The primary objective of the project is to apply evolving PEER performance-based earthquake engineering methodology to evaluate the seismic response of a section of the I-880 viaduct. A major component of the methodology involves the estimation of engineering demand parameters (EDP) for a given hazard level which is quantified by means of an intensity measure (IM). An accurate representation of EDPs for the I-880 testbed requires the development of adequate and reliable simulation models of the target system. The development of an appropriate computer model incorporating all critical elements of the system including soil-foundation interaction is one of the goals of this project. Another goal of the project is to investigate sensitivity of material and modeling parameters in estimating EDP|IM. A related objective of the project is to provide input to the development and validation of OpenSees.
Figure 1. Response Spectra of Some Typical Ground Motions Scaled to Match the Hazard Spectra at T = 0.4
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A series of OpenSees models, encompassing a range of detail and complexity, will be developed: from simple two-dimensional models of the piers and bent caps assuming fixed-base conditions to comprehensive three-dimensional models of the structure incorporating soil-foundation-structure interaction and frame-frame interaction. Preliminary studies will focus on selecting reasonable and reliable material and modeling parameters to enable both static (pushover) and transient analysis of the simulation models. Selected engineering demand parameters (EDPs) will be generated for the suite of ground motions provided for the I-880 site for different hazard levels. The EDPs will be utilized in a separate study to extract damage measures (DMs) for each hazard level.
Selection of intensity measures (IMs)
A preliminary IM that has been selected for the evaluation study is the damped elastic spectral acceleration at the natural period of the structure. Ground motions have been provided by Somerville and his research group for the I-880 bridge site corresponding to three hazard levels: events with a 50% probability of being exceeded in 50 years; events with a 10% probability of being exceeded in 50 years; and events with a 2% probability of being exceeded in 50 years. The components in the strike normal (SN) directions of each of these records were scaled so that the spectral acceleration at the natural period matches the corresponding value at the same period on the hazard spectra. The scale factor obtained for the SN direction is also used for the SP direction since it preserves the relative scaling between all components of the recording. The response spectra for a sample set of scaled records are displayed in Figure 1.
Development of simulation models
This task represents the development of accurate and comprehensive structural
models of the I-880 structure so that reliable estimates of critical
EDPs are facilitated.
Description of Structure
The selected section of the I-880 is a seven-frame structure consisting of 26 spans and a total length of approximately 1140 m. The site is located within 10 km of the Hayward Fault and is also in the vicinity of the San Andreas Fault. In addition, the soils on the site near the San Francisco Bay consist of dense fill, Bay mud and sand, covering deep clay deposits. The superstructure of the viaduct is composed of cast-in place reinforced concrete box girders. In general, the bents have two columns. However, some of the bents have three or four columns at the location of the off-ramp while some of the remaining bents have outriggers. The 55 columns for the viaduct are rectangular with circular reinforcement. While a majority of the columns have continuous moment connections at the column-deck and column-pile-cap region, some bents have pinned connections at either the column-pile-cap or column-deck location. Transverse reinforcement consists of #8 (2.5 cm diameter) hoops at 10 cm center-to-center spacing for all columns. Longitudinal reinforcement consists of varying numbers of #14 (4.5 cm) bars arranged in 5 different configurations.
Simulation Models
All simulation tasks are carried out using the PEER OpenSees computational platform.
A key element in the development of the simulation models is the validation
of material and element models. Variables such as model type (material and
element), cross-section discretization, number of elements, number of integration
points, etc. have been investigated to arrive at generally stable simulation
models for use in detailed response history analyses. An eigenvalue analysis
of each model is carried out to establish the fundamental dynamic properties
of the system. The computed eigen-frequencies were needed to establish the
scaling factors for the ground motions to be used in the time-history evaluations.
Several simulation models have been created. A typical frame in the system was first identified. A schematic of the selected frame which consists of Bents 14 – 17 is shown in Figure 2. The bents are connected by means of an elastic beam. Since the deck is composed of prestressed box-girders, linear elastic behavior is assumed. The simplest model that can be evaluated is that of a half-height column (Model Type I). The next level of detail considers a typical bent (Model Type II). Model Type III represents the entire frame composed of four bents. The ends of the beams in Model Type III are constrained by elastic springs which have assigned properties to represent the adjacent frames. The spring properties are derived through separate static analysis of the adjacent bents.
Another important feature of each of the model types shown in Figure 2 is the simulation of the soil-foundation system. Using linear elastic material properties for both soil and concrete piles, a three-dimensional model of the soil-foundation system was developed using 8-node brick elements for the soil and 3D beam elements for the piles. The stiffness of the soil-foundation system was then established by displacing and rotating the system in each co-ordinate direction.
The most detailed model (Model Type IV) of the bridge that is currently available takes into account the interaction between frames. Inelastic springs are utilized to represent the behavior of the following connection elements (as displayed in Figure 3): shear keys, vertical and longitudinal restrainers and bearing plate. Properties of the springs were estimated from material and cross-section data provided in the as-built drawings of the structure. In all cases, CALTRANS guidelines were used in estimating material parameters.
Selection of engineering demand parameters (EDPs)
Presently, the following EDPs are being considered: drift (tangential displacement at inflection point); ductility (ratio of peak drift to yield drift); and peak compressive strain in the extreme fiber of the column cross-section. The following EDPs will also be monitored in the likelihood that additional DMs will be considered in subsequent evaluation studies: relative rotation at frame-to-frame joints; displacement and Rotation at pile-caps; deformations (and derived strains) in restrainers; forces in shear key.
Sample Simulation Studies
The force-deformation response of several bents that comprise Model Type IV when subjected to a site-specific scaled ground motion is shown in Figure 4.
SFSI and Site Effects
Another important issue being addressed by the project related to soil-foundation-structure interaction effects is the propagation of the seismic waves through the soil and the relevant use of free-field motions at the base of the structure. The importance of applying ground motions at some appropriate location in the far field of the soil domain is investigated using the Domain Reduction Method (developed by Bielak and co-workers). The procedure has been augmented for use with inelastic soil material. It has been implemented within OpenSees under the name Plastic Bowl Method. Figure 5 represents a sample validation. In this particular case, the vertically propagating shear wave (continuous line) is seen as it propagates within a down-hole array. The dashed line is the vertically propagating shear wave at the boundary of the plastic bowl. The soil stiffness within the plastic bowl is controlling the shear wave velocity, observed as a shift in a peak of the traveling wave.
Figure 2: Simulation Models of Varying Detail: (a)
Model Type I – Half
Height Column; (b) Model Type II – Single Bent; (c) Model Type
III – Complete Frame
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Figure 3: Simulation Model Incorporating Frame-Frame Interaction
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Figure 4: Shear vs. deck response of selected bents
in Model Type IV when subjected to a typical 10% in 50 year event
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Figure 5: Comparison of vertically propagating shear wave at boundary
of plastic soil domain and a down-hole array
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Tasks in Progress
Time-history analyses of each model type will be carried out using the suite of ground motions generated for the I-880 project. The generated demand parameters for each model will provide a range of component and system response information that will be required to characterize damage as a function of EDP|IM. The next step in the methodology is the simulation of damage measures based on the estimated EDPs for each hazard level. This task is being coordinated with ongoing efforts on damage modeling at the University of Washington (PI: Eberhard).
Ultimately, the project will attempt to identify those uncertainties, in the analysis of elevated highway structures similar to I-880, which are important in the estimation of DMs and EDPs and those that finally impact the DVs. Consequently, the study will also reveal those uncertainties which can be ignored, and those that can be reduced by further study.
- May 31, 2003: Technical session on the I-880 testbed project at the ASCE Structures Congress in Seattle
- June 30, 2003: Prepare first draft of testbed report for circulation among I-880 testbed researchers
- September 30, 2003: Complete testbed report
I-880 Testbed report to be published as a PEER Report.