The complex fracture network in unconventional oil and gas reservoirs is the main channel for the fluid flow, and effective prediction of fracture network permeability is the basis for further accurate assessment of oil and gas productivity. On the basis of the traditional parallel-plate cube law, we introduce the tortuosity fractal dimension DTf to characterize the tortuosity of fractures. Then, combined with fractal theory, a permeability model is derived for a complex tortuous discrete fracture network (DFN). A pixel probability decomposition algorithm is used to generate ten random DFNs that conform to the fractal scale relationship, and the effectiveness of the proposed model is verified by numerical simulation. The fracture geometry parameters are further analyzed and their effect on permeability discussed. The results show that the permeability K of a fracture network increases with an increase in porosity ϕ (0.117–0.292), fractal dimension Df (1.635–1.824), maximum fracture length lmax (3.337–7.472 m), and proportionality coefficient β (0.00108–0.0164), but decreases with the increasing tortuosity fractal dimension DTf (1.0018–1.0196) and fracture dip angle θ (10°–80°). Among these parameters, Df, DTf, and β have the greatest influence on the permeability of the fracture network, followed by θ, lmax, and ϕ.

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The effect of crack angle on energy evolution during sandstone failure subjected to true triaxial cyclic loading and unloading is of great concern. However, the energy consumed in the crack initiation and compaction process is generally referred to the dissipated energy, which is inaccurate. To reveal the energy law in the breaking process of sandstone, a complex cyclic loading and unloading test is carried out on precast angled sandstone samples by employing the triaxial test system. The area integral methodology is exploited to evaluate the evolution of total energy density, elastic energy density, dissipated energy density, and plastic energy density of the rock samples of different crack angles. The variations of these four energy density levels in terms of the number of loading and unloading cycles and the upper limit of stress are explained and discussed. The obtained results reveal that during the entire cycle of loading and unloading, the variations of the above‐mentioned factors of the rock sample fairly do not rely on the crack angle. The energy density increases with the number of cycles, and the total energy density and elastic energy density significantly increase faster than the consumption mode. The growth rate of the dissipative energy density is greater than that of the plastic energy density. Additionally, the aforementioned four energy quantities grow in a quadratic manner as a function of the upper limit of the loading stress. The releasable elastic energy gradually magnifies by increasing the upper limit of the loading stress. The plasticity density first decreases and then increases, reflecting the change law of the irreversible plastic deformation caused by newly developed cracks in the rock sample. The elastic energy density, the fitting coefficient of the dissipated energy density, and the total energy density are employed to define the characteristic coefficients of the rock energy storage and energy dissipation. The results indicate that the larger the rock crack angle, the stronger the energy storage energy and the weaker the energy dissipation capacity. It also explains that how the strength of the rock sample becomes higher as the crack angle increases.

The disturbance due to coal mining causes the surrounding rock to undergo a complex process of stress changes during which the axial pressure and the confining pressure usually change accordingly at the same time. Existing studies generally investigated this process from a static perspective, which was not rigorous. The mechanical characterization of rock is very important to understand the failure of rock mass and the safety of mining during mining disturbance. Based on theoretical analysis, we conducted axial loading and radial unloading tests on the cracked sandstone, which was combined with the ultrasonic testing technology to examine its failure rules and to characterize and analyze its failure process using longitudinal wave velocity. The results demonstrated that crack length and angle had a significant impact on the strength and mechanical properties of sandstone, and the former had a greater impact on the strength of sandstone than the latter. As the crack length increased, the strength, elastic modulus, and deformation modulus of sandstone decreased, and the strength of sandstone increased as the crack angle increased. Elastic and deformation moduli first decreased and then increased. Furthermore, Poisson’s ratio increased slowly, then decreased slowly, and finally increased rapidly as the lateral pressure coefficient diminished, and Poisson’s ratio was more sensitive to changes in the angle. In this study, the change of longitudinal wave velocity reflected the whole process of sandstone failure. When the wave velocity was stable, the rock was at the yield limit point. Moreover, when the wave velocity was unstable, the sandstone was in a progressive failure period, and as a result, the wave velocity decreased and the sandstone cracked.