Elsevier

Coastal Engineering

Volume 165, April 2021, 103857
Coastal Engineering

Experimental investigation of focused wave action on coastal bridges with box girder

https://doi.org/10.1016/j.coastaleng.2021.103857Get rights and content

Highlights

  • •Wave forces acting on coastal bridge with box girder was concerned.

  • •The periodic focused waves were used as the incident wave to simulate hurricane-generated waves.

  • •The process of wave action on bridge model was visually observed by a high-speed camera.

  • •A smoothing method was employed to separate the quasi-static and slamming parts of the total wave forces.

Abstract

The waves generated by hurricanes, together with storm surges, have led to severe damage and even failures in many coastal bridges in the Gulf of Mexico. Several studies have been conducted to investigate the effects of wave action on coastal bridges over the past 15 years. However, most of the existing research, both experimental and numerical, has used a regular or irregular wave as the incident wave; this cannot accurately and efficiently reproduce the features of hurricane waves. In this study, a periodical focused wave (PFW) was employed to experimentally investigate wave actions on coastal bridges. A coastal bridge model including a deck and box girder was set up in a wave flume to measure wave forces. PFWs with different peak frequencies and main crests were calibrated in the empty flume, and then were used to observe the wave action on the bridge model at different clearances. Using a smoothing method, the quasi-static and slamming parts were separated from the total wave forces. The experimental results show that the maximum horizontal and vertical wave forces both occur at approximately the time when the overhanging deck is fully submerged and wave water begins to overlap the bridge deck. The vertical quasi-static force is almost linear in relation to the main crest and clearance, but the horizontal and vertical slamming forces show a complicated tendency. The relationships between the dimensionless wave forces and relative maximum amplitude/wave steepness are studied, along with the relative relationships between the wave force components. The experimental results are also compared with those from two existing methods.

Introduction

The waves generated by hurricanes or typhoons are a serious threat to the safety of coastal bridges. Hurricanes Ivan (2004) and Katrina (2005) almost ruined the traffic network along the Gulf of Mexico by severely damaging or destroying more than 44 coastal bridges (DesRoches, 2006). Despite not being thoroughly recognized, the enormous force of the waves was the major reason for the failure of the bridges. Prior to these catastrophic failures of coastal bridges, Denson (1978) was the only researcher to investigate the wave forces acting on bridge decks. In a hydrodynamic experiment conducted by Denson, the pressure acting on a 1:24 scale bridge model under an incident regular wave with a period of 3.0 s was observed. However, even the wave period used in Denson's experiment was not strictly similar to that of a hurricane-generated wave, and the topic of wave forces acting on bridge decks would not be revisited for another two decades.

Owing to Hurricanes Ivan and Katrina, the destructive power of hurricane waves has attracted increased attention from researchers and engineers. The civil and coastal engineering communities conducted a post-disaster survey, and three general failure conditions—unseating, drifting of the superstructures, and fractures of the guardrails—were recognized in the 44 damaged bridges, which were located in Alabama, Louisiana, and Mississippi (DesRoches, 2006). Robertson et al. (2007) surveyed the damage to coastal infrastructure generated by Hurricane Katrina. Their survey showed that the unanticipated hydrostatic and hydrodynamic forces were the main reasons for structural damage or failure; a similar conclusion was drawn by Okeil and Cai (2008). According to estimates at that time, it was expected to cost over $1 billion to repair or replace the bridges damaged during Hurricane Katrina (Padgett et al., 2008).

Both the design of new coastal bridges and the reinforcement of existing vulnerable bridges require insight into the nature of wave forces. The hydrodynamic environment during a hurricane has been investigated in the primary stages. Chen et al. (2007) investigated the surge and wave fields in Mobile Bay using two state-of-the-art numerical models, “Simulating Waves Nearshore” and “Advanced Circulation Model” (ADCIRC). The results of this integrated wave-surge numerical methodology were then employed to empirically estimate the wave loads acting on the US 90 bridge across Biloxi Bay (Chen et al., 2009). Smith (2007) simulated nearshore waves during a hurricane in four different areas around southern Louisiana using the “Steady-State Spectral Wave” model, as coupled with ADCIRC. The wave properties during hurricanes or typhoons have been further studied by several researchers (Wang et al., 2005; Fritz et al., 2007; Sheng et al., 2010; Mori, 2012). The hindcast results from surge and wave conditions near bridges supplied valuable insight into the hydrodynamic environments surrounding coastal bridges during hurricanes.

With reference to the hindcast results of wave conditions, several experiments and numerical simulations have been performed to explore the mechanisms of waves acting on coastal bridges. For both regular and irregular waves, the wave action on coastal bridges has been observed using either physical or numerical models at different scales (Mcpherson, 2008; Cuomo et al., 2009; Huang and Xiao, 2009; Bradner et al., 2011; Jin and Meng, 2011; Guo et al., 2015; Seiffert et al., 2015b). The wave forces and pressures at different deck clearances were investigated in those studies by considering the effects of the wave heights and wave periods. Using experimental data, Mcpherson (2008) verified the applicability of four different theoretical methods for calculating the forces on deck-like structures. It was concluded that the hydraulic engineering circular 25 (HEC-25) model could reasonably estimate the wave uplift forces on elevated decks (Douglass and Krolak, 2008). The general conclusions were that the wave forces contain a short-duration but large amplitude impulsive component and long-duration slow-varying component. The wave forces increase with wave height and wave period, and are significantly influenced by the clearance.

With respect to other destructive ocean waves, e.g., tsunami waves, a solitary wave is frequently used to study the wave action on bridges (Mcpherson, 2008; Hayatdavoodi et al., 2014; Azadbakht and Yim, 2015; Xu et al., 2016; Sarfaraz and Pak, 2017; Cai et al., 2018; Istrati et al., 2018); this approach has provided a valuable understanding of the wave action on coastal bridges. For bridges located in coastal zones, the specific wave characteristics should be considered (Madsen et al., 2008; Chan and Liu, 2012). Bores and dam breakers have been used to simulate such destructive waves, and to investigate the effects of the wave action on structures (Leschka et al., 2014; Chen et al., 2016a, 2018; Istrati et al., 2018). One study found that the offshore-side structural components, such as individual bearings and columns, would be able to stand larger portions of the total uplift forces generated by the bores, in comparison with those induced by unbroken solitary waves (Istrati et al., 2018).

According to the clearance, the wave action on a coastal bridge can be divided into three different scenarios: elevated, semi-submerged, and fully submerged. The elevated scenario, with the lowest chord of the bridge superstructure higher than the still water level, is the most complicated, owing of the strong nonlinearities of water waves (such as wave breaking, slamming, aeration, and air entrapment). Breaking and broken waves can generate larger forces on elevated structures than nonbreaking waves, as comparatively studied by Park et al. (2017). Trapped air can significantly amplify the uplift wave forces acting on bridges (Bozorgnia et al., 2011; Bricker and Nakayama, 2014; Hayatdavoodi et al., 2014; Seiffert et al., 2015a; Istrati and Buckle, 2019). However, it has been found that the trapped air has a limited influence on the horizontal wave force (Bozorgnia et al., 2011; Seiffert et al., 2015a; Istrati and Buckle, 2019); in addition, it will reduce the local maximum impact pressure and lengthen the load duration (Cuomo et al., 2009). The fully submerged scenario is seldom influenced by air trapping and wave slamming. However, in some studies, a negative uplift force has been observed when a wave trough passes through a structure (Xiao et al., 2010; Bricker and Nakayama, 2014; Guo et al., 2015; Huang et al., 2018b). When the top of the superstructure is lower than the wave crest, the wave water overtops the bridge deck, and reduces the uplift forces with the phase difference (Jin and Meng, 2011; Istrati et al., 2018). The semi-submerged scenario shows intermediate features between the elevated and fully submerged scenarios.

As indicated by post-disaster surveys (DesRoches, 2006; Okeil and Cai, 2008), the main reason for the failure of coastal bridges is the lack of adequate (or in some cases, any) connections between the simply supported noncontinuous spans and substructure. Both the stiffness of the connections between the superstructure and substructure and the structural response can influence the wave action on coastal bridges. The effects of elastic supports on coastal bridges under regular wave action were experimentally observed by Bradner et al. (2011). With a similar experimental setup, Istrati (2017) investigated the role of dynamic fluid-structure-interactions when sustained by unbroken solitary waves and bores impacting on coastal bridges. As expected, a movable bridge deck reduced the wave force in both the horizontal and vertical directions (Chen et al., 2016b), but the smaller restraining stiffness resulted in a larger deck displacement (Xu and Cai, 2017). It was revealed that the flexibility of the bearing connection influenced the load distribution (Istrati, 2017). Attention should also be paid to the inertial forces to consider the structural flexibilities (Xu and Cai, 2015, 2017), especially in numerical works that consider wave loads by integrating the pressure(s) over the structural surface (Istrati, 2017).

In addition, hindcast results for hurricanes have indicated that wave directions are not always perpendicular to bridge decks. Fang et al. (2019) investigated the effect of the wave angle on the wave loads of bridges. In their study, a bridge model for a hydrodynamic test included one full segment, two dummy span segments, two bent caps, and four columns. A similar bridge model was also employed in the studies of Cuomo et al. (2009) and Guo et al. (2015). In addition, three-dimensional numerical simulations were also conducted by Crowley et al. (2018) and Motley et al. (2016) for bridge decks sustaining oblique regular or solitary waves. The effect of the bridge deck inclination on wave loads was also studied by Xu and Cai (2014). It was found that an inclined bridge deck generally suffered larger horizontal and vertical wave forces.

The above-mentioned studies mainly focused on bridges with T- or I-girders. Several studies on box girder bridges have also been conducted. Based on a periodical wave, Huang et al. (2018b) experimentally investigated the wave forces acting on a box-girder bridge deck under different submergence levels, and subsequently checked the effects of co-existing currents on wave forces (Huang et al., 2018a). The solitary wave forces acting on box-girder bridges have also been studied and compared with the wave forces acting on T- or I-girder bridges (Azadbakht, 2013; Hayashi et al., 2013; Istrati, 2017). It was found that bridges with box girders experienced larger wave forces than those with T- or I-girders (Azadbakht, 2013; Istrati, 2017) or bore (Istrati, 2017).

From the above review of the literature, it can be concluded that regular waves have been the most frequently used for examining the hurricane wave action on T- or I-girder coastal bridges. The significant wave height and peak period from hindcast modeling provide a reliable guide to the wave conditions in the existing research. In contrast, there have been relatively few studies on the hurricane wave forces acting on box girder bridges. Further investigation (including of the wave nonlinearity and energy spectral distribution) is still required, as significant nonlinearities have been recognized in the waves generated by hurricanes (Soares et al., 2003, 2004; Liu et al., 2009; Mori, 2012). The nonlinearity and energy spectral distribution should be considered when studying the hurricane wave action on structures, as regular waves cannot reflect such details. Irregular waves are the preferred approach for simulating hurricane waves. However, their simulation requires a significant amount of time, and it remains difficult to predict the time and location of large waves, whether in a laboratory or a numerical simulation. An alternative approach to generating large waves in a wave flume is a focused wave. A focused wave is generated by focusing the wave crests of multiple waves (with different periods and traveling at different speeds) at the same location and time. Focused waves have been widely employed to explore extreme wave actions on different types of offshore structures or structural members, such as horizontal and vertical cylinders (Westphalen et al., 2012), platform decks (Suchithra and Koola, 1995), floating boxes (Zhao and Hu, 2012), semisubmersibles (Li et al., 2017), and wave energy converters (Hann et al., 2018).

This study experimentally investigated the wave forces acting on a box-girder-type coastal bridge under periodical focused waves (PFWs). The purpose of this study was to explore the characteristics of the wave forces exerted by hurricane waves, and to obtain further insight into the mechanisms of the hurricane-generated wave action on coastal bridges. In the present study, an experiment was performed with a scaled coastal box-girder bridge model in a wave flume equipped with a piston-type wavemaker. This paper contains five additional parts. In Section 2, the experimental setup is introduced, including the facilities, model and measurements, and test plan. In Section 3, the wave elevations in an empty flume and during the model test are presented. In Section 4, the time series of the wave forces and visual observation results are reported. In Section 5, the statistical test results are reported, and the forces under the incident PFWs are discussed. Section 6 discusses the dimensionless wave forces and existing methods for wave-force calculations. Finally, concluding remarks are provided.

Section snippets

Facility

The experiment was conducted in a two-dimensional wave flume with a length of 30 m, width of 0.8 m, and depth of 1.0 m. The water depth was kept constant at 0.5 m. One end of the flume was equipped with a piston-type wavemaker, which was driven by a computer-controlled servomotor to generate different types of waves. At the other end, a multi-layer inclined perforated plate beach slope and sponge box were used to eliminate the reflection from the end wall. An external steel frame was designed

Incident waves in empty flume

Focused waves, which have been widely used to study extreme wave actions on structures, were adopted for the present experiment. Generally, test trials are repeated more than three times, so as to eliminate potential experimental errors during the measurement of wave forces acting on bridge decks (Seiffert et al., 2014; Huang et al., 2018b). The normal practice for repeating a focused wave test is to perform another trial with the same wavemaker movement. However, this method is time-consuming,

Wave force separation

The wave forces acting on the bridge model were obtained by summing the measured results from the four load cells in the same direction. It is well-known that the wave forces acting on coastal bridges contain a slowly varying load with a duration related to the wave period, i.e., the quasi-static force, and an impact load with an extremely short duration, i.e., the slamming force (Douglass et al., 2006). Similar features have been found in the wave forces acting on columns (Wienke and Oumeraci,

Maximum wave forces in relation to wave conditions

The results from the tests of PFWs with different peak frequencies and main crests impacting the bridge model at different clearances are presented in this section. Following the discussion in the previous section, the maximum horizontal, vertical, quasi-static, and slamming forces during the main crest acting on the bridge model were extracted from the measured results, to thereby explore the changes in wave loads with respect to the peak frequency, maximum amplitude, and clearance.

Dimensionless wave forces vs. relative maximum amplitude and wave steepness

In this subsection, the relationships between the dimensionless wave forces and relative maximum amplitude and wave steepness are discussed. The dimensionless wave forces FH, FV, FVQ, and FVS are expressed as follows:FH,FV,FVQ,FVS=FH/[rglhm(AmaxC)],(FV,FVQ,FVS)/[rglhm(AmaxC)]

In the above, ρ is the water density, g is the gravitational acceleration, and hm and wd are the structural height and width, respectively, as shown in Fig. 2.

Fig. 17 shows the relationship between the

Conclusion

In this study, a hydrodynamic experiment was conducted to investigate hurricane wave actions on coastal bridge superstructures. Unlike the regular or irregular waves used in existing research, in the present study, the PFW was employed to simulate the hurricane waves. The elevations of the incident PFWs were verified to be relatively repetitive and in good agreement with the theoretical values. The wave elevations and forces were measured as the PFWs impacted a box-girder bridge model.

CRediT authorship contribution statement

Qinghe Fang: Methodology, Investigation, Writing - original draft. Jiabin Liu: Writing - original draft, Visualization. Rongcan Hong: Investigation. Anxin Guo: Project administration, Writing - review & editing. Hui Li: Supervision, Funding acquisition.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

The authors greatly appreciate the financial support provided by the National Natural Science Foundation of China (51808172, 51725801, 51921006) and Fundamental Research Funds for the Central Universities. This work was also partially supported by open funding from the Key Laboratory of Coastal Disasters and Defense of the Ministry of Education (201802).

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