# Natural Creation of Large Rock Cavern: Can We Construct Them? Jenolan Caves as a Case Study
## 2 Case Study of the Grand Arch, Jenolan Caves
### Stability Simulating of the Grand Arch
#### 2.3.3 Criteria for the Evaluation of Rock Opening Stability  
There are some criteria [64; 65; 66] to be used for the evaluation of rock-opening stability. The suggested evaluation criteria function as a guide to assessing the stability of an underground opening. These criteria require checking the deformations of the roof and wall against the opening, called the Roof Sag Ratio (RSR) and Wall Convergence Ratio (WCR), respectively. The schematic stability evaluation criteria are shown in Figure 5.  
It is recommended that the underground opening be considered unstable or unsatisfactory if the RSR and WCR are \(>\)0.50% and \(>\)1.5%, respectively. Likewise, it is regarded as stable or satisfactory if the RSR and WCR are \(\leq\)0.50% and \(\leq\)1.5%, respectively. In terms of the structural design for a beam or slab, the deflection should be controlled to less than span/250 (i.e., 0.4%), as recommended by AS3600 [67] and Eurocode 2 [68].  
Another criterion used for the evaluation of rock-opening stability is to determine yield condition around the opening when elastoplastic models are employed in numerical modeling [69; 70; 71; 72]. The Strength Factor is the number used to conclude the yield condition of the media in numerical modeling. If the Strength Factor is less than 1.0, the modeled element will be considered a failure, i.e., yielded, or unstable.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model No. 1**} & \multirow{2}{*}{**UCS** (MPa)**} & \multirow{2}{*}{**Deformation Modulus (MPa)**} & \multirow{2}{*}{**Joint Spacing (Mean) (m)**} & \multirow{2}{*}{**In Situ Stress (k) Ratio 2**} & \multirow{2}{*}{**Other Parameters (Assumed)**} \\  & & & & & & \\ \hline M1 & 35 & 11,430 & 3 & 1.4 + 75/z & Joint persistence factor = 0.8, and length = 25 m \\ M2 & 50 & 20,800 & 3 & 1.4 + 75/z & Two sets of joint dip at \(56^{\circ}\) and \(-20^{\circ}\), respectively \\ M3 & 35 & 11,430 & 2 & 1.4 + 75/z & Joint friction angle = \(28^{\circ}\) \\  & & & & & Poisson’s ratio of rock = 0.25 \\  & & & & & Unit weight of rock = 0.025 MN/m3 \\ M4 & 35 & 11,430 & 3 & 0.4 + 75/z & CSI rock quality = \(55\) \\  & & & & & Use of Heck-Brown failure criteria \\ \hline M5 & 35 & 11,430 & 3 & 1.4 + 75/z & Same as M1, but three sets of joint dip at \(56^{\circ}\), \(10^{\circ}\), and \(-20^{\circ}\) included in the model \\ \hline M6 & 35 & 11,430 & 3 & 1.4 + 75/z & Same as M1, but joint friction angle = \(26^{\circ}\) \\ \hline M7 3 & 35 & 11,430 & 3 & 1.4 + 75/z & Same as M1, but pattern bolts of 8.6 m long, 1.25 m spacing, and 200 kN working load installed at the main roof \\ \hline \hline \end{tabular}  
* For details about Models M1 to M6, refer to Section 2.3.4 below; for details about Model M7, refer to Section 3.1 below. 2 z = depth (m), below ground surface. 3 Model 7 is used for further comparison, as discussed in Section 3. Support measures are based on the Q-system [47].  
\end{table}
Table 1: Input parameters for numerical modeling of this study.