SPECIAL REPORT 96-19

Resilient Modulus Testing of Materials

from Mn/ROAD, Phase 1

Richard L. Berg, Susan R. Bigl, Jeffrey A. Stark

and Glenn D. Durell September 1996
Abstract: The U.S. Army Cold Regions Research and

Engineering Laboratory (CRREL) conducted resilient

modulus tests on materials from the Mn/ROAD test site

for the Minnesota Department of Transportation. Materials tested included samples of the lean clay subgrade

at the site and the two extreme grades of base designed specifically for Mn/ROAD. Some specimens were

tested in both frozen and subsequently “thawed” conditions; others were tested at room temperature without

ever having been frozen. Researchers performed linear

How to get copies of CRREL technical publications:

Department of Defense personnel and contractors may order reports through the Defense Technical Information Center:

DTIC-BR SUITE 0944

8725 JOHN J KINGMAN RD

FT BELVOIR VA 22060-6218

Telephone 1 800 225 3842

E-mail help@dtic.mil

msorders@dtic.mil

WWW http://www.dtic.dla.mil/

All others may order reports through the National Technical Information Service:

NTIS

5285 PORT ROYAL RD

SPRINGFIELD VA 22161

Telephone 1 703 487 4650

1 703 487 4639 (TDD for the hearing-impaired)

E-mail orders@ntis.fedworld.gov

WWW http://www.fedworld.gov/ntis/ntishome.html

A complete list of all CRREL technical publications is available from:

USACRREL (CECRL-TL)

72 LYME RD

HANOVER NH 03755-1290

Telephone 1 603 646 4338

E-mail techpubs@crrel.usace.army.mil

For information on all aspects of the Cold Regions Research and Engineering Laboratory, visit our World Wide Web site:

http://www.crrel.usace.army.mil

regression analysis on the data to develop equations

that predict frozen modulus based on unfrozen water

content and unfrozen modulus based on stress, degree of saturation and density. We also reanalyzed

data from two previously tested materials. CRREL can

use the study’s equations in the Mechanistic Pavement

Design and Evaluation Procedure under development

at CRREL to predict estimated damage in some Mn/

ROAD test sections.
Special Report 96-19

Resilient Modulus Testing of Materials

from Mn/ROAD, Phase 1

Richard L. Berg, Susan R. Bigl, Jeffrey A. Stark

and Glenn D. Durell September 1996

Prepared for

MINNESOTA DEPARTMENT OF TRANSPORTATION

Approved for public release; distribution is unlimited.

US Army Corps


of Engineers

Cold Regions Research &


Engineering Laboratory
PREFACE

This report was prepared by Dr. Richard L. Berg, Research Civil Engineer

(retired), Susan R. Bigl, Research Physical Scientist, Jeffrey A. Stark, Supervisory

Civil Engineering Technician, Civil and Geotechnical Research Division, Research

and Engineering Directorate, and Glenn D. Durell, Engineering Technician, Engineering Resources Branch, Technical Resources Center, U.S. Army Cold Regions Research and Engineering Laboratory (CRREL), Hanover, New Hampshire.

This work was funded through Agreement 64632, Task Order 1 with the Minnesota Department of Transportation (Mn/DOT) and a Construction Productivity

Advancement Research (CPAR) project between Mn/DOT and CRREL. The authors

thank George Cochran of the Minnesota Road Research Project and Dr. Vincent

Janoo of CRREL for technically reviewing the manuscript of this report.

 This report covers results from the subgrade and two base materials available in

1990 and is considered Phase 1. Additional materials were manufactured later and are

described separately as Phase 2 results.

The information reported here is the result of work done by a team of CRREL

personnel whose efforts we greatly appreciate. Arthur Peacock, Brian Charest, and

David Carbee were all involved in molding, freezing, and milling the specimens. Dale

Bull conducted some of the resilient modulus testing. Brian Charest characterized the

water content and density subsequent to resilient modulus testing.

The contents of this report are not to be used for advertising or promotional

purposes. Citation of brand names does not constitute an official endorsement or

approval of the use of such commercial products.

ii
CONTENTS

Page

Preface ............................................................................................................ ii

Executive summary ........................................................................................ v

Introduction .................................................................................................... 1

Methods .......................................................................................................... 1

Materials/conditions tested ........................................................................ 1

Specimen preparation................................................................................. 2

Test procedures .......................................................................................... 2

Previously tested materials ........................................................................ 5

Data reduction and analysis............................................................................ 7

Frozen......................................................................................................... 8

Thawed/never frozen ................................................................................. 9

Results ............................................................................................................ 10

General ....................................................................................................... 10

Frozen......................................................................................................... 10

Unfrozen..................................................................................................... 13

Conclusions .................................................................................................... 20

Literature cited ............................................................................................... 20

Appendix A: Mn/ROAD materials resilient modulus testing results ............ 21

1206 subgrade ............................................................................................ 21

Frozen .................................................................................................... 21

Unfrozen ................................................................................................ 26

1232 subgrade ............................................................................................ 44

Frozen .................................................................................................... 44

Unfrozen ................................................................................................ 48

Class 3 subbase .......................................................................................... 58

Frozen .................................................................................................... 58

Thawed .................................................................................................. 61

Class 6 base ................................................................................................ 70

Frozen .................................................................................................... 70

Thawed .................................................................................................. 74

Appendix B: Substitute materials resilient modulus testing results .............. 85

Dense graded stone .................................................................................... 85

Frozen .................................................................................................... 85

Thawed .................................................................................................. 86

Taxiway A subbase .................................................................................... 88

Frozen .................................................................................................... 88

Thawed .................................................................................................. 90

Abstract........................................................................................................... 94

iii
ILLUSTRATIONS

Page

Figures

1. Examples of triaxial cells ................................................................... 5

2. Waveform used in Mn/ROAD resilient modulus testing ................... 5

3. Comparison of Mn/DOT specifications with size gradations of

substitute materials ....................................................................... 7

4. Frozen resilient modulus data vs. temperature................................... 11

5. Effect of stress on frozen resilient modulus ....................................... 13

6. Predicted frozen resilient modulus for all Mn/ROAD materials ....... 14

7. Resilient modulus vs. degree of saturation for never frozen

subgrade materials and thawed base/subbase materials ............... 15

8. Resilient modulus vs. degree of saturation of never-frozen

1206 subgrade material illustrating the effect of dry density ....... 16

9. Resilient modulus vs. degree of saturation illustrating effect of

stress parameters ........................................................................... 16

10. Resilient modulus vs. deviator stress applied to a single 1206

subgrade specimen ........................................................................ 17

11. Resilient modulus vs. deviator stress applied to three 1206 subgrade

specimens illustrating effect of moisture condition...................... 17

12. Resilient modulus vs. deviator stress applied to two 1206 subgrade

specimens illustrating effect of dry density .................................. 17

13. Predicted moduli for all materials in unfrozen condition.................... 17

14. Comparison of frozen and unfrozen modulus data ............................. 18

TABLES

Table

1. Samples tested for resilient modulus.................................................. 2

2. Resilient modulus samples tested....................................................... 3

3. Stress conditions of resilient modulus tests in current study ............. 6

4. Stress conditions of resilient modulus tests—previous study............ 6

5. Constants for unfrozen moisture content equations ........................... 8

6. Results of regression analyses............................................................ 12

iv
EXECUTIVE SUMMARY

Laboratory resilient modulus tests were conducted on pavement materials from the

Minnesota Road Research Project (Mn/ROAD) to characterize their behavior under

seasonal frost conditions, and to provide input necessary for modeling the materials

with the Mechanistic Pavement Design and Evaluation Procedure under development at CRREL. Results of other tests to characterize their physical properties (grainsize distribution, specific gravity, Atterberg limits, organic content, hydraulic properties, and compaction) as well as tests more specifically related to freeze/thaw

processes (frost susceptibility and unfrozen moisture content) are reported separately

(Bigl and Berg 1996a).

The materials reported on here include two samples of the clay subgrade from

beneath the Mn/ROAD site (the high-heaving sample 1206 and the low-heaving

sample 1232) and the two bases with the least (class 6 special) and greatest (class 3

special) amounts of the fine fraction. When this testing was performed, the two bases

with intermediate amounts of fines (class 4 special and class 5 special) were

unavailable. However, to conduct subsequent modeling with the Mechanistic Pavement Design and Evaluation Procedure, it was necessary to approximate their

behavior using properties of similar materials. Therefore, this report includes modulus test results conducted previously on materials most closely matching the specified

size gradations of the class 4 and class 5 special subbases. A subbase from taxiway

A at the Albany, New York, airport (Cole et al. 1987) substituted for the class 4 special

subbase; dense-graded stone, from a Winchendon, Massachusetts, test site (Cole et

al. 1986) substituted for the class 5 special.

Specimens of the materials were molded at a specified moisture/density condition

and then saturated. Once saturated, they were frozen with an open system, allowing

movement of any additional water required to the freezing front. Specimens were

tested using repeated load triaxial procedures at a matrix of applied confining and

deviator stresses. Testing was first conducted at three temperatures below freezing,

and then specimens were allowed to thaw in the triaxial device and subsequently

retested in a thawed, saturated state. The same specimens of the base materials were

subsequently tested at room temperature under several moisture contents created by

drawing a suction at the base of the specimen. To obtain unfrozen data for the

subgrade materials, different specimens were molded to specific moisture conditions

and tested at room temperature without ever having been frozen. A different testing

machine was used for the unfrozen specimens of the 1206 subgrade than for all other

testing. It was discovered after testing was complete that these data include a

calibration error of unknown magnitude that produced moduli about an order of

magnitude too high.

All materials exhibited a two to three order of magnitude increase in resilient

modulus at subfreezing temperatures of –2°C and lower. The modulus of all of the

materials was stress dependent and also showed a lower magnitude increase as the

degree of saturation decreased. For the materials where a variety of densities were

tested, modulus was also dependent on density.

The resilient modulus data from the materials tested in this study were analyzed

using statistical regression techniques. Data from the two previously tested materials

were also reanalyzed. In the regression analysis, the resilient modulus was the

v
dependent variable. For the frozen condition, a function of the unfrozen water content

was the independent variable; for the thawed/unfrozen condition, various forms and

combinations of stress, density, and degree of saturation were the independent

variables. The equations resulting from this analysis have been subsequently utilized

in the CRREL Mechanistic Pavement Design Procedure to predict estimated damage

in some of the test sections at Mn/ROAD. Results of the modeling effort are described

in Bigl and Berg (1996b). Another report in this series (Bigl and Berg 1996c)

summarizes all the testing and modeling results.

vi
INTRODUCTION

This report describes resilient modulus testing

that CRREL conducted on materials from Mn/

ROAD for the Minnesota Department of Transportation (Mn/DOT). Results of other tests to determine physical and behavioral characteristics are

reported separately (Bigl and Berg 1996a). The

materials tested included samples of the subgrade

at the site and the two extreme grades of base and

subbase designed especially for Mn/ROAD: class

6 special, a clean base material, and class 3 special, a subbase material with a high percentage of

fines. Some specimens were tested in both frozen

and subsequently thawed conditions; others were

tested at room temperature without ever having

been frozen. Two intermediate grades of base—

class 4 special, class 5 special, and an R-70

subgrade—were manufactured later and results of

their testing are described in Berg (in prep.).

The resilient modulus tests were conducted using repeated-load triaxial test procedures described

by Cole et al. (1985, 1986). The tests involve

applying a confining pressure to a cylindrical specimen within a cell, while also applying a cyclical

loading of a deviator stress to the top end of the

specimen. The resilient modulus is defined as the

applied deviator stress divided by the recovered

strain upon unloading (the resilient axial strain)

for a representative loading cycle.

Linear regression analyses were performed on

the resilient modulus data from the materials tested

in this study. Data from two previously tested materials that are similar to the intermediate grades

of base/subbase materials (class 4 special and class

5 special) that will be used at Mn/ROAD were

reanalyzed. In the regression analysis, the resilient modulus was the dependent variable and various forms and combinations of stress, density, and

degree of saturation were the independent variables. The equations resulting from this analysis

have been subsequently utilized in the mechanistic pavement design procedure under development

at CRREL to predict estimated damage that would

occur in some of the Mn/ROAD test sections. Results of the modeling effort are described in Bigl

and Berg (1996b).

METHODS

Materials/conditions tested

The materials tested included the two extreme

grades of base—class 6 special and class 3 special, and the 1206 and 1232 subgrade samples that

represent, respectively, the high- and low-heaving

sandy lean clay (CL) subgrades. Specimens of the

base materials were tested in a frozen saturated

condition at three temperatures (class 6 special at

–5.0°, –3.0°, and –2.0°C; class 3 special at –7.0°,

–5.0°, and –2.0°C). The same specimens were

subsequently warmed to above freezing and tested

again at various thawed conditions in a range of

moisture levels created by drawing a suction at

the base of the specimens. Frozen, saturated

subgrade specimens were similarly tested at three

temperatures below freezing (–7.0°, –5.0°, and

–2°C) and also tested subsequently in a thawed,

saturated state at room temperature. To acquire

above-freezing resilient modulus data for the

subgrade samples at various moisture contents,

we molded specimens to specified conditions and

Resilient Modulus Testing of

Materials from Mn/ROAD, Phase 1

RICHARD L. BERG, SUSAN R. BIGL, JEFFREY A. STARK AND GLENN D. DURELL
tested at room temperature. We refer to these as a

“never frozen” specimens. Specimens of the lowheaving subgrade (1232) included replicates of

various moisture contents at a single density; for

the high-heaving subgrade (1206), replicates were

made with variation in both moisture and density

conditions. A total of 66 specimens were prepared

(Table 1).

Specimen preparation

The specimen size used for the subgrades and

the class 3 special subbase was 5.1 cm (2 in.)

diam. and 12.7 cm (5 in.) long. The coarser class 6

special material was tested using specimens measuring 15.2 cm (6 in.) in diam. and 39.4 cm (15.5

in.) in length. Gradation curves and other physical

properties of these materials are in Bigl and Berg

(1996a).

Specimens that were tested in frozen/thawed

conditions were first molded at the specified moisture/density condition, which was usually at optimum as determined from the compaction testing.

The subgrade specimens were compacted with a

CE-12 (Standard Proctor) compaction effort, while

the class 3 special and class 6 special were compacted with a CE-55 (Modified Proctor) effort to

approximate anticipated in-situ conditions (Table

2). The specimens were then prepared in a manner

similar to the procedure used in the frost susceptibility test (Chamberlain 1987). They were set on a

special base with a porous stone and saturated

from the base up with a constant head water supply. Once saturated, the specimens and their porous-stone bases were positioned with two other

special plates that could circulate temperature-regulated fluid at the top and bottom.

The bottom porous plate allowed movement of any additional water required for

open system freezing. The fluid temperatures were set to allow freezing from the

top down at the rate of about 2.5 cm (1 in.)

per day. The specimens were frozen with a

surcharge of 3.4 kPa (0.5 lb/in.2 ) placed

on the upper cold plate; this weight simulates the weight of a 15.2-cm (6-in.)-

thick asphalt concrete pavement surface.

After freezing was complete, the specimen ends were trimmed to assure that they

were smooth and flat. For the subgrade

specimens, this was done by milling the

ends flat. For the base and subbase materials, we

made a slurry of fine material that was placed in

custom-made equipment similar to that used for

capping concrete specimens with molten sulfur.

The slurry was then frozen to the ends of the

specimen and milled flat and smooth.

Subgrade specimens tested at room temperature without being frozen were molded at the specified moisture/density levels, trimmed with a knife,

and tested immediately. For the Sample 1232

subgrade, the density was held constant at about

1.76 Mg/m3 (110 lb/ft3) and the moisture content

was varied from 13% to a saturated value of 20%,

by weight (Table 2). For the 1206 subgrade, specimens were prepared at three compactive efforts,

with moisture contents intended to be at three

conditions: optimum, 2% above optimum, and 2%

below optimum (Table 2).

Test procedures

The resilient modulus tests were conducted using repeated-load triaxial test procedures, the details of which are described in reports by Cole et

al. (1985 and 1986). Testing was accomplished in

triaxial cells that were constructed to accommodate the instrumentation used to monitor load and

deformation (Fig. 1). Separate cells were used for

the 5.1- and 15.2-cm (2- and 6-in.)-diam. specimens.

The triaxial cells were designed so that the cell base

could be removed from the rest of the major cell

components. In this way, a specimen could remain

on its base while the remainder of the assembly was

used on other specimens in a rotating sequence. A

miniature, high-precision load cell mounted in the

Table 1. Samples tested for resilient modulus.

Condition

Never

Material Frozen Thawed* frozen

Sandy lean clay subgrade (CL)

1206 (high heave) 4 4† 24

1232 (low heave) 8 8† 18

Class 3 stockpile 5 4**

Class 6 stockpile 7 6**

Total 24 42

* Same samples were tested in the frozen and thawed condition

† Samples tested only in the thawed, undrained condition

** Thawed samples were tested at several moisture contents

2
Table 2. Resilient modulus samples tested.

Subgrade 1206 Subgrade 1232

Dry density Water content Dry density Water content

No. Mg/m3 (lb/ft3) (% by wt) No. Mg/m3 (lb/ft3) (% by wt)

Never frozen Never frozen

5K Compactive effort* CE 55 Compactive effort

18A 1.77 (110.3) 13.7 14A 1.76 (109.8) 13.1

18B 1.72 (107.4) 15.9 14B 1.78 (111.4) 12.9

18C 1.69 (105.3) 16.1 14C 1.78 (111.4) 13.0

21B 1.70 (106.4) 19.7 15A 1.78 (111.0) 14.4

21C 1.70 (106.1) 17.3 15B 1.77 (110.8) 14.1

15C 1.79 (112.0) 13.8

22A 1.69 (108.4) 19.0 15D 1.77 (110.3) 14.3

22B 1.73 (108.0) 19.1

22C 1.74 (108.6) 18.3 16A 1.76 (109.9) 15.7

16B 1.75 (109.0) 15.7

CE 12 Compactive effort 16C 1.76 (110.0) 15.6

16A 1.69 (105.6) 13.5 16D 1.77 (110.7) 15.5

16B 1.67 (104.4) 14.1

16C 1.89 (118.1) 14.3 18A 1.75 (109.3) 17.5

18B 1.75 (109.5) 17.5

18A 1.69 (105.4) 17.4 18C 1.76 (109.9) 17.5

18B 1.71 (106.9) 15.9 18D 1.76 (110.0) 17.2

18C 1.72 (107.3) 15.9

S1 1.70 (106.1) 20.5

20A 1.69 (105.8) 18.5 S2 1.68 (104.7) 21.3

20C 1.70 (106.1) 17.8 S3 1.70 (106.3) 20.3

CE 55 Compactive effort Frozen/thawed (saturated)

13A 1.74 (108.5) 11.0 CE 12 Compactive effort

13B 1.68 (105.1) 10.6 M4-1A 1.73 (107.8) 18.9

M4-1B 1.72 (107.5) 18.8

15A 1.88 (117.3) 13.9 M4-2A 1.71 (106.6) 19.3

15B 1.82 (113.9) 13.4 M4-2B 1.72 (107.6) 18.3

15C 1.85 (115.7) 13.5

M6-1A 1.69 (105.6) 18.9

17A 1.82 (113.9) 14.9 M6-1B 1.72 (107.1) 19.2

17B 1.86 (116.1) 14.9 M6-3A 1.68 (104.7) 19.4

17C 1.84 (114.9) 14.4 M6-3B 1.68 (104.7) 20.2

Frozen/thawed (saturated)

CE 12 Compactive effort

M5-1A 1.71 (106.5) 22.6

M5-1B 1.67 (104.1) 24.1

M5-2A 1.68 (104.6) 23.4

M5-2B 1.70 (106.0) 22.8

* 5K compactive effort = 5,000 ft-lb/ft3 applied in layers similar to the CE 12 and CE 55 test methods.

triaxial cell on the loading piston was used to

monitor the load applied to the specimen.

The axial deformation was monitored using two

LVDTs, or linear variable displacement transducers, mounted on hinged arms. The LVDT assemblies were mounted on two circumferential rings

clamped around the specimen. Radial deformation was also monitored using three noncontacting

multi-VITs (variable impedance transducers)

spaced evenly around the specimen at its midpoint. These pointed at small aluminum foil targets positioned on the specimen.

3
Table 2 (cont’d). Resilient modulus samples tested.

Class 3 Subbase Class 6 Base Course

Dry density Water content Dry density Water content

No. Mg/m3 (lb/ft3) (% by wt) No. Mg/m3 (lb/ft3) (% by wt)

Thawed Thawed

CE 55 Compactive effort CE 55 Compactive effort

Class 3-1 2.11 (131.5) 7.2 Class 6-2 2.08 (130.0) 9.6

2.12 (132.1) 3.3 2.08 (130.0) 6.0

2.12 (132.3) 0.8

Class 6-3 2.06 (128.4) 10.1

Class 3-2R 2.13 (132.7) 5.1 2.06 (128.4) 8.9

2.12 (132.6) 3.2 2.09 (130.7) 7.3

2.12 (132.3) 0.8

Class 6-4 2.09 (130.6) 9.5

Class 3-3 2.09 (130.4) 8.3 2.09 (130.6) 7.5

2.10 (131.2) 6.7 2.14 (133.8) 7.2

2.10 (130.9) 2.1 2.14 (133.8) 6.5

2.10 (131.4) 1.4

Class 6-5 2.06 (128.7) 9.3

Class 3-4 2.08 (129.6) 9.3 2.06 (128.7) 7.1

2.09 (129.8) 7.9 2.05 (128.2) 5.1

2.09 (130.5) 4.0 2.05 (128.2) 4.8

2.10 (131.0) 2.4 2.10 (131.0) 2.4

Frozen Class 6-6 2.13 (133.1) 8.9

Class 3-1 2.06 (128.3) 7.6 2.18 (136.0) 4.9

Class 3-2 2.09 (130.7) 6.2 2.18 (136.0) 4.4

Class 3-3 2.03 (126.5) 9.3 2.14 (133.3) 1.6

Class 3-4 2.02 (125.8) 10.1 2.14 (133.8) 0.7

Class 6-9 2.10 (134.2) 8.2

2.08 (136.2) 7.0

2.06 (136.2) 6.1

2.09 (136.2) 5.4

2.17 (135.3) 4.0

2.17 (135.3) 1.4

2.18 (136.3) 0.5

Frozen

Class 6-1 2.10 (130.9) 9.4

Class 6-2 2.08 (130.0) 9.6

Class 6-3 2.06 (128.4) 10.1

Class 6-4 2.09 (130.6) 9.5

Class 6-6 2.13 (133.1) 8.9

Class 6-9 2.15 (134.2) 8.2

The specimen was first positioned on one of the

cell bases with an aluminum cap placed on top.

It was then encased in a thin latex membrane with

O-rings at the top and bottom. The aluminum foil

targets for the multi-VITs were secured to this first

membrane, then a second membrane was placed

over the first to protect the multi-VITs. The remainder of the instrumentation was then attached to

the specimen and cell in the necessary positions.

Once the cell was assembled, the specimen was

tested in repeated-load triaxial compression using

a closed-loop, electrohydraulic testing machine.

4
For this study, the waveform used to apply the

cyclic deviator stress was the waveform shown in

Figure 2. The pulse length is approximately 1 second with 2 seconds between pulses. Table 3a illustrates the sequence of stress conditions applied to

the unfrozen specimens, whether thawed or never

frozen. We applied only the stress combinations

that would avoid excessive permanent strains in

the specimens (5% decrease in axial length), depending on the moisture condition and estimated

available strength. The frozen specimens were

tested holding the confining pressure constant at

69 kPa (10 lb/in.2) and varying the deviator stress

as shown in Table 3b. The frozen specimens were

tested at three temperatures: class 6 special specimens were tested at approximately –5.0°, –3.0°, and

–2.0°C (23.0°, 26.6° and 28.5°F); all other

specimens were tested at –7.0°, –5.0°, and

–2.0°C (19.5°, 23.0° and 28.5°F). The cyclical deviator stress was applied at each

test point until the resilient axial strain

remained a constant value, which occurred

at about 70–100 applied cycles.

Once the tests on the frozen specimens

were completed, they were allowed to thaw in the

triaxial device and subsequently retested in a

thawed, saturated state. For the coarser-grained

materials, the specimens were then allowed to drain

in place, and tested again. Increasing amounts of

suction were applied to the base and subbase specimens to bring them to various moisture states, and

additional test points were determined.

Previously tested materials

In order to conduct the follow-on modeling of

predicted damage at the test sections of the Mn/

ROAD facility, resilient modulus characterization

was needed for two additional Mn/DOT subbase

materials, class 4 special and class 5 special. We

looked through CRREL’s collection of material

Figure 1. Examples of triaxial cells. Cells for 15.2- (left) and 5.1-cm-diam. specimens.

1 s 2 s

Figure 2. Waveform used in Mn/ROAD resilient modulus

testing.

5
types for which resilient modulus data were available and found the two materials that most closely

fit Mn/DOT’s specifications for size gradation (Fig.

3). A dense-graded stone tested at a cooperative

study in Winchendon, Massachusetts, most closely

matched the specifications of the class 5 special

material; a subbase material from taxiway A at the

Albany, New York, airport most closely matched

the class 4 special specifications (Bigl and Berg

1996a).

The methods used during the testing of these

materials were nearly identical to the methods of

this study. Details of the testing procedures for

dense-graded stone are described in Cole et al.

(1986) and the procedures for Albany taxiway A

subbase are in Cole et al. (1987). Both materials

were molded into 15.2-cm (6-in.)-diam. specimens

in the laboratory from bulk field samples and then

Table 3. Stress conditions of resilient modulus tests

in current study.

Confining pressure Deviator stress Stress ratio

σ3, kPa (lb/in.2) σd, kPa (lb/in.2) (σ1/σ3)

a. Thawed or never-frozen specimens

48.3 (7) 48.3 (7.0) 2.0

48.3 (7) 34.5 (5.0) 1.7

48.3 (7) 27.6 (4.0) 1.6

48.3 (7) 20.7 (3.0) 1.4

48.3 (7) 13.8 (2.0) 1.3

48.3 (7) 6.9 (1.0) 1.1

48.3 (7) 3.4 (0.5) 1.1

27.6 (4) 48.3 (7.0) 2.8

27.6 (4) 34.5 (5.0) 2.3

27.6 (4) 27.6 (4.0) 2.0

27.6 (4) 20.7 (3.0) 1.8

27.6 (4) 13.8 (2.0) 1.5

27.6 (4) 6.9 (1.0) 1.3

27.6 (4) 3.4 (0.5) 1.1

13.8 (2) 34.5 (5.0) 3.5

13.8 (2) 27.6 (4.0) 3.0

13.8 (2) 20.7 (3.0) 2.5

13.8 (2) 13.8 (2.0) 2.0

13.8 (2) 6.9 (1.0) 1. 5

13.8 (2) 3.4 (0.5) 1.3

6.9 (1) 34.5 (5.0) 6.0

6.9 (1) 27.6 (4.0) 5.0

6.9 (1) 20.7 (3.0) 4.0

6.9 (1) 13.8 (2.0) 3.0

6.9 (1) 6.9 (1.0) 2.0

6.9 (1) 3.4 (0.5) 1.5

b. Frozen specimens

69 (10) 34 (5) –

69 (10) 69 (10) –

69 (10) 103 (15) –

69 (10) 138 (20) –

69 (10) 207 (30) –

69 (10) 276 (40) –

69 (10) 345 (50) –

69 (10) 483 (70) –

69 (10) 621 (90) –

69 (10) 690 (100) –

Notes:

Thawed samples: each combination of stresses normally used at each moisture condition.

Frozen samples: each combination of stresses normally used at each of three temperatures.

Table 4. Stress conditions of resilient modulus tests—

previous study.

Confining pressure Deviator stress Stress ratio

σ3,, kPa (lb/in.2) σd,, kPa (lb/in.2) (σ1 /σ3)

a. Thawed specimens

6.9 (1) 3.4 (0.5) 1.5

13.8 (2) 6.9 (1.0) 1.5

27.6 (4) 13.8 (2.0) 1.5

48.3 (7) 24.1 (3.5) 1.5

69.0 (10) 34.5 (5.0) 1.5

6.9 (1) 6.9 (1.0) 2.0

13.8 (2) 13.8 (2.0) 2.0

27.6 (4) 27.6 (4.0) 2.0

48.3 (7) 48.3 (7.0) 2.0

69.0 (10) 69.0 (10.0) 2.0

6.9 (1) 10.3 (1.5) 2.5

13.8 (2) 20.7 (3.0) 2.5

27.6 (4) 41.4 (6.0) 2.5

48.3 (7) 72.4 (10.5) 2.5

69.0 (10) 103.4 (15.0) 2.5

b. Frozen specimens

69 (10) 60 (9) –

69 (10) 138 (20) –

69 (10) 207 (30) –

69 (10) 276 (40) –

69 (10) 345 (50) –

69 (10) 483 (70) –

69 (10) 621 (90) –

69 (10) 827 (120) –

6
frozen from the top down at 2.5 cm (1 in.) per day

with open system freezing. This procedure differs

from the current study in that the specimens were

not saturated prior to freezing. Another difference

in this prior testing is the sequence of stresses

applied to the specimens (Table 4). In this case

also, the stress combinations applied were those

that would avoid excessive permanent strains in

the specimens (5% axial length shortening).

The previous regression analysis of the resilient modulus data obtained from this earlier testing had been based on characterizing the moisture

level of the unfrozen material with the measured

moisture tension. The data were reanalyzed using

degree of saturation as the indicator of moisture

condition.

DATA REDUCTION

AND ANALYSIS

For each set of applied deviator and confining

stresses, the resilient and permanent axial and ra100

80

60

40

20

0

10 1.0 0.1 0.01 0.001

Grain Size (mm)

Gravel Sand

Silt or Clay C'rse Fine C'rse Medium Fine

Percent Finer by Weight

4 10 40 200

Hydrometer 3

4

U.S. Std. Sieve Size and No.

Mn DOT Class 5 Spec.

Dense Graded

Stone

100

80

60

40

20

0

10 1.0 0.1 0.01 0.001

Grain Size (mm)

Gravel Sand

Silt or Clay C'rse Fine C'rse Medium Fine

Percent Finer by Weight

4 10 40 200

Hydrometer 3

4

U.S. Std. Sieve Size and No.

Mn DOT Class 4 Spec.

Albany, TW A

Subbase

a. Albany, New York, taxiway A subbase/class 4 special subbase.

b. Dense-graded stone, Winchendon,

Massachusetts/class 5 special subbase.

Figure 3. Comparison of Mn/DOT specifications with size gradations of substitute materials.

7
dial strains were recorded, and thus were used to

calculate a resilient modulus and Poisson’s ratio.

The resilient modulus is defined as the applied

deviator stress divided by the strain recovered upon

unloading for a representative loading cycle, or

resilient axial strain. To calculate the resilient axial

strain, the measured resilient axial deformation is

divided by the gauge length over which it is determined. Poisson’s ratio is defined as the recoverable radial strain divided by the recoverable axial

strain.

The following data were then tabulated in a

spreadsheet: confining stress, deviator stress, resilient axial strain, resilient radial strain, density,

and moisture condition or temperature. The tables

in Appendix A contain these data along with the

calculated results. The equivalent data for the previously tested materials are given in Appendix B.

These tables also show the actual stress combinations applied to each specimen.

The frozen and unfrozen data were analyzed

separately using statistical regression techniques.

The nonlinear form of the equation used to model

the resilient modulus was the same in both cases,

as given by

M KPK r = 1 2 , (1)

where K1 and K2 are constants and P is a governing parameter. This equation was linearized by

taking the natural log of both sides, resulting in an

equation of the form

ln ln , MAAP r = +0 1 (2)

where A0 and A1 are constants. To conduct the

regression, the natural log of the modulus was set

as the dependent variable and the natural log of

the governing parameter was set as the independent variable. In this general case,

K A KeA

21 1 = = 0 and .

Frozen

In attempting to represent the frozen data with

the general form eq 1, we tried three different governing parameters, all related to the unfrozen water content of the material, wu. The unfrozen water

content present in the materials at various temperatures, expressed in gravimetric form, wu–g,

had been determined in earlier characterization

tests on the Mn/ROAD materials (Bigl and Berg

1996a). It is related to the temperature in the form

w TT T ug o / ( / ) ; − = − <° α β 100 0 C (3)

where wu–g = gravimetric unfrozen moisture content, in decimal form

T = temperature, °C

To = 1.0°C

α and β = constants.

Table 5 presents the α and β constants characteristic of each material.

The first governing parameter we tried was

wu–g, expressed as a decimal, which had been normalized to the total gravimetric water content in

the sample, wt

, also expressed as a decimal. The

resulting equation was as follows:

M Kw w K

r ug t = ( /) 1 − 2 . (4)

This governing parameter has a good physical basis. When the material is very cold and solidly

frozen, there is very little unfrozen water and the

ratio wu–g/wt is a small number (<< 1). When the

material is just below the freezing point, wu–g/wt

approaches a value of 1. However, when this form

of the equation was used in the mechanistic design procedure (Bigl and Berg 1996b), the calculated amount of total water was often very high,

and the ratio of unfrozen water to total water was

unreasonably small. Therefore, other relationships

were considered.

Table 5. Constants for unfrozen

moisture content equations.

Soil α β

Subgrade

1206 11.085 –0.274

1232 8.121 –0.303

Class 3

Stockpile 1.497 –0.709

Class 4

Taxiway A 3.0 –0.25*

Class 5

Dense stone 2.0 –0.40*

Class 6

Stockpile 0.567 –1.115

* Values for these materials are estimated

8
The two other forms that were used to represent the unfrozen water content in the governing

parameter of eq 1 were directly related to the unfrozen water content, as follows: 1) wu–g, expressed

as a decimal, normalized to a unit unfrozen water

content, wo, of 1.0; and 2) the volumetric unfrozen water content, wu–v, expressed as a decimal,

normalized to a unit unfrozen water content, wo,

of 1.0. The volumetric unfrozen water content was

determined with

w w uv ug − − d = γ (5)

where γd = dry density (Mg/m3). The resulting

equations with these terms substituted as the governing parameter were:

M Kw w

K

r ug o = 1( − / ) 2

M Kw w K r uv o = / 1( − ) 2 .

In analyzing the frozen resilient modulus data,

the value of the governing parameter w w u g / , − t

wwww ug o uv o /, / − − or at each test point was determined from the temperature (and total water

content, if necessary.) Then, regression analysis

was conducted to determine the relationship between these values and the measured resilient

modulus. Data from the thawed, undrained state

(assigned to be at a temperature just barely below

freezing) were analyzed along with the frozen data.

Thawed/never frozen

For the never frozen and thawed data, the governing parameter in the general form equation (eq

1) was set to be a stress function. The constant K1

was considered to be a function of the moisture

level expressed as the degree of saturation in the

sample and, when a range of data were available,

the dry density. Thus, the general equation becomes

M Kf K r = [ ] ( ) 1 σ 2 , (6)

which includes the term

K C SS C

10 0 = 1 (/ ) (7)

or

K C SS C C

10 0 = 1 2 (/ ) ( / ) γ γ d o (8)

where f(σ) is a stress parameter normalized to a

unit stress of 6.9 kPa (1.0 lb/in.2); Co, C1, and C2

are constants; S is the degree of saturation, in %;

So is a unit saturation, 1.0%; γd is dry density, in

Mg/m3; and γo is a unit density (1.0 Mg/m3). To

conduct the regression analysis, we linearized this

equation to form

ln ln / M A A SS r = +0 0 1 ( )

+ A Af ( ) + [ ] ( ) 2 3 ln / ln . γγ σ d o (9)

For a particular set of conditions, then

K e SS K A A A A

1 23 0 0 1 2 = ( // . ) (λ γ d o ) and =

Three stress parameters were investigated to

help characterize the stress dependence of the materials tested. These included J1, the bulk stress

(or first stress invariant); τoct, the octahedral shear

stress; and J2/τoct, the ratio of the second stress

invariant to the octahedral shear stress. In our repeated-load triaxial test, where σ2 = σ3 and σ1 =

σ3 + σd, the functions are given as:

J1 3 = + 3σ σd

τoct d = σ

2

3

and

J2

3

2 9 6 3

2

/ oct

d

d

τ

σ σσ

σ = +

where J1123 =++ σσ σ

J2 12 23 13 =++ σσ σ σ σσ

τoct = − +− − 1 ( ) ( )( ) σσ σ σ σσ 2 1 2

2

2 3

2

1 3

2 .

We found that the bulk stress parameter (J1) provided the best fit to the data for the class 6 special

base material. The ratio J2/τoct was the stress parameter that best fit the data of the three subbases

class 3 special, class 4 special, and class 5 special,

and τoct best characterized the clay subgrades.

We also analyzed the data from the class 6

special base material in the thawed condition using an equation of the form

M KeK f r ( ) = [ ] 1 2 σ . (10)

9
As before, K1 was considered to be a function of

the degree of saturation and the dry density (eq 8).

In this case, the stress parameter, f(σ), was the

normalized bulk stress, J1. This form of the equation was able to accommodate negative stress values that were generated in the layered elastic analysis portion of the predictive model.

RESULTS

General

Appendices A and B give a tabulation of all the

laboratory test results of the frozen, thawed, and

never-frozen soil specimens. Appendix A contains

the data from the current study, which includes

the two Mn/ROAD subgrade samples 1206 and

1232, the class 6 special base, and the class 3

special subbase. Appendix B contains the data

determined previously from dense graded stone,

the substitute for Mn/DOT’s class 5 special subbase, and from Albany, New York, taxiway A subbase, the substitute for class 4 special subbase.

Data for the never-frozen 1206 subgrade specimens were acquired on a different testing machine than all the other data. After testing of all

specimens was completed, we discovered that this

second machine was out of calibration, such that

the moduli reported here are much higher than

they should be. However, data from the low density

(CE 5) samples are close to moduli back-calculated from falling weight deflectometer (FWD)

tests on subgrade at the site during fall of 1991.*

Table 6 summarizes the equations that resulted

from the regression analysis performed on the data,

with the frozen and unfrozen equations given in

separate sections. The number “n” in Table 6 refers to the number of points evaluated in the analysis. Each stress combination at a given moisture

level or temperature results in one data point; thus,

the test of a single specimen results in many data

points. The table also lists the coefficients of determination (r2) for these analyses.

Frozen

Figures 4a through 4f illustrate the resilient

modulus data vs. temperature for each material in

the frozen state. Also shown are the data for the

thawed, undrained condition, which are assumed

to be valid at a temperature of 0°C and were included as the warmest data point of the regression

analyses. Superimposed on the data are lines showing the moduli predicted by the three types of

regression equations. Where the predictive equation requires normalization to the total water content, that parameter was set to be the average value

for all the specimens tested. For the predictive

equation with volumetric unfrozen water, the dry

density was also set to be the average value for all

the specimens tested.

Figure 4 shows that the frozen modulus does

vary primarily as a function of the unfrozen water

content. A minor amount of variation results from

the various stress combinations acting on the specimens, as shown from the vertical spread in the

data at any particular temperature. To illustrate

this, Figure 5 shows the data from a few individual deviator stress levels plotted separately for the

subgrade samples.

All three types of predictive equations appear

to represent the data fairly well. The moduli resulting from the governing parameter, normalized

to the total water content, increases less rapidly

with decreasing temperature at temperatures just

below freezing than do moduli from the other two

equations. Unfortunately, the temperature variation of the environmental chamber of the testing

machine was too great to allow acquisition of data

at temperatures close to the freezing point for the

Mn/ROAD materials. When the two substitute materials were tested, a different chamber temperature controlling system was used, and it was possible to obtain data nearer to the freezing point. In

these cases, shown in Figures 4d and 4e, the predictive equations without normalization to total

water appear to pass nearer to the center of the

range of data collected at temperatures warmer

than –2.0°C.

Figure 4 also shows that the predictions from

the equations whose governing parameters are the

gravimetric and volumetric unfrozen water normalized to a unit unfrozen water are not very different. Predictions from the volumetric form rise

less rapidly at temperatures just below freezing,

while at the colder temperatures, they are slightly

*D. Van Deusen, Mn/ROAD, pers. comm. 1992 . larger than the gravimetric form.

10
Figure 4. Frozen resilient modulus data vs. temperature. Calculated lines are based on mean total water

content or density of all specimens tested, where appropriate.

-10 -8 -6 -4 -2 0 1

103

104

105

106

107

108

Temperature (°C)

Class 3 Subbase

c

1

1

1206 Subgrade

w /wu t

w u-g

wu-v

Calculated

-10 -8 -6 -4 -2 0

102

103

104

105

106

107

Temperature (°C)

a

Resilient Modulus

7 x 102

7 x 103

7 x 104

7 x 105

7 x 106

7 x107

(kPa) (lb/in. ) 2

1232 Subgrade

-10 -8 -6 -4 -2 0

102

103

104

105

106

107

Temperature (°C)

b

Resilient Modulus

7 x 102

7 x 103

7 x 104

7 x 105

7 x 106

7 x107

(kPa) (lb/in. ) 2

Resilient Modulus

7 x 103

7 x 104

7 x 105

7 x 106

7 x 107

7 x108

(kPa) (lb/in. ) 2

w /wu t

w u-g

wu-v

Calculated

w /wu t

w u-g

wu-v

Calculated

-10 -8 -6 -4 -2 0

103

104

105

106

107

Temperature (°C)

Class 4 Subbase

Albany Taxiway A

d

Resilient Modulus

7 x 103

7 x 104

7 x 105

7 x 106

7 x107

(kPa) (lb/in. ) 2

1

Class 5 Subbase

Dense-graded Stone

-10 -8 -6 -4 -2 0

103

104

105

106

107

108

Temperature (°C)

e

Resilient Modulus

7 x 103

7 x 104

7 x 105

7 x 106

7 x 107

7 x108

(kPa) (lb/in. ) 2

f

Class 6 Base

-10 -8 -6 -4 -2 0

103

104

105

106

107

108

Temperature (°C)

Resilient Modulus

7 x 103

7 x 104

7 x 105

7 x 106

7 x 107

7 x108

(kPa) (lb/in. ) 2

w /wu t

w u-g

wu-v

Calculated

w /wu t

w u-g

wu-v

Calculated

w /wu t

w u-g

wu-v

Calculated

11
Table 6. Results of regression analyses—test soils from Mn/ROAD.

A. Frozen condition.

Std

Material Equation (Mr in lb/in.2)* n r2 error

Clay subgrade sample 1206 (565)

Frozen M fw r u . = , ()− 1 087 5 259 207 0.99 0.319

Frozen M fw r ug . = ,() − − 1 049 2 344 207 0.99 0.275

Frozen M fw r uv . = ,() − − 1 052 2 929 207 0.99 0.262

Clay subgrade sample 1232 (566)

Frozen M fw r u . = ( )− 905 4 821 244 0.98 0.378

Frozen M fw r ug . = ( ) − − 846 2 161 244 0.98 0.423

Frozen M fw r uv . = ( ) − − 848 2 633 244 0.98 0.394

Class 3 “stockpile”

Frozen M fw r u . = , ()− 5 824 2 026 186 0.97 0.491

Frozen M fw r ug . = ,() − − 5 488 1 076 210 0.97 0.507

Frozen M fw r uv . = ,() − − 5 542 1 249 186 0.97 0.467

Class 4 (taxiway A subbase)

Frozen M fw r u . = , ()− 2 826 5 220 69 0.92 0.835

Frozen M fw r ug . = ,() − − 1 813 1 733 85 0.93 0.885

Frozen M fw r uv . = ,() − − 1 652 2 813 69 0.91 0.916

Class 5 (dense graded stone)

Frozen M fw r u . = , ()− 11 320 2 036 28 0.97 0.404

Frozen M fw r ug . = ,() − − 8 695 1 2814 28 0.95 0.511

Frozen M fw r u . = ,() − − 9 245 1 489 v 28 0.97 0.432

Class 6 “stockpile”

Frozen M fw r u . = , ()− 19 924 1 243 260 0.98 0.372

Frozen M fw r ug . = ,() − − 19 427 0 795 260 0.98 0.338

Frozen M fw r uv . = ,() − − 19 505 0 897 260 0.98 0.341

Notes: n = number of test points f(wu–v) = wu–v/wo

r2 = coefficient of determination wu–v = volumetric unfrozen

Mr = resilient modulus water content

f(S) = S/So σ = stress (lb/in.2)

S = degree of saturation (%) f

1 (σ) = J1/σo

So = 1.0 % f

2 (σ)=(J2/τoct)/σo

f(γ) = γd/γo f

3 (σ) = τoct/σo

γd = dry density (Mg/m3) σo = 1.0 lb/in.2

γo = 1.0 Mg/m3 J1 = bulk stress (lb/in.2)

f(wu) = wu–g/wt J1 = 3σ3 + σd

wu–g = gravimetric unfrozen water content J2 = 2nd stress invariant (lb/in.2)

wt = gravimetric total water content J2 = 3σ3

2 + 2σ3σd

f(wu–g) = wu–g/wo τoct = octahedral shear stress (lb/in.2)

wo = unit water content (1.0) τoct = ( ) 2 3 σd

*Output from equations can be converted to kilopascals through multiplying by 6.895

12
Table 6 (cont’d). Results of regression analyses—test soils from Mn/ROAD.

B. Unfrozen condtion

Std

Material Equation (Mr in lb/in.2)* n r2 error

Clay subgrade sample 1206 (565)

Never frozen M fS f f r . . 3 . = , , () () () − − 1 597 000 2 63 14 42 0 257 γ σ 655 0.82 0.251

Clay subgrade sample 1232 (566)

Never frozen M fS f r . . = × . () () − − 1 518 1030 13 85

3

0 272 σ 451 0.95 0.328

Class 3 “stockpile”

Thawed M fS f r . . = , () () − 283 300 1 003

2

0 206 σ 408 0.86 0.520

Class 4 (taxiway A subbase)

Thawed M fS f r . . = × . () () − 8 946 108 3 026

2

0 292 σ 149 0.86 0.168

Class 5 (dense graded stone)

Thawed M fS f r . . = , () () − 382 400 0 8759

2

0 1640 σ 64 0.77 0.164

Class 6 “stockpile”

Thawed M fS f f r . .. = , () () () − 1 391 0 507 4 04

1

0 608 γ σ 492 0.79 0.232

Thawed M fS f e f r . . . () = , () () − 5 257 0 486 4 05 0 0193 γ 1 σ 492 0.76 0.249

*Output from equations can be converted to kilopascals through multiplying by 6.895

Figure 5. Effect of stress on frozen resilient modulus.

Figure 6 compares the modulus vs. temperature for all the frozen Mn/DOT materials predicted from the regression equations in Table 6,

with the governing parameters wu–g/wt and wu–v.

At any given temperature, the subgrade specimens

have the lowest moduli. In general, the base and

subbase moduli increase with decreasing amounts

of fines in the material. The curve for the class 5

special material has a slightly different shape than

the rest, which is probably related to the estimated

choice of coefficients for the distribution of unfrozen water content with temperature.

Unfrozen

Figures 7a through 7f show the resilient modulus data vs. degree of saturation for the unfrozen

specimens. For the two subgrade materials, data

are from specimens that were never frozen, and

data from the base/subbase materials are from

specimens that were thawed subsequent to freez1206 Subgrade

-10 -8 -6 -4 -2 0

102

103

104

105

106

107

Temperature (°C)

4 & 5

15

70

σ , d Deviator Stress

lb/in.2

Resilient Modulus

7 x 10 7

7 x 10 6

7 x 10 5

7 x 10 4

(kPa) (lb/in. ) 2

7 x 10 2

7 x 10 3

1232 Subgrade

10 -8 -6 -4 -2 0

Temperature (°C)

3 & 5

15

70

σ , d Deviator Stress

lb/in.2

a. 1206 Subgrade b. 1232 Subgrade

-

13
Temperature (°C)

-12 -10 -8 -6 -4 -2 0 2

10

10

10

108

6

4

2

1206

1232

Class 3

Class 4

Class 5

Class 6

Resilient Modulus

7 x 10 8

7 x 10 6

(kPa) (lb/in. ) 2

7 x 10 2

7 x 10 4

-12 -10 -8 -6 -4 -2 0 2

Temperature (°C)

10

10

10

108

6

4

2

1206

1232

Class 3

Class 4

Class 5

Class 6

Resilient Modulus

7 x 10 8

7 x 10 6

(kPa) (lb/in. ) 2

7 x 10 2

7 x 10 4

a. Governing parameter wu–g/wt.

b. Governing parameter wu–v.

Figure 6. Predicted frozen resilient modulus

for all Mn/ROAD materials.

ing. Also shown is a line representing the predicted moduli resulting from the equations given

in Table 6, at the mean stress level tested. Where

dry density is included in the equation, it was set

at the average value of all specimens tested. It can

be seen in Figures 7a through 7f that moisture

level does influence the unfrozen moduli, but to

different degrees, depending on the material.

The vertical spread in the data points at a particular degree of saturation (Fig. 7) is the result of

the materials response to the different stress combinations applied (Table 3a). In the case of the

1206 subgrade and the class 6 special base, it also

relates to the variation in density. To show the

influence of density in the 1206 subgrade data,

Figure 8 differentiates the data from three density

ranges (high, medium, and low), along with the

corresponding predicted resilient moduli lines.

Note that the low density moduli are most representative of moduli back-calculated from FWD

deflections measured on site at Mn/ROAD.

The effect of stress combinations is shown in

Figure 9 for the low-density 1206 subgrade data,

and all of the 1232 subgrade and class 3 special

subbase data. The two subgrades display an inverse relationship between modulus and deviator

stress; the class 3 special subbase has a proportional relationship between modulus and the stress

parameter J2/τoct.

Figure 10 demonstrates the relative influence

of the deviator stress and confining pressure (σ3)

on the modulus of a single 1206 subgrade specimen at 16.1% water content. The deviator stress

has the major influence, while confining pressure

produces only minor variations in the moduli. The

figure also includes a line of predicted resilient

moduli based on a regression analysis of these

data alone, in the form:

Mr (lb/ft2) = K1 (σd)

K2,

as well as the upper and lower 95% confidence

interval around the mean line. The confidence band

brackets the variation in modulus related to σ3.

We generated several predicted curves for individual samples as described above to isolate the

influence of moisture content and density, respectively, on the resilient modulus of the 1206 subgrade material. Figure 11 shows the relationship

between modulus and deviator stress of specimens

with a similar density, but with different moisture

levels. It confirms the expected relationship that

the drier sample exhibits a higher modulus at similar stress conditions. Figure 12 compares two

samples with similar moisture, showing that the

higher density sample has higher moduli.

A comparison of the predicted modulus curves

generated by the equations in Table 6 for all the

materials studied is given in Figure 13. Among

the curves of the base/subbase materials, there is a

general increase in the predicted moduli as the

14
1206 Subgrade

100 80 60 40

103

104

105

106

Degree of Saturation (%)

Resilient Modulus

7 x 10 6

7 x 10 5

7 x 10 4

7 x 10 3

(kPa) (lb/in. ) 2

1232 Subgrade

100 90 60 80

103

104

105

106

Degree of Saturation (%)

102

70

Resilient Modulus

7 x 10 6

7 x 10 5

7 x 10 4

7 x 10 3

(kPa) (lb/in. ) 2

7 x 10 2

Class 3 Subbase

100 80 20 60

104

105

Degree of Saturation (%)

103

40

Resilient Modulus

7 x 105

7 x 104

7 x 103

(kPa) (lb/in. ) 2

100 80 60

104

105

Degree of Saturation (%)

103

40

 Class 4 Subbase

Albany Taxiway A Subbase

Resilient Modulus

7 x 10 5

7 x 10 4

7 x 10 3

(kPa) (lb/in. ) 2

100 80 60 40 20 0

103

104

105

106

Calc - Semi Log

Degree of Saturation (%)

Class 6 Base

Calc - Log Log

Resilient Modulus

7 x 10 6

7 x 10 5

7 x 10 4

7 x 10 3

(kPa) (lb/in. ) 2

f. Class 6 special base.

e. Class 5 special subbase.

d. Class 4 special subbase.

c. Class 3 special subbase.

Figure 7. Resilient modulus vs. degree of saturation for never frozen subgrade materials and thawed base/

subbase materials. Solid line represents calculated value based on mean condition of stress (and density

where included).

b. 1232 subgrade.

a. 1206 subgrade. (These data are probably in error—

see text.)

100 80 60

104

105

Degree of Saturation (%)

103

40

 Class 5 Subbase

Dense Graded Stone

Resilient Modulus

7 x 10 5

7 x 10 4

7 x 10 3

(kPa) (lb/in. ) 2

15
100 80 60 40

103

104

105

106

Degree of Saturation (%)

Resilient Modulus

115 lb/ft 3

108

105

High

Medium

Low

Density (lb/ft )3

114 - 117

107 - 110

104 - 106

7 x 106

7 x 105

7 x 104

7 x 103

(kPa) (lb/in. ) 2

100 80 60 40

103

104

105

106

Degree of Saturation (%)

0.5

1.0

4.0

10

14

σd (lb/in. ) Calculated 2

1206 Unfrozen

Resilient Modulus

7 x 10 6

7 x 10 5

7 x 10 4

7 x 10 3

(kPa) (lb/in. ) 2

Figure 8. Resilient modulus vs. degree of saturation of never-frozen 1206 subgrade material illustrating the effect of dry density.

a. Low-density (1.66–1.7-Mg/m3 or 104–106-lb/

ft3) 1206 subgrade. (These data are probably in

error—see text.)

0.5

1.0

5.0

9.0

14

σd (lb/in. ) Calculated 2

100 90 80 70 60

10 2

10 3

10 4

10 5

10 6

Degree of Saturation (%)

1232 Unfrozen

Resilient Modulus

7 x 10 6

7 x 10 5

7 x 10 4

7 x 10 3

(kPa) (lb/in. ) 2

7 x 10 2

b. 1232 subgrade.

100 80 60 40 20

103

104

105

106

Degree of Saturation (%)

Class 3 Subbase

640

330

117

58

5

Calculated (lb/in. ) 2 J2 τoct /

Resilient Modulus

7 x 106

7 x 105

7 x 104

7 x 103

(kPa) (lb/in. ) 2

c. Class 3 special subbase.

Figure 9. Resilient modulus vs. degree of saturation illustrating effect of stress parameters.

amount of fines in the material decreases, with the

exception of the class 4 special material. There is

also a decrease in the slope of the predicted curves

with decreasing fine content, indicating the expected lesser influence of moisture content on the

moduli of the coarser materials. The curves of the

two clay subgrades depart somewhat from this

pattern. The curve for the 1232 subgrade has an

extremely steep slope, showing a much stronger

influence of the degree of saturation on the modulus. The curve of predicted moduli for the 1206

subgrade is higher than those for the coarser

materials. Although this is contrary to conventional rules-of-thumb, high moduli for cohesive

materials have also been reported by Robnet and

Thompson (1973). However, it is more likely that

the high 1206 subgrade moduli are related to the

miscalibration of the testing machine. This possibility is being investigated in more detail and findings will be included in the Phase 2 report (Berg

in prep.).

For each material tested, Figure 14 shows the

frozen and thawed/unfrozen moduli data points

and curves based on the regression equations resulting from this analysis. Data in Figure 14 illustrate the rapid increase in modulus as the soils

freeze and a lower-magnitude increase in modulus values with decreasing saturation. To illustrate

these general trends, the calculated relationships

vs. degree of saturation are also shown, for one

stress condition only. As shown in Figure 9, stress

conditions also influence resilient modulus values.

16
0 10 20

104

105

Resilient Modulus

w = 16.1%

γ = 105 lb/ft d 3

2 1

2

4

7

σ (lb/in. ) 3

7 x 10 4

7 x 10 5

(kPa) (lb/in. ) 2

(lb/in. ) 2

Deviator Stress

0 70 140 (kPa)

Figure 10. Resilient modulus vs. deviator stress applied to a single 1206 subgrade specimen. Data points

illustrate level of confining stress applied. Dashed

lines indicate band of 95% confidence interval.

19.7 

16.1

w = 10.6 %

1206 Subgrade Unfrozen

0 10 20

10 3

10 5

10 6

γ = 105 lb/ft d 3

10 4

(lb/in. ) 2

Deviator Stress

0 70 140 (kPa)

Resilient Modulus

7 x 10 6

7 x 10 5

7 x 10 4

7 x 10 3

(kPa) (lb/in. ) 2

Figure 11. Resilient modulus vs. deviator stress applied to three 1206 subgrade specimens illustrating

effect of moisture condition. Dashed lines indicate

band of 95% confidence interval.

Figure 12. Resilient modulus vs. deviator stress applied to two 1206 subgrade specimens illustrating effect of dry density. Dashed lines indicate band of 95%

confidence interval.

1206 Subgrade

S = 72-75%

105.3 

0 10 20

104

105

106

γ = 113.9 lb/ft d 3

(lb/in. ) 2

Deviator Stress

0 70 140 (kPa)

Resilient Modulus

7 x 10 6

7 x 10 5

7 x 10 4

(kPa) (lb/in. ) 2

Degree of Saturation (%)

100 80 60 40 20

1232 1206

Class 3

Class 4 Class 5

Class 6

10

10

10

10

106

5

3

4

2

Resilient Modulus

7 x 10 6

7 x 10 5

7 x 10 4

7 x 10 3

(kPa) (lb/in. ) 2

7 x 10 2

Figure 13. Predicted moduli for all materials in unfrozen condition.

A significant discontinuity between thawed 0°C

and 100% saturated modulus values is shown in

Figure 14a. As indicated previously, the difference is probably due to miscalibration of the testing equipment for the unfrozen data rather than an

actual large difference in resilient modulus values

at these points. These data are currently being

reexamined and findings will be reported in the

Phase 2 report (Berg in prep.).

For the granular base and subbase materials,

essentially no discontinuity is apparent between

the modulus of the thawed, 0°C material and the

same material at 100% saturation.

17
Figure 14. Comparison of frozen and unfrozen modulus data.

100

Calculated

80 60 40 20

Degree of Saturation (%)

-10 -8 -6 -4 -2 0

103

104

105

106

107

108

Temperature (°C)

Class 3 Subbase

c

100 80 60

Degree of Saturation (%)

Calculated

90 70

Calculated

100 80 60 40

Degree of Saturation (%)

1206 Subgrade

w /wu t

w u-g

wu-v

Calculated

-10 -8 -6 -4 -2 0

102

103

104

105

106

107

Temperature (°C)

a

Resilient Modulus

7 x 102

7 x 103

7 x 104

7 x 105

7 x 106

7 x107

(kPa) (lb/in. ) 2

1232 Subgrade

-10 -8 -6 -4 -2 0

102

103

104

105

106

107

Temperature (°C)

b

Resilient Modulus

7 x 102

7 x 103

7 x 104

7 x 105

7 x 106

7 x107

(kPa) (lb/in. ) 2

Resilient Modulus

7 x 103

7 x 104

7 x 105

7 x 106

7 x 107

7 x108

(kPa) (lb/in. ) 2

w /wu t

w u-g

wu-v

Calculated

w /wu t

w u-g

wu-v

Calculated

(These data are probably in error—see text.)

18
Figure 14 (cont’d).

100 80 60 40

Degree of Saturation (%)

Calculated

-10 -8 -6 -4 -2 0

103

104

105

106

107

Temperature (°C)

Class 4 Subbase

Albany Taxiway A

d

Resilient Modulus

7 x 103

7 x 104

7 x 105

7 x 106

7 x107

(kPa) (lb/in. ) 2

100 80 60 40 20

Degree of Saturation (%)

Calculated

Class 5 Subbase

Dense-graded Stone

-10 -8 -6 -4 -2 0

103

104

105

106

107

108

Temperature (°C)

e

Resilient Modulus

7 x 103

7 x 104

7 x 105

7 x 106

7 x 107

7 x108

(kPa) (lb/in. ) 2

100 80 60 40 20 0

Degree of Saturation (%)

Calculated, Log Log

Calculated, Semi Log

f

Class 6 Base

-10 -8 -6 -4 -2 0

103

104

105

106

107

108

Temperature (°C)

Resilient Modulus

7 x 103

7 x 104

7 x 105

7 x 106

7 x 107

7 x108

(kPa) (lb/in. ) 2

w /wu t

w u-g

wu-v

Calculated

w /wu t

w u-g

wu-v

Calculated

w /wu t

w u-g

wu-v

Calculated

19
CONCLUSIONS

Laboratory resilient modulus tests on the Mn/

ROAD unbound base and subgrade materials have

resulted in the following:

1. All materials exhibited a two to three order of

magnitude increase in resilient modulus at subfreezing temperatures of –2°C and lower.

2. All of the materials exhibited an increase in

modulus as the degree of saturation decreased.

3. The modulus value of all of the materials

was stress dependent.

4. For the highly frost-susceptible 1206 subgrade and the class 6 special base course, the

resilient modulus was also dependent on the

density of the sample tested. We did not test

samples at a wide variety of densities for the

other materials, but density probably impacts

modulus values of those materials also.

LITERATURE CITED

Berg, R.L. (in prep.) Resilient modulus testing of

materials from Mn/ROAD, Phase 2. USA Cold

Regions Research and Engineering Laboratory,

Special Report.

Bigl, S.R. and R.L. Berg (1996a) Testing of materials from the Minnesota Cold Regions Pavement Research Test Facility. USA Cold Regions

Research and Engineering Laboratory, Special

Report 96-20, Mn/DOT Report 96-24.

Bigl, S.R. and R.L. Berg (1996b) Modeling of

Mn/ROAD test sections with the CRREL mechanistic pavement design procedure. USA Cold Regions Research and Engineering Laboratory,

Special Report 96-21, Mn/DOT Report 96-22.

Bigl, S.R. and R.L. Berg (1996c) Material testing and initial pavement design modeling: Minnesota Road Research Project. USA Cold Regions

Research and Engineering Laboratory, CRREL Report 96-14, Mn/DOT Report 96-23.

Chamberlain, E.J. (1987) A freeze thaw test to

determine the frost susceptibility of soils. USA

Cold Regions Research and Engineering Laboratory, CRREL Special Report 87-1.

Cole, D.M., G.D. Durell and E.J. Chamberlain

(1985) Repeated load triaxial testing of frozen

and thawed soils. Geotechnical Testing Journal, 8(4):

166–170.

Cole, D.M., D. Bentley, G.D. Durell and T.

Johnson (1986) Resilient modulus of freeze-thaw

affected granular soils for pavement design and

evaluation. Part 1. Laboratory tests on soils from

Winchendon, Massachusetts, test sections. USA Cold

Regions Research and Engineering Laboratory,

CRREL Report 86-4.

Cole, D.M., D. Bentley, G.D. Durell and T.

Johnson (1987) Resilient modulus of freeze-thaw

affected granular soils for pavement design and

evaluation. Part 3. Laboratory tests on soils from

Albany County Airport. USA Cold Regions Research and Engineering Laboratory, CRREL Report 87-2.

Robnet, Q.L., and M.R. Thompson (1973) Interim report—Resilient properties of subgrade

soils—Phase 1. Development of testing procedure.

Transportation Engineering Series 5, Illinois Cooperative Highway Research Program Series 139,

University of Illinois, Urbana, Illinois, May.

20
21

APPENDIX A: Mn/ROAD MATERIALS RESILIENT MODULUS TEST RESULTS

[The paper version of this report includes 64 pages of data that are

not reproduced here. Paper copies are available through the

National Technical Information Service. See the inside cover of

this report for ordering information.]
APPENDIX B: SUBSTITUTE MATERIALS RESILIENT MODULUS TEST RESULTS

[The paper version of this report includes nine pages of data that

are not reproduced here. Paper copies are available through the

National Technical Information Service. See the inside cover of

this report for ordering information.]
1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

6. AUTHORS

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION

 REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING

 AGENCY REPORT NUMBER

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

14. SUBJECT TERMS 15. NUMBER OF PAGES

16. PRICE CODE

17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT

 OF REPORT OF THIS PAGE OF ABSTRACT

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. Z39-18

298-102

REPORT DOCUMENTATION PAGE Form Approved

OMB No. 0704-0188

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and

maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information,

including suggestion for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington,

VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

September 1996 Final Report June 1990–October 1991

Resilient Modulus Testing of Materials from Mn/ROAD, Phase 1 CPAR Project

 Agreement No. 64632

Task Order No. 1

Richard L. Berg, Susan R. Bigl, Jeffrey A. Stark and Glenn D. Durell

U.S. Army Cold Regions Research and Engineering Laboratory

72 Lyme Road Special Report 96-19

Hanover, New Hampshire 03755-1290

Minnesota Department of Transportation

395 John Ireland Boulevard Mail Stop 330 MN/RC-96/21

St. Paul, Minnesota 55155

For conversion of SI units to non-SI units of measurement consult ASTM Standard E380-93, Standard Practice for Use of the

International System of Units, published by the American Society for Testing and Materials, 1916 Race St., Philadelphia, Pa. 19103.

Approved for public release; distribution is unlimited.

Available from NTIS, Springfield, Virginia 22161

103

Cold regions subgrades and bases Resilient modulus

Mechanistic Pavement Design and Evaluation Procedure

UNCLASSIFIED UNCLASSIFIED UNCLASSIFIED UL

The U.S. Army Cold Regions Research and Engineering Laboratory (CRREL) conducted resilient modulus tests on

materials from the Mn/ROAD test site for the Minnesota Department of Transportation. Materials tested included samples

of the lean clay subgrade at the site and the two extreme grades of base designed specifically for Mn/ROAD. Some

specimens were tested in both frozen and subsequently “thawed” conditions; others were tested at room temperature

without ever having been frozen. Researchers performed linear regression analysis on the data to develop equations that

predict frozen modulus based on unfrozen water content and unfrozen modulus based on stress, degree of saturation and

density. We also reanalyzed data from two previously tested materials. CRREL can use the study’s equations in the

Mechanistic Pavement Design and Evaluation Procedure under development at CRREL to predict estimated damage in

some Mn/ROAD test sections.