## 1 Introduction
(2004) used a two-dimensional (2D) model to calculate deflections and circumferential strains of a profiled thermoplastic pipe and examined the effectiveness of the model by a biaxial pipe test [17]. The simulation results revealed that the pipe stress was concentrated near the loose backfill area when loose backfill was placed under the haunch. Using ABAQUS, which a finite simulation model software by the SIMULIA Company in  
Figure 1: Mechanism of soil arching within the soil-pipe system. France, [PERSON] and [PERSON] (2010) established a 2D model to evaluate the deformation of HDPE and polyvinyl chloride (PVC) pipes installed in dune sand; the effects of several factors (such as relative density, backfill material, and soil cover) on the pipe performance were analyzed, and the results showed that the response of pipes increased with the increase in the relative density of the sand [18]. A three-dimensional (3D) finite element model for analyzing the deformation of pipes under normal fault motions was proposed by [PERSON] et al. (2016), and the influences of pipe diameter, thickness, buried depth, friction angle, and the density of the backfill on the bending strain of the pipe were discussed. The simulation results showed that the deformation of the pipe was sensitive to the buried depth and backfill type [19]. [PERSON] et al. (2019) established a 3D model by ABAQUS to investigate the mechanical characteristic before and after repairing the pipe with carbon fiber reinforced polymer (CFRP) layer [20]. With the development of roads and transportation, traffic load has become one of the critical factors of pipe deformation. [PERSON] et al. (1992) conducted a similar field study on buried PVC pipes and demonstrated that a PVC pipe buried in flowable fly-ash backfill was feasible and safe under continuous high-load applications [21]. At present, when dealing with the influence of traffic loads on pipes, the traffic load is often simplified to the static load without considering the pavement structure, which leads to pipe deformation that is inconsistent with the real traffic load. Many researchers believe that simplifying the traffic load to the static load results in increased pipe deformation and, therefore, safer conclusions. However, [PERSON] and [PERSON] (2017) carried out low-embankment traffic load tests on clay and found that the vertical load generated by the dynamic load was more than three times that of the static load [22]. In the 1960s, the fourth power theory proposed by the American Association of Interstate Highway Workers (AASHO) indicated that the static axle load was more suitable for simulating traffic load under low-speed and light axle load conditions [23]. For concrete pipe, the results of finite element simulation showed that pipe deformation caused by a vehicle load could be ignored when the buried depth was 1.5 times greater than the diameter of the pipe [24]. In generally, the influence of traffic load on concrete and other rigid pipelines cannot be ignored [25; 26; 27]. At the same time, a well-compacted backfill would also reduce the influence of the external load on the pipe. [PERSON] and [PERSON] (2016) found that plastic pipes were less affected and less elastically deformed by external loads when the backfill was compacted. In addition, the stress and deformation of the pipe were susceptible to the traffic load because of the shallow buried depth of the pipe [28]. [PERSON] and [PERSON] (1997) simplified the traffic load to the uniform static load in a nonlinear, two-dimensional finite element model and revealed that low-strength backfill material could significantly reduce the impact of the traffic load on PVC pipes [29]. As can be seen from the above literature review, the deformation of buried plastic pipes under traffic loads has been studied by using field tests or two-dimensional finite element models. However, there is little information about the mechanical response of HDPE pipes under a traffic load and local loose backfill soil.