EVALUATION OF THE SEISMIC PERFORMANCE OF A ... - CSU, Chico

EVALUATION OF THE SEISMIC PERFORMANCE OF A CODE-CONFORMING REINFORCED-CONCRETE FRAME BUILDING - PART II: LOSS ESTIMATION Judith Mitrani-Reiser1, Curt Haselton2, Christine Goulet3, Keith Porter4, James Beck5, and Gregory Deierlein6

ABSTRACT Performance-based earthquake engineering (PBEE) is a methodology that incorporates desired performance levels into the design process. Performance in PBEE can be economic (e.g., expected annual losses), or expressed in terms of operability and safety performance (e.g., expected downtime due to safety tagging and/or repair). These performance objectives are relevant to various types of stakeholders and should be addressed in building loss estimation procedures. In this study, we consider the structural and economic performance of a codeconforming office building. An analytical approach for PBEE is implemented to evaluate the performance of this reinforced-concrete moment-frame building. The PBEE approach used is consistent with the Pacific Earthquake Engineering Research (PEER) center’s framework, which is divided into four core analytical stages: hazard analysis, structural analysis, damage analysis, and loss analysis. Future losses of the building are uncertain because they depend on uncertain quantities, such as the shaking intensity of the earthquake, the mechanical properties of the facility, and the uncertain damageability and unit repair costs of the facility. An analytical approach is developed to propagate these uncertainties. This paper presents the mathematical foundation for the damage and loss analyses, and a description of its implementation into software. The results from running this software on multiple design variants of the building are presented, including seismic vulnerabilities as a function of shaking intensity and corresponding expected annual losses. Introduction The benchmark study presented here is a collaborative effort between Caltech, UCLA, and Stanford. The purpose of this study is to implement PEER’s PBEE methodology and evaluate the economic performance of a new reinforced-concrete moment-frame office building. 1

Ph.D. Candidate in Applied Mechanics, Caltech, Pasadena, CA 91125 Ph.D. Candidate in Civil and Environmental Engineering, Stanford University, Stanford, CA 94305 3 Ph.D. Candidate in Civil and Environmental Engineering, UCLA, Los Angeles, CA 90095 4 George W. Housner Senior Researcher in Civil Engineering, Caltech, Pasadena, CA 91125 5 Professor of Engineering and Applied Science, Caltech, Pasadena, CA 91125 6 Professor, Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305 Paper to be orally presented at 8NCEE, San Francisco, California, April 2006 2

PEER PBEE Methodology Overview Among other things, the PBEE methodology can be used to estimate the mean annual frequency with which a particular performance metric will exceed various levels for a given location (Porter 2003). The four main steps are presented in Fig. 1: hazard analysis, structural analysis, damage analysis, and loss analysis. The methodology is expressed mathematically in Eq. (1). In both the figure and the equation, p[X|Y] denotes the probability density of X conditioned on Y, λ[X|Y] denotes the mean occurrence rate of X given Y, IM denotes an intensity measure, EDP denotes engineering demand parameters, DM denotes damage measures, and DV denotes decision variables. This paper focuses on the damage and loss analyses. The complementary work to this project is described in a companion paper (Goulet et al. 2005) that focuses on the hazard and structural analyses. The first step in this approach is the hazard analysis, which evaluates the seismic hazard for a particular facility, considering nearby faults, site distance, source-to-site conditions, facility location, facility design, etc. The ground shaking at the site is parameterized via an intensity measure. The hazard curve, λ[IM|D], is the mean arrival rate of events in [IM, IM+dIM]. Some traditional intensity measures are peak ground acceleration and spectral acceleration at chosen periods (e.g., Sa(T1), the damped elastic spectral acceleration at the small-amplitude fundamental period of the structure). We use the latter in this work. The second step is the structural analysis, in which the engineer creates a soil-foundationstructure (SFS) model of the facility in order to estimate the uncertain structural response. The response is measured in terms of a vector of engineering demand parameters (EDPs), conditioned on the intensity measure IM and design. Some examples of EDPs are: directional peak transient interstory drift, directional peak diaphragm acceleration, peak plastic hinge rotation, and peak positive curvature in the beams. Note that the methodology allows for uncertainty in the structural models. The third step of this methodology is the damage analysis. This step involves using fragility functions that express the probability that a facility component (e.g., beam, column, wall partition, etc.) is in or exceeds a particular damage state as a function of an EDP. The different damage states are indicative of the corresponding repair efforts needed to restore a facility component to an undamaged state. These fragility functions, compiled based on laboratory experiments, analytical investigation, expert opinion, or some combination, are used to create a probabilistic array of damage measures. The DMs calculated in the analysis above are used in the final step of the PEER methodology, the loss analysis. This analysis, which is the focus of this paper, is the probabilistic estimation of structural performance conditioned on damage. Performance metrics that have been previously considered include repair cost, repair duration, and loss of life. The metric used in this study is repair cost. This final step of the methodology gives estimates of the mean annual frequency with which various levels of DV are exceeded; these can be used to inform a variety of risk-management decisions. Paper to be orally presented at 8NCEE, San Francisco, California, April 2006

facility definition

D

Hazard analysis

Structural analysis

Damage analysis

Loss/downtime analysis

hazard model

structural model

fragility model

loss model

λ[IM|D]

p[EDP|IM]

p[DM|EDP]

p[DV|DM]

site hazard

structural response

damage response

performance

λ[IM]

IM: intensity measure, e.g., S a(T1)

λ[EDP]

EDP: eng‘ing demand param. e.g., drift, accel.

λ [DV]

λ[DM]

DM: damage measure/state, e.g., bar buckl’g

Coll./casualty analysis λcoll fatality rate

decision making

D = OK?

DV: decision variables e.g., $ loss, downtime

Figure 1: Schematic of PEER methodology (Porter 2003).

λ [ DV | D ] = ∫∫∫ p[ DV | DM , D ] p[ DM | EDP, D ] p[ EDP | IM , D ]λ [ IM | D ]dIMdEDPdDM (1) Building and Site Information The purpose of the benchmark study was to evaluate the performance of new reinforcedconcrete structures on a site that would be most typical of the range of seismic hazards in coastal California. The benchmark structure, a 4-story, reinforced-concrete moment-frame office building, is a hypothetical structure that was designed specifically for this study according to IBC-2003, ASCE7-02, and ACI 318-02. The selected site is the LA Bulk Mail Facility in Bell, CA (coordinates N33.996°, W118.162°), located south of downtown Los Angeles. More detailed information on the site hazard characterization, the record selection methodology, the structural modeling uncertainty, and the collapse analysis may be found in the companion paper (Goulet et al. 2005). Site Information The goal for this benchmark study was to locate the building on typical site conditions for an urban region within California. It was necessary to select a site where the ground motions would not be dominated by unusual features specific to the region (e.g. basin edge effects). Other factors were also considered and are described in detail in another report (Haselton et al. 2005). One would expect some effect of near-source ground motions, since the site is within 20 km of 7 faults. However, no single major fault produces near-fault motions that dominate the site hazard, and the contributions of near fault motions from the other faults are actually typical of the Los Angeles area. This site met the benchmark selection criteria and also had the advantage of Paper to be orally presented at 8NCEE, San Francisco, California, April 2006

available high quality geotechnical data from the Resolution of Site Response Issues from the Northridge Earthquake program (ROSRINE 2005). The chosen benchmark site is located on deep sediments, mostly Quaternary alluvial deposits, near the middle of the Los Angeles Basin. The upper 30 m consist of sands and silts with traces of clay and cobbles with a corresponding average shear wave velocity Vs-30 of 285 m/s (NEHRP soil category D). Building Design Several four-story office buildings were designed according to the 2003 International Building Code (ICC 2003). The plan and elevation views of the perimeter-frame designs are shown in Fig. 2; the space-frame designs have the same layout as the perimeter-frame ones, but with frames in every bay. Some variants of the perimeter- and space-frame buildings were designed with above-code strengths (125% of code required strength) and with strengths meeting the minimum code requirements. More details on the design of this benchmark structure can be found in the benchmark report (Haselton et al. 2005). The building has a design seismic weight coefficient of 0.094g, corresponding to a calculated structural period Tcode = 0.80s7. The computed fundamental periods of the four designs range from 0.8 seconds to 1.3 seconds. Depending on the design, columns range in size from 18 in. x 24 in., to 30 in. x 40 in.; the beam dimensions range from 18 in. x 33 in., to 24 in. x 42 in. The designs were controlled by strength, the strong column-weak beam requirement, joint shear capacity provisions, and drift limitations (Haselton et al. 2005).

13 feet

120 feet

53 feet

30 feet

120 feet 180 feet

Figure 2: Plan and elevation of four-story office building. For each building, a two-dimensional model was created of a typical four-bay frame in the N-S direction. For the perimeter-frame models, an equivalent gravity frame was modeled in series, to account for the additional strength and stiffness of the gravity system. For the spaceframe models, the biaxial loading effects are not accounted for, as the models are only twodimensional. To minimize the error induced from neglecting biaxial bending, the space frames were designed for strength demands only in the N-S direction (i.e., not biaxial strength 7

This value includes the allowable 40% increase from the period computed by ASCE7-02 Eq. 9.5.5.3.2-1 (ASCE 2002). Paper to be orally presented at 8NCEE, San Francisco, California, April 2006

demands). Building Components Considered in Loss Estimates It is necessary to account for the components that, if damaged, would account for most of the repair cost effort. In the PEER PBEE methodology, a detailed list of all structural and nonstructural components would normally be populated from a building’s architectural and structural drawings. However, since the benchmark structure does not actually exist, architectural drawings were rendered for the benchmark study. The aggregate building losses depend on a variety of components: structural members, partitions, ceilings, glazing, piping, HVAC, and other building-specific components. However, Beck et al. (2002) show that the building components that contribute the most to repair cost are structural members, drywall partitions and interior paint. Thus, this benchmark study focuses on these specific building components. Fragility and Loss Distribution Functions Fragility and cost distribution functions are created using experimental data, analytical investigation, expert opinion, or some combination. A review of loss estimation research shows that lognormal distributions adequately fit loss data and are commonly used for fragility and cost distribution functions (Porter 2000, Beck et al. 2002, Aslani and Miranda 2004). To fully describe a lognormal distribution, the median and logarithmic standard deviation are needed. Therefore, the median capacity and logarithmic standard deviations of capacity (defined in terms of the EDP value that causes an assembly to reach or exceed a given damage state) are used to create the fragility functions, and then to estimate damage. Also, the corresponding median unit repair costs and logarithmic standard deviations of cost are used to create the cost distribution functions, to estimate the loss. Structural Components: Beams and Columns There are various damage indices that are used to quantify damage of reinforced-concrete (RC) structural members. Williams et al., (1997) demonstrate that the modified Park-Ang Damage Index (PADI), given in Eq. (2), is a consistently reliable indicator of severe damage and structural failure. This result and available empirical data with clear definitions of damage states (Beck et al. 2002) are the motivation for using PADI as the EDP for the RC structural members in this benchmark study: Φ − Φr PADI = m (2) Φu − Φ r where Φ m = maximum curvature attained during seismic loading

Φ u = nominal ultimate curvature capacity Φ r = recoverable curvature at unloading The fragility curves, shown below in Fig. 3, are used in the third step of PEER’s PBEE methodology to relate the modified PADI values from the structural analysis to probabilities of Paper to be orally presented at 8NCEE, San Francisco, California, April 2006

exceeding the four levels of damage. Each level of damage corresponds to a specific repair effort: the light damage state is treated with epoxy injections, the moderate damage state corresponds to a jacketed repair, and the severe and collapse damage states correspond to replacement of the member. Note that no damage is also a damage state, known as “none”. Non-Structural Components: Drywall Partitions and Finish The drywall partitions considered for the benchmark office building are 5/8” wallboard partitions on 3-5/8” metal stud at 16” centers with screw fasteners. The EDP used for the drywall partitions and finish is the peak transient drift ratio (PTDR). The fragility curves, shown in Fig. 3, were developed by Porter (2000) and are based on Rihal’s (1982) in-plane racking tests of 8’0 x 8’-0 building partitions. These fragility curves are used to relate the PTDR values from the structural analysis to probabilities of exceeding the two levels of damage. Each level of damage corresponds to a specific repair effort: the visible damage state corresponds to patching, and the significant damage state corresponds to replacement of the member. Fragility Curves for RC Moment-Frame Members

Fragility Curves for Drywall Partitions 1

Cumulative Probability

Cumulative Probability

1 0.8 0.6 Light Moderate Significant Collapse

0.4 0.2 0 0

0.5

1

1.5

2

2.5

3

0.8 0.6 0.4 Visible Significant

0.2 0 0

0.005

0.01

0.015

Peak Transient Drift Ratio

PADI

Figure 3: The left figure shows the fragility curves for RC moment-frame members and the right figure shows the fragility curves for the wallboard partitions. Loss Results The modular framework of the PEER methodology allows for straightforward software development. A MATLAB damage and loss analysis toolbox (MDLA) was created as part of this benchmark study to handle the damage and loss analyses portions of the PEER methodology. The inputs into the toolbox are: a database of fragility and cost distribution functions, tables of the damageable components of the benchmark building, and the hazard and structural analysis results. The outputs of the toolbox are the probability of exceedance of damage states for all damageable components in the structure and the DVs of the methodology described above. The DVs considered in this study are the repair costs to restore the building to an undamaged state. Damage The structural analysis results are combined with the damageable component fragility functions to compute the probability of reaching or exceeding damage state j, for a component of type i, conditioned on the structure not collapsing and on IM: Paper to be orally presented at 8NCEE, San Francisco, California, April 2006

∫

P[ DM ij | NC , im] =

P[ DM ij | edpi ] p( edpi | NC , im )dedpi

(3)

edpi

The first component of the integrand, P[ DM ij | edpi ] , is the probability of reaching or exceeding the damage states for a given building component, conditioned on EDP i appropriate for component of type i (i.e., fragility function). The second component of the integrand, p( edpi | NC , im ) , is the probability distribution of EDP i, conditioned on the structure not collapsing (NC) and on a given IM level. To evaluate this component, a lognormal distribution is used to fit the structural response data, as is done by other researchers (Miranda and Aslani 2003).

An example result of the damage analysis step is shown in Fig. 4, showing the average probability of reaching or exceeding each possible damage state for like components on each story level of the benchmark building. As expected, this figure shows that the probability of exceeding each damage state increases with increasing shaking intensity. Also, this figure shows that the probabilities of exceeding the more severe damage states are greater in the lower stories. The damage analysis results for all design variants considered in the benchmark study may be found in the final report (Haselton et al. 2005). Story

Average Probability

Columns 1 0.5 0 1 0.5 0 1 0.5 0

.1 .19.26 .3 .44 .55 .821.2

.1 .19.26 .3 .44 .55 .821.2

.1 .19.26 .3 .44 .55 .821.2

Partitions

Beams 1 0.5 0 1 0.5 0 1 0.5 0

.1 .19.26 .3 .44 .55 .821.2

.1 .19.26 .3 .44 .55 .821.2

.1 .19.26 .3 .44 .55 .821.2

1 0.5 0 1 0.5 0 1 0.5 0

1

1

1

0.5

0.5

0.5

0

.1 .19.26 .3 .44 .55 .821.2

0

.1 .19.26 .3 .44 .55 .821.2

0

4 .1 .19.26 .3 .44 .55.821.2

3 .1 .19.26 .3 .44 .55.821.2

2 .1 .19.26 .3 .44 .55.821.2

1 .1 .19.26 .3 .44 .55.821.2

Spectral Acceleration (g)

Figure 4: Average probabilities of damage per story level. Vulnerability Functions

The vulnerability functions, a product of the last step of PEER’s PBEE methodology, are the relationship between repair costs and shaking intensity level. The vulnerability functions are given by: E[TC | im] = E[TC | NC , im] ⋅ (1 − P[C | im]) + E [TC | C , im] ⋅ P[C | im] (4) where E[TC | im] is the expected total repair costs conditioned on IM and E[TC | C , im] is the replacement cost of the structure. The expected total repair cost conditioned on the structure not collapsing and on IM, E[TC | NC , im] , is calculated by:

Paper to be orally presented at 8NCEE, San Francisco, California, April 2006

na

E[TC | NC , im ] = (1 + Cop ) ⋅ Ci ⋅ CL ∑ N ui ⋅ E[ RCi | NC , im] i =1

(5)

nds

E[ RCi | NC , im ] = ∑ E[ RCi | DM ij ] ⋅ P[ DM ij | NC , im] i =1

where Cop , Ci , CL are the contractor overhead and profit, the factor for inflation, and the factor for location, respectively; na is the number of damageable component groups; Nui is the number of units in assembly group i; RCi is the repair cost for one unit in assembly group i; and nds is the number of damage states for damageable component group i. Note that each assembly group is composed of damageable components sensitive to the same EDP, and their damage states and repair costs are modeled as perfectly correlated and conditionally independent given EDP from all other assembly groups. The probability of collapse conditioned on IM, P[C | im] , is calculated as the fraction of structural simulations for a given design variant that reach a collapsed state for a given IM level over all structural simulations.

The vulnerability functions for four design variants (using Cop=0.175; Ci=1.091; and Cl=1.083) considered in this study are shown in Fig. 5, where the black dashed lines at Sa = 0.55g and Sa = 0.82g correspond to the 10% in 50yr event and the 2% in 50yr event, respectively, for the site. This figure shows a comparison of structural design choices (Fig. 5a) and of structural modeling choices (Fig. 5b). In Fig. 5a, the curve for Variant #1 (blue) corresponds to a perimeter-moment-frame design, considering the gravity frame and a flexible base; the curve for Variant #2 (red) corresponds to a similar structural model except the structural design uses the same beams and columns throughout, which makes the structure stiffer and more conservative. This more conservative design variant has smaller structural responses and thus smaller mean losses, at every level of IM. In Fig. 5b, the curve for Variant #12 (red) corresponds to a perimeter-moment-frame design not including gravity frames, modeling a flexible base and the tensile strength of the concrete; the curve for Variant #13 (blue) corresponds to a similar design except it does not model the tensile strength of the concrete. This structural model assumes that all the concrete is pre-cracked and therefore is expected not to perform as well as Variant #12, which has smaller mean losses, at every level of IM. A summary of these variants may be found in Table 1. 0.4

0.3 2.5 0.25 2 0.2 1.5 0.15 1

0.1

0.5

0.05

0.1 0.19 0.3

0.44 0.55 0.82 Spectral Acceleration (g)

1.2

0

0.45 Design Variant #12 Design Variant #13

0.4 0.35

3 Mean Repair Cost ($M)

Mean Repair Cost ($M)

3

0

3.5

0.35 Mean Damage Factor

3.5

4

0.45 Design Variant #1 Design Variant #2

0.3 2.5 0.25 2 0.2 1.5 0.15 1

0.1

0.5 0

0.05

0.1 0.19 0.3

0.44 0.55 0.82 Spectral Acceleration (g)

(a) Paper to be orally presented at 8NCEE, San Francisco, California, April 2006

(b)

1.2

0

Mean Damage Factor

4

Figure 5: (a) vulnerability functions for design variants 1 & 2, comparing two design choices and (b) vulnerability functions for design variants 12 & 13, comparing two modeling choices. Expected Annual Loss

The expected annual loss (EAL) is a valuable result for property stakeholders, which accounts for the frequency and severity of various seismic events. Here, EAL is calculated consistently with other researchers (e.g. Porter et al. 2000, Baker and Cornell 2003) as the product of the mean total rate of occurrence of events of interest and the mean loss conditional on an event of interest occurring, which may be expressed as: EAL = υ0

∫ E[TC | im] p( IM | IM ≥ im

cr

)dim

(6)

im

where υ0 is the mean annual rate of events where IM ≥ imcr = 0.1g ; E[TC | im] is calculated as in Eq. (4) and is shown for some variants in Fig. 5; and p ( IM | IM ≥ imcr ) is defined as the probability density function for IM, given seismic events of interest. A table of EAL results for the four variants considered in the previous section is shown below in Table 1. There are significant conclusions that can be made from this table: the more conservative design of Variant #2 leads to a smaller EAL value than for Variant #1; not modeling the gravity frame in Variant #12 ignores some structural stiffness and leads to a larger EAL value than for Variant #1; assuming all pre-cracked concrete in Variant #13 ignores the tensile strength of the concrete and leads to a larger EAL value than for Variant #12; and finally, the difference in EAL results for Variants #12 and 13 is drastically more than the difference of EAL results for Variants #1 and 2, because the vulnerability functions for #12 and 13 are so much further apart at low levels of IM, where the mean rate of occurrence of events is much larger. Table 1: Variant descriptions and corresponding EAL results. VID# 1 2 12 13

VID Description Perimeter moment frame; mean design; gravity frame attached; bond flexibility is captured; and column bases have elastic base spring flexibility. Modeled same as VID # 1; design is different, using the same beams and columns throughout the structure. Modeled same as VID # 1, except no gravity frame attached; bond flexibility is captured; and column bases have elastic base spring flexibility. Modeled same as VID # 1, except no gravity frame attached; no tensile concrete strength modeled; bond flexibility is captured; and column bases have elastic base spring flexibility.

EAL ($) 47,800 33,500 55,800 110,000

Conclusion

This paper describes and applies the PEER PBEE methodology, particularly, how to estimate the probability of damage and the mean total repair cost of a reinforced-concrete moment-frame office building, designed with a current building code requirements. It shows some interesting intermediate results of the methodology, such as the average probability of reaching or exceeding each possible damage state for like components on each story level. This paper also describes the vulnerability functions of four variants of the benchmark building, illustrating how structural modeling and design choices affect the loss results. Finally, it explains Paper to be orally presented at 8NCEE, San Francisco, California, April 2006

how to calculate expected annual loss, a loss metric that is significant to stakeholders, and calculates this for the four variants considered in this paper. A more detailed document (Haselton et al. 2005) shows similar results for other variants considered in this benchmark study. The focus here is on economic losses for the building; future work by some of the contributing authors will focus on other loss metrics, such as building operability and human injury. Acknowledgments

The authors would like to thank Jonathan Stewart, Ertugrul Taciroglu, and Vivian Gonzales for their insightful collaboration on this project. This work was supported primarily by the Earthquake Engineering Research Centers Program of the National Science Foundation, under award number EEC-9701568 through the Pacific Earthquake Engineering Research Center (PEER). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect those of the National Science Foundation. References American Society of Civil Engineers, 2002. ASCE-7-02: Minimum Design Loads for Buildings and Other Structures, Reston, VA. American Concrete Institute, 2002. Building Code Requirements for Structural Concrete (ACI 318-02) and Commentary (ACI 318R-02), Farmington Hills, MI. Aslani, H. and E. Miranda, 2004. Component-Level and Sytem-Level Sensitivity Study for Earthquake Loss Estimation. Proceedings, Thirteenth World Conference on Earthquake Engineering. Vancouver, B.C., Canada. Baker, J.W. and Cornell, C.A., 2003. Uncertainty Specification and Propagation for Loss Estimation Using FOSM Methods, Proceedings, Ninth International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP9). San Francisco, California. Beck, J.L., K.A. Porter, R. Shaikhutdinov, S. K. Au, T. Moroi, Y. Tsukada, and M. Masuda, 2002. Impact of Seismic Risk on Lifetime Property Values, Final Report, Consortium of Universities for Research in Earthquake Engineering, Richmond, CA. Goulet, C., Haselton, C., Mitrani-Reiser, J., Stewart, J.P., Taciroglu, E., and G. Deierlein, 2005. Evaluation of the Seismic Performance of a Code-Conforming Reinforced-Concrete Frame Building - Part I: Ground Motion Selection and Structural Collapse Simulation. Proceedings of Eighth U.S. National Conference on Earthquake Engineering. San Francisco, California Haselton, C., Goulet, C., Mitrani-Reiser, J., Beck, J.L., Deierlein, G., Porter, K.A., Stewart, J.P., and E. Taciroglu, expected 2005. Benchmarking of the Seismic Performance of a Code-Conforming Reinforced-Concrete Building, PEER Technical Report. Berkeley, California. International Code Council, 2003. 2003 International Building Code, Falls Church, VA. Miranda, E. and H. Aslani, 2003. Probabilistic Response Assessment for Building-Specific Loss Estimation. PEER Technical Report. Berkeley, California. Porter, K.A., 2000. Assembly-Based Vulnerability of Buildings and Its Uses in Seismic Performance Evaluation And Risk-Management Decision-Making, Doctoral Dissertation, Stanford University, Stanford, CA, published by ProQuest Co., Ann Arbor, MI.. Porter, K.A., 2003. An Overview of PEER’s Performance-Based Earthquake Engineering Methodology. Proceedings of Ninth International Conference on Applications of Statistics and Probability in Civil Engineering. San Francisco, California. Porter, K.A., J.L. Beck, R.V. Shaikhutdinov, S.K. Au, K. Mizukoshi, M. Miyamura, H. Ishida, T. Moroi, Paper to be orally presented at 8NCEE, San Francisco, California, April 2006

Y. Tsukada, and M. Masuda, 2004. Effect of Seismic Risk on Lifetime Property Value, Earthquake Spectra 20 (4), 1211-1237. Rihal, S.S., 1982. Behavior of Nonstructural Building Partitions During Earthquakes. Proceedings of the Seventh Symposium on Earthquake Engineering, Department of Earthquake Engineering, University of Roorke, India, November 10-12, 1982, Dehli: Sarita Prakashan, pp. 267-277. (ROSRINE) Resolution of Site Response Issues from the Northridge Earthquake, 2005. Website by Earthquake Hazard Mitigation Program & Caltrans. http://geoinfo.usc.edu/rosrine/. Williams, M.S., Villemure, I. and R.G. Sexsmith, 1997. Evaluation of Seismic Damage Indices for Concrete Elements Loaded in Combined Shear and Flexure, ACI Structural Journal 94 (3), 315322.

Paper to be orally presented at 8NCEE, San Francisco, California, April 2006