**Figure 6.**

*Method B:* In this method the GSI index is estimated by using other classification

The Cai et al. (2004) used block volume *(Vb)* and joint surface condition factor *(Jc)* to approximation the GSI. The block volume having greater number of joint sets

The *Jc* defined by the roughness of joint, weathering and infilling, these are used

The*Vb* and *Jc* are used to precisely quantify the GSI value [17]. The quantitative chart for estimation of GSI suggested by sonmez and Ulusay [1999] is shown in **Figure 6**.

The empirical methods of design do not estimate accurately the reliability supports, redistribution of stresses, rock mass deformation [18]. These parameters are very important in designing and analysis of any excavation therefore, numerical

*Vb* ¼ S1 � S2 � S3 (5)

*Jc* ¼ Jw � Js*=*Ja (6)

systems like RQD and RMR etc. when limited data is available. The GSI can be estimate from the well-known relationship presented by various researchers [17]. *Method C:* The sonmez and Ulusay considered structure rating (SR) and surface

condition rating (SCR) for approximation of GSI value [17].

to measure the joint surface condition factor by using the Eq. (6).

indicated as:

**66**

**Figure 5.**

*Slope Engineering*

where, S is joint spacing.

*Geological strength index chart [15].*

**5. Numerical methods of design**

*Quantitative estimation of GSI chart [15].*

analysis should be carried out for appropriate designing. The numerical methods are considered very useful to estimate the above parameters precisely and in minimum time as compared to other methods of design. Numerical methods used physical and strength properties of rock as input for analysis. For efficient and viable design the numerical and empirical methods are used in parallel [19–23].

Different researchers developed and present various numerical methods and models. These are divided into eight classes on the basis of four methods and two levels as shown in **Figure 7** [24, 25].
