0
Review Article

Review of Wave Loads on Coastal Bridge Decks

[+] Author and Article Information
Masoud Hayatdavoodi

Division of Civil Engineering,
School of Science and Engineering,
University of Dundee,
Dundee DD1 4HN, UK
e-mail: masoud@hawaii.edu

R. Cengiz Ertekin

Fellow ASME
Ocean and Resources Engineering Department,
SOEST,
University of Hawaii at Manoa,
2540 Dole Street, Holmes 402,
Honolulu, HI 96822
e-mail: ertekin@hawaii.edu

1Corresponding author.

Manuscript received September 27, 2015; final manuscript received May 19, 2016; published online June 21, 2016. Assoc. Editor: Chin An Tan.

Appl. Mech. Rev 68(3), 030802 (Jun 21, 2016) (16 pages) Paper No: AMR-15-1114; doi: 10.1115/1.4033705 History: Received September 27, 2015; Revised May 19, 2016

Recent natural extreme events, such as Hurricane Ike in the U.S. (2008), Tohoku tsunami in Japan (2011), and Typhoon Haiyan in Southeast Asia (2013), have caused significant damage to the decks of coastal bridges. The failure of the structure occurs when wave-induced loads on the decks of coastal bridges exceed the bridge capacity, resulting in partial removal or a complete collapse of bridge decks. Tsunami, storm waves, and storm surge are known to be the ultimate agents of such failures. An understanding of the failure mechanism and possible solutions require a better knowledge of the destructive loads on the structure. Interaction of surface waves with the bridge deck is a complex problem, involving fluid–structure interaction, wave breaking, and overtopping. Possible submergence of the deck and entrapment of air pockets between girders can increase destructive forces and add to the complexities of the problem. In recent years, remarkable progress has been made on this topic, resulting in some new findings about the failure mechanism and the destructive wave loads. A review of the key studies on wave loads on the coastal bridge decks, including those in the past and very recently, is presented here. Emphasis is given to the pioneering works that have significantly improved our understanding of the problem. Challenges associated with the existing solutions are highlighted, and suggestions for future studies are provided.

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References

Panchang, V. G. , and Li, D. , 2006, “ Large Waves in the Gulf of Mexico Caused by Hurricane Ivan,” Bull. Am. Meteorol. Soc., 87(4), pp. 481–489. [CrossRef]
Chen, Q. , Wang, L. , Zhao, H. , and Douglass, S. L. , 2007, “ Prediction of Storm Surges and Wind Waves on Coastal Highways in Hurricane-Prone Areas,” J. Coastal Res., 23(5), pp. 1304–1317. [CrossRef]
Mori, N. , and Takahashi, T. , 2012, “ Nationwide Post Event Survey and Analysis of the 2011 Tohoku Earthquake Tsunami,” Coastal Eng. J., 54(1), p. 1250001. [CrossRef]
Yim, S. C. , Cheung, K. F. , Olsen, M. J. , and Yamazaki, Y. , 2012, “ Tohoku Tsunami Survey, Modeling and Probabilistic Load Estimation Applications,” International Symposium on Engineering Lessons Learned From the 2011 Great East Japan Earthquake, Japan Association of Earthquake Engineering, Tokyo, Japan, Mar. 1–4, pp. 430–443.
Bricker, J. D. , Takagi, H. , Mas, E. , Kure, S. , Adriano, B. , Yi, C. , and Roeber, V. , 2014, “ Spatial Variation of Damage Due to Storm Surge and Waves During Typhoon Haiyan in the Philippines,” J. Jpn. Soc. Civ. Eng., 70(2), pp. 231–235.
Douglass, S. L. , Chen, Q. , Olsen, J. M. , Edge, B. L. , and Brown, D. , 2006, “ Wave Forces on Bridge Decks,” University of South Alabama, Coastal Transportation Engineering Research and Education Center, University of South Alabama, Mobile, AL, p. 74.
Riggs, H. , Robertson, I. N. , Cheung, K. F. , Pawlak, G. , Young, Y. L. , and Yim, S. C. , 2008, “ Experimental Simulation of Tsunami Hazards to Buildings and Bridges,” 2008 NSF Engineering Research and Innovation Conference, Knoxville, TN, pp. 1056–1064.
Robertson, I. N. , Riggs, H. R. , Yim, S. C. S. , and Young, Y. L. , 2007, “ Lessons From Hurricane Katrina Storm Surge on Bridges and Buildings,” J. Waterw., Port, Coastal, Ocean Eng., 133(6), pp. 463–483. [CrossRef]
Hayes, M. B. , 2008, “ Assessing the Vulnerability of Delaware's Coastal Bridges to Hurricane Forces,” M.S. thesis, University of Delaware, Newark, DE, p. 77.
Lehrman, J. B. , Higgins, C. , and Cox, D. , 2012, “ Performance of Highway Bridge Girder Anchorages Under Simulated Hurricane Wave Induced Loads,” J. Bridge Eng., 17(2), pp. 259–271. [CrossRef]
Livermore, S. N. , 2014, “ Evaluation of Tsunami Design Codes and Recommendations for Bridges Susceptible to Tsunami Inundation,” Ph.D. thesis, University of Washington, Seattle, WA, p. 122.
Maruyama, K. , Tanaka, Y. , Kosa, K. , Hosoda, A. , Mizutani, N. , and Nakamura, T. , 2013, “ Evaluation of Tsunami Force Acted on Bridges by Great East Japan Earthquake,” 10th International Conference on Urban Earthquake Engineering, pp. 7–16.
Denson, K. H. , 1978, “ Wave Forces on Causeway-Type Coastal Bridges,” Water Resources Research Institute, Mississippi State University, Department of Civil Engineering, MS, Report No. MS 39762, p. 42.
Sheppard, D. M. , and Marin, J. , 2009, “ Wave Loading on Bridge Decks,” Florida Department of Transportation, Tallahassee, FL, Technical Report No. FDOT BD545-58, UF 00056675, p. 177.
Douglass, S. L. , Hughes, S. , Rogers, S. , and Chen, Q. , 2004, “ The Impact of Hurricane Ivan on the Coastal Roads of Florida and Alabama: A Preliminary Report,” Report to Coastal Transportation Engineering Research and Education Center, University of South Alabama, Mobile, AL, p. 19.
Iemura, H. , Pradono, M. H. , and Takahashi, Y. , 2005, “ Report on the Tsunami Damage of Bridges in Banda Aceh and Some Possible Countermeasures,” 27th Earthquake Engineering Symposium, Vol. 28, pp. 214–214.
Unjoh, S. , 2006, “ Damage Investigation of Bridges Affected by Tsunami During 2004 North Sumatra Earthquake, Indonesia,” Fourth International Workshop on Seismic Design and Retrofit of Transportation Facilities, San Francisco, CA, Vol. 81, p. 10.
Robertson, I. N. , Yim, S. , Young, Y. L. , and Riggs, H. R. , 2007, “ Coastal Bridge Performance During Hurricane Katrina,” Third International Conference on Structural Engineering, Mechanics and Computation, SEMC-2007, Cape Town, South Africa, Millpress, Rotterdam, The Netherlands, pp. 1864–1870.
Stearns, M. , and Padgett, J. E. , 2012, “ Impact of 2008 Hurricane Ike on Bridge Infrastructure in the Houston/Galveston Region,” J. Perform. Constr. Facil., 26(4), pp. 441–452. [CrossRef]
Kosa, K. , 2011, “ Damage Analysis of Bridges Affected by Tsunami Due to Great East Japan Earthquake,” 27th U.S.-Japan Bridge Engineering Workshop, pp. 55–65.
Kawashima, K. , and Buckle, I. , 2013, “ Structural Performance of Bridges in the Tohoku-Oki Earthquake,” Earthquake Spectra, 29(S1), pp. S315–S338. [CrossRef]
Akiyama, M. , Frangopol, D. M. , Arai, M. , and Koshimura, S. , 2013, “ Reliability of Bridges Under Tsunami Hazards: Emphasis on the 2011 Tohoku-Oki Earthquake,” Earthquake Spectra, 29(S1), pp. S295–S314. [CrossRef]
Mas, E. , Bricker, J. , Kure, S. , Adriano, B. , Yi, C. , Suppasri, A. , and Koshimura, S. , 2015, “ Field Survey Report and Satellite Image Interpretation of the 2013 Super Typhoon Haiyan in the Philippines,” Nat. Hazards Earth Syst. Sci., 15, pp. 805–816.
Padgett, J. , DesRoches, R. , Nielson, B. , Yashinsky, M. , Kwon, O.-S. , Burdette, N. , and Tavera, E. , 2008, “ Bridge Damage and Repair Costs From Hurricane Katrina,” J. Bridge Eng., 13(1), pp. 6–14. [CrossRef]
Mimura, N. , Yasuhara, K. , Kawagoe, S. , Yokoki, H. , and Kazama, S. , 2011, “ Damage From the Great East Japan Earthquake and Tsunami—A Quick Report,” Mitigation Adapt. Strategies Global Change, 16(7), pp. 803–818. [CrossRef]
Kawashima, K. , 2012, “ Damage of Bridges Due to the 2011 Great East Japan Earthquake,” J. Japan Assoc. Earthquake Eng., 12(4), pp. 319–338.
Akiyama, M. , and Frangopol, D. , 2012, Proceedings of the Third International Symposium on Life-Cycle Civil Engineering (IALCCE'12), Vienna, Austria, Oct. 3–6, CRC Press, Boca Raton, FL. “ Lessons From the 2011 Great East Japan Earthquake: Emphasis on Life-Cycle Structural Performance,” Life-Cycle and Sustainability of Civil Infrastructure System, A. Strauss, D. M. Frangopol, and K. Bergmeister, eds., Taylor & Francis Group, London, pp. 13–20.
Yim, S. C. , 2005, “ Modeling and Simulation of Tsunami and Storm Surge Hydrodynamic Loads on Coastal Bridge Structures,” 21st U.S.-Japan Bridge Engineering Workshop, pp. 3–5.
Ghobarah, A. , Saatcioglu, M. , and Nistor, I. , 2006, “ The Impact of the 26 December 2004 Earthquake and Tsunami on Structures and Infrastructure,” Eng. Struct., 28(2), pp. 312–326. [CrossRef]
Saatcioglu, M. , Ghobarah, A. , and Nistor, I. , 2006, “ Performance of Structures in Indonesia During the December 2004 Great Sumatra Earthquake and Indian Ocean Tsunami,” Earthquake Spectra, 22(S3), pp. 295–319. [CrossRef]
Eamon, C. D. , Fitzpatrick, P. , and Truax, D. D. , 2007, “ Observations of Structural Damage Caused by Hurricane Katrina on the Mississippi Gulf Coast,” J. Perform. Constr. Facil., 21(2), pp. 117–127. [CrossRef]
DesRoches, R. , 2006, “ Hurricane Katrina: Performance of Transportation Systems,” ASCE Technical Council on Lifeline Earthquake Engineering (TCLEE), Monograph No. 29, p. 62.
Okeil, A. M. , and Cai, C. , 2008, “ Survey of Short- and Medium-Span Bridge Damage Induced by Hurricane Katrina,” J. Bridge Eng., 13(4), pp. 377–387. [CrossRef]
Aglipay, M. R. I. , Keshab, S. , Kyokawa, H. , and Konagai, K. , 2011, “ Bridges Washed Away by Tsunami in Minamisanriku, Miyagi Prefecture in the March 11th 2011 Great East Japan earthquake,” Seisan Kenkyu, 63(6), pp. 723–727.
Nishida, H. , 2011, “Proceedings of the 27th U.S.–Japan Bridge Engineering Workshop,” Center for Advanced Engineering Structural Assessment and Research, Tsukuba, Ibaraki, Japan, Nov. 7–9, p. 407.
Kuwabara, T. , and Yen, W. P. , 2011, “ U.S.–Japan Joint Reconnaissance Report of Bridge Damage Due to 2011 Tohoku Earthquake,” 43rd Joint Meeting of U.S.-Japan Panel on Wind And Seismic Effects UJNR, K. Tamura , ed., Public Works Research Institute, Tsukuba, Japan, pp. 152–164.
Suppasri, A. , Shuto, N. , Imamura, F. , Koshimura, S. , Mas, E. , and Yalciner, A. C. , 2013, “ Lessons Learned From the 2011 Great East Japan Tsunami: Performance of Tsunami Countermeasures, Coastal Buildings, and Tsunami Evacuation in Japan,” Pure Appl. Geophys., 170(6–8), pp. 993–1018. [CrossRef]
Mazinani, I. , Ismail, Z. B. , and Hashim, A. M. , 2015, “ An Overview of Tsunami Wave Force on Coastal Bridge and Open Challenges,” J. Earthquake Tsunami, 9(2), p. 1550006. [CrossRef]
Hayatdavoodi, M. , Ertekin, R. C. , Robertson, I. N. , and Riggs, H. R. , 2015, “ Vulnerability Assessment of Coastal Bridges on Oahu Impacted by Storm Surge and Waves,” Nat. Hazards, 79(2), pp. 1–25. [CrossRef]
An, S. , and Faltinsen, O. M. , 2012, “ Linear Free-Surface Effects on a Horizontally Submerged and Perforated 2D Thin Plate in Finite and Infinite Water Depths,” Appl. Ocean Res., 37, pp. 220–234. [CrossRef]
Guo, A. , Fang, Q. , and Li, H. , 2015, “ Analytical Solution of Hurricane Wave Forces Acting on Submerged Bridge Decks,” Ocean Eng., 108, pp. 519–528. [CrossRef]
Meng, B. , 2008, “ Calculation of Extreme Wave Loads on Coastal Highway Bridges,” Ph.D. thesis, Texas A&M University, College Station, TX, p. 126.
Siew, P. F. , and Hurley, D. G. , 1977, “ Long Surface Waves Incident on a Submerged Horizontal Plate,” J. Fluid Mech., 83(10), pp. 141–151. [CrossRef]
Patarapanich, M. , 1984, “ Forces and Moment on a Horizontal Plate Due to Wave Scattering,” Coastal Eng., 8(3), pp. 279–301. [CrossRef]
Boussinesq, J. , 1871, “ Thorie de l'intumescence liquide appele onde solitaire ou de translation,” C. R. Acad. Sci. Paris, 72, pp. 755–759.
Rayleigh, L. , 1876, “ On Waves,” Philos. Mag., 1(4), pp. 257–279. [CrossRef]
Korteweg, D. , and de Vries, G. , 1895, “ On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on a New Type of Long Stationary Waves,” Philos. Mag., 39(5), pp. 422–443. [CrossRef]
Green, A. E. , and Naghdi, P. M. , 1974, “ On the Theory of Water Waves,” Proc. R. Soc. London: Ser. A, 338(1612), pp. 43–55. [CrossRef]
Green, A. E. , and Naghdi, P. M. , 1976, “ A Derivation of Equations for Wave Propagation in Water of Variable Depth,” J. Fluid Mech., 78(10), pp. 237–246. [CrossRef]
Green, A. E. , and Naghdi, P. M. , 1976, “ Directed Fluid Sheets,” Proc. R. Soc. London: Ser. A, 347(1651), pp. 447–473. [CrossRef]
Green, A. E. , and Naghdi, P. M. , 1986, “ A Nonlinear Theory of Water Waves for Finite and Infinite Depths,” Philos. Trans. R. Soc. London: Ser. A, 320(1552), pp. 37–70. [CrossRef]
Ertekin, R. C. , 1988, “ Nonlinear Shallow Water Waves: The Green-Naghdi Equations,” Pacific Congress on Marine Science and Technology, PACON’88, Honolulu, HI, pp. OST6/42–52.
Naghdi, P. M. , 1991, “ A Simple Derivation of Equations of Water Wave Theory Motivated by a Direct Approach,” Mathematical Approaches in Hydrodynamics, T. Miloh , ed., Society for Industrial and Applied Mathematics, Philadelphia, PA, pp. 182–192.
Ertekin, R. C. , 1984, “ Soliton Generation by Moving Disturbances in Shallow Water: Theory, Computation and Experiment,” Ph.D. thesis, University of California, Berkeley, CA, p. 352.
Ertekin, R. C. , Webster, W. C. , and Wehausen, J. V. , 1986, “ Waves Caused by a Moving Disturbance in a Shallow Channel of Finite Width,” J. Fluid Mech., 169(7), pp. 275–292. [CrossRef]
Ertekin, R. C. , Hayatdavoodi, M. , and Kim, J. W. , 2014, “ On Some Solitary and Cnoidal Wave Diffraction Solutions of the Green–Naghdi Equations,” Appl. Ocean Res., 47, pp. 125–137. [CrossRef]
Zhao, B. B. , Duan, W. Y. , and Ertekin, R. C. , 2014, “ Application of Higher-Level GN Theory to Some Wave Transformation Problems,” Coastal Eng., 83, pp. 177–189. [CrossRef]
Zhao, B. B. , Ertekin, R. C. , Duan, W. Y. , and Hayatdavoodi, M. , 2014, “ On the Steady Solitary-Wave Solution of the Green–Naghdi Equations of Different Levels,” Wave Motion, 51(8), pp. 1382–1395. [CrossRef]
Zhao, B. B. , Duan, W. Y. , Ertekin, R. C. , and Hayatdavoodi, M. , 2015, “ High-Level Green–Naghdi Wave Models for Nonlinear Wave Transformation in Three Dimensions,” J. Ocean Eng. Mar. Energy, 1(2), pp. 121–132. [CrossRef]
Hayatdavoodi, M. , and Ertekin, R. C. , 2015, “ Wave Forces on a Submerged Horizontal Plate—Part I: Theory and Modelling,” J. Fluids Struct., 54, pp. 566–579. [CrossRef]
Jasak, H. , 1996, “ Error Analysis and Estimation for the Finite Volume Method With Applications to Fluid Flows,” Ph.D. thesis, University of London, London, UK.
Rusche, H. , 2002, “ Computational Fluid Dynamics of Dispersed Two-Phase Flows at High Phase Fractions,” Ph.D. thesis, University of London, London, UK.
Kim, J. W. , Jang, H. , Baquet, A. , O'Sullivan, J. , Lee, S. , Kim, B. , Read, A. , and Jasak, H. , 2016, “ Technical and Economic Readiness Review of CFD-Based Numerical Wave Basin for Offshore Floater Design,” Offshore Technology Conference, Paper No. OTC-27294-MS.
Xiao, H. , Huang, W. , and Chen, Q. , 2010, “ Effects of Submersion Depth on Wave Uplift Force Acting on Biloxi Bay Bridge Decks During Hurricane Katrina,” Comput. Fluids, 39(8), pp. 1390–1400. [CrossRef]
Bozorgnia, M. , and Lee, J. J. , 2012, “ Computational Fluid Dynamic Analysis of Highway Bridges Exposed to Hurricane Waves,” 33rd Conference on Coastal Engineering, ASCE, Santander, Spain, pp. 1–14.
Bricker, J. D. , Kawashima, K. , and Nakayama, A. , 2012, “ CFD Analysis of Bridge Deck Failure Due to Tsunami,” International Symposium on Engineering Lessons Learned From the 2011 Great East Japan Earthquake, Tokyo, Japan, Mar. 1–4, pp. 1398–1409.
Hayatdavoodi, M. , and Ertekin, R. C. , 2015, “ Nonlinear Wave Loads on a Submerged Deck by the Green–Naghdi Equations,” ASME J. Offshore Mech. Arct. Eng., 137(1), p. 011102. [CrossRef]
Xu, G. , Cai, C. S. , and Han, Y. , 2015, “ Investigating the Characteristics of the Solitary Wave-Induced Forces on Coastal Twin Bridge Decks,” J. Perform. Constr. Facil., p. 04015076.
Lau, T. L. , Ohmachi, T. , Inoue, S. , and Lukkunaprasit, P. , 2011, “ Experimental and Numerical Modeling of Tsunami Force on Bridge Decks,” Tsunami—A Growing Disaster, M. Mokhtari , ed., InTech, Rijeka, Croatia, pp. 105–130.
Motley, M. R. , Wong, H. K. , Qin, X. , Winter, A. O. , and Eberhard, M. O. , 2016, “ Tsunami-Induced Forces on Skewed Bridges,” J. Waterw., Port, Coastal, Ocean Eng., 142(3), p. 04015025. [CrossRef]
Lo, H. Y. , and Liu, P. L. , 2014, “ Solitary Waves Incident on a Submerged Horizontal Plate,” J. Waterw. Port Coastal Ocean Eng., 140(3), p. 04014009. [CrossRef]
Ertekin, R. C. , and Hayatdavoodi, M. , 2015, “ Hydrodynamics of Wave Forces on Coastal-Bridge Decks: Calculations by Euler's Equations Versus Nonlinear Shallow-Water Wave Equations,” Oceans 2015 Conference, MTS/IEEE, Genova, Italy, May 18–21, Paper No. 141204-084.
Chen, S. , and Doolen, G. D. , 1998, “ Lattice Boltzmann Method for Fluid Flows,” Annu. Rev. Fluid Mech., 30(1), pp. 329–364. [CrossRef]
Aidun, C. K. , and Clausen, J. R. , 2010, “ Lattice–Boltzmann Method for Complex Flows,” Annu. Rev. Fluid Mech., 42(1), pp. 439–472. [CrossRef]
Monaghan, J. J. , 1992, “ Smoothed Particle Hydrodynamics,” Annu. Rev. Astron. Astrophys., 30(1), pp. 543–574. [CrossRef]
Monaghan, J. , 2012, “ Smoothed Particle Hydrodynamics and Its Diverse Applications,” Annu. Rev. Fluid Mech., 44(1), pp. 323–346. [CrossRef]
Wei, Z. , and Dalrymple, R. A. , 2016, “ Numerical Study on Mitigating Tsunami Force on Bridges by an SPH Model,” J. Ocean Eng. Mar. Energy, 2(3), pp. 1–16.
Nakao, H. , Zhang, G. , Sumimura, T. , and Hoshikuma, J.-I. , 2013, “ Numerical Assessment of Tsunami-Induced Effect on Bridge Behavior,” 29th U.S.-Japan Bridge Engineering Workshop, pp. 1–13.
Guo, A. , Fang, Q. , Bai, X. , and Li, H. , 2015, “ Hydrodynamic Experiment of the Wave Force Acting on the Superstructures of Coastal Bridges,” J. Bridge Eng., 20(12), p. 04015012. [CrossRef]
Bradner, C. , Schumacher, T. , Cox, D. , and Higgins, C. , 2011, “ Experimental Setup for a Large-Scale Bridge Superstructure Model Subjected to Waves,” J. Waterw., Port, Coastal, Ocean Eng., 137(1), pp. 3–11. [CrossRef]
Schumacher, T. , Higgins, C. , Bradner, C. , Cox, D. , and Yim, S. , 2008, “ Large-Scale Wave Flume Experiments on Highway Bridge Superstructures Exposed to Hurricane Wave Forces,” Sixth National Seismic Conference on Bridges and Highways, Charleston, SC, Paper No. 2A3-5.
Hayatdavoodi, M. , Seiffert, B. , and Ertekin, R. C. , 2014, “ Experiments and Computations of Solitary-Wave Forces on a Coastal-Bridge Deck—Part II: Deck With Girders,” Coastal Eng., 88, pp. 210–228. [CrossRef]
Hayatdavoodi, M. , Seiffert, B. , and Ertekin, R. C. , 2015, “ Experiments and Calculations of Cnoidal Wave Loads on a Flat Plate in Shallow Water,” J. Ocean Eng. Mar. Energy, 1(1), pp. 77–99. [CrossRef]
Seiffert, B. R. , Ertekin, R. C. , and Robertson, I. N. , 2015, “ Wave Loads on a Coastal Bridge Deck and the Role of Entrapped Air,” Appl. Ocean Res., 53, pp. 91–106. [CrossRef]
El Ghamry, O. A. , 1963, “ Wave Forces on a Dock,” University of California, Berkeley, CA, Hydraulic Engineering Laboratory, Wave Research Projects, Hydraulic Engineering Laboratory, Institute of Engineering Research, Technical Report No. HEL-9-1.
Wang, H. , 1970, “ Water Wave Pressure on Horizontal Plate,” J. Hydraul. Div., 96(10), pp. 1997–2016.
French, J. A. , 1969, “ Wave Uplift Pressures on Horizontal Platforms,” Ph.D. thesis, W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology, Pasadena, CA, p. 415.
French, J. A. , 1970, “ Wave Uplift Pressures on Horizontal Platforms,” Civil Engineering in the Oceans IV, Vol. 1, pp. 187–202.
Douglass, S. L. , McNeill, L. P. , and Edge, B. , 2007, “ Wave Loads on U.S. Highway Bridges,” Coastal Structures, Venice, Italy, July, 2–4, pp. 1659–1670.
Denson, K. H. , 1980, “ Wave Forces on Causeway-Type Coastal Bridges: Effects of Angle of Wave Incidence and Cross Section Shape,” Water Resources Research Institute, Mississippi State University, Department of Civil Engineering, MS, Report No. MSHD-RD-80-070, p. 242.
Shih, R. W. K. , and Anastasiou, K. , 1992, “ A Laboratory Study of the Wave-Induced Vertical Loading on Platform Decks,” ICE—Water Maritime and Energy, Vol. 96(1), pp. 19–33. [CrossRef]
Kaplan, P. , 1992, “ Wave Impact Forces on Offshore Structures: Re-Examination and New Interpretations,” Offshore Technology Conference, Houston, TX, Paper No. OTC-6814-MS, pp. 79–86.
Kaplan, P. , Murray, J. J. , and Yu, W. C. , 1995, “ Theoretical Analysis of Wave Impact Forces on Platform Deck Structures,” Offshore Mechanics and Arctic Engineering, OMAE, ASME, Copenhagen, Denmark, Vol. 1-A, pp. 189–198.
Isaacson, M. , and Bhat, S. , 1996, “ Wave Forces on a Horizontal Plate,” Int. J. Offshore Polar Eng., 6(1), pp. 19–26.
Morison, J. R. , O'Brien, M. P. , Johnson, J. W. , and Schaaf, S. A. , 1950, “ The Force Exerted by Surface Piles,” Pet. Trans., 189, pp. 149–154.
Tirindelli, M. , Cuomo, G. , Allsop, W. , and McConnell, K. , 2002, “ Exposed Jetties: Inconsistencies and Gaps in Design Methods for Wave-Induced Forces,” International Conference on Coastal Engineering, Cardiff, Wales, J. M. Smith , ed., pp. 1684–1696.
McConnell, K. , Allsop, W. , and Cruickshank, I. , 2004, Piers, Jetties, and Related Structures Exposed to Waves: Guidelines for Hydraulic Loadings, 1st ed., Thomas Telford Press, London, UK, p. 148.
Cuomo, G. , Tirindelli, M. , and Allsop, W. , 2007, “ Wave-In-Deck Loads on Exposed Jetties,” Coastal Eng., 54(9), pp. 657–679. [CrossRef]
Marin, J. , and Sheppard, D. M. , 2009, “ Storm Surge and Wave Loading on Bridge Superstructures,” Structures Congress 2009, ASCE, Austin, TX, pp. 557–566.
Prasard, S. , 1994, “ Wave Impact Forces on a Horizontal Cylinder,” Ph.D. thesis, Department of Civil Engineering, The University of British Columbia, Vancouver, BC, p. 185.
Isaacson, M. , and Prasad, S. , 1994, “ Wave Slamming on a Horizontal Circular Cylinder,” Int. J. Offshore Polar Eng., 4(2), pp. 81–88.
Bea, R. G. , Xu, T. , Stear, J. , and Ramos, R. , 1999, “ Wave Forces on Decks of Offshore Platforms,” J. Waterw., Port, Coastal, Ocean Eng., 125(3), pp. 136–144. [CrossRef]
Bea, R. G. , Iverson, R. , and Xu, T. , 2001, “ Wave-In-Deck Forces on Offshore Platforms,” ASME J. Offshore Mech. Arct. Eng., 123(1), pp. 10–21. [CrossRef]
Cardone, V. J. , and Cox, A. T. , 1992, “ Hindcast Study of Hurricane Andrew (1992) Offshore Gulf of Mexico,” Joint Industry Project, Oceanweather, Cos Cob, CT, p. 158.
Vannan, M. , Thompson, H. , Griffin, J. , and Gelpi, S. , 1994, “ An Automated Procedure for Platform Strength Assessment,” Offshore Technology Conference, pp. 55–64.
Baarholm, R. J. , 2001, “ Theoretical and Experimental Studies of Wave Impact Underneath Decks of Offshore Platforms,” Ph.D. thesis, Department of Marine Hydrodynamics, NTNU, Trondheim, Norway, p. 161.
Baarholm, R. , and Faltinsen, O. M. , 2004, “ Wave Impact Underneath Horizontal Decks,” J. Mar. Sci. Technol., 9(1), pp. 1–13. [CrossRef]
Wagner, H. , 1932, “ Über stoiß- und gleitvorgänge an der oberfläche von flüssigkeiten,” Z. Angew. Math. Mech., 12(4), pp. 193–215 (Translated into English as Phenomena Associated With Impact and Sliding on Liquid Surfaces. N.A.C.A. Translation 1366, p. 60). [CrossRef]
Zhao, R. , and Faltinsen, O. , 1993, “ Water Entry of Two-Dimensional Bodies,” J. Fluid Mech., 246, pp. 593–612. [CrossRef]
Lai, C. P. , and Lee, J. J. , 1989, “ Interaction of Finite Amplitude Waves With Platforms or Docks,” J. Waterw., Port, Coastal, Ocean Eng., 115(1), pp. 19–39. [CrossRef]
Overbeek, J. , and Klabbers, I. M. , 2001, “ Design of Jetty Decks for Extreme Vertical Wave Loads,” Ports 01, ASCE, Norfolk, VA, pp. 1–10.
McPherson, R. L. , 2008, “ Hurricane Induced Wave and Surge Forces on Bridge Decks,” M.S. thesis, Texas A&M University, College Station, TX, p. 90.
AASHTO, 2008, “ Guide Specifications for Bridges Vulnerable to Coastal Storms,” American Association of State Highway and Transportation Officials, p. 64.
Bradner, C. , 2008, “ Large-Scale Laboratory Observations of Wave Forces on a Highway Bridge Superstructure,” Ph.D. thesis, Oregon State University, Corvallis, OR, p. 150.
Bradner, C. , Schumacher, T. , Cox, D. , and Higgins, C. , 2011, “ Experimental Setup for a Large-Scale Bridge Superstructure Model Subjected to Waves,” J. Waterw., Port, Coastal, Ocean Eng., 137(1), pp. 3–11.
Iemura, H. , Pradono, M. H. , Yasuda, T. , and Tada, T. , 2007, “ Experiments of Tsunami Force Acting on Bridge Models,” J. Jpn. Soc. Civ. Eng., 29, pp. 902–911.
Thusyanthan, I. , and Martinez, E. , 2008, “ Model Study of Tsunami Wave Loading on Bridges,” Eighteenth International Offshore and Polar Engineering Conference, Vancouver, BC, International Society of Offshore and Polar Engineers, Vancouver, Canada, pp. 174–180.
Lukkunaprasit, P. , Lau, T. L. , Ruangrassamee, A. , and Ohmachi, T. , 2011, “ Tsunami Wave Loading on a Bridge Deck With Perforations,” Sci. Tsunami Hazards, 30(4), pp. 244–252.
Rahman, S. , Akib, S. , and Shirazi, S. , 2014, “ Experimental Investigation on the Stability of Bride Girder Against Tsunami Forces,” Sci. China Technol. Sci., 57(10), pp. 2028–2036. [CrossRef]
Mazinani, I. , Ismail, Z. B. , Shamshirband, S. , Hashim, A. M. , Mansourvar, M. , and Zalnezhad, E. , 2016, “ Estimation of Tsunami Bore Forces on a Coastal Bridge Using an Extreme Learning Machine,” Entropy, 18(5), p. 16.
Chen, Q. , Wang, L. , and Zhao, H. , 2009, “ Hydrodynamic Investigation of Coastal Bridge Collapse During Hurricane Katrina,” J. Hydraul. Eng., 135(3), pp. 175–186. [CrossRef]
Booij, N. , Ris, R. , and Holthuijsen, L. , 1999, “ A Third Generation Wave Model for Coastal Regions—Part 1: Model Description and Validation,” J. Geophys. Res., 104(C4), pp. 7649–7666. [CrossRef]
Luettich, R. J. , Westerink, J. , and Scheffner, N. W. , 1992, “ ADCIRC: An Advanced Three-Dimensional Circulation Model for Shelves, Coasts, and Estuaries,” Dredging Research Program, Washington, DC, Report 1. Theory and Methodology of ADCIRC-2DDI and ADCIRC-3DL, Technical Report No. DRP-92-6, p. 143.
Luettich, R. J. , and Westerink, J. , 2004, “Formulation and Numerical Implementation of the 2D/3D ADCIRC Finite Element Model Version 44.xx,” p. 74.
Dietrich, J. , Zijlema, M. , Westerink, J. , Holthuijsen, L. , Dawson, C. , Luettich, R. , Jensen, R. , Smith, J. , Stelling, G. , and Stone, G. , 2011, “ Modeling Hurricane Waves and Storm Surge Using Integrally-Coupled, Scalable Computations,” Coastal Eng., 58(1), pp. 45–65. [CrossRef]
Hayatdavoodi, M. , and Ertekin, R. C. , 2015, “ Wave Forces on a Submerged Horizontal Plate—Part II: Solitary and Cnoidal Waves,” J. Fluids Struct., 54, pp. 580–596. [CrossRef]
Huang, W. , and Xiao, H. , 2009, “ Numerical Modeling of Dynamic Wave Force Acting on Escambia Bay Bridge Deck During Hurricane Ivan,” J. Waterw., Port, Coastal Ocean Eng., 135(4), pp. 164–175. [CrossRef]
Hirt, C. , and Nichols, B. , 1981, “ Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” J. Comput. Phys., 39(1), pp. 201–225. [CrossRef]
Sicilian, J. M. , Hirt, C. W. , and Harper, R. P. , 1987, “ FLOW-3D: Computational Modeling Power for Scientists and Engineers,” Flow Sciences, Technical Report No. FSI-87-00-1, p. 10.
Liaw, K. , 2005, “ Simulation of Flow Around Bluff Bodies and Bridge Deck Sections Using CFD,” Ph.D. thesis, University of Nottingham, Nottingham, UK, p. 251.
Bozorgnia, M. , Lee, J. , and Raichlen, F. , 2010, “ Wave Structure Interaction: Role of Entrapped Air on Wave Impact and Uplift Forces,” 32nd Conference on Coastal Engineering, ASCE, Shanghai, China, pp. 1–12.
Jin, J. , and Meng, B. , 2011, “ Computation of Wave Loads on the Superstructures of Coastal Highway Bridges,” Ocean Eng., 38(17), pp. 2185–2200. [CrossRef]
Azadbakht, M. , and Yim, S. C. , 2015, “ Simulation and Estimation of Tsunami Loads on Bridge Superstructures,” J. Waterw. Port Coastal Ocean Eng., 141(2), p. 04014031. [CrossRef]
Xu, G. , and Cai, C. S. , 2015, “ Numerical Simulations of Lateral Restraining Stiffness Effect on Bridge Deckwave Interaction Under Solitary Waves,” Eng. Struct., 101, pp. 337–351. [CrossRef]
Bozorgnia, M. , 2012, “ Computational Fluid Dynamic Analysis of Highway Bridge Superstructures Exposed to Hurricane Waves,” Ph.D. thesis, University of Southern California, Los Angeles, CA, p. 169.
Motley, M. , Lemoine, G. , and Livermore, S. , 2014, “ Three-Dimensional Loading Effects of Tsunamis on Bridge Superstructures,” Structures Congress 2014, ASCE, Boston, MA, pp. 1348–1358.
Seiffert, B. , Hayatdavoodi, M. , and Ertekin, R. C. , 2014, “ Experiments and Computations of Solitary-Wave Forces on a Coastal-Bridge Deck—Part I: Flat Plate,” Coastal Eng., 88, pp. 194–209. [CrossRef]
Constantin, A. , Escher, J. , and Hsu, H.-C. , 2011, “ Pressure Beneath a Solitary Water Wave: Mathematical Theory and Experiments,” Arch. Ration. Mech. Anal., 201(1), pp. 251–269. [CrossRef]
Wiegel, R. L. , 1964, Oceanographical Engineering, Prentice-Hall, Englewood Cliffs, NJ, p. 532.
Whitham, G. B. , 1974, Linear and Nonlinear Waves, Prentice-Hall, Englewood Cliffs, NJ, p. 532.
Sarpkaya, T. , and Isaacson, M. , 1981, Mechanics of Wave Forces on Offshore Structures, Van Nostrand Reinhold Company, New York, p. 651.
Svendsen, I. A. , and Jonsson, I. G. , 1976, Hydrodynamics of Coastal Regions, Den Private Ingeniørfond, Technical University of Denmark, Lyngby, Denmark, p. 285.
Seiffert, B. , Hayatdavoodi, M. , and Ertekin, R. C. , 2015, “ Cnoidal Wave Loads on a Bridge Deck With Girders: Experiments and Computations,” Eur. J. Mech. B/Fluids, 52, pp. 191–205. [CrossRef]
Padgett, J. E. , Spiller, A. , and Arnold, C. , 2012, “ Statistical Analysis of Coastal Bridge Vulnerability Based on Empirical Evidence From Hurricane Katrina,” Struct. Infrastruct. Eng., 8(6), pp. 595–605. [CrossRef]
Shoji, G. , and Moriyama, T. , 2007, “ Evaluation of the Structural Fragility of a Bridge Structure Subjected to a Tsunami Wave Load,” J. Nat. Disaster Sci., 29(2), pp. 73–81. [CrossRef]
Ataei, N. , and Padgett, J. E. , 2011, “ Coastal Bridge Reliability During Hurricane Events: Comparison of Fragility Curves by Static and Dynamic Simulation,” ASCE Structures Congress, Las Vegas, NV, pp. 2263–2274.
Akiyama, M. , Frangopol, D. M. , Arai, M. , and Koshimura, S. , 2012, “ Probabilistic Assessment of Structural Performance of Bridges Under Tsunami Hazard,” ASCE Structures Congress, Chicago, IL, pp. 1919–1928.
Sobanjo, J. , Thompson, P. , and Kerr, R. , 2013, “ Modeling Hurricane Hazards and Damage on Florida Bridges,” Transp. Res. Rec.: J. Transp. Res. Board, 2360, pp. 60–68. [CrossRef]
Ataei, N. , and Padgett, J. E. , 2015, “ Influential Fluid–Structure Interaction Modelling Parameters on the Response of Bridges Vulnerable to Coastal Storms,” Struct. Infrastruct. Eng., 11(3), pp. 321–333. [CrossRef]
Sheng, Y. P. , Zhang, Y. , and Paramygin, V. A. , 2010, “ Simulation of Storm Surge, Wave, and Coastal Inundation in the Northeastern Gulf of Mexico Region During Hurricane Ivan in 2004,” Ocean Modell., 35(4), pp. 314–331. [CrossRef]
Brater, E. F. , McNown, J. S. , and Stair, L. D. , 1958, “ Wave Forces on Submerged Structures,” J. Hydraul. Div., ASCE, 84, pp. 1–26.
Herbich, J. B. , and Shank, G. E. , 1970, “ Forces Due to Waves on Submerged Structures Theory and Experiment,” Offshore Technology Conference, Houston, TX, pp. 189–202.
Durgin, W. W. , and Shiau, J. C. , 1975, “ Wave Induced Pressures on Submerged Plates,” J. Waterw., Harbor, Coastal Eng., 101, pp. 59–71.
Rey, V. , and Touboul, J. , 2011, “ Forces and Moment on a Horizontal Plate Due to Regular and Irregular Waves in the Presence of Current,” Appl. Ocean Res., 33(2), pp. 88–99. [CrossRef]
Kulin, G. , 1958, “ Solitary Wave Forces on Submerged Cylinders and Plates,” National Bureau of Standards, Washington, DC, Technical Report No. 5876, p. 44.
Kojima, H. , Yoshida, A. , and Nakamura, T. , 1994, “ Linear and Nonlinear Wave Forces Exerted on a Submerged Horizontal Plate,” International Conference on Coastal Engineering, Kobe, Japan, pp. 1312–1326.
Hayatdavoodi, M. , and Ertekin, R. C. , 2012, “ Nonlinear Forces on a Submerged, Horizontal Plate: The GN Theory,” 27th International Workshop on Water Waves and Floating Bodies (IWWWFB27), Copenhagen, Denmark, Apr. 22–25, pp. 69–72.
Hayatdavoodi, M. , and Ertekin, R. C. , 2014, “ A Comparative Study of Nonlinear Shallow-Water Wave Loads on a Submerged Horizontal Box,” ASME Paper No. OMAE2014-24572.
Kerenyi, K. , Sofu, T. , and Guo, J. , 2009, “ Hydrodynamic Forces on Inundated Bridge Decks,” Technical Report No. FHWA-HRT-09-028, Turner-Fairbank Highway Research Center, McLean, VA, Technical Report No. FHWA-HRT-09-028, p. 38.
Bricker, J. D. , and Nakayama, A. , 2014, “ Contribution of Trapped Air, Deck Superelevation, and Nearby Structures to Bridge Deck Failure During a Tsunami,” J. Hydraul. Eng., 140(5), p. 05014002. [CrossRef]
Hayatdavoodi, M. , 2013, “ Nonlinear Wave Loads on Decks of Coastal Structures,” Ph.D. thesis, University of Hawaii at Manoa, Honolulu, HI, p. 186.
Bagnold, R. A. , 1939, “ Interim Report on Wave-Pressure Research,” J. Inst. Civ. Eng., 12, pp. 201–226. [CrossRef]
Mitsuyasu, H. , 1966, “ Shock Pressure of Braking Waves,” 10th Conference on Coastal Engineering, ASCE, Tokyo, Japan, pp. 268–283.
Bullock, G. N. , Crawford, A. R. , Hewson, P. J. , Walkden, M. J. A. , and Bird, P. A. D. , 2001, “ The Influence of Air and Scale on Wave Impact Pressures,” Coastal Eng., 42(4), pp. 291–312. [CrossRef]
Takahashi, S. , Tanimoto, K. , and Miyanaga, S. , 1985, “ Uplift Wave Forces Due to Compression of Enclosed Air Layer and Their Similitude Law,” Coastal Eng. Jpn., 28, pp. 191–206.
Serinaldi, F. , and Cuomo, G. , 2011, “ Characterizing Impulsive Wave-In-Deck Loads on Coastal Bridges by Probabilistic Models of Impact Maxima and Rise Times,” Coastal Eng., 58(9), pp. 908–926. [CrossRef]
Ataei, N. , and Padgett, J. E. , 2012, “ Probabilistic Modeling of Bridge Deck Unseating During Hurricane Events,” J. Bridge Eng., 18(4), pp. 275–286. [CrossRef]
Yung, T. , Sandström, R. , He, H. , and Minta, M. , 2010, “ On the Physics of Vapor/Liquid Interaction During Impact on Solids,” J. Ship Res., 54(3), pp. 174–183.
Wood, D. J. , and Peregrine, D. H. , 1998, “ Pressure-Impulse Theory for Water Impact on a Structure With Trapped Air,” 13th International Workshop on Water Waves and Floating Bodies (IWWWFB13), A. J. Hermans , ed., pp. 175–178.
Evans, D. V. , 1982, “ Wave-Power Absorption by Systems of Oscillating Surface Pressure Distributions,” J. Fluid Mech., 114(1), pp. 481–499. [CrossRef]
Suchithra, N. , and Koola, P. M. , 1995, “ A Study of Wave Impact of Horizontal Slabs,” Ocean Eng., 22(7), pp. 687–697. [CrossRef]
Cuomo, G. , Shimosako, K. , and Takahashi, S. , 2009, “ Wave-In-Deck Loads on Coastal Bridges and the Role of Air,” Coastal Eng., 56(8), pp. 793–809. [CrossRef]
Seiffert, B. , Ertekin, R. C. , and Robertson, I. N. , 2015, “ Effect of Entrapped Air on Solitary Wave Forces on a Coastal Bridge Deck With Girders,” J. Bridge Eng., 21(2), p. 04015036. [CrossRef]
Suponitsky, V. , Froese, A. , and Barsky, S. , 2014, “ Richtmyer–Meshkov Instability of a Liquid–Gas Interface Driven by a Cylindrical Imploding Pressure Wave,” Comput. Fluids, 89, pp. 1–19. [CrossRef]
Araki, S. , and Nishiyama, S. , 2015, “ Characteristics of Pressure Caused by Air Compression Acting on Underside of Bridges Time Series of Pressure,” Twenty-Fifth International Ocean and Polar Engineering Conference, Kona, HI, June 21–26, pp. 753–758.
Azadbakht, M. , and Yim, S. C. , 2016, “ Effect of Trapped Air on Wave Forces on Coastal Bridge Superstructures,” J. Ocean Eng. Mar. Energy, 2(2), pp. 139–158. [CrossRef]
Hoshikuma, J. , Zhang, G. , Nakao, H. , and Sumimura, T. , 2013, “ Tsunami-Induced Effects on Girder Bridges,” International Symposium for Bridge Earthquake Engineering in Honor of Retirement of Professor Kazuhiko Kawashima, Tokyo, Japan, p. 13.
Cuomo, G. , Piscopia, R. , and Allsop, W. , 2011, “ Evaluation of Wave Impact Loads on Caisson Breakwaters Based on Joint Probability of Impact Maxima and Rise Times,” Coastal Eng., 58(1), pp. 9–27. [CrossRef]
Salem, H. , Mohssen, S. , Kosa, K. , and Hosoda, A. , 2014, “ Collapse Analysis of Utatsu Ohashi Bridge Damaged by Tohuku Tsunami Using Applied Element Method,” J. Adv. Concr. Technol., 12(10), pp. 388–402. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

U.S. 90 Bridge from Bay St. Louis to Pass Christian, damaged by Hurricane Katrina (2005). During the event, the maximum storm surge at the site was about 6.6 m. This allowed for waves with significant wave height of about 2.6 m and period of 5.5 s to reach the bridge, see Ref.[6]. (Reprinted with permission from Riggs et al. [7].)

Grahic Jump Location
Fig. 2

Variation of the uplift force on a horizontal dock as functions of the wave height and wavelength. Solid lines are the mean lines fitted to the measured data points. In this case, the SWL is as high as the top of the deck, B=1.22 m (4.0 ft) is thewidth of the deck. In this experiment, h=0.61 m (2 ft) and tP=0.006 m (0.25 in.), where tP is the deck thickness. (Courtesy of El Ghamry [85].)

Grahic Jump Location
Fig. 3

A schematic of the wave-induced force time history on the bridge decks, a combination of the impact force and the slowly varying force, working at significantly different frequencies. The peak of these two types of forces usually does not happen at the same time; the impact force occurs slightly before the peak of the slowly varying force. (Replotted from Douglass et al. [89]. Copyright 2007 by World Scientific.)

Grahic Jump Location
Fig. 4

Mean and standard deviation of the maximum (uplift and downward) measured forces versus wave height, both rigid and flexible setups, for regular waves with h=1.89 m, deck clearance =0 m, and T=2.5 s. Error bars in this figure showone standard deviation. (Reprinted with permission from Schumacher et al. [81].)

Grahic Jump Location
Fig. 5

Maximum storm surge and crest elevation of significantwave height at the location of the U.S. 90 Bridge over Biloxi Bay during Hurricane Katrina (2005), estimated using a SWAN + ADCIRC model. All the submerged spans and those under the crest of the significant wave height were collapsed. (Reprinted with permission from Chen et al. [121]. Copyright 2009 by ASCE.)

Grahic Jump Location
Fig. 6

Comparison of the surface elevation and dimensionless vertical and horizontal forces of the laboratory measurements and calculations of Euler's equations (using openfoam) of interaction of cnoidal waves with a bridge deck with no girders, located at the SWL (h=0.071 m, H/h≈0.4, and λ=1.9 m. Fx3 and Fx1 in these figures refer to the vertical and horizontal forces, respectively. See the reference for definition of dimensionless forces. (Reprinted with permission from Hayatdavoodi et al. [83]. Copyright 2015 bySpringer.)

Grahic Jump Location
Fig. 7

Comparison of cnoidal waves: (a) horizontal force and(b) vertical force calculated by Euler's equations and theGN equations versus laboratory measurements on a submerged bridge deck (H/h=0.26 ,λ/h=26.76 ,hII/h=0.6, and h=0.071m). hII is the submergence depth measured from the SWL to the top of the deck. (Reprinted with permission from Ertekin and Hayatdavoodi [72]. Copyright 2015 by MTS/IEEE.)

Grahic Jump Location
Fig. 8

Laboratory measurements and the GN and LWA calculations of (a) vertical uplift, (b) vertical downward, (c) horizontal positive, and (d) horizontal negative forces of cnoidal waves of different wave heights and wavelengths propagating over a submerged plate (h=0.071 m and hII/h=0.6), where hII is the submergence depth. (Reprinted with permission from Hayatdavoodi et al. [83]. Copyright 2015 by Springer.)

Grahic Jump Location
Fig. 9

Two-dimensional (a) vertical uplift, (b) vertical downward, (c) horizontal positive, and (d) horizontal negative forces of the cnoidal and solitary waves on a submerged deck with no girders (B/h=2.67 and hII/h=0.6). Starting from the left data point, the cnoidal wavelengths are λ/h=12.3, 15, 16.7, 18.5, and 20.2. Bridge deck width is kept constant. (Reprinted with permission from Hayatdavoodi and Ertekin [67]. Copyright 2015 by ASME.)

Grahic Jump Location
Fig. 10

openfoam computations of gauge pressure (pressure with respect to the atmospheric pressure at sea level) at the initial stage of interaction of a solitary wave (h=0.143 m,a/h=0.407, and B/h=2.1, where a is the wave amplitude) with bridge decks (a) without openings and (b) with air-relief openings. Pressure is given in Pascal. (Reprinted with permission from Hayatdavoodi et al. [82]. Copyright 2014 by Elsevier.)

Grahic Jump Location
Fig. 11

Effect of a number of air pockets (one minus number of girders) on the oscillations of the force due to wave slamming on the bridge deck. (Reprinted with permission from Sheppard and Marin [14]. Copyright 2009 by University of Florida.)

Grahic Jump Location
Fig. 12

Effect of air entrapment on the solitary wave forces on a bridge deck, h=0.143 m, a/h=0.2, and z*/h=0.1, where a and z* are the wave amplitude and elevation from the SWL, respectively. Here, the ARO percentage refers to the percentage area of air-relief openings to the side area between girders; ARO=0% indicates no openings (full air entrapments), and ARO=100% refers to zero air entrapment. (Reprinted with permission from Seiffert et al. [173]. Copyright 2015 by ASCE.)

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