## 4 Research on the Calculation Method of Internal Force of Double-Row Skidding Pile
### Calculation of Internal Forces in Pile Body Above Shear Zero Point  
Firstly, the double-row pile without the connecting beam is regarded as two single piles to calculate the internal force; secondly, according to the force state of the double-row skidding pile without the connecting beam, especially the characteristics of the shear zero point above the sliding surface, the skidding pile is assumed to be supported by a directional hinge at the shear zero point above the sliding surface, and then it is disconnected into upper and lower parts as shown in Figure 7. The cantilever pile is used to calculate the shear zero point above the shear zero point, and the finite difference method is adopted to calculate the shear zero point below as the elastic foundation beam. The difference method is used to calculate the whole pile internal force of the fully buried double-row skid pile without connecting beams. In Figure 7, \(h_{1}\) and \(h_{2}\) are the pile lengths above and below the slip surface of the shear zero point (m), respectively. Before using the cantilever method for the calculation of internal forces above shear zero (AB section), the distribution function of the landslide thrust and soil resistance in front of the pile after the pile should be determined first. Refer to [PERSON] et al. [27] for the distribution function of soil resistance and the landslide thrust in front of the pile in the loaded section to derive the table. In order to simplify the calculation, assuming that the distribution of the landslide thrust and soil resistance in the back row pile adopts the triangular and parabolic distribution in the test as shown in Figure 8, then the location of the landslide thrust and landslide resistance in front of the pile and after the pile in the back row pile is, \(z_{a}=\frac{2}{3}H_{1}\), \(z_{b}=\frac{3}{5}H_{1}\). This section only introduces the derivation process of the formula for calculating the internal force of the rear pile, and the derivation process for calculating the internal force of the front pile is similar to that of the rear pile, so it is not specifically introduced here. Figure 8: Load distribution diagram of front and back piles. The formula for calculating the landslide thrust and soil resistance at any point z above the zero point of shear can be expressed as \((0<z\leq h_{1})\):  
\[T(z)=\int_{0}^{z}q(x)dx=\int_{0}^{z}\frac{2E_{a}}{H_{1}^{2}}xdx=\frac{E_{a}}{H_{1 }^{2}}z^{2} \tag{1}\]  
\[R(z)=\int_{0}^{z}p(x)dx=\int_{0}^{z}(\frac{-2.4E_{b}}{H_{1}^{3}}x^{2}+\frac{3.6 E_{b}}{H_{1}^{2}}x)dx=\frac{-0.8E_{b}}{H_{1}^{3}}z^{3}+\frac{1.8E_{b}}{H_{1}^{2}}z^{2} \tag{2}\]  
where \(E_{a}\) and \(E_{b}\) denote the pile back thrust (kN/m) and pile front resistance (kN/m) of the back row pile, respectively. The formula for calculating the shear force above the zero point of the pile shear is \((0<z\leq h_{1})\):  
\[Q(z)=T(z)-R(z)=\frac{E_{a}}{H_{1}^{2}}z^{2}+\frac{0.8E_{b}}{H_{1}^{3}}z^{3}- \frac{1.8E_{b}}{H_{1}^{2}}z^{2} \tag{3}\]  
The bending moment MT (z) generated by the landslide thrust \(T\) (\(0<z\leq h_{1})\):  
\[M_{T}(z)=T(z-z_{a})=\frac{E_{a}}{H_{1}^{2}}z^{2}(z-z_{a}) \tag{4}\]  
The bending moment M\({}_{R}\)(z) generated by the soil resistance \(R\) (\(0<z\leq h_{1}\)):  
\[M_{R}(z)=-R(z-z_{b})=(\frac{0.8E_{b}}{H_{1}^{3}}z^{3}-\frac{1.8E_{b}}{H_{1}^{2} }z^{2})(z-z_{b}) \tag{5}\]  
Then the bending moment above the zero point of the pile shear is calculated as \((0<z\leq h_{1})\):  
\[M(z)=M_{T}(z)+M_{R}(z)=\frac{E_{a}}{H_{1}^{2}}z^{2}(z-z_{a})+(\frac{0.8E_{b}}{ H_{1}^{3}}z^{3}-\frac{1.8E_{b}}{H_{1}^{2}}z^{2})(z-z_{b}) \tag{6}\]  
The formula for calculating the internal force above shear zero for a double-row pile is as follows:  
First, the back row of piles \((0<z\leq h_{1})\):  
\[\left\{ \begin{array}{l}Q(z)=\frac{E_{a}}{H_{1}^{2}}z^{2}+\frac{0.8E_{b}}{H_{ 1}^{3}}z^{3}-\frac{1.8E_{b}}{H_{1}^{2}}z^{2}\\ M(z)=\frac{E_{a}}{H_{1}^{2}}z^{2}(z-z_{a})+(\frac{0.8E_{b}}{H_{1}^{3}}z^{3}- \frac{1.8E_{b}}{H_{1}^{2}}z^{2})(z-z_{b})\end{array} \right.