Stability analysis of roadway surrounding rock based on complex variable function theory

In view of the analytical problem of the plastic zone of the surrounding rock in the semi-circular arched roadway with two-way unequal pressure straight walls, based on the Mohr-Coulomb strength criterion, the non-circular elastic zone of the physical plane was mapped to the image plane by the method of conformal transformation in the complex variable function. The problem of determining the boundary of the elastic-plastic region was transformed into the problem of solving the coefficients of the mapping function.The complex function solution of the surrounding rock stress of the roadway and the range of the surrounding plastic zone of the roadway were obtained, and the accuracy of the theoretical calculation was verified by FLAC3D numerical simulation. The research results show that the theoretical calculation formula of the plastic zone range of the straight semi-circular arched roadway can be obtained accurately by the complex variable function theory. Combined with the formula, it can be found that the influencing factors affecting the development of the surrounding rock plastic zone in the semicircular arched roadway with straight walls are the size of the roadway section (including the width of the roadway, the height of the straight wall and the arch height), the vertical stress, the lateral pressure coefficient, the cohesion and the size of the internal friction angle. The theory was applied to the calculation and analysis of engineering cases,and the single factor analysis method was used to carry out numerical simulation analysis on the cohesion force and internal friction angle, and the data of the numerical simulation test was extracted for comparison and analysis.It can be concluded that although there are errors in the results of theoretical calculations and numerical simulations, it can reflect the distribution of the surrounding plastic zone of semi-circular arched roadways in straight walls. When the cohesion and internal friction angle increase, the roadway presents similar elliptical failure. With the increase of cohesion and internal friction angle, the reduction of the plastic zone of the roadway decreases, and when the horizontal stress is greater than the vertical stress, the the range of the plastic zone in the vertical direction varies greatly.