考虑裂隙面粗糙度和开度分形维数的岩石裂隙渗流特性研究

Study on seepage characteristics of rock fractures considering fracture surface roughness and opening fractal dimension

岩石裂隙的粗糙度表征及其渗流特征的描述一直是岩石力学和工程地质领域的难点和热点问题。基于分形理论和流体力学基本原理,首先量化裂隙面的不规则粗糙元素,建立相对粗糙度与分形维数以及裂隙微观结构参数之间的定量关系。然后将粗糙度对渗流的影响转化为裂隙等效开度对流动特性的影响,结合裂隙开度与裂隙长度之间遵循的幂律关系,建立粗糙裂隙的渗透率计算模型。最后研究分形维数和裂隙的几何特征对渗流特性的影响,并使用相关试验数据验证模型的合理性。研究结果表明:裂隙粗糙度对渗流的影响不可忽视,渗透率与裂隙最大开度之间呈平方关系,裂隙开度和粗糙元素几何特征是影响渗流性能的关键因素。建立的渗透率模型不含任何经验常数,避免数据处理的繁琐过程,具有良好的适用性。

The characterization of the roughness of rock fractures and their seepage has been a difficult and hot issue in the field of rock mechanics and engineering geology.Based on the basic principles of fractal theory and hydrodynamics,the irregular roughness elements on the fracture surface were first quantified,and the quantitative relationship between the relative roughness and the fractal dimension as well as the fracture microstructure parameters was established.Then,the effect of the roughness on seepage was transformed into the effect of the equivalent opening of fractures on flow characteristics.Combining the power-law relationship between the fracture opening and the fracture length,a fractal model for calculating the permeability of rough fractures was established.Finally,the effects of fractal dimension and geometric characteristics of fractures on seepage properties were studied,and the rationality of the model was verified using relevant experimental data.The results show that the influence of the fracture roughness on seepage cannot be ignored.There is a square relationship between the permeability and the maximum fracture opening,and the fracture opening and geometric characteristics of rough elements are the key factors affecting seepage performance.The proposed permeability model does not contain any empirical constants,which avoids the tedious process of data processing and has better applicability.