Displacement-based Assessment Research Articles

Nonlinear seismic performance of RC bridges using the ESA, EDA, DDBA, and nonlinear analysis with various viscous damping models

Modern bridge seismic design follows a performance-based seismic design (PBSD) philosophy where the structure is designed to achieve a prescribed limit state under a defined hazard. Nevertheless, the demands may substantially diverge depending on the PBSD method applied in the assessment. This article presents a demand sensitivity analysis using the elastic (ESA) and dynamic (EDA) procedures of the AASHTO Seismic Guide Specifications and direct displacement-based assessment (DDBA). The investigation was conducted using 81 reinforced concrete (RC) bridges and ten multi-period spectra from a shallow tectonic regime. Moreover, these demands were compared with nonlinear time history analysis (NLTHA) using five viscous damping models. Seven compatible records were employed to calculate the envelopes of transverse displaced shapes and cumulative distribution functions of the column with the highest displacement ductility. These average inelastic responses were contrasted with the predictions from the ESA, EDA, and DDBA. For regular bridges, this study found that the elastic procedures considerably underestimate the deformations, while DDBA compares well with NLTHA, especially for high ductility levels. Also, a discussion about the impact of the viscous damping models is included. We expect these findings may encourage practitioners to use DDBA as a reliable alternative to evaluate the seismic performance of RC bridges.

An optimization-based rigid block modeling approach to seismic assessment of dry-joint masonry structures subjected to settlements

A rigid block modeling approach is presented for rocking dynamics and nonlinear static analysis of dry-joint masonry structures subjected to settlements and earthquake excitations. For the different types of analysis, a unified optimization-based formulation is adopted, which is equivalent to the system governing the static and dynamic structural response. Sequential solution procedures are used for time integration and for pushover analysis which take into account the effects of large displacements under the combined action of support movements and lateral loads. No-tension elastic contacts with finite shear strength are considered at block interfaces for time-history analysis and to obtain the elastic branch of pushover curves in nonlinear static analysis. A unilateral rigid contact behavior is also considered to obtain the descending post-peak branch of pushover curves corresponding to the activation of the rigid-body rocking motion, according to displacement-based assessment methods of failure mechanisms adopted in the standards. Comparisons with numerical models and experimental tests on a rocking block and on a buttressed arch are presented to show the accuracy of the developed approach. Simple tests on dry-joint tuff panels on the tilting table were also carried out to show the effects of imposed movements at support on the response to lateral loads. Finally, an application is presented to a full-scale triumphal arch subjected to the combined action of support movements and earthquake excitation to discuss, on the basis of the developed model, the effects of settlement-induced damage on seismic performance. The numerical analyses showed that the lateral force, the displacement capacity and the rocking response can be significantly affected by support movements, pointing out the relevance of the current building condition in the seismic safety assessment.

Collapse assessment of low-rise reinforced concrete special moment resisting frame systems using a simplified method

In this study, a simplified method is proposed to generate collapse fragility curves for low-rise reinforced concrete special moment resisting frame (SMRF) systems. Capacity curves are developed without carrying out structural modeling and nonlinear static analysis, to obtain equivalent SDOF parameters. Ground motion spectra that matches the conditional spectrum (CS) at specified seismic intensity levels are statistically generated and a displacement-based assessment procedure instead of nonlinear response history analysis (NLRHA) is adopted, to obtain the peak displacements necessary for the generation of collapse fragility curves, with and without considering uncertainty in modeling parameters. The proposed simplified method is applied to 3- and 5-story low-rise reinforced concrete SMRF systems for the generation of collapse fragility curves. In addition, a 8-story reinforced concrete SMRF system is considered to examine the applicability of the proposed simplified method to non low-rise reinforced concrete SMRF systems. The results show that the collapse fragility curves generated by using the proposed simplified method are in good agreement with the curves developed using NLRHA for the 3- and 5-story low-rise reinforced concrete SMRF systems; however, such agreement is not observed for the 8-story non low-rise reinforced concrete SMRF system.

Displacement-based seismic performance assessment of multi-span steel truss bridges

Simplified mechanics-based approaches for the seismic performance analysis are used for the risk assessment of large bridge portfolios. This study evaluates the applicability and effectiveness of displacement-based assessment (DBA) and nonlinear static procedures for multi-span railway steel truss bridges. Although built in the first part of the last century, these historical bridges are currently in service within the European railway networks, and their seismic performance is poorly investigated in the literature. Direct DBA algorithms and pushover-based procedures aimed at seismic performance assessment and fragility analysis of bridges are presented and tested within a set of case studies parametrically generated by using an archetype steel truss bridge. The first part of this study focuses on the seismic analysis of steel braced towers which, in many situations, compose the substructure of steel truss multi-span bridges. A simplified pseudo-pushover and an accurate equivalent viscous damping formulation are proposed to be used for the approximate performance displacement assessment of these structural components. The second part discusses the accuracy of the investigated approaches for multi-span steel truss bridges through comparisons with nonlinear time history analysis. The results of the parametric analysis are used to propose recommendations for an appropriate DBA or pushover-based strategy for the deterministic performance assessment and fragility analysis with reference to the damage state of the supporting towers or bridge serviceability in terms of superstructure transverse deformation.

Displacement-Based Seismic Assessment of the Likelihood of Failure of Reinforced Concrete Wall Buildings

To strengthen the resilience of our built environment, a good understanding of seismic risk is required. Probabilistic performance-based assessment is able to rigorously compute seismic risk and the advent of numerical computer-based analyses has helped with this. However, it is still a challenging process and as such, this study presents a simplified probabilistic displacement-based assessment approach for reinforced concrete wall buildings. The proposed approach is trialed by applying the methodology to 4-, 8-, and 12-story case study buildings, and results are compared with those obtained via multi-stripe analyses, with allowance for uncertainty in demand and capacity, including some allowance for modeling uncertainty. The results indicate that the proposed approach enables practitioners to practically estimate the median intensity associated with exceeding a given mechanism and the annual probability of exceeding assessment limit states. Further research to extend the simplified approach to other structural systems is recommended. Moreover, the research highlights the need for more information on the uncertainty in our strength and deformation estimates, to improve the accuracy of risk assessment procedures.

Validation of displacement-based procedures for rocking assessment of cantilever masonry elements

The seismic assessment of cantilever elements in masonry structures is a relevant topic because of their high vulnerability and since they often involve artistic assets (such as bell-gables, parapets or pinnacles). Due to the complexity of nonlinear dynamics of cantilever systems, displacement-based assessment (DBA) procedures have been developed with the main advantage to be less demanding and, therefore, engineering practice-oriented. Various international codes already adopt these procedures but with different choices in their implementation, e.g. in the idealisation of the single degree of freedom or the method to assess the seismic displacement demand. However, despite their widespread use, a systematic validation and comparison among them is not available yet. The aim of this paper is to assess the reliability of five DBA methods available in literature and codes. To this aim, three cantilever elements with a different slenderness were analysed, both considered as laying on the ground floor or atop a supporting structure. Then, incremental dynamic analyses (IDA) have been performed by using several recorded time histories and the results were considered as the reference solution to be compared with the ones obtained by applying the examined DBA procedures. In particular, the results were processed in terms of the peak ground acceleration (PGA) alternatively leading to the attainment of the ultimate limit condition assumed by the codes or to the block overturning. The IDA clearly highlighted that the displacement demand is very sensitive to the intrinsic features of each record. The comparison in terms of fragility curves allowed evaluating robustness, reliability and safety margins of the static displacement-based previsions. Despite the complexity of the problem, the results showed that, as long as proper definitions of the ultimate displacement capacity and proper assumptions for evaluating the seismic displacement demand are adopted, the DBA approach provides safe and reliable estimates.

ASSESSMENT OF PRECAST WIDE U BEAM-COLUMN SYSTEM FOR MITIGATION OF STRUCTURAL FAILURE FROM SEISMIC HAZARD IN THAILAND

A large number of low to moderate earthquake incidents have been witnessed in the northern and western parts of Thailand. These incidents usually lead to various damage levels in various structures. Therefore, a sufficient lateral force resisting structures should be designed for the construction in such earthquake-prone areas. This paper presents the relevance of using a typical composite wide U beam-column system for mitigation of structural failure and collapse from the seismic hazard in Thailand. The investigated composite structural system consists of precast U beams, precast columns, and cast-in-situ concrete over the precast U beams and in the joint regions. The system also includes post-tensioning in the cast-in-situ area of the composite beams. The system has widely been used in low- to mid-rise commercial building in Thailand. In order to scrutinize the seismic performance of the system, a half-scale specimen of the post-tensioned precast U beam-column joint was tested under an incremental displacement-controlled lateral cyclic load. The laboratory test revealed the drift capacity, damage pattern, strain development in the rebars etc. of the precast wide U beam-column interior joint. Based on the obtained drift capacity, displacement-based assessment of the system was carried out. In addition, the observed damages on the tested structure were evaluated using damage grading criteria for building subjected to earthquake. The assessment showed a high potential of the post-tensioned precast wide U beam-column system to mitigate the structural failure and collapse from the earthquake hazard. However, some improvements in the current seismic performance of the system are required to employ the system in high seismic zones.

Quantifying the Likelihood of Exceeding a Limit State via the Displacement-based Assessment Approach

ABSTRACT The displacement-based assessment procedure of Priestley and co-authors was formulated to provide either a pass-fail type of assessment or an indication of the likelihood of exceeding a selected limit state. To account for the effect of uncertainty in demand and capacity as part of the displacement-based assessment, it has also been shown that the SAC-FEMA approach can be adopted. In this work, the displacement-based assessment approach is improved by developing new relationships between intensity and inelastic displacement demand that permits the impact of multiple intensity levels on the likelihood of exceeding a limit state to be assessed contemporarily. The benefit of the new approach is illustrated by comparing the annual probability of exceeding key limit states as obtained through multi-stripe analyses with results obtained from the simplified approach. Results indicate that the simplified method performs reliably for the cases considered. Limitations with the new approach and future research needs are identified.

A rigid block model with no-tension elastic contacts for displacement-based assessment of historic masonry structures subjected to settlements

This paper deals with the vulnerability assessment of historic masonry structures subjected to settlements using rigid block modelling. A 2-D rigid block model with unilateral elastic contacts and finite friction is developed for the evaluation of the displacement capacity in the large displacement regime by push-down analysis. A variational formulation of the rigid block model is adopted, which relies on associative behavior for displacement rates. Under this assumption, the equation systems governing the behavior of the rigid block model can be uncoupled into two equivalent force and displacement-based problems, thus reducing computational costs. The numerical model was validated against the results of an ad-hoc experimental campaign on small scale tuff panels and against the tests on a small-scale masonry façade subjected to moving supports, from the literature. Applications of the proposed modelling approach are presented to the assessment of a full scale, monumental masonry façade. Following classic force-displacement methods that are used in the case of seismic actions, capacity curves are proposed for the damage assessment induced by settlements. Those state the relation between the base reaction at the moving supports and the displacement of a control point, which is obtained from the push-down analysis. Finally, comparisons with empirical assessment methods from the literature are presented.

Displacement-based assessment of the Gazi Hasan Pasha mosque in Kos island (GR) under the 2017 M6.6 earthquake and Eurocode 8, with proposals for upgrading

On 21/7/2017 a M6.6 offshore earthquake shook the Greek island of Kos and the Turkish coastal city of Bodrum. The Gazi Hasan Pasha mosque, a 1786 structure, suffered very limited damage: the load-bearing walls have not shown cracks or extensive deformation; the minaret and few timber members at the roof and the floor suffered serious damage. Confirmation of the damage by the results of an analysis under the nearby recorded seismic loads validated both the model and the assumptions of the analysis. In the second step the seismic performance was assessed using seismic loads from the Greek National Annex to EN1998-1 and the effectiveness of strengthening measures to upgrade the monument was studied. The assessment was based on the Greek code for interventions to masonry structures (KADET) which employs performance-based criteria. The analyses show that the mosque with strengthening measures implemented after it was damaged by an earthquake in 1933, withstands the relative drifts caused by the 2017 event. The predicted damage concurs with the observed limited damage of the structure. Analysis using seismic loads from Eurocode 8 and the performance- and displacement-based criteria of the draft KADET led to the conclusion that the structure cannot withstand these loads and needs strengthening. Insertion of steel tendons at the crest of the most displaced wall attenuates but does not eliminate the damage; addition of further tendons at the level of the top of the ground story wall appears to be very effective in achieving Immediate Occupancy performance for most elements of the building.

Effectiveness of the displacement-based seismic performance assessment for continuous RC bridges and proposed extensions

Seismic performance assessment of existing bridges, especially those designed without seismic criteria, is paramount in earthquake-prone countries. To perform this task, the Displacement-Based Assessment (DBA) represents a satisfactory trade-off between simplicity and accuracy. After describing the modal analysis-based DBA procedure, a static-based alternative is proposed in this paper, considering its strengths and limitations. Moreover, an extension of the procedure is proposed to derive the force-displacement curve of the bridge (pseudo-pushover capacity curve). The effectiveness of the DBA methodology, implemented via simplified mechanical models, is discussed through parametric analyses to address its practical applications. The DBA approach, both modal and static, is herein adopted for the transverse analysis of a set of 36 reinforced concrete continuous-deck bridges up to six spans, with pier height in the range 8–20 m and two different values of the deck transverse stiffness. Additional sensitivity analyses (24 case studies) are conducted to investigate the accuracy of the two approaches considering: 1) the length of the bridge, 2) the amount of longitudinal reinforcement in the piers; 3) different pier typologies. The results are compared to numerical pushover and time-history analyses using three suites of 10 scaled, natural ground motions respectively consistent with low-, medium- and high-seismicity sites. For the majority of the case studies, the resulting performance assessments fall within one standard deviation of the results of the time-history analyses. For this reason, the displacement-based modal or static approaches can represent a valid alternative to numerical non-linear static analyses for continuous bridges with six spans or less.

Displacement-Based Framework for Simplified Seismic Loss Assessment

ABSTRACT Loss assessment methodologies have been introduced to assess the seismic performance of buildings using more meaningful metrics like direct monetary losses. Different approaches exist, each with varying degrees of complexity and requiring different levels of detail, regarding structural behaviour characterisation or damage and loss estimation, for example. With these developments, loss assessment is increasingly becoming a more commonplace instrument in the seismic evaluation and retrofitting of existing buildings. Despite these developments, there is arguably still a need to provide practising engineers with simplified tools with which to conduct building-specific loss assessment. Displacement-based methodologies have been developed over the past number of years with a particular focus on design. The extension of this approach to loss assessment via displacement-based assessment (DBA) is the subject of this article, where a general framework for its implementation to different structural typologies is outlined and illustrated. This forms a general overview of a recently-concluded 5-year research project on the topic in Italy, where different research groups from various universities focused on specific building typologies as part of a coordinated effort to develop DBA for simplified loss assessment. An overview of the DBA method employed is presented here in addition to an overall description of the results of each working group. A summary of the developments for each typology examined is presented along with an illustration of the potential benefits of different retrofitting techniques in reducing monetary losses, whose details are found in the different typology-specific contributions to the special issue in which this paper is presented. To conclude, a comparative implementation of these simplified methodologies is described for three school buildings in Italy.

Displacement-Based Simplified Seismic Loss Assessment of Steel Buildings

ABSTRACT Evaluating losses consequent to damages induced by earthquakes has become one main paradigm in seismic performance assessment. Within this context, this paper explores a simplified seismic loss assessment methodology for steel structures that utilises displacement-based assessment in place of non-linear dynamic analyses. To this end, two case studies have been considered: (i) an archetype existing single-storey non-residential building, (ii) a prototype new multi-story residential building. Comparing results obtained using the fully probabilistic and the simplified displacement-based assessment methodologies allows the benefits of the simplified method to be highlighted. Possible difficulties encountered in applying the simplified method are also identified.

Displacement-Based Simplified Seismic Loss Assessment of Post-70s RC Buildings

ABSTRACT To help facilitate performance-based earthquake engineering (PBEE) in Italy, this study examines an existing reinforced concrete frame building damaged during the 2009 L’Aquila earthquake and compares direct monetary loss estimates computed via a simplified Displacement-Based Assessment (DDBA) method with those obtained using the refined PEER-PBEE approach. The considered case study is representative of a category of buildings that has undergone some level of seismic design, typical of post-70s construction in Italy, where previous buildings were largely designed for gravity loads only. The research finds that the expected annual loss predicted using the two approaches are comparable and thus DDBD could aid loss-assessment and hence reparability evaluations. Different retrofit options are examined and it is concluded that the DDBA approach could provide useful indications of the impact that retrofit can have on expected annual losses.

Displacement-based assessment of typical Italian RC bridges

For the effective management and maintenance of a transport network it is important to identify the most at-risk bridges within the network and subsequently implement efficient retrofit solutions. The risk assessment process adopted for this purpose usually makes use of vulnerability or fragility functions that may be either simple empirical expressions or bridge-specific expressions developed from time-consuming non-linear dynamic analyses. Fragility curves defined for bridge taxonomies are less precise because fragility curves are in general site and bridge dependent. In this work the possibility of using a simplified displacement-based assessment (DBA) procedure for the identification of bridge fragility functions is explored. The simplifications to the DBA approach are made so that the inputs required for assessment are limited to bridge characteristics that can be readily identified from a rapid visual inspection of the bridge (or from drawings). Nonetheless, by incorporating a number of input parameters that can dictate the displacement capacity of a bridge, it is argued that the simplified DBA procedure can still provide a good level of accuracy, particularly compared to simplified empirical methods. In addition to this, for portfolio risk assessment, this approach can be easily applied and is more refined than the use of fragility curves defined for bridge taxonomies. This is demonstrated in the paper by comparing fragility functions obtained via various methods, for a number of RC bridge typologies commonly found in Italy.

Quantifying seismic risk in structures via simplified demand–intensity models

Performance-based earthquake engineering (PBEE) has traditionally implied the verification of limit states at different earthquake intensities, where recent developments advocate a more risk-consistent approach. This has been primarily investigated for assessing existing structures and typically involves extensive analyses using detailed numerical models and ground motions. For new design, structures must be sized and detailed before more advanced numerical verifications are performed and the final design solution is established. In assessment, simplified procedures have been developed to incorporate further aspects of PBEE and typically comprise extensions to traditional structural analysis methods. Displacement-based assessment is one such method and while it has been extended for PBEE in the past, its use in a risk-oriented context still requires some validation. This article presents such a study, where recent developments in simplified analysis to estimate the exceedance rates of both storey drift and floor acceleration in reinforced concrete frames are described. This gives a method that is simple in its application, since it doesn’t require extensive and detailed numerical modelling or analysis, but also sufficiently accurate in its quantification of performance. While not intended as a substitute to extensive verification analysis, such a method for quantifying structural demand exceedance rates can be used to check results and provide better understanding to risk analysts. The work described herein can also be used in simplified verification analysis of new designs, whereby trial solutions may be verified in a relatively easy manner before more extensive verifications are carried out via non-linear dynamic analysis. It represents a further extension to existing simplified methods that strive toward more advanced performance quantification in line with the needs and goals of PBEE.

Seismic Vulnerability of a Rockfill Dam through Different Displacement-based Approaches

ABSTRACT The paper focuses on the assessment of the seismic performance of Menta Dam, a bituminous faced-rockfill dam located in Southern Italy. The dam was designed in the ‘70s and a comprehensive assessment of hydraulic and seismic vulnerability has been recently performed according to most recent Italian dam regulations. The present work aims at predicting the displacement capacity of the embankment as an indicator to assess the overall seismic vulnerability of the system. To this aim, different displacement-based methods, which can be classified in the framework of simplified dynamic analyses, have been applied. The results of empirical approaches and of Newmark’s type dynamic analyses are compared to the ones obtained by a novel application of Direct Displacement-Based Assessment (DDBA) method for embankment structures. The latter approach seems to be promising, since it is capable to furnish the maximum displacement experienced by the dam crest for progressively increasing seismic actions, and its probability of exceedance; hence, the likelihood of reaching a threshold damaged condition can be deduced and usefully plotted in terms of fragility curves.

Displacement-Based Seismic Assessment for Precast Concrete Frames with Non-Emulative Connections

ABSTRACT The paper develops a methodology for the seismic vulnerability assessment, Displacement-Based Assessment (DBA), of one-story and multi-story precast concrete frames with non-emulative connections. The method is based on the Direct Displacement-Based Design procedure initially developed by Priestley. The DBA is particularly suitable for the evaluation of the seismic response of flexible structures, as it considers displacements as the leading parameters to estimate the seismic vulnerability. The proposed procedure specifically accounts for the influence of beam–column connections, P-∆ effects, and second mode of vibration. The validation has been performed by means of nonlinear time history analyses.

Probability density evolution method for seismic displacement-based assessment of earth retaining structures

Earthquakes have damaged many earth-retaining structures worldwide, causing much loss of life and property as well as disrupting traffic. To assess the seismic performance of earth-retaining structures in earthquake-prone areas, a new probabilistic methodology is proposed, namely the probability density evolution method (PDEM). As a novel dynamic reliability method based on random vibration theory, PDEM combines stochastic dynamic analysis with current advanced deterministic methods. Not only does PDEM give the dynamic reliability of the global system of a structure, it also gives the probability density function and its evolution characteristics of the seismic response of interest. A tie-back wall is chosen as the type of earth retaining structures with which to show the feasibility of the method. After stochastic ground motions are generated by stochastic ground motion model, a series of deterministic seismic responses of the tie-back wall are obtained by the finite-element method. The PDEM is then used to obtain the stochastic seismic responses and the dynamic reliability of the system. Finally, the seismic performance of the tie-back wall is assessed using performance indices and displacement-based criteria selected from standards and the literature. High efficiency and accuracy of the PDEM is verified by comparing its results with those from Monte Carlo simulations. Not only can this novel method give more objective indices than can traditional evaluation methods, it can also provide a reference for the performance-based seismic analysis and design of geotechnical engineering structures.

Out-of-plane static and dynamic response of masonry panels

Out-of-plane mechanisms induced by earthquakes are typical of many masonry structures such as standing out elements (spires, battlements of fortresses, etc.) or portions of façade badly connected to the building. The displacement-based assessment procedures in standards are based on the hypothesis of rigid block, which sometimes is unable to represent their actual behaviour; furthermore, very few information is available on dissipation, which is assumed as an equivalent viscous damping, usually kept constant to 5%. The paper illustrates the results of an experimental campaign on three mock-ups subjected to static and dynamic out-of-plane actions with the aim to verify the reliability of these assumptions for traditional irregular stone masonry panels under rocking.