HYDODYNAMIC LOAD ON THE BUILDING CAUSED BY OVETOPPING WAVES Xexe Chen 1, Wael Hassan,3, Wim Uijttewaal 1, Toon Verwaest, Henk Jan Verhagen 1, Tomohiro Szki 1,,3, Sebastiaan N. Jonkman 1 Wide crested dike can redce the kinetic energy of the overtopping wave and make the overtopping wave to flow back to the seaside. If a coastal town were bilt on or near a dike, the overtopping wave rnning on the dike crest generates the force which can affect the bildings located in its path. However, qantifying the hydrodynamic load on the bilding cased by overtopping waves is not straightforward becase little empirical formlas are given in literatre for this kind of configration. Therefore, physical scale model research was carried ot. The prpose of this research is to come p with a relationship describing the force on a vertical wall exerted by the overtopping wave as a fnction of wave parameters and geometrical characteristics. Keywords: Overtopping wave; hydrodynamic load; vertical wall; wide crested dike INTODUCTION Natral disasters sch as earthqakes, tsnamis, and floods have occrred freqently in the past decades. For example, the flooding in Japan cased by a tsnami on 11 March 11, swept away boats, hoses and cars along the north-eastern Japanese coast. In late Agst 5, flooding de to hrricane Katrina also left more than 4, homes in Loisiana ninhabitable, damaged, or destroyed (FEMA, 6). And in 4, the tsnami wave cased by an earthqake in Indonesia, one of the biggest natral disasters in recent hman history, killed at least 9, people and affected the livelihood of millions of people in more than ten contries. Existing bilding codes, design practices and disaster planning methods pay little attention to flood load, related to earthqakes and wind impact on bildings. This is mainly becase the bildings are always bilt far from the coastal line or the flood defense strctre (Wilson et al, 9), bt tsnami and storm srge may bring the waves inland. If the strctres are bilt on top of the crest of the sea dike, the overtopping wave cased by tsnami, storm srge or other forms of waves occrring in coastal areas might reslt in hydrodynamic loads on them. By far, little research has been done involving the overtopping waves impacting pon the bildings. Dring the storm season, this is for example the case at the Belgian coast where hoses and hotels are constrcted on top of the dike, see Figre 1. This paper presents reslts from the physical model test which aims to nderstand the behaviors of overtopping wave cased by storm srge and its hydrodynamic load on bildings. Figre 1. Schematic of overtopping on the wide dike 1 Hydralic Engineering, Delft University of Technology, Stevingweg 1 Bilding 3, Delft, 68 CN, The Netherlands Flanders Hydralics esearch, Berchemlei 115, Antwerpen, 14, Belgim 3 Dept. of Civil Engineering, Ghent University, Technologiepark 94, B-95 Ghent, Belgim 1
COASTAL ENGINEEING 1 EXPEIMENTAL TEST Physical model set-p The physical model tests were exected on a schematized model scaled 1/3 (Chen, 11). The scaled model is simplified to clarify the basic hydralic characteristics. The simplified model consists of two parts: a schematized sea dike and a schematized bilding (a vertical plate), referring to Figre a. This bilding was secred to the both sides of the wave flme. Several aspects have been exclded in the model, sch as the foreshore profile, sea walls, and the slope of the crest and the roghness of the crest. The tests were performed in a D small wave flme (length 3 m, width.7 m, height.86 m) in the Flanders Hydralics esearch laboratory (Antwerp, Belgim) nder reglar wave condition which generated by a piston type wave generator. The testing process involved impacting the vertical plane with a series of waves and recording the force by one load cell, for pressre sensors (P1, P, P3, P4), overtopping wave maximm srface elevation by two wave probes and incident wave srface elevation by six wave gages. De to time constraint, the nmber of tests had to be restricted and so only a limited nmber of parameters cold be varied. Despite these restrictions, the experiments revealed the impact process of overtopping wave very well nder the two dike configrations inclding the dike side case and the inland case with a dike crest width of.5 meter in the model scale (referring to Figre b). (a) Physical model set-p (b) Two configrations of the test: dike side case (left) and inland case (right) Figre. Schematic of overtopping on the wide dike Figre 3. Sketch of load cell, pressre sensors and integrating method
COASTAL ENGINEEING 1 3 Data Acqisition The data were collected by a 13 channel-real time data acqisition system. In the present stdy, the water srface elevation was measred by six wave gages and two wave probes with a sampling rate of Hz. Note that the water srface elevation is not the key research target, so the highest sample rates for wave gages didn t explore in this stdy. In order to determine the sampling rate of load cell and pressre sensors, three series tests were done by the same reglar wave conditions for the dike side case, with water level.6 m, wave height.6 m and wave periods 1.8s. The sampling rates of load cell and pressre sensors were varied among 1 Hz, Hz and 5 Hz. Both of the signals of the load cell and pressre sensors reveal that the higher sampling rates can captre larger peak vales; however, the difference among the peaks of the three sample rates was not obvios. De to limitations in time and capacity of data acqisition system, the sampling rate was kept at Hz to allow for acqisition of load data dring the trials. The sampling dration was nominally 1 seconds. ESULTS Observations of raw data Figre 4 and Figre 5 show the sample signals of the force time series for overtopping waves with wave period of 1.54 seconds for both the dike side and the inland cases. In order to verify the repeatability of the test, the load cell force time series signals for the two tests are given in Figre 4 and 5 (black line and red dash line). Comparing the signals, it appears that there is a mch better repeatability for reglar wave tests in the dike side case than the inland case. In order to verify the reliability of test reslt, the measred force signals from load cell are compared with pressre sensors by integrating method (see Figre 3). For the dike side case, the force signals from the two different instrments match qite well, bt it is clear that the load cell can t catch p the load with short dration, bt the pressre sensor can do it (for example, the first peak in the pressre signal in Figre 4). However, for the inland case, there are lots of noise in the signals, this is noise can be explained by the poor cooling system of pressre sensors if they are nder wet condition. Therefore, all the data analyzed in the present stdy were based on that obtained by load cell. Measred force signal (from pressre sensors) agrees with compted force nder hydrostatic condition Figre 4. Sample of overtopping wave load time series signals for the dike side case
4 COASTAL ENGINEEING 1 Measred force signal (from pressre sensors) agrees with compted force nder hydrostatic condition Figre 5. Sample of overtopping wave load time series signals for the inland case For the hydrodynamic load of the waves on a vertical wall, it always composite by two peaks, one is de to the initial dynamic impact, and the second one is de to the reflection of rn-p water (Martin et al, 1999., Fjima et al 9). The two-peak signals were also observed from the overtopping waves. In Figre 6, t r is the rising time of hydrodynamic load, while t d is the total dration of hydrodynamic load. t d is abot.45~.55 seconds, which is closed to the 3% of wave period for the both the dike side case and the inland case. However, in the present stdy, the wave period ranges from 1. seconds to 1.8 seconds, so it is difficlt to say that t d depends on the wave period or is independent with constant time dration arond.45~.55 seconds. The green line in Figre 4 and 5 represent the force calclated nder a hydrostatic conditions sing the rn-p height recorded by wave probe (WP) in front of the wall (refer to Figre ). As a comparison grop with measred force by load cell and pressre sensors, the hydrodynamic force is smaller than the assmed hydrostatic force which is calclated by Eqation 1, in which h is the measred rn-p height. This behavior is mch obvios in the dike side case. For convenience, in the following section, this compted hydrostatic force named as the rn-p force. Fstatic.5 gh (1) It is interesting to see that there is an agreement between the measred force and the rn-p force dring the process of the water falling down in both of the dike side case and the inland case (the red frames in Figre 4 and 5). The agreement between these two forces indicates a hydrostatic condition at the wall after the overtopping wave reflected by the vertical wall. This is in line with the finding by amsden (1996), see Figre 6 (left). Figre 6. Force time series signals for trblent bore (left) (J. amsden, 1996) and force loading time series (right)
COASTAL ENGINEEING 1 5 Estimated overtopping wave force The definition of maximm wave momentm flx in Hghes (4) is the maximm depthintegrated wave momentm flx, which has nits of force per nit of wave crest and can be sed for near shore waves. According to Hghes (4), the wave force that has pshed the water p the slope at the instant of maximm rn-p, the flid within the hatched area on Figre 7a has almost no motion and the weight of the flid contained in the hatched wedge area ABC is proportional to the maximm depth-integrated wave momentm flx of the wave before it reached the toe of the strctre slope. Following the argment by Hghes (4), a similar derivation is performed for the overtopping wave force for the inland case (refer to Figre 7b) and the dike side case (refer to Figre 7c). It can be arged that the maximm overtopping wave momentm flx is integrated by water depth in front of the bilding and is proportional to the weight of water contained in the hatched area abcd ( W ) on Figre 7b for the inland case and ABC ( W ABC ) on Figre 7c for the dike side case, i.e. where is an nknown constant of proportionality, W is the weight of water Fmax W () The weight of water per nit width contained in qadrangle abcd for the inland case and triangle ABC for the dike side case shown on Figre 7b and Figre 7c are given by g 1 (3) tan Wabcd H HD abcd W g 1 tan ABC h (4) Where h is the maximm vertical srface elevation from the base of the wall, D is the minimm vertical srface elevation from the base of the wall, H is the elevation difference between h and. D For the inland case, if there is no residal water flow on the crest, D is and H approaches to h. The is an nknown angle between still water level and overtopping wave srface (which is assmed to be a straight line). Sbstitting Eqation (3) and (4) into Eqation (), it yields to a new Eqation (5), where C 1 is an nknown constant relating the angle between overtopping wave srface and still water level. For convenience, the max sbscript has been dropped from the overtopping wave force. F C gh 1 (5) Figre 7. Sketches of wave rn-p and overtopping waves in front of the bilding Figre 8 shows the plots of measred individal overtopping wave load obtained from load cell verss gh for the inland case and the dike side case. Figre 9 gives the relationship of average overtopping wave force verss gh for the inland case and the dike side case. Note that from Figre 9b, decreased scatters can be seen for longer waves. It can be explained that the estimated area ABC in Figre 7c is not trianglar anymore de to the relatively high srface level and weight of water which cased the line AC to be crved instead of a line, so Eqation (4) gives an overestimation for the force. In smmary, sing the concept of wave momentm flx gives a good estimation of overtopping wave force for both the inland case and the dike side case and C 1 is arond.33. F.33 gh (6)
6 COASTAL ENGINEEING 1 Figre 8. Individal measred overtopping wave load verss gh
COASTAL ENGINEEING 1 7 Figre 9. Averaged measred overtopping wave load verss gh
8 COASTAL ENGINEEING 1 Based on Eqation (6) which does not depend on the incident wave characters, the concept of overtopping wave tonge (Martin et al,1999) was introdced to explore the relation between incident wave and overtopping loadings, referring to Eqation (7), where S is the overtopping wave tonge thickness at the beginning of the dike crest, H m is the average vale of incident wave height near the toe of the dike, c is the crest freeboard and is the maximm wave-rn-p height for reglar wave on a smooth impermeable plane slope, recommended by Schüttrmpf (1). Note that there are many formlas which can estimate the maximm reglar wave rn-p on an infinite slope, so in this stdy, all the formlas related to the reglar wave are applied into the Eqation from Schüttrmpf (1). c S Hm (1 ) (7) Figre 1 plots the relation between the average rn p height h in front of the bilding and the wave tonge thickness S for the two cases with the straight best-fit line representing Eqation (8) in Figre 1a, and Eqation (9) in Figre 1b. Therefore, the overtopping wave force can be represented by sbstitting the relationship between the wave tonge thickness parameter ( S ) and the rn-p height ( h ), i.e. Eqation (8) and (9) directly into the Eqation (6) and get two new Eqation (1) and (11). F F h 1.4S (8) h.1s (9) c.51 g( Hm) (1 ) (1) c 1.48 g( Hm ) (1 ) (11) F C g H c ( m) (1 ) (1) Therefore, a niform eqation of the overtopping force can be rewritten as Eqation (1), where C is the coefficient related to the dike crest width, for the inland case, C is.51 while for the dike side case, C is 1.48. The redction effect for crest width of.5 meter is abot 65% in the model scale. For reglar waves, Eqation (1) can give a good estimation for the average measred overtopping wave force, especially for the waves with T 1.54s (See Figre 11). For the inland case (Figre 11a), Eqation (1) gives an overestimation for the waves with short periods ( T 1.s) and nderestimation for the waves with long periods ( T 1.8s). For the dike side case (Figre 11b), the data from T 1.8s series are tested nder one water level condition, so Eqation (11) can t give a good estimation for the waves with long periods. This relative lower level of correlation between the predictions and observation for the waves with different periods cold be explained as that the incoming waves are interrpted by the retrn flow from the previos incoming waves on the crest. This merge of the two direction flows cold weak the relationship between the overtopping wave tonge thickness ( S ) and rn p height ( h ) which will inflence the overtopping wave load on the vertical wall. In the ftre stdy, the merge effect will be discovered.
COASTAL ENGINEEING 1 9 Figre 1. Highest water srface elevation verss wave tonge thickness, (a) inland case, (b) dike side case.
1 COASTAL ENGINEEING 1 (a) B=.5 m for inland case (b) B= m for dike side case Figre 11. Overtopping wave force verss Eqation 1, (a) inland case, (b) dike side case.
COASTAL ENGINEEING 1 11 CONCLUSION AND ECOMMENDATION In this stdy, physical model tests were exected on a schematized model scaled 1/3. The aim was to come p with a relationship describing the force on a vertical plane exerted by the overtopping wave as a fnction of wave parameters and geometrical characteristics. De to time constraints, only two configrations: the inland case and the dike case were explored and the nmber of tests had to be restricted. So only a limited nmber of parameters cold be varied. Despite these restrictions, the experiments revealed the impact process of overtopping wave. The overtopping wave force cold directly be related to the overtopping wave momentm flx, reslting in a simple formlation for the prediction of it. From a theoretical point of view, it is important to increase the test range to investigate the parameters and frther research the physical meaning of the dimensionless parameters., The redction effect for crest width with.5 m is abot 65%. De to the fact that only two widths crest were tested in the present stdy, the relationship between the width and overtopping wave force cold not be presented. Therefore, in the ftre stdy, for the same scale model, variation of the width of crest shold be increased and the effect of the crest width cold be fond ot. ecommendation cold inclde testing instrments for more than 8 pressre sensors to be distribted on the srface of the vertical plane with small spaces between two sensors. The load cell and pressre sensors shold be sampled with a high sample freqency (~1 khz), to be able to catch the peak vales dring a very short time. In order to investigate the overtopping wave crest elevation propagation on the crest, at least two more wave probes shold be eqipped, or other, more accrate instrments sch as laser cold be sed. This is crcial to expand the findings of the present stdy in the ftre. The record for the water srface on the wall shold be measred more accrately and its time series shold be measred with the same sample freqency of pressre and force. For other recommendations, the findings in the present stdy can be compared with other datasets, and sing the reslts to analyses forces on bildings and actal damage to bildings. EFEENCES Chen, X. 11. Hydrodynamic loads on bildings cased by overtopping waves, Master thesis for Delft University of Technology, Delft, Netherlands; Project nmber: 77_59 for Flanders Hydralics esearch, Antwerp, Belgim. FEMA. 6. Hrricane Katrina in the Glf Coast (FEMA 549), Washington DC: Federal Emergency Management Agency. Fjima, K., Achmad, F., Shigihara, Y.,, and Miztani, N. 9. Estimation of Tsnami Force Acting on ectanglar Strctres, Jornal of Disaster esearch., 4(6), 44-49. Hghes, S. A. 4. Estimation of wave rn-p on smooth, impermeable slopes sing the wave momentm flx parameter, Coastal Engineering, 51, 185-114. Martin, F. L., Losada, M. A., and Medina,. 1999. Wave loads on rbble mond breakwater crown walls. Coastal Engineering,37, 149-174. amsden, J.D. 1993. Tsnamis-Forces on a vertical wall cased by long waves, bores and srges on a dry bed. eport No. KH--54, W.M. Keck Lab of Hydralic and Water esorce., Calif. Inst. Of Technol., Pasadena, Calif. amsden, J.D. 1996. Forces on a vertical wall de to long waves, bores, and dry-bed srges, Jornal of Waterway, Port, Coastal, Ocean Eng.,1(3), 134 141. Schüttrmpf, H. F. 1. Wellenüberlafströmng bei Seedeichen-Experimentelle nd Theoretische Unterschngen. PhD thesis. http://www.biblio.t-bs.de/ediss/data/173a/173a.html. Wilson, J., Gpta,., van de Lindt, J., Clason, M., and Garcia,. 9. Behavior of a one-sixth scale wood-framed residential strctre nder wave loading, Jornal of Performance of Constrcted Facilities, 3, 336-345.