theoretical and experimental investigation of...

Research ArticleTheoretical and Experimental Investigation ofCharacteristics of Single Fracture Stress-SeepageCoupling considering Microroughness

Shengtong Di,1,2 Chao Jia,1 Weiguo Qiao,2,3 Weijiang Yu,1 and Kang Li1

1School of Civil Engineering, Shandong University Jinan, Shandong 250061, China2Key Laboratory of Disaster Prevention and Reduction of Civil Engineering in Shandong Province, Qingdao, Shandong 266590, China3School of Civil Engineering and Architecture, Shandong University of Science and Technology Qingdao, Shandong 266590, China

Correspondence should be addressed to Chao Jia; [email protected]

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.

Based on the results of the test among the joint roughness coefficient (JRC) of rock fracture, mechanical aperture, and hydraulicaperture proposed by Barton, this paper deduces and proposes a permeability coefficient formula of single fracture stress-seepagecoupling considering microroughness by the introduction of effect variables considering the microparticle size and structuralmorphology of facture surface. Quasi-sandstone fracture of different particle size is made by the laboratory test, and the respectivemodification 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 fracturesurface of the same JRC, the permeability coefficient is different, which means the smaller particle size, the smaller permeabilitycoefficient, and the larger particle size, the larger permeability coefficient; with the increase of cranny hydraulic pressure, thepermeability coefficient increases exponentially, and under the same cranny hydraulic pressure, there is relation of power functionbetween the permeability coefficient and normal stress. Meanwhile, according to the theoretical formula, the microroughnesscoefficient of the fractures with different particle size is obtained by the calculation, and its accuracy and validity are verified byexperiments. The theoretical verification values are in good agreement with the measured values.

1. Introduction

At present, with the continuous development of national eco-nomic construction, as a result of the unceasing extending insuch project fields as the mining, tunnels, water conservancyand hydropower, nuclear waste repository, and foundationengineering, the development level of underground spaceis increasing day by day, and the confronted engineeringproblems are becoming more and more complicated. As acomplex media in almost all geotechnical engineering fields,with the jointed rock mass, which exists in a large numberof fractures and microfractures and other joints, under theaction of geological structure and human activities, thesejoints not only reduce the strength of rock mass greatly, butalso constitute an important channel for groundwater to flow

in rockmass. For the seepage hydraulic pressure, whosemainsource is the underground confinedwater, under the differentcircumstances of water storage environment and stress, it hasdifferent external impact force and permeability effect on thecrack structure of the rock mass, and the existing structuresof the fractures are destroyed; and the change of the fissurestructure 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. Theinteraction in which the seepage field of fissured rock masscan be influenced by the stress environment and the stressdistribution can be influenced by changes of the seepage fieldis called stress-seepage coupling. The coupling feature is oneof the important features of rock mass mechanics. After thedam-break of the Malpasset Dam in France (1959) and the

HindawiMathematical Problems in EngineeringVolume 2017, Article ID 6431690, 12 pageshttps://doi.org/10.1155/2017/6431690

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

2 Mathematical Problems in Engineering

landslide of the Vaiont Dam in Italy (1963), the problemgradually draws people’s attention and a large number ofstudies [1] are carried out.

As one of the key fundamental topics in the research fieldof geotechnical engineering, single fracture stress-seepagecoupling has been studied through a lot of theoretical andexperimental researches frommany aspects bymany researchscholars at home and abroad. Bandis et al. establish the rela-tionship between the fracture closure and stress, respectively,through the experiment [2–5]. Barton and Choubey divideall the joint surfaces into 10 levels from smooth to roughaccording to their roughness by analyzing the undulatingroughness of 136 joint surfaces, where JRC = 0–20, andpresent the typical roughness profile [6]. Barton proposesthe relationship among the joint roughness coefficient (JRC),the hydraulic aperture, and the mechanical aperture [7] bya large number of experiments, but the formula can only belimited to the occasions where the mechanical aperture islarger than the hydraulic aperture, and the unit of them ismicron-sized. Lomize et al. have carried out groundbreakingexperiments on the permeability law of fracture and establishthe cubic law that the seepage flux and the fracture apertureare cubically proportioned [8–10], which lay the founda-tion of the permeability law of fracture. After studying themicrofracture (10–100 𝜇m) and the extreme microfracture(0.25–4.3 𝜇m), Rommproposed that the cubic lawwill alwaysbe established, as long as the fracture aperture is biggerthan 0.2 𝜇m [9]. However, the real fractures are rough,and then, many researchers have done a lot of experimentson the roughness of fracture surfaces, and the cubic lawwas amended [11–17]. In the case of single fracture stress-seepage coupling, many scholars establish the relationshipbetween the permeability coefficient and the stress fromthe perspective of the seepage experiments or the fracturedeformation [18–30]. This paper summarizes the domesticand foreign scholars’ research results about the single fractureroughness, the relationship between the fracture deformationand the stress, and stress-seepage coupling experiments thatall of them basically adopt the natural test pieces splitting orthe artificial normal fracture and rarely involve the studiesconsidering the differences in features and laws of the seepagecapability due to the differences of microparticles and theirstructure of the surface.

Therefore, in order to investigate the effect of themicroparticle size and structure on the seepage capabil-ity of fracture, this paper tries to deduce the theoreticalformula of the permeability coefficient of single fracturesurfaces under the coupling of normal stress and the crannyhydraulic pressure by considering the influencing factors ofthemicroparticle size of fracture surfaces and introducing themicroroughness coefficient on the basis of results obtainedby Barton in 1982 through lots of experiments. Then thefractures of different particle size are prepared in the lab-oratory based on the same JRC for the use of simulatingthe different microroughness; the stress-seepage couplingtests are carried out, respectively, to obtain the permeabilitycoefficient of fracture surfaces with different particle size, andcorresponding microroughness coefficients are calculated.Finally, the accuracy and validity of the seepage theoretical

formula considering the influence of microroughness areverified through parallel tests. This study is a supplementto the theory of fracture stress-seepage coupling for thejointed rock mass, and it also has a great theoretical guidingsignificance for the phenomenon of microfracture seepage ingeotechnical engineering field, which will be the importantreference for the intensive study of the seepage law ofmicrofracture surfaces in the future.

2. Theory of Stress-Seepage Couplingconsidering Microroughness

It is assumed that the flow condition of water in the facturesis laminar flow; the water is incompressible and viscous inthe process; the water flow only seeps along fracture surfaceswithout other loss of flow; the cranny hydraulic pressureacting on fracture surfaces is regarded as the average headpressure at the inlet and outlet ends.

According to the constitutive equation of fracture defor-mation of jointed rock mass [4], the fracture deformation Δ𝑢can be expressed as

Δ𝑢 = 𝜇0 (1 − 𝑒−𝜎𝑓/𝐾𝑛) , (1)

where 𝜇0 is the maximum compression deformation offractures, 𝜎𝑓 is the normal load acting on fracture surfaces,and𝐾𝑛 is the normal stiffness of the fracture surface.

Therefore, themechanical aperture of the fracture surface𝜇 is

𝜇 = 𝜇0𝑒−𝜎𝑓/𝐾𝑛 . (2)

In 1982, considering the condition of normal stress load-ing, Barton obtains the relationship among the equivalenthydraulic aperture, the mechanical aperture, and the jointroughness coefficient (JRC) based on a large number of testresults [7]:

𝑎𝑤 = 𝜇2JRC2.5

. (3)

However, the formula only involves the macroroughnesscoefficient of the fracture, strictly speaking, the waviness ofthe fracture, without considering the viscous effect of thegeometric size and combination mode of the microparticlesof the fracture surface on the water flow. Some scholars athome and abroad have proposed somemodified formulas forthe Bartonmodel, but all of them only consider the occasionsof different JRC but not the influence of the particle sizeand distribution of fracture particles on the seepage capacityof fracture surfaces. The microroughness is the minimumlevel of rough and undulation form of the fracture surface toreflect the sublevel geometric characteristics on the surface ofthe peak valley and the concrete distribution manifestationof mineral particles or tiny crystals on joints surface, whilethe essential features of microroughness depend on thecomponent, structure size, crystal form, and combination ofthe mineral crystals of the rock on the fracture surface and itsexposure on the fracture surface [31].

Mathematical Problems in Engineering 3

Introduce the microroughness coefficient 𝐶𝑚 that ex-presses the microgeometric characteristics of the fracturesurface to measure the influence of different particle size anddistribution of fracture particles of the fracture surface onthe viscous effect of the water flow, and the value can becalculated by the stress-seepage coupling test. Among them,𝐶𝑚 = 𝑅𝑚/𝑅0, 𝑅𝑚 is the microroughness of the fracturesurface of jointed rock mass used in the test, and the valuerelies on the particle size and distribution of the componentparticles of fracture; 𝑅0 is the microroughness of test piecein the experiments adopted by Barton and regarded as thedatum reference; 𝑅𝑚 and 𝑅0 both are functions related to themicroparticle size and distribution of the fracture surface.

Therefore, formula (3) can be transformed into

𝑎𝑤 = 𝜇2𝐶𝑚JRC2.5

. (4)

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

𝑎𝑤 = 𝜇02𝐶𝑚𝑒−2𝜎𝑓/𝐾𝑛JRC2.5

. (5)

Substitute formula (5) into the cubic law, and thenget the permeability coefficient formula that considers themicroroughness as follows:

𝑘𝑓 = 𝑔𝑎𝑤212] = 𝑔𝜇04𝐶𝑚212]JRC5 𝑒−4𝜎𝑓/𝐾𝑛 , (6)

where 𝜇0 is the initial aperture of the fracture surface; 𝐾𝑛 isthe normal stiffness of the fracture surface; 𝜎𝑓 is the normalload acting on fracture surfaces; 𝐶𝑚 is the microroughnesscoefficient related to the particle size and distribution of thefracture surface; ] is the viscosity coefficient of water flowmovement; JRC is the joint roughness coefficient of rockfracture.

Formula (6) can be analyzed as follows: the permeabil-ity coefficient of the fracture is equal to the product of𝑔𝜇04𝐶𝑚2/12]JRC5, the initial permeability coefficient termconsidering JRC and microroughness, and exp(−4𝜎𝑓/𝐾𝑛),and the impact term decreased in the negative exponentiallaw. Among them, when the value of 𝜎𝑓 is smaller than 𝐾𝑛,there is the approximate simplification 𝜎𝑓/𝐾𝑛 = Δ𝑢/𝜇0 = 𝜀𝑛[5]; therefore, formula (6) can be written into

𝑘𝑓 = 𝑔𝑎𝑤212] = 𝑔𝜇04𝐶𝑚212]JRC5 exp (−4𝜀𝑛) . (7)

In the formula, 𝜀𝑛 is the normal deformation of thechanges of permeability coefficient caused by the fracturesurface.

In order to determine the amount of deformation ofthe fracture surface under the combined action of normalload and cranny hydraulic pressure, it is possible to calculatethe change of fracture aperture more easily through indoorexperiment; therefore, the following calculation is performed.Figure 1 shows the stress-seepage coupling calculation model

P

Sr

Sr

0

n

Figure 1: The calculation model of single fracture under stress-seepage coupling.

of fracture rock masses under the condition of the normalload 𝜎𝑛. When adding the hydraulic pressure 𝑃 along theside of the fracture, the total displacement of the jointed rockmass (Δ𝑢𝑡) is equal to the sum of the fracture displacement(Δ𝑢𝑓) and the displacement of the rock (Δ𝑢𝑟). The fracturedisplacement Δ𝑢𝑓 can be expressed as

Δ𝑢𝑓 = Δ𝑢𝑡 − Δ𝑢𝑟. (8)

Supposing the rock thickness is 𝑆𝑟 and the fractureaperture is 𝜇0, the strain can be expressed as

Δ𝑢𝑓 = (2𝑆𝑟 + 𝜇0) 𝜀𝑡 − 2𝑆𝑟𝜀𝑟, (9)

where 𝜀𝑡 and 𝜀𝑟 are the strain of rock masses and rocks,respectively.

The strain of rock masses can be expressed as

𝜀𝑡 = 𝜎𝑛𝐸𝑡 , (10)

where 𝐸𝑡 is the elastic modulus of monolithic rock mass thatincludes the fractures. Considering the effect of the crannyhydraulic pressure, both of it and the normal load can lead tothe compressive deformation of rocks; therefore, the strain ofrocks can be expressed as

𝜀𝑟 = (𝜎𝑛 + Δ𝑝0)𝐸𝑟 . (11)

In formula (11), 𝐸𝑟 is the elastic modulus of rocks. Sub-stitute formulas (10) and (11) into formula (9); we can get theformula

Δ𝑢𝑓 = (2𝑆𝑟 + 𝜇0) 𝜎𝑛𝐸𝑡 − 2𝑆𝑟 (𝜎𝑛 + Δ𝑝0)𝐸𝑟 . (12)

After the arrangement, the formula is

Δ𝑢𝑓 = (2𝑆𝑟 + 𝜇0𝐸𝑡 − 2𝑆𝑟𝐸𝑟 )𝜎𝑛 − 2𝑆𝑟Δ𝑝0𝐸𝑟 . (13)

The fracture strain can be described as

𝜀𝑛 = Δ𝑢𝑓𝜇0 = (2𝑆𝑟 + 𝜇0𝜇0𝐸𝑡 − 2𝑆𝑟𝜇0𝐸𝑟)𝜎𝑛 − 2𝑆𝑟Δ𝑝0𝜇0𝐸𝑟 . (14)


Substitute formula (14) into formula (7); under thecoupling of normal load and the seepage pressure, aftercomprehensively considering the joint roughness coefficientJRC and the microroughness coefficient 𝐶𝑚, the obtainedformula of permeability coefficient 𝑘𝑓 of the single fractureof the jointed rock mass is

𝑘𝑓 = 𝑔𝑎𝑤212] = 𝑔𝜇04𝐶𝑚212]JRC5⋅ exp [8𝑆𝑟Δ𝑝0𝜇0𝐸𝑟 − (8𝑆𝑟 + 4𝜇0𝜇0𝐸𝑡 − 8𝑆𝑟𝜇0𝐸𝑟)𝜎𝑛] .

(15)

Formula (15) is the theoretical mathematical model ofsingle fracture stress-seepage coupling considering micror-oughness, which comprehensively considers the compressivedeformation of the stress and seepage pressure on the fracturesurface, the joint roughness coefficient of the fracture surface(JRC), and the microroughness coefficient of the fracturesurface 𝑅𝑚. At the same time, parameters 𝐸𝑡, 𝐸𝑟, and 𝜇0 canbe calculated by the indoor tests, and they have the generalapplicability.

In the calculation, because formula (3) is the result ofdata fitting law based on a large number of experiments byBarton, and it can only be used in the micron-sized units, inthe real calculation, it is necessary to change the unit; that is,in this step of calculation, the unit should be transformed intomicron-sized unit firstly and changed into the standard unitafter the calculation.

3. Preparation of Fracture Test Pieces andExperimental Work

3.1. Test Principles. We use the steel template of the sameJRC to pour the test pieces of different particle-sized fracturesurface, adopt the same manufacturing process, and carryon maintenance in the same maintenance environment inorder to ensure the same macroroughness. Based on theanalysis of the permeability coefficient in the test results, themicroroughness coefficient of different-particle-sized frac-ture surfaces can be calculated to analyze the effect of micro-roughness on the seepage capability of fracture surfaces.

The following conversion formula is used to calculatethe measured permeability coefficient of the fracture surface;then the permeability coefficient is substituted into formula(15), and the microroughness of particle-sized fracture sur-faces can be calculated. The fracture aperture is expressed asthe hydraulic equivalent aperture.The calculation equation ofthe seepage flow of the single fracture surface is shown in thefollowing equation:

𝑞 = 𝑔𝑤𝑎𝑤3Δ𝐻12]𝐿 . (16)

According to the basic seepage theory of fracture rockmass, the permeability coefficient of the fracture of jointedrock mass can be expressed as

𝑘𝑓 = 𝑔𝑎𝑤212] . (17)

Figure 2: The stress-seepage coupling test system.

Convert formula (16) and substitute it into formula (17);we can get the following formula through conversion:

𝑘𝑓 = 3√ 𝑔𝐿2𝑞2𝛾𝜔212]𝑤2Δ𝑝2 , (18)

where 𝑘𝑓 is the permeability coefficient of the fracture testpiece; 𝑞 is the seepage flow through the fracture surface; 𝐿 isthe path length of the fracture surface where the liquid flows;] is the dynamic viscosity of water; 𝛾𝜔 is the severity of water;𝑤 is the width of the fracture surface where the liquid flows;Δ𝑝 is the difference of seepage pressure of the inlet and outletends.

3.2. Test Instruments and Systems. Thecoupled shear-seepagetest system of JAW-600 rock is adopted in the test. As themost advanced rock shear-seepage test system in China, itconsists of the loading system, the confining pressure system,the hydraulic system, the seepage box, the control system,the computer system, and other components. It can realizethe normal servo controlled test under the conditions ofconstant normal stress, constant normal displacement, andconstant normal stiffness; the seepage test under differentseepage pressures; the test of closure stress-seepage couplingunder the conditions of different seepage pressures; and thetest of shear stress-seepage coupling under the conditions ofdifferent seepage pressures.

The site experiment picture is shown in Figure 2.Considering the purpose of the test, it only involves the

normal load, regardless of the shear loading module; at thesame time, corresponding transformation of the seepage boxis done, the lateral hydraulic sealing devices of the fracturesurface are installed on both sides of the box, and the intakeis connected to the fracture hydraulic device directly throughthe distributive pipe in order to control the hydraulic sealingand to realize the real-time monitoring of the hydraulicpressure to achieve precise control of the sealing crannyhydraulic pressure through computers.

The finished test pieces are combined and assembledaccurately and sealed in a seepage box by a seal ring. Afterthe assembly of the test piece, the cavity will be injectedwith liquid plastic of a certain pressure, and the seal ringunder pressure is closely connected to the surrounding ofthe test piece; thus, the sealing of the test piece and the


Table 1: The specification and mixture ratio of fracture production material.

Material Cement Particle size of sand (mm) Water Water reducer

Specification P.O42.5

Coarse0.8

Medium0.4

Fine0.2 Common DC-WR1

Ratio 0.9 1.8 0.36 0.0135

Table 2: The parameter table of permeability coefficient calculation.

Gravitational acceleration𝐺/(m/s2)Penetrating length𝐿/(m)

Width of fracture𝑤/(m)Unit weight of water𝛾𝜔/(n/m3) Dynamic viscosity of water

]/(m2/s)9.81 0.2 0.1 1𝑒4 1.14𝑒 − 6

seepage box is realized; at the same time, contact surfacesof the upper seal ring and the lower seal ring are closelycontacted under the pressure.The schematic diagram and thesite picture are shown in Figure 3. During the experiment,the lateral hydraulic pressure is applied to the seepage boxto effectively block the fracture part of the anastomotic rockmass. Therefore, the lateral complete sealing of the fracturesurface is realized in the seepage process, and it is for surethat the direction of seepage only takes along the establishedfracture surface.

3.3. Measurement of the Roughness of Fracture Surfaces. Forthe analysis and research of the influence of microroughnesson the seepage ability, the laser tester of the jointed rocksurface and shape produced by the KEYENCE Company isapplied to measure the surface shape of the joint (JRC) afterthe generation of the test piece, of which the accuracy is±20𝜇m and the resolution is 10 𝜇m. During the laser scan-ning, the laser head remains stationary and the platform onwhich the test piece is placed will move automatically in the𝑋𝑌 direction according to the preset path;meanwhile, a com-puter is used to collect and process the data in real time. In thestudy, the distance between the measuring points on the sur-face of all rock test pieces are all 0.2mm in the𝑋𝑌 direction.

3.4. Preparation and Settlement of the Test Pieces. The artifi-cial single fracture rockmass is used as the test piece, of whichthe specification is the 100mm (width) ∗ 100mm (height) ∗200mm(length) cuboid; the group that the Barton roughnesscoefficient JRC = 6–8 recommended by ISRM is selected forthe fracture specification; the numerical control technology isused to process the corresponding steel template, and then thefracture surfaces are made by assembling the steel templateand the molds.

Three kinds of specifications sand of the particle sizeof 0.8mm, 0.4mm, and 0.2mm by the standard screen ofthe laboratory are prepared, and the P.O 42.5 cement, sandof different particles, and the benzene high efficiency waterreducing agent DC-WR1 are chosen as the materials of thetest pieces, of which the ratio is shown in Table 1.

The mold was demolished after the test pieces were madefor 24 hours, and they stay at the curing room of standardtest pieces where the temperature is 20 ± 2∘C and the relative

humidity is over 95% for 28 days. The manufacturing andmaintenance of test pieces are shown in Figure 4.

After the manufacturing and maintenance, the fracturesurface morphology of different particle size is shown inFigure 5.

3.5. Test Scheme and Process. Before starting the test, firstly,the assembled seepage box is installed to the system platformby the lifting appliance, and the water seal confining pressuresystem of the seepage box is connected to the hydraulicloading system; debugging the computer control system, itis necessary to start the test when system shows normal. Atfirst, a normal load is applied to the seepage box to reacha predetermined value; then, water seal pressure (2.5MPa)is applied to reach a steady state; at last, after applying thecranny hydraulic pressure and getting the correspondingdata, the next test is proceeded to be done.

The test sets four groups of different normal load of0.5MPa, 1.0MPa, 1.5MPa, and 2.0MPa, and the loadingis implemented step by step in the condition that theloading rate is 0.1mm/min; meanwhile, under the actionof the normal load of each group, the seepage pressure of0.2MPa, 0.4MPa, 0.6MPa, 0.8MPa, and 1.0MPa is added,respectively, and the water seal confining pressure is keptinvariant during the whole test process.

After the test, firstly, the cranny hydraulic pressure isremoved, then the water seal confining pressure, and the axialload finally.

4. Test Results and Analysis

4.1. Test Results. Formula (18) is used to calculate the per-meability coefficient, and the corresponding parameters arepresented in Table 2, of which the seepage length and fracturewidth are from the size of the sample, and the dynamicviscosity of water calculation parameter is from the reference[25] when the water temperature is 15∘C. After substitutingthe parameters, the formula of permeability coefficient canbe simplified into

𝑘𝑓 = 6.593𝑒6 3√ 𝑞2Δ𝑝2 (cm/s) . (19)


7A

A

65 8

9

10

11

500

190

A-A

12

4

3

2

1

12

11

10

9

8

7

6

5

4

3

2

1

SJH-0-7

SJH-0-6

SJH-3

SJH-0-5

M10-100

SJH-2

SJH-0-4

SJH-1

SJH-0-3

M10-30

SJH-0-2

SJH-0-1

Pressure capsule

Short shear piece

Stationary component

Shear piece

Inner hexagon screw

Ball pad

Pressing plate

Compression component

Slide plate

Inner hexagon screw

Outer plate

Bottom plate

10

2

2

2

2

2

2

1

1

1

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18

Polyurethane rubber

1Cr13

1Cr13

1Cr13

45

45

1Cr13

Num

ber

Code Name MaterialUnitprice Total

WeightNote

Sign Quantity Subarea Change file Signature Date

Stage marker Weight Ratio

HHH

Assembly drawing

SJH-00

A total of 1 piece The 1st piece

Design H Standard-

Approve

Check

Craft

ization

Quan-tity

1 : 2

Figure 3: The seepage box assembly and its diagram.


Figure 4: The process of manufacture and maintenance for quasi-sandstone body crack test pieces.

(a) (b) (c)

Figure 5: The fracture surface morphology of different particle size (from (a) to (c): coarse, medium, and thin).

4.2. Variation Law between Permeability Coefficient andCranny Hydraulic Pressure. The data of seepage flow and thedifference of seepage pressure of each group obtained in thetest is substituted into formula (19); after solving the formula,the value of permeability coefficient of each group in the testis obtained; inducing and analyzing the result, the obtainedrelation curve between the permeability coefficient and thecranny hydraulic pressure is shown in Figure 6.

Through the analysis of Figure 6, it is found that for thefracture surfaces of various particle size, under the samenormal load level, the permeability coefficient and the crannyhydraulic pressure basically present nonlinear relationship.It indicates that with the increase of the cranny hydraulicpressure, the permeability coefficient shows the exponentialgrowth approximately. Besides, with the increase of thenormal stress level, the growth rate is decreasing gradually,and the collectively presented variation law of permeabilitycoefficient among different particle size is the fracture ofcoarse sand greater than the fracture of medium sand greaterthan the fracture of fine sand. It is concluded that the inletof the cranny hydraulic pressure creates the compressioneffect on the fracture surface under the condition of constantnormal stress and causes the additional deformation of the

rock on both sides of the fracture surface, leading to theincreasing of the fracture aperture and the permeabilitycoefficient.

4.3. Variation Law between Permeability Coefficient andNormal Load. For the same cranny hydraulic pressure, thepermeability coefficient is basically in accordance with thenormal load variation. Therefore, taking the case that thecranny hydraulic pressure is 0.5MPa as an example, the varia-tion relationships between different fracture microroughnessand the normal loads are studied, as shown in Figure 7.

It can be seen from the figure that under the samecranny hydraulic pressure (0.5MPa), with the increasing ofthe normal load, the permeability coefficient of the fractureof different particle size shows a decreasing power functionapproximately. At the same time, under the same normalload, the permeability coefficients of different particle-sizedfractures are different. It indicates that the smaller the particlesize, the smaller the permeability coefficient; as the particlesize increases, the permeability coefficient increases. Thereason is that, under the same normal load, the fracturesurface is compressed and deformed, but due to its differentmicroparticle and combining structure, the particle size is


0.1 0.2 0.3 0.4 0.5 0.60.010

0.015

0.020

0.025

0.030

0.035

0.040

Fissure water pressure (MPa)

The p

erm

eabi

lity

coeffi

cien

t (cm

·Ｍ−1)

(The fracture of fine sand)

0.5－０；

1.0－０；

1.5－０；

2.0－０；

0.1 0.2 0.3 0.4 0.5 0.60.015

0.020

0.025

0.030

0.035

0.040

0.045

The p

erm

eabi

lity

coeffi

cien

t (cm

·Ｍ−1)

(The fracture of medium sand)Fissure water pressure (MPa)

0.1 0.2 0.3 0.4 0.5 0.60.020

0.025

0.030

0.035

0.040

0.045

0.050

The p

erm

eabi

lity

coeffi

cien

t (cm

·Ｍ−1)

(The fracture of coarse sand)Fissure water pressure (MPa)

Figure 6: The rule curve between permeability coefficient and cranny hydraulic pressure.


0.5 1.0 1.5 2.0 2.5 3.00.02

0.03

0.04

0.05

0.06

The normal load (MPa)

The p

erm

eabi

lity

coeffi

cien

t (cm

·Ｍ−1) Fissure water ＪＬ？ＭＭＯＬ？ = 0.5－０；

Coarse sandMedium sandFine sand

Figure 7: The rule curve between permeability coefficients andnormal loads.

bigger; the interspace generated between fracture surfacesbecomes bigger; the hindering effect on the water flowbecomes smaller; thus the permeability coefficient becomesbigger. On the contrary, the smaller the particle size, thesmaller the interspace between the fracture surfaces; underthe action of the load, the goodness of fit of the fracturesurface becomes higher, the hindering effect on the waterflow becomes bigger, and thus the permeability coefficientbecomes smaller. It can be found, therefore, that for the sameJRC roughness coefficient curve, under the same externalenvironment, the seepage capability of the fracture surfacesof different particle size is different.

The microscopic roughness mainly reduces the energy ofthe water flow caused by the viscous effect and adsorptionof water flowing through the fracture surface, which resultsfrom the influence of small particle size distribution, particlesize, and its different combination forms. However, themacroscopic roughness dissipates the energy of water mainlydependent on the wavy elevation difference of fracturesurface to affect the seepage ability of water.

4.4. Solving of the Microroughness Coefficient. In order toensure the accuracy of the solution of the microroughnesscoefficient and reduce the influence of the JRC on thepermeability coefficient, the surface roughness of the testpiece is tested by the laser tester of the jointed rock surfaceand shape.The Z2 calculationmethod [32, 33] was adopted inthis paper, coarse, medium, and fine fractures with differentparticle diameters were calculated, and the JRC values of thesurface roughness were 7.5, 7.8, and 7.2, respectively.

The stress and the strain values of the coarse particle-sized test piece are obtained from the laboratory test; 𝐸𝑡 =6325MPa and 𝐸𝑟 = 6517MPa are obtained through the fittingoperation; 𝜇0 = 54 𝜇m is obtained after the measurement.Programming formula (15) by the FISH language built-inITASCA and substituting the relating parameters to get the

The m

icro

roug

hnes

s coe

ffici

ent (

1)

Fissure

water p

ressure

(MPa)

The normal load (MPa)

0.5 0.75 1.0 1.25 1.5 1.75 2.0 0.10.2

0.30.4

0.5

0.50

0.75

1.00

1.25The fracture of coarse sand

The fracture of fine sand

The fracture of medium sand

Figure 8: The 3D plane of microroughness coefficient.

corresponding theoretical calculated value, the comparisonand solution are carried out between it and the measuredvalue. For the medium and the fine particle-sized test pieces,the corresponding values of 𝐸𝑡, 𝐸𝑟, and 𝜇0 are obtainedby the same method, and the programming calculationis used to get the microroughness coefficients of differentparticle size. The normal load (0.5–2.0MPa) and the crannyhydraulic pressure (0.1–0.5MPa) of each group, respectively,correspond to amicroroughness coefficient value; thus all themicroroughness coefficients of the fracture of each particlesize are approximatelymanifested as a plane in the graph, andthe results are shown in Figure 8.

The average value of the microroughness coefficient ofeach fracture surface is calculated, and the average valuesof the coarse, medium, and thin particle-sized fractures are,respectively, 0.772, 0.851, and 0.926. It characterized that asthe particle sizes become bigger, the microroughness coeffi-cients increase gradually with the amplifications of 10.2% and8.8%, and the permeability coefficients also increase. It canbe seen that, in the case of the same JRC, the correspondingpermeability coefficient is different due to the different parti-cle size and structural characteristics of the fracture surface.Therefore, the influence of themicroroughness of the fracturesurface on the seepage capability cannot be neglected.

4.5. Verification of the Theoretical Formula. Based on themicroroughness coefficient of the fracture surfaces of dif-ferent particle size obtained in the above analysis, the sametest pieces as the former test are selected. Five groups’ stress-seepage coupling tests are done with the cranny hydraulicpressure being 0.1 to 0.5MPa, respectively, for the two caseswhere the normal loads are 2.5MPa and 3.0MPa and thevalidity and accuracy of the microroughness coefficient areverified. The test results and the theoretical validation valuesconsidering the microroughness coefficient are shown inFigure 9.


0.0 0.1 0.2 0.3 0.4 0.5 0.60.01

0.02

0.03

0.04

0.05

0.0 0.1 0.2 0.3 0.4 0.5 0.60.01

0.02

0.03

0.04

0.0 0.1 0.2 0.3 0.4 0.5 0.60.010

0.015

0.020

0.025

0.030

0.0 0.1 0.2 0.3 0.4 0.5 0.60.01

0.02

0.03

0.04

0.0 0.1 0.2 0.3 0.4 0.5 0.60.01

0.02

0.03

0.04

0.05

0.0 0.1 0.2 0.3 0.4 0.5 0.60.010

0.015

0.020

0.025

0.030

The fracture of coarse sandThe normal ＦＩ；＞ = 2.5－０；

The fracture of medium sandThe normal ＦＩ；＞ = 2.5－０；

The fracture of fine sandThe normal ＦＩ；＞ = 2.5－０；

The normal ＦＩ；＞ = 3.0－０；The fracture of coarse sand

The normal ＦＩ；＞ = 3.0－０；The fracture of fine sandThe normal ＦＩ；＞ = 3.0－０；

The fracture of medium sand

The p

erm

eabi

lity

coeffi

cien

t (cm

·Ｍ−1)

The p

erm

eabi

lity

coeffi

cien

t (cm

·Ｍ−1)

The p

erm

eabi

lity

coeffi

cien

t (cm

·Ｍ−1)

The p

erm

eabi

lity

coeffi

cien

t (cm

·Ｍ−1)

The p

erm

eabi

lity

coeffi

cien

t (cm

·Ｍ−1)

The p

erm

eabi

lity

coeffi

cien

t (cm

·Ｍ−1)

Fissure water pressure (MPa) Fissure water pressure (MPa)

Fissure water pressure (MPa)Fissure water pressure (MPa)

Fissure water pressure (MPa) Fissure water pressure (MPa)

The measured valuesThe theoretical values

The measured valuesThe theoretical values

Figure 9: The comparison of permeability coefficient between the theoretical values considering the microroughness and the measuredvalues.

As shown in the figure, when the normal loads are, re-spectively, 2.5MPa and 3.0MPa, the goodness of fit betweenthe theoretical validation values and the measured values ofthe permeability coefficient of different particle-sized fracture

surface is higher, which means, through considering themicroroughness coefficient introduced by the nature of themicrosurface of the fracture, formula (15) is able to describethe variation law between the permeability coefficient and the


fracture water surface and show the difference in the seepagecapability of the different particle-sized fracture surface ofthe rock mass. In the case of the stress-seepage couplingof the fracture surface of the jointed rock mass, it is notcomprehensive for the seepage description to only considerthe JRC permeability of the fracture surface; therefore, theeffect of the nature and the particle distribution of themicrosurface of the fracture on the seepage capability are notnegligible.

5. Conclusion

(1) Based on the results of the test among the joint rough-ness coefficient (JRC) of rock fracture, mechanicalaperture, and hydraulic aperture proposed by Barton,the effect of different particle size and its structureon the seepage capability is considered under thesame JRC condition by introducing amicroroughnesscoefficient, and the permeability coefficient formulaof single fracture surfaces considering the micror-oughness is deduced under the condition of stress-seepage coupling, of which the parameter can becalculated through the indoor test with the feasibilityand general applicability.

(2) Through the indoor test, manufacturing the molds,and preparing the fracture surface of different particlesize, stress-seepage coupling tests are carried out,respectively, under different normal load anddifferentseepage pressure to get the permeability coefficient ofdifferent particle-sized fracture surfaces; through theanalysis of the test results, it is found that, in the caseof the same JRC, the seepage pressure, and the normalload, the seepage capability of different particle-sized fracture surface is different. With the increaseof the particle size, the permeability coefficient ofthe fracture surface increases correspondingly; thesmaller the particle size, the smaller the permeabilitycoefficient. It shows that the effect of microroughnessof the fracture surfaces on its seepage capabilitycannot be neglected.

(3) Under the same lower normal stress level, with theincreasing of cranny hydraulic pressure, permeabilitycoefficients of deferent particle-sized fractures showthe exponential growth, while for the same crannyhydraulic pressure, permeability coefficients of dif-ferent particle-sized fractures approximately show adecreasing power function with the normal load.

(4) The FISH language is used to solve the formula of thesingle fracture stress-seepage coupling consideringmicroroughness by programming in order to get themicroroughness coefficients of fracture surfaces ofdifferent particle size. The correctness and validityof the two parallel seepage tests are verified underdifferent normal load level, and the result shows bettergoodness of fit. At the same time, it also indicatesthat the theoretical formula of single fracture stress-seepage coupling deduced by the introduction of themicroroughness coefficient is reasonable and reliable.

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper.

Acknowledgments

The authors would like to express appreciation to Dr. GangWang and doctoral student Weijie Song at Shandong Univer-sity of Science and Technology for their experimental assis-tance. This project is financially supported by the NationalNatural Science Foundation of China, Grants nos. 51474135and 41272325.

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