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SUITABILITY OF USING CALIFORNIA BEARING RATIO TEST TO PREDICT

RESILIENT MODULUS

By:

Beena Sukumaran,

Associate Professor, Civil & Environmental Engineering

Rowan University

201 Mullica Hill Road, Glassboro, NJ 08028

Vishal Kyatham, Amip Shah & Disha Sheth

Research Assistants, Civil & Environmental Engineering, Rowan University

PRESENTED FOR THE FEDERAL AVIATION ADMINISTRATION AIRPORT

TECHNOLOGY TRANSFER CONFERENCE

05/02

Sukumaran et al. 1

Abstract

Resilient modulus (Mr) of subgrade is a very important factor in airport and highway

pavement design and evaluation process. Typically, this factor is evaluated using simple

empirical relationships with CBR (California-bearing-ratio) values. This paper documents the

current state of the knowledge on the suitability of this empirical approach. In addition, the paper

also documents the use of finite element analyses techniques to determine the California Bearing

Ratio. The stress-strain response of the various soils is simulated using an elasto-plastic model.

The constitutive model employed is the classical von Mises strength criteria with linear elasticity

assumed within the yield/strength surface. The finite element techniques employed are verified

against available field and laboratory test data. The model is then utilized to predict the CBR of

various soils. The empirical relationship between CBR and resilient modulus will then be

investigated based on the results obtained from the three dimensional finite element analysis and

its suitability for flexible pavement design will be evaluated.

Introduction

Most of the present methods used to design pavements utilize a mechanistic design

procedure based on elastic layer theory (Asphalt Institute, 1982; Shell, 1977; and FAA, 1995).

The elastic modulus for the soil subgrade can be obtained from repeated load triaxial tests

(AASHTO 1993). Due to the complexity of the testing and test equipment required for the

repeated load triaxial tests, it is desirable to develop approximate methods for the estimation of

resilient modulus. The AASHTO design guide suggests that the resilient modulus of fine-grained

soils can be estimated as (Heukelom and Klomp 1962):

Mr (psi) = 1,500 CBR (1)

In addition, there are various other relationships that are used around the world:

U.S. Army Corps of Engineers (Green and Hall 1975)

Mr (psi) = 5,409 CBR0.71 (2)

South African Council on Scientific and Industrial Research (CSIR)

Mr (psi) = 3,000 CBR0.65 (3)

Transportation and Road Research Laboratory (TRRL)

Mr (psi) = 2,555 CBR0.64 (4)

There has been considerable discussion on the suitability of using any of these approaches. The

CBR (California Bearing Ratio) test is a measure of the shear strength of the material and does

not necessarily correlate with a measure of stiffness or modulus such as the Mr. Thompson and

Robnett (1979) could not find a suitable correlation between CBR and resilient modulus. In

addition, it is also known that the resilient modulus is dependent on the applied stress level (Rada

and Witczak 1981). For most fine-grained subgrade soils, Mr decreases with increasing

deviatoric stress level. Model forms characterizing the relationship between Mr and deviatoric

stress have been shown to be bi-linear, hyperbolic, semilog and log-log (Witczak et al. 1995).

The CBR test can be thought of as a bearing capacity problem in miniature, in which the

standard plunger acts as a circular footing. Using the bearing capacity equation, CBR was

correlated with the undrained shear strength, su as:

Sukumaran et al. 2

CBR = 0.62 su (psi) (5)

Black (1961) found satisfactory correlation with the above value. In addition it was also shown

by Duncan and Buchignani (1976) that the resilient modulus can be predicted using the

undrained shear strength knowing the plasticity index (PI) of the soil.

Mr = 100 – 500 su PI>30

Mr = 500 - 1500 su PI<30 (6)

Combining equations (5) and (6),

Mr (psi) = 160 to 2420 CBR (7)

Thompson and Robnett (1979) suggested a relationship utilizing the unconfined compressive

strength, Qu to determine Mr. 86.0)(307.0)( +=psiQksiM ur (8)

From equation (7) and (8), it can be seen that there is a wide variation in the resilient modulus

value that can be obtained using the CBR depending on the plasticity properties of the soil. In

this study, the suitability of using equation (1) in the AASHTO and FAA design code will be

discussed. In addition, the use of three-dimensional finite element models utilizing plasticity

models will be used to predict CBR values. This study is a precursor to further studies utilizing

three-dimensional finite element models with plasticity parameters to predict the performance

and failure mechanisms of flexible pavement systems.

Some Background on Finite Element Analysis

An objective of this paper is to demonstrate that readily available displacement based and

hybrid (combined stress and displacement solution variables) based finite elements formulations

are capable of accurately, and efficiently calculating the California Bearing Ratio of subgrade

soils and thereafter the performance of pavement systems. Available displacement based and

hybrid (combined stress and displacement solution variables) based finite elements formulations

are capable of accurately and efficiently calculating limit loads for pavement systems. An

important feature in the successful use of displacement based finite element formulations is the

use of reduced integration techniques in many limit analysis investigations. The term ‘reduced’

integration refers to the fact that a lower level (fewer sampling points) of numerical integration is

being used than that theoretically required, to exactly integrate a polynomial of a certain order.

Alternatives to the use of reduced integration exist, e.g. hybrid finite elements, or very

high order displacement-based elements such as the 15-noded cubic strain triangle. Hybrid

elements are available in commercial codes, such as ABAQUS (2000), and are effective in the

analysis of incompressible materials. The term hybrid stems from the use of both displacement

and stress components as solution variables. In this case, the stress component included is the

mean pressure. Zienkiewicz and Taylor (1994) and HKS (2000) discuss this in detail. More

discussion about the suitability of these elements and analysis techniques can be found in

Sukumaran et al. (1998).

Sukumaran et al. 3

Verification of Finite Element Modeling Techniques

The adequacy of finite element modeling utilizing plasticity models are demonstrated in

the following by virtue of their performance in accurately calculating the California Bearing

Ratio for a subgrade soil. The subgrade soil utilized for the modeling purpose is the medium

strength subgrade used in the construction of the pavement test facility at the FAA technical

center. Three verification studies were conducted. The first one utilized the ultimate shear

strength as the yield strength. The properties of the soil used are shown in Table 1.

Table 1: Properties of Medium Strength Subgrade Soil

Soil Property Values

Moisture content 30.5%

Undrained shear strength 13.3 psi

Dry density 90.5 pcf

Elastic modulus 12,000 psi

The finite element mesh used for the analysis is shown below in Figure 1. The finite element

analyses were conducted using ABAQUS (HKS 2000). A von Mises shear strength idealization

was used to model the clay. The elastic-plastic material properties used for the soil are shown in

Table 1. The von Mises model implies a purely cohesive (pressure independent) soil strength

Figure 1. Finite element mesh used in the analysis

definition. A three dimensional response was simulated using quasi three-dimensional Fourier

analysis elements (CAXA) available within ABAQUS. CAXA elements are biquadratic, Fourier

quadrilateral elements. The number of elements and nodes in the mesh are 185 and 6260

respectively.

Sukumaran et al. 4

The second study was conducted using the von-Mises model with unconfined

compression stress-strain data. Stress-strain response can be better captured if stress vs. strain

data from unconfined compression tests, triaxial tests or direct simple shear test are input to

obtain the plasticity model parameters. It can be seen from Figure 2 that the zone of plastic strain

increases as penetration depth increases as would be expected. The third study conducted utilized

the instantaneous elastic modulus, which was calculated from the unconfined compression stress-

strain data. Table 2 summarizes the results obtained. It can be seen that the von-Mises model

utilizing the ultimate shear strength input predicts CBR values that are closer to the higher end of

the measured CBR values, while the other two cases predict values closer to the lower end of the

CBR values measured. Several analyses were also conducted using linear elastic models utilizing

elastic modulus values predicted using Equations (1) to (4). All these analyses rendered very

high values of CBR.

Figure 2. Plastic strain distribution at a) 0.1” piston penetration (b) 0.2” piston penetration

(b)

(a)

Sukumaran et al. 5

Table 2: Results of the Finite Element Verification Studies on the Medium Strength

Subgrade

Finite Element Model Utilized CBR values computed

Von-Mises with ultimate shear strength input

(Analysis 1) CBR at 0.1?= 8.6

CBR at 0.2?= 5.7

Von-Mises with stress-strain data input

(Analysis 2) CBR at 0.1?= 5.6

CBR at 0.2?= 4.8

Elastic model utilizing stress-dependent

elastic modulus (Analysis 3) CBR at 0.1?= 4.2

CBR at 0.2?= 4.1

Field measurements (NAPTF test pits,

November 1999) CBR at 0.1?= 3.4-8.4

CBR at 0.2?= 2.8-7.2

In order to understand the stress-strain response of the soil, stress vs. displacement plots

were studied for the three cases mentioned above and compared with the field test data. The

stress-strain plots are shown in Figure 2.

0

20

40

60

80

100

120

140

00.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Displacement (inch)

Stress (psi)

Analysis 2

Analysis 1 Field test

data

Analysis 3

Figure 3: Stress vs. displacement plot for the various verification studies compared with

field test data

Sukumaran et al. 6

The load vs. displacement response computed shows a remarkable similarity to what was

observed in the field. The prediction of the CBR value also improves as a consequence. From the

results, it can be seen that three-dimensional finite element modeling can accurately capture the

stress-strain response of the subgrade soil. Based on this conclusion, it was decided to model

various other soils for which measured resilient modulus and unconfined compressive strength

data existed (Drumm et al. 1990).

Relationship Between CBR and Resilient Modulus

The data provided by Drumm et al. (1990) was for 11 subgrade soils from Tennessee,

which had clay contents ranging from 16 to 55%. The soil properties of interest are summarized

in Table 3. Additional soil properties are given in Drumm et al. (1990).

Table 3: Index Properties of Soil Tested by Drumm et al. (1990)

Soil Classification Atterberg Limits

Designation

USCS AASHTO

Clay

content

(%) LL PL PI Unconfined

compressive

strength

(psi)

Breakpoint

resilient

modulus

(psi)

A31 CL A-4 17 30.5 22.1 8.4 63.3 15,000

B21 CL A-6 18 38.8 23.3 15.5 68.8 14,000

C11 SM A-2-4 17 20.7 19.0 1.7 30.9 11,500

D11 ML A-4 18 36.2 34.1 2.1 28.7 2,000

E21 ML A-7-6 35 37.1 27.0 10.0 67.7 18,000

E31 CL A-4 36 42.1 22.0 20.1 45.6 8,000

F11 CL A-7-6 16 29.5 20.1 9.4 53.5 6,000

H11 CL A-4 20 28.5 19.2 9.3 62.6 7,500

H21 SM-

CL A-4 16 21.0 14.1 6.9 39.7 8,000

J11 MH A-7-5 28.7 68.5 39.2 29.3 27.3 12,000

J31 MH A-7-5 55 69.5 42.6 26.9 46.0 17,000

CBR values were predicted for these soils using the elasto-plastic von-Mises model and

the finite element mesh shown in Figure 1. The soil properties used in the model are as listed in

Table 3. The unconfined compressive strength was input as the yield strength. The CBR values

computed for the various soils are listed in Table 4.

Figure 4 shows the comparison between the measured resilient modulus values and the

values predicted utilizing the computed CBR values and equations (1) to (4). In addition, the

resilient modulus was also predicted utilizing the unconfined compressive strength and equation

(8). It can be seen that equations (1) to (4) over predict the resilient modulus by a factor of 2 or

more. The best estimate of the resilient modulus is obtained from equation (8) suggested by

Thompson and Robnett (1979).

Sukumaran et al. 7

Table 4: Predicted Values of CBR from Finite Element Analyses

Soil Designation CBR values predicted from FEA

A31 40.4

B21 38.84

C11 19.3

D11 11.0

E21 40.4

E31 24.8

F11 25.3

H11 30.1

H21 21.71

J11 17.01

J31 28.61

0

10000

20000

30000

40000

50000

60000

70000

80000

a31 b21 c11 d11 e21 e31 f11 h11 h21 j11 j31

Soil Designation

Mr (psi)

Measured Mr (USACE)

Predicted Mr (Shell)

Predicted Mr USACE

Predicted Mr (CSIR)

Predicted Mr (TRRL)

Predicted Mr (Thompson

& Robnett)

Figure 4: Comparison between the measured and predicted resilient modulus values

Conclusions

Mechanistic design methods utilizing elastic layer theories require the determination of

the elastic moduli. The elastic moduli for soil subgrades can be characterized by the resilient

modulus and can be obtained from the repeated load tests. Due to the time and skill required to

conduct these tests, approximate correlations between resilient modulus and some more easily

Sukumaran et al. 8

measured parameter is utilized. The commonly used California Bearing test value is used to

obtain a prediction of resilient modulus. During the course of this research, it was found that the

resilient modulus values could not be suitably predicted using Equation (1). It was observed

during the present research that the relationship given by Equation (1) overpredicts the resilient

modulus. A more suitable estimate of resilient modulus can be obtained from Equation (8)

knowing the unconfined compressive strength of the soil.

Plasticity models should be utilized when realistic evaluations of strains and

displacements are required. Elastic models, especially the Duncan hyperbolic model (Duncan

and Chang 1970) can suitably predict deformations at failure as long as the orientation of stresses

remain constant but have limited benefit when evaluating displacements at and after failure. In

addition, the hyperbolic model is of limited suitability if realistic evaluations of pore pressure are

required. Linear elastic models are of limited benefit as they do not accurately predict stresses or

strains in the subgrade soil.

Acknowledgements

The authors wish to express their utmost gratitude to the Federal Aviation Administration

for the research grant that made this work possible. In addition, the authors would like to thank

Drs. Gordon Hayhoe and David Brill of the FAA for their assistance with the project. The

authors would also like to acknowledge Mr. Joseph Scalfaro and Mr. Steven Gomba who did

some of the preliminary work on the project.

References

1. AASHTO (1993), “Guide for Design of Pavement Structures,” American Association of

State Highway and Transportation Officials, Washington, D.C.

2. AASHTO T 294-94 (1994), “Resilient Modulus Testing of Unbound Granular

Base/Subbase materials and subgrade soils.”

3. The Asphalt Institute (1982), “Research and Development of the Asphalt Institute’s

Thickness Design Manual (MS-1),” 9th Edition, Research Report 82-2, Asphalt Institute,

1982.

4. Black, W.P.M. (1961), “The calculation of laboratory and in-situ values of California

Bearing Ratio from bearing capacity data,” Geotechnique, Vol. 11, pp. 14-21.

5. Claussen, A.I.M., Edwards, J.M., Sommer, P., and Uge, P. (1977), “Asphalt Pavement

Design –The Shell Method,” Proceedings of 4th International Conference on the

Structural Design of Asphalt Pavements, Vol. 1, pp. 39-74.

6. Drumm, E.C., Boateng-Poku, Y., and Johnson Pierce, T. (1990), “Estimation of subgrade

resilient modulus from standard tests,” Journal of Geotechnical Engineering, Vol. 116,

No. 5, pp. 774-789.

7. Duncan, J.M., and Buchignani, A.L. (1976), “An engineering manual for settlement

studies,” Department of Civil Engineering, University of California, Berkeley, 94 pp.

8. Duncan, J.M., and Chang, C.Y. (1970), “Non-linear analysis of stress and strain in soils,”

Journal of Soil Mechanics and Foundations Division, ASCE, Vol. 96, Vol. 5, pp. 1629-

1653.

9. FAA - Advisory Circular (AC) No: 150/5320-16 (1995). Airport Pavement Design for

the Boeing 777 Airplane, Federal Aviation Administration, U.S. Department of

Transportation, Washington D.C.

Sukumaran et al. 9

10. Heukelom, W., and Klomp, A.J.G. (1962), “Dynamic testing as a means of controlling

pavement during and after construction,” Proceedings of the 1st international conference

on the structural design of asphalt pavement, University of Michigan, Ann Arbor, MI.

11. HKS (2000), ABAQUS User’s Manual - Version 6.2, Hibbitt, Karlsson and Sorensen.

12. Rada, G., and Witczak W. (1981), “Comprehensive evaluation of laboratory resilient

modulus results for granular soils,” Transportation research record No. 810, pp. 23-33.

13. Thompson, M.R., and Robnett, Q.L. (1979), “Resilient properties of subgrade soils,”

Journal of Transportation Engineering, ASCE, Vol. 105, No. 1, pp. 71-89.

14. Zienkiewicz O.C., and Taylor R.L. (1994), The Finite Element Method, Vol. 1, 4th

Edition, McGraw-Hill.