# An Advanced Shear Strength Criterion for Rock Discontinuities Considering Size and Low Shear Rate
## 2 Method
### Design of the Direct Shear Test  
As mentioned in Section 2.1, in order to verify the feasibility of the new shear strength criterion and explore the applicability of the previous empirical equations (Table 1), the granite discontinuity used to establish the first empirical equation in Table 1 was selected as the counterpart and to conduct direct shear tests in this section [47]. A series of indoor direct shear tests on granite discontinuity samples with various sizes and regular sawtooth shapes under different shear rates were designed, and the experiments were conducted by making full use of a new dynamic direct shear testing device on rock joints named as TFD-500/1000-JS in the Key Laboratory of Shale Gas and Geoengineering. Institute of Geology and Geophysics, Chinese Academy of Sciences, as shown in Figure 1[58; 59]. The internal dimension (i.e., length) of the shear box for the test platform ranges from 100 mm to 1000 mm. The maximal shear rate can reach 1000 mm/s. All the index parameters of the new test platform are able to fulfill the requirement of dynamic direct shear tests [37; 60; 61]. Considering the size effects related to the discontinuity length and the undulated amplitude, the granite was cut and manufactured to artificial discontinuity samples with different dimensions and various regular sawtooth shapes by utilizing the digital control machine, as shown in Figure 2. The sawtooth profile was regarded as the first-order irregularities on the discontinuities of which the surfaces were randomly rough due to the processing uncertainty [19]. There were line-shape asperities spreading along the direction of the sample width, which belonged to the second-order irregularities [19]. The uniaxial compressive strength and the basic friction angle of granite discontinuity samples were obtained respectively via the uniaxial compression test and the tilt test on flat granite discontinuity samples [21; 37]. The geometric and strength parameters of granite discontinuity samples such as the sample length, undulated angle and amplitude, uniaxial compressive strength and basic friction angle were listed in Table 2.  
Taking the shear rate ranges in the previous empirical equations (Table 1) into account, the indoor direct shear tests on granite discontinuity samples with various sizes (i.e., lengths from 200 mm to 1000 mm and undulated amplitudes from 3 mm to 23 mm, as listed in Table 2) and regular sawtooth shapes under different low shear rates (0 mm/s to 1 mm/s) were conducted. For granite discontinuity  
Figure 1: Hardware schematic of the test platform [58; 59]. samples 1# to 3#, firstly, the normal stress was applied in the load control mode until to the pre-set value with 100 kPa or 200 kPa with the loading rate of 2.5 kPa/s, and then it remained constant. After that, the shear load was applied in the displacement control mode with a constant shear rate of 0.05 mm/s until to the displacement value with 9 mm, which was set in the test platform before the test. After the shear test, the next shear test was conducted on the identical sample under the same loading condition as mentioned above except that the shear rate was 0.1 mm/s. Then, the shear tests were conducted successively with the constant shear rate ranging from 0.2 mm/s to 1 mm/s once again. For the sample 4#, according to the above loading procedures, the normal stress was 200 kPa; the shear rates were 0.1 mm/s, 0.5 mm/s and 1 mm/s; the pre-set displacement value was 18 mm. For the granite discontinuity sample 5#, according to the above loading procedures, the normal stress was 100 kPa; the shear rate was ranging from 0.033 mm/s to 0.25 mm/s; the pre-set displacement value was 30 mm. During the direct shear tests, the shear load values were recorded in a real-time mode by the test platform.