## 3 Rock Strength and Creep Constitutive Model Based on the Hoek-Brown Failure Criterion
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Weathering Condition** & \(AWI_{0}\) & **Weathering Characteristics** \\ \hline Non-weathered & \textgreater{}0.90 & Very good fracture surface: very coarse, fresh, indicating well-sealed fresh rock matrix and no weathering \\ \hline Slightly weathered & 0.90–0.75 & Good fracture surface: coarse, relatively fresh, with the presence of rush and the slight alteration of minerals with low weathering resistance, indicating slight weathering \\ \hline Weakly weathered & 0.75–0.55 & Ordinary fracture surface: smooth with no filling, partial alteration of minerals with low weathering resistance, indicating weak weathering \\ \hline Intersively weathered & 0.55–0.35 & Poor fracture surface: the presence of slickensides, covering of tight films or filling of angular debris on the surface, high alteration of minerals with low weathering resistance, indicating intensive weathering \\ \hline Extremely weathered & \(\leq\)0.35 & Very poor fracture surface: the presence of slickensides, and soft clay films or clay filling; the vast majority of minerals with low weathering resistance are altered; indicating extreme weathering \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Representation of the rock mass weathering characteristics by \(AWI\). A correction factor \(\lambda\) is introduced to describe the effects of underground water on the weathering conditions of the jointed rock mass (Table 4). Accordingly, the rock mass weathering index, considering the effects of underground water, can be expressed as \(AWI=\lambda AWI_{0}\). By integrating the quantitative indexes in Tables 2-4 for the texture and weathering conditions of the rock mass, the geological strength index (_GSI_) quantification method (Figure 2) can be obtained. The widely applied Nishihara model can characterize the decelerating, steady-state, and accelerating creep phases of rock. Extensive experiments have shown that notable damage of the rock occurs only in the accelerating creep phase. The rock strength \(\sigma_{r}\), presented upon the failure of the rock, is the long-term strength for rock creep. The creep elements of the rock mass model are shown in Figure 3. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Production Status of Underground Water**} & \multicolumn{3}{c}{**RBI Values of Jointed Rock Mass**} \\ \cline{2-5}  & **30–10** & **10–3** & **3–1** & **1–0** \\ \hline Humid or dripping & 0.95 & 0.95–0.89 & 0.89–0.83 & 0.83–0.76 \\ \hline Rain-like or spring-like production with water pressure \textless{} 0.1 & 0.95–0.89 & 0.89–0.83 & 0.83–0.76 & 0.76–0.71 \\ \hline Rain-like or spring-like production with water pressure \textgreater{} 0.1 & 0.89–0.83 & 0.83–0.76 & 0.76–0.71 & 0.71–0.67 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Recommended values for the correction factor \(\lambda\) to capture the effects of underground water on the weathering conditions of rock mass. Figure 2: _GSI_ quantification of rock mass [31]. Note: The following example is used to demonstrate how to use the above table. In the case of \(AWI=0.52\) and \(RBI=9.7\), two vertical and horizontal lines are drawn according to the index values (the dashed lines in the table); the intersection point is found between 40 and 45; the _GSI_ value at the point is calculated via linear interpolation (the result is 41). The creep equation can be expressed as below:  
\[\varepsilon=\left\{ \begin{array}{ll}\frac{\sigma}{E_{0}}+\frac{\sigma}{E_{1}} \Big{[}1-\exp\Bigl{(}-\frac{E_{1}}{\eta_{1}}t\Bigr{)}\Big{]}&(\sigma\leq\sigma_ {r})\\ \frac{\sigma}{E_{0}}+\frac{\sigma}{E_{1}}\Big{[}1-\exp\Bigl{(}-\frac{E_{1}}{ \eta_{1}}t\Bigr{)}\Big{]}+\frac{\sigma-\sigma_{r}}{\eta_{2}}t&(\sigma>\sigma_ {r})\end{array} \right.