## 2 Numerical Model  
The concrete and soil in a footing-soil-pile system (FSPS) are idealized as non-linear, elastic-perfectly plastic and rate-independent materials obeying the upper-bound yield criterion of [PERSON] (2018). Two- and three-dimensional finite element (2D and 3D FE) models for FSPS are generated by the FEA software package of ANSYS 13.0 ([PERSON] et al., 2017). The following assumptions are made for the 2D and 3D FE models: (1) pile-walls interacting with adjacent embedded footings supporting uniformly distributed pressures; (2) soils having homogeneous and isotropic mediums; (3) no impacts of consolidation and creep on the behavior of pile-walls and footings; and (4) no influence of the ground water table on the stress-strain behavior of soils. The schematic view and sections of the 2D and 3D FE models of FSPS are shown in Figure 1. Figure 1a-d show the schematic top view, the transverse section at the pile-wall location, the longitudinal section at the symmetrical axis, and the transverse section at the footing location, respectively, with the side, out-of-plane, and bottom boundaries for the 3D FE model of FSPS. In addition, Figure 1c depicts the schematic view with the side and bottom boundaries for the 2D FE model of FSPS. The boundary conditions shown in Figure 1 are (1) side boundaries restricted from displacing in the x-direction; (2) bottom boundaries restricted from displacing in the x-, y-, and z-directions; and (3) out-of-plane boundaries restricted from displacing in the z-direction. [PERSON] et al. (2018) demonstrated that the locations of these boundaries, which are the result of a non-dimensional parametric study by a trial-and-error procedure, have a negligible impact on the behavior of an FSPS. In addition, [PERSON] et al. (2018) validated the FSPS boundaries used in this study for kaolin, silty clay, and kaolin-sand soils using previous experimental tests conducted by [PERSON] (2018), [PERSON] (2018), and [PERSON] (2018), respectively. The schematic view and sections of the 2D and 3D FE models shown in Figure 1 are meshed with linear finite elements having elastic, plastic, and large strain capabilities, as demonstrated in Figure 2. The quadrilateral four-node linear element (PLANE42) is selected for the plane strain analysis of the 2D FE model. The hexahedron eight-node linear element (SOLID45) is chosen for the analysis of the 3D FE model. The initial conditions of the geostatic or at-rest condition stresses governed by gravity and density are set for the 2D and 3D FE models ahead of the analysis. Three backfill/footing soils are considered in this study: kaolin, silty clay, and kaolin-sand. The properties of kaolin, silty clay, and kaolin-sand soils were studied by [PERSON] and [PERSON] [32], [PERSON] and [PERSON] [33], and [PERSON] et al. [34], respectively. The strength properties of the backfill/footing soils, which are the result of a test of triaxial compression consolidated drained (CD), are applicable for the long-term condition. The concrete of the piles and footings is chosen with mechanical properties studied by [PERSON] [35]. For a smooth concrete face, [PERSON] [36] recommended a friction angle at the soil-concrete interface, \(\phi_{\text{Sc}}\), between 60% and 80% of the soil internal friction angle \(\phi\). Therefore, the friction angle at the soil-concrete interface is selected as 70% of the soil internal friction angle. The properties of the backfill/footing soils and concrete for the FSPS are tabulated in Table 1.  
The width, \(\text{B}_{\text{f}}\), and depth, \(\text{D}_{\text{f}}\), of the footing are selected to be constant at 0.914 m. The driven concrete pile is chosen to have a square section with three different pile widths, \(\text{B}_{\text{p}}\): 0.254, 0.305, and 0.356 m. The total length, \(\text{L}_{\text{p}}\), and embedment length, \(\text{EL}_{\text{p}}\), of the pile are decided to be 18.593 and 12.802 m, respectively.