1. School of Mechanics and Civil Engineering,China Uuiversity of Mining and Technology(Beijing),Beijing　 100083,China;2. Sichuan University,Chengdu　 610065,China

岩体裂隙壁面的几何粗糙会引起其中流体的流动非线性,立方定律在分析此类问题时最为简便但却无法适用。旨在基于简单的立方定律,提出一个能够有效适用于岩体裂隙几何粗糙引起非线性流动的分析模型。通过对N-S方程进行量级分析得到了立方定律适用的3个条件:1足够小的壁面粗糙;2足够小的隙宽流程比;3较小的流动惯性。这些条件在粗糙岩体裂隙中难以满足。为了解决这一问题,提出了一个新的粗糙岩体裂隙的离散等效几何模型,该模型中裂隙被合理地"分割",离散成较短的单元段以使得立方定律的适用条件成立;建立了粗糙单元段的平行板等效方法,从而在粗糙单元段内应用立方定律(局部立方定律)。借助几何模型对典型粗糙岩体裂隙进行了离散和数值模拟,发现离散后的裂隙与原裂隙在流动行为上呈现极好的相似性。并基于离散裂隙导出了粗糙岩体裂隙非线性流动的流量公式,最后通过不同岩体粗糙裂隙的流动试验验证了本模型的正确性。该几何模型及其流量公式能为真实粗糙岩体裂隙的非线性流动行为分析提供有效手段。

The wall roughness causes a non-linear flow in rock fractures. For analyzing these issues,the cubic law (CL) is most convenient but maybe not adequate. The authors propose a geometric model applicable for non-linear flow in rock fractures based on the simple CL. An order-of-magnitude analysis of the Navier-Stokes equation yields three conditions for the applicability of the CL:sufficient small roughness, sufficient small ratio between length and ap- erture,and low enough flow inertial effects. These conditions may not be met in many real rock fractures because of their extended length with rough walls. To solve this problem,a new model for rough fractures on the basis of the geom- etry discretizing equivalent is developed. In applying this model to a 2-D rock fracture,the fracture is ‘ broken’ into shorter segments appropriately to meet the CL conditions. The method of rough segment equivalent to parallel plate is derived,and the CL is applied in local segments (local cubic law,LCL),thus a rock fracture can be equivalent to a series of unit parallel plate elements. Moreover,the model has been evaluated with the numerical simulation of a rough fracture,the results show that the equivalent fracture consisting of parallel plates has the similar flow behaviors with the original rough fracture. As a preliminary test,the theoretical flux values,calculated with LCL on the proposed model, are compared with experimental ones for four different fractures and found to be in good agreement. This model,togeth- er with the solution of the flow through it,can be used for modeling the processes which take place in real rock frac- tures.

国家重点基础研究发展计划(973)资助项目(2011CB201201)；中央高校基本科研业务费专项资金资助项目(2015QL06；2010YL06)；

Zhu Hongguang,Yi Cheng,Xie Heping,et al. A new geometric model for non-linear flow in rough-walled fractures based on the cubic law [J]. Journal of China Coal Society,2016,41(4):822-828.