The primary objective of this study was to develop and implement mathematical bearing capacity models originally proposed by Hopkins (1988, 1991) and Slepak and Hopkins (1993; 1995). These advanced models, which are based on limit equilibrium and are operated together, can be used to analyze the bearing capacity, or stability, of early construction of loads on a single layer of material, two-layered problems involving a layer of base aggregate and subgrade, and a foundation involving multiple layers of different materials, such as a flexible asphalt pavement. A Prandlt-type shear surface is used in the model analyses of layered foundations. In this report, the models are extended to analyzing flexible pavements reinforced with tensile elements. Although the current model does not account for strain compatibility, the strength of the tensile elements may be input for assumed strain levels. Any number of tensile elements may be analyzed in a given problem. In the limit equilibrium approach, shear strengths, the angle of internal friction, N, and cohesion, c, are entered for each layer of material. Triaxial testing of the asphalt material is performed in a manner that the shear strength parameters, N and c, are developed as a function of temperature. Hence, if the temperature of the asphalt layer is known (or assumed) at a site, then values of N, and, c, may be calculated from the relationships between the shear strength parameters and temperature. Moreover, to facilitate and provide an efficient means of analyzing early construction cases and flexible pavements reinforced with geosynthetics, “Windows” software was developed. In the case of the asphalt layer, the entire layer is divided into finite layers because N and c varies with depth of asphalt. When the surface temperature of the asphalt is known (or assumed), a temperature distribution model is used to estimate the temperature at any depth below the asphalt layer surface. Consequently, the shear strength parameters are known at any depth (of each finite layer) below the surface. To establish the validity and reasonableness of the newly developed limit equilibrium models, bearing capacity factors are derived from the limit equilibrium methods and compared to classical bearing capacity factors, Nc and Nq, developed by Prandlt and Reissner. Differences range from 1 to 10 and 1 to 3 percent, respectively. The Slepak-Hopkins model yields values of N( that are 12 to 38 larger than values published by Caquot and Kerisel. However, values of N( from the Slepak-Hopkins model are only 3 to 11 percent larger than back calculated values obtained by Debeer and Ladanyi from experimental footing tests. The Slepak-Hopkins model was also used to analyzed 237 flexible pavement sections of the 1959-1960 AASHO Road Test. Factors of safety from the model analyses showed that very reasonable results were obtained and were in line with failures recorded at the test site. Finally, actual analyses of a stretch of roadway where failures occurred were analyzed. Three sections involved tensile elements.

Report Date


Report Number


Digital Object Identifier



The contents of this report reflect the views of the authors, who are responsible for the facts and accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the University of Kentucky, the Kentucky Transportation Cabinet, nor the Federal Highway Administration. This report does not constitute a standard, specification, or regulation.