## 3 Data and Methodology
### Rock Mass Quality Evaluation
#### 3.5.2 Rock Mass Quality Evaluation Based on Geological Strength Index (GSI)  
Estimating rock mechanical parameters is a crucial step for subsequent numerical simulations of landslide deformation analysis. In this study, rock mass parameters are assessed using the GSI classification system along with the Hoek-Brown failure criterion. The generalized Hoek-Brown criterion is expressed as [36]:  
\[\sigma_{1}=\sigma_{3}+\sigma_{ci}\bigg{(}m_{b}\frac{\sigma_{3}}{\sigma_{ci}}+s \bigg{)}^{a} \tag{1}\]  
Figure 10: (**a**) Distribution of fracture sampling windows; (**b**) Sampling window for gristtone; (**c**) Sampling window for medium sandstone; (**d**) Sampling window for fine sandstone; (**e**) Sampling window for mudstone; (**f**) Sampling window for sandy mudstone.  
where \(m_{b}\), \(s\), and \(a\) are the rock mass material constants given by  
\[m_{b}=m_{i}exp\bigg{(}\frac{GSI-100}{28-14D}\bigg{)} \tag{2}\]  
\[s=exp\bigg{(}\frac{GSI-100}{9-3D}\bigg{)} \tag{3}\]  
\[a=\frac{1}{2}+\frac{1}{6}\Big{(}e^{-GSI/15}-e^{-20/3}\Big{)} \tag{4}\]  
where \(D\) represents the disturbance factor, which depends on the extent of disturbance caused by blast damage and stress relaxation, and mi is the Hoek-Brown constant.  
[PERSON] and [PERSON] [37] introduced two parameters, namely, the structural rating (SR) and surface condition rating (SCR), which are based on the volumetric discontinuity frequency (\(J_{v}\)), to quantitatively estimate the GSI. In this study, the window sampling method was employed to collect fundamental parameters, and the values were computed using the following equation [38]:  
\[J_{v}=1/S_{1}+1/S_{2}+1/S_{3}+L+1/S_{n}+N_{r}\Big{(}5\sqrt{A}\Big{)} \tag{5}\]  
where \(S_{i}\) denotes the mean spacing of each fracture set, \(N_{r}\) represents the number of fractures, and \(A\) denotes the area of the sampling window.  
Upon acquiring a GSI estimate, the mechanical parameters of rock masses were computed using the Hoek-Brown failure criterion [39]. Numerous studies have shown that the Hoek-Brown criterion followed by the rock mass can be approximated by a straight line when \(\sigma_{t}<\sigma_{3}<\sigma_{3 max}\) is satisfied. Then, the equivalent internal friction angle (\(\varphi_{m}\)) and the equivalent cohesion (\(C_{m}\)) of the Mohr-Coulomb criterion for damaged rock masses can be determined after a series of formula transformations [40]. The specific equations are as follows:  
\[\varphi_{m}=sin^{-1}\Bigg{[}\frac{3 am_{b}(s+m_{b}\varphi_{3n})^{a-1}}{(1+a)(2 +a)+3 am_{b}(s+m_{b}\varphi_{3n})^{a-1}}\Bigg{]} \tag{6}\]  
\[c_{m}=\frac{\sigma_{ci}[(1+2a)s+(1-a)m_{b}\sigma_{3n}](s+m_{b}\sigma_{3n})^{a -1}}{(1+a)(2+a)\sqrt{1+\Big{[}6 am_{b}(s+m_{b}\sigma_{3n})^{a-1}\Big{]}/[(a+1)( a+2)]}} \tag{7}\]  
where \(\sigma_{3n}^{\prime}=\sigma_{3 max}/\sigma_{ci}\).  
In addition, when \(\sigma_{ci}\) < 100 MPa, the deformation modulus of the rock mass can be estimated using the following equation:  
\[E_{m}=\bigg{(}1-\frac{D}{2}\bigg{)}\sqrt{\frac{\sigma_{ci}}{100}}\times 10^{[( GSI-10)/40]} \tag{8}\]  
when \(\sigma_{ci}\) > 100 MPa, the following formula is used  
\[E_{m}=\bigg{(}1-\frac{D}{2}\bigg{)}\cdot 10^{[(GSI-10)/40]} \tag{9}\]