MATHEMATICAL MODELING AND ALGORITHM FOR CALCULATION OF STABILITY OF REINFORCED CONCRETE TUNNEL LINING BY THE NUMERICAL FINITE ELEMENT METHOD

Abstract

This paper presents an algorithm for mathematical modeling and numerical calculation of the stress-strain state (SSS) of precast reinforced concrete linings for metro tunnels (using Almaty as an example). The calculation is implemented using the finite element method (FEM) with the Gauss-Seidel iterative procedure and the overrelaxation method to accelerate convergence. The mathematical model takes into account static loads from the weight of overlying rocks and seismic effects within a quasi-static approach based on the analysis of longitudinal and shear waves. A methodology for calculating internal forces (bending moments and longitudinal forces) and assessing the lining strength using the ultimate limit state criterion of concrete is described.