# SEISMIC PERFORMANCE OF SKEWED BRIDGES UNDER ORTHOGONAL GROUND MOTION COMPONENTS

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# Abstract

Earthquakes are a natural calamity, feared by most and cause great destruction in and around the seismic zone where they occur. Bridges, being an important component of the transportation system, are therefore required to be designed such that they can withstand these large impacts and remain functional post-earthquake event. The present study is focused on conducting a parametric study and evaluating the performance of skewed bridges under seismic activities by considering the orthogonal effects in nonlinear time history analysis, wherein, two seismic waves, in the form of time histories, act simultaneously at the structure at right angles to each other. Such a set of waves is known as the orthogonal set of time histories. Any one of the two seismic waves can be assumed to be acting in a principal direction, i.e. along the direction of the ground motion. The other seismic wave, thus, acts in a direction perpendicular to it. Responses of the bridge are obtained in the directions along the length of the bridge (longitudinal) and perpendicular to it (transverse). These responses are statistically independent of each other.

For conducting the analysis, Painter Street Overpass located in Rio Dell, CA is modeled as a dual-beam stick bridge using OpenSees.  After validating the analytical model, the bridge is subjected to a suite of orthogonal set of time histories developed for the California region. The angle formed by the seismic wave acting along the principal direction, with the central axis of the bridge, in the longitudinal is called as the angle of incidence. This angle is made to rotate from 00 to 1800 with a step of 150. Skew angle of the bridge is defined as the angle made by the bents or abutments with the axis along the transverse direction of the bridge. The above procedure is repeated for different skew angles of the bridge varying from 00 to 500 with a step of 100. The effect of the variation of these two parameters on the response of the structure is analyzed to determine the critical angle of incidence for a ground motion on the bridge. It is concluded that angle of incidence, by itself cannot determine the critical response of the structure, as critical angle of incidence, which generated the critical response in the structure, varied for different ground motions used for analysis. It is suggested to include a seismic parameter like peak ground acceleration (PGA) to the parametric study, to determine the combination that produces a critical response.

Fragility curves are developed in order to provide insight into the vulnerability of the bridge to different seismic loading conditions. The effect of change in skew angle and angle of incidence is studied on the fragility plots for different damage states of the bridge, as described by HAZUS-MH, thus linking the variation in PGA to the parametric study. It is derived that inclusion of PGA in probabilistic terms results in obtaining a range of critical incident angle and skew angle, for which the critical response can be generated in the structure. A study is conducted, in which variation of the median value of the PGA is observed along with variation in angle of incidence and skew angle of the bridge. It is inferred that the peak response in the structure occurs for incident angles ranging from 300 to 800, and for skew angles of 400 and 500.

Abstract ………………………………………………………………………………………………………………………………….. iii

List of Figures ……………………………………………………………………………………………………………………….. viii

List of Tables ………………………………………………………………………………………………………………………….. xi

Acknowledgment …………………………………………………………………………………………………………………….. xii

Chapter 1 INTRODUCTION ……………………………………………………………………………………………………… 1

1.1      Problem Statement ……………………………………………………………………………………………………. 5

1.2      Scope and Objective of the Research …………………………………………………………………………… 5

1.4      Thesis Outline ………………………………………………………………………………………………………….. 7

Chapter 2 LITERATURE REVIEW ……………………………………………………………………………………………. 8

2.1      Orthogonal Effects and Combination rules …………………………………………………………………… 8

2.2      Use of Orthogonal Effects in Seismic Analysis of Straight and Skewed Bridges …………….. 13

2.3     Modeling techniques used for the bridge models …………………………………………………………. 16

2.4      Fragility Curve Analysis ………………………………………………………………………………………….. 21

2.5      Summary ……………………………………………………………………………………………………………….. 23

Chapter 3 MODELING OF REPRESENTATIVE BRIDGES ………………………………………………………. 24

3.1      Bridge location and dimensional details: ……………………………………………………………………. 25

3.2      Modeling of the bridge: ……………………………………………………………………………………………. 28

3.2.1       Superstructure: ………………………………………………………………………………………………….. 28

3.2.2       Substructure – Abutments: ………………………………………………………………………………….. 31

3.2.3       Substructure – Bent: …………………………………………………………………………………………… 36

3.2.4       Substructure – Foundation: …………………………………………………………………………………. 38

3.3      Validation of the bridge model: ………………………………………………………………………………… 40

3.4      Summary: ………………………………………………………………………………………………………………. 49

Chapter 4 NON-LINEAR TIME HISTORY ANALYSIS OF SKEWED BRIDGES ……………………….. 50

4.1      The Study Region and Regional Seismic Hazard ………………………………………………………… 51

4.2     Variation of response with change in Angle of Incidence (θ) for a given skew angle (α) ….. 51

4.3     Variation of response with change in both skew angle (α) and angle of incidence (θ) ………. 57

4.4      Calculation of Rotation Ductility ………………………………………………………………………………. 61

4.5      Summary ……………………………………………………………………………………………………………….. 62

Chapter    5    FRAGILITY    CURVE    ANALYSIS    FOR    PAINTER    STREET    AND    OTHER

REPRESENTATIVE BRIDGES ………………………………………………………………………………………………. 63

5.1      Damage States ………………………………………………………………………………………………………… 63

5.2     Fragility Curves for the Painter Street Bridge ……………………………………………………………… 66

5.3     Variation of fragility parameters with change in angle of incidence (θ) ………………………….. 67

5.4      Variation of Fragility parameters with change in skew angle (α) …………………………………… 70

5.5          Variation of Fragility parameters with change in both angle of incidence (θ) and skew angle

(α)……………………………………………………………………………………………73

Chapter 6 CONCLUSION ……………………………………………………………………………………………………….. 81

6.1      Summary ……………………………………………………………………………………………………………….. 81

6.2      Results and Conclusion ……………………………………………………………………………………………. 82

6.3      Applications …………………………………………………………………………………………………………… 83

6.4      Limitations …………………………………………………………………………………………………………….. 83

6.5    Scope for Future Research ……………………………………………………………………………………….. 84 Bibliography …………………………………………………………………………………………………………………………… 85

Appendix A Different types of Bridges in the state of California ……………………………………………………. 91 Appendix B Time Histories for Los Angeles, CA region ………………………………………………………………. 92

Chapter 1 INTRODUCTION

Any structure that spans and provides a passage over a physical obstruction such as river, road or valley is defined as a Bridge. The first bridges ever to be built by humans have been dated back to the 13th Century B.C. This defines the importance of bridges in the transportation system. Failure of bridges due to natural calamities or human error will disrupt the normal functioning of the transportation system, causing the entire traffic to come to a standstill. This will result in major economic losses, and might also result in loss of life in the eventuality of people traversing the bridge at the time of failure. Hence safety, serviceability and performance of bridges and its components, under all loading scenarios, is of prime importance to structural engineers.

The National Seismic Hazard Map for the United States is displayed in Figure 1.1 as developed by the U.S. Geological Survey (USGS) group. The map represents levels of horizontal shaking having a 2% probability of exceeding the peak ground acceleration during 50-year time period. The shaking is measured in terms of percentage of acceleration due to gravity (g).

## Figure 1.1: Seismic Hazard Map of the USA  (Credit: U. S. Geological Survey)

As per USGS, Alaska is the most seismically active state in the U.S., with California being the second most active state. This is due to the close presence of North American Tectonic plate, which runs almost parallel to the West Coast. Since 1974, these two states constitute 80.4% of the total number of earthquakes that occurred in U.S. of magnitude greater than 3.5 on Richter scale

(USGS). Another area that was seismically active in the U.S. is known as the New Madrid Seismic Zone, where large number of intra-plate earthquakes occurred in 1811-12. Even though the area has been relatively quiet for quite some time, the probability of large earthquakes occurring in the future is very high.  Other parts of the country have relatively low seismicity.

Major earthquakes that have caused severe damage in U.S. since 1970s are the San Fernando earthquake in 1971, the Loma Prieta earthquake in 1989 and the Northridge earthquake in 1994. These earthquakes have provided insights for creating an effective structural design that is able to resist these seismic loads. Roberts (2005) stated the following major causes for the bridge failures that occurred in the San Fernando earthquake in 1971:

1. Superstructure collapsing due to unseating of girders.
2. Loss of support for suspended sections, due to separation of thermal expansion joints.
3. Bond failure between footing concrete and column reinforcing steel, causing pullout of column reinforcement.
4. Excessive deformation due to bending and horizontal shear failure of supporting columns.

Figure 1.2: Unseating of spans due to Figure 1.3: Damage caused due to rotation at narrow seats, 1971 San Fernando deck hinge joint, 1971 San Fernando

Earthquake, California (Roberts, 2005)              Earthquake, California (Roberts, 2005).

Figure 1.4: Pullout of column Figure 1.5: Shear Failure of Column, 1971 reinforcement, 1971 San Fernando San Fernando Earthquake, California Earthquake, California (Roberts, 2005) (Roberts, 2005)

As per the report by National Research Council (1994), post 1971 San Fernando earthquake, California Department of Transportation (Caltrans) upgraded their bridge design specifications to address the identified deficiencies, and initiated a state-wide seismic-retrofit program to reinforce old, non-ductile and non-seismically designed bridges. It mainly comprised of installing hinge and joint restrainers to prevent separation of deck joints. This phase was completed in 1989, with approximately 1260 state highway bridges been retrofitted after spending over \$55 million.  During the Loma Prieta earthquake on October 17, 1989, the retrofitted bridges performed really well, proving the reliability of the hinge and joint restrainers. However, failure analysis of Cypress Street Viaduct in Oakland highlighted the susceptibility of the columns to large shear forces generated during the earthquake. This led to the Caltrans’s current Seismic Safety Retrofit Program, which involves retrofitting of over 2,200 bridges at an estimated cost of \$8 billion in construction (Caltrans, 2003).

It was reported (National Research Council 1994) that the Caltrans developed a VulnerabilityAnalysis algorithm, in order to set priorities for retrofitting more than 24,000 bridges in the state. The structural and ground motion characteristics that were considered in order to set the priorities are listed as follows:

• Ground Acceleration
• Skew angle of the bridge
• Column design
• Confinement details of the column
• Length of the bridge
• Soil Type
• Abutment Type
• Hinges

This indicates the factors that were considered of high importance in risk-assessment of the bridges in California. The focus of the present research is to provide a preliminary approach for future retrofit programs, which considers the variation in the first two structural characteristics, namely the ground acceleration and skew angle of the bridge. These two factors were selected mainly due to:

1. Vast range of magnitudes of earthquakes experienced in California, ranging from 1.0 to

7.9 on Richter scale.

1. Large number of bridges in California with skew angles varying from 00 to 600.
2. Lack of sufficient knowledge to evaluate the impact of the variation of ground acceleration for a particular skew angle of the bridge on its response.

Fragility curves provide a tool to express seismic performance of bridges in a probabilistic framework. These curves describe the bridge’s vulnerability to seismic loads and provide the probability of the bridge sustaining damage beyond a given state for different levels of intensity of ground motions. Fragility curve analysis, thus, can aid in accelerating decision-making process for performance-based retrofit and cost-benefit analysis. It also proves an essential input to the Seismic Risk Assessment (SRA) methodology, aimed at evaluating the seismic risk to regions and infrastructure system (Padgett, 2007). Hence, for research purposes, a comparative study of the fragility curve analysis is undertaken, to evaluate the bridge’s performance for different ground accelerations for a particular skew angle of the bridge.

1.1 Problem Statement:

Addressing the issues as stated above, the problem statement for the research can be stated as follows:

‘To evaluate the seismic performance of a skewed bridges through a comparative

numerical study and fragility analysis incorporating possible variations in ground acceleration time history, angle of ground motion propagation (i.e., directionality) and skew angles of the bridges.’

A similar study was performed by Banerjee Basu and Shinozuka (2011). However, only the effects of directionality of the ground motions were considered. This research study adds the parameter of skew angle of the bridge.

1.2 Scope and Objective of the Research:

The present research is aimed to investigate and observe the change in seismic performance of two-span skewed bridges with the change in seismic loads. A Non-Linear Time History Analysis (NTHA) is performed to obtain the bridge response. According to AASHTO guidelines, bridge superstructure is designed such that it remains elastic under earthquake forces. Abutments are modeled as elastic elements, as the formation of plastic hinge is considered to be localized at bridge pier columns only, for this study. Hence, nonlinear properties of the bridge are considered within bridge pier. Therefore, the seismic performance of the bridge is mostly governed by the seismic performance of the bridge pier. Seismic hazard at bridge site is modeled using a suite of earthquakes having horizontal orthogonal components. The two components of the seismic waves, in the form of time histories, act simultaneously at the structure at right angles to each other. According to Penzian and Watabe (1975), any one of the two seismic waves can be assumed to be acting in a principal direction, i.e. along the direction of the ground motion. The other seismic wave, thus, acts in a direction perpendicular to it. In order to study the effects of directionality, the angle of incidence of a ground motion is varied. The angle of incidence is the angle formed by the seismic wave acting along the principal direction of the ground motion, with the central axis of the bridge structure, running along the direction of the roadway. The performance of the bridge is measured by developing fragility curves for each combination of angle of incidence of ground motion and skew angle of the bridge, for different seismic damage states.

The primary objective is to demonstrate the seismic vulnerability of skewed bridges to angle of incidence of the ground motion and to bridge’s skew angle. It is intended, with the help of observed results from this study, to support and accelerate the decision-making on retrofitting existing skew bridges and/or on seismic design considerations for new bridge constructions.

In order to realize the objective of the research, the various tasks that were conducted are broadly outlined as follows:

1. Modeling and validation of the bridge to be used for analysis.
2. Conduct Non-linear Time History Analysis (NTHA) of skewed bridges incorporating the orthogonal effects of seismic waves.
3. Perform a parametric study showcasing the variation of bridge response with respect change in angle of incidence of a ground motion for a given skew angle of the bridge and vice versa.
4. Development of fragility curves to obtain the probability of exceeding a particular damage state for different ground motions.
5. Exploration of the sensitivity of fragility estimates to change in angle of incidence of ground motions for a given skew angle of the bridge and vice versa.

1.4 Thesis Outline:

The thesis has been organized into the following chapters in order to realize all the research tasks:

1. Chapter 2 provides an insight into orthogonal effects in seismic analysis, including the current state of research studies in which the orthogonal effects have been considered for seismic analysis of skewed bridges. It explains the background theory of bridge fragility analysis and the damage states considered for this research. An overview of the modeling techniques used for design of skew bridges has also been added.
2. Chapter 3 presents the details of the skewed bridges considered for the present research. It highlights the various modeling parameters considered to model the super-structural and sub-structural elements of the bridge. Validation of the model is performed by comparing results obtained from the numerical analysis of the bridge model to those recorded during an actual earthquake in past.
3. Chapter 4 highlights the variation in peak response of the bridge with respect to the change in the angle of incidence of ground motions and bridge skew angle. Procedure to calculate the rotation ductility for a particular time instant is also discussed in this section.
4. Chapter 5 showcases the development of fragility curves for different damage states for the bridge considered. This section further highlights the sensitivity of bridge fragility characteristics on angle of incidence of ground motions and skew angle of the bridge.
5. Chapter 6 summarizes the research and lists the conclusions drawn from the obtained results. It also suggests future research work that can be undertaken following the work

done as a part of this research.