# Modified Pseudo-Dynamic Bearing Capacity of Shallow Strip Foundation near Slope on Non-Uniform Soil
## 4 Results and Analysis
### Comparisons  
#### 4.2.1 Comparison Without Considering Seismic Forces  
Before proceeding with the subsequent analyses and discussions, it is necessary to prove the reliability of the destructive mechanism proposed in the previous section. Therefore, in this subsection, the calculation results under different conditions were compared with the available data in the literature. Based on the failure mechanism presented in Figure 3, the bearing capacity of the foundations near the slope under static conditions (without considering seismic effects) was first calculated, as shown in Tables 1 and 2. The comparison of the cohesion-dominated bearing capacity factor \(N_{c}\) is given in Table 1. For the calculation of \(N_{c}\), the effect of uniform load as well as the unit weight of the soil is neglected and only the contribution of the cohesion is considered. As can be seen from Table 1, the method of this paper yields the smallest upper bound bearing capacity solution compared to the methods of the other three literature, and the results of this paper are very close to the data of [PERSON] et al. (2021) [29]. When \(L/B_{0}\) is equal to 0, the value of bearing capacity in this paper is about 15% smaller than the value given by [PERSON] et al. (1994) [30] and about 3% smaller than the value given by [PERSON] and [PERSON] (2003) [31]. When \(L/B_{0}\) is equal to 4, the value of bearing capacity in this paper is about 20% smaller than the value given by [PERSON] et al. (1994) [30] and about 12% smaller than the value given by [PERSON] and [PERSON] (2003) [31]. The reason that the results of this paper are close to the data of [PERSON] et al. (2021) [29] is because the same methodology was used.  
Table 2 demonstrates the comparison of the bearing capacity factor \(N_{\gamma}\) dominated by the unit weight of soils for different internal friction angles \(\varphi\), setback distances \(L\) and slope angles \(\beta\) considered. From Table 2, it can be seen that due to the use of upper bound theorem in both studies, the results of this paper are relatively similar to those of the other two studies. In addition, it can be noticed that at \(\varphi=40^{\circ}\), there is a slight fluctuation in some of the bearing capacity factor \(N_{\gamma}\) from the results of the other literature,  
\begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{\(L/B_{0}\)} & \multicolumn{3}{c}{\(N_{c}\)} \\ \cline{2-4}  & **[PERSON] et al. (1994) [30]** & **[PERSON] and [PERSON] (2003) [31]** & **[PERSON] et al. (2021) [29]** & **Present Study** \\ \hline
0 & 23.00 & 20.20 & 19.57 & 19.58 \\
1 & 25.85 & 23.28 & 21.80 & 21.80 \\
2 & 28.53 & 25.75 & 23.74 & 23.74 \\
3 & 31.10 & 28.81 & 25.52 & 25.51 \\
4 & 33.77 & 30.82 & 27.16 & 27.16 \\ \hline \end{tabular}
\end{table}
Table 1: The comparisons of \(N_{c}\) with the other literature.  
Figure 5: The convergence of the operation program for \(n\).  
which may be due to the optimization procedure as well as the differences in the codes. The overall consistency between this study's outcomes and the existing literature data supports the credibility of both the failure pattern interpretation and optimization approach implemented herein [32; 33; 34].