Method of successive approximation in mathematical modelling of geotechnical mechanics problems

Abstract

Abstract The purpose of this work was to develop a mathematical model by the results of mathematical modeling of the problem of loading a circular cross-sectional roadway under the action of hydrostatic pressure. Instead of finite element method, it proposed to solve this problem by method of successive approximation, which assumes finding a solution in vicinity of one point in the domain of definition in a multiplicative form where the product functions are one-dimensional functions of parameters. Such representation advantageously differs from classical representation of approximation results by visualization and convenience and by possibility to investigate function sensitivity to the parameter variation. The obtained model provides errors of 5-7%. The results of qualitative comparison of volumetric functions of the tangential stress intensity obtained by the successive approximation method with the representation of numerical results of solving the chosen classical problem presented. Mathematical models of the tangential stresses intensity function in vicinity of a roadway in analytical form are obtained. It is proposed to use this method for representing mathematical models in analytical form and determining function sensitivity to the parameter variation in the problems of geotechnical mechanics. The effectiveness of the method increases when analyzing results of multiparametric problems.