An Assessment to Benchmark the Seismic Performance of a Code-Conforming Reinforced-Concrete Moment-Frame Building

Abstract

This report describes a state-of-the-art performance-based earthquake engineering methodology 
\nthat is used to assess the seismic performance of a four-story reinforced concrete (RC) office 
\nbuilding that is generally representative of low-rise office buildings constructed in highly seismic 
\nregions of California. This “benchmark” building is considered to be located at a site in the Los 
\nAngeles basin, and it was designed with a ductile RC special moment-resisting frame as its 
\nseismic lateral system that was designed according to modern building codes and standards. The 
\nbuilding’s performance is quantified in terms of structural behavior up to collapse, structural and 
\nnonstructural damage and associated repair costs, and the risk of fatalities and their associated 
\neconomic costs. To account for different building configurations that may be designed in 
\npractice to meet requirements of building size and use, eight structural design alternatives are 
\nused in the performance assessments. 
\nOur performance assessments account for important sources of uncertainty in the ground 
\nmotion hazard, the structural response, structural and nonstructural damage, repair costs, and 
\nlife-safety risk. The ground motion hazard characterization employs a site-specific probabilistic 
\nseismic hazard analysis and the evaluation of controlling seismic sources (through 
\ndisaggregation) at seven ground motion levels (encompassing return periods ranging from 7 to 
\n2475 years). Innovative procedures for ground motion selection and scaling are used to develop 
\nacceleration time history suites corresponding to each of the seven ground motion levels. 
\nStructural modeling utilizes both “fiber” models and “plastic hinge” models. Structural 
\nmodeling uncertainties are investigated through comparison of these two modeling approaches, 
\nand through variations in structural component modeling parameters (stiffness, deformation 
\ncapacity, degradation, etc.). Structural and nonstructural damage (fragility) models are based on 
\na combination of test data, observations from post-earthquake reconnaissance, and expert 
\nopinion. Structural damage and repair costs are modeled for the RC beams, columns, and slabcolumn connections. Damage and associated repair costs are considered for some nonstructural 
\nbuilding components, including wallboard partitions, interior paint, exterior glazing, ceilings, 
\nsprinkler systems, and elevators. The risk of casualties and the associated economic costs are 
\nevaluated based on the risk of structural collapse, combined with recent models on earthquake 
\nfatalities in collapsed buildings and accepted economic modeling guidelines for the value of 
\nhuman life in loss and cost-benefit studies. 
\nThe principal results of this work pertain to the building collapse risk, damage and repair 
\ncost, and life-safety risk. These are discussed successively as follows. 
\nWhen accounting for uncertainties in structural modeling and record-to-record variability 
\n(i.e., conditional on a specified ground shaking intensity), the structural collapse probabilities of 
\nthe various designs range from 2% to 7% for earthquake ground motions that have a 2% 
\nprobability of exceedance in 50 years (2475 years return period). When integrated with the 
\nground motion hazard for the southern California site, the collapse probabilities result in mean 
\nannual frequencies of collapse in the range of [0.4 to 1.4]x10
\n-4
\n for the various benchmark 
\nbuilding designs. In the development of these results, we made the following observations that 
\nare expected to be broadly applicable: 
\n(1) The ground motions selected for performance simulations must consider spectral 
\nshape (e.g., through use of the epsilon parameter) and should appropriately account for 
\ncorrelations between motions in both horizontal directions; 
\n(2) Lower-bound component models, which are commonly used in performance-based 
\nassessment procedures such as FEMA 356, can significantly bias collapse analysis results; it is 
\nmore appropriate to use median component behavior, including all aspects of the component 
\nmodel (strength, stiffness, deformation capacity, cyclic deterioration, etc.); 
\n(3) Structural modeling uncertainties related to component deformation capacity and 
\npost-peak degrading stiffness can impact the variability of calculated collapse probabilities and 
\nmean annual rates to a similar degree as record-to-record variability of ground motions. 
\nTherefore, including the effects of such structural modeling uncertainties significantly increases 
\nthe mean annual collapse rates. We found this increase to be roughly four to eight times relative 
\nto rates evaluated for the median structural model; 
\n(4) Nonlinear response analyses revealed at least six distinct collapse mechanisms, the 
\nmost common of which was a story mechanism in the third story (differing from the multi-story 
\nmechanism predicted by nonlinear static pushover analysis); 
\n(5) Soil-foundation-structure interaction effects did not significantly affect the structural 
\nresponse, which was expected given the relatively flexible superstructure and stiff soils. 
\nThe potential for financial loss is considerable. Overall, the calculated expected annual 
\nlosses (EAL) are in the range of $52,000 to $97,000 for the various code-conforming benchmark 
\nbuilding designs, or roughly 1% of the replacement cost of the building ($8.8M). These losses 
\nare dominated by the expected repair costs of the wallboard partitions (including interior paint) and by the structural members. Loss estimates are sensitive to details of the structural models, 
\nespecially the initial stiffness of the structural elements. Losses are also found to be sensitive to 
\nstructural modeling choices, such as ignoring the tensile strength of the concrete (40% change in 
\nEAL) or the contribution of the gravity frames to overall building stiffness and strength (15% 
\nchange in EAL). 
\nAlthough there are a number of factors identified in the literature as likely to affect the 
\nrisk of human injury during seismic events, the casualty modeling in this study focuses on those 
\nfactors (building collapse, building occupancy, and spatial location of building occupants) that 
\ndirectly inform the building design process. The expected annual number of fatalities is 
\ncalculated for the benchmark building, assuming that an earthquake can occur at any time of any 
\nday with equal probability and using fatality probabilities conditioned on structural collapse and 
\nbased on empirical data. The expected annual number of fatalities for the code-conforming 
\nbuildings ranges between 0.05*10
\n-2
\n and 0.21*10
\n-2
\n, and is equal to 2.30*10
\n-2
\n for a non-code 
\nconforming design. The expected loss of life during a seismic event is perhaps the decision 
\nvariable that owners and policy makers will be most interested in mitigating. The fatality 
\nestimation carried out for the benchmark building provides a methodology for comparing this 
\nimportant value for various building designs, and enables informed decision making during the 
\ndesign process. 
\nThe expected annual loss associated with fatalities caused by building earthquake damage 
\nis estimated by converting the expected annual number of fatalities into economic terms. 
\nAssuming the value of a human life is $3.5M, the fatality rate translates to an EAL due to 
\nfatalities of $3,500 to $5,600 for the code-conforming designs, and $79,800 for the non-code 
\nconforming design. Compared to the EAL due to repair costs of the code-conforming designs, 
\nwhich are on the order of $66,000, the monetary value associated with life loss is small, 
\nsuggesting that the governing factor in this respect will be the maximum permissible life-safety 
\nrisk deemed by the public (or its representative government) to be appropriate for buildings. 
\nAlthough the focus of this report is on one specific building, it can be used as a reference 
\nfor other types of structures. This report is organized in such a way that the individual core 
\nchapters (4, 5, and 6) can be read independently. Chapter 1 provides background on the 
\nperformance-based earthquake engineering (PBEE) approach. Chapter 2 presents the 
\nimplementation of the PBEE methodology of the PEER framework, as applied to the benchmark 
\nbuilding. Chapter 3 sets the stage for the choices of location and basic structural design. The subsequent core chapters focus on the hazard analysis (Chapter 4), the structural analysis 
\n(Chapter 5), and the damage and loss analyses (Chapter 6). Although the report is self-contained, 
\nreaders interested in additional details can find them in the appendices.