USING A FINITE ELEMENT MODEL TO DETERMINE LATERAL PRESSURE OF A GRANULAR MEDIUM ON A RETAINING WALL UNDER DISPLACEMENT

Abstract

The problem of determining the pressure of a granular medium on a retaining wall depending on its displacement is an important problem in structural mechanics. Existing non-deformation methods only allow finding the pressure values at the moment of material transition to a limit state. Retaining walls, like other engineering structures, operate in a limit state. The mentioned engineering problem is considered to verify the accuracy of the developed nonlinear model. The article formulates a mathematical representation of the boundary problem that was modelled on an experimental stand. The environment that contacts the wall operates under conditions close to plane deformation, since there is no displacement in the direction perpendicular to the glass side walls. If neglect the frictional forces on the side walls, the estimation of the stress-strain state of the medium can be reduced to a two-dimensional problem based on deformation. The analysis is focused on a flat rectangular computational domain filled with a material with nonlinear deformation laws. The problem involves determining the stress state of the area under the influence of the material's own weight and the horizontal displacement of the wall.

To obtain a unique solution to the problem, it is necessary to ensure the fulfilment of static equilibrium conditions, geometric conditions of continuity (inseparability) of deformations adopted in the model of physical relationships, as well as to satisfy boundary conditions that correspond to the specific problem-solving scheme. The problem is solved using the finite element method. When choosing the calculation scheme for computer solution of the problem, the conditions of the sand mass operation in the experimental stand are considered as much as possible. The boundary conditions corresponding to the calculation scheme and the structure of the canonical equations of the displacement method of structural mechanics are considered in solving the problem. A comparison of the results of computer modelling of the problem and parallel large-scale modelling of the interaction of a rigid vertical wall with discrete filling material was made.