## 1 Introduction  
Embankment construction for infrastructure projects has considerably increased during the past few decades in soft soil, loess, and medium-compression soil regions. Among the various ground improvement methods, geosynthetic reinforced and pile-supported (GRPS) embankments are considered to be a reliable and suitable solution for time-bound construction projects and difficult ground conditions [1; 2; 3; 4; 5; 6]. GRPS embankments are piles, geogrids, and soil synergistic action of the three to bear the load; the main working principle relies on the soil arch effect and tensioned membrane effect [7]. Their advantages include faster construction, higher stability, lower cost, and wider applicability [8; 9; 10; 11]. In this integrated system, the soil arching effect develops when differential settlements between piles and soil occur because of the different pile and soil stiffness, the internal stress in the soil is redistributed, the downward tendency of the subsoli is partially restrained by the shear stress within the embankment fill on the pile caps, and the vertical component of the shear stress participates in the process of load transfer onto the piles. Consequently, soil arching has a significant influence on the ultimate bearing capacity of the foundation as well as the performance of each pile [12; 13; 14; 15; 16]. Meanwhile, the existence of the geogrid can transfer the remaining embankment load to the pile top through the tension, and the tensioned membrane effect can give full play to the bearing potential of the pile and thus improve the bearing capacity of the foundation [17; 18]. In recent years, scholars have conducted a series of research projects on the action mechanism and load-bearing capacity of GRPS embankments. [PERSON] et al. [3] studied the GRPS embankment technology over loose sandy soil. The results demonstrate that using two layers of geotextile with optimal positions over the pile heads can improve load distribution and reduce the variance in load efficiency between the piles. [PERSON] et al. [19] analyzed the stress distribution of the planar soil arch and spatial soil arch of pile embankment under static load, and the results indicated that the spatial soil arch effect is stronger than the planar soil arch effect. [PERSON] et al. [20] showed that the stress distribution of GPRS embankment is affected by the planar and spatial soil arch effects under dynamic load, and [PERSON] et al. [11] found that the existence of geogrids can reduce the influence of dynamic load on the arch effect. To improve the bearing capacity of loess foundations, [PERSON] et al. [21] and [PERSON] et al. [22] investigated GRPS embankment for loess foundations reinforced by splitting grouting piles and grouted cement fly ash gravel (CFG) piles. The results show that the structure has good bearing capacity under static load. [PERSON] et al. [23] presented a novel optimization framework for genetic algorithms and improved black hole algorithms to systematically determine the design parameters to achieve the minimum construction cost for GRPS embankments. [PERSON] et al. [24] and [PERSON] et al. [25] carried out parameter optimization of GRPS embankments and provided an economical and effective measure for the design of GRPS embankments. [PERSON] et al. [15] present an analytical model for GRPS embankments that combines several phenomena, such as the concentric arches model in cohesive fill soils, the hyperbolic model for the isochrones geogrid curve, and the subsoil's consolidation. [PERSON] et al. [26] studied the long-term performance of the GRPS embankment of a high-speed railway and carried out static load and dynamic load model tests. The analysis results show that the pile is mainly affected by friction from the surrounding soil, while its end-bearing capacity is small. [PERSON] et al. [27] established an X-type pile net composite foundation model and analyzed the mechanical characteristics of the structure under the action of a train load.