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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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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
Sukumaran et al. 1
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.
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
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
Sukumaran et al. 5
Table 2: Results of the Finite Element Verification Studies on the Medium Strength
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.
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
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
(%) LL PL PI Unconfined
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
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
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.
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.
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 Institutes
Thickness Design Manual (MS-1), 9th Edition, Research Report 82-2, Asphalt Institute,
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-
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 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.
... This study concluded that M R -CBR relationship equations are not satisfactory to predict M R of unbound granular materials. The study stated that the correlations between M R -CBR should be carefully used, because they tend to"under-predict" or "over-predict" the M R , and the same observations were reported by [12,17,18]. ...
Mechanistic pavement design procedures of flexible pavement based on elastic-layers theories require the determination or estimation of resilient modulus (MR) for each layer in the pavement structure. Considering the complexity and cost of testing required, regression models have been developed to predict resilient modulus of heavy-duty base crushed rock mixes from their physical and engineering properties. Testing results of MR for three different gradations of the same crushed rock with 15 different fines combinations of Crusher dust (CD) and Claypro (CP) have been used to calibrate a universal three-parameter deviatoric stress model. The latter relates resilient modulus to both deviatoric and confining stresses and considers shear stresses and strains developed during loading. Physical properties of these mixes were then used to develop multiple linear regression models to predict the three parameters of the calibrated deviatoric stress model. The modelling process was repeated by including California bearing ratio as a predictor with the physical properties. Both sets of models show the properties considered herein, serve to explain a high variation in the three parameters, ranging between 71-91%. However, Correlation between measured and predicted MR values from both sets of models is 0.90 and 0.87, respectively. Further, the optimum clay content (CP) for the different mixtures was also assessed. The results indicated that 1% of CP can be considered the optimum content for all three gradations.
... California bearing ratio (CBR) testing is one of the oldest and most widely used technique but it only measures the shear strength of the materials and does not necessarily correlate with the stiffness modulus (e.g. Sukumaran et al 2000). On the other hand falling weight deflectometer (FWD) is another type of apparatus used to evaluate the behaviour of the pavement layer in the actual field to a closely simulated traffic condition. ...
Conference Paper
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Use of an accelerated pavement testing (APT) facility has become one of the most popular methods around the world for testing the performance of various types of pavement materials and for determining their characteristics. In the current study using an APT facility, the model pavement structure was simulated in a steel tank of dimension 1.1 m x 1.0 m x 0.6 m. Then a sinusoidal type axial loading (at 3 Hz) was applied on the model pavement structure consisting of layers of granular base material stabilized lightly with cement-flyash overlying compacted subgrade. The consequent tensile strains induced at the bottom and middle of the stabilized base layer and the vertical deformations at various depths of the pavement structure were measured. The model test pavement was analyzed by using dynamic finite difference computer program, FLAC3D, and the stiffness moduli of the two layers used in the APT test were backcalculated.
It is crucial to accurately predict the resilient modulus of subgrade soils. The modulus is influenced by a soil’s properties, as characterised by the soil’s moisture index values. Thus, it may be feasible to predict resilient modulus based on the soil index. Consistency index, as one of the common soil indices, incorporates plasticity index and moisture content. Therefore, this study aims to establish its relationship with resilient modulus. By collecting and analysing the previous testing results, it is found that resilient modulus was well correlated and increased with consistency index. Two prediction models, a consistency index model and a modified consistency index model, were also proposed to evaluate the resilient modulus of 15 soils with plasticity indices ranging from 6 to 52 at various moisture contents. Model parameters of the consistency index model were estimated from the plasticity index and exhibited excellent correlation. The modified consistency index model incorporated stress states to predict resilient modulus. The models were validated using selected testing results. Despite some limitations, it proves reasonable as a simple alternative means to determine the resilient modulus of fine-grained soils for foundation design, in place of complex resilient modulus testing.
Most of the rural roads in India are over soft subgrade which requires improvement. Structural performance of pavement can be evaluated by Benkelman beam deflection test as well as field CBR test. Improving the soil with coir geotextiles is a good option, as coir geotextiles are natural and indigenous materials with higher durability compared to other natural geotextiles. This paper is focusing on the simulation of a numerical model which could predict the modified CBR value of coir geotextile-reinforced soil and variation in deflection with different coir geotextiles using ABAQUS. Such a model could be effectively used to choose the type of coir geotextile suitable for a particular type of soil. Numerical simulation for predicting the variation in deflection of pavement could be effectively used to evaluate the reduction in pavement deflection with the inclusion of coir geotextiles.
The subgrade strength of roads and highways is based on the California Bearing Ratio (CBR) value. In this investigation, attempts have been made to overcome the limited boundary condition approach by using advanced methods, Support Vector Machine (SVM) and Gene Expression Programming (GEP) for prediction of CBR value. A large and wide range of datasets of different types of soils have been utilized in the analysis. The grain size distribution, Atterberg’s limits and compaction characteristics of soils have been used as the input variables. Best models with different variables were developed by using GEP and the same were used for SVM analysis. The advantage of SVM over others is that it works on the principle of Statistical Risk Minimization (SRM). A comparative study of SVM and GEP models indicates that the SVM has better predictability than GEP. Further, it was found that the five-input variable (including gravel content, sand content, plasticity index, maximum dry density and optimum moisture content) model (Model III) is the best one to predict the CBR value. The detailed statistical analysis including Pearson coefficient correlation (R) and Error analysis have also been carried out. Based upon the statistical analysis, Overfitting Ratio (OR) of SVM was found to be 0.630 against the value of 1.02 in GEP analysis. Further, sensitivity analysis was carried out and it was found that the CBR value is highly dependent on gravel and sand contents. On the other hand, plastic limit plays an insignificant role in determining the CBR value of soils.
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Laboratory tests on geosynthetic-reinforced soil-aggregate systems were carried out by many researchers to understand the improvement in bearing resistance of soil-aggregate systems because of geosynthetic reinforcement. California bearing ratio (CBR) test is one among the common laboratory tests adopted for this purpose. This paper presents the influence of sample size and anchorage of reinforcement in CBR test through tests carried out using conventional and modified CBR moulds with and without anchorage of reinforcement. Clay subgrade and aggregate subbase were simulated in these tests with a geosynthetic layer placed at the interface. Modified set-up was double the size of the conventional set-up and has the provision to anchor the reinforcement. Three different types of geosynthetics namely, geotextile (GT), biaxial geogrid (BG), and geonet (GN) were used in the tests. While the size of the mould significantly affected the test results, effect of anchorage of reinforcement on the bearing resistance of reinforced soil-aggregate systems was not significant. Increase in sample size reduced the boundary interference, which otherwise resulted in over prediction of secant modulus of the reinforced systems, the effect being more pronounced for weaker reinforcement materials.Soil-aggregate system, California bearing ratio, Geosynthetics, Size effect, Bearing resistance, Anchorage.
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This study was conducted to determine the resilient modulus (Mr) and the unconfined compressive strength (UCS) of two recycled roadway materials such as recycled pavement material (RPM) and road surface gravel (RSG) with or without cement kiln dust (CKD). The recycled materials were blended with two CKD contents (5, 10 %) and 28 day curing time. Mr and UCS tests were also conducted after 10cycles of freezing and thawing to asses the impact of freeze-thaw cycling. Mr was determined conducting by the laboratory test method described by NCHRP 1-28A. Stabilized RPM and RSG had a modulus and a strength higher than unstabilized RPM and RSG. Mr and UCS of RPM and RSG mixed with CKD increased with increasing CKD content. The results indicated that the addition of CKD could be improved the strength and the stiffness of RPM and RSG. Therefore, RPM, RSG and CKD could be used as an effective materials in the reconstruction of roads.
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This paper documents the use of finite element analyses techniques to determine the failure mechanism in a pavement system under moving aircraft loads. The flexible pavement system that is modeled is on a medium strength subgrade. The stress-strain response of the medium soft clay is simulated using an elasto-plastic model. The three-dimensionality of the failure surface under actual wheel loads with wander requires that computationally intensive three-dimensional models be used. The finite element techniques employed are verified against available failure data from the National Airport Pavement Test Facility (NAPTF) of the Federal Aviation Administration based in Atlantic City. The paper will discuss the advantages and limitations of the non-linear elastic models that are currently used in pavement analysis. In addition, the paper will also discuss efficient finite element techniques that can be utilized for three-dimensional analysis that will reduce computational time without sacrificing accuracy.
A simple, practical procedure for representing the nonlinear, stress-dependent, inelastic stress-strain behavior of soils was developed. The relationship described was developed in such a way that the value of the required parameters may be derived from the results of standard laboratory triaxial tests. Comparisons of calculated and measured strains in specimens of dense and loose silica sand showed that the relationship was capable of accurately representing the behavior of sand under triaxial loading conditions.
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.
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.
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
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