Thermal–Mechanical Coupling Model of Open-Ended Microwave-Induced Borehole Fracturing of Coal and Rock

Microwave-induced borehole fracturing efficiently thermally fractures coal and rock in deep geological engineering. To elucidate the mechanism of microwave-induced borehole fracturing, this study proposes two boundary conditions: laboratory-scale conditions and engineering-scale conditions. The coal and rock surrounding the borehole are modeled using H–C and H–C–U thermal–mechanical coupling frameworks, based on these conditions. We derived analytical solutions for the stress distribution around a borehole under open-ended microwave irradiation and validated by numerical simulations and laboratory experiments. In addition, an analytical analysis of the model was conducted, introducing a factor for quick assessment of the difficulty of fracture initiation in coal and rock. The findings show that during microwave-induced borehole fracturing, radial stress around the borehole remains compressive, while tangential stress transitions from compression to tension within the temperature-changing zone. Thermal fracturing primarily occurs due to tangential tensile stress, with fracture initiation most likely at the outer boundary of the temperature-changing zone, propagating radially toward the borehole. An analytical analysis suggested that smaller boreholes, higher power, and shorter heating times are more suitable for microwave fracturing. Furthermore, when preexisting large cracks are present near the borehole, the maximum tangential tensile stress increases by 2.25 times. The external stress increases the fracture initiation threshold temperature of coal and rock, with the extent of their influence dependent on the magnitude of the second principal stress. Under similar operating conditions, the fracture initiation threshold temperature of coal and rock is influenced by the Young’s modulus, tensile strength, and thermal expansion coefficient of the coal or rock mass. The model proposed herein can predict the likelihood and location of fracture initiation during microwave-induced borehole fracturing.