Mathematical Problems in Engineering

Volume 2017, Article ID 6431690, 12 pages

https://doi.org/10.1155/2017/6431690

## Theoretical and Experimental Investigation of Characteristics of Single Fracture Stress-Seepage Coupling considering Microroughness

^{1}School of Civil Engineering, Shandong University Jinan, Shandong 250061, China^{2}Key Laboratory of Disaster Prevention and Reduction of Civil Engineering in Shandong Province, Qingdao, Shandong 266590, China^{3}School of Civil Engineering and Architecture, Shandong University of Science and Technology Qingdao, Shandong 266590, China

Correspondence should be addressed to Chao Jia; nc.ude.uds@oahcaij

Received 7 April 2017; Accepted 28 May 2017; Published 19 July 2017

Academic Editor: Mohammed Nouari

Copyright © 2017 Shengtong Di et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Based on the results of the test among the joint roughness coefficient (JRC) of rock fracture, mechanical aperture, and hydraulic aperture proposed by Barton, this paper deduces and proposes a permeability coefficient formula of single fracture stress-seepage coupling considering microroughness by the introduction of effect variables considering the microparticle size and structural morphology of facture surface. Quasi-sandstone fracture of different particle size is made by the laboratory test, and the respective modification is made on the coupled shear-seepage test system of JAW-600 rock. Under this condition, the laboratory test of stress-seepage coupling of fracture of different particle size is carried out. The test results show that, for the different particle-sized fracture surface of the same JRC, the permeability coefficient is different, which means the smaller particle size, the smaller permeability coefficient, and the larger particle size, the larger permeability coefficient; with the increase of cranny hydraulic pressure, the permeability coefficient increases exponentially, and under the same cranny hydraulic pressure, there is relation of power function between the permeability coefficient and normal stress. Meanwhile, according to the theoretical formula, the microroughness coefficient of the fractures with different particle size is obtained by the calculation, and its accuracy and validity are verified by experiments. The theoretical verification values are in good agreement with the measured values.

#### 1. Introduction

At present, with the continuous development of national economic construction, as a result of the unceasing extending in such project fields as the mining, tunnels, water conservancy and hydropower, nuclear waste repository, and foundation engineering, the development level of underground space is increasing day by day, and the confronted engineering problems are becoming more and more complicated. As a complex media in almost all geotechnical engineering fields, with the jointed rock mass, which exists in a large number of fractures and microfractures and other joints, under the action of geological structure and human activities, these joints not only reduce the strength of rock mass greatly, but also constitute an important channel for groundwater to flow in rock mass. For the seepage hydraulic pressure, whose main source is the underground confined water, under the different circumstances of water storage environment and stress, it has different external impact force and permeability effect on the crack structure of the rock mass, and the existing structures of the fractures are destroyed; and the change of the fissure structure will cause the change of the permeability channel, which will affect the stress distribution of the rock itself, and the new secondary cracks will be generated further. The interaction in which the seepage field of fissured rock mass can be influenced by the stress environment and the stress distribution can be influenced by changes of the seepage field is called stress-seepage coupling. The coupling feature is one of the important features of rock mass mechanics. After the dam-break of the Malpasset Dam in France (1959) and the landslide of the Vaiont Dam in Italy (1963), the problem gradually draws people’s attention and a large number of studies [1] are carried out.

As one of the key fundamental topics in the research field of geotechnical engineering, single fracture stress-seepage coupling has been studied through a lot of theoretical and experimental researches from many aspects by many research scholars at home and abroad. Bandis et al. establish the relationship between the fracture closure and stress, respectively, through the experiment [2–5]. Barton and Choubey divide all the joint surfaces into 10 levels from smooth to rough according to their roughness by analyzing the undulating roughness of 136 joint surfaces, where JRC = 0–20, and present the typical roughness profile [6]. Barton proposes the relationship among the joint roughness coefficient (JRC), the hydraulic aperture, and the mechanical aperture [7] by a large number of experiments, but the formula can only be limited to the occasions where the mechanical aperture is larger than the hydraulic aperture, and the unit of them is micron-sized. Lomize et al. have carried out groundbreaking experiments on the permeability law of fracture and establish the cubic law that the seepage flux and the fracture aperture are cubically proportioned [8–10], which lay the foundation of the permeability law of fracture. After studying the microfracture (10–100 *μ*m) and the extreme microfracture (0.25–4.3 *μ*m), Romm proposed that the cubic law will always be established, as long as the fracture aperture is bigger than 0.2 *μ*m [9]. However, the real fractures are rough, and then, many researchers have done a lot of experiments on the roughness of fracture surfaces, and the cubic law was amended [11–17]. In the case of single fracture stress-seepage coupling, many scholars establish the relationship between the permeability coefficient and the stress from the perspective of the seepage experiments or the fracture deformation [18–30]. This paper summarizes the domestic and foreign scholars’ research results about the single fracture roughness, the relationship between the fracture deformation and the stress, and stress-seepage coupling experiments that all of them basically adopt the natural test pieces splitting or the artificial normal fracture and rarely involve the studies considering the differences in features and laws of the seepage capability due to the differences of microparticles and their structure of the surface.

Therefore, in order to investigate the effect of the microparticle size and structure on the seepage capability of fracture, this paper tries to deduce the theoretical formula of the permeability coefficient of single fracture surfaces under the coupling of normal stress and the cranny hydraulic pressure by considering the influencing factors of the microparticle size of fracture surfaces and introducing the microroughness coefficient on the basis of results obtained by Barton in 1982 through lots of experiments. Then the fractures of different particle size are prepared in the laboratory based on the same JRC for the use of simulating the different microroughness; the stress-seepage coupling tests are carried out, respectively, to obtain the permeability coefficient of fracture surfaces with different particle size, and corresponding microroughness coefficients are calculated. Finally, the accuracy and validity of the seepage theoretical formula considering the influence of microroughness are verified through parallel tests. This study is a supplement to the theory of fracture stress-seepage coupling for the jointed rock mass, and it also has a great theoretical guiding significance for the phenomenon of microfracture seepage in geotechnical engineering field, which will be the important reference for the intensive study of the seepage law of microfracture surfaces in the future.

#### 2. Theory of Stress-Seepage Coupling considering Microroughness

It is assumed that the flow condition of water in the factures is laminar flow; the water is incompressible and viscous in the process; the water flow only seeps along fracture surfaces without other loss of flow; the cranny hydraulic pressure acting on fracture surfaces is regarded as the average head pressure at the inlet and outlet ends.

According to the constitutive equation of fracture deformation of jointed rock mass [4], the fracture deformation can be expressed aswhere is the maximum compression deformation of fractures, is the normal load acting on fracture surfaces, and is the normal stiffness of the fracture surface.

Therefore, the mechanical aperture of the fracture surface is

In 1982, considering the condition of normal stress loading, Barton obtains the relationship among the equivalent hydraulic aperture, the mechanical aperture, and the joint roughness coefficient (JRC) based on a large number of test results [7]:

However, the formula only involves the macroroughness coefficient of the fracture, strictly speaking, the waviness of the fracture, without considering the viscous effect of the geometric size and combination mode of the microparticles of the fracture surface on the water flow. Some scholars at home and abroad have proposed some modified formulas for the Barton model, but all of them only consider the occasions of different JRC but not the influence of the particle size and distribution of fracture particles on the seepage capacity of fracture surfaces. The microroughness is the minimum level of rough and undulation form of the fracture surface to reflect the sublevel geometric characteristics on the surface of the peak valley and the concrete distribution manifestation of mineral particles or tiny crystals on joints surface, while the essential features of microroughness depend on the component, structure size, crystal form, and combination of the mineral crystals of the rock on the fracture surface and its exposure on the fracture surface [31].

Introduce the microroughness coefficient that expresses the microgeometric characteristics of the fracture surface to measure the influence of different particle size and distribution of fracture particles of the fracture surface on the viscous effect of the water flow, and the value can be calculated by the stress-seepage coupling test. Among them, , is the microroughness of the fracture surface of jointed rock mass used in the test, and the value relies on the particle size and distribution of the component particles of fracture; is the microroughness of test piece in the experiments adopted by Barton and regarded as the datum reference; and both are functions related to the microparticle size and distribution of the fracture surface.

Therefore, formula (3) can be transformed into

Substitute the mechanical aperture formula (2) into formula (4) and get the formula

Substitute formula (5) into the cubic law, and then get the permeability coefficient formula that considers the microroughness as follows:where is the initial aperture of the fracture surface; is the normal stiffness of the fracture surface; is the normal load acting on fracture surfaces; is the microroughness coefficient related to the particle size and distribution of the fracture surface; is the viscosity coefficient of water flow movement; JRC is the joint roughness coefficient of rock fracture.

Formula (6) can be analyzed as follows: the permeability coefficient of the fracture is equal to the product of , the initial permeability coefficient term considering JRC and microroughness, and , and the impact term decreased in the negative exponential law. Among them, when the value of is smaller than , there is the approximate simplification [5]; therefore, formula (6) can be written into

In the formula, is the normal deformation of the changes of permeability coefficient caused by the fracture surface.

In order to determine the amount of deformation of the fracture surface under the combined action of normal load and cranny hydraulic pressure, it is possible to calculate the change of fracture aperture more easily through indoor experiment; therefore, the following calculation is performed. Figure 1 shows the stress-seepage coupling calculation model of fracture rock masses under the condition of the normal load . When adding the hydraulic pressure along the side of the fracture, the total displacement of the jointed rock mass () is equal to the sum of the fracture displacement () and the displacement of the rock (). The fracture displacement can be expressed as