分形岩石裂隙中渗流扩散运动的试验研究

Experimental study on seepage diffusion movement in fractal rock fractures

由于存在大量粗糙不规则裂隙,使得岩体中流体运动极为复杂。针对天然粗糙岩石裂隙渗流试验存在物理模型隐蔽性和不可重复性等难点,基于三维Weierstrass-Mandelbrot分形函数构建了粗糙节理面的裂隙通道,采用3D打印技术获得了透明精细的裂隙模型,使用微流体控制仪研究了不同试验条件下的裂隙渗流扩散运动,分析了裂隙通道流量与压力水头、裂隙宽度和分形维数之间的关系。研究结果表明:与平行板立方定律近似,在分形裂隙中,裂隙通道流量与压力水头成线性关系;单宽流量与裂隙通道的宽度成近似的三次方关系;考虑分形维数影响时,相同条件下流过裂隙通道的流量随着分形维数的增加而增加;粗糙裂隙渗流立方定律可采用与分形维数相关的幂指数函数进行修正。

The fluid movement in rock mass is extremely complicated due to the existence of a large number of rough and irregular fractures.To address the difficulties such as concealment and non-repeatability of physical model in natural rough rock fissure seepage tests,a fissure channel with rough joint surface was constructed based on a three-dimensional Weierstrass-Mandelbrot fractal function.Using 3D printing technique,a transparent and refined fracture channel model was obtained,and the fracture seepage diffusion movements under different conditions were studied by using microfluidic control instruments.The relationships between the discharge of fracture channel and the pressure head,the fracture width and the fractal dimension were analyzed.The results show that in fractal fractures,the discharge of fracture channel is linear with the pressure head;the single-wide discharge is approximately cubic with the width of the fracture channel,which is similar to the parallel plate cubic law.Considering the influence of fractal dimension,the discharge through the fracture channel increases with the increase of fractal dimension.The cubic law of seepage in rough fractures can be modified by the power exponent function related to the fractal dimension.