The Shape of Alluvial 

Channels in Relation 

To Sediment Type 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 352-B 

The Shape of Alluvial 

Channels in Relation 

To Sediment Type 

By S. A. SCHUMM 

EROSION AND SEDIMENTATION IN A SEMIARID 

ENVIRONMENT 

GEOLOGICAL SURVEY PROFESSIONAL PAPER 352-B 

UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1960 
UNITED STATES DEPARTMENT OF THE INTERIOR 

STEWART L. UDALL, Secretary 

GEOLOGICAL SURVEY 

Thomas B. Nolan, Director 

Reprinted, 1961 

For sale by the Superintendent of Documents, U.S. Government Printing Office 

Washington 25, D.C. -Price 35 cents (paper cover) 
CONTENTS 

Page Abstract __________________________________________ _ Effect of sediment type on downstream variations in 

Introduction ______________________________________ _ 

Page 

17 

17 

17 

18 

20 

channelshape____________________________________ 25 

Selection of a parameter representative of sediment type __ Conclusions and possible applications_________________ 28 

Methods of investigation ____ -----------------------_ lteferences----------------------------------------- 30 

Channel shape and sediment type ____________________ _ 

PLATE 

FIGURE 

ILLUSTRATIONS 

5. Stream channels illustrating range of channel characteristics at measured cross sections _________________ Facing 

8. ltelation between width-depth ratio and weighted mean percent silt-clay (M) _____________________________ _ 

9. ltelation between channel width and weighted mean percent silt-clay (M) ________________________________ _ 

10. ltelation of width-depth ratio to weighted mean percent silt-clay (M) for unstable cross sections __________ . ___ _ 

11. ltelation between width-depth ratio and weighted mean percent silt-clay (M) for cross sections with channel 

floor covered by more than 40 percent gravel, cobbles and boulders-------------------------------------

12. ltelation of width-depth ratio toM along the Smoky Hill-Kansas ltiver-----------------------------------

13. ltelation between width and depth for streams with not greatly different values of Min a downstream direction __ 

14. ltelation of channel width to depth for the Smoky Hill-Kansas ltiver--------------------------------------

15. ltelation of channel width to mean annual discharge for the Smoky Hill, ltepublican and Kansas ltivers _______ _ 

16. ltelation of channel maximum depth to mean annual discharge for the Smoky Hill, ltepublican and Kansas Rivers 

TABLE 

22 

21 

22 

23 

24 

25 

26 

27 

28 

29 

TABLE 1. Channel and sediment data _________________ ----- _____________________________________ -------________ 19 

m 

EROSION AND SEDIMENTATION IN A SEMIARID ENVIRONMENT 

THE SHAPE OF ALLUVIAL CHANNELS IN RELATION TO SEDIMENT TYPE 

By S. A. ScHUMM 

ABSTRACT 

The weighted mean percent silt-clay in the channel and banks 

of stable alluvial stream channels is used as a parameter (M) 

descriptive of the physical characteristics of sediment. Silt-clay 

is defined as alluvial material smaller than 0.074 mm. As the 

percentage of silt and clay in banks and channel increases, the 

shape of stream channels expressed as a width-depth ratio (F) 

varies according to the equation, F=255 M-J.Os Neither mean 

annual discharge nor the mean annual flood significantly affects 

this relation in spite of the importance of discharge to the absolute width and depth of a channel. 

Downstream changes in width and depth of a stream channel 

are greatly influenced by sediment type. As M increases downstream along a given river, the depth increases more rapidly and 

the width less rapidly with discharge than if M was constant, 

and width-depth ratio decreases. Conversely, as M decreases 

downstream the depth increases less rapidly and the width more 

rapidly with discharge than if M was constant, and width-depth 

ratio increases. The downstream changes in width, depth and 

width-depth ratio along the Smoky Hill-Kansas River system is 

presented as an example of the importance of sediment type to 

stream regimen. 

Unstable channels may be recognized by changes in widthdepth ratio. In general, aggrading channels have a higher widthdepth ratio than indicated by M; whereas degrading channels 

have a lower width-depth ratio than indicated by M. 

INTRODUCTION 

Lack of a simple quantitative expression of the physical properties of alluvium has hindered study of hydraulics and morphology of streams. In most studies 

of rivers and canals the median grain size {D50) has been 

used as the one parameter most descriptive of sediment 

type. However, even although of the same median 

grain size, sediment samples can vary widely in composition, depending on the sorting of the sample. If well 

sorted, the sample may consist of one type of material, 

such as sand; but if poorly sorted, a sample may be composed of several types, such as silt, sand, and gravel. 

Studies of the behavior of sediment grains under different physical environments reveal that there is a great 

change in sediment character within the range 0.05 

to 1.0 mm. For example, Hjulstrom's {1935) compilation of data, concerning the critical velocity of water required to initiate movement of sediment grains of uniform material, shows that the critical velocity increases 

as grain size decreases below 0.1 mm and increases also 

with grain size above 0.5 mm. According to Hjulstrom 

{1935, fig. 18), the velocity required to move a particle 

0.02 mm in diameter is about the same as that required 

to move a grain 2.0 mm in diameter. Bagnold (1954, 

p. 88, fig. 28) indicates that a similar relation exists between the threshold velocity of wind and grain size for 

windblown sand, although the zone of minimum velocity 

exists only for a range of about 0.07 to 0.1 mm. In addition, Rubey's {1933, p. 339, fig. 1) study of settling 

velocities of sediment shows that between 0.06 and 1.0 

mm there is a transition zone between the viscous resistance formula (Stokes Law) and the impact-of-water 

formula. His analysis suggests that in being transported by water there is a fundamental difference in the 

behavior of sediment grains smaller than 0.05 mm from 

those larger than 1.0 mm. 

It is the purpose of the present study to discuss the 

effect of one variable, sediment character, on the shape 

of alluvial stream channels. It is a simplification to 

relate any one aspect of stream morphology to one other 

variable, but this may be proper as long as both the 

writer and reader are aware that other factors may be 

important and that their importance may be identified 

as additional information becomes available. 

Valuable information on the hydrology of rivers in 

Kansas was provided by E. R. Leeson. F. F. Zdenek 

made grain-size analyses for the many sediment samples 

and calculated the values for mean annual flood and 

mean annual discharge for rivers other than those in 

Kansas. The writer also wishes to acknowledge the 

suggestions for improvement of the manuscript made 

by the following: W. M. Borland, Elliott Flaxman, 

C. R. Miller, and M. G. Wolman. 

SELECTION OF A PARAMETER REPRESENTATIVE OF 

SEDIMENT TYPE 

To obtain a valid expression of sediment type 

perhaps some grain-size parameter within the critical 

range 0.05 to 1.0 mm might be selected which would be 

more descriptive of sediment properties than median 

grain size alone. For example, Burmister (1952) has 

17 
18 EROSION AND SEDIMENTATION IN A SEMIARID ENVIRONMENT 

prepared tables from which one may estimate the permeability and drainage characteristics of a soil from the 

grain size below which 10 percent of the sample is finer 

(Hazen's effective size, D10). Other investigators have 

shown that the susceptibility .. · of soils to erosion 

(Bouyoucos, 1935) and the strength of cohesive soils 

(Trask, 1959) are related to a sand-clay ratio. 

In this study the percentage of silt and clay (taken as 

that part of each sample passing a 200-mesh sieve, 

and equivalent to sediment grains smaller than 0.074 

mm) was selected for comparison with stream-channel 

characteristics. This selection avoids the use of an 

absolute value for grain size,· the importance of which 

can be masked by sorting. of the sample. In addition, 

the value can be readily obtained from the cumulative 

grain-size curve. 

Burmister (1952, p. 20) gives some physical reasons 

for the selection of the 200-mesh sieve as the boundary 

between silt-clay and sand .. ·He states that the soil 

becomes less well drained and that capillarity increases 

with increase in material ·passing the 200-mesh sieve; 

in addition, the 200-mesh sieve is the practical lower 

limit of sieving for grain-size analyses. Any grain size 

between 0.05 mm and perhaps 0.1 mm could be used 

as the boundary between silt-clay and sand; however, 

it is convenient to use either the 200-mesh (0.07 4 mm) or 

230-mesh (0.0625 mm) sieves, and the 200-mesh sieve 

was selected for use here. · 

If, as suggested above, sediment less than 0.074 mm 

greatly influences the physical properties of sediment, 

then this fine fraction of the sample may be considered 

as the matrix in which the remainder of the sediment is 

fixed. The data available show that, in general, 

D10 decreases as percentage of silt and clay increases. 

Burmister's work (1952) indicates that a smaller value 

of D10 is associated with lower permeability and higher 

cohesion, supporting the suggestion that this fraction of 

the sediment is most effective in increasing the resistance 

of alluvium to erosion. 

METHODS OF INVESTIGATION 

Assuming that the shape of a stream channel depends 

on the resistance of sediment composing the perimeter 

of the :channel and the erosion potential of stream 

discharge, then sampling of bank and channel sediment 

at stable channel cross sections is necessary. Data 

were assembled for 90 cross sections, most of which 

were at or near Geological Survey gaging stations. 

Generally the gaging stations are located at stable 

reaches of the river. However, they often are located 

at bridges which might be assumed to affect the shape 

of the cross section. In such situations, wherever practical, the samples were collected some distance upstream 

or dowristream from the bridge. Sometimes, however, 

the depth of water necessitated obtaining samples and 

water depth from the bridge by using a small clam-shell 

type dredge. 

At most sections only the width and depth of the 

channel were measured. At others a survey was made 

of the channel cross section. The measurement of 

width and depth was to some extent subjective. Depth 

was measured to the lowest part of the channel from 

the edge of the first surface or bank above the channel 

floor. It is, therefore, a maximum depth. Width was 

measured from the edge of this bank to the corresponding elevation on the opposite side of the channel. In 

general, the upper limit of the measured depth could 

be selected not only as the edge of a terrace or bank 

but also as the lower edge of permanent vegetation 

and the upper limit of fairly recent deposition or erosion 

along tlie sides of the channel. 

The gradient of the channel at the cross sections was 

measured with a hand level for many locations. For 

others, the gradient was measured on large scale 

topographic maps. 

Composite sediment samples were taken from the 

channel floor and both banks. In general, the surface 

inch of the channel and banks was sampled along the 

selected cross sections; however, when the clam-shell 

dredge was used the samples often included a depth 

as much as 4 inches of channel material. Depending 

on channel width, samples of channel sediment were 

taken from 10 to 20 points across the stream. 

In the laboratory the samples were subjected to a 

standard grain-size analysis. The samples were first 

sieved and if they contained more than 20 percent siltclay were then prepared for hydrometer analysis. One 

important deviation from the usual procedure was 

made to aid in the dispersion of the samples (I. S. 

McQueen and R. F. Miller, oral communication). Fifty 

grams of the sediment was placed in 700 to 800 

ml of distilled water and allowed to stand overnight. 

The liquid was then decanted, removing most of the 

salts that might prevent total dispersion of the sample 

by sodium hexametaphosphate. The percentages of 

silt and clay in bank and channel samples, as well as 

the median-grain size, were taken from the plotted 

cumulative grain-size curves of each sample. 

The sediment composing the perimeter of each 

channel is expressed as a weighted mean percent siltclay, designated M, which is calculated as follows: 

M-ScXW+SbX2D 

- W+2D 

in which Sc is percentage of silt and clay in channel 

alluvium, Sb is percentage of silt and clay in bank 

alluvium, D is channel depth, W is channel width. 
SHAPE OF ALLUVIAL CHANNELS IN RELATION TO SEDIMENT TYPE 19 

Calculations of the width-depth ratio and M were 

made by slide rule and are presented in table 1 with 

other data on the cross sections and sediment. Data 

were collected at 90 cross sections, but it was later 

discovered that the channels were unstable at some of 

these cross sections. Data from 10 unstable channels 

were segregated from those for the stable channels 

because of: (a) channel aggradation (4 sections), (b) 

scour below a dam or a concrete ford (2), (c) 'Qedrock 

exposed in the channel (2), (d) bridge construction 

upstream (1), and (e) backwater effects (1 section; see 

table 1, cross sections 81-90). 

In addition, 11 other cross sections are segregated 

from the 69 stable sections listed in table 1, for these 

channels contain a high percentage of gravel, cobbles, 

and even boulders (table 1, cross sections 70-80). 

Therefore, unless otherwise stated this study is concerned primarily with channels formed in alluvium 

containing only small amounts of gravel and cobbles. 

The 11 cross sections containing the coarser sediment 

and the 10 unstable sections will be discussed separately. 

Mean a~nual :flood (recurrence interval 2.33 years) 

and mean annual discharge were obtained from data 

published in Geological Survey water-supply papers and 

unpublished reports for those sections at or near gaging 

stations. 

TABLE 1.-0hannel and sediment data 

[Location numbers in parentheses for cross sections 1-14 are author's original cross-section numbers] 

Cross 

sec- Location 

tion 

Sage Creek, S. Dak.: , 1 (2)----------------------------------- ·--- 2 (3)- -------------------------------------- 3 (4)--------------------------------------- Sand Creek, Nebr.: 4 (4)--------------------------------------- 5 !5)--------------------------------------- 6 (6)- -------------------------------------- Arroyo Calabasas, N.Mex.: 7 (A)-------------------------------------- 8 (6)- -------------------------------------- 9 (7)--------------------------------------- Bayou Gulch, Colo.: 

10 (3)- -------------------------------------- 11 (6)- -------------------------------------- Medano Creek, Colo.: 12 (1)--------------------------------------- 13 (2)--------------------------------------- 14 (3)-- ------------------------------------- 15 Saline River at Russell, Kans ________________ 

16 Paradise Creek near Paradise, Kans. _________ 

17 North Fork Solomon River near Downs Kans_ 

18 Solomon River at Bennington (Niles), Kans __ 19 Prairie Dog Creek at Norton, Kans __________ 

20 Sappa Creek at Stamford, Nebr ______________ 

21 Sappa Creek at Beaver City, Nebr ___________ 

22 Beaver Creek at Beaver City, Nebr __________ 

23 Beaver Creek at Ludell, Kans ________________ 

24 Frenchman Creek at Hamlet, Nebr __________ 

25 Blackwood Creek at Culbertson, Nebr _______ 26 Red Willow Creek near Red Willow, Nebr ___ 27 South Loup River near Cumro, Nebr ________ 

28 Niobrara River near Colclesser, Nebr ________ 

29 White River at Chadron, Nebr ______________ 

30 White River at Interior, S. Dak ______________ 

31 Cheyenne River at Edgemont, S. Dak _______ 

32 Willow Creek near Cheyenne Wells, Colo ___ _ 33 Smoky Hill River near Arapahoe, Colo _____ _ 34 Smoky Hill River near Sharon Springs, Kans. 

35 Smoky Hill River at Russell Springs, Kans._ 

36 Smoky Hill River at Gove, Kans------------

37 Smoky Hill River near Arnold, Kans _______ _ 38 Smoky Hill River near Russell, Kans _______ _ 39 Smoky Hill River at Dorrance, Kans ________ _ 

40 Smoky Hill River near Kanopolis (Longley), Kans ______________________________________ _ 

41 Smoky Hill River near Bridgeport (Lindsborg), Kans. 42 Smoky Hlll River at Abilene, Kans _________ _ 

43 Smoky Hlll River near Junction City, Kans __ _ 44 Kansas River at Wamego, Kans ___ ---------- 45 Kansas River near Topeka, Kans- -----------

Median 

grain 

size, 

Daa 

(mm) 

0.06 

.06 

.12 

• 72 

• 73 

.35 

.84 

.50 

• 75 

.58 

.55 

.24 

.24 

.24 

3.57 

.50 

.80 

.41 

.90 

.60 

• 70 

. 70 

1.10 

.27 

.02 

.11 

.25 

.33 

.15 

.50 

• 75 

1.10 

.85 

.41 

1.30 

.80 

.93 

.81 

1. 30 

.63 

.40 

.023 

1.20 

• 70 

• 75 

Silt- Silt- Weighted 

clay in clay in mean Width 

bank channel sllt-_A}ay, (feet) 

(percent) (percent) (percent) 

---

93 50 73 16 

93 68 79 20 

96 40 54 31 

70 14 23 75 

60 15 22 65 

65 10 20 36 

18 3 4.1 79 

26 3 4.8 92 

16 5 5.8 100 

13 4 4.4 130 6 4 4.1 128 

.5 1 1 340 

.5 1 1 800 

.5 .5 .5 820 

93 5. 7 11 93 

74 8 30 32 

89 1.2 16 82 90 4 11 112 82 1.5 19 45 

97 2 23 43 

96 17 43 26 

95 2 19 40 

95 2.5 36 28 

93 8. 7 31 36 

91 75 81 27 

91 30 45 45 

80 9.4 16 143 

47 2 3.3 224 86 32.5 56 25 

89 2 5.3 293 

56 .6 3 221 

Smoky Hill-Kansas Rivers system 

72 

49 

25 

21 

63 

30 

76 

69 

96 

85 

97 

90 

93 

57 

3 

3 

4 

2 

3 

2 

1 

.5 

4 

3 

87 

.5 

1 

.5 

16 

6.1 

4.5 

2.4 

4.3 

2.4 

5.3 

4.4 

14 

13 

89 

6 

3.8 

3 

15 

65 

200 

263 

226 

345 

115 

130 

92 

69 

125 

153 

636 

800 

Depth 

(feet) 

---

7 

7 

5 

7 

7 

4 

3 

4 

4 

3 

1.5 

2 

3 

2.5 

3 

7.8 

8.6 

5 

6.2 

6.0 

6.3 

4.5 

8.0 

6.5 

8.4 

7.1 

7.3 

3.4 

10.0 

5.8 

5.0 

1. 7 2.3 

2.5 

3.0 

2.5 

2. 5 3.5 

4.0 

5.5 

5.0 

18 

5.0 

10 

18 

Width· 

depth 

ratio 

(F) 

---

2.3 

2.9 

6.2 

10.7 

9.3 

9.0 

26.3 

23.0 

25.0 

43 

85 

170 

267 

328 

31 

4.1 

9.6 

22 

7.2 

7.2 

4.1 

8.9 

3.5 

5.5 

3.2 

6.3 

19.6 

65.9 

2.5 

50.6 

44.2 

8.8 

28 

80 

88 

90 

138 

33 

33 

17 

14 

7 

31 

64 

44 

Mean Mean 

Gradient annual annual Drainage (S) :flood discharge area (cfs) (cfs) (sqmi) 

------------ 0.0055 ---------- ---------- 1. 7 .0045 ---------- ---------- 3.4 

.0045 ---------- ---------- 9.5 

.0015 ---------- ---·------ 17.9 

.003 ---------- ---------- 22.2 

.001 ---------- ---------- 22.5 

.013 ---------- ---------- 3.8 

.009 ---------- ---------- 24.2 

.011 ---------- ---------- 25.8 

.010 ---------- ------·--- 19.7 

.016 ---------- .., _________ 22.9 

.017 _________ ... --------... - 25.8 

.019 ---------- ---------- 26.1 

.016 ----4~300- ----88~3-- 28.8 

---:oor-- 1,~ 1,300 11.1 

.0006 8,000 151 2,390 

---:ooos-- 7,000 558 6, 770 

2,600 33.2 721 

.0013 1.800 111 3,840 

.003 1,350 39.1 1,500 

.001 1,~~ 28.8 2,060 

.001 12.5 1,460 

.0013 850 101 1,= .0021 690 5.8 

.001 2,220 43.1 400 .003 2,080 165 1,340 

.003 ---------- --------... - 2.000 

---:002·-- 880 20.4 676 10,900 302 ---7;i43-- .0025 3,660 113 

---------- ----s:soo- ----65~2-- ---s;220-- • 00066 8, 000 215 6, 965 

. 0007 ---------- ---------- ·---------

.0005 

--·:0004-- .0008 

.0005 

9,200 314 6. 750 340 

11, 500 1, 254 

13, 000 1, 454 

39, 000 4, 398 

48, 000 5, 155 

7,857 

8,110 

18,830 

19,900 

55,240 

56,710 
20 EROSION AND SEDIMENTATION IN A SEMIARID ENVIRONMENT 

TABLE 1.-Channel and sediment data-Continued 

[Location numbers in parentheses for eross sections 1-14 are author's original cross-section numbers) 

Median Silt- Silt- Weighted Width- Mean Mean 

Cross grain clay in clay in mean Width Depth depth Gradient annual annual Drainage sec- r.ocation size, bank channel silt-clay, (feet) (feet) ratio (S) fiood discharge area tion n .. (percent) (percent) M (F) (cfs) (cfs) (sqmi) 

(mm) (percent) 

Republican River SJ&tem 

46 Arikaree River near Arikaree, Colo ___________ 1.10 82 3 4. 7 206 2.2 94 ---------- ---------- ---------- ---------- 47 Arik:aree River at Haigler, Nebr ______________ .25 65 3 8 68 3.0 23 0.002 3,500 19.6 1,460 

48 Republican River near Stratton, Nebr _ ------ .38 31 3 3.4 400 3.0 133 ---------- ---------- ---------- ---------- 49 South Fork Republican River near Benkle- .48 44 1. 5 3.4 100 2.3 43 .002 4,500 56.8 2,580 man, Nebr. 

50 Republican River near Benkleman, Nebr ____ .25 23 6 6. 7 123 2. 5 49 .003 2,175 105 4, 770 

51 Republican River near McCook, Nebr _______ .52 88 .5 4.4 115 2. 7 43 .009 ---------- ---------- 5, 760 

52 Republican River near Bostwick (Hardy), .63 29 1 2.8 154 5.0 31 .0008 12,000 843 22,400 Nebr. 

53 Republican River at Concordia, Kans •••••••• • 70 34 .2 1.4 250 5.0 50 .0007 13,000 -i;ooo··-- 23,540 

54 Republican River at Junction City, Kans •••• .60 59 1 3.4 300 6.5 46 .0007 15,000 24,900 

Powder River SJ&tem 

55 South Fork Powder River near Kaycee, Wyo. 0.63 71 9 11.3 119 2.3 52 0.004 3,900 35 1,150 56 Middle Fork Powder River above Kaycee, 22.0 60 14 20 35 2.5 14 .005 574 58 450 

Wyo. 57 Middle Fork Powder River near Kaycee, .40 69 15 23 47 4.4 11 .0015 1,630 133 980 

Wyo. 

58 Powder River below Arvada, Wyo ___________ .21 70 4 6.5 175 3.5 50 .0011 ----9~4oo· ---639 ____ ---------- 59 Powder River near Locate, Mont_----------- -~ 58 13 15 234 4.5 52 ---------- -----956"" 60 Crazy Woman Creek near Arvada, Wyo _____ .50 75 2 17 33 4.4 7.5 ---------- 1,150 40 

61 Little Powder River at Broadus, Mont ______ 4.10 82 5.5 22 40 5.5 7.3 ---------- 1,280 39 ---------- 62 Bighorn River near Kane, Wyo ______________ .16 35 20 21 220 8.5 26 ---~iio37-- 16,100 2,888 15,900 

63 Badwater Creek near Lysi~ Wyo ___________ .43 47 3 6. 7 50 2.3 22 ---------- ---------- ---------- 64 Badl\ater Creek at Lysite, yo. __ ---------- .24 58 5 7.3 109 2.5 44 .0037 ------585" ____ 34 ____ -----484"" 65 Owl Creek near Thermopolis, Wyo .. _------- .21 69 2 14 35 3.9 9.0 .0015 66 Cottonwood Creek at Winchester, Wyo ______ 1.0 15 8 8.4 133 3.5 38 ---~006--- ----··aii- ----io ____ 67 Gooseberry Creek at Pulliam, Wyo __________ 8.0 45 2.5 5. 7 59 2.4 25 371 

68 Greybull River near Basin, Wyo _____________ .50 72 7 9.9 134 3.1 43 .0015 3,140 178 1,130 

69 Bates Creek near Alcova, W-yo _______________ .00 63 14 18 69 2.8 25 .0035 500 16 377 

Gravel streams eliminated 1 

70 Powder River at Moorhead, Mont ___________ ---------- 71 Powder River at Broadus, Mont _____________ ---------- 72 Red Fork at Barnum, Wyo __________________ ---------- 73 Clear Creek at Buffalo, Wyo _________________ ----------

74 Tongue River near Acm~ Wyo.------------- ---------- 75 Little Bighorn River at Hardin, Mont _______ ---------- 76 Little Bighorn River at Lodgegrass, Mont._ ---------- 77 Popo Agie River near Riverton, Wyo __ ------ ---------- 78 Little Popo Agie River near Lander, Wyo _____ ---------- 79 Horseshoe Creek near Glendo, Wyo _______________ ------

80 North Fork Powder,River near Kaycee, Wyo. ----------

65 

38 

77 

35 

38 

59 

49 

37 

9 

85 

56 

7 

11 

1.5 

.06 

.8 

1.0 

.5 

.9 

.5 

1.0 

.3 

9.2 

12 

9.6 

2.1 

3. 7 6.3 

5.2 

4.6 

1.5 

7.5 

16 

212 

380 

35 

60 

100 

91 

60 

100 

34 

64 

21 

4.0 

5.0 

2.5 

1.9 

4.3 

4.5 

3.5 

5.5 

2.1 

2. 7 

4.0 

53 

76 

14 

31.5 

23.3 

20 

17 

18 

16.2 

23.7 

5.2 

0. 0016 7, 450 468 

: 88k4 ------64o- ----30---- -----i42--

:88g ----3~450· ---4oi____ ~~~ 

---------- 1, 820 260 ---------- .0023 ---------- ---------- ---------- 4, 910 602 2, 010 

: gg~5 ------525" ----32____ ~g~ 

Miseellaneeus sections eliminated 1 

81 Saline River near Salina, Kans _______________ 0.013 92 91 

82 White River near Rocky Ford, S. Dak _______ 1.10 88 1.2 

R3 Smoky Hill River near Weskan, Kans _______ • 70 14 3 

84 Smoky Hill River near Elkader, Kans _______ 1.20 55 4 

85 Smoky Hill River near Ellis, Kans ___________ • 72 18 .5 

86 Republtcan River near Naponee, Kans _______ .62 47 .5 

87 Powder River near Sussex, Wyo ______________ .07 64 51 

88 Powder River near Arvada, Wyo._---------- .15 78 32 

89 Badwater Creek at Bonnevillei Wyo _________ .17 32 7 90 Badwater Creek near Bonnevi Ie, Wyo _______ .37 21 7 

1 Sections not plotted on figure 8. 

CHANNEL SHAPE AND SEDIMENT TYPE 

The shape of each cross section expressed as a dimensionless width-depth ratio is plotted against Min figure 

8 for 69 cross sections (table 1). The correlation between channel shape and sediment is such that 

F=255 M-1

•

08 

where F is the channel shape expressed as a widthdepth ratio and M is the weighted mean percent siltclay. Neither the percentage of silt and clay in the 

banks nor in the channel alone show a correlation with 

width-depth ratio. 

91 56 10 5.6 ---------- ---------- ---------- ---------- 5.1 170 4 42.5 ---------- ---------- ---------- ---------- 6.3 36 3 12 --o:oo6 ___ 4.8 500 4 125 ----3:ooo· ----32T- ··-a;ooa·· 

1.9 72 3 24 --·:ooo7-- 6,500 97.7 5,630 

3.6 127 4.5 28 11,350 726 

52 177 3. 7 48 .0008 5,850 151 ·a~ooo·-

34 170 4.5 38 .0007 8,600 382 6,050 

7.5 291 3 97 ---·------ 1,280 8.37 790 

7.3 224 2.5 89.5 ---------- ---------- ---------- ----------

The wide range of channel shapes represented on 

figure 8 suggests that for alluvial channels in which 

pebbles and gravel cover only negligible parts of the 

channel, the shape of the channel is dependent on sediment type expressed as M. It is interesting to note 

that for those sections near gaging stations, the mean 

annual discharge ranged from 20 to 5,150 cfs (cubic 

feet per second). In addition, many of the streams are 

ephemeral, in contrast to the perennial flow of the 

Smoky Hill, Kansas, and Republican Rivers. Drainage 

area ranges from about 1. 7 square miles for the smallest 

ephemeral stream to 56,710 square miles for the Kansas 

River at Topeka. In spite of the wide range in stream 
SHAPE OF ALLUVIAL CHANNELS IN RELATION TO SEDIMENT TYPE 21 

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' '\~ 

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I '~ I I " I ! I 

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·" .. 

~ ~ I'; 

1.0 

0.1 1.0 10.0 100 

WEIGHTED MEAN PERCENT. SILT-CLAY {M) 

FIGURE 8-Relation between width-depth ratio and weighted mean percent silt-clay at different cross sections. The regression line was determined graphically. Standard 

error is 0.202log units, and correlation coefficient is 0.91. Point 42 is for Smoky Hill River at Abilene, Kans. 

regimen and sediment type, the correlation coefficient 

for the regression line is 0.91. The variety of stream 

types represented are illustrated in plate 5 A-F. 

The correlation of figure 8 shows that channels containing little silt-clay are relatively wide and shallow; 

whereas those composed predominantly of silt-clay are 

relatively narrow and deep. The correlation seems to 

justify the selection of Mas a parameter descriptive of 

sediment characteristics. A plot of the median grain 

size against percentage of silt and clay in the channel 

samples shows no correlation, indicating that median 

grain size has no relation to channel shape for the range 

of channels investigated. 

588578-61-2 

The scatter of points on figure 8, although not excessive, may be partly explained on the basis of normal 

stream variability. Note that the scatter of points 

appears greater where M is less than 25, if point 42 is 

disregarded. Sandy streams are generally unstable in 

that they may scour or deepen their channels during 

floods. In any event, changes in channel elevation of 

1 foot are common after a flood. Where the channels 

are hundreds of feet wide such a small change in depth 

causes a relatively large change in the width-depth 

ratio and thus greater scatter of the points representative of sandy channels. Point 42 on figure 8 is for the 

Smoky Hill River at Abilene. The introduction of 
22 EROSION AND SEDIMENTATION IN A SEMIARID ENVIRONMENT 

large amounts of silt-clay into this reach of the river 

markedly alters its appearance {pl. 5E). This may 

cause point 42 to lie well above the curve, but the 

gaging-station records suggest little change in gage 

height in this reach, and it was not eliminated as were 

sections 81 to 90. 

Also more refined techniques might further reduce the 

scatter. For example, channel maximum depth might 

be replaced by a mean depth, obtained by dividing the 

area of cross section by width. Mean depth was calculated for 20 sections at which the cross-sectional area 

was known. Where mean depth was used to calculate 

width-depth ratio, the ratio increased on the average 

by 1.5. However, neither the slope of the regression 

line nor the scatter about the regression line were 

changed. 

It is hazardous to attempt to extrapolate the relationship of figure 8 as a general law for alluvial channel 

shape, but it is interesting to note that Rubey's (1952) 

comparison of the illinois and Mississippi Rivers reveals differences similar to those noted between the 

sections characterized by high M and low M in this 

study. Fisk {1944, p. 50) concluded from studies of 

the alluvial valley of the Mississippi River that the 

~ l&J 

"" 

~ 

:i 

... 

0 

~ 

..J 

UJ 

z 

z 

<( 

:X: 

0 

1000 

100 

10 

0.1 

4 • 

• • 

1.0 

channel is wide and shallow where the river flows through 

sandy deposits and conversely is deep and narrow in 

the fine-grained materials of the deltaic plain. Most 

investigators have recognized from experience that 

sandy channels are wide compared with those cut in 

silty or clayey materials (Leopold and Maddock, 1953, 

p. 46). 

The reason for the relation between channel shape and 

percentage of silt and clay (fig. 8) is found in studies 

made by hydraulic engineers. Lane (1937, p. 124) 

states, "* * * the greater the width-depth ratio the 

greater will be the ratio of the velocity acting on the 

bottom to that acting on the sides of a channel." 

Where a narrow trench is cut in an alluvial valley, the 

tractive forces acting on the channel sides will be great, 

causing widening of the channel. Widening will 

continue until the resiStance of the banks to scour 

prevents it. If the material in which the channel is 

cut is highly cohesive (has a high percent of silt-clay) 

the channel will be narrow, but if the alluvium lacks 

cohesion (has a small percent of silt.;.clay) the channel 

will widen to a greater extent. Canals that carry a 

high bedload in friable or easily eroded material require 

high velocities 011 the bed to move the load and low 

• 

-

. • • • • •• .. • .. • 

• •• • 4 •• :2 • • • • • • . • • . 1- • ~ • . • 

• • • • 

• • 4 • • 

~ • • • • • 

• • 

10 100 

WEIGHTED MEAN PERCENT SILT-CLAY (M) 

FIGUJitE 9.-Relation between channel width and weighted mean percent silt-clay at different cross sections (M). Point 4:2 is for the Smoky Hill River at Abilene, Kans. 
GEOLOGWAL SURVEY PROFESSIONAL PAPER 352 PLATE 6 

STREA ,\1 CHANl\ELS ILLUSTHATING HA NGE OF CH Ai\"NEL CHAHACTERISTlCS AT MEASURED CROSS SECTIONS 

A, Smoky Hill lliver near Arapahoe. Colo. (cross sectio n 33 ); B, Sm oky Tlill Uive r above Cedac Bluff Reservoir, Kans. (cross section 37); C, White River nea r 

Chadron, NeLr. (cross section 29 ); D, Sappa Cree k at Stamford , X cbr. (cross section 20 ); E, Smoky Hill River near Abilene .Kans. ( cross s~r.t ion 42); F 

Kan8<tS Hi ve r near T opr. ka. K a ns. (cross sec tion 4~ . 
SHAPE OF ALLUVIAL CHANNELS IN RELATION TO SEDIMENT TYPE 23 

200.0 

~ 84• 

i\.. I 

89 

" -·I 100 .. 0 

' 90 

' 

~ 

0 

~ 0:: 

J: 

t 

liJ 

9 10.0 J: 

~ 

0 

~ 

"' """ 

86• 

85• 

1.0 

'\ 82 

• 

' " \ 

• 83 

• 87 

• 88 

,, 

I~ ' ' ' " 81.1 

,, 

'\~ 

r'\ ', 

' 

10 100 

WEIGHTED MEAN PERCENT Sll T -CLAY (M) 

FIGURE 10.-Relation of width-depth ratio to weighted mean percent sllt-clay (M} for unstable cross sections. Numbers refer to cross sections listed In table 1. Regression 

line is that determined from data on figure 8. 

velocities along the banks to prevent cutting them, 

thus a high width-depth ratio is required for a stable 

channel in friable material (Lane, 1937, p. 124). 

It is also noteworthy that the shape of the channels 

seems to be independent of discharge. Plots of mean 

annual flood and mean discharge against width-depth 

ratio showed no recognizable correlation. The absolute 

size of the channel, the width and depth in feet, is 

related to mean discharge (Leopold and Maddock, 

1953), but the ratio of width to depth is apparently 

determined by sediment type (M) for the channels 

sampled. The data show a correlation between channel 

width and M (fig. 9), but the scatter of points is such 

that the width may vary as much as 10 times for any 

one value of M. Nevertheless, the lack of correlation 

between channel depth and M, suggests that perhaps 

channel width is more sensitive to changes in M than 

depth. 

A discussion follows on the 21 cross sections eliminated because of instability or the presence of excess 

coarse sediment on the channel floor. 

In figure 10 the width-depth ratio is plotted against 

M for the 10 cross sections eliminated from prior discussion. The regression line of figure 8 has been drawn 

on figure 10 to show where the 10 points lie in relation 

to the regression line for stable channels. The two 

cross sections which show scour either downstream from 

a dam (85) or downstream from a concrete ford (83) lie 

far below the regression line. The two cross sections 

in which bedrock was exposed (82, 86) lie close to the 

regression line; whereas, those in which the rating curves 

of gage height to discharge show a progressive increase 

in gage height with constant discharge, suggesting 

aggradation, (84, 88, 89, 90) lie above the curve. The 

location of point 81 is probably the result of recorded 

backwater effects due to floods on the SmokY: Hill River, 
24 EROSION AND SEDIMENTATION IN A SEMIARID ENVIRONMENT 

1000.0 ' l 

~ ! 

~ 

~I 

" i'~ I 

,, I ', I 

I I I ' I 

~ I 

! 

I I I I 

I ' I 

"' 100.0 

' I 

•71 

; " I ', 1170 

"~ ! 

I 

73 • ' ' I 

'\ 

74• 

79 • ~I\ .. 75 

~~ 78• 77 ~76 

I . 10.0 

' .. 

! " '\ 

.so " I I 

'~ I 

I 

'" 1\ i\ ~ 

' 

1.0 10 100 

W.EIGH_TED MEAN PERCENT SILT:-CLAY (M) 

FIGURE 11.-Relation between width-depth ratio and weighted mean percent silt-clay (M) for cross sections with the channel floor covered by more than 40 percent gravel, 

cobbles, and boulders. Numbers refer to cross sections listed in table 1. Regression line is that determined from data on figure 8. 

The last point (87) lies above the regression line. 

This is attributed to bridge construction upstream which 

has caused a veneer of fine sediment to be deposited 

over the coarser material characteristic of this section. 

The relation of these points to the regression line 

suggests that the regression line of figure 8 may be used 

as a criterion of channel stability. Aggrading sections 

will have a larger width-depth ratio than expected on 

the basis of M; whereas degrading channels will have 

smaller width-depth ratios than expected on the basis 

of Malone. 

Possibly the line of figure 8 is a true regression line. 

The channel cross sections which plot above the line, 

because they are aggrading or have been aggraded, 

may be expected to regress toward a stable form by 

erosion; whereas channel cross sections which plot 

below the line, because they are degrading or have been 

degraded, may be expected to regress toward a stable 

form by a combination of bank erosion and aggradation. 

The other cross sections not plotted in figure 8 are 

those with appreciable gravel along the perimeter of 

the channel cross section. All of these sections have 
SHAPE OF ALLUVIAL CHANNELS IN RELATION TO SEDIMENT TYPE 25 

200.0 

~ • '7 " 3E 100.0 

35.' ... 

' 

10.0 

2.0 

0.1 

.. 

r\. 

"\, 

lt45 

1.0 

"':~.~~ 

144 

r\. 

'1\.: 

39 as 

• t\ ·• 43 

~3 "~ 

'~ 

~ • 

32 " ' ' 'II\. 14~ . ·~ 

~ 

r'\ 

"\ 

r\ 

10.0 ' 100 

WEIGHTED MEAN PERC~T SILT-CLAY (M) 

FIOUBB 12.-Relation of width-depth ratio toM along the Smoky Hill-Kansas River. Regression line is that determined by data on figure 8. Numbers refer to cross sections 

listed in table 1. 

greater than 40 percent of the channel floor covered 

by coarse sediment. Data from these cross sections 

are plotted on figure 11. Only three points lie far from 

the regression line. The remaining eight points fall 

reasonably close to but below the regression line. The 

reason for this is not clear for it was expected that a 

gravel or cobble veneer would prevent bottom scour 

and result in a higher width-depth ratio. 

However, data compiled on the width and depth of 

irrigation canals 1 show that channels and banks containing coarse noncohesive materials are protected by 

the larger sizes of alluvium. Therefore, the widthdepth ratio of channels containing gravel and cobbles 

should be relatively low as seen on figure 11. 

EFFECT OF SEDIMENT TYPE ON DOWNSTREAM 

VARIATIONS IN CHANNEL SHAPE 

This discussion has been concerned solely with data 

from a great variety of streams. Most studies of fluvial 

morphology and regime canals deal with the relations 

between discharge and channel dimensions along a 

1 Simons, D. B., 1957, Theory and design of stable channels in alluvial materials: 

Unpub. thesis, Colorado State Univ., 394 p. 

single river or canal. The relation shown in figure 8 

suggests that the effect of M on downstream changes 

in channel dimensions is important. 

The Smoky Hill-Kansas River system is of particular 

interest with regard to the effect of downstream variations of M to channel shape, width, and depth. To 

illustrate this M and width-depth ratio for 14 cross 

sections are plotted on figure 12. 

In eastern Colorado and western Kansas the Smoky 

Hill River is wide, shallow, ephemeral (pl. 5A, B; fig. 

12, points 33 to 37), and M is generally less than 10. 

M increases in central Kansas to about 12 (fig. 12, 

points 40 and 41); between Salina and Abilene the 

Saline and Solomon Rivers introduce large amounts of 

silt-clay into the river, and M increases sharply to 

more than 80 (pl. 5E; fig. 12, point 42). Downstream 

from Abilene the river becomes progressively more 

sandy (fig. 12, point 43) to the confluence with the 

Republican River, the beginning of Kansas River. 

The Republican River introduces large amounts of 

sand into the Kansas River, and M decreases to about 

3 (pl. 5F; fig. 12, points 44, 45). 
26 EROSION AND SEDIMENTATION IN A SEMIARID ENVIRONMENT 

20.0 

45 v 

v 

v.: 

();'/ 

/1 

5 v4 -~ f/ rr-"~ .. " <I?" ';)• ~ ~-7 I l ~-7~ 

~ 10.0 

w 

LL. 

~ 

:i 

1-

Q. 

w 

0 

~/ 

~& ~ ~ ·:::: 

" 0) ~ 

~-~~ 9~ ~ ~r c/ti 

C?."" & c;>'~V' ~;r " ..J 

w 

z 

z 

< 

J: 

(.) 

/6 

,o 'OV ~ / ~ / ,i-

'lY ~0 v 35 

33 v 34 .36 • 37 1/ 55 

2.0 

10 100 1000 

CHANNEl WIDTH, IN FEET 

FIGURE 13.-Relation between width and depth for streams with not greatly difierent values of Min a downstream direction. Number following name of stream is mean 

value of M for points forming each line, and numbers beside points refer to cross sections listed in table 1. 

Lacey (1930) showed that the depth and width of 

regime canals increase in an orderly manner with discharge and suggested that the intercept or position of 

the regression line of width to depth for each canal is 

determined by grain size. Plotting width against maximum depth for all the 69 cross sections results in an 

undecipherable pattern; however, when data for individual streams are plotted a group of curves results 

(fig. 13). 

In figure 13 each regression line is drawn in relation 

to points representing cross sections having not greatly 

different values of M. The positions of the lines 

representative of ephemeral streams are apparently 

determined by M. The Sand Creek line, with a high 

value of M, lies high and to the left. The Arroyo 

Calabasas regression line lies lower to the right as M 

decreases. However, mean annual discharge is also 

important in determining the position of the curves, 

for both the Smoky Hill River and Powder River 

curves, with a higher value of M, lie to the right of 

Arroyo Calabasas regression line. Nevertheless, the 

regression lines for rivers with approximately equal 

discharge would probably have intercepts determined 

byM. 

In contrast to the straight regression lines which may 

be drawn through points representative of cross sections 

with nearly similar values of M, the width-depth data 

for the Smoky Hill-Kansas River system reveals that 

the variability of M in a downstream direction has a 

marked effect on the relation of channel width to 

depth (fig. 14). 

In a downstream direction along the Smoky Hill 

River, M decreases from 16 to 2.4 between cross sections 

32 and 37. This change is accompanied by a relatively 

large increase in channel width in relation to depth. 

However, between cross sections 37 and 41 M increases 

from 2.4 to 13 and depth increases as channel width 

decreases to about one-fourth of its former value. The 

introduction of large quantities of silt and clay into the 

channel between cross sections 41 and 42 causes an 

abrupt increase in channel depth with a proportionally 

smaller increase in width. Downstream from cross 

section 42, M decreases from 89 to 6 and channel depth 

decreases sharply. Between cross sections 43 and 45, 

M decreases and width again increases more than depth. 

Two large dams on the Smoky Hill River are another 

probable cause of some variation in the plot of figure 14. 

The Cedar Bluffs Dam, completed in 1951, is located 

between cross sections 37 and 38. The Kanopolis Dam, 

completed in 1948, is located between cross sections 

40 and 41. 

It has been shown that the construction of a dam may 

cause upstream and downstream changes in channel 

character. For example, cross section 85, located a 

short distance downstream from the Cedar Bluffs Dam, 

was classed as an unstable channel because of recent 

degradation. However, in spite of the possible effects 

of these structures on streamflow and channel character, 
SHAPE OF ALLUVIAL CHANNELS IN RELATION TO SEDIMENT TYPE 27 

the relation between gage height and discharge for each 

cross section showed no progressive change which would 

indicate channel instability. In addition, cross sections 

37 through 41 show no unusual scatter on figure 12. 

However, if it is assumed that the dams have an 

effect on channel width and depth, then the major portion of this effect can be eliminated by discarding cross 

sections 37 through 41 from figure 14. This will cause 

some alteration of the figure, for the second and third 

segments of the graph will be replaced by a line between 

cross sections 36 and 42; however, the greater part of 

the variability of the figure will remain to be explained 

by downstream variations of M. 

Annual discharge increases progressively in a downstream direction (table 1) so the variations in channel 

shape are not the result of water losses. Therefore, 

figure 14 suggests that as M changes in a downstream 

direction neither channel width nor depth will show a 

consistent relation with mean annual discharge. Depending on the change in alluvial character either width 

or depth may decrease in a downstream direction. 

This effect of sediment type on the relation between 

width and mean annual discharge can be demonstrated 

by plotting the two variables in the manner of Leopold 

~ UJ 

LL.. 

and Maddock (1953) for cross sections for which discharge data are available (fig. 15) along the Smoky 

Hill, Republican, and Kansas Rivers. It is important 

to remember here that width and depth as used in this 

study are not the same as the width and depth for mean 

annual discharge as used by Leopold ,and Maddock 

(1953). 

The relation between mean annual discharge and 

channel width is almost a straight line for the Republican-Kansas River cross sections, in which M ranges 

from 1.4 to 8; however, the same variables show great 

irregularity for the Smoky Hill-Kansas River cross sections in which M ranges from 2.4 to 89. 

Maximum depth and mean annual discharge at the 

same cross sections (fig. 16) have a somewhat similar 

relation, for the river with the greatest variation in M 

has the greatest variation of maximum depth with 

mean annual discharge. 

Again the presence of dams on the rivers may be important. In addition to the Cedar Bluffs and Kanopolis 

Dams on the Smoky Hill River, there are two dams on 

the Republican River. The Trenton Dam, completed 

in 1955, is located between cross sections 50 and 51, 

and the Harlan County dam, completed in 1952, is lo-

~ 

:I: 

41 v ~0 ~ 

b: 

UJ 

0 

...J 

UJ· 

z 

z 

<( 

:I: 

c.J 

l.OL-----------L------L--~'~---L--~-L~~~----------~------~~~--~--~~--~~ 

10 100 1000 

CHANNEl WIDTH, IN FEET 

FIGURE 14.-Relation of channel width to depth for the Smoky Hill-Kansas River. Numbers refer to cross seetions listed in table 1. 
28 EROSION AND SEDIMENTATION IN A SEMIARID ENVIRONMENT 

cated between cross sections 51 and 52. Any effects of 

these structures on the stream channels could have been 

expected before the cross sections were studied in 1958, 

and as mentioned above scour occurred at cross section 

85 below the Cedar Bluffs Dam. In addition, channel 

degradation may also have occurred at cross section 

86, a short distance below the Harlan County dam, for 

bedrock is exposed in the channel at that cross section. 

In spite of the existence of the dams, if cross sections 37 through 41 were eliminated from the Smoky 

Hill River data and cross sections 50 through 52 were 

eliminated from the Republican River data the Smoky 

Hill River plots on figures 15 and 16 would still show 

great variation in contrast to the slight variation of 

the Republican River data. Therefore, although the 

effects of the dams should not be minimized, the writer 

believes that the cross-section data collected in 1958 

and plotted on figures 15 and 16 were not significantly 

influenced by the structures, for the upstream cross 

sections were located several miles above the water 

1000 I 

ti 

LLI 

&1. 

~ 

:i 

1-

0 

level of the reservoir and none of the downstream sections were closer than 20 miles to the dams. 

To summarize (see figs. 12-16) if M remains constant 

downstream then the width and depth of the channel 

will increase at a uniform rate with discharge, excluding the influence of other variables, and width-depth 

ratio will remain constant. If M increases, downstream 

channel depth will increase more rapidly than width, 

which may even decrease, and the width-depth ratio 

will decrease. If M decreases, downstream channel 

width will increase more rapidly than depth, which 

may even decrease, and width-depth ratio will increase. 

CONCLUSIONS AND POSSIBLE APPLICATIONS 

This study suggests that M represents the resistance 

to erosion or general behavior of sediment in a stream 

channel containing only small amounts of gravel. A 

study of this aspect of the physical properties of sediment is needed before it will be possible to suggest other 

than that the silt-clay acts as a binding agent in which 

,-I 

45 

r• 

4'\ 

-~ , 

__, V' 

.5~ ~ 

,.. """"I---"" 

Repubfican-Kansos Rlvef',......... ?; ,. ...1 

LLI 

z 

z 

< J: 

0 

100 

10 

5 

10 

_...... 47.,.1 ~ 

33 

49 ...... ...- _,.,.. 

~ 

1/ 

v 

I 

I 

I 

1/ 

I 

~ ~ 

.. v • f2 

..... ~---

"'!\. ~~ j 

~ . SmokY Hill-Kansas I River Li ~8 L.o-~ 42 

" la40 ~""' 

" v 

1"- ~ 

.41 

100 1000 

MEAN ANNUAL DISCHARGE, IN CUBIC FEET PER SECOND 

4f 

rY 

I 

1/ 

/ 

v 

1./ 

1000 

100 

10,000 

...1 

w 

z 

z 

< 

J: 

0 

FIGURE 15.-Relatlon of channel width to mean annual discharge for the Smoky Hill, Republican and Kansas Rivers. Numbers refer to cross sections listed in table 1. 
SHAPE OF ALLUVIAL CHANNELS IN RELATION TO SEDIMENT TYPE 29 

20.0 

t; 

~ 10.0 

~ 

i 

v ~ 

--:7 

~5 

/ ~" 

~ v _.... .¥ 

~ 

"' 0 

Repubtfaln-Kanses ltiver ~~ ~54 

~ ~ 

_, i..l 

"' z 

z --~~ 5' 

~ v 

47• ~ 0 

-..... 

r--...... ~ ~ ~--"'""' ~ ~ """""" V142 \s v 

vll v v 

v / - 1/ \. / 44 

/ ' / 

2.0 20 

..... 

UJ 

"' 10 Ll.. 

~ 

Smoky HW-Kansas River ~ v -I 

..... 

v v a. 

LtJ 

40•/ 43 0 

_, 

/ '"'41 UJ 

z 

z 

-----~ 38 

< :t 

0 

~ j.....oo' ~--'"'"' 

33. ~ 1--1--

~ 2.0 

10 100 1000 10,000 

MEAN ANNUAL DiSCHARGE, IN CUBIC FEET PER SECOND 

FIGURE 16.-Relation of channel maximum depth to mean annual discharge for the Smoky Hill, Republican, and Kansas Rivers. Numbers refer to cross sections listed in 

table 1. 

the larger sediment grains are fixed. Undoubtedly, the 

type of clay present and the ratio of silt to clay are also 

important. 

The importance of the percentage of silt and clay 

in the perimeter of a stream channel to channel shape 

has been demonstrated. As M increases the widthdepth ratio decreases according to the following equation: 

F=255 M-1

•

08 

Neither mean annual discharge nor mean annual flood 

affect this relation significantly, at least for the channels 

sampled in this study. 

The relation of the unstable channels (fig. 10} suggests that the position of a point in relation to the 

regression line of figure 8 may indicate that aggradation or degradation is occurring within a channel. 

Aggrading channels will have & higher width-depth 

ratio than indicated by M; whereas degrading channels 

will have a lower width-depth ratio than indicated by M. 

As M increases downstream along a given river, the 

depth increases more rapidly and the width less rapidly with discharge than if M were constant downstream, and width-depth ratio decreases. Conversely 

as M decreases downstream along a given river the 

depth increases less rapidly and the width more rapidly with discharge than if M were constant, and 

width-depth ratio increases. Changes in M downstream along the Smoky Hill-Kansas River system 

support the conclusion that width-depth ratio varies 

with M regardless of discharge, and whereas both width 

and depth of a channel may increase with discharge, 

a change in M along the river will change the rate of 

their increase downstream and may even cause either 

width or depth to decrease downstream. 

The use of percentage of silt and clay in sediment 

or some similar parameter, as an indication of the 

physical properties of alluvium, seems to open several 

profitable lines of research into fluvial morphology. 

For example, perhaps M may be of more value in 

studies of longitudinal stream profiles than median 

grain size. The adjustment of the cross sections of a 

stream to changed hydrologic conditions by widening or 

deepening of the channel may be related to M. In 
30 EROSION AND SEDIMENTATION IN A SEMIARID ENVIRONMENT 

addition, it may be possible to use the regression line 

of figure 8 and the equation derived therefrom to aid 

in the prediction of the stable form of canals or rivers 

subjected to different types of modification or increased 

discharge. 

REFERENCES 

Bagnold, R. A., 1954, The physics of blown sand and desert 

dunes: London, Methuen & Co., 265 p. 

Boyoucos, G. J., 1935, The clay ratio as a criterion of susceptibility of soils to erosion: Am. Soc. Agronomy Jour., v. 27, 

p. 738-741. 

Burmister, D. M., 1952, Soil mechanics: New York, Columbia 

Univ. Press, 155 p. 

Fisk, A. N., 1944, Geological investigation of the alluvial valley 

of the Lower Mississippi River: U.S. War Dept., Corps of 

Engineers, Vicksburg, Miss., 78 p. 

0 

Hjulstrom, Filip, 1935, Studies of the morphological activity of 

rivers as illustrated by the River Fyris: Geol. Institution, 

Univ. Upsala Bull. [Sweden], v. 25, p. 221-527. 

Lacey, Gerald, 1930, Stable channels in alluvium: Inst. Civil 

Engineers Proc., v. 229, p. 259-285. 

Lane, E. W., 1937, Stable channels in erodible material: Am. 

Soc. Civ. Eng. Trans., v. 102, p. 123-142. 

Leopold, L. B., and Maddock, Thomas, Jr., 1953, The hydraulic 

geometry of stream channels and some physiographic 

applications: U.S. Geol. Survey Prof. Paper 252, 57 p. 

Rubey, W. W., 1933, Settling velocities of gravel, sand, and 

silt particles: Am. Jour. Sci., 5th series, v. 25, p. 325-338. 

--- 1952, Geology and mineral resources of the Hardin and 

Brussels quadrangles (in Illinois): U.S. Geol. Survey Prof. 

Paper 218, 179 p. 

Trask, P. D., 1959, Effect of grain size on strength of mixtures 

of clay, sand, and water: Geol. Soc. Am. Bull., v. 70, p. 

569-580.