1 Introduction

Shear strength of rock joints is mobilized by two mechanisms: the sliding behavior between joint surfaces and the failure behavior of contacted asperities on a shearing surface (Barton et al. 1985; Swan and Zongqi 1985; Ladanyi and Archambault 1970; Lam and Johnstone 1989). Roughness that contributes to the shear strength of joint rocks is accordingly categorized into two components: a geometrical component related to the sliding behavior and the peak dilation angle, and a mechanical component representing asperity failure (Bandis et al. 1981). The former corresponds to large-scale roughness that causes dilation without failure or degradation, termed waviness; and the later is related to small-scale roughness that tends to be degraded on shearing surfaces, termed unevenness (ISRM 1981).

Normal stress is an important factor in determining the relative contribution of waviness or unevenness to shear strength because normal stress determines the number and area of local contact points of asperities (Teufel and Logan 1978; Logan and Teufel 1986; Xie et al. 1997; Hong et al. 2006a, 2008). For instance, at a low-normal stress level (e.g., σ/JCS < 0.01), small-scale asperities on a joint surface can contribute to shear strength via a sliding mechanism, increasing peak dilation angle. As the normal stress increases, however, the contribution of the small-scale asperities by sliding is expected to decrease. Instead, mechanical asperity failure becomes significant in mobilizing peak shear strength (Yang et al. 2001; Hong et al. 2006b). Therefore, the relative contribution of waviness or unevenness to shear strength, if the two can be quantified, is not constant but will vary with normal stress. Furthermore, from a strain perspective, it is known that the degradation of unevenness plays a role in mobilizing peak shear strength in a small-strain regime prior to developing peak shear displacement, whereas the dilation caused by waviness and the basic friction angle contribute shear strength regardless of the strain regime. Therefore, quantifying the unevenness on a rock joint surface and identifying the degradation characteristics during shear are important tasks for understanding the roles of unevenness and waviness in mobilizing peak shear strength and for establishing a reliable shear strength model to predict the shear strength of natural rock joints.

Many studies on the shear behavior of rock joint surfaces have been conducted, via empirical methods (Barton 1973; Bandis et al. 1983), introduction of a joint roughness coefficient (Carr and Warriner 1989; Kulatilake et al. 1995; Maerz et al. 1990; Tse and Cruden 1979), and characterization of the failure mechanisms (Lam and Johnstone 1989; Haberfield and Johnston 1994; Yang et al. 2001; Kwon et al. 2010). Micro-scale studies on the three-dimensional degradation of asperities have been performed with experimental approaches (Gentier et al. 2000; Wang and Scholz 1993), theoretical and numerical approaches (Borri-Brunetto et al. 1999; Chiaia 2002; Misra 2002), and by studying 3D joint surface morphology (Belem et al. 2009; Tatone and Grasselli 2013; Mlynarczuk 2010; Jiang et al. 2006). In spite of previous efforts, the degradation characteristics and scale of unevenness remain poorly understood. Yet, they are critical for understanding the asperity failure mechanism and to quantify roughness, and unevenness in particular.

The present study investigated the degradation characteristics and scale of unevenness on artificial rock joint surfaces. Direct shear tests were performed on tensile-fractured surfaces of artificial rock joint specimens at different normal stress levels. The degradation patterns of unevenness were obtained via an image analysis of the sheared surfaces. Spatial distributions and statistical parameters of degradation patterns, such as average, maximum, and minimum scales of the degraded area, were extracted. The effects of normal stress on the degradation characteristics and the scale of unevenness were discussed.

2 Experimental Program

2.1 Preparation of Artificial Joint Rock Specimens

A block of Hamyeol granite, 1.5 m-long, 2.5 m-wide, and 1.5 m-high, was artificially tensile-fractured to create a rough joint surface, and that created tension joint surface was chosen for the present study. Hamyeol granite is one type of Daebo granite, one of the major granites found in the central area of South Korea. It is coarse-grained granite, composed of 29 % quartz, 24 % orthoclase, 25 % plagioclase, and 9 % biotite, and the diameters of these mineral particles were analysed to be 1.0, 3.4, 0.5, and 1.7 mm (average particle size = 0.9 mm), respectively.

Silicon latex (KE-1402, Shin Etsu Co.) was applied on a 1 m × 1 m area of the created rock joint surface to replicate its surface roughness (Hong 2005; Hong et al. 2014). A mixture of the silicon latex and a hardening agent was carefully painted with a brush in a frame of 1 m × 1 m (length × width) on the rock surface and cured for 24 h. Resin has typically been used to replicate fractured surfaces in previous studies (e.g., Gale 1987; Gale et al. 1990; Gentier et al. 1989; Hakami 1995; Hakami and Larsson 1996); however, when the resin is injected, large fractures with small voids may not impregnate with the resin because of the high viscosity. Silicon latex is often used for the replication of complex objects, and we chose to brush the silicon latex liquid to minimize the smoothing of small asperities and the unintended occurrence of air bubbles. When visually inspected, the topology of the joint surface was presumed to be successfully preserved.

Four locations on the surface of the 1 m × 1 m latex replica (i.e., 1st generation replica) were selected to resize the joint specimen for laboratory direct shear tests. Using four different molds with 100 mm × 100 mm × 40 mm dimension, silicon latex was again applied at the selected locations on the 1 m × 1 m replica. Therefore, four 100 mm × 100 mm × 40 mm replica specimens (2nd generation replica), having a three-dimensional roughness, were fabricated and used to reproduce rock joint specimens for laboratory shear tests. High-strength gypsum plaster was used for the reproduction of artificial joint specimens (Hong et al. 2008). Table 1 summarizes the basic properties of the artificial rock joint specimens used in the present study. The upper section (3rd generation replica) was replicated first, and then, the lower section (4th generation replica) was replicated from the upper section. Therefore, a perfectly mated contact condition was achieved. To explore how unevenness degradation affects shear behavior, shear testing of multiple joint sets with identical surface roughness should be conducted at different normal stress levels. It is, however, extremely difficult to obtain multiple sets of natural rock joints with the same (at least, similar) joint roughness morphology. Because of this problem, the artificial rock joint sets used in this study are thought to be an optimal and useful tool to advance our understanding of the effect of normal stress on the degradation characteristics of unevenness in relation to the shear behavior of rough joint surfaces. Note that artificial rock joints made of gypsum plaster can represent sedimentary rock joints (Johnston and Choi 1986; Indraratna and Haque 2000). Thus, the results obtained from this study are applicable to sedimentary rock joints, and may have limitations for crystalline rocks.

Table 1 Material properties of the artificial rock joint specimens used
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The topology of the surfaces of the four artificial specimens (No. 1, No. 2, No. 3, and No. 4) was obtained using a three-dimensional scanner, as shown in Fig. 1 (Hong et al. 2006a). The surface roughness parameter (R S), defined as the ratio of the true surface area (A) to the apparent area projected onto the horizontal plane (A 0), was measured to be 1.0869 for Joint No. 1, 1.0876 for Joint No. 2, 1.0889 for Joint No. 3, and 1.0879 for Joint No. 4, respectively (Gokhale and Drury 1990; Gokhale and Underwood 1990). Two-dimensional roughness profiles extracted from each joint surface are presented in Fig. 2. The roughness profiles were extracted parallel to the shearing direction and with a 2-cm space interval; thus five profiles per surface in total. Each joint roughness coefficient (JRC) value was estimated by comparing each profile with the reference profiles suggested by Barton and Choubey (1977). Therefore, a representative JRC value for each surface was calculated by averaging the five JRC values. The average JRC values were 9.2 for Joint No. 1, 10 for Joint No. 2, 11.6 for Joint No. 3, and 10.8 for Joint No. 4, respectively. In addition, the average inclination angle of asperities (A i ) was obtained in the same manner. The roughness parameters obtained are listed in Table 2, and the order of roughness was No. 3 > No. 4 > No. 2 > No. 1 for R S, JRC, and A i .

Fig. 1
figure 1

Surfaces of the rock joints used: a No. 1, b No. 2, c No. 3, and d No. 4

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Fig. 2
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Roughness profiles of four joint specimens and the JRC values. The profiles were extracted with a 2-cm interval; H02 is from 1 cm above from the one side edge parallel to the shearing direction, and H06 is from 3 cm above the side edge, and H18 is from 9 cm above the side edge. The JRC values were obtained by comparing each profile with the reference profiles suggested by Barton and Choubey (1977)

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Table 2 Estimated roughness parameters of the four artificial joint specimens
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2.2 Direct Shear Test Results of the Artificial Rock Joint Specimens

A hydraulic shear apparatus (maximum loading capacity: 500 kN) was used for the joint shear tests. The shear tests were performed at five different but constant normal stresses (0.1, 0.25, 0.44, 0.78, 2.25 MPa). This low stress range can represent vertical stress to a depth from 77 to 114 m, assuming the density of overlying layers to be 2000–3000 kg/m3. This encompasses a range of interest in rock engineering practices at shallow depths, such as rock slopes (Barton 1973). The joint compressive strength (JCS) of the artificial gypsum was measured to be 40.3 MPa; thus, the normal stress normalized by the joint compressive strength (σ/JCS) was 0.0024, 0.0061, 0.011, 0.0195, and 0.056, respectively. The shearing rate was maintained at 0.5 mm/min throughout the experiments, and the shearing was halted when the peak shear stress was confirmed. The vertical displacement and horizontal displacement were monitored using linear variation displacement transducers (LVDTs), while the vertical load and horizontal load were measured using load cells.

The shear test results, shear stress-shear displacement curves and resulting peak shear stresses for different normal stresses are presented in Fig. 3a, b. The stress values are summarized in Table 3. Although the order of the roughness was measured as No. 3 > No. 4 > No. 2 > No. 1, the order of the shear strength was found to be No. 3 > No. 4 > No. 1 > No. 2. The difference between the orders of roughness and shear strength is thought to occur because the roughness parameters only contain the morphological information of average surface roughness, while the shear strength is affected by several factors, including the normal stress, local roughness, or roughest local area of the specimen.

Fig. 3
figure 3

Results of direct shear tests on the four artificial joint specimens. a Shear stress-shear displacement curves of Joint No. 1 in which the peak shear displacement (dhp) was denoted with arrows, b peak shear strength (τ/JCS) versus normal stress (σ/JCS), and c the changes in the peak shear displacement (dhp) with normal stress (σ/JCS)

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Table 3 Direct shear test results
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In an attempt to explore the role of asperity degradation in developing peak shear strength, the shearing was halted as soon as the peak shear stress was confirmed to minimize additional shear displacement and to avoid additional degradation while proceeding to a residual state (see Fig. 3a). However, because of the difficulty in determining the peak shear stress, shear displacements (dh) greater than the peak shear displacements (dhp) were unavoidable in all tests, as shown in Table 4. The ratio of the shear displacement to the peak shear displacement (dh/dhp) was approximately, 1.04–2.67, and the peak shear displacement (dhp) ranged from approximately, 0.3 to 3 mm (Table 4). A general trend was observed in that an increase in normal stress led to an increase in peak shear displacement (Fig. 3c). Typically, a residual state requires more than 10–20 % shear strain; thus, more than 10 to 20-mm shear displacement is required for our specimen size. Compared with these values, the shear displacements in our tests were less than 3.2 mm. Moreover, because the additional shear displacement after peak shear displacement, i.e., dh–dhp, was less than 1 mm (except for No. 2 under σ n  = 0.10 MPa; see Table 4), it can be justifiable to assume that this additional shear displacement would not generate significant additional degradation. Consequently, the obtained values presented in Table 5 can be considered more or less representative of the degradation occurring during the process of developing the peak shear strength of the joints. This assumption is also consistent with the previous study by Gentier et al. (2000), where they found that the major degradation of asperities took place prior to or at peak shear displacement during shear.

Table 4 Shear displacements (dh) and peak shear displacements (dhp) in the shear tests
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Table 5 Parameters extracted from the photo image analysis
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2.3 Photo Image Analysis

After joint shear testing, a total of 20 sets of joint specimens (i.e., 4 types of surfaces and 5 normal stresses) were collected. One joint set consisted of an upper joint and a lower joint. Because the surfaces of the fabricated rock joints had a pink color, the damaged areas on a sheared surface turned white in color while the undamaged area remained unchanged. Thus, the damaged asperities caused by the shear were visible with the naked eyes and a digital camera, as shown in Fig. 4. Once debris from the damaged asperities was removed with a brush, fine images of the specimen surfaces were taken with a high-resolution digital camera. To minimize distortion in the digital images, the digital camera (Nikon E3500, image resolution 2048 × 1536 dpi) was located above the center of a specimen at a fixed distance from the specimen.

Fig. 4
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Digital images of typical degradation patterns: a the bottom part of No. 2 specimen sheared at σ/JCS = 0.011, b the upper part of No. 1 specimen sheared at σ/JCS = 0.0061, c the bottom part of No. 2 specimen sheared at σ/JCS = 0.011, and d the segmentation of damaged zones on the bottom part of No. 3 specimen sheared under σ/JCS = 0.0024

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The regions of damaged asperities larger than 0.1 mm, hereafter designated degraded zones, were identified and segmented out from the obtained bitmap images via photo image analysis, as shown in Fig. 4d. The bottom parts of the twenty joint specimens, four types of joints for five different normal stresses, were analysed. Figure 5 shows the segmented images of the degraded zones. Each degraded zone was generated either from a failure of an individual asperity or from abrasive wear of a group of asperities. As expected, it appears that the number of damaged asperities and the total degraded area increased as the normal stress level increased.

Fig. 5
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Segmented images of sheared surfaces for lower joint specimens

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Based on the obtained images shown in Fig. 5, various geometric parameters were extracted. These included the number of degraded zones (N); the length of a degraded zone parallel to the shear direction (X i ); the width of a degraded zone perpendicular to the shear direction (Y i ); the average, maximum, and minimum lengths of the degraded zones parallel to the shear direction [Avg(X i ), Max(X i ), and Min(X i ), respectively]; the average, maximum, and minimum widths of the degraded zones perpendicular to the shear direction [Avg(Y i ), Max(Y i ), and Min(Y i), respectively]; the area of a degraded zone (A i ); the average, maximum, and minimum areas of the degraded zones [Avg(A i ), Max(A i ), and Min(A i ), respectively]; the sum of the degraded area on a specimen (or total degraded area; ΣΑ i ); the overall area of a joint specimen (A joint); and the ratio of the total degraded area to the overall area of a joint specimen (ΣΑ i /A joint). These values are summarized in Table 5. From these geometric parameters, the degradation characteristics and the scale of asperities were analysed, and their relation to normal stress was discussed.

3 Results and Discussion

3.1 Observations of Degradation Characteristics of Asperities

Based on visual identification of the degradation patterns of asperities, two types of typical asperity degradation characteristics were observed: (1) the individual failure of asperities, and (2) the abrasive wear of asperities (Fig. 4). The failure of asperities was presumably caused by shearing or compression. The abrasive wear indicates a condition where fractions of the solid surface are detached by external forces. Wear can be caused by the adhesion between contact surfaces and abrasion between materials (Bhushan 2002; Rabinowicz 1995). Poon and Sayles (1992) reported that rough or high modulus materials had little adhesion, and the degradation of rock joints was mainly regarded as asperity failure and abrasive wear. It was observed that small and individual asperities failed over a relatively small damaged area (Fig. 4a; the bottom part of the No. 2 specimen sheared at σ/JCS = 0.011). Fragments of failed asperities, sheared off from an undulating joint surface, were found after the completion of shear tests. On the other hand, abrasive wear of asperities was also found over a relatively large area (Fig. 4b, c; the upper part of the No. 1 specimen sheared at σ/JCS = 0.0061 and the bottom part of the No. 2 specimen sheared at σ/JCS = 0.011, respectively). This wear was pronounced in the undulating domains, producing powdery fine particles because of shallow surface degradations.

Figure 5 shows the segmented images of the degraded zones and presents the spatial distributions of the degraded zones for different specimens and different normal stress levels. Presumably, an individual asperity failure or the abrasion of a group of asperities generated each degraded zone. As expected, the number of degraded zones and the total degraded area increased as the normal stress increased. Under a low normal stress condition (σ = 0.1–0.25 MPa or σ/JCS = 0.0024–0.0061), the degraded zones are observed to be spatially scattered. When a medium level of normal stress (σ = 0.44–0.78 MPa or σ/JCS = 0.011–0.0195) was applied, the major degradation occurred at or around the relatively large-scale asperities (undulations or waviness) because of the stress concentration. At the highest normal stress level (σ = 2.25 MPa or σ/JCS = 0.056), the degradation took place over the entire area of the joint specimen, even though joint No. 3 still showed a degradation pattern that was locally concentrated around major undulations.

It is a common misconception, typically hypothesized, that the areas degraded at low normal stress would also be degraded at high normal stress. Interestingly, it was found that this was not always the case, as shown in Fig. 5. All asperities in contact at low normal stress should also be in contact at higher stress. However, asperities that are not sheared off under a low normal stress condition can be damaged at higher normal stresses because of better contact and stronger stress concentration. This additional or different asperity failure at a higher stress level changes the dilation behavior of the joints; hence, the contact domains during shear as well. Evidently, several degraded areas identified at low normal stresses (σ = 0.1–0.25 MPa or σ/JCS = 0.0024–0.0061) were not observed at high normal stresses (σ = 0.44–0.78 MPa or σ/JCS = 0.011–0.0195). It is an important implication that not all of the contact domains between joints were degraded during shear at this particular range of normal stress (i.e., σ/JCS = 0.0024–0.0195), and thus, the normal stress level plays a role in determining the spatial distribution of the asperity degradation on a joint surface. This observation is consistent with the results presented by Xie et al. (1997) and Gentier et al. (2000).

3.2 Statistical Distribution of the Scale of the Degraded Zones

Figure 6 presents the histograms of the length of the degraded zone parallel to the shear direction (X i) plotted in a logarithmic scale. As normal stress increases, the number of degraded areas (N) apparently increases. Bell-shaped distributions are observed in the log10-scale histograms. The degraded zones mostly fall into the lengths of 0.5–5 mm, i.e., the dominant scale of the degraded zones. The histograms of the width of the degraded zone perpendicular to the shear direction (Y i ) show similar results with the histograms of the length of the degraded zone (X i ). It can be found that the length and width of the degraded zones are in the same scale, independent of the shearing direction, as some parameters in Table 5 [e.g., Avg(X i ) and Avg(Y i )] indicate.

Fig. 6
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Histograms of the length of the degraded zone parallel to the shear direction (X i ) in a logarithmic scale

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The histograms of the area of the degraded zones (A i ) are shown in Fig. 7. Zones larger than 50 mm2 are often found. These outliers are hardly observed in low normal stresses (at σ/JCS = 0.0024–0.0061); however, they become frequently observed as the normal stress increases, particularly when the normal stress normalized by the joint compressive strength (σ/JCS) is greater than 0.011. It is presumed that these large degraded zones most likely resulted from the abrasive wear of small-scale asperities (unevenness) with low inclinations. Clear bell-shaped distributions can be observed as well. The degraded zones mostly fall into the area of 0.1–10 mm2, i.e., the dominant area of the degraded zones. The nominal diameters of the dominant area, i.e., equivalent diameters where the degraded zones are regarded as a circle, show a range of 0.4–3.4 mm. This is very similar to the results of X i and Y i .

Fig. 7
figure 7

Histograms of the area of the degraded zone (A i ) in a logarithmic scale

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As shown in Figs. 6 and 7, the most dominant scale of the damaged unevenness, which impacts mobilized roughness and shear strength, ranges from approximately, 0.5 to 5 mm in size and 0.1–10 mm2 in area, and this is fairly consistent regardless of normal stress. The normal stress level does not seem to significantly affect the range of scale (length and area) of the damaged unevenness.

3.3 Effect of Normal Stress on Degradation Characteristics

All X i values measured from a joint specimen are plotted against the normal stress normalized by the joint compressive strength (σ/JCS) in Fig. 8 to see the effect of normal stress on the scale of degraded zones. Although the average length Avg(X i ) or median length of the degraded zone (i.e., the peak of the histograms in Fig. 6) is not related to the normal stress, the plot reveals that the range of X i becomes wider as the normal stress increases. Moreover, the degradation appears to be more prone to small asperities [i.e., asperities with X i  < Avg(X i )] than large asperities [i.e., asperities with X i  > Avg(X i )] as the normal stress increases. For all joint types, the range of X i is the widest at the largest normal stress, and X i is spread over a range from 0.1 to 11 mm when σ/JCS = 0.056 (see Fig. 6).

Fig. 8
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Length scale of degraded zones (X i ) at different normal stress levels: a Joint No. 1, b Joint No. 2, c Joint No. 3, and d Joint No. 4

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The ratio of the total degraded area to the overall joint specimen area ΣΑ i /A joint is calculated in a range from 0.4 to 20 %, as shown in Fig. 9a. An increase in the normal stress from σ/JCS = 0.0024 to 0.056 led to an increase of ΣΑ i /A joint by more than one order of magnitude. It is found that the ratio of the total degraded area to the joint specimen area (ΣΑ i /A joint) and the normal stress (σ/JCS) show a power-law relationship (ΣΑ i /A joint = α(σ/JCS)β; Fig. 9a). The number of degraded zones (N) also shows a similar increasing trend with an increase in normal stress but with greater scattering (Fig. 9b). The number of degraded zones (N) is 27–90 at the lowest normal stress (σ/JCS = 0.0024) and 564–1215 at the highest normal stress (σ/JCS = 0.056), an increase of more than one order of magnitude.

Fig. 9
figure 9

a Changes in the ratio of the total degraded area to the joint area against the normal stress, and b changes in the number of degraded asperities against the normal stress

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Unevenness, captured by the degraded area, represents the mechanical asperity failure component that contributes to shear strength (Bandis et al. 1981; ISRM 1981), Our results provide evidence that the mechanical asperity failure component increases with an increase in normal stress at this particular regime of normal stress (i.e., σ/JCS = 0.0024–0.0195). Furthermore, given that the dominant scale of unevenness stayed fairly consistent regardless of normal stress, the increase in roughness and its contribution to shear strength with the normal stress level is mainly due to the increase in the number of damaged unevenness at this particular range of normal stress (i.e., σ/JCS = 0.0024–0.0195), rather than the size of damaged unevenness.

3.4 The Scale of the Degraded Zones: Average, Maximum, and Minimum Sizes

In Fig. 10, the average, maximum, and minimum lengths of the degraded zones parallel to the shear direction [Avg(X i ), Max(X i ), and Min(X i ), respectively], the average, maximum, and minimum widths of the degraded zones perpendicular to the shear direction [Avg(Y i ), Max(Y i ), and Min(Y i ), respectively), and the average, maximum, and minimum areas of the degraded zones [Avg(A i ), Max(A i ), and Min(A i ), respectively] are plotted against the level of normal stress. It appears that the average lengths, widths, and areas of the degraded zones [Avg(X i), Avg(Y i), and Avg(A i)] show a poor correlation with the normal stress, as shown in Fig. 10a. Thus, it is confirmed that the average scales of the degraded zones are hardly affected by normal stress.

Fig. 10
figure 10

The effect of normal stress on (a) the average length, width, and area of the degraded zones [Avg(X i ), Avg(Y i ), and Avg(A i )]; b the maximum length, width, and area of the degraded zones [Max(X i ), Max(Y i ), and Max(A i )]; and c the minimum length, width, and area of the degraded zones [Min(X i ), Min(Y i ), and Min(A i )]

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However, the maximum length, width, and area of the degraded zones [Max(X i ), Max(Y i ), and Max(A i )] are found to increase with normal stress (Fig. 10b). In contrast, the minimum length, width, and area of the degraded zones [Min(X i ), Min(Y i ), and Min(A i )] show a decreasing trend with an increase in normal stress (Fig. 10c). This is important evidence indicating that shearing under a greater normal stress can damage not only the larger asperities but also the smaller asperities on a rock joint surface.

The average area of the degraded zones Avg(A i ) has a wider range of values, scattered over one order of magnitude (i.e., 0.5–5 mm2). The average length and width of the degraded zones Avg(X i ) and Avg(Y i ) were in a considerably narrow range and consistently had a value of ~1–2 mm, independent of the normal stress (Fig. 10a). Because the area is proportional to the square of the length and width, the areal parameters always present wider ranges than the values of the length and width. The maximum length and width were calculated to be ~2–15 mm, while the maximum area was ~5–120 mm2 (see Fig. 10b; Table 5). Last, the minimum length and width were ~0.1–0.8 mm, while the minimum area was ~0.02–0.5 mm2 (see Fig. 10b).

It is noted that this minimum length or width of the degraded asperity could be limited mainly by the resolution of the image analysis conducted in the present study. If a higher resolution camera was used to capture a smaller degraded zone, the minimum length, width, and area of the degraded zones under a normal stress of 2.25 MPa (σ/JCS = 0.056) might be lower. Nevertheless, the decreasing trend of the minimum length, width, and area with increasing normal stress is still considered valid.

4 Conclusions

This study explored the degradation characteristics of unevenness (small-scale roughness) during shear, and identified the scale of the damaged unevenness in relation to normal stress at a low-normal stress range. Using laboratory direct shear tests on perfectly mated artificial rock joint specimens with three-dimensional roughness and an image analysis of the sheared joint surfaces, spatial distributions and statistical parameters of the degradation characteristics at different normal stress levels were analysed. Salient findings of this study are as follows:

  • Two types of typical degradation characteristics—the individual failure of asperities over a relatively small damaged area and the abrasive wear of asperities over a relatively large area—were readily observed by the naked eye. This wear was pronounced in the undulations, producing powdery fine particles due to shallow and surface degradation.

  • The number of the degraded zones and the total degraded area increased as the normal stress increased. Under a low-normal stress condition (σ/JCS = 0.0024–0.0061), the degraded zones were observed to be spatially scattered. When a medium level of normal stress (σ/JCS = 0.011–0.0195) was applied, the major degradation occurred at or around the relatively large-scale asperities (undulations or waviness) because of the stress concentration. At the highest normal stress level (σ/JCS = 0.056), the degradation took place over the entire area of the joint specimen.

  • It was found that not all the contact domains between joints were degraded during shear at this particular range of stress (i.e., σ/JCS = 0.0024–0.0195). As a result, several degraded zones identified at a low-normal stress level were not damaged or failed at a higher normal stress level, partially because of different dilation behavior caused by unprecedented asperity failure.

  • The histograms of the length of the degraded zone parallel to the shear direction (X i ) and the area of the degraded zones (A i ) showed bell-shaped distributions in a logarithmic scale. The dominant scale and area of the damaged unevenness ranged from ~0.5 to 5.0 and ~0.1 to 10 mm2. Some degraded areas that were larger than 50 mm2 were most likely from abrasive wear of a group of small-scale asperities (unevenness) on undulating domains. It was also found that the length and the width of the degraded zones were in the same scale, independent of the shearing direction.

  • The ratio of the total degraded area to the joint specimen area (ΣΑ i /A joint) and the number of degraded zones (N) were correlated to the normal stress (σ/JCS) by a power-law relationship. Therefore, the area of damaged unevenness on a given joint area increased with increasing normal stress because the contribution of roughness to shear strength increased at this particular range of normal stress (i.e., σ/JCS = 0.0024–0.0195). This supports the fact that the contribution of the mechanical asperity failure component to shear strength increases with an increase in normal stress.

  • The average scales of the degraded zones (or damaged unevenness) were hardly affected by the normal stress. The maximum size of the degraded zones increased, and the minimum size of the degraded zones decreased with an increase in normal stress, such that the range of damaged unevenness scale became wider. This finding indicates that smaller asperities became more vulnerable to degradation at a higher normal stress.