# Field study of post-overtopping flow impacts on a vertical wall at the crest of an upper-beach dike

Erwan Imbertie, Denis Morichon, Matthias Delpey, Benoît Larroque, Camille Lavayssière

► To cite this version:

Erwan Imbertie, Denis Morichon, Matthias Delpey, Benoît Larroque, Camille Lavayssière. Field study of post-overtopping flow impacts on a vertical wall at the crest of an upper-beach dike. Applied Ocean Research, 2025, 163, pp.104731. 10.1016/j.apor.2025.104731. hal-05262420

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https://univ-pau.hal.science/hal-05262420v1

Submitted on 16 Sep 2025

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Research paper

# Field study of post-overtopping flow impacts on a vertical wall at the crest of an upper-beach dike

Erwan Imbertie<sup>b,a</sup>, Denis Morichon<sup>a,b,d,*</sup>, Matthias Delpey<sup>b,d</sup>, Benoît Larroque<sup>a</sup>, Camille Lavayssière<sup>a</sup>

## ARTICLE INFO

Keywords:

Post-overtopping impact force

Field experiment

Coastal defense

Emergent toe

Autonomous measuring system

## ABSTRACT

In many urbanized shorelines, upper-beach sea-defenses and coastal buildings can be exposed to the impact of wave induced post-overtopping flow during energetic storm conditions. In order to properly anticipate the risk exposure of these seafront infrastructures, it is crucial to characterize and quantify the resulting assailing forces. Current knowledge on this type of configurations is mainly based on downscale laboratory experiments. Moreover, the case of sea-defense structures with an emergent toe is still scarcely documented in the literature. This study aims to provide an original insight into this topic using a new dataset collected during an experiment carried out in real conditions at a field site in the southwest of France. The instrumented site corresponds to a semi-reflective beach with a very shallow foreshore. The deployment was performed during an energetic storm (offshore significant wave height $H_s = 4.4$ m and peak period $T_p > 15$ s) concomitant with spring tide that resulted in recurrent wave-induced overtopping events, while the overtopped upper-beach seawall toe always remained emergent. The experimental setup included an innovative wave impact measuring station composed of a self supporting structure equipped with a series of high frequency pressure sensors. The station measured the loads induced by overtopping flow impacts at the crest of an upper-beach dike. Additionally, the swash flow characteristics prior to each impact and the runup against the station were captured using synchronized video recordings, complemented by an array of pressure sensors deployed on the beach foreshore. The magnitude of the measured impact force ranges between 0.38 and 9.70 kN/m. A majority of the recorded events have a twin-peak signal shape similar to that observed in laboratory studies. The joint analysis of the vertical pressure distribution and of the synchronized video images also allows to highlight different impact phases, which align with results from previous downscale experiments. However, in contrast with existing laboratory observations, our measurements show that the force peak measured during the reflection phase, which follows the maximum runup, deviates significantly from the hydrostatic prediction. The greater the intensity of the force, the more pronounced the deviation. The analysis of the pre-impact flow properties suggests a relation between the maximum impact force, the overtopping discharge and the momentum flux, while the deviation from the hydrostatic prediction seems more related to the swash flow height. Finally, the order of magnitude of the measured maximum force of the single impact events was shown to be reasonably estimated by applying an hydrostatic-like formulation to the maximum runup height, provided the application of an empirically fitted reduction coefficient. These results provide a first description of overtopping wave impacts on an upper-beach structure with an emergent toe in real field conditions. It paves the way for further measurement efforts to extend the obtained characterization to different water level and wave energy conditions.

## 1. Introduction

During the last decades, the number of people living in coastal areas has increased significantly worldwide. The dense urbanization of many low-lying shorelines creates an important vulnerability of coastal

populations and infrastructures to ocean storm impacts, which is already observed at present. At the same time, the last IPCC report confirmed the prediction of mean sea level rise due to global warming (Arias et al., 2021). With this increasing sea level trend, an essential amount of coastal defenses will be outdated in the future, leading to a

<footnote><sup>a</sup> Université de Pau et des Pays de l'Adour, E2S UPPA, SIAME, Anglet, 64600, France</footnote>

<footnote><sup>b</sup> SUEZ, Center Rivages Pro Tech, Bidart, 64210, France</footnote>

<footnote>* Corresponding author at: Université de Pau et des Pays de l'Adour, E2S UPPA, SIAME, Anglet, 64600, France. E-mail address: denis.morichon@univ-pau.fr (D. Morichon).</footnote>
further growing exposure of human activities to coastal flooding and wave overtopping.

In numerous coastal areas, urban waterfronts are comprised of a sandy beach in a shallow to very shallow environment, which is backed by a coastal defense in the form of an upper-beach dike or a seawall with a promenade on top (Chen et al., 2016; Streicher et al., 2019; Cao et al., 2022). In such configurations, waves reach the shoreline as turbulent bores after breaking on the shallow foreshore. The overtopping results in an horizontal flow on the promenade, which may subsequently impact any vertical infrastructure constructed on top of the coastal defense, such as a second coastal defense (e.g. a permanent or temporary storm wall) or directly the waterfront building facades. In order to properly anticipate the risk exposure of these infrastructures during storms, it is crucial to characterize and quantify the impacts generated by wave-induced overtopping flow.

The wave overtopping flow characteristics, velocity and thickness along with overtopping discharge, at coastal structures has already been widely studied in various configurations (Koosheh et al., 2021). In recent years, complementary investigations have also focused on the assessment of the impact forces in the above-mentioned situation of a vertical wall being collided by an horizontal flow after the overtopping of an upper-beach dike. The corresponding type of configuration is illustrated in Fig. 1. This issue has been studied through different laboratory experiments conducted on very shallow to extremely shallow foreshore environments. Based on small-scale experiments with Froude length scale ratio $λ$ between 1/35 and 1/20, Chen et al. (2015) studied the post-overtopping flow impact of regular waves. Chen et al. (2016) extended this characterization for irregular sea states. Other investigations were conducted at larger scale with the work of De Rouck et al. (2012), Ramachandran et al. (2012) and Streicher et al. (2019), who used experimental datasets with $λ$ greater than 1/5.

Common to these different studies, the quantification of the post-overtopping flow impact is assessed with two main physical quantities: the total force time series generated on the vertical wall $F(t)$ and the associated vertical pressure distribution $P(z, t)$. The vertical pressure distribution is measured using a series of pressure sensors aligned vertically over the height of the impacted wall. The total force can be consistently measured directly with load cells or indirectly by integrating the vertical pressure distribution at each time (Ramachandran et al., 2012; Chen et al., 2015; Streicher et al., 2017). These various studies have all confirmed that the force time series $F(t)$ related to an individual post-overtopping flow impact is most often composed of two consecutive peaks. The first peak F1 is dominated by the dynamic component of the impact. It exhibits a maximum pressure at the lower part of the wall. The second peak F2 is the so-called quasi-static impact component, with a nearly hydrostatic vertical pressure distribution measured at the peak time instant.

In Streicher et al. (2019), the capture of video images synchronized with the force measurements allowed to identify different impact stages and to relate them with the force signal and the time occurrence of the two force peaks F1 and F2. The first stage of the impact (S1) is the initial impact phase when the tip of the horizontal flow gets in contact with the vertical plate. The second stage is the deflection stage (S2), when the horizontal flow is deviated vertically along the vertical structure with the changing direction located at the bottom of the vertical plate. It corresponds to the force peak F1. The third stage (S3) corresponds to the moment of the maximum runup. The fourth stage (S4) corresponds to the phase when the water falls back from the maximum runup height and initiates the reflection. The quasi static force peak F2 is measured during this stage after the moment of the maximum runup. Finally, the last stage (S5) corresponds to the rest of the reflection phase, when the vertical pressure distribution measured at the wall falls in nearly perfect agreement with the hydrostatic theory. Similar impact stages were already proposed by Chen et al. (2015) for comparable beach configurations based on a smaller scale laboratory experiment, but also by Kihara et al. (2015) in the case of the impact

<figure><img src="image_2.png" /><figcaption>Fig. 1. Schematization of a vertical wall impacted by a post-overtopping flow.</figcaption></figure>

of a tsunami dry surge impact, also studied in a downscale laboratory test. In the specific configuration of short wave impact on an extremely shallow foreshore, Streicher et al. (2019) qualified the double peak shape of the impact force time series as a twin peak shape because of the comparable magnitudes of F1 and F2. Moreover, for 2/3 of the selected 60 extreme impacts that they studied, the maximum force is associated with the quasi-static peak F2.

Additional measurements of the post-overtopping flow thickness and velocity $h$ and $u$ on the promenade and of the runup height at the wall $R_h(t)$ were performed in several experiments with the aim to relate these parameters to the impact force peaks (Ramachandran et al., 2012; Streicher et al., 2018). Those studies allowed to link the magnitude of the force peak F1 and F2 with hydrodynamic parameters. The force peak F1 was shown to be well empirically predicted from the post-overtopping flow properties $h$ and $u$ on the promenade before the impact (Chen et al., 2015; Kihara et al., 2015; Streicher et al., 2018). The force peak F2 is generally predicted from the maximum runup height measured at the wall considering a hydrostatic pressure distribution (Chen et al., 2015; Streicher et al., 2018).

Despite the remarkable advances provided by these extensive downscale laboratory experiments, the transferability of the results to real study sites remains an open question. Indeed, the important effort to perform and analyze large-scale experiments was motivated by limitations due to the turbulent air entrainment during wave propagation, which is lower at small-scales with a direct effect on the generated force at the vertical wall (Blenkinsopp and Chaplin, 2007). Smaller entrained air amounts in reduced-scale experiments limits the cushioning effect, leading to higher measured forces (Bullock et al., 2001). Consequently, while upscaling the force measured at a reduced scale, an overestimation of the force is expected (Cuomo et al., 2010; Streicher, 2019). As a result, the conversion of the impact force magnitude to the real scale is still uncertain and needs field observation to be assessed. To the authors' knowledge, such acquisition in the field of post-overtopping flow impact measurements has not yet been documented or is still underway (e.g. https://www.agentschapmdk.be/nl/projecten/living-lab-raversijde).

Furthermore, each of these different laboratory studies of post-overtopping flow impact was carried out for specific beach and sea-defense configurations. Within the limits of the above-mentioned scale effects, one can expect that the empirical results obtained at reduced scale can be transposed to real sites with comparable configurations. However, their applicability is necessarily questionable as the conditions of the real study site do not fall precisely in the experimental range. In particular, all the cited experiments considered that the dike toe is constantly immersed. For such a sea-defense with an immersed toe in a very shallow foreshore configuration, the overtopping is generated by a wave-driven bore collapsing directly on the dike slope. However, in many urban waterfronts, the toe of the upper-beach defense is emerged, namely the mean water level is lower than the dike toe. In that case, the bores collapse into a swash flow on the beach face at distance from the sea-defense, and the overtopping
occurs when this swash flow exceeds the dike crest height. Although some studies can be found on overtopping volumes on this type of configurations (e.g. Altomare et al., 2016; Altomare and Gironella, 2024), the related impact on backend coastal infrastructures is still scarcely documented in the literature. Thus, it is still uncertain to which extent the overtopping impact characteristics can differ from the case with a comparable very shallow foreshore but an immersed dike toe.

In this context, the present study aims to quantify and characterize the post-overtopping flow impacts on a vertical structure located on the crest of a smooth dike in real field conditions. An experiment was carried out on a semi-reflective urban beach with a very shallow foreshore backed by a sea-defense with an emergent toe. Field measurements were collected during energetic storm conditions with a newly developed autonomous measuring station for wave impact pressure, the “WIP station”, first introduced by Imbertie et al. (2022). Concomitantly, hydrodynamic measurements were collected using different devices allowing to monitor incident waves, swash motion, flow properties before the impact and instantaneous runup height on the WIP station. Those additional measurements will be used to study the relationships between hydrodynamic parameters and the impact forces measured with the WIP station on top of the dike.

The paper is organized as follows. In Section 2, the configuration of the field experiment is presented, including the study site characteristics and the hydrodynamic conditions. Section 3 describes the different measuring systems used and the related data processing. Then, measured impact forces, pressures and the related flow characteristics are presented in Section 4. The different signals and their relationships are further analyzed and discussed in Section 5. Finally, a conclusion is drawn in Section 6.

## 2. Field experiment

### 2.1. Field site

The field experiment was conducted on the *Grand Plage* of Biarritz (GPB), located in the southwest of France and facing the Bay of Biscay. The GPB is a 600 m long urban beach, which is located in a 1.2 km wide embayment delimited by two rocky headlands at the north and south (Fig. 2(A)). The beach is backed by a protective seawall (or vertical dike) with a promenade on top separating the beach from the city waterfront buildings and gardens.

The seawall height is about 1.5 m. The GPB lies in a mesotidal environment with a spring tidal range of 4.5 m, leading to a maximum tidal elevation of +4.7 m above chart datum. Excluding any surge or

runup, it corresponds to a difference in height of approximately 3 m with the crest level of the seawall, whose average elevation is +7.6 m with limited alongshore variations.

The topo-bathymetry of the instrumented cross-shore profile is presented in Fig. 2(B). It is composed of a low-sloping zone with a 1.5% slope in the sub-tidal area at cross-shore distance from the seawall between $x = 130$ m and $x = 960$ m, punctuated by two rocky outer bars at $x = 250$ m and $x = 500$ m. This sub-tidal section ends with a flat terrace at the seaward limit with the inter-tidal zone, around $x = 100$ m. Finally, a steep sandy beachface with a slope of about 10% connects the terrace to the seawall toe. During storms, a significant amount of sand is regularly accumulated against the seawall at the top of the profile. For most energetic events, the sand accumulation rapidly reaches the crest of most exposed seawall sections.

The local wave climate is defined as moderately to highly energetic with a main direction of incoming swells from WNW (315°). The 1 year and 10 year return period storms are characterized at the study site by a significant wave height $H_s$ of 3.9 m and 6.7 m, and a peak period $T_p$ of 12.6 s and 18 s, respectively (Morichon et al., 2018). During the winter, energetic ocean storms hit Biarritz shoreline and significant hazards associated with the seawall overtopping can threaten the city waterfront (Fig. 2(C)). At the rear of the seawall, several critical infrastructures are exposed to post-overtopping flow impacts, especially the landmark buildings of the city Casino in the south and the *Hôtel Du Palais* in the north (Fig. 2(A)).

During severe storm events, a series of protective countermeasures are taken by the municipality to mitigate the impact of wave-induced overtopping. In particular, rows of sandbags are temporarily deployed on the promenade in front of the main building facades as a second coastal defense (Fig. 2(C)). It adds to the seawall height to reduce post-overtopping flow impacts on the buildings. In that configuration, the temporary defense system itself is also subject to the impacts of post-overtopping flows. In this context, a major issue for the municipality protection strategy is related to the anticipation of the loads exerted by post-overtopping flows on the sandbags installed on the promenade. This preoccupation is an important motivation for conducting the present study.

### 2.2. Experimental setup

The experimental setup was designed to study the impact generated by post-overtopping flows on a vertical structure located on the promenade. The positions of the different sensors deployed are schematized

<figure><img src="image_3.png" /><figcaption>**Fig. 2.** Configuration of the *Grande Plage* of Biarritz (GPB) experimental site. (A) Bathymetry of the embayment and identification of the instrumented cross-shore transect (black dashed line). The location of the main seafront buildings are identified with white rectangles. (B) Cross-shore topo-bathymetric profile along the instrumented transect. (C) Photograph of the waterfront during a storm at the moment of an overtopping event. The sandbags temporarily deployed at the crest of the seawall are visible in front of the Casino building.</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Fig. 3. Diagram of the upper-beach configuration along the instrumented transect with the location of the different measuring systems deployed during the campaign. The two horizontal dashed lines represent the minimum and the maximum mean water levels (MWL) measured by a nearby tide gauge during the deployment.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 4. (A) Annotated photograph of the Wave ImPact (WIP) station deployment on top of the upper-beach dike and of the complementary measuring equipment installed to monitor the local hydrodynamics before the impact. (B) Ensemble view of the instrumented section situation.</figcaption></figure>

in Fig. 3. An annotated photograph of the instrumented section of the sea-defense is given in Fig. 4.

The Wave ImPact (WIP) measurement station (Imbertie et al., 2022) was deployed to monitor post-overtopping impact pressures on the promenade. In relation to the motivation exposed in the previous paragraph, the device was installed 20 cm behind the dike crest to mimic the positioning of the sandbags that are temporarily deployed on the promenade during major storms (Fig. 2). The height of the promenade at the installation point is +7.53 m. The instrumented section was aligned with a concrete access ramp, which forms a 8 m wide sloped section along the seawall (Fig. 4). This limited section of the defense resembles of a smooth dike, which connects the promenade to the upper-beach with a 1:4 slope.

On each side of the concrete ramp, a significant accumulation of sand was rapidly observed against the seawall during the monitored storm event, with only about 30 cm of the seawall height which remained free of sand. This tended to reduce possible side effects at the lateral limits of the concrete ramp, as visually confirmed during the experiment.

In front of the WIP, three graduated poles, Pe1, Pe2, and Pe3, were fixed on the inclined concrete ramp at 1.27 m, 2.27 m, and 3.27 m from the station location, respectively. These poles were designed to characterize the ultimate swash flow properties just before the impact, hereinafter referred to as pre-impact flow thickness *h* and velocity *u*. To support the flow characterization, synchronized video images were acquired with a side-looking GoPro(R) camera designated by Cam1,

which filmed the graduated poles and the WIP station face. The later has also been graduated to allow the evaluation of the runup height against the station by analyzing the images from Cam1. More detail on this process and on the WIP station will be provided in Section 3. The synchronization of the video images with the pressure measurements of the WIP was ensured thanks to a LED fixed at the top of the station (Fig. 4). The LED was connected to the acquisition chain of the WIP station and emitted light impulses visible by Cam1 at specific times in the station time reference.

On the beachface aligned with the concrete ramp, an array of three pressure sensors was deployed. Pressure sensors CP3 and CP2 are located at distance of 72 m and 42 m from the WIP and height of +0.71 m and +3.56 m (chart datum), respectively. CP3 was located at the transition between the steep beachface and the flat low-tide terrace. This point will be referred to as the “beachface toe” or simply the “toe” in this study. CP2 is located at an intermediate position higher on the beachface slope. Both sensors will be used to characterize waves (or bores) in the inner surfzone before the collapsing or the breaking point that delimits the beginning of the swash zone. The third pressure sensor CP1 was deployed at distance 16.2 m from the WIP and height +5.91 m to measure the swash flow depth just after its generation point. Additionally, a second GoPro(R) camera, designated by Cam2, targeted the inner surf zone and the swash zone, with the aim to support the qualitative understanding of the hydrodynamics in these zones.
Finally, two topographic surveys of the instrumented profile were performed with a NRTK-GNSS at low tide before and after the monitored event. It can be noticed that variations in the topographic profile were minor between the two surveys.

## 2.3. Experimental conditions

The field deployment was conducted on the 28th of October, 2023, and post-overtopping impacts were recorded around high tide between 13:20 and 14:40 (UTC). The time window corresponds to a combination of energetic storm wave conditions with spring high tide levels, which gathers the conditions for wave overtopping to occur on the GPB.

Fig. 5 displays the evolution of tide and wave characteristics during the period of interest. Tide levels come from the official prediction by the French Naval Hydrographic and Oceanographic Service (SHOM) at the nearest tide gauge (code: 10.17183/REFMAR#95). During the deployment, the tide level varies from +4.1 m to +4.7 m. Offshore incident wave conditions are provided by a wave buoy from the French national network CANDHIS (code: 06402), which is moored in 50 m water depth offshore of the study site. The buoy recording was interrupted for almost 24 h before the deployment but fortunately it was restarted a few hours before the monitored time window. This window is characterized by energetic offshore wave conditions with $H_{S_{off}} = 4.4$ m and $15 \ s < T_{P_{off}} < 16 \ s$.

<figure><img src="image_6.png" /><figcaption>Fig. 5. (a) Tide level predicted at the nearest tide gauge (gray), offshore significant wave height $H_{S_{off}}$ (black solid) and peak period $T_{P_{off}}$ (dashed). (b) Significant wave height of the short wave $H_{SW_{short}}$ and (c) infragravity wave component $H_{IG_{short}}$ and (d) ratio $H_{IG_{short}}/H_{SW_{short}}$ measured by CP3 at the beachface toe. The red rectangle marks the time window of the WIP station recording.</figcaption></figure>

Wave energy conditions are also computed at the toe of the steep beachface using the bottom pressure measurement of CP3. At this location, the mean significant wave height and the mean peak period are $H_{S_{toe}} = 2.1$ m and $T_{P_{toe}} = 12$ s, respectively. Thus, $H_S$ is reduced by 52% before reaching CP3 location, which represents a dissipation of 73% of the offshore wave energy. In addition, the significant wave heights associated with the short waves $H_{SW_{toe}}$ and with the longer infragravity waves $H_{IG_{toe}}$ are distinguished by the integration of the wave energy spectrum for periods below 30 s and periods between 30 s and 300 s, respectively. The ratio $H_{IG_{toe}}/H_{SW_{toe}}$ varies around 0.5 (Fig. 5(d)). Additionally, the value of the spectral wave period $T_{m-1,0_{toe}} = \frac{m-1}{m_0}$ is equal to 27 s, which is almost two times larger than $T_{P_{off}}$. These elements attest of the importance of both the short and IG wave components in the study case, with a situation that is representative of an intermediate-reflective beach configuration (Wright and Short, 1984). At the time scale of a tidal cycle, $H_{SW_{toe}}$ seems

well correlated with the tidal water level. This correlation is explained by the important variation of the water depth at the beachface toe, between 4.5 m at high tide and 0.3 m at low tide, which exerts strong control over breaking wave height at that location.

In the studied configuration, the static water level (summing tide, atmospheric surge and wave setup contributions) was always lower than the toe of the ramp, resulting in an emergent toe. In terms of the foreshore characterization, the standard classification as proposed by Hofland et al. (2017) cannot be applied directly to the studied upper-beach dike because the mean sea level is lower than the dike toe. To attempt a comparison of the GPB configuration with that classification, an analogy can be proposed by assimilating the extended upper-beach section of the GPB, gathering the promenade, the seawall and the sandy beachface, to a “structure” in the sense of Hofland et al. (2017). With this analogy, the ratio of $H_{S_{off}}$ to the “structure” toe (i.e. the beachface toe) water depth $d_{toe}$ ranges from 0.3 to 1.0, which corresponds to a very shallow foreshore (Table 1).

<table><caption>Table 1
General water depth and wave bulk parameters measured during the deployment.</caption><thead><tr><th>d<sub>off</sub> [m]</th><th>d<sub>toe</sub> [m]</th><th>H<sub>S<sub>off</sub></sub> [m]</th><th>H<sub>S<sub>toe</sub></sub> [m]</th><th>T<sub>P<sub>off</sub></sub> [s]</th><th>T<sub>P<sub>toe</sub></sub> [s]</th><th>T<sub>m-1,0<sub>toe</sub></sub> [s]</th></tr></thead><tbody><tr><td>50</td><td>3.84-4.26</td><td>4.4</td><td>2.06</td><td>15</td><td>16</td><td>22.33</td></tr></tbody></table>

As mentioned above, in the experimental conditions, the dike toe is generally dry before the impact. In this situation, the broken waves propagate in the form of turbulent bores over the low-tide flat terrace and collapse on the beachface (Fig. 6(A)), where it generates a swash flow at a certain distance from the seawall. Then, the most energetic swash flows inundate the dry upper part of the beachface (Fig. 6(B)) and overtop the dike crest. Finally, the post-overtopping flow collides the WIP station on the promenade (Fig. 6(C)), which records the corresponding impact pressures. It can be noticed that the WIP station itself was never significantly overtopped by the flow, although in the most energetic cases the water uprush reached the top of the station face.

# 3. Measurement and analysis methods

## 3.1. Impact measurement

### 3.1.1. Wave impact station (WIP)

The WIP station design is illustrated in Fig. 7. It consists of a 1.7 m × 0.6 m vertical marine aluminum plate equipped with 9 piezoresistive pressure sensors of type KELLER PR-25Y, named P0 to P8, which are mounted along the central vertical axis of the plate (Fig. 7(c)). The relative pressure measurement range is 0–1 bar for P0 and 0–0.5 bar for the other sensors, with a common maximum sampling frequency of 10 kHz. The equipped vertical plate is fixed on a self-supported structure. A structural analysis and modeling of the marine aluminum frame was performed using a computer-aided design (CAD) tool, namely the SOLIDWORKS® software. This provided an estimation of the eigen frequency of 97 Hz for the structure.

The acquisition system and the power supply are integrated in a waterproof electrical box fixed at the back of the plate (Fig. 7(a)). The acquisition chain comprises a CompactRIO (real-time embedded industrial controller), providing a high-frequency synchronized acquisition of the nine pressure sensors. The CompactRIO is connected to a Raspberry Pi to remotely control the acquisition using the supervisory control and data management system PyScada (Lavayssière, 2022).

The design of the WIP acquisition system was supported by the feedback from former experiences conducted with comparable measuring systems to study wave impact on offshore dikes (Amico, 2021; Poncet et al., 2022).

When installed at the field site, the base of the WIP station was weighted down with 700 kg of lead ingot. Additionally, to ensure its
<figure><img src="image_7.png" /><figcaption>Fig. 6. Series of snapshot from Cam 2 video images illustrating (A) a bore collapsing on the beach followed by (B) the uprush phase of swash on the upper “dry” beach and (C) the impact of the post-overtopping flow on the WIP station.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 7. WIP station design: (a) back view, (b) front view, (c) geometry schema.</figcaption></figure>

stability, two metal angles fixed to the base of the WIP station and extending to the rear were used to collocate two sandbags, each weighing 1.8 tons, to ballast the WIP station. The video footage provided by Cam 1 confirmed that the WIP station remained stationary during all the recorded impacts events. Moreover, for the presented field experiment at the GPB site, the WIP station width was extended with two 1.6 m × 1.7 m wooden panels. The panels were mounted from each side of the WIP to limit edge effect and allow water accumulation in front of the pressure sensors, just like against the row of sandbags deployed on the promenade as a temporary second defense during major storms. It resulted in a vertical structure of 3.8 m wide and 1.7 m high, as visible in Fig. 4. The panels were not mechanically connected to the station, and each wooden panel were self-supported and individually ballasted, again with two pairs of sandbags of 1.8 tons each. Consequently, the WIP station stability was not affected by possible movements of the wooden panels, and the stiffness of the station was preserved.

The pressure acquisition during the campaign consists in a measurement of 3600 s duration at sampling frequency 1 kHz, following the recommendation of former studies (Schmidt et al., 1992; Streicher et al., 2019). Two different treatments are applied to the recorded raw pressure signals before they are analyzed. First, a zero-offset correction is applied on each pressure sensor before each impact. Second, the high-frequency electrical noise and potential vibration of the structure are removed using a 50 Hz second-order Butterworth low-pass filter, which also avoids disturbance from resonances at the 97 Hz eigen frequency of the station. Finally, the impact force $F(t)$ in kN/m is computed by a vertical rectangular integration of the individual filtered pressure signals at each time instant as defined in the following equation:

$$F(t) = P_0(t) \cdot 0.1 + P_1(t) \cdot 0.15 + \sum_{i=2}^{i=7} P_i(t) \cdot 0.2 + P_8(t) \cdot 0.25 \quad [\text{kN/m}] \quad (1)$$

with $P_0(t)-P_8(t)$ the measured pressure time series in kPa by the 9 sensors mounted on the WIP station.

### 3.1.2. Hydrostatic force computation

For the purpose of the study, the hydrostatic force $F_{hydro}(t)$ is estimated assuming a hydrostatic pressure distribution computed from

the instantaneous runup height $R_h(t)$ reached by the water on the face of the WIP station. The main method used to estimate $R_h(t)$ relies on the video frames captured by the camera Cam1. The related estimate is designated by $R_{h\_video}(t)$. A continuous video acquisition was conducted at 60 fps with a 2.7 K resolution (2704x × 1520x) in a linear mode to correct image distortion as in Streicher et al. (2019). The runup $R_{h\_video}(t)$ is estimated from a manual image tracking of the leading edge of the water along the vertical plate using the Tracker software (https://physlets.org/tracker/). To support this task, the face of the WIP station was vertically graduated by disposing horizontal black tape at regular 20 cm intervals (Fig. 4). An example of such a manual tracking of the runup height during one of the recorded impacts is presented in Fig. 8 at different time instants. The pixel size is evaluated at 0.27 cm along the central vertical axis of the plate where the leading water edge was tracked.

The tracking of $R_{h\_video}(t)$ is only possible for a certain time after the maximum splash-up, when a reliable visual estimation is allowed. Indeed, the tracking of the water leading edge is usually impossible during the first stage of the impact and at the moment of the maximum runup due to the location of the camera and the very turbulent nature of the vertical splash-up. When the tracking is achievable, two phenomena can affect the related precision. First, the structure where Cam1 was mounted vibrated slightly due to the energetic swash flow impacts. For the most energetic impacts, the maximum error induced by the camera vibration is estimated at 5 cm in the determination of $R_{h\_video}(t)$. Second, because of the turbulent nature of the flow and the camera angle, the exact determination of the highest point reached by water against the plate at a specific time is sometimes ambiguous. This issue leads to a maximum error estimated at around 15 cm on $R_{h\_video}(t)$ measurements for the most ambiguous cases. This uncertainty was estimated by repeating the tracking routine several times by two different operators for the most energetic impacts, which are the most challenging for the runup height estimation from the video. As the video tracking is not always achievable, $R_h(t)$ is also estimated with an alternative method relying on the pressure measurements of the WIP station. The corresponding estimate is designated by $R_h wip(t)$. It is achieved by identifying the “dry” sensors of the station. For
this purpose, a minimum pressure threshold of 0.15 kPa is used to
determine whether a sensor is “dry” or “wet”. This threshold was
calibrated empirically to filter the occasional artifacts in the pressure
signal induced by light water splashes that are not representative of the
effective water tip position. Then, if the sensor *Pi* is identified as the
lowest “dry” sensor at time *t*, the runup height *R*<sub>*h,wip*</sub>(*t*) is approximated
by: *R*<sub>*h,wip*</sub>(*t*) = (*Z*<sub>*Pi*−1</sub> + *Z*<sub>*Pi*</sub>)/2, where *Z*<sub>*Pi*</sub> is the height of *Pi*. An
example of this runup estimation method is provided in Fig. 9(a) for one
of the recorded impacts. In this case, the lowest dry sensor identified
is P6. With this method, considering the 20 cm vertical spacing of the
sensors, the exact value of the runup height *R*<sub>*h*</sub>(*t*) must be such that
*R*<sub>*h,wip*</sub>(*t*) − 0.1 m ≤ *R*<sub>*h*</sub>(*t*) ≤ *R*<sub>*h,wip*</sub>(*t*) + 0.1 m.

In order to verify the consistency of the assessment of R<sub>h</sub><sub>video</sub>(t) and R<sub>h</sub><sub>wip</sub>(t), a comparison of both estimations is provided in Fig. 9. The correlation graph in Fig. 9(b) compares the values of R<sub>h</sub><sub>video</sub>(t) and R<sub>h</sub><sub>wip</sub>(t) evaluated just after the maximum splash-up for all the impacts, which allows a proper video tracking of the runup. A specific example is also provided for one of the recorded impacts in Fig. 9(a). This figure shows that the two evaluation methods are remarkably consistent. The differences between the two runup estimations fall for most cases in the range of ±10 cm. This uncertainty range of ±10 cm on the runup estimation is retained and will be used to compute the uncertainties on the hydrostatic force estimations later in this study.

Although both methods show a good consistency with each other, the estimation of the runup height from the video is considered to be more precise because it allows to track the evolution between two adjacent pressure sensors. Thus, in the rest of this study, the runup height $R_h(t)$ is preferentially taken equal to $R_h^{\text{video}}(t)$ when a reliable video tracking from Cam1 is possible, and to $R_h^{\text{wip}}(t)$ the rest of time.

3.2. Hydrodynamics

3.2.1. Surf and swash zones

In the surf zone, the free surface elevation time series are computed
from the bottom pressure measurements provided by the two immersed
pressure sensors CP3 and CP2. A frequency-domain attenuation is used
following the linear theory (Tsai et al., 2005; Oliveras et al., 2012) with
a 0.25 Hz frequency cut-off (Bonneton and Lannes, 2017).

In the swash zone, the depth *h*<sub>swash</sub> and velocity *u*<sub>swash</sub> of the swash flow associated with each individual impact on the WIP station are estimated from the field data. The water depth time series *h*<sub>swash</sub>(*t*) is computed from CP1 bottom pressure measurements assuming hydrostaticity. The maximum value of *h*<sub>swash</sub>(*t*) in the few seconds preceding each individual impact on the WIP station is identified and associated with the subsequent impact. It will be further referred to as *h*<sub>swash</sub> for simplicity. The corresponding swash tip velocity *u*<sub>swash</sub> is estimated as

<figure><img src="image_9.png" /><figcaption>**Fig. 8.** Snapshot extracted from the *Tracker* software (https://physlets.org/tracker/) illustrating the manual tracking of *R*<sub>*h*,video</sub>(*t*) corresponding to one of the recorded impacts. (a) Snapshot corresponding to the time instant just before the impact, with the reference axis in pink and the reference length defined along the vertical axis in blue. (b) Snapshot corresponding to the maximum vertical splash-up. (c) Snapshot corresponding to the run-down of the flow. In figures (c) and (d), the red marker represents the manually tracked runup height along the vertical axis of the WIP station. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>**Fig. 9.** Comparison of the runup estimation from the video tracking *R*<sub>*h,video*</sub>(*t*<sub>i</sub>) and from the sensors of the WIP station *R*<sub>*h,wip*</sub>(*t*<sub>i</sub>) at the same time instants *t*<sub>i</sub> corresponding to the force peaks occurring after the maximum splash up. (a) Example of a runup height estimation with both methods at the same time instant for one of the energetic impacts recorded during the experiment. The vertical black line represents the WIP station face, with the locations of the nine pressure sensors P0–P9 marked with red flags. The red line represents the vertical pressure distribution measured at the examined time instant by the pressure sensors of the WIP station. (b) Correlation graph between *R*<sub>*h,video*</sub>(*t*<sub>i</sub>) and *R*<sub>*h,wip*</sub>(*t*<sub>i</sub>) for all the recorded impacts *i* for which both runup estimations are possible. The dashed lines represent the ± 10 cm difference to the line *y* = *x* (solid line). The dot in red indicates the case illustrated in (a). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
an average velocity in the area separating CP1 from the WIP station. This average velocity is computed by dividing the distance between CP1 and the WIP locations by the travel time of the swash tip between both locations. This travel time is evaluated from the video frames provided by Cam2.

In order for the swash flow properties to be related unambiguously to the individual impacts on the WIP station, the above estimations of $h_{swash}$ and $u_{swash}$ are only considered when the swash flow propagates perpendicularly to the seawall from CP1. This feature is assessed from the visual examination of Cam2 video frames. Thus, for swash flows with oblique direction in regard to the instrumented profile axis, no estimate of $h_{swash}$ and $u_{swash}$ is available.

### 3.2.2. Impact zone

In the impact zone, the pre-impact flow thickness $h$ and the tip velocity $u$ are estimated from the analysis of the Cam1 frame images using the system of graduated poles Pe1–Pe3 (see Fig. 4).

The water depth was meticulously tracked on the graduated pole Pe3 fixed on the sloped concrete ramp at distance 3.27 m from the WIP station. The same process as presented to track the runup $R_{h\_video}(t)$ is used to track the water depth $h$ on Pe3. The pixel size along the graduated pole is 0.4 cm. A possible error of 5 cm on the water depth tracking is estimated to be associated with the vibration of the aluminum structure where the camera was fixed. An additional 5 cm uncertainty is associated to the difficulty to identify the exact limit of the horizontal turbulent flow on the vertical pole. The tracking provides a water depth time series $h(t)$ synchronized with the WIP station measurements. The representative water depth of the pre-impact flow associated with each individual impact is determined from the time series $h(t)$ as the maximum flow depth measured before the time instant of the first force peak identified in the force time signal $F(t)$ provided by the WIP station.

The pre-impact swash tip velocity $u$ on the concrete ramp is computed from the tracking of the overtopping flow tip position. Using the known relative distance between the three vertical poles Pe3, Pe2 and Pe1, a length scale is defined along the axis linking Pe3 to the center of the WIP plate. The flow tip progression is assessed on each video image of Cam1, which provides a time series of the flow tip location on the ramp $x(t)$ from Pe3 up to the WIP. The related velocity is computed as the slope of the linear regression of $x(t)$.

Finally, like for the swash analysis, the pre-impact flow properties are only evaluated for cases when the flow travels along an axis perpendicularly to the WIP station. Thus, overtopping flow properties are not analyzed for oblique incidence swash flows, for which the methods presented above are not valid.

## 4. Results

### 4.1. Impact force dataset

The impact force derived from the WIP station measurements provides a time series over a 1 h 20 min time window represented in Fig. 10. The time series includes a total of 28 significant impacts. The corresponding individual force peaks are marked with a red point in Fig. 10. The dataset was limited to this time window because the last and strongest impact damaged the system, which prevents subsequent recordings to be exploited. In the first half of the measurement time window, between 13:20 and 14:00, 7 impacts are identified, while an increased number of 21 impacts are observed in the second half from 14:00 to 14:40, also with noticeably higher intensity. Considering the total measuring time, an impact occurred every 160 s, while during the last 40 min, an impact occurred every 100 s, in average. As the tidal level is the only hydrodynamic parameter that varied significantly throughout the 80 min measuring time window, the increase of the impact frequency and intensity in the second half of the time window is mostly to be attributed to the increase in the tidal level.

The main characteristics of the measured impact force peaks are summarized in Table 2. The 28 force peaks range from 0.38 kN/m to 9.70 kN/m, with a mean value of 2.58 kN/m. The duration of the individual impact events are comprised between 2.18 s and 6.38 s, with a mean value of 3.8 s. Finally, a maximum pressure of 14.46 kPa was measured on the sensor P2. The dataset of the individual maximum impact forces is characterized by a median force of 2.00 kN/m and a 75% quantile of 3.51 kN/m (Fig. 10).

<figure><img src="image_11.png" /><figcaption>Fig. 10. Impact force time series in kN/m derived from the WIP station measurements during the field experiment. Red points mark the force peaks related to the different individual impact events. The dashed horizontal lines mark the median value in blue and the 75% quantile in yellow. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

<table><caption>Table 2
Main characteristics of the collected impact field dataset.</caption><thead><tr><th rowspan="2">Number of impacts</th><th colspan="3">F<sub>max</sub> [kN/m]</th><th colspan="3">Duration [s]</th><th rowspan="2">P<sub>max</sub> [kPa]</th></tr><tr><th>min</th><th>mean</th><th>max</th><th>min</th><th>mean</th><th>max</th></tr></thead><tbody><tr><td>28</td><td>0.38</td><td>2.58</td><td>9.70</td><td>2.18</td><td>3.80</td><td>6.38</td><td>14.46</td></tr></tbody></table>

### 4.2. Shape and duration of the impact events

Considering the force time series associated with the 28 individual impacts of our field dataset, a variability in the shape of the force signal is observed. The different shapes observed can be grouped into three classes. The first two classes gather the large majority of the impact events, which all share the characteristic of exhibiting one or two peaks in the force signal occurring before 2 s from the impact initiation, while after 2 s the signal decreases rather smoothly with no visible later peak. Those two classes differ by the number of force peaks identifiable in the signal. A third specific class is proposed to distinguish a few marginal impact events of the dataset with unusual time series shapes, which exhibit a remarkable late force peak after 2 s from the impact initiation. Those three types of impact time series are illustrated in Fig. 11.

First, a majority of 21 impacts exhibit two distinct peaks, with the first peak most often occurring before 1 s from the event initiation, and the second peak between 1 s and 2 s (Fig. 11(b)). Second, 4 impacts show only one significant peak, generally occurring between 1 s and 2 s from the event initiation (Fig. 11(a)). Third, 3 impacts of the dataset cannot be properly related to the two previous classes due to their singular force signal shape. Although the first part of the force signal can be comparable to a two- or single-peak shape, those three impacts feature a distinct and strong later peak after 2 s from the impact event initiation, typically around 3 s (Fig. 11(c)). The number of impact events in each class and the related mean force values are summarized in Table 3. It can be noticed that the most populated two peaks class (75%) also corresponds to the strongest impacts, with a mean force value which is almost twice as high as the two other classes.

The variations of the duration of the individual impact events over the dataset is now examined in more detail. To compute this duration,
<figure><img src="image_12.png" /><figcaption>**Fig. 11.** Illustration of the different shapes of the impact force signal. One example is provided for each class of shape. Impact signal with (a) a single force peak and (b) two distinct force peaks before 2 s from the initiation, and no later peak. (c) Impact signal with a late force peak after 2 s from the initiation. The vertical dotted black line indicates the impact event initiation and the vertical dashed line highlights the time instant at 2 s after event initiation. The black dots materialize the relevant force peaks for the proposed classification.</figcaption></figure>

the consecutive up- and down-crossing of a minimum threshold set to $1/8 \times F_{max}$ are considered to identify respectively the beginning and end of each individual impact. This threshold was calibrated to properly isolate the signal related to individual events, while removing possible small residual values associated with remaining water in front of the station after reflection. Fig. 12 shows the obtained duration as a function of the maximum force values for the different individual impacts of the dataset. The minimum, mean and maximum duration values over the dataset are 0.8 s, 2.5 s and 4.0 s, respectively. Considering the mean value as a limit to distinguish a long-duration from a short-duration impact class, Table 4 summarizes the related statistics. The short-duration class represents 64% of the total impacts and is characterized by a mean duration of 2.0 s, against 3.4 s for the long-duration impacts. Fig. 12 highlights the general tendency for the force to increase with the impact duration. In average, the force associated with long-duration impacts is higher (3.77 kN/m) than with shorter impacts (1.92 kN/m). However, an important spreading of the values is observable around this trend. The force peaks of three of the short-duration impacts are above the 75% quantile of the force distribution, and the third maximum force peak of the dataset is associated with a short-duration impact. Finally, no clear difference is found between the mean duration of the one and two peaks impact classes in Table 3, while the class of impacts with a later peak in the force signal is logically associated with longer duration.

<figure><img src="image_13.png" /><figcaption>**Fig. 12.** Maximum force of the individual impacts as a function of the impact duration.</figcaption></figure>

<table><caption>**Table 3**

Characteristics of the 3 classes of impact shapes observed in the field dataset.</caption><thead><tr><td>Shape</td><td>One peak</td><td>Two peaks</td><td>Late peak</td></tr></thead><tbody><tr><td>Number of impacts</td><td>4</td><td>21</td><td>3</td></tr><tr><td>Ratio</td><td>14%</td><td>75%</td><td>11%</td></tr><tr><td>Mean force [kN/m]</td><td>1.59</td><td>2.90</td><td>1.63</td></tr><tr><td>Mean duration [s]</td><td>2.4</td><td>2.5</td><td>3.2</td></tr></tbody></table>

<table><caption>**Table 4**

Characteristics of the individual impacts depending on their duration.</caption><thead><tr><td></td><td>Short impacts</td><td>Long impacts</td></tr></thead><tbody><tr><td>Number of impact</td><td>18</td><td>10</td></tr><tr><td>Ratio</td><td>64%</td><td>36%</td></tr><tr><td>Mean duration [s]</td><td>2.0</td><td>3.4</td></tr><tr><td>Mean force [kN/m]</td><td>1.92</td><td>3.77</td></tr></tbody></table>

### 4.3. Impact phases

The different impact phases are examined considering the example of the energetic impact nr. 23, which is representative of the most frequently observed two peaks shape. This impact also corresponds to a normal incident swash flow direction relative to the dike. Inspired by the work of Streicher et al. (2019), a decomposition into five impact phases is proposed. Fig. 13 shows the time instant representative of each phase in the force time series, together with the associated instantaneous vertical pressure distribution. The hydrostatic pressure distribution is also computed from the runup height $R_h(t)$ and plotted in the figure at the corresponding time instant. In addition, a snapshot of the synchronized Cam1 video frames is provided at the same time instants for qualitative understanding.

The first identified phase is the initial impact phase (Fig. 13(A)), which corresponds to the instant when the swash tip gets in contact with the vertical structure and starts being deflected upward. This phase is characterized by a rapid increase in the force signal, associated with a pressure concentration on the two lowest pressure sensors of the station. During this initial phase, the measured pressure is significantly higher than the hydrostatic estimation.

The second phase corresponds to the upward deflection of the flow against the vertical structure (Fig. 13(B)). It is related to the dynamic force peak (F1). At the moment of the peak, the pressure is concentrated on the four lowest sensors (P0-P3), while a rapid decrease is observed between P3 and P4. Under the dominating dynamic effects at that time instant, the recorded vertical pressure profile differs noticeably from the hydrostatic profile. In particular, the maximum pressure recorded at P2 is significantly higher than the hydrostatic estimation.

The third phase corresponds to the moment of the maximum runup (Fig. 13(C)). It is identified to occur after approximately 1 s in the synchronized video images. This intermediate phase is generally associated
<figure><img src="image_14.png" /><figcaption>**Fig. 13.** Decomposition of the impact phases for the example of impact n°23. (A) Initial impact phase, (B) Upward deflection phase, (C) Maximum runup, (D) Initial reflection phase, (E) Hydrostatic phase. The left column gives the force time series in kN/m (red line) with the runup height along the WIP station obtained from the video analysis (solid green line) and from the pressure sensors (dashed green line). The time instant representative of each phase is marked with a black point on the force time series and the corresponding green dot on the runup time series. The impact initiation and the maximum runup time instants are identified by the black and red dashed vertical lines, respectively. The central column presents the recorded instantaneous vertical pressure distribution $P_{\text{wip}}$ (red) and the hydrostatic profile $P_{\text{hydro}}$ (blue). The right column provides the synchronized video images. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

with a plateau in the force signal between the two force peaks F1 and F2. The shape of the recorded vertical pressure distribution is comparable with that of the previous phase but the measured pressures are of lower magnitude, especially lower than the hydrostatic estimation.

The fourth identified phase is the initial reflection (Fig. 13(D)). It corresponds to the second force peak F2. This phase occurs after the maximum runup is reached, when the water accumulated against the structure falls back at the bottom of the station. It is essential to mention that this falling-down water body may interact with the incoming swash flow, which still travels toward the vertical structure, especially for most energetic impact cases. At this stage, the shape of the vertical pressure distribution changes compared to the previous phases. The force peak is associated with a primarily linear pressure distribution. However, surprisingly the pressure profile is noticeably shifted toward lower values compared to the hydrostatic profile.

The last phase is the continuation of the reflection process (Fig. 13(E)). During this phase, the recorded vertical pressure profile

matches the hydrostatic distribution. Again surprisingly, this match is reached with some delay after the peak F2. The delay can vary from one impact to another. For the impact event examined in Fig. 13, the delay after F2 to reach the hydrostatic balance estimation is about 0.4 s.

# 5. Discussion

## 5.1. Shape of the force signal

Based on laboratory experiments focusing on a shallow foreshores and overtopping of a smooth upper-beach dike, previous studies repeatedly highlighted the recurrence of a double-peak evolution shape for the post-overtopping impact force signal (e.g. De Rouck et al., 2012; Ramachandran et al., 2012; Van Doorslaer et al., 2012; Chen et al., 2015), which tends to the so-called “twin peaks” shape when the
foreshore gets very shallow (Chen et al., 2016; Streicher et al., 2018, 2019). This later denomination reflects the presence of two subsequent force peaks F1 and F2 with comparable order of magnitude in the individual impact force times series. A classification was proposed by Streicher et al. (2019) for the 30 highest impacts of their dataset, which is based on the comparison of the magnitude of the two peaks F1 and F2.

In our new field dataset, 21 (or 75%) over the 28 recorded impacts also exhibit a comparable twin peaks shape, with an average relative difference of 20% between the magnitude of the force peaks F1 and F2. Similarly to Streicher's study (considering the time in the laboratory scale), F1 generally occurs before 1 s and F2 between 1 s and 2 s after the impact initiation. The 7 remaining impacts of our dataset (or 25%) exhibit either only a single peak also recorded before 2 s, or more complex occasional shapes including one or two peaks before 2 s and an additional later peak after 2 s. A visual analysis of the synchronized videos recorded by Cam1 and Cam2 was carried out to understand the possible reason for these different shapes. Firstly, this analysis reveals that the one peak signal shape corresponds to events when the swash flow initial impact does not occur exactly on the WIP station sensors but slightly next to their location on the wooden panels. Then, the water that has accumulated against the structure flows alongshore up to the sensor location, which for some cases is accentuated by the oblique incidence of the impacting swash flow. In this configuration, the first force peak F1 is actually much attenuated in the measurements and the force peak F2 appears largely dominant, leading to the one peak overall shape in the recorded signal ($F1 \ll F2$). Moreover, examining the video recordings for the force signals displaying a second or third peak after 2 s suggests that they are all related to complex 3D effects, and in some cases to the catch up of two subsequent swash flows in the impact zone. In any case, for these impacts of unusual shape, the first force peak F1 is always of lower magnitude compared with the following force peak(s).

Hence, for the 28 impacts recorded at our field site, we can distinguish the impacts for which $F1 > F2$ from those for which $F1 < F2$. The corresponding mean characteristics are given in Table 5. Both cases are illustrated in Fig. 14 for 3 examples taken from the dominant impact class with the two peaks shape. In the class $F1 < F2$, impacts have a larger average duration and force. Among the 7 most energetic impacts exceeding the 75% percentile of the maximum impact force distribution, 2 impacts are in the class $F1 > F2$ and 5 in the class $F1 < F2$. Regarding the duration, among the 9 impacts in the class $F1 > F2$, 8 are considered as short-duration impacts in Fig. 12 (duration < 2.5 s). On the opposite, 9 of the 10 long-duration impacts are in the class $F1 < F2$. However, the duration of the individual impacts in the class $F1 < F2$ is equally spread over the short- and long-duration categories.

<figure><img src="image_15.png" /><figcaption>Fig. 14. Examples of force time series in kN/m for impact events dominated by (a) the first force peak ($F1 > F2$) and (b) the second force peak ($F1 < F2$). The vertical dashed lines indicate the impact initiation (black) and the moment of the maximum runup (color). The square and circle symbols mark the force peaks F1 and F2, respectively.</figcaption></figure>

<table><caption>**Table 5**
Characteristics of the impact events depending on the dominant force peak.</caption><thead><tr><th>Impact type</th><th>F1 > F2</th><th>F1 < F2</th></tr></thead><tbody><tr><td>Number of impact</td><td>9</td><td>19</td></tr><tr><td>Ratio</td><td>32%</td><td>68%</td></tr><tr><td>Mean duration [s]</td><td>2.2</td><td>2.7</td></tr><tr><td>Mean rise time [s]</td><td>0.6</td><td>1.3</td></tr><tr><td>Mean force [kN/m]</td><td>2.14</td><td>2.78</td></tr></tbody></table>

## 5.2. Non-hydrostatic deviation of the second force peak F2

During the impact phases A, B and C, the evolution of the vertical pressure distribution presented in Fig. 13 is comparable to that described in previous laboratory studies focusing on wave overtopping on very shallow foreshore configurations (Streicher et al., 2016, 2019) or on tsunamis surge (Kihara et al., 2015; Tan et al., 2023; Li and Liu, 2024). The largest pressures on the lowest part of the vertical structure, and the rapid decrease at higher levels, were explained in Kihara et al. (2015) using precise 2D velocity measurements on a vertical plane close to the wall. During the upward deflection phase, the formation of two opposite rollers was highlighted close to the bottom of the vertical structure. The formation of a counterclockwise roller at higher levels is then hypothesized to be responsible for the rapid vertical decrease of the pressure. In contrast, the formation of a clockwise roller affecting the bottom of the vertical wall is hypothesized to be responsible for the higher pressures measured in this area due to the downward acceleration of the fluid. Ko and Yeh (2018) showed that the momentum equation of the inviscid fluid along the wall can explain the vertical pressure distribution associated with the fluid dynamic during that phase. The relevance of these hydrodynamic processes were also confirmed by numerical studies based on Reynolds Averaged Navier Stokes (RANS) models that focus on the impact of bichromatic waves or surge on a vertical wall (Gruwez et al., 2020; Rozki et al., 2025). The corresponding force peak F1 (phase B) is qualified as “dynamic” because of these dominant acceleration effects. Consistently, the classification proposed by Streicher et al. (2019) considers the impact events of dynamic type when F1 is dominant over F2. This qualification can be applied to the 9 impact events in our field dataset for which $F1 > F2$ (Table 5).

Furthermore, in previous laboratory studies of post-overtopping impact on very shallow foreshores (e.g. Chen et al., 2015, 2016; Streicher et al., 2018), the second peak F2 is generally observed during the reflection phase and is qualified as “quasi-static”. This denomination was used because the corresponding vertical pressure distribution was comparable to a hydrostatic distribution computed from the instantaneous

<figure><img src="image_16.png" /></figure>
runup height. This fit of the measured vertical pressure distribution is ascribed to the fact that the velocities close to the wall at the moment of the initial reflection phase become negligible (Chen et al., 2015; Tan et al., 2023). Consistently, Streicher et al. (2019) proposed to classify the impact events as quasi-static when the force signal is such that $F1 < F2$. In contrast, in our dataset, the pressure distribution associated with F2 can largely differ from the hydrostatic prediction. A first aspect of this discrepancy is that the F2 force peak value is significantly lower than the hydrostatic prediction for a portion of the impacts recorded in the field. This peculiar behavior is especially clear for the most common impact events with a twin peaks shape. To highlight this aspect, Fig. 15 displays the corresponding correlation between the force F2 derived from the WIP station measurements and the hydrostatic force estimation $F2_{hydro}$ computed from the instantaneous runup height $R_h(t)$ at the corresponding instants. A remarkable trend is visible of an increase of the deviation of F2 from $F2_{hydro}$ with the increasing values of F2.

<figure><img src="image_17.png" /><figcaption>**Fig. 15.** Correlation of the force peaks F2 measured in the field by the WIP station and the hydrostatic force $F2_{hydro}$ computed from the instantaneous runup height $R_h(t)$ at the corresponding instants for the twin peaks impact events of the dataset. The vertical lines indicate the uncertainty on the hydrostatic force computation due to the uncertainty on the estimation of $R_h(t)$ (±10 cm; see paragraph 3.1.2).</figcaption></figure>

To provide a further insight into the impacts with a large deviation $dF2_{hydro} = F2_{hydro} - F2$, the measured force signal related to the four most energetic twin peaks impacts of the field dataset is plotted in Fig. 16 (left panel, solid lines). The hydrostatic force computed from the runup height time series $R_h(t)$ for the same impact events is superimposed (dashed lines). The corresponding measured and hydrostatic vertical pressure distributions at the time instant of F2 are plotted in the right panel of the figure. For the four examined impact events, $dF2_{hydro}$ values are again always positive and comprised between +2.87 and +6.52 kN/m. Here, a second important aspect of the observed discrepancy from the hydrostaticity is visible: not only the hydrostatic computation from $R_h(t)$ overestimates the pressures measured by the station at the different sensor levels, but also the measured profiles do not exactly show the expected linear hydrostatic pressure increase with depth. In contrast, measured pressure gradients rather exhibit diverse fluctuations, which are especially visible near the bottom for the two impacts with the largest intensity and deviation $dF2_{hydro}$ (n°9 and n°10). Consequently, in the presented dataset, the nature of the second peak cannot be considered as quasi-static for the most energetic impacts.

For the 4 impact events examined in Fig. 16, the measured force eventually fits the hydrostatic force but after a specific delay from the

peak F2, similarly to the impact previously illustrated in Fig. 13. This delay ranges from 0.4 s to 0.8 s for the examined events. In contrast, the study by Streicher et al. (2019) of post-overtopping impacts on shallow foreshore suggest a clear agreement with the hydrostatic force prediction during the initial reflection phase right from the moment of the force peak F2. Moreover, for comparable maximum force magnitudes, the impact duration in their study is of the order of 1.5 s (laboratory scale), which is much lower than the duration computed from our field dataset, which ranges from 2.5 s to 3.0 s, so up to twice longer.

Several hypotheses can be proposed to explain the reason for the non-hydrostatic deviation of the second force peak F2 observed in our the field dataset. First, the measurement set-up could be expected to deform under the energetic loading, effectively absorbing part of the impact energy. However, it has been verified with qualitative video analysis that the WIP station remains static during the most severe impacts (n°9–10–23–25). Moreover, the design of the vertical plate of the WIP station (material and dimensions) should not allow for any deformation for the magnitude of the pressures recorded during the field campaign. Second, the uncertainties on the runup height estimation used to compute the hydrostatic force can be questioned. In Section 3, an uncertainty of ±10 cm was estimated on the evaluation $R_h(t)$. The induced uncertainties on the hydrostatic force estimation are displayed in Figs. 15 and 16. For the four impacts presented in Fig. 16 especially, the non-hydrostatic deviation $dF2_{hydro}$ is 2.0 to 3.8 times larger than the uncertainties attributed to the evaluation of $F2_{hydro}$. Thus, the magnitude of the non-hydrostatic deviation of F2 is significantly higher than the uncertainties inherent to the hydrostatic force computation.

Third, a possible contribution to the observed deviation between the measured force peak F2 and the hydrostatic prediction could be related to the entrainment of air in the impacting water uprush. Indeed, in our field experiment, the post-overtopping flow accumulated in front of the WIP station during the energetic impact events is significantly aerated due to their very turbulent nature. The substantial aeration of the impacting swash flow in the field is visible in Fig. 13. The entrapped air can be responsible for a non-negligible reduction in the fluid density, which directly affects the magnitude of the hydrostatic force, as mentioned in the early study of Ramsden (1996). Recently, Li and Liu (2024) reported an overestimation of the measured impact force by the hydrostatic prediction during the initial reflection phase based on a downscale laboratory study of a surge impacting a vertical (or inclined) seawall. The authors ascribed the lower measured impact force to the important aeration of the upper part of the water uprush against the wall. Moreover, the authors also emphasize that the air entrainment into the water column accumulated against the wall could also result in a deviation of the vertical pressure gradient from the hydrostatic theory. In our analysis, neither our runup estimation nor our computation of the hydrostatic force account for this aspect, which could reduce the recorded pressures compared to that induced by a non-aerated water body. The effect of air entrainment on impact forces during the reflection phase, although present in downscale laboratory experiments, could be exacerbated at real scale, as the presence of entrained air should be more pronounced in field conditions than in laboratory settings.

Finally, the remarkably long duration of the impacts recorded in the field might be another contribution to the different nature of the force peak F2. More precisely, the qualitative analysis of the synchronized video frames suggests that the swash flow still travels toward the station during the early reflection phase. The water inflow toward the structure seems significantly prolonged in our field experiment compared to the cases studied by Chen et al. (2015, 2016) or Streicher et al. (2018, 2019). This prolonged inflow during the initial reflection phase could generate dynamic effects that add to the usually quasi-static reflection process, resulting in the nonlinear pressure profiles observed in our measurements (Fig. 16). It could be expected that the extended upward acceleration of the swash flow reduces the hydrostatic
<figure><img src="image_18.png" /><figcaption>**Fig. 16.** (a) Force signal of the 4 most energetic two peaks impacts (solid line). The corresponding hydrostatic force time series is superimposed (dashed line) with the associated uncertainties due to the estimation of $R_h(t)$ (color band). The colored dots indicate the measured force peak F2 and the colored squares give the estimated hydrostatic force $F2_{hydro}$. (b) Vertical pressure distribution at the instant of F2. The solid line represents the measurement and the dashed line is the computed hydrostatic pressure profile at the same time instant with the associated uncertainties represented by the color band. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

impact while the continuous in-stream of water interacts with the opposite flow reflected by the vertical plate.

In their study of tsunami surge impact on storm walls, considering much longer impact duration (~80 s), Kihara et al. (2015) commented that at the moment of the initiation of the reflection by the downward flow accelerated by gravity, a continuous burst of incident flow close to the structure bottom is still at play. The impact pressure at this moment was mentioned to result from a combination of dynamic and hydrostatic pressures. Tan et al. (2023) also observed such a secondary flow near the wall toe inducing significant variations in the vertical velocity and accelerations along the impacted wall during the reflection phase, which result into a non-hydrostatic pressure profile. Li and Liu (2024) again observed such a deviation from the hydrostatic pressure distribution when studying a surge impact process on a wall and commented about the crucial role of the water's acceleration along the wall, although focusing on slightly different instants of the impact before and after the actual reflection force peak. To a certain extent, the observation of post-overtopping swash flow impacts collected at our field site could reflect such situations, which were previously described in studies of surge impacts. In particular, it seems consistent with the visual observation of the most energetic impact events from the video recordings, which suggests that the water velocities against the WIP station front could still be very significant during the initial reflection phase. It is also coherent with the pressure distribution observed in the lower part of the WIP station for the most energetic impact events, which features a vertical profile that somewhat resembles the profile observed during the dynamic deflection phase (Fig. 16).

### 5.3. Relationship with the pre-impact hydrodynamics

In this paragraph, the relationship between the impact force and the pre-impact flow depth and velocity is investigated. Here, the methods used to estimate the swash ($h_{swash}$, $u_{swash}$) and pre-impact ($h$, $u$) flow properties require that the flow travels perpendicularly to the WIP station. This reduces the dataset to 13 individual impact events with maximum individual force ranging from 0.38 to 5.90 kN/m. Although the available impact events sample is limited, preliminary trends will be examined.

Fig. 17 summarizes the values of $h_{swash}$, $h$, $u_{swash}$ and $u$ computed from field measurements for the selected impacts. The flow depth $h$ on the concrete ramp ranges from 0.15 to 0.75 m, and the corresponding flow tip velocity $u$ is comprised between 2.2 and 7.6 m/s. The respective comparison of $h$ and $u$ with $h_{swash}$ and $u_{swash}$ shows that flow depth and tip velocity have similar orders of magnitude whether they are estimated in the swash zone or on the concrete ramp. This supports the consistency of the computation methods used to derive these quantities from the field data. In general, flow tip velocities and depths are larger in the swash zone, which is consistent with the expected decrease of these quantities when the swash flow travels toward the upper-beach. The resulting discharge $hu$ ranges from 0.6 to 5.2 m³/s/m, a range that is also consistent in the swash zone and on the ramp.

The relationships between the maximum force $F_{max}$ of the individual impacts and the quantities $h$ and $u$ are investigated in Fig. 18, as well as the dependency of $F_{max}$ on the overtopping discharge $hu$ and on the

<figure><img src="image_19.png" /><figcaption>**Fig. 17.** Flow depth and tip velocity estimated from field data in the swash zone ($h_{swash}$, $u_{swash}$) and on the concrete ramp ($h$, $u$) for the 13 selected 1D impacts of the dataset.</figcaption></figure>
related momentum flux $hu^2$. The figure shows a clear tendency for the force to increase with the overtopping flow depth, but a significant spreading of the values is observed around this general trend. For example, the three impacts with a flow depth of about 0.25 m relate to forces that vary noticeably from 0.45 to 1.91 kN/m. Similarly, the four other impacts with comparable flow depths of about 0.4 m correspond to $F_{max}$ ranging from 2 kN/m to almost 5 kN/m. The physical explanation for this variability can be found by looking at the corresponding tip velocities: for a given flow depth, an increase in the tip velocity appears to be related to an increased force value.

These observations suggest that both the flow depth and the tip velocity are linked to the maximum impact force. This is confirmed by the quite significant correlation between $F_{max}$ and the discharge $hu$ in Fig. 18(b), which shows much less scatter than with $h$ or $u$ individually. These results are in agreement with the previous findings of e.g. De Rouck et al. (2012). The correlation of $F_{max}$ with the momentum flux $hu^2$ of the impacting flow (Fig. 18(c)) is also found significant. This is consistent with previous studies which proposed to estimate the impact force from the maximum momentum flux characterizing the incoming impacting flow (Cross, 1967; Wüthrich, 2017; Streicher et al., 2018). Here, the scatter could be considered more pronounced for the three events with moment flux comprised between 13–20 m³/s². Following the same method, the relationship between the non-hydrostatic deviation $dF_{2_{hydro}}$ and the pre-impact flow properties is examined in Fig. 19. A possible relationship between $dF_{2_{hydro}}$ and the overtopping flow depth $h$ is visible (with a possible polynomial shape). In contrast, the correlation plot between $dF_{2_{hydro}}$ and $hu$ or $hu^2$ is more scattered, suggesting a more limited role of the tip velocity $u$ in the determination of the non-hydrostatic deviation of F2.

The relation between the pre-impact flow characteristics ($h, u$) and the impact force $F_{max}$ is further investigated, now also considering the runup height against the WIP station. First, we examine the relation between ($h, u$) and the maximum runup height $R_{hmax}$. Similarly to Li

and Liu (2024), and continuing the possible analogy of our configuration with a surge impact, we propose to apply the formula from Shafiei et al. (2016) based on the Bernoulli equation to compute an estimation of $R_{hmax}$ from $u$ and $h$. The corresponding expression is given by :

$$R_{computed} = h + c_R \cdot \frac{u^2}{2g} \quad [m], \quad (2)$$

where $g$ is the acceleration of gravity and $c_R$ an empirical coefficient that accounts for the transfer between the kinetic energy and the potential energy. In the case with no energy loss, $c_R = 1$. In our case, the lower value $c_R = 0.45$ was empirically fitted when minimizing the root mean square difference between $R_{computed}$ obtained from Eq. (2) and the observations of $R_{hmax}$. The comparison of the computed values $R_{computed}$ with this fitted coefficient and the observed values of $R_{hmax}$ is presented in Fig. 20(a), again focusing on the subset of 13 individual impact events with a pre-impact flow traveling perpendicularly to the WIP station. It shows that the fitted formula (2) provides a consistent order of magnitude compared to the measured $R_{hmax}$ values, as well as a coarse reproduction of the related variation range from 0.3 m to 1.8 m over the dataset, with a root mean square error of 0.26 m. Most discrepancies are obtained for a set of 3 impacts with $R_{hmax}$ between 1.3 and 1.7 m, which are sensibly underpredicted by expression 2 (2) with $R_{computed}$ between 0.8 and 1.2 m.

Secondly, following Streicher et al. (2018), we propose to compare the measured maximum impact force $F_{max}$ to an estimation obtained from the maximum runup $R_{hmax}$ by applying an hydrostatic-like formulation given by :

$$F_{computed} = \frac{1}{2} \cdot \rho_{\omega} \cdot g \cdot (c_F \cdot R_{hmax})^2 \quad [N/m], \quad (3)$$

with $\rho_{\omega}$ the water density and $c_F$ an adjustment coefficient. This later coefficient may account for the fact that the accumulated water body in front of the wall at the moment of the maximum runup has a triangular shape and not a horizontal water surface, thus only a certain

<figure><img src="image_20.png" /><figcaption>Fig. 18. Evolution of the maximum individual impact force $F_{max}$ with (a) the overtopping flow depth $h$ and tip velocity $u$, (b) with the overtopping discharge $hu$, and (c) the momentum flux $hu^2$.</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>Fig. 19. Evolution of the non-hydrostatic deviation $dF_{2_{hydro}}$ with (a) the overtopping flow depth $h$ and tip velocity $u$, (b) with the overtopping discharge $hu$, and (c) the momentum flux $hu^2$.</figcaption></figure>
amount of $R_{hmax}$ is considered to compute the force ($c_F < 1$). When trying to estimate the reflected force peak F2, the coefficient $c_F$ may also account for the timing of F2, which actually does not coincide with the timing of $R_{hmax}$ but is rather observed slightly later when $R_h < R_{hmax}$ (Streicher et al., 2018). Here, the coefficient $c_F = 0.65$ was empirically fitted to our field dataset, considering the $F_{max}$ and $R_{hmax}$ values derived from the WIP station measurements. The best-fit value, $c_F = 0.65$, is then used in Eq. (3) to calculate two estimates $F_{computed}$ of $F_{max}$ that are displayed in Fig. 20(b) : one estimate from the observed $R_{hmax}$ values (red points), and another estimate from the computed $R_{computed}$ values with Eq. (2) (yellow points). Results obtained suggest that the fitted formula (3) provides a fair estimation of the measured $F_{max}$ when applied to the $R_{hmax}$ observed, with a root mean square error of 0.6 kN/m. The scatter is more pronounced for the computation of the force using the estimated runup $R_{computed}$, with a root mean square error of 1.3 kN/m. The largest deviation from the observations is obtained for the same 3 impact events for which $R_{computed}$ was significantly underestimated, which are much better estimated when using the observed $R_{hmax}$ values. For the rest of the impacts, the range of $F_{max}$ variations is rather consistent for both $F_{computed}$ estimations.

These last results must be analyzed carefully, as they depend on the measurement of the maximum runup height, which remains a challenge in both laboratory facilities and field conditions, as well as the limited number of impact events that limits the statistical representativity. However, the orders of magnitude obtained appear rather consistent when estimating the maximum runup height and impact force using the pre-impact flow characteristics, providing the preliminary fitting of the coefficients $c_R$ and $c_F$ on the field dataset. The value $c_R = 0.45$ is significantly lower than 1, which would represent a perfect transfer between kinetic and potential energy. This possible energy loss can be hypothesized to be attributed to the significant amount of entrained air in the pre-impact flow and the dissipation induced by the important turbulence level. When estimating $F_{max}$ from $R_{hmax}$ with Eq. (3), the fitted coefficient $c_F = 0.65$ is also lower than the one proposed by Streicher et al. (2018), $c_F = 0.8$. This lower value of $c_F$ seems consistent with the overestimation of the F2 force peak by the hydrostatic prediction in our case, which was commented in previous paragraphs. The hypothesized contributions to this overestimation, namely the aeration of the flow and the possible dynamic effects during the reflection phase, could be roughly represented in our lowered $c_F$ best-fit value.

## 5.4. Perspectives of the study

To the authors' knowledge, the present study provides the first acquisition and analysis of field measurements of post-overlapping

wave impacts on a vertical structure at a real site with a very shallow foreshore. Although such an acquisition remains very challenging in practice, which currently limits the size of the available dataset, it also highlights the importance of collecting data in the field as a complement to downscale lab experiments. The confrontation of the processes observed in laboratory experiments against those observed at real sites is an important task to confirm (or not) the results obtained at reduced scale and thus verify the full adequacy of the downscale experiment setting. Indeed, any laboratory experiment is still a reduce-scale model of the reality, which requires a number of assumptions and parameterizations of the real-scale features. Even if conducted with a lot of care, it cannot be totally guaranteed that no bias or deviation is introduced in the lab, until the observations are confirmed at full scale.

In particular, a major scaling issue relates to the effect of entrained air on the magnitude of the pressures generated on a vertical structure and the resulting force. It has been shown that the magnitude of the measured maximum pressures decreases with the increasing inclusion of air bubbles in the water due to the so-called cushioning effect (Bullock et al., 2001). Due to this cushioning effect, the force peaks occurring during the initial impact phase or the upward deflection phase could lead to an overestimation while upscaling the impact force (Streicher et al., 2019). Additionally, the relationship between the force magnitude during the initial reflection phase and the runup on the vertical structure directly depends on the water density, which is altered by the quantity of entrained air (Ramsden, 1996; Li and Liu, 2024). Despite the importance of these two processes, it remains very challenging to this day to generate the right amount of entrained air in the impact zone while downscaling real configurations (Chen et al., 2016; Van Doorslaer et al., 2017; Streicher, 2019). In this context, the in-situ measurements presented in this study enable us to characterize real-scale processes, thereby overcoming the problems of scale and model effects encountered when studying the impacts of overtopping on vertical upper-beach infrastructures.

Next to these advances, several aspects have been identified as needing improvement to confirm and better understand the processes at play in the studied configuration. First, despite an important effort to collect data in the field during a storm event, the number of overtopping impacts recorded is limited to 28. The characterization of the impacts and especially of the non-hydrostatic deviation of the second force peak F2 presented in this field study should be confirmed with an extended dataset covering a wider range of conditions with a large variety of impacts. A related perspective is currently underway with the permanent installation of an adapted version of the WIP station at the GPB site. This effort could be complemented with measurements in a

<figure><img src="image_22.png" /><figcaption>Fig. 20. (a) Comparison of $R_{hmax}$ observed on the field and $R_{computed}$ obtained with the fitted formula (2). (b) Comparison of $F_{max}$ observed on the field and computed with the fitted formula (3) using $R_{hmax}$ observed (red points) and using $R_{computed}$ (yellow points). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>
more controlled laboratory environment focusing on this specific beach and sea-defense configuration. Such additional observations should also allow to confirm the hypotheses proposed in the present work as a possible source of explanation for the non-hydrostatic deviation of F2.

Second, it was mentioned that aeration and air entrainment could be key in modulating the impact force and pressures, including the possible generation of non-hydrostatic effects during the initial reflection phase. Many previous studies have emphasized this aspect as a major issue while downscaling the studied configurations in laboratory facilities. Therefore, it would be very interesting to measure the void fraction in future experiments in order to quantify the proportion of air in the water uprush and better understand the related effects. In the same perspective, the vertical velocities and accelerations along the impacted wall were also hypothesized to affect the pressure profile during the reflection phase, possibly contributing to the divergence from the hydrostatic prediction. Thus, velocity measurements along the wall could be highly useful to further investigate this aspect, in addition to the ensemble of sensors deployed in this study.

Third, regarding the estimation of the runup on the WIP station, the interpretation of the video data is limited because of important vertical water projections in front of the camera during the upward deflection phase. An alternative location for the camera installation could avoid this limitation and allow a continuous runup estimation from the video. Moreover, the quantification of the runup height on the station is highly dependent on the quality of the video images. Those estimations are of poor quality if the lens of the camera is dirty or wet. Finding a more robust method to estimate the runup on the vertical structure in the field is an important component for improvement. The use of resistive type gauges as in Streicher et al. (2017), or step gauges fixed on the vertical structure as used in Ramachandran et al. (2012) and De Rouck et al. (2012), could be possible solutions. An alternative option is to make the vertical structure transparent, as adopted by Li and Liu (2024). With this solution, a camera can film the back of the structure and provide images to estimate the runup height on the vertical structure, as well as to qualify the nature of the flow along the plate during the entire impact duration.

Fourth, in the pre-impact zone, the measurement systems employed only permit the estimation of a mean flow tip velocity before the impact on the WIP station. A more precise and detailed measurement of the velocity using one or several current meters could refine the assessment of this quantity. Moreover, the access to the temporal evolution of the overtopping velocity would allow a more accurate estimation of the duration of the swash inflow toward the station. During the initial reflection phase especially, this could permit to quantify the inflow velocity at the moment of the force peak F2, which is suggested in the present work as a possible contribution to the non-hydrostatic deviation. Furthermore, the flow depth estimation from the graduated poles is also highly dependent on the video image quality and clarity. It is very challenging to process the images automatically, and the overall video images require high storage capacity. An alternative solution could be to use the same resistive type or step gauges as for the runup, or pressure sensors with high-frequency acquisition.

Finally, in the studied field deployment, significant three-dimensional (3D) effects were observed qualitatively through video analysis in the inner surfzone and the swash zone. These 3D effects seem responsible for a significant part of the variability observed in the impact shape and type. It would be certainly interesting to characterize the 3D hydrodynamics of the inner surfzone and the swash zone, and to combine it with directional flow measurements in the impact zone, in order to analyze the effect on the impact events. One option considered resides in using a 3D LiDAR (Light Detection And Ranging) system as done e.g. in the work of Almeida et al. (2020) or a lidar-camera fusion system as in the study by Matsuba et al. (2025). This type of measurements would also provide quantitative data to study bore interactions in the inner surfzone, such as bore catching, and bore interactions in the swash (Bergsma et al., 2019). These processes could also have a significant effect on maximum swash flow excursions (Stringari and Power, 2020; Barale et al., 2024) and on the post-overtopping impact forces (Streicher et al., 2019).

## 6. Conclusion

This study presents the first field dataset of wave induced post-overtopping flow impact pressures generated on a vertical structure located on top of an upper-beach dike with an emergent toe. The field site of the Grande Plage of Biarritz (SW France) was characterized as a semi-reflective beach and a very shallow foreshore environment. In the field conditions, overtopping of the dike is induced by a swash flow previously generated on the beachface at a distance from the defense structure. Post-overtopping impact pressures were measured during an energetic winter storm event with a dedicated monitoring system, the WIP station, installed at the crest of the dike. A total of 28 impacts were recorded over a sampling duration of 1h20 min, with maximum forces of the single impacts ranging from 0.38 to 9.7 kN/m. The instantaneous runup height against the WIP station front was estimated through a tracking performed on synchronized video images and using the station pressure measurements. Additionally, the pre-impact flow depths and tip velocities were derived from measurements in the swash zone and on the dike.

The main results and conclusion arising from the analysis of this unprecedented field dataset are summarized in the following items:

* The combined analysis of the force time series, the vertical pressure profiles and the synchronized video images allowed to identify the following different impact phases: (A) Initial impact, (B) Upward deflection, (C) Maximum runup height, (D) Initial reflection and (E) Hydrostatic phase. This decomposition is very much in line with the previous results obtained from laboratory experiments (Streicher et al., 2019).

* A majority of 21 over the 28 recorded impact events exhibit a twin peaks shape, with two distinct force peaks of comparable magnitude : a first peak F1 during the upward deflection phase (B) and a second peak F2 during the initial reflection phase (D), again consistently with previous laboratory studies. In total, 68% of the impact events are dominated by F2 ($F1 < F2$).

* The analysis of the vertical pressure distribution during the deflection phase is in good agreement with the laboratory measurements of Kihara et al. (2015) and Streicher et al. (2019). However, during the initial reflection phase, the vertical pressure distribution at the moment of F2 deviates sensibly from the expected linear hydrostatic profile computed from the runup height. Moreover, the magnitude of the force is overestimated by the hydrostatic prediction and this overestimation is shown to increase drastically with the force peak value. This observation differs notably from previous downscale studies (Ramachandran et al., 2012; Chen et al., 2015; Streicher et al., 2019). Possible contributions for the highlighted non-hydrostatic deviation are hypothesized to relate (i) to the aeration of the impacting flow and (ii) to superimposed dynamic effects due to the prolonged swash inflow during the initial reflection phase, with a possible analogy to a long wave induced surge impact.

* The analysis of the pre-impact flow properties suggests a possible relationship between the maximum individual impact force $F_{max}$ and the overtopping discharge $hu$ or the momentum flux $hu^2$. Moreover, it was found that the deviation of F2 from the hydrostatic force prediction could be rather related to the overtopping flow depth $h$. Finally, the observations of $F_{max}$ were compared to estimations obtained from the maximum runup height using an hydrostatic-like formula, which provided rather consistent order of magnitude and range of variation, provided the application of an empirically fitted damping coefficient.

This study proposes the first field characterization of post-overtopping wave impacts on an upper-beach sea-defense. It is based on an original dataset obtained from a very challenging deployment in real storm conditions, which offers a valuable but limited amount of data. The
dataset will have to be extended in the near future to confirm and complement the presented results. Another originality of the study relates to the emergent toe condition of the instrumented upper-beach defense, which results in an overtopping by a swash flow, a configuration that is still scarcely documented in the literature. Comparisons were made with different existing laboratory studies identified as the most comparable to the present field site configuration. However, to the authors' knowledge, the specific impact force exerted by swash overtopping on vertical structures has never been studied neither in laboratory experiments nor in the field so far. This type of wave overtopping should be studied under controlled laboratory conditions, in addition to complementary measurements in the field, to further characterize the physical processes at play.

### CRediT authorship contribution statement

**Erwan Imbertie:** Writing – review & editing, Writing – original draft, Methodology, Investigation, Formal analysis. **Denis Morichon:** Writing – review & editing, Validation, Supervision, Project administration, Methodology, Funding acquisition, Conceptualization. **Matthias Delpey:** Writing – review & editing, Validation, Supervision, Project administration, Methodology, Funding acquisition, Conceptualization. **Benoît Larroque:** Writing – review & editing, Methodology. **Camille Lavayssière:** Writing – review & editing, Methodology.

### Declaration of competing interest

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: IMBERTIE reports financial support was provided by SUEZ EAU FRANCE (Centre Rivages Pro Tech). If there are other authors, they declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Acknowledgments

This research was carried out under the framework of the joint laboratory KOSTARISK, which is part of the E2S UPPA program managed by the French National Research Agency (ANR-16-IDEX-0002) and supported by the French Government's "Investissements d'Avenir" (PIA). The joint laboratory KOSTARISK is co-funded by E2S UPPA, the AZTI Foundation and the center Rivages Pro Tech of SUEZ.

The authors would like to thank Lionel Elissalde and the Port of Bayonne (Region Nouvelle Aquitaine) for their contribution to the creation of the WIP station, as well as the city of Biarritz for its logistical support during the field campaign.

Finally, the authors would like also to express their gratitude to the different anonymous reviewers who examined this manuscript for their constructive suggestions and observations, which were greatly appreciated and helped to improve the presented work significantly.

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