Stresses around an underground opening with sharp corners due to non-symmetrical surface load

Abstract

The paper aims at analyzing the stress distribution around an underground opening that is subjected to non-symmetrical surface loading with emphasis on opening shapes with sharp corners and the stress concentrations developed at these locations. The analysis is performed utilizing the BIE method coupled with the Neumann's series. In order to implement this approach, the special recurrent relations for half plane were proven and the modified Shanks transform was incorporated to accelerate the series convergence. To demonstrate the capability of the developed approach, a horseshoe shape opening with sharp corners was investigated and the location and magnitude of the maximum hoop stress was calculated. The dependence of the maximum hoop stress location on the parameters of the surface loading (degree of asymmetry, size of loaded area) and of the opening (the opening height) was studied. It was found that the absolute magnitude of the maximum hoop stress (for all possible surface loading locations) is developed at the roof points when the opening height/width ratio is relatively large or when the pressure loading area is relatively narrow (compared to the roof arch radius), and contrarily, when the opening height/width ratio is relatively small or when the surface pressure is applied to a relatively wide area, the absolute magnitude of the maximum hoop stress is developed at the bottom sharp corner points.