A wing-crack extension model for tensile response of saturated rocks under coupled static-dynamic loading

Saturated rocks, widely existing in various deep underground engineering, are likely to be encountered coupled static-dynamic loading. It is thus vital to acquire the combined effect of water saturation and static pre-tension on the dynamic tensile strength, and establish a reasonable crack extension model for describing the fracturing mechanism of saturated rocks under coupled static-dynamic tension. In this study, from the perspective of meso-mechanics, the relationship between pore water pressure and static pre-tension loading are first deduced, and then the analytic solution of stress field of elliptical crack orifice under coupled pore water pressure and far-field stress is solved using complex function. The effect of pore water pressure is considered into Griffith theory, and the most dangerous fracture azimuth angle of elliptical crack in rocks under combined far-field stress and pore water pressure are determined. Second, the length of fracture process zone of initial crack in saturated rocks under static pre-loading is estimated based on Schmidt's maximum tensile stress criterion. Finally, a wing-crack extension model is proposed to analyze the dynamic fracturing behavior of saturated rocks under pre-tension, and the theoretical calculation formula for tensile strength of saturated rocks under combined static-dynamic loading is obtained. To validate this new model, nine coupled static-dynamic tension tests with different pre-static loading ratio are performed on saturated flattened Brazilian disc (FBD) specimens, in virtue of the split Hopkinson pressure bar (SHPB) specialized with an axial confining apparatus. A rational consistency is observed between the experimental and theoretical results in terms of the dynamic tensile strength of saturated rocks.