The main objective in this project is to develop a methodology to estimate the economic losses in buildings from earthquakes. Instead of having discrete qualitative performance levels of a structure, this project aims at describing the seismic performance of the building in a continuum way, and more specifically in terms of dollar losses. In this project, emphasis is on losses associated with damage to structural components. This project is being conducted in connection with the seven-story reinforced concrete building PEER testbed structure. Loss estimation associated to non-structural components is being conducted in another project (Project # 5242002).

The PEER mission is to develop and disseminate technologies to support performance-based earthquake engineering. In particular, one of PEER’s goals is to providing quantitative tools for characterizing and managing seismic losses. This project aims at implementing PEER’s framework to evaluate dollar losses in buildings by using a component-based approach. The methodology is fully probabilistic and permits the explicit incorporation of various sources of uncertainty in the estimation of earthquakes losses.

The PEER framework equation permits the estimation of EDPs from IM’s and DV’s from EDP’s. The equation has been modified to be able to estimate damage states in different components, referred to as damage measures, DM. In particular we have modified the framework equation to be able to consider discrete damage states, which facilitate the estimation of repair or replacement cost associated with each damage state as opposed to estimating losses directly as a function of the EDP as originally developed. Based on the modified equation, a step-by-step procedure is proposed to evaluate the building loss.

The procedure uses four basic steps to estimate the annual expected loss in buildings:

1. Estimation of the seismic hazard at the site;
2. Estimation of structural response parameters at different locations of the structure as a function of the ground motion intensity;
3. Estimation of the level of physical damage (damage state) in each component as a function of structural response parameters;
4. Estimation of the economic loss in each component associated with each damage state.

In year 5, efforts were primarily aimed at the development of motion-damage relationships in structural components present in the Van Nuys 7-story reinforced concrete testbed structure. The DM’s have carefully been selected based on the course of actions required to be taken to either repair or replace the component. The probability of exceeding a damage state conditioned on the EDP has been presented in terms of fragility functions. The development of fragility functions for structural components was demonstrated and carefully documented for slab-column connections. Fragility functions for four damage states as a function of interstory drift ratios were developed using the results of 8 experimental programs, including a total of 73 specimens. Two of the damage states also require the vertical shear ratio, introducing the concept of fragility surfaces.

Figure 1. Fragility functions for two damage states of slab-column connections of the building

In year 6, we are developing of cost functions that permit the estimation of economic losses conditioned on knowing that the component is in a certain damage state. Damage functions are being developed for slab-column connections.

In its present form the methodology is capable of providing information on the expected annual loss in the building. This annualized loss provides valuable information on average annual losses that are expected to occur in the building, thus provide basis for comparisons with rate of return of the current investment with other investments, with annual insurance premiums, etc. However, it does not provide information of the probability of exceeding economic losses or different size. In year 6 we are working towards extending the methodology to be able to compute the mean annual frequency of exceedance of any dollar loss in the building. This information will be able to answers questions such as what is the probability that I may face a loss of more than 4 million dollar in my structure?. This type of information provides more complete information to risk managers in deciding whether to retain, eliminate, transfer or partially transfer the risks involved. More importantly, this kind of information will provide information that will allow to make decisions regarding seismic risk in the same format in which owner’s, lenders, insurers and other stakeholders currently evaluate and manage real state risks.

Computation of the mean annual frequency of exceedance of dollar losses is significantly more complex than the estimation of the expected annual loss. It involves the estimation of the dispersion of the losses in individual structural and nonstructural components but also the estimation of the correlation between these individual losses. During year we are conducting sensitivity studies to evaluate the influence of correlation between economic losses of individual components of the estimation of the economic loss in the building.

Within PEER economic loss estimation is also being conducted by Prof. Beck and Dr. Porter at Caltech in relationship with the Life Sciences Building on the Berkeley campus. Their approach is based on Monte Carlo simulation. Some work is being conducted at the Mid-America Earthquake center, although their approach is based on estimation of regional consequences, as opposed to goal of this project which is aimed at the estimation of earthquake losses in particular structures.

In year 7 the effort will be devoted to sensitivity studies to identify the influence of various types of uncertainties involved in the process of estimating losses in a building. A procedure will be developed to disaggregate losses to identify the components, the story levels, the response parameters, etc that contribute more significantly to economic losses. Similarly, the disaggregation procedure will permit the identification of the ground motion intensities that contribute more to economic losses in particular structures. This will provide additional information to stakeholders on how economic losses can be mitigated and to provide tools for better risk management.

Our efforts are currently being considered in the ATC-58 project that deals with performance-based design procedures. That project is being developed by the Applied Technology Council with funding from FEMA.

• Cost functions for slab-column connections. May, 15, 2003
• Cost functions for other structural components. August, 1, 2003
• Estimation of losses considering all structural components of the testbed building. September 30, 2003. For this purpose we will use fragility functions being developed by PEER researchers at the University of Washington for columns and beam-column joints.

• Cost functions for structural components.
• Sensitivity analysis on the effects of different sources of uncertainty on the loss in the building.