UCL Institute for Risk and Disaster Reduction


ENFRAG: ENhancing state-dependent FRAGility through experimentally validated energy-based approaches

An eighteen-month project that aims at advancing state-dependent earthquake fragility assessment methodologies.

Machine shaking a small wall to replicate an earthquake

1 February 2024

The ENFRAG research project is part of the ERIES project (engineering research infrastructures for European synergies). ENFRAG aims at advancing state-dependent earthquake fragility assessment methodologies. The project involves sequential quasi-static cyclic displacement-controlled in-plane (IP) and shaking-table dynamic out-of-plane (OOP) tests on four nominally identical masonry infill walls. Different load protocols are employed to induce the same peak-based engineering demand parameters (EDPs) while modulating the energy-based demands. A multi-fidelity approach is employed to integrate the experimental data with synthetic datasets including IP cloud-based analysis, IP quasi-static, push-pull analyses with different load protocols, OOP dynamic analyses, and IP-OOP combined analyses. The results are used to explore the potential of energy-based EDPs for interpreting damage states and damage accumulation. This allows experimentally validating methodologies to derive state-dependent fragility functions that account for multiple sources/mechanisms of damage accumulation. This contribution provides an update on the numerical and analytical components of ENFRAG, as well as linking them with the specific research objectives.

Challenge being addressed 

Fragility functions play a crucial role in seismic risk assessment, allowing for the prioritisation of retrofitting efforts, the development of more effective building codes, and the allocation of resources for disaster preparedness and response. Fragility functions describe the probability of different assets reaching or exceeding different damage states (DSs) conditioned on an earthquake intensity measures (IMs). DSs are usually represented by thresholds of engineering demand parameters (EDPs) often represented by peak deformation quantities such as displacements, drifts or accelerations (i.e., ground or floor). Monotonic or quasi-static cyclic testing can conveniently provide such deformation thresholds for a given structural system or component, thus providing proxies of the peak structural demand under different ground motions. This is ideal from an economic point of view since such tests do not depend on a specific ground-motion excitation input (thus not requiring several tests).

Recent research (Di Trapani and Malavisi, 2019; Papadopoulos et al., 2020) has investigated damage state-dependent fragility relationships useful for structures subjected to ground motion sequences (e.g., mainshock-aftershock). Most studies use the peak inter-storey drift as the measure of damage, although some models also take residual drift into account (Zhang et al., 2020). Peak or residual quantities, however, cannot properly capture damage accumulation since they do not monotonically increase with ground-motion intensity. Moreover, using these EDPs for state-dependent fragility analysis can lead to statistical inconsistencies. For example, a structure subjected to a given peak deformation (e.g., drift) will sustain a certain level of damage. If the structure is subsequently subjected to the same deformation level, the actual damage level is likely to increase. If damage is measured with peak deformation-based DS thresholds, the structure will not be assigned a higher DS, which is inconsistent.

Integral quantities, such as hysteretic energy, can solve the above inconsistency since they monotonically increase with the ground-motion excitation (or sequence) length. A recent study by Gentile and Galasso (2021) provides a hysteretic energy-based framework for state-dependent fragility. The framework takes advantage of the demonstrated pseudo-parabolic relationship between the peak global deformation (e.g., maximum inter-storey drift) and the hysteretic energy of a system. By characterising the median of this relationship via numerical analyses, it is possible to convert deformation-based damage thresholds into energy-based ones and characterise state-dependent fragility functions. The authors highlight that even though the framework is theoretically sound, an experimental validation is needed.

Aims and objectives 

The ERIES-ENFRAG project (ENhancing state-dependent FRAGility through experimentally validated Energy-Based Approaches), led by University College London, sheds some light on the above research gap. ERIES-ENFRAG explores the experimental validation of hysteretic energy-based fragility assessment approaches, which are: 1) Currently based only on analytical and/or numerical validations; 2) Only considering one type of action/damage mechanism. The project focuses on masonry infill walls experiencing cumulative states of damage due to combinations of in-plane (IP) and out-of-plane (OOP) actions, commonly quantified through two different peak-based engineering demand parameters (EDPs). Extensive analytical and numerical studies are adopted to define specific loading protocols adopted for this study. This allows the experimental results to be used in a multi-fidelity statistical approach – combining experimental and numerical data – and to maximise the statistical power of the inferences drawn from the results.

Funding details: European Commission, Horizon Europe, ERIES: engineering research infrastructures for European synergies
Project duration: 18 months
Principal Investigator: Roberto Gentile
Project team: Fatemeh Jalayer (UCL IRDR); Jingren Wu (UCL IRDR); Fabio Freddi (UCL CEGE); Fabrizio Mollaioli (Sapienza University of Rome); Giulia Angelucci (Sapienza University of Rome); Gerard O’Reilly (IUSS Pavia); Riccardo Milanesi (EUCENTRE Laboratory, Pavia)

Watch a video of the out of plane collapse of the first specimen on LinkedIn.


Di Trapani, F., Malavisi, M., 2019. Seismic fragility assessment of infilled frames subject to mainshock/aftershock sequences using a double incremental dynamic analysis approach. Bulletin of Earthquake Engineering 17, 211–235. https://doi.org/10.1007/s10518-018-0445-2

Papadopoulos, A.N., Kohrangi, M., Bazzurro, P., 2020. Mainshock-consistent ground motion record selection for aftershock sequences. Earthq Eng Struct Dyn. https://doi.org/10.1002/eqe.3263

Zhang, L., Goda, K., De Luca, F., De Risi, R., 2020. Mainshock-aftershock state-dependent fragility curves: A case of wood-frame houses in British Columbia, Canada. Earthq Eng Struct Dyn 1–20. https://doi.org/10.1002/eqe.3269

Gentile, R., Galasso, C., 2021. Hysteretic energybased statedependent fragility for groundmotion sequences. Earthq Eng Struct Dyn 50, 1187–1203. https://doi.org/10.1002/eqe.3387