## 4 Analysis of Test Results
### Calculation and Analysis of the Shaft Resistance of the Pile  
A compressive pile with no soil at the bottom is a pure friction pile, and its bearing capacity is the sum of the shaft resistance on the pile surface area, i.e., its bearing capacity represents the shaft resistance of the pile.  
According to [PERSON] et al. (2018), the initial shaft resistance of pile \(\tau_{\text{s}}\) can be expressed as:  
\[\tau_{\text{s0}}=\sigma_{\text{n}}^{{}^{\prime}}\tan\delta=K\sigma_{\text{v}}^{ {}^{\prime}}\tan\delta \tag{1}\]  
where the \(\sigma_{\text{n}}^{{}^{\prime}}\) is the normal effective stress on the pile surface; the \(\delta\) is the friction angle between the pile surface and soil. According to [PERSON] et al. (2018), \(\delta/\varphi\) of smooth concrete piles is 0.8-1.0, \(\delta/\varphi\) of rough pile surfaces is 1.2, and \(\varphi\) is the internal friction angle of the soil. The \(K\) is the coefficient of vertical effective stress converted to the horizontal effective stress, which is 1.2 (2018); the \(\sigma_{\text{v}}^{{}^{\prime}}\) is the vertical effective stress of soil.  
When there is vertical additional stress \(\sigma_{\text{z}}\) in soil, Equation (1) can be rewritten as:  
\[\tau_{\text{s1}}=\sigma_{\text{n}}^{{}^{\prime}}\tan\delta=K\Big{(}\sigma_{ \text{v}}^{{}^{\prime}}+\sigma_{\text{z}}\Big{)}\tan\delta \tag{2}\]  
We can calculate the shaft resistance of the pile by Equation (2) when considering the additional stress in the soil.  
According to Equations (1) and (2), the calculated initial shaft resistance of pile \(\tau_{\text{s0}}\) and shaft resistance \(\tau_{\text{s1d}}\) after accounting for the influence of additional stress in the soil are shown in Table 5. \((\tau_{\text{s1d}}-\tau_{\text{s0}})/\tau_{\text{s0}}\) represents an increased value of the shaft resistance of pile. The shaft resistance of pile \(\tau_{\text{s1d}}\) increases after considering the additional stress in Table 5. A shorter distance to the loading point corresponds to a greater increase in the shaft resistance of the pile. This result indicates that the loading effect of pile side soil caused by compressive piles is more obvious. At the depth of 300 mm, 600 mm, 900 mm, and 1200 mm, the improvement rate of the shaft resistance is 25.4%, 10.4%, 5.4%, and 3.8%, respectively.  
The initial shaft resistance of pile \(\tau_{\text{s0}}\) calculated by Equation (1) and the shaft resistance of the pile \(\tau_{\text{s1u}}\) after accounting for the influence of additional stress calculated by Equation (2), are shown in Table 6. Considering the additional stress after the unloading effect, the calculated shaft resistance of the pile \(\tau_{\text{s1u}}\) is less than the initial shaft resistance of the pile \(\tau_{\text{s0}}\). A shorter distance to the loading point corresponds to a more obvious decrease in shaft resistance of the pile and a more obvious unloading effect of the pile side soil due to the uplift pile. The vertical stress decrease rate is 22.8% at 300 mm from the loading point,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Depth (mm)** & **Fitting Formula** & **Squared Mean Square Error** & \(\sigma_{\text{s0}}\) **(kPa)** \\ \hline
300 & \(\sigma_{\text{z}}=-0.00002\text{x}^{2}+0.0098\text{x}-1.345\) & 0.9949 & \(-1.1125\) \\
600 & \(\sigma_{\text{z}}=-0.00002\text{x}^{2}+0.009\text{x}-1.2175\) & 0.9896 & \(-1.005\) \\
900 & \(\sigma_{\text{z}}=-0.00002\text{x}^{2}+0.0083\text{x}-1.1075\) & 0.9913 & \(-0.9125\) \\
1200 & \(\sigma_{\text{z}}=-0.00002\text{x}^{2}+0.009\text10.3% at 600 mm, 6.2% at 900 mm, and 4.3% at 1200 mm, and the average shaft resistance decrease rate of the entire pile is approximately 11%.