# Application of ANN in Predicting the Cantilever Wall Deflection in Undrained Clay
## 2 Materials and Methods  
### Generation of Database  
In this study, the database was constructed through a series of numerical simulations. The finite element model of the soil-cantilever wall system was built by Plaxis 2D, a commercial software. The typical numerical model is shown in Figure 1. As the soil small strain behavior is well recognized from the case histories, the Hardening Soil model with small strain stiffness (HSsmall) available in Plaxis is used for the simulation of clays in this study. The HSsmallmodel includes not only the stress dependency but also the strain dependency of the soil stiffness. The undrained condition was assumed for the analyses [28; 29]. The retaining wall is linear elastic. A half width of the excavation was modeled because of symmetry of the problem. The size of the finite element mesh depends on the excavation size for each case history. The adopted finite element mesh is presented in Figure 1. Basically, four times the wall length was required for the distance from the wall to the right-side boundary [6]. The bottom boundary was set to 50 m deep to minimize the effect of the presence of bottom boundary on the wall deflection [15], and it was restricted from both horizontal and vertical movements, while the left- and right-side boundaries were only restricted horizontally. Moreover, the soil mass and the retaining structure were modelled by about 1200 15-node triangular soil elements and 15 5-node plate elements, respectively.  
It is worth noting that the finite element method (FEM) analysis was rigorously verified based on 14 centrifuge tests and 45 field cases [30]. Figure 2 presents the comparisons between the cantilever wall deflections \(\delta_{FEM}\), i.e., the wall top displacements, calculated by Plaxis 2D and the measured displacements \(\delta_{m}\). Since the results of FEM were quite close to the 45\({}^{\circ}\) trend line, the rationality of the analysis of FEM was demonstrated. Therefore, the use of database from the verified finite element model in ANN is appropriate and reliable. More detailed information about the numerical models used and the validation process can be found in the authors' previous work [30]. As a result, a total of 191 numerical simulations of the soil-cantilever wall system were conducted, and the corresponding numerical data of the cantilever wall deflection \(\delta\) as well as other associated parameters were obtained.  
Figure 1: Finite element model in Plaxis.  
From the above numerical results, it is noted that the cantilever wall deflection \(\delta\) is significantly influenced by the excavation width \(B\), the excavation depth \(H_{c}\), the wall thickness \(t\), the at-rest lateral earth pressure coefficient \(K_{0}\), the soil shear strength ratio at mid-depth of the wall \(s_{u}/\sigma_{v}\), and the soil stiffness ratio at mid-depth of the wall \(E_{ur}\)/\(s_{u}\). Therefore, these six important parameters were selected as the main influential factors used in the following ANN model. Finally, as described previously, a total of 191 results of finite element analyses of the cantilever wall deflection were used, and the statistical analysis of these data sets is presented in Table 1. In this database, the excavation width \(B\) is distributed between 10.00 and 150.00 m, the excavation depth \(H_{c}\) is distributed between 0.50 and 6.00 m, the wall thickness \(t\) is distributed between 0.60 and 1.60 m, the at-rest lateral earth pressure coefficient \(K_{0}\) is distributed between 0.50 and 1.10, the soil shear strength ratio at mid-depth of the wall \(s_{u}/\sigma_{v}\) is distributed between 0.30 and 0.70, and the soil stiffness ratio at mid-depth of the wall \(E_{ur}\)/\(s_{u}\) is distributed between 199.38 and 900.00.  
Figure 3 presents the relationship between each input and output parameter. The results in Figure 4 indicate that the correlation between all input parameters is weak, so the input datasets used in this study are appropriate.