Numerical Modelling of Deformation of Soil Foundations

Abstract

The algorithm for investigation of soil foundations under its own weight and surface loading is considered. A soil is presented as a continuous medium, which has specific physical and mechanical properties. Structurally, there are three groups of soils, the first – sand, the second – clay and the third – rocks. The main difference is a bonding strength between the individual crystal grains and the medium continuum.Kinematics of a medium continuum is described by the spatial gradient of rate tensor, the deformation rate tensor and the rate of rotation tensor. The state of stress is described by the Cauchy stress tensor and objective Jaumann rate of Cauchy stress. An isotropic elastic-plastic material is considered. The linearized constitutive equations of elastic deformation are obtained as a function of objective Jaumann rate of Cauchy stress in the current state. The theory of a flow and an additive representation of the total deformation rate on elastic and plastic parts are used. The Drucker-Prager yield criterion is applied.The research algorithm is based on the incremental method. The principle of virtual work in terms of the virtual velocity is used. After linearization, the system of linear equations is obtained, where an increment of displacement in the current state is unknown. The radial return method with an iterative refinement of the current mode of deformation is applied. This procedure is based on the introduction into constitutive equations a work of the additional stresses in virtual deformation of the rate.The numerical implementation is based on the finite element method. An eight-node isoparametric hexahedron element is used. The calculation of the soil foundation is considered as an example. The fields of displacements and stresses are obtained. The intensity of stresses and plastic deformations are shown.