基于分形理论的岩体粗糙裂隙中溶质运移预测模型研究

Predictive model for solute transport in a rough rock fracture based on fractal theory

为研究裂隙面粗糙度对粗糙裂隙中溶质运移过程的影响,以及粗糙度对水动力弥散系数D_(L)和溶质运移速度V_(t)的控制作用,基于分形理论计算了不同裂隙的粗糙度和定水头下的水力开度,讨论了裂隙面粗糙度对粗糙裂隙中溶质运移过程的影响以及不同分形维数裂隙的渗流量和流速。通过耦合Navier-Stokes方程和对流−扩散方程(advection-diffusion equation,简称ADE)获得了裂隙中溶质运移穿透曲线,利用ADE经典解析解耦合直接模拟的穿透曲线,得到了水动力弥散系数D_(L)和溶质运移速度V_(t),讨论了D_(L)和V_(t)对溶质的控制作用及其与粗糙度的相关性,建立了基于分形理论的粗糙裂隙中溶质运移预测模型,并将该模型与直接模拟和基于几何特征的预测模型进行了对比验证。研究结果表明:分形维数D和幅度参数K_(v)表征裂隙面粗糙度的效果较好,D_(L)和V_(t)与分形参数DK_(v)的相关性较高,所建立模型对于岩体粗糙裂隙中的溶质运移模拟具有很好的适用性和准确性。

To investigate the effect of fracture surface roughness on solute transport in a rough fracture and the effect on the hydrodynamic dispersion coefficient D_(L)and transport velocity V_(t),roughness and hydraulic aperture of various fractures under constant head were calculated using fractal theory.The study discussed the influence of roughness on solute transport in rough fractures,as well as the seepage flow and solute velocity with different fractal dimensions.Breakthrough curves were generated by integrating the Navier-Stokes equation and the advection-diffusion equation(ADE).The breakthrough curves from direct simulation were coupled using the classical ADE approach.Subsequently,D_(L)and V_(t)were determined.The study explored the control exerted by D_(L)and V_(t)on solutes and their correlation with roughness.A prediction model based on fractal theory for solute transport in rough fractures was established and compared with direct simulation and geometric feature-based models.Results indicate that fractal dimension D and amplitude parameter K_(v)effectively characterize surface roughness,with a strong correlation between D_(L),V_(t),and fractal parameter DK_(v).The established model demonstrates high applicability and accuracy in simulating solute transport in rough fractures.