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RESULT AND DISCUSSION
Correlation of reflection coefficient to surf parameter
In the condition of the submerged breakwater was removed, the correlation of the reflection coefficient to the surf parameter by the test result was obtained as shown in Figures 6 and 7.
Fig.6 correlation between Kr and ξs (smooth)
Fig.7 correlation between Kr and ξs (step)
From the figures, we can see the steeper the dike slope, the bigger the reflection coefficient. Its relation equation can be obtained.
Due to the wave runup profile will changed on different incident wave steepness and the dike slope. Therefore, the correlation between the coefficients N and M to the surf parameter at different dike slope can be obtained as shown in Figures 8-11.
Fig.8 Correlation between N and ξs (smooth)
Fig.9 Correlation between M and ξs(smooth)
Fig.10 Correlation between N and ξs(step) step
dike surface
Fig.11 Correlation between M and ξs(step)
After the regression analysis, the correlation formula between N or M and the surf parameter can be obtained as follows.
For smooth dike surface
N =1.447(ξs)0.23, M =0.661(ξs)-1.59;cosθ=1.5 (28)
N =1.30(ξs)0.41, M =0.486(ξs)-1.87;cosθ=2.0 (29)
N =1.423(ξs)0.52, M =0.134(ξs)-1.33;cosθ=3.0 (30)
For step dike surface
N =1.388(ξs)0.26, M =0.914(ξs)-1.97;cosθ=1.5 (31)
N =1.772(ξs)0.11, M =0.348(ξs)-1.75;cosθ=2.0 (32)
N =1.761(ξs)0.05, M =0.184(ξs)-1.59;cosθ=3.0 (33)
Correlation between energy loss and the surf parameter
When the incident wave assails the dike, the wave runup on the dike slope and the wave reflection from the sloping dike will to happened simultaneously. Meanwhile, the wave runup height as well as the wave energy loss will to changed at different incident wave and the dike condition. In this study, the correlation between the wave energy loss and the surf parameter was obtained as shown in Figures 12 and 13. From the figures, we can see the wave energy loss was bigger in big incident wave. Besides, we can see the bigger the wave energy loss, the milder the dike slope too. The reason was the milder the dike slope; the longer distance the wave to climbed. So that the bigger the wave energy loss will to generated. In addition, from these two figures, we also can find the wave energy loss was bigger at the step dike surface than the smooth dike surface in the same incident wave condition.
After the Kl value can to estimated then use the above mentioned formula, the values of N, M, Kr as well as the runup wave height can to computed. The comparison of the computed wave runup height with the measured wave runup height was shown in Figures 14 and 15 (without submerged breakwater). The correlation coefficient (R2) for the smooth surface dike and the step dike are equal to 0.9195 and 0.9484 respectively. It indicates that this wave runup height prediction model was quite reliable.
Fig.12 Correlation between Kl and ξs (smooth)
Fig.13 Correlation between Kl and ξs (step)
Fig.14 Comparison of wave runup (smooth)
Fig.15 Comparison of wave runup (step)
Influence of submerged breakwater to wave runup height
The main function effect of the submerged breakwater was to reduce the wave energy of the incident wave. After the incident wave passes over the submerged breakwater, its energy was break down, so that the runup height on the sloping dike decreases down also. In this study, the submerged breakwater was impermeable and the surface of submerged breakwater was smooth, so that the frictionless assumption was made. Due to the wave reflection coefficient (Kr) can to obtained and the transmission coefficient (Kt') can to computed also. Therefore, using equation (25), the wave height at the place where between the submerged breakwater and the sloping dike can be calculated. The comparison of the computed wave height and the measured wave height was shown in Figure 16 (smooth dike surface). The correlation coefficient R2 = 0.8940. This result can say acceptable.
At last, in advantage of equations (20) and (23), the wave runup height on the sloping dike can to computed. The comparison of the computed wave runup height to the measured wave runup height was shown in Figure 17 (smooth dike surface). The correlation R2 = 0.8614. This result can say acceptable also.
Fig.16 comparison of wave height after transmission (smooth)
Fig.17 Comparison of wave height after transmtssion (smooth)
CONCLUSIONS
1. The correlation equation between the reflection coefficient from the sloping dike and the surf parameter (ξs) was obtained as shown in equations (26) and (27).
2. The runup wave profile coefficients N and M are function of the surf parameter and can be obtained by use equations (28) to (33). It can to computed by use equations (17) and (14).
3. The correlation between the coefficient of energy loss in wave runup and the surf parameter was obtained as shown from Figures 12 to 15.
4. The wave energy loss was bigger at the step dike than at the smooth surface dike in the same incident wave and dike slope conditions.
5. Although the wave height will reduced after it pass over the submerged breakwater. But due to the reflection effect from the sloping dike. Sometime the wave height will grow up again at the place where between the submerged breakwater and the sloping dike. The reason may be the wave-wave interaction can to induced in this place.
6. The prediction model of wave runup under the influence of submerged breakwater was conduct in this study. Although the primary result can says acceptable. However, the advance study on the effect of wave transmission over rough and permeable submerged breakwater as well as the influence of the wave runup on step dike were suggest.
ACKNOWLEDGEMENT
The financial support by the National Science Council of Taiwan (NSC89-2611-E-242-001) who made this study possible, are gratefully acknowledged. Thanks also due to Ms. Y. C. Chin for her assist on typewritten and proofread.
REFERENCES
Ahrens, J.P. 1981. Irregular wave runup on smooth slopes. Tech. Report No. 81-17. Coastal Engineering Research Center. Waterways Experiment Station. Vicksburg. Mississippi.
Cross, R.H. and C.K. Sollitt 1972. Wave Transmission By Overtopping. Journal of Waterways, Port. Coastal and Ocean Eng. ASCE. Vol.98. pp.295-309.
Seabrook, S.R. and K.R. Hall. 1998. Wave Transmission at Submerged Rubblemound Breakwaters. Coastal Eng.. pp.2000-2013.
Van der Meer, J.W. and C.J.M. Stam 1992. Wave Runup on Smooth and Rock Slope of Coastal Structures, Journal of Waterway, Port, Coastal and Ocean Eng.. ASCE. No.5.
Yamamoto, Y., K. Tanimoto and K.G. Harshinie. 1994. Run-up of Irregular Wave on Gentle Sloping Beach. Coastal Eng.. pp.689-703
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