Analytical stress solution for rock mass containing two holes based on an improved Schwarz alternating method

In this study, the accuracy and generality of stress calculation for a plate containing double holes via Schwarz alternating method was investigated. The original Schwarz alternating method with inverse mapping function shows a good performance in terms of the stress solution for a plate containing two arched holes. However, for a plate containing two holes with corners, evitable error may be produced during the calculation because of the unsatisfying accuracy of inverse mapping function. This error is particularly obvious in the stress calculation for a plate containing two triangular holes. To address the problem, an improved Schwarz alternating method without the consideration of inverse mapping function was proposed in this study. The coordinate transformation of points around hole boundaries is realized by an optimization method instead of the inverse mapping function, which leads to little error during the calculation and thus improves the stress solution accuracy especially for plates containing holes with corners. With the employment of the improved method, the influences of connecting angle and lateral pressure coefficient on stress solutions for plates containing double U-shaped holes were discussed. In addition, DEM simulations were further conducted to study the influence of stress characteristics on the failure patterns of rock mass. The result shows that the hoop stress linearly relates to lateral pressure coefficient in the elastic plate and fractures always initiate around hole boundaries where high stress concentrates.