Figure 4 shows the flow structures through the experimental domain with different types of BM without any rotation ($\mathsf{\theta }=0^{°}$) following an EM for the experimental case EM-BM. In this study, four basic flow types were observed, i.e., Type-1 (see 2–5 cm results in Figure 4a) and Type-2 (see 6 cm results in Figure 4a) hydraulic jump within the gap region of the BM and the EM. Furthermore, a bow wave including a detached hydraulic jump (see Figure 4b) and the wall-jet-like bow wave (see Figure 4c) at the front face of the BM as well as the front face of the piloti-type column have been observed, respectively [6,8]. Moreover, the hydraulic jump was classified based on the location of the jump toe. When the hydraulic jump toe was lying within the gap between the EM and BM, the jump was identified as a Type-1 hydraulic jump, and when the starting position of the hydraulic jump was observed on the downstream surface slope of the EM, the jump was defined as a Type-2 hydraulic jump [27].

Moreover, when the BM had a specific porosity (like BM_B and BM_C), the overtopping flow becomes supercritical in the gap region, while forming a detached hydraulic jump with a bow wave due to the flow passing through the BM, as shown in Figure 4b. Meanwhile, when increasing the overtopping depth from the EM, the detached length slightly increased, while the bow wave running along the front face of the BM was extended for the BM_B and BM_C (see Figure 4b). When the BM was elevated by using an array of piloti-type columns, no hydraulic jump formed due to the arrangement of the piloti-type columns, which allowed a free flow below the BM (see Figure 4c). This phenomenon was classified as a no-jump except for the wall-jet-like bow wave in front of the piloti-columns. Furthermore, a similar flow phenomenon has been observed when increasing the water depth within the cylinder array below the BM, as shown in Figure 4c [8,16].

Moreover, to characterize the flow behavior at the non-piloti-type BMs, the ratio of the non-dimensional water depth $H_{\mathrm{F}} \left(=h_{\mathrm{FB}}/h_{\mathrm{E}}\right)$ measured in front of the non-piloti-type BM, obtained for the highest non-overtopping depth $H_{\mathrm{o}} \left(=h_{\mathrm{o}}/h_{\mathrm{E}}\right)$, presented in Figure 5 as a function of the Froude number ($F{r}_{\mathrm{FB}}$), was measured in front of the BM for the EM-BM case. The results presented in Figure 5 show that a Type-2 hydraulic jump was generated when the BM frontal water depth exceeded the limit of 0.5 times the embankment height ($h_{\mathrm{E}}$). The hydraulic jump-starting point was lying on the EM downstream surface slope with a subcritical Froude condition concerning the BM total porosity (${\eta }_{\mathrm{tot}}$) and the orientation angle ($\mathsf{\theta }$). Furthermore, with the increased porosity of the BM towards the flow direction, the Type-2 hydraulic jump was converted to a Type-1 hydraulic jump or detached bow wave, as shown in Figure 4b [16,17]. The error bars in Figure 5 represent the standard deviation of the measured water depths in front of the BM for all the approaching flow depths under the EM-BM case. In addition, the hydraulic jump formation conditions concerning the experimental setup are discussed in the next section.

The numerical model’s sensitivity to the grid size and the chosen turbulence model were assessed utilizing a statistical indicator such as the root mean square error (RMSE), normalized root means square error (NRMSE), normalized mean square error (NMSE), mean absolute percentage error (MAPE), mean absolute error (MAE), and determination coefficient (${\mathrm{R}}^2$) [23,28,29]. To check the model sensitivity, over the mesh resolution, the numerical model simulated for the non-overtopping depth $H_{\mathrm{o}}$ equals to 0.41 (see Table 1) was evaluated. The numerical model sensitivity analysis was conducted with the control case, which used BM_A when the rotation angle ($\mathsf{\theta }$) equals zero.

The results of the numerical model sensitivity based on the streamwise velocity ($U_{\mathrm{x}}$) are listed in Table 2 and concern the grid size and the turbulence model selected using the listed indicators. From the sensitivity results listed in Table 2, the highest correlation was given by the k–ω SST turbulence model for Mesh 1. Furthermore, Figure S2 in the Supplementary Figures shows the streamwise horizontal velocity profiles observed over the embankment crest concerning the mesh and the turbulence model selected in the numerical model calibration. According to the results shown in Figure S2, the velocity profiles belong to Mesh 1, showing good agreement between the numerically predicted velocities and the experimentally observed velocity profile for the k–ω SST turbulence model.

Moreover, to check the accuracy of the developed numerical model, the accuracy of the predicted and measured water surface profile along the channel center line, concerning the mesh and the turbulence model selected, was evaluated. The free surface obtained by the numerical simulation, performed with the VOF, and each turbulence model selected concerning the mesh is shown in Figure S3 of Supplementary Figures. According to Figure S3a, the calculated free surface profile for the $k–\omega \mathrm{SST}$ turbulence model reasonably matched the measured profile of the other two. However,, when reducing the number of cells in the numerical grid, as shown in Figure S3b,c, the accuracy of the free surface of the numerical prediction was reduced, which concerned the measured profile in the experimental study. According to Figure S3a, $k–\omega \mathrm{SST}$ turbulence model captured the formation conditions of the hydraulic jump toe and the entire free surface profile than the other two selected. Therefore, according to the data in Table 2 with the graphical representations in Figures S2 and S3, the $k–\omega \mathrm{SST}$ turbulence model was selected to carry out the numerical simulation in this study.

After the flow interacts in front of the BM, a submerged hydraulic jump occurs when the flow changes from a supercritical to subcritical condition after overtopping from the EM. For the present study, the type of hydraulic jump forming in a rectangular prismatic channel with a zero upstream slope and nearly horizontal downstream slope are characterized using the non-dimensional overtopping depth ($H_{\mathrm{o}}$). The quick dissipation of the overtopping flow from the EM increased the safety of the BM when it had enough opening space in its frame while flowing through it. This experimental study observed a hydraulic jump between the downstream gap region between the EM toe and the BM front or EM toe and the VM front (see Figure 2a–c) concerning the experimental arrangement. Out of the selected BMs, the BM_A and BM_B gave more attention due to their geometric arrangement, as shown in Figure 2f. Figure 6 shows the normalized position of the hydraulic jump over the BM_A and BM_B according to the experimental settings of EM-BM and EM-VM_C-BM, respectively.

To define the location of the hydraulic jump in this study, three values of the non-dimensional position of the hydraulic jump $P_{\mathrm{J}}$ (= $P_{\mathrm{j}}/S$) were defined based on the starting position of the jump within the system, which was measured according to the BM front or VM front, as shown in Figure 2a–c. When the non-dimensional position of the jump was $P_{\mathrm{J}}<1$ the hydraulic jump’s starting position was within the gap region when $P_{\mathrm{J}}=1$ the hydraulic jump’s starting position was on the EM’s toe, and when $P_{\mathrm{J}}>1$ the hydraulic jump’s starting position was on the EM’s downstream surface slope as shown in Figure 4a [22]. For the piloti-type BMs (BM_D and BM_E), the $P_{\mathrm{J}}$ value was not calculated due to the absence of a hydraulic jump except for the bow wave along the piloti-column surface. Moreover, in front of the BM_C, the wall-jet-like bow wave was observed with a detached hydraulic jump while increasing the overtopping flow from the EM, which is because the porosity of the BM_C promoted quick dissipation of flow from its four-sided opening, as shown in Figure 4b. When a Type-1 hydraulic jump formed, the value of the $P_{\mathrm{J}}$ was less than 1, as shown in Figure 6, with a BM_A and BM_B under the experimental cases of EM-BM and EM-VM_C-BM, respectively. Additionally, when the overtopping flow depth increased, the hydraulic jump position moved closer to the embankment toe, and when the $P_{\mathrm{J}}$ was greater than 1, the hydraulic jump position was seen on the downstream surface slope of the EM while rotating both the BMs, as shown in Figure 6. Furthermore, when a hydraulic jump transferred to Type-2 from Type-1, the water depth in front of the BM increased. This phenomenon further increased the force at the BM. The increasing water depth in front of the BM was directly related to its total porosity (${\eta }_{\mathrm{tot}}$) and the orientation angle ($\mathsf{\theta }$).

According to the experimental EM-VM_D-BM case, the hydraulic jump was observed within the gap region of the EM toe and VM front, as shown in Figure 2c. Moreover, for all the BMs used under the experimental EM-VM_D-BM case, while increasing the overtopping depth, Type-1 and Type-2 hydraulic jump was observed. Figure 7 shows the relative position of the hydraulic jump over the non-dimensional overtopping depth ($H_{\mathrm{o}}$) for the EM-VM_D-BM case. In this case, the hydraulic jump position was measured from the VM front towards the EM toe, as shown in Figure 2c. The VM in the gap region (see Figure 2) absorbs the turbulence of the overtopping flow and slows down the flow velocity toward the BM. The velocity towards the VM downstream completely depends on the VM thickness ($dn$); while lowering the vegetation thickness, the flow velocity of the VM downstream also increases and vice versa. As shown in Figure 7a,b, the Type-2 hydraulic jump was further extended with the BM_A and BM_B under the experimental EM-VM_D-BM case. For the BM_C, due to the VM in the gap region, the wall-jet-like bow wave converted to a hydraulic jump under the EM-VM_D-BM case while increasing the flow depth in front of the BM_C.

Meanwhile, for the EM-VM_D-BM case, the formation conditions of the wall-jet-like bow wave had vanished except for the submergence of the piloti-type columns of the BM_D and BM_E while increasing the overtopping depth from the EM. In addition, Figure 7d,e shows that piloti-type BM would be the most appropriate hybrid approach to reduce the formation of the Type-2 hydraulic jump which could facilitate the reduction in the self-destruction of the embankment structure under disastrous situations on the prototype scale [30]. This would further enhance the resilience of the coastal community under disaster situations [1].

This section discusses the variation in the tsunami force at the BMs considered in the experimental EM-BM case. The variation in the x-, y-, and z-direction forces on the BMs concerning the non-dimensional overtopping depth are shown in Figure 8 for both the non-piloti-type BMs. As shown in Figure 8, for the BM_A, the force on the building in three directions ($F_{\mathrm{X}}$, $F_{\mathrm{Y}}$, and $F_{\mathrm{Z}}$) was higher than the other two non-piloti-type BMs, BM_B and BM_C. As shown in Figure 8, the recorded forces of $F_{\mathrm{X}}$, $F_{\mathrm{Y}}$, and $F_{\mathrm{Z}}$ are proportional to the rotational angle ($\mathsf{\theta }$) due to the decreased and increased effective area concerning the total porosity of the BM (${\eta }_{\mathrm{tot}}$) [7,16,17]. According to the field observations and damages of the existing tsunamis mentioned by Fraser et al. [31] and Ruangrassamee et al. [14], when the buildings are fully enclosed, the lift force ($F_{\mathrm{Z}}$) becomes more critical than the drag forces ($F_{\mathrm{X}}$ and $F_{\mathrm{Y}}$), which were similar to the observations of the present study. This is because the pressure difference (static and dynamic pressure) acting on the front and back faces of the BM plays a vital role, even if the flow cannot dissipate quickly enough with respect to the overtopping depth. This phenomenon leads to an uplift in the BM while increasing drag forces $F_{\mathrm{X}}$ and $F_{\mathrm{Y}}$ due to the partial reflections from the adjacent structures, which are represented by the side walls of the experimental flume [16,17]. Even when the BM has a specific porosity, the lift force ($F_{\mathrm{Z}}$) might be higher due to the turbulence of the flow inside the building structure, like the observations of the present experiment, as mentioned by Fraser et al. [31] and Ruangrassamee et al. [14] (see Figure 8 for BM_B and BM_C).

Furthermore, forces acting on the piloti-type BMs (BM_D and BM_E) are shown in Figure 9 by the rotation angle ($\mathsf{\theta }$) for the experimental EM-BM case. For the piloti-type BMs, the z-direction force $F_{\mathrm{Z}}$ (uplift force) was prioritized over the x- and y-directional forces due to the wall-jet-like flow phenomenon observed along the front surface of the piloti column pillars below the BM. In addition, when increasing the overtopping depth, the uplift force $F_{\mathrm{Z}}$ increased gradually except for the BM_E when it was rotated at a 45° angle, as shown in Figure 9. Moreover, with less number of piloti column pillars, the lifted wall-jet-like bow wave along the surface of the piloti-pillar tended to travel along the bottom ceiling level and an increase in the overtopping depth was observed [16].

This phenomenon further increased the lift force ($F_{\mathrm{Z}}$) over the BM_D, as shown in Figure 9a–c. However, when the number of piloti column pillars like in the BM_E model increased, it disturbed the traveling of the elevated wall-jet bow wave along the ceiling level. As a result, it reduces the lift force ($F_{\mathrm{Z}}$), as shown in Figure 9d–f. Furthermore, when the piloti-type BMs were rotated, the number of piloti-pillars exposed to the water flow increased. In this situation, the drag force ($F_{\mathrm{X}}$) and the lift force ($F_{\mathrm{Z}}$) increased, as shown in Figure 9b,e, respectively [16,17]. Furthermore, when the porosity (${\eta }_{\mathrm{tot}}$) of the non-piloti-type BMs was increased, under the EM-BM case, the force at the BM reduced in relation to the overtopping depth, except for the BM_B when the $b_{\mathrm{B}}/W$ ratios were equal to 0.43 and 0.51, as shown in Figure 8e,f. This is due to the flow interaction and the energy transition of the flow at the BM due to its rotation against the incoming overtopping tsunami flow current concerning the increased effective area of the BM_B. Furthermore, when the BM_C was rotated, it increased the porosity further than its frontal condition, which reduced the drag characteristics further, as shown in Figure 8h,i.

As shown in Figure 2, the present experimental study considered three alternative settings to check the overtopping tsunami force reduction and its variability concerning the experimental arrangement and the BM’s orientation. Case EM-BM was used as a reference case for the comparison in this section. Figure 11 shows the force reduction in $F_{\mathrm{X}}$, $F_{\mathrm{Y}}$, and $F_{\mathrm{Z}}$ for all the non-piloti-type BMs (BM_A, BM_B, and BM_C) related to the non-dimensional overtopping depth $H_{\mathrm{o}}$ ($=h_{\mathrm{o}}/h_{\mathrm{E}}$) when the BM rotation angle ($\mathsf{\theta }$) equals to $0^{°}$. Depending on the layout of the experimental arrangement and the geometric features of the BM, the overtopping tsunami flow from an embankment could approach the building from a different direction concerning the orientation of the BM. Recent tsunami damage to the structures was observed, and the extent of the damage varied depending on the direction of the approaching wave [31].

The most effective method for tsunami force reduction was the utilization of the VM within the gap region (EM-VM_D-BM case) of the EM and BM (see Figure 2c) as an additional alternative approach for the primary defense measures. In addition, when the BM had enough outer frame opening, the reduction in the tsunami force at the BM was high if the vegetation could grow after the first defensive measure, as shown in Figure 11, which would be an added advantage to minimize the total structure failures (toppling, overturning or collapsing) and reduce the rebuilding cost when necessary [17].

Moreover, for the piloti-type BMs (BM_D and BM_E), the tsunami force at the BM would be significantly reduced according to the experimental arrangement, as shown in Figure 12. The pressure introduced by the turbulent intensities in front of the non-piloti-type BM directly influenced the structure and increased the overtopping depth. Furthermore, under the experimental case EM-VM_D-BM conditions (for details, see Figure 2c), the turbulent intensities were ineffective beyond the VM when remaining in the gap region. Behind the VM within the gap region, the static pressure head of the flow transferred as the tsunami force was over the BM, with a low-velocity head due to the absorbance of turbulence lowering the dynamic pressure head. Due to the VM in the gap region under the experimental EM-VM_D-BM case, the force at the non-piloti-type and piloti-type BMs was drastically reduced (see Figure 11 and Figure 12). The percentage reductions in the drag force in the x-direction ($F_{\mathrm{X}}$) at the BM under the EM-VM_D-BM case conditions ranged between 7.1 and 80.1%, 21.7 and 92.9%, 9.9 and 64.4%, 36.5 and 89.1%, and 47.1 and 77.5% for the BM_A, BM_B, BM_C, BM_D, and BM_E, respectively. Furthermore, the physical configuration of the BM_D and BM_E, which consisted of a series of circular shape cylindrical pillars with significant space, enabled the tsunami overtopping flow current to flow underneath the BM with minimal disruption due to its less effective area, as shown in Figure 12 [16].

During the experiment, the difference in the flow depth reduction between the upstream and downstream of the BM was observed when the overtopping flow reached the BM in relation to its total (${\eta }_{\mathrm{tot}}$) porosity and the experimental layout. This phenomenon led to a reduction in the drag characteristics of the tsunami force at the BM while increasing the overtopping depth from the EM. The supercritical overtopping flow from the EM might maintain the supercritical condition or become subcritical depending on the experimental arrangement, BM orientation, or porosity [16,17]. The drag force became severe with the bluntness, and it was primarily reduced over the piloti-type buildings due to the circular cylindrical shape of the pillars used in this present experiment, as suggested by Dissanayaka and Tanaka [8].

Therefore, it is crucial to define the relationship between the front and back water depth reduction and the choked flow condition due to the drag related to the experimental setup, orientation of BM, and porosity for the non-piloti-type BMs. For evaluating the drag characteristics of the non-piloti-type building models, the BM_A model in the EM-BM arrangement was selected as the base case. The empirical drag coefficient $C_{\mathrm{D}}$ was defined over the non-piloti-type BMs with the upstream Froude number as a function of the blockage ratio ($b_{\mathrm{B}}/W$), which assumed that the flow depths of the front and back of the BM was $h_{\mathrm{FB}}\approx h_{\mathrm{BB}}$ as defined by Wüthrich et al. [17] for the post-tsunami overland flows. For the present experimental study $h_{\mathrm{FB}}\gg h_{\mathrm{BB}}$ and the difference in the flow depths upstream and downstream became noticeable by the porosity of the non-piloti-type BM and their orientation. Moreover, due to the steady-state flow conditions used in the present experiment, the chocked characteristics of the flow at the BM were observed [17,32]. Hence, the empirical drag coefficient ($C_{\mathrm{D}}$) was replaced by the resistance coefficient ($C_{\mathrm{R}}$). Referring to Equations (5) and (6) the resistance coefficient ($C_R$) was calculated. For the fully impervious building model (BM_A), the total porosity (${\eta }_{\mathrm{tot}}$) was equal to zero, and the porosity coefficient $\mathsf{\Phi }$ equalled one. Equation (6) calculated the percentage of the porosity of the BM_B and BM_C which were equal to 16.6% and 35.9%, respectively.

The maximum water depth in front of the BM was observed for the EM-BM case; however, for the EM-VMC-BM case, the water depth in front of the BM decreased with increasing velocity. Meantime, when the VM was present at the gap region, the velocity was further lowered in front of the BM, even when the BM was impervious or not, due to the reduced turbulence by the VM. Therefore, the resistance coefficient ($C_{\mathrm{R},0}$) was calculated for the BM_A and plotted over the initial Froude number ($F{r}_{\mathrm{o}}$), as shown in Figure 13. Moreover, the resistance coefficient $C_{\mathrm{R},0}$ for the impervious BM_A varied between 4.0 and 1.5, 1.9 and 0.9, and 2.9 and 1.2 for the EM-BM, EM-VM_C-BM, and EM-VM_D-BM cases, respectively, for all the rotations ($\mathsf{\theta }$) considered in relation to the experimental layout, as shown in Figure 13. These values were higher than those recommended by the ASCE-7 [33] for the post-tsunami overland subcritical flow conditions in front of the impervious BM. However, the values of $C_{\mathrm{R},0}$ were consistent with the finding of Qi et al. [32] for flows with similar features and varying blockage ratios.

Figure 14 represents the relationship of the non-dimensional difference in water depth [($h_{\mathrm{BF}}-h_{\mathrm{BB}}$/$h_{\mathrm{o}}$)] of upstream and downstream of the BM over the $H_{\mathrm{o}}$ when the rotation angle $\mathsf{\theta }$ = $0^{°}$ for the $b_{\mathrm{B}}$/$W$ = 0.36, for all the non-piloti-type BMs considered. Moreover, Figure 14a represents the variation in the resistance coefficient ($C_{\mathrm{R},0}$) with the non-dimensional overtopping depth ($H_{\mathrm{o}}$) for the BM_A as an inset figure. Furthermore, for the BM_B and BM_C, the normalized resistance coefficient $C_{\mathrm{R}}/C_{\mathrm{R},0}$ are illustrated in Figure 14b,c, according to the experimental arrangement. As shown in Figure 14, with the imperviousness of the BM, the difference in the non-dimensional upstream to the downstream water depth at the BM increased with increasing resistance coefficient, as shown in Figure 14a. Furthermore, when increasing the porosity of the BM, the difference in the non-dimensional from upstream to downstream water depth ratio was reduced while reducing the relative resistance coefficient ($C_{\mathrm{R}}/C_{\mathrm{R},0}$) for the BM_B and BM_C, as shown in Figure 14b,c. This makes it possible of reducing the overtopping tsunami force acting on the BM in relation to the increased percentage of the total porosity in the BM frame. The overall consistency of the results shown in Figure 14 shows that when the frontal porosity predominated, the flow passing through the building (regardless of its orientation) was essential in determining the resistance coefficient [16,17]. This figure revealed a higher influence on the resistance coefficient reduction for the configurations with a BM_C, which had larger openings on the outer frame (see Figure 2f). Moreover, for the BM_C with the VM in the EM-VM_D-BM arrangement, it was the most effective solution under the non-piloti-type building category in force reduction due to tsunami overtopping flow from the EM, as shown in Figure 14c.