Experimental Investigation of the Permeability Measurement of Radial Flow through a Single Rough Fracture under Shearing Action

Ph.D. Student, State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi’an University of Technology, Xi’an 710048, China Professor, State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi’an University of Technology, Xi’an 710048, China Master’s Student, State Key Laboratory Base of Eco-hydraulic Engineering in Arid Area, Xi’an University of Technology, Xi’an 710048, China


Introduction
Joints with varying surface roughness and gouge content occur in underground rock masses and are the main channels of groundwater flow.ese rock joints possess low shear strength [1].When water seeps into rock joints, the rock is compressed and the joint surface is shear-dilated, closed, or even destroyed [2].As a result, a complex seepagestress state emerges.
is complex stress state affects the stability of many large-scale rock engineering projects.erefore, analysis of the hydraulic characteristics of fractured rock masses is an important topic in many areas of engineering, such as hydraulic structures, hydrogeology, rock mass mechanics, and mining engineering.
Few studies have considered the seepage-stress coupling effect of a joint fracture.e results reported to date have been obtained largely by laboratory test methods or experimental and numerical simulations.Researchers firstly considered the effect of normal stress on the joint surface, and many scholars carried out studies of normal stress and seepage, obtaining the classical cubic law.e mechanical behavior of rock is controlled mainly by shear displacement of discontinuities [3].Shear dilation occurs during shear, but there are few studies on joint deformation characteristics under varying shear rate.Kleepmek et al. [4] believed that the peak shear strength of a rough fracture increases with displacement velocity.Li et al. [5] studied the strength characteristics of rock joints under different shear rates by using artificial concrete joint samples and found that the peak shear strength of rock joints decreased with the shear rate.However, the geometrical characteristics of the fracture surface also affect shear strength and hence weaken rock asperities [6] and affect the relationship between the hydraulic aperture and mechanical aperture [7].Fractures produce gouge material under shear deformation and normal stress.e gouge material fills in the fracture, affecting the overcurrent capability of the fracture.Chen et al. [8] believed that the plastic and liquefaction effects of fracture fillings significantly improve the permeability of fractures.And, Liu et al. [9] suggested that the modified cubic law cannot be used to simulate the motion of fracture fluid in the presence of gouge material.
In a partial laboratory test, through the modification of a biaxial or triaxial testing machine, a seepage device can be added to an original testing machine to create a device capable of testing the seepage-stress coupling system in joints [10][11][12][13].
e pore water pressure can be increased substantially in such a biaxial or triaxial testing machine, to be as high as 30-50 MPa [14,15].However, biaxial and triaxial tests do not consider the effect of direct shear; therefore, special test equipment must be developed to consider this effect.Some researchers have completed the shear-seepage coupling tests under the condition of uniflow [15][16][17][18].However, the geometric heterogeneity of a natural fracture surface leads to flow anisotropy, which is related to the direction of the injection pressure [19,20].Compared to uniflow flow, radial flow does not require consideration of the tightness issue on both sides of the joint sample; thus, many scholars have performed studies on radial flow.Tanikawa et al. [21] designed special test equipment that can use a thermocouple to heat nitrogen and calculate the seepage characteristics of granite fractures under thermohydro-mechanical conditions.Additionally, to study the effect of shearing stress, Yeo et al. [22] designed a special shear box for conducting shear-seepage tests under the condition of radial flow; however, its method of water injection was from the top down and the shear displacement was only 2 mm, to ensure sealing.A limitation of the tests was that the hydraulic pressure was low.
e above analysis of current experimental systems illustrates that a shear and radial flow coupling test technique for rock joints is still lacking.e test conditions do not tend to accurately represent natural conditions.In particular, there is no test that uses appropriate sealing technology.In addition, the maximum hydraulic pressure of the existing equipment is not high enough to reflect natural conditions.Based on the existing research and the urgent need to develop such equipment, we contacted the manufacturer to develop a new type of shear flow coupling test system.As a result, the YZS-600 microcomputer-controlled rock joint direct shear-seepage coupling test system was developed.
In this study, the newly designed system was used to test fluid flow in a series of cases in which normal stress, shear velocity, and roughness of fracture surface were varied.

Test System.
e test system is composed of the main engine, servo oil source, stress system, multi-05 full-digital, multichannel, closed-loop control system, and sealed shear box. Figure 1 shows a photograph of the main components of the test system.e shear loading frame is composed of a closed-loop controller, hydraulic servo oil source, force and displacement transducer, and sealed shear box.e shear force and normal force loading systems are controlled by an electrical displacement control (EDC) closed-loop controller developed by the Doli Company (Germany).e system has multiple measuring channels, and each channel can perform independent control, such as load control, deformation control, and displacement control.e testing machine can apply three boundary conditions, namely, constant normal displacement, constant normal load (CNL), and constant normal stiffness, in the normal direction.e stability of the normal rigidity can be ensured by feeding back the measured normal stress and normal deformation conditions during testing to the EDC.e EDC controller then adjusts the applied load as necessary to maintain constant rigidity.e hydraulic servo oil source controls the application of normal and shear loads.
e force and displacement transducer monitors the normal and shear loads as well as the displacement change.
e samples are placed in a closed shear box, which is similar to a cube divided into upper and lower parts.e sample in the lower part of the shear box is fixed, whereas the sample in the upper part of the shear box is enveloped by an independent square rigid copper casting.e normal stress and shear stress act through pistons pushing on the rigid copper casting.e top of the shear box is arranged with a rigid roller to prevent the upper sample from moving independently.O-shaped rubber sealing rings are used where the sample is fixed to the shear box and around the normal and shear pistons to ensure that the shear box is airtight.A schematic of the shear box is shown in Figure 2. e hydraulic loading system is composed of a water tank and nitrogen cylinder.Fixed pressure, with a maximum value of 3 MPa, is transmitted to the water tank through the relief valve on the nitrogen cylinder.Water is injected from the middle of the lower shear box base and then spreads onto the surface of the joint fissure.e water outlet is arranged on the surface of the lower shear box. is geometry allows for radial flow seepage mode.e mass of the water outflow is determined by an electronic scale and fed back to the computer.e flow direction is shown in Figure 3. e main technical parameters of the testing machine are provided by the manufacturer, as shown in Tables 1 and 2.

Sample Preparation.
e shape of the sample box in this test system is a cylindrical flute; thus, the geometrical surface of the sample is a regular round shear surface.e fracture plane of natural rock is kaleidoscopic with gouge of different properties.Compared with natural rocks, the rock-like materials used in this study have better homogeneity and were selected for ease of specimen preparation [23,24].e rock-like samples were composed of a super strong gypsum sample with a regular sawtooth surface.To avoid inaccurate test results caused by differences in the physical and 2 Advances in Civil Engineering mechanical properties and deformation intensity properties of the sample, the same test material was adopted for each batch of samples.e same mixing proportion and a mold of the same specifications were used to make each sample.e test material was extremely strong gypsum that is fully mixed with the proportions 25 g of water : 100 g of gypsum powder.
e slurry, which has good liquidity, is similar to glue and was slowly cast in a rigid mould for coagulation over 10-15 min.e duration of the stripping operation was 40-60 min.e stripped sample is shown in Figure 4. Upon drying, the compressive strength of the samples reached 47.82 MPa, as shown in Table 3. Advances in Civil Engineering e rock-like samples were cylindrical with a basal diameter D of 200 mm and a height H of 75 mm.Two di erent types of fracture planes (smooth and rough) were considered as shown in Figure 4. e teeth on the plane of the rough sample were regularly spaced.e length of a single tooth was 10 mm, and there were 20 teeth (Figures 4(b) and 4(d)).
e cross section of each tooth was a right triangle, and the undulant angle was 60 °(Figure 4(b)).e smooth sample was free of undulant angles (Figures 4(a) and 4(c)).
Because of the di erences in the joint surfaces of the samples and the existence of multiple sample directions for rough samples, many potential shear box placement orientations exist.Four feature combinations were selected in this test and are shown in Figure 5 (the pink arrow is the shear stress direction)-combination I: the upper and lower samples are smooth samples; combination II: the upper sample is a smooth sample, the lower sample is a rough sample, and the teeth ridges of the rough surface are oriented perpendicular to the shear direction; combination III: the upper and lower samples are rough samples, and the teeth ridges of both rough surfaces are oriented perpendicular to the shear direction; combination IV: the upper and lower samples of combination III are counter-rotated by 90 °, so that the teeth ridges of both rough surfaces are oriented parallel to the shear direction.

Testing
Procedure.Before the test, the gypsum sample was soaked until saturated.Subsequently, the following steps were performed:   Advances in Civil Engineering Step 1. Open the instrument, place the rock-like sample in the shear box, and set the normal stress value and shear velocity in the computer program.
Step 2. Load the normal stress until it is stable.
Step 3. Open the nitrogen relief valve to increase the hydraulic pressure until the flow is stable.

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Step 4. Begin shearing until the shearing displacement is maximized.
e boundary condition of this direct shear test was CNL, which is mainly used for rock slope stability analysis [25,26].Barton pointed out that when engineering problems related to a rock mass occur, the effective normal stress is commonly between 0.1 MPa and 2.0 MPa [27].erefore, the direct shear tests were carried out under a normal stress of about 2 MPa.Eight test cases were designed, as listed in Table 4.

Shear Stress Evolution.
ree distinct stages of shear stress evolution with increasing shear displacement were observed, and these are compared in Figure 6. e shear stresses under all working conditions first increased rapidly, then decreased, before a final stable stage was reached.e value of shear stress after achieving stability was slightly higher than the initial value.e evolution of shear stress can be related to the extent of surface fracture damage.

Failure State of Fracture Surface.
Experiments were performed to test whether the failure state of the fracture surface was directly related to the contact state of the rocklike samples.
For Group A, a larger normal stress led to higher shear stress (Figure 6(a)).Increasing shear stress increased damage to the sawtooth surface, as illustrated in Figure 7.After the shear test, abundant gouge material filled the fissures.ese gouge material moved along the fissures due to fluid flow and shear displacement.It can be clearly seen that grain size of the gouge decreases with an increase in shear stress.us, the abrasive effect of shear stress on the fracture surface also increases.e shearing process can amplify the plastic and liquefaction effects of the gouge.Although all teeth were pulverized, the roots of the teeth were preserved and rough fissures remained which formed dominant channels for water flow, as shown in Figure 8.
For Group B, no obvious increase in peak shear strength was observed with an increase in shear velocity.After the shear tests, all teeth were pulverized and a large amount of gouge material filled the fissures (Figure 9).Residual shear strength increased with an increase in shear velocity (Figure 6(b)).After reaching the peak shear strength, under the action of gouge fragments and flow disturbance, increasing shear velocity caused the upper and lower sample blocks to slide along the fissures more easily, so the residual peak strength decreased with an increase in shear velocity.
e size and distribution of gouge did not show obvious regularity.
For Group C, greater shear stress was required when the fracture surface was more complex (Figure 6(c)).e fracture surface failure varied across all four combinations.Figure 10(a) shows both upper and lower samples that are smooth.After the shear test, there were no obvious signs of damage, and the upper and lower surfaces remained smooth.
It was not even possible to find traces of water pressure erosion.Figure 10(b) shows the case of the upper sample being smooth and the lower sample being rough.After loading normal stress, the smooth surface of the upper sample became textured due to contact with the lower sample.After loading shear stress, displacement lines were observed on the upper sample.A small portion of the lower sample was damaged due to the shear displacement.e sample surfaces shown in Figures 10(c) and 10(d) all began rough.e physical properties of the samples are the same, but the way they are placed in the shear box determines the final failure state.Case 2 (Figure 10(c)) is severely damaged, but Case 8 (Figure 10(d)) is hardly damaged.It can be seen that parameters such as undulant angle i, the Barton term for joint rock coefficient (JRC), and shear strength [28] are related to the shear direction and fracture surface matching of the samples.

Fissure Width.
e distribution of fissure width b during shear can be expressed by the following equation [29]: where b 0 is initial mechanical fissure width, δ n is the change in mechanical fissure width due to normal stress, and Δδ n is the change in mechanical aperture induced by shear deformation.e fissures are filled with water before shearing, and the initial mechanical fissure width b 0 under the radial flow can be calculated by the following equation [22,30]: where Q is the steady state fluid flow rate, ΔH is the head difference, the constant C � (2π/ln(r 1 /r 2 ))(g/12μ) for radial flow, r 1 and r 2 , represents the outside and inside radius of the fracture surface, respectively, g is the gravitational acceleration, and μ is the fluid dynamic viscosity.
Because the fracture widths are not always equal, the true initial fissure width b 0 in equation ( 2) is replaced by the equivalent hydraulic fissure width b 0 ′ , and equation ( 2) can be rewritten as follows: where C ′ � 2π/ln(r 1 /r 2 ).
Under the CNL boundary condition, δ n is equal to 0. Finally, the equivalent fissure width can be obtained from the following equation: e calculated data points are grouped in Figure 11.In Figure 11, when the test begins, there is only normal stress and hydraulic pressure, and the fissure width is 6 Advances in Civil Engineering relatively small.After the shear stress is loaded, the fracture surface is dislocated and the teeth are gradually destroyed.With increasing shear displacement, the fracture surface is gradually destroyed and the ssure width gradually increases.e following conclusions can be obtained according to the gures for each group: Group A: there is more compaction of the upper and lower samples when the normal stress is larger.After the shear stress is loaded, the teeth of the fracture surface are destroyed, gouge in the fracture is pressed tightly, and the ssure width exhibits a decreasing trend.

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Group B: as shown in Figures 6(b) and 9, under the action of gouge and ow disturbance, an increase in shear velocity makes the upper and lower surfaces slide more easily.e ssure width decreases with an increase in the shearing velocity of the fracture surface.Group C: Figure 10 shows that after the shear test, except for combination III, evolution of the fracture surface of the other three groups is relatively complete.e ssure width of combination III increases dramatically during shear, and the nal value is much higher than for the other three cases (Figure 11(c)).
e other three cases remain stable.is suggests that the gouge material has a strong in uence on ssure width.Hydraulic conductivity can be expressed as where K is permeability and ρ is liquid density.After the teeth of the rough fracture surfaces are pulverized, abundant gouge material is produced in the ssures.
e gouge lls the dominant channels of water ow and the fracture.e gouge is a porous media.As can be seen from Figure 8, normal stress changes the grain size of the gouge fragments.Liu et al. obtained the following equation by experiment [9]: where b is ssure width, D m is grain size, and m and n are coe cients related to the geometric parameters of both fracture and rock.Equation (6) implies that K increases with increasing b/D m .Considering the obvious change in permeability with shear displacement and the larger change in gouge grain size under di erent normal stress N, equivalent ssure width b ′ and shear displacement d can be shown to follow a natural logarithmic relationship (Figure 13), written as follows: where α, β are parameters, d > 0. Figure 14 and Table 5 show that α and β are linear with normal stress N, written as follows: Hydraulic conductivity under di erent normal stress can be obtained by substituting equations ( 6) and (7) into equation (5): In addition, for this study the values of a, b, c, and d in equation ( 8) are 0.251, 0.1001, −0.1522, and 0.6036, respectively, when equation ( 9) is applied to other researches; the values of α and β can be ensured by referring equations ( 7) and ( 8) and the test conditions.

Conclusions
is study examined the hydromechanical coupling of a single rough fracture.e microcomputer-controlled rock joint direct shear-seepage coupling test system used in this study was based on advanced virtual technology.Under radial ow, eight test cases of arti cial fractures were tested to observe changes in deformation behavior with changing normal stress, shear velocity, and roughness of the fracture surface.After testing, variations in the mechanical properties and the permeability of rough fracture surfaces during shear were determined.e grain size of gouge produced by rough fracture surface deterioration was shown to decrease with an increase in normal stress during shear.e ssure width of rough fractures was determined mainly by gouge fragment size.High normal stress was shown to cause liquefaction or plasticization of gouge material.Gouge lled the preserved roots of teeth on rough surfaces to form the dominant channels of water ow.e grain size of the gouge a ected fracture permeability.e in uence of shear velocity on the test results was mainly observed after the peak strength; the faster the shear velocity, the smaller the observed shear stress.A shared orientation of shear direction and teeth on the fracture surface had a considerable in uence on the shear stress, undulant angle, and JRC. e ssure width of rough fractures was shown to correlate with the change in shear displacement.erefore, a new expression describing uid ow in gouge-lled fractures under di erent normal stress was proposed.In this study, the parameters α and β of equation (7) were related to normal stress, and α increased, while β decreased, with increasing normal stress.When equation (7) was used in other tests, the reference values of α and β were con rmed by equation (8).Because of the limitations of sample processing and testing equipment, only three normal stress tests were carried out in this study.However, although our data were somewhat limited, this expression should provide a reference for the study of permeability of rock joints.
As water ows from the center of the specimen to the edge, there is a head drop and a gradient in hydrostatic pressure forms across the specimen (from the applied pressure on the inside to zero on the outside).Future works will focus on the in uence of this gradient on the overall e ective stress.

Figure 3 :
Figure 3: Flow direction of the seepage-stress coupling test system.

Table 1 :
Main technical parameters of the normal force and shear force electrohydraulic servo systems.Vertical force electrohydraulic servocontrol Horizontal force electrohydraulic servocontrol Maximal testing force 700 kN E ective measurement range of the testing force 20-80% F.S Indicating accuracy of the testing force ±1% Resolution of the testing force 1/200,000 Displacement piston formation (force measured by a radial load sensor) ≥200 mm ≥100 mm Measuring range of the displacement 0-200 mm 0-100 mm Discrimination of the displacement 0.025 (5,000 yards) Indicating accuracy of the displacement <±5% F.S Measuring range of the deformation 0-100 mm Indicating accuracy of the deformation ±5%

igure 4 :
Structure of the test sample surface: (a) cross section of the smooth sample; (b) cross section of the rough sample; (c) surface of the smooth sample; (d) surface of the rough sample.

Figure 6 :
Figure 6: Evolution of shear stress with increasing shear displacement.(a) Increasing normal stress.(b) Increasing shear velocity.(c) Changes in the ssure plane combination mode.

Figure 12 : 2 Figure 13 :
Figure 12: Variations in ow with increasing shear displacement.(a) Increasing normal stress.(b) Increasing shear velocity.(c) Changes in the ssure plane combination mode.

Table 2 :
Main technical parameters of the hydraulic pressure stabilizing system.

Table 5 :
α and β for di erent normal stresses.