a b s t r a c tDriven by the rapid progress in exploiting unconventional energy resources such as shale gas, there is growing interest in hydraulic fracture of brittle yet heterogeneous shales. In particular, how hydraulic cracks interact with natural weak zones in sedimentary rocks to form permeable cracking networks is of significance in engineering practice. Such a process is typically influenced by crack deflection, material anisotropy, crack-surface friction, crustal stresses, and so on. In this work, we extend the He-Hutchinson theory (He and Hutchinson, 1989) to give the closed-form formulae of the strain energy release rate of a hydraulic crack with arbitrary angles with respect to the crustal stress. The critical conditions in which the hydraulic crack deflects into weak interfaces and exhibits a dependence on crack-surface friction and crustal stress anisotropy are given in explicit formulae. We reveal analytically that, with increasing pressure, hydraulic fracture in shales may sequentially undergo friction locking, mode II fracture, and mixed mode fracture. Mode II fracture dominates the hydraulic fracturing process and the impinging angle between the hydraulic crack and the weak interface is the determining factor that accounts for crack deflection; the lower friction coefficient between cracked planes and the greater crustal stress difference favor hydraulic fracturing. In addition to shale fracking, the analytical solution of crack deflection could be used in failure analysis of other brittle media.

In order to reduce the shock and vibration caused by torque disturbance of the gearbox in vehicles equipped with automatic transmission in the process of in situ shift, a novel semi-active hydraulic damping strut is introduced in the powertrain mounting system. The dynamic response evaluation indexes of vehicle in situ shift are put forward, and a 13-degree of freedom vehicle dynamic model including the semi-active hydraulic damping strut is established. The optimized dynamic characteristic parameters are acquired according to the principle of sharing force and the 13-degree of freedom vehicle dynamic model. The dynamic response evaluation indexes with and without the semi-active hydraulic damping strut are calculated using the 13-degree of freedom vehicle dynamic model in the process of in situ shift, and the calculation results show that the vibration of a vehicle can be reduced by the introduction of a semi-active hydraulic damping strut. Experiments are carried out to analyze the vibration response of the vehicle with and without a semi-active hydraulic damping strut, and the results show that the shock and vibration of the vehicle are reduced by introducing the semi-active hydraulic damping strut. The theoretical calculation values of active-side acceleration of the engine mount and torque strut are consistent with the experimental values, which show that the 13-degree of freedom vehicle dynamic model is reasonable.

a b s t r a c tCracks in kerogen-rich shales and other brittle rock-like materials have a tremendous impact on their elastic properties and strength. In this paper, we investigate the effective mechanical properties of shale plates with pre-existing cracks. We employ the extended finite element method (XFEM) to investigate a pre-cracked medium with an elastic, isotropic and brittle shale matrix. We show how the mechanical properties of the orthotropic shale plates are dependent on the crack density and the standard deviation of crack angles. Both the Young's modulus and the Poisson's ratio of the cracked media exhibit a linear dependence on the standard deviation of crack angles, in contrast to the nonlinear dependence of the strength on the angle deviation. Finally, we propose mechanical models to capture the relationship between the mechanical properties and the distribution characteristics of pre-existing cracks in shales. These phenomenological models could be applied to estimate the fracking behavior of shales in engineering practice.