Mechanism of Elastic–Plastic Crack Initiation in Unsaturated Rock Cracks under Gas–Ice Pressure at Low Temperatures

While analyzing the frost heaving and cracking of rock mass in cold regions, it is generally assumed that the cracks are fully saturated. However, rock mass cracks are often in an unsaturated state in actual engineering practice. Upon moisture freezing, the volume of ice increases, the volume of gas decreases, and the gas pressure increases, while the crack walls are subjected to gas pressure, freezing pressure, and the frictional force of the ice, resulting in complex stress conditions. In this paper, the mechanism of crack initiation in unsaturated rock cracks under the influence of gas–ice pressure is investigated. Assuming a small yield range, the calculation formulae for gas pressure after freezing, plastic zone, stress intensity factor, crack initiation angle, and crack initiation stress were derived from the complex variable function and elastic–plastic crack mechanics theory. Critical parameters such as freezing temperature Ti, volume ratio of filling water sw, and crack shape were analyzed and discussed. The results showed that effective gas pressure (>1 atm) is generated after freezing only when sw>0.7; the lower the Ti, the smaller the gas pressure after freezing. Further, the more the crack shape tends toward a circular shape, the easier it is to generate effective gas pressure after freezing, whereas the lower the Ti, the more the crack shape tends toward an elliptical shape. Also, the smaller the Ti, the larger the crack initiation angle, while changes in sw and crack shape have almost no effect on the crack initiation angle.