Stochastic Model for Damage Accumulation in Rubble-Mound Breakwaters Based on Compatibility Conditions and the Central Limit Theorem
Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 138, Issue 6
Abstract
Motivated by existing damage accumulation modeling difficulties, some suggestions on how to build consistent stochastic models for damage accumulation in breakwaters are given. The models avoid the selection of easy to use mathematical functions, which are replaced by those resulting from a set of properties that are expected in the model. It is shown how an inadequate selection of damage progression models leads to inconsistencies, which are avoided by using the proposed consistent mathematical structures. Dimensional analysis, compatibility conditions, and the central limit theorem are the bases for building a model aimed at reproducing the stochastic damage progression on breakwater as a result of general random wave actions. Four elements are identified as essential for a damage accumulation analysis: (1) the statistical distribution of the initial damage, (2) the mathematical structure of damage growth curves, (3) the damage function, which accounts for how the variables affect damage, and (4) the integral form in which damage accumulates, which permits relating its random character to the normal distribution. These four elements are combined to derive a general structure of models for determining the damage produced by any wave history, and to obtain the evolution of densities of cumulative damage with time. Finally, the proposed methods are illustrated by means of a real case example, and one of the models proposed is shown to be convenient in reproducing damage progression in breakwaters. The proposed method is valid not only for breakwaters but to other evolutive processes appearing in the maritime and coastal engineering field.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
We are indebted to the Spanish Ministry of Science and Technology (Projects BIA2009-10483 and TRA2010-17818) for partial support.
References
Aczel, J. (1966). Lectures in functional equations and their applications, Vol. 19, Academic Press, New York.
Ahrens, J. P. (1975). “Large wave tank tests of riprap stability.” Technical Memorandum 51, U.S. Army Engineer Waterways Experiment Station, Coastal Engineering Research Center, Vicksburg, MS.
Ahrens, J. P., and McCartney, B. L. (1975). “Wave period effect on the stability of riprap.” Proc., Civ. Eng. Oceans III, ASCE, Reston, VA, 1019–1034.
Bazant, Z. P. (2006). “Mechanics-based statistics of failure risk of quasibrittle structures and size effect on safety factors.” Proc. Natl. Acad. Sci. USA, 103(25), 9434–9439.
Bazant, Z. P., and Pang, S. D. (2007). “Activation energy based extreme value statistics and size effect in brittle and quasibrittle fracture.” J. Mech. Phys. Solids, 55(1), 91–131.
Burcharth, H. F. (1984). “Fatigue in breakwater armour units.” Proc., 19th Int. Conf. Coastal Eng., Vol. 3, ASCE, Reston, VA, 2592–2607.
Burcharth, H. F. (1994). “Reliability evaluation of a structure at sea.” Proc., Int. Workshop Wave Barr. Deep Water, Port and Harbour Research Institute, Yokosuka, Japan.
Burcharth, H. F. (1997). “Reliability based design of coastal structures.” Advances in coastal and ocean engineering, Vol. 3, WS Publishing, Singapore, 145–214.
Burcharth, H. F. (2000). “Reliability based design of coastal structures.” Chapter 6, Coastal Engineering Manual Part VI (CEM), Coastal Engineering Research Center, Vicksburg, MS, VI.6.1–VI.6.47.
Burcharth, H. F., and Sorensen, J. D. (1998). “Design of vertical wall caisson breakwaters using partial safety factors.” Proc., 25th Int. Coastal Eng., Vol. 2, ASCE, Reston, VA, 2138–2151.
Carver, R. D., and Wright, B. L. (1991). “An investigation of random variations in the stability response of stone armored, rubble mound breakwaters.” Technical Rep. CERC-91-17, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.
Castillo, C., Mínguez, R., Castillo, E., and Losada, M. (2006). “An optimal engineering design method with failure rate constraints and sensitivity analysis. Example application to composite breakwaters.” Coast. Eng., 53(1), 1–25.
Castillo, E., Fernández-Canteli, A., and Hadi, A. S. (1999). “On fitting a fatigue model to data.” Int. J. Fatigue, 21(1), 97–106.
Castillo, E., Fernández-Canteli, A., Pinto, H., and Ruiz-Ripoli, M. L. (2008a). “A statistical model for crack growth based on tension and compression Wöhler fields.” Eng. Fract. Mech., 75(15), 4439–4449.
Castillo, E., Fernández-Canteli, A., and Ruiz-Ripoli, M. L. (2008b). “A general model for fatigue damage due to any stress history.” Int. J. Fatigue, 30(1), 150–164.
Castillo, E., and Hadi, A. S. (1995). “Modeling lifetime data with application to fatigue models.” J. Am. Stat. Assoc., 90(431), 1041–1054.
Castillo, E., Iglesias, A., and Ruiz-Cobo, R. (2004a). Functional equations in applied sciences. Mathematics in science and engineering, Elsevier, New York.
Castillo, E., Losada, M., Mínguez, R., Castillo, C., and Baquerizo, A. (2004b). “Optimal engineering design method that combines safety factors and failure probabilities: Application to rubble-mound breakwaters.” J. Waterw. Port Coast. Ocean Eng., 130(2), 77–88.
Castillo, E., and Ruiz Cobo, M. R.(1992). Functional equations and modeling in science and engineering, Vol. 161, Marcel Dekker, New York.
Davies, M. H., Mansard, E. P. D., and Cornett, A. M. (1994). “Damage analysis for rubble mound breakwaters.” Proc., 24th Coast. Eng. Conf., Vol. 1, ASCE, Reston, VA, 1001–1015.
Font, J. B. (1968). “The effect of storm duration on rubble mound breakwater stability.” Proc., 11th Coast. Eng. Conf., Vol. 1, ASCE, Reston, VA, 779–786.
Hudson, R. Y. (1958). “Design of quarry-stone cover layers for rubble-mound breakwaters.” Research Rep. 2-2, U.S. Army Engineer Waterways Experiment Station, Vicksburg, MS.
Hudson, R. Y. (1959). “Laboratory investigation of rubble-mound breakwaters.” J. Wtrwy. Harb. Div., 85(WW3), 93–121.
Iribarren, R. (1938). “Una fórmula para el cálculo de los diques en escollera [A formula for the calculation of rock-fill dikes].” Technical Rep. HE-116-295, Revista de Obras Públicas, Madrid, Spain (in Spanish).
Jensen, O. J. (1984). A monograph on rubble-mound breakwaters, Danish Hydraulic Institute, Hørsholm, Denmark.
Jensen, T., Andersen, H., Grønbeck, J., Mansard, E. P. D., and Davies, M. H. (1996). “Breakwater stability under regular and irregular wave attack.” Proc., 25th Coast. Eng. Conf., Vol. 2, ASCE, Reston, VA, 1679–1692.
Losada, M. A., and Giménez-Curto, L. (1982). “Mound breakwaters under oblique wave attack.” Coast. Eng., 6(1), 83–92.
Medina, J. M., and McDougal, W. G. (1990). “Discussion on “Deterministic and probabilistic design of breakwater armor layers”. J. Waterw. Port Coast. Ocean Eng., 116(4), 508–510.
Medina, J. R. (1996). “Wave climate simulation and breakwater stability.” Proc., 25th Coast. Eng. Conf., ASCE, Reston, VA, 1789–1802.
Medina, J. R., Garrido, J., Gómez-Martín, M. E., and Vidal, C. (2003). “Armor damage analysis using neural networks.” Proc., Coast. Struct., ASCE, Reston, VA, 236–248.
Melby, A., and Kobayashi, N. (1999). “Damage progression and variability on breakwater trunks.” Coastal structures, 1999, Balkema, Rotterdam, Netherlands, 309–316.
Melby, J. A. (1999). “Damage progression on rubble–mound breakwaters.” Technical Rep. CHL–99–17, U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, MS.
Melby, J. A., and Kobayashi, N. (1998). “Progression and variability of damage on rubblemound breakwaters.” J. Waterw. Port Coast. Ocean Eng., 124(6), 286–294.
Mínguez, R., Castillo, E., Castillo, C., and Losada, M. (2006). “Optimal cost design with sensitivity analysis using decomposition techniques. application to composite breakwaters.” Struct. Saf., 28(4), 321–340.
Pfeiffer, H. L. (1991). “Comparison of four rubble-mound stability equations with prototype data from burns harbor breakwater.” M.S. thesis, Civil Engineering Dept., Texas A&M Univ., College Station, TX.
Pilarczyk, K. W., and Den Boer, K. (1983). “Stability and profile development of coarse materials and their application in coastal engineering.” Proc., Int. Conf. Coast. Port Eng. Devel. Countr., World Association for Waterborne Transport Infrastructure (PIANC). Brussels, Belgium, 43–61.
Scotto, M. G., and Guedes-Soares, C. (2007). “Bayesian inference for long-term prediction of significant wave height.” Coast. Eng., 54(5), 393–340.
SPM84 (1984). Shore protection manual. U.S. Army Engineer Waterways Experiment Station, U.S. Government Printing Office, Washington, DC.
Thompson, D. M., and Shuttler, R. M. (1975). “Riprap design for wind wave attack. A laboratory study in random waves.” Rep. EX707, H. R. Wallingford, Wallingford, U.K.
Torum, A., Mathiesen, B., and Escutia, R. (1979). “Reliability of breakwater model tests.” Proc., Coast. Struct., ASCE, Reston, VA, 454–469.
Van der Meer, J. W. (1988). “Rock slopes and gravel beaches under wave attack.” Ph.D. dissertation, Delft Hydraulics Laboratory, Emmeloord, Netherlands.
Vidal, C., Losada, M. A., and Mansard, E. P. D. (1995). “Suitable wave-height parameter for characterizing breakwater stability.” J. Waterw. Port Coast. Ocean Eng., 121(2), 88–97.
Vidal, C., Losada, M. A., and Medina, R. (1991). “Stability of mound breakwater’s head and trunk.” J. Waterw. Port Coast. Ocean Eng., 117(6), 570–587.
Vidal, C., Martín, F. L., and Migoya, L. (2003). “Parámetros de oleaje para la descripción de la evolución del daño en diques rompeolas.” Actas de las VII Jornadas Españolas de Costas y Puertos, Balkema, Rotterdam, Netherlands, 1–10 (in Spanish).
Vidal, C., Medina, R., and Lomónaco, P. (2006). “Wave height parameter for damage description of rubble-mound breakwaters.” Coast. Eng., 53(9), 711–722.
Vidal, C., Medina, R., Martín, F. L., and Migoya, L. (2004). “Wave height and period parameters for damage description on rubble-mound breakwaters.” Proc., 29th Int. Conf. Coast. Eng., Jane McKee Smith (ed.), Vol. 4, World Scientific, Hackensack, NJ, 3688–3700.
Information & Authors
Information
Published In
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 138 • Issue 6 • November 2012
Pages: 451 - 463
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Apr 15, 2011
Accepted: Feb 14, 2012
Published online: Feb 16, 2012
Published in print: Nov 1, 2012
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.