Fluid Flow Behavior of Sheared Rough Fractures Subjected to Different Stress State

Min Wang,Bing Dai,Qifeng Guo,Yakun Tian,Pengfei Shan

doi:10.3390/cryst11091055

Abstract

The hydraulic properties of fractures are greatly affected by the stress. Knowing the fluid flow behavior of fractures is of great importance to underground engineering construction and environmental safety. The main purpose of this paper is to study the fluid flow characteristics of rough fractures under different stress states. First, rough fracture surfaces were generated by using the corrected successive random addition (SRA) algorithm. Then, the sheared fracture models subjected to different stress condition were obtained under the boundary condition of constant normal stiffness (CNS). Finally, the hydraulic characteristics of the three-dimensional rough rock fractures were analyzed by numerically solving the full Navier–Stokes equation. It has been found that (1) the aperture of fractures all obeys the Gaussian distribution. The dilatancy effect is gradually obvious and aperture becomes larger with the increase of shear displacement. (2) When the initial normal stress increases, the contact area of fracture becomes larger and the reverse flow can be observed around the contact area. (3) The relationship between hydraulic gradient and flowrate exhibits nonlinearity which can be described by the Forchheimer’s law. The linear coefficient a and the nonlinear coefficient b gradually decrease with the increase of shear displacement and finally stabilize. The values of a and b are reduced by 1–2 and 1–3 orders of magnitude respectively during the shear. The critical Reynolds number increases with the increase of shear displacement and decrease as the initial normal stress increases.

Highlights

There are a large number of fractures with different sizes and occurrences in natural rock masses
For deep underground projects and rock slopes reinforced with bolts, the normal stress imposed on the fracture surface changes with shear and the fracture dilatancy is constrained by the surrounding rock
Where vpeak is the peak dilation rate that can be obtained through Equation (6); c1 and c2 are decay constants which can be calculated from experimental data; for rough fractures it is usually assumed that the value of c0 is 0.3 when the shear dilation appears

Summary

Introduction

There are a large number of fractures with different sizes and occurrences in natural rock masses. To consider the influence of fracture geometry on flow characteristics, many scholars have developed different modified cubic law to improve the applicability of the traditional one This was achieved by considering the factors of aperture, roughness, and contact area. For deep underground projects and rock slopes reinforced with bolts, the normal stress imposed on the fracture surface changes with shear and the fracture dilatancy is constrained by the surrounding rock At this time, the conventional constant normal load boundary is no longer applicable, and the constant normal stiffness boundary condition should be adopted [21,22]. Indraratna et al [23] developed a shear test instrument of rock joint based on the condition of CNS and experimentally studied the shear behavior of rough fractures with different initial normal stress. Where ∆x is the interval, M is the number of intervals and zi is the height of surface asperity

Aperture Distribution

Boundary Conditions

Fluid Flow Behavior of Sheared Rough Fractures