LABORATORY EXPERIMENTS ON WAVE OVERTOPPING OVER SMOOTH AND STEPPED GENTLE SLOPE SEAWALLS

Transcription

1 Asian and Pacific Coasts 23 LABORATORY EXPERIMENTS ON WAVE OVERTOPPING OVER SMOOTH AND STEPPED GENTLE SLOPE SEAWALLS Takayuki Suzuki 1, Masashi Tanaka 2 and Akio Okayasu 3 Wave overtopping on gentle slope seawalls was investigated in a laboratory wave flume. Overtopping rate was measured by a water tank placed behind the seawall. Velocity and water depth of overtopping water were simultaneously measured by using a Laser Doppler Velocimeter and a wave gage. It was found that overtopping rate for stepped seawalls is smaller than that for smooth seawalls. Steps on the front face of stepped seawalls reduce the wave reflection coefficient. Velocity of overtopping water has a peak just after the initiation of each overtopping event and overtopping volume could be estimated by using the velocity and water depth of overtopping water. Keywords: Wave overtopping, irregular wave, gentle slope seawall, overtopping velocity 1. Introduction Recently in Japan, coastal structures are constructed witonsideration in various aspects such as environment and utilization under ordinary conditions as well as disaster prevention. In that context, stepped gentle slope seawalls that give good accessibility to waterfront are now often used as the near-end protective facility in Japan s Complex Coastal Protection Concept. It is, however, important to estimate accurate wave overtopping rate in the storm conditions, because disaster prevention is the fundamental function of them. In laboratory experiments, Goda and Kishira (1976) measured overtopping rate over gentle slope seawalls and provided charts for smooth gentle slope seawalls. They conducted experiments also for stepped seawalls, but description on them is very limited. Kobayashi and Raichle (1994) suggested the measured overtopping probability and averaged overtopping rate are affected noticeable by the spectral shape and wave grouping of the incident waves measured just outside the surf zone. Shankar and Jayaratne (23) showed the wave steepness is a good parameter for describing the combined effect of wave height and period on wave run-up and 1 Graduate Student, Dept. of Civil Eng., Yokohama National Univ., 79- Tokiwadai Hodogaya-ku, Yokohama 24-81, Japan, d1sc11@ynu.ac.jp 2 Graduate Student, ditto, d2gc113@ynu.ac.jp 3 Associate Professor, Department of Marine Science and Technology, Tokyo University of Fisheries, okayasu@tokyo-u-fish.ac.jp

2 overtopping rate. Tamada et al. (22) performed experiments for various smooth slopes, but most of recent gentle slope seawalls are stepped in Japan. Wijayaratna et al. (2) simulated overtopping volume by using two-dimensional Large Eddy Simulation (LES). They concluded that it can simulate the wave overtopping well, if the water depth at the toe of seawall is small. Richardson et al. (22) measured water elevation and velocity of overtopping water to compare with numerical models. They mainly focused on overtopping for sloped, vertical, battered and composite seawalls. In the present study, experiments on wave overtopping over both smooth and stepped gentle seawalls were performed in laboratory. The slope of seawall surface was 1/3, that is considered to be the typical slope for the present gentle slope seawall design. Overtopping rates between smooth and stepped seawalls were compared. Velocity at the top of seawalls was measured. Reflection coefficients that affect the scour at the toe of seawalls were also investigated. 2. Outline of Laboratory Experiment 2.1 Experimental condition Figure 1 shows the setup of the flume and measuring instruments. The wave flume was 17 m long,.6 m wide and. m high with a 1/2 seabed. A 1/3 gentle slope seawall, made of acrylic, was placed at the on-shore end of the seabed. Both smooth and stepped surfaces were used for the slopes of seawalls. Table 1 shows the design parameters of the seawalls. Six wave gages and two Acoustic Doppler Velocimeters (ADVs) were installed in the flume to measure incident and reflected waves. A Laser Doppler Velocimeter (LDV) was placed beneath the top of the seawall to measure velocity of overtopping water at 2mm above it. 1 ~ 6: Wave gage, 7 and 8: ADV, 9: LDV 7 2 Wave h h C 4 1/ h 1/ 2 1. m 3. m 3. m Fig. 1. Wave flume and experimental setup

3 Irregular waves were generated by an absorption-type wave generator. Table 2 shows the experimental wave conditions, where H 1/3 is the significant wave height and T 1/3 is the significant wave period. Table 1. Design parameters of seawalls Offshore water depth (h ) Crest elevation from SWL ( ) Water depth at the toe of seawall (h) Case A Case B Case C Unit: cm Table 2. Wave conditions A B C Case H 1/3 (cm) T 1/3 (s) Setup of LDV A LDV optical probe was fixed on a measuring tank, which was placed behind the seawall, to measure velocity of overtopping water as shown in Fig. 2. The laser beams were irradiated offshore and were changed the direction upward by a mirror. The focal point was adjusted to be at 2 mm above the top of the seawall. Water depth of overtopping water was simultaneously measured by using a wave gage at a point about 2 cm offshore of the velocity measuring point.

4 Wave Seawall (Acrylic frame) Wave gage Focal point 2 mm 1 mm Plastic cover Mirror LDV Water tank Fig. 2. Schematic figure of LDV setup 2.3 Data acquisition Overtopping rate was evaluated from water surface elevation in a small water tank placed behind the seawall with a wave gage. The incident and reflected waves were separated by a method proposed by Kubota et al., (1989) using water surface elevation and cross-shore velocity in the offshore constant depth region. The outputs from wave gages and ADVs were recorded in a digital data recorder with a frequency of 1 Hz. For each trial, the data were stored for seconds from the still water condition. The data of LDV, which were recorded to a personal computer, were synchronized after the experiment. Overtopping rates were calculated from the data of 1 seconds (about 2 waves) after the wave field had been considered to become the steady state condition. The data were taken three times for each of four different wave conditions. 3. Experimental Results 3.1 Difference of overtopping rates between smooth and stepped seawalls Figure 3 shows relationship between ratios of overtopping rates for stepped seawalls against smooth seawalls and crest elevation to offshore wave height ratios. In the figure, overtopping rates of stepped seawalls are less than 4% of those of smooth seawalls in all cases. It can be said that stepped seawalls can reduce the overtopping rates considerably.

5 Overtopping rate (stepped/smooth) Case A Case B Case C Crest elevation/offshore wave height Fig. 3. Relationship between overtopping ratio and crest elevation to offshore wave height ratio 3.2 Relationship between crest elevation and overtopping rates Figure 4 shows relationship between ratios of crest elevation of seawalls to offshore wave heights and overtopping rates, sorted by the water depth at the toe of seawalls h. For the same overtopping rate, crest elevations of stepped seawalls are about 7% of these of smooth seawalls. Crest elevation/offshore wave height Case A stepped (h=cm) Case A smooth (h=cm) Case B stepped (h=cm) Case B smooth (h=cm) Case C stepped (h=cm) Case C smooth (h=cm) Overtopping rate (cm 3 /cm/s) Fig. 4. Relationship between crest elevation to offshore wave height ratio and overtopping rate

6 3.3 Wave reflection coefficients by seawalls Figure shows relationship between wave reflection coefficient by seawalls and wave steepness. In this figure, all results of the trials that were conducted three times for each of four different wave conditions were shown. The figure for Case A, in which the water depth at the toe of seawalls was equal to zero, shows almost same values for both smooth and stepped seawalls. In the cases that the water depth at the toe of seawalls exists (Case C), reflection coefficients show larger values, and the reflection coefficients for stepped seawalls are smaller than those of smooth seawalls. It can be considered that energy dissipation rate is increased by steps on the seawalls. Wave reflection coefficient Case A Case C Stepped Smooth Stepped Smooth Fig.. Relationship between wave reflection coefficient and wave steepness 3.4 Overtopping velocity Wave steepness Relationship between overtopping velocity and overtopping water depth Figure 6 shows an example of velocity and water depth of overtopping water. Water depth rises rapidly due to an overtopping event and the depth is hold for a while as overtopping water goes through the top of the seawall, then decreases gradually. However, velocity has a sharp peak just after the initiation of each overtopping event and it decreases immediately after the peak. It should be noted here that since LDV is very sensitive to the condition, the velocity couldn t be measured in a relatively large number of overtopping events as seen in Fig. 7.

7 2 Case C (Smooth) Velocity of overtopping water Water depth of overtopping water Velocity (cm/s) Wave depth (cm) Time (s) Fig. 6. Measured velocity and water depth of overtopping water 2 1 Case B (Smooth) Velocity of overtopping water Water depth of overtopping water Velocity (cm/s) Water depth (cm) Time (s) Fig. 7. Time series of measured overtopping velocity and water depth Calculate overtopped volume from velocity and water depth The solid lines in Fig. 8 give accumulated volume of overtopped water that was evaluated from water surface elevation in a small water tank installed behind the seawall. The squares show overtopped volume calculated from measured velocity and water depth of overtopping water. In this case, the measuring condition for the LDV (data rate) was quite good and the lack of velocity data for overtopped water was little. The figure shows that the accuracy of overtopped volume calculated from velocity and water depth is enough.

8 Overtopping volume (cm 3 /cm) Case C-3(Smooth) H 1/3 =1.9 cm, T 1/3 =1.42 s Solid line: Measured from a water tank Square: Calculated from velocity and water depth Time (s) Overtopping volume (cm 3 /cm) 1 1 Case C-3(Stepped) H 1/3 =1.9 cm, T 1/3 =1.42 s Solid line: Measured from a water tank Square: Calculated from velocity and water depth Time (s) Fig. 8. Time series of overtopped volume (Case C)

9 In some cases, overtopped volume calculated from velocity and water depth was much smaller than that evaluated by the small water tank as shown in Fig. 9. It was found for these cases that the LDV couldn t capture the overtopping velocity well. Overtopped volume (cm 3 /cm) Case B-4 (Smooth) H 1/3 =1.9 cm, T 1/3 =1.42 s Solid line: Measured from a water tank Square: Calculated from velocity and water depth Overtopped volume (cm 3 /cm) Time (s) Case B-4 (Stepped) H 1/3 =1.9 cm, T 1/3 =1.42 s Solid line: Measured from a water tank Square: Calculated from velocity and water depth Time (s) Fig. 9. Time series of overtopped volume (Case B)

10 3.4.3 of overtopping water Histograms of for each overtopping event are shown in Figs. 1 (for the smooth seawalls) and 11 (for the stepped seawalls). was calculated from maximum velocity and maximum water depth of overtopping water for each overtopping event. Total number of waves was about 3 for each figure. Since overtopping flow is supercritical in general, data less than 1 are considered to show that the velocity of overtopping water was not appropriately measured. For the cases of smooth seawalls (Fig. 1), the maximum frequency is around 2, and the numbers distribute up to around 8. As for the stepped seawalls (Fig. 11), distribution of Froude number is lower than the cases of smooth seawalls Case C-1 =11cm,H 1/3 =8.38cm,T 1/3 =1.4s Case C-3 =11cm,H 1/3 =1.9cm,T 1/3 =1.42s Case B-2 =8cm,H 1/3 =8.38cm,T 1/3 =1.4s Case B-4 =8cm,H 1/3 =1.9cm,T 1/3 =1.42s Fig. 1. Histograms of (Smooth seawall)

11 8 7 6 Case C-1 =11cm,H 1/3 =8.38cm,T 1/3 =1.4s Case C-3 =11cm,H 1/3 =1.9cm,T 1/3 =1.42s Case B-2 =8cm,H 1/3 =8.38cm,T 1/3 =1.4s Case B-4 =8cm,H 1/3 =1.9cm,T 1/3 =1.42s Fig. 11. Histogram of (Stepped seawall) 4. Conclusions Wave overtopping rate on gentle slope seawalls and velocity of overtopping water were investigated in a laboratory wave flume. From the experimental results, it can be concluded as follows. 1) Stepped seawalls reduce overtopping rate in comparison with smooth seawalls. 2) With relatively large water depth at the toe of seawalls, the wave reflection coefficients of stepped seawalls are smaller than those of smooth seawalls. 3) Velocity of overtopping water has a peak just after the initiation of each overtopping event. 4) Overtopped volume can be estimated by using velocity and water depth of overtopping water. ) of overtopping water is distributed up to 8 in cases of smooth seawalls. Acknowledgements The authors thank Prof. Tomoya Shibayama and Mr. Manabu Shimaya of Yokohama National University for their kind advises and suggestions on conducting the experiments and analysis. This research was partially supported by the Ministry of Education, Culture, Sports, Science and Technology, Japan, Grant-in-Aid for Scientific Research (B) (2), 13423,

12 References Goda, Y., and Kishira, Y. (1976): Experiments on Irregular Wave Overtopping Characteristics of Seawalls of Low Crest Types, Technical Note of PARI, No. 242, p 28. (In Japanese) Kobayashi, N., and Raichle, A. (1994): Irregular wave overtopping revetment in surf zones, Journal of Waterway, Port, Coastal, and Ocean Engineering, ASCE, 12 (1), pp Kubota, S., Mizuguchi, M., Hotta, S., and Takezawa, M. (1989): Field Observation of Wave Reflection and Swash Oscillation, Proceedings of Coastal Engineering, JSCE, Vol. 36, pp (In Japanese) Richardson, S., Pullen, T., and Clarke, S., (22): Jet velocity of overtopping waves on sloping structures: Measurements and computation, Abstracts for 28th International Conference on Coastal Engineering, ASCE, paper No. 347 Shankar, N. J. and Jayaratne, M. P. R. (23): Wave run-up and overtopping on smooth and rough slopes coastal structures, Ocean Engineering, 3, pp Tamada, T., Inoue, M., and Tezuka, T. (22): Experimental Studies on Diagrams for the Estimation of Wave Overtopping Rate on Gentle Slope-Type Seawalls and These Reduction Effect on Wave Overtopping, Proceedings of Coastal Engineering, JSCE, Vol. 49 (1), pp (In Japanese) Wijayaratna, N., Okayasu, A., and Noma, T. (2): Numerical simulation of overtopping rate on stepped seawall, Proceedings of Coastal Engineering, JSCE, Vol. 47 (1), pp (In Japanese)