Numerical experiments to determine the lateral-thrust coefficient of a loose medium

Abstract

1. An understanding of the lateral-thrust coefficient is basic to the development of approximate schemes for computation of the pressures developed by a loose material. If the pressure problem is solved in the strict statement, there is no need to introduce a lateral-thrust parameter. Only a mathematical model of the deformation, the characteristics of the medium, and the edge conditions are given In this case. Relationships between stresses, which can be interpreted as the lateral-thrust coefficient, can be derived even after solution of the specific problem-Applied problems are usually solved using an approximate schemes, one of the premises of which is the introduction of an additional characteristic of the medium -the lateral-thrust coefficient -and a number of a priori assumptions on stress distribution [1]. The basic assumptions are contained in the hypothesis that the lateral-thrust coefficient k is constant.This hypothesis contaIns a whole series of assumptions on the fact that the lateral-thrust coefficient is independent of the yield of the enclosing surfaces, the character of the stress distribution, the material' s load history, etc. It is known, however, that the quantity k depends on these and many other factors. All hypotheses contaIning the assumption k = const are therefore only specific approximations. We can expect that depending on the specific situation, sone of these hypotheses will be proven rather accurate, others less accurate, and a third will be unsatisfactory. Of major Interest is the theoretical evaluation of various assumptions, which can be made from the solution of problems posed strictly.2. For this purpose, it is necessary to select a mathematical strain model, the load range, and the proper edge conditions. Let us restrict ourselves to the case of plane strain within the framework of the model described by Revuzhenko [2], which describes the basic properties of the medium and does not assume limitingstate conditions. In approximate computational schemes, the hypothesis k = const is introcklced as a generalization of Pascal's law; In this case, the magnitude of the coefficient itself characterizes the capacity of thin layers of material to transmit a load distributed over their entire length in the direction of the lateral enclosing surfaces. We will therefore treat the thIn layer as a loadingregion. The conditions on the boundaries of the layer depend on the method of loading and the entire strain region from which this layer is isolated. To evaluate the hypothesis, however, it is sufficient to restrict ourselves to certain characteristic cases when the condltious on the layer boundaries are given directly, and are not determined by the complete problem.Let us examine the case where there are no tangential stresses on the boundaries, and the lateral surfaces are orthogooal surfaces AB (Fig. 1). Let us assign normal-stress or displacement distributions to the surface AB, Wlnkler yield conditions to the lateral surfaces, and the condition of no vertical displacements to the surfac...