Application of stress function and Fourier’s series for calculation of multilayer reinforced road structure

Abstract

The article is devoted to the development of a method for static load calculation of a multilayer reinforced road structure. Unlike the traditional calculation practice of such structures, in which both reinforced and unreinforced layers are considered as isotropic layers, in this paper reinforced layers are presented as orthotropic layers, and unreinforced layers as isotropic. The computational model of the structure with isotropic and orthotropic layers is considered in the framework of the plane problem of elastic theory. The width of all layers in the crosswise direction is the same. The resolving equations are derived from the equations of strain compatibility involving the stress function and Fourier’s series. The unknown constants are obtained from the boundary conditions and layer coupling conditions. Formulas for determining the maximum deflections are derived. As an example, the two-layer structure calculation is given, the upper layer of which is reinforced with a geocell and the lower layer is unreinforced. A uniform loading is applied on a limited part of the upper layer surface. The paper presents a maximum deflections dependence diagram of the two-layer system on the number of terms of the series. The calculated deflections of the two-layer structure are compared with the maximum deflections of an equally thick unreinforced single-layer structure, as well as with the results of field experiments. The effect of reinforcing the upper layer of the structure is defined as the ratio of the difference between the unreinforced and reinforced maximum deflections of structures and the unreinforced structure maximum deflection. The reinforcement effect calculated according to the proposed theory was 16 %, while the effect obtained as a result of field experiment was 10 %. The difference is explained by the difference in the size and shape of the load deck, as well as the difference between the plane and volume deformation models of the theoretical model and the real structure.