NONLINEAR SEISMIC ANALYSIS OF A BRIDGE GROUND SYSTEM

Joel P. Conte1, Member ASCE Ahmed Elgamal1, Member ASCE Zhaohui Yang1, Member ASCE

Yuyi Zhang1 Gabriel Acero1

Frieder Seible1, Member ASCE

ABSTRACT

This paper presents a two-dimensional yet advanced nonlinear finite element model of a real bridge system, the Humboldt Bay Middle Channel Bridge near Eureka in Northern California, and its response to a seismic input motion. The computational model of the Middle Channel Bridge is developed using the new software framework OpenSees developed by the Pacific Earthquake Engineering Research (PEER) Center to combine advanced structural and geotechnical seismic response simulation capabilities. The model incorporates soil-pile-structure interaction. Realistic nonlinear material models are used for the concrete (confined and unconfined), reinforcing steel, and soil materials under cyclic/dynamic loading. The materials in the various layers of the supporting soil medium are modeled using an effective-stress, multi-surface plasticity model incorporating liquefaction effects. A seismic response analysis is presented, with soil properties weaker than the actual ones, in order to test the robustness of the numerical framework, and explore potential effects of liquefaction on the various components of the bridge system. The simulated response shows that liquefaction-induced lateral spreading may have severe implications on the seismic demand imposed on the bridge structure (piers, piles, approach slab).

Keywords: Bridge, earthquake response analysis, soil-pile-structure interaction, nonlinear finite element analysis, soil plasticity, soil liquefaction

INTRODUCTION The Pacific Earthquake Engineering Research (PEER) center is developing probabilistic

seismic performance assessment methodologies (Cornell and Krawinkler, 2000). The Humboldt Bay Middle Channel Bridge, near Eureka in northern California, was selected as one of the testbeds, and all reported modeling efforts are motivated by its structural configuration, site characteristics, and seismicity. This bridge (Fig. 1) is a 330 meters long, 9-span composite structure with precast and prestressed concrete I-girders and cast-in-place concrete slabs to provide continuity. It is supported on eight pile groups, each of which consists of 5 to 16 prestressed concrete piles, in soils potentially vulnerable to liquefaction (under extreme earthquake shaking conditions). The river channel has an average slope from the banks to the center of about 7% (4 degrees). The foundation soil is composed of mainly dense fine-to-medium

1 Department of Structural Engineering, University of California at San Diego, La Jolla, CA92093. E-mails:

jpconte@ucsd.edu, elgamal@ucsd.edu, zhyang@ucsd.edu, y8zhang@ucsd.edu, gacero@ucsd.edu, seible@ucsd.edu.

2

sand (SP/SM), organic silt (OL), stiff clay layers (Fig. 2). In addition, thin layers of loose and soft clay (OL/SM) are located near the ground surface (see Fig. 2). The bridge was designed in 1968 and built in 1971 and has been the object of two Caltrans (California Department of Transportation) seismic retrofit efforts, the first one designed in 1985 and completed in 1987, and the second designed in 2001 to be completed in 2002. The probabilistic seismic performance assessment methodology under development at the University of California at San Diego (USCD) is based on advanced mechanics-based computational modeling and probabilistic analysis. The objectives of this paper are twofold: (1) describe the two-dimensional yet advanced nonlinear computational model of the soil-pile-structure system developed for the Humboldt Bay Middle Channel Bridge, and (2) present preliminary results of seismic response simulation performed using the model. The computational model was developed using the new software framework OpenSees (McKenna and Fenves, 2001) developed under the auspice of the Pacific Earthquake Engineering Research (PEER) center to combine advanced structural and geotechnical seismic response simulation capabilities.

FIG. 1. Humboldt Bay Middle Channel Bridge (Courtesy of Caltrans)

FINITE ELEMENT MODELING A two-dimensional nonlinear model of the Middle Channel Bridge, including the

superstructure, piers, and supporting piles was developed using OpenSees as shown in Fig. 2. The bridge piers are modeled using 2-D nonlinear material, fiber beam-column elements (with five Gauss-Lobato points) formulated using the flexibility approach based on the exact interpolation of the internal forces (Spacone et al. 1996). The discretization of the column cross-section into concrete and steel fibers is shown in Fig. 3(c). The concrete material is separated into confined (inside shear reinforcement/stirrups) and unconfined concrete (outside stirrups). The uniaxial Kent-Scott-Park model with degraded linear unloading/reloading stiffness shown in Fig. 3(a) is used to model the concrete fibers, while the uniaxial bilinear model (or uniaxial J2 plasticity

FIG. 2. OpenSees finite element model of structure-pile-soil system (based on blue prints courtesy of Caltrans, mesh constructed using GID software)

Eureka Channel (South-East)

Samoa Channel (North-West)

C1 C2 C3 C4 C5 C6 C7 C8

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model with linear kinematic hardening) shown in Fig. 3(a) is used to model the reinforcing steel. The unconfined concrete is characterized by a smaller compressive strength, smaller crushing strength and smaller ductility as compared to the confined concrete. Each pile group supporting each pier is modeled by an equivalent single pile currently kept linear elastic (see Fig. 2). Similarly, the superstructure is idealized using equivalent linear elastic beam-column elements. The interior expansion joints (in third span near column C3 and in sixth span near column C6) and the abutment joints are modeled using zero-length elasto-plastic gap-hook elements as shown in Fig. 4. The kinematic constraints due to the abutment walls are modeled using rigid diaphragm constraints.

FIG. 3. Uni-axial stress-strain law for (a) concrete (Kent-Scott-Park model), and (b) reinforcing steel (bilinear inelastic model with kinematic hardening), and (c) fiber

discretization of column cross-section

FIG. 4. Abutment joint: zero-length element with elasto-plastic gap-hook material

The materials in the various layers of the supporting soil medium are modeled using an effective-stress constitutive model incorporating liquefaction effects. This model is based on the original multi-surface plasticity concept (Prevost, 1985), in which a set of Drucker-Prager yield surfaces with a common apex and different sizes form the hardening zone as shown in Fig. 5(a). The outmost surface is the shear strength (or failure) envelope. A purely deviatoric nonlinear kinematic hardening rule (Prevost, 1985; Elgamal et al., 2001) is employed. A non-associative flow rule is used in order to describe the soil contractive/dilative (dilatancy) behavior under shear loading (Elgamal et al., 2001), with the non-associativity restricted to the volumetric component of the plastic flow (Prevost, 1985). This model attempts to capture the following salient features of soil response (see Fig. 5(b)): (1) dependence of soil stiffness and shear strength upon effective pressure, (2) dependence of pore water pressure on shear loading, and (3) reproduction of large cyclic-mobility shear strain accumulation mechanisms. The latter is directly related to assessment

(a) (b) (c)

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of lateral spreading in liquefied sands, which is one of the most important damage measures for liquefiable soil sites (Elgamal et al., 2001). This soil constitutive model framework may be adapted for representing cohesionless soils (e.g., sand) under general loading conditions as well as cohesive soil materials (e.g., clays under fast loading conditions such as earthquake excitations). In order to simulate undrained response in saturated soils, the above effective-stress soil model is embedded within a pore water linear elastic material model with high bulk modulus (i.e., nearly incompressible). This approach is often referred to as partial solid-fluid coupling in the geomechanics literature.

FIG. 5. Yield surfaces and undrained performance of the sand model

The above soil model has been extensively validated and calibrated for both drained (or dry) and undrained conditions through numerous sources including laboratory tests (Arulmoli et al., 1992; Kammerer et al., 2000), centrifuge experiments (Dobry and Taboada, 1995), and downhole-array seismic records (Elgamal et al., 2001). The soil domain is analyzed under the assumption of plane strain condition. It is spatially discretized using four-noded, bilinear, isoparametric finite elements with four integration points. The above-described soil constitutive model was embedded in this plane strain finite element and implemented in OpenSees. The thickness of the soil domain (out of plane) is taken as 6.10 m corresponding to the width of the pile groups supporting the bridge piers, while a thickness of 10.4 m (separation distance between wing walls) is used for the embankment/abutment sub-domain. These thickness assumptions are preliminary and are the subject of current research. Soils below the water table are modeled as undrained materials, and soils above as dry materials. Different sets of material constitutive parameters are used for the various soil types in the supporting soil medium. The elasto-plastic liquefiable soil domain is linked directly to the piles enforcing compatibility of the horizontal and vertical degrees of freedom between the pile nodes and corresponding soil nodes (simplifying assumption, with no relative motion allowed between soil and piles). The lateral boundary and base conditions for the soil medium are handled as follows. A semi-infinite soil profile to vertically propagating shear waves (e.g., earthquake-like motions) usually behaves and is approximated as a shear beam. Therefore, the lateral boundaries (vertical sides) of the soil medium are constrained to deform similarly in the lateral direction. This is achieved by imposing equal horizontal degree of freedom constraints to pairs of lateral nodes. The input motion of

(a) (b)

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seismic acceleration is applied to all nodes at the base of the soil domain. Thus, the base of the soil medium is assumed to move rigidly, neglecting spatial variability (due to wave passage and incoherence effects) of the input motion. More realistic techniques for imparting seismic motion are being considered currently.

RESPONSE SIMULATION RESULTS As a preliminary test-run, a near-field strong motion record, the 1994 Northridge earthquake recorded at the Rinaldi station (first comp. - 228 degrees horiz., PGA = 0.89g, PGV = 1.85 m/sec, PGD = 0.60 m), is applied to the base of the soil-pile-structure model shown in Fig. 2. In this preliminary simulation, loose soil properties are employed (instead of the actual denser ones), in order to test the bridge-soil computational model under extreme loading conditions and potential soil liquefaction scenarios. The abutment foundation piles are not included either. Figure 6 shows the deformed mesh (exaggerated scale) at the end of the earthquake. A main characteristic in this figure is that the abutments and river banks moved (flowed) towards the center of the river channel (as indicated by the arrows in Fig. 6) due to a lateral spreading mechanism associated with reduction in soil strength. The latter results from an increase in pore-pressures within the cohesionless soils. Due to this permanent soil deformation mechanism, the approach slabs settle by up to 34 cm (point C in Fig. 6). Notice the deformed configuration of the ground surface along the river channel with the kinks at the foot of the bridge piers. This is due to the fact that in a two-dimensional model, the foundation piles act as barriers to the flow of surrounding liquefied soil (compared to the more realistic partial flow of soil in 3-D). Improvements of the 2-D model presented here are underway in order to remove this artifact. More specifically, special 1-D elements (nonlinear or P-Y springs) are being added as interface between the nonlinear soil medium and the piles, allowing the flow of liquefied soil around the piles in a 2-D model as well as gapping effects between the soil and the piles near the ground surface (Boulanger et al. 1999).

FIG. 6. Permanent deformation of bridge-foundation-soil system at the end of the earthquake (exaggerated scale)

The horizontal displacement response histories of the top and bottom of the bridge piers relative to the base of the soil foundation are plotted in Fig. 7(a) and (b), respectively. It is observed that the pier tops have almost the same motion due to the high axial stiffness of the bridge superstructure. However, the pier bottoms undergo significantly different motions depending on their distance to the center of the river channel. Due to the tendency for lateral spreading of portion of the foundation soil along the piles, the bottom of each pier moves permanently towards the center of the channel in a combination of quasi-static and dynamic response components. The moment-curvature responses at the bottom section of the first and eighth columns are shown in Figs. 7 (c) and (d), respectively. Consistent with the lateral spreading response of the foundation soil, the bottoms of columns 1 and 8 undergo uni-directional (i.e., without any yield reversal) inelastic flexural response with opposite curvatures and very large peak flexural ductility (= ratio of maximum absolute curvature to effective yield curvature) of ~14 and ~18, respectively. The red dots in Figs. 7 (c) and (d) indicate the residual state of the bottom section of columns 1 and 8 at the end of the earthquake, and therefore very large residual flexural ductilities. Figs. 8 (a) and (c) show a sample of the excess pore pressure ratio history during the earthquake at material points A and B (see Fig. 6) in the soil medium. The excess pore pressure ratio is

C

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defined here as the ratio of the excess pore pressure (above the hydrostatic pore pressure) to the mean initial effective soil pressure. It is seen that the excess pore pressure undergoes a sharp and significant build-up between 2 and 4 sec due to the large pulse of the near-field Rinaldi record occurring within this time segment. The soil liquefies at Point A 8 sec into the earthquake, while the soil never liquefies at point B. The soil shear stress - strain response at point A shown in Fig. 8(b) shows a large stress excursion due to the large pulse of the input seismic record. Subsequently, a dramatic strength deterioration and stiffness degradation occurs at point A due to soil liquefaction. The shear stress - strain response at point B given in Fig. 8(d) shows also a large yield excursion due to the input pulse, followed by a second large yield excursion later on. Notice that the soil material at point B exhibits much smaller losses of strength and stiffness than at point A.

FIG. 7. Seismic response of bridge columns (to elucidate consequence of a liquefaction scenario)

A color map of the deviatoric stress ratio, an index of the shear stress intensity relative to the soil shear strength for a given confinement (mean effective pressure), is plotted in Fig. 9. Soil having reached its shear strength for a given confining pressure is represented in dark red. This spatial distribution of the shear stress response is given at the instant of peak input seismic acceleration, which corresponds to the apex of the large seismic input pulse. Clearly, at this instant, large portions of the foundation soil is experiencing intense shearing. A color map of the excess pore pressure in the soil medium at the same instant is displayed in Fig. 10. Liquefied soil appears in dark red color. It is observed that at this instant of time, liquefaction appears mainly under the bridge abutments and within a thin surface layer along the river channel.

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FIG. 8. Seismic response of foundation soil

FIG. 9. Deviatoric stress ratio at instant of peak input acceleration

FIG. 10. Excess pore pressure ratio at instant of peak input acceleration

CONCLUSIONS This paper presents a seismic computational modeling and response analysis effort motivated by an existing bridge-ground system, the Middle Channel Bridge at Humboldt Bay near Eureka in Northern California. The model of the soil-pile-structure system is two-dimensional yet advanced incorporating realistic nonlinear material models for the concrete, reinforcing steel, and soil materials. The soil constitutive model incorporates liquefaction effects. In a preliminary seismic response simulation, loose soil properties were employed (instead of the actual denser ones), in order to test the bridge-soil model under extreme loading conditions and potential soil liquefaction scenarios. This seismic response simulation predicts a lateral spreading mechanism induced by soil liquefaction. This response mechanism has important implications in terms of seismic demand to and permanent/residual deformation of the bridge system (piers, approach

Point A

Point A

Point B

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slabs, foundation piles). It is important to emphasize that the predicted seismic response is related to the assumed properties of the foundation soil, which are not representative of the actual soils at the Humboldt site. Further improvement of the model presented here are underway, especially in order to model the flow of liquefied soil around foundation piles in a 2-D model. The presented pilot effort is part of the PEER Center ongoing development of a probabilistic seismic performance assessment methodology for highway bridges. This methodology integrates probabilistic seismic hazard analysis, advanced computational modeling of the bridge ground system, probabilistic seismic demand analysis, and probabilistic damage analysis or fragility analysis (Cornell and Krawinkler, 2000).

ACKNOWLEDGMENTS Support of this work was provided primarily by the Earthquake Engineering Research Centers

Program of the National Science Foundation, under Award Number EEC-9701568 through the Pacific Earthquake Engineering Research Center (PEER). This support is gratefully acknowledged. The authors wish to thank Mr. Patrick Hipley, Mr. Cliff Roblee, Mr. Charles Sikorsky, and Mr. Mark Yashinsky of Caltrans for providing all the requested information regarding the initial design and retrofits of the Middle Channel Bridge. Prof. Greg Fenves, Dr. Frank McKenna, Mr. Michael Scott (U.C. Berkeley) and Prof. Boris Jeremic (U.C. Davis) helped with the OpenSees modeling and analysis framework. Prof. Pedro Arduino (Univ. of Washington, Seattle) suggested and helped with the use of GID (http://gid.cimne.upc.es/), a commercial pre- and post-processing system for geometric modeling and visualization. Their help is gratefully acknowledged.

REFERENCES Arulmoli, K. et al. (1992), "VELACS: Verification of Liquefaction Analyses by Centrifuge

Studies, Laboratory Testing Program, Soil Data Report," Report, The Earth Technology Corporation, Project No. 90-0562, Irvine, CA.

Boulanger, R. W. et al. (1999), "Seismic Soil-Pile-Structure Interaction Experiments and Analyses," Journal of Geotechnical and Geoenvironmental Engrg., ASCE, 125(9), 750-759.

Cornell, C. A. and H. Krawinkler (2000), "Progress and Challenges in Seismic Performance Assessment," PEER Center News, 3(2), Spring 2000.

Dobry, R., V. Taboada, and L. Liu (1995), "Centrifuge Modeling of Liquefaction Effects During Earthquakes," Keynote Lecture, Proc. 1st Intl. Conf. On Earthquake Geotechnical Engineering (IS-Tokyo), Ishihara, K. (Ed.), Balkema, Netherlands, 3, 1291-1324.

Elgamal, A., Lai, T., Yang, Z., and He, L. (2001), "Dynamic Soil Properties, Seismic Downhole Arrays and Applications in Practice," (CD-ROM), State-of-the-art paper, Proc. 4th Intl. Conf. on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, San Diego, CA, March 26-31, 2001, S. Prakash, (Ed.).

Kammerer, A. et al. (2000), "Cyclic Simple Shear Testing of Nevada Sand for PEER Center Project 2051999," Research Report No. UCB/GT/00-02, Univ. of California at Berkeley, CA.

McKenna, F. and G. L. Fenves (2001), "The OpenSees Command Language Manual, Version 1.2," Pacific Earthquake Engineering Research Center, University of California at Berkeley. (http://opensees.berkeley.edu/ )

Prevost, J.H. (1985), "A Simple Plasticity Theory for Frictional Cohesionless Soils," Soil Dynamics and Earthquake Engineering, 4(1), 9-17.

Spacone, E., F. C. Filippou, and F. F. Taucer (1996), " Fibre Beam-Column Model for Non-Linear Analysis of R/C Frames: Part I. Formulation," Earthquake Engineering and Structural Dynamics, 25 (7), 711-725.