Research on Algorithm and Coupling Damage Model of Rock Under High Temperature and Loading Based on Mohr–Coulomb Criterion

Abstract

For the coupled damage problem caused by the surrounding rock of tunnel under high temperature and external load under fire conditions, an elastoplastic damage model is established based on the Mohr–Coulomb (M-C) criterion and the theory of continuous damage mechanics by introducing high temperature and load coupling damage factors. In order to solve the “singularity” problem of the model in the numerical integration process, the fully implicit return mapping algorithm in the principal stress space is deduced by region and including three steps of elastic prediction, plastic correction and damage correction. The finite element solution program of the model is written in C++ language, and uniaxial compression test and tunnel cavern calculation examples are used to verify and analyze the program calculation results. The results show that the difference between the peak intensity calculated by the model and the peak intensity data of the uniaxial test under each temperature is within 5% and the stress–strain curve calculated by the model is consistent with the overall trend of the test curve. The conclusion that damage around the cavity increases with increasing temperature is obtained by the simulation calculation of the cavern, which verifies the accuracy and feasibility of the model and calculation program. The safety and stability evaluation of the surrounding rock of tunnel under the action of fire is provided with a certain theoretical basis by the research content of this paper.