1. Introduction
According to the Korea Meteorological Administration (KMA), 70.8 earthquakes with a magnitude of 2.0 or higher occurred on average each year near the Korean Peninsula from 1978 when digital observations began to 2023. Among them, 12 earthquakes (32.4%) occurred under the sea. The main question asked is whether Korea is safe from tsunamis. The answer can be obtained from the past and recent cases. The 7.6 magnitude earthquake and tsunami off the Noto Peninsula, Japan, at around 16:00 on January 1, 2024, served as a reminder of such risks. The resulting tsunami measured up to 82 cm on the east coast of Korea (KMA, 2024). It was recorded as the first significant tsunami in the 2000s after 1940, 1964, 1983, and 1993, when the tsunamis off the west coast of Japan recorded in the 1900s affected the east coast of the Korean Peninsula. After the tsunami caused by the earthquake off the Noto Peninsula, Japan first reached the east coast of the Korean Peninsula; the maximum tsunami height was observed between two hours to two hours and 30 minutes (KMA, 2024). In Japan adjacent to the epicenter, after the tsunami first arrived, the maximum tsunami height was reached in 20 minutes to one hour. A tsunami height of up to 5.1 m was observed in Shika-machi, Ishikawa Prefecture, and an inundation trace of 6.6 m was observed at Funami Park in Joetsu City, Niigata Prefecture (NOAA, 2024).
As noted from past damage cases, tsunamis cause significant damage to major coastal facilities (e.g., ports, power plants, and marine industrial complexes) and the entire social infrastructure (e.g., roads, railways, and residential facilities adjacent to the coast). Rossetto et al. (2007) reported that fluid forces, scour, and collisions by drifting objects are the leading causes of damage to structures. From the 2004 Indian Ocean tsunami (Rossetto et al., 2007; Suppasri et al., 2012), the 2010 Chile tsunami (Palermo et al., 2013), the 2011 East Japan earthquake (Takahashi et al., 2011; Suppasri et al., 2012; Naito et al., 2014), and the 2018 Indonesia tsunami (Stolle et al. 2020; Krautwald et al., 2021), a number of collision damage cases by the debris from collapsed structures and large drifting objects (e.g., vehicles, containers, and ships) were reported. Collisions of drifting objects by tsunamis cause structural damage to most facilities and structures, such as columns that support loads (Palermo et al., 2013, Naito et al., 2014). Collisions with slabs lead to collapse by promoting scour at the foundation (Krautwald et al., 2021). Chavet et al. (2015) revealed through vulnerability analysis that the collision of drifting objects is an important factor that determines the collapse probability of a building. Therefore, an analysis of the collisions of drifting objects by tsunamis is required to quantify the risks of facilities in coastal areas and to design tsunami-proof structures (Kaida et al., 2024).
The collision speed and weight are important parameters in calculating the collision force caused by a drifting object. The maximum flow velocity around a structure or drifting object presented in ASCE (2022) can be applied, but it does not consider the effects of complex flow phenomena around a structure (Krautwald et al., 2022; Kihara and Kaida, 2019). The drift behavior of an object is significantly affected by buoyancy (Stolle et al., 2020; Krautwald et al., 2021), and the interaction between drifting objects affects the moving trajectory, diffusion, and drift speed (Stolle, 2016). The initial position of an object or the direction of a fluid force also has a significant impact on the drift behavior (Kimoto and Toita, 2021). In the results of the hydraulic experiment by Oda et al. (2020), the probability of fully floating objects (e.g., ships) colliding with seawalls was significantly affected by wave breaking or eddies, and they drifted more rapidly as the area under water pressure increased. Nonlinear interactions occur between the behavior of drifting objects and fluid motion. Moreover, the formation of the flow field is affected by the size, geometry, buoyancy, and weight of the object (Miyokawa et al. 2017). Derschum et al. (2018) examined the effects of the flow field and the effects of the initial conditions of a container and the contact conditions with a structure on collision forces in repeated experiments that used breaking waves. The splitting streamline and stagnation by the obstacle caused the nonlinear motion of a drifting container and reduced the collision speeds. The initial conditions of the container had no significant impact on the contact between the two objects when the distance between the initial position of the container and the structure was sufficient because of the uncertainties generated during the drift process. The numerical analysis conducted by Lee et al. (2024) using LS-DYNA also showed that the contact conditions between drifting objects and fixed structures had a significant impact on the collision forces. This indicates that the maximum collision forces of containers are dominantly affected by the contact conditions with structures.
According to de Costa et al. (2019), complex structures with coastal forests, moats, and embankments reduce the tsunami inundation height and the maximum drift speeds of objects by approximately 50% and 32%, respectively. Coastal forests can reduce damage to inland areas by decreasing the inundation speed and inundation height of tsunamis and significantly reducing damage through debris collection (Tanaka and Onai, 2017). Coastal forests, however, may experience damage caused by current concentration and driftwood. The numerical analysis by Como and Mahmoud (2013) reported that the collision between driftwood by a tsunami and wooden structures may cause collapse due to the weakening of structural components. Kharade and Kapadiya (2013) analyzed the reaction of structural elements to the impact load caused by collisions between driftwood from a tsunami and reinforced concrete structures through numerical analysis. They reported that structural damage was different depending on the collision location or height. The force acting on the entire structure increased when the collision occurred at a level 0.5 m higher than the water level. It was most vulnerable when the drifting object collided with the pillar at the edge of the building.
As described above, studies on drifting object collisions by tsunamis were mostly conducted under inclined beach conditions. In Korea, as of May 2024, the lengths of natural and artificial coastlines are 9,670 km (63%) and 5,571 km (37%), respectively (KHOA, 2024). Artificial coasts have increased continuously by approximately 16.16 km compared to 2023. In particular, most revetments for main coastal facilities (e.g., nuclear power plants, ports, and power plants), coastal roads, and coastal cities are upright or have concrete blocks installed together. Few studies have examined the drift behavior or collision of objects during the overtopping and inundation processes of tsunamis on such artificial revetments. Recently, some studies have been conducted on the hydraulic characteristics of tsunamis, drift of objects, and collisions on artificial coasts. The effects of the revetment type on the overtopping (Lee et al., 2022a) and inundation (Lee et al., 2022b) of tsunami waves (solitary waves) were analyzed through hydraulic experiments and numerical analysis. Kim et al. (2023) developed Open CV-based object recognition software to track the drift behavior of containers by tsunamis on a vertical revetment (VR) and wave absorbing revetment (WAR). Hwang et al. (2023) and Hwang et al. (2024a) analyzed the experimental images of Kim et al. (2023) using motion analysis software DIPP-Motion. They compared the travel path, drift speed, and maximum drift distance according to the tsunami height, container weight, and revetment type. Containers on land drifted faster and farther on a WAR than on a VR as the flow cross-section decreased gradually in the inclined breakwaters of the WAR and the horizontal flow velocity developed. Hwang et al. (2024b) carried out collision experiments on VR considering the tsunami height, detached distance of the container (distance between the container and port crane), and container weight. They reported that the contact conditions between the two objects varied according to the floating condition of the drifting container, and the uncertainty increased as it completely floated. In other words, the collision speed of the fully floating container increased because of the reduced bottom friction. Nevertheless, the probability of face-to-face collisions (head-on collisions) decreased due to floating body motion. For this reason, larger collision forces occurred under experimental conditions with relatively low collision speeds (face-to-face collisions) compared to the experimental conditions of fully floating conditions (high collision speeds).
In this study, hydraulic experiments were performed to understand the collision between a drifting container and a port crane under WAR conditions. In addition, the characteristics of the collision between the drifting container and port crane leg were examined according to the tsunami height, detached distance of the container (distance between the two objects), and the load and weight of the container. Furthermore, the collision characteristics of the drifting container according to the revetment type and the experimental results considering VR conditions (Hwang et al., 2024b) were compared and analyzed.
2. Hydraulic Experiments
2.1 Wave Flume
In this study, 1/40-scale hydraulic experiments were performed in a wave flume with a piston-type wave paddle with a length, width, and height of 37 m, 0.6 m, and 1 m, respectively, as shown in Fig. 1. This system was used by Hwang et al. (2024b) who applied VR to analyze the collision characteristics of the container drifting by a tsunami on a WAR. The depth of the flume (h) was 47 cm, and an impermeable vertical wall (VR) was placed 27.05 m away from the wave paddle. A 1:2 WAR composed of a rubble mound and wave-dissipating blocks (tetrapod, TTP) was installed on the sea side of the vertical wall. Here, the rubble mound was composed of crushed stone with an average particle diameter, average weight, and porosity of 7.72 mm, 2.2 g/ea, and 0.46, respectively. In addition, TTP, with an average weight of 368 g/ea and a porosity of 0.5, was placed in two layers. The revetment height was 52 cm, and the crest height (Fb) from the water surface was 5 cm. A container model with free movement and a crane leg model with a load cell on top was placed on the impermeable land area with a length of 750 cm.
In this study, the bottom of the crane could not be fixed because of the experimental conditions, and quasi-static experiments that fixed the top were performed.
2.2 Models of Container and Crane
In the experiments, this study used the 1/40-scale acrylic container and crane leg model used by Hwang et al. (2024b), and the targets were the 20 ft International Organization for Standardization (ISO) container and the leg of the J100 ship-to-shore (STS) crane. The 20 ft container had a weight (W0), maximum loading weight (Wmax), and maximum weight (Wtotal) of 2,080 kg, 28,230 kg, and 30,480 kg, respectively. The following two container models were used in the experiments: Model-A (Whalf =W0 +Wmax/2) with half of the maximum loading weight and Model-B (Wfull =W0 +Wmax) with the maximum loading weight. Table 1 lists the detailed specifications of the container prototype and the models.
The leg of the J100 STS crane was placed on land 100 cm away from the coast, and a load cell was fixed at its top to measure the collision force. The specifications of the leg were 1,340 to 2,830 mm × 1,730 mm, and its cross-sectional area decreased toward the top (Kosbab, 2010). In this study, for the convenience of experiments, the cross-section of the crane leg was simplified and set to a 40 mm × 40 mm cross-section by applying a square (1,600 mm × 1,600 mm). The leg height of the crane was also set to 560 mm to meet the conditions of the wave flume because it was not possible to consider 17,560 mm.
Acrylic container and crane models were used in this study. Hence, their properties are different from those of the actual materials.
2.3 Experimental Conditions
Three initial positions of the container were considered in the experiments, and the detached distances (D) from the coast were 10, 50, and 80 cm. In this instance, the gaps (G) between the crane leg at x = 100 cm (x/h = 2.13) and the container were 83.9, 43.9, and 13.9 cm. Thus, the non-dimensional detached distances (D/h) for the initial position of the container were 0.21, 1.06, and 1.7, and the non-dimensional gaps (G/h) were 1.79, 0.93, and 0.3.
The maximum water level (ηmax) measured at WG1, where the waveform of the tsunami generated by the piston-type wave paddle stabilizes, is defined as the incident wave height (H0). In this instance, the position information of the wave paddle required to generate tsunami waves was calculated based on the equation reported by Katell and Eric (2002). In the container drift experiment (Kim et al., 2023), the three tsunami conditions shown in Table 2 were used for the drift of the container to the x = 100 cm point where the crane leg was fixed. Considering the scale applied in the experiment, the wave heights were 4, 5.8, and 7.48 m, which corresponded to a wave height similar to the tsunami height (5.1 m) that occurred in Japan after the Noto Peninsula earthquake, a lower wave height, and a higher wave height. In Table 2, Le is the effective wavelength (
= 4.24 h ∊
2.4 Measurement and Analysis
The collision forces of the drifting container were measured using Bongshin Loadcell’s B3X23 fixed at the top of the STS crane leg. This three-axis load cell can measure the forces in the x, y, and z directions by up to ±500 N. The electrical signals transmitted from the load cell were converted into forces in HIOKI’s LR8450 data logger.
Images were captured using the two cameras (Canon’s XA45) placed on the top and side of the flume to record the inundation of tsunamis, the drift of the container, and the collision process. The imaging sections on the top and side were 160 and 120 cm, respectively, including some of the breakwaters of the WAR and the STS crane leg. The position, speed, and acceleration during the drift-collision process of the container were calculated from the images captured using the camera installed on the top, as shown in Fig. 1. Numbers were assigned to each side of the container model, and markers were attached to four corners and the center. In addition, a grid of 10cm intervals was displayed at the bottom of the land area for distance calibration in the captured images. Motion analysis software DIPP-Motion (DITECT, 2024) was used for image analysis. DIPP-Motion tracks markers through the binarization of grayscale, and it corrects the radial and tangential distortions of the camera and lens through its processes. Hwang et al. (2024a) and Hwang et al. (2024b) examined the reliability of DIPP-Motion. These studies can be referred to for detailed analysis methods and verification.
3. Experimental Results
3.1 According to Tsunami Height
Fig. 2 presents the collision characteristics of the drifting container Model-A(Whalf) according to the tsunami height under the D/h = 0.21 (G/h = 1.79) condition. The (a) location of the container, (b) spatial distribution of non-dimensional drift speeds (
V / g h V c / g h
The drifting container was further accelerated, and the drift speed also increased as ∊ increased (Figs. 2(a) and 2(b)) because the fluid force acting on the container increased due to the increase in the inundation height of the land area and the bottom friction decreased because of buoyancy. Therefore,
V c / g h
In the hydraulic experiment that considered a WAR (Lee et al., 2022b), Table 3 lists the maximum inundation height (IH ) at the x/h = 2.13 point where the crane leg was located when the tsunami waves under the conditions of ∊ = 0.21, ∊ = 0.31, and ∊ = 0.4 caused inundation. The critical depths (dcr ) required for Model-A and Model-B to fully float were calculated to be 2.78 and 5.17 cm, respectively, using Eq. (1) proposed by Yao et al. (2014), and is also listed in Table 3. Because Model-A met IH/dcr >1.0 under all tsunami incident conditions, the drifting container collides with the crane leg when it is fully floated, as shown in Fig. 3. In addition, the tsunami wave height and the collision force have a linearly proportional relationship because face-to-face collisions occur mostly under all conditions.
where ρs and hs are the density and height of the drifting object, and is the density of water.
3.2 According to Detached Distance
In Fig. 4, with the same configuration as Fig. 2, the collision characteristics of Model-A that drift due to the tsunami of the ∊ = 0.4 condition were compared and analyzed according to D/h or G/h. The black, blue, and red colors in Fig. 4 represent the initial positions of D/h = 0.21 (G/h = 1.79), D/h = 1.06 (G/h = 0.93), and D/h = 1.7 (G/h = 0.3), respectively. As with Fig. 3, Fig. 5 shows the images of the collisions between the drifting container and crane leg viewed from the side according to D/h.
The drifting container in the fully floating condition can move freely because IH caused by the tsunami under the ∊ = 0.4 condition is 2.23dcr at the location of the crane leg. In addition, because D/h increases as the non-dimensional detached distance D/h decreases, the distance for sufficient acceleration of the drifting container is secured, and the influence of the bottom friction decreases. Therefore,
V / g h V c / g h V c / g h V c / g h
3.3 According to Container Weight
Fig. 6 compares the behavior of Model-A (Whalf) and Model-B (Wfull) to understand drift-collision characteristics according to the container weight. Here, the incident condition of the tsunami was ∊ = 0.4. The black solid lines and symbols represent Model-A, and the red dashed lines and symbols represent Model-B.
dcr required for full floating increases as the container weight increases. The dcr values of Model-A and Model-B were 2.78 and 5.17 cm, showing a 1.86-fold difference (see Table 3). Therefore, the heavier Model-B had lower drift speed, acceleration, and collision speed than Model-A under the larger influence of bottom friction (Figs. 6(a) to 6(c)). Model-B drifts and collides in the fully floating condition because IH/dcr at ∊ = 0.4 is 1.2 in Table 3, as shown in Fig. 7(c). On the other hand, at ∊ = 0.21 and ∊ = 0.31, the drifting container collides with the crane leg while it is not under fully floating conditions because IH/dcr is lower than 1.0, as shown in Figs. 7(a) and 7(b). In Fig. 6(d), larger was caused by Model-A with a higher collision speed at ∊ = 0.21 and by heavier Model-B at ∊ = 0.31. The results were similar at ∊ = 0.4.
These phenomena occurred because collision forces are significantly affected by the contact conditions between the two objects, as discussed by Lee et al. (2024) and Hwang et al. (2024b). In other words, of Model-A is larger than that of Model-B because a face-to-face collision occurred for Model-A under the ∊ = 0.21 condition, whereas a face-to-line collision occurred for Model-B due to the yawing caused by uneven bottom friction and fluid force, as shown in Fig. 8. A comparison of Fig. 3 and Fig. 7 showed that Fh,max of heavier Model-B was larger at ∊ = 0.31, which mostly causes face-to-face collisions because there is no significant difference in the collision speed between Model-A and Model-B. In addition, Fh,max of Model-B is similar to that of lighter Model-A with a face-to-face collision because a line-to-face collision occurs for Model-B that drifts by the tsunami of ∊ = 0.4 due to pitching in the fully floating condition.
3.4 According to Revetment Type
The experiment results that considered the VR (Hwang et al., 2024b) and WAR (this study) conditions, respectively, were compared and analyzed to assess the drift-collision characteristics of the container located at D/h = 0.21 (G/h = 1.79) according to the revetment type. Fig. 9 shows the drift-collision process of the container on land because of the invasion of the tsunami of ∊ = 0.4 over time. Fig. 10 was configured in the same manner as Fig. 2, and the collision characteristics of the VR and WAR were compared. The black dotted lines and symbols represent the VR, and the blue dotted lines and symbols represent the WAR.
The bottom of the container was submerged and subjected to fluid force for the VR at the time point when the container began to move (t = 0 s) because of the wedge-shaped tsunami bore (Fig. 9(a)). On the other hand, the container began to drift for the WAR because of the tsunami bore with a certain water level or higher, as shown in Fig. 9(b). On the VR, the drift of the container began at a lower water level than the WAR and the drift speed was low under the influence of bottom friction. The container collided with the crane at a higher water level than the WAR because the drift speed was much lower than the tsunami inundation speed. Furthermore, the inundation speed was higher because the VR had a higher maximum water level than WAR during tsunami overtopping, increasing the difference in the drift speed of the container.
According to Lee et al. (2022b), the runup height of the tsunami on VR was higher than the WAR because of the rapid development of the vertical flow velocity at the front of the revetment, but the water level decreased rapidly as the vertical flow velocity was converted into the horizontal flow velocity on land and flow separation occurred at the corner. On the WAR, the inundation speed increased because of the development of the horizontal flow velocity caused by the reduced water cross-section while the tsunami passes through inclined breakwaters. The momentum flux, which is the numerical analysis results for tsunamis by Kim et al. (2023), was larger for the WAR than the VR, and it was maintained further. On the WAR, the tsunami of ∊ = 0.4 was maintained to the point of D/h = 2.13 at which the crane leg was located. Therefore, the acceleration and travel speed of the drifting container were higher for the WAR compared to the VR, as shown in Figs. 10(a) and 10(b). Consequently,
V c / g h
Hwang et al. (2024b) that the VR. They reported that Hwang et al. (2024b) that the VR. They reported that
V c / g h
4. Conclusion
Hydraulic experiments were performed to investigate the collision characteristics of drifting containers and port cranes by tsunamis flowing into land through a wave-absorbing revetment (WAR). The drift and collision behaviors of a container were analyzed using the images obtained from the experiments and DIPP-Motion. In addition, the collision forces of the drifting container were measured through the load cell installed at the top of the crane leg model. The major experiment results according to the tsunami wave height, initial position of the container (detached distance and separation distance), container weight, and revetment type were as follows.
(1) The inundation height of the land area increased as the incident wave height of the tsunami increased. In addition, the drifting container floats due to buoyancy, reducing bottom friction. Consequently, the drift speed increased as the wave height increased, resulting in collision speeds of 1.59, 2.28, and 2.48 m/s and collision forces of 45.18, 65.53, and 77.68 N, which were 15.58, 10.4, and 6.45 times larger than when there was no drifting object.
(2) The distance and time for free movement of the drifting container increased as the detached distance decreased. This decreased the probability of face-to-face collisions between the drifting container and the crane leg.
(3) The critical depth required for the container to float increased as the weight increases. Therefore, the drift speed and collision speed of Model-B filled with cargo were 0.88 and 0.89 times those of lighter Model-A under the significant influence of bottom friction. The collision force of the drifting container was dominated by the weight and collision speed, but it was also significantly affected by the contact conditions.
(4) The overtopping and inundation phenomena of tsunamis varied according to the revetment type. Therefore, in the case of the WAR that significantly developed horizontal flow velocity because of the gradually reduced water cross-section in inclined breakwaters, the acceleration and drift speed of the drifting container were higher than the VR, increasing the collision speed and collision force by 1.32 and 1.48 fold.
In summary, the factors that affect the collision forces of drifting objects include the size of the tsunami, the weight of drifting objects, the location of objects (detached/separation distance), and the revetment type. On the other hand, the contact conditions discussed by Lee et al. (2024) and Hwang et al. (2024b) also had a significant impact on the collision forces. Moreover, the probability of face-to-face collisions decreased as the inundation height increased (full floating of the drifting object). The distance between the two objects increased, and the weight of the drifting object decreased. Hence, it is difficult to generalize the collision force calculation in collisions of drifting objects because the contact conditions are significantly affected by the floating conditions. Therefore, in the design that needs to consider the collisions of drifting objects, it is essential to apply face-to-face contact conditions that cause the maximum collision force. Meanwhile, incident wave conditions similar to actual tsunamis (Lee et al., 2022c) will be examined further because solitary waves cannot perfectly replace tsunamis. In addition, numerical analysis methods (Hwang et al., 2022; Seo et al., 2022) that can directly analyze fluid-structure interactions will be used to predict the collision forces of large objects and their drift and collision behavior.
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