The effects of the deck inclinations on the peak moments (both positive and negative moments) are presented in Fig. 4.13. Again, while the left part of each plot shows the positive and negative peak values, the right part shows the ratios or the normalized values, i.e., 𝑀𝑚𝑜𝑚𝑒𝑛𝑡
|𝑀0| , where 𝑀𝑚𝑜𝑚𝑒𝑛𝑡 and 𝑀0 are similarly defined as the
cases of the horizontal and vertical forces. It is noted that for some inclination angles, there is only either positive or negative moment, not both.
For the case of E7.2/CS(-0.889), higher waves do not always generate larger moments, and the trends of the ratios are not clear. For the case of E7.5/CS(-0.667), the ratios of the positive moments decrease, then increase with the increase of the bridge deck inclinations from negative to positive values. However, the ratios of the negative moments increase, then decrease with the increase of the bridge deck inclinations.
(a) E7.2/CS(-0.889)
(b) E7.5/CS(-0.667)
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(c) E7.8/CS(-0.444)
(d) E8.1/CS(-0.222)
(e) E8.4/CS(0)
Fig. 4.13 (continued) Moments considering bridge deck inclinations
For the other five cases, E7.8/CS(-0.444), E8.1/CS(-0.222), E8.4/CS(0), E8.7/CS(0.222) and E9.0/CS(0.444), the general trends of the positive and negative moments are much clear. It can be observed that larger moments, positive or negative, are companied with higher wave heights. For the cases of E8.7/CS(0.222) and E9.0/CS(0.444), the trends of both the positive and negative moments increase as the
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bridge deck inclinations increase; and the ratios vary with the wave heights. For the cases of E8.4/CS(0), E8.7/CS(0.222) and E9.0/CS(0.444), the dominating moments with negative bridge deck inclinations are negative moments, and are positive moments with positive bridge deck inclinations.
(f) E8.7/CS(0.222)
(g) E9.0/CS(0.444)
Fig. 4.13 (continued) Moments considering bridge deck inclinations
The values of the moments depend on the corresponding horizontal forces and vertical forces. In the calculation process, all the horizontal and vertical forces are integrated by the pressure along the whole bridge model surface. While some local pressure changes may not affect the total horizontal or vertical forces, they influence the moments. As a result, the normalized ratios of the moments either increase or decrease with the increase of the bridge deck inclinations. In addition, both the bridge deck inclination and the wave heights play important roles on the moments.
4.4 Concluding Remarks
From this research concerning wave forces due to solitary waves on bridge decks with inclinations, conclusions can be drawn as follows:
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(1) Higher waves are accompanied with larger wave forces on the bridge decks, especially for the wave-induced horizontal forces and vertical forces. However, there are some exceptions for the moment forces when the bridge deck is fully submerged into the water. Generally speaking, the wave forces on the inclined bridge decks under solitary waves are affected by the following factors: wave heights, bridge deck inclinations, and the relative position between the wave peak (the height of water depth plus the wave height) and the top of the seaward girder. The wave heights and bridge deck inclinations play more significant roles than the other factors.
(2) Generally speaking, the increment of the normalized ratios of the horizontal forces for the bridge deck inclinations from −6o to 0o is smaller than that for the bridge
deck inclination from 0o to 6o when the wave peak is higher than the top of the seaward
girder. The ratios generally increase with the increase of the bridge deck inclinations from −6o to 6o.
(3) The increment of the normalized ratios of the vertical forces for the bridge deck inclination from −6o to 0o is larger than that for the bridge deck inclination from 0o
to 6o. The normalized ratios increase as the bridge deck inclinations increase, especially
when the bridge deck is partially or fully submerged into the water.
(4) The ratios of the moments do not have consistent trends for the seven different bridge elevations studied in the present study. The dominating moments with negative bridge deck inclinations are negative moments, and are positive moments with positive bridge deck inclinations when the leveled bridge decks are above the SWL. However, the dominating moments with negative bridge deck inclinations are positive moments when the levelled bridge decks are under the SWL.
The limitations of the current study and future work are described as follows: (1) In the present study, 2D numerical simulations have been conducted. However, 3D models may provide more reliable results, but maybe much more computational expensive. (2) The bridge models employed in the present study are simplified without considering the railing and the diaphragm. Hence, more studies are needed to further investigate the wave forces due to solitary waves on coastal bridge decks with inclinations. (3) In this study, laminar flow is adopted. In the future work, effects of the turbulence need to be considered.
4.5 References
Bozorgnia, M., Lee, J., and Raichlen, F. (2010). “Wave Structure Interaction: Role of Entrapped Air on Wave Impact and Uplift Forces.” Proceedings of 32nd
Conference on Coastal Engineering, Shanghai, China.
Bozorgnia, M., and Lee, J. (2012). “Computational Fluid Dynamic Analysis of Highway Bridges exposed to Hurricane Waves.” Proceedings of 3rd
Conference on Coastal Engineering, Santander, Spain.
Bradner, C., Schumacher, T., Cox, D., and Higgins, C. (2011). “Experimental Setup for a Large-Scale Bridge Superstrcuture Model Subjected to Waves.” Journal of
103
Bricker, J.D., Kawashima, K., and Nakayama, A. (2012). “CFD Analysis of Bridge Deck Failure due to Tsunami.” Proceedings of the International Symposium on
Engineering Lessons Learned from the 2011 Great East Japan Earthquake,
March 1-4, Tokyo, Japan. pp.1398-1409.
Bricker, J.D., and Nakayama, A. (2014). “Contribution of trapped air, deck superelevation, and nearby structures to bridge deck failure during a tsunami.”
Journal of Hydraulic Engineering, ASCE, 05014002-1 to 7 (in press).
Cuomo, G., Shimosako, K., and Takahashi, S. (2009). “Wave-in-deck loads on caostal bridges and the role of air.” Coastal Engineering, 56:793-809.
Denson, K. H. (1980). “Wave forces on causeway-type coastal bridges: Effects of angel of wave incidence and cross section shape.” Water Resources Research Institute, Mississippi State University, 242 pp.
FHWA (2008). “Highways in the coastal environment.” Hydraulic Engineering Circular No.25. 2nd edition. Publication No. FHWA-NHI-07-096. Washington, D.C.
French, JA. (1969). “Wave uplift pressure on horizontal platforms.” Report No. KH_R_19. Pasadena (CA): W.M. Keck Laboratory of Hydraulics and Water Resources, California Inst. of Tech.
Gilberto, M. (2005). “US 90 to I-10 Ramp Bridge over Mobile Bay Baldwin County, Alabama just east of Mobile.” MCEER, <http://mceer.buffalo.edu> (Feb. 22, 2014).
Ghobarah, A., Saatcioglu, M., and Nistor, I. (2006). “The Impact of the 26 December 2004 Earthquake and Tsunami on Structures and Infrastructure.” Journal of
Engineering Structures. 28(2), pp:312-326.
Graumann, A., Houston, T., Lawrimore, J., Levinson, D., Lott, N., McCown, S., Stephens, S., and Wuerts, D. (2005). “Hurricane Katrina: A climatological perspective— Preliminary report.” Technical Rep. No. 2005-01, NOAA’s Climate Data Center, Washington, D.C.
Huang, W., and Xiao, H. (2009). “Numerical Modeling of Dynamic Wave Force Acting on Escambia Bay Bridge Deck during Hurricane Ivan.” Journal of Waterway,
Port, Coastal, and Ocean Engineering, ASCE, 135(4), 164-175.
McPherson, R.L. (2008). “Hurricane Induced Wave and Surge Forces on Bridge Decks.” Texas A&M University (Master’s thesis).
Riggs, H.R. (2007). “JWPCOE Special Issue: Tsunami Engineering (Introduction).”
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Shoji, G., and Moriyama, T. (2007). “Evaluation of the Structural Fragility of a Bridge Structure Subjected to a Tsunami Wave Load.” Journal of Natural Disaster
Science, Vol. 29, No. 2, pp:73-81.
U.S. Agency for International Development (USAID). (2005). Tsunami relief, Bureau for Legislative and Public Affairs. Washington, D.C.
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.” Computer &
Fluids, 39, 1390-1400.
Xu, G., Cai, C.S., and Deng, L. (2015). “An improved method for investigating wave forces of Biloxi Bay Bridge Decks by solitary waves.” Journal of Waterway, Port,
Coastal, and Ocean Engineering, ASCE. (submitted).
Yeh, H., Francis, M., Peterson, C., Katada, T., Latha, G., Chadha, R.K., Singh, J.P., and Rahghuraman G. (2007). “ Effects of the 2004 Great Sumatra Tsunami: Southeast Indian Coast.” Journal of Waterway, Port, Coastal, and Ocean Engineering, 133, pp.382-340.
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CHAPTER 5. NUMERICAL SIMULATIONS OF LATERAL RESTRAINING