The problem begins with the behaviour factor, the famous q-factor of Eurocode 8, which scales down the elastic seismic demand to account for a structure’s capacity to deform inelastically and dissipate energy. In the newest generation of the code, q is decomposed into three contributions: one for generalized ductility, one for overstrength arising from the redistribution of forces in redundant structures, and one for other sources of reserve strength. It is the second term, often called the system overstrength ratio or OSR, that has proved so troublesome for masonry. When a masonry building is pushed laterally, the first wall to reach its strength does not usually signal the end of the road. If that wall retains deformation capacity, the surplus load flows to its stiffer or stronger companions, and the building keeps picking up lateral resistance until several walls have exhausted both their strength and their displacement capacity. The ratio between this ultimate base shear and the shear at first yield can range widely, from a theoretical minimum of 1.0 in structures with no redundancy to values between roughly 1.4 and 2.5 for most unreinforced masonry configurations, and occasionally beyond 3.0.

That variability is the crux of the difficulty. The overstrength ratio depends on the wall layout, the pattern of openings, the number of storeys, the presence of reinforced concrete ring beams or masonry spandrels, the stiffness of the floor diaphragms, and the connection details, all of which vary enormously with regional building traditions. It also depends on modelling choices: whether walls are discretised as continuum finite elements, equivalent frames or macro-elements, what constitutive laws are adopted, and how coupling between intersecting walls is treated. Previous studies have shown that calculated overstrength ratios do not even depend strongly on the assumed deformation capacity of individual walls, which makes the task of tabulating representative values for design codes nearly hopeless. A single conservative default value, derived from statistics across many configurations, could impose seismic demands far higher than any specific building actually needs, forcing designs to fail strength checks that nonlinear analysis would comfortably pass.

The Pavia team’s answer is elegant in its simplicity: set the overstrength contribution to unity, and instead of encoding redundancy in a code-specified factor, let the designer exploit it explicitly through force redistribution, bounded by the physics of wall deformation. The logic rests on a simple observation about walls acting in parallel within a storey. All walls connected to a rigid floor diaphragm share the same top displacement, so the system’s ultimate state is reached when the wall with the lowest displacement capacity gives out, regardless of how much reserve the others still hold. Wall displacement is expressed through the chord rotation at the wall base, multiplied by the wall’s effective height and a kinematic conversion factor close to unity for typical single-storey boundary conditions. The ultimate displacement of each wall follows from its ultimate chord rotation capacity, which is governed by its failure mechanism, whether shear, flexural or a hybrid of the two.

This kinematic picture immediately reveals why redistribution cannot be unlimited. Consider a storey containing a very short, stiff squat wall alongside taller, more flexible companions, a scenario common in practice wherever foundations step or openings vary in height. The squat wall attracts a disproportionate share of the elastic shear and is also the first to hit its displacement limit. Once it reaches its ultimate chord rotation, the whole system has exhausted its capacity, and the taller walls may never have developed their full strength. The maximum shear that can be transferred to any of those taller walls is therefore capped by a simple similarity-of-triangles argument: the increment is proportional to the difference between the limiting system displacement, set by the weakest wall’s ultimate capacity, and the displacement computed in the linear elastic analysis. A deliberately conservative simplification assumes the governing wall is the shortest one in the storey, failing in pure shear in double bending at the minimum possible ultimate chord rotation, a value for which reference figures are provided by the new Eurocode 8 Part 1-2.

Extending the criterion to buildings that twist under seismic loading required a careful treatment of torsion. When the centres of mass, stiffness and strength do not coincide, different walls experience different displacement demands, and the neat assumption of equal top displacements breaks down. The researchers distinguish torsionally restrained systems, which possess at least one adequately stiff, strong and well-spaced wall couple in the perpendicular direction capable of developing restraining torque, from torsionally unrestrained systems, where in-plan rotation runs free. For restrained systems, they propose dividing the floor plan into two zones around the critical wall. In the soft-edge zone, ultimate displacements are conservatively taken equal to the critical wall’s capacity; in the stiff-edge zone, they are assumed proportional to the elastic displacement field, which is safe because nonlinear analyses consistently show that in-plan twist diminishes as walls yield. For unrestrained systems, no general rule is offered, and the authors argue such layouts should simply be avoided in new construction.

The validation campaign is one of the most thorough aspects of the work. Two single-storey case-study buildings were deliberately configured at the borderline of plan regularity and torsional restraint, with wall heights ranging from 1.00 to 3.40 metres to generate marked eccentricities. Walls were modelled in the Ruaumoko3D program as nonlinear beam-column elements with lumped plasticity, assigned flag-shaped hysteretic rules for flexural response and modified Takeda or Schoettler-Restrepo rules for shear response, calibrated against full-scale cyclic tests of clay-unit masonry walls conducted at the EUCENTRE and University of Pavia laboratories. Incremental dynamic analyses were then run under seven bi-directional ground-motion pairs selected for two Eurocode soil classes, applied with all four sign combinations, across three period variants and three hysteretic assumptions, yielding 1,008 simulations in total. The results were strikingly consistent: once nonlinear behaviour was mobilised, the in-plan twist dropped markedly relative to the elastic case, the shortest wall always governed the attainment of ultimate conditions, and soft-edge displacements never exceeded 0.70 centimetres against the 1.02-centimetre limit, confirming a substantial margin of conservatism in the proposed redistribution bounds.

The practical payoff is demonstrated through worked examples, including a three-storey terraced house whose weak direction exhibits an overstrength ratio of 3.2. Analysed linearly with the overstrength factor set to unity and the new deformation-based redistribution applied storey by storey, with wall capacities recomputed at each step as force eccentricities changed, all walls and ring beams passed their checks up to a design base shear of 1,200 kilonewtons, roughly 2.3 times the demand at which verification would have failed without redistribution, and far beyond the maximum overstrength factor of 1.4 the new code would otherwise admit. By contrast, the older heuristic limits tied to a code-specified overstrength factor proved so restrictive in one example that a building verifiable by other means could not be checked at all, a consequence of fixed percentage thresholds being disconnected from the actual redistribution capacity of the system. The authors also discuss a cautious extension to low-rise multi-storey buildings, adding an upper bound on redistributable shear increments and capping the ultimate chord rotation at the severe-damage rather than near-collapse state to cover the additional uncertainties of multi-storey response.

The criterion now underpins the provisions of the forthcoming Eurocode 8 Part 1-2 for new masonry buildings, giving practitioners a rational alternative to both conservative default factors and full nonlinear analysis. The authors are careful to note that nonlinear static procedures, where applicable, remain more convenient, since no automated software yet exists for post-linear redistribution, and that further dynamic validation of multi-storey applications is a future task. But the significance of the work lies in closing a forty-year-old gap: since the late 1970s, when the inadequacy of linear methods for masonry was first recognised in Europe, the profession has redistributed forces on the basis of analogy and judgement. It can now do so on the basis of displacement compatibility and measured deformation capacity, bridging the persistent gap between the elastic models of everyday design and the stubbornly nonlinear reality of masonry under earthquake attack.

Subject of Research: A deformation-based criterion for limiting seismic force redistribution in masonry buildings after linear elastic analysis

Article Title: A deformation-based criterion for redistribution of seismic forces in masonry buildings after linear analysis

Article References: Damiani, N., Manzini, C. F., & Magenes, G. (2026). A deformation-based criterion for redistribution of seismic forces in masonry buildings after linear analysis. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02685-5

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02685-5

Keywords: masonry buildings, seismic design, force redistribution, linear analysis, Eurocode 8, overstrength ratio, chord rotation, torsional response, nonlinear dynamic analysis, unreinforced masonry, behaviour factor, earthquake engineering

The starting point is the Da.D.O. platform, the Database of Observed Damage maintained by the Italian Department of Civil Protection and Eucentre. Across fifty years of Italian earthquakes, from Friuli in 1976 to Emilia in 2012, the platform now holds damage data for roughly 320,000 surveyed buildings, about 78 percent of them masonry structures and 8 percent reinforced concrete. For the Irpinia event specifically, the researchers drew on inspections carried out in forty-one municipalities in Southern Italy, chosen to span the full range of macroseismic intensities generated by the shock. The stock is dominated by masonry, particularly rubble stone and tuff, with reinforced concrete buildings a small minority, most of them built between 1960 and 1980 and designed for gravity loads alone, with no consideration of seismic forces.

But the archive has a serious flaw. Nearly 47 percent of the reinforced concrete buildings have no recorded construction age, more than double the missing fraction among masonry buildings. That gap matters because construction age is one of the strongest proxies for seismic vulnerability: it encodes the design code in force, the quality of materials, and the construction practices of the era. Rather than discarding nearly half the reinforced concrete inventory, the researchers trained a supervised machine-learning classifier to infer the missing ages from the attributes that inspectors did record, including vertical and horizontal structural systems, roof type, number of storeys, number of housing units, average floor area, municipality, and even observed damage.

The team compared a full arsenal of algorithms in MATLAB’s Classification Learner environment, including decision trees, support vector machines, logistic regression, k-nearest neighbors, naive Bayes classifiers, and neural networks. The best performer was an optimizable ensemble that achieved a cross-validated accuracy of 59.8 percent, automatically selecting a bagged ensemble of 449 classification trees from a set of ten predictors. Accuracy rose above 90 percent in area-under-curve terms for the two extreme building periods, pre-1900 and 1972 to 1980, while intermediate classes proved harder to separate, an expected result when structural features evolve gradually over time. Crucially, Shapley value analysis showed the classifier leaned on physically meaningful signals: the horizontal structural system was the most influential predictor, reflecting the historical shift from wooden and vaulted floors to reinforced concrete slabs, with vertical structure and municipality close behind. Damage variables had negligible influence, which reduces the risk of circular reasoning in the subsequent fragility analysis.

The second, arguably more consequential innovation concerns how the ground shaking itself is handled. Empirical fragility studies typically rely on ShakeMap-derived intensity measures, which blend ground-motion prediction equations with instrumental recordings. These products carry inherent uncertainty, and most studies simply ignore it. That omission produces a classic statistical pathology known as attenuation bias, or regression dilution: measurement error in the predictor variable gets absorbed into the response model, artificially inflating the dispersion of the estimated fragility curves. Del Gaudio and Verderame instead modeled ShakeMap uncertainty explicitly, treating the true intensity at each municipality as a latent variable drawn from a spatially correlated random field, with correlations between locations decaying with distance in the manner described by Jayaram and Baker.

Within a Bayesian framework, the researchers used Markov Chain Monte Carlo sampling, specifically the Metropolis-Hastings algorithm, to estimate the parameters of lognormal fragility functions, which describe the probability of exceeding a given damage state as a function of ground motion intensity. Twenty thousand iterations were run, with 3,000 discarded as burn-in, and prior distributions for the median and dispersion parameters were constructed from European and Italian fragility models, including the European Building Vulnerability Database, the Global Earthquake Model’s vulnerability model, and the European Seismic Risk Model ESRM20. The observed damage of each building entered the likelihood as a Bernoulli variable, and posterior samples captured uncertainty in both the fragility parameters and the latent intensity field simultaneously.

The results are striking. When intensity uncertainty was ignored, dispersion parameters ballooned to implausible values: 1.82 for reinforced concrete buildings at the first damage state, 2.14 for tuff masonry, 1.36 for brick, 1.46 for rubble. Once the latent intensity field was introduced, dispersions collapsed into a narrow band of roughly 0.6 to 0.8 across all typologies and damage states. In other words, much of the apparent scatter in historical damage data was never a property of the buildings at all; it was an artifact of treating interpolated shaking estimates as if they were certain. The corrected curves also show a cleaner, monotonic progression across damage states, with medians rising as severity increases and minimal overlap between thresholds, exactly what a physically credible fragility model should look like.

The refined taxonomy then delivers a detailed vulnerability hierarchy of the Irpinia building stock. Rubble stone masonry emerges as the most vulnerable typology, followed by tuff and then brick masonry, consistent with the irregular geometry and weak mechanical properties of rubble construction. Within each vertical typology, the horizontal system proves decisive: buildings with wooden floors or vaults consistently perform worse than those with steel or reinforced concrete diaphragms, and high-rise masonry buildings are generally more fragile than low-rise ones. Reinforced concrete buildings show their own pattern, with pre-1970 construction more vulnerable than later buildings and tall structures more fragile at low damage states. The authors suggest this taxonomy, which exploits every attribute in the original inspection forms rather than collapsing buildings into broad EMS-98 vulnerability classes, offers a template for future empirical fragility work.

Perhaps the most provocative finding concerns which ground motion descriptor best explains the observed damage. Comparing peak ground acceleration, peak ground velocity, and spectral acceleration at 0.3 seconds, the researchers evaluated efficiency in two independent ways: through the standard deviation of residuals in a probit representation of the damage data, and through Bayesian Information Criterion-based likelihood comparisons. Both methods converge on the same answer. Peak ground acceleration, long the default choice in seismic risk practice, generally performs the worst, showing the largest residual scatter. Peak ground velocity provides the strongest and most consistent explanatory power, especially for moderate-to-high damage states, a result the authors link to its closer connection with the kinetic energy imparted to structures and the deformation demands that govern severe damage. The agreement between two methodologically independent tests strengthens the case that velocity-based intensity measures deserve a larger role in regional empirical fragility assessment.

Finally, the team compared their Irpinia curves against fragility models derived from the 2009 L’Aquila earthquake, another Da.D.O. dataset from a very different building culture. The comparison reveals how much regional practice and the history of seismic classification matter. Most L’Aquila municipalities had been designated seismic since 1915, while many Irpinia towns were first classified only after 1980, so their reinforced concrete buildings differ fundamentally in design provenance. For tuff masonry, the correspondence is telling: buildings with wooden or steel slabs most resemble the bad-quality masonry classes defined in L’Aquila’s AeDES survey, while those with reinforced concrete slabs align with good-quality classes, and the match shifts with damage severity. Rubble masonry maps onto bad-quality classes, brick onto good-quality ones. The lesson is that fragility is not just a function of a structural label; it is woven from materials, floor systems, regulatory history, and even the survey forms used to describe them, and any national risk model that ignores that texture is smoothing away exactly the information that matters most.

Subject of Research: Empirical seismic fragility assessment of the Irpinia 1980 building stock using machine learning and Bayesian updating

Article Title: Bayesian updating of seismic fragility curves of the Irpinia 1980 building stock with machine-learning-supported data analysis

Article References: Del Gaudio, C., & Verderame, G. M. (2026). Bayesian updating of seismic fragility curves of the Irpinia 1980 building stock with machine-learning-supported data analysis. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02669-5

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02669-5

Keywords: seismic fragility curves, Bayesian inference, machine learning, 1980 Irpinia earthquake, masonry buildings, reinforced concrete, ShakeMap, intensity measures, Markov Chain Monte Carlo, Da.D.O. database, vulnerability ranking, ground motion uncertainty