Fracture Behavior Investigation of a Typical Sandstone Under Mixed-Mode I/II Loading Using the Notched Deep Beam Bending Method

The brittle fracture behavior of rocks under mixed-mode loading is important in rock engineering. First, a new configuration called the notched deep beam (NDB) specimen was introduced for the fracture testing of rock materials under mixed-mode I/II loading, and a series of finite element analyses were performed to calibrate the dimensionless fracture parameters (i.e., Y _I, Y _II and \(T^{*}\)). The results showed that an NDB specimen subjected to three-point bending is able to generate pure mode I loading, pure mode II loading, and any mixed-mode loading in between. Then, several NDB specimens made of sandstone were used to investigate the brittle fracture behavior of rock under mixed-mode I/II loading. The fracture surfaces were theoretically described using a statistical method, and the results indicated that all the fracture surfaces generated under different mixed-mode loading were statistically identical; to some extent, these results experimentally showed that only tensile fracture occurs under mixed-mode I/II loading. The obtained fracture strengths were then analyzed using several brittle fracture criteria. The empirical criterion, maximum energy release rate criterion, generalized maximum tangential stress (GMTS) criterion, and improved R-criterion accurately predicted the fracture strength envelope of the sandstone. Finally, based on the concepts of point stress and mean stress, the micro-crack zones (MCZs) under different mixed-mode loading were theoretically estimated based on the MTS and GMTS criteria. The critical radius of MCZ in the crack propagation direction was not a constant for all mixed-mode loading conditions regardless of whether the T-stress was considered. This result suggests that the size of the core region used to predict the crack initiation direction and fracture strength based on the GMTS criterion should be chosen more carefully.