BUILDING LOSS MODELING AND BENCHMARKING: EDP TO DV

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1 BUILDING LOSS MODELING AND BENCHMARKING: EDP TO DV Author Name: Vivian D. Gonzales Home Institution: University of California, San Diego REU Institution: California Institute of Technology REU Advisor: Keith A. Porter, Judith Mitrani-Reiser

2 Abstract The approach pursued by the Pacific Earthquake Engineering Research (PEER) Center to performance-based earthquake engineering is developed in four stages: hazard analysis, structural analysis, damage analysis and loss analysis. This paper summarizes the last two stages of the approach - damage and loss analysis conducted at the California Institute of Technology. In the damage analysis, engineering demand parameters (EDP) such as accelerations, ground failure and drifts are used with fragility functions of the many components (assemblies) that constitute a facility. Once the EDP s are used with the fragility functions one can determine the measures of damage (DM) of the components of a facility. In the loss analysis, the DM s obtained are used to evaluate the decision variables (DV) of a facility. The decision variables measure the seismic performance of the facility in terms of death, dollars, and downtime. The main objectives of this project is to evaluate and benchmark the performance of new reinforced-concrete building, and to simplify and package the algorithms that describe the probability distribution of damage measures (DM) and decision variables (DV). The packaged algorithms will facilitate implementation by other users of OpenSees or other automated performance based earthquake engineering generation II (PBEE-2) evaluation code. Also, the packaged algorithms and data will facilitate the evaluation of the probabilistic relationship between EDP and DM, and DM and DV.

3 Introduction There are various methodologies for developing performance-based earthquake engineering (PBEE). This particular methodology is through the Pacific Earthquake Engineering Research (PEER) Center. PBEE is a framework by which many structures (existing or new) are analyzed for their seismic performance. PBEE focuses on the seismic performance of the structure through decision variables (DV). The decision variables measure the performance of a facility in terms of repair costs, fatalities, risk of collapse and post-earthquake operability (Porter, 2003). PEER s PBEE approach has four stages: hazard analysis, structural analysis, damage analysis and loss analysis. Research conducted at Caltech, Stanford and UCLA are making this project possible. Each university focuses on a specific stage of the project. As shown below in Fig.1, is PEER s methodology. The UCLA team research on the hazard analysis, Stanford on the structural analysis and Caltech on the damage and loss analysis (circled in red). Thus, one of Caltech s goals is to Benchmark PEER s PBEE-2 methodology for calculating damage and loss for IBC-2003 compliant buildings. Calculating the damage and loss of buildings would be very beneficial for facility stakeholders since it would provide them with valuable information such as repair cost, fatalities and downtime (Porter, 2003). PEER PBEE ANALYSIS METHODOLOGY Hazard analysis Structural analysis Damage analysis Loss analysis hazard model g[im D] struct l model p[edp IM] frag'y model p[dm EDP] loss model p[dv DM] facility def. D site hazard g[im] structural response g[edp] damage response g[dm] performance g[dv] decision making D OK? D: Location & Design IM: intensity measure EDP: eng'ing demand param. DM: damage measure DV: decision variable Fig. 1 (PEER Analysis Methodology, Mitrani 2004)

4 My contribution to the project The algorithms of dollars, death and downtime were packaged by creating libraries of logarithmic medians and standard deviations for capacity and for repair costs of damageable assemblies. For example, I found the logarithmic median and standard deviations for the capacity of different assemblies using fragility curves illustrated below in Fig. 2. Fragility functions were obtained from different sources such as, lab experiments, analytical, earthquake data, and engineering judgment. Fig. 2 (Fragility curves for drywall partitions, Mitrani 2004) Once the algorithms are packaged they are used with a Matlab toolbox that will run a Monte Carlo Simulation a method for propagating uncertainties. As shown above, in Fig. 2 after using the information from the fragility curves of assemblies (in this case, drywall partitions) and using it in a Matlab program, we get a probability of the assembly performance in terms of: dollars, death and downtime. However, before running this analysis with Matlab and packaging all the algorithms, it is necessary to have an inventory of a specific structure to be tested. Thus, with the floor plans of an imaginary building at UC Merced, it was possible to learned about the different assemblies that make up a building. Reviewing the floor plans of that building was very informative. With the help of the UC Merced library floor plans, I created an imaginary building. The design was made with Microsoft Office Visio 2003; however the structural design (columns, beams and dimensions) was provided by the team at Stanford as shown in Figs. 3, 4.

5 Fig. 3 (Mean Frame Elevation) Fig. 4 (Plan View)

6 Up Up Up Up The imaginary building has 4 levels and the inside design for levels 1 and 2-4 are shown in Figs. 5, 6. E D C B A Fig. 5 (Level 1, author s work) (Level 2-4, author s work) Fig. 6

7 After creating the design of this imaginary building, it was necessary to create an inventory of all the assemblies (of structural importance) that make up the building. Creating an inventory of all the assemblies is necessary in order to have a table that includes the logarithmic medians and standard deviations for capacity and for repair costs of all the damageable assemblies. Shown below in Fig. 7 is an example of the inventory of assemblies with the logarithmic medians and standard deviation for capacity and repair cost, depending on their limit state. The limit state ranges from 1-4, from least damage to complete collapse, respectively. This particular example was taken from a 66,000sf, seven-story hotel building located in Van Nuys, California. The imaginary building that was created with Visio has not been tested yet; however, the example of the Van Nuys Hotel will suffice to explain the process of this project. Fig. 7 (Matlab Toolbox Packaging, Mitrani 2004)

8 Outcomes After having all the information necessary which includes, logarithmic median and standard deviations for the capacity of different assemblies using fragility curves one can run the analysis to see the building performance. Below in Fig. 8 are the results for one simulation of one ground motion and structural model pair for an earthquake scaled to Sa = 0.5g of the same Van Nuys Hotel. Fig. 8 (Van Nuys Hotel Building Performance, Mitrani 2004) Fig. 8 shows the performance of each specific assembly at different damage measurements. For example, above in Fig. 8 the first column describes the assembly by giving it a number, the second column gives the total number of assemblies that will be evaluated for performance, in the following columns 3-7, it gives the number of assemblies with DM (0-4) from least damage to complete collapse, respectively. The Damage measurements are explained in detail below in Fig. 9. Qualitative term Translation Example Negligible, few, little 0-1% Generally negligible [ceiling] damage: less than 1% of ceiling area is damaged. Some, minor 1 10% Some cracked [glazing] panes; none broken: Between 1% and 10% of lites visibly cracked; no glass fallout. Distributed 10 30% Distributed [partition] damage: between 10% and 30% of partitions need patching, painting or repair, measured by lineal feet. Many 30 60% Many fractures at [steel moment frame] connections: between 30% and 60% of connections suffer rejectable damage. Most % Most [HVAC equipment] units do not operate: at least 60% of HVAC components inoperative. (Quantify Damage Measure, Porter et al. 2001) Fig. 9 After obtaining the building performance by running the simulation, we can obtain a probability histogram that shows the performance of the entire structure in terms of repair cost, fatalities and

9 downtime operability. Below in Fig. 10 is the total cost histogram, after running 200 simulations for the Van Nuys Hotel Total Cost Histogram for 200 Simulations prob Tota l Re pair Cost (in Do llars) x 10 6 Fig. 10 (Van Nuys Hotel Cost Histogram, Mitrani 2004)

10 Conclusions, Future Work This paper has summarized the two stages (damage and loss analysis) of a performance-based earthquake engineering methodology by the Pacific Earthquake Engineering Research (PEER) center; also, my contribution to the project during the summer of 2004 at the California Institute of Technology. The project objectives focus on informing stakeholders about the seismic performance of their structures in terms of cost, fatalities and downtime; furthermore, to hopefully implement the design code or provide different ways to meet the design code. The probabilistic approach of this project contains many uncertainties and these uncertainties could be diminished by using different techniques and programs. Currently the Matlab toolbox includes loss estimation based on Monte Carlo Simulation (MCS), but in the future it will be expanded to include First-moment second order (FOSM) and moment matching (MM) estimation (Mitrani, 2004). These techniques of propagating uncertainties are far more accurate and effective than the Monte Carlo Simulation. Furthermore, the toolbox with capacity and cost parameter for different assemblies will be available from a complete database for the use people interested in this type of research.

11 Acknowledgments: I want to thank PEER for giving me the opportunity to participate in the summer internship program. Many thanks to my advisor, Keith A. Porter for sharing his knowledge and mentorship with me and finally, I am very thankful to Judith Mitrani-Reiser for being such a great advisor and friend. References: Mitrani-Reiser, J. Methodologies in Performance Based Earthquake Engineering and Proposed Extension to other Disasters- Group Meeting. Pasadena, CA 2004 Porter, K.A., 2003, An Overview of PEER s Performance-Based Earthquake Engineering Methodology, Proc. Ninth International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP9) July 6-9, 2003, San Francisco, CA. Civil Engineering Risk and Reliability Association (CERRA). Porter, K.A., J.L. Beck, and R.V. Shaikhutdinov, 2002b, Investigation of Sensitivity of Building Loss Estimates to Major Uncertain Variables for the Van Nuys Testbed, Report to Pacific Earthquake Engineering Research Center, Berkeley. Porter, K.A., A.S. Kiremidjian, and J.S. LeGrue, 2001, Assembly-based vulnerability of buildings and its use in performance evaluation, Earthquake Spectra, 17 (2),

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