In this chapter, the earthquakes' simulation test series have been post-processed. The input signal has been taken from the norm IEC 60068-3-3 and properly scaled in amplitude and frequency to simulate the seismic characterization of the region of interest in Mioveni (Romania) (\S\ref{parag:creation_input_signal_seismic}). To study the sloshing processes during this norm-seismic signal on ALFRED's model, the pseudo spectra of acceleration develops from a maximum value plateau that starts for $f=0.89$ Hz, while the amplitude is multiplied by ten times the original one.\\
In the first part of the chapter, a description of the sloshing processes is reported during the norm-base seismic signal applied only in the x-direction when the three steam generators' configuration is set-up and the water depth is $h_{model}=8.84$ cm. The comparison with the fundamental harmonic base excitation, for a forcing amplitude of $a_y=5$ mm and a forcing frequency of $f_y=0.98$ Hz, helps for a better understanding of the randomness of sloshing processes when a seismic event is experienced.\\
In the second part of the chapter, the shifted-scaled norm-base seismic signal is performed to three different setup. Firstly the effect of water depth is tested for a percentage variation of $\pm11\%$ and then a hazardous internal configuration is tested when $h_{model}=8.84$ cm.\\
In the last part, the shifted-scaled norm-base signal is applied in the three direction, so the output from the capacitance probes is compared with the one-direction signal.
%=============================================================================
\section{Norm-base seismic input in one direction}
The norm-base seismic simulation in the x-direction of the reference frame attached to the experimental setup it's a simplification of the signal in the three direction. Fundamental harmonic base excitation with a forcing amplitude $a_y=5$ mm and forcing frequency $f_y=0.98$ Hz is selected to compare with the results of the seismic simulation, so the dimensionless time is scaled by the pulsation $\omega_{1}=2\cdot\pi\cdot 0.98$ Hz$=6.158\mathrm{rad/s}$, and wave amplitude is divided by $D$.
The Figure \ref{fig:time_history_seismic_sim_x_direction} presents the dimensionless time history from the capacitance probes P1 and P2. The motion is nonlinear, as it's suggested in Figure \ref{fig:cine_video_seismic_sim_x_direction} by the video captures of the free-liquid surface motion taken in the dimensionless time range from 67.738 to 73.896 ($t\approx{[}11,12{]}$ s). The very last part of the signal is not so useful to study because the input signal, which is amplified by ten times in amplitude, gives a little shock to the shake table to return to the homing position of zero in the three axis of the Cartesian reference frame. The component of displacement due to the instantaneous arrest is not of interest because is not related to any imposed acceleration by the input signal.
\begin{figure}[H]
    \centering
    \includegraphics[width=0.90\textwidth]{immagini/seismic_simulation/cine_video_seismic.png}
    \caption{Video captures of the free-liquid surface motion taken in the dimensionless time range from 67.738 to 73.896 ($t\approx{[}11,12{]}$ s): surface motion is not planar; internal cylinder sloshing system can be spotted in the second and the fourth capture.}
    \label{fig:cine_video_seismic_sim_x_direction}
\end{figure}
\begin{figure}[H]
    \centering
    \includegraphics[width=0.65\textwidth]{immagini/seismic_simulation/Sloshing231012_15h56_Norm_scaled_shifted_x10_x_only_subplot_time_history.png}
    \caption{Dimensionless time histories for shifted-scaled norm-base test series (which is 10 times increased in amplitude from the original): P1 is in blue and P2 is in green}
    \label{fig:time_history_seismic_sim_x_direction}
\end{figure}
The PSD plots, in Figure \ref{fig:PSD_seismic_sim_x_direction} are studied in confrontation with the one for the selected harmonic test series. The seismic case represents the first four peaks according to the Pseudo Spectra of Acceleration in the range of 0.89 Hz, as outlined in \S\ref{parag:creation_input_signal_seismic}. Then, in the PSD is way difficult to identify exactly which are the nonlinear component. Higher peaks amplitude is near the harmonic tests one, but on a span of frequencies and not only one peak.\\
The phase plane plots are very powerful in the comparison within seismic and harmonic study case. as it's shown in Figure \ref{fig:phase_plane_plot_seismic_sim_x_direction}. When the harmonic input at low amplitude is applied, the orbits are on a limited and common curve, while the orbits for the seismic case doesn't follow a path or a specific curve. The greater difference is recorded for the capacitance probe P2, which is near the inner cylinder: sloshing processes are more intense on the internal structure than the harmonic study case.
\begin{figure}[H]
    \centering
    \includegraphics[width=0.75\textwidth]{immagini/seismic_simulation/harmonic_seismic_confrontation_PSD_semilogy_probes_plot_2023_10_12_Norm_scaled_shifted_x10_x_only_Summary_png.png}
    \caption{Dimensionless PSD plots for the seismic simulation in one direction and the fundamental harmonic in y-direction at $a_y=5$ mm and $f_y=0.98$ Hz: the seismic one reflects the plateau in the 0.89 Hz range of the Pseudo Spectra of the Acceleration, while the harmonic case is easier to comment.}
    \label{fig:PSD_seismic_sim_x_direction}
\end{figure}
\begin{figure}[H]
    \centering
    \includegraphics[width=0.75\textwidth]{immagini/seismic_simulation/harmonic_seismic_confrontation_Phase_subplot_2023_10_12_Norm_scaled_shifted_x10_x_only_Summary_png.png}
    \caption{Dimensionless phase plane plots for the seismic simulation in one direction and the fundamental harmonic in y-direction at $a_y=5$ mm and $f_y=0.98$ Hz: the seismic case is highly random if compared to the harmonic one.}
    \label{fig:phase_plane_plot_seismic_sim_x_direction}
\end{figure}
%===================================================================================
\section{Effect of water depth}
The effect of water depth is studied for the nominal value $h_{model}=8.84$ cm, $h=7.84$ cm and $h=9.90$ cm for simulating an $\pm11\%$ of the $h_{model}$, and $h=6.50$ cm. The tested setup always represents a shallow water condition.\\
The dimensionless time history in Figure \ref{fig:effect_of_water_depth_seismic_sim_x_direction} exhibits higher wave amplitudes when the water depth is increasing. Similar time evolution of the free-liquid surface is spotted when the water depth is equal to $h_{model}$ and its $\pm11\%$. The same observation it's about the PSD plot in frequency ratio $f_y/f_1=$(0.6,2.2) ($f_y={[}0.59,2.16{]}$ Hz) range: except from the forcing frequency plateau around 0.89Hz of the input signal, the other nonlinear frequency components very small in amplitude are in common for the three higher test series.\\
The previous observation is not effective for the lower water depth test series at $h=6.50$ cm because the similarities cannot be distinctly found: in the zoom of the time history in Figure \ref{fig:effect_of_water_depth_seismic_sim_x_direction} happens that peak/trough for $h=6.50$ cm doesn't correspond to the one of the other series.
\begin{figure}[H]
    \centering
    \includegraphics[width=0.90\textwidth]{immagini/seismic_simulation/time_history_effect_of_water_depth_seismic_MOD.png}
    \caption{Dimensionless time history and PSD plots at different water depth: the wave amplitude is higher in time window within time range $t={[}9.7,12.9{]}$s; PSD plot is computed on the complete signal.}
    \label{fig:effect_of_water_depth_seismic_sim_x_direction}
\end{figure}
%===================================================================================
\section{Simulation of hazard in the primary pool}
The simulation of a hazard in the primary pool is simulated by the removal of the three steam generators out of the model, as in the fundamentals harmonic test series (\S\ref{parag:effect_of_hazard_harmonic}).\\
Time history in Figure \ref{fig:effect_of_hazard_seismic_sim_x_direction} for the capacitance probe P2 exhibits higher peaks and deeper troughs in the hazardous configuration. The observation is according to the fundamentals harmonic test series. Since the position of the probe is near to the inner cylinder, representing likewise the central nuclear core, more critical sloshing processes are experienced in the hazardous configuration. The PSD plots exhibits the same peaks at the input forcing frequency, and higher secondary peaks related to the nonlinear component are spotted for the modified internal structure. The nonlinear components don't match completely within the two configurations' PSD, suggesting different values as the structural damping in the model is changed.
\begin{figure}[H]
    \centering
    \includegraphics[width=0.75\textwidth]{immagini/seismic_simulation/internal_hazard_config_MOD.png}
    \caption{Dimensionless time history, phase plane plots PSD plots by the capacitance probe P2 for the seismic test series in one direction at $h_{model}=8.84$ cm and the configuration with and without the three SG: the wave amplitude is higher in the hazardous configuration and the PSD outline several different nonlinear components.}
    \label{fig:effect_of_hazard_seismic_sim_x_direction}
\end{figure}
\clearpage
%=============================================================================
\section{Norm-base seismic input in three direction}
The norm-base seismic input signal in one direction, which is shifted in frequency and scaled in amplitude, is finally applied in the three directions, basically using the very same signal for the x direction but also in y and z direction of the Cartesian reference frame of the shake table. Results are shown in Figure \ref{fig:3d_vs_no3d} for the capacitance probe P1 and in Figure \ref{fig:cine_video_seismic_sim_all_directions} for a sight on the sloshing processes in the model's pool. The wave amplitude confrontation is ten times higher than the \textit{x-only} series when the peaks occur. The simply three dimensions input signal is more critical if compared to any of the previous seismic test series with different water depths or with a hazardous internal configuration but applied in one direction. The norm-base seismic test series only in the x-direction gives back an external acceleration in x equal to $0.629\,\mathrm{m/s^2}$, so applying in the 3DoF case the same norm-base shifted and scaled signal means applying at the same time a peak of equal intensity in all the directions.\\
Finally, moving the input signals in three directions makes the free-liquid surface motion more critical and harder to predict in the complicated ALFRED's model annular geometry. The wave-structure interaction affects the sloshing processes since the 1 DoF test series, and the effect is way more crucial. The main observation after this comparison within the one DoF and the three DoF cases is the dangerous increasing of the wave amplitude when moving to more realistic seismic simulations. It's critical than studying the simpler cases for moving to the more complicated simulations.
\begin{figure}[H]
    \centering
    \includegraphics[width=0.85\textwidth]{immagini/seismic_simulation/3d_vs_no3d.png}
    \caption{Video captures of the free-liquid surface motion taken in the dimensionless time range from 67.738 to 73.896 ($t\approx{[}11,12{]}$s): \textit{a, b, c, d} are consecutive in time; surface motion is not planar and the wave amplitude is greater than the test series in one direction (Figure \ref{fig:cine_video_seismic_sim_x_direction}).}
    \label{fig:cine_video_seismic_sim_all_directions}
\end{figure}
\begin{figure}[H]
    \centering
    \includegraphics[width=0.90\textwidth]{immagini/seismic_simulation/3d_xonly_confrontation.png}
    \caption{Dimensionless time history, phase plane plots PSD plots by the capacitance probe P1 for the seismic test series in one direction and three directions at $h_{model}=8.84$ cm: when the peaks occur, in the three DoF series the wave amplitude is ten times higher than the one from the \textit{x-only} series.}
    \label{fig:3d_vs_no3d}
\end{figure}
\clearpage
%============================================================================
\section{Scale effect assessment}\label{parag:full_scale_discussion_seismic}
The scale effect assessment for the norm-base test series is made taking into account the five parameters already investigated in \S\ref{parag:full_scale_discussion_harmonic}: forcing amplitude, forcing frequency, wave amplitude, water depth and internal configuration. The wave amplitude for ALFRED upscaling is computed as in Eq. \ref{eq:Fr_ALFRED_model_wave_amplitude} based on the Froude scaling. When the norm base excitation is applied in one direction along x, the peak of the external forcing acceleration is computed for the forcing frequency of $f_x=0.89$Hz and the maximum forcing amplitude imposed of 20mm:
\begin{equation}
        \Ddot{a}_t=A_{ALFRED}\times(2\pi f_{ALFRED})^2=\frac{A_{model}}{0.054}\times\left(2\pi \frac{f_{x,model}}{4.29}\right)^2=0.629\,\mathrm{m/s^2}
\end{equation}
when the conventional water depth is equal to $h=8.84$ cm.\\
In Table \ref{tab:full_scale_seismic} is reported an overview of the most interesting results.
\begin{table}[H]
\centering
{\fontsize{11}{10}\selectfont
\begin{tabular}{|cr|rrr|rrr|}
\hline
\multicolumn{2}{|l|}{}                                                                                                                          & \multicolumn{3}{c|}{Model}                                                                                                                           & \multicolumn{3}{c|}{ALFRED}                                                                                                                             \\ \hline
\multicolumn{1}{|l|}{\textbf{Test series}}                                                                  & \multicolumn{1}{l|}{\textbf{3SG}} & \multicolumn{1}{l|}{\textbf{h {[}m{]}}} & \multicolumn{1}{l|}{\textbf{$\Ddot{a}_y$ {[}$\mathrm{m/s^2}${]}}} & \multicolumn{1}{l|}{\textbf{$\zeta_m$ {[}m{]}}} & \multicolumn{1}{l|}{\textbf{h\_A {[}m{]}}} & \multicolumn{1}{l|}{\textbf{$\Ddot{a}_t$ {[}$\mathrm{m/s^2}${]}}} & \multicolumn{1}{l|}{\textbf{$\zeta_A$ {[}m{]}}} \\ \hline
\multicolumn{1}{|c|}{\begin{tabular}[c]{@{}c@{}}Norm base signal \\ scaled and shifted\\ 1DoF\end{tabular}} & Yes                               & \multicolumn{1}{r|}{0.088}              & \multicolumn{1}{r|}{0.652}                               & 0.016                                           & \multicolumn{1}{r|}{1.627}                 & \multicolumn{1}{r|}{0.629}                               & 0.068                                           \\ \hline
\multicolumn{1}{|c|}{\begin{tabular}[c]{@{}c@{}}$a_y=0.015$m\\ $f_y=0.98$Hz\\ 1DoF\end{tabular}}            & Yes                               & \multicolumn{1}{r|}{0.088}              & \multicolumn{1}{r|}{0.190}                               & 0.015                                           & \multicolumn{1}{r|}{1.627}                 & \multicolumn{1}{r|}{0.180}                               & 0.065                                           \\ \hline
\multicolumn{1}{|c|}{\begin{tabular}[c]{@{}c@{}}Norm base signal\\ scaled and shifted\\ 1DoF\end{tabular}}  & No                                & \multicolumn{1}{r|}{0.088}              & \multicolumn{1}{r|}{0.652}                               & 0.024                                           & \multicolumn{1}{r|}{1.627}                 & \multicolumn{1}{r|}{0.629}                               & 0.102                                           \\ \hline
\multicolumn{1}{|c|}{\begin{tabular}[c]{@{}c@{}}Norm base signal\\ scaled and shifted\\ 3DoF\end{tabular}}  & Yes                               & \multicolumn{1}{r|}{0.088}              & \multicolumn{1}{r|}{1.158}                               & 0.040                                           & \multicolumn{1}{r|}{1.627}                 & \multicolumn{1}{r|}{1.10}                                & 0.170                                           \\ \hline
\end{tabular}}
\caption{Scale effect on some selected test series in the earthquakes'reproduction norm base excitation with different forcing amplitudes, frequencies, water depths and internal configurations; the uncertainty on the displacements for the wave amplitude in model from capacitance probe P1 is equal to $\simeq$0.0058 m (\S\ref{parag:total_uncertainty}).}\label{tab:full_scale_seismic}
\end{table}
The 1DoF series for the configuration with the three steam generators exhibits highly nonlinear motion, and the maximum wave amplitude reached in the model is equal to $\simeq$15.8 mm$\pm$1.351 mm (total uncertainty on the probes measurements \S\ref{parag:total_uncertainty}). The maximum wave amplitude can be compared to the one in output from the horizontal harmonic base excitation at forcing amplitude 5mm and first sloshing frequency of 0.98 Hz, which is equal to $\zeta=$0.068 m.\\
The confrontation within the test series results for the configuration with and without the three steam generators is particularly descriptive, as it is when the horizontal harmonic base excitations are applied. The peak of wave amplitude reached is equal to 0.102 m when the hazardous configuration is set up, which is 1.5 times the one when all the tubes in the pool are considered.\\ 
The greatest discrepancy in terms of magnitude order is obtained when the norm-base seismic signal is applied in all the direction. The ground acceleration has components in all the three direction at the same time, so when a peak is applied along x then is simultaneously along y and z. The external acceleration vector in its maximum peak has a nominal module equal to:
\begin{equation}
    \Ddot{a}_t=\sqrt{3 \times A_{ALFRED}\times(2\pi f_{ALFRED})^2=\frac{A_{model}}{0.054}\times\left(2\pi \frac{f_{x,model}}{4.29}\right)^2}=1.10\,\mathrm{m/s^2}
\end{equation}
The case is an estimation of the seismic loads built on the region of interest ground acceleration of $\Ddot{a}_t=1\,\mathrm{m/s^2}$ in Mioveni \cite{ALFRED_Mockup}. The wave amplitude in ALFRED reaches peaks 2.5 times higher than in the 1DoF case, for a maximum value of 0.170 m.\\
The fundamentals harmonic test series make the point on how the maximum wave amplitude can qualitatively increase in the model. Moreover, in the respective scale effect assessment in \S\ref{parag:full_scale_discussion_harmonic}, some theoretical horizontal ground accelerations $\Ddot{a}_t$ were of the same magnitude order if compared to the $\Ddot{a}_t$ peaks of Mioveni \cite{ALFRED_Mockup} and Turin \cite{Protezione_civile} of 1$\mathrm{m/s^2}$, which is a medium-low value, and to the mean one of Belgium \cite{Earthquake_ground_acceleration} of 0.40$\mathrm{m/s^2}$.\\
The same value from the report and the literature are represented in the seismic simulations' tests, with the 1DoF signals that make a connection with the previous 1DoF harmonic test series and the following 3DoF seismic tests.\\
Finally, the importance of the integrity of the internal component in the nuclear reactor is here highlighted. The sloshing processes demand a strong structural damping component in the primary pool. The problem of possible hazard is something that must be avoided and if it occurs have to be stabilized. It's here reported that one of the very first nuclear accident in 1960, that happened in the US on the SL-1 reactor \cite{Additional_Analysis_of_the_SL-1_Excursion}, has demonstrated how many damages the cooling water caused hitting the top of the primary pool during that dramatic event.