Accurate determination of the surface roughness is of significant importance in estimating the mechanical and hydraulic behaviors of rock joints. The correlation between joint roughness coefficient (JRC) and various statistical roughness parameters calculated from digitized Barton’s roughness profiles was explored with Pearson’s correlation coefficient method. The results show the strongest correlation between the standard deviation of the roughness angle and JRC following an excellent linear relationship. In addition, the correlation in the JRC with textural parameters is better than its correlation with amplitude parameters. Twenty-nine rock joint surfaces from fine sandstone, coarse sandstone and granite joint samples with a wide range of surface morphology were digitized using a high-resolution 3D scanner instrument. Further, the statistical roughness parameter values were calculated for each joint profile at eight different sampling intervals for sensitivity analysis of these statistical roughness parameters with regard to the sampling interval. The result indicated that textural parameters generally have a certain degree of dependency on sampling interval, following a power-law relationship. Specifically, when the sampling interval increases, the structure function value increases whereas it decreases for other textural parameters. In contrast, the dependence of the amplitude parameters on the sampling interval is not significant.

The mechanical evolution of coal is evident when the pore pressure and the surrounding stress alone influence it. However, the evolution of the mechanical response of saturated coal under the coupling effect of pore pressure and confining pressure needs further investigation. This study identifies the mechanical behaviors of burst tendency dry and saturated coal under the stress condition where confining and pore pressure simultaneously increase but keep the constant difference by conducting a series of triaxial compressions on high burst tendency dry and saturated coal samples. The results show that the elastic modulus (E) and strength (σ_peak) of dry coal increase from 3.4 to 4.8 GPa and 78.5 to 92.6 MPa, respectively, and the macro shear failure angle decreases from 64.2° to 56.5° when the confining pressure increases from 9 to 15 MPa. However, these parameters show the opposite evolution law when the pore pressure increases. Furthermore, the E and σ_peak of saturated coal decrease from 3.84 to 2.75 GPa and 73.4 to 60.3 MPa, respectively, and the macro shear failure angle of saturated coal increases from 64.7° to 72.4° when the confining pressure and pore pressure increase simultaneously. The coefficient μ is proposed to reveal the evolution of strength at the effective confining pressure. Furthermore, the Mohr–Coulomb failure criterion, including μ, is ameliorated for application in coal under pore pressure conditions. In addition, a model was developed to reveal the effect of a pore-rich layer on the angle of macrocracks, which was confirmed by acoustic emission. The research reveals the mechanical behavior of coal under high pore pressure. Improved Mohr–Coulomb criterion criteria provide new guidance and vision for the analysis of coal instability in high pore pressure coal seams.

Equivalent hydraulic aperture and fracture surface roughness are two significant factors affecting the fluid flow behaviors in rock fractures. To understand the role of fracture surface roughness and aperture in the fluid flow through 3D self-affine rough fractures, roughness fracture surfaces with joint roughness coefficients equal to 2.5, 7.5, 12.5, and 17.5 were established, and the Navier–Stokes equation was used to compute the fluid flow in these 3D self-affine rough fractures with a mechanical aperture increase from 0.2 mm to 0.8 mm with a gradient of 0.2 mm. The results show that when the fracture mechanical aperture is 0.2 mm, the impact of fracture surface roughness on fluid flow is considerable, while this effect decreases obviously with the increase of fracture mechanical aperture. Comparing the permeability obtained by the Navier–Stokes equation with the cube law under different hydraulic gradients, we found that their deviation increased with the increase of hydraulic gradients. This allows for the definition of a critical hydraulic gradient (), below which the permeability can be properly predicted using the cubic law for its simplicity, and above which Forchheimer’s equation should be applied, and Forchheimer’s coefficients , , and can be calculated by the prediction equations established in this study.

Geothermal recovery involves a coupled thermo-hydro-mechanical (THM) process in fractured rocks. A fluid transient equilibrium equation, considering thermal conduction, convection, and heat exchange, is established. The evolution of the reservoir permeability and the variance in the fracture aperture due to a change in the stress field are derived simultaneously. THM coupling is accomplished through iterative hydromechanical and thermo-hydro processes. To overcome the difficulty of geometric discretization, a three-dimensional THM coupler model embedded with discrete fracture networks, using a zero-thickness surface and line elements to simulate fractures and injection/production wells, is established to evaluate the geothermal production. The reliability of the method is verified by a case study. Then, this method is applied to evaluate the influence of the geometric topological characteristics of fracture networks and the fracture aperture on the reservoir temperature evolution and heat extraction effectiveness. The results show that the power generation efficiency and geothermal depletion rate are significantly affected by the injection–production pressure. Injection wells and production wells with pressures higher than the initial fluid pressure in the fractures can be used to significantly increase power generation, but the consumption of geothermal energy and loss of efficiency are significant and rapid. To achieve better benefits for the geothermal recovery system, an optimization algorithm based on simultaneous perturbation stochastic approximation (SPSA) is proposed; it takes the power generation efficiency as the objective function, and the corresponding program is developed using MATLAB to optimize the position and pressure values for each production well. The results show that the heat transfer for the entire EGS reservoir becomes more uniform after optimization, and the heat transfer efficiency is greatly improved.

Understanding the fluid pattern is of special significance for estimating the hydraulic conductivity of fractured rock masses. The nonlinearity of fluid flow in discrete fracture networks (DFNs) originates from inertial effects and is enhanced by complex geometric topologies, which produces additional viscous friction and is subject to inertia effects, consequently transitioning the fluid to the nonlinear flow regime. Therefore, it is important to obtain the critical conditions for the transition of a fluid from laminar to turbulent flow. To investigate the role of fracture aperture and fracture intersection on the onset of the transition of a fluid to nonlinear flow in fractured rocks, the fluid dynamic computation was performed by solving Navier–Stokes (N–S) equations in DFN models. The results show that the flow flux initially linearly correlates with the hydraulic gradient ($J$) and the permeability of DFNs initially remains constant. As the hydraulic gradient increases, the flow flux presents a strong nonlinear relationship with the hydraulic gradient, and the permeability decreases dramatically. In particular, significant inertial effects appear earlier with a large fracture aperture or a dense fracture intersection. A critical hydraulic gradient ($J_c$) is proposed to judge the onset of nonlinear flow. The mathematical expression of $J_c$ and Forchheimer coefficients A and B involving the fracture aperture and fracture intersection density is established through a multiple regression algorithm. Finally, the reliability of the predictive model was verified by comparing the results of the prediction and fluid dynamic computation of a series of DFN models with well-known geometric distributions. The consistency of the fitted equations and a correlation coefficient greater than 0.9 between them indicate that the predictive model proposed in this study is reliable.