SIMULATION OF INUNDATION CAUSED BY TSUNAMI VIA UNDERGROUND CHANNELS

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1 SIMULATION OF INUNDATION CAUSED BY TSUNAMI VIA UNDERGROUND CHANNELS Kazunor ITO 1, Yuknobu ODA 1, Atsush FURUTA 1 and Yurko TAKAYAMA 1 Approprate seawalls can protect landsde from tsunam nundaton. But, n a case that a coastal ndustral faclty has an underground water channel, even f a seawall works properly aganst tsunam attack, sea water comes nto landsde va the channel. So, ths study focused on tsunam nundaton va an underground channel caused by tsunam. Numercal smulaton methods were dscussed and verfed by usng physcal model test results. Keywords: tsunam; nundaton; underground channel; overflow; two-phase smulaton INTRODUCTION Tohoku Earthquake Tsunam, whch has occurred on 11 March 11, made us re-realze the mportance and dffculty of protectng human lfe and nfrastructures from devastatng tsunams (Mor and Takahas 1, Suppasur et al. 1). Hence, we have to re-consder whether we can expect all tsunam rsk events wthout oversght from the vew pont of Busness Contnuty Plan (BCP). Usually, seawalls and dkes are constructed to stop the tsunam nundaton. In case of ndustral facltes facng to sea, such as a power plant, a chemcal factory and so on, seawalls and dkes could protect the facltes from tsunam nundaton. However, these facltes are often connected to the sea by the underground channels such as ntake/outfall and dranage channels. Even f seawall functons properly aganst the tsunam nundaton, sea water could come nto the landward sde va underground channels. Ths event s descrbed as `nundaton nsde seawall` (IIS). Ths research s focused on IIS, whch was often overlooked as tsunam rsk, and we studed about the smulaton method of nundaton on the landward sde of the seawall comparng wth a physcal model test. In hydraulc desgn phase of an underground ntake/outfall channel and dranage channels connectng to the sea, surgng analyss s executed normally n order to avod overflow from pts. Surgng phenomena n underground channels such as an ntake/outfall and dranage channels s encouraged by hgh waves and tsunams. In ths process, water nsde pts oscllates vertcally durng the tme of hgh wave and tsunam attack. Snce magntude of the water oscllaton s orgnated due to the resonant phenomena between confguraton of the channels and wave perod, a conventonal one dmensonal surgng smulaton s appled to confrm whether or not hghest water levels n pts are below the ground level under the desgn condtons. If the conventonal one dmensonal smulaton has an applcablty to evaluate nundaton on the landward sde of the seawall caused by tsunam, t s very effectve from an engneerng vew pont. So that, physcal model tests were conducted to examne whether or not surgng phenomena and nundaton on the landward sde of the seawall are smlar (Fg. 1). And, two knds of smulaton methods were studed here. One of them s three dmensonal smulaton based on Volume of Flud method (VOF). The other one s mproved one dmensonal surgng smulaton. There s a possblty that nundaton on the landward sde of the seawall could occur due to storm surge. In a case of storm surge, lead tme, that someone makes counter measures such as gate operaton, pluggng to avod occurrence of nundaton on the landward sde of the seawall, s enough long. However, snce earthquake and tsunam occur suddenly and people have to evacuate from tsunam, t s very dffcult to make the counter measure actons n a case of tsunam. Ths s a dfferent pont about the nundaton on the landward sde of the seawall between a storm surge and tsunam. HYDRAULIC PHYSICAL MODEL TESTS Model Equpment and Experment Cases Hydraulc physcal model test shown n Fg. was conducted to nvestgate whether or not surgng phenomena and nundaton on the landward sde of the seawall are smlar phenomena. If dstrbuton of overflow volume from pts corresponds to dstrbuton of surgng ampltudes n each pt, surgng phenomena and nundaton on the landward sde of the seawall would be smlar. The physcal model tests were carred out by usng wave flume of Technology Center, Tase Corporaton. Slope type bathymetry was set n the flume. Long perod regular wave was appled by 1 Technology Center, Tase Corporaton, Nase-cho Totsuka-ku, Yokohama, Kanagawa, 45-51, Japan 1

2 COASTAL ENGINEERING 1 non-reflected wave generator. Generated wave perods were 1s and s. The wave heghts were 3cm, 5cm and 7cm. Underground ppe channels wth 16mm and 31mm dameters were nstalled and fve pts Sea wall Overflow nsde the sea wall Sea wall Tsunam attack Tsunam attack A B C D E A B C D E (a) Illustraton of nundaton nsde the sea wall (b) Surgng phenomena Fgure 1. Explanaton vew of IIS and surgng phenomena. WAVE MAKER 6.5m Hgh seawall s nstalled to avod tsunam nundaton from quay. 31mm,Horzontal ppe s nstalled avobe water level. 31mm,Horzontal ppe s nstalled below water level. 3m.3m 6m 33.5m.m.4m.m.4m 15.5m (a) Model set for nundaton nsde the sea wall.m.5m@5=.5m.11m WAVE MAKER Addtonal ppes are used to measure surgng ampltude..5m@5=.5m 33.5m (b) Model set for surgng Fgure. Schematc vew of physcal model test. were also mounted. Interval between pts was kept as.5m constantly. Horzontal poton of the channels was set at two elevatons. Dfference of those was that horzontal poton was set under the water or n the ar. Enough hgh sea wall was nstalled n order to stop land over flow from quay. Overflow water volume from pts was measured for dfferent cases of IIS experments shown n Fg. (a). Snce generated wave perod was long, the overflow volume was measured as sum up volume of frst wave and second wave to mnmze the nfluence of reflecton wave from wave generator. Addtonal pts were mounted to measure the surgng ampltude n the pts n case of surgng experments shown n Fg. (b). The surgng ampltude was measured by usng wave gauge n the case that ppe dameter was 31mm. But, snce wave gauge was not able to be mounted nsde 16mm dameter pt, the surgng ampltude was not able to measure n the case of the 16mm dameter. The detaled descrpton of the experment condtons are presented n Table 1. Results of Physcal Model Test and Numercal Smulaton Objectve of physcal model test and numercal smulaton s to evaluate whether or not surgng s smlar phenomena to nundaton on the landward sde of the seawall. So, dfference between spatal

3 COASTAL ENGINEERING 1 3 dstrbuton of surgng ampltude and spatal dstrbuton of overflow volume from a pt s dscussed as follows. Fg. 3 shows tsunam wave profle n front of a quay and tme seres of surgng at pt E. Locaton of pt E s shown n Fg.. Measurement results and numercal smulaton results are ndcated n Fg. 3. Two dmensonal VOF method based on Naver-Stokes equatons was appled for reproducton of tsunam wave profle. The smulaton code s CADMAS-SURF (Isobe et al. 1999a, Isobe et al. 1999b, CDIT 1). Conventonal one dmenson surgng analyss was appled to reproduce tme seres of surgng n pt E. Experment result of tsunam wave profle n Fg. 3 (a) has the solton fsson. Although there s dscrepancy around crest poton of the wave profle wth solton fsson, smulaton results by usng CADMAS-SURF reproduced experment result qualtatvely. It was a same stuaton about surgng profle shown n Fg. 3 (b). Agreement between the experment result and the conventonal surgng analyss results was substantally good. There s a clear dfference between tsunam wave profle and surgng profle. Tsunam profle has orgnal s perod oscllaton mode and 1s perod oscllaton mode came from solton fsson. On the other hand, a surgng profle shown n Fg. 3(b) has oscllaton mode wth about 5s. Ths 5s mode could be resonant mode of an underground ppe channel. Table 1. Experment condtons. Case Horzontal ppe Ppe and pts dameter [mm] Wave heght [cm] Wave perod [s] AW-1 Under the water 31 7 AW- Under the water 31 5 AW-3 Under the water AW-4 Under the water AA-5 In the ar 31 7 AA-6 In the ar AA-7 In the ar 31 5 BW-1 Under the water 16 7 BW- Under the water 16 5 BW-3 Under the water BW-4 Under the water BA-5 In the ar 16 7 BA-6 In the ar BA-7 In the ar 16 5 Fg. 4 ndcates dstrbuton of maxmum surgng ampltude n a pt. Fg. 5 shows dstrbuton of overflow water volume from a pt. In the case of maxmum surgng ampltude, the dstrbuton was nearly flat or gradually ncreasng from A to E. But, n case of overflow water volume, the dstrbuton was not flat and t was J shape. It means that overflow volume of pt A and E are larger among all pts whle overflow volume of pt E s the largest. Dstrbuton of overflow water volume s not smlar to that of maxmum surgng ampltude. If both dstrbutons would be smlar, we thought that surgng analyss could be evaluaton method to extract a large overflow volume pt before mplementaton of ths experment seres. However, as shown n Fg. 4 and 5, snce results of experments was not smlar between surgng and overflow, t was found clearly that conventonal surgng analyss does not have applcablty to estmate overflow water volume from pts. Ths s one conclusons of ths experment seres (Ito et al. 1). A mechansm of dfference between surgng phenomena and overflow phenomena s dscussed here. Backwater nsde channel s governed by water dfference of a pt back and forth. For nstance, overflow volume from pt A ncreases n the occason when water dfference between pt B and tsunam heght n front of a seawall s large. When overflow from each pt s contnung, the pezometrc head of each pt s lmted by ground elevaton. It s nevtable that water dfference of a pt

4 4 COASTAL ENGINEERING 1 back and forth s very small. Dvdng flow between a horzontal ppe and pt becomes week and domnant momentum of backwater transports to termnal poton of channel. Snce termnal poton s just bend shape, overflow from termnal pt ncreases. But, snce tsunam surface elevaton n front of a seawall s hgh, water dfference between tsunam and pt B s always large. So, overflow from pt A s larger than pt B and C. Water surface elevaton [m]..1. Experment result CADMAS-SURF Tme [s] (a) Tsunam wave profle n front of a quay Exprment result Conventonal surgng analyss Water surface elevaton[m] Tme [s] (b) Surgng n Pt E Fgure 3. Tme seres of tsunam and surgng profle. (Case AW-1) Max. Surgng amp. [cm] AW-1 AW- AW-3 AW-4 AA-1 AA- AA Sea sde [cm ] Land sde Fgure 4. Dstrbuton of maxmum surgng ampltude Overflow volume [cc] AW-1 AW- AW-3 AW-4 BW-1 BW- BW-3 BW Sea sde [cm ] Land sde Overflow volume [cc] AA-5 AA-6 AA-7 BA-6 BA-5 BA Sea sde [cm ] Land sde (a) Horzontal ppe s set below SWL (b) Horzontal ppe s set above SWL Fgure 5. Dstrbuton of overflow water volume

5 COASTAL ENGINEERING 1 5 THREE DIMENSIONAL NUMERICAL SIMULATION OF TSUNAMI OVERFLOW VIA UNDERGROUND CHANNELS Smulaton Method and Reproduce Smulaton of Physcal Model Test As the smulaton method, three dmensonal two- phase (water and ar) smulaton model (CDadapco 1) was appled to reproduce the tsunam overflow volume. Governng equatons are Naver- Stokes equatons and Contnuty equaton. Smulaton scheme s Fnte Volume Method (FVM) and water surface was smulated usng Volume of Flud Method (VOF). Turbulence model, whch had been used, s the standard k- model. Unstructured mesh system was employed as computatonal flexble mesh. Mesh sze for both x and y vares from.4m to 1m. In case of z, mesh sze vares from.4m to.1m. Fg. 6 shows the comparson of overflow volume between physcal model test and three dmensonal numercal smulatons. Smulaton carred out for case AA-5 s shown n Fg. 6. Tsunam overflow volume gven by the two- phase smulaton has good accuracy. It was found hgh applcablty of the two-phase smulaton (Furuta et al. 11). Fg. 5 and Fg. 6 ndcate very mportant matter from the vew pont of Busness Contnuty Plan (BCP). Overflow volume of termnal pt E, located landward sde s largest. If an underground water channel shown n Fg. s a water ntake channel or a dscharge channel of a power plant, normally a pump system s nstalled at pt E. Further, electrc faclty and devces are also set around pt E. Hence, there s hgh possblty of overflow attacks to the electrc facltes and devces n ths stuaton. In the case of a bg tsunam attack to the ndustral faclty such as a power plant, an energy storage base and a chemcal factory, a hgh seawall wll be constructed n order to avod land overflow from a quay. But, even f a hgh seawall worked properly, sea water comes nto land sde va an underground channel. Physcal model test shown n Fg. does not have a specal model scale. If the model scale s assumed as 1/1, dameter of the underground channel s nearly 3m and total length s 5m. Tsunam heght s 7m. These sze and condton are correspondng to a large-scale channel of power plant etc. So that, experment results presented n ths paper descrbed that nundaton nsde seawall (IIS) s a rsk event of tsunam BCP for ndustral facltes located n seasde. Further, t emphaszes that IIS should not be gnored. Overflow volume (cc) Experment -phase smulaton Seaward sde locaton of pts landward sde Fgure 6. Comparson of overflow volume between experment and numercal smulaton Case Study of Inundaton Insde Seawall for Realstc Dranage Channel Network An underground channel shown n Fg. has smple shape and confguraton. But, n the case of a real underground dranage channel for an ndustral faclty, the confguraton s complex. Because dameter sze of channel changes dependng on locaton and some channels are connected at a pont of a manhole. In ths secton, behavor of nundaton on the landward sde of the seawall n the case of a realstc underground dranage channel network s dscussed.

6 6 COASTAL ENGINEERING 1 Fg. 7(a) shows an mage of a faclty that has a realstc underground dranage channel network. It s assumed that the faclty s some materal storage base and plan scale s 3m x 3m. The faclty has an enough hgh seawall that can stop tsunam overflow from a quay. There are roads n the model faclty. A dranage channel network s bured under the roads. Parameters of the dranage channel network are plotted n Fg. 7(b). The dranage channel network conssts of 4 lnes (A, B, C, and D seres). A1 to D are locatons of each manhole. Parameters of the dranage channel network were desgned based on Japanese water works desgn manual. Dameter of ppes vares from.3m to1m. Dameter of manhole s 1m. Ppes are nstalled wth slope. The slope s vares from 1/1 to 1/. One dran pont at quay s set to 1.8m below the stll water level. Fg. 8 shows computatonal mesh of a manhole poton. Computaton was carred out accordng to the three dmensonal two- phase (water and ar) smulaton model as descrbed n prevous secton. Incdent tsunam wave was long perod regular wave wth perod s. Computatonal mesh sze along the ppe axs drecton vares from.1m to 3.8m. The mesh sze along the rght-angled drecton to the ppe axs vares from.46m to.94m. The mesh sze of vertcal drecton of manhole vares from.75m to.17m. (a) Model mage of a faclty (b) Model parameters Fgure 7. Model of a realstc underground dranage channel network Fgure 8. Computatonal mesh of a manhole poton. Fg. 9 and Fg. 1 show the case study result for a realstc dranage channel network. Fg. 9 shows tme seres of water surface elevaton n front of a seawall. As shown n Fg. 9, maxmum water surface elevaton s 9.4m. But, snce heght of a seawall s more than 9.4m, overflow from a seawall does not occur. In ths case, overflow on the landward sde of the seawall comes from each manhole. Fg. 1 shows snapshots of numercal smulaton. These snapshots are stuaton of second tsunam attack. At frst, overflow appeared at manhole A1, located just behnd seawall. Overflow from other manholes also occurred and sea water comes from manhole A6 located at most landward sde fnally. Stuaton of frst tsunam attack was smlar to the stuaton of second attack. But, overflow from manhole A6 due to frst tsunam attack s smaller than second wave attack. Fg. 11 shows numercal smulaton results under the ground. There s closed ar n the ppe. When frst tsunam attacked to a quay, an underground dranage channel was flled wth sea water. And, overflow from a manhole started. In the occason of backrush tsunam, seawater nsde an

7 COASTAL ENGINEERING 1 7 underground dranage channel started to return to the sea. Then free surface appeared n the ppes. Snce dscharge from the underground dranage channel took long tme, second tsunam attack started before the completon of the dscharge. Then, closed ar was generated n the ppes. Snce ppe system has slope as mentoned n prevous secton, seasde elevaton of a ppe s lower than landsde. If there s no flow velocty nsde a ppe, closed ar n a ppe could move toward the landsde by the buoyancy and s exhausted va a manhole. However, closed ar generated by second tsunam attack moved wth sea water toward landsde, t pushed sea water that remanng nsde a ppe. So, the closed ar encouraged overflow from landsde manholes smlar to the plug flow. Water elevaton(m) 1 t=4s 8 t=44s 4 t=46s t=48s Tme(s) Fgure 9. Tme seres of water surface elevaton n front of a seawall Fgure 1. Snapshots of numercal smulaton on the ground (a) t=415s (b) t=83s Fgure 11. Snapshots of numercal smulaton under the ground Fg. 1 shows overflow volume from each manhole. Snce overflow volume of manhole A1 s much larger than the others, the result of manhole A1 s not ncluded n Fg. 1. The volume n Fg. 1 s total volume due to frst and second tsunam attack. There s a specfc characterstc n overflow

8 8 COASTAL ENGINEERING 1 volume dstrbuton of A1 to A6 located n lne. Overflow volume from seaward sde manholes s large and the volume from landward sde manholes s small. Ths trend s dfferent from expermental results shown n Fg. 5. Snce an underground dranage channel shown n Fg. 7 s more complex than the experment model shown n Fg., form loss of the underground dranage channel s also larger than the experment model. It s a reason why there s the dfferent trend. But, overflow volume from a termnal manhole A6 s larger than one of A5. It could be smlarty between the underground dranage channel and the experment model shown n Fg.. As the results, t was found that even f an underground dranage channel has complex confguraton, nundaton on the landward sde of the a seawall could occur. Further, overflow from a termnal manhole located landward sde occurs, even f the overflow volume s not so much. Ths concluson has an mportance from a vew pont of BCP. Ths result descrbes that nundaton nsde a seawall (IIS) should be consdered as one of the crucal tsunam rsk events. Because, f the overflow reaches electrc devces, the devces are defntely damaged. When the volume of the overflow s large, we could lose evacuaton roots. Moreover, f evacuatng people observe overflow n ther ahead evacuaton root, t could be hard to keep gentle refuge acton. Overflow volume(m^3) Termnal Termnal A A3 A4 A5 A6 B1 B B' B3 B4 C1 C D1 D Fgure 1. Snapshots of numercal smulaton under the ground STUDY OF ONE DIMENSIONAL SIMULATION MODEL Applcablty of three dmensonal two-phase smulaton for nundaton nsde seawall (IIS) was dscussed n prevous secton. As an advantage of the smulaton, output such as overflow volume, nundaton area of overflow, the velocty and flud force can be obtaned. On the other hand, the smulaton needs much effort to setup a model and takes long CPU tme. These are dsadvantages of the smulaton. However, a smple smulaton method, that s not much computatonally expensve, s requred from the vew pont of engneerng. Even f an output from the smple smulaton s only overflow volume, t could be enough as prmary assessment of nundaton on the landward sde of the seawall. So that, one dmensonal smulaton model s studed here. STUDY OF ONE-DIMENSIONAL SIMULATION MODEL The three dmensonal two-phase smulaton for nundaton nsde seawall (IIS) was dscussed n the prevous secton. That smulaton can provde much nformaton for nundaton such as volume, nundaton area, velocty and flud force by the overflow water. However, that smulaton requres much computatonal effort such as model settng and long CPU tme. From an engneerng standpont, practcal use gves an advantage on a smple smulaton method. Then we developed a one-dmensonal smulaton model to estmate only the overflow volume, whch gves prmary assessment of nundaton on the landward sde of the seawall. Formulaton of One-Dmensonal Smulaton Model Fg. 13 shows notatons for the one-dmensonal smulaton model. For the sake of smplfcaton, the cross-secton areas of the man (horzontal) ppe and the vertcal pt ppes are assumed to be constant as A h and A v respectvely n ths paper. In a common model for surgng smulaton, the pressure at the bottom of the pt (vertcal ppe) s assumed to be equal to the water level of the pt, and

9 COASTAL ENGINEERING 1 9 the acceleraton of the water of the man ppe unt s estmated as lnear to the water level dfference between the both end ppes ( -1 ). The dfference equatons derved from the contnuty equaton and the momentum equatons for the common model are expressed as the followng equatons: A t h v 1 A v v (1) v g t L -1 [loss] where the loss denotes the energy loss of head by the frcton and the ppe form. () z x n wn pn vn w+1 +1 Av v+1 Ⅰ Ⅱ w Ⅲ v Ah -1 w-1 v-1 L L+1 L Fgure 13. One-dmensonal smulaton model. Fg. 14 shows the maxmum surgng ampltude and the overflow volume estmated by the abovementoned common model compared wth the model test results. As for the surgng ampltude (Fg. 14(a)), the estmatons show good agreement wth the model tests. On the other hand, the estmated over flow volumes are much larger than the model test at the sea sde pts, especally for large overflow cases. The local pressure dfferences n the vcnty of the bottom of pts (e.g., between I and III on Fg. 13) are neglected on the common model and t s consdered to cause ths error. Max. surgng amp. [cm] AW-1 AW- AW-3 AW-4 model test common model Sea sde Land sde (a) Maxmum surgng ampltude Overflow volume [ml] model test AW-1 AW- AW-3 AW-4 common model Sea sde Land sde (b) Overflow volume Fgure 14. Comparson of the estmaton by the common model wth the model test. As for the control area enclosed by the sectons I, II and III n Fg. 13, the veloctes at the sectons are respectvely represented as v I, w II and v III. In the case of nflow (v III < ), the pt s also nflow (w II > ) and the bottom of pt s to be dverson. The absolute velocty of the secton III s larger than that of the secton I, so that the pressure at the secton III should be less than that of the secton I. On the common model, ths pressure dfference s neglected and t causes overestmatons of the overflow of the sea sde pt. The energy loss coeffcent for dverson s gven as the followng equaton (Gardel 1957): f.58q.6q.3 (3) d B where q B s represented as the rato of the flow rate of the branch ppe of the man ppe before dverson,.e., q B = - w II / v I here. The pressure dfference between the sectons I and III are shown n Fg. 15 wth the parameter of q B. The broken lne s derved from the dfference of the velocty heads at the secton I and III, whch s calculated consderng the energy loss by Eq. (3). The postve value means that the pressure at the secton I s larger than that of the secton III. The pressure dfference B

10 1 COASTAL ENGINEERING 1 shown by the sold lne n Fg. 15 s derved from only the dfference of the velocty heads, not consderng the local energy loss. When w II s small, the energy loss s small and the pressure dfference can be equal to the velocty head dfference. When w II becomes larger, the local energy loss cannot be neglected and the pressure dfference becomes smaller than the velocty head dfference. In ths model, the pt veloctes are assumed to be small compared wth the man ppe velocty. The pressure dfference generated at the vcnty of the pt bottom s assumed to be equal to the velocty head dfference. p p v v p (4) Ⅰ Ⅲ 1 (Δp/ρg)/(v (III) /g) Dfference of velocty head Equaton (3) w (II) /v (III) Fgure 15. Dfference of the pressure at dverson pont. In the case of confluence (e.g., v III <, w II < ), the energy loss coeffcent s gven as the followng equaton (Gardel 1957): B.97.6 q f q (5) c where q B s represented as the rato of the flow of branch ppe to the man ppe after confluence, and q B = - w II / v I here. denotes the rato of area A v /A h. Fg. 16 shows the pressure dfference between the sectons I and III derved wth Eq. (5) n the same way of Fg. 15. In Fg. 16, the dot lne shows the pressure dfference calculated as the velocty head dfference, and the sold lne shows the pressure dfference calculated as the momentum dfference assumng that the momentum flux from the vertcal pt s neglgble. Opposte to the case of dverson, the pressure of the secton I s less than that of the secton III, because the velocty of the secton I s larger. Fg. 16 shows that when s nearly equal to, the pressure dfference calculated wth Eq. (5) s equal to the momentum dfference. Because the area of the pt A h s much small and the velocty of the nflow from the pt s vertcal lke jet flow, there s no horzontal momentum flux from the pt. Therefore the pressure dfference between the sectons I and III occurs to balance the dfference of the momentum. On the other hand, when =.5, the pressure dfference may be approxmated by the pressure dfference calculated from the velocty head dfference. When s enough large, the vortex nduced at the pt bottom s small, so that the energy loss s small. Hence the pressure dfference equvalent for the dfference of velocty head s occurred. Then the pressure dfference s assumed to be lnearly changng between the velocty head dfference and the momentum dfference accordng to n ths model, gven as: where p p B 1 v v Ⅰ pⅢ 1 (6) 1.4 for.5 for.5 The pezometrc head of the man ppe at the upstream sde for the pt (e.g., the secton III for v < ) s assumed to be equal to the total head. Then the pressure s represented wth Eq. (7) and the momentum equaton of the man ppe unt s expressed as Eq. (8) when v <.

11 p COASTAL ENGINEERING 1 11 p g w Ⅰ Ⅲ g w 1 v v when v 1 (7) v t g - 1 w w 1 1 1v v 1 [loss] when v L L (8) Comparng to Eq. (), the second and the thrd terms of the rght-hand are newly consdered n ths model. (Δp/ρg)/(v (III) /g) Dfference of velocty head Dfference of momentum Equaton (5) w (II) /v (III) α=.5 α=. α=1.5 α=1. α=.5 α Fgure 16. Dfference of the pressure at confluence pont. Valdaton of One-Dmensonal Smulaton Model Fg. 17 shows the comparson of the estmaton by usng Eq. (8) n the same way of Fg. 14. As for the surgng (Fg.17 (a)), the proposed model reproduces the result of the model test wth good accuracy smlar to the common model (Fg. 14(a)). As for the overflow (Fg.17 (b)), the proposed model also has a good agreement wth the model test result, comparng wth the common model that cannot reproduce the model test shown n Fg. 14(b). It s found that t s necessary to consder the pressure dfference at the bottom of the pt to estmate the overflow from the pt. The valdaton comparng the calculaton results by the proposed model and the common model wth the model test result s shown n Fg. 18. The common model sometmes gves much overestmaton, but the proposed model can reproduce the model test result wth good accuracy. Max. surgng amp. [cm] AW-1 AW- AW-3 AW-4 model test proposed model Sea sde Land sde (a) Maxmum surgng ampltude Overflow volume [ml] AW-1 AW- AW-3 AW-4 model test proposed model Sea sde Land sde (b) Overflow volume Fgure 17. Comparson of the estmaton by the proposed model wth the model test.

12 1 COASTAL ENGINEERING proposed model common model Calculatom [ml] Model test [ml] Fgure 18. Comparson of the calculatons wth the model test. CONCLUSION Ths study s focused on tsunam nundaton va an underground channel caused by tsunam. Approprately nstalled seawall can protect landsde from tsunam nundaton. But, snce coastal ndustral facltes such as a power plant and a chemcal factory and so on, use sea water, those are connected wth underground water ntake/water dscharge channel. Even f a seawall functons properly aganst the tsunam attack, sea water could come nto the landsde va the channel. Ths phenomenon was called as nundaton nsde seawall (IIS) n ths paper. Characterstcs of IIS were researched through hydraulc physcal model test and three dmensonal two-phase numercal smulaton. In desgn phase of an underground channel, surgng analyss s carred out n order to examne a relatonshp between the channel elevaton and ground elevaton. If the surgng analyss has potental to evaluate IIS, t could be effectve analyss. So that, surgng phenomena and IIS were compared by usng physcal model tests. As the result, t was found that they have dfferent characterstcs. Especally, a remarkable characterstc of IIS was that overflow volume due to IIS was larger at landward sde termnal pt. It was confrmed quanttatvely usng three dmensonal two-phase numercal smulatons, whch could reproduce IIS phenomena ncludng the remarkable characterstc. And t was ponted out that IIS s should be consder as an mportant event from a vew pont of Busness contnuty plan for coastal ndustral facltes. Addtonally, t was demonstrated by usng computatonal case study such that IIS could occur n case of a realstc underground dranage channel wth complex shape and confguraton, too. It was ndcated that IIS closely related to losng of evacuaton routs durng tsunam attack. Although three dmensonal two-phase numercal smulatons has a hgh performance to evaluate ISS, the larger computatonal loads s one of the man dsadvantage. Therefore, a smple smulaton method, whch s not computatonally expensve, s requred from a vew pont of engneerng. Accordngly, one dmensonal smulaton method was developed and verfed by usng experment results. REFERENCES CD-adapco 1, METHODOLOGY STAR-CD VERSION.4.14, CD-adapco. Coastal Development Insttute of Technology of Japan, 1. Research and development of a numercal wave flume; CADMAS-SURF, Report of the research group for development of numercal wave flume for the desgn of martme structures, (n Japanese). Furuta. A., K. Ito and Y. Oda. 11. Smulaton of Overflow Phenomena va Underground Dranage Channels and Pts caused by Tsunam. Journal of JSCE, Ser. B (Coastal Engneerng), Vol.67, pp.6-1. (n Japanese)

13 COASTAL ENGINEERING 1 13 Gardel,A, 1957, Les pertes de charge dans les ecoulements au travers de branchments en te, Bulletn Technque de la Susse Romande, No.9-1. Isobe.M., X.Yu, K.Umemura and S.Takahash. 1999a. Study on Development of Numercal Wave Flume, Proceedngs of Coastal Engneerng, JSCE, Vol.46, pp (n Japanese) Isobe, M.; Takahash, S.; Yu, S.P.; Sakakyama, T.; Fujma, K.; Kawasak, K.; Jang, Q.; Akyama, M., and Oyama, H., 1999b. Interm development of a numercal wave flume for martme structure desgn. Proceedng of Cvl Engneerng n the Ocean 15, JSCE, (n Japanese) Ito. K., Y. Oda, Y. Takayama and A. Furuta. 1. Basc Study on Overflow Phenomena va Underground Dranage Channels and Pts caused by Tsunam. Journal of JSCE, Ser. B (Coastal Engneerng), Vol.66, pp (1). (n Japanese) Mor. A., and T. Takahash. 1. Natonwde post event survey and analyss of the 11 TOHOKU EARTHQUAKE TSUNAMI. Coastal engneerng journal, JSCE, Vol.54, No.1, pp Suppasr. D., S. Koshmura, K. Ima, E. Mas, H. Gokon, A. Muhar and F. Imamura. 1. Damage characterstc and feld survey of the 1 great east Japan tsunam n Myag prefecture. Coastal engneerng journal, JSCE, Vol.54, No.1, pp