# An Advanced Shear Strength Criterion for Rock Discontinuities Considering Size and Low Shear Rate
## 4 Discussion  
As shown in Figure 7, it can be seen that the theoretically predicted results calculated by the Barton shear strength empirical equation keep invariant with the shear rate increasing. For small samples (1# to 4#), the theoretically predicted shear strength results overestimate the experimental results while they underestimate the test data for the large sample (5#). It has no capability of prediction on the rate-dependent increasing tendency of granite discontinuity samples. It also displays that previous empirical Equations (a) to (c) cannot predict the peak shear strength of granite discontinuity samples accurately. For one thing, the theoretically predicted results calculated via previous empirical equations are obliviously different from the experimental results. For another, the variation trends  
Figure 7: Comparison on the peak shear strength between the experimental data and the predicted results for granite discontinuity samples (a) Case of sample 1#; (b) Case of sample 2#; (c) Case of sample 3#; (d) Case of sample 4#; (e) Case of sample 5#. Note that in case of sample 1#, the predicted results calculated via Equation (c) are negative which were not drawn. of the theoretically predicted results are opposite to those of the experimental results. In detail, the theoretically predicted shear strength results calculated by Equation (a) are almost invariable and basically independent on the shear rate; while the theoretically predicted results calculated via Equations (b) and (c) decrease with the shear rate increasing. Nevertheless, the results predicted by the new shear strength criterion agree well with the experimental results in terms of both the value and the variation tendency. As mentioned above, it indicates that Equations (a) to (c) are not applicable from two aspects, i.e., the value and the variation trend to predict the shear strength of granite discontinuity samples taking into account the shear rate. The reason for this may be attributed to the difference of the material property. It is reported in Section 1 that there exists two types of rock materials. One has the shear rate-strengthening effect for the shear strength of the rock discontinuities such as concrete, the other has the shear rate-weakening effect for the shear strength of the rock discontinuities such as cement [49; 52; 54]. Equations (b) and (c) were established respectively based on the shear tests of cement and cement mortar discontinuities [51; 53]. Thus, the theoretically predicted results from Equations (b) and (c) are not applicable to predict the experimental results of granite discontinuity samples, which increase with the shear rate increasing. Compared with previous equations (Equations (a) to (c)), the new shear strength criterion is applicable to predict the shear strength of both the rock discontinuities with the shear rate-strengthening effect such as granite and discontinuities with the shear rate-weakening effect such as cement under various shear rates, by setting different values of coefficient \(M\). According to Equation (9), the intercept value is much closer to the basic friction angle than that (36.432\({}^{\circ}\)) obtained by [54], which indicates that the new shear strength criterion has a better prediction accuracy than the previous equation, such as Equation (d) proposed by [54]. This equation did not take both the discontinuity length and the undulated amplitude into account simultaneously. According to Figure 7, the error values indicate that the larger the scale of the rock discontinuities, the higher the accuracy of the new shear strength criterion. In practical applications, the length of the rock discontinuity ranges from meters to kilometers. Hence, the new shear strength criterion is applicable and feasible for the evaluation of the stability of the rock mass.