Practical Model to Estimate Behavior of Tsunami-Drifted Bodies. Takashi Tomita 1 and Kazuhiko Honda 2

Transcription

1 Practical Model to Etimate Behavior of Tunami-Drifted Bodie by Takahi Tomita 1 and Kazuhiko Honda ABSTRAT Hitorical record of tunami damage have hown u that tunami caue variou damage: inundation, detruction of houe, drift of veel and other. If veel are drifted by a tunami, they have the potential to collide with houe and building and then to caue econdary damage to them in addition to the damage by tunami fluid force. To control and mitigate the damage by the drifted-bodie, we hould undertand and predict the damage at firt. We have, therefore, developed a numerical model to etimate behavior of multiple tunami-drifted bodie practically. The preent model calculate drift motion of each body in term of drag and inertia force acting on the body, and furthermore conider colliion between drifted bodie and between the drifted body and any tructure. After the preent model i implemented into the STO ytem which calculate tunami damage in ocean and coatal area, it i validated qualitatively in comparion with ome imple tet run and applied to the calculation in a model area with actual bathymetry and topography. KEYWORDS: olliion, Drifted Body, Numerical Modeling, Tunami 1. INTRODTION Japan ha good ytem to iue tunami warning. The Japan Meteorological Agency (JMA) i the organization in charge. Local government alo iue evacuation order and adviory if happen of tunami damage i etimated in their region. However, even if the tunami warning and evacuation order are iued, many reident tay at their houe and office to get further information of tunami and do not evacuate actually. I thi good behavior? Each peron decide finally whether he/he hould evacuate or not. Therefore, it i important that each peron image tunami diater which he/he may uffer, before encounter of the tunami. To help the enhancement of people imagination of tunami diater, we have developed numerical imulation and viualization ytem on tunami damage, which i named the STO ytem [1]. A introduced in the 40th panel meeting in the NIST, the STO ytem conit of the numerical imulation model named STO (Storm urge and Tunami imulator in Ocean and oatal area) and a diplay tool which how eaily numerical reult uch a the variation of water urface elevation and water particle velocity a well a damage occurrence area by uing the moving image. Another feature of the diplay tool i that uer of the tool can ee the reult from any viewpoint they want. A hown in hitorical damage record, tunami caue inundation, detruction of houe a well a drift of many veel and other. If veel are drifted by a tunami, they may collide with houe and building, and then caue econdary damage to them in addition to the damage by tunami fluid force. To control and mitigate damage by the drifted bodie, we hould undertand and etimate their behavior. A new numerical model i, therefore, developed and implemented in the STO ytem to etimate the behavior of tunami-drifted bodie. The attractive feature of the model are a follow: 1) it can deal with a large number of bodie, ) calculate not only tranlational motion of each body but rotational motion in the horizontal plane, and 3) conider colliion between the drifted bodie and between the body and any tructure 1 Reearch Director, Tunami Reearch enter, Port and Airport Reearch Intitute, Nagae Yokouka , Japan Reearcher, ditto.

2 . NMERIAL SIMLATOR OF STO FOR ESTIMATION OF TSNAMI DAMAGE The STO ytem i compoed of two part: numerical imulation model and diplay toll of it reult. The imulation model alo conit of 3 ub-model: STO-ML, STO-I and STO-DM. Figure 1 how an example of arrangement of STO-ML, STO-I and STO-DM. STO-ML Tunami ource Port area and other coatal area STO-I STO-DM which tunami reduction wa invetigated around a tunami breakwater, howed that the tunami wa not enitive to the model coefficient in the eddy vicoity coefficient [4]. Therefore, we may ue the default value of the coefficient. STO-DM i the new model added into the STO ytem to calculate the tunami-drifted veel, car, container and other. To calculate behavior of the tunami-drift bodie, thi model ue temporal and pecial variation data of water urface elevation and horizontal velocity calculated by STO-ML and STO-I. The detail of the model are in the next ection. Eay howing of numerical imulation reult i important for reident who may not necearily have enough knowledge to ee the reult. For Fig. 1 Arrangement of STO-ML, STO-I and STO-DM in the numerical imulation model of the STO ytem 1 STO-ML [1] i a multi-level model which i developed with the ue of hydrotatic preure aumption, and therefore can be applied in wide area uch a ocean. To conider vertical ditribution of horizontal velocity, STO-ML deal with a water bain vertically divided into ome layer. STO-I [1] i the fully three-dimenional model, whoe governing equation are the continuity equation to expre the ma conervation and the Reynold-Averaged Navier-Stoke (RANS) equation a the momentum equation in three dimenion. The porou body model by Sakakiyama and Kajima [] i introduced in the dicretized equation of the governing equation to conider the configuration of ea bottom and the hape of tructure oothly. The eddy vicoity i alo conidered in term of implementation of the eddy vicoity coefficient which depend on velocity tructure and a model coefficient in the ame way a Fujima et al. [3]. omparion with the hydraulic experiment, in Fig. Snahot of diplay on water urface elevation uing the STO ytem Fig. 3 Snahot of diplay on damage occurrence area uing the STO ytem (Black bar indicate damage occurrence area)

3 example, a reident may want to ee the reult of tunami damage etimation in the whole area of their city a well a in hi/her reidential area. To atify uch a demand of each reident and diater mitigation officer, the diplay tool of the STO ytem ha the function of howing the reult from any viewpoint. Furthermore, the diplayed reult are not only inundation area and it depth but fluid velocity and wave preure, which are calculated by the STO ytem. Figure and 3 how example of tunami inundation and tunami-damaged area indicated by the diplay tool. Actually the tool how the reult by the moving image, although the figure indicate nahot. 3. NMERIAL MODEL TO ESTIMATE DRIFT MOTION OF BODIES BY TSNAMIS 3.1 Drift Motion Model To calculate drift motion of many bodie by a erie of tunami wave with le computational effort, the numerical model to olve drift motion of bodie doe not calculate water urface elevation and water particle velocity of tunami directly, and utilize the reult on them which are calculated by the other numerical model of tunami. Then, each body i horizontally moved by the tunami-induced drag and inertia force acting on each body. For practical calculation, the hape of each drifted body i approximated by a rectangular olid. Three mode of motion are calculated in the model: urging, waying and yawing, a hown in Fig. 4. It hould be noted that the vertical motion of heaving i conidered o a to keep draft of the body on the water urface. Therefore, the vertical motion i induced by the buoyancy force of the body. heave yaw way urge Fig. 4 onidered motion of drifted body With reference to Ikeya et al. [5], horizontal force in the urging and waying direction, F x and F y, repectively, and momentum around the z-direction, M z, are determined by the following equation: FX (1 ) FDX 1 FDX FMX F (1) Y (1 ) FDY1 FDY FMY M Z (1 ) M DZ1 M DZ M MZ in which 0.95 h h : D D () h 0.05 : 1. D FDX 1 DX 1, dydz DX 1, n n n dydz n F DY1 V V dxdz bvb Vb dxdz (3) b M DZ1 DX 1, YdYdZ DX 1, n n n YdYdZ n V V XdXdZ bvb Vb XdXdZ b G FDX DX G VG BD G VG FDY DY G VG LD (4) VG M DZ l FDX FDY n FMX M LD dy dy t n t V V b F MY M BD dx dx t b t n M MZ M LD Y dy Y dy t n t V V b M BD X dx X dx t b t (5)

4 L, B and D are the length, width and draft depth of floating body, and h the water depth, a hown in Fig. 5. In Eq. 3,, n, V and V b are the ditributed flow velocitie on the ide face of body, a hown in Fig. 6. It i neceary that thee velocitie hould be calculated in the ituation of no drifted body. In Eq. 4, G and V G are the flow velocitie in the urging and waying direction at the poition of the center of gravity of the body a hown in Fig. 6. The firt and econd term in the right-hand ide of Eq. 1 mean drag force induced by the flow going under the bottom of body and running through the ide, repectively. The third term are for inertia force. In the calculation of F DX1, F DY1 and M DZ1, velocity ditribution in the horizontal plane i conidered, becaue eddie hedding from the bottom may not be uniform horizontally depending on the non-uniform velocity. It hould be noted that M DZ1 i modified becaue a drifted body with rotational motion and the ame drift peed a the urrounding flow make rotation indefinitely uing the original M DZ1 by Ikeya et al. Horizontal Plane Vertical Plane Fig. 5 Definition of ize of body Fig. 6 Definition of flow velocitie to calculate fluid force The coefficient uch a DX1, and other are a follow: 0.4 : 0 DX 1, 0.8 : : n 0 DX 1, n 0.4 : n 0 (6) 0.4 : V : V : Vb 0 b 0.4 : V 0 b X Y.0 co 1. in co (7).0 in. in co.0 (8) M 0.09L in( ) l 0.09L in( ) : in( ) 0 :in( ) 0 (9) 3. olliion Model For eaily earching a contact point of a drifted body to another body or a tructure, it i aumed that a contact face i et o a to cover all main part of the body, a hown in Fig. 7, which how an example of a fihing boat. The horizontal hape of a hip which i incribed in the rectangular indicated by the actual body length of L and actual body width of B i urrounded by a contact face line with circular curve with the radiu of R (m) and parallel line with the pacing of R (m). The vertical ection of contact face i the rectangular to cover main part which may collide with anybody. It hould be noted that the volume formed by the contact face i different from the volume for calculation of drift motion, which i indicated in term of L, B and H in Fig. 5. The value of L and B are determined by Eq. 10, conidering Eq. 11. Eq. 10 expree the balance of ma and buoyancy of the body, in which M i the ma of body, D the draft depth of body and w the denity of water. In deed M LBH w (10) L L B B H D (11)

5 At the moment that the drift body collide with anything, it i aumed that the moving peed of the drift body uddenly become zero in the normal direction of the contact face without deformation. B H L R L Subtantial volume for drift motion calculation R D B ontact face Fig. 7 ontact face and ubtantial volume of ma to calculate drift motion H gradually turned to the flow direction a it i drifted by the uniform flow, and the moving peed of the body i alo accelerated. After colliding with a corner of tructure, the body rotate in anti-clockwie direction around the corner, and the body collide again with the ide of tructure. Figure 9 and 10 how the motion velocity of the drifted body and rotation angle, repectively. ntil 350 when the drifted body contact the tructure firt, the direction of body change toward 45 which i the flow direction, the motion peed i alo accelerated toward the flow velocity. After colliding, the motion peed i uddenly down. olliding point with the tructure niform flow 4. TEST ALLATIONS IN SIMPLE ONDITIONS Validation of the drift model i conducted under very imple calculation condition. In the phae 1 of tet run, drift motion of a floating body in a uniform flow ha been invetigated, in which the initial body angle in the flow, the partition number of the body to conider the velocity ditribution in pace, and ratio of water depth and draft depth have been changed. The number of tet run i eight. In the phae, a moving body contacting with a tructure and two bodie colliding with each other have been checked. The number of tet run i even. In total 15 run, the developed drift model provided good reult qualitatively. Initial et point of floating body Fig. 8 Motion of the drifted body in a uniform flow (ae 1-1) Fig. 9 Motion peed of the drifted body Figure 8 how a reult of the tet calculation in the phae, in which a floating body i initially et in the flow of u= 0.5 m/ in the x-direction and v = 0.5 m/ in the y-direction. The body cale are 3 m in the x-direction, 15 m in the y-direction, and 1 m of draft depth, the ma of body i 45 t. In the figure, location of the drifted body are indicated every 30. Before colliding with the tructure, the angle of body Fig. 10 Direction angle of the drifted body

6 5. APPLIATION OF STO SYSTEM INLDING WITH DRIFT MODEL TO ATAL BATHYMETRY AND TOPOGRAPHY The STO ytem i applied to a model area with actual bathymetry and topography, a hown in Fig. 11. Many fihing boat are moored in the water area covered by the dahed thin line, a hown in Picture 1. Since air-born laer profiler data i available in the model area, we can ue the calculation grid ize of m in the area urrounded by the dahed thick line in the figure where STO-I i applied to calculate the tunami in detail. In the outer region, STO-ML with a ingle layer i applied, and the grid ize of 6 m i epecially ued in the area indicated in the figure. STO-ML and STO-I i connected to conduct equence of tunami calculation. The generated tunami in the calculation ha the tunami height of m approximately and wave period of 0 minute at Point A in Fig. 11 in the ituation of no breakwater. If there are the breakwater a hown in the figure, the tunami doe not overtop them, and they can reduce the tunami intruion into the harbor area. If a ubmerged breakwater i additionally intalled in the opening ection of the breakwater, it i anticipated to reduce further the tunami height in the harbor area. A a trial to check the performance of the STO ytem, tunami calculation by the STO ytem i conducted in the ituation of exitence of the breakwater with the ubmerged breakwater, becaue experimental validation of the STO ytem ha hown that it can olve the tunami paing through breakwater with the ubmerged breakwater [4, 5]. The calculation condition are a follow: in ae 1 no breakwater are intalled, and in ae there are breakwater with the ubmerged breakwater which narrow their opening ection area from 7,000 m to 1,800 m. The number of moored veel i 158 in the harbor area. In thi trial, only the firt tunami i picked up in a erie of tunami wave. The initial water urface level i 0.7 m above the mean water level. Point B Point A Depth(m) Fig. 11 Model area where the STO ytem i applied Picture 1 Moored veel in the model area Figure 1 how variation of water urface elevation at Point A and Point B. The water urface elevation at Point B rie 3. m from the initial water urface level (3.9 m from the mean water level) in the cae of no breakwater. However, in the ituation of exitence of the breakwater, it decreae to. m (.9 m). Since the ground height i approximately 0.8 m above the initial water level (1.5 m above the mean water level) around Point B, the tunami run up on the land even if the breakwater are intalled. However, inundation depth i le than m, and then may not caue evere detruction of houe by the tunami. Indeed, Shuto [6] and damage report on the 004 Indian Ocean Tunami have indicated that the tunami of m or more provide complete detruction of wooden houe.

7 The breakwater have another function to control tunami damage. In thi trial, they delay the tart of tunami inundation 90 econd in reidential area near the coat line. Thi time duration provide evacuating people with advantage. Fig. 1 Time variation of water urface elevation The fluid velocity i alo reduced from 3.5 m/ to.1 m/, a hown in Fig. 13 by the intallation of the breakwater. However, it hould be noted that at the opening ection of breakwater (at Point A) the fluid velocity i fatened depending on narrowing of the opening ection. Therefore, we hould conider uch a fat fluid velocity for deign of the breakwater. The reduction of water urface elevation and fluid velocity alo provide reduction of the number of drifted veel. Figure 14 how the ituation jut before inundation tart and 3 minute after the tart of inundation. Both of them are of the cae of no breakwater. In the cae of no breakwater, the tunami with high water urface elevation and fat fluid velocity drift 56 veel: 49 veel broken the mooring ytem, and 7 veel ettled on the land. All boat are not necearily wept by the tunami in the cae of no breakwater. However, if the breakwater i intalled, the firt tunami wave wee only 7 veel on the land. (1) Jut before inundation tart Fig. 13 Time variation of fluid velocity () 3.6 minute after the tart of inundation Fig. 14 Snahot of drifted veel in the cae of no breakwater, uing STO diplay tool

8 6. ONLDING REMARKS The new numerical model i implemented in the STO ytem to calculate the drift behavior of veel and other by tunami. The model can deal with their colliion with tructure and another drifted body. Validation of the model i conducted in the very imple tet run, and it i confirmed that the model give u good reult. Furthermore, we need to validate the model quantitatively. A a trial to how how damage etimation we do by the STO ytem including the drift model, the ytem i applied to a model area with actual bathymetry and topography. Exitence of breakwater, on which the STO ytem i already validated in comparion with experimental reult quantitatively, reduce inundation depth, fluid velocity in the harbor area and the number of drifted veel, and delay the tart of inundation. AKNOWLEDGEMENT We expre incere thank to the Geographical Survey Intitute Japan for upplying the airborne laer canning urvey data of the model area. REFERENES 1. Tomita, T., K. Honda, and T. Kakinuma Application of three-dimenional tunami imulator to etimation of tunami behavior around tructure. Proceeding of the 30 th International onference on oatal Engineering, ASE, Sakakiyama, T., and R. Kajma Numerical imulation of nonlinear wave interacting with permeable breakwater, Proceeding of 3 rd International onference on coatal Engineering, ASE, Fujima, K., K. Maamura, and. Goto. 00. Development of the d/3d hybrid model for tunami numerical imulation, oatal Engineering Journal, JSE, 44(4), Tomita, T. and K. Honda Tunami inundation imulation by three-dimenional model, Proceeding of the 31 t International onference on oatal Engineering, ASE (in pre). 5. Ikeya, T., R. Aakura, N. Fujii, M. Ohmori, T. Takeda and K. Yanagiawa Experiment on tunami wave force acting on a floating body and development of an evaluation method, Proceeding of Annual Journal of oatal Engineering, JSE, 5, (in Japanee). 6. Shuto N Tunami intenity and diater. In Tunami in the world, edited by Tinti, S., Kluwer Academic Pre,