AN EXPERIMENTAL STUDY OF WAVE FORCES ON VERTICAL BREAKWATER

Journal of Marine Science and Technology, Vol., No. 3,. -17 (7) AN EXPERIMENTAL STUDY OF WAVE FORCES ON VERTICAL BREAKWATER Yung-Fang Chiu*, Jaw-Guei Lin**, Shang-Chun Chang**, Yin-Jei Lin**, and Chia-Hsin Chen** Key words: vertical breakwater, wave force, hydraulic model test. ABSTRACT In this study, a series of hydraulic model tests with regular/ irregular waves was carried out in a wave flume to investigate the wave forces acting on a comosite-tye breakwater. Waves in front of the breakwater, wave ressures on the vertical wall and at the bottom of caisson were measured simultaneously. The imum horizontal force and ulift force were calculated and comared with Goda s wave force theories. The results had shown that Goda s theories offer higher safety factor. However, the measured ulift force was smaller than Goda s and nonzero at the land-side end of the bottom which might be caused by the ath of water flow in the orous media beneath the caisson. It also shows that the results from different irregular wave train with the same sectrum are different, and thus the effectiveness of conventional irregular wave tests with several reeats of the same wave train should be reconfirmed. INTRODUCTION Comosite-tye breakwater is the most oular structure for the harbors around Taiwan coast. However, due to the characteristic of Taiwan coast, most of them are constructed on sandy seabed, esecially at Taiwan West Coast. Vertical caisson, large wave force and sandy seabed create a very sensitive circumstance that several kinds of structure failure might occur. From revious relevant studies, such as Oumeraci [] and Coastal Engineering Manual by U. S. Army Cors of Engineering [13], the causes of structure failure can be classified into three tyes: (1) the material strength destruction or the mechanical instability of the structure, () the excetional hydraulic conditions including extreme wave force or excess water level, and (3) the foundation or the seabed instabilities including the scouring and the settlement. However, excet for all these Paer Submitted //, Acceted /9/. Author for Corresondence: J.G. Lin. E-mail: jglin@mail.ntou.edu.tw. *Center of Harbor and Marine Technology, Institute of Transortation, Taiwan. **Deartment of Harbor and River Engineering, National Taiwan Ocean University. individual failure mechanisms, the dynamic behavior of a Comosite-tye breakwater under the interaction among waves, vertical caisson, rubber mound foundation and sandy seabed, might also be the cause of structure failure. Three different tyes of wave force acting on the vertical breakwater are identified: non-breaking waves, breaking waves with almost vertical front, and breaking waves with large air ockets, and therefore hydraulic model tests erformed in the final stage of the coastal structure design become a common sense and a necessary ste [3]. Several wave force theories have been romoted for the evaluation of the wave force acting on vertical wall. For examle, under the assumtion of uniformly distributed loads with averaged wave ressure acting on vertical wall, Hiroi, in 19, roosed the first wave ressure formula. Sainflou, in 19, theoretically derived a simle form of standing wave force formula. In 19, Minikin formula was roosed from the studies of imact force tests. Based on the Ito s continuous loading and imum wave height concets, and the exerimental/field data, Goda, in 1973, obtained four equations for the design load on vertical walls and becomes the most oular equations in the recent coastal structure design. The equations are shown as follow, and the related sketch is shown in Figure 1. η * =.7 (1 + cosβ) H (1) P 1 =. (1 + cosβ) (α 1 + α cos β) ρgh () P = 1 cosh (πh/l) (3) P 3 = α 3 P 1 () P u =. (1 + cosβ) α 1 α 3 ρgh () where, β is incident wave angle; H is the imum wave height in the design sea state at the location just in front of the breakwater; L is wave length; h is the wave deth at a distance of H s seaward of the breakwater

Y.F. Chiu et al.: An Exerimental Study of Wave Forces on Vertical Breakwater 9 front wall; H s is the significant wave height; α 1 =.+. α = min h c h b d 3h b η* h Fig. 1. Goda s wave force distribution. π h / L ; sinh (π h / L) () H d, d H ; (7) α 3 =1 h* h 1 1 cosh (π h / L). () On account of the comlexity of wave behavior in front of a vertical breakwater, the evaluation of wave forces on vertical breakwater are mostly done by hydraulic exeriment in a wave flume. For examle, Oumeraci et al. [11], Schmidit et al. [1], Oumeraci and Kortenhaus [9], Hattori et al. [], Klammer [], Kortenhaus and Oumeraci [], Oumeraci et al. [1]. Regular/irregular wave trains are usually selected as incident waves. Regular wave tests emloyed the reresentative wave height/eriod of incident waves, but u 3 1 d h irregular wave tests emloyed their sectrum. In order to retain the statistical accuracy, the exeriments are always reeated at least three times in both regular/ irregular wave tests. Due to the randomness of ractical waves, however, the wave trains with the same sectrum are always different. So, not only the results obtained from regular/irregular wave exeriments are different, but also the results from each irregular wave tests with different wave train from the same sectrum are different. Such henomenon leads to the suitability investigation of regular/irregular wave exeriments. In this aer, the exerimental data from a series of regular/irregular hydraulic model tests of a comosite-tye breakwater deloyed on a sandy seabed, carried out by Center of Harbor and Marine Technology, Institute of Transortation (hereafter, IHMT) and Deartment of Harbor and River Engineering, National Taiwan Ocean University (hereafter, NTOU), were used to investigate the wave forces on the caisson. Full discussions of the exeriments can be found in Chen [1] and Lin [7]. EXPERIMENTAL SETUP The exeriments were carried out in the wave flume (see Figure ), which is located in Wind Tunnel Laboratory, IHMT. A comosite-tye breakwater (see Figure 3) was built on a sandy seabed (see Figure ) in the wave flume. As shown in Figure, the wave flume is 1 m long, 1. m wide and. m high with iston tye wave maker. The system can generate regular waves and irregular waves with JONSWAP and Bretschneider sectra. The suggested wave frequency range is between. Hz and Hz, the exerimental suggested Wave absorber nd Observation section 1 st Observation section 1.. 31. Wave addle. 1.. 1. 3.. Fig.. Layout of exerimental wave flume (unit: m).

1 Journal of Marine Science and Technology, Vol., No. 3 (7) 31. 9.7.. Armor layer with rock Concrete block Caisson..3 1.. 11. 1. 13.9.. 1. Rubber mound foundation 7.1.. 11. 1.. Filter Fig. 3. Layout of the breakwater (scale 1:3, unit: cm).. 13.9 1.... Fig.. Exerimental setu (unit: cm) 11. Table 1. Exerimental regular wave cases (Case ID in arentheses) Wave eriod T (s) Wave height H (cm).33 13.9 19.. 1. (HT1) 1.33 (HT13) (H13T13) 1.7 (HT1) (H13T1) (H19T1). (HT) (H13T) (H19T) (HT) Remarks 7 reeats without breakwater; 7 reeats with breakwater water deth is 1 m and the imum wave height is.3 m. The model scale of the exeriments is 1:3. In order to simulate the nearshore waves in front of the breakwater (see Figure ), the seabed was combined with one 1:1 sloing bottom with m long to change the water deth from 1.1 m to. m, a fixed horizontal seabed with m long, a sand trench with. m long and.m dee, and a 1. m long fixed bed behind the breakwater to maintain the trench. The water deth in front of the breakwater is. m, and the caisson was set at the distance of.139 m measured from the front edge of the sand trench. According to the model scale, the offshore water deth (1.1 m) is around m in ractice. Two incident wave tyes are carried out in the exeriments. Table 1 shows ten regular wave cases tested in the exeriments, the arentheses show their case ID numbers. The imum wave height was chosen to avoid the wave breaking. The irregular wave cases introduced the reresentative waves shown in Table 1 as significant wave height (H ) and related eriod (T ) into JONSWAP sectrum [] shown as follow

Y.F. Chiu et al.: An Exerimental Study of Wave Forces on Vertical Breakwater 11 S( f )=β J H T P f ex 1.(T f ) where γ ex [ (T f 1) /σ ] (9). β J.3 +.33γ.1(1.9 + γ) 1[1.9.19ln γ ] (1) T T /[1.13 (γ +.).9 ] (11) In order to take into account the hase change effects of each comonent waves in the irregular wave train, each sectrum were generated three wave trains according to different random hases. Table shows the irregular wave cases, each wave train was reeated twice for the cases with breakwater, and once for the cases without breakwater. By considering the daming effect of sandy seabed, the incident waves at different locations were firstly measured before the breakwater was deloyed. A caacitance wave gauge was set right on the location of the breakwater, and 7 reeats for all 1 regular wave cases and one run with 3 wave trains for all irregular wave cases were tested. After the breakwater was set on Table. Exerimental irregular wave cases Wave cases 1 3 f (Hz).9.9.. H (cm).33 13.9 19.. T (sec) 1. 1.33 1.7. Wave trains JHT1-1 JH13T13-1 JH19T1-1 JHT-1 (case ID) JHT1- JH13T13- JH19T1- JHT- JHT1-3 JH13T13-3 JH19T1-3 JHT-3 Remarks 1 without breakwater; reeats with breakwater the seabed, 7 reeats for all regular wave cases and reeats of for all irregular wave cases with 3 wave trains were executed. For the measurements of wave ressure on the breakwater, ressure gauges along the sea-side vertical wall of the caisson for horizontal ressures and ressure gauges on the bottom of the caisson for ulift ressures were deloyed. Figure shows their locations, and the ressure gauges were labeled resectively as V1 ~ V from to to toe along the vertical wall, and U1 ~ U from right to left along the caisson bottom for the following discussions. The locations of V1 and V are adjustable according to the wave case to be tested, the dimensions marked at the left side of vertical wall in Figure are the locations of ressure gauges used in regular wave cases with H =.33 cm and 13.9 cm, and the dimensions marked at the right side of the vertical wall are the locations of ressure gauges used in regular wave cases with H = 19. cm and cm and in irregular wave cases. The waves and ressures were all samled with Hz rate for 9 seconds in each test. The time series of wave rofiles and ressure rofiles are analyzed by s of zero-u-crossing method after de- and de-trend rocesses. Wave forces acting on the breakwater are calculated from the distributions of wave ressures with following equations (see Figure ). The ressures at two ends of the vertical wall and of the caisson bottom were linearly extraolated from the measured data. Total horizontal force F H = Total ulift force F U = 3 Σ i =1 13 Σ i =1 Area i Area i Acting location of total horizontal force X = (1) (13) 13 Σ Area i * X i i =1 (1) F H : gauge 1. Used for H =.33/13.9 regular cases 1... 1. 1. 1. Used for H = 19./. regular cases and for irregular cases 17.1 17.1 17.1 Fig.. Locations of ressure gauges (unit: cm)

1 Journal of Marine Science and Technology, Vol., No. 3 (7) Acting location of total ulift force Y = 3 Σ i =1 Area i * Y i F U () where X i (i = 1 ~ 13): The horizontal distance of the centroid of Area i from origin Y i (i = 1 ~ 3): The vertical distance of the centroid of Area i from origin EXPERIMENTAL RESULTS The discussions of the exerimental results are divided into two arts: regular waves and irregular waves, and then the comarisons are resented. 1. Regular wave results Table 3 shows the wave heights/eriods measured at dee water zone as incident waves and at the location Case ID Table 3. Measured Progressive waves Incident waves Waves at breakwater H o (cm) T o (s) H (cm) H (cm) HT1.33 1... HT13.33 1.33.. HT1 13.9 1.33.9.73 HT.33 1.7 9. 9.1 H13T13 13.9 1.7 1.9 1.33 H13T1 19. 1.7 11. 1.97 H13T.33..7.1 H19T1 13.9.. 1. H19T 19.. 1.3. HT...17 3.97 of breakwater. Due to the side effect of the wave flume, the shoaling effect of the sloing bottom and the daming effect of sandy seabed, the regular wave heights arrived at the location of breakwater is different from the incident wave heights. Figure 7 shows the wave rofiles (3 reeats in each case) at the location of the breakwater and the wave s nonlinearity can be found in large wave cases. Figure shows, as an examle, the rofiles of horizontal ressure on the wall and of ulift ressures at the bottom of the caisson in Case HT. As referred to Figure, the water elevation during the wave trough action might below the locations of gauges V1, V and V3 and causes these gauges obtained incomlete ressure rofiles and zero ressures as water level below their locations. One noticeable henomenon is that even though the wave rofile is highly nonlinear, the ulift ressures still look quite linear which should be caused by the form of wave ressure transmission in water and wave energy dissiation on orous foundation and seabed. Area 3 Area : Measured : Extraolated P L U Area 1 Area 3 Area Area 7 Area 9 Area 11 Area 13 Area Area 1 Area 1 U 3 U P U V 1 P U R 1 Area 1 Area 19 Area 17Area Fig.. Wave forces calculations. V P S V 3 P D V V Area 1 Area Area Area Area Area 1 Area 1 1-1 - 1-1 - 1-1 - 1-1 - 1-1 - 1-1 - 1-1 - 1-1 - 1-1 - (a) CaseHT1 (b) Case H13T13 (c) Case H19T1 (d) Case HT Fig. 7. Wave rofiles at the location of breakwater in regular wave exeriments. 1-1 - 1-1 - 1-1 -

Y.F. Chiu et al.: An Exerimental Study of Wave Forces on Vertical Breakwater 13 From Goda s theories, the variations of horizontal/ulift wave forces are directly roortioned to wave height and wave eriod, and the horizontal wave ressure and ulift wave ressure are equal at the sea-side toe of the caisson. Figures 9 and 1 resent the relations between the imum horizontal/ulift wave ressures and wave heights/eriods from Case HT U1 U U3 U 1-1 - 1-1 - 1-1 - 1-1 - Fig.. 1 3 7 9 Time (s) (a) At the bottom V1 1-1 - V 1-1 - V3 1-1 - V 1-1 - V 1-1 - 1 3 7 9 Time (s) (b) On the vertical wall Time series of wave ressures on caisson (Case HT, ressure unit: gf/cm ). resectively. The solid/hollow circles in the figures are resectively the imum and minimum wave ressures, linear regression curves are also included. Linear and roortional relations can be found between wave ressures and wave height/eriod. By comaring the V ressures in Figure 9 and U ressures in Figure 1, one can find that the ressures at the toe of the vertical wall aear to be larger than the ressures at the sea-side end of the bottom, which is different from Goda s theories that assuming to be equal. Furthermore, the non-zero ressures at the landside end of the caisson bottom are also different from Goda s. Such henomena might be caused by the existence of footing of the caisson and orosity of the rubber mound foundation that change the flow attern in the foundation. Figure 11 shows the comarisons of wave forces on caisson. Linear regressions of measured and theoretical horizontal/ulift forces vs. wave heights are lotted. The measured horizontal/ulift forces are all smaller than Goda s wave forces, and the larger the wave height, that larger the difference. From the observations on the time series of wave forces and rofiles, the occurrence times of imum/ minimum horizontal forces are found not consistent with the arrival of wave crest/trough. Such henomenon causes the discussions on the definition of imum wave force. Figure 1 shows the horizontal and the ulift forces calculated as wave eaks (crest/trough) Wave ressure (gf/cm ) Wave ressure (gf/cm ) Wave ressure (gf/cm ) (a) Gauge V1 1 - -1 - - 1 3 (b) Gauge V 1 - -1 - - 1 3 (c) Gauge V3 1 - -1 - - 1 3 Wave ressure (gf/cm ) Wave ressure (gf/cm ) (d) Gauge V 1 - -1 - - 1 3 (e) Gauge V 1 - -1 - - 1 3 (a) Gauge V1 1 - -1 - -. 1 1.. Wave eriod (sec) (a) Wave height (b) Wave eriod Fig. 9. Relations between wave height and imum horizontal wave ressures (Case HT). Wave ressure (gf/cm ) Wave ressure (gf/cm ) Wave ressure (gf/cm ) (b) Gauge V 1 - -1 - -. 1 1.. Wave eriod (sec) (c) Gauge V3 1 - -1 - -. 1 1.. Wave eriod (sec) Wave ressure (gf/cm ) Wave ressure (gf/cm ) (d) Gauge V 1 - -1 - -. 1 1.. Wave eriod (sec) (e) Gauge V 1 - -1 - -. 1 1.. Wave eriod (sec)

1 Journal of Marine Science and Technology, Vol., No. 3 (7) (a) Gauge U (b) Gauge U3 (a) Gauge U (b) Gauge U3 Wave ressure (gf/cm ) 1 - -1 - Wave ressure (gf/cm ) 1 - -1 - Wave ressure (gf/cm ) 1 - -1 - Wave ressure (gf/cm ) 1 - -1 - - 1 3-1 3 -. 1 1.. Wave eriod (sec) -. 1 1.. Wave eriod (sec) (c) Gauge U (d) Gauge U1 (c) Gauge U (d) Gauge U1 Wave ressure (gf/cm ) 1 - -1 - Wave ressure (gf/cm ) 1 - -1 - Wave ressure (gf/cm ) 1 - -1 - Wave ressure (gf/cm ) 1 - -1 - - 1 3 (a) Wave height - 1 3 -. 1 1.. Wave eriod (sec) (b) Wave eriod -. 1 1.. Wave eriod (sec) Fig. 1. Relations between wave height and imum ulift wave ressures (Case HT). Force ( g/cm) 1 11 1 9 7 3 1 Regression Goda Horizontal force Ulift force 1 1 1 1 1 Fig. 11. Comarisons of wave forces on the caisson. actions, the wave ressures at these moments might not be the largest. Figure 13 shows the horizontal and the ulift forces calculated from imum/minimum wave ressures of all wave gauges. Linear regression curves are also included in Figures 1 and 13. Figure 1 collects their regression curves and shows there are a slightly difference between them, esecially on the horizontal force. For convenient use in engineering design, wave forces at wave crest action with a roer safety factor are suggested. Wave force (gf/cm) 1 - - - - -1 1 3 (a) Horizontal force at wave eak/trough Wave force (gf/cm) 1 - - - - -1 1 3 (b) Ulift force at wave eak/trough Fig. 1. Maximum horizontal and ulift forces (calculated at wave crest/trough). Wave force (gf/cm) 1 - - - - -1 1 3 (a) Horizontal force at P /P min Wave force (gf/cm) 1 - - - - -1 1 3 (b) Ulift force at P /P min Fig. 13. Maximum horizontal and ulift forces (calculated from all imum ressures).

Y.F. Chiu et al.: An Exerimental Study of Wave Forces on Vertical Breakwater 1 Wave force (gf/cm) 1 1 - - - - -1-1 Force from Max. ressure imum minimum Force at wave eak imum minimum 1 3 (a) Horizontal Force. Irregular wave results 1 - - - - -1 1 3 Wave force (gf/cm) Force from Max. ressure imum minimum Force at wave eak imum minimum (b) Ulift Force Fig. 1. Comarisons of wave forces calculated from wave crest and imum ressures. H (cm) H (cm) 3 1 3 1 3 1. 1 1.. 3. 1 1.. 3 T (s) T 1/1 (s). H 1/1 (cm) H / m 3.. 1 1.. 3. 1 1.. 3 T (s) T (s) This study also investigates the irregular wave forces acting on the caisson. As mentioned above, JONSWAP sectra for four different wave conditions are selected and combined with three different hase sets of comonent waves to generate the wave trains in the exeriments. Totally, 1 wave trains are used in this investigation, and each wave train is reeated twice for the cases with breakwater (standing wave cases), and once for the cases without breakwater (rogressive wave cases). Figure shows the relations of characteristic wave heights and related wave eriods, and the ratio of H / m vs. T of the irregular rogressive waves measured at the location of the breakwater. The figures show that different wave train may induce different imum wave height and eriod, thus, it causes different wave forces acting on the breakwater; however, for significant wave height/eriod and for wave height/eriod, three different wave trains only cause a slightly difference with the imum of % in wave height and the imum of % in wave eriod. The ratio of H / m is also not a constant and lies between 3.7 and.. From the investigation, one can find that different wave trains with the same sectrum and different comonent wave hases contain different wave characters. Figure 1 shows the characteristic standing wave heights/eriods in front of caisson. H, H 1/1, and H of all irregular wave cases with two reeats are resented. Due to the random roerty of waves and of the interactions among waves, sandy seabed, rubber mound foundation and vertical breakwater, Figure 1 shows that, even using the same wave train, the wave height/eriod measured from two reeat tests are still not equal, not to mention the results from three different wave trains with the same sectrum. Again, the investigations oint out the uncertainty of the irregular wave test results, and should not be tested with only one wave train with several reeats. DISCUSSIONS 1. Comarisons of regular wave forces and irregular wave forces In order to comare the results of regular waves and irregular waves, Figure 17 resents the wave ressure distributions on vertical wall and at the bottom for all wave cases. Each figure contains the results of three irregular wave trains with two reeats (in symbols) and the distribution of imum regular wave ressure (in solid line). For horizontal and ulift wave ressure distributions, the regular wave ressures are found close to the imum irregular wave ressures in HT1 and JHT1 cases, close to highest 1/1 irregular wave.. 3. ( : JHT; : JH19T1; : JH13T13; : JHT1) Fig.. Characteristic rogressive wave heights/eriods at the location of the breakwater. 3 1 3 1 JHT 1 3 Wave train no. 3 1 1 3 Wave train no. JH13T13 JHT1 3 1 1 3 Wave train no. 1 3 Wave train no. ( : H : H 1/1 : H ) JH19T1 Fig. 1. Characteristic standing wave heights/eriods in front of the caisson.

1 Journal of Marine Science and Technology, Vol., No. 3 (7) (a) (b) (c) (a) (b) (c) 3 3 1 3 3 1 3 3 1 3 3 1 1 3 (P H ) (gf/cm ) 1 3 (P H ) 1/1 (gf/cm ) 1 3 (P H ) (gf/cm ) (d) (e) (f) (P U ) (gf/cm ) (P U ) 1/1 (gf/cm ) (P U ) (gf/cm ) Cases HT1 vs. JHT1 1 3 (P H ) (gf/cm ) 3 3 1 1 3 (P H ) 1/1 (gf/cm ) 3 3 1 1 3 (P H ) (gf/cm ) (d) (e) (f) (P U ) (gf/cm ) (P U ) 1/1 (gf/cm ) (P U ) (gf/cm ) 3 1 1 3 3 1 1 3 3 1 1 3 1 1 3 1 Cases H19T1 vs. JH19T1 1 3 1 3 (a) (b) (c) (a) (b) (c) 3 3 1 1 3 (P H ) (gf/cm ) 3 3 1 1 3 (P H ) 1/1 (gf/cm ) 3 3 1 3 3 1 3 3 1 3 3 1 1 3 (P H ) (gf/cm ) (d) (e) (f) (P U ) (gf/cm ) (P U ) 1/1 (gf/cm ) (P U ) (gf/cm ) (P U ) (gf/cm ) (P U ) 1/1 (gf/cm ) (P U ) (gf/cm ) 1 Cases H13T13vs. JH13T13 1 3 (P H ) (gf/cm ) 1 3 (P H ) 1/1 (gf/cm ) 1 3 (P H ) (gf/cm ) (d) (e) (f) 1 3 1 3 1 3 1 1 1 1 1 1 3 1 1 1 1 1 Cases HT vs. JHT 1 3 1 3 Fig. 17. Comarisons of regular wave forces (solid line) and irregular wave forces (symbols) (a) imum horizontal force; (b) highest 1/1 horizontal force; (c) highest horizontal force; (d) imum ulift force; (e) highest 1/1 ulift force; (f) highest ulift force.

Y.F. Chiu et al.: An Exerimental Study of Wave Forces on Vertical Breakwater 17 ressures in H13T13 and JH13T13 cases and in H19T1 and JH19T1 cases, but only close to highest irregular wave ressures in HT and JHT cases. With these comarisons, one can see that the regular wave test for the wave forces acting on comositetye breakwater might be under-estimated. As a conclusion of this section, on evaluating the wave force acting on a coastal structure by s of hydraulic model test, irregular wave tests with different wave train of the same sectrum is a much roer way.. Comarisons of theoretical wave forces and irregular wave forces In this section, the irregular wave ressure distributions are comared to Goda s wave force theories. Figures 1 to 1 resent the horizontal and ulift wave ressure distributions of all wave cases. Each figure contains three wave trains with two reeats, and the exerimental imum(p ), highest 1/1(P 1/1 ), highest (P ), and averaged(p ) ressures are comared with the wave ressures obtained from Goda s theories with the reresentative wave height of H (solid line) or 1.H (dotted line). For the cases of JHT1 and JH13T13, Figures 1 and 19 show that the theoretical horizontal/ulift ressures of 1.H are slightly smaller than P, but larger than P 1/1, P and P. However, for the cases of JH19T1 and JHT, Figures and 1 show that the theoretical horizontal/ulift ressures of 1.H are larger than all characteristics ressures. From the analyses of the exeriments, in irregular wave cases, Goda s wave force theories underestimate the wave forces acting on caisson in small wave condition, and overestimate in large wave condition. As mention above, such henomenon might be caused by the random roerty of waves and of the interactions among waves, sandy seabed, rubber mound foundation and breakwater. CONCLUSIONS 1. Due to the shoaling effect for waves traveling on 3 3 3 3 3 3 1 1 1 1 1 1 1 3 1 3 1 3 1 3 1 3 1 3 3 3 3 1 1 1 1/1 1/1 1/1 1 3 1 3 1 3 3 3 3 1 1 1 1 3 1 3 1 3 3 1 1 3 1 3 1 3 (g/cm) (g/cm) (g/cm) (a) Wave train 1 3 1 (b) Wave train (c) Wave train 3 3 1 3 1 1/1 3 3 1/1 1/1 1 1 1 3 1 3 1 3 3 3 1 1 1 3 1 3 1 3 3 3 3 1 1 1 1 3 1 3 1 3 (a) Wave train 1 (b) Wave train (c) Wave train 3 Horizontal ressures Ulift ressure Fig. 1. Comarisons of theoretical/irregular wave forces in Case HT1 (solid line: theoretical H ; dashed line: 1.H ; solid symbol: exerimental data).

1 Journal of Marine Science and Technology, Vol., No. 3 (7) 3 1 1 3 3 1 1/1 1 3 3 1 1 3 3 1 1/1 1 3 3 1 1 3 3 1 1/1 1 3 3 3 3 1 1 1 1 3 1 3 1 3 3 3 1 1 1 3 1 3 1 3 (a) Wave train 1 (b) Wave train (c) Wave train 3 Horizontal ressures 3 1 3 1 3 1 3 1 3 3 1 1 13 1 3 1 3 3 3 1/1 1/1 1/1 1 1 13 1 3 1 3 3 3 1 1 13 1 3 1 3 3 3 1 1 13 1 3 1 3 (a) Wave train 1 (b) Wave train (c) Wave train 3 Ulift ressure Fig. 19. Comarisons of theoretical/irregular wave forces in Case H13T13 (solid line: theoretical H ; dashed line: 1.H ; solid symbol: exerimental data). 3 3 3 1 1 1 1 3 1 3 1 3 3 1 3 3 1 1 1 3 1 3 1 3 3 3 3 1 1 1/1 1 1/1 1/1 1 3 1 3 1 3 3 3 3 1 1 1 1 3 1 3 1 3 3 3 1 1 1 3 1 3 1 3 (a) Wave train 1 (b) Wave train (c) Wave train 3 Horizontal ressures 3 1 3 1 1/1 3 1/1 3 1/1 1 1 1 3 1 3 1 3 3 3 1 1 1 3 1 3 1 3 3 3 3 1 1 1 1 3 1 3 1 3 (a) Wave train 1 (b) Wave train (c) Wave train 3 Ulift ressure Fig.. Comarisons of theoretical/irregular wave forces in Case H19T1 (solid line: theoretical H ; dashed line: 1.H ; solid symbol: exerimental data).

Y.F. Chiu et al.: An Exerimental Study of Wave Forces on Vertical Breakwater 19 3 3 3 1 1 1 1 3 1 3 1 3 1/1 3 3 3 1 1 1 1 3 1 3 1 3 3 3 3 1 1 1 1 3 1 3 1 3 3 3 1 1 1 3 1 3 1 3 (a) Wave train 1 (b) Wave train (c) Wave train 3 1/1 Horizontal ressures 1/1 3 1 3 1 3 1 3 3 1 1 1 3 1 3 1 3 1/1 3 3 1/1 1/1 1 1 1 3 1 3 1 3 3 3 1 1 1 3 1 3 1 3 3 3 3 1 1 1 1 3 1 3 1 3 (a) Wave train 1 (b) Wave train (c) Wave train 3 Ulift ressure Fig. 1. Comarisons of theoretical/irregular wave forces in Case HT (solid line: theoretical H ; dashed line: 1.H ; solid symbol: exerimental data). nearshore sloing bathymetry, the wave nonlinearity will become dominant. However, as wave ressures transmit into the orous media of seabed, their nonlinearities might be decayed, and aroach to linear as deth increased.. The occurrence times of imum/minimum horizontal and ulift forces are not consistent with the arrival of wave crest/trough. But the total forces have only slightly difference in our cases. Wave forces at wave crest action with a roer safety factor are suggested. 3. Regular wave test underestimate the wave force acting on vertical breakwater, irregular wave test was suggested.. Wave forces will be increased as wave height/eriod increased. However, Goda s wave force theories underestimate the wave forces acting on caisson in small wave condition, and overestimate in large wave condition. As mention above, such henomenon might be caused by the random roerty of waves and of the interactions among waves, sandy seabed, rubber mound foundation and breakwater.. Due to the randomness and uncertainty of the results, the irregular wave tests should not be tested with only one wave train and reeated several times. Otimal number of wave trains with the same sectrum but different comonent wave hases, and their statistical interretations should be investigated further. REFERENCES 1. Chen, C.-H., Dynamic Behavior of Vertical Breakwater Induced by Irregular Waves, Master Theses, Deartment of Harbor and River Engineering, National Taiwan Ocean University ().. Goda, Y., Random Seas and Design of Maritime Structures, World Scientific, Singaore (19). 3. Goda, Y., Technical Standards and Commentaries for Port and Harbour Facilities in Jaan, The Overseas Coastal Area Develoment Institute of Jaan, Jaan ().. Hattori, M., Arami, A., and Yui, T., Wave Imact on Vertical Wall under Breaking Waves of Various Tyes, Coastal Engineering, Vol.,. 79-11 (199).

17 Journal of Marine Science and Technology, Vol., No. 3 (7). Klammer, P., Oscillatory Motions and Permanent Dislacements of Caisson Breakwaters Subject to Imulsive Breaking Wave Loads, Proceedings of the th International Conference on Coastal Engineering, Venice ASCE, Vol.,. 1-1 (199).. Kortenhaus, A. and Oumeraci, H., Classification of Wave Loading on Monolithic Coastal Structure, Proceedings of the th International Conference on Coastal Engineering, Venice ASCE, Vol. 1,. 7- (199). 7. Lin, Y.-J., Dynamic Behavior of Vertical Breakwater Induced by Regular Waves, Master Theses, Deartment of Harbor and River Engineering, National Taiwan Ocean University ().. Oumeraci, H., Review and Analysis of Vertical Breakwater Failures- Lessons Learned, Coastal Engineering, Vol.,. 3-9 (199). 9. Oumeraci, H. and Kortenhaus, A., Analysis of the Dynamic Resonse of Caisson Breakwaters, (Secial Issue on Vertical Breakwaters), Coastal Engineering, Vol.,. 9-13 (199). 1. Oumeraci, H., Kortenhaus, A., and Klammer, P., Dislacement of Caisson Breakwaters Induced by Breaking Wave Imacts, Proceedings of the International Conference of the Institute of Civil Engineers Advanced in Coastal Structures and Breakwaters, London, UK,. -3 (199). 11. Oumeraci, H., Partenscky, H.W., Kohlhase, S., and Klammer, P., Imact Loading and Dynamic Resonse of Caisson Breakewater-Results of Large-Scale Model Tests, Proceedings of 3rd International Conference on Coastal Engineering, Venice, ASCE, Vol.,. 17-1 (199). 1. Schmidit, R., Oumeraci, H., and Partenscky, H.-W., Imact Loads Induced by Plunging Breakers on Vertical Structure, Proceedings of the 3 th International Conference on Coastal Engineering, Venice, ASCE, Vol.,. - (199). 13. U.S Army Cors of Engineers, Coastal Engineering Manual, Coastal Engineering Research Center, USA ().