## 4 Results and Discussion
### Failure Mode  
This section displays some failure modes observed within the soil (\(c\)-\(\phi\) soils) at some selected locations of the cavity (\(r\) = 1 m, 5 m, and 10 m with the cavity size \(D\) = 2 m) considering the same geometrical settings for different shear strength parameters. The general deformed models revealed the existence of 2 main failure modes. The Bearing failure where the plastic domain expands only beneath the footing. This failure mode is similar to the condition where there is no cavity within the soil--then, the Bearing and Void failure. This is a combined failure due to the cavity and footing interaction where the plastic domain expands between the underneath of the footing and the vicinity of the  
Figure 8: Distributions of the BC/BC\({}_{\rm NV}\) within the \(X\) and \(Y\) directions for the intermediate soils. (a) \(c\) = 10 kPa, \(\phi\) = 20 deg; (b) \(c\) = 10 kPa, \(\phi\) = 30 deg; (c) \(c\) = 50 kPa, \(\phi\) = 20 deg; (d) \(c\) = 50 kPa, \(\phi\) = 30 deg. cavity. The strain rate concentrates at the footing base as well as the cavity's edge. The interaction is dependent on the range of distance between the footing and the cavity. So, the interaction ranges from less, medium, or strong interaction regarding the strain rate (see Figure 6). The void failure, where the plastic domain is located mainly at the cavity edges and roof, portrays a possibility of collapse due to the soil's self-weight. This latter, however, is out of the range of this study. The results show at least the bearing failure as being triggered by the loading conditions and occurs mostly at the shallowest depths. Figure 9a,b displays the failure modes for the cavity located at the depth (\(h\)-\(D/2\)) = 8 m and the horizontal distance \(r\) = 1 m. The condition case in Figure 9a (Bearing and Void failure) shows that the strain rate is also concentrated at the cavity wall (lower parts). The farther the cavity exists horizontally, the less the interaction between the footing and the cavity occurs. Figure 9b shows that for the identical geometrical conditions with Figure 9a, a change of the failure mode in the case only \(\phi\) is higher is observed. The change of failure to the Bearing failure is remarkable as opposed to Figure 9a. This is due largely to the value of \(H\) of the failure domain generated considering this typical shear strength. The failure mechanisms are in agreement with those obtained by [PERSON] et al. [15] who discussed the bearing capacity and failure mechanism of a rough strip footing located above the cavity by introducing a method that considers random and complex shapes based on an Inverse Discrete Fourier Transform (IDFT). In Figure 9c,d, with the cavity located at \(r\) = 5 m, \(h\)-\(D/2\) = 6m, the Bearing and Void failure is observed for the case \(\phi\) = 30 deg (Figure 9c). The footing and the cavity strongly interact, and the failure domain around the cavity portrays a high strain rate. However, when \(\phi\) is higher (\(\phi\) = 40 deg), the failure mode is drastically changed (Figure 9d) to the Bearing failure, similar to Figure 9b. Figure 9b,d reveals that for large shear resistance angles, the influence of the cavity in deeper layers is not significant on the performance of the footing. Figure 9e,f, with the cavity located at \(r\) = 10 m, \(h\)-\(D/2\) = 2 m, an interesting observation of the failure changes against the shear resistance angle reveals that for the low shear resistance angle \(\phi\) = 30 deg; the influence of the cavity on the footing at shallow depths is ceased at large distance \(r\). This is supported by the only Bearing failure observed in Figure 9e. However, for the case with a large shear resistance angle \(\phi\) = 30 deg, the strong interaction of the footing-cavity system is observed. Briefly, the analyses of the typical failure modes revealed an interesting role of the shear resistance of the soil on the overall stability and expansion of the influence zone of the cavity.