ANALYSIS OF BRIDGE PERFORMANCE UNDER THE COMBINED EFFECT OF EARTHQUAKE AND FLOOD- INDUCED SCOUR

Transcription

1 The Pennsylvania State University The Graduate School College of Engineering ANALYSIS OF BRIDGE PERFORMANCE UNDER THE COMBINED EFFECT OF EARTHQUAKE AND FLOOD- INDUCED SCOUR A Thesis in Civil Engineering by Gautham Ganesh Prasad 2011 Gautham Ganesh Prasad Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 2011

2 The thesis of Gautham Ganesh Prasad was reviewed and approved* by the following: Swagata Banerjee Assistant Professor of Civil Engineering Thesis Adviser Andrew Scanlon Professor of Civil Engineering Jeffrey A. Laman Professor of Civil Engineering Peggy A. Johnson Professor of Civil Engineering Head of the Department of Civil Engineering *Signatures are on file in the Graduate School. ii

3 ABSTRACT Earthquake in the presence of flood-induced scour is a critical multihazard scenario for bridges located in seismically-active, flood-prone regions of the United States. Bridge scour causes loss of lateral support at bridge foundations and results in increased seismic vulnerability of bridges. The present study evaluates the combined effect of earthquake and flood-induced scour on the performance of four example reinforced concrete bridges with different number of spans. For the analysis, Sacramento County in California is considered as the study region where the annual probabilities of occurrence of earthquakes and floods are reasonably high. The seismic hazard of the study region is considered through a suite of ground motion time histories which were generated for this region. Regional flood hazard is expressed in the form of a flood hazard curve that provides the annual peak discharges corresponding to flood events with various annual exceedance probabilities. Bridge scour, an outcome of the flood events, are calculated and used in the development of finite element models of these bridges. Nonlinear time-history analyses are preformed to evaluate the seismic performance of the example bridges having scour at bridge piers. In parallel, analyses are performed to evaluate bridge seismic performance in the absence of scour. Fragility curves are developed to represent the performance of example bridges under this multihazard scenario. Comparison of bridge fragility characteristics obtained in the presence and absence of scour presents the increased seismic vulnerability of the bridges in the presence of iii

4 flood-induced scour. The study identifies the most sensitive range of bridge scour for which the rate of degradation of bridge seismic performance is significant. A sensitivity study is performed to investigate the influence of various input parameters on the overall performance of the example bridges. For this, the 5-span example bridge is chosen to analyze under a 100-year flood event. Risk curves of this example bridge are developed that determine annual probability of exceeding different levels of societal loss arising from bridge seismic damage in the presence and absence of flood-induced scour. This societal loss is measured in terms of postevent bridge repair/restoration cost. Results show that the seismic risk of the example bridge may increase significantly in the presence of scour. iv

5 TABLE OF CONTENTS List of Figures... vii List of Tables...x Acknowledgement... xi Chapter 1 INTRODUCTION Scope of present research Major objectives and orientation of the thesis...5 Chapter 2 LITERATURE REVIEW Introduction Flood-induced bridge scour Seismic response of bridges Combined effect of scour and earthquake...13 Chapter 3 FLOOD AND SEISMIC HAZARD IN THE STUDY REGION The study region Regional flood hazard Regional seismic hazard...20 Chapter 4 ANALYSIS OF EXAMPLE BRIDGES IN THE STUDY REGION Example bridges Foundation of example bridges Calculation of scour depths Modeling of bridges Time History Analysis and bridge response...43 Chapter 5 SENSITIVITY ANALYSIS Variability in hazard models Regional flood hazard curve with 90% confidence interval Parameter sensitivity in the calculation of scour depth Variability in regional seismic hazard Variability in bridge response : Seismic risk curves of the example bridge...83 Chapter 6 SUMMARY AND CONCLUSION Research significance Assumptions and limitations Major observations Future study...95 REFERENCES...96 Appendix A: p-multiplier design curve v

6 Appendix B: Post-earthquake restoration cost (C RPm ) of the 5-span example bridge with d eq = 0.97 m vi

7 List of Figures Figure 1.1: Natural hazard maps of US and Puerto Rico (USGS) ; (a) seismic hazard: red, orange and pink zones represent high probability of strong shaking and (b) flood hazard: red zones represent the regions with high flood hazard...2 Figure 2.1: Schematic diagram of local scour...8 Figure 3.1 (a) Historic flood data and (b) flood hazard curve for Sacramento County in CA...19 Figure 3.2: Acceleration time history for Los Angeles with a probability of exceedance (a) 10% in 50 years (b) 2% in 50 years and (c) 50% in 50 years...25 Figure 4.1: Schematic diagram of 2 span bridge...27 Figure 4.2: Schematic diagram of 3 span bridge...27 Figure 4.3: Schematic diagram of 4 span bridge...27 Figure 4.4: Schematic diagram of 5 span bridge...27 Figure 4.5: Cross-section of pier...28 Figure 4.6: Typical section of bridge...28 Figure 4.7: Elevation of abutment...28 Figure 4.8: Abutment plan...29 Figure 4.9: Pile layout...29 Figure 4.10: Soil profile...34 Figure 4.11: Expected local scour at foundations of example bridges under flood events with various frequencies...34 Figure 4.12: Moment-rotation behavior for bridge piers...38 Figure 4.13: Schematic of soil-foundation-structure interaction model; (a) without flood-induced scour and (b) with flood-induced scour...38 Figure 4.14: p-y curves developed for the equivalent pile with 0.97 m diameter...41 vii

8 Figure 4.15: Example bridge models...42 Figure 4.16: Acceleration time history data for LA03 ground motion...43 Figure 4.17: Direction of earthquake loading...44 Figure 4.18: First five mode shapes of 2 span reinforced concrete bridge with deq = 0.97 m...47 Figure 4.19: First five mode shapes of 3 span reinforced concrete bridge with deq = 0.97 m...48 Figure 4.20(a): First five mode shapes of 4 span reinforced concrete bridge with deq = 0.97 m (No scour)...49 Figure 4.20 (b): First five mode shapes of 4 span reinforced concrete bridge with deq = 0.97 m (1.50 m scour)...50 Figure 4.21(a): First five mode shapes of 5 span reinforced concrete bridge with deq = 0.97 m (No scour)...51 Figure 4.21(b): First five mode shapes of 5 span reinforced concrete bridge with deq = 0.97 m (1.5 m scour)...52 Figure 4.22: Example model for determining the displacement ductility from rotational ductility...54 Figure 4.23: Time histories of displacement ductility for 2-span bridge under a strong motion; The diameter of equivalent pile is taken as (a) 0.97 m and (b) 4.2 m...56 Figure 4.24: Change in fragility curve for 2 span bridge with d eq = 1.20 m for different scour depth for (a) minor damage state and (b) moderate damage state (c) major damage state...58 Figure 4.25: Change in fragility curve for 3 span bridge with d eq = 1.20 m for different scour depth for a) minor damage state b) moderate damage state c) major damage state Figure 4.26: Change in fragility curve for 4 span bridge with d eq = 1.20 m for different scour depth for a) minor damage state b) moderate damage state c) major damage state...61 viii

9 Figure 4.27: Change in fragility curve for 5 span bridge with d eq = 1.20 m for different scour depth for a) minor damage state b) moderate damage state c) major damage state...63 Figure 4.28: Three dimensional plots for 2 span bridge...68 Figure 4.29: Three dimensional plots for 3 span bridge...68 Figure 4.30: Three dimensional plots for 4 span bridge...69 Figure 4.31: Three dimensional plots for 5 span bridge...69 Figure 5.1: Comparison of flood hazard curves developed from empirical and analytical methods...75 Figure 5.2: Flood hazard curve with 90% confidence interval...77 Figure 5.3: Tornado diagram developed for the 5-span example bridge...81 Figure 5.4: Seismic fragility curves of the 5-span example bridge with d eq = 0.97 m in presence and absence of flood-induced scour; (a) no scour, (b) 0.56 m scour, (c) 1.22 m scour, (d) 2.85 m scour, (e) 3.08 m scour, (f) 3.30 m scour and (g) 3.45 m scour...87 Figure 5.5: Risk curve of the 5-span example bridge under the combined effect of earthquake and flood-induced scour...89 Figure 6.1: Flowchart for seismic performance analysis of bridges located in flood-prone regions...92 Figure A1: Proposed p-multiplier design curve ix

10 List of Tables Table 3.1: Annual peak flood discharge magnitudes for the Sacramento County...18 Table 3.2: PGA values of LA ground motions having various hazard levels...21 Table 4.1: Details of example bridges...30 Table 4.2: Calculation of scour for example bridges...35 Table 4.3: Soil profile...40 Table 4.4: Fundamental time periods (in sec)...46 Table 4.5: Median PGAs for all combinations of Y s and d eq for all example bridges Table 5.1: Peak discharge flow calculated using analytical method for different exceeding probability...73 Table 5.2: Peak flood discharges with 5% and 95% statistical confidence...76 Table 5.3: Calculation of scour for different flood events...83 Table A5.1: Post-earthquake restoration cost (C RPm ) of the 5-span example bridge with d eq = 0.97 m at no scour condition Table A5.2: Post-earthquake restoration cost (C RPm ) of the 5-span example bridge with d eq = 0.97 m at 0.56 m scour Table A5.3: Post-earthquake restoration cost (C RPm ) of the 5-span example bridge with d eq = 0.97 m at 1.22 m scour Table A5.4: Post-earthquake restoration cost (C RPm ) of the 5-span example bridge with d eq = 0.97 m at 2.85 m scour Table A5.5: Post-earthquake restoration cost (C RPm ) of the 5-span example bridge with d eq = 0.97 m at 3.08 m scour Table A5.6: Post-earthquake restoration cost (C RPm ) of the 5-span example bridge with d eq = 0.97 m at 3.30 m scour Table A5.7: Post-earthquake restoration cost (C RPm ) of the 5-span example bridge with d eq = 0.97 m at 3.45 m scour x

11 ACKNOWLEDGEMENT This research would not have been possible without the support from many individuals. I would like to express my sincere thanks to people have contributed to this project in various ways. First, I would like to thank my advisor, Dr. Swagata Banerjee for all her comments and suggestions as I worked on this thesis. Without her support, guidance and advice this project would not be possible. I would like to thank my thesis committee members, Dr. Andrew Scanlon, Dr. Jeffrey Laman and Dr. Peggy Johnson for their support and guidance. I would also like to thank my colleagues and staffs in the Department of Civil & Environmental Engineering for letting me use the facilities in the CEE dept, consultations and moral support. Last but not the least I would like to thank my family for their encouragement and support. xi

12 Chapter 1: Introduction Bridges are important components of highway and railway transportation systems. Past experience indicates that bridges are extremely vulnerable to natural and manmade hazards such as earthquakes, floods, high wind, blast and vehicle/vessel impact at bridge piers. Bridge damage due to such extreme events may cause significant disruption of the normal functionality of transportation systems, and thus may result in major economic losses to the society. Therefore, safety and serviceability of bridges have always been great concerns to the practice and profession of civil engineering. A large population of bridges (nearly 70% according to the National Bridge Inventory, or NBI) in the United States is located in moderate to high seismically active and flood-prone regions. Figure 1.1a presents the nationwide relative shaking hazard map provided by the US Geological Survey (USGS), where California falls under the category of highly seismically active region. In last four decades, failure of a large number of highway bridges is observed during the 1971 San Fernando, 1989 Loma Prieta and 1994 Northridge earthquakes. These extreme natural events significantly disrupted the normal functionality of the regional highway transportation networks. Besides seismic events, several damaging flood events are also recorded in this region (Figure 1.1b represents the flood hazard map of the United States, USGS). The 1995 California flood (total casualty $1.8 million) and the 1997 Northern California flood (total casualty $35 million) are two examples of such events that caused notable damage in the state of California. Present state-of-the-art practice of bridge engineering considers these extreme events as discrete events to evaluate the 1

13 performance of bridges. Consequently, loss estimation methodologies and risk mitigation techniques for bridges are developed based on their failure probabilities under discrete hazard conditions. However, these two natural hazards (i.e., earthquake and flood) must be treated as multihazard condition for reliable evaluation of bridge performance located in regions with high seismic and flood hazards. (a) Seismic Hazard (b) Flood Hazard Figure 1.1: Natural hazard maps of US and Puerto Rico (USGS); (a) seismic hazard: red, orange and pink zones represent high probability of strong shaking and (b) flood hazard: red zones represent the regions with high flood hazard The present research evaluates the combined effect of earthquake and flood on bridge performance considering that these two natural events occur successively. Flood-induced soil erosion, commonly known as scour, causes loss of lateral support at bridge foundations (Bennett et al., 2009). This can impose additional flexibility to bridges which amplify the adverse effect of seismic ground motions on bridge performance. Hence, an earthquake in the presence of flood-induced scour is a critical multihazard for bridges located in seismically active, flood-prone regions. Although 2

14 the joint probability of occurrence of earthquake and flood within the service life of a bridge is relatively small, past experience indicates that one natural event can occur just after another (even before the aftermath of the first event is taken care of). For example, an earthquake of magnitude 4.5 struck the state of Washington on January 30, This seismic event occurred within three weeks after the occurrence of a major flood event in that region. Such successive occurrences of extreme events can significantly increase structural vulnerability from that under discrete hazard events. The importance of consideration of possible multihazard events for the reliable performance evaluation of bridges is well understood, however, the availability of relevant literature is extremely limited. NCHRP Report 489 (Ghosn et al., 2003) documents reliability indices of bridges subjected to various combinations of extreme natural hazards. Ghosn et al. (2003) assumed each extreme event to be a sequence of independent load effects, each lasting for equal duration of time. The service life of a bridge was also divided into several time intervals with durations equal to that of load. Occurrence probabilities of independent natural events within each time interval were calculated and combined to obtain joint load effects. This methodology, however, cannot be applied for load combinations involving bridge scour. This is because scour itself does not represent a load; rather it is a consequence of flood hazard. Therefore, load combination, or load factor design, as proposed in NCHRP Report 489, may not provide a reliable estimation of bridge performance under a natural hazard in presence of flood-induced bridge scour. Rigorous numerical study is required for this purpose. 3

15 1.1 Scope of the Present Research The present study evaluates the performance of reinforced concrete bridges under the combined effect of flood-induced scour and earthquake. Sutter County in California, a region with high seismic and flood hazards, is chosen as the study region. Four example reinforced concrete bridges with different lengths are considered to examine their relative vulnerability under the combined natural hazards. Flood hazard of the study region is expressed in the form of regional flood hazard curve. This flood hazard curve is developed using the historic flood discharge data reported by USGS for this region. Flood hazard with various intensities are considered and resulting scour depths at bridge foundations are estimated. Seismic hazard of the same region is modeled through a suite of earthquake ground motions that were generated for Los Angeles in California. Finite element models of the example bridges with and without flood-induced scour are developed using SAP2000 Nonlinear (Computer and Structures, Inc. 2000) and analyzed under these ground motions. Bridge seismic performance in the presence and absence of flood-induced scour is represented in the form of fragility curves. Change in bridge seismic fragility characteristics with scour depth demonstrates the change in bridge vulnerability with the combined demand of these two natural hazards. Bridge performance under the multihazard condition may vary depending on the variability involved in various analysis modules. Sensitivity analysis is performed to identify major uncertain parameters to which bridge performance is greatly sensitive. Seismic risk curves of bridges are generated as an ultimate outcome of this research. 4

16 1.2 Major Objectives and Orientation of the Thesis The broader objectives of this research include: - Development of fragility curves to determine bridge failure probabilities due to the combined effect of earthquake and flood-induced scour. These fragility curves are a useful tool for the evaluation of risk and resilience of highway transportation networks under similar multihazard scenario. - Investigation of parameters sensitivity in the calculation of flood-induced scour depth. Four input parameters (discharge rate, bed condition and angle of attack coefficient, and effective pier width) are considered for this and their possible variations are taken from existing knowledge-base. - Development of risk curves to express the annual exceedance probabilities of various levels of societal loss due to seismic damage of bridges located in flood-prone regions. The thesis is organized in the following five chapters: Chapter 2 focuses on the review of existing literature on the evaluation of bridge performance under floodinduced scour, earthquakes and the combination of these two natural hazards. Regional seismic and flood hazard of the study region is discussed in Chapter 3. Chapter 4 contains the description of example bridges under consideration and the evaluation of their performance under the combined effect of earthquake and floodinduced scour. Sensitivity analysis and the expected seismic risk of bridges are discussed in Chapter 5. Chapter 6 summarizes the present research and presents conclusions based on the research outcomes. Research significance and recommendations for further studies on this topic are also presented in this chapter. 5

17 Chapter 2: Literature Review 2.1 Introduction Literature review for the present study is done by categorizing literatures on bridge performance evaluation in three groups: (i) due to flood events, (ii) under earthquake ground motions and (iii) under the combined effect of earthquake and flood-induced scour. The following sections provide the details. 2.2 Flood-Induced Bridge Scour The extent of flood impact on bridges is commonly measured in terms of scour depth at bridge foundations. Scour is defined as erosion caused by fast flowing water which results in removal of sand, earth, or silt from the bottom of the river (Liang et al., 2009). Bridge scouring has three components (HEC 18, 2001): 1) Local scour: - Local scour occurs at bridge piers, abutments or any other structural parts that obstruct the normal flow of water. 2) Contraction scour: - Contraction scour occurs when normal stream flow gets contracted by external objects such as bridge piers. Such contraction reduces the overall width of the channel and results in accelerated stream flow which causes scour. 3) Degradation and Aggradations scour: Degradation and aggradations scour occurs over time due to continuous flow of water. Contraction scour and local scour at bridge piers are the expected outcome of accelerated stream flow due to one-time flood event. In this study, the contraction 6

18 scour is estimated to be less than 10% of the local scour at bridge piers for all range of discharge values. Hence, only the pier local scour is considered here as the immediate outcome of flood events. The guidelines given in HEC -18 (2001) is used to calculate the pier local scour. Schematic diagram of the local scour is shown in Figure 2.1. Numerous researches have been performed to predict scour at bridge piers and a number of equations have been proposed. Johnson (1995) performed a comparative study with the scour calculation equations proposed by the Colorado State University (CSU) (as given in HEC ), Melville and Sutherland (1988), Breusers et al. (1977), Shen et al. (1969), Laursen and Toch (1956) and Jain and Fischer (1979). It was observed that the equations proposed by CSU provided accurate estimates of bridge scour at very low Froude number (~ 0.1) and hence, suggested to use to evaluate scour depth at bridge piers. In the present study, Froude numbers calculated for various intensity flood events fall in a range of 0.11 to Thus, scour calculation equations given in HEC 18 (Richardson and Davis, 2001) are used here which are the modified version of that originally proposed by CSU. 7

19 Figure 2.1: Schematic diagram of local scour (mo.water.usgs.gov/current_studies/scour/index.htm) According to HEC-18 (Richardson and Davis, 2001), local scour Y s is expressed as Y s 0.65 a hK1K2K3K4 Fr1 (2.1) h where h is the flow depth directly upstream to the bridge pier (in m), a is the pier width (in m), K 1, K 2, K 3, and K 4 are correction factors representing pier nose shape, angle of attack of flow, bed condition, and particle size of soil, respectively. The Froude number Fr 1 is defined as 0. 5 V gh, V and g being the mean velocity of the flow directly upstream to the pier (in m/sec) and acceleration of gravity (9.81 m/s 2 ), respectively. Values of K 1, K 2, K 3 and K 4 are determined from HEC-18. V is the velocity of flow measured at the pier location where scour is calculated and h is the 8

20 measured flow depth. The flow depth for a given flood discharge rate is calculated as (Gupta, 2008): Q h b V (2.2) where Q is the discharge rate (m 3 /sec) and b is the passage width. Velocity of the flood (V) is calculated using the following equation (Gupta, 2008): V 2/3 1 bh 1/ 2 S (2.3) n b 2h Here n and S represents manning s roughness coefficient and slope of bed stream, respectively. For a given flood event, the annual peak discharge Q is the only known quantity. To calculate corresponding values of flow velocity V and flow depth h, the passage width b is assumed to be equal to the total length of the bridge. Note that the scour depth calculation discussed here provides a rapid estimation of scour at bridge piers caused by regional flood events. For exact calculation of bridge pier scour, separate hydraulic analysis at each bridge pier is required. Johnson and Torrico (1994) suggested another correction factor K w in Equation 2.1 for h/a < 0.8 in a subcritical flow and uniform noncohesive sediments with a/d 50 > 50. In such cases, K w should be multiplied with the value of scour depth calculated using in Equation 2.1. K w is calculated as K w 2.58 h a 1.00 h a Fr Fr for for V V c V V c (2.4) where V c represents critical velocity which is defined as the velocity required for initiating the motion of bed materials (Richardson and Davis, 2001). This critical 9

21 velocity can be calculated following the equation below where K u is taken as 6.19 and D represent soil partial size. V c K u h 1/6 D 1/3 (2.5) Bennett et al. (2009) performed analytical study to determine the behavior of a laterally loaded pile group subjected to scour. The pile group consisted of 8 piles and each pile in the pile group had a diameter of 0.25 m and length of m. The pile group was converted into group equivalent pile based on the procedure defined in Mokwa et al. (2000). Effect of scour depth and pile head boundary condition on the deflection profile of the pile was studied in this paper. Five different scour depths, measured from the ground level, were considered to evaluate the effect of scour depth on the pile system. The result showed that the deflection of pile head was insignificant when the scour depth was less than the depth of the pile head (i.e., scour did not reach the pile cap). Once the scour depth reached the pile head and proceeded to further depth, a significant amount of deflection of pile was observed. Deflections of the pile head under two fixity conditions (fixed and free) were compared. The study found that the deflection of the pile head under free-head condition was more than the deflection of the pile head under the fixed-head condition. Increase in scour depth resulted in reduction of lateral bearing capacity of the pile group. Under the fixed head case it was observed that the maximum shear force and bending moment developed at the pile head and these maximum values increased with increase in the scour depth. From these observations, it can be easily visualized that when the scour is accompanied by an earthquake, the damage to the structure will be much more 10

22 intense. This indicates the significance of assessing bridge damageability under scour and earthquake. 2.3 Seismic Response of Bridges During last few decades, a number of numerical and experimental studies are performed to simulate bridge seismic performance. It is well recognized that the development of fragility curves is one of the most efficient techniques to express bridge seismic vulnerability. The fragility curves represent the probability of bridge failure in a particular damage state under certain ground motion intensity (such as peak ground acceleration or PGA). Such curves are developed either through empirical method (i.e., using the damage data of the bridges associated with the past earthquake) or through analytical method (i.e., by simulating damage states based on dynamic characteristics of bridges). Basoz and Kiremidjian (1997) developed the fragility curves using the data from 1989 Loma Prieta earthquake and 1994 Northridge earthquake using the regression analysis. Bridges were categorized into 11 different classes based on substructure and superstructure type and material. Empirical fragility curves were developed for each of the bridge class. Shinozuka et al. (2000a) developed empirical fragility curve using the damage data from 1995 Kobe earthquake and 1994 Northridge earthquake. Along with the empirical method, studies have been carried to develop the fragility curves based on analytical method (Hwang et al. 2000, Mander and Basoz 1999, Shinozuka et al. 2000b, Banerjee and Shinozuka 2008a). This is done through the numerical simulation of bridge seismic performance using different structural analysis methods 11

23 such as response spectrum analysis, nonlinear static and dynamic analyses. Hwang and Huo (1994) developed the fragility curves based on Monte Carlo simulation of the dynamic characteristics of structures. In most of these above literatures, fragility curves are generally expressed using a two-parameter lognormal distribution function. The distribution parameters median PGA m and log-standard deviation, referred to as fragility parameters, respectively represent PGA corresponding to 50% probability of exceeding the damage state and the dispersion of fragility curve. At a damage state k (= minor, moderate, major, complete collapse), fragility parameters PGA mk and k can be estimated using the maximum likelihood method. Under the lognormal assumption, the analytical form of the fragility function F( ) for the state of damage k is given as, F PGA, PGA i mk, k ln PGAi PGA k mk (2.6) PGA i represent PGA of a ground motion i. Care should be taken while developing the fragility curves in order to make sure that the fragility curves of different damage state do not intersect each other. This can be achieved by considering a common logstandard deviation for all damage sates. For the further details on likelihood method and fragility curve development, readers are referred to Banerjee and Shinozuka (2008a). 12

24 2.4 Combined Effect of Scour and Earthquake While a number of research studies have been conducted to evaluate bridge performance under earthquake and flood-induced scour considering these are discrete natural disasters, not much attention is given to evaluate bridge response under the combined effect of these natural hazards. In relation to this, Tsai and Chen (2006) studied the seismic capacity of a three span reinforced concrete bridge having scoured group piles. The length and diameter of bridge columns were 10 m and 2.2 m, respectively. The bridge was supported on a group pile foundation consisting of nine piles with diameter of 0.7 m and having length equal to 30 m. In numerical analysis, soil springs were provided in lateral direction of piles to incorporate the pile soil interaction. For scour condition, these springs were removed up to the scour depth. Results from this numerical study showed that the scouring of pile group resulted in lower seismic capacity of the bridge. Exposure of piles due to scour resulted in shifting of plastic hinges from bottom of the pier to the top of the pile which resulted in lesser lateral force resistance. Chen (2008) performed a small-scale experiment to demonstrate the effect of scour and earthquake on a bridge pier. The experimental set-up consisted of a flume of 10 cm wide, 2 m long and 20 cm deep that was filled with sand. The pier model of length 14 cm and diameter 1.27 cm made out of aluminum plate was placed in the flume box. Two linear motors were installed in the flume for the purpose of shaking the entire system. The test was performed for different flow rates and different shaking frequencies. Scour depth around the piers were evaluated for concurrent 13

25 application of scour due to flow and earthquake and then compared with that obtained from sequential application of these two independent events. The result showed that the scour depth for the concurrent event case and sequential event case is different. In general it was observed that sequential event case resulted in shallower scour depth as compared to scour depth due to concurrent event case. Thus, this study confirmed the higher structural vulnerability under this combined hazard scenario. Another related study on the combined effect of earthquake and scour on bridge performance is done by Alipour et al. (2010). In this study, three bridges, one short, one medium and one long span, were modeled in OpenSees (2009). These bridge models were supported by pile shaft foundations. Soil-structure interaction was modeled using American Petroleum Institute (API) guidelines. These were incorporated in the model using bi-linear springs along the length of the shaft. Seismic performance of bridges under 16%, 50% and 84% probability of occurrence of scour is evaluated. The effect of scour was modeled by removing the bilinear springs from the pile shaft up to the scour depth range. Both pushover and timehistory analyses were performed to investigate bridge performance. For the push over analysis, the strength of the bridge was evaluated in terms of base shear capacity. From the study it was concluded that bridges subjected to higher scour have a lesser base shear capacity. The response of the bridge for time history loading was evaluated in terms of deck drift ratio and the bridge was subjected to 60 ground motions. For the evaluation of seismic performance of bridges, fragility curves were plotted. Ductility limits were developed for each damage state (i.e., slight, moderate, extensive and complete collapse damage state) and was compared with bridge 14

26 ductility to evaluate the performance of the bridge. Fragility curves for the medium span bridge at minor and moderate damage states were plotted for different scour levels. In the result, change in the fragility curves was observed with the change in scour levels. The probability of exceeding a particular damage state increased with higher scour depth. The above three studies show the importance of considering earthquake and flood-induced scour for bridge performance evaluation. However, none of these studies have strategically modeled the seismic and flood hazards for any region and investigated the combined impact of these hazards on performance of bridges populated in that region. However, for multihazard analysis, it is very important to identify the region specific seismic and flood hazard levels as bridge safety depends on maximum demands of these two natural disasters. In addition, many of the analysis parameters and modules may be associated with uncertainties. A sensitivity analysis is needed to identify the critical input parameters and the influence of their variability on the seismic performance of bridges in the presence of flood-induced scour. 15

27 Chapter 3: Flood and Seismic Hazard in the Study Region 3.1 The Study Region Overlapping of seismic and flood hazard maps (shown in Figure 1.1) indicates that California, Washington and partly Oregon in Western US and the New Madrid Seismic Zone in Eastern US are regions with high seismic and flood hazards. In this study, Sacramento County in California is chosen as the bridge site. Nevertheless, the method presented in this study is transportable and can easily be applied to any other region of interest. 3.2 Regional Flood Hazard Regional flood hazard is generally expressed in the form of flood hazard curve that provides probability of exceedance of annual peak discharges in the region. Such curve can be developed through flood-frequency analysis (Gupta, 2008) performed using (1) empirical method, (2) analytical method and (3) graphical method. In this section, empirical method is used to develop the flood hazard curve. For the study region, 104 data (from year 1907 to 2010) of annual peak discharge is collected from USGS National Water Information System (USGS 2011). Table 3.1 and Figure 3.1a display the magnitudes of these annual peak flood discharges. Plotting of these data in a log-normal probability paper provides the probability of exceedance of different annual peak discharges (Figure 3.1b). This represents the flood hazard curve of the study region. Thus the relation between flood hazard level and physical measure of flood characteristics (i.e., peak discharge rate) is established. Federal Highway 16

28 Administration or FHWA requires all bridges over water must be able to withstand the scour associated with 100-year floods (i.e., flood events having probability of exceedance once in 100 years) (Richardson and Davis, 2001). Hence, 100-year flood events are considered in this study as extreme flood scenario. From the hazard curve (Figure 3.1b), annual peak discharge corresponding to 100-year flood (exceedance probability 0.01) is estimated to be equal to 2200 m 3 /s. Five other more-frequent flood events with exceedance probabilities of 0.90, 0.50, 0.10, 0.05, and 0.02 (respectively for 1.1-year, 2-year, 10-year, 20-year, and 50-year flood) are also considered. Corresponding annual peak discharges are estimated to be 60 m 3 /s, 305 m 3 /s, 900 m 3 /s, 1300 m 3 /s, and 1900 m 3 /s. Amount of bridge scour resulting from the above various frequency flood events are estimated and presented in Chapter 4. 17

29 Table 3.1: Annual peak flood discharge magnitudes for the Sacramento County Year Annual peak discharge (m 3 /sec) Year Annual peak discharge (m 3 /sec) Year Annual peak discharge (m 3 /sec) Year Annual peak discharge (m 3 /sec)

30 Annual peak discharge (m 3 /s) Annual peak discharge (m 3 /s) (a) Year (b) 1 Probability of exceedance (Probability of annual discharge being equal or exceeded) Figure 3.1 (a) Historic flood data and (b) flood hazard curve for Sacramento County in CA; Dots represent 104 data and the solid curve indicates mean hazard curve 19

31 3.3 Regional Seismic Hazard Seismic hazard of this region is modeled by considering sixty ground motions with various hazard levels. These motions were originally generated by FEMA for the area of Los Angeles in California ( These include both recorded and synthetic motions and are categorized into three sets having annual exceedance probabilities of 2%, 10% and 50% in 50 years. Each set has 20 ground motions; LA01 to LA20 represent moderate motions with annual exceedance probability of 10% in 50 years, LA21 to LA40 represent strong motions with annual exceedance probability of 2% in 50 years, and LA41 to LA60 represent weak motions with annual exceedance probability of 50% in 50 years. Table 3.2 represents the range of PGA values of the ground motions under each of these three sets. Figure 3.2 shows the acceleration time history of one ground motion from each set of strong, moderate and weak motions. 20

32 Table 3.2: PGA values of LA ground motions having various hazard levels Los Angeles Ground Motions Having a Probability of Exceedance of 10% in 50 Years SAC Name LA01 LA02 LA03 LA04 LA05 LA06 LA07 LA08 LA09 LA10 LA11 LA12 LA13 LA14 LA15 LA16 LA17 Record Imperial Valley, 1940, El Centro Imperial Valley, 1940, El Centro Imperial Valley, 1979, Array #05 Imperial Valley, 1979, Array #05 Imperial Valley, 1979, Array #06 Imperial Valley, 1979, Array #06 Landers, 1992, Barstow Landers, 1992, Barstow Landers, 1992, Yermo Landers, 1992, Yermo Loma Prieta, 1989, Gilroy Loma Prieta, 1989, Gilroy Northridge, 1994, Newhall Northridge, 1994, Newhall Northridge, 1994, Rinaldi RS Northridge, 1994, Rinaldi RS Northridge, 1994, Sylmar Earthquake Magnitude Distance (km) Scale Factor Number of Points DT (sec) Duration (sec) PGA (cm/sec 2 )

33 LA18 LA19 LA20 Northridge, 1994, Sylmar North Palm Springs, 1986 North Palm Springs, Los Angeles Ground Motions Having a Probability of Exceedence of 2% in 50 Years SAC Name Record Earthquake Magnitude Distance (km) Scale Factor Number of Points DT (sec) Duration (sec) PGA (cm/sec 2 ) LA Kobe LA Kobe LA23 LA Loma Prieta 1989 Loma Prieta LA Northridge LA Northridge LA Northridge LA Northridge LA Tabas LA Tabas LA31 LA32 LA33 LA34 LA35 LA36 LA37 LA38 Elysian Park (simulated) Elysian Park (simulated) Elysian Park (simulated) Elysian Park (simulated) Elysian Park (simulated) Elysian Park (simulated) Palos Verdes (simulated) Palos Verdes (simulated) LA39 Palos Verdes

34 LA40 (simulated) Palos Verdes (simulated) Los Angeles Ground Motions Having a Probability of Exceedence of 50% in 50 Years SAC Name LA41 LA42 LA43 LA44 Record Coyote Lake, 1979 Coyote Lake, 1979 Imperial Valley, 1979 Imperial Valley, 1979 Earthquake Magnitude Distance (km) Scale Factor Number of Points DT (sec) Duration (sec) PGA (cm/sec 2 ) LA45 Kern, LA46 Kern, LA47 Landers, LA48 Landers, LA49 LA50 LA51 LA52 LA53 LA54 LA55 LA56 LA57 LA58 Morgan Hill, 1984 Morgan Hill, 1984 Parkfield, 1966, Cholame 5W Parkfield, 1966, Cholame 5W Parkfield, 1966, Cholame 8W Parkfield, 1966, Cholame 8W North Palm Springs, 1986 North Palm Springs, 1986 San Fernando, 1971 San Fernando, LA59 Whittier, LA60 Whittier,

35 Acceleration (g) Acceleration (g) Time (sec) (a) probability of exceedance: 10% in 50 years Time (sec) (b) probability of exceedance: 2% in 50 years 24

36 Acceleration (g) Time (sec) (c) probability of exceedance: 50% in 50 years Figure 3.2: Acceleration time history for Los Angeles with a probability of exceedance (a) 10% in 50 years (b) 2% in 50 years and (c) 50% in 50 years ( 25

37 Chapter 4: Analysis of Example Bridges in the Study Region 4.1 Example Bridges The example bridges used in this study are adopted from the five-span (two exterior 39.6 m and three interior 53.3 m) reinforced concrete bridge model presented by Sultan and Kawashima (1993). The bridge was designed following bridge design aids (Caltrans, 1988). The bridge deck is composed of 2.1 m deep and 12.9 m wide prestressed concrete hollow box-girders. This literature does not provide the reinforcement in the bridge girder. In fact, this is not a crucial factor for the seismic performance analysis of bridges as bridge girders generally remains elastic during earthquakes. Bridge piers are 19.8 m long and have circular cross sections (2.4 m diameter). Keeping all structural conditions the same, the present study considers three additional example bridges with 2, 3 and 4 spans by omitting one or more interior spans from the original five-span bridge model. Figures 4.1 to 4.4 present these bridge models. The pier and girder cross-sections of these bridges are shown in Figures 4.5 and 4.6, respectively. The elevation and the plan of abutment are presented in the Figure 4.7 and Figure 4.8 respectively. Details of the exterior and interior (as applicable) span lengths, cross-sectional and material properties, and bridge foundations of the example bridges are given in Table 4.1. Figure 4.9 represents the pile layout for the bridge. Cross section of bridge girder generally changes with change in span numbers. However, to avoid complexity in developing the numerical models of these bridges, the same girder cross-section is used here for all example bridges. 26

38 Figure 4.1: Schematic diagram of 2 span bridge (not to scale) Figure 4.2: Schematic diagram of 3 span bridge (not to scale) Figure 4.3: Schematic diagram of 4 span bridge (not to scale) Figure 4.4: Schematic diagram of 5 span bridge (After Sultan and Kawashima 1993) (not to scale) 27

39 CL # 14, total m 6.5 m 6.5 m 0.53 m 2.13 m Column 2.4m Ø # m Center Line of Bridge Figure 4.5: Cross-section of pier Figure 4.6: Typical section of bridge 5.5 m 0.91 m 1.14 m 4.58 m 1.22 m 0.61 m 3.05 m 1.83 m 0.84 m 0.61 m Figure 4.7: Elevation of abutment 28

40 0.3 m 3.05 m m m Figure 4.8: Abutment plan 0.45 m 0.38 m Ø pile 5.5 m 6.4 m 0.45 m 5.5 m 6.4 m Figure 4.9: Pile layout 29

41 Table 4.1: Details of example bridges Span Total Interior Exterior Deck Type, height and Foundation at # span span span type diameter of piers pier bottom m N/A 39.6 m Forty (40) m 53.3 m 39.6 m m 53.3 m 39.6 m Hollow boxgirder Circular, 19.8 m long and 2.44 m diameter 0.38 m diameter and 18.3 m long m 53.3 m 39.6 m concrete piles 4.2 Foundation of Example Bridges As shown in Figure 4.9, Sultan and Kawashima (1993) assumed a group of forty 0.38 m diameter, 18.3 m long piles as the foundation below each pier of the five-span model bridge. In this study, the same foundation is used for all example bridges for the purpose of modeling simplicity. The movement of ground due to seismic shaking imposes lateral load to the pile foundation. For pile groups, Brown et al. (2001) suggests the use of reduction factors (p-multipliers) that should be applied to the p-y curve for each single pile to obtain a set of p-y curves for piles acting as a group. The p value in the p-y curve for the group equivalent pile is adjusted by considering the reduction factors which are defined in the Mokwa et al. (2000). Values of these reduction factors depend on the location of a pile in the pile group with respect to the point of load application. The equivalent pile p value is obtained by adding all the adjusted p values of the each pile in the pile group. GEP p value is obtained using the Equation

42 (4.1) where p i is the p-value for the single pile, f mi is the p-multiplier obtained from the Figure A1 (Mokwa et al., 2000) and N is the number of piles in the group. Randolph (2003) outlined an approach to calculate the stiffness of an axially loaded pile group using an equivalent pile that will represent the functional behavior of the pile group. Yin and Konagai (2001) adopted the same approach for laterally loaded pile groups. The pile group is replaced by an equivalent pile with bending stiffness EI eq (where E is modulus of elasticity for the pile material and I eq is the moment of inertial for the equivalent pile cross section) equal the bending stiffness EI Group (where I Group is the moment of inertia for the entire group) of the pile group. Additionally, pile foundation may have sway and/or rocking motions during seismic excitations. The load-deflection characteristic and the bending stiffness of a pile group vary under these two types of seismic motion. Accordingly, the dimension of the equivalent pile will be different for sway and rocking motions. For sway motion, the bending stiffness of the equivalent pile is calculated as the summation of stiffness of all piles in the group (Yin and Konagai, 2001) EI eq EI n EI (4.2) Group p p where n p is the number of piles in a pile group and I p is the moment of inertia of a single pile cross section. To calculate EI eq under a rocking motion, the relative location of each individual pile (with respect to the center of gravity of the group) is considered in addition to the bending stiffness EI p of an individual pile. According to 31

43 Yin and Konagai (2001), EI eq for a pile group subjected to rocking ground motion can be calculated as EI eq EI Group n p 2 E pi p E p Ap x pi x i 1 0 (4.3) where A p is the cross-sectional area of a single pile, x pi and x 0 are, respectively, the coordinates of pile i and the centroid of the pile group with respect to a fixed origin. The present study uses p-y curve of an equivalent pile which is functionally (with respect to bending stiffness) identical to the pile group that it represents. Using equations (4.2) and (4.3), the diameters of equivalent piles d eq under sway and rocking motions are calculated to be equal to 0.97 m and 4.2 m, respectively. These values of d eq indicate that the pile foundation has much higher rotational rigidity against lateral rocking motion compared to that under lateral sway motion. As identical foundation is considered for all example bridges, the above calculations of d eq remain the same for all four example bridges. The length of the equivalent pile is considered to be the same as of the individual piles. The value of d eq will change according to the geometry and dimensions of a bridge foundation. Therefore, to facilitate the identification of the effect of d eq on bridge dynamic characteristics in presence and absence of flood-induced scour, a parametric study is performed as part of the present study. Five different d eq values (4.2 m, 2.4 m, 1.6 m, 1.2 m, and 0.97 m) are considered with an upper bound calculated for lateral rocking motion and a lower bound calculated for lateral sway motion. 32

44 4.3 Calculation of Scour Depths The subsurface soil profile assumed by Sultan and Kawashima (1993) at the model bridge site is considered for this study. Bridge scour is not a prominent phenomenon in fine-grained soils (e.g., clays, plastic silts); however, for coarsegrained soils (e.g., sand or silty sand) scouring is very common. Therefore, to account for the worst possible scenario of flood-induced scouring, the present study considers an example bridge site that consists of sand and silty sand down to infinite depth. The soil profile considered for this study is shown in Figure Using the Equations 2.1, 2.2 and 2.3, and the flood data provide in Figure 3.1, the scour depths for all example bridges are calculated. As all bridge piers considered here have circular shape, the K 1 is taken as 1.0. K 2 is taken as 1.0 considering zero angle of attack of flow. K 3 is 1.1 for clear-water scour. K 4 is taken as 1.0 for the size of soil particles D 50 and D 95 being less than 2 mm and 20 mm. For coarser particles (i.e., D 50 > 2 mm and D 95 > 20 mm), K 4 is less than 1.0 and this results in less scour. This is apparent because coarser particles require higher flow velocity to be eroded. For this study, n = 0.08 (FEMA 2008) and S = 0.1% which represents Mannings roughness coefficient and slope of bed stream are used in Equation 2.3 to calculate the velocity of flow and this calculated velocity is used in Equation 2.1 to calculate scour. The calculated scour depth values are given in Table 4.2 and plotted in Figure

45 Local scour Y s (m) Figure 4.10: Soil profile span bridge 3-span bridge 4-span bridge 5-span bridge Annual peak discharge (m 3 /s) Figure 4.11: Expected local scour at foundations of example bridges under flood events with various frequencies 34

46 Table 4.2: Calculation of scour for example bridges Flood event 1.1-year 2-year 10-year 20-year 50-year 100- year Exceedance probability Discharge rates (m 3 /s) Local scour at bridge piers Y s (m) 2-span span span span Figure 4.11 shows that the scour depths calculated for the four example bridges for the flood events considered in this study spread over a wide range from 0.73 m to 4.55 m. To investigate the relative impact of different combinations of earthquake and flood-induced scour depths on the performance of all example bridges, it is important to consider the same ground motions and scour depths for the numerical analyses. Thus, three representative values of Y s (= 0.6 m, 1.5 m, and 3.0 m) are used for seismic analysis of example bridges under the 60 ground motions described in Chapter 3. Seismic performance of example bridges does not change for pier scour more than 3.0 m (will be demonstrated further in this chapter). Thus, the scour depth beyond 3.0 m is not considered here. In addition, analyses are performed for a no scour condition (i.e., Y s = 0). The analysis results will demonstrate the relationship between bridge seismic performance and increasing scour depth and will identify the 35

47 critical range of scour depth within which bridge performance degradation is significant. 4.4 Modeling of Bridges Finite element (FE) analyses are performed using SAP2000 Nonlinear (Computer and Structures, Inc. 2000). During earthquakes, bridge girders are expected to respond in the elastic range. These are modeled in SAP2000 by using linear beamcolumn elements. These elements are aligned along the center line of bridge decks. At the two extreme ends, bridge girders are generally supported on abutments which provide full restraint against the vertical movement (translation) of girders at these locations. The horizontal (longitudinal) movement of girders at these locations is allowed up to an initially provided gap (in couple of centimeters) between girder and abutment. To numerically simulate bridge failure, the present study assumed no constraint at abutment locations for the longitudinal movement of girders. This allowed the bridge models to translate freely in this direction. Hence, at abutments, bridge girders are modeled to have unconstrained degrees of freedom along the longitudinal translation (along the axis of the bridge). This type of modeling is also adopted by the Washington State Department of Transportation (Kapur, 2011). The degrees of freedom for vertical movement at these locations are taken as fully constrained. The girders are also allowed to have in-plane rotations at abutments. Probability of bridge failure under seismic shaking is then calculated by measuring the horizontal displacement of the bridge at superstructure level. Failure (i.e., 36

48 complete collapse) is said to occur when the maximum displacement reaches to the ultimate limit state which is defined in the following section of this chapter. Bridge piers are modeled as single column bents. During seismic excitation, maximum bending moment generates at pier ends which can lead to the formation of plastic hinges at these locations if the generated moment exceeds the plastic moment capacity of these sections. To model such nonlinear behavior of bridge piers, nonlinear rotational springs (Plastic Wen Nlink) are introduced in FE model at the top and bottom of each pier where plastic hinges are likely to form. The properties of these nonlinear links are decided based on the bi-linear moment-rotation behavior of bridge piers (Figure 4.12; Priestley et al., 1996). This bi-linear behavior is approximated from the original nonlinear moment-rotation relationship (also shown in Figure 4.12) in order to input this in SAP2000. Rigid elements are assigned at girder-pier connections to ensure full connectivity at these intersections of monolithic concrete bridges. The equivalent pile is assumed to be drilled in sand as the conhesionless soil is considered in the present study. Nonlinear p-y springs are used along the length of the equivalent pile to model the soil-foundation-structure interaction (Figure 4.13a). In presence of scour, a part of the bridge foundation system loses lateral support from soil. To model this loss of lateral support, springs within a length Y s from the top of the equivalent pile are removed (Figure 4.13b). For example, if flood results in bridge scour of 1.5 m depth, p-y links upto a depth of 1.5 m from the top of pile are removed to model scouring. Hinge condition is assumed at the tip of the equivalent piles (Priestley et al., 1996). 37

49 Figure 4.12: Moment-rotation behavior for bridge piers (1 kip-ft = 1.36 KN-m) p-y springs p-y springs (a) (b) Figure 4.13: Schematic of soil-foundation-structure interaction model; (a) without flood-induced scour and (b) with flood-induced scour 38

50 Stiffness of p-y springs is calculated following API recommendations (API 2000). The nonlinear lateral soil resistance deflection (p-y curve) behavior of sand is expressed in the equation below (API 2000). p A p u k H tanh A pu y (4.4) where p and y are the lateral soil resistance and corresponding lateral deflection at a depth H, respectively. A represents the factor to account for static or cyclic loading condition which is given as 0.9 for cyclic loading. p u is the ultimate bearing capacity of soil at a depth H and k is the initial modulus of subgrade reaction (1220 ton/cubic meter). p u is depth dependent; API (2000) proposes two equations (Equations 4.5 and 4.6) to calculate p u for shallow and deep depths. The smaller of these two values is used as the ultimate lateral resistance in the calculation of p-y curve (Equation 4.4). For shallow depth: p u C H C d H 1 2 (4.5) For deep depth: p u C d H 3 (4.6) where coefficients C 1, C 2 and C 3 are determined according to the friction angle of sand (Figure of API 2000), d is the average pile diameter measured from top of the pile to depth H (in m) and γ is the effective soil weight (0.92 ton/cubic meter). For all equivalent piles (with various d eq ), p-y curves are developed for an interval of 0.3 m along the length of the piles. The pile is driven into cohesionless soil with properties shown in the Table 4.3. Using the properties of piles and the properties shown in Table 4.3, load deflection curve for pile soil interaction is calculated using the Equation

51 Table 4.3: Soil profile Soil type Frictional angle (deg) Soil layer depth (m) Cohesion (KN/m 2 ) Silty Sand Sand Sand Figure 4.14 shows two example curves developed at depths of 7.3 m and 11.3 m for 0.97 m diameter equivalent pile. As expected, increasing lateral resistance of soil is achieved at greater depths. Such curves are assigned to the pile nodes (at 0.3 m interval) of the FE bridge model to characterize the nonlinear behavior of soil during seismic events. These p-y curves are incorporated in to the SAP2000 bridge model by assigning multi-linear elastic links (having nonlinear properties). Figure 4.15 shows the line diagram of all four example bridges modeled in SAP

52 Lateral Resistance (KN) p-y curve at 11.3 m depth p-y curve at 7.3 m depth Deflection (m) Figure 4.14: p-y curves developed for the equivalent pile with 0.97 m diameter 41

53 (a) Two span Reinforced Concrete Bridge (b) Three span Reinforced Concrete Bridge (c) Four span Reinforced Concrete Bridge (d) Five span Reinforced Concrete Bridge Figure 4.15: Example bridge models (from SAP2000) 42

54 4.5 Time History Analysis and Bridge Response Time history analysis results in dynamic response of a structure subjected to arbitrary loading which varies with time (like earthquake). Nonlinear modal time history analysis is performed on the bridge model and only material nonlinearity in terms of Nlinks is considered. Modal analysis is performed using Ritz vector as it is recommended for nonlinear time history analysis. Constant damping of 5% is considered for all the modes. The acceleration versus time history data which is developed by FEMA is imported into SAP2000 using the time history function command. Figure 4.16 below shows the acceleration time history data for one of the earthquake ground motion (LA03) that is used in the study. Figure 4.16: Acceleration time history data for LA03 ground motion (FEMA) Common loads such as thermal load, wind load (regular wind) and live load act on the bridges simultaneously with extreme loads due to earthquakes and floods. This research primarily focuses on the bridge performance under extreme loads, and 43

55 hence, simultaneous occurrences of other common loads and their effects on bridge performance are not studied here. Earthquake loading is considered to act along the longitudinal direction of bridge as shown in the Figure As the bridge is modeled in 2D, the earthquake loading is considered only in longitudinal direction of bridge. No phase lag of earthquake at various bridge supports is considered. Figure 4.17: Direction of earthquake loading Nonlinear time history analyses of the example bridges are performed in the presence and absence of flood-induced scour (for Y s = 0, 0.6 m, 1.5 m, 3.0 m; d eq = 0.97 m, 1.2 m, 1.6 m, 2.4 m, 4.2 m). For each combination of Y s and d eq, 60 ground motions are considered that represent the seismic hazard of the bridge site. Thus 4800 numerical simulations are performed in total for all bridges considered herein. The fundamental time periods of these bridges are given in Table 4.4. The fundamental time period increases with increasing bridge scour indicating higher flexibility of bridges obtained due to the release of lateral resistance at foundations. Time-histories of bridge response are recorded at various bridge components. To characterize the global nature of bridge performance under the combined action of earthquake and 44

56 scour, the study considered bridge responses measured in terms of longitudinal displacement (along the bridge axis) at the bridge girder level for the fragility analysis. It is reasonable to consider that flexible bridges (due to scour at foundation) have higher tendency to deflect laterally. During earthquake, the abutment and the girder may deflect in the longitudinal and transverse directions. In the present study, bridge deflection only in the longitudinal direction (i.e., along the bridge axis) is considered as the example bridges are modeled in 2D. Axial force develops at the interface of girder and abutment when the girder and abutment strike, which may eventually lead to the failure of abutment backwalls. In case of out-of-phase movement of abutment and girder, excessive separation among these two components may occur resulting in the unseating of bridge girders. The present study assumed an unrestrained longitudinal movement of bridge girders at abutment locations. Thus, with this assumption, bridge failure is defined here in terms of released degree of freedom (i.e., longitudinal deflection of girder). The first five mode shapes for reinforced concrete bridge with d eq = 0.97 m is shown in Figure 4.18, 4.19, 4.20 and 4.21 for 2 span, 3 span, 4 span and 5 span bridges respectively for no scour and 1.5 m scour. 45

57 Table 4.4: Fundamental time periods (in sec) d eq (m) Scour depths Y s (m) Scour depths Y s (m) span bridge 3-span bridge span bridge 5-span bridge Following figures (Figure 4.18 to 4.21) show the first five modes of the example bridges for 0 m scour and 1.5 m scour along with their modal periods. 46

58 0 m scour 1.5 m scour Mode 1: 2.39 sec Mode 1: 3.40 sec Mode 2: 0.25 sec Mode 2: 0.25 sec Mode 3: 0.20 sec Mode 3: 0.20 sec Mode 4: sec Mode 4: 0.10 sec Mode 5: sec Mode 5: sec Figure 4.18: First five mode shapes of 2 span reinforced concrete bridge with d eq = 0.97 m 47

59 0 m scour 1.5 m scour Mode 1: 2.19 sec Mode 1: 3.12 sec Mode 2: 0.46 sec Mode 2: 0.46 sec Mode 3: 0.23 sec Mode 3: 0.23 sec Mode 4: 0.22 sec Mode 4: 0.22 sec Mode 5: 0.16 sec Mode 5: 0.16 sec Figure 4.19: First five mode shapes of 3 span reinforced concrete bridge with d eq = 0.97 m 48

60 Mode 1: 2.12 sec Mode 2: 0.53 sec Mode 3: 0.39 sec Mode 4: 0.23 sec Mode 5: 0.22 sec Figure 4.20(a): First five mode shapes of 4 span reinforced concrete bridge with d eq = 0.97 m (No scour) 49

61 Mode 1: 3.02 sec Mode 2: 0.53 sec Mode 3: 0.40 sec Mode 4: 0.23 sec Mode 5: 0.22 sec Figure 4.20(b): First five mode shapes of 4 span reinforced concrete bridge with d eq = 0.97 m (1.50 m scour) 50

62 Mode 1: 2.09 sec Mode 2: 0.56 sec Mode 3: 0.45 sec Mode 4: 0.34 sec Mode 5: 0.18 sec Figure 4.21(a): First five mode shapes of 5 span reinforced concrete bridge with d eq = 0.97 m (No scour) 51

63 Mode 1: 2.97 sec Mode 2: 0.57 sec Mode 3: 0.45 sec Mode 4: 0.37 sec Mode 5: 0.22 sec Figure 4.21(b): First five mode shapes of 5 span reinforced concrete bridge with d eq = 0.97 m (1.5 m scour) 52

64 Measured displacements are converted to displacement ductility (µ Δ ) which is used here as signature representing bridge seismic performance. By definition, displacement ductility is the ratio of displacement of the bridge pier to the yield displacement (Caltrans, 2006). Displacements at top of bridge piers are found to be the same as the displacements of their immediate nodes in girder due to the monolithic pier-girder connections of example bridges. µ Δ corresponding to the ultimate state (i.e., complete collapse) is calculated to be equal to 5.0. This value is in accordance with Caltrans recommendation for target displacement ductility (Caltrans, 2006). Beyond yielding and before complete collapse, three intermediate states of bridge damage namely minor (or slight), moderate and major (or extensive) damage (definition follows HAZUS 1999 physical descriptions of bridge seismic damage) are considered. Banerjee and Shinozuka (2008a, b) quantified these intermediate bridge damage states in terms of rotational ductility. In this study in order to convert the rotational ductility values at different damage states to their corresponding displacement ductility values a simple beam was modeled in SAP2000 (Figure 4.22). The beam was subjected to nonlinear push over analysis at the top. The rotation of the plastic wen link and the corresponding displacement at the top of the beam was measured. Based on the rotational ductility in the intermediate damage states as defined in Banerjee and Shinozuka (2008a, b), the corresponding displacement ductility was calculated. The values of µ Δ corresponding to minor, moderate and major damage states are thus calculated to be equal to 2.25, 2.90 and 4.60, respectively. These values represent the threshold limits (lower bound) of their corresponding damage states. The state of bridge damage under a specific ground 53

65 motion is decided by comparing the calculated displacement ductility µ Δ with the threshold limits of all damage states (i.e., minor, moderate and major). Thus, bridge damage state under a ground motion can be decided as 2.25; ; ; 4.60; No damage M inor damage M oderatedamage M ajor damage The ultimate displacement using the above procedure is calculated to be 0.81 m. The ultimate displacement is also calculated using the procedure provided in Priestley et al. (1996). The ultimate displacement from Priestley et al. (1996) is calculated to be 0.83 m. Hence, the procedure used above to calculate the displacement ductility can be declared to be accurate. Push over load Roller support Plastic wen link Figure 4.22: Example model for determining the displacement ductility from rotational ductility 54

66 Figures 4.23a and 4.23b show the time histories of displacement ductility for 2- span bridge with 0.97 m (purely sway motion) and 4.2 m diameter (purely rocking motion) equivalent piles under one of the strong motions. As observed the bridge has increased displacement ductility with increasing scour depth if the foundation has purely sway motion during earthquake (Figure 4.23a), however, no such change is observed in case of pure rocking motion (Figure 4.23b). 55

67 Displacement ductility Displacement ductility Time (sec) 0m scour 0.6m scour 1.5m scour 3.0m scour (a) Time (sec) 0m scour 0.6m scour 1.5m scour 3.0m scour (b) Figure 4.23: Time histories of displacement ductility for 2-span bridge under a strong motion; The diameter of equivalent pile is taken as (a) 0.97 m and (b) 4.2 m 56

68 Probability of Exceeding a Damage State Figures 4.24 to 4.27 represent the fragility curves of all four example bridges at three damage states. Fragility curves are developed based on the median PGA s value presented in Table 4.5 and the log-standard deviation of As shown in all of these figures, fragility curves shift from right to left with increasing depth of scour. Hence for a specific PGA value, the probability of exceeding any damage state increases with increasing scour. This indicates higher seismic damageability of bridges in presence of flood-induced scour m 1.5 m 0.6 m 0.0 m PGA (g) (a) 57

69 Probability of Exceeding a Damage State Probability of Exceeding a Damage State m 1.5 m 0.6 m 0.0 m PGA (g) (b) m 1.5 m 0.6 m 0.0 m PGA (g) (c) Figure 4.24: Change in fragility curve for 2 span bridge with d eq = 1.20 m for different scour depth for (a) minor damage state and (b) moderate damage state (c) major damage state 58

70 Probability of Exceeding a Damage State Probability of Exceeding a Damage State m 1.5 m 0.6 m 0.0 m PGA (g) (a) m 1.5 m 0.6 m 0.0 m PGA (g) (b) 59

71 Probability of Exceeding a Damage State Probability of Exceeding a Damage State m 1.5 m 0.6 m 0.0 m PGA (g) (c) Figure 4.25: Change in fragility curve for 3 span bridge with d eq = 1.20 m for different scour depth for a) minor damage state b) moderate damage state c) major damage state m 1.5 m 0.6 m 0.0 m PGA (g) (a) 60

72 Probability of Exceeding a Damage State Probability of Exceeding a Damage State m 1.5 m 0.6 m 0.0 m PGA (g) (b) m 1.5 m 0.6 m 0.0 m PGA (g) (c) Figure 4.26: Change in fragility curve for 4 span bridge with d eq = 1.20 m for different scour depth for a) minor damage state b) moderate damage state c) major damage state 61

73 Probability of Exceeding a Damage State Probability of Exceeding a Damage State m 1.5 m 0.6 m 0.0 m PGA (g) (a) m 1.5 m 0.6 m 0.0 m PGA (g) (b) 62

74 Probability of Exceeding a Damage State m 1.5 m 0.6 m 0.0 m PGA (g) (c) Figure 4.27: Change in fragility curve for 5 span bridge with d eq = 1.20 m for different scour depth for a) minor damage state b) moderate damage state c) major damage state Comparison of bridge fragility characteristics obtained for different combination of d eq and Y s is made in terms of median PGA (PGA m ) in Figures 4.28 to Higher median PGA represents stronger curves (i.e., less vulnerable). This is because, fragility curves move towards right with increase in median value and thus, result in less probability of exceeding a specific damage state. For example, seismic fragility curves developed for 2-span bridge at minor damage state have median PGAs equal to 0.65g and 0.48g for no scour (solid curve with solid dots) and 3.0 m scour (solid curve without dots), respectively (Figure 4.24a). Among these, the former is stronger as it requires higher PGA to reach to a certain level of failure probability. 63

75 The horizontal axes of the three dimensional (3D) plots shown in Figures 4.28 to 4.31 represent scour depths (Y s ) and diameter of equivalent pile (d eq ). Obtained median PGAs for all combinations of Y s and d eq are plotted along the vertical axis of these 3D plots. These median PGAs values are represented in Table 4.5. In each of these plots, three surfaces are shown representing three states of bridge damage. The lowermost surface represents minor damage and the uppermost represents major damage. These surfaces show the change in bridge fragility characteristics with scour depth and diameter of equivalent pile. In general, seismic fragility characteristics of example bridges degrade with increasing scour depth. The rate of degradation (i.e., rate of change of median PGA) is significant for lower values of d eq. As observed from Figures 4.28 to 4.31, very high rate of degradation is observed for d eq less than 1.6 m when scour condition at bridge foundation changes from zero to 0.6 m. During this phase, more than 20% reductions of median PGAs are estimated at minor damage for all example bridges with d eq = 0.97 m. For any further change in scour depth beyond 0.6 m, degradation of bridge seismic performance is not significant and the rate of change gradually becomes zero (corresponding to the flat regions of surfaces in Figures 4.28 to 4.31 for sour 1.0 m). For higher d eq (more than 1.6 m), bridge seismic performance is almost independent of scour depth. This is quite expected due to higher foundation stiffness contributed by bigger diameter piles. Observed tends are nearly identical for all example bridges. In general, weaker fragility curves are obtained for the 2-span bridge than that for other three bridges. However, the difference is not significant for any damage state in particular. 64

76 Table 4.5: Median PGAs for all combinations of Y s and d eq for all example bridges Bridge Type Equivalent pile diameter Damage state 0 m scour Median PGAs value 0.6 m scour 1.5 m scour 3.0 m scour 2 span bridge 3 span bridge d eq = 0.97m d eq = 1.20m d eq = 1.60m d eq = 2.40m d eq = 4.20m d eq = 0.97m d eq = 1.20m Minor Moderate Major Minor Moderate Major Minor Moderate Major Minor Moderate Major Minor Moderate Major Minor Moderate Major Minor Moderate

77 Major span bridge d eq = 1.60m d eq = 2.40m d eq = 4.20m d eq = 0.97m d eq = 1.20m d eq = 1.60m d eq = 2.40m d eq = Minor Moderate Major Minor Moderate Major Minor Moderate Major Minor Moderate Major Minor Moderate Major Minor Moderate Major Minor Moderate Major Minor

78 4.20m Moderate Major span bridge d eq = 0.97m d eq = 1.20m d eq = 1.60m d eq = 2.40m d eq = 4.20m Minor Moderate Major Minor Moderate Major Minor Moderate Major Minor Moderate Major Minor Moderate Major

79 Figure 4.28: Three dimensional plots for 2 span bridge Figure 4.29: Three dimensional plots for 3 span bridge 68

80 Figure 4.30: Three dimensional plots for 4 span bridge Figure 4.31: Three dimensional plots for 5 span bridge 69

81 Chapter 5: Sensitivity Analysis The analysis modules and parameters may be associated with uncertainties. For reliable performance evaluation of bridges under the combined action of earthquake and flood-induced scour, it is therefore important to quantify these uncertainties and estimate their influences on bridge seismic performance. Parametric uncertainty may get introduced in the analyses from various sources such as the calculation of discharge rate, flow depth and velocity of flood flow, occurrence rate and peak intensity of seismic motions, geometry and material properties of bridges (Johnson and Dock 1998, Ghosn et al. 2003, Perkins 2002). Approximate characterization of underlying mechanism for different physical processes (e.g., scouring, ground shaking) induces model uncertainty. Statistical uncertainty, which is due to the limited number of available observation data, also has a high potential to introduce significant uncertainty in the final outcome (Banerjee et al., 2009). For example, annual peak discharge rates corresponding to certain flood hazard are estimated from regional flood hazard curve. This curve is generated based on the measured data. Hence, the values of annual peak discharge obtained for given flood hazard levels may be associated with significant statistical uncertainty. For reliable estimation of peak discharges, it is thus important to develop the confidence bounds of flood hazard curves (Gupta, 2008). This chapter presents a sensitivity study to identify major uncertain parameters. For this, variability of different analysis parameters is determined based on available knowledge. 70

82 5.1 Variability in Hazard Models Regional Flood Hazard Curve with 90% Confidence Interval As mentioned in Chapter 3, regional flood hazard curve can be developed through (1) empirical method, (2) analytical method and (3) graphical method. The flood hazard curve of the study region shown in Figure 3b is developed using empirical method. Estimation of confidence intervals of this curve, however, requires the curve to be developed using analytical procedure (Gupta, 2008). Therefore the same 104 data of annual peak discharges collected for the study region is used here to perform analytical method in order to generate the mean flood hazard curve and its 90% confidence interval. In the analytical method, flood hazard curve is developed using a probability distribution function. The present study used Gamma-Type distribution as this distribution has been adopted by US Federal agencies for flood analysis (Gupta, 2008). Other distributions such as Gaussian, Lognormal and Gumbel can also be used for this purpose. The annual peak discharge (Q) of a specified flood event is expressed in terms of the mean ( X ) and standard deviation ( ) of logarithmic values of sample annual peak discharges ( Qˆ ) collected over years for a specific watershed. The relations are given as: Q ln X K (5.1) X E ln Qˆ (5.2) 71

83 2 2 ln Qˆ X E (5.3) where K, known as the frequency factor, represents the property of the probability distribution under consideration at specified annual occurrence probability (or return period T) of flood events. For Gamma-Type distribution, values of K can be obtained using the coefficient of skewness (g) of sample annual peak discharges ( Qˆ ). For a sample of size n, g is obtained as n g n i 1 ln Qˆ X n 1 n 2 3 i 3 (5.4) For the present set of 104 data of annual peak flood discharge Qˆ collected for the study region (Table 3.1), X,,and g are calculated to be equal to 3.16 m 3 /sec, 0.50 and 0.65 respectively. Using these statistical parameters, values of K for various flood occurrence probabilities are estimated from Table 8.7 (IACWD, 1982) of Gupta (2008) and presented in Table 5.1. The table also provides the values of Q obtained for these flood events (Equation 5.1). Developed flood hazard curve (Q vs. annual exceedance probability of flood events) is presented in Figure 5.1. The same obtained from empirical method (Figure 3b) is also plotted in the same figure to make a comparison between these two curves. The observed difference is purely due to different procedures undertaken in empirical and analytical methods to establish the flood discharge-frequency relationship. 72

84 Table 5.1: Peak discharge flow calculated using Analytical method for different exceeding probability Probability of exceedance Frequency factor (K) Logarithimic discharge (ft 3 /sec) Probability of exceedance Frequency factor (K) Logarithimic discharge (ft 3 /sec)

85 Probability of exceedance Frequency factor (K) Logarithimic discharge (ft 3 /sec) Probability of exceedance Frequency factor (K) Logarithimic discharge (ft 3 /sec)

86 Annual peak discharge (m 3 /s) Analytical curve 10 Empirical curve 1 Probability of exceedance (Probability of annual discharge being equal or exceeded) Figure 5.1: Comparison of flood hazard curves developed from empirical and analytical methods 75

87 Developed flood hazard curve through analytical method (Figure 5.1) is associated with 50% statistical confidence. It provides the most expected (or mean) estimates of annual peak discharges corresponding to various flood hazard levels. To develop the 90% confidence interval of this mean hazard curve, error limits on both sides of the mean estimate for various probability of exceedance are estimated (Gupta, 2008). Table 5.2 represents these error limits for 5% and 95% statistical confidence and the corresponding values of peak discharge are calculated. Figure 5.2 represents flood hazard curves of the study region with 5%, 50% and 95% statistical confidence. Lower statistical confidence indicates higher exceedance probability. Thus, for a particular flood hazard, the annual peak discharges obtained for 5% statistical confidence is always higher than that obtained for other two confidence levels. Table 5.2: Peak flood discharges with 5% and 95% statistical confidence Probability of exceedance 5% confidence Error limit 95% confidence Error limit Standard deviation ( ) 5% confidence 95% confidence A B 1 B 2 C 1 C 2 Q ln = Discharge (ft 3 /sec) 5% 95% confidence confidence D 1 D 2 (Table (Table 5.1 C 1 ) C 2 )

88 Annual peak discharge (m 3 /s) % statistical confidence 50% statistical confidence 95% statistical confidence 1 Probability of exceedance (Probability of annual discharge being equal or exceeded) Figure 5.2: Flood hazard curve with 90% confidence interval 77

89 5.1.2 Parameter Sensitivity in the Calculation of Scour Depth Depending on expected scour depth from flood events, bridge seismic response may change to a great extent (Figures 4.28 to 4.31). Parameters involved in the scour depth calculation have high variability which introduces variability in calculated scour depth. To estimate the level of variability associated with calculated scour depths and to investigate the sensitivity of different input parameters, a sensitivity study is performed here. This is done by considering the 5-span example bridge and a 100-year flood event. This particular bridge is chosen as it is directly adopted from the literature without any alteration. Based on the bridge response observed in Chapter 4, it is expected that other example bridges will have the similar trend as of the 5-span bridge. Sensitivity of four input parameters (discharge rate, coefficient for angle of attack of flow, and bed condition coefficient and effective pier width) are studied. Variability of these parameters is discussed in the following section. Annual peak discharge (Q): Uncertainties associated with Q for any particular flood hazard level can be estimated from the flood hazard curve with 90% confidence interval (Figure 5.2). This may have significant impact on the expected bridge scour depth. To demonstrate the impact, present study considered 100-year flood event. Values of Q corresponding to 5%, 50% and 95% confidence levels are estimated to be equal to 2720 m 3 /sec, 1960 m 3 /sec and 1280 m 3 /sec, respectively. Respective values of flow velocity and flow depth are calculated using Eqs. 2.2 and 2.3. These two variables (i.e., flow velocity and flow depth) are considered here as independent variables although, in reality, some correlation may exist among them. The 78

90 randomness of these two variables is assumed to be the sole result of the randomness observed in the annual peak discharge. Correction factors for HEC equation (K): This study considered K 1 and K 4 as deterministic variables and K 2 and K 3 as random variables. The correction factor K 1 corresponds to the shape of the bridge piers which are considered to be circular. Therefore K 1 has no variation. K 4 corresponds to the size of subsurface soil particles and remains constant (equal to 1.0) for D 50 < 2mm and D 95 < 20mm. Any variation in soil particle size distribution assumed not to alter this criterion. K 2 and K 3 correspond to the angle of attack and bed condition, respectively. During flooding, the angle of attack may vary depending on the direction of flood water to the bridge site. Therefore, some variability may be present in K 2. This variation is taken here following the recommendation of Johnson and Dock (1998). K 3 depends on the bed condition. Many a times it is very difficult to accurately predict the type of bed condition, particularly during flood events. This prediction uncertainty is accounted here by considering a variation in K 3 (Johnson and Dock, 1998). As presented in Johnson and Dock (1998), K 2 is assumed to follow a normal distribution with mean and coefficient of variation equal to 1.00 and Similarly, K 3 is considered as a random variable having a mean equal to 1.10 with 5% variation (Johnson and Dock, 1998). Therefore the values of mean ± 2(standard deviation) are calculated to be 0.9 and 1.10 for K 2 and 1.21 and 0.99 for K 3. These values are considered in the sensitivity analysis. 79

91 Effective pier width (a): For analysis purpose, it is assumed that diameter of bridge piers has 10% variation. Hence the values of mean ± (standard deviation) of a becomes 2.16 m and 2.64 m, where the mean value is 2.4 m. Other input parameters for the calculation of scour depth (Chapter 2) are considered to be deterministic assuming these parameters can be measured with relatively high certainty. Values of these deterministic parameters are kept unaltered from the previous analysis presented in Chapter 4. In the sensitivity study, all uncertain parameters are first kept at their mean values and the scour of the 5-span example bridge is calculated. This scour depth is referred to as the most expected scour depth and calculated to be 3.44 m for a 100-year flood event. Following this, value of one uncertain parameter is changed (with the assigned variation) at a time keeping all other parameters at their respective mean values. Scour depths are calculated for each case and are plotted in Figure 5.3. This figure, known as Tornado diagram, shows the parameter sensitivity in the bridge scour calculation. The result indicates that the calculated scour depth is most sensitive to angle of attack of flow (K 2 ) and bed condition coefficient (K 3 ). 80

92 Figure 5.3: Tornado diagram developed for the 5-span example bridge The scour depth is directly proportional (has linear relation) to coefficient of angle of attack of flow (K 2 ) and bed condition coefficient (K 3 ) (Equation 3.1). Thus, scour depth increases with increase in K 2 and K 3. Due to the variability in annual peak discharge (Q) obtained for 5% and 95% confidence levels, almost the same amount of change in scour is observed on both sides of the most expected scour depth. Increase in effective width of bridge piers (a) results in increase in scour depth due to the fact that more flow is obstructed by a bigger pier. Note that this analysis considered all bridge piers have the same diameter irrespective of the variability considered in its value. 81