Mixed-mode (I-II) fracturing is a prominent mechanical characteristic of hydraulic fracture (HF) deflecting propagation. At present, understanding the effect of injection rates on HF deflecting propagation remains challenging and restricts the control of HF deflecting propagation bearing tensile and shear stresses with fluid injection rates. Our recently published experimental results show that the fracture process zone (FPZ) length of mixed-mode (I-II) fractures in rock-like materials increases with the rising quasistatic loading rate. Both the deformation in FPZ and the generation of real fracture surfaces are tensile. On this basis, the rate-dependent mixed-mode (I-II) cohesive fracture model was proposed under quasistatic loading, and a couple of theoretical outcomes were obtained. Under different injection rates, the deflecting HF propagates step-by-step under mixed-mode (I-II) fracturing, and the HF extension path is supposed to be straight in each step. With the increment of injection rate, the increased (tensile) FPZ length is the stable propagation distance of deflecting HF in each step and besides deteriorates the fracture resistance discontinuity of FPZ developing to be a real tensile fracture. Thus, the mixed-mode (I-II) fracture tends to propagate unstably driven by kinetic energy once FPZ develops completely under fast loading. Moreover, two injection rate-dependent (IRD) HF deflecting propagation modes were determined, i.e., the step-by-step stable-propagation and step-by-step unstable propagation modes. HF deflection occurs in the step alternation of fracture propagation. With the increasing fluid injection rate, the increased FPZ length and kinetic energy (from fracture resistance discontinuity) extend the stable and unstable HF propagation distance along the initial direction in an extension step, respectively. Therefore, fast fluid injection improves the HF deflecting propagation radius; i.e., it inhibits the HF deflecting propagation or promotes HF extension along the initially designed direction. The injection rate-dependent HF deflecting propagation modes (based on the proposed model) were validated by further processing of published true triaxial physical simulation tests of hydraulic fracturing. The ordinal response of Fiber Bragg grating sensors embedded along the fracture propagation path, and the continuous fluctuant injecting pressures validate the step-by-step propagation of the hydraulic fracture. The test-measured deflecting HF trajectory indicates that high fluid injection rates remarkably increase the HF deflecting radius, which is consistent with the theoretical analysis in this work. The above findings can provide theoretical bases for controlling the HF deflecting propagation in the surrounding rock of mines and oil-gas reservoirs.
Effect of fluid injection rate on the hydraulic fracture propagation characteristics