# Applicability of CADMAS-SURF to evaluate detached breakwater effects on solitary tsunami wave reduction

- Minoru Hanzawa
^{1}Email author, - Akira Matsumoto
^{2}and - Hitoshi Tanaka
^{3}

**64**:13

https://doi.org/10.5047/eps.2011.06.030

© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences; TERRAPUB. 2012

**Received: **29 October 2010

**Accepted: **10 June 2011

**Published: **22 February 2012

## Abstract

Detached breakwaters, made with wave-dissipating concrete blocks such as Tetrapods, have been widely applied in Japan, but the effectiveness of such kinds of detached breakwaters on tsunami disaster prevention has never been discussed in detail. A numerical wave flume called CADMAS-SURF has been developed for advanced maritime structure design. CADMAS-SURF has been applied mainly to ordinary wave conditions such as wind waves, and little attempt has been made for expanding its application to tsunami waves. In this study, the applicability of CADMAS-SURF for evaluating the effectiveness of detached breakwaters on a solitary tsunami wave reduction is investigated by comparing the calculated results with those from hydraulic experiments. First, the effectiveness of a detached breakwater on the reduction of wave height and wave pressure was confirmed both by hydraulic experiments and numerical simulations. Finally, CADMAS-SURF has been found to be a useful tool for evaluating the effects of detached breakwaters on tsunami wave height and pressure reduction, as a first step in a challenging study.

## Key words

## 1. Introduction

Coastal and port-related structures have been designed based on design formula as well as hydraulic model tests. Although hydraulic model tests can precisely reproduce actual physical phenomena, it usually requires time and cost to create seabed configurations and model structures, and to measure various kinds of data such as wave height, wave pressure, overtopped water and the movement of targeted structures. Also, the design formula is usually limited by the range of model conditions that the formula is based on. In addition, more information is required from the viewpoint of reliability-based performance design taking damage level into consideration.

Based on the above situation and recent advances in computer simulation technology, a numerical wave flume called CADMAS-SURF (e.g. Isobe et al., 1999) has been developed for advanced maritime structure design. CADMAS-SURF has been applied mainly to ordinary wave conditions such as wind waves, e.g. wave force onto breakwaters and wave overtopping of seawalls (e.g. Isobe et al., 2002; Goda and Matsumoto, 2003). So far, little attempt has been made to extend its application to tsunami waves.

Maritime structures are exposed to not only wind waves, but also tsunami waves. Damage to coastal structures such as seawalls were actually reported at the time of the South West Hokkaido earthquake tsunami in 1990, and the Japan Sea earthquake tsunami in 1983 (Tanimoto et al., 1983; Tanaka et al., 1993). Researchers have focused their efforts on the study of disaster prevention from tsunamis, especially with seawalls, e.g. Mizutani and Imamura (2000), Asakura et al. (2002) and Kato et al. (2006). In Japan, detached breakwaters have been widely applied, but the effectiveness of detached breakwaters on tsunami disaster prevention has never been discussed in detail. At the time of the Indian Ocean Tsunami in December, 2004, in Male, the main island of the Maldives, detached breakwaters effectively protected the island from the tsunami (Fujima et al., 2006). However, the effectiveness of detached breakwaters on tsunami reduction has not been discussed in detail.

In recent years, the risk of the occurrence of tsunamis generated by near the shore large earthquakes, such as Tokai, Tonankai, Nankai and off-Miyagi earthquakes, is considered to be high. In addition, the occurrence of the great Chilean earthquake in February 2010 caused a large trans-Pacific tsunami. In this study, the applicability of the numerical simulation model called CADMAS-SURF for evaluating the effects of detached breakwaters on a solitary tsunami wave reduction will be discussed.

## 2. Numerical Wave Flume

### 2.1 Basic equations

*t*is the time,

*x, z*are the horizontal and vertical coordinates, respectively,

*u, w*are the horizontal and vertical velocities, respectively,

*ν*

_{ e }is the molecular kinematic viscosity,

*γ*

_{ v }is the porosity,

*γ*

_{ x },

*γ*

_{ z }are the horizontal and vertical sectional transform ratios, respectively,

*p*is the pressure,

*ρ*is the mass density of the fluid, and

*g*is the acceleration due to gravity.

### 2.2 Free surface

*F*of the VOF function is:

## 3. Hydraulic Model Tests

### 3.1 Method of wave generation

*H*is the wave height,

*c*is the wave celerity, and

*h*is the water depth.

*X*(

*t*) in the right-hand part and the non-linearity of

*X*(

*t*). Therefore, the wave paddle position

*X*

_{i+1}at

*t*=

*i*+ 1 is calculated based on Eq. (13), using

*X*

_{ i }at

*t*=

*i*by the Newton-Raphson method:

*κ*(

*ct*−

*X*(

*t*)) of Eq. (12) should be considered, because the wave length of the solitary wave is theoretically infinity. In this study, the time

*t*

_{0}giving the value −0.999 to tanh

*κ*(

*ct*−

*X*(

*t*)) is obtained by Eq. (14) following Goring and Raichlen (1980). From this, the following wave paddle position

*X*

_{ i }, at each time

*t*

_{ i }, can be calculated by Eq. (13) with the initial time

*t*

_{0}.

### 3.2 Sea bed and structures

*x*= 0 m. The slope of 1/5 begins at

*x*= 3.75 m and ends at

*x*= 4.25 m. The slope of 1/30 begins at

*x*= 4.25 m and ends at

*x*= 13.25 m. The flat bed is constructed from

*x*= 13.25 m to 14.75 m followed by a 1/20 slope. This topography represents the typical cross-section around Japanese coasts.

In total, 13 wave gauges were installed from *x* = 2.25 m to 14.25 m (St. 1 to 13) for water surface monitoring as shown in Fig. 1.

*x*= 11.25 m (St. 9) as shown in Figs. 1 and 2. The detached breakwater is made using wave-dissipating concrete blocks of Tetrapods of 59 g with a porosity of 50%. The crown width of the detached breakwater is equivalent to 3 rows of Tetrapod units. The crown height is set with a clearance of 4 cm above the sea-water level which is 0.5 times the wave height equivalent to the stability limit of Tetrapods of 59 g based on ordinary design against wind waves. This is the common method for detached breakwater design in Japan.

*x*= 13.75 m (St. 12), and 7 wave pressure gauges with a capacity of 1.96 N/cm2 were installed on the surface of the seawall as shown in Fig. 3.

*H*

_{0}= 5.3 cm.

Hydraulic model test cases.

Case | Off-shore water depth | Structures | Meas. item | ||
---|---|---|---|---|---|

Detached breakwater | Seawall | Run-up | Wav e pressure | ||

1-1 | 0.43 | — | — | 엯 | — |

1-2 | 0.40 | — | — | 엯 | — |

2-1 | 0.43 | 엯 | — | 엯 | — |

2-2 | 0.40 | 엯 | — | 엯 | — |

3-1 | 0.43 | — | 엯 | 엯 | 엯 |

3-2 | 0.40 | — | 엯 | 엯 | 엯 |

4-1 | 0.43 | 엯 | 엯 | 엯 | 엯 |

4-2 | 0.40 | 엯 | 엯 | 엯 | 엯 |

## 4. Numerical Simulations

As described before, in the hydraulic experiments, solitary tsunami waves were generated based on Eqs. (7) to (14). In the simulation in the numerical wave flume, the same method of wave generation was applied, i.e., the water level and velocity at each time obtained by Eqs. (7) and (9) were given at the wave generation boundary, *x* = 0 m, with the initial time of *t*_{0} as given by Eq. (14). Behind the wave maker, a wave damping area, called the sponge layer, of 4 m from *x* = −5 m to −1 m, was added to suppress wave reflection from the offshore end of the flume.

In the numerical simulations, the horizontal and vertical mesh sizes were set as Δ*x* = 1.0 cm and Δ*z* = 1.0 cm, respectively. Referring to previous researches, the appropriate horizontal mesh size should be chosen by satisfying the equation, *L*/ Δ*x* > 80, where *L* is a wave length. In this study, the wave length *L*, corresponding to the time *t*_{0} obtained by Eq. (14), was 10.85 m for high tide, and 9.74 m for low tide, to satisfy the above criteria. On the other hand, the vertical mesh size was recommended to satisfy equations, *H* /Δ*z* > 10 for general wave conditions, and *H* /Δ*z* > 5 for the weak-linear wave with a wave height smaller than a breaking wave. In this study, *H*_{0} = 5.3 cm satisfies the condition *H*/Δ*z* > 5.

*t*in the simulations is automatically calculated as Eq. (16), where Δ

*t*

_{ c }, determined based on the following CFL condition of Eq. (15), is multiplied by a safety factor

*α*. In this study,

*α*is set as 0.2 based on a preliminary calculation.

The porosity *γ*_{
v
} of the detached breakwater is 50% as mentioned before. The coefficients of drag force and inertia are set as *C*_{
D
} = 1.0 and *C*_{
M
} = 1.2, respectively, by following Sakakiyama and Imai (1996).

The wave flume set-up, as shown in Figs. 1 to 3, is also used in the numerical simulations, where water surface and wave pressure are calculated for the cases shown in Table 1.

## 5. Results and Discussions

### 5.1 Water surface

#### (1) Case 1-1

*H*

_{0}= 5.3 cm. Figures 6(a) and (b) show the hydraulic experimental results and the simulated results, respectively. The wave deformation phenomena from the shoaling process up to St. 10 (

*x*= 12.25 m) is successfully simulated by the numerical wave flume. Even though around St. 12 (

*x*= 13.75 m) within the flat area the simulated result is biugger than that in the hydraulic experiment, the overall shape of the simulated wave agrees well with that of the hydraulic experimental wave.

#### (2) Case 1-2

*x*= 12.25 m). The numerical simulation results agree well with the hydraulic experimental results, but the wave shape landward from the wave breaking point shows less agreement.

#### (3) Case 2-1

#### (4) Case 2-2

As shown in Figs. 6 to 9, the time series of the water surface can be well simulated by CADMAS-SURF before wave breaking. Some discrepancies between the simulated results and the experimental results of the detailed shape of the time series, after wave breaking, can be seen. This might be caused by the difficulty of simulating air bubble inclusion, due to wave breaking, in the numerical simulation.

In the numerical simulation, the water surface at later times tends to descend to a level lower than the initial sea-water level compared with the experimental results. The reason for these discrepancies has not yet been explained and will be considered in future work.

Although there are still problems to be solved, CADMAS-SURF merits application in maritime structure design against solitary tsunami waves with regard to tsunami disaster mitigation, because the incident mode of such waves is generally of critical relevance.

### 5.2 Wave height

*z*= 1.0 cm was chosen by taking the computing time into account. The use of a smaller vertical mesh size to improve the accuracy of the numerical simulation is left for future research.

### 5.3 Wave pressure on the seawall

#### (1) Time series of wave pressure

#### (2) Wave pressure distribution

As discussed in the section concerning water surface comparison, the maximum wave pressure should be taken into account with regard to the design of seawalls against tsunamis.

*p*

_{max}at each elevation is defined as the maximum wave pressure of the time series for each point. Therefore, the time of each

*p*

_{max}is not necessarily the same.

The overall shape of the wave pressure distribution for the high-tide case (Fig. 14(a)) by numerical simulation shows a fairly good agreement with the experimental results. However, the position of the maximum pressure is a little different. As for the low-tide case (Fig. 14(b)), the overall shape of the wave pressure distribution by numerical simulation also agrees well with the experimental results. Better agreement can be seen in the lower area than the upper area.

#### (3) Effect of detached breakwater

As shown in Figs. 14, 15 and 16, the wave pressure distribution can be well simulated by CADMAS-SURF; however, some discrepancies can be noted. These might be caused by difficulties of simulating air bubble inclusion due to wave breaking and wave collision at the seawall in the numerical simulation, as discussed in Section 5.1. Improvement of the numerical simulation to address this discrepancy will be considered in future work.

## 6. Conclusions

- (1)
Water surface variation before the wave reaches the wave breaking point, and up to the front of a detached breakwater was well simulated by the numerical simulations.

- (2)
Wave pressure on a seawall was also well simulated.

- (3)
The effectiveness of a detached breakwater on the reduction of wave height and wave pressure was confirmed both by hydraulic experiment and numerical simulations.

- (4)
The applicability of CADMAS-SURF for tsunami disaster mitigation has been validated.

## Authors’ Affiliations

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