Project Title/ID Number Computational Reliability for Design—4132002
Start/End Dates 10/1/02—9/30/03
Project Leader Joel Conte (UCSD/Faculty)
Team Members Yuyi Zhang (UCSD/Grad Student), Gabriel Acero (UCSD/Grad Student), Quan Gu (UCSD/Grad Student)
Project goals and objectives
  • Develop, implement, and document sensitivity and reliability analysis modules in OpenSees to facilitate solution of the PEER PBEE framework equation.
  • Identify and model uncertainties (characterizing the seismic loading, system parameters, modeling assumptions, etc.) and track their propagation through nonlinear earthquake response analysis (using OpenSees) for the Humboldt Bay Bridge testbed structure.
  • Demonstrate the various ingredients required in the solution of the PEER probabilistic framework equation as well as their integration for the Humboldt Bay Bridge testbed structure.
  • Investigate seismic reliability assessment of non-ductile structures with degrading components.
Role of this project in supporting PEER’s vision

This project will contribute to the development, assessment and validation of the computational tools for probabilistic and reliability analysis in OpenSees based on finite element modeling of an actual testbed bridge structure using OpenSees. This real-world application example will foster the integration of the methodologies and numerical tools developed, will naturally bring up some deficiencies and gaps in these methodologies, and thus will point the way to their refinement and completion.

Methodology employed

This project is based on advanced numerical modeling of the Humboldt Bay Bridge testbed structure using the PEER software framework OpenSees. Soil, foundation, and structure are all modeled using state-of-the-art material models and finite elements recently developed and implemented in OpenSees by other PEER researchers. The probabilistic assessment methodology consists of integrating probabilistic seismic hazard analysis, nonlinear seismic response analysis of the bridge structure-foundation-soil system performed using OpenSees, and probabilistic capacity analysis (or fragility analysis) for various potential limit-states or failure modes. The nonlinear seismic response analysis is performed for ensembles of real ground motion records corresponding to different seismic hazard levels as defined by the surrounding seismicity and the spectral acceleration at the predominant period of the structure-foundation-soil system. Parametric investigations (sensitivity analyses) are performed around a representative model of the HBB system to assess the effects and relative importance of a number of system parameters on the bridge performance. Effects of system parameter uncertainty and modeling uncertainty on the probabilistic estimate of bridge performance are also investigated.

Brief description of past year’s accomplishments and more detail on expected Year 6 accomplishments

The 2-D nonlinear model of the bridge structure-foundation-soil system previously developed in OpenSees was augmented to include:

  1. pile groups (piles and pile caps) modeled using force-based fiber beam-column elements,
  2. extended soil region in both horizontal and vertical directions (see Figure 1).

In collaboration with Prof. Jacobo Bielak of Carnegie Mellon, we developed a simplified yet improved method for defining the seismic excitation around the lateral and bottom boundaries of the soil region. This seismic excitation assumes vertically propagating shear waves and a linear elastic, undamped, and homogeneous semi-infinite half-space underlying the soil region modeled in OpenSees. It is also consistent with free field (rock and soil) actual earthquake records representative of the local seismicity (seismic hazard) provided by Dr. Paul Somerville. The proposed treatment of the boundary conditions includes simple (of the Lysmer type) transmitting/absorbing boundaries, in order to incorporate the seismic excitation and limit the occurrence of spurious seismic wave reflections along the boundaries of the modeled soil medium. The proposed seismic input definition requires deconvolution of the free field soil motions provided by Somerville through an 1-D equivalent linear model of the layered soil region shown in Figure 1, in order to obtain incident seismic motions at the base of the modeled soil region. The computer program SHAKE is used for this purpose and convergence problems are encountered.

Ensembles of ground motions representative of the seismicity of Humboldt Bay were scaled to three hazard levels (50% in 50 years, 10% in 50 years, and 2% in 50 years) based on the 5 percent damped pseudo-acceleration spectral value at the predominant frequency (1.90 Hz) of the bridge structure-foundation-soil system, see Figure 2.



Figure 1. 2-D Nonlinear model of Humboldt Bay Bridge
Larger View


Figure 2. Transfer function of Humboldt Bay Bridge System
Larger View

Seismic response analysis for these three hazard levels is underway. Several limit-states are considered with corresponding pairs of Engineering Demand Parameters (EDP’s) and capacity terms. Preliminary results of probabilistic seismic demand analysis (for rock site records only) related to three failure modes (rupture of shear key(s), unseating, and pier failure) are shown in Figure 3. Probabilistic capacity analysis of spliced columns/piers against flexural/shear failure is also being performed in collaboration with Prof. Marc Eberhard, Univ. of Washington, and based on experimental data on spliced columns (UCLA, Prof. John Wallace).
Other similar work being conducted within and outside PEER and how this project differs

Some work has been conducted outside PEER on some individual aspects (e.g., fragility analysis of bridge components) of this project. However, to our knowledge, the integration of seismic hazard analysis, seismic demand analysis of a bridge structure-foundation-soil system, and probabilistic capacity analysis (or fragility analysis) has not been achieved outside PEER. We are and will keep reviewing the literature to identify and possibly take advantage of related work outside PEER.

Plans for Year 7 if this project is expected to be continued

In parallel with the expected research work described above for Year 6, we anticipate completing the application of an alternative approach of probabilistic performance assessment of the HBB during Year 6 and into Year 7. This alternative approach consists of the finite element reliability method, several ingredients of which are being implemented in OpenSees by Prof. Der Kiureghian and co-workers at UC Berkeley, with whom we collaborate.

The two probabilistic performance assessment methodologies will be directly compared in the context of the Humboldt Bay Bridge testbed.

At the completion of the probabilistic performance assessment of the HBB using a 2-D OpenSees model, we will naturally be interested in extending this work to 3-D with the new challenges that this will bring up (e.g., porting of OpenSees to a high performance computing environment such as SDSC, definition of seismic input, etc).

Describe any instances where you are aware that your results have been used in industry
Expected milestones
  1. PEER report on Humboldt Bay Bridge testbed including hazard analysis, structural model, structural analysis, damage analysis, and documenting probabilistic performance assessment of the HBB using the PEER probabilistic framework (October 2003).
  2. Documentation of probabilistic performance assessment of HBB using the finite element response sensitivity analysis and time-variant finite element reliability analysis tools available in OpenSees (December 2003).
  3. Probabilistic Performance assessment of the HBB based on 3-D modeling and analysis in OpenSees (June 2004).

Documentation of probabilistic performance assessment of the Humboldt Bay Bridge testbed based on advanced numerical modeling in OpenSees and using the PEER probabilistic framework.