# Stability Numbers for Unsupported Conical Excavations in Multi-Layered Cohesive Soils
## 3 Results and Discussion
Figure 11: The effect of thickness of the soil layer to the rigid body at a toe of slope, where \(D/H=1\), \(H/B=0.5\), (**a**) \(\beta=15^{\circ}\), (**b**) \(\beta=30^{\circ}\), (**c**) \(\beta=45^{\circ}\), and (**d**) \(\beta=60^{\circ}\). Increasing the thickness ratio (\(T/H\)) means increasing the thickness of the soil layer to the rigid body at the toe of the slope. [PERSON] and [PERSON] [5] showed that as the thickness ratio (\(T/H\)) increases in homogeneous soil, the slope stability number gradually decreased and then converged. To confirm the effects of the thickness ratio (\(T/H\)), and strength difference between two layers (\(c_{u1}\)/\(c_{u2}\)), the width ratio (\(H/B\)) was fixed at 0.5 and depth ratio (\(D/H\)) was set to 1. In addition, \(c_{u1}\) was fixed and \(c_{u2}\) was changed to change \(c_{u1}\)/\(c_{u2}\). When \(c_{u1}\)/\(c_{u2}\) was less than 1, which is \(c_{u2}\) was greater than \(c_{u1}\), the stability number had a value similar to \(T/H=1\) regardless of thickness. When \(c_{u1}\)/\(c_{u2}\) was greater than or equal to 1, the slope stability number decreased and converged as thickness ratio (\(T/H\)) increased, it is similar to the results of [PERSON] and [PERSON] [5]. Figure 11a shows the result for \(\beta=15^{\circ}\). When the thickness ratio (\(T/H\)) \(>\) 1.6, stability number (\(N\)) did not change. Figure 11b shows the result for \(\beta=30^{\circ}\). The stability number was reduced and stability number did not change when the thickness ratio (\(T/H\)) \(>\) 1.4. Figure 11c,d shows the result for \(\beta=45^{\circ}\) and \(\beta=60^{\circ}\), respectively. The stability number (\(N\)) did not change when the thickness ratio (\(T/H\)) \(>\) 1.2. Through this, it can be seen that the effect of the thickness ratio (\(T/H\)) was larger the lower the slope. Figure 12 shows the effect of the ratio of excavation height to the radius of the circular excavation ratio (\(H/B\)), and strength difference between two layers (\(c_{u1}\)/\(c_{u2}\)) on the slope stability number for a purely two cohesive soil layers on the rigid base. The value of the thickness ratio and angle of inclination was fixed as the thickness ratio (\(T/H\)) was 2, and \(\beta=30^{\circ}\) to confirm the effects of the width ratio (\(H/B\)). Figure 12a shows the result for \(D/H=0.5\), which is the top layer thickness was smaller than the excavation depth. The stability number (\(N\)) did not change when the width ratio (\(H/B\)) was \(>\) 5. Figure 12: The effect of the width ratio on the stability numbers, where \(T/H=2\), \(\beta=30^{\circ}\), (**a**) \(D/H=0.5\), (**b**) \(D/H=1.0\), and (**c**) \(D/H=1.5\). Figure 12b shows the result for \(D/H=1.0\), which is the top layer thickness was equal with excavation depth. Figure 12c shows the result for \(D/H=1.5\), which is the top layer thickness was deeper than excavation depth. It was confirmed that the variation of the stability number was increased as the depth ratio (\(D/H\)) increased. However, the effect on the strength ratio (\(c_{ul1}/c_{ul2}\)) was reduced as the depth ratio (\(D/H\)) increased. As the width ratio (\(H/B\)) increased, which is the height of the slope increased or the radius of excavation decreased, the slope stability number increased. This finding can be seen that the sharp increase in \(H/B<1\). This is because the collapse type changes from deep seated failure to toe failure. Figure 13 shows the effect of the depth ratio (\(D/H\)), which is the relative top layer thickness to excavation depth on the slope stability number. In the multi-layered soil, the relative top layer thickness and strength was a significant influence factor on stability. Figure 13a shows the stability numbers in \(\beta=15^{\circ}\). The stability number when \(c_{ul1}/c_{ul2}<1\) was larger than the stability number when \(c_{ul1}/c_{ul2}=1\), which was a homogenous soil layer, but the stability number when \(c_{ul1}/c_{ul2}>1\) was smaller than the stability number when \(c_{ul1}/c_{ul2}=1\).