# Assessment of the Bearing Capacity of Bridge Foundation on Rock Masses
## 4 Results and Discussion  
### Bearing Capacity for Weightless Rock  
We studied the comparison of the numerical and analytical results on rock mass through a sensitivity analysis, where the influence of four geotechnical and geometrical parameters (\(m_{i}\), _UCS_, _GSI_, and _B_) is observed. In Figure **1**, the correlation between the numerical (\(P_{hFDM}\)) and the analytical (\(P_{hSGO}\)) results can be observed, thus concluding that the value of \(P_{hFDM}\) is always higher than \(P_{hSGO}\), with a variation between the results of up to 60%. Figure 4 shows that the two parameters that mostly influenced the relation between \(P_{hFDM}\) and \(P_{hSGO}\) were \(m_{i}\) and _GSI_, because the dispersion range changes considerably in function of the \(m_{i}\) and _GSI_ value (represented in the abscissa axis). Mathematical correlations will be indicated in the next section for a more detailed analysis. Figure 4a clearly demonstrates the influence of the rock type (\(m_{i}\)) on the correlation between \(P_{hFDM}\) and \(P_{hSGO}\), with the results for adjusted greater values of \(m_{i}\) being worse. Figure 3: The bearing capacity vs. velocity increments diagram of the central node of the footing (\(m_{i}\) = 5, \(B\) = 4.5 m, _UCS_ = 5 MPa, and _GSI_ = 10). The results for \(P_{hFDM}\) in the cases with lower \(m_{i}\) (\(m_{i}=5\)) were very similar to the results for \(P_{hS\in O}\) presenting a variation lower than 15%, while for higher values of \(m_{i}\) (\(m_{i}=32\)) the numerical results (\(P_{hFDM}\)) could exceed up to 60% of the analytical results (\(P_{hS\in O}\)). Figure 4b does not show a clear influence of \(B\) on the relation between \(P_{hFDM}\) and \(P_{hS\in O}\), by increasing the dispersion ratio with the enlargement of \(B\). This sensitivity influence is clearer in Figure 5 where the correlation of the results between \(P_{hFDM}\) and \(P_{hS\in O}\) is presented as a function of \(P_{hS\in O}\). For a large footing (\(B=22\) m), the values of \(P_{hFDM}\) are slightly above the values obtained for the smaller footing (\(B=4.5\) m). However, there is hardly any variation between widths of 16 and 22 m, or between 4.5 and 11.5, respectively. In other words, the influence of the foundation width has little influence (less than 15%) due to the non-incorporation of self-weight. Regarding the _UCS_ parameter, Figure 4c shows that this parameter does not influence the correlation of \(P_{hFDM}\) and \(P_{hS\in O}\). The cause of this fact is that the numerical and analytical solution is proportional to the value of _UCS_; that is, the relationship \(P_{hFDM}/P_{hS\in O}\) (and therefore the deviation of results) is independent of _UCS_. Table 2 shows two examples of the correlation of \(P_{hFDM}\) and \(P_{hS\in O}\) with the variation of _UCS_. The first group of case studies (1, 2, 3, and 4) correspond to a rock type of claystone with \(m_{i}=5\) and a similarity in the results of \(P_{hFDM}\) and \(P_{hS\in O}\) can be observed. The second group of case studies (5, 6, 7, and 8) have sandstone with \(m_{i}=20\), the results of \(P_{hFDM}\) and \(P_{hS\in O}\) present a dispersion close to 25%. Based on these two examples, it is observed that a higher value of \(m_{i}\) implies a greater dispersion between \(P_{hFDM}\) and \(P_{hS\in O}\) and the same dependence of the value of \(P_{\rm h}\) with the _UCS_. In contrast, Figure 4d shows that the dispersion and the difference between the results decrease with the increase of _GSI_. With higher values of _GSI_, the dispersion range between  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{1}{c}{**Cases**} & \multicolumn{2}{c}{_UCS_ **(MPa)**} & \multicolumn{1}{c}{\(P_{hFDM}\) **(MPa)**} & \multicolumn{1}{c}{\(P_{hS\in O}\) **(MPa)**} \\ \hline \(m_{i}=5\) & 1 & 5 & 0.22 & 0.22 \\ \(B=11\) m & 2 & 10 & 0.46 & 0.44 \\ \(GSI=10\) & 3 & 50 & 2.22 & 2.22 \\ \(GSI=10\) & 4 & 100 & 4.47 & 4.44 \\ \hline \(m_{i}=20\) & 5 & 5 & 1.05 & 0.82 \\ \(B=11\) m & 6 & 10 & 2.1 the results is less than 20%.