In the modified formula for the cubic law, the roughness correction coefficient C serves as a parameter that indicates the characteristics of the roughness of a rock’s surface. In this study, surface data for natural rock samples were acquired through high-precision 3D scanning and combined with publicly accessible CT scan data on rough rock fractures to generate spatial coordinates. The roughness correction coefficient C was calculated and analyzed using both formulaic and numerical methods. The analysis revealed significant effects of scale on the roughness correction coefficient for rock fractures within a size range of 5 to 10 cm (determined based on the actual sample size), with tensile fractures demonstrating greater variations compared to shear fractures. When calculating the roughness correction coefficient on the same fracture surface in different directions, significant directional effects were observed. Furthermore, elliptical fitting demonstrated favorable results. The conclusion drawn was that the roughness correction coefficient for fracture surfaces can be represented effectively using a tensor form, thereby simplifying the expression of directionality. Calculating and analyzing the fractal dimension of a rough surface further confirmed the existence of effects of size on roughness.

The Dahai Pb-Zn mining area is located in the northwestern Pb-Zn district in northeastern Yunnan Province in the Sichuan-Yunnan-Guizhou Pb-Zn metallogenic triangle (SYGT), east of the Xiaojiang fault. Numerous Pb-Zn deposits (spots) occur in clastic rocks in this area. In this study, the Maliping, Laoyingqing, and Jinniuchang Pb-Zn deposits, representative clastic rocks in the Dahai mining area, were selected as research objects. The results of H-O-S-Sr-Pb isotope analyses show that the three deposits mainly formed through the mixing of a basinal brine with a hydrothermal fluid derived from deep within the underlying (deformed) basement, and brines leached organic matter from wall rocks. The δ³⁴S values range from −2.62–30.30‰. The S isotope results show two different sources of reduced S: one in the Laoyingqing deposit derived from the S reduction generated by the pyrolysis of sulfur-bearing organic matter in the carbonaceous slate of the Kunyang Group, and the second in the Maliping and Jinniuchang deposits derived from the S reduction generated by the thermochemical sulfur reduction (TSR) of seawater sulfate in the Lower Cambrian Yuhucun Formation and Sinian Dengying Formation. The Pb isotope results show that the Pb sources of the three deposits are derived from basement rocks (Kunyang Group) with a small portion derived from Devonian–Permian carbonate rocks and Dengying Formation dolomite, both of which have undergone homogenization during mineralization. The Sr content varied from 0.09629 to 0.2523 × 10⁻⁶, and the study shows that the main source of Sr is a mixture of ore-forming fluid flowing through basement rocks (Kunyang Group) and through sedimentary cover. However, most of the Sr in the Maliping deposit is derived from marine carbonate, and in the Laoyingqing deposit, it is provided by basement rocks (Kunyang Group). Based on a comparative study of the deposits, the Pb-Zn deposits in the clastic rocks of the Dahai mining area and the SYGT belong to the same metallogenic system and were formed under the same metallogenic geological background. Finally, a unified metallogenic model of the two types of fluid migration and mixed mineralization of the Pb-Zn deposit in clastic rocks of the Dahai mining area is proposed. The metallogenic model provides a basis for the study of the Pb-Zn metallogenic system and guidance for deep and peripheral prospecting in this area.

The seepage performance of a rock mass mainly depends on the rock fractures developed in it. Numerical calculation method is a common method to study the permeability properties of fractures. Seepage in rock fractures is affected by various factors such as fracture aperture, roughness, and filling, among which aperture and roughness are the two most widely influenced factors. The Navier-Stokes (NS) equation can be solved directly for the seepage flow in rock fractures with good accuracy, but there are problems of large computational volume and slow solution speed. In this paper, the fracture aperture space data is substituted into the local cubic law as an aperture function to form a numerical calculation method for seepage in rough rock fractures, namely, the aperture function method (AFM). Comparing with the physical seepage experiments of rock fractures, the calculation results of AFM will produce a small amount of error under the low Reynolds number condition, but it can greatly improve the calculation efficiency. The high efficiency of calculation makes it possible to apply AFM to the calculation of large-scale 3D rough fracture network models. The pressure drop of fluid in the fracture has viscous pressure drop (VPD) and local pressure drop (LPD). VPD can be calculated using the AFM. After analyzing the results of solving the NS equation for fracture seepage, it is concluded that the LPD includes the pressure drop caused by area crowding in the recirculation zone (RZ), kinetic energy loss in the RZ, kinetic energy loss in the vortices, and other reasons.

The roughness correction factor ( C ) mentioned in the cubic law correction formula is a parameter that reflects the roughness characteristics. In this study, high precision three‐dimensional (3D) scanning was used to scan natural rock samples, and both analytical and numerical simulation methods were employed to investigate the size effect and anisotropy of the C . The results show that C exhibits both size effects and anisotropy. Through ellipse fitting analysis, it was found that the C can be expressed in tensor form. Based on this, a new method for representing the permeability tensor is proposed by combining the roughness correction tensor and the average aperture. By comparing experimental results from 3D printed models, traditional cubic law, corrected cubic law, and Navier–Stokes (N–S) equation simulations, it is demonstrated that the roughness correction tensor, in conjunction with the average aperture, can effectively quantify the permeability characteristics of complex rough fractures. This provides a new quantitative approach for single‐fracture flow studies.