STRESSES AND DEFLECTIONS IN A LAYERED PAVEMENT SYSTEM

Abstract

The present study deals with the problem of layered pavement systems in which elastic moduli, instead of being constant, v:ry with stress. The analysis considers the possibility of pavement materials possessing different elastic moduli in compression and tension and the varia tion in elastic moduli with stress. Experimental and theoretical evidence indicates that difference between practice and the existing layered theory solutions exists mainly in that, in practice the surface deflections are higher, the pattern of deflections around a load is more concentrated and reduction in deflection with depth is more rapid, than indicated by the theory. These differences appear largely due to the simplifying assumptions made in the layer theory. Amongst other assumptions, the theory assumes constant elastic moduli for the layers of a pavement. The elastic moduli in compression and tension ere further assumed eaual and independent of stress. Pavement materials, on the other h?nd* are known to have a much lower value of elastic modulus in tension than in compression. Further, experi mental evidence indicates that the elastic modulus in any layer of a loaded pavement does not remain uniform but varies with the level of stress imposed. In order to reduce the gap between theory ?nd practice, the above -11- facts should be recognised and incorporated in the analysis of layered pavement systems. The present studv is an attempt in this direction. Experiments have been conducted which suggest, a practical approach for obtaining possible variations in elastic moduli with stress. Triaxial tests .-*t various confining pressures have been used to establish variations in elastic modulus with stresses when horizontal stresses in the loaded pavement are compressive. These tests have been performed on triaxial specimens of bituminous concrete, soil cement, soil bitumen, soil and sand. From these tests relationships expressing variations in the elastic moduli with confining pressures have been obtained for their use in the analysis. A. test method, based on the concept of thick hollow cylinder under internal radial pressure, has been developed to study stress-strain behaviour of pavement materials subjected tc horizontal tension and vertical compression. In this test, hollow cylindrical specimens, subjected to internal radial pressure, have been tested to express variations in elastic moduli with stresses when the hori zontal stresses in the loaded pavement are tensile. This stress condition is likelv to occur in the upper layers of a pavement ne?r the interfaces. These tests have been performed on hollow cylindrical specimens of bituminous concrete, soil cement, and soil bitumen. Relationships, -inexpressing variation in elastic moduli with stress, have been obtained and used subsequently in the analysis. (V' i The theoretical analysis, which has to include, the variations in elastic modulus with stress and also the possibility of elastic modulus in compression and tension being unequal, is obviously not possible by Burmister's method. Finite element method, which offers a powerful technioue for solving such complex problems, has therefore been used in the present study. In th*^ analysis nonlinear material properties have been approximated in the solution by iterative technique choosing for each successive cycle of solution a vnlue of modulus for each element correspond ing to the state of stress calculated for that element in the preceding cycle. The whole process was clone automatically and sequentially on a computer. A. A finite element computer program has been written for the computation of stresses and displacements. The computer program consists of a main program (MAIN) and four subroutines (SM, MATINV, SKLC, SOLN). No standard subroutine has been used. The program is written in FORTRAN II language and was executed on IBM 70^4. The pr-gram may be used for analysis of layered pavement systems composed of materials, with linear or nonlinear stress-strain behaviour. The finite element analysis, which considers the possibility of pavement materials having different elastic moduli in compression and tension and also includes the -ivvariations in elastic moduli with stress indicates that surface deflections are higher, deflection profiles have a sharper curvature and the reduction in deflection with depth is more rapid than indicated by the analysis which assumes constant values of elastic moduli for the layers of a pavement. These results were found to compare with similar observations reported, by other investigators, for differences between measured deflections and deflections computed by linear elastic theory. The comparison indicated that the proposed analysis is more realistic than the analysis which assumes constant elastic moduli for pavement layers. This has been further supported by comparing a few typical results of the proposed analysis with some field data. The comparisons with field data indicated that the surface deflection profile obtained by the proposed analysis was closer, in shape and extent, to the observed deflection profile than that predicted by Burmister's analysis. The maximum surface deflections given by the proposed analysis were found to be nearer to measured values than those calculated by Burmister's analysis. The observed variation in deflection with depth was found to resemble more the variation indicated by the proposed analysis than that predicted by existing linear analysis. " For the load and material data used in the present study, an empirical correlation has been obtained between -vmaxirnum surface deflections computed by the proposed analysis and Burmister's deflection values. This correlation was found to agree closely with a correlation reported between the observed surface deflections and deflections computed by existing layered system analysis. The correlation indicates the extent of modification required in Burmister's deflection value to obtain realistic estimates of surface deflection on which design of pave ments is generally based. The empirical correlation has been applied to deflections computed by Burmister's method for pavement model sections and compared with measured deflections. The modified deflection values were found to be quite close to the measured values. For an accurate analysis of layered pavement systems, in which elastic moduli in tension and compression may not be equal and independent of stress, the finite element computer program, shown in Appendix 4.1, can be directly used with a high speed digital computer. The relationships, expressing variations in elastic moduli, which are used in the computer program can be obtained experimentally as suggested in the present study.