# Impact of Rock Mass Strength Anisotropy with Depth on Slope Stability Under Excavation Disturbance
## 2 Disturbance Concept in the Hoek and Brown Failure Criterion  
The excavatability of a rock mass is closely related to the intact rock strength and the overall rock mass strength together with its discontinuity properties. Many studies in the rock mechanics literature discuss the excavatability of rock masses [8, 15, 16, 17, 18]. While mechanical excavation methods such as digging with excavators and ripping can be used to excavate weak rock masses, as the strength of the rock material and the quality of the rock mass increases, there is a need to loosen the rock mass in situ and reduce it to smaller block sizes through blasting. Clearly, the degree of disturbance due to every different technical process, such as digging, ripping, and blasting, can vary in a rock mass. After disturbance of the rock mass, depending on the excavation method, the apertures of the existing discontinuities increase (the loosening of the rock mass) and the block size decreases with the development of new cracks. [PERSON] et al. [19] schematically illustrated the concept of disturbance together with the effect on rock mass strength as shown in Figure 1a-d.  
During the period when the Rock Mass Rating (RMR) was used to assess the quality of rock masses within the Hoek-Brown failure criterion, two separate equations were recommended for determining the \(m\) and \(s\) constants--one for disturbed and one for undisturbed rock masses (Equations (1a)-(1e)). However, this approach posed a limitation in accurately defining varying degrees of disturbance. \[\sigma_{1}=\sigma_{3}+\sqrt{m\sigma_{3}\sigma_{ci}+s\sigma_{ci}^{2}}\] (1a) For disturbed rock mass: \[\frac{m}{m_{i}}=exp\left(\frac{RMR-100}{14}\right) \tag{1b}\] \[s=exp\left(\frac{RMR-100}{6}\right)\] (1c) For undisturbed rock mass: \[\frac{m}{m_{i}}=exp\left(\frac{RMR-100}{28}\right)\] (1d) \[s=exp\left(\frac{RMR-100}{9}\right) \tag{1e}\]  
The Geological Strength Index (GSI) was subsequently incorporated into the Hoek and Brown failure criterion in place of the Rock Mass Rating (RMR), due to RMR's inefficiency in rating very weak rock masses (RMR < 25). [PERSON] et al. (2010) replaced GSI with RMR\({}_{76}\) (1976 version of ratings of RMR parameters), which varies between 0 and 100, in their update, without providing any information about the disturbance condition, and used the relations related to the undisturbed rock mass condition from the 1988 version of the criterion. Figure 1: Schematic representation of disturbance effects on rock masses: (**a**) in situ undisturbed rock mass, (**b**) illustration of new crack development, (**c**) losing of rock mass, and (**d**) illustration of disturbance effects on shear strength envelope ([PERSON] and [PERSON], 2014). The concept of degree of disturbance by using a continuous relationship from an undisturbed rock mass to a completely disturbed rock mass was firstly introduced to the Hoek and Brown criterion by [PERSON] and [PERSON] [6]. To achieve this aim, a reduction factor, namely, a disturbance factor (D\({}_{t}\)) ranging from 0.8 for a completely disturbed condition to 1 for an undisturbed condition, was used in the denominator of the m and s equations to join continuously undisturbed to completely disturbed condition, as given in Equations (1b)-(1e). After this modification by [PERSON] and [PERSON] [6], it became possible to account for different degrees of disturbance, from basic mechanical excavation to uncontrolled blasting. Similar to the innovative disturbance degree approach proposed by [PERSON] and [PERSON] [6], a disturbance factor (D) ranging from 0 to 1 for an undisturbed and completely disturbed condition, respectively, was also adopted in the criterion by [PERSON] et al. [4]. The latest form of the criterion as presented by [PERSON] et al. [4] is given in Equations (2a)-(2d).