# Damage Characteristics and Dynamic Response of RC Shells Subjected to Underwater Shock Wave
## 3 Validation of the Numerical Simulation  
A field test of RC slab underwater explosion [25] was used to verify the accuracy of numerical methods and material models. The Arbitrary Lagrangian-Eulerian (ALE) method amalgamates the benefits of Lagrangian and Eulerian methods [5] and was used in this model. It should be noted that the material model, solver type, and Euler-Lagrange coupling method are the same as those used in the bottom-sitting shell structures under underwater explosive loads. A numerical analysis model of the 1/2 RC slab under the underwater explosion was established, as shown in Figure 4. The dimensions of the water domain are 0.7 m \(\times\) 0.7 m \(\times\) 0.35 m. The dimensions of the RC slab are 0.5 m \(\times\) 0.5 m \(\times\) 0.06 m. The fixed boundary is set at the ends of the RC slab. The nodes located on 1/2 symmetrical surface of the model are set to be symmetrical constraints. The outer surface of the water domain is set to be non-reflecting. The RC slab is simulated using the Lagrange algorithm, while the water and TNT are modeled using the Euler algorithm. The interaction between the RC slab and water is simulated through a fluid-structure coupling method. The explosive is set in volume fraction form. The steel bar is simulated using a beam element. The dimensions of the numerical model of the RC slab are shown in Figure 5. Subsequently, based on the experimental data of the dynamic response of the RC slab under underwater explosion [25], the accuracy of the numerical method and material models was verified. As shown in Figure 6, the comparison of the damage characteristics between the underwater explosion test [25] and numerical simulation demonstrates a better consistency. The front side of the plate exhibits minimal damage, characterized by a few distributions of compression cracks. The back side of the plate displays more severe damage, with a large number of tensile cracks dispersed across its surface. Meanwhile, the back side of the plate displays a damage characteristic that the cracks extend from the center to the periphery of the plate.  
In addition, as shown in Figure 4, consistent with the underwater explosion test, the pressure measure point 1 and measure point 2 of the underwater explosive are located at the upper and lower surfaces of the plate 130 mm away from the explosive center, respectively [25]. The comparison of the pressure time history curve obtained by the water explosion test [25] and numerical simulation is shown in Figure 7. The overall change trend of the pressure time history curve obtained by numerical simulation is basically consistent with the test data, but there are still some differences. The peak pressure obtained by numerical simulation and underwater explosion test at point 1 is 35.8 Mpa and 40 Mpa, respectively, with a difference of about 10.5%. The peak pressure obtained by numerical simulation and underwater explosion test at measure point 2 is 14.4 Mpa and 16 Mpa, respectively, with a difference of about 10%. The difference between the pressure time  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Mass density RO (kg/m\({}^{3}\)) & 7850 \\ Young’s modulus E (GPa) & 206 \\ Poisson’s ratio PR & 0.3 \\ Yield stress SIGY (MPa) & 400 \\ Strain rate parameter C (s\({}^{-1}\)) & 35.27 \\ Strain rate parameter P & 5 \\ Tangent modulus ETAN (GPa) & 2.06 \\ \hline \hline \end{tabular}
\end{table}
Table 5: The parameters of the rebar.