Ubiquitiformal Fracture Energy under Triaxial Compression Incorporating Stress Triaxiality

Most studies on ubiquitiformal fracture energy focus on tensile loading, whereas rock materials in engineering practice are predominantly subjected to compressive and confining stresses. In this paper, the complexity and the upper and lower bound to scale invariance are introduced into the expression of the fracture parameters, and a theoretical expression for fracture energy under triaxial compression is derived. The stress triaxiality is introduced into the calculation of the ubiquitiformal fracture energy, and Method 2 is proposed for the calculation of the ubiquitiformal fracture energy under triaxial compression. The two methods are compared in combined with numerical simulations. The results show that the calculation of the ubiquitiformal fracture energy under both methods is very close to the critical strain energy release rate obtained from the fracture toughness relation. However, method 2 is limited to slate materials, and Method 1 should be used for the calculation of the ubiquitiformal fracture energy under arbitrary materials. Therefore, the fracture toughness of crack initiation can be directly obtained through the ubiquitiform theory, combined with mechanical tests and scanning electron microscope tests, which overcomes the shortcomings of traditional methods that cannot directly measure the fracture toughness.