# Optimized Analysis Method for Evaluating the Shear Strength Parameters of Rock Joint Surfaces

Authors: Yao Xiao; Huafeng Deng; Jingcheng Fang; Hengbin Zhang; Jianlin Li
Journal: Advances in Civil Engineering
 (2020)

---

## Abstract

The results obtained from the mechanical test of rock samples inevitably suffer dispersion owing to discrepancies between test specimens. In view of these deficiencies, the present study proposes a method based on the empirical equation of shear strength developed by Barton to determine the shear strength parameters of joint surfaces using a single test specimen. This approach is then applied to optimize the analysis of multiple specimens. An analysis of experimental results verifies that the shear strength parameters of joint surfaces obtained by the proposed method can more accurately reflect the shear mechanics of multiple specimens than conventional multiple sample analyses; meanwhile, the results are reasonable and reliable. More importantly, the optimized method ensures the shear strength parameters are no longer affected by the sequence of specimens employed during shear test. The optimized analysis method eliminates the effect of differences between specimens and the influence of subjective factors on test results and therefore provides more realistic evaluations of shear strength parameters.


---

## Body

## 1. Introduction

The overall and local deformations and stability of an engineering rock mass are often controlled by discontinuous joint surface. Therefore, the reliability of rock mass deformation and stability analyses in engineering projects are directly affected by the accurate determination of the shear strength parameters of the joint surface. These parameters are commonly obtained by shear test, which is a type of destructive test employed to evaluate the shear strength of individual rock joint specimens. To obtain more generally applicable test results, multiple joint specimens are usually prepared to perform shear test under different normal stresses. Specifically, for the intact rock, its shear strength conforms to Mohr–Coulomb criterion, and its shear strength parameters are cohesionc and internal friction angle ϕ, while, for rough joint without filling, its cohesion c is zero, but a lot of experimental research studies show that for no filling rigid joint surface, there is a certain degree of cohesion [1], and in the action of stress, the joint surface will show damage characteristics of cutting tooth; theoretically cutting tooth of internal friction angle of the joint surface and friction angle of the tooth surface is different because they are close, so we approximately set friction angle of the tooth surface as internal joint angle of the joint surface [2]. Therefore, the cohesion and internal friction angle of the specimen surfaces are obtained by a fitting analysis conducted according to the Mohr–Coulomb criterion. However, the roughness and fluctuation of joint surfaces directly affect shear strength of joint specimens, and the difference between shear strength obtained for different joint surfaces can be significant even for shear tests conducted under equivalent normal stresses. Moreover, regardless of whether shear test is conducted with natural joint specimens collected on-site [3–6] or artificially prepared, joint specimens [7–13] have been widely studied, and it is impossible to ensure that all specimens have the same morphological feature on the joint surface. For example, by the study of Shang et al. [14], even for some rock joints with the same areal persistence, the measured shear strength is still different. At the same time, Ji et al. [15] found it is different to remove the effect of surface irregularity from the test results. In this case, different sections of structural plane surfaces are quite likely to yield significantly different results. As a result, the results obtained from shear test of the rock sample inevitably suffer dispersion owing to discrepancies between test specimens. In fact, specimen discrepancies can even mask the effects of the normal stresses, and shear strength can remain constant or even decrease with the increased normal stresses, depending on the order of rock specimens selected during the test. To reduce the impact of specimen discrepancies on the results of shear test, repeated tests are usually performed using multiple specimens at each level of applied stress in studies. However, repeated test has been demonstrated to be unable to effectively compensate for specimen discrepancies owing to the test time limitations in the study of You and Hua [16]. Therefore, the influence of specimen discrepancies on the shear strength parameters of the joint surface is an unavoidable problem when employing multiple joint specimens during mechanical test.To alleviate these deficiencies in conventional multiple specimen analyses, this paper proposes a method based on the empirical formula for the shear strength of rock joints proposed by Barton [17, 18] for determining the shear strength parameters of rock joints using a single test piece. This approach is then applied to optimize the analysis of multiple specimens. The proposed method seeks to eliminate the effect of specimen discrepancies and the effect of the test sequence on the results of shear test.


## 2. Shear Test Arrangement of the Rock Joint Specimen

Fresh sandstone blocks with weak structural planes are collected within the Three Gorges Reservoir area, and standard cubic specimens are prepared with dimensions of 100 mm × 100 mm × 100 mm. The cubic specimens are split along the middle to prepare single-joint specimens with relatively flat interfaces. A typical single-joint specimen is shown in Figure1.Figure 1
Typical single-jointed rock specimen.
(a)
(b)The shear tests are conducted under four normal stresses of 1.0 MPa, 1.5 MPa, 2.0 MPa, and 2.5 MPa. The repeated shear test is carried out on the YZW1000 microcomputer control electric direct shear instrument which is shown in Figure2. Shear direction is indicated by the arrow in Figure 1. According to Dieterich [19], different shear rates have different influences on the degree of wear on the structural surface of rock mass, thereby affecting the sliding friction coefficient of the structural surface; Sun [20] points out that the static loading rate limit of rough and clean joints is 0.01 mm/s, so the shear rate adopted in this paper is 0.005 mm/s. When shear strength of the rock sample reached a stable state, it is determined to be the termination condition of the test, and repeated shear tests are conducted for three samples under each normal stress condition.Figure 2
YZW1000 microcomputer control electric direct shear instrument.The loading process of shear test is shown in Figure3. After the sample is loaded into the shear box, the normal preload is first performed to ensure that the normal pressure probe is in good contact with the shear box; then, the normal load is applied (e.g., 1.0 MPa, 1.5 MPa, 2.0 MPa, and 2.5 MPa) followed by tangential preloading, which is to fix the upper shear box; finally, the tangential load is applied until the shear stress-strain curve shows a peak intensity and reaches a steady state.Figure 3
Schematic diagram of shear test loading process.


## 3. Test Results and Discussion

### 3.1. Analysis of Shear Test Data

The shear strength test value of each specimen in ascending order and the average shear strength value for each applied stress are listed in Table1. We note that the difference between the maximum and minimum shear strength values obtained under the four normal stresses of 1.0 MPa, 1.5 MPa, 2.0 MPa, and 2.5 MPa is 0.14 MPa, 0.30 MPa, 0.60 MPa, and 0.40 MPa, respectively. The dispersion in the shear strength results under equivalent normal stresses is obvious. The analysis clearly demonstrates that, although the joint specimens are prepared by an equivalent method and are macroscopically identical, the roughness coefficient values of the joint surfaces are not the same, and this variability in the microtopography of the joint surface affects the shear strength result of the individual specimen.Table 1
Experimental shear strength values of the joint specimens.
σ
n (MPa)
τ (MPa)
Average value ofτ (MPa)
1.0
1.07
1.13
1.21
1.14
1.5
1.30
1.51
1.60
1.47
2.0
1.70
1.96
2.30
1.99
2.5
2.46
2.60
2.86
2.64


### 3.2. Conventional Multiple-Specimen Method for Determining the Shear Strength Parameters

The shear strength parameters of joint surfaces are usually analyzed either by fitting the average values obtained under the various normal stresses (denoted as method 1) or by fitting the individual values obtained under the normal stresses (denoted as method 2). The fitting results for methods 1 and 2 are given in Figures4 and 5, respectively. The cohesion c1 and internal friction angle ϕ1 values for method 1 and those for method 2 (i.e., c2 and ϕ2) are then obtained by fitting to the respective curves from methods 1 and 2, respectively.Figure 4
Shear strength parameters obtained by fitting average shear strength values of the joint specimens (method 1).Figure 5
Shear strength parameters obtained by fitting individual shear strength values of the joint specimens (method 2).It can be noted from Figures4 and 5 that the shear strength parameters of the joint surface obtained by the two methods are the same, where the cohesion c1 = c2 = 0.05 MPa and the internal friction angle ϕ1 = ϕ2 = 45.15°. Because the joint surfaces are prepared by the splitting method, the fitting degree given by the correlation coefficient R2 is very high (i.e., 0.9701 and 0.8955 for Figures 4 and 5, respectively). According to the shear strength theory of joint surfaces proposed by Patton, a joint surface will exhibit two different types of stress and damage associated with tooth cutting interactions and the climbing slope effect under the action of shear test. Due to tooth cutting interactions, the joint surfaces exhibit some degree of cohesion.While the value ofR2 obtained for method 1 is greater than that obtained for method 2, previous research has suggested that the use of method 2 presenting the discrete distribution of the test results is more intuitive and faithful in previous research by You and Hua [16]. However, neither of these methods effectively consider the influence of specimen discrepancies on the test results. Without distinguishing the difference between specimens, the shear strength parameters obtained by directly fitting the data can neither faithfully reflect the effect of normal stress on the shear strength nor can faithfully reflect the shear strength of a group of specimens even if the value of R2 is high. Nevertheless, shear test under varying normal stresses provides a considerable amount of useful information that should be fully analyzed and applied [14, 15]. As such, developing a suitable analysis method to obtain shear strength parameters that can better reflect the shear characteristics of the rock mass joint surface is of paramount importance.


## 3.1. Analysis of Shear Test Data

The shear strength test value of each specimen in ascending order and the average shear strength value for each applied stress are listed in Table1. We note that the difference between the maximum and minimum shear strength values obtained under the four normal stresses of 1.0 MPa, 1.5 MPa, 2.0 MPa, and 2.5 MPa is 0.14 MPa, 0.30 MPa, 0.60 MPa, and 0.40 MPa, respectively. The dispersion in the shear strength results under equivalent normal stresses is obvious. The analysis clearly demonstrates that, although the joint specimens are prepared by an equivalent method and are macroscopically identical, the roughness coefficient values of the joint surfaces are not the same, and this variability in the microtopography of the joint surface affects the shear strength result of the individual specimen.Table 1
Experimental shear strength values of the joint specimens.
σ
n (MPa)
τ (MPa)
Average value ofτ (MPa)
1.0
1.07
1.13
1.21
1.14
1.5
1.30
1.51
1.60
1.47
2.0
1.70
1.96
2.30
1.99
2.5
2.46
2.60
2.86
2.64


## 3.2. Conventional Multiple-Specimen Method for Determining the Shear Strength Parameters

The shear strength parameters of joint surfaces are usually analyzed either by fitting the average values obtained under the various normal stresses (denoted as method 1) or by fitting the individual values obtained under the normal stresses (denoted as method 2). The fitting results for methods 1 and 2 are given in Figures4 and 5, respectively. The cohesion c1 and internal friction angle ϕ1 values for method 1 and those for method 2 (i.e., c2 and ϕ2) are then obtained by fitting to the respective curves from methods 1 and 2, respectively.Figure 4
Shear strength parameters obtained by fitting average shear strength values of the joint specimens (method 1).Figure 5
Shear strength parameters obtained by fitting individual shear strength values of the joint specimens (method 2).It can be noted from Figures4 and 5 that the shear strength parameters of the joint surface obtained by the two methods are the same, where the cohesion c1 = c2 = 0.05 MPa and the internal friction angle ϕ1 = ϕ2 = 45.15°. Because the joint surfaces are prepared by the splitting method, the fitting degree given by the correlation coefficient R2 is very high (i.e., 0.9701 and 0.8955 for Figures 4 and 5, respectively). According to the shear strength theory of joint surfaces proposed by Patton, a joint surface will exhibit two different types of stress and damage associated with tooth cutting interactions and the climbing slope effect under the action of shear test. Due to tooth cutting interactions, the joint surfaces exhibit some degree of cohesion.While the value ofR2 obtained for method 1 is greater than that obtained for method 2, previous research has suggested that the use of method 2 presenting the discrete distribution of the test results is more intuitive and faithful in previous research by You and Hua [16]. However, neither of these methods effectively consider the influence of specimen discrepancies on the test results. Without distinguishing the difference between specimens, the shear strength parameters obtained by directly fitting the data can neither faithfully reflect the effect of normal stress on the shear strength nor can faithfully reflect the shear strength of a group of specimens even if the value of R2 is high. Nevertheless, shear test under varying normal stresses provides a considerable amount of useful information that should be fully analyzed and applied [14, 15]. As such, developing a suitable analysis method to obtain shear strength parameters that can better reflect the shear characteristics of the rock mass joint surface is of paramount importance.


## 4. Single-Specimen Method for Determining the Shear Strength Parameters

Barton [17, 18] established an empirical equation to evaluate the shear strength τ of the joint surface based on a statistical analysis of shear test data obtained for more than 200 artificial shear joints. The accuracy of this formula has been confirmed in vast studies [1, 21–27]. The equation is given as follows:(1)τ=σntanJRClog10JCSσn+ϕb,where σn is the normal stress, JRC is the joint roughness coefficient, JCS is the compressive strength of the joint surface (given as 50 MPa which is measured by the rebound method), and ϕb is the basic internal friction angle of the joint surface (given as 30° from the test results). By rearranging equation (1), we obtain the calculation equation of JRC:(2)JRC=arctanτ/σn−ϕblog10JCS/σn.We present a method based on equations (1) and (2) to calculate the shear strength parameters of the joint surface using shear test data obtained for a single specimen. The specific steps of the method are given as follows.Firstly, calculate JRC using equation (2) according to the test value of τ obtained under a single value of σn, as shown in Table 2.Table 2
Joint roughness coefficients (JRC).
Serial number
σ
n (MPa)
Experimental value ofσ (MPa)
JRC
1
1.0
1.07
9.97
2
1.13
10.88
3
1.21
12.02
4
1.5
1.30
7.17
5
1.51
9.97
6
1.60
11.06
7
2.0
1.70
7.41
8
1.96
10.32
9
2.30
13.58
10
2.5
2.46
11.17
11
2.60
12.39
12
2.86
14.48Secondly, calculate the values ofτ expected for the specimen under other values of σn using equation (1). In this way, the values of τ can be obtained under multiple values of σn by calculations based on a single shear test.Thirdly, the experimental values and calculated values ofτ obtained under different values of σn are subjected to linear fitting to determine the shear strength parameters of the joint specimen. This is referred to herein as the single-specimen method.The proposed single-specimen method was applied to the test results of the twelve specimens discussed in the previous section. The results are shown in Table3.Table 3
Shear strength parameters calculated using the proposed single-specimen method.
Serial number
σ
n (MPa)
Experimental value ofτ (MPa)
Theoretical value ofτ (MPa)
c (MPa)
ϕ (°)
1
1.0
1.07
—
0.24
39.99
1.5
—
1.51
2.0
—
1.93
2.5
—
2.33
2
1.0
1.13
—
0.28
40.85
1.5
—
1.58
2.0
—
2.02
2.5
—
2.43
3
1.0
1.21
—
0.33
41.90
1.5
—
1.68
2.0
—
2.13
2.5
—
2.56
4
1.0
—
0.91
0.15
38.34
1.5
1.30
—
2.0
—
1.68
2.5
—
2.05
5
1.0
—
1.07
0.24
39.31
1.5
1.51
—
2.0
—
1.93
2.5
—
2.33
6
1.0
—
1.14
0.29
40.99
1.5
1.60
—
2.0
—
2.03
2.5
—
2.45
7
1.0
—
0.91
0.16
37.52
1.5
—
1.32
2.0
1.70
—
2.5
—
2.07
8
1.0
—
1.09
0.25
40.32
1.5
—
1.54
2.0
1.96
—
2.5
—
2.37
9
1.0
—
1.33
0.40
42.98
1.5
—
1.83
2.0
2.30
—
2.5
—
2.74
10
1.0
—
1.15
0.29
41.12
1.5
—
1.61
2.0
—
2.03
2.5
2.46
—
11
1.0
—
1.24
0.34
41.92
1.5
—
1.72
2.0
—
2.17
2.5
2.60
—
12
1.0
—
1.41
0.46
44.06
1.5
—
1.92
2.0
—
2.40
2.5
2.86
—Table3 shows that the calculated values of c for the twelve specimens range from 0.15 MPa to 0.46 MPa with a mean of 0.28 MPa, and the calculated values of ϕ range from 37.52° to 44.06° with a mean of 40.78°.Histograms of the shear strength parameters listed in Table3 are given in Figure 6. It is noted that both histograms obey normal distributions.Figure 6
Histogram of the cohesion calculated for the joint surfaces: (a) cohesion; (b) internal friction angle.
(a)
(b)Shear strength parameters of the specimens given in Table3 suggest two aspects that should be explained.(1)
The cohesion values obtained for the twelve specimens range from 0.15 MPa to 0.46 MPa, and the internal friction angle values range from 37.52° to 44.06°. Accordingly, the shear strength parameters of each specimen are notably different.(2)
The shear test conducted under different normal stresses employed many samples with obvious difference. Therefore, the shear strength parameters obtained from the analysis should represent a comprehensive embodiment of the shear strength of the group of samples employed. Theoretically, an analysis of the shear strength parameters of the joint surface should be consistent with the mean values ofc and ϕ given in Table 3. However, compared with the values of c and ϕ given in Table 3, we note that the conventional analyses of multiple specimens provide a value of c that is significantly less than the average of Table 3 (0.05 MPa versus 0.28 MPa) and a value of ϕ that is significantly greater than the average of Table 3 (45.15° versus 40.78°). These results further illustrate the deficiencies of the standard multiple-specimen method. The cause of these deficiencies is mainly related to the order of selected samples during the test. A detailed analysis of this effect will be introduced in the following section.


## 5. Optimization Method for Determining the Shear Strength Parameters

To address the above problems, we plot the experimental and theoretical values ofτ obtained for the joint specimens in Figure 7; we note the values of τ obtained for all specimens lie between the upper and lower limit envelopes, and the results are presented in Table 4.Figure 7
Optimization analysis of the shear strength parameters of joint specimens.Table 4
Analysis results of the shear strength parameters of joint specimens.
Analysis method
c (MPa)
ϕ (°)
Extreme value line 1
0.98
23.12
Extreme value line 2
−0.40
52.49
Conventional multiple-specimen method
0.05
45.15
Single-specimen method
0.28
40.80
Optimization method
0.29
40.85The difference between the specimens produced a significant effect on the selection of which the specimens should be tested by the multiple-specimen method under which normal stress. This can be examined according to the two extreme values in the analysis shown in Figure7 and Table 4. According to the general data analysis method, the first extreme value is obtained as a line between the specimen with the largest value of τ at the lowest value of σn and the specimen with the smallest value of τ at the highest value of σn. The corresponding fitted line is shown by extreme line 1 in Figure 7, where the value of c obtained by the fitting is the largest and the value of ϕ is the smallest, i.e., 0.98 MPa and 23.12°, respectively. The other extreme value is obtained as a line between the specimen with the lowest value of τ at the lowest value of σn and the specimen with the highest value of τ at the highest value of σn. The corresponding fitted line is shown by extreme value line 2 in Figure 7, where the value of c obtained by the fitting is the smallest and value of ϕ is the largest, i.e., −0.40 MPa and 52.49°, respectively. Because the order of specimen selection in the multiple-specimen method is random, the obtained shear strength parameters must lie between extreme value line 1 and line 2, with a value of c between −0.40 MPa and 0.98 MPa and a value of ϕ between 23.12°and 52.49°. We note that the possible ranges of c and ϕ are very extensive, and a negative value of c and greater than 50°of ϕ are obviously not consistent with the shear mechanics of the structural plane itself.The previous analysis suggests that the experimental values and calculated values ofτ for each specimen shown in Figure 7 should be fitted altogether to more comprehensively reflect the shear strength of the entire group of samples. The value of c obtained by this optimized analysis method is 0.29 MPa, and the value of ϕ is 40.85°.As can be seen from Table4, the results obtained by this optimized analysis method are very close to the average shear strength parameters of the twelve specimens obtained by the single-specimen method, which indicate that the optimized analysis method is reasonable and credible. Simultaneously, the results obtained by the proposed optimized analysis method are not affected by the order with which multiple specimens are subjected to shear test, which eliminates the influence of the specimen sequence on the results of fitting analysis and thus also eliminates subjective factors affecting test results.


## 6. Conclusions

Individual shear tests of joint specimens can only represent the shear strength of the joint surface under the applied normal stress; therefore, this kind of shear test cannot completely reflect the shear mechanics of the specimen under other normal stresses. Accordingly, the results obtained from the shear test of multiple rock specimens inevitably suffer discrete phenomenon owing to discrepancies between test specimens. The single-specimen method proposed in this paper based on the empirical equation for the shear strength of the joint surface which is proposed by Barton can determine the JRC of the joint surface, determine the shear strength of a joint surface under different normal stresses through a single shear test, and then determine the shear strength parameters of the individual joint surface by conducting linear fitting of the single experimental data point along with the calculated data points. This approach is then applied to optimize the analysis of multiple specimens. As a result, the obtained shear strength parameters are the same as those of the group. Analysis of the shear strength parameters of multiple joint surfaces obtained by the optimized method verified that the calculation results are reasonable and reliable.The results of shear strength parameters of the joint surface obtained according to the proposed method are not affected by the sequence of specimens employed during shear test. This eliminates the effect of difference between specimens and the influence of subjective factors on the test results, therefore provides more realistic evaluation of shear strength parameters. An analysis of experimental results verified that the shear strength parameters of the joint specimen obtained by the proposed approach are obviously more reasonable and credible than those obtained by conventional multiple-specimen fitting analyses.The work in this paper is based on Barton’s empirical shear strength formula. For other similar joint surface shear strength empirical formulas, they can also be directly applicable as long as they can better reflect the difference characteristics of the joint surface and the correlation of shear strength.



---

*Source: 8914015-2020-01-03.xml*