Analysis of stress intensity factor for a crack emanating from elliptical hole subjected to compressive stress and shear stress

Underground caves often exist in karst areas, which will cause many difficulties in tunnel construction. The underground caves are often subjected to compressive stress, shear stress and internal pressure come from rock, faults and groundwater, respectively. The crack emanating from the cave will propagate under the effect of external forces, leading to the disaster of cave collapse and water gushing. To research the stability of crack emanating from the elliptical cave, a model of a plane containing an elliptical hole with a single crack under the compressive stress, shear stress and internal pressure was established. The theoretical solutions of stress intensity factors (SIFs) for crack tip were derived using complex variable function and conformal mapping function. The theoretical results were compared with the results of numerical simulation to verify the correctness of the theoretical solutions. The effects of crack length, ellipse shape, compressive stress, shear stress, internal pressure and crack inclination angle on SIFs were discussed. We can conclude that when the crack inclination angle is varied from 0 degrees to 30 degrees, the initiation pressure is small, and the cave is easily destroyed by groundwater. The flatter the elliptical hole, the easier the crack propagates. With an increasing of crack length, the value of SIFs at the crack tip increase quickly first and then increase linearly. When the crack inclination angle is 45 degrees, the initiation angle of the crack reaches the maximum value.

Automated summary

This study investigates the stability of cracks in underground caves in karst areas. A model of a plane with an elliptical hole and a single crack under different stresses was established, and theoretical solutions were derived for stress intensity factors. The effects of crack length, ellipse shape, stress, pressure, and inclination angle on the intensity factors were discussed.