# Review of the Double-Row Pile Supporting Structure and Its Force and Deformation Characteristics
## 5 Calculation Model of Pile-Soil Interaction  
At present, the calculation model of pile-soil interaction is mainly based on the classical earth pressure theory, the soil arch effect theory, and the Winkler theory. The process of innovation and optimization of computational models essentially goes through theoretical field investigation, theoretical analysis, numerical simulation verification, and model establishment. The pile-soil effect is taken into account in the calculation model of the earth arch effect and the Winkler theory, so it has been more widely used [124]. This section mainly reviews the calculation model based on three theories and introduces the optimization process and development status of the calculation model based on the Winkler theory. In the calculation model based on the classical theory of earth pressure, it is usually considered that excessive soil displacement is one of the main reasons for excessive lateral displacement and even the failure of double-row pile supporting structures. To quantitatively study the relationship between soil displacement and pile internal force, [PERSON] et al. [125], based on the Rankine earth pressure theory, which is based on soil pressure in the limiting state of a retaining wall, assumed that soil pressure was triangularly distributed along the depth direction of the pile in the pile row support, and then calculated the displacement and internal force of the pile, as shown in Figure 4.  
Subsequently, domestic scholar [PERSON] et al. [126] first proposed to assume the soil as a rigid-plastic body for rigid-plastic analysis. On this basis, [PERSON] et al. [127] proposed the \"volume ratio coefficient method\" to determine the distribution coefficient according to the ratio of the weight of the sliding soil on both sides of the row pile. \[\alpha=\frac{2L}{L_{0}}-\left(\frac{L}{L_{0}}\right)^{2}, \tag{1}\]In the formula, \(L\) is the row distance and \(L_{0}\) is the width of the sliding crack surface. However, because the distribution coefficient of this model is simple, it often causes an uneven distribution of passive earth pressure between the front and back rows of piles, resulting in an unclear value of the maximum bending moment. Then, based on the research of [PERSON] and [PERSON] et al., [PERSON] et al. [128] assumed the sum of earth pressure between piles as Rankine active earth pressure and the pile row supporting structure as a steel truss statically indeterminate structure embedded in the soil [129], and then calculated the earth pressure. \[e_{aF}=\epsilon_{a}+\alpha e_{\alpha} \tag{2}\]  
\[e_{aB}=\epsilon_{a}-\alpha e_{\alpha} \tag{3}\]  
\[\alpha=\frac{2\cdot b\cdot z\cdot cgt\eta-b^{2}}{\left(z\cdot cgt\eta-b\right) ^{2}} \tag{4}\]  
In the formula, \(\eta\) is the rupture angle; \(z\) is the depth; \(b\) is the width; \(\alpha\) is the distribution coefficient of earth pressure; and \(e_{\alpha}\) is the main earth pressure distribution intensity. In the assumption of the model, it is considered that the steel frame structure only bears the horizontal load, and the method of automatically adjusting the internal force of the double-row pile supporting structure is different in the process of not considering the change of external force. The model considers the beam connected by pile row and pile top as a steel frame structure with only the bottom fixed together, so that the pile row supporting system only shifts under the soil pressure without considering the angle caused by the uneven force, and then ignores that the pile row structure also bears the force couple action, the effect of soil between piles on supporting piles is ignored, and the soil arch effect is also ignored. Because it is based on the solution of force balance or moment balance under simple boundary conditions, the calculation is relatively simple, but the error is large, and the application is limited.