BRIDGE ABUTMENT INTERACTION UNDER ...

In Proceedings of 2nd International Conference on Structural Condition Assessment, Monitoring and Improvement Changsha, China, 19-21 November 2007

BRIDGE ABUTMENT INTERACTION UNDER SEISMIC LOADING André R. Barbosa, Manuel A. G. Silva Civil Engineering Department Univ. Nova de Lisboa, 2829-516 Caparica, Portugal Abstract: Abutments may undergo significant damage of difficult repair due to earthquakes.

Simultaneous consideration of all intervening factors is difficult to achieve at present and simplified models that integrate most representative features are required. The study illustrates a simplified methodology for considering non-linear aspects and interaction abutmentsuperstructure for a bridge actually built and examines the influence of some parameters on the response. 1. Seismic damages in abutments Damages on bridges and abutments due to earthquakes have shown the need to consider the abutment–embankment participation on the response, unlike previous practice. Abutments may undergo significant damage of difficult repair due to earthquakes especially when the bridges have integral type abutments; however, seat type abutments may also experience damage once the gap between superstructure and abutments backwall closes during an earthquake. This mode of failure may result in unacceptable post event repair cost and lifelines downtime, and should be avoided. For seat abutments, this may be accomplished by providing gaps that are wide enough or by inserting fluid dampers or locking devices to limit the relative motion of bridge sections under transient motion. However, as shown in the next series of figures, extensive, serious damages in both integral and seat type abutments have been reported. Fig. 1-a) shows the failure of an abutment of Mouken Bridge due to the Chichi earthquake (Taiwan, September.1999) and b) the damages caused to one of the abutments at the Moss Landing bridge due to liquefaction (Loma Prieta, October.1989). Fig. 2-a) shows a failed support bent at one abutment of a bridge in Highway 8A East of Bhachau (Bhuj, India, January. 2001), and Fig 2-b diagonal cracking at bridge on road Moquegua-Tacna (Atico, Peru, June.2001). The result of longitudinal impact between deck and abutment is shown in Fig. 3-a) while b) illustrates wall cracking caused by the transversal motion of the backfill soil of an abutment in a Californian bridge (Northridge, January.1994). These and similar failures motivated a large experimental program at The Network for Earthquake Engineering Simulation (NEES) where the behavior of 4-span bridges including abutments and foundations was examined. The studies comprised static and dynamic tests that were

performed on the shaking table at the Englekirk Center of UCSD, Fig.4 (http://nees.unr.edu/4spanbridges/).

Fig. 1- a) Mouken Bridge(Taiwan, September.1999); b) Moss Landing. U.S.G.S. (Loma Prieta, October.1989) The dynamic response of bridges may be affected by the interaction with foundation, abutments and embankments. Werner et al. (1987, 1990), Wilson and Tan (1990a,b). Goel (1997), and, Goel and Chopra (1997) showed that the response was, indeed, influenced by the abutments, soil nonlinearities and SSI. The influence of SSI was also addressed by Zhang and Makris (2002) and Price (1997) who studied the peak spectral values for the abutments and the transversal frequency of


bridges. Short bridges without expansion joints showed that the stiffness and mass of the embankments substantially reduced the influence of the columns on the overall response at high shaking intensities, Inel and Aschheim (2004).

with elastomeric bearings and fluid dampers. They considered SSI at the end abutments and found that neglecting SSI (i)the response of the isolated structure was underestimated; and (ii) in general, both transverse and longitudinal forces at the backwall were underestimated, by as much as 100% for some of the quakes considered.

Fig. 3- a)Impact deck -abutment; b)Abutment cracking (Northridge, California, 1994)

Fig. 2 - a) Bhachau (Bhuj, India, 2001) b)Moquegua-Tacna (Atico, Peru, 2001) Soil-abutment interaction owes its nonlinearities, mostly, to large deflections in the backfill, at the abutments. Incorporation of abutment stiffness leads to a more reliable estimate of the distribution of seismic loads among bents and abutments and to better estimates of displacements, Karantzikis and Spyrakos (2000). Based on parametric studies, the authors concluded that, if the bridge analyzed considering backfill stiffness reduction, the forces and moments at the piers are greater by 25%-60% and the displacements by 25%-75%, depending on soil properties. Price and Eberhard (2004) computationally modeled three bridges and compared the results with available records of actual response. They concluded that the influence of nonlinear soil behavior appeared even for moderate shaking and interaction between structure and the embankment decreased the abutment response. Makris et al. (2004) analyzed a bridge

Fig. 4: Cross-section and photo soil container placed on the shaking table at UCSD Simplified methods that rely on a model where the inertial part of SSI is given more attention than the kinematic, due to the relatively higher stiffness of the superstructure, may underestimate the SSI. Some of the reported studies represent soil, piles, abutments and embankments in detail, or consider very refined modeling that requires lengthy and expensive computations. The kinematic response of embankments may have a substantial effect on


the response of bridges, Zhang et al. (2004). Adequate approximations need further study and this note shows such an approach.

2. Computational Model The bridge used for the study is located at Coja, Portugal, crosses River Alva, and has 115.0m between abutments, span divided in two hanging lateral segments of 35m and a central span of 45m, Fig.5. The bridge piers are rigidly connected to the post-tensioned deck. At both ends the bridge is simply supported at counterforted abutments. The gap between the superstructure and abutments is 15cm. The backwall is 1.75m high. Measuring from the top, for the first 0.95m it is 0.35m wide while for the remaining backwall height it is 0.60m wide.

based on Caltrans’s design provisions and borrows procedures from Siddharthan (1994). Caltrans method is based on experimental work by Maroney (1995) and assumes that the backwall fails before complete mobilization of soil-abutment. Only the soil behind the wall is considered as effective with an initial stiffness, Ki, 11.5 kN/mm/m. The stiffness of the abutment is:

k abut = k i w

h 1 .7

(1)

where w = distance between wing walls, and h= abutment height without footing thickness. Elastoplastic behaviour is assumed, with maximum capacity given by

 h  Pabut = 239 Ae    1.7 

(S.I. units)

(2)

where Ae is a cross-section. Longitudinal (SL), vertical (SV) and transversal (ST) stiffness coefficients are taken from Siddharthan et al.(1997), assuming that the spring forces act when the deck pushes against the embankment. Under static conditions, the secant stiffness Si for directions i = L,V, T is

x  Si = Di Ei  i  H γBW 2 ET = H2

Fig. 5 – Bridge, over Rio Alva (Profico, Lda.) Modeling the seismic actions was achieved by selecting seven records from the PEER earthquake record database (http://peer.berkeley.edu/nga/). They were made compatible with two elastic Eurocode 8 (EC8) code spectra and the Portuguese National Directive, for soil type A Both spectra correspond to the main sources of seismic activity in the Iberian Peninsula for a 475 year return period. The first is representative of near-fault earthquakes whose sources are mainly concentrated near the Lisbon area. The second corresponds to sources located in the Atlantic Ocean, around 200 km off the coast of Portugal. This is the region where the 1755 earthquake (magnitude 9.0) had its epicenter. The seven earthquake records were scaled, independently, to both spectra, resulting in a set of 14 ground motions used for analysis. Computational models were considered (e.g. Xu et al. (2003)). The study hereafter is primarily

−0.96

, E L = EV =

γB 3 H2

and

(3)

with Di as an adimensional function of geometry and Ei a normalization factor. For full description on how to determine Di refer to original work, Siddharthan et al.(1997). The computational model was implemented on OpenSees, an open source software framework that uses object-oriented methodologies. The foundations are modeled by equivalent linear springs. Materials (concrete and steel) are represented in agreement with their nonlinear properties. The confinement of concrete was taken into account both on the resistance and the ductility of reinforced concrete and Mander’s model was selected, Fig. 6, Mander (1988). A 3-D FEM model, with 38 bar elements and 121 DOF, Fig.7, represents the main structure and piers with equivalent springs for abutments and soil. Based on the geometry shown in Fig. 7, three different models were created. For Model 1, the reference model, the bridge is considered to be simply supported on both abutments. For the other two models, Model 2 and Model 3, the connection of the main structure to the abutment is done using


zero-length elements that have a uniaxial elasticperfectly-plastic gap behaviour.

3. Main Results In this section, the simulated responses of 210 finite element analyses are discussed (3models x 7 ground motions x 2 code earthquake spectra x 5 intensity levels). The nonlinear finite element model was first subjected to gravity loads before the modal frequencies and modal shapes, shown in Fig. 9, were computed. f 1 = 0.54 Hz

Fig. 6 - Model proposed by Mander (1988) Maxima responses were obtained using a Newton-Raphson algorithm and the Newmark integration scheme with parameters γ = 0.5 and β = 0.25. An integration time step of 0.005 seconds was used for all analyses.

f 2 = 14.07 Hz

f 3 = 30.11 Hz

Abutment

Abutment 0 0 . 7 2

CP Piers

Pier Base

Fig. 9 - First three longitudinal modal frequencies and mode shapes.

0 0 . 5 3

0 0 . 5 4

0 0 . 5 3

Fiber elements

Rigid Link

Fig. 7 - View of 3D computational model For the force-displacement relationship shown in Fig 8, the backfill stiffness is only active once when the deck displaces enough to close the gap provided by the zero-length elements. F gap

F Fy

K

K gap

∆ Fy

∆

Tension Gap

Compression Gap

Fig. 8 – Tension and compression elasto-perfectlyplastic gap elements The gaps for models 2 and 3 are 10cm and 15cm, respectively. Based on the design of the original bridge, it is assumed that the backwall fails prior to complete mobilization of soil passive resistance behind it, thus shearing off. The springs stiffness are, therefore, determined according to the Caltrans design code.

The set of 14 ground motions was applied to each model for 5 different seismic intensity levels. These intensity levels are obtained by amplifying the design earthquake spectra compatible ground motions (Intensity for Design, ID – 475 year return period), by 0.30, 1.50, 2.0 and 3.0. For example, the 0.3ID amplified ground motion corresponds to a 72 years return period. Fig.-10a) and Fig.-10b) show maximum displacement, velocity and accelerations for the set of selected ground motions and 5 different excitation levels, both for Models 1 and 3, respectively. Void and filled markers correspond to ground motions scaled to the code spectra 1 and 2. From Fig. 10 the main observations that can be made are: (i) the EC8 earthquake spectra with higher frequency content, spectra 1, produce higher values of maximum accelerations, and lower displacements; (ii) the maximum displacement for model 3 is smaller when compared to the results of model 1 and the reverse applies to the base shear forces.


exceeded are the markers and lines joining them distinct.

Model 1 4000

Gap - model 3

4000

0.25

0.2

0.15

0.1

0.05

Displacement [m]

4000

3000 2000 3.0 ID

1000

1.5 ID

0 0

2000

2.0 ID

0.15

0.1

0.05

Displacement [m] 0 0

0.6

0.5

0.4

0.3

0.2

0.1

Model 1 - EQ spect 1 Model 1 - EQ spect 2

0.7

Velocity [m/s] 4000

1.00 ID 0.30 ID 1.50 ID 2.00 ID 3.00 ID

2000 0 0

5

4

3

2

1

Acceleration [m/s2]

Model 3 4000 2000

Base Shear [kN]

0 0

0.1

0.05

0.2

0.15

0.25

Model 2 - EQ spect 1 Model 2 - EQ spect 2

0.2

Model 2 - EQ spect 2 Model 3 - EQ spect 1 Model 3 - EQ spect 2

Fig. 11 – Simulated responses for all 3 models in terms of mean maximum displacement response to 7 ground motions compatible with 2 earthquake spectra and amplified to 1.5ID, 2.0 ID and 3.0ID Fig. 12 presents (i)the mean maximum displacement for model 2, and (ii)the 16th and 84th percentile for the base shear and fixed mean displacements. It is apparent that the variability of the base shear for fixed mean displacement is greater when this displacement is near the gap dimension.

Displacement [m] 4000

1.00 ID 0.30 ID 1.50 ID 2.00 ID 3.00 ID 0.7 0.6

2000 0 0

0.2

0.1

0.3

0.4

0.5

Velocity [m/s]

4000

Base Shear [kN]

Base shear [kN]

0 0

Base Shear [kN]

2000

Gap - model 2

3000 2000

84th percentile µ

1000

16th percentile

4000 0 0

0.05

0 0

0.1

0.15

Displacement [m]

2000

1

2

3

4

5

Acceleration [m/s2]

Fig. 10 (a), {b} - Maximum response quantities for 5 ground motion intensities, for (Model 1) and {Model 3}. Void markers correspond to spectra 1 and filled markers to spectra 2. Fig. 11 illustrates the results from each of the models, for the mean maximum displacements, for ground motions scaled to both codified earthquake spectra. Only the responses for 1.5 ID, 2.0 ID and 3.0 ID levels are shown. The maximum displacements decrease for smaller gap, and this is accompanied by an increase in the base shear forces. The equivalent stiffness increases as the mean maximum is greater than the provided gap. Note that if a the displacement, for a specific ground intensity level, is less than the gap dimension, for all three models the results are exactly the same and the markers overlap each other and therefore once the gap dimension is

Fig. 12 – Mean displacement vs. base shear response and 16th and 84th percentile of the base shear for fixed mean displacements.

4. Conclusions The study summarized here illustrates a simplified methodology for considering non-linear aspects and interaction abutment-superstructure for a bridge actually built in Portugal and examines the influence of some parameters on the response. A total of 210 non linear finite element analyses was performed using earthquake ground motions made compatible to EC8 code earthquake spectra. The main conclusions of this work are: (i) the behavior of the bridge supported on seat type abutments is substantially altered if the gap joint closes; (ii) for this study, the EC8 earthquake spectra with higher frequency content, spectra 1, produce higher values of maximum accelerations, and lower displacements than the EC8 earthquake spectra 2;


(iii) for smaller gap dimensions, the maximum displacements decrease with an increase in the base shear forces. The equivalent stiffness increases as the mean maximum displacement is greater than the provided gap; (iv) the variability of the base shear for fixed mean displacement is greater when this displacement is near the gap dimension. The simplified methodologies described herein show shortcomings that justify further work in the future. The use of different abutment springs should account for the latest results of the on going NEES project. The importance of modeling the covibrating mass of soil of the backfill needs to be examined. The influence of soil-structure interaction was well established, but has to be verified for different types of soil and correlated stiffness. The influence of damping requires careful consideration. Integral abutments have to be studied in a manner that allows a more enlarged view de of the overall problem. The use of lock up devices and their correct modeling to establish the corresponding behavior of the abutments is another topic to be examined.

Acknowledgements The authors acknowledge the Portuguese Science and Technology Foundation for partially funding this work through the project POCTI/ECM/36019. References Goel, R.K. (1997). “Earthquake characteristics of bridges with integral abutments.” Journal of Structural Engineering, ASCE, 123(11), 1435-1443. Goel, R.K., and Chopra, A.K. (1997). “Evaluation of bridge abutment capacity and stiffness during earthquakes” Earthquake Spectra, 13(1), 1-21 Inel, Mehmet, Aschheim, M. A. (2004), "Seismic Design of Columns of Short Bridges Accounting for Embankment Flexibility", Journal of Structural Engineering, Vol. 130, No. 10, October 1, pp1515-152 Karantzikis, M.J. and Spyrakos, C. C., (2000), "Seismic Analysis of Bridges Including SoilAbutment Interaction", 12 WCEE, #2471 Mander, J. B., Priestley, J. N., and Park, R. (1988). “Theoretical stress-strain model for confined concrete.” J. Struct. Eng., 114(8), 1804– 1826.

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