Analysis of surrounding rock stress and plastic zone of two-way unequal pressure circular roadway based on complex variable theory

In order to solve the non-axisymmetric elastoplastic problem of circular roadway under bidirectional unequal pressure conditions, the analytical solution of stress and plastic zone of circular roadway is determined.Based on the complex theory, this paper uses the method of conformal transformation in complex variable function to derive the tangential stress equation of surrounding rock in circular roadway in two-way unequal stress field.Furthermore, combined with the Mohr-Coulomb strength criterion, the plastic zone calculation formula of the circular tunnel under the bidirectional unequal pressure condition is obtained and the stress distribution state and the size and shape of the plastic zone under different lateral pressure coefficients are calculated.Based on the specific geological parameters of coal mines, the influence of mechanical properties of different surrounding rocks on the tangential stress distribution and plastic zone around the roadway is analyzed and verified by numerical simulation software FLAC^3D5.0.The analysis results show that the mathematical formula is consistent with the numerical simulation results, which verifies the accuracy of the calculation method.The lateral pressure coefficient and buried depth are the main factors affecting the tangential stress distribution of surrounding rock around the roadway.When the lateral pressure coefficient is greater than 1, the circular tunnel starts to rotate 360° from the surrounding rock of the roof.The tangential stress value is distributed as a sine function, and the lateral pressure coefficient is larger, the curve amplitude is larger.The lateral pressure coefficient, roadway radius and surrounding rock mechanical parameters (cohesion, internal friction) are the main factors affecting the shape and size of the plastic zone of the circular roadway.The lateral pressure coefficient is the decisive factor of the shape of the plastic zone.When the lateral pressure coefficient is 1, the shape of the plastic zone is circular, and the lateral pressure coefficient is not 1.The circular roadway transitions from a circular shape to an elliptical shape, and finally becomes a two-headed “hoist” shape, and its long axis is always parallel to the direction in which the ground stress is small.There is a critical value for the influence of the size of the plastic zone, so that the circular roadway does not form a closed plastic zone.