## 1 Introduction  
The high-density polyethylene (HDPE) corrugated pipe is a type of flexible pipe that has played a significant role in municipal engineering. The earth's pressure of buried flexible pipes is shared between the pipe and soil. Since the stiffness of the pipes is smaller than that of the surrounding soil, when a load is applied to the soil surface, the relative downward deflection of the adjacent soil prism is less than that of the central soil prism, the central soil prism is subjected to an upward friction force (Figure 1), and the earth pressure acting on the pipe is less than the weight of the central soil prism [1]. Therefore, the structural behavior of a buried flexible pipe is influenced by the hoop stiffness of the pipe and the stiffness of the backfill [2]. The stiffness of the backfill depends mainly on the degree of compaction [3], water content [4], soil properties [5], and grade [6]. Therefore, the influence of the earth pressure above a flexible pipe on pipe deformation cannot be ignored, and the load acting on pipes can be divided into soil loads and external loads. At the same time, under different soil conditions, the force transmitted from external load to the crown of the pipe is different [7; 8]. In many previous studies, scholars have mainly analyzed the mechanical deformation law of flexible pipes by laboratory tests and numerical simulations. During the installation of a pipe, its deformation is affected by the compaction method [9], compaction equipment [10], groove width, backfill material, the thickness of the backfill pipe cover, pipe diameter, and pipe hoop stiffness [11]. [PERSON] and [PERSON] (2017) studied the deformation of a flexible pipe during its installation and proposed a formula for calculating the peak deflections of a thermoplastic pipe by backfilling the soil to the crown of the pipe [12]. On the basis of field test data and numerical simulation data, [PERSON] et al. proposed a calculation formula for the deflection of an HDPE pipe during backfilling [11]. Through field tests, [PERSON] et al. measured the deflection and hoop strain generated during the pipe backfilling process, and they proposed an empirical relationship to predict the hoop strains that were generated on HDPE pipes in the construction phase [13]. For a flexible pipe buried in backfill with asymmetrical compactness, weak support on the springline leads to an increase in the lateral displacement of the pipe; hence, the haunch exhibits strain concentration behavior [14]. [PERSON] et al. (2011) designed a new technique to measure the radial contact pressure applied to a buried pipe and the deflection of the pipe under static vertical loading, and the measurement results indicated that the radial contact pressure and deflection of the pipe were sensitive to the compaction backfill [15]. [PERSON] et al. (2012), through a series laboratory tests on HDPE pipes buried in poorly graded sand with different compaction, found that the stress and deformation of these pipes were higher when the surrounding backfill was loose, and the maximum stress appeared at the invert, whereas the crown stress and invert stress were higher when the backfill was compact [16]. In addition, the method of installation and the type of backfill material were also key factors that affected the deformation of the pipe. A laboratory experiment was carried out by [PERSON] et al. (2008) to compare the effects of compaction methods, gradation, and soil material on the strain within profiled thermoplastic pipes; the empirical strain coefficient was derived by using measured data, which simplified the calculation of the maximum local bending strain in a special-shaped pipe design method [9]. With the popularization of finite element analysis software, numerical simulation has been widely applied to the calculation of pipe deformation. [PERSON] et al.