## 4 Numerical Calculation Case  
In order to further illustrate the applicability of the equivalent simulation method proposed in this research, this method was applied to high- and low-rise buildings in Beijing, China, as a numerical calculation case. The entire raft was used as the foundation of the complex of buildings. CFG piles were used to reinforce the foundation of the high-rise, and the natural foundation was used in the basement and the low annex. The effect of the settlement control of the raft was analyzed using the equivalent simulation method of the strengthened zone mentioned above. The modeling method used was the same as in the previous section. The integral equivalent simulation method was used to simulate the reinforcement effect of the CFG piles by increasing the strength and stiffness parameters of the reinforcement zone. Moreover, to consider the influence of the stiffness of the superstructure on the settlement of the raft, a model of the superstructure was created using a slab element, and a floor load of 15 kPa was applied to each floor. The roof load of the underground garage was 90 kPa. The overall size of the model was 100 m \(\times\) 200 m \(\times\) 30 m (\(x\times y\times z\)), and it was divided into 73,437 10-node tetrahedral elements and 162,202 nodes, which included 41,675 plate elements, 450 beam elements, and 1698 interface elements. Figure 15 shows the meshes of the 3D model of the foundation reinforcement of the high-rise buildings. The model parameters of the soil are shown in Table 1. The parameters of the beam element of the basement pillar were as follows: elasticity modulus \(E\) = 3 \(\times\) 10\({}^{7}\) kPa, sectional area \(A\) = 0.36 m\({}^{2}\), and moment of inertia of area \(I\) = 0.01 m\({}^{4}\). The model parameters of the plate element were as follows: thickness of the raft of the foundation of high-rise structure \(d\) = 0.8 m, thickness of the other raft \(d\) = 0.5 m, elasticity modulus \(E\) = 3.25 \(\times\) 10\({}^{7}\) kPa, thickness of foundation raft \(d\) = 0.8 m, and thickness of other raft \(d\) = 0.5 m. The model parameters of the superstructure were as follows: thickness of the wall of superstructure \(d\) = 0.3 m, floor thickness \(d\) = 0.2, and elasticity modulus of the floor \(E\) = 3 \(\times\) 10\({}^{7}\) kPa. The equivalent parameters of the reinforced zone of the composite foundation were as follows: elasticity modulus \(E_{1}\) = 1.0 \(\times\) 10\({}^{4}\) kPa, \(E_{2}\) = 1.2 \(\times\) 10\({}^{5}\) kPa, [PERSON]'s ratio \(v_{1}\)= \(v_{2}\) = 0.3, \(G_{2}\) = 4.62 \(\times\) 10\({}^{4}\) kPa, cohesion force \(c\) = 270 kPa, and \(\varphi\) = 0\({}^{\circ}\). The construction processes were simulated as follows: (1) calculation of initial stress field; (2) excavation of foundation pit; (3) construction of CFG pile using equivalent treatment method to improve the parameters of the strengthened zone; (4) construction of basement by considering the temporary load on the roof of the basement; and (5) construction of superstructure by applying a load on each floor. Figures 16 and 17 show the settlement nephogram in the entire raft and the settlement distribution in the center section of the raft of the high-rise buildings, respectively. Following CFG pile reinforcement, the settlement of the high-rise building was controlled to within 40 mm, the maximum settlement of the raft slab was 40.3 mm, and the maximum differential settlement was approximately 0.5%, which was lower than the differential settlement control value of 2% ([PERSON] et al., 2016). According to the theoretical method mentioned in the foregoing, the maximum settlement of the raft was 20.3 mm and the maximum differential settlement was 0.8%, similar to the results of settlement obtained by the 3D numerical simulation in this section.