Theoretical Analysis of Stress Intensity Factor for Two Asymmetric Cracks Emanating from Water Conveyance Tunnel

The water conveyance tunnel has been widely applied in tunnel engineering, which may be subjected to compressive stress and shear stress from rock and faults, respectively. The internal pressure caused by water in the tunnel will make the appearance of cracks and propagation, resulting in disasters. In order to study the effects of the cracks and compressive stress on the cracked tunnel model, a plane model containing a circular hole with two unequal cracks under the compression loads, shear stress and internal pressure was established in this study. Complex variable function and conformal mapping function were implemented to theoretically derive the stress intensity factors (SIFs) at the crack tip in the rock mass, the numerical simulation was conducted to validate the theoretical solutions. The results indicate that the numerical results using the ABAQUS code were in good agreement with the theoretical solutions. The effects of compressive stress, shear stress, internal pressure, crack length and crack inclination angle on model II SIFs were discussed, the initiation angle and initiation pressure of different rock materials were also studied. When the crack inclination angle changes from 0 degrees to 30 degrees, the tunnel is easily destroyed. With the increase of the right crack length, the increasing rate of the SIFs increases quickly first and then linearly, however, the left crack length has a slight effect on SIFs. When the crack inclination angle is 45 degrees, the crack initiation angle reaches the maximum value.