岩石裂隙压剪变形破坏与非线性渗流特性

Deformation,Failure and Nonlinear Flow Characteristics of a Fracture Subject to Normal Stress and Shear Displacement

探索岩体中流体的流动机理对解决隧道开挖和地下工程施工过程中的突涌水问题具有重要意义,定量描述岩石单裂隙受压剪共同作用下的渗流特性是理解裂隙渗流机理的基础,但已有研究尚未建立应力、位移、开度、惯性系数等关键控制参数之间的定量关系。本文制作了含单裂隙的花岗岩试样,采用固定剪切位移后逐渐增加法向应力的方式开展变水头渗流试验,得到裂隙渗透率的演化规律;通过高精度3维轮廓仪获取裂隙表面的形貌数据,在自主开发的基于接触力学变分原理框架的裂隙受压变形计算程序的基础上,表征不同剪切错位和不同应力条件下裂隙面的变形特性和内部空腔结构演化规律;提取裂隙开度分布数据,在COMSOL软件中求解Navier–Stocks方程,实施不同剪切位移和受压状态下的裂隙非线性渗流数值模拟;定量分析剪切位移、法向应力、空腔几何特征与非线性渗流控制参数之间的关系。结果表明:试验得到的裂隙表面破坏区域与数值模拟结果基本吻合,验证了裂隙变形计算程序的可靠性。法向应力、剪切位移分别与力学开度呈幂函数递减和指数函数递增的关系,且剪切位移的增加会导致裂隙内的接触面更集中。Forchheimer方程中的惯性系数B和临界水力梯度J_(c)可以定量刻画裂隙的非线性渗流特性,B和J_(c)与剪切位移之间呈幂函数递减关系,且随着剪切位移的增大,J_(c)和B的增加速率和波动范围逐渐降低:当剪切位移从2 mm增加到8 mm时,J_(c)的波动范围从6.10×10^(–3)减少到1.20×10^(–3),降低了80.32%;B的波动范围从2.97×10^(14) Pa·s^(2)·m^(–7)减少到2.43×10^(13) Pa·s^(2)·m^(–7),降低了91.28%。裂隙开度的相对标准偏差RSD与惯性系数B和临界水力梯度J_(c)之间均存在相似的幂函数关系,并据此建立了计算渗流从线性转换为非线性临界点的预测公式。

Exploring the fluid flow mechanism in rock masses is of great significance for preventing water inrush during excavation of underground constructions such as tunnels.Quantitative descriptions of the hydraulic properties of single rock fracture subject to normal stresses and shear displacement are the basis for understanding the coupled hydro-mechanical processes in fractured rock masses;however,the quantitative relationships among stress,deformation,aperture,inertial coefficients have not been developed in previous works.Granite specimens with single fracture were prepared and flow tests with variable water heads were carried out,in which incremental normal stresses were applied at each fixed shear displacement to characterize the evolution of permeability.The surface morphology of fractures was digitalized using a three-dimensional high-resolution scanning system.A self-designed numerical code was employed to calculate the deformation of fractures under normal stresses based on the framework of variational principles in contact mechanics.The fracture deformation and void space variation under different shear displacements and normal stresses were investigated.By extracting the aperture data and solving Navier–Stokes equations using COMSOL software,a series of numerical simulations were performed to investigate the nonlinear flow behavior of fluids within fractures under different shear displacements and normal stresses.The relationships among shear displacement,normal stress,void space distributions and parameters describing the nonlinear flow were quantitatively analyzed.The results showed that the fracture surface damage areas obtained from the experiment agreed well with the numerical simulation results,which verified the reliability of the deformation calculation code.The normal stress and the shear displacement exhibited a decreasing power function and an increasing exponential function with the fracture aperture,respectively.The increase in the shear displacement resulted in the concentration of contact areas.The inertia coefficient B in the Forchheimer equation and the critical hydraulic gradient J_(c) could quantitatively characterize the nonlinear flow behavior.B and J_(c) exhibited decreasing power functions with the shear displacement.The increasing rates and ranges of J_(c) and B decreased gradually as shear advances.When the shear displacement increased from 2 to 8 mm,the range of J_(c) decreased from 6.10×10^(–3) to 1.20×10^(–3) by a rate of 80.32%.The range of B decreased sharply from 2.97×10^(14) Pa·s^(2)·m^(–7) to 2.43×10^(13) Pa·s^(2)·m^(–7) by a rate of 91.28%.A similar power function relationship existed between RSD-B and between RSD-J_(c).Finally,a predictive function was proposed to quantify the onset of nonlinear fluid flow through fractures.