Performance-based Seismic Assessment Research Articles

Performance-Based Seismic Assessment of School Building Using Fragility Curve and Capacity-Demand Response Spectrum

Performance-Based Seismic Assessment of School Building Using Fragility Curve and Capacity-Demand Response Spectrum

Study on seismic failure mechanism and damage model of unconstrained adobe block walls

Through the quasi-static cyclic in-plane loading test of three kinds of unconstrained adobe block walls, namely plain adobe wall, modified mud adobe wall and modified adobe wall, the failure mode and seismic performance of each specimen were clarified. Using residual deformation and cumulative energy dissipation as failure parameters, a two-parameter seismic damage model of unconstrained adobe block walls was established. and a calculation method for the adjustment coefficients of energy consumption items was provided. The results showed that the failure mode of the typical unconstrained adobe block wall under earthquake action was not affected by the modification of adobe materials, and the final failure mode was shear failure along the mud crack and the inclined crack extending through the block. Furthermore, the proposed seismic damage model can well reflect the evolution law of earthquake damage of adobe block walls, and the recommended damage index boundary values for five performance levels were given, providing a reference for performance-based seismic design and damage assessment of adobe block walls.

Generation of synthetic spectrum-compatible bi-directional ground motions with specific directionality

Ground motions compatible with the maximum-direction response spectrum (RotD100) condition are emphasized in performance-based design and seismic risk assessment of civil structures in different regions. Due to the complex nature and uncertainty of earthquakes, the comprehensive inclusion of essential characteristics of ground motions is crucial. Recently, the directionality effect of horizontal bi-directional ground motions, representing the variation of the response spectral ordinate amplitude along various directions, on the seismic performance assessment of certain structures or key structural elements has received increasing attention in seismic analysis. However, from the seismic design perspective, there is still a lack of a method that can generate bi-directional ground motions comprehensively reflecting the directionality effect. This study focuses on the correction of ground motion directionality when generating synthetic bi-directional ground motions for a given target response spectrum. An efficient and integrated algorithm is proposed. To demonstrate the applicability of the proposed algorithm, three different target RotD100 response spectra are determined according to modern seismic design codes, and 20 pairs of bi-directional ground motions are generated using the proposed algorithm for each target spectrum. It is shown that with the proposed algorithm, the generated motions present a close match to the target RotD100 response spectrum and meet the specific directionality requirement. In addition, due to the iterative modification of the envelope function, the energy of the generated ground motion is also consistent with the scaled natural records.

The probabilistic performance-based seismic assessment of concrete bridge piers with SMASC reinforcing bars: Effect of pulse-like ground motion and vertical load-to-capacity ratio

Concrete bridge piers are critical components of bridge structures and their performance under seismic loading is of utmost importance. Traditional reinforced concrete bridge piers have shown limitations in terms of residual deformations and seismic resilience. This has led researchers to explore alternative reinforcement materials, such as Shape Memory Alloy (SMA) coupled with steel reinforcing bars, which have demonstrated promising attributes like energy dissipation as well as self-centering capacity. This study aims to fill this gap by evaluating the performance of concrete bridge piers with SMA-Steel coupled (SMASC) reinforcing bars under various intensities of vertical gravity loads and the action of pulse-like ground motion components, throughout a probabilistic framework. To this end, a group of bridge piers with different reinforcement types, including pure steel and SMASC are considered. These piers are subjected to 55 near-fault (NF) pulse-like records as well as 32 far-fault (FF) ground motions, throughout the Incremental Dynamic Analysis (IDA). The influence of distinct frequency components is analyzed by decomposing NF records into low-frequency pulses and high-frequency residual components. Also, the role of pulse to the 1st modal period of the piers (Tp/T1) is investigated by evaluating the piers’ response under the action of NF records, which were clustered into four groups. Results were assessed by evaluating the intensity measure and capacity of the studied piers at the desired performance objectives according to the FHWA manual. Moreover, the mean annual frequencies of exceeding performance limit states and the confidence levels of meeting performance objectives are studied. The results of the study indicate that the dominance of the component of NF ground motions depends on factors such as the intensity of gravity loads, ground motion characteristics, and the Tp/T1 ratio. The components of NF records within certain clusters of the Tp/T1 ratio are necessary for accurate response assessment, while FF records can be used for conservative design purposes, depending on the level of ground motion intensity and the intensity of applied gravity load. The SMASC-reinforced piers with specific λ factors (i.e. λ = 0.5 or λ = 1.0) and low intensity of gravity loads lead to a higher (1.6 times higher) mean annual frequency of exceeding a limit state, compared to pure steel rebars. Also, the confidence levels for meeting performance objectives vary depending on the ground motions, but, as gravity load intensity increases, confidence levels decrease, particularly for piers with a λ factor of 0.5.

Efficient beam-based model for reinforced concrete walls considering shear-flexure interaction

This paper presents an efficient beam-based modelling scheme for the seismic analysis of reinforced concrete structural walls. The model combines a force-based beam element with a fibre section for flexural response and a zero-length element for shear response. The fibre-based element simulates the nonlinear flexural behaviour through uniaxial material laws that account for concrete cracking, concrete crushing, and yielding and rupture of reinforcing bars. The zero-length element represents the shear behaviour with a trilinear lateral force-displacement curve representing, in a phenomenological way, nonlinear deformations caused by diagonal cracking. The reduction of shear resistance caused by inelastic flexural deformations is accounted for in the model to reproduce failures due to shear-flexure interaction. The model has been validated using data from 52 tests on wall specimens exhibiting flexure, shear and mixed shear-flexure modes from experimental campaigns reported in the literature, showing good accuracy in predicting the effective stiffness, maximum strength and displacement capacities obtained in the tests. Model results for ultimate displacement capacity correlate better with experimental results than simplified code-oriented expressions in performance-based evaluation standards and recommendations. Considering its balanced accuracy and computational efficiency, it is concluded that the proposed modelling scheme can effectively be used for performance-based seismic design and assessment of RC wall buildings.

Constant-strength inelastic displacement ratio spectra for assessment of superstructures in seismically isolated buildings

A reliable estimation of maximum displacement demands of seismically isolated inelastic superstructures is crucial for assessment of base-isolated buildings under beyond-design earthquakes. Constant-strength inelastic displacement ratio, CR, spectra, as applied in the performance-based seismic assessment procedure, can be used to estimate the inelastic displacement demands of structures. Currently, a suitable analytical expression of CR is lacking for base-isolated structures considering the influencing parameters comprehensively. This paper seeks to fill this gap. The constant-strength spectra are computed from nonlinear dynamic analyses of simplified two-degree-of-freedom models considering the inelastic behavior of the superstructure and isolator system, using a set of earthquake ground motions recorded on stiff soil sites. The effects of strength reduction factor of superstructure, superstructure elastic period, secondary stiffness ratio of superstructure, mass ratio, isolation period, normalized strength of isolation system and superstructure viscous damping on the mean and dispersion of CR are investigated. In particular, the effects of variations in earthquake intensity and isolator strength on CR are taken into account by the normalized strength of isolation system. Besides, limiting values of CR as the superstructure elastic period tends to zero or infinity are discussed and verified using the statistical values of CR. Finally, based on the trends of CR with respect to the design parameters of the superstructure and isolation system, and the boundary conditions to the CR formula, an analytical estimating equation with reasonable accuracy is developed to approximate the mean constant-strength inelastic displacement ratios during seismic assessment of base-isolated building structures built on stiff soil sites.

Consequences of consequence models: The impact of economies of scale on seismic loss estimates

The detailed evaluation of expected losses and damage experienced by structural and nonstructural components is a fundamental part of performance-based seismic design and assessment. The FEMA P-58 methodology represents the state of the art in this area. Increasing interest in improving structural performance and community resilience has led to widespread adoption of this methodology and the library of component models published with it. This study focuses on the modeling of economies of scale for repair cost calculation and specifically highlights the lack of a definition for aggregate damage, a quantity with considerable influence on the component repair costs. The article illustrates the highly variable and often substantial impact of damage aggregation that can alter total repair costs by more than 25%. Four so-called edge cases representing different damage aggregation methods are introduced to investigate which components experience large differences in their repair costs and under what circumstances. A three-step evaluation strategy is proposed that allows engineers to quickly evaluate the potential impact of damage aggregation on a specific performance assessment. This helps users of currently available assessment tools to recognize and communicate this uncertainty even when the tools they use only support one particular damage aggregation method. A case study of a 9-story building illustrates the proposed strategy and the impact of this ambiguity on the performance of a realistic structure. The article concludes with concrete recommendations toward the development of a more sophisticated model for repair consequence calculation.

Performance Assessment of Reinforced Concrete Bridges Under Coupled Horizontal and Vertical Ground Motions Using Fragility Surfaces

ABSTRACT The objective of this study is to explore the seismic fragility of reinforced concrete bridges, specifically in response to the vertical components of ground motions, utilizing fragility surfaces. The examination of bridge responses involves the application of optimally selected intensity measures through three-dimensional nonlinear time-history analyses, encompassing uncertainties in both superstructure materials and soil–structure interaction effects. In this investigation, an extended Probabilistic Seismic Demand Model (e-PSDM) is employed, leveraging fragility surfaces to concurrently consider vertical and horizontal excitations. The results obtained from this approach are compared with traditional fragility curves. This study emphasizes Pile-cap displacement and drift ratio as pivotal engineering damage parameters, acknowledging their sensitivity to the influences of both soil–structure interaction effects and vertical ground motion. The fragility surfaces derived from the study reveal a correlation between increased vertical spectral accelerations and elevated probabilities of surpassing both slight damage and collapse limit states. These observations underscore the critical significance and practical utility of fragility surfaces in the context of performance-based seismic assessment and design for reinforced concrete bridges. The findings from this research contribute valuable insights into the nuanced behaviour of reinforced concrete bridges under seismic conditions, emphasizing the relevance of incorporating vertical components in fragility assessments for a more comprehensive understanding of structural vulnerability.

Performance-based plastic design and seismic fragility assessment for chevron braced steel frames considering aftershock effects

Observations from past earthquakes demonstrated that buildings in high seismic regions might be exposed to several aftershocks following the mainshock which can significantly increase the damage level. Since aftershocks have the potential to increase the vulnerability of buildings damaged under mainshocks, it is crucial to consider aftershock effects in the structural design phase. Performance-based Plastic Design (PBPD) method is an innovative seismic design method in which the building designed by this method shows a desirable performance under severe ground motions. PBPD allows the designer to avoid time-consuming trial and error process of analyses that are usually done in Performance-based Design method to reach a desirable performance. However, this efficient method is only valid for mainshocks only and does not consider aftershock effects in the structural design process. In this study, initially, the seismic performance (interstory drift and plastic hinges distribution) of the three 3-, 6-, and 9- story PBPD designed Chevron-braced Steel frames (CBSF) are compared under mainshocks (MS) and mainshock-aftershock (MS-AS) sequences. Subsequently, a PBPD method is developed for CBSFs considering the aftershock effects in the structural design process. Incremental dynamic analysis (IDA) has been performed using a suite of mainshocks and aftershock ground motions to develop a design base shear modification factor. Using the developed method, the performance of CBSFs under MS and MS-AS sequences is evaluated and compared with the existing PBPD method. Fragility curves are developed to compare the seismic vulnerability of the frames designed based on PBPD and proposed PBPD methods under MS-AS sequences. The outcomes of this study provide a practical design approach for CBSFs under MS-AS sequences and shows that the structures designed using developed PBPD method show more desirable behavior under MS-AS sequences compared with the structures designed using the conventional PBPD method.

Seismic Repair Cost-Based Assessment for Low-Rise Reinforced Concrete Archetype Buildings through Incremental Dynamic Analysis

This study presents the performance-based seismic assessment of low-rise reinforced concrete archetype buildings, considering repair costs for ordinary moment-resistant frames (OMF) and dual systems consisting of OMF plus special shear walls (SSW). Historically, the OMF systems, conceived for residential purposes in Ecuador resulting from informal construction, have reported poor responses under seismic forces. This study analyzes damage levels through fragility curves as a function of the maximum global drift reached through incremental dynamic analysis. For this, two archetypes with OMF and two with a similar configuration, including structural walls, are modeled to define a loss function and annual collapse probabilities. As a result, it is noted that systems with structural walls significantly reduce repair costs by between 75 and 90% of the total cost of the building, and prevent collapse. Systems with ordinary moment frames report total losses, implying their use should be limited in areas of high seismicity.

Performance-Based Seismic Assessment and Design of Long-Span Concrete Deck Arch Bridges

Performance-Based Seismic Assessment and Design of Long-Span Concrete Deck Arch Bridges

Performance-based seismic design and vulnerability assessment of concrete frame retrofitted by metallic dampers

Concrete frame has been one of the most widely employed structural types in engineering practice and would also have widespread application in the future. However, severe failure even collapse behavior were also detected for the pure concrete frame in strong earthquakes. So it is necessary to improve the seismic performance of pure concrete frame. This paper aims to analyze the seismic performance of metallic damper retrofitted concrete frame. Three concrete frames with metallic damper were selected as the research objects. The performance-based seismic design using the equivalent energy method was employed to design the prototype buildings, in which the multi performance objectives were considered. The concrete beam and column was designed taking the additional forces caused by the metallic damper into consideration. Further, the numerical model of the concrete frame with metallic damper was developed and verified by the test results. Time-history analyses were performed under frequently-occurred, design-based and maximum considered earthquakes to validate that the seismic performance of prototype buildings complied with the design objectives. Subsequently, seismic vulnerability of three prototype buildings were evaluated in terms of non-collapse and collapse fragilities. The analytical results indicated the performance-based design method is suitable to design the concrete frame with metallic dampers and the metallic damper could significantly improve the seismic vulnerability of pure concrete frame. This paper is beneficial for the design and application of metallic damper in concrete frames.

Performance-based seismic assessment of a historical masonry arch bridge: Effect of pulse-like excitations

Seismic analysis of historical masonry bridges is important for authorities in all countries hosting such cultural heritage assets. The masonry arch bridge investigated in this study was built during the Roman period and is on the island of Rhodes, in Greece. Fifteen seismic records were considered and categorized as far-field, pulse-like near-field, and non-pulse-like near-field. The earthquake excitations were scaled to a target spectrum, and nonlinear time-history analyses were performed in the transverse direction. The performance levels were introduced based on the pushover curve, and the post-earthquake damage state of the bridge was examined. According to the results, pulse-like near-field events are more damaging than non-pulse-like near-field ground motions. Additionally the bridge is more vulnerable to far-field excitations than near-field events. Furthermore, the structure will suffer extensive post-earthquake damage and must be retrofitted.

A new framework for ground motion selection for structural seismic assessment

Performance-based structural seismic assessment generally requires the selection of ground motions wherein the target acceleration response spectrum (Sa) should be matched in a desired period range. The pros and cons of the commonly used uniform hazard spectrum (UHS), conditional mean spectrum (CMS) and conditional spectrum (CS) are thoroughly examined. Aiming at combining the merits and overcoming the challenges of these methods, a new framework is proposed to construct a series of conditional target spectra for selecting ground motions. The response spectrum is expressed as the product of peak ground acceleration (PGA) and the normalized spectra (β = Sa/PGA) which can be smoothed by four spectral shape parameters. The proposed framework provides the expected median and covariance of the spectral shape parameters conditioned on specified design values of PGA and PGV/PGA (peak ground velocity/PGA). Efficient step-by-step procedures are developed for the application of the proposed alternative approach, and a sample application is illustrated and compared with the CS approach. It is demonstrated that the proposed methodology is capable of incorporating conventional probabilistic seismic hazard analysis (PSHA), considering spectral shape and spectral variability of realistic ground motions while avoiding the choice of the conditioning period. Site class effects can also be incorporated into the proposed approach.

Non-linear modeling parameters for new construction RC columns

Modeling parameters (MP) of reinforced concrete columns are a critical component of performance-based seismic assessment methodologies because in these approaches damage is estimated based on element deformations calculated using non-linear models. To ensure model fidelity and consistency of assessment results, performance-based seismic assessment methods in ASCE 41, ACI 369.1, and ACI 374.3R prescribe modeling parameters calibrated using experimental data. This paper introduces a new set of equations to calculate reinforced concrete column non-linear modeling parameters optimized for design verification of new buildings using response history analysis. Unlike modeling parameters provided in ACI 369.1 and ASCE 41, intended for columns of older non-ductile buildings, the equations for modeling parameters anl and bnl presented in this study were calibrated to simulate the load-deformation envelope of reinforced concrete columns that meet the detailing requirements of modern seismic design codes. Specifically, the proposed equations are intended for use with provisions in ACI 374.3R, Chapter 18 and Appendix A of ACI 318-19 and Chapter 16 of ASCE/SEI 7-16. The proposed equations were calibrated using the ACI Committee 369 column database, which includes column configuration parameters, material properties, and deformation capacity modeling parameters inferred from the measured response of columns under load reversals. Dimension reduction techniques were applied to visualize different clusters of data in 2D space using the negative log-likelihood score. This technique allowed decreasing the non-linearity of the problem by identifying a subset of columns with load-deformation behavior representative of new construction conforming to current codes requirements. A Neural Network model (NN) was calibrated and used to perform parametric variations to identify the most relevant input parameters and characterize their effect on modeling parameters, and to stablish the degree of non-linearity between each input variable and the model output. Developing equations for modeling parameters applicable to a wide range of columns is challenging, so this research considered subsets of the database representative of new construction columns to calibrate simple practical equations. Linear regression models including the most relevant features from the parametric study were calibrated for rectangular and circular columns. The proposed linear regression equations were found to provide better estimates of new construction column modeling parameters than the available tables in ACI 374.3R and ASCE 41-13, and the equations ASCE 41-17.

Impact of ground-motion duration on nonlinear structural performance: Part I: spectrally equivalent records and inelastic single-degree-of-freedom systems

In current seismic performance-based assessment approaches, nonlinear dynamic analysis of structures generally relies on ground motions selected based on their pseudo-spectral accelerations, with little or no consideration for ground-motion duration. Part I of this study, presented in this article, attempts to comprehensively quantify the impact of ground-motion duration on the nonlinear structural performance of case-study inelastic single-degree-of-freedom systems for shallow-crustal seismicity conditions. The effect of duration is decoupled from that of ground-motion amplitude and spectral shape by assembling sets of spectrally equivalent long- and short-duration records. Such sets are employed in incremental dynamic analyses of a wide range of computational models incorporating in-cycle and cyclic strength and stiffness deterioration. The structural response is quantified in terms of peak- and cumulative-based engineering demand parameters. Formal hypothesis testing is used to assess the statistical significance of duration’s impact on the median structural capacity of the considered structural systems. Furthermore, the derivation of duration-dependent fragility and vulnerability relationships demonstrates that ground-motion duration effectively impacts the nonlinear structural performance of various systems, and it should be accounted for in current practice. The fragility median values for highly deteriorating structural systems under long-duration ground motions are found to be up to 21% or 34.0% smaller than the short-duration counterpart if a peak- or cumulative-based engineering demand parameter is adopted, respectively.

Performance-based seismic assessment of slope systems

The calculated seismic slope displacement provides a valuable index of the seismic performance of earth embankments and natural slopes. Sliding block models are often employed. The specific features of each sliding block method determine its reliability. Rigid sliding block models should not be used except for the limited case when the sliding mass is rigid. A coupled nonlinear deformable stick-slip sliding block model calculates reasonable seismic slope displacements. The primary source of uncertainty in assessing the seismic performance of an earth slope is the input ground motion. Hence, many ground motion records for each tectonic setting should be employed. Seismic slope displacement depends primarily on the earth structure's yield coefficient and the earthquake ground motion's spectral acceleration at the effective fundamental period of the sliding mass. Coupled nonlinear sliding block models enable the sensitivity of the seismic slope displacement and its uncertainty to key input parameters to be assessed. These procedures can be implemented within a performance-based design framework to estimate the seismic slope displacement hazard, which is a more rational approach.

Experimental Investigation on the Performance Levels and Drift Capacity of SRC Columns

To promote the performance-based seismic design and assessment of steel-reinforced concrete (SRC) structures, 27 SRC columns, varying axial load ratio n, steel ratio ρss, and shear span ratio λ, were tested under quasi-static cyclic loadings. The failure modes, hysteretic response, performance levels (PLs), damage states and drift limits of the SRC columns were reported and discussed. The results showed that the failure mode shifted gradually from flexural to shear as λ decreased, but the deformability was not weakened obviously. Six PLs were defined based on the backbone curve of the SRC columns. Each PL was correlated to a damage state that represents a specific macroscopic damage extent. The relative error of drift limits between performance levels and damage states was less than 9% on average. Parametric analysis showed that n and ρss were the most influential factors for drift limits, whereas λ had an ignorable effect. Then, practical regression formulas were established in terms of n and ρss for drift limits of three key PLs (PL1, PL5, and PL6) of the SRC columns, and they were in good agreement with the experimental results. Finally, the average damage indices of PL1 to PL6, calculated using the model proposed in this paper, were 0.26, 0.45, 0.65, 0.83, 0.95, and 0.99, respectively.

Development of Fragility Models for Precast Concrete Shear Walls and Columns Connected by Grouted Sleeves

Performance-based seismic design and assessment of precast concrete (PC) structures have been widely studied. Fragility models for PC components have rarely been developed; however, it is a critical foundation for the above-mentioned design and assessment. Hence, this study was focused on developing fragility models for PC shear walls (PCSWs) and columns (PCCs) connected using grouted sleeves. To this end, 46 full-scale PCSWs and 45 full-scale PCCs, connected using grouted sleeves, were collected, and their test results were analyzed. Six damage states (DSs) were recommended based on the typical damage characteristics and with reference to the associated reinforced concrete (RC) components. Subsequently, the fragility models of PCSW and PCC were established for each DS using the drift ratio as the engineering demand parameter. In addition, the influence of the design axial load ratio on the fragility models was revealed. Through the comparison of fragility models between the PC and RC components, differences in parameters and curves of fragility models were quantitatively compared. These study achievements can serve as valuable references for performance-based seismic design and assessment of PC structures connected using grouted sleeves.

Deformation limits of corroded reinforced concrete columns

Steel reinforcement corrosion is one of the main causes of the mechanical degradation of reinforced concrete (RC) members. Selecting proper performance indexes and quantifying their limits for structural components is an important issue in the life-cycle performance-based seismic design. In this study, the damage levels of flexure-dominated RC members are defined mainly based on the material strain. The mechanical and deformation behavior of corroded RC columns are analyzed by numerical simulation performed with Abaqus software. The corrosion ratio, the axial compression ratio, the longitudinal reinforcement ratio, the stirrup ratio and the shear-span ratio are considered in the parametric analysis. It is found that the performance of slightly corroded columns is approximate to that of noncorroded columns, although the deformation capacity significantly degrades if the column corrosion is severe. An increase in the axial compression ratio leads to a decrease in the deformation capacity of RC columns. Increases in the longitudinal reinforcement ratio and stirrup ratio are beneficial to improving the deformation capacity of slightly corroded columns but have little effect on the ultimate deformation of severely corroded columns. According to the numerical results, formulas of the yield and ultimate deformation of corroded RC columns are derived, and the deformation limit of each damage level are proposed, which can both be applied in the life-cycle performance-based seismic design and assessment of RC structures.