# An Advanced Shear Strength Criterion for Rock Discontinuities Considering Size and Low Shear Rate
## 1 Introduction  
Discontinuities commonly exist in the natural rock mass, occurring at different scales, such as the fault and the joint [1; 2; 3; 4]. They are weak and discontinuous interfaces along which the failure and mobilization of the rock mass initiate under both gravity and earthquakes. Namely, the mechanical behavior of the rock mass is prominently influenced by the discontinuity [5; 6; 7; 8; 9]. In the past few decades, strong earthquakes have taken place all over the world, triggering thousands of co-seismic landslides. According to post disaster investigations, it was found that these co-seismic landslides were mainly controlled by discontinuities in the slope rock mass [10; 11; 12]. As a matter of fact, the instability of the rock mass under the earthquake mainly resulted from the dynamic response of the rock discontinuity, which interacted with the stress wave and further produced dynamic deformation and failure [13; 14; 15]. The key to evaluate the stability of the rock mass under an earthquake is to quantitatively describe the dynamic characteristics of the rock discontinuity, among which the dynamic shear strength is the most important property [16; 17]. Many researchers experimentally explored the shear characteristics of the rock discontinuities mainly taking into account the roughness and friction angle of the discontinuity, the compression strength of the rock as well as the normal stress [18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29]. It was found that the peak shear strength of the rock discontinuities increased with the values of these factors increasing. Due to the irregularity of the geometrical morphology of the rock discontinuities, it was often very difficult to theoretically characterize their roughness [30; 31; 32; 33; 34; 35; 36]. As a result, the shear strength of the rock discontinuities was usually characterized by empirical equations [18; 19; 20; 21; 22; 24; 25; 26; 27; 28; 29], among which the Barton shear strength empirical equation is now the ISRM-suggested equation and has been widely used to evaluate the stability of the rock mass under the gravity [37; 38]. Furthermore, [PERSON] and [PERSON] [39; 40] found that the peak shear strength of the rock discontinuities had an obvious size effect, i.e., the shear strength decreased with the increase of the discontinuity length along the shear direction (discontinuity length for short in the following). On this basis, they put forward the empirical equations of influence factors for shear strength considering the effect of discontinuity length. Nevertheless, it showed that the size effects of shear strength for the rock discontinuities were induced by not only the discontinuity length but also the discontinuity undulated amplitude of the shear contact surfaces (undulated amplitude for short in the following) [41; 42; 43; 44; 45; 46]. An important finding was that the shear strength increased with the increase of the undulated amplitude. However, in the above studies, the shear characteristics of the rock discontinuities were researched without taking into account the shear rate, while many experimental studies showed that it significantly influenced the shear strength of the rock discontinuities [47; 48; 49; 50; 51; 52; 53; 54; 55; 57]. They indicated that the shear strength of the rock discontinuities, such as serine and concrete discontinuities, increased with the shear rate, rising in the range of 0 mm/s to 1 mm/s. Meanwhile, for the rock discontinuities such as sandstone and cement, the shear strength decreased with the shear rate's increase. Additionally, many researchers established an empirical equation (Table 1) to characterize the shear strength of the rock discontinuities under different shear rates [48; 51; 53; 54; 55]. Among the empirical equations in Table 1, Equations (c) and (d) were improved based on the Barton shear strength empirical equation [53; 54]. Nevertheless, there still existed some defects for these equations.