# Effects of Heavy Rainfall on Shallow Foundations in Bukit Timah Granite in Singapore
## 2 Methodology
### Finite Element Modelling and Input Parameters  
The 2D plane-strain finite element model for the analysis of rainfall infiltration into Bukit Timah Granite (BTG) soil was developed. The SIGMA/W was used to create the shallow foundation model with a 10 B in width and 5 B in height, where B (=5 m) is the width of the footing in the FEM. The mesh of the model was discretized into a global size of 0.75 m, with secondary nodes enabled for 8-noded element mesh for strain-stress analysis. The left and right side of the model was fixed in the horizontal direction, while the bottom of the soil model was fixed in both a horizontal and vertical direction. A no-flow boundary condition was also applied to the sides and bottom of the model, and less water flowed out of the model in those directions. Floods and run-off resulting from the rainfall and the lack of infiltration capacity of the soil were also disregarded in this study. Figure 2 shows the FE mesh and boundary conditions. Loads were applied to simulate a load of a building in increments of 100 kPa, starting from 100 kPa and ending at 500 kPa, and were applied at the surface of the soil in the center of the model to investigate the load-settlement response.  
The soil parameters of residual soil in BTG were adapted from [PERSON] et al. [14; 25], which were obtained from a study area in Orchard Boulevard situated in the southern part of Singapore. The residual soil was modelled in SIGMA/W using the Mohr-Coulomb model. The soil parameters, along with the hydraulic parameters are presented in Table 1[14; 25]. The soil-water characteristic curve (SWCC) and the unsaturated permeability function were both fitted using the Fredlund and Xing [32] function and were both implemented natively in the SIGMA/W hydraulic modules in GeoStudio. The SWCC and unsaturated permeability functions are presented in Figures 3 and 4.  
Figure 2: The 2D finite element (FE) model used in this study.  
Rainfall events of 8 mm/h, 20 mm/h and 32 mm/h were applied for 1, 2, 3, 4 and 5 days to the ground surface [4]. A rainfall event of 0 mm/h rainfall for similar durations was also modeled to study the 0 rainfall condition and understand the scenario of a lack of rainfall. The rainfall intensities and durations were adapted from [PERSON] et al. [4], which were  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Properties** & **Residual Soil** \\ \hline Unit Weight, \(\gamma\) (kN/m\({}^{3}\)) & 18 \\ Saturated Volumetric Water Content, \(\theta_{\mathrm{s}}\) & 0.51 \\ Residual Volumetric Water Content, \(\theta_{\mathrm{r}}\) & 0.253 \\ Saturated Permeability, \(k_{\mathrm{s}}\) (m/s) & \(1.00\times 10^{-6}\) \\ [PERSON] and [PERSON] (1994) SWCC Fitting & \\ Parameters & \\ \(a\) (kPa) & 20 \\ \(n\) & 2.6 \\ \(m\) & 0.41 \\ Effective Cohesion, \(c^{\prime}\) (kPa) & 5 \\ Effective Friction Angle, \(\phi^{\prime}\) (\({}^{\circ}\)) & 28 \\ Effective Elastic Modulus, \(E\) (mPa) & 20 \\ Initial Void Ratio, \(e_{0}\) & 0.8 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Soil and hydraulic parameters for BTG residual soil [14; 25].  
Figure 4: Unsaturated permeability function for BTG residual soil.  
Figure 3: Soil–water characteristic curve for BTG residual soil.  
determined based on historical maximum daily rainfalls and obtained from meteorological stations in Singapore. The adapted values had a slight increase in intensity to factor in the impacts of climate change. Initial groundwater tables of 1 B m and 2 B m below the surface were adopted, which gave an initial matric suction of 50 kPa and 100 kPa, respectively. These controlling parameters used in the simulations are summarized in Table 2. The coupled flow-deformation analyses were performed to simulate the time-dependent transient water flow/infiltration and the deformation response in response to flux boundary conditions [4]. No ponding boundary condition at the surficial layer was considered. The sequential analysis procedure used in this study is summarized in Figure 5.