Rubble Mounds: Numerical Modeling of Wave Motion
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 111, Issue 5
Abstract
A mixed numerical model is developed to simulate wave motion in rubble‐mound structures. The mixed model utilizes a combined finite difference method of characteristics scheme to integrate the unsteady continuity and momentum equations in the plane to obtain the internal water levels while the two‐dimensional properties of the flow are found from a finite element solution for the internal flow domain, plane, at any time t. The two‐dimensional solution is used to update pressure distribution coefficient and hydraulic conductivity values in the plane. The model is applied to the Sines breakwater in order to check the dynamic stability of the seaward slope under severe wave attack. The predicted values for the internal water surface are found to be in fair agreement with a physical model measurement. Furthermore, the model indicates a lower factor of safety than the traditional analysis. Special provisions are included in the model to account for added mass and to detect and correct for internal wave breaking and the entrainment of air near the interface.
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References
1.
Baird, W. F., “The Design of Rubble‐Mound Breakwaters,” Proceedings of Recent Developments in Ocean Engineering, University of California, Berkeley, Calif., Feb., 1981.
2.
Barends, F. B. J., Van der kogel, H., Uijttewaal, and Hagenaar, J., “West Breakwater‐Sines, Dynamic‐geotechnical Stability of Breakwater,” Proceedings of Coastal Structures '83, ASCE, 1983.
3.
Chow, C. Y., An Introduction to Computational Fluid Mechanics, John Wiley & Sons, Inc., New York, N.Y., 1979, pp. 207–208.
4.
Failure of the Breakwater at Port Sines, Portugal, ASCE Port Sines Investigation Panel, ASCE, New York, N.Y., 1978.
5.
Hannoura, A. A., “Numerical and Experimental Modelling of Unsteady Flow in Rockfill Embankments,” thesis presented to the University of Windsor, at Windsor, Ontario, Canada, in 1978, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
6.
Hannoura, A. A., and McCorquodale, J. A., “Stability of Rockfill Slopes under Wave Action,” Proceeding of the 7th Canadian Congress of Applied Mechanics, 1979, pp. 533–534.
7.
Hannoura, A. A., and McCorquodale, J. A., “Wave Motion in Rockfill Embankments,” Advances in Water Resources, Vol. 2, Sept., 1979, pp. 149–152.
8.
Hannoura, A. A., and McCorquodale, J. A., “Air‐Water Flow in Coarse Granular Media,” Journal of the Hydraulics Division, ASCE, Vol. 104, No. HY7, July, 1978, pp. 1001–1010.
9.
Harlow, E. H., “Large Rubble‐Mound Breakwater Failures,” Journal of Waterway, Port, Coastal, and Ocean Division, ASCE, Vol. 106, No. WW2, May, 1980, pp. 275–278.
10.
Hudson, R. Y., “Laboratory Investigation of Rubble‐Mound Breakwaters,” Journal of Waterways and Harbors Division, ASCE, Vol. 85, No. WW3, Proc. Paper 2171, Sept., 1959, pp. 93–119.
11.
Johnson, J. W., Kondo, H., and Wallihan, R., “Scale Effects in Wave Action Through Porous Structures,” Proceedings of the 10th Conference on Coastal Engineering, ASCE, Tokyo, Japan, 1966.
12.
Kondo, H., “An Analytical Approach to Wave Transmission Through Permeable Structures,” Coastal Engineering Conference, Vol. 13, Japan, 1970, pp. 31–42.
13.
Lean, G. H., “A Simplified Theory of Permeable Wave Absorbers,” Journal of Hydraulic Research, IAHR, Vol. 5, No. 1, 1965.
14.
Madsen, O. S., “Wave Transmission Through Porous Structures,” Journal of the Waterways Harbors and Coastal Engineering Division, ASCE, Vol, 100, No.WW3, Aug., 1974, pp. 169–187.
15.
Madsen, O. S., and Stanley, M. W., “Wave Transmission through Trapezoidal Breakwaters,” Proceeding XV, Coastal Engineering Conference, Vol. 3, Chapter 15, 1976.
16.
McCorquodale, J. A., “Wave Energy Dissipation in Rockfill,” Proceedings, 13th Conference on Coastal Engineering, ASCE, Vol. 111, Vancouver, Canada, 1972, pp. 1885–1903.
17.
McCorquodale, J. A., “Variational Approach to Non‐Darcy Flow,” Journal of Hydraulics Division, ASCE, Vol. 96, No. HY11, Nov., 1970, pp. 2265–2278.
18.
Nasser, M. S., and McCorquodale, J. A., “Wave Motion in Rockfill,” Journal of Waterways, Harbor and Coastal Engineering Division, ASCE, Vol. 101, No. WW2, Proc. Paper 11286, May, 1975, pp. 145–159.
19.
Nasser, M. S., “Theoretical and Experimental Analysis of Wave Motion in Rockfill Structures,” thesis presented to the University of Windsor, at Windsor, Ontario, Canada, in 1974, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
20.
Sweet, J., Barends, F. B. J., Van Loon‐Engels, C. H., and Van der koghel, “A Method for Dynamic Soil‐Structure Interaction Problems,” Proceedings of International Conference on Numerical Methods for Non‐Linear Problems, Swansea, Sept., 1980, pp. 197–208.
21.
Sollitt, C. K., and Cross, R. H., “Wave Reflection and Transmission through at Permeable Breakwaters,” Report No. 147, R. M. Parsons Laboratory, MIT, 1972.
22.
Vinje, T., and Brevig, P., “Numerical Simulation of Breaking Waves,” Advances in Water Resources, Vol. 4, June, 1981, pp. 77–82.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 111 • Issue 5 • September 1985
Pages: 800 - 816
Copyright
Copyright © 1985 ASCE.
History
Published online: Sep 1, 1985
Published in print: Sep 1985
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