# Impact of Rock Mass Strength Anisotropy with Depth on Slope Stability Under Excavation Disturbance
## 3 Approaches to the Use of Disturbance Factor on Rock Slope Excavations
In our study a schematic representation of the input parameters given in Figure 2 was prepared to clarify the terminology used by [PERSON] et al. [10]. While the disturbance factor is equal to one (D = 1) from the excavated surface to the depth of the FDL, Equations (3a) and (3b) were proposed by [PERSON] et al. [10] for a gradual decrease of D from 1 to zero. \[D=\frac{ln(H)-ln(H_{i})}{decay} \tag{3a}\] \[decay=-\left(\frac{FDL}{H}\right) \tag{3b}\]  
where D: [PERSON] et al. 's [4] the disturbance factor, H\({}_{i}\): increase in slope height, H (or UDL): general slope height, FDL: total disturbance depth. [PERSON] et al. [10] proposed a classification, namely, the Rock Mass Disturbance Rating (DR in percentage), which includes nine input parameters to determine the depth of the fully disturbed zone (FDL) from the excavation surface. The Rock Mass Disturbance Rating proposed by [PERSON] et al. [10] is openly accessible on the web. The FDL can be estimated by multiplying the DR with the UDL. Among the parameters in the DR classification, particularly the structural elements such as \"Fore dipping structure\", \"Back dipping structure\", and \"Perpendicular structure\", it can be argued that using these parameters in the rating aimed at determining the depth of the fully disturbed zone (FDL) may be debatable. This is because these parameters are related to the anisotropic behavior of the rock mass. However, as is well known, the Hoek and Brown criterion is only applicable to the isotropic rock mass condition. Therefore,  
to depth. However, it is an acceptable reality that the excavation disturbance of a rock mass decreases gradually from the surface to a depth. Similarly, with this inference, as can be seen from a graphical presentation given by [PERSON] et al. (2010), the yielded rock mass in percentage versus depth graph for both the southeast wall of the HVC Lornex Pit and northeast of the HVC Valley Pit exhibit an inverse \"S\" shaped trend. In this study, an inverse \"S\" shaped equation was proposed to define the continuous decrease in transitional rock mass disturbance from the surface to a depth (Equation (5)). The structure of [PERSON] et al. 's ([PERSON] et al., 2016) equation was used in the derivation of the equation. In the developed inverse \"S\" shaped equation degree of decreasing in rock mass disturbance with depth is less until DfL (disturbed rock mass limit); after DfL, the decreasing trend of the transitional rock mass disturbance is similar to the exponential trend. \[D(z_{n})=D_{f}\bigg{(}1-\frac{50}{50+k^{(100-100z_{n})/15}}\bigg{)}\bigg{(} \frac{100z_{n}}{100z_{n}+1}\bigg{)} \tag{5a}\] \[k=1.8254e^{2.8249 DfL_{n}}\] (5b) \[z_{n}=z/UDL \tag{5c}\]  
where Df is the maximum disturbance factor on the face of the excavation, DfL\({}_{n}\) is the DfL (disturbed rock mass limit) normalized to UDL, z is the depth from excavation surface, z\({}_{n}\) is the normalized depth (z) to UDL, and the k value determined with DfL is related to the extremum point of the developed equation, which satisfies the yielded rock mass of \(\sim\)90% \(\pm\) 5, consistent with the southeast wall of the HVC Lornex Pit and northeast of the HVC Valley Pit cases studied by [PERSON] et al. (2010). In order to obtain reasonable inverse S shaped curves, k should not be taken to be less than 3. For the approaches listed above, representative graphical presentations depending on the normalized depth to UDL are given in Figure 3 in order to understand them well. The approaches for the use of transitional disturbance factors consider a determination of disturbance factors for every slice above the failure surface by considering a depth of slice from the bottom surface of the slope. Figure 3: _Cont._