天然岩石裂隙面粗糙度尺寸效应及方向性研究

Research on Size Effect and Directionality of Roughness of Natural Rock Fracture Surface

为探究岩石裂隙粗糙面尺寸效应及方向性,对立方定律修正公式中表征天然岩石粗糙裂隙性质的粗糙度修正系数C进行分析。采用高精度3D扫描仪扫描天然岩石样品,得到其表面粗糙度数据,结合网络公开发布的高精度粗糙岩石裂隙CT扫描数据,生成空间坐标,采用公式法和数值法计算分析粗糙度修正系数C。根据公式法计算结果得出粗糙度具有尺寸效应;根据数值法结果得出粗糙度具有方向性,且粗糙度方向性可使用张量形式来表达。通过计算粗糙裂隙JRC值、表面及隙宽分形维数对研究结果进行印证,证明裂隙面粗糙度具有尺寸效应和各向异性。进一步研究发现:可采用粗糙度修正系数张量或粗糙度张量结合裂隙平均隙宽,形成单裂隙渗透张量,量化复杂粗糙裂隙网络中模型的粗糙面。

To delve into the size-related effects and directional properties of the roughness on rock fracture surfaces,this paper focus on analyzing the roughness correction coefficient C within the refined formula of the cubic law,as it effectively characterizes the roughness of natural rock fractures.Since Louis first introduced the cubic law,numerous scholars have since proposed numerous modified formulas,including those by Zhang Youtian,Zimmerman,and Xiong et al.Through conversion,we acquire the calculation formula for the roughness correction coefficient and utilize collected natural fractures for related computations.High-precision 3D scanning technology was used to scan natural rock samples and acquire roughness data of fracture surfaces.By combining this data with publicly available high-precision CT scan data of rough rock fractures,we generate spatial coordinates.Both formulaic and numerical methods were used to calculate and analyze the roughness correction coefficient C.Using the formulaic approach,the roughness correction coefficient for sample sizes ranging from 10%to 100%of the fracture surface were calculated and varying results were obtained,which indicates that roughness exhibits a scale effect.According to the numerical method,a well-fitting ellipse was obtained,indicating that the roughness correction coefficient possesses directionality and can be expressed using tensor notation.This conclusion is further supported by calculating the JRC value of rough fractures and their surface and crack width fractal dimensions,revealing that the roughness of fracture surfaces exhibits scale effects and anisotropy.Upon further investigation,it is discovered that the roughness correction coefficient tensor or roughness tensor,when combined with average crack width,can be utilized to form a single crack permeability tensor that quantifies the rough surface in complex rough crack network models.