TESTS OF BOULDER DAM

mercury surface was at elevation 1400, when a deflection of 0.000,02

inch was observed. This indicated an average tensile strain of 2.8

millionths of an inch per inch, corresponding to a stress of 0.28 pounds

per square inch. This was the average stress over a gage length of

7.25 inches. The peak stress near the surface ,vas undoubtedly greater,

but a more refined system of measurements would have been required

to determine it.

~

..

0

rr: !!"Q9______--

'"

0

.J

"~ 1-9.92______-

...

0

~" 2QQ.--_---

;:

..

>

'"..J soo iii --------

'"

z

0

~ !QQ-----

..

:::

0:

0:: 600

0 -----

"

TABLE OF DEFLECTIONS

Positive signs indicate lengthening', negative signs indicate shortening.

Goge readings given in ten-thousandths of an inch,

,

Positi on of -,,~' '<"- ~\...

measurements \ -

Valu€s in table are overages of two or more

tests for eoch loading condition.

Load applied to model with mercury bog No.

2; and to canyon walls with bogs Nos. 3

and. 4.

Holes drilled in model to required depth and

inver roqs with expansion ends anchored

in them.

Outside end's of rods supported by flexible

couplings at downstream face and allowed

to bear against "Last Wordn gages.

Movement of interior of model at point of

anchorage, with respect to downstream

face, registered on the dial gages.

~Q.L

--

SECTION ON CENTER LINE OF CANTILEVER E

FIGURE 1I8-DEFLECTION OF INTERIOR OF CROWN CANTILEVER

FLOW TEST

110. Plastic Flow.-In making the tests of the model, some plastic flow occurred during the first two or three tests each day. After

these tests had been made, the action of the model became elastic,

and repeated measurements of strains or deflections agreed very

closely. Apparently the movement of the model during the first test,

after being idle for several hours, was partly plhtic and partly elastic.

Flow tests of cylinders had shown that the deformation increased

rapidly when load was first applied, but became practically stationary

after being under load for a few hours. Since only elastic deformations were desired in the deflection and strain measurements, tests

in which some plastic flow had obviously occurred were always disr;ardec1. In order to determine the magnitude and rate of flow of the
MISCELLANEOUS TESTS 187

model, a test was made under continuous Joad with mercury surface at

elevation 1232.

111. Calibration of Instrument Stand.-As the flow test would

require several days, temperature variations were expected. Although temperature changes in the testing room were relatively small

and probably did not affect the model materially, they might be expected to affect the instrument stand which was equipped with a steel

reference plate, as shown in figure 71. This plate was rigidly fastened

to the concrete abutments, and any change of temperature caused it

to deflect like a steel arch with fixed ends. To check the movement

of the plate, a dial gage had been mounted on an in val' rod, between

the plate and the concrete pit, so that the movement of the plate

could be measured. Since the usual test observations required less

than an hour, the change in temperature was not sufficient to cause

appreciable movement of the plate. However, in a test lasting several days some movement was probable.

A calibration of the steel plate of the instrument stand was therefore made for knovvn changes in temperature. Mercurial thermometers

were placed adjacent to the plate at a number of locations. The temperature was changed by opening the windows and shutting off the

steam radiator. Temperatures were read at intervals, and positions

of the model and instrument stand determined. From data thus obtained, curves were plotted showing movements of the plate caused

by temperature changes.

112. Procedure.--The flow test was started on the morning of

December 10, 1931. Dial gages and thermometers were read and the

mercury load applied. ,Vhen the mercury surface reached elevation

1232, the gages and thermometers were read again. Readings were

made at intervals of 15 minutes during the first few hours of the test.

then at 30-minute intervals during the remainder of the first day. As

the rate of flow diminished, the interval between readings was increased. After eight days the model was unloaded and allowed to

recover. Deflection readings were continued for four days. At the end

of the fourth day the upper portion of the model had returned to its

original position, but complete recovery had not taken place in the

lower part.

In plotting the data from the plastic flow test, a number of minor

discrepancies were encountered. Small variations of temperature and

atmospheric conditions seemed to affect the model and the apparatus
:,NEVAOA ABUTMENT

-I

..0 [

INSERT NUMBERS "'RIZONA A8UTMEN~

20

>0

4

"

1;

~

50

0

~&O

... 0

~

z to

...

m

z,

2

:;!

0

!>O

0

~

,

~

Z

~

20

30

.....

00

00

ELEVATION 900

10

is:

0

t:I tI:J

t:-<

20

>-3

I?':!

w

>-3

w

0

':rJ

1;0

0

c::

t:-<

t:I

tI:J

::d

t:I

>

is:

>0

10

~

- LOADED DEfLECTION

UNLOADEO DEFLECTION

CURVE TI~~A~iNTGER

0

0.10 DAYS

0.50

1.00

- 3.00

8.00

TIME AFTER

UNLOADING

0.25 DAYS

0.50

1.00

4-.00

FIGURE 119-INCREASE IN ARCH DEFLECTIONS DUE TO FLOW,

LOAD A T ELEVATION 1232
20 30

m

r

~

<

~IIOO

~

J.. .G ,

..

\

\

i\

1!1 ,I' ,,,

II,I

I

SECTION B

SECTION C

20 30

I

,il

'I' ',I

h' "0 ,\\\..c;

~\~~

100 t'tt",

,I" ,'II

1"'1 Ir'

~ 900 I

; \~~~\

<5 \\'\

z eOQ 1\\

1111 ,,11

1", III/

I

II

Ii

III

III

1I't---G

III\-.H

'It~.~

'I' Il'

","

1,1

1\\

II'

\\\ IIII

IIII

\\'1

JIll "I' III/ 1111

SECTION H

SECTION,

7°1232

1100

-

LOADED DEFLECTION

UNL.OAOEDDEFLECTION

1000 CURVE TI~UI~ER

~ 0

I'T1 0.10 DAYS

<

OOO~

~

~

00

n

trJ

t"'

t"' >Z

trJ

0

d

00

>-:3

trJ

00

>-:3

00

700

000

,

A.. 1232

"00

'000

NOTE

UNL.OADED OEFLECTION CURVES FOR

SECTIONS

"A"

AND

"H"

NOT OeTAINED.

FIGURE 120-INCREASE IN CANTILEVER DEFLECTIONS DUE TO FLO\Y,

LOAD AT ELEVATION 1232

-'m

""
190 MODEL TESTS OF BOULDER DAM

more than had been anticipated. After correcting for the change of

temperature of the steel plate, the observed points varied periodically.

Observed deflections were greater in the morning than in the afternoon. These periodic variations were disregarded and smooth curves

drawn through the general trend of the plotted points. Most of the

variations occurred above elevation 900, where the measurements were

made with reference to the steel plate of the instrument stand. Below

elevation 900 the plotted points fell on smooth curves with practically

no irregularities.

113. Results of Flow Test.-Results of the flow test are shown

in figures 119 and 120. The maximum deflection at the top of the

crown section, elevation 1232, increased from 0.004,92 inches to 0.005,35

inches in eight days. This increase was 8.75 per cent of the original

deflection. After unloading, the upper part of the structure recovered

almost to its original position in four days. At lower elevations the

flow was greater in proportion to the original deflection, due to the

higher stresses in the material. At insert 3, elevation 600, the original

deflection increased from 0.000,65 inches to 0.001,00 inches, 53.9 per

cent, in eight days. The lower part of the model did not recover so completely as the upper part in the period of time allotted to recovery.

Although the increase in deflection observed during the test must

have been principally due to flow, small proportions of the increase

probably were caused by the cracking of the model, discussed in the

following section.

114. Condition of Model.-As soon as the flow test was completed the upstream form and rubber bags were removed from the pit.

A careful inspection of the upstream face was then made to determine

if any cracks had formed. The results of the inspection are shown in

figure 121. The model had cracked from the abutments nearly all the

way around the upstream face. The width of the crack was small,

but it showed definitely through the protective coat of shellac. There

was also a small horizontal crack, about six inches long, at the Nevada

abutment near elevation 1150. These cracks must have formed during

the flow tests, as several inspections of the upstream face, prior

to the beginning of the test, failed to reveal any indications of cracking.

The plaster-celite material had an ultimate strength in tension

of about thirty pounds per square inch, about one-sixth of its ultimate strength in compression. The cracks along the abutments at

the upstream edge may have affected the action of the structure as an
MISCELLANEOUS TESTS 191

arch. After the model was dismantled, examination showed that the

cracks around the abutments varied from one to one and one-half

inches in depth. Some proportions of these depths prohably were

caused by tests made after the flow test was completed. The horizontal crack extended only through the surface coating of shellac.

A close examination of the downstream face of the model failed to

show any cracks, even in the area of known tensile stresses.

CANTILEVER MEASURING SECTIONS

"

E D C

,...

'000

~

,,"

~

900 ,;

~

'"

..

~

",$2

~y

41"-

"

~

~

.f ,f

g

v

,,>0

-NOTICEABLE CRACK

PROBABLE CRACK BUT NOT DEFINITE

"-hCRACK CONTINUES INTO SUPPLE.IWIENTAL

BASE FROM THIS POINT

DEVELOPED UPSTREAM ELEVATION

(f.PPRoxIMATE)

FIGURE 121-CRACKS AT UPSTREAM FACE ON COMPLETION

OF FLOW TEST

115. Effect of Cracking.-Since cracking in the model reduced

the effective section, an increase in radial deflection was expected.

Accordingly, a series of radial deflection measurements was made to

determine the effect of the cracks on the action of the model. The

results of the measurements, plotted along the arch elements, are

shown in figures 122, 123, and 124. They should be compared with

the results obtained from former tests, made before any cracking

occurred, see figures 87, 83, and 85, respectively. In the former tests.

the model acted as an arch fixed at the abutments. By applying mer-
~~0

~120

0 130~ m

~r

m

n 1>0

~~,60

Z "0

~m

z

~r

0

c

~~Z

0

~r

~~Z

0

'

20

'070

'\

90

100 I

"0 E LEV. 1100

0'

~

'~.

'--~' _h~~j=---+_- . ~:

.

J. '~~.'~_i ~Z/ /~

.

:~

.....

'"

~

ELEV 900

q~4~ t+- -=-c-- -~~-~I ::

ELEv 800

~

0

c:I

l':I

r

>-3

M

00

H

r.i:.

~~~-+--!

I~

E LEV. 700 0

"'J

tJ:I

0

c::

r

c:I

~

::c

c:I

>

~

~'U'7-:':::j

I~

ELEV. 600

30

0 0 0 Test No 1176 usi ng mercury bogs Nos. 2,3,and 4. June 13,1932.

Test No- 1177 using mercury bog NO.2.June 13,1932

Mercury pressure 'IS applied to model with mercury bog Na2,

and to canyon walls with bogs 3 tiJnd 4.

"

FIGURE 122-RADIAL DEFLECTIONS OF ARCH ELEMENTS AFTER CRACKING,

LOAD A T ELEVATION 1400
.' ~3 0 7 . II 13 IS 17

" ~~-d

~/-

,

"'-. .-/

.::--,. -#'

,~

~'~ ./"

NEVADA ABVTMENT INSERT NUMBERS "RIZCNA ABUTMENT

~;:

~ ELEV. 800

0

10

20

50

ELEV. 1232

'"

1;

~

:;:

~

...

..

<>....

~

z

~

.... %

I

~

10 14 15

°m

2- 4 .

.~o

20

30

40

50

.0

ELEV. 700

is:

....

Ul Q

l"J

....

r-o

>z(g

0

d

Ul

>':3 (g

Ul

>':3 Ul

. 1

,.

20

30

00

ELEV.IIOO

0

~

3

7'"13

10

20

p'

30

~

40

50

ELEV. 1000 m'

3 0 .

.- 10

20

3.

40

o.

ELEV.600

~

z

!i

20,:~

:~

, I---~; ;

ELEV. 900

c c--o Te5t NO.1191u5mg mercury bogs NOS.2,3,ond 4. June 14,1932

If "I( Test No. 1192using mercury bog No 2. June 14,1932

Mercury pre5sure was opplied to model with mercury bog

No.2, and fa canyon walts with bogs 3 ond 4

FIGURE 123-RADIAL DIDFLECTIONS OF ARCH ELEMENTS AFTER CRACKING,

LOAD AT ELEVATION 1232

......

<:

'-'0
.5NEVADA ABUTMENT ARllONA ABUTMENT--

'. I 2 INSERT NUMBERS

0 Ie

--

, 1 .

"

13

"

11

---- ==- -- -

"

.0

~~'0

20

!:

~i

..

..z

..

'"0c:

...z

i

!i1

.z

~'"

, . . . to 12 ,. I

-~ ...-

-- --- - --

.....

'"

...

00

30

"" ~

___3

,

'_'0

- 10

20

30

40

SO

eo

ELEV 800

so

eo

ELEV 1232

.

~~

~.oELEV 700

::::

0

tJ

l"J

r

>-3

l"JCD

>-3 CD

0

t:z;I

tC

0q

r

tJ

t:;J

~

tJ

>

::::

30

.0

00

eo

ELEY 1100

~ ELEV 1000 m~ELEV 600

~§j--+-H 30

.0

' ELEV 900

Test No.1201 using mercury boos Nos. 2,3 ond 4.

,, Test No. 1203 using mercury bag No. 2

Mercury pressure was applied to made I with mercury bog

No.2. and to canyon wolls with boos 3 ond 4.

FIGURE 124-RADIAL DEFLECTIONS OF ARCH ELEMENTS AFTER CRACKING,

LOAD AT ELEVATION 1100
Deflection Before Cracking*

Elevation

of Pressure Pressure

Mercurv on on

Surface Model Model and

Canyon

1400 155.0 152.8

1350 117.7 119.9

1300 83.5 86.2

1250 54.0 64.7

1232 48.0 60.2

1200 34.0 50.3

1150 22.8 41.0

1100 14.6 28.1

- -

Pressure

on

Model

168.8

132.2

I

99.0

62.0

52.5

37.0

22.0

12.1

MISCELLANEOUS TESTS 195

cury pressure to the abutments, the deflection of the model was

changed materially. After the model cracked at the abutments, it

acted more like a hinged arch. It was more flexible, as shown by the increased downstream deflection at the crown and the increased upstream deflection of the upper arch elements at the abutments. Mercury pressure on the canyon walls had practically no effect on the deflection of the model after cracking.

The differences in deflection caused by the cracking of the model

along the abutments at the upstream face are shown in table 3. In

this tabulation, radial deflections of the model at insert 9, elevation

1232, before and after cracking, are listed for the two loading conditions and for partial, normal, and overloads of mercury.

TABLE 3-RADIAL DEFLECTIOXS OF MODEL AT I~SERT 9,

ELEVATION ]232, SHOWING EFFECTS OF CRACKING

1 Deflection After Cracking *

~

Pressure

on

Model and

Canyon

------

165.8

130.2

95.5

62.3

53.0

39.2

22.1

12.0

*Each unit represents 0.0001 inch.

TEMPERATURE TESTS

116. Purpose of Tests.-The arches which make up the top

portion of Boulder Dam are comparatively slender and their action

under temperature changes can be predicted. The lower arches, having a much larger area in contact with the abutments than exposed

to the reservoir or atmosphere, have a more complex action. Temperatures a short distance within the rock abutments remain fairly

uniform, which tends to maintain uniform temperatures along the

contact with the dam. For a period of several years before the

rc:;erYQiris filled, the upper portion of the dam will be exposell to the
196 MODEL TESTS OF BOULDER DAM

atmosphere on both faces, while the lower part of the upstream

face will be at the temperature of the reservoir water.

It was not feasibJe to duplicate on the model the actual conditions

at the dam. It was possible, however, to expose both faces of the

model to uniform temperatures, both higher and lower than actual

conditions, and therefore to produce much higher temperature stresses.

The purpose of the temperature tests on the model was to obtain distribution of temperature in the interior of the model for known

temperatures at the faces, and to measure the model deflections

caused by the imposed temperature conditions.

FIGURE 125-UPSTREAM PART OF MODEL JACKET

117. Temperature Control.-In making temperature tests of

concrete models, water had been used as the medium for producing

temperature changes. Water could not be used in temperature tests

of the Boulder model, owing to the nature of the plaster-celite
MISCELLANEOUS TESTS 197

FIGURE 126-DOWNSTREAM PART OF MODEL JACKET

FIGURE 127-DOWNSTREAM PART OF JACKET BEING INSTALLED

Cardboard Vanes on Face are for Distributing Flow of Air
198 MODEL TESTS OF BOULDE,R DAM

material. Frozen carbon dioxide, dry ice, was chosen for the cooling

medium and warm air for the heating medium. This necessitated

building a jacket around the model so that vapor from the dry ice

could circulate along the model faces and not over the abutments.

It was desired to keep the abutments at as near a constant temperature as possible.

FIGURE 128-JACKET IN PLACE OVER MODEL

118. Construction of Jacket.-The jacket was made by casting

plaster shells, one-fourth of an inch thick, over the forms used in

casting the model. The shells were reinforced with burlap to prevent cracking. The two shells are shown in figures 125 and 126.

In figure 127 the lower part of the downstream shell is shown as it

was being installed one inch from the downstream face of the model

A mixture of asbestos and building plaster was used for sealing the

shells to the abutments. This mixture was rather soft and did not

prevent the canyon walls from deforming. The holes in the top {)f
MISCELLANEOUS TESTS

FIGURE 129-MODEL READY FOR TEMPERATURE TEST

the finished jacket, shown in figure 128, were for attaching flues

through which vapor could be circulated. Deflection rods extended

through small holes in the jacket. These were sealed with cotton,

which prevented escape of air but did not affect movements of the

rods. Apparatus for cooling the model is shown in figure 129. Carbon

dioxide was placed in the container on the support above the model,

and an electric fan forced the vapor into the manifold attached to

the top of the jacket. Dampers were placed in the branches of the

manifold for the purpose of equalizing the flow of vapor inside the

jacket. After the vapor passed over the faces of the model it was

allowed to exhaust into the open air. The fan shown in the bottom
g Q

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SECTION ON LINE OF CENTERS

10,

SCALE OF INCHES

FIGURE 130-LOCA TIONS OF THERMOCOUPLES
MISCELLANEOUS TESTS 201

of figure 129 circulated air at room temperature through a ventilating

system in the supplemental base.

119. Equipment.--Temperatures at different locations in the

model were measured with thermocouples and mercurial thermometers. The locations of the thermocouples, which were installed while

constructing the model, are shown in figure 130. The potentiometer

and equipment used in measuring temperatures are shown in figure

131. Cold junctions of the thermocouples were placed in the thermos

jug which was filled with melting ice. Next to the thermos jug in

figure 131 is the thermocouple switchboard. The standard cell, potentiometer, and storage battery are in the center of the figure, while the

galvanometer is in the extreme left. This apparatus was borrowed

from the Physics Department of the University of Colorado. Measurements of temperature by thermocouples were supplemented by 15

mercurial thermometers. The locations of the thermometers are

shown in figure 132.

The steel plate of the instrument stand was removed and one built

of laminated wood installed. This was done because wood is much

less susceptible to temperature changes than steel.

120. Cooling Test.-The method of procedure adopted for the

cooling test was as follows: .

FIGURE 131-TEMPERATURE MEASURING APPARATUS
1232

"

J 100

1000

~

~

900

-i eoo

a

Z 700

505

DOWNSTREAM ELEVATION

.'

'PLASTER CEUTE

BASE)

.'

:.PLASTER

CEUTE

SASE-:

"

-'

CONCRETE':

BASE-., "

,

CONCRETE

eASE,.

,

PLAN

r

900

- ~ eoo -4

~

~~- 505

UPSTREAM ELEVATION

hermorne1er

I

2

3

4

~

6

7

8

9

10

II

12

13

14

10

LEGEND

DESCRIPTION

In i e under dam at Elev. 485.

In u stream exhaust ducl.

In Nevada bufment- U str m -

I v. ,

In Arizona abut ment

-

U stream -

Elev. 800.

In ArizoM abutme,lt at to

-

Elev. 1200.

Irl Nevada abutment at to

-

lev. I

In inlet air duct at to of model.

In inlet air duct at fa of model.

In inlet air t t t fm I.

In Arizona abutment-Downstream -

EI '1.10 0

In Neva a tment- ownstr m- I v.1

In dam at Elev. 800.

!n downstream e"aust duc!.

11'1Nevada abutment-Downstream -

lev.8 .

In Arizona abutment

-

Downstream- Elev. 8 O.

FIGURE 132-LOCATIONS OF THERMOMETERS

r-::.

I..:;

1100

IQOO

'"0

t:I [rj

t"'

""

[rj

rn

rn""

0

":J

tJj

0

c::

t"' t:I [rj

::0

t:I p;.

~
MISCELLANEOUS 1iI<~STS 203

1. The model was brought to a stable condition of temperature and radial movement by circulating air at room temperature

through the jacket system.

2. The model was cooled to as Iowa temperature as possible

by circulating carbon dioxide vapor through the system.

3. The model was returned to the approximate starting conditions of temperature and position by circulating air at room

tem perature.

Observations of temperature and radial deflection were made at

frequent intervals, so that the action of the model could be studied.

The test was commenced on the morning of June 23, 1932. Air at

room temperature was circulated through the system until stable conditions were reached. At 10:40 a. m., June 23, the temperature and

position of the model being fairly stable, carbon dioxide was placed in

the cooling system. Cooling by carbon dioxide was then continued

until the model temperature had been lowered as much as possible.

121. Results of Cooling Test.- The average temperature of the

model at the beginning of the test was about 68 degrees Fahrenheit.

The material of which the model was made had fairly good insulating

qualities. Consequently, considerable time was required to cool the

model to a stable temperature. Graphs showing the temperature

range as determined by the thermocouples and thermometers are

shown in figures 133 and 134. All temperatures are in degrees Fahrenheit.

It is obvious that in a structure such as Boulder Dam, the upper

portion of the structure, which is relatively thin, will respond more

quickly to a change in outside temperature than the lower portion.

The lowest temperature reached during the cooling test was indicated

by thermocouple 10, where a temperature of 40 degrees, giving a drop

of 28 degrees, was observed. Thermocouple 1, which was located in the

supplemental base underneath the dam, indicated a drop in temperature of only 6 degrees. This was the smallest change noted.

Temperature observations were made hourly during the early

part of the test and at intervals of about two hours after the temperature changes became less rapid. At the end of one week the model

became stationary with respect to temperature and position. The

conduction of heat from the abutments into the model was equal to

the radiation of heat from the model into the carbon dioxide vapor,

so that the temperature of the model became stationary. The average
THERMOCOUPLE No. I

I

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I

THERMOCOUPLE No. 3

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THERMOCOUPLE No. 4

j ~I j

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THERMOCOUPLE No. 5

---

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THERMOCOUPLE No. 6

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T>lERMOCOUPLE No. 7

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THERMOCOUPLE No. II

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THERMOMETER No. I

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THERMOMETER No. 3

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THERMOM E TER No. 4

I I

T T

THERMOMETER No. 5

204 MODEL TESTS OF BOULDER DAM

TI ME IN DAYS

JUNE 23,1932-+- 2'4" f- 25 +

26 +- 27 -+~ 28 -~- 29 +- 30 -+.JULY 1-+ 2

+-

3

-+-

4

-+- 5 -+- 6 +.,

0

7D

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10 12 13

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50

70

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OB5, NO.4

I

23

I

40

I

55 71 87 102 lIi5--117...119 130 141 144

I I I I III I I I

RELATION OF OBSERVATIONS TO TIME AND TEMPERATURE.

148

I

FIGURE 133-TEMPERATURE RECORD DURING COOLING TEST

For L,ocations of Thermocouples and Thermometers see Figures 130 and 132
I

I

THERMOMETER No. 6

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THERMOMETER No, 13

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THERMOMETER No. 14

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THERMOMETER No. 15

MISCELLANEOUS TESTS 205

TIME IN DAYS,

"

"U~E. 23,19 ~2

"":'"

24-'- "':-< ""25 .-+"""26 ---+---27 -

,..

-28 ---~_..U ._"'; 5Q-""';"'JULY 1';--- 2

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0 I 2 3 .. 5 6 7 8 9 '10 1\ t2 13 14

10

00

10

60

60.

10

60

50

40

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80

10

60

50

40

'0

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20

W 10

:r

z

~

80

X 70

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~ 60

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50

~ 40

~

30

~

20

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50

10

60

50

40

10

50

40

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60

50

OBS. NO.4 , 23I

>0, 5tj ~I aT Iqi 1I~"1~/1I9 ~~o I~I

~ELATION OF OBSE~VATIONS TO TIME ANO TEMPE~ATU~E

'44, 148I

FIGURE 134-TEMPERATURE RECORD DURING COOLING TEST

(CONTINUED)

For Locations of Thermometers see Figure 132
206 MODEL TESTS OF BOULDl<lR DAM

decrease in temperature was about twenty degrees when the model

had reached its coolest condition.

Radial deflections caused by the lowering of the temperature are

shown in figures 135 and 136. Deflections measured at the lower

elevations showed the effect of the high coefficient of expansion of the

material, o.ooo,exn of an inch per inch per degree Fahrenheit. Deflection measurements were made at the downstream face of the model

instead of at the center line of the arch elements. The shrinkage of

the model at the surface, below elevation 800, was greater than the

downstream deflection at the center line. Consequently, the net movement of the downstream face below elevation 800 was upstream.

The dry ice was removed from the cooling system on June 30,

1932. Air at room temperature was circulated until the model

returned approximately to its original temperature and position. This

required about one week. Deflection curves observed during this

period are shown in figures 137 and 138. The final observed position

of the model is shown by deflection curves numbered 148. At elevations 800 and 1100 some deformation still remained in the model. This

deformation was probably the result of flow under the severe stresses

caused by the cooling operations.

122. Heating Test.-Before starting the heating test, the dial

gages were removed and cleaned, the tray which held the dry ice was

removed, and the fan in the ice box was reversed so as to draw air

from the top of the jacket. Two 550-watt electric heating elements

were used to furnish heat, which was admitted to the system through

openings in the bottom of the jacket. The warm air was drawn

upward over both faces of the model.

The method of procedure adopted for the test was essentially

the same as in the cooling test, except that the temperature of the

model was increased instead of lowered. In detail the procedure was

the same as the cooling test described in section 120. A temperature

of 125 degrees was the maximum to which the plaster-celite material

could be exposed without danger of dehydrating the plaster.

Heat was admitted to the system July 11, 1932, and applied for

one week. At the end of that time the model was fairly stationary

as regards position and temperature. The range of temperature during

this period is shown in figures 139 and 140. In the lower elevations

of the model the temperature increased from 70 to 100 degrees. At

10:15 p. m., July 11, electric power was turned off at the plant anq
f'lEVAOA. ABUTMENT I

10

20

>0

4.

..,

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00 40~

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INSERT NUMBERS ARIZONA ABUTMENT--....

"' ELEV. 1000

~

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4

0

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,.,.,.

102'

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20

30

ELEV. 900

20

10

ELEV.800

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-~-40

ELEV. 700

~g-_"'t::''L0

ELEV. 600

Date

NOTES

Obs. Time 43

40

71 6-27-32

87 6.28-32

102 6- -32

115 6-30-32

. A..

Positive deflection indicates downstreom movement

Negative deflection indicates upstream movement

FIGURE 135-RADIAL DEFLECTIONS OF ARCH ELEMENTS DUE TO COOLING "". co

-->
2>f -

100

....

..

!

0

z

eoo I I

I I I I

\;.\\ I

SECTION E

RADIAL DEFLECTIONIN TEN- THOUSANDTHS OF AN INCH

SECTION B

SECTION C

~

I

f!

700

"

~"

SECTlON F

eoo

V

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-

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SECTION 0

no

1,,~~~~ 1100 §~

/i/ 7V

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Positive deflection indicates downstreorTI movement

Neootive deflection indicates upstream movement.

FIGURE 136-RADIAL DEFLECTIONS OF CANTILEVER ELEMENTS DUE TO COOLING

toO

0

00

...

1100

1000

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20

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130-"

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2 4

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~- ----...:

130""

119"" 117'-

......... II!J'- --

, 3 . 7

4

119-

"1 144--

-.130

.>115

Ob, Date Time Remarks

115 6.30.32 8:30.9:08 AM. Drv Iced at 7:30A.M.

.-~ 117 6.30.32 11:30'11:54A.M. Drv ice removed I 1:25 A.M.

119 6.30'32 1:35'1:57 P.M.

f-:lt- -H* 11:20-11:55 AM.

580- 5:5i P. M.

144 7-4-32

~~1487.5-32

..N V MENT

0

r

20

'"

-10

40

INSERT NUMBERS

7

ARIZONA ABUTME"ff

-10

10

20

30

148--

144'"

117,.-

ELEV. 900

'0

115.

ELEV. 1232

146/-

30

ELEV. 600 .0

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ELEV. 1000

0

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'-1154117

15 8-20

. -10 , .1

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0

ELEV. 700

~en

C':I L;j

r:

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0

c::

en

>-3

C';I

en

>-3

en

-20

Positive deflection indicates downstream movement.

Negative deflection indicates upstream movement.

FIGURE 137-RADIAL DEFLECTIONS OF ARCH ELEMENTS SHOWING

RECOVERY FROM COOLING ""

0

~
'~t ;'[

,1171);1 .J.. \

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t i

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RADIAL DEFLECTION IN TEN.THQUSANDTHS or AN INCH

-10 0 10 ~ ~ ~ ~ ~ w ~ ~ -ro -10 0 10 2'0 30 40 50 eo 70 80 90 1001232

m

r

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Positive deflection indicates downstream movement

Negative deflection indicates upstream movement

FIGURE 138-RADIAL DEFLECTIONS OF CANTILEVER ELEMENTS SHOWING

RECOVERY FROM COOLING
THERMOCOUPLE No. I

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-r--

MISCELLANEOUS TESTS 211

TIME IN DAYS

JULY 11,1932-";"- 12 -+-13 -+-14 -..;..- 15 -+- 16

-+-

17 -1---18 -~- 19 '+-20 -+-21 -+. 22 -+- 23 +.24

+-

25 ...;..-26 +-27 +- 28

-+

29

+-

30

0 10 II 12 13 14 15 16 17 18 19

90

80

90

80

70

mo

90

80

70

mo

90

80

70

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'00

90

80

70

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90

80

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100

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110

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:

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110

100

90

80

70

90

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'70

160

150

140

130

120

"0

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90

80

70

90

80

70

90

80

70

80

70

oes. NO.2 6

II '8I

55

I

617 719 90'lrt99 (1\0 1~4 1~2 161S

RELATION OF OBSERVATIONS TO TIME AND TEMPERATURE

30I 4', 172

I

176

I

FIGURE 139-TEMPERATURE RECORD DURING HEATING TEST

For Locations of Thermocouples and Thermometers see Figures 130 and 132
I

HERMOMETER No.6

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THERMOMETER NO.7

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THERMOMETER No. 14

. I I

I I

THERMOMETER No.15

212 MODEL TESTS OF BOULDER DAM

T1ME IN DAYS

JULY 11,1932 +12 +- 13 +

14 +- 15 +- 16 + 17 ,.:...18 ,.:..,19 ,..:..20 ,.:..,21 ~ 22 ~ 23 ~ 24 ,..L.25 ~ 26 ;.:..,21 ..;...28 ,..:...,29 ~ 30

0 t 2

I

7'

,

'to' It '12 '13 '14 "5 '1& "7 "8 "9

60

70

60

70

130

120

110

100

90

60

70

130

120

110

100

90

60

70

130

120

110

100

t: 90

~ 80

~

70

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80

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200

190

160

170

160

100

140

130

120

110

100

90

80

70

60

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DBS.NO 26

II

18

I

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43

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55

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67 79 90, ,92.,99 ,.JIO 134 162 168

I I II I I r I I

RELATION OF OBSERVATIONS TO TIME AND TEMPEijATURE

172

I

176,

FIGURE 140-TEMPERATURERECORD DURING HEATING TEST

(CONTINUED)

For Locations of Thermometers see Figure 132
MISCELLANEOUS TESTS 213

remained off for two hours. This accounts for the irregularities in

the temperature graphs shown in figures 139 and 140.

123. Results of Heating Test.-Radial deflections of the model

during the heating test and recovery are shown in figures 141 to 144.

The deflection curves contained more erratic points than were encountered in the cooling test. This was due to the fact that the dial

gages were mounted so that upstream deflections were recorded as

negative movements on the gages. The dial gages did not register

negative movements as satisfactorily as positive movements, partiCtllarly when the measurement was about one hundred dial divisions,

because of the changing tension in the springs of the gages. Frequently, the gages above elevation 800 went out of range and had to

be reset, which involved some errors.

The heat was turned off on the morning of July 18. After 12

days the model had returned approximately to its original position

and temperature. The mean temperature of the air had risen during

the three weeks devoted to the test so that the model temperature at

the completion of the test was slightly higher than at the beginning.

The upper part of the model, where arch elements were relatively

thin, deflected upstream due to expansion of the arch rings. Below

elevation 800, where the model was relatively thick, the expansion of

the heated model caused the measured deflections to be downstream in

direction. These deflections were opposite to those measured in the

cooling test.

124. Condition of ModeL-After completion of the temperature

tests the jacket was removed and both faces of the model carefully

inspected for cracks. The crack around the upstream face at the foundation and abutments, originally started in the flow tests, apparently

had been extended by the temperature tests. Additional cracks on

both faces of the dam were also observed. It was found later, after

the model was dismantled, that these additional cracks were almost

entirely on the surface, due, probably, to the brittle film of shellac

and varnish being more affected by temperature than the plastercelite. The abutment cracks were about 10 inches deep at the top

and decreased to about 1 inch deep at the base. There was no way of

determining what proportions of these depths were caused by the

plastic flow test and by the temperature tests.

125. Effect of Cracking.-Radial deflection measurements were

next made to determine the effect of the additional cracking on the
30 90-,

'2110 55,

'0 43-:

.

"" ,

7

30,

11'/, '- c"-'- 5

--16

---- '- , '-"-'!>

20 --- ------

, '- 2"

,

--f---- 2

"0 ~19-~ 9O~ ;------ --- ,

---- ~0 55'

'/./ ,,43

"

"'"

70

eo 30"

"-

3( IS'

"--

,

2-" .-

0

,

-ISO

-140

,30

-'20

-110

-'00

-90

-00

-70

-60

-50

-40

-30

;0 -20

g -10

;; 0

~

'0

~

20

~ 30

~

m 4

0,

~

z

m-<

z,

I

~

,.Z

~

\

NEVADA ABUTMENT

I

_2_3

'3

ARIZONA ABUTMENT-;-

IS 17

-,

2_.

INSERT NUMBERS 4- __7

---

9

-

_II

61--

55)

,--43

IS---

',.

2..

ELEV. 900

I 3 5 1 9

-10

fo!~~ I~ 1'~"~:1~,~

ELEV. 800 "4

0

~

2

"4,,,,' '-'~

19

"

,

- --9 ,-~&67

~

.43,- -30

ELEV. 700 _: - 0

~I~', -.'

-

'=.~:90

.

~

~4" . =--

55 30

ELEV. 800

Remarks

-I ndicotes upstreom deflection

+ !ndicotes downstreom deflection.

FIGURE 14I-RADIAL DEFLECTIONS OF ARCH ELEMENTS DUE TO HEATING

':IS

,--

---

2" -jELEV, 1232

L- C

"

ELEV. 1100

-90

-8

ELEV. 1000

-100

-90

-eo

-70

-eo

-50

-40

-30

-20

-'00

'0

""

.....

...

:::::

0

t1[rj

r<

>-3 [rj

r:n

>-3

r:n

0

"]

OJ

0

q

r<

t1[rj

::0

t1

>

~
~i\

~~.

1\

~1000 :\ --

r 1\ ~,,

< \'

~-I900

~\

~lill,\

\

\\~I\

700 SECTION GI \

600 1\

SECTION F \ I II

-60 -40 -20 0 20

~

r

~

1100

~

"

Z

1000

N

g..! ~

~

~

"'

;

0

"

'00

SECTION C

SECTION D

12i~20 -100 -eo -(10 40 -20 0 20 -100 -80 -60 -40 -20 0 20 -eo -40 -20

". '. '1-1

.

r\

~

~~ !!\'io \ ~'o!! k~

~

~ 1\ ~ N

0 20

",I\\\\[.

'&~\~N

~l\~

~

ll;t\\,\\ \

\\ \

"

\\ II'

SECTION H

SECTION E

+ INDICA.TES DOWNSTREAM DEFLECTION

-

INDICATES UPSTREAM OEFLECTION

1232

1100

1000

m

900 5~

-I

"

800 Z

is:

......

UJ

(')

t'i t-<

t-<

:>-

Z

t'i 0

q

UJ

700

800

1\11' I 1\ I

"

I 505

Remarks

>"'3

t'i UJ

>"'3 UJ

Heat off at 8: AM

FIGURE 142-RADIAL DEFLECTIONS OF CANTILEVER ELEMENTS DUE TO HEATING ""......

."
rNEVADA ABUTMENT INSERT NUMBERS ARIZONA ABUTMENT.--- , 2 . . 7 . "

'3 ,. 10 J7

00--

./ ........

92-' .......

./

r-..

"

..--

~.IIO .................

'-

"

134--

I-- .........~

'62' --....: r-.................... ........

16e--'

1--:-- ~172. -..:

176"

~---- t'-. ~-

---

......- 90-- ........

92--

/' -.... "- r-..

"- ./ 110'--

---

"

134--- "-

- 162-' 'ee- ./ 172.- ........

17e-,

---

-.....:::

90-

'--'92

~-

"

--:::

.........

-....

---- 110-"

'34

---162

S --

166-.'

116.."

90,

---

:.-- 92-

---

-

110.

10

.

134',

---- 172

&I

-

-j!lO

-140

-130

-/20

~J 10

-100

-90

-00

-70

-80

-50

.-40

-30

-20

~ -10 "

0

i:. 10 r

20

~ 30 ~ 40 m0

...~z

... mz

... "0C~,.Z"

... "~~

,.Z~"

ELEV. 1232

-130

J

-'20

-"0 .100

-90

-00

-70

-00

-50

-40

-30

-20

-'00

10

20

10 12 14

ELEV. 1100

-110

-'00

-90

-80

-70

-50

-50

-40

-30

-20

-100

10

E LE V. 1000

'0 '"f-'

""

-00

-90

-80

-70

-80

-50

-40

-30

-20

-100

ELEV. '0 900

13579_10

~O

~'O ELEV.800

~

,

0

tj

t:IJ

t"'

>-'J t:IJ w

>-'J w0

':1J

td0d

t"' tj

t:IJ

::0

tj~~

"

3.

-162,1 172 &176 -20

'00

'020

30

nI

--:--

92-

90-'

ELEV. 800

O~serva. Date ilon No.

90

92

99

110

134

162

168 m

:=176

Remarks

)-18-32

)-18-32

)-18-32

)-19-32

)-21-32

)-23-32

)-26-32 )

28-32

)- 30'-32

-

Indicates upstream deflection

+ Indicates downstream deflection.

FIGURE 143-RADIAL DEFLECTIONS OF ARCH ELEMENTS SHOWING

RECOVERY FROM HEATING
( : ~J1/- ~.

~g:~, ~:

\ ~; ~~~: ;~ -

I}.,~

~-

" ~" ~g

~JI

~V Illil , I

I

SECTION H

1\

-- ,

L

1 I

1\

~" \ Ij~

SECT ION G 1,,1/ j

-120 -Ioo-eo 1232

a

m ~

r

fI1 1100

~

"

Z

1000

900

SECT ION C

SECT ION D

.232120 -160 -80 -60 -40 -20 0 20 -100 -80 -60 -40 -20 0 20 -60 -40 -20 0 20 1232

'000

m

~

m

<

~ 900

~

'00

700

'00 SECTION F III II I J

SECT ION E

O~serva- Dale lion No.

90

92

99

110

134

162

168

172

176

+

INDICATES DOWNSTREAM DEFL.ECTION.

-

INDICATES UPSTREAM DEFL.ECTION.

FIGURE 144-RADIAL DEFLECTIONS OF CANTILEVER ELEMENTS SHOWING

RECOVERY FROM HEATING

1100

1000

m

r

900 IT1

~

.00 "

z

700

~~

U"J. ()

tr.J

r,...,

>Z

tr.J

0

c;

U"J.

...,

tr.J

U"J.

...,

U"J.

'00 I

I, \

.05

Remarks

"".....

-1
218 MODEL TESTS OF BOULDER DAM

flexibility of the arch. Downstream deflections at the crown increased

about eight per cent for the overload conditions and about five per

cent for load at elevation 1232. The differences were less for partial

loads. The increase in deflection changed the shape of the deflection

curves only slightly from those shown in figures 122 to 124. Applying mercury pressure to the canyon walls had practically no effect on

the radial deflections. Frequently, the two deflection curves coincided, particularly at elevation 1100.

COMPUTEO TENSION ;"'-

~~

AREA-"",-.

"

,

/~~i;~

-,

\\

"-I" ..-

Ir..nOF'EN SLOTS

, ,

, ,

1232

0

, ,

0" ,/ \ 50' 50',

~

;J

'"'" i

'"~'-

~

t

i:::

t

;;j

0

"

ttl

700 it

!§

v

DEVELOPED DOWNSTREAM ELEVATION (APPROXIMATE)

,

I I I

SCALE OF INCHES "

,

FIGURE 145-LOCATION OF SLOTS IN TENSION AREA

TENSION AT DOWNSTREAM FACE

126. Slots in Tension Area.-The strain measurements showed a

zone of tension in the arch elements at the downstream face of the

model. Since Boulder Dam was built in blocks, separated by joints,

the development of similar stresses in the dam would probably result

in the opening of vertical radial joints in the tension area. To

obtain a similar condition in the model, vertical slots were sawed

into the downstream face at the locations of the joints, as shown in

figure 145.
~w w w

"'

,, ", "' " "'

;;\

'" " w w '"

w w w w

"'

w :;; I- I- I- :;; I- I- :;; ~~w ~::;

'" '" '"

w

'" " "

~~"

" ~"

z

"'

z z 0 0

~"

w w

"

0 0

I- t;;

"

I-

"

"' ~:.J :5"' "' "

Q. Q. a!

.w w w

"' "'

"' ;;\ ;;\

" w w w w w w'" w :;; I- I- :;; :;; I- ~::; :;;

~'" w

'" '" '"

" " " " " " "

z

"' "

z z 0 0 0 ~z

"

w w 0

I- I-

" "

I-

"

"' "' :5 "'

:.J ~Q. Q.

w w

"' "'

" " w w'" w'" W

I-W I- I- :;; ~COMPUTEDLINE OF

~5 0 10 20

'"

ZERO ARCH STRESS

'"

" " "

t" "I I I Z

0 ~~Z 0 SCALE OF 1NCHES

"

I- I-

"

"' "'

MISCELLANEOUS TESTS

ELEVATION 900 ELEVATION 850

ELEVATION 800 ELEVATION 750

ELEVATION 700

FIGURE 146-DEPTHS OF SLOTS IN TENSION AREA

219
""" 0"" Deflection Before Cracking Deflection After Cracking Deflection With Slots t1

Elevation l".J

of Pressure Pressure Pressure Pressure Pressure Pressure t'"

Mercury on on on on on on ..,

Surface Model Model and Canyon Model Model and Canyon Model Model and Canyon l".J 00

~--_.__._---- ~------- ..,

1400 155.0 152.8 177.5 174.5 174.6 173.2 00

1350 117.7 119.9 139.4 137.6 140.0 142.6 0

"'J 1300 83.5 86.2 103.0 101.0 99.8 98.0 1:0

1250 54.0 64.7 66.0 60.5 66.2 63.4 0

d

1232 48.0 60.2 55.0 52.2 54.4 51.5 t'"

1200 34.0 50.3 39.5 36.9 39.8 36.1 t1

l".J

1150 22.8 41.0 23.0 22.1 22.3 21.4 ;0

1100 14.6 28.1 14.0 12.8 15.0 12.2 t1

>- I!:

'One unit. of deflection equals 0.0001 inch.

""""

0

TABLE 4-RADIAL DEFLECTIONS AT INSERT 9, ELEVATION 123'2.

SHOWIKG EFFECT OF SLOTS IN DOWNSTREAM FACE'
"

y

~.. MERCURY SUR,ACe. AT L YA>

"" ""

13100

"" ". .

'" "

... ,.. ,..

,.,

.. ,.. ,.. .. ... ~, , ,.,

'.' .. ... ... .. ,..

'"

~,.. ,., ,. .., ,.. ,.. ,.. ,..

." ... '.'

,., .., ,.. ,.. ... ..,

""

,., ,.,

"

,.. ,.. ... ...

'"

,

.., ... ,.. ,., ,., ,.. ,.. ,..

B' ., ,.. ,..

"

,.,

...

,.. ..

... :

,.. ... ... u ...

,., ,.. ...

-

,.. ,., ,.. ,. ,.. ,.. ,.. ,..

-

,

... .., .., ,.. ... ,.. ... ,..

MISCELLANEOUS TESTS 221

The limits of tension stresses in the model, due to a mercury

load, were calculated from stresses determined by a trial load analysis.

Using computed stresses at the faces and assuming a straight line

variation of stress between the faces, tension areas in the arch elements were computed as shown in figure 146. Depths of the slots

sawed into the downstream face were determined from the data shown

in figure 146.

127. Radial Deflections.-After the slots were cut in the model

a series of radial deflection tests were run. It was found that relieving tension by cutting slots had very little effect on radial deflections.

Apparently, at these elevations, the load was carried by arch thrust

and cantilever bending; and cutting the slots did not appreciably alter

the arch thrust in the uncracked portion and had virtually no effect

on the cantilever loads. In table 4, observed deflections at the top of

the crown cantilever are compared with original deflections and with

deflections after cracking at the abutments.

HO TE

Units in t,bln art in O.oooC

No closina of slots W.ISfOllnd

inilln.tuts.

loCI

'.00 '~50 900 ,

1.5 1.3

-

3 2.0 1.5

8!iO I 2.3 I." eo :I- I.' ',5

-

1 1.2 LO

-

a I.' '-I

YSO I 2.0 '.1 150 3 J.O 2.4

100 ,

,.0 0.1

100 1 1.0 :t.,

,..

,..

,..

,..

,.,

'.' ,..

...

IEVATION

'",..

..,

...

..,

,..

,..

,..

,..

,..

,..

OA

...

...

...

...

...

...

...

...

0.'

,

DO

...

..

...

...

...

,..

M

..

...

SI.OT

NO.""", {,'SI.OTItO.S

I

!

.:

I

!

DEVELOPED DOWNSTREAM ELEVATION

"PPROXIMATD .

()oooOooINDltAtE:STWO INSUlTS_1W[£N

WItICHN£A5UR[MtNTSWERE

M"'~

,',

FIGURE 147-0PENING OF SLOTS 1 AND 3

128. Slat Openings Due to' Laad.-Additional inserts were set

in the downstream face of the model, so that dial gages could be

mounted to register changes in the width of the slots. Two sets of

measurements were made as shown in figures 147 and 148. A maximum increa5e of 0.001,27 inches in width occurred at slot 2, which coin-
222 MODEL TESTS OF BOULDER DAM

cided with cantilever section E. This increase was measured at elevation 850, with the mercury surface at elevation 1400 and with pressure

applied to both the model and the canyon walls. For the same conditions of loading, with the mercury surface at elevation 1232, the

spreading was 0.0008 inches. The opening and closing of the slots was

elastic, since the recovery on unloading was nearly always 100 per

cent. No closing of the slots during loading was observed in these

tests.

NOTE

Urlihin tables are in 0.000.:'

Nodosing ofslo!s wufound

inlhuetesls.

""

MERCURY BAGS NO.23AND4

tUWo"... s~':. 1400 1350 ME~~~AY~~:;"'CE'2~; EL~~~rON 11.50 1100

~ 2 ~ U ~1 ~o 5.8 ~z 4.4 ~

~o l 12.1 11.11 10.4 9.0 &.0 7.2 8.0

4.'1" 800 2 II..

IU'

8.0 0.1 5.11 5.8 4.7 3.0

150 2 5.6 5.04 4.11

".!

3.5 3.3 2.1 2.3

700 Z 4.1 3.7 3.11 2.6 2.2 2.1 1.7 1.2

.

100°-g

9.o!L §

.:;

I~¥

I 700 !

DEVELOPED DOWNSTREAM ELEVATION

,""PPRQ)(IMATEI

M Y AG .

ScOT MERCURY SURFACE AT ELEVATION

'''''..0. 1400 1350 1300 12!>O 1232 1200 1150 1100

~: :.~ ::: ~:: :.~ ::~ ::~ :_~ :~

800 2 8.0 7.3 6.$ $.$ 4.1 4.3 3.5 2.9

150 2 4.7 4.3 3.8 3.4 2.9 2.7 l.2 1.9

700 2 JA 3.0 2.9 2.3 2.1 1.9 1.5 1.3

1>-<1 i'NOICATE$ TWO tN5£!lTS 8£TW[EN

WHICi'i r.tEASUREMENTS WERE MADE

"

FIGURE 148-0PENING OF SLOT 2

129. Slot Openings Due to Flow.-A study of the action of the

open slots under sustained load was made. Slot 2 always had a

greater increase in width while being loaded than slots 1 or 3. For

this reason, as many dial gages as possible were mounted across this

slot for measurements under sustained load. Gages were mounted

across slot 2 at elevations 700, 800, 850, and 900, and across slots

1 and 3 at elevation 750. Gages were also set to register radial

deflections at all other inserts which were not used for measuring

changes in width of slots.

The radial deflection measurements indicated that the model was

more flexible and considerably weaker, due to cracking and repeated

loading and unloading. The amount of radial flow in previous tests

had caused permanent set at points of high stress.

The action of the open slots under sustained load is of considerable interest. The first few observations indicated that the

change in width was negligible in most cases, with a slight tendency
,

No.2 ELEV.900

z

JOINT

,

.

, "

".

.

I

,

,

JOINT No.2 ELEV.650 -

Unitsore 0.00010100 incb.

+lndicatesopenintjjJofjoists

.

-!ndicotesclosingofjoints.

.'

,

.

~JOINTNo-2ELEV. 600

, III

.'

I I---+--r I

.,

N"O.IELEV. 750 -I

JOINT

.

"'

JOINTNo.3 ELEV.750 .'

"'

-I-

.,

..

.,

JOINTNo.2 ELEV.700

"'0 .., .,

"

..

., .. 0.1080.9'.0

" " "

,

"

'.0 " " "

... ..,

'"

.. .

"D

MISCELLANEOUS TESTS 223

to close as shown in figure 149. After an interval of one day all three

slots had opened, They continued to open for about four days, after

which the width remained practically constant.

~

,

~.

~.

~.

<

.

~.

v.r

FIGURE 149-CHANGE IN SLOT OPENING DUE TO FLOW

CHAPTER VII-TRIAL LOAD ANALYSIS OF

MODEL

INTRODUCTION

130. General.-The trial load method of analyzing arch dams

is described in detail in another bulletin of the Boulder Canyon

reports.12 Only a brief description, showing the application of the

method to the analysis of the plaster model, is presented herein. For

the purpose of the analysis, the model was replaced by two systems

of elements, a system of vertical cantilevers and a system of horizontal

arches. The mercury load was divided between the arches and cantilevers, and equal and opposite tangential and twist loads were applied

to the two systems until geometrical continuity was established

throughout the structure. The required loads were determined gradually, by trial, until calculated deflections and rotations in the two

systems were equal at all conjugate points. Since this satisfied the

conditions of continuity, stresses and strains due to the applied loads

were then calculated for both systems of elements. Seven arches and

nine cantilevers, spaced at approximately equal intervals throughout

the model, were used in the analysis.

The mercury load at the upstream face of the model produced

movements in radial and tangential directions, and rotations in horizontal planes. These movements and rotations were considered in

the radial, tangential, and twist adjustments, respectively. In the

radial adjustment, the. mercury load was divided between the arches

and cantilevers in such a way a.s to produce radial continuity in the

two systems of elements. In the tangential adjustment, equal and

opposite internal tangential loads were introduced in such a way

as to restore tangential continuity. In the twist adjustment, equal

and opposite internal twist loads were introduced in such a way as

to produce the same rotations in the arches and cantilevers.

12"Trial Load Method of Analyzing Arch Dams," Bull. 1, Part V-Technical

Investigations, Boulder Canyon Project Final Reports, 1938.

225
226 MODEL TESTS OF BOULDER DAM

131. Data and Assumptions.- The principal structural data and

assumptions made for the analysis are listed as follows:

1. Scale of the model, 1 :240.

2. Elevation of mercury surface, 1232.

3. Density of mercury, 13.6.

4. Modulus of elasticity of plaster-celite in tension and compression, 90,000 pounds per square inch.

5. Modulus of elasticity of plaster-celite in shear, 37,500

pounds per square inch.

6. Normal stresses vary as a straight line from the upstream

to the downstream face of the model.

7. Cantilever stresses at the faces of the model act parallel

to the slopes of the faces.

505

~U_"-{

-

'K--'

4 u 31.28"

-

nn 32.58'

,

n--nu

n__-

- - ----

1232

1200

1100

1000

900 Z

0

~;;;

d 600

700

600

k.2~-..i

+I

'1;

"'.,/-".

'-~::-"...PLASTER-CELITE BASE...

"""""",

.~

10 5 10

J I I I I I I I I 1 I I

SCALE Of INCHES

FIGURE 150-CANTILEVER SECTION E
TRIAL LOAD ANALYSIS OF MODEL 227

8. The foundation deformation was adjusted to conform

to the model measurements.

9. The concrete support around the plaster-celite base and

the sand-plaster support at the downstream side of the plastercelite base were considered to be rigid.

132. Cantilever Elements.-Cantilever elements were assumed

to be one inch wide at the axis of the model and to have radial sides

that converged from the upstream face to the downstream face. They

were elastic units, set on elastic bases, and resisted shear and bending

in radial directions, shear in tangential and vertical directions, and

torsion in horizontal and vertical planes. Cantilever section E, as

constructed, is shown in figure 150.

The mercury load on the upstream face of the model was divided

into vertical and horizontal components and the vertical components

assigned to the cantilevers. Horizontal components were divided and

applied to the arches and cantilevers, using unit radial pattern loads.

Unit loads on the cantilevers were triangular in shape and varied

from one pound per square inch pressure at a given arch elevation to

zero pressure at the arch elevations directly above and below, see

figure lSl-a. This made it possible to supply any horizontal load that

varied as a straight line between the elevations of the sample arches

used in the analysis. Shears, moments, and deflections were computed for each of the unit pattern loads to provide data for use in the

following steps of the analysis.

Equal and opposite tangential forces, one set acting on the arches

and the other on the cantilevers, were necessary to produce equal

tangential deflections in the two systems. In the application of tangential forces, it was also found convenient to use a triangular unit

load system. Unit tangential loads applied to the cantilevers were

similar to the unit radial loads except that they represented tangential

shearing forces applied at the center lines instead of radial forces

applied at the upstream face, see figure lSl-b.

Equal and opposite twisting moments, one set applied to the

arches and the other to the cantilevers, were required to make angular

rotations of the arches coincide with the rotations of the cantilevers.

As in the case of the tangential loads, it was found convenient to

use a triangular unit load system. Unit cantilever twist loads, representing twisting moments applied to the cantilevers, are shown in

figure lSl-c.

Radial cantilever loads deflected the cantilevers in radial direc-
228 MODEL TESTS OF BOULDER DAM

Load applied at upstream

face of cantilever.

?~?..-

5~?-

TYPICAL UNIT RADIAL lOAD (0)

\'1:,":/1,/

I

I'J

per sq.

Thrusts applied at centers of

gravity of cantilever.

"?9~/

TYPICAL UN!T TANGENTIAL LOAD (b)

\'I-?,'I:-

Momenfs applied 01 centers

ofgrovily of can1ilever.

Intensity of twist IOOd

~

' ,

]

in-lb. per sq. in:"'

,

~r}7

TYPICAL UNIT TWIST LOAD (c)

FIGURE 151-TYPICAL UNIT CANTILEVER LOADS
TRIAL LOAD ANALYSIS OF MODEr.. 229

tions only, but tangential loads produced tangential deflections and

also rotations in horizontal planes. These rotations existed because

the center lines of the cantilevers were not vertical. Tangential

thrusts applied near the top of a cantilever produced twisting moments

in horizontal planes at all lower elevations. Twist loads not only

rotated the cantilevers, but also deflected them radially. These radial

deflections appeared because the rates of change of the applied twisting moments along the arch center lines produced rates of change

of bending moments in the cantilevers.

Deflections were computed for unit radial, tangential, and twist

loads. These were tabulated so they could be used easily in the trial

load adjustments. The tabulations simplified the problem of estimating the amounts of loads to be applied to the arches and cantilevers.

After the loads had been determined by the adjustments, stresses in

the cantilevers were calculated by ordinary stress formulas.

133. Arch Elements.-Horizontal arch elements were circular

and of constant radial thickness. They were assumed to be one inch

high and to have horizontal top and bottom faces. Abutments of the

arches were radial at the top elevations, half radial at elevations 1100

and 1000, and gradually approached directions parallel to the canyon

walls at the lower elevations. The arch elements were statically

indeterminate, set on elastic abutments, and were assumed to resist

moments, thrusts, and shears in horizontal planes. Calculations for

arch elements included effects of irregular abutments and a lack of

symmetry between the crown cantilever and the arch crowns.

Unit pattern loads were used in applying horizontal mercury

loads to the arch elements. Radial pattern loads included a uniform

load over an entire arch, and triangular loads varying from a maximum

pressure at the abutment to zero pressure at the quarter points, see

figure 152-a. With these unit loads it was possible to apply any

load to an arch that varied as a straight line between quarter points.

Uniform loads, with one pound per square inch radial pressure at the

upstream face, and triangular loads, with one pound per square inch

radial pressure at the abutment, were computed for all arches used

in the analysis.

Tangential thrust loads, applied at arch center lines, were required

for the tangential adjustment of deflections. Unit loads, needed to

build up tangential loading, consisted of triangular loads varying from

one pound per square inch tangential thrust at each abutment to zero

thrust at the different quarter points, as shown in figure 152-b.
230 MODEL TESTS OF BOULDER DAM

--

LOAD APPLIED AT UPSTREAM

FACE OF DAM

\1 LB. PER SQ. IN.

CROWN

I

i

,J i

~~,

~ ~ I

'~ '

~ I

'~ '

~j

(0) TYPICAL UNIT RADIAL LOAD

INTENSITY OF TANGENTIAL

LOAD.\..

,m' THRUSTS APPLIED AT It

//

.' OF ARCH

I LB. PER SQ.

CROWN

I

~\' I

:.. J '

I

:,~,

I'~

,

IN""""'!~'~

I

.~~ I

.~.

.

,1

(b) TYPICAL UNIT TANGENTIAL LOAD

MOMENTS APPLIED AT It

OF ARCH INTENSITY OF TWIST LOAD

I IN. LB. PER SQ. IN../

CROWN

I

~\' I

J I

"'.,'~~.~

I

'~ I

~. '

,I

(C) TYPICAL UNIT TWIST LOAD

FIGURE 152-TYPICAL UNIT ARCH LOADS
TRIAL LOAD ANALYSIS OF MODEL 231

Besides radial and tangential loads, twist loads were required

for the purpose of establishing equal rotations in the arches and

cantilevers at conjugate points. Unit twist loads were also triangular

in shape. They varied from a moment of one inch-pound per square

inch at an arch abutment to zero moment at the quarter points, as

illustrated in figure 152-c.

Concentrated loads at the arch abutments were introduced for

the purpose of transferring cantilever shears, thrusts, and moments

from the cantilever foundations to the arch abutments. In this way

forces were conveniently transferred between the two systems at

abutment locations. Concentrated radial, tangential, and twist loads

were a radial shear of one pound, a tangential shear of one pound, and

a moment of one inch-pound, respectively.

As only part of the unit arch loads were necessary for the adjustments, the loads needed were calculated as the adjustments were made.

Deflections due to required unit arch loads were tabulated, so they

could easily be used in the deflection adjustments. After the proper

arch loads had been determined by the trial load method, arch stresses

were calculated by ordinary stress formulas.

RADIAL ADJUSTMENT

134. Procedure.-The radial adjustment was the first step in

the analysis of the model by the trial load method. Figure 153 shows

the adjustment at the arch elements, including the division of mercury

load between the two systems and the final adjusted radial deflections

of the arches and cantilevers. The positions indicated on the drawing apply to the developed center lines of the arches. Locations

of arch quarter points and cantilevers are also shown. The plotted

points, representing calculated movements of the arches and cantilevers for the final distribution of mercury load, show that a very

satisfactory agreement of radial deflections was obtained at all conjugate points.

As previously mentioned, concentrated loads were introduced at

the arch abutments for the purpose of maintaining equilibrium and

continuity. Figure 154 shows that the center-line width of a cantilever resting on the end of an arch element of unit height is equal to

tan t{;. As the assumed unit cantilever used in the analysis vvas

one inch wide at the axis, the radial shear at the base of a cantilever

1

.

I' d 1 h f

Rami.

was mu tIp Ie t ' h

)y t e actor - an t{; to gIve t e correct amount

Reenter line
, ,

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,

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ELEV 1232.

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LOAD

,

i t

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I fI ,

I ,

I ,

I

I

,

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ELEV. 900

:1

D, CROWN CANTILEVER

F'

M' ,M'

ELEV. 600

NOTES

MERCURY SURFACE AT ELEV. 12J2

x RADIAL DEfLECTION OF ARCH CENTER LINE.

0 RADIAL DEFLECTION OF CANTILEVER CENTER OF GRAVITY.

ABUTMENT DEFORMATIONS ADJUSTED TO CONFORM TO MODEL

MEASURE MENT$,

*

LOCATION OF CANTILEVER AT END Of ARCH AT ELEV. 900.

THESE CANTILEVERS USED IN ADJUSTING LOAD DISTRIBUTION.

FIGURE 153-RADIAL ADJUSTMENT AT ARCH ELEMENTS
TRIAL LOAD ANALYSIS OF MODEL 233

Abutment '--_/

,/ Upstream

fa7:'

I

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I

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I

~~n_-

/

/

/

/

/

Downstream face /

Abutment

RAXls=Radius to axis of dam

Rt =Radius to center line

¥ =Angle abutment makes

with vertical at t.

Downstream face

"

,

,-

FIGURE 154-CONTACT OF ARCH AND CANTILEVER AT ABUTMENT
234 MODEL TESTS OF BOULDER DA:vr

of concentrated radial load which should be applied to an arch of oneinch height. For the same reason tangential shears and twisting

moments at the cantilever foundations were corrected by the factor

R.

ax's tan If, to determine concentrated tangential and twist loads

Reenter line

for the arches. Since the base of each cantilever, except the crown,

rested on the end of an arch, the abutment deflection of the arch

was added algebraically to the cantilever deflections.

135. Distribution of Load.--For the first estimate of load distribution, crown cantilever deflections were adjusted to crown deflections of the arches. In this step only uniform and concentrated loads

were used on the arch elements. After the crown cantilever was

adjusted, deflections of other arch and cantilever points were computed

and plotted on an adjustment sheet in the same manner as the final

deflections shown in figure 153. By comparing preliminary deflections, additional loads were estimated and applied to the structure

until the calculated arch and cantilever deflections were approximately

the same at all conjugate points. After several trials the deflections

were brought into close agreement, thereby completing the first stage

of the radial adjustment. Since the subsequent twist and tangential

adjustments caused radial arch and cantilever movements, radial readjustments were required to restore continuity. Altogether ten radial

adjustments and readjustments were made before arriving at the final

deflections shown in figure 153.

As different trial loads were applied to the two systems, it was

necessary to have the sum of the arch and cantilever loads equal to

the horizontal mercury load at each point. This was done by plotting

the arch load and also the total mercury load on each of the developed

center lines of the arches. The difference between the arch load and

the total load represented the cantilever load.

The radial adjustment constituted the most important step in the

trial load analysis. Although twist and tangential adjustments were

required, they were of secondary importance compared with the radial

adjustment. The reason for this was that the radial movements were

much greater than the tangential or angular movements.

TANGENTIAL ADJUSTMENT

136. Tangential Arch Deflections.-After radial deflections due

to radial loads had been adjusted, the tangential adjustment was made.
TRIAL LOAD ANALYSIS OF MODEL 235

Results of the tangential adjustment at the arch elements are shown

in figure 155. This drawing gives initial positions and final tangential displacements of the arch center lines; also, amounts of tangential

loads required for the adjustment. Positive tangential loads and

movements shown in figure 155 act toward the right abutment. Negative loads and movements act toward the left abutment. Following

this convention, it is seen that tangential displacements are toward

the left abutment in the left part of the model and toward the right

abutment in the right part of the model. Tangential loads applied

to the arches are away from the left abutment in the left part of the

model, and away from the right abutment in the right part of the

model. The right abutment is the end of the arch on the observer's

right when looking upstream.

An analysis of the effects of the radial adjustment showed that

the radial loads deflected the arch center lines in tangential directions as well as in radial directions. Therefore conjugate points of

the two systems were out of agreement in tangential directions. These

initial tangential arch movements were computed by combining tangential deflections of the unit loads used in the first stage of the radial

adjustment. Since the base of each cantilever moved with the abutment of the corresponding arch, the initial deflection of the cantilever

equalled the movement of the arch abutment.

137. Tangential Shear Loads.-Equal and opposite tangential

shear loads, one on the arch and the other on the cantilever, were

introduced to remove relative tangential deflections. Required amounts

of the loads were estimated and applied to the two systems. As in

the radial adjustment, it was expedient to use unit arch and cantilever

loads in determining tangential loads and deflections. For the purpose of simplifying the estimate of the first tangential loads to apply

to the structure, only cantilevers Band C were investigated. After

these elements were brought into approximate agreement with the

arches by trial tangential loads, tangential deflections of other arch

and cantilever points were computed. The relative tangential deflections of all points were then compared and additional loads estimated

until tangential deflections were approximately the same at all conjugate points. A close agreement of deflections was secured after

several trials, thus completing the first stage of the tangential adjustment.

Subsequent readjustments of tangential deflections were required

because twist adjustment and radial readjustment loads deflected the
7~o*D ,~AOWN ~"'NTILEVER

[:',..+

L 1

F 70!G:'00*10oc1tH

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ELEV. 1232

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SCALE OF INCHiS

to:>

<:.00

cr>

..or

A8T,-

ELEV.800

7oo0CROWN CANTILEVER, 700

"

1 : : : : : Ii )

j

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0

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pj l'J

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ELEV.600

NOTES

MERCURY SURFACE ATELEV. 1232

X TANGENTIALDEFLECTION OF ARCH CENTER LINE,

0 TANGENTIALDEFLECTION OF CANTILEVER CENTER OF GRAVITY.

ABUTMENT DEFORMATIONS ADJUSTED TO CONFORM TO MODEL

MEASUREMENTS

*

LOCATION OF CANTILEVER AT END OF ARCH.

THESE CANTILEVERSUSED IN AOJUSTING LOAO DISTRIBuTION

FIGURE 155-TANGENTIAL ADJUSTMENT AT ARCH ELEMENTS
TRIAL LOAD ANALYSIS OF MODEL 237

arches tangentially. Nevertheless, the adjustments converged rapidly

and only four sets of trial loads were required to produce the close

agreement shown in figure 155. Satisfactory adjustment was obtained

by applying tangential loads to the top four elevations only, no loads

being required at elevations 600, 700, and 800.

It was necessary at all stages of the adjustment to keep tangential loads equal and opposite at all points in the two systems. To

insure that this condition was satisfied, arch loads were plotted on

developed center lines and amounts of unit loads for the cantilevers

determined from the arch load diagrams.

Tangential loads and deflections were small compared with radial

loads and deflections. This indicated that tangential loads had a

comparatively small effect on the total movements of the model. However, the tangential loads had a considerable effect on arch stresses,

since they changed the arch thrusts without causing appreciable movement in the structure.

TWIST ADJUSTMENT

138. Twist Loads.-Rotations of arch and cantilever elements

about vertical axes were considered in the twist adjustment. Figure

156 shows the twist loads and final adjusted rotations, or twist deflections. Rotations are designated as twist deflections to make them

comparable with radial and tangential deflections. The final rotations were clockwise in the left part of the model and counterclockwise in the right part, viewed from above. The twisting moments

applied to the arches were in the opposite direction and opposite to

the cantilever twisting moment loads.

Radial and tangential loads from previous adjustments rotated

the arches, and tangential loads rotated the cantilevers. The rotations, or twist deflections, of the arches were calculated by combining

twist deflections of all unit loads used in the first stages of the radial

and tangential adjustments. In the same manner, twist deflections of

the cantilevers were calculated by adding rotations due to applied

unit tangential loads and combining them with abutment rotations of

the corresponding arches. Resulting relative rotations were removed

by introducing equal and opposite twist loads which acted on the

arches and cantilevers. The required amounts of the twist loads were

estimated and gradually adjusted by trial. As in the preceding adjustments, it was found expedient to use unit arch and cantilever load~

in the application of successive trial loads.
238 MODEL TESTS OF BOULDER DAM

139. Procedure.-The first set of trial twist loads applied to the

model gave approximate deflection agreements at arch and cantilever

intersections at cantilevers C and G. Successive sets of trial loads

were applied until the deflection agreements were close enough at all

cantilevers to complete the first stage of the adjustment. Since subsequent radial and tangential readjustments rotated the arches and

cantilevers, twist readjustments were made for the purpose of restoring agreement between the twist deflections. After the required readjustments had been completed, the resulting loads and deflections

were drawn on the adjustment sheet, see figure 156.

Twist loads caused radial and tangential deflections in the arches

and radial deflections in the cantilevers. The cantilever deflections

appeared because the rates of change of the applied twisting moments

along the arch center lines produced rates of change of bending moments in the cantilevers. It was found that resulting bending moments

were relatively large and amounted to approximately twenty-five per

cent of the moments due to radial loads. The following steps show

the procedure used in calculating these deflections:

1. Twisting moments were computed for all cantilevers at

all arch elevations.

2. Twisting moments were differentiated along arch center

lines. This gave rates of change of twisting moments along arch

center lines which were equal to rates of change of radial bending

moments in the cantilevers.

3. Rates of change of radial bending moments were integrated from the top of each cantilever to the lower elevations,

giving bending moments in the cantilevers.

4. A double integration of the M/EI curve from the base

of each cantilever gave cantilever deflections.

The twist adjustment indicated that twist resistance stiffened

the structure considerably, thereby reducing deflections and stresses

in the structure. Although effects of twist were greater than effects

of tangential movements, they were still relatively small when compared with the results of the radial adjustment.

140. Additional Adjustments.-After the first stage of the twist

adjustment had been completed, there remained secondary movements

which had not been considered. These were radial deflections due to

tangential and twist loads and tangential deflections due to twist

loads. The secondary radial movements were considered in the first
-,

7CJ! D rOUNN CANTILEVER

I

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.

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>-::J

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'(NTE!'IL'N[Or,o.I«:IO'"

. 1°

"

I, I

SCALE OF INCHES

1

:

1

1

1

I

ELE V, eoo

NOTES

MERCURY SURfACE AT ELEII. 1232.

X TWIST DEFLECTION Of ARCH CENTER LINE.

0 TWIST DEFLECTION Of CANTILEVER CENTER OF GRAVITY.

ABUTMENT DEFORMATIONS ADJUSTED TO CONfORM TO

MODEL MEASUREMENTS.

*

LOCATION OF CANTILEVER AT END OF ARCH.

THESE CANTILEVERS USED IN ADJUSTING LOAD

DISTRIBUTION.

I~IGUREJ 156~TWJST ADJUSTMENT AT ARCH ELEMENTS ""

wOJ:>
240 MODEL TESTS OF BOULDER DAM

radial readjustment. This required additional radial loads, causing

new tangential and twist movements. Next, the first tangential readjustment was made to correct discrepancies caused by twist loads and

radial adjustment loads. Likewise, a twist readjustment and subsequent radial, tangential, and twist readjustments were required, since

each readjustment produced movements which had to be considered

in the following readjustments. However, the effects converged

rapidly. After a few readjustments, the secondary movements became

so small that they did not change the adjustments by appreciable

amounts.

The complete analysis, including all adjustments and readjustments required ten radial, four tangential, and four twist load trials.

These adjustments determined the total movements of the model, also

the distribution of the different types of loads. \Vith this information, arch and cantilever stresses were calculated by usual stress

formulas.

RESULTS OF ANALYSIS

141. Stresses and Deflections.--The most important results of

the analysis are shown in figure 157. In this drawing, arch and cantilever stresses are shown on the developed profile at the axis of the

model. Final radial loads and deflections are shown at the assumed

cantilever elements. Cantilever deflection curves show deflections due

to the weight of the plaster-celite material, deflections due to the

plaster-celite material plus vertical components of the mercury load

on the upstream face, and deflections due to weight of the model plus

vertical and horizontal components of the mercury load.

142. Comparison with Experimental Stresses.-Arch stresses

determined by the trial load analysis are compared with those determined from the model measurements in figure 158. The agreement

was very close at the lower elevations, but some differences occurred

along the abutments above elevation 1000. The greatest differences

occurred at elevation 1232 at the abutments.

The discrepancies in stress were due to inadequacies in both

analytical and experimental procedures. In the first place, formulas

for abutment deformations and accompanying stresses had been developed on the assumption that the foundation was infinite in extent.

Actually, the model had a supplemental base of highly elastic plastercelite material, about twelve inches thick, supported by a compara-
I

1150 \

,.

1100 ,

I

I.

1000

900

TRIAL LOAD ANALYSIS OF MODEL 241

600

EXT" Stress at eJ!trados of arch.

INT= Stress at intrados of arch.

D=Stress at downstream edge

of cantilever.

U=Stress at upstream edge

of cantilever.

+=Compression. -

:Tenslon

EXT.+8.17

INT.+4.36

\242

1232

EX1.+\4.17:

INT.-4.79

1150

A

CROWN

CANTILEVER E

1100

U+2.07

0-2.31

U+2.22

0-2.45

U+O.45

0-0.06

U+O.88

0-0.70

Exr.+IO.17

INT.+4.B9

EX1,-I.77

INT.+IG.03

1000

U+O.69

0+0.15

U-I.96

0+502

U-1.59

0+4.33

£X1.+10.81

INT.+2.IO ::;

«

a

....

« 900

z

5?

....

«

~ 800

UJ -'

U-1.59

0+6.31

U-I,1S

0+6.37

EXT.+9.79

INT.-2.59

EXT.-1.32

INT.+11.48

U+O.21

0+4.53

U-D,51

0+5.55

EX1.+7.47

INT.-3.83

700 EX1.+0.81

INT.+3.23

0 :i to 15 It, I I I

,

r

SCALE OF MODEL IN INCHES

505

600

DEVELOPED PROFILE ON AX IS Mercury surfoce at top of

LOOKING UPSTREAM dam ot E11232.

r- Dowstream movement during fitling of rubber bog. 1242

1232- I

\

I

\

Model is built r above £1.1232 to

.. protect inserts at that elevation.

\

"

I

I

I

\,

1100

~

«

a

1000 !q

Z

900 ~....

«

>

800 ~

UJ

5

B

NOTES

Arch stresses are octing in horizontal directions

parallel to the edges of the arches.

Cantilever stresses are acting in inclined directions

parallel to the edges of the cantileversAll stresses and horizontal mercury load in

pounds per square inch.

Foundation deformation adjusted to conform

to model measurements.

No change in temperature.

!! JO

..J ~ Foundation deformation

c 700

+10- +, 0 -5 -10

11111111"1 1.,,.1

RACIAL DEFLECTION IN

THOUSANDTHS OF AN INCH

1242

1232

..

«

a

....

«

z

a

....

«

~

-' UJ

BOO

505

5

G

~ Downstream deflection,mercury

surface at E1.I232.

--' Upstream deflection}no mercury load.

Upstream deflection,vertical mercury

lood.

0 Cantilever deflection.

x Arch deflection.

0

700

FIGURE 157-RESULTS OF TRIAL LOAD ANALYSIS
I I I

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242

NEVADA ABUTMENT

0

,

+40

+'0

+20

+10

-10

MODEL TESTS OF BOULDER DAM

dA

CANTILEvER MEASURING SECTIONS

D' D E FF'

G

G'

ARIZONA ABUTMENT

16 17 B'B c' c H 'H'

ELEVATION 123.2

ELEVATION 1100

+'0

+20

+10

- x-----

-'0 ELEVATION 1000

+20

-'0 ELEVATION 900

+20

~

, ;

+10

I

.

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-'0 "ELEVATION 600

+20C

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+10 I

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-10

ELEVATION 700

NOTES

+I:~

-'0 ELEVATION 600

/1, )( Computed stress.

<>--0 Measured stress, load on model only.

11---:t!: Meosure.d stress, load on mode! and canyon walls.

Reservoir mercury surface at elevation 12J:2.

+ Compression.

- Tension

FIGURE 158-COMPARISON OF EXPERIMENTAL AND COMPUTED

ARCH STRESSES
TRIAL LOAD ANALYSIS OF MODEL 243

tively rigid concrete primary base. It was therefore necessary to

use some approximation in determining abutment deformation. In the

second place, strain measurements along the abutments would have

been more accurate if more sensitive measuring apparatus had been

available. A more sensitive type of strain gage, operating over a gage

length of 0.25 or 0.50 inches, was needed.

Figure 159 shows lines of equal arch stress plotted on the developed downstream face of the model. Stresses determined from

strain measurements were slightly greater than those determined

from the analysis. At the time strains were measured, over 800 tests

had been made, and some small cracks in the model may have developed along the upstream abutments. The occurrence of cracks at

such locations would be accompanied by increases in stress at the

downstream face, as shown in figure 159. The width of the tension

area was about the same for the two sets of stresses shown in the

figure. However, the height of the tension area was somewhat greater

in the case of the stresses determined from the model measurements.

Along the abutments between elevations 900 and 1150, analytical

stresses were more concentrated than experimental stresses, although

the latter were slightly greater in magnitude.

Cantilever stresses determined analytically are compared with experimental stresses in figure 160. In the central part of the model

where stresses were not affected by the abutments, the agreement was

very close, as shown by the curves at cantilever sections D', E', and

F'. Along the abutments, stresses at sections B', C', and G' showed

considerable variation. This variation is also shown by the lines

of equal stress at the downstream face in figure 161. In the experimental stresses, the tension area occurred between cantilever sections

C' and G' above elevation 1075. Analytically, the tension area extended

to both abutments. This was due to the inadequacy of the mathematical method in computing deformations and accompanying stresses for

abutment conditions in the model.

An inspection of the load-distribution diagrams in figure 157

shows that the proportions of load carried by arch action were considerably greater than those carried by cantilever action. Arch stresses

were therefore materially greater than cantilever stresses. The agreement between analytical and experimental stresses was very close for

the higher stresses. Discrepancies found between the two sets of

stresses were in regions of low stress. Consequently, the agreement

of arch stresses was better than the agreement of cantilever stresses.
~~~0

0

0

m

~~~z

800

0

~0

z

i

244 MODEL TESTS OF BOULDER DAM

CANTILEVER MEASURING SECTIONS

C D E F

1242

Stresses are computed from strain

measurements using a modulus -of

elasticity of 90,ooolb.per sq. in.

~~

c

~

~

0

m

!i

~

z

0

;::

~

0

z

I

ARCHSTRESSES '0' FROM STRAIN MEASUREMENTS

C 0 E F G

o~ ~

t~?~ 1242

Stresses -are computed from trial

load analysis assuming linear

distribution of stress.

'0' ARCH STRESSES BY TRIAL LOAD ANALYSIS

NOTES

Plotted stresses ore in pounds per square inch.

Reservoir mercury surface at elevation 1232.

Load on model only.

+

Compression

- Tension.

FIGURE 159-COMPARISON OF LINES OF EQUAL ARCH STRESS
I

'\

I

I

1

/

1

\ 1/ \

II

/.

,\

I

I

'\ \

-

\

-

-'\

I

I \

*I I

I

i

1

/

- r '~

/

I

I

I

I i

/.

In

I

I

I

I

I

k

SECTION S'

-5 0 +5 +10

SURFACE STRESSES AT DOWNSTREAM FACE IN POUNDS PER SQUARE INCH

a +5 +10

I

/

I

I

I

\

\

\

\

I

I

, i

SECTION c'

0 +5 +10

SECTION D'

0 +5 t10

.\

I

,I

/

f.

d

I' i!

I

I

I

\

SECTION

E'

NOTES

SECTION F'

505

X 4( Computed stress.

0---0 Measured stress. load on model only.

r.r o Measured stress, load on model and canyon wolls.

Reservoir mercury surface otelevation 1232..

+

Compression

-

Tension

0 +5 +10

-1232

700

600

l"IGURE 160-EXPERIMENTAL AND COMPUTED CANTILEVER STRESSES

1100

z

0

;:

1000

ffi

>-'3

::0

~

t"

t"

0

;..

tj

;..

Z

;..

t"

><:

Ul

......

Ul

0

':rJ

900

690

.....

......

0

tj

t':I

t"

""....

""
246 MODEL TESTS OF BOULDER DAM

Stresses are computed from

strain measurements uSing a

modulus of elasticity of 90.000

pounds per square inch.

CANTILEVER MEASURING SECTIONS

a 0 E F 1242

~

~

"

~

0m

~

~

.,

%0

;:

~

.,

%

I

Stresses ore computed from

triol load analysis assuming

lineor distribution of stress.

505

CANTILEVER STRESSES FROM STRAIN MEASUREMENTS

8 C D r:: F' G J242

". "...AREA OF LOW E.NSION.. __0-

~

~

"

~

0

m

~

~

.,

%0

~

.,%

I

CANTILEVER STRESSES BY TRIAl. LOAD ANALYSIS

NOTES

Plotted stresses Ore in pounds per square inch.

Reservoi r mercury surface ot elevation 1232.

load on model only.

+ Compression.

- Tension.

Oevelopementof downstreamface is approximate.

FIGURE 161-COMPARISON OF LINES OF EQUAL CANTILEVER STRESS
CROWN SECTION-;

r---4f'-+

m

5"

out on

S"out'm 5~ t ---5" ---t--- S" :~,,~ S"-_-"r'nn 5" not nuS"__' f "'S" -'-+-"S.".+1'1--tgB~_-

'°

,

lQ

,~

f

t

;;j

/J'

.." ..' ..' ,004 C,O

iJ'v4;

Q

"

Q' q.'

.."::0

>

t"'

t"' 0

>tJ

>

Z

>

t"' ><U1

......

U1

0

"'.:I

is:

0

tJt;j

t"'

SCALE OF INCHES .008

MEASURED DEf"LEC1'IONS

- CALCULATED DEf"LECTIONS

-----

DEFLECTIONS AT DEVELOPED DOWNSTREAM FACE

MODULUSOf"ELASTICITYFORMODEL~ 90,000 POl)NDS PER SQUARE INCH

SCALE Of MODEL I TO 240 DENSITY OF MERCURY ~ J3.6.

ACTUAL DEfLECTION CURVES FOR MODEL PLOTTED fROM TEST NO. 85,

CALCULATED DEFLECTIONS CORRECTED TO APPLY TO DOWNSTREAM FACE.

MERCURY SURfACE AT ELEVATION 1232

FIGURE 162-COMPARISON OF COMPUTED AND MEASURED DEFLECTIONS

<.0

....

""
248 MODEL TESTS OF BOULDER DAM

143. Comparison with Measured Deflections.-The comparison

of deflections calculated by the trial load method with those measured

on the model, given in figure 162, shows a remarkably close agreement.

The small discrepancies which appear at some locations may be partly

due to differences between actual thicknesses of the model and uniform thicknesses assumed at the different elevations considered in

the trial load analysis. The differences between calculated and

measured deflections probably would have been less if more sample

arches and cantilevers had been used in the analysis. Nevertheless,

sufficient elements were investigated to give an adequate solution.

The unusually close agreement of calculated and measured deflections

at all locations at the downstream face, shown by the curves in figure

162, constitutes a very satisfactory check on the accuracy of the trial

load method of analysis.
CHAPTER VIII-INVESTIGATION OF RUBBERLITHARGE MATERIAL

144. Introduction.-After completing the test program on the

plaster model of Boulder Dam, the test results, together with further analytical studies, indicated that an improvement in stress distribution could be obtained by adding arch fillets at the downstream

face. A new model incorporating these changes in design was then

proposed. The rubber-litharge compound developed by the Aluminum

Corporation of America was selected for building the new model, and

20 tons of this material was ordered from the Republic Rubber Company of Youngstown, Ohio.

When the rubber-litharge arrived at the laboratory, preliminary

investigations of the physical properties of the material were immediately made. The tests indicated different elastic properties along

different axes, showing that the material was anisotropic. Consequently, mathematical studies of the stress-strain relations of anisotropic materials were made in order to interpret properly the results

of the tests and to aid in developing testing procedures.

STRESS-STRAIN RELATIONS

145. Characteristics of Material.-In the process of manufacture,

the rubber-litharge compound acquired different elastic properties in

different directions. The blocks or sheets into which the rubber was

molded may be considered to have three mutually perpendicular

axes of elasticity. In the following discussions, these reference axes

are assumed to be parallel to the edges of the blocks. The rubber blocks

were similar in their elastic properties to a block of wood cut from

the outer portion of a tree in such a way that two faces are perpendicular to the direction of the wood fibers, two faces intersect the

rings of growth at right angles, and two faces are tangent to the rings

of growth. The structure of such a material is different in the

three directions and has a different modulus of elasticity in each di249
250 MODEL TESTS OF BOULDER DAM

rection. Tests show that such materials have three shear moduli and

six Poisson's ratios, two for each axis.

The rubber-litharge compound presented an additional difficulty

in that it was not possible, as in the case of the wood block, to determine the direction of the three axes by inspection. Some of the blocks

were smooth, apparently having been cured against the steel face of

a press; others showed cloth prints, probably caused by curing against

a cloth-covered press; others, which were originally too thick, had

been dressed with a sanding machine and showed the marks of the

sander. There was no difficulty in recognizing the axis perpendicular

to the thickness of the block, but the other two axes could only be

distinguished by determining the modulus of elasticity in each tranverse direction. In order to follow a logical procedure in investigating

the physical properties of the material, the mathematical development described in the following sections was used as a basis for the

test program.

146. Notation.-The notation used in subsequent formulas and

discussions is as follows:

x, Y, Z =

coordinates of three mutually perpendicular axes.

€x = strain in the x direction.

€ = y strain in the y direction.

€ =

strain in the z. direction. z

Y =

chan!!e in angle between the x and y axes. .xy ~

Y.l/Z =

change in angle between the y and z axes.

Yzx = change in angle between the z and x axes.

a = direct stress.

T = shear stress.

fL

= Poisson's ratio.

E = modulus of elasticity.

[{

= volume modulus.

A, B, 0, F, G, Ii = elastic coefficients.

L, JJf, LV= shearing moduli of elasticity in the directions of the pairs of axes y, z; x, z; and

x, y, respectiveJy.
RUBBER-LITHARGE MATERIAL 251

147. Elastic Symmetry.-The report on tests of similar material, made by the Aluminum Company of America,13 indicated that the

material had three planes of elastic symmetry which were mutually

perpendicular. These planes were parallel to the faces of the material, which was molded in blocks. The strain energy function for

a material with three planes of symmetry is :14

i1V=L1E2+BE'+{E'+BFEE +

B(}E E +2IJE E X !J 2;' ./JZ I~',r XJJ

+L'y yz + .11'Y zx + LV'y xy (19)

Stresses in terms of strains are:

II =

LiE + 11E + OE x {f.' y z; (fdO)

(fd1) IIy =IlE +BE +FE x 11 ,zIIZ = (lEx + P\; + CE., (B2)

T = L,y

1/Z 1IZ

(B3)

T

zx =

illy

e:l'

(24)

(25) T =N, xy Y.ry

Young's modulus for each of the three principal directions is

given by the following equations:

~=BC-F'

E x

(B6)

~=CA-(}'

E y

(27)

~=AB-Jl'

E iii

(28)

--

13Templin, R. L., and R. G. Sturm, "Methods for Determining the Physical

Properties of Certain Rubber Compounds at Low Stresses," Proc. Am. Soc.

Test. Mats., Vol. 31, Part II, p. 882, 1931.

"Love, A. E. H., "Mathematical Theory of Elasticity," 4th Ed., 1927, pp.

106-107 and pp. 160-163, Cambridge UniverBity PreBB, London.
A H G

d= H B F

G F 0

eH - FO

(29) ft

Be -- F' xy

BO-FI!

(30) ft =---- xz; BO-F'

OH - FO (31) ft =-- yx AO - G'

AF-GH

(32) ft

AO-G' yz

BO-FI!

(33) ft =-- zx AB-H'

AF-GH

(34) ft

AB - H'

zy

252 MODEL TESTS OF BOULDER DAM

where the value of d is given by the determinant:

In terms of the coefficients, the values of Poisson's ratio may be

expressed by the following equations:

where ft is the ratio of the extension in the 1J direction to the con- xy .

traction in the ;E direction produced by a compressive load acting in

the X' direction. By this definition, the sign of ft is always negative.

Three other coefficients related to Poisson's ratio may be defined

as follows:

~=AF-GH

Fx (35)

d

-=BG-HF

F y

(36)

d

-=OH-FG

Fz (37)
1 P-yz /Lzy

-=-=-

Fx F ~y E z

1 P-zx /Lxz

-=~=-

F y Ez Ex

1 /LXY /Lyx

-=~=-

F Ex Ey z

RUBBER-LITHARGE MATERIAL 253

These coefficients may be determined experimentally from the

relations:

(38)

(,'g9)

(40)

It should be noted that since the sign of /L is negative, the sign of

F ,F , and F must also be negative.

x

y z

Strains may be expressed in terms of stresses by means of these

coefficients as follows:

<I

.t'

<IY

<I,

( (41) =-----

x Ex Fz Fy

<Iy <I" <Ix

(

y =------

E y F F x z

(42)

<Iz <Ix <Iy

( (43)

=--------

z Ez Fy Fx

148. Elastic Constants.-Nine constants of the material may be

determined experimentally; namely, three values of Young's modulus

and six values of Poisson's ratio. Since these may be expressed in

terms of the coefficients A, B, 0, F, G, and n, it is evident that three

relations must exist between them. These relations, obtained from

equations 38, 39, and 40 are

E z/Lxz =

E aPzx

E x/Lyx = E yP-Xy

(;,;,)

(45)

(46)

E /I. =E' /I.

y.zy z.yz

A relation which involves the different Poisson's ratios only may

be obtained from the product of the above equations as follows:
254 MODEL TESTS OF BOULDER DAM

fLzyfLxzfLyx = fLyzfLzxfLxy (47)

The coefficients L, M, and N, as stated in section 146, represent

shearing moduli of elasticity in the directions of the pairs of axes

y,z; w,z; and w,y, respectively. By torsion tests on specimens of circular cross section, average values of the two shearing moduli in the

plane normal to the axis of the specimen may be determined. If test

specimens are built up with the different planes of symmetry normal

to the axis of the cylinder, as shown on figures 176 and 177, averages

of the shearing moduli on the m, y, and z planes may be obtained experimentally. Each shearing modulus so obtained is independent of

the others.

149. Volume Modu1us.-The volume modulus of elasticity for

an anisotropic material is given by the equation:

111 122 2

-=-+-+-------- J{ E E E FF y F x

y

z x z

where J{ is the volume modulus. Equations 38, 39, and 40 show that

each value of F is a function of two separate values of fL and E. Since

the experimentalIy determined values of fL and E in these equations

were not identical, the average values of these quantities were used

to compute K. If all values of fL and E are averaged, the expression

for J{ becomes the same as that for an isotropic material:

(48)

J{= E

3(1 - 2fL)

(49)

It is evident from the above equation that when fL equals 0.50, K

becomes infinite. If fL is slightly greater than 0.50, K will have a large

negative value; and conversely, if fL is slightly smaller than 0.50, K

will have a large positive value. Small experimental errors in determining fL wiII, therefore, greatly influence the value of K computed

from equation 48. According to Karl Pearson and St. Venant/5 negative values of the volume modulus of elasticity are not impossible in

the case of anisotropic materials. This would mean that the material

would increase in volume when subjected to pressure.

150. Axis of Symmetry.-Preliminary tests on the material indicated that the lowest modulus of elasticity was obtained in the di15Todhunter, Isaac, and Karl Pearson, "A History of the Theory of Elasticity," 1893, pp. 110 and 208. Cambridge University Press, London.
RUBBER-LITHARGE MATEJRIAL 255

rection normal to the thickness of the sheets. It was not possible to

determine, by inspection, the transverse directions of the sheet to

which the other two reference axes corresponded. Since the sheets

were laid horizontally in building the model, it may be expected that

half of the sheets had their transverse reference axes turned in one

direction, and the other half in the direction at right angles. For

such a condition, the material may be expected to act as if it were

isotropic in the transverse direction of the sheets. The reference

axis normal to the sheet is then the axis of symmetry.

151. Isotropic Conditions in Two Directions.-If the axis of symmetry is taken as the z axis, the strain energy function is

2 lV = A(£x' + £y') + C£z' + 'EF(£y + £x)£z

+ 2( A - 'EN)£X£y + L(/yZ + /zx) + N/XY (50)

Stresses in terms of strains are:

ux= A£x+ (A -,q?N)£y+ F£z

u =

( A - 2N ) £ + ./1£ + F£ Y x

y

z

(51)

(52)

(53)

(54)

(55)

(56)

u

z = F£x + F£y + C£z

T yz =

Ly yz

T

zx =

Ly

zx

T -N y

xy xy

The elastic constants may be expressed in terms of coefficients by

the following relations:

!1 !1

"

-=-=AG-F

E E I1J y

(57)

!1

-

!. A ~!

-

!.~!' --l/JUf .!flf

Ez

(58)

AC -2CN -F'

ftxy = ftyx = =t (}

- F'

(59)

2FN

ftxz = ftyZ=

AO -F'

12FN

ft

~x = ftzy = 4AN -qN'

(60)

(61)
256 MODEL TESTS OF BOULDER DAM

~-=~=2FX

F F x

y

(62)

.1

-=AO-130N-F'

Fz

(63)

where .1 is the determinant:

A ( A -2N) F

.1 = (A -

2N) A F

F F 0

or .1 = 4N( AO - ON -F') (64)

Values of F , F , and F may be obtained from experimentally

x

y

z

determined values of IL and E by the relations:

1 1 P-xz ILzx

F x

F y E x

E z

-=-=-=- (65)

1 P-xy

Fz E x

--=- (66)

From equation 65, the relation between the experimentally determined constants is

E -E xP-zx - zP'xz; (67)

A second relation may be obtained from equations 57, 63, and 64;

namely,

~=2 AO-13 ON -13F'=~ + ~ 2N Ex Fz

whence

G=

.z 2 ( 1 + P- )

Xll

E:£

(68)

where the symbol Gz for the shear modulus is used in place of

N. This is the same as the relation which holds for an isotropic material.
RUBBER-LITHARGE MATERIAL 257

The volume modulus of elasticity is given by the equation,

121 4 B

--=-+------ K E E F F x z x z

(69)

ELASTICITY TESTS

152. Specimens.-Three types of specimens were made and

tested. The first type, specimens A, B, and C, were rectangular

prisms, approximately 6 by 6 by 12 inches in dimension. They were

made by cementing together twelve 6 by 6 by I-inch blocks and

grinding the faces of the prisms to plane surfaces. Specimen A was

made from blocks cut from a single 24 by 24 by I-inch sheet. A small

arrow was marked on each block before the sheet was cut, and the

specimen was built up with the arrows all turned in the same direction, so that the assembled specimen had the same directional properties as the individual blocks. This specimen was made to determine

the elastic properties in the direction of its three principal axes.

Specimen B was made from blocks cut from a single sheet, but

the arrows on alternate blocks were turned at right angles to each

other. This specimen was made to determine whether the rubber,

under such conditions of assembly, behaved as an isotropic material in

one plane.

Specimen C was made from a group of 6 by 6 by I-inch slabs

selected at random from the stock pile. No regular arrangement of

the transverse axes of the individual blocks was made since these

axes could not be identified. This specimen was, therefore, representative of the material as it was assembled in the model.

The second type of specimen, D and E, consisted of circular

cylinders, three inches in diameter and about 12 inches long. Specimen D was made of 12 circular disks, 3 inches in diameter and 1

inch thick, cemented together without regard to the directions of

the transverse axes, and turned to a true circular section in a lathe.

This specimen was tested in tension, compression, and torsion. Specimen E had a middle section 7 inches long turned from 3 sheets

cemented together, with the joints parallel to the axis of the specimen. The reference axes of the three sheets were parallel. At each

end was a section 3 inches long with transverse joints for use in

gripping the specimen.

The third type of specimen was used to find the modulus of elas-
258 MODEL TESTS OF BOULDER DAM

ticity of the material in flexure. Specimen F was a rectangular prism,

3 by 3 by 16 inches in size, made by cementing together three strips

cut from a 24 by 24 by 1-inch slab. It was tested on a 15-inch span,

with the cemented joints vertical.

FIGURE 163-COMPRESSION TEST OF RUBBER-LITHARGE PRISM

SHOWING END RESTRAINT

153. End Conditions.-The 6 by 6 by 12-inch prisms were tested

in compression, using a hydraulic testing machine equipped with a

dial graduated in 20-pound divisions over a 10,000-pound range. In

testing such a soft material, relatively large strains were produced

by small loads. Considerable bulging of the specimen occurred, as

shown in figure 163. This resulted in a complex strain condition near

the ends of the specimen, due to friction between the material and

the bearing plates through which the load was applied. The bulging

in the middle and the restraint at the ends was eliminated by greasing

the ends of the specimen with cup grease. The same specimen, with
RUBBER-LITI-IARG E MATERIAL 259

the ends greased, is shown in figure 164. No bulging occurred when

the load was applied. Therefore, bearing surfaces of the specimen

were greased in all subsequent compression tests.

FIGURE 164-COMPRESSION TEST OF RUBBER-LITHARGE PRISM

WITH ENDS GREASED

154. Compression Tests.-In testing specimens A, B, and C,

loads were applied in increments of 400 pounds in the direction of the

short axes of the specimens, and 200 pounds in the direction of the long

axes. This made the unit stress increments in the specimen slightly

less than six pounds per square inch. Longitudinal deformations of the

specimen were determined by measuring changes in length between

the base of the testing machine and reference marks at each of the four

corners of the block at the upper end of the specimen, using a steel

scale graduated in hundredths of an inch. Lateral deformations were

measured with calipers, between gage points made by cementing small
OBSERVED DATA REDUCED DATA

TOTAL LONG. DEF. LATERALDEFORMATION UNIT UNIT UNIT LATERAL DEFORMATION

LOAO ,

. . 4 A . C 0 E

, G H J X L M LOADLONG. A . C 0 E,

DEF. G H J X L M

'00 6.06 6.09 6.01 6.10 5.11 5.69 5.6'3 5.69 5.6'3 5.11 5.12 5.11 5.11 12.26 12.28 12.31 0 0 0 0 0 0 0 0 0 0 0 0 0 0

'00 5.99 6.00 6.00 5.99 5.74 5.12 5.72 5.74 5.73 5.15 5,15 5.74 5.75 12.34 12.36 12,39 5.67 0.015 0.005 0005 0,005 0,009 0,001 0.0.07 0.005 0.005 0.001 0.007 0.006 0.006

900 5.92 5.96 5.93 5.94 5.16 5.75 5.15 5.77 5.75 5.77 5.78 5.77 5.18 12.43 12.44 12.47 11,23 0.025 0.009 0.010 0.010 0014 0.011 0.010 0.010 0.01 I 0.012 0.014 0.013 0.013

1300 5.84 5.87 5.87 5.87 5.19 5.77 5,79 5.81 5.78 5.81 5.82 5.80 5,82 12.51 12.53 12.56 16.62 0,038 0,014 0.014 0.017 0,021 0.016 0,017 0.OL1 0.016 0019 0.020 0.020 0.020

1100 5.78 5.80 5.80 5.81 5.82 5.80 5.81 5.83 5.82 5.83 5.86 5.83 5.86 12.59 12.62 12,64 22.0 0.050 0.019 0,019 0.021 0.024 0,023 0.021 0.024 0.021 0.026 0.021 0.028 0,021

2100 5.71 5.13 5.13 5.13 5,86 5.84 5.85 5.81 5.85 5.86 5.89 586 5.88 12,68 12,71 12.73 21.0 0.063 0026 0,026 0.028 0.031 0.028 0,026 0.030 0026 0.029 0.034 0,035 0,034

2500 5.64 5.65 5.67 5.66 5.89 5.87 5.89 5,90 5.88 5.90 5.92 5.90 5.92 12.18 12.81 12.83 32.0 0.076 0.031 0.031 0,035 0.036 0.033 0.033 0.035 0.033 0.036 0.042 0,042 0.042

2900 5.59 5.58 5.59 5.60 5.92 5,90 591 5.94 5.93 5.93 5.95 5.93 5.95 12.86 12.89 12.92 36,9 0.090 0.036 0036 0,039 0.043 0.041 0.039 0.040 0039 0.041 0049 0,049 0.049

3300 5.51 5.53 5,53 5.53 5,95 5.93 5.95 5.97 5.95 5.96 5.98 5.96 5,99 12,94 12,98 13,00 41.7 0.101 0,041 0.041 0.045 0.046 0.045 0.043 0.045 0.043 0.049 0.054 0.056 0055

DIRECTION OF LOAD--

STEEL PLATE...H,

NOle: 8eorln, .urlgc.. of specimen grea..d for

the..telts.

POSITION OF LATERAL MEASUREMENTS

.A

~

XJ.'1f...

J'..; ""

J

1- 0

POSITION OF LONGITUDINAL MEASUREMENTS

MODULUS OF ELASTICITY. 410 LBS.PER SQ.IH.

AVERAGE POISSON'S RATIOS. 0.42 AND 0.56

t.o

ao

0 '" POISSON'SRATIO POISSON'S RATIO POISSON'S RAT'IO

=~.~.43 .~'0.43 '~'0.4j

~

g

E

W

~'"

~

~

0

tj

t:rJ

t"'

>-3

t:rJ

w

>-3

w

0

"OJ

t:C

0

C

t"' tj

t:rJ

::0

tj

>

""

'""

POISSON'S RATIO

=~~25: '0.46

POISSON'S RATiO

.~O25; '0.42

!40

~

EW

~.o

;

~

0,

UNIT OEFORMATION

FIGURE 165-COMPRESSION TEST OF SPECIMEN A LOADED IN X DIRffiCTION
T[STING MACHINE TABI.E"--

NOfO. eoorino surfoces of Ipteimen ...ert ortOsed

forltlfttfnh

C

POSITION OF LATERAL MEAsUREMENTS

w

;30

'OSITION OF LONGITUDINALIUASUREMENTS z

MODULUS Of' UASTLCIT't .'68 L8S.PEA SQ.IN.

AVERAGE. POiSSON'S "ATIOS. 0.41 AND 0.60

50

POISSON S RATIO

s~.0.4.)

POISSON'S RATIO POISSON'S RATIO POISSON'S RATIO' POISSON'S RATIO POISSON'S RATIO

s%Jlj-0.42 :%ftI"0.43 =&¥ti"0.42 _&fllsO.4' =~.O~'7

!4

g

~30

~

.

r

~

d

tC

tC

~

t'">-I

>"J

~

~

~tr:I

~

~

>"J

t::J

~

:;

t'"

~40

:;i

0"'.0.04"--":

OBSERVED DATA REDUCED DATA

~~~; I

L02Na. ~EF.

4 A 8 C 0

L~TER:I. O~fOA:ATI:H

K L M

~61T ~~~J A e C 0

UNI7ELATE;A'" O:fORM:TlON

J K L M

100 5.985.'2 5.99 5.96 5.12 5.81 5.81 5.82 5.81 5.82 5.8.4 5.83 5.84 12.29 12.28 12.32 0 0 0 0 0 0 0 0 0 0 0 0 0 0

500 5.91 5.n 5.92 5.87 5.85 5.79 5.79 5.85 5.84 5.85 5.86 5.865.87 12.,)9 12.40 12.<t2 5.560.0140.0050,0030.00.) 0.005 0.005 0.005 0.003 0.005 0.005 0.008 0,0/00.008

900 5.835.76 5.845.81 5.875.86 5.87 5.88 5.87 5.88 5.88 5.90 5.90 12.50 12.50 12.52 10.960.0270.0080,0080,0100.0100.0100.0100.0070,012 0.010 0.017 0.0180.016

/3005.755.675,785.73 5.925.905.915,925.91 5,91 S;91 5.925.92 t2.61 12,60 12,63 16.20.0420,0170.0/50.0170.0170,017 0.015 0.012 0.015 0.014 0.026 0.026 0.025

17005.635.605.705.655.945.945,904 5.96 5.95 5.95 5.95 5.95 5.96 /2.71 12.71 12.704 21.J 0.058 0.0200.0220.0220.0240.0204 0.022 0.019 0,0200,0200.034 0.035 0.034

2100 5.605.53 5.&2 5.58 5.98 5,96 5.98 5.97 5.97 5.97 5.99 5.98 6.00 12.82 12,82 12,85 26.30.0690.0270.0260.029 0.0.26 0.027 Q..026 0,026 0.026 0.027 0.042 0.043 0.042

2500 5.53 5.46 5.55 5.51 6.01 6.006.0/ 6.926.01 6.006.02 6.00 6.03 12.93 12.94 12.95 3 U 0.0830.0320,032 0.034 0.OY4 0,0340.031 0.031 0.0290.0320.051 0.0530.050

2900 5.046 5.39 5.48 5.43 6.056.046.036,056.046.05 6.056.046.06 13.04 13.05 13.06 35.8 0.097 0.03~ 0,039 0.037 0,03900390.039 0.Q36 0,0360.037 0.059 0.061 0.059

3300 5.39 '5.335.41 5.376,086.056.076.096.086.086.086.076.0913.14 13,15 ').1740,30.1090.00440.0400.0440.0460.046 0.044 0.040 0040 0,042 0.067 0069 0.067

FIGURE 166-COMPRESSION TEST OF SPECIMEN A LOADED IN Y DIRECTION """"

.....
OBSERVED DATA REDUCED DATA

TOTAL LONG.DEF. LATERAL OEFORMATION UNIT

"'

UNIT LATERAL DEFORMATION

LOAD , , , .

, , ,

0 E F

, H

, , LOADLON"G , , , , E

, , H , ,

400Lb. 11.95 11.95 11,98 12.00 5.85 $.86 5.90 5,90 5.96 590 $.91 ':;,92 5.91 $.95 0 0 0 0 0 0 0 0 0 0 0 0

600 11.74 11,71 11.14 11.79 5.89 $.92 5.94 5.96 6.01 5.95 5.96 $.96 5.9$ 5.98 5.B5 0.018 0.001 0.010 0.001 0.010 0009 0,009 0.009 0.001 0.001 O.OO~

000 11.54 11.56 11.60 11.60 5,95 5.91 5.99 6,02 6.01 600 6.01 6.01 6.01 6.03 11.50 0.034 0.011 0.019 0.015 0.021 0,019 0,011 0.011 0.015 0.011 0,014

1000' 11.36 11.31 11.42 11.42 6.01 6.03 6.04 6.06 6.11 6.04 6.05 6.05 6.04 6.06 11.00 0.050 0021 0.029 0024 0.021 0.026 0.024 0.024 0.022 0,022 0.019

1200" 11.19 11.20 11.25 11.25 6.05 6.09 6.10 6.12 6.16 6.01 6.10 6.10 6.09 6.11 22.30 0.065 0,034 0.031 0,034 0.031 0.03-4 0.029 0,032 0,031 0,031 0.021

1400- 11.02 11.04 11.09 11.09 6,10 6.13 6.14 6,11 6.21 6.12 6.14 6.13 6.!3 6.15 21.43 0.019 0,042 0046 0041 0.046 0.042 0,031 0,039 0.036 0.031 0.034

1600- 10.85 10,86 10.90 10.90 6,15 6.18 6.20 6.23 6.21 6, I ~6.18 6.19 6.18 6.20 32.40 0.096 0.051 0.054 0.051 0.055 0.052 0,042 0.046 0.046 0.046 0.042

1900" 10.69 10,11 10.10 10.15 6.21 6.24 6,24 6.29 6.32 6.20 6.22 6.22 6.22 6,23 31.20 0,110 0,060 0.064 0051 0.065 0.060 O.O~) 0.052 0,051 0.052 0.041

262 MODEL TESTS OF BOULDER DAM

steel plates to opposite points on the lateral faces of the specimen. Nine

such sets of gage points were provided on the 6 by 12-inch faces of

specimens A and B, and three sets on the rest of the faces of A and B

and on all faces of specimen C. The results of the tests are shown

in figures 165 to 173, inclusive.

DIRECTION OF 1..0..0-1

STEElPl.ATE---'~.'.':~ECI"EN

A''''''.

TESTINO MACHINE TABlE'"

POISSON'S RATIO

=~M8

PO~S;:~.::TIO POI~~o-::TlO POI~;¥~o~:TIO PO~&;i;o~~TlO

MODULUSOF ELASTICITY' 350 L8S. PER SQ.lN

AVERAGE POISSON'S RATIOS '0.56 AND0.41

g

~

Nof.:Blorln"lurfocuofsplclrun

<;Jrlosedforfhnetutl. ~2

,-OIRECTIONOF GRAIN

~"-..

\, OF RUB~ER

H

X AXIS ,

<- POSITIONOFLONGITUDINAL

MEASUREMENTS

FIGURE 167-COMPRESSION TEST OF SPECIMEN A LOADED

IN Z DIRECTION

155. Tension Tests.--Specimens D and E were tested in tension,

using the machine developed for plaster-celite specimens, see figure

46. Flat-headed tacks, with small conical holes in their heads, were

driven in opposite sides of the specimen, 5.3 inches apart, and cemented

in place. These served as gage points for measuring longitudinal

deformations. Strains were measured with a pair of sharp-pointed

dividers and a micrometer caliper. Small steel plates were cemented

to the specimen for lateral gage points, and lateral deformations

measured with a micrometer caliper. The load was applied in three-
.

B

I

~ i

MODULUS OF ELA~TlCITY. 388 LBS.PER SQ.'N. E

20

: AVERAGE POISSON S RATIOS.0.43 AND 0.61 ~ 3

DIRECTION OFLOAD.

STEEL PLATE--

(12"-20" .1')

TESTING MACHINE TABLE"-

Nole Bearing surfaces of specimen ..ere

greostdintheselesls.

"

C

POSITION OF LATERAL MEASUREMENTS

~

:Ai~

.

Z .

'..

d

POSITION OF LONGITUDINAL

MEASUREMENTS

50

POISSON'S RATIO

'~~O.40

POISSON'S RATIO POISSON'S RATIO POISSON'S RATIO POISSON'S RATIO POISSON'S RATIO

:~'O.48 :~"O.35 .%fH-O.43 '~'O.40 =~'O,47

,;

a

~

30

~

c::

tD

tD

t?'J

:;0

t'"......

~

~

:>-

~

0

l;j

~

tJ;.

>-3

~

>

t'"

50

POISSON'S RATIO POISSON's RATIO ,,~~;: .0.46

=

gm.'O.40

~40

g

;30

o.

;.. ..O.O4~..:"; UNIT' DEFORMATION

OBSERVED DATA REDUCED DATA

~":ci I

LO:G. O,EF.

4 ABC 0

L:TER~L D~FOR~ATlO..N

I< L tot ~~~ ~~~F~ A 8 C 0

UNIT

E

LATE~ALO:FORM:TION

J

I( L M

100 6.08 6.03 6.106.08 5.92 5.935.93 5.92 5.93 5.94 5.95 5.95 5.96 11.83 11.19 11.80' a a a a a a a a a a a

0' 0' 0'

50'0' 6.0'1 5.96 6.0'25.99 5.97 5.96 5.97 5.975.97 5.97 5.96 5.97 6.0'0' 11.95 I r.91 11.90' 5.7 0'.0'14 0'.0'0'8 0'.0'0'5 0'.0'0'7 0'.0'0'8 0'.0'0'7 0'.0'0'5 0'.0'0'2 0'.0'0'3 0'.0'0'7 0'.0'10' 0'.0'10' 0'.0'0'9

90'0' 5.925.875.945.91 6.0'0' 5.99 6.0'1 6.0'0' 6.0'1 6.0'1 6.0'1 6.0'26.0'3 12.0'4 12.0'1 12.0'1 11.20'.0'28 0'.013 0'.0'10' 0'.0'13 0'.0'13 0'.0'13 0'.0'12 0',0'10 0'.0'120'.0'120',0'180'.0'19 O'.O'r7

130'0' 5.845.795.865,846.0'46.0'36.0'36.0'46.0'46.0'66.0'56.0'5 6.0'6 12.15 12.11 '12.1 I 16.50'.0'420'.0'20' 0'.0'17 0'.0'17 0'.0'20' 0'.0'18 0'.0'20' 0'_0'17 0'.0'17 0'.0'17 0'.0'27 0'.0'27 0'.0'26

170'0' 5.75 5.11 5.785.766.0'16.0'86.0'86.0'86.0'86.0'86.0'76.10' 6.10' 12.26 12.21 12.22 21.70'.0'570'.0'250'.0'250.0'250'.0'270'.0'250.0'230'.0'20' 0'.0'25 0.0'23 0'.0'36 0'.0'35 0'.0'35

210'0' 5.67 5.63 5.70' 5.68 6.11 6.10' 6.11 6.12 6.12 6.12 6.12 6.13 6.] 5 12.36 12.32 12.32 26,8 0'.0'72 0'.0'32 0'.0'28 0'.0'30' 0'.0'33 0'.0'32 0'.0'30' 0'.0'280'.0'30' 0'.0'32 0'.044 0'.0'44 0'.043

250'0' 5.60' 5.55 5.635.61 6.176.156.166.166.166.166.156.166.18 12.46 12.42 12.42 31.70'.0'860'.0'420'.0'370'.0'380'.0'40' 0'.0'38 0'.0'37 0'.0'330'.0'350'.0'31 0'.0'52 0'.0'520'.0'51

290'0' 5.525.48 5.545.51 6.20' 6.19 6.20' 6.19 6.20' 6.20' 6.19 6.20' 6.22 12.58 12.54 12.54 36.40'.10'20'.0'460'.0'430.0'450'.0'450.0'450.0'430'.0'40' 0.0'41 0.0'430.0'62 0.0'620.0'62

330'0' 5.445.40' 5.47 5.46 6.23 6.226.226.226.236.246.216.236.2612.69 12.65 2.65 41,0' O'.lr5 0'.0'510'.0'480'.0'480'.0'50' 0'.0'50' 0'.0'50' 0'.0'43 0'.0'46 0'.0'50' 0'.0'710'.0110.0'10

FIGURE 168-COMPRESSION TEST OF SPECIMEN B LOADED IN X DIRECTION '"

<:!>

~
OBSERVED DATA REDUCED DATA

TOTAL LONG. OEF LATERALDEFORMATION UNIT UNIT UNIT LATERAL DEfORMATION

LOAD I 2

,

4 A . C 0 E

, G

"

, . L

"

LOADLONG.A . C 0 E

, G

"

J . L

"

DEF

100 6.20 617 6.14 6,20 5,84 5.82 5,83 584 583 5,84 5.83 5,83 5.84 11.81 11.80 11.81 0 0 0 0 0 0 0 0 0 0 0 0 0 0

'00 6.12 6,08 6.07 6.12 5,86 5.86 5.87 587 5,87 5.87 5.86 5.86 5.86 11.97 11.9J 11,91 5.8 0014 0.003 0007 0007 0005 0007 0,005 0.005 0005 0.003 0.014 0.009 0.009

.00 6.02 5,99 5.97 6.02 5.90 5.89 5.90 591 5.90 591 5.90 5.90 5.90 12,05 12.01 12,02 11.4 0,031 0.011 0012 0012 0.012 0012 0012 0,012 0.012 0.011 0.020 0,018 0018

1300 5.94 5.90 5.89 5,95 594 5,93 5.94 594 5,93 5.94 593 593 5,93 12.16 12,JI 1212 16,9 0045 0,017 0019 0019 0011 0,017 0.011 0011 0.017 0.015 0029 0,026 0,026

1700 5.84 5.82 5.81 5.86 5.98 5.96 5.98 5.98 5.98 5.98 5.98 5.96 598 12,27 12.22 12.22 22.2 0,060 0:-024 0024 0025 0024 0025 0,024 0025 0022 0,024 0039 0,035 0.034

2100 5.78 5.74 5.72 5.18 6.01 6.00 6.01 6,02 6.01 6,01 6.01 6.01 6,01 1237 12.32 12.32 27,3 0074 0.029 0030 0.031 0030 0030 0.029 0.030 0031 0,029 0048 0,043 0042

2500 5.70 5,66 5,64 5.72 605 6.03 6.05 6.05 6,04 606 605 6.04 6,06 1248 12,43 12,43 32.2 0088 0035 0035 0,037 0035 0035 0.037 0037 0035 0.037 0056 0.052 0.051

2900 5.62 5,60 5.56 5.62 6.10 6,07 6.09 6,10 6,08 609 6,08 6,01 6.10 12.59 1254 12.54 370 0103 0,044 0.042 0044 0.044 0042 0042 0,042 0040 0044 0.056 0.061 0.060

3300 5,55 5.50 548 5,55 6.12 6,11 612 612 6,12 613 612 6,11 614 12,68 1264 1266 41.7 01 I 8 0047 0049 0049 0047 0,049 0,049 0049 0,047 0050 0072 0069 0070

DIR[CTIO

~

OF LOADITIElELPLAT£.o.n SP£CIMEN

.-6M.fI'.'2M

'

TUTING ..ACHIH£' TAeLE.""

Ho'. a.arino ,lIr'ae.. of ,plelm,n war, grUSld in

,...,.t..t,.

Tlu, ,...el"',,,,,, "'O~, fro... on, 24M. 24M, IM,lab.

TII'''',.dl.n 0' '", "ai.. otlh, ,.tlb.,...

01t.,n"',4 In'aclllift.Th. n'II'" .ata IIlIall'

on

'''0 4"°''''0.

o,...t tll, ero.. IIcliono'

'"'

...cl_n un'., I....

C

P081TION OF LATERAL MEASUREMENTS

~

,}..

;1 z t.

ii 1

.

J- (I

1II081TION OF LONGITUDINAL MEASUREMENTS

IIIODULUS OF [LASTICIT\( .3'2 LBS. PER sa. IN.

AVERAGE POISSON'S IIATIOS .. 0.41 AND 0.57

'0 ""0'>....

POISSON'S RATIO POISSON'S RATIO POISSON'S RATIO

..g:?::-0.4. .mt-O.41 .SfH.040

i40

g

~30

z

~

0

t:I

t':'J

t"'

>-:3

t':'J rn

>-:3

rn

0

"'1

tC

0

d

t"' t:I

t':'J

::c

t:I

:.-

~

~40

g

«

~ 30

.

0

:- 0.04~ ~

UNIT OEFOAMATJON

FIGURE 169-COMPRESSION TEST OF SPECIMEN B LOADED IN Y DIRECTION
OBSERVED DATA REDUCED DATA

TOTAL. LONG.DEf. LATERAL DEFORMATION UNIT UNIT UNIT LATERALDEFORMATION

'""

, , , 4,

"

, D

, ,

. H J

, LOADL8E'1=G

,

"

, D

, , G H J

,

IOOLb. 11.72 11.83 11.79 11.69 6.01 6.02 6.04 '.00 6.02 6.04 6.00 6.01 ~.94 6.01 D D 0 0 0 0 0 0 0 0 0 0

300" lUll 11.62 11.58 11.47 6.05 6.07 6.08 6.05 6.08 6.08 ,.. 6.06 5.98 6.07

"

0.018 0.007 0.008 0,007 o,ooe 0.010 0.007 0.010 0008 0.007 0,010

>00" 11.32 11.45 11.41 11.30 6.086.11 6.13 610 6.13 6.(36.11 6.11 6.06 6.11 110 0.034 0.012 0.015 0.015 0.017 0.018 0.015 0.018 0.017 0.020 0.017

roo" 11.13 11.26 11.22 11.11 6.13 6.18 6.18 6.15 6.18 6.19 6.15 6.16 6.08 6.16 16.3 0.051 0.020 0027 0.023 0.025 0.027 0.025 0,025 0.025 0.023 0.025

900" to.95 11.07 11.03 10,92 6.18 6.23 6.23 6,20 6.23 6,256.21 6.21 6.13 6.20 2\.4 0.068 0.028 0,035 0,032 0.033 0.035 0.035 0.0:35 0.033 0.032 0.032

ItOO" 10.13 10.90 10.89 10.15 6.23 6.29 6.28 6.26 6.28 6.30 6.24 6.26 6.2:3 6.24 26.3 0.08:3 0.036 0.045 0.040 0,043 0.04:3 0.043 0.040 0.041 0,048 0,038

1300" 10.62 10.14 10.69 10.58 6.28 6.34 6326.31 6.3:3 6.35 6.30 6,31 6.28 6.29 31.0 0.099 0.045 0.05:3 0.046 0.051 0.051 0,051 0.049 0.049 0.056 0.04G

1500~ 10.44 10.56 10.53 10.40 6.34 6.38 6.39 6.36 6.38 6.40 .... 6.37 6.28 6,34 35,6 0.116 0.054 0.059 0.057 0.059 0.059 0.059 0.059 0.059 0.056 0.052

1100" 10.28 10.40 10.36 10.25 6,31 6.45 6.436.41 8.44 6.45 6.41 6.42 6.35 6.38 40.0 0,132 0.059 0.010 0,064 0.061 0.069 0.061 0.067 0.061 0.067 0.060

RUBBER-UTHARGE MATERIAL 265

pound increments. These specimens were also tested in compression

and the results of both tests are shown in figures 174 and 17S.

156. Torsion and Flexure Tests.-Specimens D and E were

tested in torsion in the machine shown in figure 50. The load was

applied in increments of one pound, causing a unit shearing stress oi

1.12 pounds per square inch at the outside fiber of the specimen. Deformation measurements were made by measuring distances between

reference points of the troptometer. The results of the torsion tests

are shown in figures 176 and 177.

STEELPl..ATE.'''.

(8'.".!4)

SPECIMEN

/ff.6".12~

TESTING MACHINE TABLE"-

Note: Bloring surloel of sPle;men

O",o$ldfo" thu. tuts

"

ta

'

D ,

, ,

=

C 0;

,

/

,

8

,

J 50

POSITION OF lATERAL MEASUREMENTS

~

,-'.,"

-f !i f

~ i ¥ ~

: "> ~

: .."', '..~. ;-1 i

POllnoN OF' LONGITUDINAl.

MEASUREMENTS

MOOULUS OF ELASTICITY. 318 LBS. PER SQ.IN.

AVERAGE POISSON'S RATIO. 0.49 10

~30

~40

~

~30

FIGURE 170-COMPRESSION TEST OF SPECIMEN B LOADED

IN Z DIRECTION

Specimen F was tested in flexure as a simply supported beam on

a IS-inch span. As the beam was very flexible, the load was applied

at the center in increments of 200 grams. Deflections at the center

were measured with a dial gage reading to one-thousandth of an

inch. Results of the flexural test are given in figure 178.
OBSERVED DATA REDUCED DATA

TOTAL LONGITUDINAL OEF. LATERAL DEFORMATION UNIT

"'

LATERAL DEFORMATION LONG. lOAD I 2 3 4 A . C D E F LOAD OEF. A . C 0 E F

IDOLb. 6.20 6.18 6.14 6.18 6.02 6.03 6.03 12.20 12.22 12.21 0 0 0 0 0 0 0 0

500 6.13 6,11 6.07 6.10 6.06 6.06 6.06' 12,28 12.31 12.30 5.6 0.013 0.007 0.005 0.005 0.007 0.008 0.008

900 6.07 6.04 5.98 6.03 6.09 6.10 6.09 12.39 12,40 12.38 11.0 0.025 0.012 0.012 0.010 0.015 0.016 0.014

1300 5.98 5.97 5.92 5.96 6.11 ,6.13 6.12 12.47 12.50 12.47 16.3 0,037 0.015 0,017 0.015 0.022 0.023 0.02!

1700 5.92 5.89 5.84 5.88 6.15 6.18 6,15 12.56 12.59 12.56 21.5 0.05! 0.022 0.025 0.020 0.030 0.030 0.029

2100 5.84 5.82 5.77 5.81 6.19 6.22 6.19 12.65 12.69 12.65 26.4 0.063 0.028 0.032 0.027 0.037 0.038 0.036

2500 5.78 5.75 5.70 5.74 6.21 6.25 6.21 12.74 12,78 12.73 31.4 0.076 0.032 0.033 0.030. 0.044 0.046 0.042

2900 5.70 5.68 5.63 5.66 6.25 6.28 6.25 12,83 12.88 12,84 36,2 0.089 0.038 0.042 0.037 0051 0054 0051

266 MODEL TESTS OF BOULDER DAM

DIRECTION OF LOAD-,

.,,",,~:.::l .."". ~6""2"

TESTINGMACHINETABLE-/

~

D

~

~~

E

A

'" C

D .

E A

POSITION OF LATERAL. MEASUREMENTS

.

~

,'!1<

I . Y

0

"Z ',Iii'

1~ d

)

POSITION OF LONGITUOINAL MEASUREMENTS

50

POISSON'S RATIO

~~:: =0.40

~ 40

g

~

w

~30

~

~

0

0

W

~

~

0

50

POISSON S RATIO

g:?:: "0.56

~

w

~30

~ . z

MODULUS OF ELASTICITY =403 LBS. PER SO.IN. ;;

AVERAGE' POISSON'SRATIOS;rO.44 AND.Q.59 ,,~20

t;

~

t: :

~ 105

~40

g

o.

~-O.o4"--":

POISSON'S RATIO POISSON'S RATIO

~.?26: =0.50 ~=O.41

UNIT DEFORMATION

POISSON S RATIO POISSONS RATIO

g:?::=O.63 ~.O.59

UNIT DEFORMATION

FIGURE I7l-COMPRESSION TEST OF SPECIMEN C LOADED

IN X DIRECTION

ELASTICITY DATA

157. Elastic Constants.-E1astic constants of the material, obtained graphically from the test data and based on original dimensions of the specimens, are given in table 5. The z axis is perpendicular to the thickness of the slabs, while the x axis is in the direction

of the greatest modulus of elasticity. The first subscript in the symbols for Poisson's ratio indicates the direction of the longitudinal

strain. The second subscript indicates the direction of the lateral

strain . Thus ,

/I. is the ratio of the lateral strain in the y direction '-xy

to the strain in the x direction when a load is applied to the speci-
RV ATA R TA

TOTAL LONGITUDINALDEF. LATERALDEFORMATION UNIT \R,~G LATERALDEFORMATION LOAD I 2 3 4 A . 0

°

E F LOAD A . 0

°

E F

IDOLb. 6.23 6.20 6.20 6.25 6.00 6.01 6.00 12.21 12.21 12.20 0 0 0 0 0 0 0 0

500" 6.15 6.13 6.12 6.16 6.03 6.05 6.04 12.29 12.31 12.29 5.5 0.014 0,005 0.007 0.Q07 0007 0.008 0.008

900" 6.08 6.05 6.04 6.09' 6.06 6.07 6.07 12.38 12.40 12,37 10.9 0.027 0.010 0,010 0.012 0.014 0.or5 0.014

1300" 6.00 5.97 5.97 6.02 6.10 6.10 6.10 12.48 12.48 12.46 16.2 0.040 0.017 0.015 0.017 0.022 0.022 0,021

1700" 5.93 5.89 5.89 5.94 6.13 6.13 6.14 12.59 !2.60 12.57 21.3 0.053 0.021 0.020 0.023 0.031 0.032 0.030

2100" 5.85 5.82 5.82 5.87 6.17 6.18 6.17 12.69 12.69 12.67 26.2 0.067 0.028 0.028 0.028 0.039 0,039 0.038

2500" 5.77 5.75 5.74 5.80 6.20 6.20 6.21 12.79 12.79 12.75 31.0 0.080 0.033 0.031 0.035 0.047 0.047 0.045

2900" 5.70 5.68 5.68 5.73 6.22 6.24 6.24 12.89 12.89 12.86 35.8 0.093 0.036 0.038 0.040 0.055 0.055 0.053

RUBBER-LITHARGE MATERIAL 267

OIREOTIO_OFLOACSTEEL PLATE'--.~ SPECIMEN

6"1( 6-1( 12"

TESTING MACHINE TABLE.'

~

o

B

.~ tV Er

A

....

0

°

POSITION OF LATERAL MEASUREMENTS

~

y

/f~

""!'

z

"

:

i 1. :f.- 0

POSITION OF lONGI~UDINAL MEASUREMENTS

MODULUS OF ELASTICITY. 410 LBS.PER SQ. IN.

AVERAGE POISSON'S RATIOS .O.4~ AND 0.54

50

POISSON'S RATIO

>:g:~2~ ..0.45

POISSON'S RATIO POISSON's RATIO

:~:O.43 =g:?ZS; .0.42

~ 40

g

'"~~

~3

z

50

POISSON'S RATIO

:~;O.57

POISSON'S RATIO POISSON'S RATIO

"&PH,;D.56 "~.O.50

~ 40

~

~30

~m

-'=

FIGURE I72-COMPRESSION TEST OF SPECIMEN C LOADED

IN Y DIRECTION

men parallel to the x axis. It should be emphasized that the elastic

constants given in table 5, being based on original dimensions, are

usually different from those given on figures 165 to 178, which were

based on actual dimensions.

158. Changes in Dimension.-For a material which deforms

greatly under small loads, the usual method of computing unit stress,

by dividing the total load by the original cross-sectional area, gives

rise to considerable error. Error is also involved in computing the

unit strain by dividing the deformation by the original length of the

specimen.

In the compression tests of specimens A, B, and C, the cross-
'" DIRECTION OF LOAD-, POISSON'S RATIO POISSON'SRATIO POISSON'S RATIO

"~.O.37 ,,~.~;~ .0.51 "SfR-aO.sa

~<co""jl~ .~'"" ~40 (tlxe.xa') _,,.---6"1(6"1.12."

T£STING ""'CHINE UBLE~

.

No~:B.orlflQ'Ul"focIIOf.p.cim.n9r'a"dforthlS' tnfs.

TIIII.pIclmen wo. iliad. from 12- 6".11. 6"..I"slobl with

the dlrectlORof It" groin of rubber at random.

~E

.

A~:'" J! 0

UNIT DEFORMATION F C

B ':.}" i< E

50

C F POISSON'S RATIO POISSON'SRATIO POISSON'S RATIO

POSITION OF LATERAL MEASUREMENTS "g.~5~ aO.51 "g:~;: 0.57 "gf,':. 0.49

~40

Z g

--l

'(]b'

. 3C

~, ~I ,

~~;i

~/; "', J

POSITIONOFLONGITUOINALMEASUREMENTS

MOOULUS OF ELASTICITY. 362 LeS.PER SQ.IN.

°i<- 0,04" ~>j UN IT DEFORMATION AVERAGE POISSON'SRATIOS .0.47 AND0.52

.5 RVE D TA R DU D A

TOTAL LONGITUDINAL OEF. LATERAL DEFORMATION UNIT .~ti~1. LATERAL DEFORMATION

LOAD ,

2 3 4 A B C D E F LOAD A B C D F

100 Lb 11.62 1159 11,57 11.62 605 6.05 6.07 6.03 6.02 6.04 0 0 D 0 D 0 0 0

300 11.42 11.39

"":

I

".42 6.09 6.10 6.10 6,07 6,08 6,08 5.6 0.017 0.007 0,008 0.005 0,007 0.010 0.007

SOD 11,23 11.21 11.20 11.25 6.13 6,14 6,14 6.12 6.13 6,12 11.1 0.032 0.013 0.015 0.012 0.015 0.019 0.014

7CO 11.08 11.05 11.04 11.08 6,16 6.19 6.19 6.17 6.19 6.16 16.4 0.046 0.018 0.023 0.020 0.023 0.028 0.021

900 10.88 10.88 10.85 10.90 6,21 6.24 6.23 6.22 6.23 6.22 21.5 0.062 0.027 0.032 0.027 0.032 0.035 0.030

1100 10,72 10.69 10,68 10.69 6.25 6.29 6.28 6.26 6.28 6.27 26.4 0.078 0.033 0.040 0.035 0.038 0.043 0.038

1300" 10.56 10.53 10.52 10.57 6.31 6.34 6.32 6.31 6.33 6.31 31.2 0.092 0.043 0,048 0.041 0.046 0.051 0.045

1500" 10.41 10.37 10.36 10.42 6.38 6.39 636 6,35 6.37 6.39 35.8 0,106 0054 0056 0,048 0.053 0,058 0.058

268 MODEL TESTS OF BOULDFJR DAM

FIGURE I73-COMPRESSION TEST OF SPECIMEN C LOADED

I;\T y, DIRECTION

sectional area of the specimen at a stress of 40 pounds per square inch

was about ten per cent greater than the area of the specimen under no

load, so that discrepancies might be expected in values of stress and

strain computed by usual methods. To reduce the discrepancies,

stresses were computed by dividing each value of the load by the corresponding area of cross-section. Similarly, strains were obtained

by dividing each deformation by the mean of the initial and final length

for the particular strain observation. Stress-strain and lateral deformation curves, shown on figures 165 to 173, were determined by

this method.

159. Plotting Test Data.-In plotting test data, measurements

of longitudinal deformations at the four corners of the block were
COMPRESSION TENSION

TOTAL I:INIT AVER. UNIT AVER UNIT TOTAL UNIT AVER UNIT AVER UNIT

LOAD LOAD LONG. LONG LAT LAT LOAD LOAD LONG LONG LAT LAT.

DEF. OEF. DEF. DEF. DEF DEF DEF DEF

0 0 0 0 0 0 0 0 0 0 0 0

6 0.84 0.0194 0.0024 0 0033 0,0011 6 084 00210 00026 0 0040 0,0013

12 1.68 0.0384 0.0048 0.0072 0.00;1:3 12

"8

0.0423 0 0052 0.0075 0.0024

18 2.52 0.0573 0.0072 0.0113 0,0035 18 2 52 0 0619 0.0077 00115 0003-6

24 3.36 0.0776 0.0097 0.0155 00049 24 3.36 0 0952 0.0105 0 0155 0 0049

30 4.20 0.0950 0.0120 0.0190 00060 30 4 20 01051 00132 00198 0,0063

.. 5.04 0.1139 0.0142 00225 00070 .. 504 01274 00158 0.0237 0,0075

42 5.88 01331 0.0166 Q. 02&0 00081 42 5.88 0.1503 0.01B6 0.0215 0,0081

48 6.12 0.1518 0.0190 0.0297 0 0093 48 6.72 0,1716 00212 a 03!3 0.0099

54 7 56 0.1928 0.0238 0.036 00113

RUBBER-LITHARGE MATERIAL 269

0- z2

"

0.012 0.016

TENSION TEST

"'ODULUS OF ElASTICITY -350 LIS. PER SQ. IN.

POISSON" RATIO -0.4$

0.008 0.012 0.016 0.020 0.024

~6

...

..

..

"

~~

..

...

..

..04

z

~

z

-30

..

0

...

TEST SPECIMEN

FIGURE 174-RESULTS OF TESTS ON SPECIMEN D

averaged for each increment of applied load, and the average values

plotted as shown in the upper left-hand diagram of figure 165. A

curve was then drawn through the plotted points and the initial tangent modulus of elasticity determined from the curve. In the case

of lateral deformations, separate measurements made along each axis

of the block were not averaged before plotting. Instead, results of

measurements along each gage line were plotted on a separate diagram, a curve drawn through the plotted points, and Poisson's ratio

determined for each gage line, as shown in figure 165. The different

values of Poisson's ratio obtained for a given axis of the block were

then averaged and the average value recorded at the left of the diagrams. Thus figure 165 shows two average values of Poisson's ratio,

one for each direction at right angles to the applied load.
COMPRESSION TENSION

TaTAL UNIT AVER. UNIT AVER. UNIT AVER. UNIT TOTAL UNIT AVER UNIT AVER UNIT AVER. UNIT

LOAD LOAD LONG. L.ONG LAT. LAT. LAT. LAT. LOAO LOAD LONG. LONG LAT. LAT. LAT. L.AT.

OEF. OEF. OEF.H DEF'-I DEF2-2 D£F,2-2 OfF. OEF. OEFI-! OEF.I-! DEF.2-2 OEF.2-2

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

6 0.87 0.0118 0.0022 0.0030 0.0010 0.0037 0.0012 6 0.87 o.or 14 0.0021 0.0030 0.0010 0.0043 0.0014

12 1.74 0.0201 0.0038 0.0055 0.0018 0.0062 0.0020 12 1.74 0.0249 0.0047 0.0050 0.0019 0.0080 0.0026

16 2.61 0.0290 0.0055 0.0080 0.0026 0.0110 0.0035

"

2.61 0,0353 0.0066 0.0083 0.0027 0.0117 0.0037

24 3.48 0.0396 0.0075 0.0102 0,0033 0,0137 0.0044 24 3.48 0.0466 0,0085 0.0113 0.0036 0.0147 0.0047

30 4.35 0.0487 0.0092 0.0132 0.0042 0.0170 0,0054 30 4,35 0.0607 0.0114 0.0140 0.0045 0.0180 0.0057

36 5.22 0.0592 0.0112 0.0!47 0.0047 0.0207 0,0066

'6

5.22 0,0727 0.0136 0.0167 0.0053 00220 0.0070

42 6.09 0.0706 0.0134 0.0175 0.0056 0.0240 0.0077 42 6.09 0.0820 0.0154 0.0190 0.0061 0.0250 0.0080

48 6.96 0.0806 0.0152 0.0207 0.0066 0.0280 0.0090

270 MODEL TESTS OF BOULDER DAM

..

~

TENSION TEST

MOOUL.US OF EL.ASTICITY .396 LBS. PER SQ. IN.

POISSON'S RATIO ,., . 0.39

POISSON'S RATIO 2.2~ O.~I

%

U

Z

r

~4

0

a

z

f3

z

0.024

2

#

'

, ,

:!

I

~-~:::

-

2

TEST SPECIMEN

FIGURE 175-RESULTS OF TESTS ON SPECIMEN E

If the separate measurements of lateral deformation along each

axis of the block had been averaged for each load increment before

plotting, the resulting curves would have been smoother than the

individual curves shown in the figures. In this case Poisson's ratios,

determined from the curves, would have represented average values

for the different axes of the block. The latter method was used in

computing the elastic constants, based on actual dimensions of the

loaded specimens, given in table 6. The values given in table 6 are

sometimes slightly different from those shown on the figures, due to

the different methods of determination. For example, in figure 165

the modulus of elasticity of specimen A is 410 pounds per square

inch and the average values of Poisson's ratio 0.42 and 0.56, whereas

in table 6, the corresponding values are 420 pounds per square inch, 0.47

and 0.58, respectively. Although the differences are small, the quantities in table 6 more nearly satisfy the stress-strain equations.
I

I Modulus of Elasticity Poisson's Ratio I

I

I

I Lb. per Sq. In.

Specimen Direction Test -- - - - -- - --

I

of Slabs I

I

EorG Ex Ey E, /Lxy /Lu /Lyx fLy, /Lu /L,y

I -- - - -. - --

Compression

A Parallel 475 430 395 0.48 0.60 0.43 0.68 0.47 0.57

B Alternate 430 430 370 0.46 0.65 0.47 0.68 0.55 0.53

C Random 460 435 390 0.46 0.61 0.42 0.64 0.51 0.58

D Random 350 0.50 0.50

E Parallel 455 0.40 0.57

Tension

D Random i315 0.46 0.46

E Parallel

I

Torsion

I

395 0.39 0.51

D Random I 120

E Parallel

I Flexure

I

135

F Parallel

'

I

I 405

i

TABLE 5-ELASTIC CONSTANTS BASED ON ORIGINAL DIMENSIONS

~

d

tJ:I

tJ:I

l".J

~

S

>-3

iI1

>

~

0

l".J

::::

>

>-3 l".J

::>:I

......

>

t"'

.",

->

>-'
.

7

V

/

/"

/

/

,/

/'

V

./

/

,

V

TORSION TEST

MOOUL.US OFEI...ASTICITV.120LSS.PERSQ.IN

0

,

'//

0

APPLIED

UNIT AVER4G£ AVERAGE

LOAD ~!~ir TOTAL UNIT

POUNDS PERSQ,I OfF.

"" " " " "

,

1.12 0.'6 0.0078 ,

2.23 0,43 0.0209 ,

335 0.58 0.0282

., 446 0.80 0.0369

5.59 0,98 0,0476 ,

6.70 1,11 0,0569

Modulus of

Elasticity * Poisson's Ratio

Com- Direc- - - - - - - - - -

pression tion

Specimen of SJabs Ex Ey E, fLxy fLu fLy% fLy, fLu fL.y

- - - - - - - -

A Parallel 420 355 340 0.47 0.58 0.40 0.62 0.47 0.55

B AJternate 350 340 320 0.42 0.58 0.41 0.58 0.54 0.54

C Random 400 375 335 0.42 0.56 0.42 0.58 0.50 0.53

272 MODEL TESTS OF BOULDER DAM

0

0.005

00'

0.015 0.02 0.03 0.035 004

UNIT DEFORMATION

0,045 005 0.06

%

U%

W

..00.

.

0Z0

0

.

Z

.

0Z

~

Z

.

Unit shearing stress 5S. If'' ~"1.116P

Unit shearing strain 6s" M "

5.~45xl~_71 =

O.0486e

T" Applied torque

p

=

Applied load

a =

Radius of specimen

e"

Totol observed deflection of froptometer

R=Lever arm of troptometer

L

=

Gage length of specimen

I TEST SPECIMEN

FIGURE 176-TORSION TEST ON SPECIMEN D

TABLE 6-ELASTIC CONSTANTS BASED ON ACTUAL DIMENSIONS

*Pounds per Square Inch.

160. Consistency of Results.-Nine elastic constants were determined in the compression tests of specimens A, 13, and C. According

to the theory of elasticity, only six are independent. Consequently,

there must be three necessary relations between the nine constants.

These relations are expressed by equations 44, 45, and 46, and in an

alternate form by equation 47.
/"

/'

/

/

V

/

/

[7

2 V

/

TORSION TEST

/'

MOOULUSOFELASTlCIT.... 140LB5. PER SQ. IN.

,

/'

/0 0.005 0,01 0,015 0,02 0025 003 0.035 u.04 0.045 0.05 0,0 5 0.06

APPLIED

\~~~~~~

AV[RAGE ""[RAGE

LOAD TOTAL Ut<llT

PQU"IOS ~~~~g~OEf. CEF.

0 0 0 0

I 1.1 85 0.177 0.0084

2 2.370 0.360 0.0171

, 3.555 0.540 0.0251

. 4.7400.737 0.0351 ,

5.925 0.893 0.0425

6 7.11 1.053 00501

Specimen Mean Maximum Mean Maximum

-----~-_._._- ~--- --------~

.

A 6 10 3 8

B 5 10 1 2

C 2 4 5 7

RUBBER"LITHARGE MATERIAL 273

0

0

«

~

0,

0

z

«

.w%

0

~

Z

~

7

Z

U

Z

«

i6

«w

;!:'

z

~

~

~.

UNIT DEFORMATION

NOTES

Unit shearing stress 5s" -¥-

"

~2:3" US5p

Unit sheorlng strain Os" *:: 5.~84_8;.78" O.0476e

T =-Applied torque

p" A pplied load

0" Radius of specimen

e:: Totol observed deflection of troptometer

R:: Lever, arm of troptometer

l" Gage length of specimen

~

'

1j

:~~::

TEST SPECIMEN

FIGURE I77-TORSION TEST ON SPECIMEN E

The exactness with which theoretical relations are satisfied by

experimentally determined constants furnishes an indication of the

consistency of the experimental work. Results obtained by substiTABLE 7~-COKSISTENCY OF TEST RESULTS DETER MIXED

BY EQUATIOKS 44 TO 46, INCIXSIVE*

Original Dimensions Actual Dimensions

~- ------.-.-----.---.

*Tabular quantities are percentages, as explained in the text.
V

/

/

V

'/

a

j

/

a /

V

/

:/

a /

a _/

°V

/ FLEXURE TEST

AYRAG~ MODUlUS OF ELASTIC'iTY

42 e La. PER 5,Q.IN.

a 001 002 0 . 004 00' 00" 00' 008 009 10 I

274 MODEL TESTS OF BOULDER DAM

20

2000

1800

'.00

U)1400

a

~120

z

c..

..

"~IOO

~::;

~

80

0

c

~

.0

40

DEFLECTIONAT MIDSPAN IN INCHES

Modulus of elasticity determined from

Load-deflection diagram as follows:

E.7/a ;}f. '~gox~~~~02.~~5S.. 428 lb.per sq.Inch

E =Mo dulus of elasticity

p. Applied load in grams

A= Deflection of midspan

I = Moment of inertia

p

ATEST SPECIMEN

3".:''' _16"

FIGURE 178-FLEXURE TEST ON SPECIMEN F

tuting the values of the elastic constants found for specimens A, B,

and C, in the theoretical equations, are summarized in table 7. The

amount by which the larger of the two sides of the equation exceeded

the smaller was expressed as a percentage of the smaller. Values of

maximum and average variations are given in the table for three

relations of equations 44 to 46, inclusive. Computations were made

for elastic constants based on original dimensions, as given in table

5, and for those based on actual dimensions, as given in table 6.

161. Computed Volume Modulus.-Values of the volume modulus of elasticity, as computed by equation 48, are given in table 8.

As explained in section 149, the large negative values are the result

of Poisson's ratios slightly larger than 0.50.
Specimen

I

Original Dimensions Actual Dimensions

A -1,890 - 4,170

B -1,200 - 4,540

C -1,890 - 25,000

RUBBIDR-LITHARG E MA TIDRIAL 275

TABLE 8-VOLUME MODULUS OF ELASTICITY

162. Discussion of Results.- The determination of the proper

value of the modulus of elasticity to use in analyzing test data obtained

on the model was complicated by the following causes:

1. There were some variations in the elastic properties of

the material due to variations in curing different batches at the

manufacturing plant.

2. The modulus of elasticity differed in different directions

and there was no way of determining how the transverse axes of

the different slabs were oriented in the model.

3. Two sets of values for elastic constants were obtained

for specimens A, B, and C, depending on whether original or

actual dimensions were used in computing stresses and strains.

The effect of variation in the material was minimized by building up a specimen from sheets selected at random. This was done in

the case of specimen C. The uncertainty as to direction of the transverse elastic axes was also taken into account in specimen C, due to

the method of assembling the block. Effects of differences in elastic

properties along different axes were averaged in specimen B, where

horizontal directions of blocks cut from the same slab were alternated

in building the specimen. Values of Ex and Ey were the same for

specimen B, indicating that the specimen was isotropic in the transverse plane. There was a difference of about six per cent in these

values for specimen C. For specimen A, which had the reference axes

parallel, Ex, computed on the basis of actual dimensions, was 18 per

cent larger than Ey. When average values of Ex and Ey were computed

for the three specimens, they were found to be consistent.

Whether elastic constants, computed on the basis of original dimensions or those based on actual dimensions, should be used in

analyzing the model is problematical. First of all, it is certain that

some error is involved in the determination of at least one set of

values, due to the assumption that the stress-strain curve was a
276 MODEL TESTS OF BOULDER DAM

straight line. Since the change from original to actual dimensions

involved a correction of the second degree, if one stress-strain curve

was a straight line, the other must have had a small curvature.

An isotropic material cannot increase in volume under uniform

pressure. Consequently, the maximum value which Poisson's ratio

can have for an isotropic material is 0.50. For this condition the volume modulus is infinite. If these restrictions are assumed to hold for

the anisotropic rubber-litharge material, they are best satisfied by

the values of Poisson's ratio based on actual dimensions. These have

an average for the three specimens of 0.510 as compared with an

average of 0.544 for the values based on original areas. The values

computed for the volume modulus, as given in table 8, also favor the

constants based on actual dimensions, since the computed volume

modulus more nearly approaches infinity.

Two specimens, D and E, were tested in compression under small

values of load, so that the effect of using actual dimensions in determining the elastic constants was small. These tests gave values of

moduli slightly larger than the values found for specimens A, B, and

C, based on actual dimensions.

The moduli of elasticity in tension for specimens D and E were

found to be about 90 per cent of the corresponding compression

moduli. If actual dimensions were used in computing values of stress

and strain, the tension moduli would be increased and the compression moduli decreased, so that the values would be very nearly equal.

The modulus of elasticity in shear for specimen D, with transverse joints, satisfied very closely the relation of equation 68, namely,

that the shear modulus should be one-third of the tension or compression modulus when Poisson's ratio equals 0.50. The modulus

of elasticity in flexure is subject to a small correction for the effect

of shear stress.

In the analysis of the model, it was important that the ratio of

the modulus of elasticity in the vertical or z direction to that in the

transverse direction be determined as closely as possible. This ratio

was approximately y/g, with very little variation in the specimens

tested.

163. Conc1usions.-In view of the test results and the foregoing

discussions, the following value~ of the elastic moduli are considered
RUBBffiR-LITHARGE MATERIAL 277

to be the average for the rubber-litharge material used in building the

model.

Stress Condition Modulus of Elasticity,

lb. per sq. in.

343

389

120

Tension and 1

Vertical

compression: J

Transverse

Shear: Vertical

The average value of Poisson's ratio is considered to be 0.50.

THERMAL EXPANSION

164. Specimens and Apparatus.-Determination of the coefficient of thermal expansion was made by using 3 by 4 by 24-inch

beams, built up from strips three inches wide, cut from one 24 by 24

by I-inch slab. The apparatus was the same as that used in determining the coefficient of thermal expansion of soft plaster beams, illustrated in figures 64 and 65. Small steel bearing plates were cemented

to the ends of the beam for use in the measurements. Changes in

length were measured with two dial gages reading to one tenthousandth of an inch. The gages were supported by the steel yoke

and rested against the steel plates on the ends of the specimen.

Changes in length of the specimen were determined by comparing

observations made on the specimen with those made on a reference

bar kept at constant temperature.

165. Determination of Coefficient.-Two sets of tests were made.

In the first set the beam was cooled from an initial temperature of

75 degrees Fahrenheit. In the second set the beam was heated from

a temperature of 75 degrees. The rubber-litharge beam was so soft

that there was considerable difficulty in placing it in the measuring

yoke so that it would be unrestrained. Finally, the beam was placed

on a greased plank so that it would be free to expand or contract, and

the yoke placed over it.

The results of the tests of thermal expansion showed that the

coefficient was not a linear function of temperature. In considering a temperature test of the model, it was evident that the value of

the coefficient would depend on the range of temperature change. The

initial temperature of the model would probably be the same as the

atmospheric temperature in the testing room, which usually was
278 MODEL TESTS OF BOULDER DAM

about 75 degrees. If the model were cooled to 35 degrees, the coefficient of expansion to be used in analyzing the results would be

0.000,065 inches per inch per degree Fahrenheit. If the model were

heated to a temperature of 100 degrees, the coefficient of expansion

would be 0.000,078 inches per inch per degree Fahrenheit. The temperature tests of the model are described in chapter XII.
CHAPTER IX-CONSTRUCTION OF RUBBERLITHARGE MODEL

MODEL BASE

166. Reconstruction of Testing Pit.-The rubber-litharge model

was constructed in the pit where the previous models had been tested.

In order to accommodate the new model, considerah1e reconstruction

was necessary. First the concrete base and abutments for the p1astercelite model were removed. As the height of the new model was

greater than the depth of the pit, it was necessary to add heavy concrete curbs along the tops of the sides. Concrete cross-walls, joining

the ends of the curbs, completed the model enclosure. The shape

of the inside of the pit was determined by the requirements for the

rubber supplemental base. The reconstructed testing pit is shown in

figure 179.

167. Boundary of Supplemental Base.-Some uncertainties had

arisen concerning boundary conditions of the bases of previous

models. Methods of analyses have been developed for the deformation

of the foundation and abutments of dams, based on the assumption

that the rock is homogeneous, isotropic, and infinite in extent. Although such conditions never exist at actual dams, it was considered

desirable to make the supplemental base of the rubber-litharge model

somewhat thicker than the supplemental base of the p1aster-celite

model. Consequently, a minimum thickness of two feet was assumed

for the supplemental base, with a minimum extension of two feet upstream and downstream from the base of the model. This was twice

the minimum thickness used for the p1aster-celite model. For the

scale selected, the thickness of the supplemental rubber-litharge base

was one-half the height of the model. Figure 180 shows the design of

the reconstructed testing pit, rubber-litharge model, and supplemental

base.

168. Reservoir.- The upstream cross-wall of the testing pit

enclosed a space upstream from the dam to provide a reservoir. Drain

279
280 MODEL TESTS OF BOULDER DAM

FIGURE 179-RECONSTRUCTED TESTING PIT

and overflow pipes were provided as shown on figure 180, and suitable

valves were installed to control the reservoir water surface. A drain

pipe was laid in the bottom of the pit to carry discharged water to

the sump at the downstream end of the pit. The original sump was

enlarged and connected to a larger sump, outside the pit, where a

pump was installed for emptying the sump and filling the supply tank.

The supply tank, located in the basement adjacent to the testing room,

had a capacity of about forty cubic feet. A gas heater was attached

to the supply tank, for controlling the temperature of the water. Two

1 ~-inch diameter pipe lines were laid from the supply tank to the

reservoir, so that the reservoir could be quickly filled.

169. Laying Rubber-Litharge Slabs.-The method of building

the supplemental base is shown in figure 181. The rubber-litharge

slabs were not exactly uniform in thickness. Consequently, considerable fitting was necessary before a layer could be cemented in

place. The usual procedure was to fit the slabs for an entire layer

before cementing. This included trimming the slabs along the edges

of the layer and grinding off excess thickness where necessary. The

slabs were cut and trimmed with a band saw. A jet of water was

allowed to impinge on the saw blade, just above the rubber, to prevent the blade from binding. The saw was equipped with a device

for tilting the table, so that bevel cuts could be made as required. A

motor-driven sanding drum was used in grinding the slabs to the

proper thickness.
CONSTRUCTION OF RUBBER-LITHARGE MODEL

10< 21'.0"

r<>--- -5'-0"-- ~ n_- --11"0"

Sr>-

A

AL- -5A

sL>-

PLAN

-~/'r--

_u

8'-0"

i-- --5'-3f'

1232

SECTION A-A

'"'"

SECT ION B-B

FIGURE 180-TESTING PIT, RUBBER-LITHARGE MODEL,

AND SUPPLEMENTAL BASE

281

~~
282 MODEL TESTS OF BOULDER DAM

FIGURE 181-CONSTRUCTING THE SUPPLEMENTAL BASE

As soon as the slabs for a layer had been fitted, each was carefully cleaned with benzol. Rubber cement was then applied to the

bottom faces and edges of the slabs and the slabs placed in position.

The cement caused the slabs to shrink slightly while the cement was

wet, but the rubber regained its normal volume as soon as the cement

dried. The shrinkage of the slabs caused the vertical joints to open

slightly. As soon as the cement was thoroughly dry, the joints were

closed by hammering until a tight fit was obtained. The joint between

the rubber slabs and the concrete support was filled with quick-setting

building plaster to complete the layer. The supplemental base, built

to elevation 505, is shown in fig-ure 182.
CONSTRUCTION OF RUB,BERcLITHARGE MODEl

FIGURE 182-SUPPLEMENTAL BASE BUILT TO ELEVATION 505

NSTRUCTION OF MODE

170. Plans for Model.=-Plans for the model were made from

the design drawings for Boulder Dam, changing all dimensions to

conform to the scale of the model. Figure 183 shows the plan of the

dam, study 37, and figure 184 shows thicknesses and radii at the

crown cantilever, reduced to the scale of the model. Figure 185 shows

the abutment excavation lines at the dam.

A contour map of the dam and adjacent canyon, on a scale of I

to 180, was drawn on wallboard; and lines for the abutment excavation

were added by transference from figure 185. The adopted scale of

1 to 180 made one inch on the model correspond to 15 feet on the dam.

In constructing the model, slabs having a thickness of one inch were

used, so that each layer had a thickness corresponding to 15 feet on

the dam. This facilitated the laying out of the patterns for the model

and the topography of the canyon. When completed, the top of the

model was at elevation 1236 or about one-fourth of an inch higher

than the scale requirement.

In placing each layer, the arch element of the model was cut out

from patterns and cemented first. The abutments and canyon topography were next placed. This procedure insured a tight fit of the

model against the abutments. Any variation in the width of the
284 MODEL TESTS OF BOULDER DAM

\0

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II

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~j

FIGURE 183-PLAN OF BOULDER DAM, STUDY 37

vertical joints was allowed to accumulate at the joint between the

rubber and the concrete, and the space filled with quick-setting building plaster, as in the construction of the model base.

171. Installation of Apparatus.-Tests of the plaster-ce1ite model

of Boulder Dam had shown that radial deflections were greater at

the arch center lines than at the downstream face. In the case of the

rubber-litharge model, greater differences were expected, because of

the large value of Poisson's ratio. To measure deflections at the arch

center lines and at the upstream face, invar steel rods were anchored

in the model at elevations 595, 700, and 915, as shown in figure 186.

Grooves, with sufficient clearance to prevent binding of the rubber

on the deflection rods, were cut in the top of the sJabs after placing.
CONSTRUCTION OF RUBBER-LITHARGE MODI~L 285

k--_uunuu---uu Radius to axis 33.33"

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RD 29.83"

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FIGURE 184-DIMENSIONS OF MODEL AT CROWN SECTION

The rods were then inserted, and the grooves filled with cup grease.

A piece of thin paper was placed over the slot and the next layer of

the model added.

In planning the experimental program, a test to determine the

effect of temperature was included. Temperature changes had been

satisfactorily determined with thermocouples and a potentiometer in

the plaster-celite model tests. As a similar set of measurements was

desired for the rubber model, nineteen thermocouples were placed

in the model and adjacent foundation. The thermocouples consisted

of two wires, one of copper, the other constantan, each about twelve

feet long. The ends of each pair were soldered together and one connection was embedded in the model at the point where the tempera.

ture measurement was desired. The wires were placed in spaghetti

tubing for insulation.

172. Waterproofing the Upstream Face.-As soon as the model

was completed, the entire upstream face was carefully cleaned and

covered with uncured gum rubber to prevent uplift pressure from

occurring within the model. This type of rubber had no elastic prop.

erties, so the action of the model wa5 not affected by the waterproof
FIGURE 185-ABUTMENT EXCAVATION LINES AT BOULDER DAM

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CONSTRUCTION OF RUBBER.LITHARGE MODEL 287

FIGURE 186-MODE,L AND CANYON BUILT TO ELEVATION 595

Rods in Place for Measuring Downstream Movement of Upstream

Face and Center Line

membrane. The edges of the gum rubber sheet were sealed with asphaltic putty at the junction of the upstream face and the abutments.

Figure 187 shows the completed rubber-litharge model.

Tests of the reservoir upon completion of the model revealed a

few small leaks through the abutments. These were sealed by painting

the entire reservoir with several coats of rubber cement. The junction of the supplemental base and the concrete was sealed with a

strip of inner tube rubber, which was caulked into a groove in the

concrete wall and cemented to the rubber base. All seams and joints

that might possibly leak were coated with asphaltic putty.
288 MODEL TESTS OF BOULDER DAM

FIGURE 187-THE COMPLETED RUBBER-LITHARGE MODEL

173. Reference Structure.-After completing the model, the

structure shown in figure l&g was constructed for reference use during the progress of the testing work. Since temperature changes in

the reference piers and steel instrument stands of other models had

introduced small errors, an effort was made to reduce such errors by

using laminated wood construction. The reference structure consisted of two parts, a beam fifteen feet long by twelve inches square

and a laminated wood instrument stand. The beam was built of

2 by l2-inch planks which had been thoroughly seasoned. The planks

were bolted together and fastened to the curb which supported the

supplemental base, as shown in figure 188. 1'he detachable reference

pier, for supporting instruments, was made of 1 by 8-inch planks,

glued and bolted together. This stand was used to support micrometers, gages, and other apparatus used in measuring deflections.
CONSTRUCTION OF RUBBER-LITHARGE MODEL

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SECTION A-A

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END ELEVATION

FIGURE 188-REFERENCE STRUCTURE FOR DEFLECTION

MEASUREMENTS

CHAPTER X-DEFLECTION MEASUREMENTS

RADIAL DEFLECTION TESTS

174. Apparatus.- The general layout of appara' us for measuring radial deflections was similar to that used in the plaster-celite

model tests. Inserts were set in the downstream face for measuring

deflections of cantilever and arch elements at the locations shown in

figure 189. Inserts consisted of specially made aluminum tacks with

spherical heads which were forced into the rubber at the points of

measurement. Invar steel rods were fastened to the laminated

wood reference pier and alined so that dial gages could 1;e mounted

in directions radial to the axis of the model. Gages were set to bear

against the inserts in the downstream face.

Owing to the low modulus of elasticity of the rubber-litharge

material, this model was more flexible than any model previously

tested. Radial deflections were much greater than the range of available dial gages which measured to one ten-thousandth of an inch.

I t was therefore necessary to procure additional dial gages which had

a range of 0.25 inches and measured to one-thousandth of an inch.

Figure 190 shows a typical arrangement of gages for radial deflection measurements. The top row of gages are set to measure

deflections at the downstream face. The two pairs of gages at the

center and lower part of the model are set to measure radial movements of the rods anchored at the center line and at the upstream face.

As there were not sufficient gages available to measure deflections at

all inserts at one time, it was necessary to make a large number of

tests to complete the deflection measurements.

175. Test Procedure.- The method of making radial deflection

tests was as fol1ows. Initial readings of the gages were made with

the reservoir empty. Temperatures of the air, model, and reservoir

water were also noted. As the coefficient of linear expansion of the

rubber-litharge material was rather high, about ten times that of

concrete, an effort was made to have the three temperatures the same.

The temperature of the water in the supply tank was regulated by

231
CANTILEVER MtASURING SECrION$

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FIGURE 189-INSERTS FOR DEFLECTION MEASUREMENTS
DEFLECTION MEASUREMENTS 293

FIGURE 190-TYPICAL ARRANGEMENT OF GAGES FOR RADIAL

DEFLECTION MEASUREMENTS

using a gas water heater attached to the tank, or by adding cold

water from the city supply. Water was allowed to flow by gravity

from the supply tank to the reservoir. It required about twenty

minutes to fill the reservoir to elevation 1232. Hook gages were used

to determine the water surface elevation. Gages at the downstream

face of the model were read and the reservoir allowed to drain. The

water drained into a sump and was then pumped back into the supply

tank. Thirty to forty-five minutes were usually allowed for the

model to return to its initial position.

Deflection measurements were made for full load and for a range

of partial loads. For partial loads, observations were made with the

reservoir surface at elevations 900, 950, 1000, 1050, 1100, 1150, and

1200.
294 MODEL TESTS OF BOULDER DAM

176. Full Load Deflections.--Results of radial deflection tests

made with the reservoir surface at elevation 1232 are shown in figures

191 and 192. In general, the deflection curves were similar to those

obtained in the tests of the plaster-celite model. As shown in figure

191, the arch element at elevation 1232 deflected upstream at the

abutments about the same as in the plaster-celite model. The maximum upstream deflection of 0.006 inches occurred at the Nevada abutment. The maximum downstream deflection of 0.166 inches occurred

at the crown of the top arch. At elevation 1100 the deflection of the

arch at the Arizona abutment was greater than at the Nevada abutment. Deflections were 0.015 inches and zero at these respective

locations. A similar condition existed at elevation 1000 where the

deflection was 0.022 inches at the Arizona abutment, and 0.011 inches

at the Nevada abutment. This lack of symmetry in deflections at the

abutments was also found in the tests of the plaster-celite model.

Between elevations 900 and 600, appreciable deflections occurred

at both abutments. As the arch elements were relatively thick in this

part of the model, the opportunity for bending was small. Deflections at the abutments were primarily due to shear. Owing to the

greater depth and extent of the foundation, abutment deflections

were relatively larger than in the tests of the plaster-celite model. In

the lower elevations of the model, the deflections at the abutments

were large in proportion to the deflections at the crown section. At

elevation 700, the deflection was 0.024 inches at the abutments and

0.039 inches at the crown. Deflections at elevation 600 were 0.024

inches, 0.028 inches, and 0.020 inches at the Arizona abutment, crown,

and Nevada abutment, respecti\'ely.

Radial deflections of cantilever elements are shown in figure 192.

As in the case of the arch abutments, there was considerable deflection at the foundations of the cantilever sections. Due to the flexibility of the rubber-litharge material, the restraining effect of negative loads on the cantilevers, caused by the upper arches, was not pronounced.

177. Squeezing of Model.-Considerable differences between the

deflections of the upstream and downstream faces of the model were

noted. The rods for measuring deflections at the upstream face

and at the arch center lines were located as closely as possible

to cantilever section E. The results of these measurements for the

full water load are shown on the deflection curve for cantilever E in

figure 192. The deflection of the model at elevation 600 at the upstream
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Neqatlve deflection denotes upstream movement.

FIGURE 191-RADIAL DEFLECTIONS OF ARCH ELEMENTS, LOAD AT ELEVATION 1232

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FIGURE 192-RADIAL DEFLECTIONS OF CANTILEVER ELEMENTS, LOAD AT ELEVATION 1232
DEFLECTION MEASURE'MEN'fS 297

face was about twice the deflection at the downstream face. At the

higher elevations the differences were smaller. Differences between

deflections at the arch center lines and the downstream face were

relatively small. indicating' that most of the squeezing of the model

occurred between the upstream face and the arch center lines.

178. Partial Load Deflections.--Radial deflection measurements

were made for partial load conditions with the reservoir water surface

varying at 50-foot increments between elevations 900 and 1200. Results of partial load tests were very similar to those obtained in the

tests of the plaster-celite model. \Vhen the reservoir water surface

was above elevation 1100, the maximum deflection occurred at elevation 1232. \Vith the reservoir water surface at elevation 1100 or lower,

the maximum deflection occurred below the top of the model, indicating the presence of vertical tensile strains at the downstream face.

Table 9 gives deflection data for loads at elevations 1232, 1100. and

1000.

179. Consistency of Repeated Tests.- The radial deflection tests

showed that the model was highly elastic if load was applied for

short intervals of time. Variations between repeated tests, performed

under the same conditions, were always small. Table 10 contains

measured deflections of cantilever section E, obtained in several different tests. The tabulations show that the observations agreed very

closely. Recovery after unloading was very consistent if a sufficient

interval of time was allowed in each test. The small discrepancies

which sometimes occurred were usually traceable to a change in temperature, insufficient time for recovery, or some local cause such as a

gage sticking or working loose on its support.

The model flowed appreciably under sustained loads. As flow

was not desired in deflection tests, the reservoir was filled as rapidly

as possible and the measurements made before appreciable flow occurred. Zero readings of the gages could be recorded, the model

loaded, and load deflections measured in about half an hour. Draining the reservoir required only ten or fifteen minutes, so that the

entire test could be completed in less than an hour.

TANGENTIAL DEFLECTION TESTS

180. Installation of Micrometers.-For measuring tangential deflections of the model, it was planned to use dial gages, mounted on
Deflections Deflections

Insert Reservoir Water Insert Reservoir Water

Elev. No. Surface Elevation Elev. No. Surface Elevation

--- - --- -

1232 1100 1000 1232 1100 1000

-- - --~-- - -

3 -6 -4 -2 2 18 10 6

4 -5 -3 -2 3 26 16 9

5 -3 -6 -3 4 46 25 17

6 28 0 -1 800 5 55 33 20

7 85 14 3 6 50 29 17

8 137 30 9 7 31 18 10

1232 9 166 38 12 -- -- -

10 146 31 9 2 21 14 9

11 93 16 5 3 32 20 12

12 39 3 1 700 4 39 23 14

13 5 -3 -2 5 36 22 14

14 -3 -4 -2 6 24 15 9

15 -3 -2 0 --- -- - - -

-~-- -- - -- - 2 20 14 8

4 0 -1 -1 600 3 28 19 12

5 22 6 3 4 24 16 11

6 70 21 7

7 112 36 12 Deflections at 1100 8 128 42 15 Interior Points 9 109 36 12

10 77 23 7 Upstream Face

11 30 7 2

12 15 3 -1 El. 915 90 47 24

- -' El. 700 64 43 30

4 11 4 2 El. 595 50 37 28

5 46 20 9

6 86 38 17 Arch Center Line

1000 7 103 45 21

8 91 42 19 El. 915 82 42 22

9 56 24 11 El. 700 47 31 21

10 22 10 2 El. 595 32 22 16

--

NOTES

3 16 7 4 The unit of measurement is 0.001 of

4 28 15 8 an inch.

5 59 30 16 Positive values denote downstream

900 6 74 39 21 deflection.

7 67 35 19 Negative values denote upstream de8 39 20 11 flection.

9 27 12 5 For location of inserts, see figure 189.

298 MODEL TESTS OF BOULDER DAM

TABLE 9-RADIAL DEFLECTIONS FOR FULL AND PARTIAL LOADS

IIwar rods, similar to those 11sed for measuring radial deflections.

Some difficulty was encountered in mounting the gages so that local

strains would not occur around the inserts. By using micrometer

screws which measured to 0.001 of an inch this difficulty was avoided.

As the available micrometers were of much lighter weight than the

gages and contained no springs to actuate their movement, they
eva IOn ---~~ -----~

98 99 100 123 124 125 996

4-28-33 4-28-33 4-28-33 4-28-33 5-4-33 5-4-33 10-7-33

-- - --

1232 166 166 166 166 167 169 163

1100 127 129 128 129 129 130 126

1000 102 102 101 101 101 102 ......

900 75 75 75 74 73 74 76

800 55 55 56 55 55 55 54

700 39 38 38 38 38 38 40

I

608

I

28 28 28 28 28 28 29

DEFLECTION MEASUREMENTS 299

TABLE lo-RADIAL DEFLECTIONS OF CANTILEVER SECTION E

(Thousandths of an Inch)

Test Number and Date

El t"

proved very satisfactory. The general arrangement of apparatus is

shown in figure 193.

The micrometers were mounted in a tangential direction on invar

steel rods. Brass pins, having polished pointed heads, were bent to

an L shape and forced into the rubber at points where measurements

were desired. The micrometers were adjusted to bear against the

pointed heads of the pins. Contact was determined by a 2-volt electric circuit which caused a flashlight bulb to glow. This system was

very satisfactory, as repeated readings checked within 0.001 of an

inch. The micrometers were mounted about one-half inch from the

downstream face of the model; so it was necessary to apply small

corrections to the observed readings to obtain deflections at the face

of the model.

181. Procedure.-The method of testing was similar to that used

in making radial deflection tests. Zero readings were made with the

reservoir empty. The reservoir was filled and readings made for the

loaded condition. The reservoir was then emptied and a period of

about thirty minutes allowed for recovery. Usually the micrometers

were set to measure the tangential deflection of one arch element at

a time, so that the test could be completed before appreciable flow

occurred in the model.
300 MODEL TESTS OF BOULDER DA~

FIGURE 193 APPARA IS FOR MEASURING

AT ELEVATION I:

'ANGENTIAL DEFLECTIONS

2

182. Full Load Deflections.- Tangential deflection measurements, maqe with the reservoir water surface at elevation 1232, are

shown in 6gure 194. The symmetry of the deflection curves obtained at the different elevations was remarkable. The line of zero

deflection coincided with cantilever section E, except at elevations

1232 and 800. At elevation 1232, the point of zero deflection was about

tbree-fourtbs of an inch toward the Nevada abutment from section

E, and at elevation 800, it was about one inch toward the Arizona

abutment from section E. Tangentiat deflection curves reached their

maximum values n~ar the quarter points of the arch elements, except

below elevation 800 where arch elements were relatively thick. Below

etevation 800, maximum tangential deflections occurred at the abutm~nts.

'he angential deflection, 0.057 inches, occurred at ele argest
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DEFLECTION MEASUREMENTS 301

,-CROWN CANTILEVER E

ARIZONA ABUTMeNT

13 1-'

15 NEVADA ABUThilEN'T

60 3 4

IN5ERl NUMBERS,'

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ELEVATION 1100

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-

Indicates deflection to left when looking upstream

For locotion of inserts see Figure 189

FIGURE 194-TANGENTIAL DEFLECTIONS OF ARCH ELEMENTS,

LOAD AT ELEVATION 1232
TABLE ll-TANGENTIAL DEFLECTIONS FOR FULL AND PARTIAL LOADS

Deflections Deflections

Elev. Insert --- Elev. Insert

No. Reservoir Water No. Reservoir Water

Surface Elevation Surface Elevation

-- - ---

1232 1100 1000 1232 1100 1000

-- -- -- - ----

3 -12 -

6 - 2 4 -34 -20 -12

4 -19 - 6 - 3

5 -28 -11 -

7

5 -37 - 9 - 3 900 6 -

2 0 0

6 -57 -16 -

5 7 27 12 6

7 -52 -15 - 5 8 39 21 11

8 -28 -10 - 3 -----

1232 9 3 0 0 2 -22 -12 - 7

10 32 9 2 3 -25 -15 - 9

11 47 14 6 4 -18 -11 - 6

12 54 15 5 800 5 - 5 - 2 -2

13 40 11 4 6 14 8 5

14 25 8 4 7 25 15 8

15 22 7 3 ---

- - 2 -13 -11 - 5

4 -34 -13 - 5 3 -10 - 6 - 3

5 -45 -16 - 5

700 4 0 1 0

6 -53 -20 - 7 5 12 11 5

7 -30 -10 - 3 6 14 9 5

1100 8 0 1 0 ---

9 29 11 4 2 -12 - 7 - 4

10 51 19 6 600 3 - 1 2 - 1

11 50 19 6 4 5 4 3

12 36 12 7

The unit of measurement is 0.001 of

-- -

4 -38 -16 - 8

an inch.

5 -44 -18 - 7 Positive values indicate deflection to

6 -30 -13 - 5 right when looking upstream.

1000 7 - 2 - 1 - 1

8 27 12 6 Negative values indicate deflection

9 48 22 10 to left when looking upstream.

10 35 16 7 For location of inserts, see figure 189.

302 MODEL TESTS OF BOULDER DAM

vation 1232, insert 6, on the Nevada side of the model. The corresponding deflection at the same elevation on the Arizona side, insert

12, was 0.054 inches. At elevation 1100 the maximum deflections

were slightly smaller, being 0.053 inches on the Nevada side and 0.052

inches on the Arizona side.

183. Partial Load Deflections.-In general, partial load deflection curves were similar to those shown for full loads, except that the

tangential movements were smaller. With the reservoir water surface

at elevation 1000 or lower, most of the tangential movement occurred

below elevation 1000. Tangential deflections in the upper part of

the model were practically negligible. Data from observations of

tangential deflections during full and partial loads are given in table 11.
DEFLECTION MEASUREMENTS 303

SLOPE DEFLECTION TESTS

184. Apparatus.-Since slope deflections of the arch elements

were relatively small, a precise system of measuring angular changes

in the order of one one-hundred-thousandth of a radian was necessary.

The optical lever system, developed for the plaster-celite model tests,

was used for the slope deflection measurements on the rubber-litharge

model, see section 91.

Small optical flats, one and one-half inches in diameter, were

used as mirrors for the optical lever system. These were much lighter

in weight than those previously used. They were mounted in an

aluminum frame with trunnions supported by an adjustable yoke. The

yoke was attached to the rubber with small wood screws which were

coated with rubber cement before placing. vVith this system of support, an optical flat could be set in any desired direction. In order to

obtain sufficient length of radius for the optical lever system, transits

were mounted on concrete pedestals outside the building, in line with

a window and the model.

185. Procedure.-In making observations for sJope deflections,

the transit and mirror were set so that the telescope could be focused

on the reflection of the scale in the mirror. The scale reading was

noted by the observer and the reservoir filled to the desired elevation.

As the model deflected under load, the optical flat rotated slightly, due

to the angular or twist deflection. This rotation could be noted by

the change of the scale reading. The amount of rotation could then

be computed after correcting for the radial and tangential deflection

of the model at the insert at which the mirror was mounted. Since

it was not possible to move the transit during an observation, two instruments were used in this series of tests. Measurements were made

at the 48 inserts shown in figure 189. In filling the reservoir, the water

surface was held at four different elevations long enough to make an

observation at each elevation. The reservoir was then lowered to

the same elevations and check readings made.

186. Full Load Deflections.-Slope deflections measured with

the reservoir water surface at elevation 1232 are shown in figure 195.

With the exception of the slight irregularity at the Nevada abutment,

elevation 900, the curves were symmetrical about cantilever section E.

Maximum deflections of 0.0089 radians occurred at stations 7 and 11

at the top of the model. Slope deflections were materially smaller
.. / i'...

/

"

1/ ""-

--...., / -

'\. /

\.

/

60

40

20

-20

::: l

z

60

< 40 a

< 20

-20

-40

-60

z

,.

,0

z

0

,

u

u

0

h

./" "-

./

'-... /'"

'r---"

304 MODEL TESTS OF BOULDER DAM

NEVADA ABUTMENT

3 4 5

INSERT NUMBERS /"

CROWN CANTILEVER E

8 9 -' 10 12

ARIZONA ABUTMENT

I?I 14 15

20

so

60

40

-20

-40

-

60

-80

ELEVATION 1236

7 8 9

ELEVATION 1100

6 7 8 10

ELEVATION 1000

:~ ELEVATION 900

-20

:~ ELEVATION 800

2:~

-20 ELEVATION700

-:~ ELEV.600

NOTES

MeaSurements otelevotion 1236 mode ot

arch center line

AII others ot dOwnstream face of arch eleme nts.

-

Indicates clocKwise deflection when viewed

from above

+

Indicates counter clockwise deflection when

viewed from above.

For location of inserts see Figure 189

FIGURE 195-SLOPE DEFLECTIONS OF ARCH

LOAD AT JDL1DVATION 1232

ELEMENTS,
DEFLECTION MEASUREMENTS 305

at the lower elevations where the arch lengths were shorter and the

thicknesses greater.

The slope deflection curves were consistent with the radial deflection curves shown in figure 191. The radial deflection was upstream at both abutments at elevation 1232. The slope changed from

counterclockwise at the Nevada abutment, when viewed from above,

to clockwise as the radial deflection changed to downstream in the

Nevada half of the arch. At the Arizona abutment the slope was

clockwise at the end of the model where the deflection was upstream.

As the radial deflection became downstream the direction of the slope

changed. The maximum radial deflection of the arch at elevation 1232

occurred at insert 9. At this point the slope of the neutral axis of

the model was zero, and the measured slope deflection was zero.

187. Partial Load Deflections.-Measurements of slope deflections during partial loads were made with the reservoir water surface

varying at 50-foot intervals from elevation 900 to elevation 1200. The

deflection curves were similar to those shown for the full load tests,

except that the movements were smaller. Table 12 gives slope deflections measured at the different inserts during tests with the reservoir

water surface at elevations 1000, 1100, and 1232.

VERTICAL DEFLECTION TESTS

188. Effect of Squeezing.-In making deflection measurements

at cantilever sections, it was noticed that considerable vertical movement occurred at both upstream and downstream faces of the model.

The vertical movement was the result of squeezing that took place in

the model when water load was applied. The horizontal radial deflection of the upstream face was greater than that of the downstream

face; and, since it is difficult to compress compounds of soft rubber,

due to their high Poisson's ratio, the model deflected in the direction

of least restraint when the reservoir was filled. The result was that

vertical deflections were observed at both faces of the model. Tests

were next made in which vertical deflections of the model were

measured.

189. Apparatus.-Invar steel rods were attached to the upstream

face along horizontal arch elements below the top of the model, and

were alined so that vertical deflections were registered on dial gages

reading to 0.001 of an inch. Micrometers were mounted in vertical
Angle of Deflection Angle of Deflection

in Radians in Radians

Elevation Insert Reservoir Water Elevation Insert Reservoir Water

No. Surface Elevation No. Surface Elevation

1232 1100 1000 1232 1100 1000

3 0.000109 0.000016 -0.000021 3 -0.001161 -0.000810 -0.000540

4 0.000333 0.000313 0.000090 4 -0.001188 -0.000870 - 0 .000606

5 -0.001823 -0.000025 -0.000041 5 -0.001587 -0.001064 -0.000686

6 -0.007195 -0 001662 -0.000527 900 6 -0.000428 -0.000136 -0.000055

7 -

0 .008926 -0.002602 -0.000747 7 0.001682 0.000926 0.000531

8 -0.005023 -0.001840 -0.000596 8 0.002496 0.001625 0.000991

1236 9 0.000031 -0.000103 -0.000051

10 0.005363 0.001675 0.000502 3 -0.000968 -0.000708 -0.000512

11 0.008886 0.002609 0.000852 4 -0.000847 -0.000614 -

0 .000450

12 0.007578 0.001767 0.000529 800 5 0.000279 0.000094 0.000019

13 0.002903 0.000364 0.000145 6 0.001402 0.000898 0.000618

14 -0 .000373 -0.000184 - 0 .000092 7 0.001116 0.000926 0.000677

15 -0.000694 - 0 .000288 -0.000114

-~-. 2 -0.000699 -0.000577 - 0 .000465

4 -0.000709 - 0 .000355 -0.000179 3 -0.000717 -0.000573 - 0 .000401

5 -0.003275 -0.001245 -

0 .000442 700 4 -0.000142 -0.000116 - 0 .000056

6 -0.005528 -0.002213 -0.000771 5 0.000961 0.000670 0.000452

7 -0.003673 -0.001637 -0.000613 6 0.001410 0.000977 0.000722

1100 8 -0.000317 -0.000313 -0.000130

9 0.003657 0.001457 0.000573 2 -0.000762 -0.000560 -0.000413

10 0.005614 0.002178 0.000786 600 3 -0.000146 -0.000037 - 0 .000002

11 0.004247 0.001450 0.000519 4 0.001725 0.00114] 0.000744

12 0.00157] 0.000683 0.000311

-~-~~ All measurements made at downstream face of arch element

4 -0.000387 - 0 .000302 - 0 . 000205 except at El. ]236 where measurements were made along

5 -0.002997 -0 00]554 -

0 .000779 center line of arch element.

6 -0.002989 -0.001519 -0.000723 Positive values indicate counterclockwise deflection when viewed

WOO 7 -0.000130 -0.000311 -0.000207 from above.

8 0.002294 0.001134 0.000567 Negative values indicate clockwise deflection when viewed from

I

9

I

0.004568 0.00202] 0.00093] above.

W 0.002321 0.001190 0.000525 ,

TABLE 12-SLOPE DEFLECTIONS FOR FULL AND PARTIAL LOADS ""

0

""

;:::

0

t:I

trJ

r<

>'3 trJ

rn

>'3

rn

0

"'J

b:I

0

d

r<

t:I

trJ

::0

t:I

>

;:::
DE~"'LECTION MEASUREMENTS 307

directions at the downstream edges of the arch elements and at the

top arch at the upstream face. The arrangement of apparatus for

measuring vertical deflections at the top arch is shown in figure 196.

Contacts of the micrometers were determined by an electric circuit,

as in preceding tests. Dial gages were installed for measuring vertical

deflections at the crown cantilever, as shown in figure 197.

FIGURE 196-MICROMETERS FOR MEASURING VERTICAL

DEFLECTIONS OF TOP ARCH

190. Results.-\Tertical deflections of the arch elements during

full load are shown in figure 198. A comparison of full load and partial

load deflections is given in table 13. Vertical deflections of arch elements were consistent with horizontal radial deflections. In the central

portion of the model, where the radial deflection was downstream,

bending in the cantilever section caused the upstream edge of the

model to deflect higher than the downstream edge. At the abutments

of the upper part of the model, where the radial deflection was upstream, bending of the cantilever elements caused the downstream

edge of the model to deflect higher than the upstream edge.

During full load tests, vertical deflections at the top of the model
308 MODEL TESTS OF BOULDER DAM

were about 40 per cent of the horizontal radial deflections at the upstream side and about 25 per cent of the radial deflections at the downstream side. For partial reservoir loads, ratios of vertical deflections

to horizontal radial deflections were slightly higher. Such conditions appear to be abnormal and probably occur only in models made of

soft materials having a high Poisson's ratio.

FIGURE 197-DIAL GAGES FOR MEASURING VERTICAL DEFLECTIONS

AT THE CROWN CANTILEVER

Figure 199 shows results of vertical deflection measurements at

the crown cantilever, also results of horizontal and normal deflection

measurements at the same section, measured movements being plotted

on an exaggerated scale in all cases. The deflection diagrams show

the effect of squeezing between the upstream and downstream faces

of the model. Downstream movements were greater at the upstream

face than at the downstream face. The greatest vertical movement

occurred at the upstream edge of the top of the section. The vertical

deflection measurements showed a slight rising of the supplemental

base downstream from the model, and a relatively greater lowering
8 9

'0 " " "

, '0 : I

I

,

, ,

,

I

"

..--...X---- -X-... I

"

,

'

,

,

,X' 'X , ,

,

/

0'

,

,

"

:

"

,

:

: ~I//' ~"- ' 0' I

O~

~1__-/ " 1-- :

------""")' " '--

-- - - -

-----1I,

,

: '

'

0 8 7 ---_.'~" 9

'0 "

,

/_x'T

I 0 '~" :

-+- ",

W-- "'- ~I

:

'

.'"

"

j ,

,

'

,

,

I

I

0 "X-- 7

'

8,

,

/,-::l/ "'

,

,

' ~,

'

-I ,

'-~

,

,

I :

'

DEFLECTION MEASUREMENTS 309

NEVADA ABUTMENT INSERT NUMBERS ARIZONA ABUTMENT

00

ELEVATION 1236

00

00

10

80

.0

10

00

~UPSTREAM ABUTMENT

r

-

DOWNSTREAM ABUTMENT

30

20

,0

~

U

Z

Z

<

~

..

~

~

0

Z

<..

~

~z

ELEVATION 1100

x :..

30

'0

z

0

~

~

<U

~

ELEVATION 1000 "EB==f~ 201 / -

X./--

"""" ",

:

IO~

0

"

,I

~ ' ELEVATION 900

20~

10 I

- -

. I

,x ,

,

'

0

ELEVATION 800

20~

101

: /

Xu ,

'"

;

0 L--i... ~

ELEVATION 700 'x

~:EJEEm :2

3 0

!

'x 0 '

ELEVATION600 '

>( x Deflection at upstream face.

~ Deflection at downstream face.

FIGURE 198-VERTICAL DEFLECTIONS OF ARCH ELEMENTS,

LOAD AT ELEVATION 1232
Elevation Insert 1

1232 1100 1000 No. i

U.S.* D.S.* U.S. D.S. U.S. D.S.

i-~I

3

I

18 18 9 10 5 5

4 21 24 10 12 7 7

5 23 30 II 14 7 8

6 29 37 13 16 7 9

7 43 41 16 17 7 9

8 56 42 19 17 8 8

1236 9 66 43 21 17 8 8

10 67 42 20 17 8 8

II 47 40 15 17 7 9

]2 32 34 12 15 7 9

]3 20 27 11 13 6 8

]4 19 23 11 ]3 7 7

]5 18 20 II 12 7 7

---

4 u-- 21 ]4 8

5

----

27

----

17

'u

8

6 31 3] II 19 6 9

7 39 34 13 19 6 10

1100 8 43 35 14 ]8 6 10

9 37 33 12 18 5 9

10 28 28 10 ]7 4 9

II 18 21 8 15 4 8

---_._--------~." .-- -----

4 15 17 7 14 4 9

5 27 19 10 ]5 5 ]3

6 35 20 ]2 17 5 14

1000 7 36 20 13 17 6 15

8 33 19 12 16 6 14

9 25 18 10 14 5 12

10 18 17 8 12 5 9

------------

A

**

I

13 15 7 II 4 8

4 22 15 8 12 3 10

5 27 16 9 14 2 II

900 6 29 16 9 14 1 12

7 '

I 25 15 8 13 1 II

8

I

I 18 12 6 12 2 9

A** I

I 7 4 3

----

hn

---- I--!

3 7 9 2 8 1 7

4 II 5 4 10 0 7

800 5 ]2 5 5 II 0 7

6 11 8 4 10 0 7

7 9 12 2 9 1 9

~_..~--- .~

A** -1 7 -4 7 -4 4

3 4 5 -1 6 -2 6

700 4 7 3 1 6 -1 6

5 5 3 0 5 -1 6

6 -3 4 -1 4 -2 5

1

I

2 2 3 3

600 3 3 -1 4 2 3 2

, 4 i

1 un 3 2

310 MODEL TESTS OF BOULDER DAM

TABLE 13-VERTICAL DEFLECTIONS OF ARCH ELEMENTS

(In Thousandths of an Inch)

Reservoir Water Surface Elevation

.U.S. indicates Upstream face. D.S. indicates DOWTll'tream face.

uA indicates Abutment.

For location of inserts, see figure 189.
DEFLECTION MEASURffiMENTS 311

VERTICAL DEFLECTION,

(RE5ER~51~V J.,)JiR SURFACE (f

..:L-:

'

,

'

,

ORIGINAL POS'TJON-~ "\,

123Z

"

'"

D

1100~

'3:>

1000g

~

~

900 5

;:

'">

800 ~

..MODEL OF BOULDER DAM\

"

Z

700 ~

0

~

600 ~

8

~.r~.

i-:-~§§9-

-.

-- - - - -

-_./

-----

< SUPPLEMENTAL BASE ,-.-

SECTION ON CENTER LINt OF MODEl..

100 0

I f I

..,

"'"

, -

,

SCAL~ OF DEFLECTION

IN THOUSANDTHS OF AN INCH

NOTES

x Deflection measured in" horizontal rodiol direction.

.. Deflection measured in vertical direction.

. Deflection measured in normal rodial direction.

iii Position determined by verticol and horizontal measurements.

. Position determined by vertical and normal measurements.

FIGURE 199-RESULTANT DEFLECTION OF CROWN CANTILEVER

of the supplemental base upstream from the model.

formation was caused by the reservoir weight.

The latter deCANYON MOVEMENTS

191. Downstream Movements.-Horizontal deflection rods were

attached at the junction of the downstream face with the canyon

walls. The rods were set parallel to the line of arch centers, so that

downstream movements of the canyon could be measured. A typical

arrangement of the apparatus is shown in figure 200. Gages were

mounted on the concrete curb at the downstream end of the test pit.

Observations were made with the reservoir water surface at elevation

1232 and at vertical intervals of 50 feet between elevations 900 and

1200. Results of the measurements are shown in figure 201.
312 MODEL TESTS OF BOULDER DAM

With the reservoir water surface at elevation 1232, the maximum

movement on the Arizona side occurred at elevation 1100 and

amounted to 0.0340 inches. At elevation 900 the movement was

slightly smaller, being 0.0334 inches. On the Nevada side the maximum movement occurred at elevation 900 and amounted to 0.0245

inches. At elevation 1100 the deflection corresponding to the maximum on the Arizona side was only 0.0200 inches.

FIGURE 200-MEASUREMENT OF DOWNSTREAM MOVEMENTS

AT ABUTMENTS

Maximum movements when the reservoir was partially full occurred at lower elevations than for full load conditions. Magnitudes

of the deflections are shown in the table in figure 201. \Vhen the

reservoir water surface was at elevations 950 and 900, deflections were

very small.

The data in figure 201 show that full load deflections on the Arizona side of the canyon were about one-third larger than on the
ELEV. OF

ELEVATION OF

POINT OF

RESERVOIR WATER SURFACE

MEASURE- 1232 1200 1150 1100 105011000

MENT DEFLECTIONS

1232 100 90 60 40 30 20

1100 200 170 1-20 60 60 .0

1000 206 177 128 97 72 .0

900 245 217 170 135 98 71

BOO 232 205 167 135 103 BO

700 221 192 163 135 106 83

600 131 122 92 69 70 72

ELEV. OF

ELEVATION OF

RESERVOIR WATER SURFACE

POINT OF

MEASURE- 1232120011150]11001050]1000

MENT DEFLECTIONS

1232 180 130 90 60 40 20

1100 340 270 IBO 120 70 50

1000 254 290 210 148 101 67

900 334 284 222 165 124 90

800 253 221 180 142 119 90

715 200 171 14B liB 92 70

600 150 140 121 90 BO 63

DEFLECTION MEASUREMENTS 313

§ 0

i5 0

12

0

~

,_,Line of contact between

..- dam and canyon wall.

§

..0

..

>

'"

z

..

z

0

N

a:

..

00

(

PLAN OF MODEL

0,. , , 100 200 300

S~~~~' OF DAM I~ FEET'

0 1000 2000

"""""

.

DEFLECTION IN TENTHOUSANDTHS OF AN INCH

NEVADA ABUTMENT ARIZDNA ABUTMENT

Deflections in ten-thousandths of on inch.

FIGURE 201-DOWNSTREAM MOVEMENTS AT ABUTMENTS
WATER ARIZONA GAGE LOCATIONS NEVADA GAGE LOCATIONS SURFACE

ELEVATION 1300 1232 1160 1100 1000 900 800 700 600 1300 1232 1160 1100 ,000 900 800 700 600

900 6 10 5 8 3 0 I 3 3

,

6 9 II 7 7

,

I 4

950 12 18 13 8 7 I 6 6 6 4 II II 8 7 I I 0 -6

1000 13

'0

13 II 7

,

3 7 8 4 15 15 15 9 7 -, -4 8

1050 19 26 23 16 8 I 0 5 6 6

'0 '0 19 7 I -4 -7 0

1100 23 30 '4 '0

10 I -, 4 6 6 25 '5 '4 9 0 -4 -II -,

1150 32 40 33 '48 -, -, 4 5 9 31 23 27 9 -, -5 -II -7 1200 43 50 33 25 5 -8 -II 3 4 13 45 46 38 12 -3 -4 -12 -II

1232 49 58 40 25 3 -14 -14 ,

0 16 50 53 4' 9 -0 -6 -13 -16

UPSTREAM CANYON WALLS

950 12 93 78 10 101 128

1000 50 139 109 25 116 13' 1050 61 154 103 .9 158 157

1100 103 194 131 74 154 157

1150 100 190 120 117 21' 187

1200 127 219 149 14' 220 197

1232 115 '09 131 170 '0. 107

314 MODEL TESTS OF BOULDER DAM

Nevada side. The differences between the movements on the two

sides of the canyon decreased with the lowering of the reservoir water

surface. The lack of symmetry of the measurements was consistent

with the radial deflection measurements which showed larger deflections on the Arizona side of the canyon. The difference was largely

due to the lack of symmetry in the structure, the upstream portions

of the arch elements being longer on the Arizona side.

192. Spreading of Reservoir Walls. - Measurements of the

spreading of the reservoir walls were difficult, since it was necessary

to make all observations under water. A vertical post was placed

between the concrete cross-wall and the 12 by 12-inch beam which

supported the reference pier. The post was located at the intersection

of the line of centers and the upstream gage line, as shown in figure

202. Horizontal measurements of the movement of each canyon

wall with reference to the vertical post were made at elevations 600,

800, and 1000. As in other derlection tests, dial gages and invar rods

were used for the measurements. It was necessary, however, to proNEVADA ARIZONA

"Central reference on all

downstream meosurements

PLAN

SECTION

NOTES

0 0 Position of measurement at

downstream canyon walls.

- Positionof measurement at

upstream conyon walls.

The unit of measurement is 0.0001

of on inch.

In the table of deflections, positive values indicate lengthening between

measuring points, and negative

values indicate shortening between

measuring points.

A possible error of approximately

10 percent moy hove been introduced due to submerginQ the

gages.

TABLE OF DEFLECTIONS

DOWNSTREAM CANYON WALLS

FIGURE 202-MEASUREMENTS OF SPREADING OF RESERVOIR WALLS
DEFLECTION MEASUREMENTS 315

teet the gages from water by covering them with a membrane of thin

rubber. When a gage was mounted with its face upward, the dial

could easily be read through the water with a pair of low-power field

glasses.

A table of measured deflections is shown in figure 202. With the

reservoir water surface above elevation 1100, movements were greater

at the Nevada abutment than at the Arizona abutment, due to lack of

symmetry. The maximum full load deflection was 0.0266 inches and

occurred at elevation 800 on the Nevada side. The corresponding

movement on the Arizona side was 0.0209 inches. \Vith the water

surface at elevation 1100, the deflection on the Arizona side at elevation 800 was 0.0194 inches, as compared with 0.0154 inches on the

Nevada side. The measurements may contain small errors due to the

use of dial gages covered with rubber membranes, located under water.

193. Spreading of Downstream WaIls.-Measurements of the

spreading of the canyon walls downstream from the model were made

along the gage line shown in figure 202. A vertical post was also

used as a central reference for these measurements, so that displacements of each side of the canyon could be obtained. Measurements

were made between elevations 600 and 1300. The section of the

canyon where the measurements were made was more symmetrical

than the section in the reservoir. Consequently the deflections were

more symmetrical. .When the reservoir was full the maximum spreading was 0.0058 inches at elevation 1232 on the Arizona side. The

corresponding measurement on the Nevada side was 0.0050 inches.

Below elevation 900, the spreading was negative, apparently due to

the effect of Poisson's ratio. The negative movements of the canyon

walls below elevation 900 decreased as the reservoir water surface

was lowered. Measurements made at elevation 1300 showed that the

spreading of the canyon above the top of the model was greater on

the Arizona side than on the Nevada side.

194. Changes in Chord Lengths.-Changes in chord lengths were

measured at the downstream face of the model, at elevations 1232 and

at 100-foot intervals between elevations 1100 and 600. The installation

of equipment for measuring changes in chord lengths is shown in

figure 203. Invar steel rods were fastened to the abutments at the

ends of each arch element, with pivot mountings, and held together

by flexible couplings. A dial gage was mounted on one bar so that

it would register the relative movement of the other bar. By using
316 MODEL TESTS OF BOULDER DAM

FIGURE 203-MEASURING CHANGES OF CHORD LENGTH

this system of mounting, bending of the bars due to the deflection

of the model while under load was etiminated.

Results of the measurements of changes in chord lengths are

shown in figure 204. The chords increased in length in all tests.

The maximum increase of 0.0143 inches occurred at elevation 1232,

with the model under full water load. At elevations 1100 and 1000

the deflections were only slightly smaller, being 0.0135 and 0.0102

inches, respectively.

195. Resultant Movement of Model.-The resultant horizontal

movement of the model was determined by combining data Qbtained

from the radial, tangential, and foundation deflection tests" Figure
RW5 CHORD VE.DEE RW5. CHeRt! AVE.DEE

1232 21 1232 18

1100 ~~,. 1100 7.5

1000 ,.. ~!060 82

900 900 1..4 1100 900 54

Z

800 1.4 800 4~0

J> 700 '.2 700 2~6

'"

~600 034 600 0.55

<

1232 3.2 12.32 9.6

J>

N

I'

00 2.8 1100 9.7

0

0 1000

-

2.3 1000 77

-

J>

Z 950 900 2.3 1150 900 82

J> 800 1.7

~-

800 42

J>

700 '4

100 2.8

<D

J> 600 0.45 600 0.48

C

<D 1232 4.2 1232 12.3

-t

C -.!Igo 4~0 1100 12.1

'"

-t 1000 3.4 1000 9.5

'" '"

1000 -sfoo 3.3 1200 900 7.4

600 24 800 5.0

Z

'"

7QO

'8

700 3.'

-t

Z

-t 600 0.51 600 0.40

1232 58 1232 14.3

1100 5.7 1100 '35 1000 46 1000 102

1050 900 4.' 123.2 900

U

8.:)0

--

3.0 800 5.' 700 24 700 3.' 600 0.60 f).00 0.17

UNIT MEASUREMENT~.OO' O. AN INCH

CHOPOS INCREASED IN LENGTH IN ALL TESTS

.,

'00, 200,

SCALE Of" FEET

RESULTS OF TESTS

Ij

l':J~

l':J 0j0Z~

l':J

q;. >q~

l':J

i!:

l':J Z

>-3

Ul

FIGURE 204-TESTS FOR CHANGES IN CHORD LENGTH ""~

-->
318 MODEL TESTS OF BOULDER DAM

. CONCRETE > SUPPORT h_-- -~-

. RUBBER ABUT ENT------

1100

1000

600

600

GOO

LINE OF ARCH CENTERS""

600 60

600

'"..

-:.00

.'

- - -

RUBBER ABUTMENT

--

"""",u_-.

- - CONCRETE SUPPORT'

0 5 10 .IS

I I I I

SCALE OF MODEL I N INCHES

NOTES

Original position of model shown thus n___-

Deflected position shown thus -

Deflected position is obtained from radiol,

tangentiol and abutment deflections with

the reservoir water surface at EL1232.

0 50 100

I J

SCALE OF DEFLECTION

IN THOUSANDTHS OF AN INCH

FIGURE 205-RESULTANT HORIZONTAL MOVEMENT OF MODEL
':,<:!

0

:::

..MEASUREMENTS ON ARC HAYING SAME CENTER

OF CURV...TURE A$ ...RCM AT EI..EVATION 600

_:

~r i

' 900

0 2 i 8

0 I():ii:

~ ,"'"

-1+°0

-H700

~L16oo

RADIAL MEASUREMENTS TO UPSTREAM AND DOWNSTREAM f"ACES

fROM CENTER OF CURVATURE rop EACH ELEVATION

~

6

1100---------------------

if'" S

1050 "--------- 0

, Q)

1000 ,.. lo.8" ~ -o.~" ,

"

:

<? 950 13.80"' ,

~

'

0

'

;::: 900 I5.'''' >i --I.tO

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FIGURE 206-DIMENSIONS OF MODEL AFTER COMPLETION OF 700 TESTS

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320 MODEL TESTS OF BOULDER DAM

205 shows the results of the calculations. Some interpolation was

necessary in combining the data, since all components of movement

were not measured at each point. In plotting the movements, only

those measured at the model dam were used, foundation movements

remote from the dam being neglected. The squeezing of the material

between the faces of the model is quite apparent from the figure.

196. Changes in Shape of Model.-The shape of the model

changed gradually, due to flow and to cumulative effects of repeated

loadings. The changes occurred slowly and were hardly noticeable

between tests. However, after a period of four months, when about

seven hundred tests had been completed, it was realized that the

shape of the model had changed considerably. The model was carefully

measured and the results are shown in figure 206. A comparison with

original dimensions may be made by referring to figure 184. Appreciable proportions of the changes probably represent flow caused by

the weight of the material.

The greatest change in the shape of the model occurred above

elevation 900. The thickness of the model along cantilever section E

increased about three-tenths of an inch. The arch had been carefulIy

alined while being built, and the position of each piece of rubber was

checked before being cemented in place. After seven hundred tests

had been made on the model, the arch elements were no longer circular

as constructed, but varied considerably. The downstream radius of

the top of the model was originally 30.33 inches. After deforming, the

distance from the original center to the downstream face varied from

29.37 to 30.25 inches.
CHAPTER XI-STRAINS AND STRESSES

197. General.-It was realized at the beginning of the tests that

the stress and strain distribution would be considerably different

from that obtained in a model with a lower Poisson's ratio. The

squeezing effects observed in the deflection tests showed that the

top of the model moved upward at both faces, causing vertical tensile

strains. This, however, does not necessarily indicate vertical tensile

stresses if the horizontal strain was compressive. From equation 12,

section 96, it is evident that <Tvis a compressive stress if I-' is 0.50. £v

is a tensile strain, and £H

is a compressive strain more than twice as

large as £v'

Methods of computing strains and stresses from experimental

measurements were developed in chapter V. The same methods were

followed in analyzing data obtained on the rubber model. A large

number of detailed strain diagrams were prepared as intermediate

steps in calculating stresses, in the same manner as in the plastercelite tests. Since these were important only as an aid in compiling

final results, detail strain diagrams are not included in this chapter.

APPARATUS

198. Gages at Upstream Face.-The use of water for the loading

medium permitted the measurement of strains at the upstream face, a

testing operation which was not possible on the plaster-celite model.

For this purpose, specially designed gages, which could operate under

water, were constructed. The gages were essentially the same as

those developed by the Aluminum Company of America, except for a

change in gage length.16

The general assembly of the gages is shown in figure 207, where

three gages are mounted on horizontal, vertical, and diagonal gage

lines. Details of the vertical strain gage are shown in figures 208

and 209. The other gages were similar, except for the shape of the

16Karpov, A. V., and R. L. Templin, "Building and Testing an Arch Dam

Model," Civil Engineering, Jan., 1932, pp. 11-16.

321
322 MODEL TESTS OF BOULDER DAM

'Indicator

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FIGURE 207-STRAIN GAGES FOR UPSTRE'AM FACE

gage frame, The gage consisted of a lever and fulcrum attached to

the face of the model by pins, Relative movements between pairs of

pins were registered by pointers on graduated scales, The movement

of the pins was magnified approximately thirty times by the pointerThe gages were constructed of aluminum with jewel bearings at the

pivot pins, Since it was impossible to obtain identical dimensions

in constructing the gages, each gage was calibrated separately,

against a ten-thousandth micrometer on a special calibration jig.

The apparatus was designed so that an assembly of three gages

could be mounted on a rosette, making angles of 0, 90, and 135 degrees

with the horizontal. A jig with holes drilled at proper locations was

used to set the pins in the face of the modeL When assembled on

the model, very thin rubber bands were stretched between the strain
STRAINS AND STRESSES 323

. ~IN

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FIGURE 208-FRAME DETAILS FOR VERTICAL STRAIN GAGE

pins and pivot heads to maintain a slight pressure on the deflection

rods. Figure 210 shows gages assembled on the face of the model.

As constructed, the pins which actuated the gages were all the

same length, requiring different depths of penetration in the model

to obtain proper clearance between different gages. In conducting

the tests it was observed that the pins having the deepest setting

gave the most consistent results. Gages having the least penetration

were affected by friction which caused erratic readings. At a number

of points it was necessary to repeat the tests, using single gages with
324 MODEL TESTS OF BOULDER DAM

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FIGURE 209-PIN DETAILS FOR VERTICAL STRAIN GAGE

pins set to maximum depth. The water used for loading was very

clear and it was possible to read gages at any location on the upstream

face with a pair of low..power field glasses,

199. Gages at Downstream Face.-Strains at the downstream

face of the model were measured with the gage shown in figure 211,

which was developed for measuring surface strains in soft rubber.

I t consisted of a dial gage mounted on a steel frame. Atone end of

the frame was a fixed arm with a pointed end, and at the other was a

movable arm with a pointed end. The plunger of the dial bore against

a smooth area on the upper end of the movable arm. The dial spring

was balanced by a light-weight rubber band, so that virtually no force

was exerted on the strain pins. To make a strain observation, points

of the arms of the gage were set in countersunk holes in the heads of

tacks, driven in the rubber to form rosettes, as shown in figure 212.

The tacks were set with a template so that the gage lines intersected

in a point. The lever arm of the gage had a two to one ratio so that
STRAINS AND STRESSES 325

average unit strains over 2-inch gage lengths could be read directly

on the dial. Two gages were assembled, carefully calibrated, and

adjusted to 0.0001 of an inch so that unit strains could be read exactly,

thereby eliminating mathematical computations or corrections.

FIGURE 210-STRAIN GAGES MOUNTED ON UPSTREAM FACE

200. Directions 0£ Measurements.-Sufficient data for computing principal strains and stresses could be obtained by making strain

measurements along any three gage lines intersecting at a point. In

order to simplify computations of stresses from strains and to take

advantage of a number of arithmetical checks in the computations, the

gage lines at the downstream face were set horizontal, vertical, and

at 45 and 135-degree diagonal directions. At the upstream face, the

45-degree diagonal strains were omitted from the water load measurements because of the difficulty involved in setting up four gages at

the same location. When strains are measured along four gage lines
326 MODEL TESTS OF BOULDER DAM

FIGURE 21l-HAND-OPERATED STRAIN GAGE

intersecting at a point, a valuable check on the accuracy of the measurements is obtained from the relation that the sum of the strains

measured along any two perpendicular gage lines is a constant.

WATER LOAD CONDITIONS

201. Water Load Strains.-Strains due to water load were measured on the upstream and downstream faces at locations shown in

figures 213 and 214. Rosettes on the downstream face show gage lines

used with the dial strain gage. Rosettes on the upstream face show

four gage lines, only three of which were used during the water load

tests. The fourth gage line was added later, for use in the dead load

strain measurements.

In conducting tests, zero gage readings were made on both faces

with the reservoir empty. Temperatures of model and canyon walls

were determined by mercurial thermometers placed at convenient locations. The temperature of the water in the supply tank was regulated

until it was the same as the average temperature of the canyon and

model. The reservoir was then filled and full load readings made.

Since dead load strains remained constant, changes in gage readings

represented strains due to water load only. Because of the high
STRAINS AND STRESSES 327

FIGURE 212-STRAIN GAGE ROSETTES ON DOWNSTREAM FACE

Poisson's ratio, definite conclusions could not be drawn from the

strain measurements until they had been converted to stresses.

202. Arch Stresses.-Arch stresses at extrados and intrados locations, due to full water load, are shown in figure 215. Stresses were

largely compressive, except for a small area below elevation 1200 at

the center of the downstream face. Tension probably occurred at

the upstream face along the abutments, but the width of the tension

area was probably small, since strain measurements on a 3-inch gage

length did not show tension. The maximum compressiop shown on

the curves was 1.48 pounds per square inch. This stress occurred at

the downstream face at cantilever section B. elevation i 100. and also
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FIGURE 213-LOCATIONS OF ROSETTES ON DOWNSTREAM FACE
CANTILEVER SECTION E--

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FIGURE 214-LOCATIONS OF ROSETTES ON UPSTREAM FACE

NEVADA ABUTMENT

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330

NEVADA ABUTMENT

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MODEL TESTS OF BOULDER DAM

CANTlL.EVER MEASURING SECTIONS

C 0 E F

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ELEVATION 600 := 1.1 Pounds per s"quare inch..

FIGURE 215-ARCH STRESSES, LOAD AT ELEVATION 1232
STRAINS AND STRESSES 331

between sections G and H at elevation 1000. At elevation 1050 at the

Arizona abutment, a peak stress of 1.78 pounds per square inch was

found. This stress occurred in the region of maximum stress shown

by the plaster model tests.

The effect of adding fillets at the downstream face is shown in

figure 215. Compressive stresses which occur at the abutment ends

of the intrados curves were reduced considerably. At the elevations of

the fillets, arch stresses were larger at distances of two to eight inches

from the abutments than at the abutments.

203. Cantilever Stresses.-Cantilever stresses at the upstream

and downstream faces, due to full water load, are shown in figure 216.

These were considerably smaller than the arch stresses, the maximum being only 0.62 pounds per square inch. The maximum stress

occurred at the Arizona abutment at elevation 1050. Below elevation

1000 both upstream and downstream stresses were compression. Tension occurred above elevation 1100 at the downstream face.

An abnormal condition of stress existed in'the upper part of the

model between sections E and F. Strain measurements showed that

tensile cantilever strains existed at both faces of the model when the

water load was applied. This was due to the fact that the soft rubber

compound deforms at constant volume. When stresses were computed

from strains, including the effect of 'Poisson's ratio, most of the tension disappeared. This was because the compressive arch strains were

much larger than the cantilever strains. However, between sections

E and F and above elevation 1100, vertical tensile stresses were found

at both faces of the model. This condition is abnormal and would

not occur in a dam made of concrete.

204. Horizontal Shear.-Horizontal shearing strains and stresses

at extrados and intrados locations, due to full water load, are shown

in figure 217. These stresses were relatively small, being less than

0.4 pound per square inch. With the exception of some variation at

elevations 900 and 1000, where the fillets were of maximum thickness.

shearing stress curves at the upstream and downstream faces were

similar. This shows the consistency of the strain measurements made

with two radically different types of strain gages.

205. Principal Stresses.-Principal stresses at the upstream and

downstream faces of the model, due to full water load, are shown in

figure 218. Stresses at the upstream face are shown in the upper diagram, and stresse5 at the down5tream face in the lower diagram.
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FIGURE 216-CANTILEVER STRESSES, LOAD AT ELEVATION 1232
I A B C D E F G H 1

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STRAINS AND STRESSES 333

NEVADA ABUTMENT CANTILEVER "'EASURING SECTIONS ARIZONA ABUTMENT

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NOTE

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multiplied by average shear

modulus of elastIcity of 125

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NOTE

Positive shear is caused by shear

forces acting thus: ~

+0.002

-0.002

ELEVATION 600

FIGURE 217-HORIZONT AL SHEARING STRAINS AND STRESSES,

LOAD AT ELEVATION 1232
334 MODEL TESTS OF BOULDER DAM

CANTilEVER M EASURtNG SECTIONS

G FED C

NEVADA

ABUTMENT

ARIZONA

ABUTMENT

APPROXIMATE DEVELOPED UPSTREAM ELEVATION

£1. 1236"\ CANTILEVER MEASURING SECTIONS

C D E F G

EI.I232 ~-

NEVADA

ABUTMENT

ARIZONA

ABUTMENT

0'

,

I J I

SCALE OF STRESS IN MODEL IN

POUNDS PER SQUARE INCH

,

.

COMPRESSION

TENSION

APPROXIMATE DEVELOPED DOWNSTREAM ELEVATION

FIGURE 218-PRINCIPAL STRESSES DUE TO WATER LOAD
STRAINS AND STRESSES 335

Considering the upstream face, major principal stresses were

nearly horizontal at the central sections. All major principal stresses

were compression, as were most of the minor principal stresses. Tension occurred as a minor principal stress at section F, elevation 1200.

Major principal stresses calculated from strain measurements nearest

the abutments were inclined approximately normal to the abutments.

Minor principal stresses were compression, except along the Nevada

abutment at elevations 900, 1100, and 1200. It is possible that some

unmeasured tension existed as a minor principal stress nearer the

abutments. The maximum principal stress of 1.33 pounds per square

inch was approximately horizontal at elevation 1000.

Principal stresses at the downstream face, given in the lower

diagram of figure 218, show the effect of adding fillets at the ends

of the intrados curves. In the case of a circular arch under normal

load, stresses at the downstream face are relatively high compressions

along the abutments and relatively low compressions or tensions at the

crown. The general effect of adding fillets was to reduce the arch

stresses at the abutments, thus causing some changes in the directions

of principal stresses.

Below elevation 800, where the arch is circular, major principal

stresses along the abutments at the downstream face were compression. The general direction of the stresses was almost normal to the

abutment lines. Above elevation 800, where fillets were added, slopes

of the principal stresses were changed until the major principal

stresses were almost horizontal. This condition prevailed along both

abutments between elevations 950 and 1100. Above elevation 1100,

slopes were inclined still further until the major principal stresses

made acute angles with the abutments.

The downstream face of Boulder Dam cannot be developed exactly

because of its warped shape. Consequently, the developed downstream

elevation shown in the lower diagram of figure 218 is approximate.

The diagram contains considerable distortion along the abutments,

particularly in the region of the fillets, so that the directions of principal stress are somewhat exaggerated.

Tension occurred as a minor principal stress in the central part

of the downstream face. Such stresses were nearly horizontal below

elevation 1100. Above elevation 1100, tension occurred in diagonal

directions between sections G and H. The maximum tension. which

occurred at section D, elevation 1100, was only 0.35 pounds per square

inch.
336 MODJ<~L TESTS OF BOULDER DAM

DEAD LOAD CONDITIONS

206. Strain Measurements.-In building the model and canyon,

many uncertainties arose in connection with the strains and stresses,

due to the weight of the structure. It was necessary to build the

model and canyon in continuous layers from abutment to abutment,

because of the relatively large deformations in the soft rubber caused

by its own weight. Strains in the model were affected by the deformation of the canyon walls, since it was not practical to build the walls

first and then put in the model. The measurement of dead load strains

was therefore postponed until all other tests had been completed.

Dead load strains were measured as the model was removed from the

testing pit.

Dead load strains were measured with the dial gage shown in

figure 211. Locations of rosettes for strain measurements are shown

in figures 213 and 214. The rosettes were located at the intersections

of the arch and cantilever elements, as far as possible. Additional

measurements were made along the abutments at the downstream

face and at points halfway between the cantilever sections on the

lower part of the upstream face.

The procedure in making dead-load strain measurements was as

follows: An observer took zero readings on all rosettes on both faces.

These readings were checked by a second observer who repeated the

observations. A layer of rubber one inch in thickness, corresponding

to a height of 15 feet on the dam, was then carefully removed from

the top of the model and readings on all rosettes repeated and checked.

This procedure was continued until the entire model was removed

from the canyon.

Curves were plotted to show the magnitude of strains due to dead

load above the center of each rosette. As no observations could be

made when the rubber containing a rosette was removed, the curve

was extended until it reached the elevation of the center of the

rosette. Values obtained in this way, reversed as to tension and compression, gave d~ad load strains at the rosettes. From these strains

dead load stresses at each arch element were calculated.

207. Dead Load Stresses.-Arch stresses due to dead load are

shown in figure 219. Stresses at the downstream face were largely

compression, although some tension occurred at the abutments. Tension stresses were relatively small and did not exceed 0.5 pounds per

square inch, except at the Arizona abutment at elevation 1000 where
,

-- '

,

.,-EXTRADOS

'

,

"="='- -

.... ....::....---- -

~' ---- '~INTRADOS ---- , --- -- - j

,

,

,

: EX RADOS, :

,

, ,

, .-, TRADOS

- -+- - :--- '

'

.5,

J

'

.0, '

'-- -""..- EXTRAOOS '

I

'

:

'

.0 I

,

,

:

.5'

' .-

~ADOS :

,

0

.5 :0"""'/ "

STRAINS AND STRJ<~SSES 337

+0.5

CANTILEVER MEASURING SECTla,.S

0 E F G

ARIZONA ABUTMENT

1 J

NEVADA ABUTMENT

1

+1.0

-0.5

ELEvATION 1200

+1.5

+i.o

"'0.6

ELEVATION 1100

+2.0 ,

,

+I.S

:

+I.°t

,

+0.51

,

0:

-O.SI,

,

-1,0

I

,"UPSTREAM ABUTMENT

"-r---DOWNSTREAM ABUTMENT

tg

~

~.m

~"

8"

z

z

0

0

~

~

~

0

~

u

i

ELEVATION 1000

+1.5,

,

+1.0I

: +0.51

0':

-0.5

ELEVATION 900

+2

+1

+

COMPRESSION

-

TENSION

+2

+1

+0

-0

ELEVATION 800

+1.5

+1.0

+0,5

-0,5

ELEVATION 100

~

I STRESS-STRAIN COMPUTATIONS

+0.: :

,

--INTRADOS

:

:

E (JH=j:ji!(EH+j-LEv)

-0.5

ELEVATION 600 =1~6.~5{-Q,OOOI-O.5KO.OOO5)=-O.09LB./IN.1

FIGURE 219-DEAD LOAD ARCH STRESSES
I

........

~PSTRlA"

It

\

.-DOWNSTREAM f'--

~- J

V

I

\

........ UPSTREA~

f'\

/ V

I'"

"DOWNSTREAM

\

w 0 +, +2.0 +3.0 +4..0 +5.0"'&~

\ I""-- r\PSTREAM '

/

'

,

'-

1'\ DOWNSTREAM

l/

J

'"'"

<

>

12321.0 0 +1,0 +2.0

"ooFfillR""

"°0crt] SECTION A

-[H""

SECTIONB

0

z

1232.0 +1.0 +2.0 +30 +4.0 +5.0 +6.0

12.00

1,100

'000

'"~

'"

<

!:i 900

g

'00

TOO

'°0

SECTIONf

+1.0 +2.0 +3,.0 +4 t ,.0

SURFACE STRESS IN La. PER SQ,IN.

.0 H,Q +2.0 +3.0 +4.0 +5.0

SECTION C

.0 +1.0 +2..0 +30 +4..0

SECTION G

SECTION D

-1.0 .0 +1.0 +2.0 +30

"'

JOWNlTREd. lfEfJ SECTION t

"'" "'"

00

232

200

'00

000

'"

'" 9.00

~

a

.00 z

a::

0

t:J

t':J

t"

>-3

t':J w.

>-3 w.

0

"'.1

to

0

c:

t"t:J

t':J

~

t:J

II>

a::

SECTION H

TOO

GOO

50S

SECTION E

-'~o

LLLU SECTION J

... COIoiPRESSION

-

TENSION

STRESS-STRAIN COMPUTATlO6lS

0;. ~. _~f( €v + f!-€M)

J-36_~5 (.OO4o.-.o.5'OOO4}*1.9 Lb per sq In

FIGURE 220-DEAD LOAD CANTILEVER STRESSES
STRAINS AND STRESSES 339

0.75 pounds per square inch was found. At the upstream face, arch

stresses were materially larger. Between elevations 700 and 1000

they were about two pounds per square inch, the peak stress of 2.3

pounds per square inch occurring at cantilever section F, elevation

800. No tension due to dead load was found at the upstream face.

Cantilever stresses due to dead load are shown in figure 220. At

the downstream face, cantilever stresses were small. At section E,

the stress was almost zero between elevations 800 and 1000, with a

negligible amount of tension between elevations 700 and 800. At section G, elevation 900, the stress at the downstream face reached its

maximum value of 1.5 pounds per square inch. At the upstream face,

cantilever stresses were considerably larger. Stresses between three

and five pounds per square inch occurred between sections C and G.

The peak stress occurred at section F, elevation 800, and was 5.5

pounds per square inch.

Horizontal shearing strains and stresses due to dead load are

shown in figure 221. Since shear stress is equal to shear strain

multiplied by the average shearing modulus of elasticity, one set

of curves shows both strains and stresses. Two scales are provided

so that either the strain or the stress can be read from the curves

as desired. In the upper elevations of the model, shearing stresses

were small. In the lower part, where the model was thicker, shearing

stresses were larger and fairly symmetrical. The maximum shearing

stress was 1.0 pound per square inch and occtlrred at the Nevada abutment at elevation 600.

Principal stresses due to dead load are shown in figure 222. At

the upstream face, major principal stresses were almost vertical.

Major principal stresses and all except one of the minor stresses were

compression. A negligible amount of tension occurred at cantilever

section F, elevation 1200. At this elevation the stresses were so

small that their values hardly exceeded the limits of accuracy of the

strain gages. Below elevation 1100, the stresses increased in magnitude toward the lower part of the model. The largest principal stress,

5.85 pounds per square inch, occurred at section E, elevation 580.

Principal stresses at the downstream face were much smaller than

at the upstream face. Considerable tension was found along both

abutments. The maximum tension of 1.38 pounds per square inch

occurred at the Nevada abutment near elevation 600. The maximum

compression, 1.63 pounds per square inch, occurred near the Nevada

abutment at elevation 700.
i EXTRADOS,' - - '

,

, -- INTRAOOS-. --- '----

'

I

,

i I '

,

- : --INTRA?OS '

,

,

EXTRA~O~

1->< ,,

r-- '

,

,

I I '

, .

340 MODEL 'l'ESTS OF BOULDER DAM

NEVADA ABUTMENT

+0.002 I

CANTILEVER MEASURLNG SECTIONS

0 E F G

ARIZONA ABUTMENT

J

-o.OOZ

l

:o...

-0.2

-0.4

-0.004

ELEVATION 1200

+0.002

[

:0..

-0.2

-0,4

-0.002

-0.004

ELEVATION 1100 -"UPSTREAM ABUTMENT

-"OOWNSTREAM ABUTMENT +0.004 ,

I

+0.0021

I

0.,

I

-0.0021

,

-0.004

~

g

~

~

~

~

z

~

..

~

~

~

~

~

"

~

z

~

I +0.4

I

I

+0.2

I

0.

I

-0.2

I

I -0.4

ELEVATION 1000

z

u

z

~

~

~

~

~

z

u

z

+0.004

0.,

,

-0.002 '!Oz

~~

"

~

~

ELEVATION .00

+0.004

:

+0.4

:

+0.2

:0.

,

!

-0.2

I -0.4

: -0.6

,

,

-0.004

:

-0,006 -0.8 ELEVATION 800

NOTE

Positive shear is caused by shear

forces acting thus: ~.

+0.8 +0.006

+0.004

:

+0,6

I +0.4

I

I +0.2

I

I

I

-0.2

:

-0.4

: -0.6 ,

-

0.006 -0.'

+0.002 :

+0.2

,

0.

,

:

-0.2

:

-0.4

,

I -0.6

NOTE

Shear stress equals shear strain

multiplied by average shear

modulus of elasticity of 125

pounds per square inch.

-0.002

I -0.8

,

ELEVATION 600

,.0

FIGURE 221-DEAD LOAD HORIZONTAL SHEARING

STRAINS AND STRESSES
ARIZONA

ABUTMENT

£1. 1236-~.,

EI.I232.~

ELl200~"

-

NEVADA

ABUTMENT

,

.

I I

SCALE OF'STRESS IN MODEL IN

POUNOS PER SQUARE INCH

STRAINS AND STRESSES 341

CANT,ILEVER MEASURING SECTIONS

G FED C EI. 1236"~'

EI.1232~-'

El.1200

NEVADA

ABUTMENT

APPROXIMATE DEVELOPED UPSTREAM ELEVATION

CANTILEVER MEASURING SECTIONS

C D E F G

£1.1000

ARIZONA

ABUTMENT

II

COMPRESSION

.

TENSION

FIGURE 222-PRINCIPAL STRESSES DUE TO DEAD LOAD

APPROXIMATE DEVELOPED DOWNSTREAM ELEVATION
342 MODEL TESTS OF BOULDER DAM

COMBINED LOAD CONDITIONS

208. Combining Strains.-To obtain actual horizontal, vertical,

and shearing stresses in the model during the application of reservoir

load, dead and live load stresses were added at the different locations

when strains were measured. Since directions of principal stresses

varied during different load conditions, these stresses could not be

added directly. It was necessary to combine original strain readings

and to compute magnitudes and directions of principal stresses from

the combined values.

209. Arch Stresses.-Arch stresses due to combined loads, weight

plus full reservoir pressure, are shown in figure 223. When the two

sets of stresses were combined, the most important result was the

elimination of tension from the arch elements. Some tension may have

existed along the abutments at the upstream face, beyond the region

of measured strain; but all tension at the downstream face was eliminated. The weight of the model caused it to deflect upstream, thereby

producing horizontal tension along the downstream abutments and

horizontal compression in the central portion of the downstream face,

see figure 219. The water load produced stresses of an opposite

nature; compression occurred along the abutments at the downstream

face with tension in the central portion. \Vhen the two sets of stresses

were combined, compressive stresses predominated. In the central

part of the downstream face, the stresses had no magnitude at elevations 1000 and 1200, and were small at elevations 600, 700, and 800.

The largest arch stress for the combined load was 3.1 pounds per

square inch. This stress occurred at elevation 800, at the upstream

face near the Arizona abutment.

210. Cantilever Stresses.-Cantilever stresses due to combined

loads are shown in figure 224. Cantilever stresses at the upstream

face of the model were from three to five times as large as those at

the downstream face. The largest stress, 5.5 pounds per square inch,

occurred at elevation 800 between sections D and G at the upstream

face. Stresses at the downstream face were approximately uniform in

magnitude, being about one pound per square inch. Some variation in

the downstream stress occurred at cantilever D, below elevation 800.

This condition did not occur at other cantilever sections.

No tension of any consequence was found after the stresses were

combined. Dead load cantilever stresses were compression, except for
!

I

EXTR~DOSj" !'--

1

,

'-..... I ..-

,/ .....,

.......- -r-.: ', IINTRADOS)

, 1

,

,- EXTRAOO5

'

, ,

->-- ,

.....r - >-C'INTRA 0$ ,

I

"""""

'

,

I

,

.,

+2

0

0

.

.

.

~~~~0

0

>

0

.

~~~0

.

.

°

,

,

--EXT ADOS ~1

°,, ,

°

......

"""""

INTAAOOS , ,

I r-.. ./ '

,

°, ,-EXTADOS , ,

,0 '

, ,

, ,

°

,

'-- .....t:.--INT ADOS -

,

,

,

'

~EXTRADOS

,

, ,

, 1

, ,

, I

1"-

,-IHTRAOO ,

,

I '

, ,

,

(

-EXTRAOiS ,

I .INTRADOS

"

STRAINS AND STRESSES 343

NEVADA ABUTMENT

+2.0 I A

CANTILEVER MEASURING SECTIONS

, F

ARIZOHA ABUTMENT

I J

+1.0

-1.0

ELEVATION 1200

""3.0

+1.0

+2.0

ELEVATION 1100

"'~~~UPSTREAM ABUTMENT

-~,DOWNSTREAM ABUTMENT

ELEVATION 1000

.,

ELEVATION 900

+4.0

+2.0

+ COMPRESSION

-

TENSION

+3.0

+

1.0

ELEVATION 800

,'°

+\.0

~ IHTRADO

STRESS STRAIN COMPUTATIONS

Ot.'~(€M+J..l(V)+~O'Z

:~{O.OOI8+0.~)(a.oo04J+~ 0.011

: 0.92 LB. PER SQ. IN.

---EX RADOS

+2.0

ELEVATION 700 NorE O'z IS ZERO ON DOWNSTREAM SURFACE

+3.0

+1.0

+2.0

ELEVATION 600

FIGURE 223-ARCH STRESSES, DEAD LOAD COMBINED WITH

FULL RESERVOIR LOAD
\

I" ~UPSREA

\

i'-

/

'oowSTRAM LL

-- -

0 H +2.0 +3.0 +4.0 ..

UP TRE/P->

\

fD WN$REA

\

,.

"

., . .. . ..

r----

""

/

'<

STR AM

/ '-OOW

1"- STR M

\

1'\ V

V

,/'

C>O

....

....

02" 200

'00

000

a::

0

t1

tr:I

t'

>-3

tr:I

00

>-3

00

0

"'J

to

0q

t't1

l':::

itI

t1

>

s::

"

+20'" +4." +.0

r----.

'

"-

,

!\U STRAM ,

"

.........

OOWSTREM /V

/

~ ::fr'f]

-!.D 0 '10 "0.

~

DOW STREAM

~

1100

SECTION A

mJ-.

S1j

SECTION B

123210 0 +10 +20 +3.0+40 +5.0+60

0200

"00

'000

m

r

m

<

!i 900

~

'00

700

600

SECTION F

SURFACE STRESS IN LB. PER SQ. IN.

SECTION C

...10 ...2.0 +3.Q...2"_~.O~5.0 + 6.0

SEC-TION G

SECTION 0

-1.0 +1. +2.0

U 5TR AM

SECTION E

D NS R~_M

SECTION H

'00

700

600

'f:=:L::D'

~REAM

SECTION J

STRESS-STRAIN COMPUTATIONS

OV~~e(€~+fL€H)+tp. 0;

OV.I_3~.~5(O.OO24+0.5 XO.Oo.03J'" I~O~5 0.077

~ 50Qx 0.002."55 +1 X0.071: 1.35 Lb.lSq.llI.

NOTE: OZ is zero on downstream surface.

FIGURE 224-CANTILEVER STRESSES, DEAD LOAD COMBINED WITH FULL RESERVOIR LOAD
,

, I

'

,

\

I

I INTRAQ ' 5---'/ V

I

I -

,

, ~-~EXTRADOS ,-"

\

g

~f'

~~I

+02 ~I

~0 ~,

~I-0.2

~~~~~.

~r' ~~I

+0.2.

,

0 ,

)

-0.2.

t -0.4

I

STRAINS AND STRESSES

NEVADA ABUTMENT

+0.04 I A

CANTILEVER MEASURING SECTIONS

E F G

+0.02 ,

,

I

-0.02 I

-0.04

+0.04

+0.02

-0.02

ELEVATION 1100

+0.04

I

+0.021

,

0',

-0.02 ~-INTRAas

~

!

~

~

~

~

~

~

ELEVATION 1000

~

ELEVATION 900

%

~

~

.~~

~

-+0.04

I

+0.02

ELEVATION 800

+0.06

+0.04

NorES

Cantilever measuring sections are

radial.

Positive shear is caused by shear

forces acting thus: ~

ELEVATION 600

ARIZONA ABUTMENT

J

[

+0.'

TO.2

0

-0.2.

: '-UPSTREAM ABUTMENT

"DOWNSTREAM ABUTMENT

:

[

+0.

I +0.2 I

, 0

I

-0.2

: +0.6

:

+0.4

I +0.2

I

I

I

-0.2

:

-0.4

-0.6

+0.2

I

+0

I

I

-0.2

:

-0.4

: -0.6

I

-O.B

, -1.0

I

-1.2

NOTE

Shear stress equals shear strain

multiplied by overage shear

modulus of elasticity of 125

pounds per square inch.

FIGURE 225-HORIZONTAL SHmARING STRESSES, DEAD LOAD

COMBINED WITH FULL RmSERVOIR LOAD

345

I

~O.4

I

,

.0.2

I

I -0.2 ,

I -0.4
346 MODEL TF.JSTS OF BOULDER DAM

a small area at the downstream face between elevations 700 and 900.

Small tensile stresses existed in the upper elevations of the model

on both faces as a result of applying water load. When the two

stresses were combined, most of the tensile stresses were offset by

the larger compressive stresses, only a negligible amount of tension

remaining at sections D and F.

211. Horizontal Shear.-Horizontal shearing strains and stresses

are shown in figure 225. In the upper part of the model, where the

structure was relatively thin, shearing stresses were small, being less

than 0.4 pounds per square inch. The maximum shearing stress was

1.20 pounds per square inch. This stress occurred at the downstream

face at elevation 600 at the Nevada abutment.

212. Principal Stresses.-Principal stresses at the upstream face,

due to combined loading, are shown in the upper diagram of figure

226. The major principal stresses due to dead load were approximately vertical while those due to water load were roughly horizontal.

The effect of dead load on the stresses was much greater than the

effect of water load. Consequently, major principal stresses were

almost vertical in direction. The largest major stress occurred at

elevation 580, cantilever section E, and was 6.12 pounds per square

inch. No tension occurred as a minor stress.

Principal stresses at the downstream face, due to combined loading, are shown in the lower diagram of figure 226. The stresses were

larger along the abutments than in the central part of the downstream

face. Directions of principal stresses along the abutments, in the

regions of fillets between elevations 800 and 1100, are slightly distorted in the diagram, owing to the method of development. The

maximum compression occurred at elevation 700 near the Nevada

abutment and was 2.04 pounds per square inch. The maximum tension, which occurred as a minor principal stress, was 1.23 pounds per

square inch. This stress occurred at elevation 600 near the Nevada

abutment. Tensile stresses at the downstream face always occurred

as minor principal stresses and were small in magnitude.

It must be remembered that the method of obtaining dead load

stresses did not conform with the construction procedure; also that

the effect of this lack of conformity was increased by the high Poisson's ratio of the rubber. Had the canyon been constructed before

building the model, stresses obtained by removing the model would
ARIZONA

ABUTMENT

EI. 1236-..,

E1.1232.

'

EI.I100

NEVADA

ABUTMENT

0 I

I

,

I

SCALE OF STRESS IN MOOEL IN

POUNDS PER ,-SQUARE INCH

STRAINS AND STRESSES 347

CANTILEVER MEASURING SECTIONS

FED C ,-- EI. 1236

EI.1200

NEVADA

ABUTMENT

EI.550

APPROXIMATE DEVELOPED UPSTREAM ELEVATION

CANTI LEVER M EASURI NG SECT! ONS

C D E F G

ARIZONA

ABUTMENT

COMPRESSION

TENSION

Ei'IGURE 226-PRINCIP AL STRESSES DUE TO DEAD AND LIVE LOADS

APPROXIMATE DEVELOPED DOWNSTREAM ELEVATION
348 MODEL TESTS OF BOULDER DAM

have been fairly similar to those occurring in the prototype. Since

the dam and canyon walls were built as a unit, and the dam removed

separately, the expansion of the canyon walls after a portion of the

model was removed caused squeezing in the lower portions of the

model. Such squeezing undoubtedly had some effect on the measured

strains. This effect appears in the horizontal stress components

shown in figure 222.
CHAPTER XII-FLOW AND TEMPERATURE

TESTS

FLOW TEST

213. Effect of F1ow.-In tests of previous models it was noticed

that when load remained on the model for a considerable length

of time, deflections were increased due to flow. Flow tests had been

made on the concrete model of the Stevenson Creek test dam and the

plaster-celite model of Boulder Dam. The rubber-litharge material

was so different from concrete and plaster-celite that it was believed

a sustained load would cause the material to flow appreciably. A

gradual change of shape due to repeated loadings was mentioned in

chapter X.

The effect of flow on a model of an arch dam is usually most

noticeable in changes of radial deflection. Tangential and twist deflections undoubtedly change slightly, but since the initial magnitudes of

these deflections are small, it is not feasible to measure the small

changes due to flow. The same condition prevails in the strains. Flow

probably causes a slight redistribution of strain which would require

very precise instruments to measure. A test was therefore made

to determine only the effect of flow on the radial deflections of the

model.

214. Method of Making Flow Test.-The flow test was similar

to the radial deflection tests, except that the water load was allowed

to remain on the model for an extended period of time. As the model

deflected the reservoir water surface became lower, and it was necessary to add water to the reservoir to maintain the proper surface

elevation. The water in the reservoir cooled slightly during the test;

so it was necessary to add warm water to maintain the proper temperature. This was usually done each morning.

.

Radial deflection measurements were made with micrometers and

dial gages reading to 0.001 of an inch. The micrometers and gages

were set to measure radial movements at the inserts shown in figure

,189. An initial reading with the model unloaded was made at 8 :15

349
350 MODEL TESTS OF BOULDER DAM

a. m., October 9, 1933. The reservoir was filled and radial deflection

measurements made immediately, before flow of any consequence

occurred. These observations were repeated at intervals of one~half

hour during the first day and at greater intervals during succeeding

days. Differences between readings at any time during the test and

the first set of readings, made with the reservoir full, constituted the

deflections due to flow.

Curves were plotted showing flow at individual inserts. At the

beginning of the test, slight irregularities in deflections were noticed.

These irregularities were apparently due to small variations of temperature. At the lower elevations, where the arch was thicker, such

irregularities were not encountered. A small periodic variation

occurred daily above elevation 700.

The model became practically stationary at the end of the tenth

day of observation, and it was planned to unload the model on the

fourteenth day of the test. However, on the fourteenth day the deflection began to increase rapidly. Unloading was therefore postponed

for a few days. During this time, the deflection increased rapidly

until the twenty-third day, when the model was unloaded.

The cause of the increase in deflection could not be seen at the

time of the test. Later, when the model was being dismantled, the

cause was discovered. The rubber cement in the horizontal joint at

elevation 580 had failed near the Arizona abutment at the upstream

face. About three hundred square inches of the cemented joint had

opened. This made the cantilever elements more flexible and caused

the rapid increase in deflection.

After the load was removed, observations for radial deflections

were continued, so that the amount of recovery could be observed.

Very little recovery occurred after the model had been unloaded two

days. The remaining deflection was due to the open joint and plastic

flow. The proportion of the deflection due to each factor could not

be determined.

215. Results of Test.-Radial deflections of arch elements are

shown in figures 227 and 228. In general, flow tended to increase the

radial deflection. This increase was very consistent below elevation

1000. At the upper elevations of the model, particularly at elevation

1232, some irregularities were encountered, owing to the reversal of

directions of movement. At the abutments the model deflected upstream while at the crown the deflection was downstream. The

initial upstream deflection was small and the increase due to flow
.

4..

,

.9 '0

"

"

03 ..

0

"

~. 0 ~h . ~11 0 ~f/ . "..~~'B ,,-C, E., ff//

:X A'.

.

,j

~----,.)'

. ELEIl1232 . .

..

.0

,.

'00

..0

".

200

ELEV.1100

0

4

.

,

'0

20

.0

,.

,00

'20

..0

NEVADA ABUTMENT

-2

10

'"~0

ii~

20

~z

::I

!i: ~z~

INSERT NUMBERS ARIZONA ABUTMENT '

Dim4 . . , .

9:.

.

.A

.B,C.D

E"

.0"

'00

,..

ELEV. 900

"

2

~'

4"B'C'D'E'.

':.

.0"

'00 ELEV.800

~O

t=El:u::

ELEV.700 2 3

4

"

0

~:ELEIl 600

"'J

t"0~>Ztj

0-,3

t:::I ~

"d

t:::I ~>0-,3 q~

t:::I

0-,3

t:::I

U1

0-,3

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FIGURE 228-RADIAL ARCH DEFLECTIONS DUE TO FLOW AND RECOVERY
FLOW AND TEMPERATURE TESTS 353

was less than the minor fluctuations caused by temperature changes.

The results of observation G, made on the fourteenth day of the test,

were assumed to represent flow. The results of the later observations

were complicated by the failure of the rubber cement at elevation 580.

The radial deflection due to flow was consistent above elevation

700. It varied from 20.0 per cent at elevation 800 to 23.1 per cent at

elevation 700. At elevation 600, the flow amounted to 35.6 per cent

of the original radial deflection. This was rather large compared with

the flow at higher elevations, and may have been due to the beginning

of failure at elevation 580.

The effect of the failure of the joint was to increase the flexibility of the structure. At elevation 1232 the initial deflection at the

crown of the arch was 0.166 inches. At the end of 14 days, flow

increased this deflection to 0.202 inches. At the end of 23 days, the

combined effects of the open joint and flow increased the deflection

to 0.238 inches. At elevation 600, the effect was relatively greater.

The initial deflection was 0.028 inches; at the end of fourteen days,

the deflection was 0.038 inches; and at the end of 23 days it had

increased to 0.073 inches.

At the end of the twenty-third day, the model was unloaded and

allowed to recover. For 1.5 days after unloading, the model recovered

rapidly. After that it became practically stationary. Observations

made ten days after unloading showed that the model lacked 0.027 to

0.041 inches from recovering to its initial position. The deflection

curves, designated by J in figure 228, show the final position of the

model on the completion of the test.

216. Condition of Mode1.-After the model had been unloaded

for two weeks, a radial deflection test was made to determine the effect

of the open joint on the action of the model. The results of the

test are shown in figure 229, where radial deflections after failure

of the joint are compared with those obtained from previous tests.

The differences between the two sets of deflections were relatively

small. During the two weeks that the model remained idle, the weight

of the material caused the joint to close and the rubber cement apparently reunited the two layers. In the investigation of properties of

various brands of rubber cements, it was found that the cement used

in building the model would allow surfaces to read here after being

torn apart, if no dust or dirt entered the joint while it was open.

In the case of the torn joint, the upstream edge was covered with an

uncured sheet of crude rubber which prevented the entrance of foreign
,

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FIGURE 229-RADIAL ARCH DEFLECTIONS BEFORE AND AFTER FLOW TEST
FLOW AND TEMPERATURE TESTS 355

matter, so that the conditions for readhesion were ideal. The torn

joint developed sufficient strength after the idle period to permit the

application of full load without causing much change from previously

measured deflections.

TEMPERATURE TEST

217. Purpose of Test.--Temperature changes in arch dams produce deformations and stresses which may be of considerable magnitude. Temperature changes occur in a dam with the reservoir empty,

partially full, or full. If the reservoir is empty, both faces of the dam

are exposed to atmospheric temperature changes. If the reservoir is

full, the upstream face is subject to water temperature changes, while

the downstream face is subject to atmospheric temperature changes.

In investigating temperature effects in arch dams by means of models,

tests had been made on the concrete model of Gibson Dam17 and the

plaster-celite model of Boulder Dam. In both tests, effects of a

decrease and an increase of temperature on unloaded models were

investigated. \Vhen cold water is impounded behind a dam which is

relatively warm, the upstream face cools rapidly while the downstream

face remains at nearly constant temperature for a period of time

depending on the thickness of the cross-section. This condition, which

causes shrinkage at the upstream face, was investigated in the temperature test of the rubber-litharge model.

218. Procedure.- The procedure adopted for the temperature

test was as follows:

1. The model was hrought to stahle conditions of temperature and radial movement by allowing it to remain unloaded

in a room of fairly uniform temperature for a period of ten days.

2. The reservoir was filled with water at air temperature

and a complete set of temperature and radial deflection measurements made.

3. The temperature of the reservoir water was lowered by

adding chipped ice and the deflection and temperature conditions

of the model observed at convenient intervals until stable conditions were reached.

17"Arch Dam Investigation, Report by Committee," Vol. II, pp. 292-325,

Engineering Foundation, May, 1934.
356 MODEL TESTS OF BOULDER DAM

4. The model was returned to its original temperature by

adding warm water to the reservoir.

5. The reservoir was drained and the model allowed to

return to its original position as it recovered from the deformation due to load and flow.

During the construction of the model, thermocouples had been

placed at the locations shown in figure 230. Apparatus for obtaining

temperature readings from thermocouples was the same as in the

temperature tests of the plaster-celite model.

Stable conditions were reached at 10:00 a. m., November 27,1933.

The reservoir was filled with water at air temperature and observations for temperature and deflection made. Ice was added to the

reservoir water and observations repeated at intervals of approximately three hours for four days, when stationary conditions of temperature and deflection were again reached. The ice was removed

from the reservoir and warm water added until the temperature of

the water had returned to normal. Observations for temperature and

deflection were continued for eight days. At the end of this period,

the temperature of the model was approximately the same as the

initial temperature. The reservoir was drained and observations for

deflections continued during a six-day period. At the end of this

time the model had recovered from flow due to water load until it was

almost at its initial position. The observations were then terminated.

219. Initial Temperature Conditions.-All temperatures in the

test are expressed in degrees Fahrenheit. Temperatures existing in

the model at the beginning of the test varied from 68.0 to 69.9 degrees,

see table 14. The minimum occurred at elevation 505, at thermocouple 3, located 12.8 inches from the upstream face. The maximum

occurred at elevation 505 at thermocouple 2, 14.5 inches from the

downstream face; also at elevation 1125 at thermocouples 16, 17, and

19. The model was slightly cooler below elevation 700 than in the

thinner portions of the model above that elevation.

220. Conditions at End of One Day.-At the end of one day with

ice in the reservoir, the temperature of the model had been lowered

considerably, as shown in the third column of table 14. The temperature of the upper part of the model had been reduced about twenty

degrees. Near the upstream face, at elevation 600. a temperature

change of about 10 degrees was found. In the central part of the
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358 MODEL TESTS OF BOULDER DAM

TABLF 14-TEMPERATURES IN MODEL

I

Thermocouplel Initial

No. I

TemperI

ature

Deg-.F.

Temperature at End of

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

69.9

68.0

68.1

68.4

68.4

68.2

68.2

68.8

69.1

68.8

69.1

69.5

69.5

69.5

69.9

69.9

69.5

69.9

model and near the downstream face, there was less change in temperature.

The effect of cooling the material in the upper part of the model

and at the entire upstream face was to deflect the model upstream.

Radial deflections of the arch elements at the beginning of the test

and at the end of one day are shown in figure 231. At insert 9, elevation 1232, the initial radial deflection was 0.166 inches. Cooling- the

model for one day reduced this deflection to 0.097 inches. At the ahutments, a similar upstream movement was noted. At insert 5. elevation 1232, the deflection chang-cd from --0.002 inches to -0.028 inches;

and at insert 13 at the opposite end of the arch element. the chang-e in

deflection was from 0.007 inches to --0.045 inches. At lower elevations, deflections were less hut a general upstream movement was

observed.

Cantilever deflection curves in figure 232 show a pronounced

upstream movement at the top. Vertical shrinkage of the cantilever,

causing upstream movement, was more effective than the horizontal

shrinkage of the arches, which normally causes downstream move-
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In table L4

FIGURE 231-RADIAL DEFLECTIONS OF ARCHES AT END OF ONE DAY

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SECTION B

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RADIAL DEFLECTION IN THOUSANDTHS OF AN INCH

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EL.IIOO

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NOTES

Original deflection of madel- Reservo.r

water surface at elevation 1232

- Deflection af model after temperature

change

+ Indicates downstream deftection

Indicates upstream deflection

Distribution of temperature In model is shown

in table 14

FIGURE 232-RADIAL DEFLECTIONS OF CANTILEVERS AT END OF ONE DAY
FLOW AND TEMPERATURE TESTS 361

ment. The upstream movement of the lower portion of the cantilevers was fairly uniform.

221. Conditions at End of Two Days.--Temperatures existing in

the model at the end of two days are shown in the fourth column of

table 14. At elevation 1125 the average temperature was 48.3 degrees,

a decrease of 21.5 degrees from the initial temperature. A general

decrease in temperature had occurred in the upstream half of the model

below elevation 900. At the base of the section on line of centers, the

temperature was 64.5 degrees at thermocouple 3, a decrease of 3.5

degrees.

At that time, flow of the rubber-litharge material was beginning

to affect the deflection of the model. A slight increase in radial

deflection occurred at the crown section of the arch element at elevation 1232, as shown in figure 233. Below elevation 1000 the arch

elements continued to deflect upstream as the decreasing temperature

caused the model to shrink.

Deflections of the cantilever elements at the end of two days are

shown in figure 234. The effect of vertical shrinkage of the upstream

face was similar to that of the first day of observation.

222. Conditions at End of Four Days.- The temperature distribution in the model at the end of the fourth day is shown in the

fifth column of table 14. At that time, model temperatures had become

almost stationary. Since the minimum temperature of the reservoir

water was 32 degrees, further cooling of the model was impossible.

At elevation 1125, the average temperature was 44.5 degrees, a decrease of 25.3 degrees from the initial temperature. Temperatures of

about fifty degrees existed in the lower part of the model near the

upstream face. At elevation 505, the temperature at thermocouple 2,

located 14.5 inches from the downstream face, was 68.5 degrees, a

decrease of 1.4 degrees from the initial temperature of the test.

Radial deflections of the arch elements are shown in figure 235.

Above elevation 900, deflections continued to increase due to flow of

the rubber-litharge compound. At elevations 1000 and 1100, crown

deflections were almost the same as the initial deflections; but along

the abutments there was some variation. At elevations 600 and 700,

deflections continued to decrease due to shrinkage.

Deflections of the cantilever elements are shown in figure 236.

Temperatures at thermocouples 13, 14, and 15 indicated that cooling

had become effective at the downstream face. The resulting shrinkage
'N~VADA ABUTMENT INSERT NUMBERS ARIZONA ABUTMENT-;: 3 4 , 6 1 . . 10 "

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Originol deflection of model

- Reservoir

water surface at elevafion 1232

-

Deflection of model after temperature

change.

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Indicates upstream deflection.

Olstribuhon of temperature in model is shown

in table 14
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NOTES

Original deflection of model-Reservoir

water surface at elevation 1232

-

Deflection of model after temperature

change

+ Indicates downstream deflection.

Indicates upstream deflection.

Distribution of temperature in model is shown

in ta ble 14

FIGURE 234-RADIAL DEFLECTIONS OF CANTILEVERS, END OF TWO DAYS

0 EL.123

"'"

""

~.:.
364 MODEL TESTS OF BOULDER DAM

caused downstream deflections at elevations 1000 and 1100 in cantilevers D and E. Deflections at sections A and H showed the effect of

abutment deformation.

At that time the model had become practically stationary in temperature distribution and position. A very slow increase in deflection

was occurring due to flow. As there was no possibility of obtaining

greater deformation with reservoir water having a temperature of 32

degrees, the ice was removed and warm water added until the reservoir

temperature reached 68 degrees.

223. Conditions at End of Twelve Days.-At the end of twelve

days the temperature of the model had risen until it was within about

two degrees of the original temperature. Observed temperatures

at that time are shown in the last column of table 14. The greatest

variation from the original temperature occurred between elevations

600 and 700, where an average temperature of 66 degrees existed, 2.2

degrees lower than the initial temperature.

Deflections of the arch elements at the end of twelve days are

shown in figure 237. At elevation 600 the deflection was slightly

less than the initial deflection. This was to be expected as the temperature of the model was less than the initial temperature at that

elevation. At elevation 700 the deflection was almost the same as the

initial deflection. Above elevation 700, a general decrease in deflection occurred. The difference in deflection in the upper part of the

model was largely due to flow. The maximum deflection at the top

of the model was 0.202 inches. In the flow test the corresponding

deflection, after being unloaded for 12 days, was 0.205 inches. The

close agreement of these two deflections indicated that the joint which

was torn apart during the flow test had knit together satisfactorily.

The reservoir was drained and the model allowed to recover.

Observations for temperature and deflection were continued for four

days. At the end of that period the average temperature was 68 degrees, which lacked one degree of being the initial temperature. The

corresponding deflections are shown in figure 238. The recovery from

the flow at the end of four days was very good, since the position

of the model was almost the same as the initial position before filling

the reservoir.

224. Conc1usions.--The results of the temperature test indicate

that the effect of cooling the upstream face of an arch dam is to

cause an upstream deflection. If the reservoir is full at the time of
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NOTES

Origlnol deflection of model- Reservoir

water surface at elevation 1232.

- Deflection of model ofter temperature

chdnge.

+ Indicates .downstream deflection.

Indicates upstream deflection.

Distribution of temperature in model is shown

in foble 14.

FIGURE 235-RADIAL DEIFLECTIONS OF ARCHES AT END OF FOUR DAYS

w

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SECTION 8

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IEL 100

n. IDa

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SECTION E

RADIAL DEFLECTION IN THOUSANDTHS OF AN INCH

0 .30 0 30 60 90 120 ISO

SIECTION C

70

RADIAL DEFLECTION IN THOUSANDTHS OF AN INCH

60

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lEt. 700

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SECTION D

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SECTION"

SECTION 8

NOTES

Original deflection of model~ Reservoir

water surface at elevation 1232.

- Deflection of model after temperature

change.

+ Indicates downstream deflection.

Indicates upstream defleclion.

Distribution of temperature in model is shown

in table 14.

FIGURE 236-RADIAL DEFLECTIONS OF CANTILEVERS AT END OF FOUR DAYS
"NEVADA ABUTMENT INSERT NUMBERS ARIZONA ABUTIoIENT.

3

, , . 1 . 9

,

" " "

,.

--- -- --

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NOTES

Orlglnol deflection of model- Reservoir

water surfoce ot elevation 1232.

- Deflection of model ofter temperature

change.

Indicates downstream deflection

Indicates upstream deflection

Distribution of temperature in model is shown

in table 14.

FIGURE 237-RADIAL DEFLECTIONS OF ARCHES AT END OF TWELVE DAYS

0.:>

->""
---- -----

--- --

---- --- Permanent seh, ~- -,

...

---

'~" '""',-~ -0 Finalrecover:.---I ---;-;3::

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on unloading ~~,

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Decrease

'"

deflection

" dc' 10 COOling,tp,.."

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"-'.. .Increase In deflection doe

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period. I

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NEVADA ABUTMENT

0..>

a>00 ARIZONA ABUTMENT NEVADA ABUTMENT

INSERT NUMBERS

ARIZONA ABUTMENT

5 6 7 8 9

-'0

INSERT NUMBERS

8 9 10

-'0

ELEVATION 900

'

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ELEVATION 100

150

ELEVATION 1100

. 1

EXPLANATION

A-Initial deflection reservoir full normal

temperature'

,

8- Deflection at end of four days, reservoir full,

minimum temperature conditions

C- Deflection at end of twelve days, reservoir

full, normal temperature.

D- Position on unloading, reservoir empty,

normal temperature.

EPosition four doys after unloading, reservoir

empty, normal temperature.

+ Indicates dOwnstream deflection

-

Indicates upstream deflection m"

4_'0

--

-,~,

0:,

-

0

..:.:..-;;;~~j ~:~-:. -':' 30

A".

'0 ELEVATION 600

150

ELEVATION 1000

FIGURE 238-DEFLECTIONS SHOWING RECOVERY FROM TEMPERATURE TEST
FLOW AND TEMPERATURE TESTS 369

cooling, a general reduction of the maximum deflection occurs. This

is opposite from the effect of a uniform cooling of an arch dam which

results in a downstream deflection. The difference is due largely to

the vertical shrinkage of the upstream face of the cantilevers. The

large upstream movement near the abutments, as shown on the arch

deflection curves, indicates that shrinkage of the canyon walls may

have been responsible for a portion of the upstream movement. The

canyon walls, being continuous with the model and exposed to the

same reservoir temperature conditions, tended to pull the model

upstream.

CHAPTER XIII-TRIAL LOAD ANALYSIS OF

RUBBER-LITHARGE MODEL

225. General.-A brief description of the trial load method was

given in chapter VII, in discussing the analysis of the plaster-celite

model. This chapter presents the application of the method to the

rubber-litharge model with certain additions required to fit the peculiar properties of the model material. The most important additional

consideration was the vertical movement, a feature not required in

previous analyses.

Similar to the plaster-celite model analysis, seven sample arches

and nine cantilevers were selected for consideration as representative

structural elements. Elastic properties, determined in the materials

investigations, were used with proper consideration of the differences

in vertical and horizontal planes.

PROCEDURE

226. Data and Assumptions.- The principal items of structural

data, together with the assumptions made for the purpose of the

analysis, are listed as follows:

1. Scale of model, I to 180.

2. Reservoir water surface at elevation 1232.

3. Unit weight of water, 62.5 pounds per cubic foot.

4. Unit weight of rubber-litharge material, 150 pounds per

cubic foot.

5. Average modulus of elasticity of rubber-litharge material for tension and compression in the cantilevers, 343 pounds

per square inch.

6. Average modulus of elasticity of rubber-litharge material

for tension and compression in the arches, 389 pounds per square

inch.

7. Average modulus of elasticity of rubber-litharge material for shear in the cantilevers, 114.33 pounds per square inch.

371
372 MODEL TESTS OF BOULDER DAM

8. Average modulus of elasticity of rubber-litharge material for shear in the arches, 129.67 pounds per square inch.

9. Average value of Poisson's ratio, 0.5.

10. Normal arch and cantilever stresses vary as a straight

line from the upstream to the downstream face of the model.

11. Foundation movements made to conform to the model

measuremen ts.

12. The concrete pit assumed to be rigid.

13. The rubber-litharge material assumed to remain in contact with the concrete of the testing pit at a1l10cations.

Note that values of the shearing modulus of elasticity for arches

and cantilevers are slightly different from experimentally determined

values. It was necessary to use the above values in order to maintain mathematical compatibility in the stress-strain relations.

227. Cantilever Elements.- Vertical cantilever elements were

assumed to be one inch wide at the axis of the dam and to have radial

sides, converging from the upstream face to the downstream face.

The cantilevers were elastic units, set on elastic bases. They resisted

radial forces applied at the upstream faces, tangential and vertical

forces applied at the center lines, and horizontal and vertical moments

applied at the center lines. Tabulations of unit radial, tangential, and

twist loads were made for cantilever elements as described in section

132. Equal and opposite sets of vertical forces acting on arches

and cantilevers were required to make vertical arch mOvements agree

with vertical cantilever movements. In these considerations it was

found convenient to use triangular loads at the center lines.

Figure 239 shows a plan of the arches and cantilevers used in

the analysis. Due to changes in direction of radial lines at different

elevations, the cantilevers were warped slightly. Consequently, radial

cantilever loads caused not only radial deflections but also slight tangential, angular, and vertical movements.

Figure 151, chapter VII, shows typical unit radial, tangential,

and twist loads applied to the cantilever of the plaster-celite model.

Figure 240-a shows the additional unit vertical loads applied to the

cantilevers of the rubber-litharge model.

228. Arch Elements.-The horizontal arch elements shown on

figure 239 were assumed to be one inch high and to have horizontal
ELEV. "

LEFT HALF RIGH-i~A

1232 70.00' 70"00'

1100 59"00' 52"00'

1000 45"00' 40"00'

.00 33"00' 29"00'

800 20"00' 21"00'

700 13"00' 16"00'

600 ANALYZED AS A BEAM

0 I 2 3 4 5 6

sCAli OF I~CHE5

.

,

::d

>

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t'"

0

>

tJ

>

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>

t'"K:

w

-w

0

":J

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tJ

t'j

t'"

CENTRAL ANGLES <I> OF ARCHES (AS ANALYZED)

FIGURE 239-PLAN OF MODEL SHOWING ARCHES AND CANTILEVERS ""

->

""
374 MODEL TESTS OF BOULDER DAM

top and bottom faces. The extrados of each arch was circular. The

intrados followed a three-centered curve in which the central part

had the same center as the extrados. The abutments of the arches

were radial at the top elevations and gradually changed to lines that

were closely parallel to the canyon walls at the lower elevations.

The abutment lines of the arches, as they were constructed and

analyzed, are shown on figure 239. I

At elevation 600, the arch was

shaped more like a rectangle than <in arch, so it was analyzed as a

rectangular beam.

Calculations for arch elements considered effects of irregular

abutments, thickening of arches due to fillets, and lack of symmetry

between the crown cantilever and the arch crowns. Calculations of

Intensity of

vertiCOIIOO~

Onepound p~

square inch:'-'

One pound per

square inch'-----

'?;;\ 'ltt. ,

~-<... "-Load applied at center

~ ~ of arch.,

-~t-.

_5g_~

(a) UNIT VERTICAL CANTILEVER LOAD (b) UNIT VERTICAL ARCH LOAD

FIGURE 240-UNIT VERTICAL LOADS

deflections caused by unit radial, tangential, and

made in the same manner as described in section

These unit loads are shown in figure 152.

Besides the radial, tangential, and twist loads, vertical loads

were required to make the vertical arch deflections agree with the

vertical cantilever deflections. The required unit loads included a

uniform load of one pound per square inch vertical shear, and triangular loads which varied from one pound per square inch vertical

shear at the abutment to zero shear at the different arch quarter

points, as shown on figure 240-b. Other features of the arch calculations were the same as described in section 133.

twist loads were

133, chapter VII.
TRIAL LOAD ANALYSIS OF MODEL 375

ADJUSTMENTS

229. Radial Adjustment.--The radial adjustment was the first

step in the analysis. Figure 241 shows the final adjustment for the

arch elements, including the division of water load as well as the

adjusted deflections of the arches and cantilevers. The initial positions indicated on the drawings are the developed center lines of

the arches. Locations of arch quarter points and intersections of

the cantilevers with the arch center lines are also indicated on the

diagrams. Deflections were measured from these points.

The horizontal component of the water load was divided into

two parts, both radial, one acting on the arches and the other on the

cantilevers. The vertical component of the water load was assigned

to the cantilevers, and the resulting cantilever deflections combined

with the deflections caused by the horizontal water load assigned to

the cantilevers, before adjusting with the arch deflections.

Details of the application of concentrated loads at the abutments

to maintain continuity were presented in section 134. Subsequent

readjustments of radial deflections were necessary because loads introduced in the tangential, twist, and vertical adjustments, in addition

to effects of Poisson's ratio, caused radial arch and cantilever movements. Altogether, thirteen trial adjustments and readjustments

were made before arriving at the final loads and deflections shown on

figure 241.

The radial adjustment constituted the principal step in the trial

load analysis. Although tangential, twist, and vertical adjustments

were required, they were of secondary importance compared with

the radial adjustment. Radial movements were much greater than

tangential, angular, and vertical movements. Poisson's ratio had considerable effect on radial deflections because of its high value.

230. Tangential Adjustment.-After radial deflections due to

radial loads were adjusted, tangential movements were considered in

the tangential adjustment. Figure 242 shows the initial position and

final tangential displacements of arch center lines, also the tangential

loads required for the adjustment. Positive tangential loads and movements act toward the right abutment; negative loads and movements

act toward the left abutment.

The first stage of the radial adjustment showed that radial arch

loads caused larger tangential movements of the arch center lines

than radial cantilever loads. Consequently, conjugate points of the
II

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"ABUT iI

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I'.~ I:~ oCR1:* I i t~ ~i !'ABUT r r 'r : ri I I r : t I i i i I i

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ELEY. 600

NOTES

Water surface at elevation 1232

>(Rodlol deflection of arch center line 0 Radial deflection of cantilever center of

gravity

>,}Location of cantilevers at ends of arches

at elevations 1000 and 800

These arches used In determining load

distnbutlOn

Foundat,on deformation adjusted to can.

form 10 model measurements

Analysis includes effects of tongenhal

shear, twist, Poisson's ratio, vertical

adjustment,and foundation deformation

FIGURE 241-FINAL RADIAL ADJUSTMENT AT ARCH ELEMENTS
.

..

"00,'001

0900 ~Ol 0 700

)1 II

44 \!~

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*600 ..

700 900 1000 1100 I

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SCALE OF INCHES

600 CAO...~CANTILEvER600 I

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,,: 'I

ELEV. 1232

1100 10°

1

°

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r' I

800 700 600 CROWN J ' I ' 1

4131 ABUT, 4;1 1'II . 4,'1 k~ 1,4 ~ 1 r r I : I I I I :

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IIII

III

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ELEV. 700

'-~rl

ELEV. 600

NOTES

Woter surface at elevation 1232. )(

Tangentlol deflection bf orch center line

0 Tangential deflection of cantilever

center of gravity.

~, Location of cantilevers at ends of

arches ot elevations 1000 and 800.

These contdevers used in determining

lood distribution. .

Foundation deformation adjusted to

conform to model measurements.

Analysis includes effects of Poisson's.

ratio, vertical adjustment,and foundation deformation.

FIGURE 242-FINAL TANGENTIAL ADJUSTMENT AT ARCH ELEMENTS

~

-1-1

ELEV. 1100

,,,

~-+ i:

ELEV. 1000

800

600 700 900 "

'>

~'

12: :.4:

4 ABUT.

r,r: ' I , :I' : i : ,, , , I , I , I I i

EL.EV. 900
378 MODEL TESTS OF BOULDER DAM

two systems were out of agreement in tangential directions. For the

purpose of simplifying the estimate of tangential loads required to

bring arches and cantilevers into agreement, two cantilevers, 700 and

900, were investigated first. Relative tangential deflections of all

points were then compared and an estimate made of the additional

loads necessary to produce approximately the same deflections at

conjugate points. After several trials, close agreement was obtained.

Subsequent readjustments of tangential deflections were required,

since twist adjustment loads, radial readjustment loads, vertical

loads, and effects of Poisson's ratio produced additional tangential

movements. A total of twelve sets of trial tangential loads were required for the first stage and subsequent readjustments to obtain the

resulting loads and deflections shown on figure 242.

231. Twist Adjustment.-Radial loads on the arches produced

angular movements about vertical axes while radial loads on cantilevers produced very little rotation about vertical axes. To bring the

conjugate points of the two systems into tangential agreement, further rotations of the arches and cantilevers were introduced. The first

trial adjustment was made between the arches and cantilevers 900

and 700. From this adjustment a fairly close estimate was made of

the loads required for the remainder of the structure. Since the vertical adjustment, radial and tangential readjustments, and the effects

of Poisson's ratio all produced additional angular movements in the

arches and cantilevers, subsequent twist readjustments were made to

restore angular agreement. Figure 243 shows the loads and movements after the twist readjustments were completed.

232. Vertical Adjustment.-Before the rubber-litharge model

of Boulder Dam was tested, vertical movements in a dam had not

been seriously considered. Since appreciable vertical deflections occurred in the rubber-litharge model, these movements were measured

at sufficient points to determine vertical deflection curves. The trial

load analysis was, therefore, extended for the purpose of considering

vertical loads and deflections.

Results of the vertical adjustment at the arch elements are given

in figure 244. The diagrams show initial and final vertical displacements, also vertical loads required for the adjustment. Positive deflections are upward and positive vertical loads act in a downward

direction on the arches. Figure 244 shows that the model was deflected

vertically in an upward direction, except at elevation 600 where the
ELEV. 1232

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'"~~,', ijt~fr"" I i Inl~ ELEv. 900

°

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SCALE OF INCHES

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.., ~>

t"S>tj>Z>~U1 H

U1 0

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t:I

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ELEV.700

""rrl'

ELEV.600

NOTES

Water surface 01 elevation 1232 x Angular movement of arch center hne. a Angular movement of cantilever center

of gravity-

~:-Location of conlilevers at ends of

arches at elevations 1000 and 800

These cantilevers used in determining

lood dlstrlbulion

Foundation deformation adjusted to conform to model measurements

Analysis includes effects of Poisson's

ratio,vertical adjustment,and foundation deformation.

FIGURE 243-FINAL TWIST ADJUSTMENT AT ARCH ELEMENTS ""-><:>
~ ."

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0

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m" W§~

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ABUT'l

900 700 1100

:3

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600 CROWNCANflL(VER '.' .Jfl .

,c<

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ELEV. 1232

I

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ELEV. 1100

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ELEV.900

O~~6

SCALE OF INCHES

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ELEV. BOO

600 600

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ELEV.700

'''m"'

ELEV. 600

NOTE5

Water surface at elev. 1232 x Verhcol deflection of arch at

axis of dam.

0 Verticol deflection of cantilever

at aXIs of dam.

Foundation deformotion adjusted

to conform to model meosurement

Analysis includes effects af poisson's

rotio and foundation deformation

FIGURE 244-FINAL VERTICAL ADJUSTMENT AT ARCH ELEMENTS
TRIAL LOAD ANALYSIS OF MODEL 381

deflection was downward. In general, the loads on the arches actt>d

in an upward direction.

An analysis of the effects of radial, tangential, and twist adjustments showed that the arches and cantilevers moved in vertical directions. The major reason for the vertical movements was the

effect of Poisson's ratio on the cantilevers. If the cantilever is

visualized with the water pressure acting on its upstream face and

the arch stresses acting on its sides, it is evident that Poisson's ratio

causes vertical movements.

Equal and opposite vertical loads, one set on the arches and

the other on the cantilevers, were introduced to remove relative vertical deflections. Required amounts of loads were estimated and gradually adjusted by trial. As in other adjustments, it was expedient to

use unit arch and cantilever loads. In the first estimate of vertical

loads, crown cantilever deflections were adjusted to the crown deflections of the arches. After the crown cantilever was adjusted,

deflections of other arch and cantilever points were computed. All

vertical deflections were then compared and additional loads estimated

until conjugate points of the two systems were relatively close together. After five successive trials, a satisfactory deflection agreement was obtained, thus completing the first stage of the vertical

adjustment.

The vertical loads caused radial, tangential, and angular movements in the arches and cantilevers. These movements were considered in subsequent readjustments. However, it was found that

additional radial, tangential, and twist loads, used to correct for movements due to vertical loads, were not of sufficient magnitude to produce significant additional vertical deflections. Therefore, subsequent

vertical readjustments were not required. Although vertical deflections were rather large, vertical adjustment loads produced only

small radial, tangential, and angular movements. The major effect

of vertical loads was to increase cantilever stresses at the upstream

face. The loads caused only minor changes in normal arch stresses.

233. Sequence of Adjustments. - Movements not considered

prior to the completion of the first stage of the twist adjustment were

radial deflections due to tangential and twist loads, and tangential

deflections due to twist loads. These radial movements, considered

in the first radial readjustment, introduced additional radial loads,

causing new tangential and twist movements. Next, the first tans'ential readjustment was made to correct for discrepancies caused by
382 MODEL TESTS OF BOULDER DAM

twist loads and the first radial readjustment loads. Likewise, a twist

readjustment and subsequent radial, tangential, and twist readjustments were required because each readjustment produced movements that had to be considered in the following readjustments. The

effects converged rapidly. After a few radial, tangential, and twist

readjustments, they became so small that they did not change the

other adjustments by appreciable amounts.

The next step in the analysis was to determine the effect of

Poisson's ratio in the radial, tangential, and twist adjustments.

Poisson's ratio produced movements in the arches and cantilevers.

Consequently, additional loads were introduced to restore continuity

throughout the structure. The procedure of adjustments and readjustments was the same as described above.

N ext, vertical movements due to Poisson's ratio were considered

in the vertical adjustment. The resulting vertical loads caused radial,

tangential, and angular movements that were considered in subsequent readjustments. However, effects of additional vertical loads

were small, and only one set of readjustments was required.

The complete analysis, including all adjustments and readjustments, required thirteen radial, twelve tangential, twelve twist, and

five vertical sets of trial loads. These adjustments determined the

total movements of the model, also the amount and distribution of

the different loads. vVith this information, arch and cantilever stresses

were calculated by the usual stress formulas.

RESULTS OF ANALYSIS

234. Computed Stresses.-Computed arch and cantilever stresses

are shown on the developed profile in the upper part of figure 245.

Final radial loads and deflections at the assumed cantilever elements

are shown in the lower diagrams.

Arch stresses are given for extrados and intrados locations at

crown and abutment sections. The maximum compression in the

arches occurred at the extrados of the arch at elevation 600 and

amounted to 3.15 pounds per square inch. The maximum tension

occurred at the extrados at the left abutment of the arch at elevation

1100 and amounted to 1.24 pounds per square inch.

Cantilever stresses are given for upstream and downstream faces

at all arch elevations. Cantilever stresses were smaller than arch

stresses, because the moments of the vertical and horizontal loads
100L 600L CROWN CANT! LEVER 6001'1

£-+-U4

1+.39

[""1,'" 1+.11

...

""

U+.39 U+.34

0-.08 0-.23 0-,13 D-.22

EH.57

U+.21

1+ 06

Uf., 4

U"'.21 U+.2"

0+.26 0+.01 0+.27 0+,10

[+1.60

1+.20

U".13 U+,24 U+.28 U+.24

0+.40 0+.25 0+.46 0+.30

£+1.94

r+.02

U+.30

0+.24

U+.38

0+.48 g::;~

TRIAL LOAD ANALYSIS OF MODEL 383

0+.02 -.'

7001'1 900R 1232

-1.1

1- .19

900L

~Q 900

..C

Z

0

roo

ARCH STRESSES ARE ACTING I~

HORIZONTAL DIRECTIONS PARALLEL

TO THE EDGES OF THE ARCHES.

[-STRESS AT EXTRADOS OF ARCH.

I-STRESS AT INTRAOQ.S OF ARCH.

CANTILEVER STRESSES ARE ACTING

IN INCLINED DIRECTIONS PARALLEL

TO THE EDGES OF THE CANTILEVER.

V-STRESS AT UPSTREAM EDGE OF

CANTILEVER

C'STRESS AT DOWNSTREAM EDGE

OF CANTilEVER.

~ 900 !.;(

<{ ,T , If, ,Ir

z

SCALE OF LNCHES 0

.00

~ STRESSESINCLUDEEFFECTS ;;::

~:~O~O ~~'~~::~~i~?~~~~t:5~j:- 7 0

ICAI. AOJUSTMENT,ANO ADJUhlNG

COMPUTED FOUNDATION DEFORMATIONS

TO MODEl. MEASUREMENTS. AI.\.

+3.06 STRESSES IN 1.8 PER SQ. IN.

1-.10

+. COMPRESSION

-. TENSION

PROFILE ON AXIS LOOKING UPSTREAM (DEVELOPED)

~_..

(Mid-point of trlor'1gular abutment of cantilever is assumed at

elevation indicated by deflection diagram """"""""--

~

'00 ..c

z

0

.00

~

'00

DOWNSTREAM MOVEMENT OUR ING

FILI.I"IG OF_:~S_E~~~I~)

~

~

1000

"

C

~

900

~

~

eoo

+01 0 -0.1

Lu..uki.J

RADIAl.. DEFLECTION IN INCHES

LOAD DISTRIBUTION AND

RADIAL ADJUSTMENT

NOTES

0 Cantilever deflection.

x Arch deflection

Foundation deformation adjusted to

conform to model measurements.

FIGURE 245-RESULTS OF TRIAL LOAD ANAL,YSIS
EH04

t-.11

.

1

~~900

z

0

!

700

505

1232 [t.33

1-.\8

1100

.

~1000

"

~z

900 0

;::

~~900

"

~600

505

123

[-.156

1-.159

1100

10

~~900

z

0

!

600

600

505

.00 CROWN

.

""'"

CANTILEVER 6 1232

E-.I' Et." 1-.35 1-.01

1100

U-,\5 0-.01 U-. 1 Ot.21 "... 0+.09

1000

~0-,09 Ut.02 Ot.11 0-.03 ~!:8%~

900

~U+.o9 Z

O-,11t 0

600

~600

50.

STRESSES DUE TO TANGENTIAL SHEAR AND TWIST

CROWN

CANTILEVER

[+.21 E+.29

'-.00 1-20

384 MODEL TESTS OF BOULDER DAM

1100

0 10 20

1111i/llldl 11111111

SCALE OFINCHES

~ 1000 0

~

900 ~

E

800 ~

600

50.

STRESSES DUE TO POISSON's RATIO

900L CROWN

CANTILEVER EiOaR

[-.08\

1-.032

[-.I

1-,159

70aL 600 1232

1100

~

10000

"

~

900 ~

~ 800 ~

700

600

505

NOTES: Arch stresses Ofe acting in horizontal directions parallel to

the edges of the arches.

E =Stress at extrodos of arch. I =Stress at intrados of arch.

Cantilever stresses are octing in inclined directions parallel to the

U =e~~~:s~~/~~st~~~~I~d~e of cantilever.

0" Stress at downstream edge of cantilever.

All stresses are i!" poun.ds per square inch.

Profiles are on aXIs looking upstream (developed).

+:: Compression

-:: Tension

FIGURE 246-ARCH AND CANTILEVER STRESSES
TRIAL LOAD ANALYSIS OF MODEL 385

tended to balance each other. A maximum cantilever compression of

0.73 pounds per square inch occurred at the downstream face of

cantilever 700-R at elevation 900. A maximum tension of 0.25 pounds

per square inch occurred at the downstream face of cantilever 600-L

at elevation 600. All cantilever stresses shown in the figure are acting

in inclined directions parallel to the edges of the cantilevers.

The load distribution diagrams indicate that the greater part

of the water load was carried by arch action; also that the load on

each arch was fairly uniform. The load carried by cantilever action

was a maximum at the base of the crown cantilever, and varied to a

negative load at the top of the model. The negative load developed

because the top arches resisted downstream cantilever movements.

Figure 246 shows changes in arch and cantilever stresses due

to tangential shear and twist, Poisson's ratio, and vertical adjustment. Tangential shear and twist action changed both arch and cantilever stresses considerably. In general, tangential shear and twist

effects reduced arch stresses at the intrados of the abutments and

the extrados of the crowns. In the cantilevers, upstream stresses

were increased at the lower elevations and decreased at the upper

elevations. Downstream cantilever stresses were decreased in the

lower part of the model and increased in the upper part.

Poisson's ratio effects did not change stresses as much as did tangential shear and twist. Nevertheless, the changes were appreciable.

The effect of Poisson's ratio would be much less in a concrete dam

where the ratio is approximately 0.20 instead of 0.50. The vertical

adjustment changed arch stresses only slightly; and, in general, increased cantilever stresses.

235. Experimental and Analytical Stresses.-A comparison of

experimentally determined arch stresses at the upstream face of the

model, with those obtained in the trial load analysis, is shown in figure

247. Strain measurements could not be made at the upstream face

at elevation 1232, where stresses were computed, as there was not

sufficient space for mounting strain gages. However, the stress curve

determined from strain measurements at elevation 1200 has the same

general shape as the computed curve at elevation 1232. At elevations

1100 and 1000, the agreement between the two sets of stresses is satisfactory. At lower elevations, where the model was thicker, the two

stress curves are somewhat farther apart, the analytical stresses being

larger than the stresses determined from strains. Discrepancies

between the two sets of stresses were probably due to effects of
---

- --- -----

-" ""''''''' ",.

/

-...

/

/ '

/

"

"

z

w .0.

~4

~0

-0 ..

~..

0

Z

~0

.

WJ

8

~~..

..

~~U

4

~~~..

,

-

- - --,

, ..../ -.

.--- --

,

0

386 MODEL TESTS OF BOULDER DAM

""'.5

NEVADA ABUTMENT

, A

CANTILEVER MEASURING SECTIONS

0 E F G

ARIZONA ABUTMENT

J

----

...---

"" , ""

ELEVATION 1232

TI.5

',-

ELEVATION 1200

+1.5

+'.0

+0.5

-0.5

-1.0

-1.5

ELEVATION 1100

'1"1.0

ELEVATION 1000

'1"1.5

-_x ,,---

+1.0

+0.5

ELEVATION 900

::~

~

- --._--

+'.5 ---

+1.0

1-0.5

ELEVATION 800

::

.

~m:1j - --- - -

+2.0

+1.5

., 0

i'0.5

0

ELEVATION 700

NOTE

Reservoir water surface

at elevation 1232

.','

~

+ .0 ----

+2.5

+2.0

t 1.5

+

1.0

+0.5

ELEVATION 600

NOTES

+ Compression

-

Tension

0-0 Stresses from measured strains

x---x Analytical stresses

FIGURE 247-EXPERIMENTAL AND ANALYTICAL ARCH STRESSES

AT UPSTREAM FACE
i--

~- ---04 ~'::::::- - --

"

---- --- - -- ---

"

/

r-..... -........

"

./

"- .,-:::.--

-

-""- ~-- -.-.

+-0.5

~~.0.5

.

~" 0

~.

0

"

Z

~".

~~W

"

0

2

0

0W

~~0

WU

..

~~0

TRIAL LOAD ANALYSIS OF MODEL 387

NEVADA ABUTMENT

I

+1.5

+LO

CANTILEVER MEASURING SECTIONS

D E f G

ARIZONA ABUTMENT

I J

to.5

0

-0.5

-1.0

-1.5

ELEVATION 1232

+1.5

+1.0

+0'

ELEVATION 1200

+2.5

+2.0

+1.5

tl.O

ELEVATION 1100

tUS ...

HO

+0.5

ELEVATION 1000

+I.'

~

+10

+Q.5

0 -- --- --"- ----

ELEVATION 900

HO

~

+0.5

0 - --

..J,

-0.5

ELEVATION BOO

HO

~

+0.5

0)<-><-"

---

-0.5

ELEVATION 700

NOTE

Reservoir water surface

at elevation 1232.

+l.0

+°;,,-- ~-----.----- -0.5

ELEVATION 600

NOTES

+ Compression.

-

Tension.

0-0 Stresses from measured strains.

,,---x Analytical stresses.

FIGURE 248-EXPERIMENTAL AND ANALYTICAL ARCH STRESSES

AT DOWNSTREAM FACE
388 MODEL TESTS OF BOULDER DAM

ARIZONA ABUTMENT NEVADA ABUTMENT

1232

~

~

a

0

a

m

4

00

Z

a

~

z

i

1232

.

4a

~

a

m

~

4

00

Z

a

4

>

J

z

I

FIGURE 249-LINES OF EQUAL ARCH STRESS AT UPSTREAM FACE

STRESSES FROM MEASURED STRAINS

ANALYTICAL STRESSES

DEVELOPED UPSTREAM ELEVATIONS

APPROXIMATE

NOTES

+ Compression.

- Tension.

Stresses are in pounds per square inch.

Reservoir water surface at elevation 1232.
TRIAL LOAD ANALYSIS OF MODEL 389

Poisson's ratio, the proximity of the canyon walls, and the fact that

the arch thicknesses were considerably greater than the arch lengths.

Arch stresses at the downstream face, determined by experimental and analytical methods, are compared in figure 248. \Vith

the exception of some variation along the abutments, the two sets

of stresses show a good agreement above elevation 700. At elevation 600, experimental stresses were compressive at the abutments and

decreased to zero at the crown, while analytical stresses were tensile

from abutment to abutment. However, both stresses were small at

all locations along the arch, and the greatest difference between the

two was about one-half pound per square inch.

Lines of equal arch stress at the upstream face, determined experimentally and analytically, are compared in figure 249. It should

be remembered that strains on the upstream face were measured

over 3-inch gage lengths, so that the measurements indicated average

strains over the 3-inch lengths. Consequently, stresses computed from

the measurements do not show complete stress variations. The greatest differences occurred below elevation 700 where the model was

relatively thick.

A similar comparison of stresses at the downstream face is shown

in figure 250. The agreement between the two sets of stresses was

much better, since the strains were measured with a more accurate

instrument having a shorter gage length than was used at the upstream face. The line of zero stress, determined experimentally, extended from elevation 1200 to the base of the model. The corresponding line, determined analytically, crossed the downstream face between elevations 690 and 790. Both methods indicated a concentration of stress along the abutments between elevations 900 and 1100.

Cantilever stresses at the upstream face are compared in figure

251. In the central part of the model, the agreement was satisfactory, but some discrepancies occurred near the abutments. A similar

comparison of cantilever stresses at the downstream face is shown

in figure 252. The agreement between the two sets of stresses was

close, the greatest discrepancy being about one-half pound per square

inch.

Lines of equal cantilever stress at the upstream and downstream

faces are shown in figures 253 and 254. Magnitudes of maximum tensile and compressive stresses agreed closely in both figures. Some

variations occurred in locations of lines of zero stress between areas

of tension and compression.
390 MODEL TESTS OF BOULDER DAM

NEVADA ABUTMENT

A

CANTILEVER MEASURING SECTIONS

C 0 E F G

ARIZONA ABUTMENT

STRESSES FROM MEASURED STRAINS

00

ANALYTICAL STRESSES

DEVELOPED DOWNSTREAM ELEVATION

APPROXIMATE

NOTE5

+ Compression

- Tension

Stresses are in pounds per square inch

Reservoir water surface ot elevation 1232.

g

«

~

0

J

~

0

m

~

~

~

z

0

~

"

z

I

8

g

«

~

0

J

~

0

m

!<

~

z

0

§

"

z

I

8

FIGURE 250-LINES OF EQUAL ARCH STRESS AT DOWNSTREAM FACE
\

I

I,

,

,

I

I

,

\

.0ffE

SECTION A

-05 Ot05 tlO 1232

1200

,

100

~

~

1000

~(I)

900

.00

SECTION F

.~

SECTION B

STRESS IN POUNDS PER SQUARE INCH

.mJ

SECTION C

STRESS IN POUNDS PER SQUARE INCH

.aE

SECTION G

'00'

SECTION H

-0.5 a +0.5 +r,o -0.5 0 +0.5 +1.°1232

1200

,f

,

I

,

,

I

I

1100

1000

~

<

900 !4

~

>-3

::0

>-<

>

t"'

t"' 0

>Ij

>

Z

>

~rn

>-< rn

0

"'J

Ie' 0

Ij

trj

t"'

SECTION 0

SECTION E

-OEfEO

SECTION J

NOTE 5

+

Compressi'On

-

Tension

0 0 Stresses (rom measured strains

X---ot< Analytical stresses

Reservoir water surface at elevation 1232

.00

700

600

FIGURE 251-EXPERIMENTAL AND ANALYTICAL CANTILEVER STRESSES AT UPSTREAM FACE "'" ~

I-'
f

~:\

\

\

\

/

/

/

(

,

1\\

I

I

I

- Lt

'\t"\

1\

\

\

I

I

I,

I

I

I

\

\..

\

\

\

\

IiI

I

,I

,

"'"

t::

""

1100

'000

~c

~<

900 !j

i is:

800 0

tI

l':j 100 t'"

>-3

600 l':j

00

>-3 00

0

"'J

td

0

q

t'"tI

l':j

::d

tI

>....

....,

-lfET SECT! ON I

-0.5 0 "to.5 +1.0

1232

>200

1100

.000

~

<

~ 900

~

800

100

600

SECTION F

00"

SECTIONA

-0.5 0 "0.5 +1.0

SECTION G

STRESS INPOUNDS PER SQUARE INCH

-05 0 +05 +10

HE

t

,\

-0.5 0 +0.5 +1.0

SECTION 0

-OffEr

SECTION J

NOTES

+

Compression.

- Tension.

- Stresses from measured strainsK oto:Analytical stresses.

Reservoir water surface at elevatIon 1232:.

-05 01-05 +10 1232

'200

SECTION E

-OEE~~r

SECTION K

FHHJRE 252-EXPERIMENTAL AND ANALYTICAL CANTILEVER STRESSES AT DOWNSTREAM FACE

SECTION B

I

I

SECTION C

STRESS IN POUNDS PER SQUARE INCH

lr;n"cm"

SECTION Ii
TRIAL LOAD ANALYSIS OF MODEL

ARIZONA ABUTMENT NEVADA ABUTMENT

"o.'/..!>

STRESSES FADM MEASURED STRAINS

ANALYTICAL STRESSES

DEVELOPED UPSTREAM ELEVATIONS

APPROXIMATE

NOTES

+

Compression.

-

TensiOn

Stresses are in pounds per square inch.

Reservoir water surface ot elevation 1232

1232

~

~

w

C

J

~

C

G

~

.

0

z

c

~

c

z

I

1232

~~

w

c

~

C

G

.

0

z

c

~

..

z

i

FIGURE 253-LINES OF EQUAL CANTILEVER STRESS

AT UPSTREAM FACE

393
394 MODEL TESTS OF BOULDER DAM

NEVADA ABUTMENT

A

CANTILEVER ~EASURING SECTIONS

C 0 E F G

0

ARIZONA ABUTMENT

H 1232

STRESSES FROM MEASURED STRAINS

ANALYTICAL STRESSES

DEVELOPED DOWNSTREAM ELEVATION

APPROXIMATE

NOTES

+ Compression.

-

Tension.

Stresses ore in pounds per square inch.

Reservoir water surface at elevation 1232.

FIGURE 254-LINES OF EQUAL CANTILEVER STRESS

AT DOWNSTREAM FACE

"11

~~

"~

~

..z

"

~

0z

~

~

~

"

u

g

~~

"

~

"

Ii:

~

..z

":i

~

0z

~

~~

"

"
TRIAL LOAD ANALYSIS OF MODEL 395

236. Comparison of Deflections.-Comparisons of movements

calculated by the trial load method with those measured on the model

are shown in figures 255 to 258, inclusive. The comparison of radial

deflections indicates a satisfactory agreement between the two sets of

deflections. The tangential deflections, angular movements, and vertical deflections did not agree as well with the measured values; but,

with the exception of the angular movements near the top of the

model, the agreement was fairly satisfactory. The probable reasons for

the discrepancies were:

1. Variations between actual thicknesses of the model and

values assumed in the analysis.

2. The rubber-litharge base was not securely bonded to

the concrete base.

3. The modulus of elasticity and Poisson's ratio in the vertical direction were different from those in radial and tangential

directions.

4. The correction of calculated movements at the center

lines to apply to the downstream face could only be approximated.

The calculated movements would have been slightly more accurate if more arches and cantilevers had been used in the analysis.

However, the results indicated that the elements investigated were

sufficient to give a satisfactory solution.

237. Conclusions.-In the trial load analysis it was necessary

to assume that the rubber-litharge compound was a homogeneous

material, isotropic in the horizontal plane. Tests of the material gave

three different moduli of elasticity in three mutually perpendicular

directions, and two different Poisson's ratios for each direction. The

only attempt that could be made to fit these conditions was to use

different moduli of elasticity for the arches and cantilevers. It was

necessary to assume in the analysis that the foundation was continuous. Since the rubber-litharge supplemental base was not securely

bonded to the concrete support, movements may have occurred at the

contact between the two materials. These movements probably caused

deflections in the model that could not be accounted for in the trial

load analysis.

It is believed that the discrepancies between calculated and

measured data were due to the characteristics of the model rather

than to the trial load analysis. Consideration should be given to the

fact that agreements of stress in regions of high stress were much
Crown secfion-"

...

Developeddownstream

face of model.-------------

Measured deflections

Calculafed deflections

-

Indicates downstream deflection.

RADIAL DEFLECTIONS AT DEVELOPED DOWNSTREAM FACE

(LOOKING UPSTREAM)

NOTES

Modutus of elasticity for arches: 389 pounds per square inch

Modulus of elasticity for cantilevers: 343 pounds per square inch.

Poissons ratio:Q.5 Scale of model I to 180.

Measured deflections plotted from Figure 191.

Calculoted deflections corrected to apply to dOwnstream face

Water surface at £1.1232

<»

'"' ""

_£!-J~t

-

,,~

0 o~

,+

,+

-O.lO ~+"

-0.30 ~~ ,V

-0.40 Q4t;

O,..V

.>

~

0

Ij

t<J

t"

>-'3

l"i

Ul

>-3 Ul

0

"'j

t:tI

0

Ci

t"Ij

l"i

::0

Ij

>

~

~~LE' 0: INCHE~O

FIGURE 255-COMPUTED AND MEASURED RADIAL DEFLECTIONS
Developed downslream

face of modeL-------------

Crown section \

-__~!-",'-2_~~__-

I

n_t!::..119P_-

cl~8J

___~k_~~~Q 

#- .'::>

~

,~

,v

-0.05 ~

~,.v

,,~."

Measured deflections

Calculated deflecttons

----------

+ Indicates deflectIOn to the right when looking upstream

-

Indicates deflection 10 the left when Iookll"lg upstream.

.J:hl!.QQ.__--

,.

,

SCALE Of INCHES

...,

::0

......

:>-

t-<

t-<

0

:>-

t!

:>-

Z

:>-

~00

......

00

0

''OJ

s::

0

t!

t"J t-<

Developed downstream

foce of model.

TANGENTIAL DEFLECTIONS AT DEVELOPED DOWNSTREAM FACE

(LOOKING UPSTREAM)

NOTES

Modu Ius of elasticity for arches:: 389 pounds per square inch.

Modulus of elasticity for cantilevers. 343 pounds per square inch.

POIsson's ratIO- 0.5 Scale of model I to 180

Measured deflections plotted from Figure 194.

Calculated deflections corrected to apply to downstream face.

Water surface at elevation 1232.

FIGURE 256--COMPUTED AND MEASURED TANGENTIAL DEFLECTIONS

""

~

-->
""<10

00

Developed downstream

face of model.---------

"--~-I,.""-~~_L_.

+0.010 ...,+~

.0

~

,+

,'>

~+

~..

0< ..

.~

#'v .

~

0

tI

M

t""'

>-3

Mrn

>-3

rn

0

"':J

I;1j

0

r.

t""' tI

M

::>:I

tI

>

""

"'"

("1-- Developed \ \

downstream

foce of model.

Measured deflections

Calculated defleclrons

--- --------

+ Indlcoles counter ctockwise movement when viewed from above.

-

Indicates clockw!semovement when viewed from above. ~!"_-.!!9Q...- ,.,

SCAL.E OF THCMES

ANGULAR MOVEMENTS AT OEVELOPED DOWNSTREAM FACE

(LOOKING UPSTREAM)

NOTES

Modulusof elasticity for arches: 389 pounds per square Inch

Modulusof elasticity for cantilevers: 343 pounds per square inch

POisson'sratio =0.5 Scale of mode! I to 180.

Measured deflections plofted from Figure 195.

Colculated deflections corrected to opply to downstream face.

Water surface at EI.1232

FIGURE 257-COMPUTED AND MEASURED ANGULAR MOVEMENTS
<

.

r~

J

z

-.06 i

Measured deftections

Calculated deflections ---------

-~I,.,,"g:t2_---

..,

::0

>

t"'

t"' 0

:>-

t:!

:>-

Z

:>-

~UJ

UJ ""

0

":I

~

0

t:!

trJ

t"'

J_L-,!i!Q(L___-

0

,

10 15

I I

"

I I I I

SCALE OF INCHES "

I

-_~_L..:_6.9_0___--

VERTICAL DEFLECTIONS AT DEVELOPED AXIS

o..OOKING UPSTREAM)

NOTES

Modulus of elasticity for arches" 389 pounds per square inch.

Modulus of elosticity for cantilevers" 343 pounds per square inch.

Poisson's rafro. 0.5 Scale of model I to 180.

Measured deflections plotted from Figure 19B.

Water surface at elevation 1232.

Foundation deformation adjusted to cont:lrm to model measurement.

FIGURE 258-COMPUTED AND MEASURED VERTICAL DEFLEC'fIONS

10->

""""
400 MODEL TESTS OF BOULDER DAM

closer than in regions of low stress. In general, agreements of observed and computed deflections were closer than agreements of stress.

Referring to the trial load analyses of the plaster-celite model,

the reader will observe that a better agreement with experimental

results was obtained. It is therefore concluded that the results of

the plaster-celite model tests represent more closely the action of a

concrete dam than do the results of the rubber-litharge model tests.
LIST OF BULLETINS

The following list shows tentative titles of final reports on the

Boulder Canyon Project now being prepared for publication. Titles

and prices of printed reports now ready for distribution are also included. Appropriate announcements will be made in engineering

periodicals as additional bulletins become available.

PART I-INTRODUCTORY

General Description of Project

History of Project

Legal and Financial Problems

PART II-HYDROLOGY

Stream Flow and Reservoir Operation

Lower Basin Utilization

Upper Basin Utilization

PART III-PREPARATORY EXAMINATIONS AND CONSTRUCTION

Geologic Investigations

Surveys and Preliminary Construction

(Topographic surveys, highways, raihvays, po,ver lines, substations, and

Boulder City).

PART IV-DESIGN AND CONSTRUCTION

General Features

Boulder Dam

Diversion Structures and Spillways

Intake Towers and Outlet Works

Concrete Manufacture, Handling, and Control

Penstocks and Outlet Pipes

Hydraulic Valves and Gates

Handling Facilities

(Cableway, cranes, and other permanent handling facilitil's).

Power Plant Building

Generating, Transforming, and Switching Equipment

Turbines, Governors, and Mechanical Auxiliaries

Control, Communication, and Electrical Auxiliaries

Imperial Dam and Desilting Works

All-American Canal and Canal Structures

401
402 MODEL TESTS OF BOULDER DAM

LIST OF BULLETINS-(Continued)

PART V-TECHNICAL INVESTIGATIONS

Trial Load Method of Analyzing Arch Dams*

Slab Analogy Experiments*

Model Tests of Boulder Dam

*

Stress Studies for Boulder Dam *

Penstock Analysis and Stiffener Design

Model Tests of Arch and Cantilever Elements

Research Measurements at Dam

(paper, $1.50; cloth, $2.00')

(paper, $1.00; cloth, $1.50)

(paper, $1.50; cloth, $2.00)

(paper, $1.50; cloth, $2.00)

PART VI-HYDRAULIC INVESTIGATIONS

Model Studies of Spillways*

Model Studies of Penstocks and Outlet Works*

Studies of Crests for OverfaU Dams

Model Studies of Imperial Dam and Desilting Works

Model Studies of All-American Canal Structures

Silt Movement in Colorado River

(paper, $1.00; cloth, $1.50)

(paper, $1.00; cloth, $1.50')

PART VII-CEMENT AND CONCRETE INVESTIGATIONS

Thermal Properties of Concrete

Investigation of Portland Cements

Cooling of Concrete Dams

Mass Concrete Investigations

Contraction Joint Grouting

Volume Changes in Mass Concrete

(Largely Investigations at Owyhee Dam, Owyhee Project, Oregon).

"For Sale at Offices of the Bureau of Reclamation in Denver, Colo., and Washington, D. C.

The Bradford-Robinson Ptg. Co., Denver, Colo. 7-5-39 3000