The length of fracture process zone deciphers variations of rock tensile strength

Tensile strength is one of the most critical design factors in many rock engineering projects. However, despite many available testing techniques, an accurate estimation of the true tensile strength of quasi-brittle rock-like materials is yet a controversial problem since it can vary by the shape and size of a test specimen, the adopted test method, and applied loading conditions. Different studies have tried to address this issue by providing (mainly empirical) laws for determining variations of rock tensile strength as a function of a particular test parameter such as specimen size. In this study, however, a new general approach is presented that can decipher the tensile strength variations of rock under various testing conditions. Using coupled Finite Fracture Mechanics (FFM), it is first proved that the length of the Fracture Process Zone (FPZ) can be determined with accuracy and ease using the energy criterion of coupled FFM. Then, the length of FPZ is used in the stress criterion of coupled FFM to determine rock tensile strength. The failure stress of a material is then proved to be mainly a function of the FPZ length following a power law originated from the Linear Elastic Fracture Mechanics (LEFM). The results assist in deciphering variations of rock tensile strength related to the sample size and test method.