Introduction
Building code provisions for earthquake safety have largely been developed based on judgment informed by observed performance of buildings in past earthquakes, laboratory testing of structural components, and analysis of idealized models. While building codes imply that code-conforming structures have a low likelihood of collapsing, the actual safety of modern code-conforming buildings is unknown, as is the safety of structures built according to earlier out-dated building codes.
Recent developments in earthquake engineering research have enabled simulation of structural collapse under seismic loading, providing quantitative measures of collapse risk. Using these tools, we examine the seismic collapse risk of reinforced concrete (RC) frame structures in the U.S. By assessing the collapse safety of modern code-conforming structures, we “benchmark” the safety provided by current code provisions. These assessments are useful in quantifying the relative safety of different building systems and the impact of changes to design requirements, and to quantify the effectiveness of retrofitting to reduce the collapse risk of older, non-ductile structures.
As part of this research, the authors have worked closely with researchers and practitioners involved in the ATC-63 project of the Applied Technology Council. The ATC-63 effort has developed a systematic method to assess collapse safety, for the purpose of assessing the adequacy of newly proposed structural design standards and building code provisions (ATC 2007). The collapse performance assessments described here have contributed to the development and validation of the ATC-63 methodology.
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(b)
Figure 1. Analytical model for frame structures, showing
(a) generalized 2D model configuration and
(b) nonlinear material features of beam-column hinges.
Figure 2. Calibration of RC beam-column model to experimental test by Saatcioglu and Grira (1999) [specimen BG-6].
Methodology for Performance-Based Collapse Assessment
To evaluate structural collapse performance we use the performance-based earthquake engineering (PBEE) methodology developed by the Pacific Earthquake Engineering Research (PEER) Center, which provides a overall framework for relating ground motion intensity to the structural response through analytical models and structural simulation, and finally to potential dollar losses, deaths and downtime (Deierlein 2004). This study focuses on collapse prediction, accomplished through inelastic dynamic analysis to directly simulate sidesway collapse.
Simulation of global sidesway collapse is based on the incremental dynamic analysis technique (Vamvatsikos and Cornell, 2003). In incremental dynamic analysis, an analysis model is subjected to a recorded ground motion, and the motion is scaled to increased intensity until the building becomes dynamically unstable and collapse occurs. This process is repeated for a suite of ground motion records. Collapse performance is represented by a cumulative distribution function, which describes the probability of collapse as a function of ground motion intensity. This collapse distribution is corrected to account for the spectral shape of rare ground motions (Haselton and Deierlein 2007) and the effect of uncertainties in modeling parameters (Liel et al. 2007).
Nonlinear Modeling of Reinforced Concrete Frames
Nonlinear time-history analysis is a central ingredient of the collapse assessment, the accuracy of which depends on how faithfully the model captures the strength and stiffness degradation that causes structural collapse. In this study, the reinforced concrete frames are modeled using the two-dimensional, three-bay model shown in Figure 1a. The beams, columns and beam-column joints are modeled using hinge models developed by Ibarra et al. (2005) that capture the post-peak softening branch of the monotonic backbone curve and the degrading hysteretic response. These features are essential to simulating collapse due to the combined effects of inelastic softening and P-Δ effects. To determine the modeling parameters for reinforced concrete beam-columns, Haselton et al. (2007) calibrated the concentrated spring model to results from more than 250 experimental tests. A comparison of the cyclic test data with model predictions for one of these columns is illustrated in Figure 2.
Collapse Assessments, and Building Code Applications
Collapse Predictions for Code-Conforming Reinforced Concrete Moment Frames
Using the method and models described above, Haselton and Deierlein (2007) assessed the collapse risk of 30 code-conforming reinforced concrete special moment frame structures, designed for a high seismic site in California. All structures are office buildings, and were fully designed according to the governing code provisions (2003 IBC, ASCE 7-02 and ACI 318-02). Haselton examined both space and perimeter frame systems with heights ranging from 1 to 20 stories. The results are illustrated in Figure 3a in terms of the conditional probability of collapse, that is the probability of collapse of the structure given that a rare ground motion (with 2% likelihood of being exceeded in 50 years) occurs. The collapse results are relatively consistent over structures of different heights, though the 1-story and mid-rise (8- and 12-stories) have slightly worst performance. It is clear that perimeter frame structures have consistently higher collapse risk than the space frame structures. Space frames tend to have higher lateral overstrength because the relative dominance of gravity and lateral loads in the design. In addition, perimeter frames are more flexible, which increases P-Δ effects, causing deformations to concentrate in a smaller number of stories.
The collapse assessment methodology also allows us to directly evaluate the effects of changes to building code provisions. In ASCE 7-05, the minimum base shear requirement was changed from the previous 2002 edition, leading to a significant reduction in design base shear for tall buildings at some sites. To examine the impacts of the revised provisions, Haselton redesigned the 12- and 20-story buildings according to ASCE7-05. Because of the reduced minimum base shear requirement, these structures have a lower design base shear than their ASCE 7-02 counterparts (eg. the design base shear of the 20-story building decreased from 0.044g to 0.022g). Figure 3b shows the collapse safety predictions for these redesigned (ASCE7-05) structures. Under the 2% in 50 year ground motion, the buildings designed according to ASCE 7-05 have a significantly higher probability of collapse. We also observe that the collapse safety of the ASCE 7-05 buildings reduces significantly as building height increases, and the predominant collapse mechanism tends to be more localized for the weaker ASCE 7-05 designs. These findings suggest that the minimum base shear requirement in ASCE 7-02 are an important component of ensuring relatively consistent collapse risk for buildings of varying height. Based largely on this study, the ASCE 7 committee has recently issued an addendum to reinstitute the minimum base shear requirement of the previous 2002 edition.
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Figure 3. Predicted collapse performance of reinforced concrete special moment frames, measured in terms of probability of collapse for a 2% in 50 year ground motion. Comparison of figures (a) and (b) illustrates the minimum base shear requirements change between ASCE 7-02 and ASCE 7-05. The building images show the predominant collapse mechanism for the 12-story structure, which is more localized for the weaker ASCE 7-05 designs.
Comparison of Modern and Older RC Moment Frames
This collapse assessment procedure can also be used to evaluate the performance of structures designed according to out-dated building codes. Liel has assessed the seismic collapse risk of California’s older (pre-1975) reinforced concrete frame structures, whose deficiencies, principally the lack of ductile detailing of reinforcement and potentially brittle failure modes, have been exposed by damage in past earthquakes. This study is based on the design, modeling and assessment of 26 non-ductile reinforced concrete frame structures designed according to the 1967 Uniform Building Code. These structures are designed for the same Los Angeles site as the code-conforming structures. We also use the same model (Figure 1), though the parameters defining the monotonic and cyclic behavior of beams and columns reflect the reduced ductility of these systems, and possible joint shear failure is explicitly modeled. In addition, we examined and modified results of the dynamic analysis account for column shear failure. As shown in Figure 4, the 1967 moment frames have a significantly larger probability of collapse than the code conforming structures. When collapse safety is measured instead in terms of collapse rate (mean annual frequency of collapse), we find that the older reinforced concrete frame structures are approximately 40 times more likely to collapse than the code-conforming reinforced concrete frame structures. These metrics can be used to explicitly evaluate the costs and benefits of retrofitting these deficient structures.
Figure 4. Predicted collapse performance of code-conforming (2003) and existing (1967) reinforced concrete moment frames.
Due to changes in building code provisions, particularly related to reinforcement detailing and capacity design, the 2003 structures are much safer.
Conclusions
As described here, quantitative assessment of collapse performance for the first time allows us to compare the collapse safety of different structures and structural systems in order to systematically examine the implications of design standards and provisions. These assessments are enabled by research to improve understanding of ground motions and their effects on structural response, nonlinear behavior and computer response simulation of structures, and practical probabilistic approaches to account for the inherent uncertainties in design and analysis. The ATC-63 project has implemented these advancements in a practical framework to assess the collapse safety of buildings and their underlying design basis.
References
American Concrete Institute. (2005). Building Code Requirements for Structural Concrete (ACI 318-05) and Commentary (ACI 318R-05), Farmington Hills, MI.
American Society of Civil Engineers. (2005). ASCE7-05: Minimum Design Loads for Buildings and Other Structures, Reston, VA.
American Society of Civil Engineers. (2002). ASCE7-02: Minimum Design Loads for Buildings and Other Structures, Reston, VA.
ATC 63 (2007), “Recommended Methodology for Quantification of Building System Performance and Response Parameters,” 75% Interim Draft Report, Applied Technology Council, Redwood City, CA.
Deierlein, G.G. (2004). “Overview of a Comprehensive Framework for Earthquake Performance Assessment,” Performance-Based Seismic Design Concepts and Implementation, Proceedings of an International Workshop, Bled Slovenia, P. Fajfar and H. Krawinkler, Eds. PEER Report 2004/05, pp. 15-26.
Haselton, C.B., and Deierlein, G.G. (2007), “Assessing Seismic Collapse Safety of Modern Reinforced Concrete Moment Frame Buildings,” Blume Center TR 156, Stanford University, CA.
Ibarra, L.F., Medina, R.A., and Krawinkler, H. (2005). “Hysteretic models that incorporate strength and stiffness deterioration,” Earthquake Engineering and Structural Dynamics, Vol. 34, pp. 1489-1511.
Liel, A.B., C.B. Haselton, G.G. Deierlein and J.W. Baker, “Incorporating Modeling Uncertainties in the Assessment of Seismic Collapse Risk of Buildings,” Structural Safety (accepted).
Saatcioglu, M and Grira, M. (1999). “Confinement of Reinforced Concrete Columns with Welded Reinforcement Grids,” ACI Structural Journal, American Concrete Institute, Vol. 96, No. 1, January-February 1999, pp. 29-39.
Vamvatsikos, D. and C. Allin Cornell (2002). “Incremental Dynamic Analysis,” Earthquake Engineering and Structural Dynamics, Vol. 31, Issue 3, pp. 491-514.
Acknowledgments
The support of the Pacific Earthquake Engineering Research Center, the Applied Technology Council and the National Science Foundation (Graduate Research Fellows Program) is gratefully acknowledged.
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