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  


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 realworld 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 stateoftheart 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 structurefoundationsoil system performed using OpenSees, and probabilistic capacity analysis (or fragility analysis) for various potential limitstates 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 structurefoundationsoil 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 2D nonlinear model of the bridge structurefoundationsoil system previously developed in OpenSees was augmented to include:
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 semiinfinite halfspace 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 1D 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 pseudoacceleration spectral value at the predominant frequency (1.90 Hz) of the bridge structurefoundationsoil system, see Figure 2. 
Figure
2. Transfer
function of Humboldt Bay Bridge System 

Seismic response analysis for these three hazard levels is underway. Several limitstates 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 structurefoundationsoil 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 coworkers 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 2D OpenSees model, we will naturally be interested in extending this work to 3D 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  


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