Dynamic flexural failure of rocks under hydrostatic pressure: Laboratory test and theoretical modeling

Dynamic flexural failure of rocks is commonly encountered near deep underground openings due to the bending load derived from earthquakes or production blasts in rock engineering. Meanwhile, deep underground rock is also generally subjected to static hydrostatic pressure. Thus, it is desirable to investigate dynamic flexural failure characteristics and mechanisms of rocks under static hydrostatic pressure. In this study, the dynamic flexural tensile strengths of Laurentian granite (LG) under five hydrostatic pressures (i.e., 0 MPa, 5 MPa, 10 MPa, 15 MPa and 20 MPa) were measured by using a triaxial split Hopkinson pressure bar (SHPB) system in combination with the semi-circular bend (SCB) method. The experimental results indicate that dynamic flexural tensile strength under a certain hydrostatic pressure rises with the loading rate, and dynamic flexural tensile strength at a certain loading rate increases with the hydrostatic pressure due to the closure of microcracks in rocks. In addition, an empirical formula is proposed to successfully predict both the rate dependence and the hydrostatic pressure effect on the dynamic flexural tensile strength. Moreover, the parameter in terms of the hydrostatic pressure is first introduced in the two-parameter tensile strength model, which is improved in this study to quantitatively rationalize the discrepancy between the dynamic intrinsic tensile strength and the dynamic flexural tensile strength for rocks under hydrostatic pressures, and to further establish the relationship between the hydrostatic pressure and the characteristic material length δ for rocks. Meanwhile, the characteristic material length is optimized by the particle swarm optimization method and the value of δ decreases with the hydrostatic pressure due to the closure of microcracks and pores. Besides, an equation is established to describe the relation between the hydrostatic pressure and the characteristic material length. In addition, the morphology of the main fracture in the tested SCB specimens is digitized and the fractal dimension is applied to quantitively describe the fracture surfaces roughness. There is no clear trend to indicate the influence of hydrostatic pressure on the surface roughness, whereas there is generally a decrease of fractal dimension with increasing loading rate for LG under each hydrostatic pressure.