Analytical Solution for Stress Distribution around Arbitrary Stopes Using Evolutionary Complex Variable Methods

Abstract

In this study, we proposed an evolutionary complex variable method (ECVM) to find the analytical solution for the stress distribution in an infinite homogeneous, isotropic, and elastic rock mass. This ECVM was a combination of conformal mapping functions, firefly algorithm (FA), and the complex variable theory. Conformal mapping functions were determined by FA to transform arbitrary stope configurations into unit circles. The complex variable theory was then utilized to calculate two complex potential functions, resulting in stress distribution around arbitrary stope configurations solved. A case study involving the analytical solution around rectangular stopes was performed and validated by Abaqus finite-element software. The implementation of the proposed method for arbitrary stope configurations was discussed, and conformal mapping functions for several complex stope configurations were provided. The results showed that there was a good agreement between the analytical solution and numerical modeling. The difference between the analytical solution and Abaqus were mainly around stope corners, which might be because the grid size in Abaqus is not small enough. FA was found to be efficient and advantageous in the determination of conformal mapping functions. The proposed analytical solution has practical significance because it could be used for parameter sensitivity analysis, feasibility studies, and verification of numerical modeling.