## 4 Application of the Improved \(p\)-\(y\) Curve Method in Layered Soil
### Validation  
The improved \(p\)-\(y\) curve method was applied to the above tests, and the displacement and bending moment of the pile were compared with the measured results.  
(1) Pile displacement  
The comparison between the calculated and measured value of pile displacement along with depth is shown in Figure 5a, and the comparison between the calculated and measured value of pile top displacement is shown in Figure 5b.  
Figure 5a shows that the calculated value of pile displacement was consistent with the measured value. When the load was below 300 kN, the pile displacement mainly occurred within 10 m underground. When the load increased to 350 kN, however, the displacement value and the depth of displacement influence, increased rapidly. Similarly, Figure 5b shows that when the load increased from 150 kN to 350 kN, the error between the calculated value of pile top displacement and the measured value was between \(-9.8\%\) and 10.3%. When the load reached 400 kN, however, the calculated and measured values of pile top displacement increased sharply, to 161.2 mm and 220.4 mm, respectively, and the error increased to 26.9%. This may have been because the pile foundation had been damaged and the measured value of the pile top displacement was thus too large. Thus,  
Figure 5: Comparison between the calculated and measured value of the pile body displacement with depth.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Type of Soil Layer** & **Thickness/m** & \begin{tabular}{c} **Mass** \\ **Density/(kg/m3)** \\ \end{tabular} & \begin{tabular}{c} **Compression** \\ **Modulus** \\ **Es/MPa** \\ \end{tabular} & \
\begin{tabular}{c} **Poisson’s** \\ **Ratio** \\ \end{tabular} &
\begin{tabular}{c} **Friction** \\ **Angle/(c)** \\ \end{tabular} \\ \hline Miscellaneous fill & 4.8 & 1845 & - & 0.38 & 12.8 \\ Silt & 8.3 & 1676 & 2.09 & 0.40 & 10.2 \\ Silty clay with silt & 4.8 & 1915 & 4.31 & 0.35 & 12.8 \\ Silty clay & 12.6 & 1769 & 3.24 & 0.35 & 11.2 \\ Silty clay & 12.7 & 1777 & 4.63 & 0.30 & 12.3 \\ Silty clay & 1.8 & 1810 & 3.77 & 0.30 & 11.3 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Soil physical and mechanical property parameters.  
within a certain allowable range, the improved \(p\)-\(y\) curve method has good applicability in calculating the internal forces and deformation of piles loaded at large displacement levels, before a pile foundation is likely to be damaged.  
(2) The bending moment of the pile shaft  
The comparison between the calculated and measured value of the pile shaft bending moment with depth is shown in Figure 5(a), and the comparison between the calculated and measured value of the pile shaft maximum bending moment is shown in Figure 5(b).  
According to Figure 5(a), the calculated and measured bending moment values were mainly distributed within 12 m below the ground. With an increase in load, the calculated depth of the maximum pile bending moment appeared about 5 m below the ground, which was consistent with the measured value. Figure 5(b) shows that when the load increased from 150 kN to 350 kN, the error between the calculated value of the maximum pile shaft bending moment and the measured value was \(-\)17.4% to 9.8%. When the load was increased to 400 kN, however, the calculated and measured values of the maximum pile bending moment increased to 1995 kN and 2789 kN, respectively, with an error of 28.5%. Combined with the comparative analysis of the pile top displacement, the improved \(p\)-\(y\) curve method also has good applicability in calculating the internal forces and deformation of a pile loaded at a displacement level, within a certain allowable error range, in addition to when the pile foundation is not damaged.