Tenth U.S. National Conference on Earthquake EngineeringFrontiers of Earthquake Engineering July 21-25, 2014 Anchorage, Alaska 10NCEE

EXPERIMENTAL EVALUATION OF SEISMIC PERFORMANCE OF SEAT-TYPE ABUTMENTS IN A CURVED HIGHWAY

BRIDGE

J. D. Wieser1, E. M. Maragakis2, and I. G. Buckle3

ABSTRACT Expansion gap closure in seat-type bridge abutments during strong earthquakes results in seismic pounding. This pounding affects the behavior of the bridge and yet there are limited experimental studies focused on this phenomenon. As a part of a Federal Highway Administration funded project, a 2/5 scale curved bridge model was tested on the four shake tables in the University of Nevada, Reno Large Scale Structures Laboratory. Two of the six configurations of the bridge model were used to isolate the influence of seismic pounding at the abutments on the overall response of the bridge. In the configuration considering abutment pounding, a backwall system simulated the expansion gap, a realistic contact surface, and nonlinear backfill. In this configuration, the superstructure is forced to impact a backwall supported by nonlinear springs with initial stiffness similar to that of typical embankment soil. Numerical models of the experimental configurations with and without abutment pounding show good correlation with the experimental results. Validation of the numerical models provides confidence in the analytical techniques employed which will be used in further analytical parametric studies.

1Graduate Research Assistant, Department of Civil and Environmental Engineering, University of Nevada, Reno, 1667 N. Virginia St. MS 0258 Reno, NV 89512 2Dean, College of Engineering, University of Nevada, Reno, 1667 N. Virginia St. MS 0256 Reno, NV 89512 3Director, Center for Civil Earthquake Engineering Research, University of Nevada, Reno, 1667 N. Virginia St. MS 0258 Reno, NV 89512 Wieser, J.D., Maragakis, E.M., Buckle, I.G. Experimental Evaluation of Seismic Performance of Seat-Type Abutments in a Curved Highway Bridge. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

Experimental Evaluation of Seismic Performance of Seat-Type

Abutments in a Curved Highway Bridge

J.D. Wieser1, E.M. Maragakis2and I.G. Buckle3

ABSTRACT Expansion gap closure in seat-type bridge abutments during strong earthquakes results in seismic

pounding. This pounding affects the behavior of the bridge and yet there are limited experimental studies focused on this phenomenon. As a part of a Federal Highway Administration funded project, a 2/5 scale curved bridge model was tested on the four shake tables in the University of Nevada, Reno Large Scale Structures Laboratory. Two of the six configurations of the bridge model were used to isolate the influence of seismic pounding at the abutments on the overall response of the bridge. In the configuration considering abutment pounding, a backwall system simulated the expansion gap, a realistic contact surface, and nonlinear backfill. In this configuration, the superstructure is forced to impact a backwall supported by nonlinear springs with initial stiffness similar to that of typical embankment soil. Numerical models of the experimental configurations with and without abutment pounding show good correlation with the experimental results. Validation of the numerical models provides confidence in the analytical techniques employed which will be used in further analytical parametric studies.

Introduction Curved highway bridges are particularly vulnerable to earthquakes due to their inherent eccentricity between the center of mass and center of stiffness. Under seismic loads, this eccentricity induces increased in-plane rotations of the superstructure in curved bridges compared to their straight counterparts. Excessive in-plane rotations have been shown to result in unseating and collapse of curved bridges in several recent earthquakes [1,2,3,4]. Unseating occurs in seat-type abutments when the support length provided cannot sufficiently accommodate the relative displacements of the superstructure. Seat-type abutments are commonly used in curved bridges to avoid large, unbalanced stresses in the superstructure and embankment backfill due to thermal expansion and contraction. Seat-type abutments allow thermal expansion by providing a gap between the end of the bridge and the abutment backwall. However, this gap is not always sized to accommodate the seismic displacement demands and during significant earthquake events the gap is closed resulting in abutment pounding. Seismically induced abutment pounding is a highly nonlinear phenomenon. Essentially 1Graduate Research Assistant, Department of Civil and Environmental Engineering, University of Nevada, Reno, 1667 N. Virginia St. MS 0258 Reno, NV 89512 2Dean, College of Engineering, University of Nevada, Reno, 1667 N. Virginia St. MS 0256 Reno, NV 89512 3Director, Center for Civil Earthquake Engineering Research, University of Nevada, Reno, 1667 N. Virginia St. MS 0258 Reno, NV 89512 Wieser, J.D., Maragakis, E.M., Buckle, I.G. Experimental Evaluation of Seismic Performance of Seat-Type Abutments in a Curved Highway Bridge. Proceedings of the 10th National Conference in Earthquake Engineering, Earthquake Engineering Research Institute, Anchorage, AK, 2014.

the superstructure collides with the abutment structure which instantaneously changes the dynamic characteristics of the bridge system. Large inertia forces generated by the superstructure mobilize the passive resistance of the backfill soil behind the abutment backwall which can result in nonlinear soil behavior. Typically in straight bridges it is accepted that this interaction reduces superstructure displacements by adding stiffness and dissipating energy. In curved bridges, abutment pounding dissipates energy, but instantaneous variations in the location of the center of stiffness may amplify the aforementioned in-plane rotations of the superstructure resulting in increased displacement demands. In an attempt to improve the understanding of the dynamic behavior of curved highway bridges, a series of large-scale shake table experiments were conducted at the University of Nevada, Reno. The Federal Highway Administration sponsored research project investigated six configurations of a 2/5th-scale curved bridge. Two of these configurations were used to isolate the effect of abutment pounding on the response of the bridge. The conventional configuration (CB1) provided a benchmark for the abutment pounding configuration (CB5). This paper presents the findings of the experimental investigation and discusses an analytical approach to simulating the response of the experimental model.

Curved Bridge Model The physical curved bridge model employed in the experimental investigations was a 2/5th-scale, 3-span, steel plate girder bridge. The bridge model was 145 ft (44.2 m) long with a radius of 80 ft (24.4 m) and a subtended angle of 104° (1.8 rad). The three girders were spaced at 54 in (1.37 m) on center and the width of the reinforced concrete deck was 144 in (3.66 m). The four supports were distributed symmetrically along the bridge creating three spans of 42 ft (12.8 m), 61 ft (18.6 m), and 42 ft (12.8 m), respectively. A rendering of the curved bridge model spanning the four shake tables at the University of Nevada, Reno Large Scale Structures Laboratory is shown in Fig. 1.

Figure 1. Rendering of curved bridge model.

The superstructure was comprised of a reinforced concrete deck that was composite with three steel I-girders. The reinforced deck was 3.25 in (83 mm) thick with a 0.75 in (19 mm) haunch. The girders were built-up sections consisting of 0.625 in (16 mm) by 9 in (229 mm) flange plates and 0.375 in (10 mm) by 26 in (660 mm) web plate. The cross-frames between the girders are spaced every 72 in (1.83 m) throughout the length except at the middle of the bridge where two cross-frames are spaced at 78 in (1.89 m). The piers were single columns with dropped caps. The model columns had a diameter of 24 in (610 mm) and a clear height of 92 in (2.34 m). The columns were designed with 1% longitudinal steel ratio and a 5% axial load ratio. The specified concrete strength was 5 ksi (38 MPa) and the steel reinforcement was A706 Gr. 60 steel. The abutment supports were supplied by steel reaction towers. These lightweight, rigid

towers were designed to transfer the acceleration input from the shake tables to the superstructure with minimal distortion. In addition, the towers were required to provide a multitude of support conditions, including: large displacement slider bearings, two types of isolation bearings, shear keys, and abutment backwalls. The two bridge configurations of interest in this study (CB1 and CB5) had the same superstructure support conditions with the exception of the abutment backwalls. Pin bearings connected each of the girders to the pier caps, as shown in Fig. 2a. These bearings were designed to carry shear and axial forces through the bearing while allowing rotation. The lateral, compressive, and tensile load capacity of the pin bearings were 50 kip (222 kN), 100 kip (445 kN), and 40 kip (178 kN), respectively, and the rotational capacity was 4.3° (0.075 rad). At the abutments, the vertical support was provided by flat slider bearings, shown in Fig. 2b. These bearings allowed translation in both horizontal directions as well as uplift. The slider bearings were comprised of a sliding pot bearing with a Teflon surface which was attached to the underside of the girder, and a stainless steel plate on which the slider was free to move with a low coefficient of friction. These bearings could accommodate a displacement range of ±18 in (±457 mm) in the tangential and radial directions.

Figure 2. Types of bridge bearings at support locations.

In addition to the slider bearings a two-way internal shear key was mounted on the bottom chord of the cross frame at the abutment supports. The shear keys were designed to be sacrificial. They were to provide radial restraint to the end of the bridge for low to moderate level shaking but fail during the 75% DE level excitation. This coincides with the current practice as shear keys are commonly detailed as structural fuses to protect the abutment foundation. The fracture strength of the shear keys employed in the curved bridge model was 25 kip (111 kN). Each shear key was comprised of three components: i) the shear pin, ii) the “dog-bone”, and iii) the trough. These components fit together as shown in Fig. 3. The “dog-bone” is attached to the bottom chord of the cross frame and holds the top of the shear pin. The bottom of the shear pin fits into a brass bushing that slides freely in the trough. The trough is mounted to the abutment reaction tower and oriented in the tangential direction. When fully assembled the shear key restrains the radial movement of the bridge through shear in the shear pin and accommodates tangential movement by sliding in the trough. The stainless steel shear pin was notched to ensure shear failure at the design capacity of 25 kip (111 kN). Static load tests were conducted on the shear key components to verify the strength of the shear keys prior to shake table testing of the bridge.

(a) Pin Bearing @ Piers (b) Slider Bearing @ Abutments

Figure 3. Shear key assembly.

The abutment backwalls were designed to provide a realistic contact surface between the end of the superstructure and the abutment. Using a reinforced concrete wall facilitated the assessment of energy losses due to impact as well as any potential localized damage states of the backwall or girders. Each backwall was made of reinforced concrete confined by a steel frame, shown in Fig. 4a. The 144 in x 34 in x 6 in (3.66 m x 0.84 m x 0.15 m) backwalls spanned the width of the bridge deck and weighed 4.0 kip (17.8 kN) each. The concrete strength of the backwalls was 5.5 ksi (38 MPa). The backwalls were supported on two casters which travel along a rail attached to the abutment tower which was oriented in the tangential direction, depicted in Fig. 4b. Four nonlinear soil springs were used in parallel to simulate the passive resistance of the embankment backfill, illustrated in Fig. 4c. The initial gap between the end of the bridge and the backwall, shown in Fig. 4d, was 0.75 in (19 mm). This gap length was determined from temperature load analysis of the prototype bridge and was scaled down for the model. Ideally the passive resistance of the embankment backfill would have been provided by laminar soil boxes atop the shake tables. However due to laboratory limitations this was not an option. Instead, the soil behavior was simulated with nonlinear soil springs mounted between the backwall and the rigid abutment tower. An iterative process of prototyping and testing was employed in the development of the soil springs. The goal was to emulate the nonlinear behavior of the code prescribed soil as closely as possible. Static compressive load testing of the final soil spring design is summarized in Fig. 5. The soil spring design offered a nearly elasto-perfectly-plastic behavior with the accumulation of permanent plastic deformation, very similar to idealized soil behavior.

(a) “Dog-Bone” and Shear Pin (c) Shear Key Assembly

(b) Trough and Brass Sliding Sleeve (d) Deformed Shear Pins

25 kip (111 kN)

Figure 4. Experimental abutment backwall assembly.

The targeted soil stiffness and strength of each abutment were calculated according to the provisions of Caltrans SDC [5]. The targeted total abutment stiffness and strength was determined from the following equations:

⎟⎟⎠

⎞⎜⎜⎝

⎛××=

ft

hw

ft

inkipK abut 5.5

/50 or ⎟

⎠⎞

⎜⎝⎛××=

m

hw

m

mmkNK abut 7.1

/7.28 (1)

⎟⎟⎠

⎞⎜⎜⎝

⎛××=

ft

hksfAP ebw 5.5

5 or ⎟⎠⎞

⎜⎝⎛××=

m

hkPaAP ebw 7.1

239 (2)

In which, h and w are the effective height and width of the abutment backwall, respectively, and Ae is the effective area of the backwall. The initial stiffness of embankment fill equal to 50 kip/in/ft (28.7 kN/mm/m) is based on a backfill soil satisfying the Caltrans Standard Specifications. This value should be reduced by 50% if these specifications are not satisfied. The passive force capacity of the soil, Pbw, is calculated based on the effective backwall area and the maximum passive soil pressure obtained from full scale abutment testing, 5 ksf (239 kPa). The

height proportionality factor ft

h

5.5 ⎟

⎠⎞

⎜⎝⎛

m

h

7.1 is also derived from the full scale abutment tests

conducted at the University of California Davis [6]. The achieved total stiffness and strength of the simulated abutment backfill in the experimental model is compared to code prescribed estimates in Table 1. Due to shake table limitations the total soil force capacity per abutment was limited to 40 kip (178 kN). This was 17% of the Caltrans prescribed strength and 23% of the AASHTO [7] prescribed strength. As a result, yielding of the experimental soil springs occurred at significantly less force in then would be expected in the field. The total stiffness of the soil springs was 33% of the Caltrans prescribed estimate for a standard backfill soil and 66% of a substandard backfill soil. However, the experimental soil stiffness was 260% of the AASHTO estimate for a clay backfill. Therefore,

(b) “T-Rail” Radial Restraint

(c) Radial View of North Abutment Backwall

(a) Backwall Frames

(d) Above View of South Abutment Gap

while on the flexible side, the stiffness of the simulated backfill in the experimental abutments was considered to be within an acceptable range.

Figure 5. Soil spring calibration.

Table 1: Abutment backfill soil properties.

Abutment Model

Prototype Model

Fult K Fult K

kip kip/in kip kip/in

Experiment (CB5) 250 650 40 260

Caltrans Standard 1430 1975 230 790

Caltrans Substandard 1430 990 230 395

AASHTO Sand 1050 1205 165 485

AASHTO Clay 1085 250 175 100

Loading Protocol

The design spectrum was based on a rock site in Reno, Nevada. The peak ground acceleration was 0.472 g, the short-period spectral acceleration was 1.135 g, and the 1-second spectral acceleration was 0.41 g. The horizontal components of ground motion recorded at the Sylmar Station during the 1994 Northridge Earthquake was used as the only shake table input motion for CB1 configuration. During the CB5 configuration additional earthquake motions were applied namely, the El Centro #9 recording of the 1940 Imperial Valley Earthquake, and the Hachinohe Station recording of the 1968 Tokachi Oki Earthquake in Japan. These motions were added to the protocol to impose longer duration of shaking and induce a greater number of abutment pounding events. In the experiments, the ground motions were increased incrementally in terms of their equivalent Design Earthquake (DE) intensity. The equivalent DE was determined by scaling the amplitude of the major component of the recording such that the spectral acceleration matched the design spectrum acceleration at a period of 1.0 second. As a result, the corresponding amplitude scale factors for the El Centro (ELC), Hachinohe (HAC), and Sylmar (SYL) motions were 0.84, 0.77, and 0.475, respectively. In order to maintain similitude, the input motions were time scaled by a factor equal to 0.632.

0.0 6.4 12.7 19.1 25.4

0.0

8.9

17.8

26.7

35.6

44.5

53.4

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.00 0.25 0.50 0.75 1.00

Deformation (mm)

Forc

e (k

N)

For

ce (

kip)

Deformation (in)

(a) Undeformed Soil Spring

(b) Deformed Soil Spring

Experimental Observations In order to isolate the effect of abutment pounding the results from CB5 were compared to those of CB1. During the experiments it was observed that there was a reduction in column cracking in CB5. Also, shear key failure was delayed from 75%DE in CB1 to 100%DE in CB5. This would indicate abutment pounding has a beneficial effect on the performance of the bridge. However, upon further review of the experimental data it was observed that the shake table input motion during CB1 had overshot the target motion rather significantly, particularly at the north abutment which was the location of the first shear key failure. Due to better tuning of the shake tables throughout the duration of experimentation, the input motions to CB5 were much closer to the target motion. As a result, the PGA applied to CB5 was only 73% of the PGA applied to CB1. In addition, the spectral acceleration of the CB5 motions were consistently 10%-15% lower than those of the CB1 motions over the fundamental period range of the bridge. Thus, the preliminary conclusion that abutment pounding reduces the level damage to the bridge contains some level of uncertainty due to the variation in shake table input motion. To address this uncertainty, a strong emphasis was placed on developing analytical models which could simulate the response of each experimental configuration.

Analytical Simulation A full finite element model was developed using OpenSees [8] to simulate each of the experimental configurations. The superstructure was modeled with elastic shell elements representing the reinforced concrete deck and steel girders. The elastic modulus of the concrete deck was reduced to 10% of Ec to account for cracking incurred during the erection process. The cross frames were modeled explicitly with elastic frame elements. The abutment towers were included in the model with elastic frame elements. The additional masses mounted on the bridge deck and bent caps were simulated with nodal masses. Nonlinearity was introduced in the column elements, slider bearing elements, soil springs, and impact elements. In addition, to material nonlinearity geometric nonlinearity was accounted for with p-delta geometric transformations of the column elements. The columns were modeled with nonlinear elements employing a two-point Gauss-Radau integration scheme to the hinge regions of the column. The interior region of the column was assumed to behave elastically. The elastic region of the column was assigned the cracked section properties by reducing the effective EI based on the first yield point determined in a moment-curvature analysis. The nonlinear sections were discretized with 16 fibers representing the unconfined cover concrete, 81 fibers representing the confined core concrete, and 16 fibers representing the longitudinal steel reinforcement. The concrete constitutive models were based on Mander’s confinement model [9] while the steel reinforcement was modeled with a parabolic strain hardening model. The material models were calibrated from properties determined by material sample testing. An example of the experimental moment-curvature verses the analytical model moment curvature during the 75%DE run of CB1 is shown in Fig. 6a. Note that the analytical model slightly under estimates the strength of the section which is also reflected in the overall shear strength of the column depicted in Fig. 6b. The slider bearings were modeled with an element that allows uplift and incorporates a velocity dependent friction model. The friction model was calibrated from experimental data. The same friction model was assigned to all six slider bearings. The shear keys were modeled

with a series of springs. A gap was included to emulate any small slop in the shear keys due construction tolerances. This gap was in series with a strength degrading hysteretic model that was capped with an ultimate strain. This complex model was needed to simulate the timing of the shear key failure observed in the experiment. The comparison of the shear key forces during the 75% DE run of CB1 is illustrated in Fig. 7.

Figure 6. Analytical comparison of CB1 column response to 75% DE.

The displacement of the mid-span of the deck is compared in Fig. 8. The analytical model does a good job of simulating the results of the CB1 experiment. With the confidence obtained in modeling the CB1 experiment the model was adapted to incorporate the abutment pounding present in CB5. The soil springs were modeled with a Giuffre-Menegotto-Pinto model. The soil springs were used to support elastic backwall shell elements. The Kelvin impact approach [10] was used to model the pounding of the end of the superstructure with the backwall. This approach employs a linear spring in parallel with a linear damper which is in series with a gap element. A total of 18 impact element assemblies were included at each abutment matching every node at the end of the bridge with a corresponding node on the backwall. The resulting soil spring response is compared for the 75% DE Sylmar motion in Fig. 9.

Figure 7. Analytical comparison of CB1 shear key response to 75% DE.

-0.02 -0.01 0.00 0.01 0.02

-565

-283

0

282

565

-5000

-2500

0

2500

5000

-4.00 -2.00 0.00 2.00 4.00

Curvature (rad/m)

Mom

ent

(kN

-m)

Mom

ent

(kip

-in)

Curvature (10-4 rad/in)

Experiment

Analysis

a)-50.8 -25.4 0.0 25.4 50.8

-177.8

-88.9

0.0

88.9

177.8

-40.0

-20.0

0.0

20.0

40.0

-2.0 -1.0 0.0 1.0 2.0

Displacement (mm)

Shea

r (k

N)

Shea

r (k

ip)

Displacement (in)

Experiment

Analysis

b)

-111.2

-55.6

0.0

55.6

111.2

-25.0

-12.5

0.0

12.5

25.0

6.0 7.0 8.0 9.0 10.0

Shea

r (k

N)

Shea

r (k

ip)

Time (sec)

South Abutment

-111.2

-55.6

0.0

55.6

111.2

-25.0

-12.5

0.0

12.5

25.0

6.0 7.0 8.0 9.0 10.0

Shea

r (k

N)

Shea

r (k

ip)

Time (sec)

North Abutment

ExperimentAnalysis

Figure 8. Analytical comparison of CB1 deck displacement response to 75% DE.

Figure 9. Analytical comparison of CB5 soil spring response to 75% DE.

Conclusion

An experimental investigation into the effect of abutment pounding on the overall seismic performance of a curved highway bridge was presented. A 2/5th scale curved bridge model was tested on shake tables at the University of Nevada, Reno under two configurations isolating the influence of abutment pounding. Though preliminary conclusions indicated a beneficial effect, uncertainty due to variation in the achieved experimental input motions requires further inspection through numerical modeling. Finite element models emulating the experimental configurations were shown to simulate the experimental results with a good level of accuracy. Validation of the numerical models has provided the authors with confidence in performing a variety of analytical parameter studies in the upcoming future. The objective of future parameter studies is to establish a definitive conclusion on the influence of abutment pounding and develop a set of design recommendations for bridge engineers.

-76.2-50.8-25.40.025.450.876.2

-3.0-2.0-1.00.01.02.03.0

4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0

Dis

plac

emen

t (m

m)

Dis

plac

emen

t (i

n)

Time (sec)

Experiment Analysis

0.00 6.35 12.70

0

45

89

134

178

0

10

20

30

40

0.00 0.25 0.50

Displacement (mm)So

il F

orce

(kN

)

Soil

For

ce (

kip)

Displacement (in)

0

45

89

134

178

0

10

20

30

40

6.0 7.0 8.0 9.0 10.0

Soil

For

ce (

kN)

Soil

For

ce (

kip)

Time (sec)

North Abutment

Experiment

Analysis

0.00 6.35 12.70

0

45

89

134

178

0

10

20

30

40

0.00 0.25 0.50

Displacement (mm)

Soil

For

ce (

kN)

Soil

For

ce (

kip)

Displacement (in)

0

45

89

134

178

0

10

20

30

40

6.0 7.0 8.0 9.0 10.0

Soil

For

ce (

kN)

Soil

For

ce (

kip)

Time (sec)

South Abutment

Experiment

Analysis

Acknowledgements This project is funded by the Federal Highway Administration under contract number DTFH61-07-C-00031: Improving the Seismic Resilience of the Federal Aid Highway System. The FHWA Contracting Officer’s Technical Representative is Dr Wen-huei (Phillip) Yen. In addition, the authors would like to thank the UNR Large Scale Structures Laboratory manager, Dr. Patrick Laplace, and staff for their valuable input into the design of the backwall systems. The team also appreciates for the hard work of the steel fabricators at Yajima USA and Reno Iron Works and the bearing and shear key manufacturers at Dynamic Isolation Systems. In addition to the authors, the project team at UNR consists of co-investigators include Drs Ahmad Itani, Gokhan Pekcan, and David Sanders. The project manager is Kelly Doyle. A number of graduate students are working on this project including Nathan Harrison, Ebrahim Hormozaki, Michael Levi, Ahmad Saad, and Chunli Wei, also Moustafa Al-Ani (Visiting Researcher) and Arash E. Zaghi (former post-doc researcher). The authors also acknowledge the National Science Foundation for the use of NEES Shake Table Array at the University of Nevada, Reno under a Shared-Use Agreement with NEEScomm at Purdue University. Joseph Wieser was supported by the National Science Foundation GK-12 Program, Grant DGE No. 1045584 during the completion of this paper. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.

References

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2. Jenning, P.C. 1971, “Engineering Features of the San Fernando Earthquake.” Report No. EERL 71-02, Caltech, Pasadena, CA.

3. Priestley, M.J.N., Seible, F., and Uang, C.M. (1994). The Northridge Earthquake of January 17, 1994: Damage and Analysis of Selected Freeway Bridges, Structural Systems Research Project Report No. SSRP 94/06, University of California, San Diego, CA.

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5. Caltrans. (2010). Caltrans Seismic Design Criteria, Version 1.6, California Department of Transportation (Caltrans), Sacramento, CA.

6. Maroney, B.H., 1995, Large Scale Abutment Tests to Determine Stiffness and Ultimate Strength Under Seismic Loading, Ph.D. Dissertation, University of California, Davis.

7. AASHTO. (2012). Guide Specifications for LRFD Seismic Bridge Design, American Association of State Highway and Transportation Officials, Washington, D.C.

8. McKenna, F., Fenves, G. L., & Scott, M. H. (2000). Open system for earthquake engineering simulation. University of California, Berkeley, CA.

9. Mander, J. B., Priestley, M. J., & Park, R. (1988). Theoretical stress-strain model for confined concrete. Journal of structural engineering, 114(8), 1804-1826.

10. Muthukumar, S., and Desroches, R. (2004). Evaluation of impact models for seismic pounding. In Proceedings of the 13th World Conference on Earthquake Engineering, Vancouver, Canada.