Some beaches that had erosion issues were sampled to determine the research area. Because previous studies of ACRs did not examine the longshore current and drift, beaches with a pocket or spiral shape were preferred. Therefore, Cheonjin-Bongpo beach was used as the research area, which is denoted as ‘GW 12 littoral cell’ in South Korea. Fig. 2 shows the location of the research area.

Field observations were conducted to investigate the characteristics of the research area. During the observation, echo sounder devices (Sonar-tech, AquaRuler 200S; CEE HydroSystem, CEESTAR; and VALEPORT, MIDAS) were used, and the water depth was measured until 25 m. Global Navigation Satellite System (GNSS) devices (Leica, GX1230; Leica, Viva GS16) were used to obtain shoreline data when the wave height was less than 0.7 m. The wave data were acquired using an acoustic wave and current profiler (Nortek AS, AWAC). The median grain size (D₅₀) of the sand particle was determined to be 1.493 mm, and the calculated settling velocity was 16.7 cm/s using the van Rijn(1984)’s equation.

SWAN (Simulating waves nearshore) model 3^rd generation was developed by Delft University of Technology (Booij et al., 1999), which aims to simulate the deformation of multi-direction irregular waves based on the wave action balance equation. The SWAN model is considered a practical method to predict wave deformation because it can consider wave reflection, diffraction, shoaling, and wave breaking. Because of these advantageous features, the 3^rd generation model (Version 41.31) of SWAN based on the field observation data was used to examine the impacts of an ACR under high wave conditions. In this study, SWAN modeling was conducted with two procedures. At first, the winter wave condition for the absence of an ACR was simulated to find the incident wave height for a physical model test.

After determining both the transmission and reflection coefficient from the physical model test, second SWAN modeling was performed for both winter and summer wave conditions to examine the wave height distributions in the presence of an ACR. During SWAN modeling, the maximum wave (H_1/250) was used as an incident wave for simulating the high wave condition. Moreover, bathymetry was rotated 45° counter-clockwise to perform easier modeling. Table 1 lists the specific conditions for SWAN modeling. As the SWAN model has been used widely in both the research and business practice field, an additional model verification process was omitted.

The transmission and reflection coefficient values are required as input parameters to simulate the ACR installation conditions in the SWAN model. As there was no prior research explaining the transmission and reflection coefficient according to the ACR design, a physical model test was conducted to find its values. Therefore, it was assumed that the ACR installation locations refer to the designs of a submerged breakwater in the research area from the basic plan for the 2^nd coastal maintenance project (Ministry of Ocean and Fisheries, 2014). The incident wave height for the physical model was determined using both cross-sectional and planar designs for the ACR. The wave height values for the incident and transmission are located 10 m away from the ACR offshore side and 20 m away from the onshore side in the points of the prototype scale. In addition, the Froude scale with a ratio of 1 : 25 in the length scale and 1 : 5 in the time scale was applied to the physical model test. A seabed slope of 1/30 was applied because the beach slope of the east sea is generally 1/30. The capacity type of wave gauge (Kenek, CH-608E) and wave probes (Kenek, CHT-30E) were used during the physical model test. Wave calibration processes were conducted at every measuring point to obtain precise and reliable wave data. The transmission coefficient was defined as the ratio of the incident wave height (H_i ) to transmitted wave height (H_t), as shown in Eq. (1).

Healy’s formula (Healy, 1953) was applied to calculate the reflection coefficient (K_R ), as shown in Eq. (2), which is based on the partial standing wave theory. To apply this equation, both the largest (H_max) and smallest (H_min) wave height at antinode and node of the partial standing wave, respectively, were used (see Fig. 3).

Six representative beach profile (BP1∼BP6) lines, which are the normal direction to the shoreline, were set to investigate the erosion-mitigation effects of the ACR (see Fig. 4,). Generally, the trends of the wave height distribution are different between the open inlet and behind the submerged structure. In this regard, the beach profile lines were determined at the open inlet of the ACR (BP1, BP3, and BP5). Moreover, BP2, BP4, and BP6 represent the beach profile lines, which are located behind the ACR structure.

With these beach profiles, the critical wave heights at each water depth condition were calculated based on the McCowan (1894)’s wave breaking parameter (κ), which has a general value of 0.78 (see Eq. (3)).

Subsequently, wave-breaking locations were determined, where the wave height value given by SWAN modeling is greater than that of the wave breaking parameter cases. The height (H_b) and depth (h_b) of the breaking wave were decided. The slope for the beach profile (tanβ) was defined as an angle from the wave breaking point to the shoreline.

The Dean’s parameter (Ω) introduced by Dean (1977), mass flux (M), undertow (u_b), maximum wave setup (η̄_max), and surf-scaling parameter (∊_s), which are relevant factors to elucidate the high wave control performance of the ACR, were computed. where, H_b, w_f, and T represent the wave height at breaking point, settling velocity of a sand particle, and wave period, respectively. where, ξ_b and L_o mean the surf similarity parameter and wavelength for deep water, respectively.

SWAN modeling was first carried out to determine the incident wave for the physical model test and examine the wave height distribution without an ACR. In this regard, the wave heights in front of three ACRs, denoted as H₁, H₂, and H₃, were averaged (see Fig. 5). Consequently, the incident wave was determined to be 2.40 m for performing the physical model test, as shown in Table 3.

To determine the relevant transmission and reflection coefficient, the structure geometry and wave condition were designed based on the Froude similarity scales (Table 4). A regular wave was generated until it reproduced the target wave (H = 9.56 cm, T = 1.80 s) at the incident wave measuring point.

Fig. 6 shows the experimental design for this physical model. The incident and transmitted wave heights were measured at WP1 and WP2, respectively. Moreover, the wave measurement was conducted from 17.2 m to 23.5 m to determine both the transmission coefficient (K_T) and reflection coefficient (K_R).

Fig. 7 shows the results of the wave measurement. The results indicate that remarkable wave attenuation occurred from the ACR. Moreover, a partial standing wave occurred in front of the ACR. In this regard, the calculated transmission coefficient (K_T) was 0.36 based on the H_i (9.44 cm) and H_t (3.40 cm) values. Moreover, the calculated reflection coefficient (K_R) was 0.39. These K_T and K_R values were applied to both the winter and summer wave simulations.

The second SWAN modeling was performed to investigate the wave height distribution trends with ACR installation for winter and summer wave conditions. Fig. A1 provides detailed information on the ACR structure. Fig. 8 shows the wave height distribution results in the presence of the ACR for a winter wave.

Table 5 lists the wave height percentile in the presence and absence of an ACR case calculated at each beach profile line. The results of significant wave reduction indicate that ACR installation plays a crucial role in wave attenuation at the rear side of its structure for both winter and summer cases. Moreover, greater wave height mitigation (58.95∼70.90%) occurred in the presence of an ACR, whereas no significant wave reduction occurred without ACR installation (83.95∼96.15%).

The wave breaking trends also differed according to the ACR installation. Fig. 9 shows the wave-breaking height and wave-breaking distance from the shoreline. In the case of ACR installation, waves with smaller heights break near the shoreline, whereas relatively larger waves break further from the shoreline. The ACR induced breaking for larger waves in advance, allowing only smaller waves to propagate over the ACR. A significant difference was not observed between the winter and summer high waves, which means that the ACR plays a positive role in terms of wave height reduction.

The mass flux (M), undertow (u_b), and maximum wave setup (η̄_max) at each beach profile were calculated and compared to investigate the impacts of wave-induced current. Table 6 lists the computed values of M, u_b, and η̄_max . According to average values for the winter and summer results, smaller mass flux (∼50%), undertow (∼80%), and wave set up values (∼61%) were observed with ACR installation, highlighting the positive impacts on shoreline stability.

As a wave is a key parameter that determines the shape of the shoreline, the Dean’s parameter (Ω) and surf-scaling parameter (∊_s) were computed to determine the impacts of the waves in terms of shoreline changes (Table 7 and Table 8). Under winter and summer high wave conditions, the Dean’s parameter decreased in the ACR cases, which is closer to the reflective wave type compared to the dissipation wave type.

When waves propagate over the ACR, a decrease in surf-scaling parameters usually occurs, particularly in BP2, BP4, and BP6, suggesting that wave-induced erosion can be mitigated. Moreover, the planar design of the ACR suggested in this study appears to be more effective for summer waves (improved in six beach profiles) than winter waves (improved in four beach profiles) in terms of high wave control. Overall, an ACR can mitigate erosion caused by high waves.