# Model Tests on Jacked Pile Penetration Characteristics Considering a Static Press-in Piling Machine
## 3 Test Results and Analysis
### Test Data Processing and Analysis
#### 3.1.3 Theoretical Introduction  
According to the classical tribology theory, the sliding friction is the sum of the adhesion and plough effect. The \"adhesion-plough\" theory was first proposed and used in the friction between metal surfaces [28; 29], while this paper applies the theory to the pile-soil interface to analyze the experimental results. In the process of pile jacking, the soil body is subjected to the pile body's ploughing action and produces slurry water film, which affects the adhesion force and the play of plough furrow force and causes a different side friction resistance form. Therefore, the pile side friction resistance is mainly divided into three sections, L1, L2, and L3, which are analyzed by the \"adhesion-plough\" theory, respectively. The distribution of pile side friction force is shown in Figure 6.  
The \(L1\) section is the upper part of the pile body. In this section, the soil around the pile is repeatedly plughed by the pile body, leading to the generation of a slurry water film that separates the pile from the soil and to the loss of adhesion force and plough force between the pile and the soil. Consequently, the side friction of the pile is primarily generated by the friction between the slurry water film and the pile body, as shown in Formula (5).  
\[F_{L1}=A_{f-p}\tau_{f} \tag{5}\]where \(A_{f-p}\) is the actual contact unit area between the slurry water film and the pile body; \(\tau_{f}\) is the average shear strength of slurry water film.  
The \(L2\) section is the middle of the pile body. In this section, the ploughing effect of the soil around the pile becomes less, resulting in a thinner slurry water film and the generation of plough force. However, because the presence of the slurry water film prevents the adhesion force from working, the pile side friction resistance is primarily composed of the furrow force between the pile and the soil and the friction between the pile and the slurry water film, as shown in Formula (6).  
\[F_{L2}=F_{p}+F_{f}=\mu_{p}W+A_{f-p}\tau_{f}=\frac{\pi}{2}\cot\beta\cdot\text{W} +A_{f-p}\tau_{f} \tag{6}\]  
where \(F_{p}\) is the furrow force; \(F_{f}\) is the friction force between the slurry film and the pile body; \(\mu_{p}\) is the furrow friction coefficient; \(\beta\) is the conical half-angle of the hard asperity at the pile-soil interface; \(W\) is the positive pressure between pile and soil.  
The \(L3\) section represents the lower part of the pile body. In this section, the ploughing effect of the soil around the pile is the weakest. The slurry water film gradually becomes thinner or even disappears. As a result, the adhesion force works, and the ploughing force gradually becomes larger. However, the friction between the slurry water film and the pile body is basically lost, so the pile side friction resistance is mainly influenced by the ploughing force and the adhesion force, as shown in Formula (7).  
\[F_{L3}=F_{a}+F_{p}=\mu_{a}W+\mu_{p}W=\frac{\tau_{5-p}}{H}W+\frac{\pi}{2}\cot \beta\cdot W \tag{7}\]  
where \(F_{a}\) is the adhesive force; \(\mu_{a}\) is the adhesive friction coefficient; \(\tau_{5-p}\) is the shear strength of the contact surface between pile and soil; \(H\) is the soil hardness.  
The relevant parameters of the formula in the above theory are difficult to determine, making it challenging to obtain a quantitative solution. Therefore, this paper primarily utilizes this theory to conduct an effective qualitative analysis of the test results.