In recent decades, significant research efforts have been devoted to developing fragility and vulnerability models for mainshock-damaged buildings, i.e., depending on the attained damage state after a mainshock ground motion (state-dependent fragility/vulnerability relationships). Displacement-based peak quantities, such as the maximum interstory drift ratio, are widely adopted in fragility analysis to define both engineering demands and structural capacities at the global and/or local levels. However, when considering ground-motion sequences, the use of peak quantities may lead to statistical inconsistencies (e.g., fragility curves’ crossings) due to inadequate consideration of damage accumulation. In this context, energy-based engineering demand parameters (EDPs), explicitly accounting for cumulative damage, can help address this issue. This paper provides an overview of recent findings on the development of aftershock-fragility models of mainshock-damaged buildings. Particular focus is given to state-of-the-art frameworks for fragility analyses based on cumulative damage parameters. Moreover, a literature review on damage indices and energy-based concepts and approaches in earthquake engineering is reported to better understand the main advantages of the mostly adopted energy-based parameters, as well as their limitations. Different refinement levels of seismic response analyses to derive fragility relationships of mainshock-damaged buildings are also discussed. Finally, the benefits of adopting energy-based EDPs rather than, or in addition to, peak quantities in state-dependent fragility analyses are demonstrated on a reinforced concrete frame building. Specifically, a refined lumped plasticity modeling approach is adopted, and sequential cloud-based time-history analyses of a Multi-Degree-of-Freedom (MDoF) model are carried out. The results highlight that energy-based approaches for fragility analysis effectively capture damage accumulation during earthquake sequences without inconsistencies in the obtained statistical models. On the other hand, estimating global or local structural capacity in terms of cumulative EDPs is still challenging. Further experimental data are needed to better calibrate the quantification of energy-based damaged states.

When dealing with seismic risk assessment at a large scale, the collection of relevant building data is still deemed a challenging task, often leading to limited building knowledge and, consequently, high uncertainties. Therefore, innovative yet standardized frameworks and adaptive tools are needed to support the seismic risk assessment of buildings. Towards this goal, this paper proposes a simplified multi-knowledge seismic assessment methodology involving the analytical-mechanical SLaMA (Simple Lateral Mechanism Analysis) method. An ad-hoc data collection form is first developed to identify the building vulnerabilities by merging and building on existing institutional forms at the international level and integrating new input data. The data are then used to implement the SLaMA-based methodology, at different building knowledge levels, to assess the seismic safety and the economic losses of buildings. The proposed data structure and approach is planned to be included in the “Seismic-Response” module for PELL (Public Energy Living Lab)-School platform, aiming to become a standardized and interoperable database for relevant data of Italian schools and a dashboard for allowing stakeholders to continuously monitor their energetic and static/seismic conditions. The paper discusses the potential and effectiveness of the proposed procedure for large-scale applications and its integration into platforms assessing the energy efficiency of buildings.

The severe socio-economic impact of recent earthquakes has further highlighted the crucial need for a paradigm shift in performance-based design criteria and objectives towards a low-damage design philosophy, in order to reduce losses in terms of human lives, repair/reconstruction costs, and recovery time (deaths, dollars and downtime). Currently, displacement-based parameters are typically adopted to design/assess the seismic performance of the structures, by limiting the maximum displacement or the maximum interstorey drift ratio (IDR) reached by the structure under different earthquake intensities. However and arguably, displacement-based quantities are characterized by inherent weaknesses, since, for instance, they are not cumulated parameters, thus not able to capture directly the effects of multiple cycles, deterioration and damage cumulation. Therefore, in the last decades, energy-based approaches were investigated and developed in order to establish alternative engineering demand parameters for the assessment of post-event damage through a dynamic energy balance. Towards the main goal of developing an integrated Displacement and Energy-Based Design/assessment procedure (DEBD) for actual use in practice, this research work proposes an innovative approach based on the use of inelastic spectra correlating the energy components with the corresponding maximum displacement response parameters of the structure. In practical terms, the proposal is to further integrate and develop the well-known Direct Displacement-Based Design, by directly adopting the hysteretic energy as an additional design parameter. The energy inelastic spectra are developed through an extensive parametric analysis of Single-Degree-of-Freedom (SDoF) systems, with different nonlinear hysteretic models. In such an approach, the maximum seismic energy demand imparted to a structure can be directly predicted and controlled, whilst distinguishing the various components of the energy balance, including the hysteretic one. The effects of near-field and far-field earthquakes are also investigated. Results show that in the first case the seismic demand is concentrated in the peak of a few large cycles that absorb the demand energy induced by the high component in peak ground velocity in the second case the higher equivalent number of plastic cycles tends to become critical for structures with inadequate structural details and prone to suffer by cumulative cycles and overall plastic fatigue mechanisms.

NUMERICAL INVESTIGATIONS ON THE RESIDUAL CAPACITY AND ECONOMIC LOSSES OF EARTHQUAKE-DAMAGED REINFORCED CONCRETE WALL STRUCTURES - 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering - 28-30 June 2021, Streamed from Athens, Greece

During an earthquake, the detachment and local interaction between infill wall panels and surrounding frame can occur, potentially leading to significant local damage to both structural and non-structural elements, if not global collapse. Yet, a procedure to assess the relative deformation mechanism in terms of detachment shape and values, rather than, and in addition to, the diagonal compression strut mechanism and associated internal panel strain and stress path, is still missing in the literature. Therefore, in this paper the concept of shape functions is proposed and adopted to assess the seismic displacement incompatibility between infill walls and the surrounding frame structure. A parametric study on different typologies of infilled frames is developed to investigate the key parameters affecting the infill-frame detachment. The proposed concept of shape functions can support the design/retrofit of improved construction details, such as shear keys and/or steel dowels, in view of either decoupling or strengthening retrofit/repair strategies. Moreover, as infill-frame detachment can lead to damage to energy enhancement rehabilitation solutions, such as external thermal insulation systems, which are becoming more common nowadays in view of the international target towards a significant reduction of energy consumption and CO₂ emission, it is suggested to implement the proposed displacement-compatible design check to assess and detail for adequate displacement capacity.