# Study on Load Transfer Mechanism of Pile-Supported Embankment Based on Response Surface Method
## 1 Introduction  
Pile-supported reinforced embankments are complex geotechnical structures composed of foundations, piles, pile caps, reinforced cushions, and filled embankments. Through the soil arching effect and the membrane effect, most of the load is transferred to the pile, effectively controlling the embankment settlement. In recent years, many scholars have studied the load transfer mechanism of pile-supported reinforced embankments. In a study on the calculation method of the load transfer, [PERSON] and [PERSON] [1] considered the soil arch to be a hemispherical shell and split it into one spherical soil arch and four plane soil arches. This model was adopted by the British standard, BS 8006-1 [2]. [PERSON] and [PERSON] [3] proposed a multi-arch model, which assumed that soil arches are a system composed of a series of spherical shell elements with different centers and different radii. [PERSON] et al. [4] modified the [PERSON] and [PERSON] and introduced a coefficient, \(\alpha\), to determine whether the soil has entered a plastic state. [PERSON] [5] proposed a wedge-shaped soil arch model with a top angle of 30\({}^{\circ}\), assuming that the load acting on the soil between piles is equal to the weight of the wedge under any embankment height. This model was adopted by the Nordic Geotechnical Group [6]. On the basis of the Hewlett and Randolph model, as well as the [PERSON] and Kempfert model, [PERSON] et al. [7] proposed the concentric arch model. [PERSON] [8] assumed that the deformation curve of reinforcements under a vertical load follows a catenary distribution and deduced the calculation formula of reinforcement tension. [PERSON] [9] assumed that the deformation shape of reinforcements is a circular arc and deduced the calculation formula of reinforcement tension. [PERSON] [5] proposed a simplified method to calculate the maximum deflection and tension of reinforcements in a two-dimensional plane based on the wedge-shaped soil arch model; on that basis, [PERSON] [10] added a correction coefficient while considering the three-dimensional effect. [PERSON] [11] simulated the settlement form of reinforcements between two piles by a plane arc and simulated the deformation mode of reinforcements between four piles by a three-dimensional spherical equation. [PERSON] [12] studied the strain and force characteristics of bars in a three-dimensional state. Because of the different assumptions about the shape of soil arches and the deformation of reinforcements in pile-supported reinforced embankments, there are differences between the calculation methods. In researching the load transfer mechanism, [PERSON] [13] considered the effect of the interfacial friction between the reinforcement and the soil, and used the Winkle elastic foundation model to simulate the foundation soil and analyze the load transfer law. [PERSON] [14] proposed a new design method for geogrid-reinforced piled embankments. The method was based on the soil arching effect and the membrane effect, and bearing capacity of the subsoil was considered. [PERSON] [15] studied the effect of different embankment heights and reinforcement stiffness on the load transfer. [PERSON] [16; 17] analyzed the embankment load and deformation response by changing the embankment height, the net pile spacing, the internal friction angle of the filler, and the porosity. [PERSON] [18; 19] studied the influence of embankment filler properties, embankment height, and pile spacing on the soil arching effect through the discrete element model. [PERSON] [20] showed, through model tests, that the load transfer efficacy could be improved by increasing the cohesion of the embankment filler and reducing the pile spacing. [PERSON] [21] and [PERSON] [22] also used model tests to study the influence of pile-soil relative displacement, embankment height, and horizontal reinforcement on the soil arching effect.