Analysis of Elastic-Plastic Crack Initiation and Evolution at the Tip of an Unsaturated Inclined Open Crack under Ice–Gas–Ice Pressure

The surfaces of mountain slopes in high-altitude and cold regions contain numerous microdefects and macrodefects. These exposed cracks on the rock mass surface provide favorable channels for the flow of water and gas. As the external temperature decreases, the outer surface of the crack tends to freeze, trapping internal gas and subjecting the ice to compression, leading to the problem of crack initiation in unsaturated cracks. Under the assumption of small-scale yielding, this study derives calculation formulas for the gas pressure, crack plastic zone, stress intensity factor, and crack initiation strength based on weight functions and the elastic-plastic fracture mechanics theory. The influence of relevant parameters on crack initiation is analyzed. Finally, the theoretical solutions are compared and validated using the phase-field method. The results indicate that during the initial freezing stage, ice growth and subsequent expansion compressing the gas only occur after the freezing depth exceeds a minimum value, lmin. When the gas volume fraction is 0.1, the gas pressure can reach up to 6 MPa. A higher gas volume fraction leads to lower crack initiation stress and a smaller crack initiation angle. Furthermore, a higher gas volume fraction results in more branch cracks during propagation and a larger propagation zone.