## 1 Introduction  
Geogrid-reinforced piled embankments (GRPEs) have been widely used in highway and railway projects built on soft soil foundations. The soil arching and tension membrane effects play an important role in the load transfer mechanism of GRPEs. A large number of experimental and numerical studies on this topic have been conducted by many researchers [1, 2, 3, 4, 5, 6, 7, 8]. The bearing capacity of the subsoil should not be neglected in design, and it provides certain support to the upper embankment, although it usually has high compressibility, low shear strength, and a long consolidation time. [PERSON] and [PERSON]'s [9] method considered the influence of subsoil when calculating the deflection of geosynthetics under linear elastic conditions and demonstrated that the subsoil contributes to the support of the embankment's residual load. [PERSON] et al. [10] presented that subsoil has a major contribution to the overall vertical equilibrium of GRPEs. [PERSON] and [PERSON] [7] demonstrated the non-negligible bearing capacity of subsoil in long-term conditions, and the support of subsoil reduced the reinforcement tension. Therefore, a design that does not take into account the bearing capacity of the subsoil may become overly conservative. In addition, engineering practices have shown that soils with different stress histories have diverse strains under the same stress. [PERSON] et al. [11] and [PERSON] et al. [12] noted that the stress history affects the soil stiffness, which in turn causes differences in soil settlement. Different stress histories would cause various consolidation coefficients of the subsoil [13], which determines the consolidation rate of the soil. Therefore, the stress history is an important factor in calculating the settlement of subsoil. Many researchers have developed design methods to analyze the performance of GRPEs. However, the current design methods mainly target either one or some aspects of the load-transfer mechanism, and there is an absence of clear and comprehensive guidelines available for the design of GRPEs. British standard BS8006 [14; 15] provides engineers with a relatively recognized design method for GRPEs, but the support of the subsoil was not considered. [PERSON] et al. [16] and [PERSON] and [PERSON] [5] analyzed and modified the BS8006 [14] in terms of the calculation method of the tensile force and the reinforcement sag for the 3D situation, respectively. The bearing capacity of the subsoil was, however, not taken into account in both approaches. [PERSON] et al. [17] proposed a design method for GRPEs and considered the bearing capacity of the subsoil. The method was used to estimate the magnitude of arching taking place in the embankment fill material and to calculate the tension in the reinforcement. [PERSON] et al. [10] built a simplified model to simulate the GRPE. The model was then used to assess the contributions of the reinforcement and the subsoil. [PERSON] and [PERSON] [18] developed an analytical solution for GRPEs where the load-transfer mechanisms accounting for soil arching, tensioned-membrane effects of the reinforcement, and the role of the subsoil were investigated. [PERSON] and [PERSON] [19] presented a simplified model for the analysis of GRPEs considering subsoil consolidation. However, all the methods mentioned above ignore the effect of stress history on subsoil settlement. This was also the case in some other related studies (e.g., [PERSON] and [PERSON] [20]; EBGEO [21]; [PERSON] and [PERSON] [22]; [PERSON] et al. [23]; [PERSON] et al. [24]; [PERSON] et al. [25]; [PERSON] [26]). In addition, previous design methods were usually expressed in the form of complicated equations, to be solved by software or difficult mathematical operations, which entailed higher requirements for engineers and proved inconvenient for promoting the application. EBGEO [21] solved this problem by expressing the design methods through diagrams, based on the soil arching model proposed by [PERSON] et al. [27; 28] and [PERSON] [29; 30].