Performance‐based earthquake engineering (PBEE) is a probabilistic framework developed to improve seismic risk decision‐making, characterising building performance in terms of metrics such as ...casualties, economic losses and anticipated downtime. Building upon PBEE, expected annual loss (EAL) and collapse safety expressed in terms of mean annual frequency of collapse (MAFC) have been recently proposed as fundamental objectives within an integrated performance‐based seismic design (IPBSD) framework. This article, following the parametric investigations conducted, proposes a refined design loss curve and demonstrates the capabilities of IPBSD to target a certain MAFC and limit EAL through its application to several reinforced concrete case‐study buildings. The performance was evaluated using both incremental dynamic analysis and a storey‐based loss assessment procedure to estimate MAFC and EAL of risk‐targeted designs, respectively. The agreement and consistency of design solutions and intended performance objectives were then checked to demonstrate the validity of the IPBSD framework, with MAFC being effectively targeted and the EAL limited as initially foreseen by the method. Further scrutiny of the results highlighted the validity of the assumptions made in the IPBSD framework and shed further light on the pertinent sources of economic losses, namely the ones deriving from structural and non‐structural elements, when designing buildings, in addition to influential parameters like initial period range and the influence of design engineering demand parameter profiles. This is seen as part of the next‐generation risk‐targeted and loss‐driven design approaches in line with modern PBEE requirements.
Summary
Decision models for the verification of seismic collapse safety of buildings are introduced. The derivations are based on the concept of the acceptable (target) annual probability of ...collapse, whereas the decision making involves comparisons between seismic demand and capacity, which is familiar to engineering practitioners. Seismic demand, which corresponds to the design seismic action associated with a selected return period, can be expressed either in terms of an intensity measure (IM) or an engineering demand parameter (EDP). Seismic capacity, on the other hand, is defined by dividing the near‐collapse limit‐state IM or EDP by an appropriate risk‐targeted safety factor (γim or γedp), which is the only safety factor used in the proposed decision model. Consequently, the seismic performance assessment of a building should be based on the best possible estimate. For a case study, it is shown that if the target collapse risk is set to 10−4 (0.5% over a period of 50 years), and if the seismic demand corresponds to a return period of 475 years (10% over a period of 50 years), then it can be demonstrated that γim is approximately equal to 2.5 for very stiff buildings, whereas for buildings with long periods the value of γim can increase up to a value of approximately 5. The model using γedp is equal to that using γim only if it can be assumed that displacements, with consideration of nonlinear behavior, are equal to displacements from linear elastic analysis.
The problem of seismic fragility and risk assessment of Reinforced Concrete (RC) structures considering aging due to corrosion is addressed. Aging of RC structures is often followed by deterioration ...mechanisms, such as corrosion of the reinforcing steel due to chloride ions, especially in marine environments. The corrosion model adopted is a combination of equations that exist in the literature while the parameters that primarily affect the initiation of corrosion were defined performing a sensitivity analysis. Furthermore, the paper aims to shed light on what are the cover values that minimize the effect of chloride-induced corrosion and thus improve the seismic performance during the lifetime of a structure that is built in corrosive environments. For this purpose, a risk-targeted design methodology is proposed in order to determine the minimum cover depth values for the desired target risk. A four storey RC building designed according to contemporary code provisions is adopted as a case study in order to investigate the methodology proposed.
Abstract
In the ongoing quest for improved seismic design codes, there is currently substantial focus on risk‐targeted design, which aims to achieve more uniform seismic risk across code‐compliant ...buildings. Such an approach has already been adopted in ASCE 7, which uses lognormal fragility functions, with a single assumed value for dispersion, to generate uniform risk spectra. One challenge to this approach is that fragility functions have been shown to vary depending on the site being considered. This article, therefore, explores the extent to which site location influences the dispersion of fragility functions through the study of inelastic single‐degree‐of‐freedom systems. Twenty‐four different sites across New Zealand are considered so that a diverse range of seismic hazard settings, including multiple tectonic region types, are examined. The resulting dispersion values for the cases examined range from 0.14 to 0.29 and they are shown to be influenced by both the spectral shape and variance of the target spectra used for ground motion selection. The study is then extended to the consideration of scenario‐based seismic risk analysis. It is shown that fragility functions derived using ground motions selected on the basis of probabilistic seismic hazard analysis are, in theory, not suitable for use in scenario‐based risk analyses. The potential ramifications of this work on other risk‐targeted design methods are also discussed. Overall, this work sheds important light on the importance and potential implications of site dependence for what concerns risk‐targeted design.
The approximation of seismic hazard curve H(x) affects the determination of risk-targeted design ground motion SaR significantly. The traditional first-order approximation of H(x) for obtaining SaR ...may result in a relatively large error. Therefore, this study employs a second-order approximation of H(x) with three parameters to define the fitted parabolic functions. Three scenarios are proposed to determine the second-order approximation of H(x). Scenario 1 utilizes the ground motion intensity values of the three points along with their corresponding annual exceedance probabilities. Scenario 2 is essentially the same as scenario 1, with the difference that scenario 2 uses the tangent of the parabola at the frequent-level earthquake when the ground motion intensity is less than that of the frequent-level earthquake. Scenario 3 involves the utilization of two points and a symmetry axis. The suitability of the three scenarios is verified by comparing the risk-targeted maximum considered earthquake (MCER) obtained from the approximated H(x) with that from the actual H(x). The suitability is further examined by studying the ground motion intensity interval which significantly affects the determination of SaR through the lower and upper integration limits. Subsequently, the maps of MCER, collapse risk, and risk coefficient (i.e., the ratio of MCER to MCE) for mainland China are developed, and the sensitivity analysis is studied. It is shown that the ranges of the collapse risk in 50 years and risk coefficients for mainland China are 0.86%–1.03 % and 0.94–1.01, respectively. Therefore, only minor adjustments to the MCE in the current Chinese seismic design code are required to achieve the target collapse risk of 1 % in 50 years.
•Three scenarios are proposed for second-order seismic hazard curve approximation.•Ground motion intensity interval that significantly impacts RTGM is determined.•Sensitivity analysis for RTGM is conducted with various decision parameters.
Abstract The design of structures depends on the performance requirements that are usually defined through structural codes for single units. This approach may not be optimal because major ...earthquakes affect the built environment and can also trigger domino effects due to fires, explosions or toxic dispersion. To overcome this issue, we introduce a probabilistic framework for defining unit performance requirements by means of risk‐targeted fragility functions that account for potential domino effects and an overall system performance requirement. The system performance requirement is demonstrated by the potential loss of life, which represents the tolerated number of fatalities per year expected in the earthquake‐affected area. The proposed framework decomposes the problem into a damage‐based fatality analysis, population analysis and seismic hazard analysis, which can be performed and improved independently by engineers with the relevant expertise. The damage‐based fatality analysis includes a series of Monte Carlo simulations using logic trees to account for domino effects. These analyses are then coupled with an iterative risk estimation aimed at identifying the critical units in a system and estimating their risk‐targeted fragility functions, which can then be used for the design of a single unit. The methodology is demonstrated by estimating the potential loss of life due to a seismic event in an urban industrial area. It is shown that the risk‐targeted fragility functions of hazardous storage tanks can be estimated in a few iterations based on disaggregating the potential loss of life. The pilot research presented in the paper provides new possibilities for defining seismic design parameters of structures.
Abstract
New construction technologies are evolving in the market faster than codes for earthquake‐resistant building design. Earthquake‐resistant design of nearly zero‐energy buildings that are ...constructed throughout Europe and thermally insulated system below the foundation is not yet supported by the codes. However, major earthquakes can cause the sliding of these buildings and damage lifelines, potentially triggering domino effects such as fire or explosions. To address this issue, a numerical framework to evaluate the risk‐targeted engineering demand parameter is introduced and applied to establish a database of risk‐targeted sliding displacements in Slovenia for low‐rise buildings with a specific type of thermally insulated system below foundation pads. The database of risk‐targeted sliding displacement accounts for seismic hazard at the location of the building, the soil type, the thermally insulated foundation pad system variant, and the characteristics of the structure above the thermal insulation layers. The database of the risk‐targeted sliding displacement was then used to introduce a code‐based verification model to design the diameter of the penetration in the structure of low‐rise buildings, with the aim of preventing the failure of hazardous lifelines entering the building. Engineering practitioners can easily apply this simple verification model to design the diameter of the penetrations. However, the model shows that the maximum sliding displacement corresponding to the annual target risk of 2·10
−4
is expected to be only about 4 cm for the thermally base‐insulated low‐rise buildings in Slovenia investigated in this study.
With the introduction of performance-based earthquake engineering (PBEE), engineers have strived to relate building performance to different seismic hazard levels. Expected annual loss (EAL) and ...collapse safety described by mean annual frequency of collapse (MAFC) have become employed more frequently, but tend to be limited to seismic assessment rather than design. This article outlines an integrated performance-based seismic design (IPBSD) method that uses EAL and MAFC as design parameters. With these, as opposed to conventional intensity-based strength and/or drift requirements, IPBSD limits expected monetary losses and maintains a sufficient and quantifiable level of collapse safety in buildings. Through simple procedures, it directly identifies feasible structural solutions without the need for detailed calculations and numerical analysis. This article outlines its implementation alongside other contemporary risk-targeted and code-based approaches. Several case study reinforced concrete frame structures are evaluated using these approaches and the results appraised via verification analysis. The agreement and consistency of the design solutions and the intended targets are evaluated to demonstrate the suitability of each method. The proposed framework is viewed as a stepping stone for seismic design with advanced performance objectives in line with modern PBEE requirements.
Seismic isolation has been used to improve the seismic performance of buildings for the last decades. However, it has been shown that the code-based displacement capacity of isolation members does ...not provide adequate collapse probabilities for different Risk Categories of ASCE 7–16. Seismic design codes stipulate to determine maximum isolator displacement at the Risk-Targeted Maximum Considered Earthquake (MCER) level. Although the code-based isolator displacement capacity is checked with the mean displacement of the MCER level nonlinear time history analysis results, extreme event effects and incorporating uncertainties into fragility curves create additional displacement demands. Therefore, there is a need to amplify the code-based displacement capacity of isolators to obtain sufficient collapse performance. A previous study, assumed elastic behavior and rigid mass model for the superstructure, proposes an iterative probabilistic approach. In the present study, seven different seismically isolated buildings are modeled, and the nonlinear behavior of isolators and superstructures is considered in the incremental dynamic analyses achieved for all models to obtain fragility curves. Although the seismic isolation considerably decreases the spectral accelerations of the superstructure, it is shown that the R-μ-T relations for diaphragm level accelerations, transferred accelerations from base to superstructure, become more sensitive to nonlinear behavior at the superstructure mode periods. The fragility curves of five case study buildings are obtained using the FEMA P695 procedure, and it is figured out that the collapse probability of isolation units is highly correlated with the required isolator displacement to code-based maximum isolator displacement (D/DM) ratio. Then, two simple equations with high correlation coefficients are acquired to estimate the required displacement capacity for prescribed risk-target levels. Further, the obtained equations are verified for two different isolated building models, and their results are compared with the Incremental Dynamic Analysis (IDA) results. The verification results show that the given equations can be used in the preliminary design phase of seismically isolated mid-rise reinforced concrete buildings.
•Code-based displacement capacity of isolators does not provide adequate collapse probabilities.•R-μ-T relations for diaphragm level accelerations become more sensitive to nonlinear behavior.•Collapse probability of isolation unit is highly correlated with the required isolator displacement to code-based maximum isolator displacement ratio. .•Two equations are acquired to estimate the isolator required displacement capacity for prescribed risk-target levels.
•A risk-targeted decision model for the operational limit state is presented.•The limit-state displacement is controlled by the risk-targeted safety factor.•The safety factor depends on the target ...risk, location and seismic intensity measure.•The decision model is demonstrated by designing a pipe rack of a petrochemical plant.
A simplified risk-targeted decision model for the verification of the seismic performance of infrastructure components to the operational limit state is presented. It assumes linearity between the intensity measure and the engineering demand parameter and requires the evaluation of the displacement demand for a hazard-targeted design earthquake and of the displacement capacity. The latter is defined as the ratio between the operational limit-state displacement and a risk-targeted safety factor, which depends on the seismicity of the relevant location, on the randomness of the intensity measures causing the operational limit-state, and on the acceptable (target) probability of exceeding this limit state. In the paper, the theoretical background of risk-targeted safety factor is first explained, followed by a discussion on the sensitivity of the risk-targeted safety factor to the input parameters. The design procedure involving the simplified risk-targeted decision model is then introduced and demonstrated by means of an example of a simple pipe rack located at a petrochemical plant. Within the scope of the presented example, the operational limit-state displacement of the pipe rack is estimated on the basis of the limit-state strains of a pipe attached to the frame. The risk-targeted safety factor is then evaluated, and the frame is designed. It is shown that the application of the proposed procedure is straightforward once the operational limit-state displacement has been determined. The advantage of the procedure is that the target risk is accounted for by the risk-targeted safety factor, which can be calculated with respect to the importance of the equipment of the critical infrastructure. Additionally, the proposed decision model can be easily adopted by engineers, because the seismic demand is calculated by analogy to the Eurocode. However, at this stage of the research, the application of the proposed decision model is limited to structures that do not exhibit any significant nonlinear seismic response at the operational limit state, and to structures where the equal displacement rule applies.
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