Final Research Report

for

RESILIENT MODULUS OF GRANULAR SOILS WITH FINES CONTENTS

Prepared by

Nien-Yin chang, Ph.D., P.E. Hsien-Hsiang Chiang, Ph.D.

and Lieu-Ching Jiang, Doctoral Candidate

for

Colorado Department of Transportation and

Federal Highways Administration

under

Contract No. COOT 91-379

Expansive Soil Research Center Department of Civil Engineering university of Colorado at Denver

Denver, Colorado 80204-5300

May 1994

The contents of this report reflect the views of

authors who are responsible for the facts and the

accuracy of the data presented herein. The

contents do not necessarily reflect the official

views of the Colorado Department of Transportation

or the Federal Highway Administration. This report

does not consti~ute a standard, specification, or

regulation.

i

Technical Rep0l1, Documentation Page

1. Report No. 2. GoVel"lllllellt Accessioll No.

CDOT-DTD-R-95-9

4. Tille and Subtitle

Resilient Modulus of Granular Soils With Fines Contents

7. Author(s)

3. Recipient's Catalog No.

5. RepOl·t Date

Apri11995

6. Perfol"luing Organization Code

8. Ped"orming Organization Rpt.No.

Nien-Yin Chang, Hsien-Hsiang Chian.l~;, Lieu-Ching Jiang CDOT-DTD-R-95-9

9. Pcrrol"luing O.·galli7.ation Namc anel Add.·css

Colorado Department of Transportation

4201 E. Arkansas Ave. Denver Colorado 80222

12. Sponsol"ing Agcncy Namc and Addl'css

Colorado DepaJ1ment of Transportation

4201 E. Arkansas Ave. Denver, Colorado 80222

15. Supplcll1cnhll")' Notes

10. WOI'k Unit No. (TRAYS)

11. Contract 01' GI'ant No.

13. Type or Rpt. and Pel'ioel COVCI'Cel

Final Reoort 14. SI)Onsm'ing AgenL'Y Code

Prepared in Cooperation with the U.S. Department of Transportation Federal Highway Administration

16. Ahslrad

This study examined the relationship of resiJient modulus with the stabilometer R-values, and with the index properties of Colorado soils.

A total of 39 resilient modulus tests were conducted, 20 in this test program and 19 in an earlier test program. Soil types ranged from A-I-a

to A-7-6 with valying amounts of fines. Regression analyses were

performed to formulate the functional relationship lIsing the least square fit.

Two regression equations were formulated to relate resilient modulus to R-value (one linear and one nonlinear), and four linear regression equations to relate

resilient modulus to percent fines content, plasticity index, uniformity coefficient, and mean grain size. In general, the values of the Correlation coefficients are small

llnd care should be taken when using these equations, particularly for granular soil samples with less than 30% of fines.

Implcmcnt"t ion:

It is recommended to abandon the effort to formulate a relationship between resilinet modulus and R-vaJue because of the inability of R-value jn reflecting dynamic behavior of soils.

l7. Kcy Words

Resilient Modulus,

R -vallle,I ndex properties

19.5ccmity Classif. (reIWI'I)

Unclassified

20.SeclII·ity CIassif. (page)

Unclassified

18. Distl"ihutiol1 Stalell1cl1t

No Restrictions: This report is

available to the public through

the National Technical Info. Selvice. Springfield, VA 22161

21. No. of l'ilges

ii

EXECUTIVE SUMMARY

After several decades of development, the design of pavement

using theory of elastic layers has matured to an extent that its

introduction for general acceptance by pavement engineers becomes

feasible. This led to the adoption of the elastic layer theory

in pavement design by the American Association of state Highway

and Transportation Officials (AASHTO) in its "AASHTO Guide for

Design of Pavement structures - 1986. 11 The use of elastic layer

theory involves two elastic material parameters, namely resilient

modulus and Poisson's ratio. The major difficulties in the

implementation of the 1986 AASHTO Guide include: 1) the lack of

proper/affordable testing equipment, 2) the lack of

understanding of the physical meaning of resilient modulus, and

3) site (or soil type) dependency of resilient modulus. Thus,

each state is advised to develop its own design curve and/or

design equation.

Objectives of this research project are three fold: · 1) to

determine the resilient modulus and the stabilometer R value of

soils of different index properties, 2) to formulate the

functional relationship between the resilient modulus and R­

value, and between the resilient modulus and different index

properties of soils, and 3) to provide detailed test procedures

for resilient modulus. Because of the recent nature of the

implementation of resilient modulus in pavement design, its data

base is extremely small compared to the data base for the

iii

stabilometer R-value. Thus, the functional relationship between

the resilient modulus and the R-value with a large data base

would seem desirable. Once the equation is formulated., the

resilient modulus of a subgrade soil can be evaluated for a R­

value that can be easily determined. However, the R value does

not reflect the dynamic property of soils that is required in the

design of pavement. It would be extremely desirable to determine

the resilient modulus of soils and then relate the resilient

modulu.s to their index properties.

The resilient modulus is a dynamic property of soil.

Previous studies indicate that the dynamic properties of soils

are strongly related to the index properties of soils. These

index properties include percent fines content, gradation

characteristics and Atterberg I s limits. Thus, the resilient

modulus can be formulated as a function of index properties of

soils. Given the functional relationship, a resilient modulus

can be determined using the index properties that can be easily

determined.

This study aims to provide the functional relationship where

the resilient modulus is related to the stabilometer R value

and/or index properties of Colorado soils. The statistical

sample size is, however, too small to obtain a good functional

relationship because of the large number of influencing factors

involved. To form a bigger statistical data base, the results

from the twenty resilient modulus tests from this research and

the nineteen tests conducted earlier for the Colorado Department

iv

of Transportation are merged. Test results are found to be quite

scatter, particularly for the granular soils. This is believed

to be caused by a large number of factors affecting the dynamic

behavior and properties of soils.

Both linear and nonlinear regression analyses were performed

to relate the resilient modulus to the stabilometer R value.

Both linear and nonlinear regression equations give nearly the

same result as the one recommended by Yeh and Su (1989). The

correlation relationship between the resilient modulus and the R

value is weak. This weak correlation between MR and R values

could be because of the inability of the stabilometer R value in

reflecting the dynamic properties of soils.

Linear regression analyses are also performed to relate the

resilient modulus to each of the following index properties of

soils: mean grain size 050, uniformity coefficient, Cu, percent

fines content, FC (passing u. s. standard sieve #200), and

plastic index, PI. The resilient modulus was found to be weakly

correlated to these index properties in a descending order of the

strength of correlation: % fines content, FC, plasticity index,

PI, uniformity coefficient, CU, and mean grain size, 050.

This study reveals the fact that the many factors affect the

value of resilient modulus. These factors include density (or

void ratio), moisture content, percent fines content, Atterberg's

limits of fines, uniformity and mean grain size of coarse grain

soils with grain size greater than US Standard Sieve #200,

conf ining stress, and cyclic stress amplitude and the number of

repeti tion, etc.

v

To formulate an equation for an effecti ve

evaluation of the resilient modulus, it is recommended to conduct

a systematic resilient modulus test program involving soils with

a wide range of values for each index property. To facilitate

technology transfer, it is recommended to hold resilient modulus

training sessions for material and pavement design engineers

throughout the state aiming at an eventual transfer the resilient

modulus technology including the method of testing and the

analysis of test results to the Colorado Department of

Transportation.

1

I. INTRODUCTION

A highway pavement system includes pavement and subgrade

materials, and, sometimes, base (and subbase) course. Its design

naturally requires the mechanical properties of pavement

materials and all base course and subgrade materials.

Conventionally these mechanical properties are lumped in one

single parameter, namely the stabilometer R-value or CBR. The

continual distress of pavement designed using R-value indicates

the shortcoming of using R-value in the pavement design.

Besides, in the last three decades, the development of the

elastic layer theory for pavement design has matured to an extent

that its implementation in pavement design becomes feasible.

This leads to the adoption of the 1986 AASHTO Guide for Design of

Pavement structures.

In the elastic layer theory, the material is assumed to be

isotropic linear elas.tic with two independent material

parameters, namely Poisson's ratio and Young's modulus. In the

repetitive loading environment, the resilient Young's modulus (or

resilient modulus) of subgrade varies with the number of

repetition, amplitude of repetitive loading, confining pressure,

and index properties of soils including density, void ratio,

moisture content, gradation characteristics of soils, amount of

fines passing #200 sieve and their Atterberg's limits. Major

difficulties for the implementation of this design guideline in

the state of Colorado include: 1) the lack of an appropriate test

2

apparatus, 2) many factors influencing the resilient modulus of

soils, and 3) the lack of a technology transfer program. To

conduct cyclic triaxial tests for resilient modulus determination

requires both a closed-loop hydro-electric universal testing

machine and good analytical skills. In this study, twenty cyclic

triaxial tests were conducted for different soils. Because of

the variability of soils from one state to the other, AASHTO

recommends each state to develop its own formula for resilient

modulus. Many factors affect the resilient modulus of soils.

This makes the task of formulating resilient modulus complex.

Objectives of this research project are three fold: 1} to

determine the resilient modulus and the stabilometer R value of

soils of different index properties, 2) to formulate the

functional relationship between the resilient modulus andR­

value, and between the resilient modulus and its influencing

factors, and 3) to provide detailed test procedures for resilient

modulus. These influencing factors include gradation charac-

teristics (uniformity coefficient, effective and mean diameters

and coefficient of curvature), fines content and plasticity,

density, moisture content, cyclic stress amplitude and repetition

and confining pressure, etc.

Regression equations were formulated to relate resilient

modulus, individually, to R values, mean diameter, uniformity

coefficient, %fines content and plasticity index. However, the

number· of resilient modulus tests is too small and the

influencing factors too many to provide equations for effective

3

evaluation of resilient modulus in terms of some easily

determinable index properties of soils. Additional research is

needed for accomplishing the effort in characterizing the

resilient modulus of Colorado soils. This should involve a well

designed experimental program to provide a sufficient data base

for the statistical modeling.

4

II. LITERATURE REVIEW

11.1 AASHTO Pavement Design Guide

Based on the information provided by the AASHTO Road Test

(AASHTO, 1962) conducted between 1958 and 1961, AASHTO published

"AASHTO Interim Guide for Design of Pavement structures - 1972"

(AASHTO, 1972). This design guide takes into account of the soil

support by incorporating the soil support value and strength

coefficients in the design procedures. The soil support value

and strength coefficients are determined from the California

Bearing Ratio (CBR) and the stabilometer R-value, respectively.

The Interim Guide had served its main objectives for many years

without serious problems. The state highway agencies were

generally satisfied with the Interim Guide but acknowledged that

some improvements could be made.

After many years under the Interim Guide, the AASHTO Design

Commi ttee recommended that some revisions and additions were

required to incorporate the information developed since 1972.

This effort resulted in "AASHTO Guide for Design of Pavement

structures - 1986 {AASHTO, 1986)." This revised design guide,

while retaining the basic algorithms developed from the AASHTO

Road Test as used in the Interim Guide, adopts the resilient

modulus of soils for characterizing soil support and assigning

layer coefficients. The AASHTO test method T-274 was recommended

as the definitive test for evaluating the resilient modulus of

subgrade soils.

5

Additionally, the concept of reliability was

introduced to permit a designer to use the concept of risk

analysis for various classes of roadways.

II.2 stabilometer R-Value

The R-value (resistance value) is a parameter representing

the resistance to the horizontal deformation of a soil under

compression at a given density and moisture content. This

parameter is an indication of the ability of soil to carry a

load. The better can a subgrade soil resist horizontal

deformation under a traffic load, the less surface pavement

material is required to carry the design traffic load.

The R-value is derived from the result of a test (AASHTO T-

190) conducted in a Hveem stabilometer as shown in Figure II.1.

A cylindrical specimen with 4 inches (10.16 cm) in diameter and

2.5 inches (6.35 cm) in height is enclosed in a membrane. As a

vertical load of 2000 lb (8896 N) is applied over the full face

of the specimen to produce a pressure, Pv ' the resulting

horizontal pressure, Ph' is read. The vertical load is then

reduced to 1000 lb (4448 N), and the horizontal pressure is

adjusted to 5 psi (34.5 kPa) with a displacement pump. By

turning the pump handle to raise the horizontal pressure from 5

HEAD Of TESTING MACHINE

FOLLOWER fOR APPL YING LOAD TO SPECIMEN

NOT TO SCAL E

AIR CHAMBER MANUALLY OPERATE

f"""'~~ ~ SCREW TYPE PUMP ... ,,#, ." !O'¥' """"" :;"""" ~I

~j lIaUID UNDER SMALL r, -= j INITIAL PRESSURE .... flEXI BLE DIAPHRAGM

PLATEN OF TESTING MACHINE

NOTE-The specimen is given lateral support by the nexible sidewaU. which transmits horizontal pressure to the liquid. The magnitude of the pressure can be read on the gauge.

Figure II.l Schematic diagram of Hveem stabilometer.

0'1

7

to 100 psi (34.5 to 689.5 kPa), the number of turns is recorded

as the turn displacement, 0, of the specimen. The Stabilometer

R-value is then determined using the equation below:

R • 100 ~ 100 ,

(1)

where Pv is usually 160 psi (1103.2 kPa) .

The R-value provides the information of relative quality of

subgrade soils and empirically relates to the field performance

of pavement materials. It has been correlated with CBR, soil

classification, and other properties of different soil types.

The R-value test, while being time and cost effective, does not

have a sound theoretical base and it does not reflect the dynamic

behavior and properties of soils. Its development and use are

mainly based on trial and error, previous experience and

observations, and engineering judgments. The R-value test is

static in nature and irrespective of the dynamic load repetition

under actual traffic.

II.3 Resilient Modulus

A pavement structure is designed to sustain millions of

repeated wheel loads during its service life and it is more

realistic to obtain and use in pavement design the repetitive

8

load property of pavement materials. The resilient modulus, MR,

in AASHTO T292 and T294 is an elastic rebound stress-strain

relationship. It measures the elastic rebound stiffness of

flexible pavement materials, base courses and subgrades under

repeated loading.

At a point under investigation, each moving wheel imparts a

dynamic load pulse to all layers of a pavement system. It is

followed by a period of zero dynamic load, relaxation period,

before the next moving wheel arrives that causes the dynamic load

cycle to be repeated. Therefore, the resilient modulus is

determined from a repetitive pulse load triaxial compression test

(AASHTO T-274) with a suggested pulse duration of 0.1 second

followed by a 1.9 second rest period.

The test is conducted on a cylindrical specimen with 2.8 or

4 inches (7.11 or 10.16 cm) in diameter, depending on particle

size, and at a desired density and moisture content. Before

starting a test sequence, a series of axial load repetitions

under various deviator stresses is applied for sample

conditioning. The test is then conducted by varying the deviator

stress and confining pressure, respectively, and by applying 200

repetitions under each load condition. The decreasing load and

recovered deformation at the 200th repetition of each load

condition are recorded for calculating the unloading stress and

recovered strain. The resilient modulus at certain stress

condition is defined as the secant modulus of the 200th unloading

curve and is expressed as

M • R

,

9

(2)

where 0d is deviator stress and Er is recovered axial strain at

the 200th repetition.

The resilient modulus test closely simulates the pavement

materials at different depths under various traffic loads in

field. It provides a fundamental dynamic stress-strain property

of materials in a flexible pavement system that governs its

response under a traffic load. However, the test needs

sophisticated and expensive equipment, which many state highway

agencies do not have. Based on the AASHTO procedure, the

required testing time to determine a modulus is at least 2.5

hours for cohesive soils and 4.5 hours for granular materials,

excluding the time for sample preparation and test setup. For

lack of equipment and being very time consuming, Yeh and su

(1989) indicated that it would be impractical to attempt a large

scale testing program for investigating every aspect of resilient

modulus of all types of Colorado soils. The revised guide

provided correlations of MR with CBR, R-value, and other soil

properties for some types of soil. Nevertheless, The AASHTO

still recommended that each state should develop its own

correlations due to the geographic dependency of resilient

modulus.

10

II.4 Factors A~~ectinq Resilient Modulus

A number of factors affect the resilient modulus of subgrade

soils. Previous studies by Seed, et ale (1967), TRB (1975),

Thompson and Robnett (1976), Thornton and Elliott (1986), Elliott

and Thornton (1987), etc. have shown the influence of various

factors on resilient modulus. Among these factors are grain size

distribution, plasticity, density, moisture content, compaction

method, freeze-thaw cycle, confining pressure, and deviator

stress. The effect of these factors is discussed below.

11.4.1. Index properties

The grain size distribution, fines content, liquid limit,

plasticity index, and group index may influence the dynamic

behavior of subgrade soils. Thompson and Robnett (1976)

performed a detailed study on the effect of these properties of

Illinois soils on their resilient moduli. However, this study

did not find any significant correlation between resilient

modulus and any single soil property.

11.4.2 Moisture content and Density

The influence of moisture content has been found to be

significant in some studies. As illustrated in Figure 11.2,

Thompson and Robnett (1976) presented the variations of resilient

modulus of the AASHTO Road Test subgrade. with six different

moisture contents ranging from o.~% below to 1.9% above optimum,

the resilient moduli decrease with the increase of moisture

11

16

AASHO'

Symbol w". MR (ksi)

14\ D 0-0.8 9.29 0 0-0.5 6.07 £ 0+0.4 3.51

• 0+0.5 3.27

12 X 0+ 1.3 2.89 + 0+ 1.9 2.4\3

,-... .... g Compacted y = 95". T-99

~

:;E 10 .

III ::J ::J

'"0 0 ~

-c cu -III 6 cu

.~

4

10 15 20 25 30

R~p~ated Deviator Stress. 0'0' psi

Figure II.2 Variation of resilient modulus with moisture contents ranging from 0.8% below to 1.9% above optimum (from Thompson and Robnett, 1976).

12

content. Robnett and Thompson (1976) studied the relationship

between resilient modulus and moisture content of two fine­

grained soils and AASHTO Road Test subqrade. Figure II.3 shows

that the resilient modulus evidently decreases as the compaction

moisture content increases. Thompson and Robnett (1976) also

reported the influence of moisture content in terms of the degree

of saturation. As plotted in Figure II.4, the general trend of

resilient modulus decreases significantly with the increase of

soil saturation. Therefore, the selection of an appropriate and

representative moisture content for design, and the control of

moisture content during sample preparation and field construction

can be crucial.

Although Figure II.4 reveals the difference in the

relationships between resilient modulus and soil saturation for

95% and 100% of compaction, the degree of saturation reflects the

combined effect of moisture content and density. Robnett and

Thompson (1973) conducted tests on two different cohesive soils

at 1.7% and 2.5% over the optimum moisture content, respectively.

Each sample was compacted to 95% and 100% of the standard proctor

density. The results as presented in Figure II.5 indicates that

the higher density results in higher resilient modulus but the

difference in modulus is small. The investigation performed by

Elliott and Thornton (1987) also concluded that resilient moduli

of two Arkansas cohesive soils were not affected significantly by

the variation of density.

14~-----'------~--~--~-------r------,

12

DrlJ . en

6 /)]~e,. & a. 0 10 II ~. a 'il-b "0 - ~d'.

<:( 8 ~ q, ,..... 0(0 .-

~ '-' % I>:

/-. ::E 6 ~ - 0 en ~ 0 ::J

'S7J'~ ::J -0 0 0

02,<h :2: 4 :l"Q

C ~ (U

0 en Q)

0: 2

oL------L------L-----~~--~~----~ -1.0 Optimum +1.0 +2.0 +3.0 +4.0

(AASHO T-93)

Compact ion Moisture Content. ~o

Figure II.3 Relationship between resilient modulus and moisture content of two fine-grained soils and AASHO Road Test subgrade (from Robnett and Thompson, 1976).

1 3

i .~ u .. ... .. .. ~ a .. 3 ~

"a o :e c .. = ·iii ..

16

I~

12

10

8

6

a: ~

2

o

a

", a 0 ., rfJ

0 0 ", 0

\..,0 0 ~o ~ 0

~ P 0' 0 0 0 0

t> '" 0

~ ;> 0

~ 0 o 0 0 (

~ 1'\ " 0 "' R ..

rrA.~ o 0 0 0

0 0

.... LC o 0 Q,

0

/' 0

~ '0

00

o 0 0 0

o 0 n ~ 00 r---. 95 .,.

p OB ERi" 3~334 s,1 J 0 0 0 0 0

o 0 0 O~ R "0.64 Sit = 2.69 ksi 0 0 '0.

0 0

8 p -lOp 0 0 p 0 o 00

80

-0

60 70 80

"10 Saluration. S r

a /0'0.,. AASH~0-T99 o 95". AASHTO - T 99

1

0 1100 .,.

M R= 45.2 - 0 . 428 S

11'"0' n7.6 ''=~' '" ' -

a

1'" a'" a

, ° I' []o a

"" P o ~ ~

a 00 ~

O,~ 0" 000 0"":: 0

~ooo -"<

0 ~ 0

90 100

Figure II.4 Relationship between resilient modulus and degree of saturation at 95% and 100% of compaction (from Thompson and Robnett, 1976).

14

12

FlonaClon B, Optimum Moisture + 1.7 '7'0

10-- ... 95'7'0 AASHO T-99 Density 10

~IOO'7oAASHO T-99 Density

Wisconsinan Loam Till Optimum Moisture + 2.5'70

0---095'70 AASHO T-99 Density 8 0---0 100'70 AASHO T -99 Dens i t y

,-.. .... ~ NOTE: 0·0 3

c.: :a 6

." :::J

:::J "0 0 ::E

-C 4 cu

." cu cr

2

°O~------~---------ILO--------~15~-------2~O---------2~5--------~30

Figure 11.5

Applied Deviator Stress, ps i

Effect of density on resilient modulus of specimens compacted at 95% and 100% of AASHTO T-99 density (from Robnett and Thompson, 1973):

15

16

Some studies demonstrated that the method of compaction

affects the resilient modulus as well, The results of test using

static or kneading compaction method are compared in Figure 11.6.

Both Robnett and Thompson (1973) and Elliott and Thornton (1987)

found that the specimen made by using static compaction has a

higher resilient modulus than that using kneading compaction.

Generally, the kneading compaction produces soil structures

similar to that under field compaction, and generates more

consistent test results. Thus, the standard resilient modulus

test procedure CAASHTO T-274) specifies kneading compaction

(AASHTO T-99) as the method for sample preparation.

11.4.3 Climate

The variation in resilient modulus throughout a year is

expected because of the seasonal moisture changes of subgrade

soil. Based on the analysis of deflection measurements taken

during the AASHO Road Test, the seasonal variation in subgrade

resilient modulus is shown in Figure 11.7. The modulus has the

lowest value in the spring and the highest value in the winter

coinciding with freezing and thawing seasons. The spring thaw

modulus of roadbed is typically 10% to 30% of the summer modulus

while the frozen roadbed modulus is typically two orders of

magnitude greater than the summer modulus. As a result, the

roadbeds are softer in the spring than at other time of the year.

,..... ..... g

1 CII ::J

::J "0 0

:::E -.::::: CII

en CI)

a:

12~-------.--------r--------r--------r--------r--------'

Fayette B (95 "1. Density)

q .-til Kneading Compaction Opt. +2.5 "10

\ ...... Stalic Compaction Opl.-t-2.5"10 IO~----~~~-------;---------1

8

6

"'

Wisconsinan Loam Till (100 "I. Density)

0--0 KneadinQ Compaction Opt.-t-2.8"1o

0--0 Sialic Compaction Opl.+2.6"l0 ~--~~-r~------r--------;

NOTE: a l • 0

---2~----~~----~------~~----~-------t-------;

°OL-------~L-------~IO--------~1~5--------~2~O------~2~5~------~30

App l ied Deviator Stress, psi

Figure II.6 Variation of resilient modulus of specimens made by using static and kneading compaction methods (from Robnett and Thompson, 1973).

17

A &

-. .... ~ 7 '-"

i 6 .. .= ::J

"0 S 0 ~ Q C , ~ 4

, , .- , .. , • a: • s "0 0 ... 01 ..a ::J 2 en ,

\ • , ,

0 Jan

?\ . , I

, \

I , b.

I I I I

, . b'

Time of Year

~ I' I ~ • 1 : ,

I • • • . , I

f'J , • • I • • •

6 1958 o 1959 c 1960

(Only Time Periods in Which 4 or More SeclIOM Wen Available are Plotted)

1 8

Figure II. 7 Seasonal variation of subgrade resilient modulus during the AASHO Road Test.

19

It has been recognized that the freeze-thaw cycle has a

major impact on the resilient modulus of subgrade soil. Robnett

and Thompson (1976) investigated the effect of freeze-thaw cycles

on the resilient modulus of fine-grained soils. Figure 11.8

reveals that the first freeze-thaw cycle caused a dramatic

reduction in the resilient modulus and the subsequent cycles

caused additional minor reductions. Elliott and Thornton (1987)

also reported that one freeze-thaw cycle significantly reduced

the resilient modulus of three Arkansas soils.

II.4.4 stress states

The effect of stress state on resilient modulus of subgrade

soil has been studied extensively in the past two decades.

Howard and Lottman (1977) conducted resilient modulus tests on

four Idaho soils, including two fine sands, silt, and silty clay,

under various stress conditions. The test results demonstrated

that all four soils showed an increase in resilient modulus as

deviator stress decreases, and resilient modulus exhibited a

drastic increase for deviator stress less than 0.75 psi (5.17

kPa). It was also found that the resilient modulus of granular

soils was predominantly dependent on confining pressure. The

resilient modulus of soils, however, was not so sensitive to the

variation of confining pressure, rather was more a function of

deviator stress. Elliott and Thornton (1987) confirmed that in

15

TAMA B

14

12 jNUmbef or Freeze - Thaw ,-." Cycles ..... ~ '-" 0

r:r: 10 ~

.. II)

:J :J 8

"0 0 ~

- 6 c u .-en u

Q: 4

2

°0~-------4~------~8---------1~2--------~16---------J20

Repeated Deviator Stress t uo' psi

Figure 11.8 Effect of number of freeze-thaw cycles on resilient modulus of fine-grained soil (from Robnett and Thompson, 1976).

20

21

no case was the effect of confining pressure of major significant

for cohesive soils.

Because the resilient modulus varies with axial load and

confining pressure, the resilient modulus has usually been

plotted against deviator stress and confining pressure. Based on

the results of early resilient modulus studies, Thornton and

Elliott (1986) concluded that the modulus of granular base

materials had a positive linear relationship with the sum of

principal stresses on a log-log plot. As for cohesive soil, the

test results are reported in an arithmetic plot of resilient

modulus versus deviator stress at each confining pressure.

22

III. USE OF RESILIENT KODULUS IN PAVEMENT DESIGN

The surface deflection of a pavement results from the

accumulation of load induced strain within the pavement and

subgrade with the subgrade being a major contributor. In the

AASHO Road Test (AASHO, 1962), 60% to 80% of the deflection

measured at the surface was found to develop within the subgrade.

Thus, the resilient modulus of subgrade is a maj or factor

governing the surface deflection and the performance of flexible

pavement and the procedure for its evaluation is included in the

revised AASHTO pavement design procedure (AASHTO, 1986). In this

procedure, resilient modulus is used in determining an effective

resilient modulus as a direct input in pavement design and in

selecting layer coefficients in determining layer thicknesses.

The effective resilient modulus of a roadbed soil is an

average modulus weighted by relative damage and adjusted for

seasonal variations. The following steps are involved in

determining the effective resilient modulus:

1. Perform laboratory tests to develop a relationship

between resilient modulus, MR, and moisture content.

2. Estimate the seasonal variations of moisture content in

subgrade.

3. Determine the monthly or bimonthly resilient modulus for

a year from the above relationship.

23

4. Select a relative damage, u f , value for each seasonal

resilient modulus based on the MR-U f scale provided by the design

guide.

5. Calculate the average of relative damage values for the

year.

6. Select effective resilient modulus corresponding to the

average relative damage from the MR-U f scale.

The effective resilient modulus which accounts for the

combined effect of temperature, moisture, and seasonal damage is

then used in design.

The revised guide provides a design chart as shown in Figure

111.1 for the flexible pavement design. Reliability and overall

standard deviation are introduced ·at the beginning of the design

procedure. This uncertainty factor accounts for the combined

effect of the variation in all the design variables so that the

designer no longer need to use conservative estimates for the

other input parameters. The traffic factor is then considered by

entering the cumulative expected l8-kip equivalent single axle

load (ESAL) during the design period. In terms of effective

roadbed soil resilient modulus, the material properties and

environmental effects are then included in the design. By

incorporating the loss in design serviceability, which is the

change between initial and terminal serviceability indexes, the

nomograph leads to a structural number. "structural number" is

a parameter used in the design of layered pavement structure.

It relates to the thickness of each layer by a layer coefficient.

tOD:>RAFH SOINmz

10910 4.2 - 1.5 f

t. PSI ~ 1091:'18 .. ZR*So+ 9.36*I0910 (SN+1) - 0.20 + + 2.32*I091h - 8.07

1094

1.

99.9

_ 199

~ ~ It:

~ :g .~ 0; It:

10

70

60

50

Figure III.1

~l _i c~

0.40 + --519 (SN+l) •

Design Serviceability Lass, 6P51 ) .!!!. I!

L V I

~ .; -$~ o.~ =-=8 1._ IID--Ill. 0: 0'" 1- 0 ... ~ .. - .. D-E .. :::<t .n.! I

EKample'

WII : 5 K 10'

R=95 %

50 = 0.35

-.;; ~~ ... ::E .. ... -..... o " 0-a:~ .. 0 .?: ::E uc .f .! ... = w :

a:

M" & 5000 psi

6PSI = 1.9

Solution: SN = 5.0

...

~ /~~

LV ~ ,.

/ V ~ ~

/V ~ ~ / / /.

/ ~ 05/ /; ~ 1.'/ /~ til I.i',

2.0 % 'I 7 6 5 4 3 2

Deslg" Slruclural Number, SN

Design chart for flexible pavements based on using mean values for each input (form AASHTO, 1986).

I\J

"'"

25

The revised guide employs layer coefficients, ai' to express

the empirical relationship between structural number and layer

thicknesses, 0i' as formulated in the following equation:

(3)

Based on the resilient modulus of each pavement material, the

layer coefficients are individually estimated for asphalt

concrete pavement, base course,. and subbase layer. Once the

structural number and layer coefficients are determined, the

thickness of each layer can be calculated from the above

equation. This equation does not provide a unique solution

because many combinations of layer thicknesses all satisfy the

design load-carrying capacity.

26

IV. TESTING PROGRAM, PROCEDURES, AND RESULTS

IV.l Testing Program

Twenty resilient modulus tests were performed in this

research program. Initially, twenty two bags of row soils were

provided by the Materials Laboratory of Colorado Department of

Transportation (COOT). The bag soils were first sieved through

a stack of sieves including u.s. standard sieves #4, #8, #20,

#40, #60, #100, #200 and bottom pan. After sieving the soils,

the amount of fines passing #200 sieve was found to be sufficient

for preparing only eight samples, Nos. 1 to 8, of a desired

gradation characteristics for this test program. with the COOT's

agreement, additional soils were carefully selected and delivered

to the Geotechnical and structural Laboratory at the university

of Colorado at Denver (UCD) for preparing the other twelve

samples, Nos. 9 to 20.

In order to test a broad spectrum of soil types for this

research program, twenty soil samples were prepared of different

gradation characteristics with the mean diameter (050) ranging

from 0.0053 inches (0.135 rom) to 0.187 inches (4.75 rom), and the

coefficient of uniformity, Cu ' from 6.3 to 75.4, and the percent

fines content by weight from 6% to 32%. However, all samples

except Nos. 17 and 19 do not have measurable plasticity index and

their classification ranges from A-1-a to A-2-4 with the AASHTO

classification. The gradation curves of twenty soil samples are

27

reported in figures in Appendix A, and the AASHTO classifica­

tion, gradation characteristics, and plasticity index, PI, of

each sample are included in Table IV.1.

Soil samples were mixed for compaction in the Geotechnical

and Structural Laboratory at the University of Colorado at Denver

(UCO). The compaction (AASHTO T-99) and R-value test (AASHTO T-

190) were carried out in the Materials Laboratory at the Colorado

Department of Transportation (COOT). A mechanical kneading

compactor was used to compact all soil samples and the correction

was then made for rock fraction. Results of the compaction test

including maximum dry density, Yd , and optimum moisture content,

~oPt' provided by the COOT are summarized on Table IV.1. The R­

value of tested samples ranges from 48 to 81, and are also listed

on Table IV.l.

The cyclic triaxial test system at UCO was used in this

resilient modulus test program. An MTS-810 series closed-loop

electro-hydraulic universal testing machine with a capacity of

200 kips (890 kN). Figure IV.l shows the test system, which

consists of a stiff load frame, MicroConsole Model 458.20

providing the closed-loop control of the servo electro-hydraulic

system, and data acquisition apparatus. Other system components

include LVOT, load cell, actuator, servovalves, hydraulic

pressure supply, and hydraulic service manifold.

28

Table IV.1 Soil classification, gradation characteristics, and laboratory test results of each soil sample.

No Class. D50 Cu -#200 PI Yd cuopt R MR & G.I. (rom) (%) (pcf) (%) (ksi)

1 A-2-4 (0) 4.75 13.6 6 NP 132.6 5.7 78 13.6

2 A-1-a 4.75 22.8 6 NP 133.0 5.9 81 10.3

3 A-1-b 1.8 18.0 8 NP 128.0 8.0 72 28.8

4 A-1~b 1.6 25.5 8 NP 129.3 7.0 75 29.0

5 A-1-b 1.5 38.6 9 NP 130.6 6.6 78 13.0

6 A-1-b 1.3 57.7 13 NP 129.2 6.8 77 15.4

7 A-1-b 0.35 9.3 14 NP 122.7 9.6 78 10.0

8 A-1-b 0.54 16.0 14 NP 124.4 9.0 81 12.4

9 A-1-b(0) 1.9 41.3 10 NP 121.7 8.3 64 10.3

10 A-1-b(0) 1.68 11.2 2 NP 110.2 10.8 71 16.7

11 A-1-b(0) 0.63 11.1 . 9 NP 117.6 8.4 72 13.6

12 A-2-4(0) 0.14 7.0 28 NP 116.3 12.8 55 10.6

13 A-2-4(0) 0.135 9.3 32 NP 118.0 10.4 67 13.0

14 A-2-4(0) 0.25 9.5 18 NP 118.5 11. 7 73 9.6

15 A-2:"4CO) 0.24 6.3 15 NP 118.7 9.45 81 13.0

16 A-2-4(0) 0.4 25.0 22 NP 116.9 13.4 50 6.8

17 A-2-4 (0) 0.147 11.5 32 4 123.5 10.1 62 20.0

18 A-1-aCO) 2.5 75.4 11 NP 133.3 6.1 77 11.0

19 A-2-4(0) 0.3 30.5 27 7 129.1 8.2 48 12.6

20 A-1-a(0) 2.24 55.4 8 NP 132.0 5.8 81 12.0

NP: Non-plastic

Figure IV.l Cyclic triaxial test system MTS-801 at the UCD. I\)

\0

30

V.2 Procedures of Resilient Hodulus Test

Twenty specimens for resilient modulus tests were prepared

and compacted. A large size triaxial tests were used because

samples contained large particles of over 1 inch (25.4 rom). The

cylindrical sample dimensions were 6-inch (15.24-cm) in diameter

and 12-inch (30.48-cm) in height. Soils samples were first cured

at the optimum moisture content for 24 hours before testing. The

specimen was then compacted in a 6-inch (15.24-cm) diameter mold

by the standard Proctor method. To maintain the specimen

uniformity and to achieve the maximum dry density, samples were

compacted in eight 1.5-inch (3.81-cm) lifts. All specimens were

consolidated in the triaxial chamber under a confining pressure

for 24 hours. The procedure for sample preparation for resilient

modulus test is detailed in Appendix B.

Because of the non-plastic nature of soils used in this

research, the standard procedures for determining resilient

modulus of granular soils as described in AASHTO T-274 were

followed. During the test, 200 repetitions of axial load are

applied under each load condition. Each axial load repetition

comprises a O.l-second load pulse followed by a 1.9-second zero

load period.

The resilient modulus test for granular soils begins the

sample conditioning under a cyclic load: 200 repetitions of each

deviator stress, ad' of 5 and 10 psi (34.48 and 68.95 kPa) under

a confining pressure, 0c' of 5 psi (34.48 kPa), then, 200

repetitions of cyclic ad at 10 and 15 psi (68.95 and 103.43 kPa) ,

31

respecitvely, under a a c of 10 psi (68.95 kPa), and, finally,

another 200 repetitions of ad at 1"5 and 20 psi (103.43 and 137.90

kPa) are applied under a a c of 15 psi (103.43 kPa). This load

condi tioning eliminates the effects of the interval between

compaction and loading, initial loading versus reloading, and

initially imperfect contact between the end platens and the

specimen.

In the resilient modulus test, each sample was tested under

all combinations of a c of 20, 15, 10, 5, to 1 psi (137.90,

103.43, 68.95, 34.48, to 6.90 kPa) , and ad from 1, 2, 5, 10, 15,

to 20 psi (6.90, 13.79, 34.48, 68.95, 103.43, to 137.90 kPa).

Load and deformation were recorded throughout the test. The

recorded load and deformation for the 200th repetition of each

load condition are used in determining the MR under each stress

condition. The confining pressures, deviator stresses, and the

number of repetitions used during the sample conditioning and

testing are summarized on Table IV.2. The detailed procedure for

resilient modulus test is presented in Appendix c.

IV.3 Results of Resilient Modulus Test

The resilient modulus was calculated from the recorded axial

load and recovered deformation after complete unloading under

each load condition. since the samples tested in this research

were granular soils, the resilient moduli are reported in two

forms:an arithmetic plot of resilient moduli versus deviator

Table IV.2 Confining pressures, deviator stresses, and number of repetitions used in resilient modulus test for granular soils.

Confining Deviator Repetitions Pressure stress at

(psi) (psi) Each Load

5 5, 10 200 Condi-tioning 10 10, 15 200

15 15, 20 200

20 1, 2, 5, 10, 15, 20 199 + 1

15 1, 2, 5, 10, 15, 20 199 + 1

Testing 10 1, 2, 5, 10, 15 199 + 1

5 1, 2, 5, 10, 15 199 + 1

1 1, 2, 5, 1'0 199 + 1

32

33

stresses at various confining pressures, as presented in

Appendix D and a log-log plot of resilient moduli versus the sum

of principal stresses, e, as presented in Appendix E.

The arithmetic plots exhibit an increase in MR as O"d

increases from 5 psi (34.48 kPa), although the trend grows vaguer

at O"d below 5 psi (34.48 kPa). These plots illustrate the strong

dependency of ~ on O"c. This dependent relationship between the

resilient modulus and confining pressure for granular soils

agrees with the findings of previous research. The test results

also demonstrate a strong linear relationship between MR and e on

a log-log plot. The equation of least-square line relating MR

and e for each sample is presented at the bottom of each log-log

plot in Appendix E.

Yeh and Su (1989) concluded in their research report that

the MR under the stress condition of O"d of 6 psi (41.37 kPa) and

o"c of 3 psi (20.69 kPa) is the most appropriate value for

adoption in pavement design. From the arithmetic plots shown in

Appendix D, the ~ under such stress condition was determined for

each sample and was included in Table IV.1. These values of

resilient modulus are used in developing the functional

relationship between the MR values and R values and index

properties of soils. To enlarge the database for the statistical

modeling of MR , the results of the nineteen samples from the

previous test program (Yeh and Su, 1989) with soil types ranging

from A-1-b to A-7-6 per AASHTO classification are included in

this study. The AASHTO classification, fines content, plasticity

34

index, PI, maximum dry density, Ydl and optimum moisture content,

Wopt' resilient modulus values and R values of these samples are

included in Table IV.3.

35

Table IV.3 Soil classification of soil samples and laboratory test results from previous test program (From Yeh and Su, 1989).

No Class. -#200 PI Yd Cl)opt R MR & G.I. (%) (pcf) (%) (ksi)

21 A-7-6(17) 69 28 108.0 17.8 6 3.5

22 A-7-6(2) 42 22 108.5 17.1 15 4.2

23 A-6(11) 69 19 109.1 16.4 11 -4.6

24 A-6(2) 44 13 110.8 15.2 30 8.4

25 A-4(1) 42 10 119.0 11.6 26 7.8

26 A-2-6(1) 25 14 119.9 11.1 39 10.5

27 A-2-4(0) 20 10 116.2 12.1 41 6.4

28 A-1-b(0) 25 4 130.0 7.2 34 8.5

29 A-2-4(0) 23 9 115.4 13.5 37 11.2

30 A-4 (3) 57 9 114.4 14.4 37 7.2

31 A-2-4(0) 34 8 116.7 12.8 42 10.3

32 A-4(0) 44 6 116.2 12.1 39 7.7

33 A-4(0) 36 9 117.9 16.0 40 6.8

34 A-4(0) 48 1 120.3 11.3 70 8.7

35 A-2-4 (0) 16 NP 119.9 10.9 77 8.6

36 A-1-b(0) 10 NP 118.2 6.2 79 15.5

37 A-1-b(0) 10 NP 127.7 8.0 62 11.0

38 A-1-b(0) 17 3 120.9 11.3 72 8.7

39 A-1-beO) 9 NP 129.9 8.5 80 21.9

NP: Non-plastic

36

V.l STATISTICAL MODELING

V.l Introduction

Descriptive statistics and inferential statistics are the

two major branches in statistics. The descriptive statistics

deals with summary and description of data.

statistics concerns with analysis of sample

The inferential

data to make

inferences about a large set of data - a population, from which

the sample is selected. Experimental research in engineering

involves the use of experimental data - a statistical sample, to

infer the nature of some conceptual population that characterizes

a phenomenon of interest to the .experimenter. One of the most

important application of inferential statistics in engineering

involves estimating the mean value of a response variable or

predicting some future value of the response variable based on

the knowledge of a set of related independent variables. A

relationship used to relate a dependent (response) variable toa

set of independent variables is generally referred to as a

regression model or a statistical model (Mendenhall and Sincich,

1991) • The regression modeling was used in this study to

formulate the functionial relationship between the resilient

modulus and their influencing parameters.

V.2 Reqression Analysis

Regression equation relates a dependent variable, Y, to a

set of independent variables, Xi' where i is a nonzero integer.

37

In this study, the dependent variable, resilient modulus, MR , is

related to the independent variable, stabilometer R-value and

index properties of soils including uniformity coefficient, Cu '

mean diameter,Dso ' % fines content, FC, and plasticity index, PI.

The least-squares approach is used to determine the best estimate

of a regression equation. In general, the least-squares method

chooses the best-fitting model which minimizes the sum of squares

of the distances between the observed responses and those

predicted by the fitted model. Once a regression model is

obtained, it is desirable to test the contribution of each

independent variable involved in predicting the response variable

so that the model may be refined.

V.3 Regression Hodel between ~ and Stabilometer R-Value

Over a period of eight years, UCD has conducted resilient

modulus tests on 39 different samples under the CDOT sponsorship.

The data base from the results of the resilient modulus test on

these samples is used in the statistical modeling. The type of

soils tested ranges from clay to granular soils with various

percentages of fines of minus #200 sieve. Besides the R-value,

the gradation characteristics, including coefficient of

uniformity, coefficient of curvature, and percent fines content

by weight, are included as independent variables in the analysis.

However, only 20 out of 39 samples have the information on

gradation characteristics.

38

The regression analysis was performed to formulate the

functional relationship between MR and R-value and index

properties. A commercially available statistical graphics system,

"STATGRAPHICS" developed by statistical Graphics corporation was

used. As shown in Figure V.1, data points of MR versus Rare

quite scattered, particularly at the R-value above 60. Thus, it

is extremely difficult to use one regression curve to represent

the complete population of data points. After many experiments,

the "best" regression equation is:

log MR - O.llB + 0.517 . log R , (4)

or

M _ 1. 312 . R 0.517. R (5)

The above statistical formulation gives the intercept of

0.118, the slope of 0.517, the R2 of 42.79% and the standard

error of estimate of 0.155. The value of R2 is much less than

desired. This is mainly due to the scatter of data points.

Figure V.1 shows the regression curve, upper and lower bound

curves for one and two standard deviations, respectively. The

predicted resilient modulus, MRP ' is plotted against MR obtained

the laboratory test in Figure V.2. The linear comparison between

them has a R2 value of 25.11%. Again this low R2 value reflects

the scatter of data points.

34.67

21.88

13.80 -.. .... ~ '-"

Pi:

:E 8.71

5.50

3.47

Figure V.l

.j ......... ...... ..... . } ...... .. ... ......... + ......... · · ··········1····· ···· ············i········ ·· ···/' ····· ~ ..

• • • 1 )/// .

: : : : /. /: 4~"""""""""'" .~ •• ••••• - •• ••••• ······"f··········· ..... .... . ~ ...... ,oJ " ......... ~ .... .......... .. )".~ ..

• : • /,,/ 0 • /// :

! ! l / 0 i / ~ ~ ~ / ~/ /. :

iU J~~>j0.UJ.:U~:/" /> ~ , .: .............. /.. .... : ....... ... ............ ~ ......... ,/. .. --:. .... : ....... ( ............ /) ...... .. ............. i..

~ / ~ : /00;/ . ;.

: /: ;/:" / : / : /. r, · . / L: r ~ // / o ~ 0

· . / /:0

..... /

/

:...-...-; /

... ... ?; ... I. .. ............. ~ .............. -/-. :':'oi ...... .......... ..... ~ .. · ...-. ." .......... ~ ........ -:.- ........... .

0 /

/

;/ /

/; / / ; /

..... . /. . . . .~ •••.. 0 •..• _ .•••••••• ~ ••••• ~ _, •••••••• ••••• ~ ••• 0_ •• •• '" •••••••••• ~ •• ••••••• _ •• ••••••••• !, ........ _ .... .. ..... ~ ..

5 10 20 40 80 160

R-value

Scatter plot of log ~ versus log R with regression curve, upper and lower bound curves for one and two standard deviations, respectively.

39

13 . 3

11. 3

'1.3

7.3

5 . 3

3.3

Figure V.2

. . . -... -.. ... ... ... ;: . -. . . --....... .. - _. ~ . .. -............ ".

[] :[] [] [] []

.:. [] [] []

[] [] []

[]

[] 0:

0 0 0

[]

0

• ••••• •• •••••• • •• "!,C' ••••••••••••••• ..... ..... -- .. .. .. ;. ..... ...... ...... ; ..... . .. ..... __ ... : .. · . · . · . []

· . · . · . · . · . · . · . · . · . : 0 · . · . · . · . · . o · . · . · . · . [] · . · . · . · . . . . . .~ ................. -: .. ............ .. . -:' ................. ~ ..... ............ -:: -... .. ....... ... .. ; .. ... ... . _ .. .. ... ":-' · . . . . . . : : :0 : : : : • • 0 • - • .

~ ~ [] 0 :0 ~ ~ ~ ~ : : 0 : 0 : • : : ., . .. . . . . . .. . . . : : D: : : . , . . . .. . . , .. . . ' . . . . , . . . . . • • D . • • . , . .' . , . .. .. -i- o .............. . .. ~ ••• 0 •••• 0 •••• •• •• i··· · 0 •••• •••• 'o ••• ~. 0 ••• 0' , _ ••• • •••• ~ ••••• 0 •• •• •• _oo • •• ~ • • o . o . 0 0 ••••• •••• :' .

: : [] : : : : : : : : : : : : : : : : : : : · . . . . . . · . . . . . -· . . . . . -; ~ ~ ; ~ i ~ : : : : : : : · . . . . . . · . . . . . . · . . . . . . · . . . . . . · . . . . . . · . . . . . .

.\ •••• ••• ••••••• D •• j. ••••••••••••••••• \ •••••••••••••••••• i •••••.. ... . . . • •. . ..:; . .. ..•. .. .••• . .... ; . ···· . · .• ····· .••. .: ••

· . · . ., . , .: ............ ~ .... : ................. : ................... : ....... . .. ... .. .. ; ...... .... ... ..... : .. .. .... ...... "':"

o 5 10 15 20 2S 30

comparison of predicted ~ wi th 1\ obtained from laboratory test.

40

41

Linear regreeeson analyses were performed to formulate the

functional relationships between the resilient modulus and R­

value and each of the following index properties: percent

fines content, FC, plasticity index, PI, uniformity coefficient

, Cu ' and mean grain size, D50 • Results of these linear

regression are shown in Figures V.3 to 7. Values of R2 for these

regression analyses are quite small.

The above-mentioned regression functions are less than ideal

because of the scatter of data points. The scatterness of data

points is caused by the fact that many factors can affect the

value of resilient modulus and one single independent parameter

is simply insufficient as a predictor. Instead, all significant

influencing factors should be included in the formulation of the

regression equation as independent parameters. These factors

include gradation characteristics, liquid limit, plasticity

index, confining pressure, deviator stress amplitude, number of

loading cycles, etc. This will require additional tests with

well documented index properties and test conditions.

30

25

~20 (/)

~15 c::: ~ 10

5

0

MRvsR f).f).

Rearession output: Constant 3.20046 1

Std Err of Y Est 4.659746 R SQuared 0.32965 No. of Observations 39 .... __ ._._._._. . ......... _._ ............... _._._.6 ... _ ............... _ ............. _ .... _._ ......... f). ._._ ............... _._._ .....•......•.. -.-._._ ........... __ . Degrees of Freedom 37

X Coefficient(s) 0.14543 Std Err of Coef. 0.034094

_ .. _. __ ._ .......... _ ...... _._._ ............ -._._ ... _ .... --............. -...... ~ ... -.-.-.-.~ ............ -.-.-._ •..........•.. _.- ._._ ..... -

f). - ~~ -._._ .... _ ...... _ .... _._ ............... __ ... _._ ...... -.-.--...... - .... -.-.. -......... --.--.---::~ ... ...c:.._ ..... ~ .. ···--··LS·-·-···~·-·A.·-·-····-····-·-······· .. ·········-._ ............... _._.

f). f). f). .

6.

0 20 40 60 80 100 R

Figure V.3 Linear Regression Equation of Mr vs. R-value

~

N

30

25 ~20 (/)

c15 Cl:: ~ 10

5

0 0

~ M~vs-#200

Recression OutDut: Constent Std Err of Y Est R Squared No. of Observations ....................•.............. ~ ..•......................................................•.............. ································6····················· .. _ .• Decrees of Freedom

f:::, ~ Coefficient(s) Std Err of Coef.

f:::, f:::, f:::,L->~f:::,

- ................ ~ ............ ~ ........ 6 ........... zs: ... _._ ....... _ .... A ..... _-=' •.•.... ~. ~ . f:::,

f:::,L:::. L:::.

f:::,

10 20 30 40 - #200 (0/0)

50

-0.18359 0.04375

60

Figure V.4 Linear Regression Equation of M vs. Fines Content r

16.00795 4.684633 0.322471

39 37

70

of>, w

30

25

:=-20 en ~15 0:: ~ 10

5

0 0

MRVS PI·

Rearession Output: Constant . 13.53223 Std Err of Y Est 4.847377

............................................ & .............................................................................................................................................................. .. . R Squared 0.274578 No. of Observations 39 Degrees of Freedom 37

. ~ Coefficlent(s} -0.42362 Std Err of Coef. 0.113198

6. 6.

~ .... __ .... _ ...... _ .. _ ..... _ ... _ ............. _.6. ......................... __ ............ _ .... _ .... _ .......... _ ...... _ ................ _ .... _ ...... __ ._ ...... _ ..................... _ .. _. __ . __

6.'6. 6.

5 10 15 PI

20 25 30

Figure V.S Linear Regression Equation of M vs. Plasticity Index r .;:.

01:>0

30

25 ..---.. --~ 20 "'-"

0:: 15 ~

10

5 0

6. 6. MRvs. CU

Rearession Outout Constant 14.n62 std Err of Y Est 5.918286 R Squared 0.00889 No. of Observations 20

.. __ ..... _ .......... _._._._ ............. & .. _ ............ _.-._._._ ............ _._.-._ ............. -._.-._ ....... __ ._._._._._ ............ __ .-._ .... -........ _.-.... _. Degrees of Freedom 18

IX Coefficient(s) -0.02793

----.:-.-.. -.----;----;-.;;-----~-:-------~---6.6. 6. 6. 6

6 6 6 6

Stet Err of C~ef. 0.069501

_._._ .............. _Q_ .. ~" ... _._._ .......... _._._._._ ........... _ ... .6. ... __ .... _._ .... _ ....... _ ... _. __ ._._ ...... _._._._ ..... _6 ._. ___ ............ _ ._._ ............ _._._._ ......... " ... _._ ........ _ .. _. __ . __ ....... _ ... _._._._. __ ..... _ .. _. __ ._. __ ..... __ ._.

6

10 20 30 40 Cu

50 60 70 80

Figure V.6 Linear Regression Equation of M vs. C r u

.r::.. lJ1

30

25 ..-.... .-~ 20 ...........

0::: 15 ~

10

5

6. 6. MRvs. D50

Regression Output: Constant 13.79n Std Err of Y Est 5.937036 R Squared 0.002601 No. of Observations 20 Dearees of Freedom 18

I .... ;6 .................................................................................... _ ........................................................................................... _ .. .

IX Coefticient(s) 0.21162 Std Err of Coef. 0.976782

6. _ ..... .................... _ .......... A .......... ..... - ... _ .................. - ... . ..... __ .... _. 6. ....................... . .... . . • .~ 1:::,.

" "'" " -" -.,,--z;"'---:-------------------------"----------<:---------------------------------------- ------1:::,.

0 1 2 3 4 5 D50 (mm)

Figure V.7 Linear Regression Equation of Mr vs. DS O oj:>.

0'1

47

VI. SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

VI. 1 Summary

The AASHTO Guide for Design of Pavement structures - 1986

uses the theory of elastic layers in the design of pavement,

which, in turn, requires the resilient modulus, MRf of pavement

materials, base course and subgrade. However, its implementation

has met some technical difficulties resulted from 1) the lack of

and the complexi ty of testing equipment, 2) the scarci ty of

resilient modulus data base, 3) the soil type dependency of

resilient modulus, and 4) many influencing factors of resilient

modulus.

Because of the recent nature of its implementation, the Mr

data base is extremely small. Conversely, the StabilometerR­

value has been in use in the pavement design for decades and has

a very large data base. To remove this shortcoming and to take

the advantage of the large R-value data base, numerous attempts

have been made to establish the correlation between Mr and R­

value and to establish their functional relationship. The state

of Colorado has also invested in this endeavor through the

sponsorship of the resilient modulus research at the Univeristy

of Coloradoat Denver by the Colorado Department of

Transportation. A total of 39 resilient modulus tests were

conducted, 20 in this test program and 19 in an earlier test

program.

48

Regression analyses were performed to formulate the

functional relationship using the least square fit. Two

regression equations were formulated to relate the resilient

modulus to R-value (one linear and one nonlinear) and four linear

regression equations relate the resilient modulus to percent

fines content, plasticity index, uniformity coefficient, and mean

grain size. These equaitons , however, have small values of

coefficient of representation called R square. The use of the

equation relating the resilient modulus to the R-value can give

the value of resilient modulus smaller than that obtained from

the in-situ deflectometer test on subgrade and base course.

V~.2 Conclusions

From the data base of 39 samples with the soil type ranging

from A-1-a to A-7-6, two regression equations, one linear and one

nonlinear, were formulated in which the resilient modulus was

wri tten as a function of the stabilometer R-value. These

equations do not represent significant improvement over the one

provided in the study by Yeh and su (1989).

Four linear equations were also formulated to express the

resilient modulus in terms of fines content, plasticity index,

uniformity coefficient and mean grain size. The values of the

coefficients of representation are also small. This implies any

one single independent parameter is ineffective as a predictor.

The correlation is weak for samples of granular soils

containing varying amounts of fines of up to around 30%. For

49

granular soils with less than 30% fines, the index properties of

granular constituencies may have an important influence on the

resilient modulus of soils. These influencing factors include

gradation characteristics, relative density and grain shape of

the granular soils and percent fines content and fines

c6nsistency. These factors are responsible for the scatter of MR

values at the stabilometer R-value greater than 60 and the poor

functional relationship.

The inability of the Stabilometer R-value to realistically

reflect the engineering properties of granular soils with less

than 30% fines has also contributed to its poor functional

relationship to resilient modulus.

To appropriately evaluate the resilient modulus of soils

requires a sophisticated universal testing machine capable of

simulating the pulsating load from traffic, and continual

monitoring of lateral deformation, vertical deformation and the

amplitude of pulsating load, etc.

To strengthen the equation, the multiple regressioin analysis

is needed to formulate an equation expressing the resilient

modulus in terms of a number of significant influencing factors.

VI.3 Recommendations

1. Use the MR vs. R-value equations with caution, particularly

for granular soil samples with less than 30% of fines.

50

2. Conduct a systematic research to study the influence of

various factors affecting the resilient modulus of soils.

For soils containing less than 30% fines of minus #200

sieve, the factors should include: gradation characteristics,

relative density, grain shape, fines contents and plasticity,

degree of saturation, confining pressure, cyclic stress

amplitude, and number of cycles of repeated stress. For

clayey soils, the effect of density, moisture content, liqid

limit and plastic index should investigated.

3. When formulating the regression equation for MR, it would be

more reasonable to separate the granular (or nonplastic)

soils from the clayey (or plastic) soils because of the

different factors affecting the resilient modulus of these

two types of soils, as discussed above.

4. Mutiple regression analysis should be performed to formulate

the resilient modulus in terms of all significant

influencing factors. With the combined effort of Items 2, 3

and 4, the authors of this report believe that a good set of

re9ression equations can be formulated to effectively

evaluate the resilient modulus in terms of factors that can

be easily determined.

5. It is recommended to abandon the effort to formulate a

functional relationship between resilient modulus and

stabilometer R-value because of the inability of R-value in

reflecting the dynamic behavior/properties of soils.

51

6. Develop design charts for the selection of resilient modulus

with given index properties of soils.

7. Hold training sessions in different regions of COOT, cities

and counties in Colorado for the purpose of effecti ve

technology transfer.

8. To strengthen the equation, the multiple regressioin analysis

is needed to formulate an equation expressing 'the resilient

modulus in terms of a number of significant influencing

factors.

52

REFERENCES

AASHO, "The AASHO Road Test, Report 5 - Pavement Research," Special Report 61E, Highway Research Board, 1962.

AASHTO, "AASHTO Interim Guide for Design of Pavement Structures -1972," American Association of state Highway and Transportation Officials, 1972.

AASHTO, "AASHTO Guide for Design of Pavement Structures - 1986," American Association of State Highway and Transportation Officials, 1986.

Elliott, R.P. and Thornton, S.I., "Interim Report - Resilient Properties of Arkansas Subgrades," Report No. UAF-AHTRC-86-002, Arkansas Highway and Transportation Research Center, University of Arkansas, Fayetteville, Arkansas, 1987.

Howard, H.R. and Lottman, R.P., "A Test Procedure and Analysis of Resilient Modulus for Highway Soils," Proceedings of the 15th Annual Engineering Geology and Soils Engineering Symposium, Pocatello, Idaho, 1977, pp. 243-256.

Mendenhall, W. and sincich, T., " statistics for Engineering and the Sciences," Third Edition, Dellen Publishing Company, San F~ancisco, 1991.

Seed, H.B., Mitry, F.G., Monismith, C.L., and Chan, C.K., "Factors Influencing the Resilient Deformations of Untreated Aggregated Base in Two-Layer Pavements Subjected to Repeated Loading," Highway Research Record, No. 190, National Research Council, 1967.

Robnett, Q.C. and Thompson, M.R., "Interim Report - Resilient Properties of Subgrade Soils, Phase I - Development of Testing Procedure," Transportation Engineering Series, No. 5, University of Illinois, Urbana, Illinois, 1973.

Robnett, Q.C. and Thompson, M.R., "Effects of Lime Treatment on the Resilient Behavior of Fine-Grained Soils, II Transportation Research Record, No. 560, Transportation Research Board, 1976.

Thompson, M.R. and Robnett, Q.C., "Final Report - Resilient Properties of Subgrade Soils," Transportation Engineering Series, No. 14, University of Illinois, Urbana, Illinois, 1976.

53

Thornton, S.I. and Elliott, R.P., "Resilient Modulus - What Is It ?" Proceedings of the 3 7th Annual Highway Geology Symposium, Montana Department of Highways, Helena, Montana, 1986, pp. 267-282.

TRB, "Test Procedures for Characterizing Dynamic Stress-strain Properties of Pavement Materials," Special Report 162, Transportation Research Board, National Research council, 1975.

Yeh, S.T. and Su, C.K., "Final Report - Resilient Properties of Colorado Soils," Report No. CDOH-DH-SM-89-9, Colorado Department of Highways, Denver, Colorado, 1989.

54

APPENDIX A

GRADATION CURVES OF SOIL SAMPLES

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75

APPENDIX B

SAMPLE PREPARATION PROCEDURES

B.l preparing soil

1. Mix sieved soils with different particle sizes in designed amounts to obtain a designated gradation curve.

2. Prepare a soil mass not less than 30 pounds (13.6 kg), W" for a 6-inch diameter specimen, and determine its moisture content, (d,.

3. Determine the weight of water, Ww' required to reach the optimum moisture content, (dopt.

w. = tor (1)

4. Add the water Ww to the soil mass in small amounts and mix thoroughly after each addition.

5. Place the mixture in Ziploc plastic bags. Seal the bags and store them in a humidity room for 24 hours.

B.2 Initial Measurements

1. Carefully check the pressure system, triaxial cell, and rubber membrane under pressure for any possible leakage.

2. Measure the thickness of rubber membrane. Take four measurements, two at the top and two at the bottom. Take an average for double thickness, dm•

3. Obtain two dry porous stones and two filter paper discs. The filter paper should not be larger than the porous stone.

4. Place two porous stones, two filter papers and loading cap on base pedestal. Measure the height of the stack at three different locations. Take an average as an initial height, hi' without specimen.

5. Remove the loading cap, filter papers and porous stones.

B.3 Weighing Soil for Specimen

1. Obtain the soil prepared in Step B.1, and check the moisture content which should maintain at (dopt. Adjust moisture content to (dopt if it is necessary.

2. Measure the inner diameter of split compaction mold. The expected diameter of specimen, Do' is subtracting the double thickness of membrane, dm, determined in Step B.2.2 from this

76

measurement.

3. Measure the total height of mold sitting on triaxial cell base. The expected height of specimen, ho' is subtracting the initial height, hi' determined in step B. 2 . 4 from this measurement. The ho snould be at least two times D.

4. Determine the expected volume of compacted specimen, Va' to be prepared.

1 4

(2)

5. Determine the total weight of the soil, Wt , to be compacted.

W t = (1 + (,.) opt ) • Yd' VO' (3)

where Yd is the maximum dry density.

6. Specimen is to be compacted in eight layers. Divide the soil mass into eight equal portions. Seal each portion of soil in a Ziploc bag.

B.4 Mountinq split compaction Mold

1. Apply a thin layer of grease sealant around the side of base pedestal.

2. Place a porous stone and a filter paper on the base pedestal.

3. Place the bottom of rubber membrane over the base pedestal, and smooth it around the side of base pedestal.

4. Fix the rubber membrane in place with three O-rings.

5. Apply a thin layer of grease sealant to the splitting surfaces of mold.

6. Tighten the split mold on base pedestal, and draw the rubber membrane up through the mold.

7. stretch the top of rubber membrane over the rim of mold.

8. Apply a vacuum of 10 psi (68.95 kPa) to the inside of mold, and remove membrane wrinkles.

9. Measure the distance from the bottom filter paper to the rim of mold.

77

B.5 compacting specimen

1. carefully place a bag of soil prepared in step B.3.6 in the mold, and level the surface of soil.

2. compact the soil in the mold with a Proctor hammer until the thickness of the first layer is slightly over 1/8 of ho determined in step B. 3 . 3 . The thickness of each layer compacted should be progressively smaller than the previous layer so that the compaction effort would be more uniform throughout the specimen. Thus, the thickness of each layer varies from slightly over ho/8 for the first layer to hol8 for the top layer.

3. scarify the surface of the compacted layer.

4. Carefully place the next bag of soil in the mold, and repeat Steps B.5.2 and B.5.3 for each new lift.

5 . Level and smooth the final surface .

B.6 Removing Mold

1. Place a filter paper and a porous stone on the top of compacted specimen.

2. Apply a thin layer of grease sealant around the side of loading cap, and place it on top of the porous stone.

3. Check the level of the loading cap in two opposite directions. The maximum allowable tilt is 0.2% of D.

4. Carefully unfold the top of rubber membrane, and smooth it around the side of loading cap.

5. Fix the rubber membrane in place with three O-rings which already hung on the pressure line connecting to the loading cap.

6. with vacuum still in the mold, apply a vacuum of 5 psi (34.48 kPa) to the top of specimen.

7. Release the vacuum from the mold.

8. Carefully open and remove the split mold, and check the specimen for any irregularity on the surface.

B.7 Final Measurements

1. Measure the sample diameter including rubber membrane at

78

three different heights. Take an average as a final diameter, Df • The actual diameter of specimen, D, is subtracting the double thickness of membrane, ~, determined in step B. 2.2 from Df •

2. Measure the total height to the top of loading cap at three different locations. Take an average as a final height, h t , wi th specimen. The actual height of specimen, h, 1S

subtracting the initial height, hi' determined in step B.2.4 from h f •

3. Determine the actual volume of specimen, v,

v 1 4

• 1t • D2 • h.

4. Determine the unit weight of specimen, Ytl

(4)

(5)

where Wt is total weight of soil determined in step B.3.5.

5. Check any leakage around rubber membrane and fittings by spreading some water on them. If necessary, carefully install a second rubber membrane or reinstall fitting to stop leakage.

B.8 Mounting Triaxial Chamber

1. Clean the contact surface of triaxial cell base, and apply a thin layer of grease sealant.

2. Apply a thin layer of grease to the large O-ring, and place it on the triaxial cell base.

3. Assure the loading ram is fully lifted and locked in place.

4. Clean the bottom surface of the triaxial chamber, and apply a thin layer of grease sealant.

5. Open the valve at the top of chamber to the air.

6. Carefully place the chamber on the cell base, and lock it in place by a rim locking band.

7. Gently lower the loading ram to check if the specimen is properly centered. Then, raise and lock the loading ram back in place.

79

B.9 Applying confining Pressure

1. with the chamber top valve open, fill the chamber with water, and leave about 0.5 inches short from the chamber top for an air pocket.

2. Turn off the water, disconnect the water supply line from the cell, and then close the chamber top valve.

3. with the pressure valves at the cell base closed, connect an empty confining pressure line at atmospheric pressure to the chamber top valve, and an empty drainage line at atmospheric pressure to the bottom of specimen.

4. Slowly release the vacuum from the specimen, and gradually raise the confining pressure to 5 psi (34.48 kPa) by slowly opening the chamber top valve.

5. Connect the transducer to the triaxial cell base.

6. Calibrate the transducer.

7. The specimen is ready for resilient modulus test after cured over night.

80

81

APPENDIX C

TEST PROCEDURES

C.1 Testing setup

1. Turn on the material testing system MTS-810 and the hydraulic pressure system.

2. setup the MicroConsole and data recording system as required.

3. with the drainage valve at the bottom of specimen closed and the confining pressure valve open, carefully place the triaxial cellon the platform of the loading machine.

4. Center the triaxial cell, and raise loading piston to couple the loading ram of triaxial cell with load cell. The testing setup at this step is shown in Figure C.l.

5. Apply an axial load about 5 psi (34.48 kPa) which slightly over compensates the chamber pressure to lower the loading ram slowly until it contacts the loading cap.

6. Open the drainage valve to dissipate the excess pore water pressure caused by possible disturbance in the steps C.1.3 through C.1.5.

C.2 conditioning

1. Set the confining pressure to 5 psi (34.48 kPa) and apply 200 repetitions of an axial deviator stress of 5 psi (34.48 kPa). Then, apply 200 repetitions of an axial deviator stress at 10 psi (68.95 kPa).

2. Set the confining pressure to 10 psi (68.95 kPa) and apply 200 repetitions of an axial deviator stress of 10 psi (68.95 kPa) • Then, apply 200 repetitions of an axial deviator stress at 15 psi (103.43 kPa).

3. Set the confining pressure to 15 psi (103.43 kPa) and apply 200 repetitions of an axial deviator stress of 15 psi (103.43 kPa) . Then, apply 200 repetitions of an axial deviator stress at 20 psi (137.90 kPa).

4. with the drainage valve open, let the specimen sit for a few minutes to fully dissipate any possible excess pore water pressure.

C.3 Recorded Resilient Modulus Test

1. Rebalancing the measuring devices and recording system.

2. Begin the recorded testing by increasing the confining pressure to 20 psi (137.90 kPa).

82

8 3

Figure C.l Triaxial cell is on the loading machine and coupled with load cell ready for test.

-84

3. Apply 200 repetitions of a deviator stress of 1 psi (6.895 kPa) and record the vertical recovered deformations for the 200th repetition.

4. Repeat step C. 3 • 3 for deviator stress levels of 2, 5, 10, 15, and 20 psi (13.79, 34.48, 68.95, 103.43, and 137.90 kPa) and continue to record vertical recovered deformations for each 200th repetition.

5. Reduce the confining pressure to 15 psi (103.43 kPa), and repeat step C.3.3 for deviator stress levels of 1, 2, 5, 10, 15, and 20 psi (6.895, 13.79, 34.48,68.95,103.43, and 137.90 kPa).

6.

7.

8.

Reduce repeat and 15

Reduce repeat and 15

Reduce repeat 10 psi

the confining pressure to 10 psi (68.95 kPa) , and step C.3.3 for deviator stress levels of 1, 2, 5, 10, psi (6.895, 13.79, 34.48, 68.95, and 103.43 kPa).

the confining pressure to 5 psi (34.48 kPa) , and step C.3.3 for deviator stress levels of 1, 2, 5, 10, psi (6.895, 13.79, 34.48, 68.95, and 103.43 kPa).

the confining pressure to 1 psi (6.895 kPa) , and step C.3.3 for deviator stress levels of 1, 2, 5, and (6.895, 13.79, 34.48, and 68.95 kPa).

9. stop the loading after 200 repetitions of the last deviator stress level or when specimen fails.

C.4 post-Testing

1. Reduce the sitting load set in step C.1.5, and slowly lower the loading piston to fully raise the loading ram.

2. Disconnect the loading ram from load cell, and lock the loading ram in place.

3. Reduce the chamber pressure to zero, and disconnect the transducer and pressure lines.

4. Remove the triaxial cell from the loading machine, and dismantle the cell.

5. Turn off the hydraulic pressure system and the material testing system.

6. Use a part of specimen to determine the moisture content after test.

85

APPENDIX D

ARI~TIC PLOT OF TEST RESULTS

RESILIENT MODULUS

:[ r-. 30 .-m ~ '--"

a::: 20 2

10

-x-

--+-*- -+---

./ e a--a

Sample No. 1

---x-

--+

__ x

GeeeE)

)He X*'f(

4AAA ..

+++++

a c = 20 psi 15 psi 10 psi

5 psi 1 psi

o ~l~~~~ __ ~~ __ ~~~~~~ __ ~-L __ ~~ __ ~~~ __ ~~ __ ~~ __ ~~~~~

o 5 10 15 20 25

Deviator Stress (psi)

co 0"1

87

It) N

N '-'ij'ij'ij'ij [a.a.a.a. olt)OIt)~ . N ........

0 n Z " b 0

N Q)

UBI - / 0...

E / ,,-... .-0 /

(/)

0.. (f) t

It)'-'" .... \ (/)

en (f) \ \ <U

L..

\ +-' :J \ U1 ---1 \ t o L.. :J x .- 0

\ +-' 0 \ 0

0 > 2 \ <U

0

~ z It)

W ---1

L _I -(f) W et:: I I I 1 I I I J I I I I I 0

0 0 0 0 0 0 It) .q- ...., N ....

(!S>\) HV'J

88

n I '-'-iil~ .- J) en en en ~Q.Q.Q.Q.

. 010010

-- I 0

N.- .....

Z II u , b 0

N OJ

UBI -0..

E ,-... .-0 en

(f) D-10"'-/

+ ..-\ en I \ (f)

(l,) (f) , L..

:J \ -+-'

I (/)

--1

J, ::::J r o L..

..- 0

0 -+-'

I 0

0 > :2 I

Q)

0

1-- I \ Z , + 10

W \

--1 -(f) ~ -W 0::: _LJ--L-L-J I I 1 I I 1.-1 I I I I a

0 0 0 0 0 0 10 v 1'1 N .....

(!S>I) ~V'J

RESILIENT MODULUS Sample No. 4

::r ,--..30 .-m ~ '--"

20 0.::

:2 ~ 10 E

.

- --- -

-+ - -+

G&eee )H(X_

& ......... .a +++++ ae&BEJ

ac == 20 psi 15 psi 10 psi

5 psi 1 psi

o ~I~~~~ __ ~-L __ ~-L~~~-J __ ~-L __ L--L __ ~~~ __ ~~ __ ~~ __ L--L~~~

o 5 10 15 20 25

Deviator Stress (psi)

00 \.0

90

10 N

L() ._.;;.ij.ij9ij s.o.o.o.o.

0 100 11') .... . N ........

0 Z II

u

If b 0

N Q)

\ UUI -0..

E \ r-.

0 Cf)

(Jl Q.

~ + 10'--"

\ ....

\ Cf) Cf)

if) Q) L.

:=:> +-' (f)

---1 \ :J • 1

o L. .... 0

0 +-' 0

0 > 2

Q)

0

I- l. I

Z 1 w '\ -1 -(f) W 0:: I I I I I I I I I I J I

0 0 0 0 0 II) v t') ('II ....

(!s>!) ~~

RESILIENT MODULUS Sample No. 6 50 ~

40

'\ ~ --ok --tc

-:; 30 t-.::L -'--'"

-+ -.-+-et:: 20 ~ ~ -+--

~ B

10

I oC 1

o 5

-El

L I I I

Gee&EI O'c = 20 psi - )CofH( 1 5 psi

10 psi 5 psi 1 psi

10 15 25

Deviator Stress (psi)

~ I-'

92

III C'I

'" "ij"ij "ij "ij'ij a. a. a.. a.. a..

• 0 100111 ....

0 C'I .... ....

Z II u

b

Q) x

- HBI \

0

0..

C'I

E \

".-...

0 (f)

VJ

)(

C-

\ 1 Ill""""" ....

\ \ VJ VJ

(f)

=:J \ \

OJ

~

L

\ ....,

:::J

(/)

0 t o L

..... 0 ...., c

0 2

> OJ

0

l-Z t w ~

(f) -W - ---n::: 0 0 0 ....

~~

93

I() N

OC) .-'g;'g;'g;'g; [a.a.a.a. o I() 0 I() or-

0 Nor- .-

Z II u

b 0 N

<V

UBI 0..

E ,,-.... (J) 0 0.. U)

+ I()"--" r-

Ul

\ (J) Q)

(f) L

\ -+-' =:l (f)

~ ;. ~ o L

=:l .- 0 I -+-' 0 I c .-0 I >

I Q) 2

I 0

J- ! z W ~ / ---.J -U) W n:: I I I I I LL I I I I L...L...LL I I 0 ..

0 0 0 0 0 0 I() v I') N .-

(!s>j) ~V'J

RESILIENT MODULUS Sample No. 9 50 ~I--------------------------------------------------------------~

40

~30 .-en .:Y. '--" ! ........

(t: 20 r- .; ........ )f-::;;; r,,- ..-----Is lao ....6.

10 +-+- ........ - ......

-+

-£I

t3- B

G&&eQ a c = 20 psi )H( x.....c 1 5 psi A666~ 10 p~ +++++ 5 psi Ge&ee 1 psi

tc

o ~I ~~~~~~~--~~~~--~~~~--~~~~--~~~~~~~~ o 5 10 15 20 25

Deviator Stress (psi)

1.0 ~

50

40

,-... 30

en ..:::£ '--'

RESILIENT MODULUS Sample No. 1 0

e

~ O'a = 20 psi _x_ 15 psi &6AAA 10 psi +++++ 5 psi

1 p:si

e --Q -_ ....... ~

A

- - -+

o ~1~~~~ __ ~-L __ ~-L~~~~ __ 4--4 __ ~-L __ ~~~ __ ~~ __ ~-L __ ~~~~~

o 5 10 15 20 25

Deviator Stress (psi)

\0 U1

50

40

,--... 30

en ..::x -....-

D:: 20 :2

10

RESILIENT MODULUS Sample No. 11

Gee&EI Uc - 20 psi )He X*tC 1 5 psi A666A 10 p~ +++++ 5 psi

1 psi

~

--* -*

- -+ +-+- -+-

+-

--IiI ~ a

o ~ I I I I I I I I I I I I I o 5 to 15 20

Deviator Stress (psi) 25

1.0 m

97

LO

N N

~ "ij",;"ij";;";; 0.0.0.0.0.

. 0 10010 ..-

0 N"-"-

Z II

b OJ

UBI , 0

-0...

N

E \

r--.

0 (f)

rn , Q.

+ It)'--'"

I -1

(f) I

rn

:J I

rn Q)

\ L ......., (f)

----1 :J 1 0

t o L

I .,.... 0 .......,

0 a :2

.-> (])

0

~ I Z w

+ I

LO

----1 \

-(f) -~\-<

I

w +-0:::: 0

0 0 ..-

(!S>\) ~~

RESILIENT MODULUS Sample No. 13 50 r------------------------------------------------------------,

40

GG&eQ a c = 20 psi - x*'C 1 5 psi .666. 10 p~ +++++ 5 psi Geee-EI 1 psi

~30 ~ '-/ ~ ~ 20 L-

Q e

....x -.-.c _ .-.c

/"

~ - -,..- --+-- -+ ~

10 ~-- w

o I ..J

o 5 10 15 20 25 Deviator Stress (psi)

\.C OJ

RESILIENT MODULUS Sample No. 14 50 ~------------------------------------------------

40

,,-... 30

en ~ '--'

0::: 20 ::E

10 ~ .......... -

~

a--

--+ -+

-EI

G&eeQ )H(X_

!l6666

+++++ [H!66EI

ac = 20 psi 15 psi 10 psi

5 psi 1 psi

_x

o ~i ~~~~~-L~ __ ~~~~ __ ~~-L~ __ ~~~~~~~~~~~~~

o 5 10 15 20 25

Deviator Stress (psi)

~ ~

50

40

".--... 30

CIl ~ -....-

~ 20 L

10

RESILIENT MODULUS

_.-ac .-ac

""It--

-+ .........

~ .... ----+ I!I .......£I

I

Sample No. 15

G6&eQ JHCX_

+++++ IHt£Ht6

Uc = 20 psi 15 psi 10 psi

5 psi 1 psi

-

o !~~~~~ __ ~~~~ __ ~~-L~ __ ~~~~~~~~~~~~~-L~

o 5 10 15 20 25

Deviator stress (psi)

~ a a

RESILIENT MODULUS Sample No. 1 6 50 ~--------------------------------------------------------~

40

....... 3J en

.Y "'-J

a:::: 20 ~

10

- -- --..... -

G&e&e _ X-tHC

+++++ GaeeG

ac == 20 psi 15 psi 10 psi

5 psi 1 psi

---o I I I I I I I I I I I I

o 5 10 15 20 25

Deviator Stress (psi)

I-' o I-'

50

40

r--. 30 .-Cfl ~ "'--'"

0:: 20 ::2

10

RESILIENT MODULUS Samp le No . 1 7

~ "-* --+-- -of- -+

Ge6&E)

)H()(~

AAAA6

+++++

.-.c

~=W~ 15 p~ 10 p~

5 p~ 1 p~

o I~~~~ __ ~~~~~~~~ __ ~~-L~ __ ~~~ __ ~~-L~ __ .~~~~

o 5 10 15 20 25

Deviator stress (psi)

t-' o I\J

RESILIENT MODULUS Sample No. 18 50

40 r-

. \

C' 30 ~ \ &-----e-----e----m \ e ~ G

'--' ~ ~ e __ x- ___ x- - - _x- -

_ -x

0:= 20 2

6 ~

10[:""'-+- - -f- - - - -+- - - ---+ GeeeQ C1e = 20 psi

15 psi _XofHC

.666616. 10 psi +++++ 5 psi I3-&S9S 1 psi

o ~'~~~~~~~ __ ~~~~ __ ~~-L~ __ ~~~~~~~~

o 5 10 15 20

Deviator stress (psi) 25

..... a w

RESILIENT MODULUS Sample No. 1 9 50

40

030~ en

.:::L. ""--'"

~ 20 ~

10

" I \ \

- -lit-" - *"" ot(

_--4-+-+- - +- - - - +- -

'- -e B Ge&&E)

IHC XotHC

AAAA6

+++++ IHt&&EI

O'c = 20 psi 15 psi 10 psi

5 psi 1 psi

o I L

o 5 10 15 20 Deviator Stress (psi)

25

...... o ~

RESILIENT MODULUS Sample No. 20

50 F

40

_x ........ x- _ _ -x-- -- -

-+ ---+-'+- --

G&e&e a c = 20 psi 10 ~ Ii... ------- -

)He X_ 15 psi AAAAA 10 psi +++++ 5 psi IHHHH!.I 1 psi

at I I I I a 5 10 15 20 25

Deviator Stress (psi)

I--' o U1

106

APPENDI% E

LOG-LOG PLOT OF TEST RESULTS

100

I

2

,....... en

.:::, 10

0::

~ 5

2

"" .,.../

2

RESILIENT MODULUS Sample No. 1

0

0 ~ ~ ..",r

~ ~

:,.- .....

~ ~ ~

" .......,

~ ~ "

1 10 100 Sum of Principal Stresses, 9 (psi)

MR = 4.988 X 8 0.461

1 07

100

5

2

--.. rn ~ 10 ~

II::

::2 II

2

1

/

RESILIENT MODULUS Sampl e No. 2

0 QCP

~ ~ pt

k<' ~ ~ ~

:>

A ,/

..Air"'"

./ ."

./ V

2 5 2

". ~i-'

10 100 Sum of Principal Stresses, e (psi)

MR = 2.977 X 8 0.550

108

100

2

~

CI) ..Y. 10 -..-

0:: :2

5

2

2

RESILIENT MODULUS Sample No. 3

0

~ 0 n :nO u u ~u

0 0 0

I

I 2

~c

I

10 100 Sum of Principal Stresses, e (psi)

MR = 27.502 X e 0.061

109

100

a

2

~

rJ) ..Y. 10 -...-

0:: 2

5

RESILI ENT MODULUS Sample No. 4

0 ... b

~ 0 g po ----t-'lp 0 ~ ~ ~

~

2 a

~o .... ~

1 10 100 Sum of Principal Stresses, 8 (psi)

MR = 21.089 X 8 0.156

110

.--­U)

100

6 10

1

5

2

5

2

/' V'

RESILIENT MODULUS Sample No. 5

90l

~ ~

o~

~~ ~O 0

~~

.JI' Jt'

...... "" v

~

2 5 2 5

'" ).0' "

10 100 Sum of Principal Stresses, e (psi)

MR = 3.568 X e 0.550

III

100

~

rn o 10

a: ~

1

II

2

...-,.....

5

2

RESILIENT MODULUS Sample No. 6

u P Igj ~

~ ~ b .........:

... .:::0-0 I""

"I..- J

...... i--" 0

~ ~ C ~

~ .....

z II 2 II

~ i""

1 10 100 Sum of Principal Stresses, e (psi)

MR = 7.278 X 8 0.374

112

100

II

2

---en ~ 10

II:::

2 II

2

r---

/""

RESILIENT MODULUS Sample No. 7

D

0 ~

~ rr ~o ~~ 0

" .... ~

.,'" ~

2 2

~ t'" ~

10 100 Sum of Principal Stresses, 8 (psi)

MR = 3.910 X e 0.449

113

100

II

2

..-(I)

25., 10

It: I--"'" 2

II

2

--

RESILIENT MODULU S Sample No. 8

.., ~ :>

0

~ ...-~

~~ ClfO I'"'

0

,1--~

.... 0 ~

~ .......

2 II 2

~

ro it'"

10 100 Sum of Principal Stresses, 8 (psi)

6.345 X e 0.359

114

100

....-rn

.:::f. 10 -...-

a:: :=!!

~-

5

2

~.

5

V

2

RESILIENT MODULUS Sample No. 9

p -

I ~ ~ 0 . ;ao1

~ ~O ~

v

....-! I"

./ ./

./ .....

2 5 2 5

~ ...

~

1 10 100 Sum of Principal Stresses, 8 (psi)

MR = 3.208 X 8 0.523

115

100

,-... en -=.. 10

II:::

~

5

2

~

5

2

2

RESILIENT MODULU S Sample No . 1 0

0 ~

o 0 ~O I=>

O~ ....

1 10 100 Sum of Principal Stresses , 8 (psi)

MR = 1 3. 207 X 8 0.139

116

100

5

2

---rn ~ 10

a:;

~ I' 5

2

1

...........

RESILIENT MODULUS Sample No. 11

~ AI ~

~ ~ II) P

..... .... ~ ~ ~

...-

2 :I 2 :I

~

10 100 Sum of Principal Stresses, 8 (psi)

MR = 5.5 24 X 8 0.385

117

100

5

2

----rn o 10

0: ~

5

2

----

2

RESILIENT MODULU S Sample No. 12

~

0 00

.Qo1 ~

I--~ ~ iTo

0 -f-'" f--'" ~ n -

I 2

~ .,.. .... 1--1-'

10 100 Sum of Principal Stresses, e (psi)

6.935 x e 0.304

118

100

5

2

.......... CIl

c., 10

a:: ~

5

2

...... --

2

RESILIENT MODULU S Sampl e No . 13

0

~ ~ ,... ......

~~ foQ ~. P p

"... ,; .... 0

--~ -

5 2

~ I'-" ....

10 100 Sum of Principal Stresses, 8 (psi)

MR = 6 .866 X e 0.333

119

100

'2

,........,. en ~ 10 '-"

a::: ~

5 ......-

2

RESILIENT MODULUS Sampl e No. 14

b

~ ~ ~

~ p

-..... ~

~ .... ........... 1"'"

2 5 '2

..oc tl... i""' .... r-i"""

10 100 Sum of Principal Stresses, 8 (psi)

4.339 X 8 0.374

100

5

2

,...-.. CI) ~ 10 ---

a:: ::?:

5

2

--

RESILIENT MODULU S Sample No. 15

~

0 ~ ~ ,~ '"' ~O ~~ ~ ... , ~ 0

... ~ ~ ---

1 5 2 5

i-" ,....

10 100 Sum of Principal Stresses, 8 (psi)

MR = 6.544 X 8 0.346

121

100

5

2

,......... en ~ 10 '-"

a:: ~

5

2

2

RESILIENT MODULUS Sample No. 1 6

p

.n O 0

"-

~

'" 0

5 2

10 100 Sum of Principal Stresses, e (psi)

MR = 11.192 X 8 -0.073

122

100

5

~

.r--...

CII ~ 10 '--'"

0::

:2 5

----

RESILIENT MODULUS Sampl e No. 1 7

- p 0

oW-! p-~( ~ 8 fIJ'

I-

~ -. ~ p

0

~Ot l--

10 100 Sum of Principal Stresses, 8 (psi)

M R = 1 5. 2 1 1 X 8 0.162

123

100

:I

,.---...

Ul .::{. 10 '-'

0::

.2 5

2

/:

RESILIENT MODULU S Sampl e No. 1 8

ro n.

~ ~

..........

~ ~u

0

100' ..... 00

~

./ /

/

~

./ "

2 2 5

~ .....

"

10 100 Sum of Principa l Stresses , 8 (psi)

2 .880 X 8 0.610

124

100

2

----.. en

.:::, 10

a:: ..... ~

5

2

",.,.

RESILIENT MODULU S Sampl e No. 19

n

1'-'0

a.,.... ~ ~

~~ ~o :'> :>

~ ~~

v ~ ,

0 ,. -,.,.

2 2

~

f ~

10 100 Sum of Principa l Stresses, 8 (psi)

6.565 X 8 0.348

" 125

100

2

,,--.... Cf)

~ 10 "--'"

0::

~ 5

2

./ ~

2

RESILIENT MODULU S Sample No. 20

~ ~ D"I 11 ">

~~ ~U p-

..... ~ ...... 0

..... ~

~ L'

o~ ~ ....

10 100 Sum of Principal Stresses, 8 (psi)

MR = 4.196 X 8 0.490

126