Analysis of Interference Effects and Calculation Model for Crack Initiation Strength in X-Type Jointed Rock Mass After Freeze–Thaw Cycles

Rock masses characterized by X-type joints are prevalent in cold region rock engineering projects. A precise understanding of the mechanical mechanisms governing the fracture initiation strength of these jointed rock masses after experiencing freeze–thaw damage is paramount for ensuring the safety and stability of associated engineering structures. Leveraging the mutual constraint relationship between the displacements at the tips of intersecting joints under compressive shear conditions, a computational approach has been developed to determine the stress intensity factor at the tip of the main joint, taking into account the interference effects arising from both main and subjoints. Furthermore, the fine-grained defects within the rock mass are abstracted as elliptical microcracks, and deterioration equations for rock cohesion and fracture toughness under freeze–thaw cycling are derived using frost heave theory. Taking into account the mutual interference effects between main and subjoints, as well as the degradation of rock mechanical properties caused by freeze–thaw cycles, a computational approach for determining the initiation strength of X-type jointed rock masses has been developed. The validity of this method has been confirmed through rigorous model testing. The findings reveal that the wing cracks in X-type jointed rock masses predominantly propagate along the tips of the main joints, while the extension of subjoints is constrained. When the X-joints have the same inclination, the initiation strength of the subjoint exceeds that of the single-joint rock mass when its inclination is less than the main joint’s but is lower when the subjoint’s inclination exceeds that of the main joint. The interference effect between oppositely inclined intersecting joints enhances the initiation strength of the rock mass, with the maximum occurring when the subjoint is at an inclination of 120°. When the freezing time is less than 18 h and the temperature is below −16°C, variations in both time and temperature are more sensitive in affecting the initiation strength of the X-jointed rock mass. Rocks with a high elastic modulus and low tensile strength experience a greater rate of freeze–thaw damage, and brittle rocks are more susceptible to frost heaving failure.