# Safety Evaluation of a RC Structure with Multiple Openings under High Water Depth Inundations
## 4 Numerical Simulation
### Resistance of the Prototype Building to HYDRODYNAMIC Pressure  
Taking advantage of the results discussed in Section 4.2, the behaviour of the prototype building under hydrodynamic pressures was examined. The prototype building was introduced in Section 2.1. The ground floor of the building was discretised. As shown in Figure 8a, the Y axis was parallel with the NS direction of the prototype building. The model had three types of windows. There were large-operable, large-fixed and small operable ones as discussed in Section 2.1 (see, Figure 1c). The model was composed of 14,209 nodes and 13,319 four-node quadrilateral shell elements (Figure 8a). The model was fully constrained at the bottoms of the structure. The same material parameters and failure criteria as discussed in Section 4.1 were adopted. Two analyses were performed. As the first analysis, hydrodynamic pressures from nonbreaking waves were applied to the model. They were added to the hydrostatic pressures by increasing the assumed water depth. This approach is considered appropriate in case the flow velocity is lower than 3 m/s [(40,68)]. The study focused on zones at least 1 km away from rivers as discussed in Section 2.1 and the flow velocity of inundations usually does not exceed 3 m/s in such zones [(69,70)]. In addition, this value is the expected lower bound as a design flow velocity for 3-m level flows [(33)]. For these reasons, the flow velocity was considered equal to 3 m/s in this analysis. The equivalent surcharge height, _dh_ was calculated in the following Equation (1). \[dh=\frac{1.25v^{2}}{2g} \tag{1}\]  
Figure 8: Hydrodynamic analysis of the prototype building: (**a**) numerical model and (**b**) deformation distribution contours at the 3-m water depth. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**(mm)** & **W1 OP** & **W2F** & **N1 OP** & **N2F** \\ \hline
**experiment** & 16 & 10 & 6.4 & 10 \\ \hline
**numerical** & 15.4 & 9.3 & 5.8 & 11.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of deflection between the numerical model and real structure. where:  
\(\
u\) is the velocity of a fluid flow. \(g\) is the gravitational acceleration. The surcharge height was equal to 0.6 m and therefore the resultant water depth was 3.6 m in the considered analysis. The deflection was 18.1 mm, 15.5 mm and 10.2 mm at the mid-spans of the large operable, large fixed and small windows, respectively. The RC walls showed very little deformation. The maximum deflection was observed in the large operable windows (Figure 8b). At this state, the loads acting on the large and small windows were equal to 15.2 kN and 6.8 kN, respectively. The large operable windows were close to failure at the considered flow velocity, taking into account the allowable deflection of the sole windows discussed in Section 4.2. As the second analysis, dynamic pressures from nonbreaking waves were applied to the north elevation (see, Figure 8a). The north elevation was selected as it had all three types of the windows: i.e., large operable, large fixed and small operable windows. The purpose of the analysis was to examine the influences of equations on results. The model was subject to the hydrostatic and hydrodynamic pressures. In this analysis, the hydrodynamic pressures were calculated according to Equation (2) [33]. \[p_{d}=\frac{1}{2}\rho C\varv^{2}A \tag{2}\]  
where:  
\(p_{d}\) is a horizontal drag load acting on a wall due to hydrodynamic pressures. \(\rho\) is the density of a fluid (=1000 kg/m\({}^{3}\) for water). \(C\) is a drag coefficient (=1.25 in this analysis). \(A\) is a surface area experiencing the drag load. The surface area was calculated by multiplying the width of the wall normal to the flow by the water depth. The flow velocity was considered equal to 3 m/s like the previous analysis. The resultant hydrodynamic load was 136.6 kN. The load was uniformly distributed over the surface areas. The value was 5.6 kN/m\({}^{2}\). It was added to the hydrostatic pressures of the 3-m water depth.