Modeling of Temperature-Dependent Mode I Fracture Toughness in Rock Materials
摘要
Understanding the fracture behavior of rocks under high temperatures is crucial for the safety of rock engineering projects such as geothermal energy extraction from hot, dry rock. Model I fracture toughness is a key parameter that characterizes the capacity of a rock to withstand crack initiation and extension, which is significantly affected by temperature. However, it is a tough challenge to obtain the fracture toughness of rock materials at elevated temperatures conveniently. In this study, from the perspective of energy equivalence, the maximum energy storage density for failure of rock materials is proposed, and a temperature-dependent Model I fracture toughness theoretical characterization model is developed. The model establishes a quantitative relationship between parameters, such as temperature, fracture toughness, Young’s modulus, Poisson’s ratio, characteristic length, and melting point without fitting experimental data. Since experimental data, such as Young’s modulus can be conveniently obtained by nondestructive experiments, the model can accurately predict the fracture toughness of rocks at elevated temperatures without the need for destructive fracture toughness experiments at the corresponding temperatures. The accuracy of the model is verified with 11 sets of experimental data at different temperatures. This model can serve as a novel method for evaluating the properties of rocks at high temperatures, as its utilization circumvents the need for inconvenient and destructive experiments conducted at elevated temperatures. This study offers theoretical insights for analyzing the safety and stability of engineering structures.