# Influence of Rock Slide Geometry on Stability Behavior during Reservoir Impounding
## 3 Rock Slide Characterization and Dam Reservoir-Related Mechanisms
### Block Model  
In order to study and present the impact of reservoir impounding on the stability evolution of deep-seated rock slides in detail, an analytical block model was developed, comprising the essential features and geometries. For this block model, the geometry of the rock slide is divided into four individual blocks, each with a planar plane representing the basal shear zone. In reality, sections of planar shear zones are rare, but a major advantage of this approach over methods such as those of vertical slices is its simplicity and comprehensibility  
The dip angles of the planar basal shear zone sections of blocks 1, 2, 3, and 4 were assigned to \(\alpha=37.4^{\circ}\), \(\beta=29.7^{\circ}\), \(\varepsilon=18.0^{\circ}\), and \(\delta=8.1^{\circ}\), respectively (Tables 1 and 2). For this calculation, cohesion is neglected and assumed as c = 0 kPa. According to the back-calculations, a friction angle of the basal shear zone for each block of \(\varphi_{b}=24.2^{\circ}\) is needed to meet equilibrium state (FoS = 1) if no reservoir is available. This means that blocks 1 and 2 are unstable, pushing onto the resisting blocks 3 and 4. The effective cohesion c\({}_{\rm r}\) and friction angle \(\varphi_{\rm r}\) along the steeply inclined contact planes between the individual blocks are set to c\({}_{\rm r}\) = 0 kPa and \(\varphi_{\rm r}\) = 30\({}^{\circ}\). In order to investigate the influence of the reservoir on the stability of the rock slide, water pressures related to the reservoir level were applied. The water pressures are given by a horizontal phreatic level based on the assumption that the rock slide mass is highly permeable and overlying a compact, less permeable bedrock. For the sake of simplicity and comparability, a rising groundwater table within the rock slide and bedrock was neglected, but it is obvious that such a water table exists in natural conditions. The calculation is based on the equilibrium of forces; moments were not taken into account. The factor of safety against sliding is defined by the ratio of the sum of the shear resistance, \(\sum T_{i}\), on the base of the individual blocks (n = 4) to the sum of the applied shear forces, \(\sum S_{i}\), and is calculated by \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Block No.** & **Block Area** & **Shear Zone Dip** & **Shear Zone** & **Contact** \\  & **[m\({}^{2}\)]** & **[\({}^{\circ}\)]** & **Length [m]** & **Plane [m]** \\ \hline Block 1 & 128,676 & \(\alpha=37.4\) & OA = 1145.3 & AB = 236.5 \\ Block 2 & 122,635 & \(\beta=29.7\) & AC = 504.8 & CD = 272.2 \\ Block 3 & 143,402 & \(\varepsilon=18.0\) & CE = 569.6 & EF = 246.7 \\ Block 4 & 45,915 & \(\delta=8.1\) & EF = 276.6 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Geometrical parameters of the rock slide profile (see Figure 1). Figure 2: Geometry and internal and external forces acting on block 1 (**a**), block 2 (**b**), block 3 (**c**), and block 4 (**d**). \[FoS=\frac{\sum_{i=1}^{n}T_{i}}{\sum_{i=1}^{n}S_{i}} \tag{1}\]  
The shear resistance on the base of the blocks is given by the Mohr-Coulomb failure criterion, transformed into forces, yielding  
\[T_{i}=c_{b}\cdot A_{b}+\text{N}_{i}\cdot\tan(\phi_{b}), \tag{2}\]  
where \(N_{i}\) is the sum of the normal reaction forces at the base of the individual blocks, \(\varphi_{b}\) the friction angle, \(c_{b}\) the cohesion, and \(A_{b}\) the area of the basal shear zone section. The block geometries and external and internal forces of individual blocks are shown in Figure 2.  
The shear force \(S_{1}\) of block 1 acting down the plane is calculated as  
\[S_{1}=W_{1}\cdot\sin(\alpha)-Z_{1}\cdot\cos(\alpha/2)-Q_{1}\cdot\sin(\alpha/2), \tag{3}\]  
where \(W_{1}\) is the weight force, and \(Z_{1}\) and \(Q_{1}\) are interaction forces. For block 2, the calculation procedure of the shear force is similar.