# Natural Creation of Large Rock Cavern: Can We Construct Them? Jenolan Caves as a Case Study
## 4 Discussion of the Findings Based on Two Parts of Stability Simulations
### In Situ Stress Field  
The in situ stress field is another driven factor to control the cave/opening size and the stability condition [20; 22; 23; 38]. Referring to the simple fixed-beam model [91], the beam is exposed to a vertical load (\(Vq\)), and the horizontal reaction load (\(Hq\)) acts on the two ends of the abutment. A pressure line will exist within the beam, as depicted in Figure 11a. It can be found that the in situ horizontal stress provides a certain amount of horizontal reaction force to the abutment of the roof support beam of the opening. Figure 11: Illustration of beam support and configurations: (**a**) arching effect in a fixed-end supported beam due to loads and (**b**) simple fixed parabolic arch beam and equation. This pressure line configuration is under the same vertical load, but in a high horizontal load case, a thinner beam depth (\(B\)) is required, as shown in Figure 11a. The shape of the pressure line with an inclination angle (\(\alpha\)) at the fixed end is controlled by the resultant stress of the vertical and horizontal loads. Hence, the inclination angle (\(\alpha\)) is small for the high horizontal load case. Similarly, if the horizontal load is small but the vertical load remains unchanged, a thicker beam depth is needed, and a greater inclination angle (\(\alpha\)) is formed for this case. The Grand Arch Model M4 was formed in a small horizontal-to-vertical stress ratio (i.e., k = 1.76) of rock condition. It is expected that the pressure line was developed relatively close to the upper boundary of the beam depicted by the fixed-beam model [91]. In this case, it is the bedding thickness of the limestone. For Model M1, formed in a higher in situ stress ratio of k = 2.76 in rock strata, the pressure line is expected to be developed a bit far away from the upper boundary of the beam compared with Model M4. Due to the difference in the shape of the pressure line developed within the same size of the beam, i.e., same thickness of the bedding, the utilization of the beam stiffness capacity under the given rock condition in Model M1 is better than in Model M4. Hence, the deformation of the roof beam in Model M1 of 66 mm is less than that of Model M4, i.e., 81 mm, as shown in Figure 6a,d, respectively. These two models demonstrate that high horizontal stress would give a higher horizontal reaction force at the hinge points of the opening to compensate for the rock support beam [23]. When detecting stress change in Models M1 and M4, a stress plot along Line 1 (see Figure 6a for this query line location) from the top hinge point of the opening to the ground surface is obtained, as presented in Figure 12b. This plot is a horizontal stress (Sigma 1) against elevation (y-axis). It can be found that a higher horizontal stress response at the hinge point of the opening in Model M1 is obtained in comparison with Model 4, i.e., about 18.4 MPa and 8 MPa, respectively. Figure 12: _Cont._  
Another stress plot along Line 2 (see Figure 6a for this query line location) from the mid-span of the Arch opening to the ground surface is also obtained, as presented in Figure 12a. This plot is a vertical stress (Sigma 3) against elevation (y-axis). A smaller vertical stress of \(-\)51 kPa at the roof boundary of the opening in Model M1 is detected; however, Model M4 gives a relatively high vertical stress value of \(-\)36 kPa in comparison with M1. Basic rock mechanics shows that when a joint presents in rock mass under the principal stress acting vertically and horizontally, a normal stress is formed perpendicular, acting on the joint plane, and a tensile stress is also formed along the joint plane. The principal stresses magnitude and orientation are then altered when meeting a joint based on the resultant of normal stress and tensile stress acting on the joint. Therefore, both the Sigma 1 and Sigma 3 plots contained in Figure 12 are shown as irregular sharps rather than smooth linear or curved lines.