## 3 Numerical Modeling  
### Project Overview  
A large culvert intersection project with a backwater canal is used as the background. The type is an assembly culvert, and the main design index is as follows: the design length is 234 m, design flow rate is 53.9 m\({}^{3}\)/s, the design water depth is 3.5 m, the structure of the pipe body is box-type, the section size is 2 \(\times\) 4.0 m \(\times\) 4.0 m, the length of gate section is 10 m, and the length of building arrangement is 154 m. The culvert axis intersects with the backwater canal at an angle of roughly 77\({}^{\circ}\), which is convenient for traffic. The design dimensions of the culvert are shown in Figure 2.  
The stratum within the scope of engineering geological exploration is the upper Pleistocene alluvium of the Fourth Series, and the lithology is mainly light, medium, and heavy powdery loam, fine sand, and pebbles, divided into five soil units. Layer 1 is pebbles (Q\({}_{3}^{\text{alp}}\)), composed mainly of quartz sandstone, followed by quartz sand and andesite. Layer 2 is fine sand (Q\({}_{3}^{\text{alp}}\)), composed mainly of feldspar and quartz, mostly fine sand with uneven quality, locally containing a small amount of mud and occasionally small gravel and occasional calcium colloid in XHCSX4. Layer 2 is loess-like heavy powdery loam (Q\({}_{3}^{\text{alp}}\)). It is plastic, with a soil texture, rusty yellow streaks, occasional calcium reticulation, and slightly low local clay content near medium powdery loam. Layer 2 is loess-like medium powdery loam (Q\({}_{3}^{\text{alp}}\)). It is plastic with uneven soil texture, snail shell fragments, occasional rusty yellow streaks, and slightly high local clay content near the medium powdery loam. Layer 2 is loess-like heavy powdery loam (Q\({}_{3}^{\text{alp}}\)). It is brownish yellow, wet and plastic, and has uneven soil texture, a plant root system and snail shell fragments.  
The physical parameters of the soil layer used in the numerical model are shown in Table 1. The permeability coefficient is determined according to the geological exploration data, and the geological profile is shown in Figure 3.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Materials**} & **Density** & **Angle of Internal** & **Modulus of Elasticity** & **Poisson’s Ratio** & **Cohesion (kPa)** & **Permeability Coefficient (m/s)** & **Pore Ratio** \\ \hline Heavy chalky loam & 1530 & 18 & 5 & 0.3 & 20 & 3.0 \(\times\) 10\({}^{-6}\) & 0.807 \\ Medium chalky loam & 1580 & 18 & 5.1 & 0.3 & 14 & 5.0 \(\times\) 10\({}^{-7}\) & 0.914 \\ Heavy chalky loam & 1540 & 19 & 6 & 0.3 & 21 & 8.6 \(\times\) 10\({}^{-8}\) & 0.716 \\ Medium-fine sand & 1500 & \(\backslash\) & 20 & 0.3 & \(\backslash\) & 8.0 \(\times\) 10\({}^{-5}\) & \(\backslash\) \\ Sand and pebbles & 1700 & \(\backslash\) & 150 & 0.2 & \(\backslash\) & 3.0 \(\times\) 10\({}^{-3}\) & \(\backslash\) \\ C20 concrete & 2400 & \(\backslash\) & 22,500 & 0.2 & \(\backslash\) & 1.0 \(\times\) 10\({}^{-9}\) & 1.5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Suggested values for physical parameters of soil layers and structural materials in the site area.  
Figure 2: Culvert design size.