## 2 Materials and Methods  
### Key Studies on Rock Mass Disturbance  
A simple definition of a rock mass is an engineering volume composed of rock material and the discontinuity planes that bound it. In engineering applications such as dams, tunnels, and slopes, it is inevitable that the virgin stress state of the rock mass will change. Excavation of rock masses is required in many rock mechanics applications, such as dam construction, mining activities, and highway construction. For such technical initiatives, from an engineering perspective, excavation costs should be minimized as much as possible by using optimum excavation methods (e.g., blasting, digging, ripping, drilling) based on the mechanical properties of the rock masses. Depending on the excavation method applied in slope excavations, new cracks develop, with their abundance decreasing from the excavation surface to the depth. As discussed by [PERSON] and [PERSON] [6], another disturbance effect that increases in significance with increasing slope excavation depth is the removal of the rock mass, resulting in stress relief. This causes the surrounding rock mass to relax and dilate. The guidelines for estimating the disturbance factor (\(D\)) proposed by [PERSON] et al. [3] were revised by [PERSON] and [PERSON] [6], considering both stress relaxation and blasting damage. However, the updated guideline, which includes stress relaxation and blasting damage, provides descriptions of rock masses that define only two classes based on the scale of slopes. The first description, based on the disturbance viewpoint, refers to relatively small-sized slopes typically encountered in civil engineering applications. For this category of relatively small slopes, \(D=0.5\) is recommended for controlled presplit or smooth-wall blasting with moderate rock mass damage. The second description, based on the disturbance viewpoint, pertains to relatively large open-pit mine slopes. According to the rock mass disturbance description for large-scale slopes provided by [PERSON] and [PERSON] [6], stress reduction damage primarily due to stress relief occurs, even when mechanical excavation methods are applied to excavate slopes in some weak rock masses. In this case, the use of \(D=0.7\) as the minimum disturbance factor is recommended. On the other hand, \(D=1.0\) is recommended for production blasting, regardless of the slope scale. Although the most recent version of the Hoek-Brown failure criterion incorporates continuous relations for the disturbance factor, no accepted relationship exists between the lower (\(D\) = 0.5 or \(D\) = 0.7, depending on the rock mass disturbance description) and upper (\(D\) = 1.0) limits of \(D\) values. In other words, the selection of intermediate \(D\) values at the design stage is entirely left to the practitioner's experience. [PERSON] et al. [7] derived a continuous relation of \(D\) by considering the ratio of disturbed to undisturbed rock from existing empirical relations in a deformation modulus (Equations (5) and (6)). \[E_{m}= \begin{cases}\left(1-\frac{D}{2}\right)\sqrt{\frac{\sigma_{c}}{100}}10 \frac{GSI-10}{40}(\sigma_{c}\leq 100\;\text{MPa})\\ \left(1-\frac{D}{2}\right)10\frac{GSI-10}{40}(\sigma_{c}>100\;\text{MPa})\end{cases}  \tag{5}\]  
\[\frac{E_{ud}}{E_{d}}=\frac{1}{1-\
icefrac{{D}}{{2}}} \tag{6}\]  
where \(\sigma_{c}\) is the uniaxial strength of rock material, \(D\) is the disturbance factor of the rock mass, \(E_{m}\) is the deformation modulus of the rock mass, \(E_{ud}\) and \(E_{d}\) are the deformation modulus of undisturbed and disturbed rock masses, respectively. Moreover, in addition to the empirical relation between \(E_{m}\) and \(RMR\) proposed by [PERSON] et al. [10], the empirical relation between the Basic Quality Index (\(BQ\)) and \(RMR\) was also considered by [PERSON] et al. [7] in the derivation of a continuous type relation between \(D\) and \(BQ\) (Equations (7) and (8)).