Characteristic of tsunami force acting on shelter with mooring

Applied Ocean Research 64 (2017) 70–85

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Characteristic of tsunami force acting on shelter with mooring Andi Ardianti a,b,∗ , Hidemi Mutsuda a , Kento Kawawaki a , Yasuaki Doi a , Takuso Fukuhara c a

Department of Energy and Environmental Engineering, Hiroshima University, Higashi-Hiroshima, Hiroshima, Japan Department of Naval Engineering, Hasanuddin University, Makassar, Indonesia c Tsuneishi Iron Works Co., Ltd, Fukuyama, Hiroshima, Japan b

a r t i c l e

i n f o

Article history: Received 7 October 2016 Received in revised form 28 December 2016 Accepted 15 February 2017 Keywords: Tsunami shelter Mooring Interaction between tsunami and structure Particle based method

a b s t r a c t Tsunami shelter has been designed and built as a refuges in case tsunami occurs. In recent year, different kinds of tsunami shelter have been proposed and developed, which is either a building type or a floating one. The main purpose of this research is to propose a new type of tsunami shelter with elastic mooring in comparison with a fixed type of shelter and to investigate tsunami force acting on the shelter and motions due to tsunami wave. Three different kinds of tsunami shelter were compared, rectangular, trapezoid and streamline type, with two conditions such as fixed on the ground and floating with elastic mooring. To compute interaction between run-up tsunami wave and the tsunami shelters with mooring, the numerical model has been developed by using particle based method, Smooth Particle Hydrodynamic (SPH) coupling with Extended Discrete Element Method (EDEM) for elastic mooring. Based on the validation of tsunami force and shelter motions with experimental results, the numerical results indicated that the model can simulate interactions between tsunami wave and shelter in fixed and mooring case. The result also shows that the tsunami force on the fixed tsunami shelter can be higher than that on the tsunami shelter with elastic mooring and then the mooring system can reduce tsunami force, 35% for averaged value and 50% for maximum one and the surge and pitch motions can be also reduced. The tsunami shelter with elastic mooring system could be a useful option for evacuating from tsunami attacking. © 2017 Elsevier Ltd. All rights reserved.

1. Introduction Tsunami caused by earthquake becomes natural disaster at coastal area in the world, including Japan area. In Tohoku region in Japan on March 2011, the huge earthquake and the tsunami disaster cause lost in lives and properties. According to the data from Cabinet Office [1], more than 21,000 people lost their lives at the time. The recent research reveals that another huge scale earthquakes following with tsunami will attack on Japan coast near future, which is Nankai trough earthquakes that could damage many important cities near coast in Japan. When the source region of tsunami is very close to a populated zone along the coast, evacuation rotes and facilities become a critical factor in lives and properties, especially during tsunami attacking. Ashar, F., et al., [2] suggested that some of tsunami options such as higher building, tsunami tower and tsunami shelter are required in this areas where accessibility to escape from tsunami attacking would be an important factor for a few minutes after earthquake, especially at a

∗ Corresponding author at: Department of Energy and Environmental Engineering, Hiroshima University, Higashi-Hiroshima, Hiroshima, Japan. E-mail address: [email protected] (A. Ardianti). http://dx.doi.org/10.1016/j.apor.2017.02.005 0141-1187/© 2017 Elsevier Ltd. All rights reserved.

residence area near coastal line. According the research by National Tsunami Hazard Mitigation Program [3], there are seven principles for planning and designing area that is vulnerable to tsunamis. The cabinet office in Japan also published a design guideline for tsunami evacuation buildings. Nayak, et al., [4] has examined these guidelines based on the recent tsunami events. Some of the countries including Japan have researched tsunami options as mentioned above for withstanding tsunami attacking near future. Huge breakwaters and tsunami towers over 30 m height have been constructed along coastal line and also underground shelter was constructed as an evacuation place. A small-sized floating shelter for a family has been proposed and developed and the floater improving a lifeboat was also developed. However, there are some disadvantages in these tsunami options such as construction cost, maintenance, a capacity, and accessibility for child, senior citizens and physical handicapped person and safety for floating debris such as car, ship, house and wooden floater. The most important point for tsunami options is to adapt social needs, composition of population and main industry in an evacuated area near coastal region. Therefore many tsunami options should be existed and then they should be selected and combined to protect lives and properties from tsunami under consideration of the disadvantages as above mentioned.

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Fig. 1. Illustration of tsunami shelter with easy access for child, senior citizens and physical handicapped person.

Designing tsunami options such as shelter, tower and protecting structure, tsunami force acting on tsunami options must be accurately predicted. Wave force acting on tsunami options has been investigated in many experimental and numerical studies. Hur, D.-S., et al., [5] have investigated tsunami wave force acting on an asymmetric structure on a submerged permeable breakwater using direct numerical simulations and experimental works in a three-dimensional non-breaking wave field. Nakamura, et al., [6] has performed numerical and experimental works by using fluidsediment interaction model to investigate tsunami run-up and tsunami force on a square onshore structure. Mutsuda, H., et al., [7–10] has conducted numerical works to compute fluid force and impact pressure caused by tsunami wave on a building. Moon, W. C., et al., [11] have performed the experimental works to evaluate pressure on a simplified onshore building. Wei, Z., et al., [12] has investigated impact of tsunami bore on simple bridge piers. They have confirmed that their numerical method can be a useful tool to investigate tsunami force on structure. However, most of the studies have focused on fixed structures. On the other hand, to investigate tsunami force acting on a floating structure, Madurapperuma, et al., [13] has computed impact force on RC columns caused by collision of floating ship containers and Ardianti, A., et al., [14–16] has evaluated a suitable arrangement of buildings and their shaded area in a large populated zone to evacuate from a huge tsunami impact and influence on floating obstacles such as car, ship, house and floating debris, by numerical and experimental works. The results in this study could be useful for revising existing design guidelines, but the validation with experimental result is not enough for evaluating interaction between tsunami wave and floating obstacles. Considering the above mentions, the final goal of this research is to propose and develop a new type of tsunami shelter that is capable of accommodating for one hundred or more people for evacuating from run-up tsunami. In this study, the coupling method Smoothed Particle Hydrodynamics, SPH with Extended Distinct Element Method, EDEM has been developed to compute a fully nonlinear interaction between run-up tsunami with splashing/breaking and tsunami shelter with fixed and elastic mooring. Characteristics of tsunami force acting on shelter and its motions in experimental and numerical works considering fluid structure interaction problem is examined as a preliminary work. This research also focus on configuration of tsunami shelter and its mooring system comparing with a typical and existing shelter.

2. Overview of floating/submerged tsunami shelter with mooring A new type of tsunami shelter, floating/submerged type, has been proposed in our previous works by Mutsuda, H., et al., [10]. The original concept has been proposed by our research group. Figs. 1 and 2 show concept design of tsunami shelter with easy access for child, senior citizens and physical handicapped person and arrangement of seats and equipment including life support system in the shelter. The floating/submerged tsunami shelter has an important concept that is not only to protect tsunami attacking with high water level and strong velocity but also to avoid from them. The research focuses on a large-sized tsunami shelter located near coastal area. The shelter is capable of accommodation for at least one hundred people and even more from run-up tsunami to survive for a few week or more after tsunami disaster. As shown in Fig. 2, the front and back face can be protected by double hull structure which is normally applied for ship building. There are many prepared facilities consisting of emergency medical system, oxygen cylinder, life support system, food storage area, power generation and its battery, communication network system and so on for surviving during a few weeks or more. The windows and doors are stronger for high pressure and watertight. The evacuated people should be supported by seatbelt during tsunami attacking. On the other hand, in usual condition, the seats can be

Fig. 2. Arrangement of equipment and seats in tsunami shelter.

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Fig. 3. Illustrated motion of a floating/submerged tsunami shelter.

packed under the floor and the wider open-space can be provided as a community zone. The floating/submerged tsunami shelter can be supported by a mooring system attached on the ground because a huge tsunami can easily flush the shelter away to inland area or offshore region. This paper focus on elastic mooring system using rubber binding tubes to keep it stable position even though secure situations are occurred. One example of elastic mooring system has been already installed in the international ferry terminal at Hongkong since 2012, to adopt for variability of tidal level (e.g Superflex, www. supflex.com). Fig. 3 shows illustrated motion of a proposed floating/submerged tsunami shelter during low/high water level of tsunami conditions. Using a mooring system and ballast water control, the shelter can be floated on water surface to reduce drag force when low water level of tsunami is less than 3–5m, on the other hand, it can be submerged under tsunami wave when high water level is more than 5–10 m or more to reduce wavy motion caused by run-up tsunami. After tsunami hitting, the floating/submerged tsunami shelter can be used as temporary accommodation and emergency medical center. In usual condition, this shelter can be used as communication space for community hall, storage space for fish or marine product and disaster prevention goods.

reduce numerical diffusion and to keep stable computation and velocity-pressure coupling method is applied with the fractional step method, in which the pressure with a specified jump condition is solved by Poisson equation given by the following equation:

∇ ·(

∇ P n+1 ∗

)=

∇ · u∗

(3)

t

where * denotes a physical value after advection step. The algorithm is similar with SMAC method to avoid pressure fluctuation in SPH method. The computed pressure acting on obstacle can be used in calculating acceleration and solid motion, e.g tsunami shelter, floating debris such as car, wood and some garbage. The governing equations for solid are the continuity equation and momentum equation as follows: D ∂ui + =0 Dt ∂xi 

(4)

Dui ∂ ij i + g i − Ffsi = 0 = Dt ∂xj

where  is the density, ui is the velocity, x is the position vector for j component, ␴ is the stress tensor of solid phase, and Ffsi is the fluid structure interaction term as shown in Eq. (2). The stress tensor in Eq. (5) is given by the following equation, ij

 s = −Pıij + S ij

3. Numerical method

(5)

(6)

where Sij

Robustness and capability for fluid-structure interaction problems using particle based method, especially tracking breaking wave and splashing, have been widely acknowledged. In recent years, fluid-structure interaction problems modelled by using the Smoothed Particle Hydrodynamics (SPH) have been applied in wide range of applications (e.g. Monaghan, J., [17]; Barreiro, A., et al., [18]. Based on particle based method, the proposed and developed model in this study are explained in this section. 3.1. Governing equations In this study, the numerical model has been developed by using the model (Mutsuda, H., et al., [10]) based on SPH to compute fluid force and impact pressure acting on obstacle, this method can also track breaking wave and splashing after colliding with obstacle. The governing equations for fluid phase consist of the continuity equation and the incompressible Navier-Stokes equation:

is the deviatoric stress tensor, P is the pressure computed by eq. (3). The present model can also consider a large deformation of an elastoplastic body to compute collapsing and destroyed structure due to tsunami attacking. The stress on solid obstacle changes at every calculation step by using the following equation:

{dS ij } = [Dep ]{dεij }

(7)

where D is the elastoplastic matrix, dεij is the strain increment of a time, and dSij is the increment of the deviatoric stress for a certain time. To compute rotations of solid obstacle during solid motions in 3D, the Jaumann derivative is used to ensure material frame with respect to the rotation as follow:



dS ij 1 = 2 εij − ıij εij 3 dt



+ S ik ωjk + ˝ik S kj

(8)

where ε the strain rate tensor and is the spin tensor. 3.2. Fluid-structure interactions

∂ui =0 ∂xi

(1) 2

∂ui ∂u 1 ıP  ∂ ui + uj i = − + + gi + Ffsi  ∂xi  ∂xj ∂xj ∂t ∂xj

(2)

where ui is the velocity for each particle i in 3D, gi is the gravity acceleration, Ffsi is the fluid structure interaction term between fluid and solid particles to consider solid motion caused by tsunami force,  is the density of the fluid and  is the viscosity. The governing equations can be solved by using the splitting method as a well-known conventional multiphase technique to

The term Ffsi can be achieved based on the pressure and acceleration of particle in SPH. In the model, the Ffsi in Eqs. (2) and (5) can be given by the following equation: Ffsi (ra ) = −

P(rb ) 1  mb ∇ a · W (ra − rb , h) (ra ) (rb )

(9)

b

where W is the kernel function characterized by a distance between particles, P is the pressure,  is the density, ra and rb is the particle positions, h is the reference area where interaction between particles can be considered, and m is the particle mass. To achieve

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Fig. 4. Two different kinds of spring and dashpot model in Extended Distinct Element Method, EDEM (Left: Normal direction, Right: Tangential direction).

computational robustness and stability, the time increment for solid phase is approximately 1/10 to 1/50 of that for fluid phase.

DOF motions of floating obstacle such as tsunami shelter and debris in this paper. More details can be seen on the previous researches by Ardianti, A., et al., [16] and Mutsuda, et al., [7–10].

3.3. Solid motion 3.4. Mooring motions All obstacles for solid phase are modelled by SPH particles to capture their motions and deformation. Therefore, for three dimensional motions, six degrees of freedom (6 DOF) of obstacle, can be represented by describing translational and rotational motions of obstacle using the following equations: 2

∂ xs,k Fs,k = − Ffsi mi ∂t 2 I

∂ωi = Ti ∂t

(10) (11)

∂ i = ωi ∂t

(12)

where i is the rotational angle, ␻ is the angular velocity, Ti is the torque, I is the inertia moment. In addition, the center of gravity of obstacle can be obtained by solving the inertia moment of SPH particles, and this is based on Baraff’s theory [19], in which the equations of motions in 3D can be given by: rg =

n 1

N

ri

(13)

i=1

 N

I=

m[ri − rg ]2

(14)

i=1

where N is the number of particle for obstacle, rg is the position of the center of gravity, I is the inertia moment, ri is the position of i th particle and m is the mass of the particle. If a rigid body was employed, the inertia moment is assumed to be the same as the initial condition. It should be noted that the inertia moment should be exchanged at every time step for computing motions of an elastoplastic body. In SPH, the coordinates of particles representing obstacle in every time step can be tracked by using the rotation matrix. In general, the Euler angles are conventionally used in rigid body dynamics as a rotational matrix. However, the Gimbal lock phenomena can be sometimes occurred when a body is largely rotated. In this study, the mooring motion caused by tsunami force is unsteady and large in time and space. Especially, when snap impulsive load due to tsunami wave is occurred, the mooring cable is largely deformed and bending at a local segment during a short time. To avoid the gimbal lock and compute a local bending of mooring motion, the quaternion can be used instead of the Euler angles as rotational matrix. This method is enhanced to be applied for 6

In this study, EDEM (Extended Distinct Element Method) proposed by Megro, et al., [20] are employed to compute mooring motions for 6DOF in 3D. To reproduce mooring motions using particles, the continuum condition should be considered by using relationship between neighboring particles. Therefore, in this model, two kinds of springs and dashpots model are used to consider both elastic mooring motions and their collapsing/collision due to fluid force. The two spring-dashpot models including element dashpot model and void dashpot model, are illustrated as shown in Fig. 4. The element dashpot model plays a role of considering contact force between particles and then the void dashpot model for computing connect force between particles assuming the continuum condition. If a collapsing condition is imposed for the void dashpot model, the connect force is released to reproduce it. The governing equations for elastic mooring motions can be represented by Eqs. (15) and (16). ¨ + Ci u˙ + Fi = 0 Mi u

(15)

Ii ϕ ¨ + Di ϕ˙ + Mi = 0

(16)

where u is the vector of deformation, Fi is the force acting on particle i, Mi is the moment on particle i, ␸ is the vector of rotation, Ci and Di are coefficients of damping. The quaternion is also used instead of the rotation matrix in 3D to compute a large motion of mooring and to consider a snap impulsive load caused by impact tsunami force. Based on Heltz theory on the elastic-contact, the spring coefficient kn and ks, and the viscosity-dashpots cn and cs are respectively defined by: kn = [ ks =

2 2 di dj E ( ) en (t − t)] 9 di + dj 1 − 2

1 kn 2(1 + )



cn = 2

cs = cn

mi kn



1 2(1 + )

1/3

(17) (18) (19) (20)

where the subscripts n and s indicate the normal and tangential direction, d is the diameter, en is the drag force due to the spring in the normal, E is the Young modulus and m is the mass for each

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Fig. 5. Computational domain and boundary conditions.

particle and  is the Poisson ratio. These coefficients should be sometimes improved by experimental result to work well in trial and error. 3.5. Numerical conditions In this study, the tsunami shelters are assumed as solid phase without their deformations based on Eqs. (7) and (8) as a preliminary work. The computational domain is X/L = 4.14, Y/L = 4.02 and Z/L = 0.46 height, where L is the length of the shelter, as shown in Fig. 5. The initial water column as tsunami wave is located at the upstream side and also the outflow condition is imposed at the downstream side. The side and bottom walls are supposed with free slip condition. The diameter of particle dp /L is set to be 0.01 for the tsunami shelter and 0.04 for the tsunami wave and walls at the initial condition. The number of particles is about 20,000 for water column and about 30,000 for ground and side walls to work well at each case. To set a designed tsunami as the same experimental wave condition with water level and velocity at the front of the shelter, the distance between the shelter and the water column at the initial condition was decided in trial and error. The length of each mooring lm /L is set to be 0.4 and the motions of the shelter in 6 DOF is considered at the mooring case. The density of particles for the shelter and particle distribution can be decided considering the draft based on buoyancy and gravity center of the shelter. The referenced radius for interaction among particles in SPH is set to be a few times of particle diameter in all phase. The initial water column for tsunami wave is decided by the width and the length and the initial position to generate the same incident tsunami wave in experimental conditions. The time increment tf for fluid phase is set to 0.001 s and the time increment ts for solid phase is controlled to be stable running at each time step, normally ts = 1/20 to 1/100 tf . 3.6. Shelter models To investigate characteristics of maximum impact force and averaged one on the tsunami shelter, the motions of the shelter during tsunami wave attacking, three different types of the tsunami shelter are employed in this research: (1) rectangular type, (2) trapezoid type and (3) streamline type as shown in Fig. 6. The dimension is normalized by the shelter length to wave direction. At the initial condition, the total number of particles for the shelter is about 33,000 to 53,000 to consider a smoothed face. The capacity for evacuation and the shelter height are almost the same condition in all shelters. The rectangular type is one of the typical building as a referenced model. In our previous works, the trapezoid and

streamline types without mooring were proposed to reduce tsunami force and its motions. In the next step, to develop a more sophisticated shelter, mooring system for the shelter is examined to keep the stable condition and safety for evacuated people including small children and senior citizens under tsunami attacking. In this study, to investigate effect of mooring system for the tsunami shelter as mentioned in chap.1, four-points mooring system with 45 deg. at each corner of the shelter in horizontal plane is applied. More detail experimental and numerical conditions for mooring can be shown in the next section. 4. Experimental work 4.1. Experimental set-up The experimental works were conducted in the tsunami wave tank with 40 m length × 1.2 m width × 2.5 m depth as illustrated in Fig. 7. The slope beach with variable ranging from 1/3 to 1/100 at the upstream side of the tank was set up to generate different tsunami wave and velocity for design condition. The plunger type of wave maker is located at about 5 m distance away from the slope. The initial water depth is about 1.25 m. The flat bottom as ground is located for propagating run-up tsunami with several tsunami conditions with considering water level and velocity. The shelter model was located at the rotating table on the ground away from the toe of the slope. The distance between the toe and the gravity center of the shelter model is about 0.95 m. Two different support system such as fixed case and mooring one were performed in the experiment. The tsunami force was measured by the dynamometer supported on the fixed jig with wires, the one used for the fixed shelter case and two dynamometers used for the floating shelter with mooring case. Run-up tsunami wave height was initially measured by the water gauge located on the toe of the slope. The initial tsunami velocity was also measured by using the current meter installed at the same position. The wireless sensor of motions was located inside of the shelter to measure the shelter motions in six degree of freedom such as surge, sway, heave, roll, pitch and yaw. The two video cameras were used to clearly record tsunami attacking phenomena between wave motion and the shelter from the front and back sides. 4.2. Experimental conditions The model scale in this experiment is set to be 1/30 to 1/100 for real scale. Considering the field survey of TOHOKU tsunami earth quake tsunami (Mori, N., et al., [21]), the tsunami wave height

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Fig. 6. Shelter models.

and velocity were decided considering survival conditions based on Froude number. The wave height is set to be 5.9–14.2 cm and the velocity is less than 2.0 m/s at the toe of the slope. The incident wave period in regular wave is set to be two seconds to avoid water disturbance caused by the forgoing wave. The measured data such as wave height, velocity, force and motions were averaged for each periodic wave because the phenomena is quite sensitive for fluid motion with splashing on the shelter. To validate the numerical results, the same types of the tsunami shelter such as rectangular type, trapezoid type and streamline type, were installed in this experiment. The models have the same dimension with the numerical setup as shown in Fig. 8. The mooring conditions are chain, wire and elastic mooring with loose tension. The elastic coefficient for mooring was already selected in the previous works before performing the experiment. The initial setup for the shelter in the experiment is shown in Fig. 8. For the fixed case, the shelter was placed in the center of the rotating table and the dynamometer was placed above the center of the shelter to measure tsunami force on the shelter. Fig. 9 shows the enlarged mooring supported by both the elastic part at the ground and the shelter sides. The dimension of elastic mooring is 50 mm length and 5 mm square. To decide the elastic coefficient considering the existing mooring system, Super Flex (www.supflex. com), the tensile stress experiment was conducted to compare the strain of some elastic materials with different elastic coefficients.

As shown in Fig. 10, the elastic coefficient (2.98 N/cm) was selected in the model scale of this study. For the floating with mooring case, the shelter was located with the mooring at every corners of the shelter, which was four-points mooring system as mentioned in chap. 3. The six-points mooring system was also conducted as shown in sec. 5.1. The dimension of the shelter was 49.7 cm × 14 cm × 4.9 cm for the rectangular and the trapezoid type, 56 cm × 14 cm × 5 cm for the streamline type in model scale as mentioned above. The weight and material of the shelters were decided considering the draft for buoyancy and the gravity center in real scale. 5. Results and discussion In this chapter, the experimental and computational results are presented to clarify a useful mooring condition for tsunami shelter and to investigate characteristics of tsunami force on three different types of shelter and their motions caused by tsunami attacking. The useful conditions in configuration of tsunami shelter and mooring system are examined. 5.1. Experimental results Effect of elastic mooring for reducing tsunami force on tsunami shelter are evaluated in this section. Firstly three different kinds

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Fig. 7. Experimental setup.

of mooring systems attached with a standard rectangular type of shelter were compared in experimental result to decide a useful mooring system. To make clear reliability for supporting tsunami shelter with mooring, three types of mooring such as chain, elastic and wire were employed. The chain mooring could be flexible for multidirectional fluid force and the elastic mooring plays a role of damping

for impact force. In the rectangular type, the comparison of maximum tsunami force acting on tsunami shelter with different kind of moorings is shown in Fig. 11, where H2 is the incident wave height at the toe of horizontal ground and d is the height of the shelter in the projected area from the front view. The result shows that the maximum forces in the elastic and chain mooring cases are lower than those in the wire case,

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Fig. 8. Set up of tsunami shelter on horizontal bed.

Fig. 9. Elastic mooring attached on the corner of tsunami shelter.

Fig. 10. Strain of elastic mooring at each tensile force.

especially the elastic mooring can reduce the impact force caused by collision due to tsunami attacking. The reduced impact forces are almost the same level for the cases of the different wave height. The results mean that the elastic mooring could be a useful technique for reducing tsunami attack and therefore the mooring cost could be also reduced because the mooring cable can be shortened at a smaller constructed area. To evaluate tsunami force on shelter and motions with fourpoints elastic mooring, the rectangular and streamline types of the tsunami shelter were employed as shown in Fig. 6. The tsunami wave height H2 at the toe of the horizontal ground in Fig. 7 was used as the normalization parameter. Fig. 12 shows comparison of the averaged and the maximum tsunami forces in wave direction acting on two different types of tsunami shelter. The averaged force, Fxave , and the maximum one, Fx1max on the dynamometer at the upstream side on the streamline shelter were normalized by g H2 , where the water density is  and the gravity acceleration is g. Fig. 13 shows comparison of

Fig. 11. Comparison of maximum tsunami force acting on tsunami shelter with different kinds of mooring.

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Fig. 12. Comparison of averaged and maximum tsunami forces in wave direction acting on different types of tsunami shelter.

Fig. 13. Comparison of shelter motions caused by tsunami wave.

shelter motions caused by tsunami wave in x, y and z directions respectively. The maximum accelerations Axmax , Ay max and Az max for surge, sway and heave directions, respectively, were averaged using maximum values for each wave, where the tsunami wave height H2 in x axis was normalized by the shelter height d. The yawing motion was quite small comparing other motions and then it can be ignored in this paper. The result shows that the maximum and the averaged tsunami forces on the streamline type are significantly lower than those on the rectangular type in all wave conditions. The averaged reduction rate is also 50% or more and their values are less than 1.5 times for hydrostatic pressure normalized by the tsunami wave height, H2 , which is lower than the regulation for designing on shelter in Japan. The maximum surge motion Axmax is dominant component in the shelter motion and it is quite small in the streamline type, which is the same level with a standard regulation for a ship. The maximum sway Ay max and heave Az max motions are also less than 0.2 normalized by the gravity acceleration. The pitching motion in the streamline type is also lower level than that in the rectangular type. The averaged pitch angle is approximately 3–4◦ .

On the other hand, the rolling motion in the streamline type is relatively larger than that in rectangular type. This is because the overtopping tsunami flow on the streamline shelter is relatively stronger and therefore the pressure on the surface of the shelter would be unstable and the negative pressure causes lift force. Although the maximum value is less than 3 deg., the rolling motion should be reduced with improving the mooring system in the next step. It is evident that the streamline type with elastic mooring could be one of the safety options to evacuate small children, elder and handicap people from tsunami accident. To reduce the tsunami force and the motions, especially the rolling motion, acting on the shelter with four-points elastic mooring as shown in the above results, six-points elastic mooring system was examined in experiment. Fig. 14 shows arrangement of mooring system on tsunami shelter. The mooring No. 5 and 6 were supported at the side of the shelter to reduce the rolling motion. Fig. 15 shows comparison of motions of tsunami shelter supported by different number of mooring. The vertical axis means the reduction rate of motions (surge, sway, and heave) acting on the tsunami shelter with six-points mooring to that with four-points mooring.

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Fig. 14. Different arrangement of mooring system with tsunami shelter (Lower: experimental setup, Upper: layout of mooring).

Fig. 15. Comparison of motions of tsunami shelter supported by different number of mooring.

The tsunami wave height H/d is 0.651, which is one of the survival condition. In Fig. 15, it can be seen that the motions in the six-points mooring are smaller than those in the four-points mooring under the all conditions. The maximum reduction ratio is 50% over in sway motion related with rolling motion. This means that the shelter motions in the six-points mooring can be more constrained than those in the four-points mooring attached on the shelters. The reduction ratio in streamline type is considerably higher level in all motions. The motions in the streamline type can be more stable comparing with other types. It is clarified that the six-points mooring system attached on the shelter could make the shelter stable and therefore it can keep more safety position but the flexibility of the shelter motions between run-up tsunami and return flow would be weakened.

5.2. Numerical results and validations In this section, the developed numerical model coupling SPH with EDEM is validated with experimental results and then

numerical investigation is conducted to evaluate usefulness and effectiveness in streamline shelter with mooring in more detail. Snapshots of tsunami wave attacking with splashing and running on tsunami shelter without mooring supported by the dynamometer are shown in Fig. 16. The numerical results are also visualized with the experimental results just before and after tsunami attacking in different time step. Fig. 17 shows comparison of time histories of tsunami water elevation and tsunami velocity near the front edge of the ground. It can be seen that the computational results are in good agreement with the experimental ones. However, there is small discrepancy in the rising tendency and the fluctuation of the water elevation. Because it is difficult to consider the effect of friction on the steel ground in the experiment and to reproduce unsteady and strongly breaking phenomena with splashing near the free surface at the first stage of the runup tsunami wave, that is, a bore propagating. In near future work, the model should be improved by a specific numerical technique. Fig. 18 shows comparison of time histories of tsunami force for each tsunami shelter, where the vertical axis represents the nondimensional force in x direction, Fx divided by the water density ␳, the gravity acceleration g, and the tsunami wave height H2 . The

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Fig. 16. Snapshots of tsunami wave with splashing and running on tsunami shelter (Top: experiment, Bottom: computation).

Fig. 17. Comparison of time histories of tsunami water level and tsunami velocity at the front edge of the ground.

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Fig. 18. Comparison of time histories of tsunami force acting on tsunami shelters.

horizontal axis represents the non-dimensional time. Fig. 19 shows comparison of maximum and averaged tsunami force on tsunami shelters. In Fig. 18, the results show that the computational results are in good agreement with the experimental ones and they are reasonable to predict the fluid force caused by run-up tsunami acting on the shelter. However, there is small discrepancy in the rising tendency at the start time. It is difficult to consider the effect on the surface friction of the ground in the computational model. As shown in Fig. 17, the front face of the run-up tsunami propagating on the ground has small different between the experiment result and computational one. Therefore, the friction effect on the ground should be carefully considered and the boundary layer near the ground also should be modelled using particles in near future effort. It can be also found that there is fluctuation with high frequency in numerical results. This is because the particle distribution is low around the shelter, especially at the downstream side where the dead water region is emerged and there is not enough number of

particle to compute accurate pressure on the shelter. However, the computational cost and time are larger as the particle density is higher in particle distribution. The high accurate prediction needs a large number particle in near future effort. Fig. 19 indicates that there is same tendency of the tsunami force versus tsunami shelter type. The forces on the streamline type are lower than those on the rectangular and trapezoidal types in the experimental and the numerical results. It is quite evident the front face of the shelter plays an important role to reduce the sudden tsunami attack with breaking during run-up region on the shelter location. But there is small discrepancy in the maximum tsunami force for the trapezoidal type. The inconsistency is about 26% overestimate in numerical result. This is caused by particle resolution and distribution around the shelter as mentioned above. All of the validation indicate that the developed model coupling SPH with EDEM are one of the useful tool for computing interaction between tsunami wave and the shelter.

Fig. 19. Comparison of maximum and averaged tsunami force on tsunami shelters.

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Fig. 20. Snapshots of tsunami wave acting on tsunami shelter with elastic mooring and running on it (Top: experiment, Bottom: computation).

Next validation is related with not only tsunami force but also shelter motions with elastic mooring case. Fig. 20 shows snapshots of tsunami wave acting on tsunami shelter with elastic mooring and running on it to compare numerical results and experimental ones. Fig. 21 shows comparison of tsunami forces and motions caused by tsunami wave to validate the numerical results, where same non-dimensional parameters are used in the above figures. The mooring forces Fx , Fy and Fz were recorded at the locations

No.1 and No.2 as shown in Fig. 14 and the shelter motions Ax , Ay and Az were measured at the gravity center of the shelter. The small discrepancy can be found in peak value and phase shift between the numerical and experimental results. However the numerical results in the motions and forces acting on the shelter are acceptable for computing a strong interaction between shelter motion with elastic mooring and tsunami wave with splashing and breaking. The

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Fig. 21. Comparison of tsunami forces and motions caused by tsunami wave.

coupling method SPH with EDEM could be used to evaluate a shelter type and a mooring system and to optimize them. Fig. 22 shows comparison of computed time histories of tsunami force Fx acting on each tsunami shelter in fixed case and elastic mooring one as shown in Fig. 6. It can be found that the maximum

tsunami force and its averaged level in the elastic mooring case are quite lower than that in the fixed case without mooring. The effect of the elastic mooring to reduce the tsunami force on the shelter can be clearly found, in terms of its maximum impact forces and occurred time of impact forces.

Fig. 22. Comparison of time histories of tsunami force for x-direction, which is acting on tsunami shelter in fixed case and elastic mooring one.

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Fig. 23. Comparison of maximum and averaged tsunami force acting on tsunami shelter with mooring.

To investigate the maximum and the averaged tsunami force in more detail, comparisons between them are shown in Fig. 23. The left figure indicates experimental result and the right one is numerical result. The tsunami forces can be considerably reduced in the mooring case and then they are almost the same level in all

shelters. Using the elastic mooring system, all of the shelter types can be employed as a useful evacuation facility. The numerical model can reproduce the tendency of the forces in both fixed and elastic mooring cases versus the tsunami shelter.

Fig. 24. Comparison of reduction ratio of maximum and averaged tsunami force on tsunami shelter with six points elastic mooring.

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Fig. 24 also shows comparison of reduction rate of maximum and averaged tsunami force acting on tsunami shelter with sixpoints elastic mooring in experimental and numerical result. The reduction ratio is divided by the force in four-points elastic mooring. The reduction ratio in numerical result is consistency with the experimental result and then the averaged ratio is about 35% and the maximum one is over 50%. This result suggests that the sixmooring system can reduce maximum and averaged tsunami force and then the developed numerical model could be reasonable for investigating strong interaction between tsunami shelter and runup tsunami wave and for designing the shelter considering tsunami force and its motion. 6. Conclusions This paper has proposed and developed a new facility for evacuating from tsunami disaster, which is a floating tsunami shelter with mooring to reduce tsunami force and its motion comparing with existing tsunami options. The streamline type of the shelter can reduce the tsunami force and the shelter motions caused by tsunami wave comparing with the rectangular and the trapezoidal type of the shelters. The elastic mooring is also one of the useful technique to drastically reduce the impact pressure caused by tsunami attacking. This paper has also developed the coupling method Smoothed Particle Hydrodynamics, SPH with Extended Distinct Element Method, EDEM to compute a fully nonlinear interaction between run-up tsunami with splashing/breaking and tsunami shelter with fixed and elastic mooring cases. All of the numerical results are reasonable with experimental ones for reproducing the tsunami force and the motions of the shelter. The model could be utilized to design a tsunami shelter with mooring system. In near future effort, the optimization of the shelter size and configuration and the more sophisticated mooring system should be examined based on the results in this paper. The numerical model should be also improved to compute more realistic condition considering arrangement of surrounding buildings in a downtown and also floating debris acting on shelter such as vehicle, house, rubbish and garbage should be considered in this model. Acknowledgements The research work was partially performed by Mr. Fujii at KUBOTA Co. Ltd. The research was supported by Grants-in-Aid for Scientific Research “KAKENHI”, Grant-in-Aid for “Chugoku-SangyoSouzou Center” and Grant-in-Aid for “Challenging Exploratory Research and adaptive and seamless technology transfer program (A-STEP) of Japan Science and Technology Agency”. The authors express thanks to the supports. References [1] Director General for Disaster Management Cabinet Office, Disaster management in Japan, Tech. rep., Director General for Disaster Management Cabinet Office, Tokyo (2015).

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