Response Sensitivity for Probabilistic Damage Assessment of Coastal Bridges Under Surge and Wave Loading

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1 Response Sensitivity for Probabilistic Damage Assessment of Coastal Bridges Under Surge and Wave Loading Navid Ataei, Matthew Stearns, and Jamie E. Padgett The susceptibility of coastal bridges to damage during hurricane-induced storm surge has been illustrated along the U.S. Gulf Coast in several hurricane events. This factor poses a significant threat to the safety of nationwide transportation systems, effectiveness of postevent emergency response and recovery activities, and socioeconomic stability further afforded by functioning transportation infrastructure. Nationwide risk and loss assessment packages currently lack any reliable input models of bridge fragility to assess the risk to the transportation infrastructure posed by hurricane-induced storm surge and wave. However, these tools are essential for comparing the vulnerability of different bridge types, conducting regional risk assessment or loss estimates, and supporting decision making on risk mitigation activities. As a first step in the development of probabilistic models of bridge vulnerability subjected to hurricane scenarios, sensitivity studies are conducted to assess the significance of varying hazard and bridge parameters on the dynamic response of coastal bridges. Three-dimensional nonlinear finite element models are used to assess these demands under varying input modeling parameters, and an analysis of variance is conducted to evaluate the significance of each parameter. The sensitivity study reveals that the potential variation in wave parameters has the most statistically significant impact on the response of the bridge. Additionally, a second-level sensitivity study reveals that the most critical structural parameter is the deck mass followed by connection modeling parameters. The results of this study provide insight into modeling parameters that should receive careful treatment in probabilistic analysis of bridge vulnerability. More than 50% of the U.S. population lives within 50 mi of the shoreline, and development continues to occur at a rapid pace in regions susceptible to coastal hazards (1). The performance of the infrastructure in these regions, such as bridge and transportation infrastructure, is critical to support the safety and vitality of coastal communities. Only recently has the performance of coastal bridge infrastructure during hurricane events become a central focus of research studies. One of the contributing factors to this delay is the ability to evacuate before hurricane landfall and hence a limited threat of fatality due to bridge collapse. However, the substantial damage to roads and bridges during Hurricane Katrina (44 highway Department of Civil and Environmental Engineering, Rice University, 6100 Main Street, Houston, TX Corresponding author: J. E. Padgett, Jamie. padgett@rice.edu. Transportation Research Record: Journal of the Transportation Research Board, No. 2202, Transportation Research Board of the National Academies, Washington, D.C., 2010, pp DOI: / bridges damaged) has highlighted the potential inhibition to postdisaster emergency response and recovery activities for a region, as well as substantial direct and indirect economic losses from a nonfunctioning transportation system. For example, the total losses during Hurricane Katarina, considering all direct and indirect losses (e.g., job losses), are estimated to exceed $100 billion (2). Bridges were revealed to be the most vulnerable critical component of the transportation system, suffering damage during hurricane-induced storm surges and wave loads (Figure 1), and costing a total of $1 billion (3) for repair and replacement. The occurrence of coastal bridge damage in hurricane-induced storm surge events is not isolated to the 2005 Hurricane Katrina. In retrospect to the history of hurricanes, one can find many bridges that were fully destroyed or severely damaged. Bridges were destroyed during Hurricane Camille (1969), at Escambia Bay, Florida, during Hurricane Ivan (2004) (4), in Hokkaido, Japan, during the Songda Typhoon (2004) (5), and in Houston and Galveston, Texas, during Hurricane Ike (2008). Moreover, global climate change influencing sea level rise could likely yield more coastal bridges susceptible to inundation or surge and wave loading during future hurricanes (6). Despite the above mentioned facts, there is currently no reliable method to probabilistically assess the vulnerability of existing bridge inventories in hurricane-prone zones. Most research has addressed the estimation of wave and surge loads on bridge superstructure (7 10) as a reconnaissance lesson and assessment of empirical data for limited bridges (2, 3, 11) or hindcasting the previous hurricane data and prediction of storm wave and water surge in coastal regions (1, 7). However, probabilistic models of bridge vulnerability are essential to assessing the risk posed to existing bridge inventories and to making decisions about retrofitting of susceptible ones. As a first step in the development of probabilistic models of bridge vulnerability during hurricane-induced loading, sensitivity studies are conducted to estimate the significance of varying hazard and bridge parameters in affecting the dynamic response of bridges. A detailed nonlinear finite element bridge model is analyzed in this paper with different structural and wave load parameters in order to capture potential accumulated damage and dynamic behavior of the bridge. A brief overview of wave and surge load models in the literature is presented and the numerical bridge models and load models adopted for this study are defined. Finally, an experimental design and the results of sensitivity studies are discussed to identify which hazard and bridge parameters have the most significant effect on the response of critical bridge components. The results provide insight into hazard intensity measures of interest in conditional reliability studies of coastal bridges, parameters by which to bin vulnerability models of different structural characteristics, and key uncertain parameters that should be carefully treated in probabilistic models 93

2 94 Transportation Research Record 2202 FIGURE 1 US-90 bridge crossing Biloxi Bay. of bridge performance under hurricane-induced surge and wave loading. REVIEW OF SELECT WAVE AND SURGE LOAD MODELS IN LITERATURE To better understand and characterize the wave loads on coastal bridge decks, the interaction of waves with the decks must first be analyzed. One of the primary considerations in analytical studies of coastal bridges subjected to hurricanes is the accuracy of wave and surge loading models. Fluid structure interaction is a complex phenomenon, due to air entrainment, turbulence, and wave diffraction. Hence, it cannot be simulated completely with computational fluid mechanics and a combination of theoretical analyses and experiments is required to properly address this problem (12). Petroleum and oil industries have devoted considerable effort to study the effects of wave loads on offshore platform decks. Hence, many of the approaches for estimating the wave loads on bridge decks are developed based on available formulations for offshore structures. However, considering that coastal bridges are usually located in shallow bodies of water with unique design features, the application of these models to coastal bridges is questionable and has received increased attention in recent years. One of the first related studies on wave forces was carried out by El Ghamry on a dock (13). Kaplan et al. proposed a mathematical model for estimating the forces on cylinders and plates of offshore structures (14). Their method is based on Morison s equation that includes drag and inertial terms. His approach estimates the forces for offshore platforms with large clearance between deck and still water level. Hence, it is not appropriate for coastal bridges, because they typically have smaller clearance. In addition, Morison s equation is valid when the structural members dimensions are very small in comparison to wave length, which is not the case for coastal bridges. The general equation for fluid flow is Navier Stokes. However, the numerical simulation of Navier Stokes equations for turbulent flow is extremely demanding. Therefore, in advanced simulations, usually methods such as time-averaged equations (e.g., Reynolds-averaged Navier Stokes equations) supplemented with turbulence models are used in practical computational fluid mechanics (9). Recently, more research has focused on hazard modeling of the event itself and estimation of wave forces on bridge superstruc- tures. Chen et al. present a method of hindcasting the wave conditions during the storm using the two state-of-the-art numerical simulation programs, ADCIRC and SWAN models (7). The surge heights, wave periods, and significant wave heights from their models matched well with recorded data from Hurricane Katrina. Cuomo et al. investigated the role of trapped air under the bridge decks in more detail through experimental testing (15). The experimental setup consisted of a 1:10 Froude scale model of a concrete girder-type bridge. The model was subjected to a series of wave loads with differing water depths, wave periods and heights, and deck opening configurations. Douglass et al. provided an extensive literature review of available methods to calculate wave forces on bridge superstructures (8). They presented a case study conducted on the US-90 Bridge at Biloxi Bay damaged during the 2005 Hurricane Katrina and estimated the wave forces using various existing wave force prediction methods. Finally, based on experimental testing conducted at Texas A&M in a wave basin, they proposed new equations to estimate maximum horizontal and vertical forces on bridge decks (8). These equations are based on the assumption that wave forces are linearly proportional to the hydrostatic reference load, which is the equivalent force acting on bridge deck if there is air on the other side of the deck. This is the basic approach of many previous formulations. However, in the Douglass et al. work, they implemented an empirical coefficient to adjust the value of the force based on the bridge geometry and wave parameters. By reviewing the available literature on storm surge and wave forces on bridge decks, one can conclude that most of them provide maximum horizontal and vertical forces acting on the deck. Although this information is valuable in preliminary risk assessment, complete time histories of wave forces are required for detailed nonlinear dynamic analysis of coastal bridges. Marin and Sheppard reported on the development of a mathematical model to predict the forces due to storm surge and wave loads in the time domain (16). The proposed model breaks the wave loads into components of drag, inertia, buoyancy, and slamming forces. They developed a program to calculate these components over time. The basis of their method builds on the work of Kaplan et al. and Morison s equation. However, they significantly improve the estimation by adding the added mass computations and discretizing the domain. The proposed algorithm was tested with field data of the I-10 Escambia Bay Bridge and gave acceptable agreement (16). Huang and Xiao (9) developed a program that uses the Reynoldsaveraged Navier Stokes (RANS) equations to simulate the wave loads on bridge decks. After verification of model, by comparison with French s tests (17), Huang and Xiao investigated the forces on the I-10 Bridge s deck. The maximum horizontal and vertical loads were compared to empirical formulas of Bea et al. (12) and Douglass et al. (8). The value of maximum uplift force derived from Douglass et al. s empirical method is slightly lower, and from Bea formulas is about 20% higher. However, the value of horizontal force from these equations is more conservative. The method used in this research to illustrate the structural response to wave force time histories on the bridge deck is derived from the new AASHTO specifications for bridges vulnerable to coastal storms (18). These forces were derived from the extensive studies of Marin and Sheppard and have been selected due to their accuracy with experimental and field data. The force models have also been implemented in a physics-based model in their work and have been determined to be accurate in both theory and practice. The time-dependent models adopted herein make simplifying assumptions regarding the

3 Ataei, Stearns, and Padgett 95 Vertical Load (kips) FIGURE 2 Time (s) Schematic vertical wave force on bridge deck. evolution of peak forces proposed in AASHTO based on Marin and Sheppard s work. The vertical force is composed of a drag force, inertial force, buoyant force, and the impact force. The drag, inertial, and buoyant forces comprise what is known as the quasistatic force. As the wave comes in contact with the girders of the bridge, the water traps pockets of air in between the wave and the bottom of the bridge deck, which causes a sudden force taken here to be the impact force (18). The impact forces will also take place in the horizontal direction, as the wave impacts each of the girders over time in the horizontal direction. These impact forces are taken to be the same magnitude as the vertical impact forces in this research. The schematic view of force is depicted in Figure 2. The negative portion of the force is caused by the suction force that arises from the wave pulling down on the air pocket and the force from the water mass on top of the bridge deck. This force can be equal in magnitude to the positive quasistatic force. The complete equations of wave peak forces are presented in Modjeski and Masters, Inc. (18). These force quantities will be used for the estimation of the peak vertical quasistatic load, the horizontal quasistatic load, and the vertical slamming force. A simplified model for deriving a time history of the wave forces has not been analyzed in great detail to date in the literature, but it has been found that the wave forces are in phase with the wave (14). Based on this finding, the wave forces in this research have been taken as a sinusoid with a period equal to that of the wave and maximum amplitude equal to that of the maximum quasistatic load. The impact loads are then superimposed on the quasistatic forces. The impact loads were observed to have an effect on the bridge for approximately 5 8 the period of the wave, based on visual observation of results given by Marin and Sheppard (16). In addition to the vertical and horizontal forces, moment induced by wave should also be considered. When a wave passes over a bridge deck, the forces imparted change dramatically with time, and those forces cause moments on the bridge deck. The moment is calculated about the center of the bridge deck at each time step using the moment arm method. The time-varying moment arm follows a linear time history, as it is assumed that the wave is moving at a constant velocity. Parameters used in the estimation of wave loads on superstructure are shown in Figure 3. NUMERICAL SIMULATION OF COASTAL BRIDGE RESPONSES In this study, the behavior of simply supported multiple-span concrete girder bridges is investigated since it is one of the most common bridge types found in the coastal regions of the United States and has been the subject of significant damage in past events. To simulate the response of bridges under wave and surge loads, a three-dimensional nonlinear finite element model was developed using the OpenSees platform (19). A brief summary of the model is provided herein. A representative multispan concrete girder bridge is selected for the nonlinear dynamic analysis to illustrate potential behavior of critical elements and conduct the sensitivity analysis. However, the approach presented can be used to test the sensitivity of other bridge types or geometric configurations. The bridge model consists of three spans with varying length: the outermost spans with a length FIGURE 3 Parameters affecting wave load model for the superstructure. [Adapted from Marin and Sheppard (16).]

4 96 Transportation Research Record 2202 of 40 ft and the middle span length of 80 ft. This bridge is used as a representative case study, since most bridges found along the coastal U.S. regions are short to medium length span bridges usually without any proper vertical connection between super and substructure (7 9). Therefore, the most common severe mode of failure observed for coastal bridges during hurricane events is deck unseating (3, 7 12). The deck width is 49.2 ft, with eight girders of depth of 3.7 ft at 6-ft spacing. The substructure consists of two bent caps, each supported with three 36-in.-diameter circular concrete columns all of them with 12 Number 9 longitudinal reinforcement. The bent caps have a rectangular 3.5-ft width and 4-ft depth cross section with a total of 15 Number 9 reinforcing bars. The outermost spans of the bridge are supported by seat-type abutments. The numerical model is developed based on recommendations by Nielson (20) for typical multispan concrete girder bridges in the central and southeastern United States and modified to capture the response of the bridge to the coupled vertical and horizontal forces of wave appropriately. The current study considers simply supported decks using nonlinear zero-length elements representative of the elastomeric bearings, both fixed and expansion. A vertical contact element has been incorporated to allow the deck to be uplifted from the supports and settle back on the bent beam when the vertical force reduces during wave passage. The superstructure of the bridge is modeled with elastic beamcolumn elements since plastic deformation is not expected in the deck. A nonlinear beam-column element is selected for modeling the columns and bent caps. Hence, the nonlinear response of critical bridge components can be captured. A deterministic response analysis is conducted to illustrate the dynamic response of the representative bridge under hurricaneinduced surge and wave loading. A coastal bridge may experience a range of relative surge elevation and wave parameters during an extreme hurricane event, ranging from its clearance from mean sea water level to complete submergence. The influence of this range of parameters is discussed in the section on sensitivity analysis. The deck displacements for many possible combinations of wave and surge parameters quickly range from negligible response to larger values of deck displacement that result in unseating of the deck. For this illustration, the wave properties adopted are similar to those presented by Douglass et al. (8) observed for Hurricane Katrina. While the relative surge elevation will range significantly depending on the event, siting of structure, and original height over mean water level, the relative surge elevation implemented for the deterministic analysis is selected to demonstrate the model s ability to capture deck uplift before complete unseating, where interesting phenomena, such as accumulated deformations and displacements or vertical slamming of the deck back on the supports, can be observed. The deterministic wave conditions as well as the structural properties for the representative bridge are summarized as follows: Wave parameters: Wave length, λ=120 ft Maximum wave height, H max = 12.3 ft Crest height, η max = 8.06 ft Wave period, T = 6 s Relative surge, Z c = 4.1 ft Structural parameters: Width, W = 49.2 ft Girder height, d z = 4.6 ft Deck thickness, d b = 0.58 ft Concrete strength, f c = 4.9 ksi Yield steel, f y = 69 ksi The results of the analysis of the representative bridge with the above parameters are discussed in this section. The maximum vertical wave load for the first and last deck is 237 kips; the weight of the deck is 226 kips, which is the only resistant force in vertical direction because there is no positive vertical connection between the deck and its supports. Since the weight of the deck is less than the peak vertical force, the movement of the decks in upward direction is inevitable, as shown in Figure 4. This uplift of the deck off of the supports further permits the horizontal wave forces to transversely displace the deck, since the bearings no longer engage in the transverse direction once uplift occurs and fails the bearings. Also, Figure 4 illustrates that the vertical displacement of waveward side of deck is greater than the leeward side, which is reasonable due to moment induced by wave loading as the wave passes across the superstructure. The transverse force-deformation diagram for one of the fixed elastomeric bearings in the first deck is depicted in Figure 5a. Figure 5b shows the force time history of one of the contact elements. This force is in phase with the vertical wave load on the superstructure. Note that the contact element force becomes zero after the deck FIGURE 4 Displacements of nodes of deck on the bent caps of first and last spans. The first and last nodes refer to waveward and leeward, respectively. (a) (b)

5 Ataei, Stearns, and Padgett Bearing Force (kips) Axial Force in Contact Element (kips) Displacement (in.) (a) Time (s) (b) FIGURE 5 (a) Elastomeric bearing force-deformation response and (b) contact element force. has been uplifted by wave loads, and the bearing no longer engages after uplift. It is observed that the initial horizontal load from wave impact is sufficient to yield the bearings in the transverse direction. The vertical uplift forces then exceed the deck weight and the bearing elements no longer engage. Figure 6 illustrates the moment curvature response of a column in the pier supporting Decks 1 and 2, as well as moment time history. The column capacity can be estimated based on moment axial load interaction diagrams. For the column sections used in the bridge model, the nominal moment capacity is over 700 kips/ft for axial loads ranging from 3,000 kips in compression to minor loads in tension. The axial loads in the column are always in this range. Hence, this figure illustrates that the column does not reach its ultimate capacity due to hurricane loading. However, the columns undergo several cycles due to impacts in the vertical and horizontal force direction and also deck movement in the vertical direction. Overall, this deterministic analysis reflects a potential failure mechanism of uplift and transverse deck displacement given wave loads that exceed the deck weight (when vertical connection elements are lacking) and lateral force in the bearings. The potential for accumulated deformations, for example, in the bearings under lateral loading, is illustrated as well as accumulated deck displacements over repeated cycles of the loading. Additionally, while the primary components of interest were the deck and bearing elements, the dynamic response of the three-dimensional structure revealed the potential for significant interaction effects between the superstructure and substructure. For example, before uplift of the deck, the moment induced in the columns due to the lateral motion of the superstructure is less than 100 kips/ft, but after the deck has been uplifted and slammed back, the moment demand increases to 590 kips/ft. Additionally, the peak deck displacements were a function not only of bearing yielding or shifting of the deck off of its supports, but also substructure response. It is noted that the study here does not separately consider transient loads on the piers but rather only forces transferred from deck loading. The next section presents a sensitivity study based on the model described above to investigate which bridge and loading parameters have the greatest impact on the peak response quantities of the components. (a) (b) FIGURE 6 Column: (a) moment curvature and (b) moment time history.

6 98 Transportation Research Record 2202 SENSITIVITY STUDY Bridge and Wave Parameters Given the potential nonlinear behavior indicative of damage under surge and wave loading, as well as the potential range in conditions affecting not only the input wave load model but also the bridge model, a sensitivity study is warranted. With an effective bridge model and wave load model, it is possible to design an experiment to evaluate which of the parameters of the models have the greatest affect on the response of the bridge to the hurricane surge and wave forces. In order to determine the sensitivity of the model to the variation in input parameters, an analysis of variance study is conducted with 12 different input variables (factors) that affect the wave force model and the bridge model. The suite of variables has been selected based on past studies on bridge modeling parameters (21) and previous research on wave forces (8). For example, potential variation exists in the wave height, wave period, depth of the girders, and stiffness of the bearings, among other properties. A probability distribution is assigned to each parameter based on the aforementioned literature review. The 5% and 95% percentiles for each random variable have been used as the low and high levels for the parameters in the sensitivity study. The median of the distribution is used as the center point, or middle level, for each parameter. For variables with unknown distributions or little information to determine a probability distribution, uniform distributions were assumed. This is a conservative assumption, for example, with the relative surge elevation, which could vary significantly across different locations and events. Using the parameters as threelevel categorical variables, the sensitivity study is conducted using the Taguchi method for experimental design. This method uses 27 runs with various combinations of the three levels of the factors to determine the sensitivity of the vertical displacement of the bridge to the various input parameters. For each combination of factors (run) a three-dimensional nonlinear dynamic analysis is conducted for one wave passing on the bridge structure. The runs and their variables can be found in Table 1, where a plus sign represents the high value of the parameter, a minus sign represents the low value of the parameter, and a 0 represents the median of the parameter. A single run consists of the execution of the wave model with the different wave input parameters defined above. The wave forces are then used by an execution of the bridge model in OpenSees, using the bridge model parameters defined in Table 2. The output of the OpenSees model is then analyzed using MATLAB to find the maximum vertical displacement of the bridge decks. Once the vertical displacement is found for each run of the experiment, an analysis of variance can be performed. The software package JMP is used to aid in the analysis of variance and hypothesis testing of the significance of the main effects and select two factor interactions. The p-value is defined as the probability of rejecting the null hypothesis, or the probability that the variation between conditions occurred by chance. For this study, the null hypothesis is that the effect of varying the parameter is negligible with respect to the deck displacement. By observing the calculated p-values for the various parameters shown in Table 1, it can be seen which variables have the greatest affect on the vertical displacement of the bridge deck. For this study, parameters with a p-value of less than.05 are taken to be the most significant. It can be seen that for this analysis, the relative surge elevation, wave height, and wave period are the most TABLE 1 Taguchi Method Design of Experiments Parameter Values for Runs Run H λ T Z c d g f c f y μ k i F u m ζ significant parameters, whose variation has a statistically significant impact on the resulting deck displacement. The analysis of variance is also carried out for other responses of the bridge, such as transverse displacement, column drift, and bearing deformation. These responses were found for each of the original 27 runs, and an analysis of variance revealed the p-values for each of the input parameters with respect to each response. The p-values for each of the input variables are shown in Table 3, and the parameters with p-values of less than.05 are highlighted. It can be seen from these results that the parameters with the most influence on the response of the bridge are the wave load model input parameters. None of the two-factor interactions of the parameters were determined to be of statistical significance in the response of the structure. This first phase of sensitivity analyses reveals the relative variability introduced into a response assessment given variation in loading parameters as opposed to structural modeling parameters. While this is a rather intuitive result, the findings provide insight into which wave modeling parameters may be viable intensity measures for conditioning vulnerability estimates or probabilistic demand models of the bridge under surge and wave loading. The first phase of analysis reveals that wave height, period, and relative surge elevation are the most critical parameters that may be viable for conditioning demand models (e.g., P[deck displacement > d H, T, Z c ]). Furthermore, while not as critical, the variation in wave length may

7 Ataei, Stearns, and Padgett 99 TABLE 2 Variables for Sensitivity Study with Distributions and Values Parameter Distribution High Median Low Units Wave height (H) Uniform ft Relative surge elevation (Z c ) Uniform ft Wave length (λ) Uniform ft Period (T) Uniform s Girder depth (d g ) Uniform ft Concrete strength ( f c ) N(33.8,4.3) ksi Steel strength ( f y ) LN(6.13,0.08) ksi Coefficient of friction for elastomeric pads (μ) LN( 1.022,0.1) Initial stiffness for elastomeric pads (k i ) Uniform % Ultimate dowel strength (for two dowels) (F u ) LN(4.75,0.08) kips Mass (m) Uniform % Damping ratio (ζ) N(0.045,0.0125) ratio be significant enough to include as a random variable when simulating the bridge responses for demand modeling. Most Significant Bridge Modeling Parameter In order to find the structural input parameters that have the most influence on the response of the bridge model, a second-level analysis is conducted. This analysis assumes a storm event with constant wave values for height, period, length, and relative surge elevation. The values used for this study were taken from research done by Douglass et al. (8) and Marin and Sheppard (16), as shown in the list on page XX, and are typical values for a storm surge and wave load during Hurricane Katrina. Using this deterministic wave load time history, the structural parameters that were considered during the first-level analysis are analyzed to identify which have the most significant effect on the dynamic response and demand placed on critical bridge components. A similar experimental design is selected to determine the combinations of values for each of the 27 runs of the analysis; however, only combinations of the eight bridge modeling parameters are considered. After the 27 runs of the Taguchi design of experiments (DOE), an analysis of variance can be conducted for the vertical displacement, transverse displacement, column drift and fixed and expansion bearing deformation of the bridge. The results of this analysis are shown in Table 4; parameters with p-values of less than.05 are highlighted. It can be seen from the results that the mass of the bridge is the utmost structural modeling parameter, because it is statistically significant in each of the responses. It may be intuitively concluded that the connectivity between deck and substructure will affect the response of the bridge. In the bridge type that has been reported here, weight of the deck is the only parameter opposing the vertical load, and because the dominant mode of failure is deck shifting or unseating, weight of the deck is the most critical parameter. Other items of interest are girder depth and the bearings initial stiffness. The girder depth has a significant effect on vertical response, as the wave loading changes by change of the girder depth. Additionally, as long as the bearings are engaged (i.e., before uplift), their stiffness affects the response. However, it is interesting that they act more effectively on the vertical response than the transverse displacement. But it should be noted that this observation is dependent on the wave TABLE 3 p-values for Sensitivity Analysis of Joint Wave Load Model and Bridge Modeling Parameters Vertical Transverse Fixed-Bearing Expansion-Bearing Parameter Displacement Displacement Deformation Deformation Column Drift H λ T Z c d g f c f y μ k i F u m ζ

8 100 Transportation Research Record 2202 TABLE 4 p-values for Second-Level Analysis of Variance Vertical Transverse Fixed-Bearing Expansion-Bearing Parameter Displacement Displacement Column Drift Deformation Deformation m d g k i F u μ ζ f y f c m m m d g NA d g d g.0001 NA NA NA NA m k i.0001 NA NA NA NA d g f y.0121 NA.716 NA NA k i f y.0325 NA.0059 NA NA F u F u NA F u m NA NA.0429 NA NA F u d g NA NA.0062 NA NA loading magnitude. In this section, the adopted loading causes a small uplift at the climax of vertical force. As the wave and surge loading increases, the bearings disengage faster and their influence decreases. The influencing parameters in this phase of study are important, since they provide insight into categorization of bridge inventory in coastal regions with respect to hurricane hazard. CONCLUSION Since recent hurricane events have revealed the vulnerability of the transportation network, particularly coastal bridges, to surge and wave loading, a reliable method to probabilistically assess the vulnerability of existing coastal bridge inventories is required. As the first step in developing fragility models for coastal bridge vulnerability, this paper presents a sensitivity analysis of the response of typical concrete girder coastal bridges under potential variation in parameters affecting the wave load and bridge modeling. A three-dimensional nonlinear finite element model was developed for the sensitivity study that is presented in this paper. The proposed numerical model has the capability to capture the complicated responses of bridges, such as uplifting of the deck from the bent cap or abutment, slamming back on the supports, and accumulation of deformations or displacements during wave passage. The results of the subsequent analysis of variance reveal that the potential variation in wave parameters has the most statistically significant impact on the dynamic response of the bridge. The findings underscore the importance of considering such parameters as wave height, period, or relative surge elevation as potential intensity measures for conditional reliability analyses of coastal bridges. Furthermore, the second-level sensitivity study revealed that among a suite of random variables considered in the finite element bridge modeling, the most critical parameter was the deck mass affecting a range of bridge component responses (e.g., deck displacement, bearing deformation, column drift, etc.). Additional statistically significant parameters include those primarily associated with connectivity and bearing modeling, such as the coefficient of friction at the elastomeric pads, initial stiffness of elastomeric pads, or ultimate dowel strength. These parameters therefore provide insight into potential important sources of uncertainty in response assessment and fragility modeling of bridges subjected to hurricane-induced surge and wave loads. Furthermore, they also indicate parameters that warrant careful field assessment for bridges along the coast in order to improve predictive models of their response or vulnerability to hurricane loads. Future work will address the rigorous selection of appropriate intensity measures for conditioning probabilistic demand models and the development of analytical fragility curves, or vulnerability models, for the coastal bridges. ACKNOWLEDGMENTS The authors acknowledge the Houston Endowment for support of this work, as well as the Brown Undergraduate Research Internship Program, which partially supported the participation of the second author. REFERENCES 1. Chen, Q., L. Wang, H. Zhao, and S. L. Douglass. Prediction of storm surges and wind waves on coastal highways in hurricane-prone areas. Journal of Coastal Research, Vol. 95, No. 5, 2007, pp Mosqueda, G., K. A. Porter, J. O Connor, and P. McAnany. Damage to Engineered Buildings and Bridges in the Wake of Hurricane Katrina. Proc., Forensic Engineering Symposium, Long Beach, Calif., Padgett, J., R. DesRoches, B. Nielson, M. Yashinsky, O.-S. Kwon, N. Burdette, and E. Tavera. Bridge Damage and Repair Costs from Hurricane Katrina. Journal of Bridge Engineering, Vol. 13, No. 1, 2008, pp Douglass, S. L., S. A. Hughes, S. Rogers, and Q. Chen. The Impact of Hurricane Ivan on the Coastal Roads of Florida and Alabama: A Preliminary Report. Coastal Transportation Engineering Research and Education Center, University of South Alabama, Mobile, 2004.

9 Ataei, Stearns, and Padgett Okada, S., H. Mitamura, and H. Ishikawa. The Collapse Mechanism and the Temporary Restoration of Omori Bridge Damaged by the Storm Surge of Typhoon No. 18 in Technical Memorandum of Public Works Research Institute, pp , The Potential Impacts of Global Sea Level Rise on Transportation Infrastructure, Phase 1 Final Report: The District of Columbia, Maryland, North Carolina and Virginia. ICF International, 2007, p Chen, Q., L. Wang, and H. Xhao. Hydrodynamic Investigation of Coastal Bridge Collapse During Hurricane Katrina. Journal of Hydraulic Engineering, Vol. 135, No. 3, 2009, pp Douglass, S. L., Q. Chen, J. M. Olsen, B. L. Edge, and D. Brown. Wave Forces on Bridge Decks. FHWA, U.S. Department of Transportation, Huang, W., and H. Xiao. Numerical Modeling of Dynamic Wave Force Acting on Escambia Bay Bridge Deck During Hurricane Ivan. Journal of Waterway, Port, Coastal and Ocean Engineering, Vol. 135, No. 4, 2009, pp Meng, B., and J. Jin. Uplift Wave Load on the Superstructure of Coastal Bridges. Proc., Structures Congress: New Horizons and Better Practices, Long Beach, Calif., Okeil, A. M., and C. S. Cai. Survey of Short- and Medium-Span Bridge Damage Induced by Hurricane Katrina. Journal of Bridge Engineering, Vol. 13, No. 4, 2008, pp Bea, R. G., T. Xu, J. Stear, and R. Ramos. Wave Forces on Decks of Offshore Platforms. Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 125, No. 3, 1999, pp El Ghamry, O. A. Wave Forces on a Dock. Hydraulic Engineering Laboratory, Institute of Engineering Research Technical Report HEL-9-1, University of California, Berkeley, 1963, p Kaplan, P., J. J. Murray, and W. C. Yu. Theoretical Analysis of Wave Impact Forces on Platform Deck Structures. Proc., International Conference on Offshore Mechanics and Arctic Engineering, Copenhagen, Denmark, Cuomo, G., K.-i. Shimosako, and S. Takahashi. Wave-in-Deck Loads on Coastal Bridges and the Role of Air. Coastal Engineering, Vol. 56, No. 8, 2009, pp Marin, J., and D. M. Sheppard. Storm Surge and Wave Loading on Bridge Superstructures. ASCE, Austin, Tex., French, J. A. Wave Uplift Pressure on Horizontal Platforms. California Institute of Technology, Pasadena, Calif., Modjeski and Masters, Inc. Guide Specifications for Bridges Vulnerable to Coastal Storms. Task Order DTFH61-06-T AASHTO, The Open System for Earthquake Engineering Simulation. berkeley.edu. 20. Nielson, B. G. Analytical Fragility Curves for Highway Bridges in Moderate Seismic Zones. In Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, 2005, p Padgett, J., and R. Desroches. Sensitivity of Seismic Response and Fragility to Parameter Uncertainty. Journal of Structural Engineering, Vol. 12, 2007, pp The Structural Fiber-Reinforced Polymers Committee peer-reviewed this paper.

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