Numerical study on mechanical and failure properties of sandstone based on the power-law distribution of pre-crack length

It is of great significance to study the mechanical properties and failure mechanism of the defected rock for geological engineering. The defected sandstone modeling with power-law distribution of pre-cracks was built in this paper by Particle Flow Code software. Then the mechanical properties of sandstone and the corresponding failure process were meticulously analyzed by changing the power-law index (PLI) and the number of pre-cracks (NPC). The results show that (1) With the increase of the PLI, the proportion of prefabricated long cracks gradually decreases. (2) When the NPC is the same, the uniaxial compressive strength (UCS) of sandstone increases with the PLI; while when the PLI is the same, the UCS decreases with the NPC. (3) The damage model of rock strength is established based on the Mori-Tanaka method, which can be used to better describe the strength evolution of damaged rock. (4) The failure mode of the specimen is closely related to the total length of the pre-crack. As the total length of the pre-crack increases, the failure intensity of the specimen gradually becomes weaker. In addition, for the specimens with the total pre-crack length between 0.2-0.55 m, significant lateral expansion occurred during their failure process. (5) For the specimens with smaller PLI in the pre-peak loading process, the concentration of the force field inside is more serious than that of the specimens with larger PLI.