# Influence of Suction on Capacity of Pile Foundation
## 4 Results
### Tip Resistance  
Total ultimate bearing capacity of the bored pile is determined by Equation (24) [25].  
\[Q_{ult}=Q_{t}+Q_{s} \tag{24}\]  
where \(Q_{t}\)--tip resistance or end bearing capacity; \(Q_{s}\)--shaft bearing capacity or skin friction of the pile.  
Following the calculations made above, the end-bearing capacity for the Type 1 and Type 2 piles was calculated.  
In saturated conditions, \(Q_{s}\) can be calculated using Equation (25) [25]:  
\[Q_{s}=A_{p}*q_{p}=A_{p}*\left(c^{\prime}*N_{c}^{\prime}+q^{\prime}*N_{q}^{ \prime}\right) \tag{25}\]  
where \(A_{p}\)--cross-sectional area of the pile; \(q_{p}\)--unit resistance; \(q^{\prime}\)--effective vertical stress; \(N_{q}\), \(N_{c}\)--bearing capacity factors; \(c^{\prime}\)--cohesion of a soil.  
In unsaturated conditions, the end bearing capacity is found using Equation (26) [31]:  
\[Q_{s}=N_{c}\Big{[}c^{\prime}+(u_{a}-u_{w})*S^{k}*tan\delta\Big{]}*A_{p} \tag{26}\]  
where \((u_{a}-u_{w})\)--matric suction; S--degree of saturation; k--fitting parameter; \(\delta\)--degree of internal friction [31].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Length (m)** & \(\lambda\) & \(Q_{S}\) **(kPa)** \\ \hline
0 & 0.29 & 0 \\ \hline
1 & 0.29 & 106.85 \\ \hline
2 & 0.29 & 248.64 \\ \hline
3 & 0.29 & 412.50 \\ \hline
4 & 0.29 & 586.22 \\ \hline
5 & 0.29 & 647.64 \\ \hline
6 & 0.29 & 821.80 \\ \hline \hline \end{tabular}
\end{table}
Table 16: Values of shaft capacity of Type 2 using modified \(\lambda\) method.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Depth (m)** & \(\beta\) & \(\sigma_{p}^{\prime}\) **(kPa)** & \(Q_{s}\) **(kPa)** \\ \hline
4 & 0.5828 & 72.8 & 363.16 \\ \hline
5 & 0.5385 & 83.5 & 477.99 \\ \hline
6 & 0.5385 & 100.2 & 658.14 \\ \hline \hline \end{tabular}
\end{table}
Table 14: _Cont._  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**\(\alpha\)** & \(\epsilon_{\text{\emph{sumst}}}\))** & \(\pi\) & _d (m)_ & _L (m)_ & \(Q_{s}\) **(kPa)** \\ \hline
0.453 & 84 & 3.14 & 0.6 & 0 & 0 \\ \hline
0.453 & 88.6 & 3.14 & 0.6 & 1 & 76.65 \\ \hline
0.453 & 95.5 & 3.14 & 0.6 & 2 & 162.96 \\ \hline
0.453 & 100.8 & 3.14 & 0.6 & 3 & 258.04 \\ \hline
0.453 & 100.7 & 3.14 & 0.6 & 4 & 343.84 \\ \hline
0.332 & 77.5 & 3.14 & 0.6 & 5 & 242.49 \\ \hline
0.332 & 76.1 & 3.14 & 0.6 & 6 & 285.76 \\ \hline \hline \end{tabular}
\end{table}
Table 15: Values of shaft capacity of Type 2 using modified \(\alpha\) method.  
Generally, the obtained results indicate the greater capacity of the pile in unsaturated conditions. For the Type 1 pile, the calculated shaft capacity undergoes a sudden decrease at the depth of 3 m due to the high value of the fitting parameter \(\mu\) in the clay layers. This is the same for the Type 2 pile, where the decrease occurs at a depth of 4 m. Overall, in both saturated and unsaturated conditions, the \(\lambda\) method showed the biggest value of the shaft capacity and the beta method showed the lowest.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{4}{c}{**Saturated**} & \multicolumn{4}{c}{**Unsaturated**} \\ \hline \multirow{2}{*}{**Depth, m**} & \multicolumn{4}{c}{**Bearing Capacity, kPa**} & \multirow{2}{*}{**Depth, m**} & \multicolumn{4}{c}{**Bearing Capacity, kPa**} \\ \cline{2-2} \cline{5-8}  & \(\alpha\) & \(\beta\) & \(\lambda\) & & **Modified \(\alpha\)** & **Modified \(\beta\)** & **Modified \(\lambda\)** \\ \hline
0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline
1 & 30.74 & 15.08 & 65.84 & 1 & 75.65 & 28.28 & 106.85 \\ \hline