Conditional spectrum (CS) record selection is a standard tool for the selection of ground motion ... more Conditional spectrum (CS) record selection is a standard tool for the selection of ground motion recordings consistent with the hazard at a site of interest. For many important applications the seismic hazard is computed for reference rock conditions and the effects of local site conditions are investigated downstream via soil dynamics. Ideally, when selecting for rock conditions, the recordings should be real, recorded on rock sites, and strong enough to push the structure into its severe nonlinear range. However, rock-recorded ground motions are often scarce and the analyst is usually left with the suboptimal option of augmenting the set with scaled motions and motions recorded at soil stations. We investigated how this practice can affect the structural response estimates by means of nonlinear dynamic analyses of a comprehensive set of single-degree-of-freedom (SDOF) systems. We first performed site and structure-specific CS record selection using ground motion databases of only soil-recorded motions versus databases of only rock recorded ones. In addition, we performed the CS based on extreme cases of using ground motions scaled by either only small or only large factors. Our focus was on the statistical comparison of the common intensity measures (IMs) of the selected records and, more importantly, of the structural response estimates when these extreme opposite selection choices are made. We show no significant statistical differences in the distributions of the IMs and structural responses, while the fragility and response hazard remain almost identical, for all practical purposes. These results imply that, as long as hazard consistency is accurately enforced in the ground motion record selection, using CS, selecting soil-recorded motions or record scaled up to 10, will not bias the response estimates. Finally, repeating the above procedure for response prediction of one multiple degrees of freedom (MDOF) system suggests that our conclusions are applicable also to more complex structural systems.
iii ACKNOWLEDGMENTS iv CONTENTS v LIST OF FIGURES vii LIST OF TABLES xi 1 GUIDELINES AND PROCEDUR... more iii ACKNOWLEDGMENTS iv CONTENTS v LIST OF FIGURES vii LIST OF TABLES xi 1 GUIDELINES AND PROCEDURE 1 1.1 Objective 1 1.2 PG&E Building Inventory 3 1.3 Procedure 4 1.4 Discussion of the Six Steps 7 1.4.1 Step 1: Nonlinear Static Procedure (NSP) Curve for Intact Building 7 1.4.2 Step 2: NSP Curves for Damaged Building 11 1.4.3 Step 3: Inferring Dynamic Response from Static Response 13 1.4.3.1 Intact Structure 15 1.4.3.2 Damaged Structure 16 1.4.4 Step 4: Occupancy Status for Damaged Building 24 1.4.5 Step 5: Ground Motion Level Associated with Structural Limit State 36 1.4.6 Step 6: Computation of Fragility Curves 45 2 APPLICATION OF THE GUIDELINES 51 2.1 Case Study No. 1: Three-Story Steel Moment-Resisting Frame (SMRF) Building...... 51 2.1.1 Structural Model 52 2.1.2 Connection Model 52 2.1.3 Application of the Guidelines 53 2.1.3.1 Step 1: NSP of Intact Structure and Identification of Damage States.... 53 2.1.3.2 Step 2: NSP Curves for Damaged Structure 54 2.1.3.3 Step 3: From SPO to IDA 56 2.1.3.4 Step 4: Occupancy Status for Damaged Building 64 2.1.3.5 Step 5: Ground Motion Level at Incipient Structural Limit State 65 2.1.3.6 Step 6: Computation of Fragility Curves 66 2.1.4 Validation 67 2.2 Case Study No. 2: Tilt-up Building 69 2.2.1 Structural Model 70
Page 1. Multidirectional Seismic Excitation Effects in Building Response Estimation: Collaborativ... more Page 1. Multidirectional Seismic Excitation Effects in Building Response Estimation: Collaborative Research with USGS (Dr. Nicolas Luco) and AIR AWARD No. 06HQGR0011 Drs. ... in collaboration with Dr. Nicolas Luco(USGS) ...
Earthquake Engineering & Structural Dynamics, May 31, 2023
Design spectra are commonly defined for a constant value of hazard associated to an “ultimate” li... more Design spectra are commonly defined for a constant value of hazard associated to an “ultimate” limit state (LS) of reference, typically 10% in 50 years. Given a specific structure, this approach results in different limit‐state exceedance risk levels even for sites characterized by the same design peak ground acceleration (PGA), mainly because of differences in hazard curve shape/slope. Instead, Risk Targeted design maps (first applied in ASCE7‐10) suggest the application of suitable spectra adjustment factors, the so‐called risk coefficients, in order to ensure a uniform collapse risk across different sites and buildings. Making use of simplified single‐degree‐of‐freedom (SDoF) structures for several configurations of vibration period and ductility, we test the effectiveness of the adjustment factors computed under different assumptions in matching a specific target risk or, at least, in harmonizing the risk of multiple buildings at different sites with respect to different LSs. Although risk matching is shown to be only theoretically possible and unachievable in practice, we claim that harmonization remains a viable target, and we offer insights for possible future adoption of Risk Targeted Spectra in the European code provisions.
This paper introduces First-Order Reliability Methods (FORM) and presents in a condensed form exa... more This paper introduces First-Order Reliability Methods (FORM) and presents in a condensed form examples from recent applications of FORM in structural analyses.
Present building-specific loss assessment state-of-art involves the convolution of seismic hazard... more Present building-specific loss assessment state-of-art involves the convolution of seismic hazard and building seismic demands. The latter is conditioned on spectral acceleration, Sa( T1), at the building's first mode as the ground motion intensity measure (IM) and is typically estimated by carrying out nonlinear dynamic analyses on a two-dimensional (2-D) model. By new proposals on the use of improved IMs that can introduce higher fidelity, the accuracy in loss estimation becomes an open question. In reply, we offer a uniform basis for comparing the loss estimates for a set of eight different scalar and vector IMs whose hazard can be predicted with existing GMPEs. Despite all eight being legitimate IMs, and despite the consistent use of conditional spectrum record selection, we find large differences in the estimated loss hazard. This points to the large uncertainty still lingering when connecting hazard to loss. Among the IMs considered here, the vector IMs and at least a scalar average of spectral accelerations showed a remarkable stability in their predictions for the three-dimensional (3-D) buildings, pointing to a potential for reliable applications.
. Understanding seismic risk at both the national and sub-national levels is essential for devisi... more . Understanding seismic risk at both the national and sub-national levels is essential for devising effective strategies and interventions aimed at its mitigation. The National Earthquake Risk Model of Switzerland (ERM-CH23), released in early 2023, is the culmination of a multidisciplinary effort aiming to achieve, for the first time, a comprehensive assessment of the potential consequences of earthquakes on the Swiss building stock and population. Having been developed as a national model, ERM-CH23 relies on very high-resolution site-amplification and building exposure datasets, which distinguishes it from most regional models to-date. Several loss types are evaluated, ranging from structural/nonstructural and contents economic losses, to human losses, such as deaths, injuries and displaced population. In this paper, we offer a snapshot of ERM-CH23, summarize key details on the development of its components, highlight important results and provide comparisons with other models.
Conditional spectrum (CS) record selection is a standard tool for the selection of ground motion ... more Conditional spectrum (CS) record selection is a standard tool for the selection of ground motion recordings consistent with the hazard at a site of interest. For many important applications the seismic hazard is computed for reference rock conditions and the effects of local site conditions are investigated downstream via soil dynamics. Ideally, when selecting for rock conditions, the recordings should be real, recorded on rock sites, and strong enough to push the structure into its severe nonlinear range. However, rock-recorded ground motions are often scarce and the analyst is usually left with the suboptimal option of augmenting the set with scaled motions and motions recorded at soil stations. We investigated how this practice can affect the structural response estimates by means of nonlinear dynamic analyses of a comprehensive set of single-degree-of-freedom (SDOF) systems. We first performed site and structure-specific CS record selection using ground motion databases of only soil-recorded motions versus databases of only rock recorded ones. In addition, we performed the CS based on extreme cases of using ground motions scaled by either only small or only large factors. Our focus was on the statistical comparison of the common intensity measures (IMs) of the selected records and, more importantly, of the structural response estimates when these extreme opposite selection choices are made. We show no significant statistical differences in the distributions of the IMs and structural responses, while the fragility and response hazard remain almost identical, for all practical purposes. These results imply that, as long as hazard consistency is accurately enforced in the ground motion record selection, using CS, selecting soil-recorded motions or record scaled up to 10, will not bias the response estimates. Finally, repeating the above procedure for response prediction of one multiple degrees of freedom (MDOF) system suggests that our conclusions are applicable also to more complex structural systems.
iii ACKNOWLEDGMENTS iv CONTENTS v LIST OF FIGURES vii LIST OF TABLES xi 1 GUIDELINES AND PROCEDUR... more iii ACKNOWLEDGMENTS iv CONTENTS v LIST OF FIGURES vii LIST OF TABLES xi 1 GUIDELINES AND PROCEDURE 1 1.1 Objective 1 1.2 PG&E Building Inventory 3 1.3 Procedure 4 1.4 Discussion of the Six Steps 7 1.4.1 Step 1: Nonlinear Static Procedure (NSP) Curve for Intact Building 7 1.4.2 Step 2: NSP Curves for Damaged Building 11 1.4.3 Step 3: Inferring Dynamic Response from Static Response 13 1.4.3.1 Intact Structure 15 1.4.3.2 Damaged Structure 16 1.4.4 Step 4: Occupancy Status for Damaged Building 24 1.4.5 Step 5: Ground Motion Level Associated with Structural Limit State 36 1.4.6 Step 6: Computation of Fragility Curves 45 2 APPLICATION OF THE GUIDELINES 51 2.1 Case Study No. 1: Three-Story Steel Moment-Resisting Frame (SMRF) Building...... 51 2.1.1 Structural Model 52 2.1.2 Connection Model 52 2.1.3 Application of the Guidelines 53 2.1.3.1 Step 1: NSP of Intact Structure and Identification of Damage States.... 53 2.1.3.2 Step 2: NSP Curves for Damaged Structure 54 2.1.3.3 Step 3: From SPO to IDA 56 2.1.3.4 Step 4: Occupancy Status for Damaged Building 64 2.1.3.5 Step 5: Ground Motion Level at Incipient Structural Limit State 65 2.1.3.6 Step 6: Computation of Fragility Curves 66 2.1.4 Validation 67 2.2 Case Study No. 2: Tilt-up Building 69 2.2.1 Structural Model 70
Page 1. Multidirectional Seismic Excitation Effects in Building Response Estimation: Collaborativ... more Page 1. Multidirectional Seismic Excitation Effects in Building Response Estimation: Collaborative Research with USGS (Dr. Nicolas Luco) and AIR AWARD No. 06HQGR0011 Drs. ... in collaboration with Dr. Nicolas Luco(USGS) ...
Earthquake Engineering & Structural Dynamics, May 31, 2023
Design spectra are commonly defined for a constant value of hazard associated to an “ultimate” li... more Design spectra are commonly defined for a constant value of hazard associated to an “ultimate” limit state (LS) of reference, typically 10% in 50 years. Given a specific structure, this approach results in different limit‐state exceedance risk levels even for sites characterized by the same design peak ground acceleration (PGA), mainly because of differences in hazard curve shape/slope. Instead, Risk Targeted design maps (first applied in ASCE7‐10) suggest the application of suitable spectra adjustment factors, the so‐called risk coefficients, in order to ensure a uniform collapse risk across different sites and buildings. Making use of simplified single‐degree‐of‐freedom (SDoF) structures for several configurations of vibration period and ductility, we test the effectiveness of the adjustment factors computed under different assumptions in matching a specific target risk or, at least, in harmonizing the risk of multiple buildings at different sites with respect to different LSs. Although risk matching is shown to be only theoretically possible and unachievable in practice, we claim that harmonization remains a viable target, and we offer insights for possible future adoption of Risk Targeted Spectra in the European code provisions.
This paper introduces First-Order Reliability Methods (FORM) and presents in a condensed form exa... more This paper introduces First-Order Reliability Methods (FORM) and presents in a condensed form examples from recent applications of FORM in structural analyses.
Present building-specific loss assessment state-of-art involves the convolution of seismic hazard... more Present building-specific loss assessment state-of-art involves the convolution of seismic hazard and building seismic demands. The latter is conditioned on spectral acceleration, Sa( T1), at the building's first mode as the ground motion intensity measure (IM) and is typically estimated by carrying out nonlinear dynamic analyses on a two-dimensional (2-D) model. By new proposals on the use of improved IMs that can introduce higher fidelity, the accuracy in loss estimation becomes an open question. In reply, we offer a uniform basis for comparing the loss estimates for a set of eight different scalar and vector IMs whose hazard can be predicted with existing GMPEs. Despite all eight being legitimate IMs, and despite the consistent use of conditional spectrum record selection, we find large differences in the estimated loss hazard. This points to the large uncertainty still lingering when connecting hazard to loss. Among the IMs considered here, the vector IMs and at least a scalar average of spectral accelerations showed a remarkable stability in their predictions for the three-dimensional (3-D) buildings, pointing to a potential for reliable applications.
. Understanding seismic risk at both the national and sub-national levels is essential for devisi... more . Understanding seismic risk at both the national and sub-national levels is essential for devising effective strategies and interventions aimed at its mitigation. The National Earthquake Risk Model of Switzerland (ERM-CH23), released in early 2023, is the culmination of a multidisciplinary effort aiming to achieve, for the first time, a comprehensive assessment of the potential consequences of earthquakes on the Swiss building stock and population. Having been developed as a national model, ERM-CH23 relies on very high-resolution site-amplification and building exposure datasets, which distinguishes it from most regional models to-date. Several loss types are evaluated, ranging from structural/nonstructural and contents economic losses, to human losses, such as deaths, injuries and displaced population. In this paper, we offer a snapshot of ERM-CH23, summarize key details on the development of its components, highlight important results and provide comparisons with other models.
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