1. Introduction
The Great East Japan Earthquake (magnitude 9.0) and the resulting tsunami of March 11, 2011, caused serious damage to Japan’s fishing ports and villages. It is believed that the fishing port facilities suffered external forces that far surpassed the conventional design requirements.
Field surveys, conducted after the earthquake, reported that a large number of “onshore” seawalls, built behind the fishing ports to protect the villages, collapsed because of the tsunami attack. Although a major reason for the collapse was scouring due to tsunami overflow, frequent reports of the seawalls collapsing without the scouring were also confirmed. On the other hand, conventional methods used to calculate the tsunami-induced forces were often based on the hydrostatic pressure profile that corresponded to a tsunami’s inundation depth. Although recent researches had examined the wave forces on breakwaters and onshore structures, the effects of the slope of bottom topography, the slope of seawall structure, and the distance of the structure from the shoreline were not fully understood. Furthermore, few studies also investigated the wave-force characteristics of the onshore structures under the tsunami overflow conditions. Hence, we had to consider the methods to calculate the tsunami-induced forces on the seawalls.
In this study, we conducted hydraulic model experiments to evaluate the tsunami-induced forces on the onshore seawalls, by changing the conditions of the slope of bottom topography, the slope of seawall structure, and the distance of seawall from the shoreline. Based on the results obtained, we explored the methods to calculate the wave forces under non-overflow and overflow conditions.
2. Hydraulic Model Experiments
The experiments were performed in a wave flume (100 m in length, 2 m in height, and 1 m in width) on a scale of 1/81. Beginning at the wavemaker, the bathymetry consisted of a 47–68 m flat-ocean bottom section, a 17–38 m slope section, and a 15-m flat-land surface section. We installed three kinds of bottom slopes in the ratio of 30:1, 20:1, and 10:1. The seawall was positioned 0–150 m landward from the shoreline (note that the experimental parameters mentioned here and thereafter are described according to the corresponding local scale). The seawall height was set to the one that satisfactorily exceeded the tsunami inundation height for non-overflow conditions, and at 4.6–8.3 m for the overflow conditions. The shoreward slope of the seawall was set to 1:0 (vertical), 1:0.2, and 1:0.5, whereas the landward slope was set to 1:0.5. Using forward paddle movement, the tsunami was modeled as an idealized solitary wave with a half-period of 113–180 s.
3. Results
We analyzed the experimental results by focusing on the “maximum” wave pressure (pmax), which is the wave pressure when its vertically-integrated value (wave force) was maximum. Under the non-overflow conditions, we first examined the vertical profile of the normalized wave pressure, pmax/ρgη (where ρ is the density of water, g is the acceleration of gravity, and η is the inundation depth of the front of the seawall at a time when pmax was measured). We found that pmax/ρgη was not remarkably affected by the change in the slope of bottom topography, the slope of seawall, the period of incident wave, or the distance of seawall from the shoreline, and that pmax/ρgη is 1.0–1.1 times larger than the normalized hydrostatic pressure, z/η (where z is the height from the land surface). Next, we examined the vertical profile of pmax/ρgηmax where ηmax is the maximum inundation depth obtained from experiments that did not use a seawall. It was shown that pmax/ρgηmax increased with the increasing distance from the shoreline. In the non-seawall experiments, along with an increase in the distance from the shoreline, an increase of the horizontal velocity (U), decrease of ηmax, and the resulting increase of the Froude number (proportional to Uηmax-1/2) were also confirmed. Based on the results obtained, we proposed formulae to estimate the wave pressure on the seawalls by combining a function using hydrostatic pressure and its correction factor of 1.1 and a function using ηmax and the Froude number.
Under the overflow conditions, pmax/ρgη did not show a significant dependence on the slope of bottom topography, the slope of seawall, the period of incident wave, or the distance of seawall from the shoreline, and the value was 1.0–1.2 times larger than the normalized hydrostatic pressure. As the magnitude of overflow became smaller, the ratio of the wave pressure to hydrostatic pressure, pmax/ρgz , approached 1.0–1.1, which agreed with the results obtained from the non-overflow cases. Based on the results obtained, we proposed the formulae of the wave pressure for both the shoreward and the landward of the seawall as functions using hydrostatic pressure and correction coefficients.
These findings were mentioned in the design guideline for onshore seawalls, published by the Fisheries Agency and the Ministry of Land, Infrastructure, Transport and Tourism in Japan (November, 2015). We hope that the results of this study will provide useful information in promoting disaster prevention and mitigation measures that will be effective against tsunamis.