## 5 Case Verification
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Case No.**} & **Soil Type (Around** & **Diameter** & **Length** & **Measured** & \multirow{2}{*}{**\(q_{e}\)/MPa**} & \multirow{2}{*}{\(\phi f^{\circ}\)} & **Predicted Toe** & **Predicted to** \\  & **the Pile Tip** & **/mm** & **/m** & & **Capacity/kN** & & **Capacity/kN** & **Measured Ratio** \\ \hline \hline \multirow{2}{*}{\(1\)} & Medium-dense & \multirow{2}{*}{324} & \multirow{2}{*}{16.8} & \multirow{2}{*}{315} & \multirow{2}{*}{3} & \multirow{2}{*}{27} & \multirow{2}{*}{310.6} & \multirow{2}{*}{0.986} \\  & sand & & & & & & & & \\ \hline \hline \multirow{2}{*}{\(2\)} & Medium-dense & \multirow{2}{*}{324} & \multirow{2}{*}{31.1} & \multirow{2}{*}{180} & \multirow{2}{*}{2} & \multirow{2}{*}{19} & \multirow{2}{*}{192.1} & \multirow{2}{*}{1.067} \\  & sand & & & & & & & & \\ \hline \hline \multirow{2}{*}{\(3\)} & Sand & \multirow{2}{*}{273} & \multirow{2}{*}{9.2} & \multirow{2}{*}{355} & \multirow{2}{*}{4} & \multirow{2}{*}{32} & \multirow{2}{*}{348.6} & \multirow{2}{*}{0.982} \\  & Sand & & & & & & & & \\ \hline \hline \multirow{2}{*}{\(4\)} & Sand & \multirow{2}{*}{609} & \multirow{2}{*}{34.25} & \multirow{2}{*}{1650} & \multirow{2}{*}{5} & \multirow{2}{*}{26} & \multirow{2}{*}{1814.5} & \multirow{2}{*}{1.100} \\  & Sand & & & & & & & & \\ \hline \hline \multirow{2}{*}{\(5\)} & Silty sand & \multirow{2}{*}{500} & \multirow{2}{*}{8.7} & \multirow{2}{*}{2000} & \multirow{2}{*}{8} & \multirow{2}{*}{33} & \multirow{2}{*}{2351.1} & \multirow{2}{*}{1.176} \\  & Sand & & & & & & & & \\ \hline \hline \multirow{2}{*}{\(6\)} & Medium-dense & \multirow{2}{*}{400} & \multirow{2}{*}{9.4} & \multirow{2}{*}{310} & \multirow{2}{*}{2} & \multirow{2}{*}{23} & \multirow{2}{*}{284.6} & \multirow{2}{*}{0.918} \\  & sand & & & & & & & & \\ \hline \hline \multirow{2}{*}{\(8\)} & Medium-dense & \multirow{2}{*}{508} & \multirow{2}{*}{35.85} & \multirow{2}{*}{3000} & \multirow{2}{*}{15} & \multirow{2}{*}{33} & \multirow{2}{*}{4710.9} & \multirow{2}{*}{1.570} \\  & sand & & & & & & & & \\ \hline \hline \multirow{2}{*}{\(9\)} & Medium-dense & \multirow{2}{*}{508} & \multirow{2}{*}{43} & \multirow{2}{*}{2600} & \multirow{2}{*}{16} & \multirow{2}{*}{31} & \multirow{2}{*}{3492.8} & \multirow{2}{*}{1.343} \\  & sand & & & & & & & & \\ \hline \hline \multicolumn{2}{c}{\(10\)} & Sandy clay & \multirow{2}{*}{273} & \multirow{2}{*}{13} & \multirow{2}{*}{245} & \multirow{2}{*}{3} & \multirow{2}{*}{28} & \multirow{2}{*}{208.0} & \multirow{2}{*}{0.849} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of pile case record data and predicted ultimate toe capacity. Figure 15: (**a**) Computed versus measured toe resistance by proposed method; (**b**) ratio of computed to measured values of ultimate toe capacity by proposed method. method gives results consistent with the measured values, their results generally overestimate the ultimate toe capacity by more than 20%. Compared with these two methods, the proposed method shows a good agreement with the measured values. For those cases wherein the ultimate toe capacity is low, the predicted values provided by the proposed method are quite accurate, while for the cases where the end-bearing capacity of piles is high, there is a certain degree of overestimation. This indicates that for cases where the ultimate toe capacity is high, the failure zone at the boundary of which the equivalent frictional strength fully mobilized may expand, and \(\alpha_{SA1}=37.5^{\circ}\) may cause deviation. Figure 16: (**a**) Computed versus measured toe resistance by [PERSON]’s method; (**b**) ratio of computed to measured values of ultimate toe capacity by [PERSON]’s method. Figure 17: (**a**) Computed versus measured toe resistance by [PERSON]’s method; (**b**) ratio of computed to measured values of ultimate toe capacity by [PERSON]’s method. Figure 18: Computed versus measured ultimate toe capacity by different methods.