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SUITABILITY OF USING CALIFORNIA BEARING RATIO TEST TO PREDICT RESILIENT MODULUS

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Resilient modulus (M r) 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.
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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.
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Base/Subbase materials and subgrade soils.
3. The Asphalt Institute (1982), Research and Development of the Asphalt Institutes
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.
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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,
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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-
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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
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11. HKS (2000), ABAQUS Users 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.
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Mechanistic pavement design procedures based on elastic layer theory require the specification of elastic moduli for each material in the pavement section. Repeated load tests yielding a resilient modulus are frequently used to characterize the soil subgrade. Due to difficulties associated with cyclic testing, approximate methods are often used for design estimates of resilient modulus. These approximations are often based only on shear strength measures and do not account for the dependence on the magnitude of cyclic deviator stress. A procedure is described to relate the soil-index properties and the moduli obtained from unconfined compression tests, to resilient modulus. Two statistical models are described and demonstrated for 11 soils from throughout the state of Tennessee. One model provides an estimation of the breakpoint resilient modulus, or the modulus at a deviator stress of 6 psi (41 kPa). The second model provides a general nonlinear relationship for the modulus of fine-grained soils as a function of deviator stress. Both models are demonstrated for a range of soils and are shown to provide a good characterization of the response for the soils investigated. Similar relationships can be developed for other subgrade soils, and may prove useful to agencies that use deterministic pavement design procedures, but lack the capability for high-production repeated-load testing.
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Synopsis The Paper briefly reviews the factors which affect the results of in-situ and laboratory California bearing ratio tests. A relation between CBR and bearing capacity is developed which enables the in-situ CBR value to be calculated from a knowledge of the cohesion, true angle of internal friction, and suction of the soil. A method of correcting the in-situ value to take into account the confining action of the mould used in labortory tests is proposed. Laboratory investigations made on a single-sizee sand and on a heavy clay are reported in which close agreement was found between computed and measured CBR values. Cet article esquisse les facteurs qui influent sur les résultats des essais CBR in situ et au laboratoire. On developpe un rapport entre le CBR et la capacité portante qui permet de calculer la valeur CBR in situ si on connaît la cohésion, l'angle de frottement interne véritable et la suction du sol. On propose une méthode pour corriger la valeur in situ afin de tenir compte de la contrainte exercée par le moule proposed. employé dans les essais au laboratoire. On décrit des recherches faites au laboratoire avec un sable élémentaire et avec une argile lourde et on constate un bon accord entre les valeurs calculées et les valeurs mesurées.
Article
Resilient properties of 50 typical Illinois fine-grained soils were evaluated. Soil resilient properties can be related to soil characteristics (texture, plasticity, organic carbon content, AASHTO group index). Current soil classification procedures do not group fine-grained soils into groups with distinctive resilient properties. Moisture-density conditions and degree of saturation significantly influence the resilient properties of fine-grained soils. Average resilient properties for various soil classification groups were determined. Regression equations were developed for estimating resilient properties based on soil characteristics and degree of saturation.
Research and Development of the Asphalt Institute’s Thickness Design Manual (MS-1),” 9th Edition
  • The Asphalt
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.
Asphalt Pavement Design –The Shell Method
  • A I M Claussen
  • J M Edwards
  • P Sommer
  • P Uge
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.
An engineering manual for settlement studies
  • J M Duncan
  • A L Buchignani
Duncan, J.M., and Buchignani, A.L. (1976), " An engineering manual for settlement studies, " Department of Civil Engineering, University of California, Berkeley, 94 pp.
Guide for Design of Pavement Structures American Association of State Highway and Transportation Officials
AASHTO (1993), " Guide for Design of Pavement Structures, " American Association of State Highway and Transportation Officials, Washington, D.C.