# Review of the Double-Row Pile Supporting Structure and Its Force and Deformation Characteristics
## 5 Calculation Model of Pile-Soil Interaction
In the exploration of the mechanical model of double-row piles and earth pressure by foreign scholars, [PERSON] [130] and [PERSON] [131] and other scholars calculated the distribution of earth pressure, the distribution of the bending moment, and the displacement of piles to explore the distribution of the pile-soil interaction force but did not consider the influence of the soil arching effect. With the gradual establishment of the soil arching effect theory, [PERSON] et al. [132], [PERSON] et al. [133], and [PERSON] et al. [91] provided the stress  
Figure 4: Diagram of earth pressure distribution model. calculation formula considering the soil arching effect, in which the vertical average stress \(\sigma_{av}\) and the pile side soil pressure \(\sigma_{h}\) are, respectively:  
\[\sigma_{av}=\frac{V}{B}=\frac{\sigma B}{2\mu K_{w}}[1-e^{(-\frac{2K_{w}\mu B}{B}h )}]+q_{0}e^{(-\frac{2K_{w}\mu B}{B}h)} \tag{5}\]  
\[\sigma_{h}=K_{w}\frac{V}{B}=\frac{\gamma B}{2\mu}[1-e^{(-\frac{2K_{w}\mu B}{B} h)}]+K_{w}q_{0}e^{(-\frac{2K_{w}\mu B}{B}h)} \tag{6}\]  
In the formula, \(h\) is the soil depth along the vertically downward direction of the surface; \(V\) is the total vertical load when \(h=0\), \(V=q_{0}\); \(K_{w}\) is the lateral earth pressure coefficient; \(\gamma\) is the weight of soil; \(B\) is the influence range of the soil stress arch; \(\mu\) is the friction coefficient of the wall back, \(\mu=tan\delta\), \(\delta\) is the friction angle of wall soil. For rough wall backs, \(\delta=\varphi\) (friction angle) can be taken. The model assumes that the side wall of two adjacent piles is a parallel wall with a certain length, roughness, and no deformation. When the influence range of the soil arching effect in a row pile retaining structure is \(B\), the soil pressure can be calculated by the geotechnical principle. However, the model is only for the analysis of lateral earth pressure when a single foundation pit is supported by a row pile. The deformation and internal force of the double-row pile supporting structure is not fully considered by the connection beam and crown beam. In analyses of pile-soil interaction in double-row pile-supporting structures, the elastic foundation beam method proposed by [PERSON] based on pile-soil interaction is widely used [134]. [PERSON] et al. [135] considered the front pile, back pile, and connecting beam as three independent parts and, based on first studying the joint action of the connecting beam, lower elastic soil, and pile side soil pressure on the front and back pile, equivalent foundation soil was used as an independent equivalent spring to simulate its deformation properties to calculate the lateral resistance of soil to pile, as shown in Figure 5.  
\[p_{x}=b_{0}\cdot c_{y} \tag{7}\]  
In the formula, \(b_{0}\) is the calculated width of the pile; \(c_{y}\) is calculated according to China's method; and \(x\) is the lateral displacement of the pile. The model assumes the soil is a linear elastic body, which is quite different from the actual situation, so the calculation model does not apply to all cases. Scholars then, based on [PERSON]'s model, further assumed that the soil around the pile was a discrete linear spring, and the internal force and deformation of the pile body were calculated by numerical modeling according to the  
\[\alpha=\frac{2L}{L_{0}}-\left(\frac{L}{L_{0}}\right)^{2}, \tag{1}\]0 Elastic soil model diagram. finite element method of the elastic foundation beam [136]. At this time, the earth pressure borne by the supporting pile can be regarded as the reaction force caused by the spring deformation caused by the deformation of the pile supporting structure. However, the model assumes that the soil pressure, horizontal displacement, and angle of the pile are all distributed in a parabolic shape, neglecting the cohesive force and friction resistance between the pile and soil. In addition, [PERSON] et al.