The core of the proposal is a dual-parameter damage index built from two quantities: the Area Loss Ratio, abbreviated ALR, and the Residual Height Ratio, or RHR. The ALR describes the fraction of the tower’s horizontal cross-sectional area that has been lost as blocks detach and fall away, while the RHR captures how much of the original height remains standing after partial collapse. Together, the two parameters trace a damage trajectory that a single measure cannot. A tower might lose a modest amount of area near its crown while retaining most of its height, or it might shear through at mid-height and shed an entire upper story; the combination of ALR and RHR distinguishes these very different failure modes and allows them to be ranked on a common severity scale.

To calibrate the index, the researchers modeled seven representative masonry pagodas in three dimensions using the discrete element method, a computational technique originally developed for rock mechanics. Unlike continuum finite element models, which treat masonry as a smeared material, the discrete element approach represents the structure as an assembly of individual polyhedral blocks interacting through contacts. That matters for pagodas, because their failure under earthquake shaking is fundamentally a process of blocks cracking loose, sliding, rotating and toppling. The formulation traces back to the distinct element schemes introduced by Peter Cundall and collaborators in the late 1980s, and it allows the simulation to capture progressive detachment and collapse rather than merely the onset of cracking.

Within the numerical models, the team systematically varied the key structural parameters that govern pagoda behavior. Three stood out: the condition of the internal infill, the height-to-width ratio of the tower, and the opening ratio, meaning the proportion of the facade occupied by doorways, windows and arched niches. Each of these features varies widely across the surviving stock of ancient pagodas, and each plausibly changes how the structure responds to shaking. By building models that span this parameter space, the researchers could isolate the influence of each factor on displacement demand and collapse susceptibility, rather than studying a single iconic tower in isolation.

The nonlinear dynamic analyses subjected the seven pagoda models to multiple ground motion records at two hazard levels drawn from Chinese seismic design practice: a frequent earthquake with a peak ground acceleration of 0.07 g, and a rare earthquake with a peak ground acceleration of 0.40 g. The gap between those two levels is enormous, roughly a factor of nearly six in acceleration, and the simulations show how dramatically the damage picture changes across it. Under frequent shaking, the towers largely remain intact, with cracking confined to vulnerable zones around openings. Under rare shaking, the response escalates into block detachment and partial collapse, particularly for the most vulnerable configurations.

The parameter study yielded clear and intuitive trends. Internal infill, the material packed inside the hollow shell of many pagodas, significantly enhances global stiffness and reduces seismic responses, effectively bracing the tower from within. Conversely, increasing the height-to-width ratio amplifies displacement demand at the top of the structure, and larger opening ratios weaken the load-bearing walls and concentrate stress around voids. The most striking results came from hollow-core towers and fully opened configurations under rare earthquakes: these models exhibited pronounced block detachment and partial collapse, with area loss ratios reaching 10 to 20 percent and residual height ratios dropping to approximately 80 percent. In other words, a fifth of the tower’s footprint could be lost and its standing height reduced to four-fifths of the original before the process stabilized.

From the evolution of ALR and RHR across the simulation suite, the team distilled a four-level collapse classification framework that spans the entire damage process, from initial cracking through to global collapse. The lowest level corresponds to the appearance of cracks without meaningful geometric loss, while the intermediate levels capture progressive block detachment and partial sectional failure. The highest level denotes global collapse, the point at which the residual structure can no longer carry its own weight. Because the classification is anchored to measurable geometry rather than subjective inspection categories, two assessors looking at the same damaged tower should, in principle, arrive at the same severity rating, which is precisely what post-earthquake triage requires.

A crucial test for any damage index is whether it works in the messy reality after a real earthquake, when survey teams may have only photographs and rough sketches rather than laser scans. The researchers validated their method against damage observed in masonry pagodas during the 2008 Wenchuan earthquake, the catastrophic event in Sichuan Province that damaged thousands of heritage structures. The comparison demonstrated that the proposed index can reliably quantify collapse severity even when detailed geometric loss data are unavailable, which is a decisive practical advantage. Emergency responders and heritage authorities rarely have the luxury of complete documentation in the days after a major quake, so an index that tolerates incomplete data is far more useful in the field than one that demands it.

The significance of the work extends beyond China’s borders. Masonry towers and pagodas are a global heritage category, from Italian campaniles to Nepalese temple towers, and seismic risk assessments for such structures have proliferated in recent years, using tools ranging from ambient vibration monitoring and Bayesian model updating to limit analysis and shaking table tests. What most of these methods share is a focus on predicting damage before it happens or detecting it through dynamic signatures. The new dual-parameter index addresses a different and complementary question: once damage has occurred, how bad is it, quantitatively? That question drives triage decisions, such as which towers need immediate shoring, which can await scheduled restoration, and which are safe for the public to approach.

The authors suggest the method can serve as a robust and practical tool for post-earthquake damage assessment and for decision making in the conservation and seismic risk mitigation of historic masonry structures. Because ALR and RHR are geometric ratios, they can in principle be estimated from visual inspection, photogrammetry or laser scanning, and they translate directly into the language conservators use when planning interventions. The research was supported by the National Natural Science Foundation of China, the Key Research and Development Program of Shaanxi Province and a doctoral dissertation innovation fund from Xi’an University of Technology. For the custodians of ancient towers standing in one of the world’s most seismically active regions, the study offers something rare: a damage scale designed for their buildings, validated against a real catastrophe, and simple enough to be used when it matters most, in the chaotic hours and days after the ground stops shaking.

Subject of Research: A dual-parameter geometric damage index for quantifying seismic collapse severity in historic masonry pagodas using discrete element modeling

Article Title: A novel dual-parameter method for evaluating seismic collapse severity in masonry pagodas

Article References: Li, M., Lu, J., Wang, D., Jia, X., Wu, X., Mao, D., Yun, Z., & Wang, Z. (2026). A novel dual-parameter method for evaluating seismic collapse severity in masonry pagodas. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02661-z

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02661-z

Keywords: masonry pagodas, seismic collapse, damage index, discrete element method, area loss ratio, residual height ratio, earthquake engineering, cultural heritage, Wenchuan earthquake, structural health assessment, nonlinear dynamic analysis, post-earthquake assessment

The research, conducted by Resat Oyguc and Evrim Oyguc of the Institute of Disaster Management, Earthquake Engineering Department at Istanbul Technical University, focuses on a class of buildings that keeps structural engineers awake at night: non-ductile reinforced concrete frames. These are structures designed before modern seismic codes demanded the careful reinforcement detailing that allows a building to bend and deform without collapsing. Many such buildings across seismically active regions, from Türkiye to California, remain in service today, and retrofitting them has become a global engineering priority.

Two of the most common retrofit strategies anchor the study. The first involves wrapping columns with bonded carbon fiber-reinforced polymer, or CFRP, jackets—thin, immensely strong composite sheets that confine the concrete and delay brittle failure. The second deploys steel buckling-restrained braces, ingenious devices in which a steel core designed to yield in both tension and compression is housed within a tube that prevents it from buckling, allowing the brace to dissipate seismic energy stably through hundreds of loading cycles. Both approaches can dramatically improve a frame’s performance, but they do so in fundamentally different ways, and this difference has long frustrated attempts at unified assessment.

The problem, as the authors explain, lies in the very design of existing damage indices. Scalar indices calibrated against one intervention family record how much damage has occurred rather than which mechanism produced it. An index tuned to the behavior of CFRP-retrofitted frames transfers poorly to braced frames, and neither can sound an alarm when a brittle mode—such as joint panel shear failure or sliding—is about to take control of the response. In a severe earthquake, that distinction can mean the difference between a repairable structure and a catastrophic collapse.

The researchers’ answer is the Mechanism Evolution Index, or MEI, a framework that condenses six independently measurable response quantities into a bounded scalar on the unit interval, while simultaneously decomposing the structural state into a ternary coordinate that separates demand into three interpretable channels: ductility, shear, and connection. The six constituents include quantities familiar to any experimentalist: the normalized hysteretic energy dissipated during a run, the ratio of peak base shear to design-level capacity, the peak interstorey drift ratio, the residual drift left after shaking stops, the dynamic amplification between the shaking table and the structure above it, and the period softening ratio that captures how much the structure’s fundamental frequency has degraded from one excitation to the next.

What makes the framework remarkable is its economy of calibration. The six constituents are combined through a single frozen weight set, anchored once at the joint-panel cracking and sliding thresholds of a three-specimen calibration series. Each constituent passes through a sigmoid normalization function whose half-saturation value is fixed to the measured response of the bare specimen at design intensity. Once these anchors are set, the weights are frozen and applied without any re-tuning across retrofit type and shaking intensity. This is a deliberate departure from the prevailing practice, in which every new structural configuration demands its own bespoke index calibration, rendering comparisons across interventions nearly impossible.

The ternary coordinate is where the index earns its diagnostic power. The three components—ductility, shear, and connection—sum to one, placing every response state as a point within a triangular coordinate space whose corners represent pure ductile, pure shear, and pure connection demand. As a frame is shaken progressively harder, its point traces a trajectory through this space, and the leading axis at any moment names the mechanism that governs. The framework also defines a dominance margin, the difference between the two largest coordinates, which quantifies how decisively one mechanism leads over the others—a measure of confidence in the diagnosis itself.

To build and test the framework, the researchers drew on a one-third-scale specimen series: a bare non-ductile frame, the same frame retrofitted with a three-ply CFRP jacket, and a version strengthened with an innovative tube-in-tube buckling-restrained brace. All three configurations were reproduced by a single calibrated OpenSees finite element model, whose joint hysteresis was tuned to match measured displacement traces, base shear histories, hysteretic energy, and the fundamental periods identified from white-noise excitation before and after each strong-motion run. The calibration objective weighted all four error measures simultaneously, ensuring the simulation platform captured not just peak responses but the degradation pathways that unfold between them.

The findings tell a story that should concern anyone responsible for retrofit decisions. Under design-level intensity, the bare frame became connection-dominated, its ternary point migrating toward the joint sliding threshold exactly as its unreinforced beam-column panels began to fail. The CFRP jacket, perhaps counterintuitively, suppressed joint engagement through the design band but then collapsed through the very same connection channel when pushed to the ultimate level—the strengthening shifted the brittle mode upward in intensity rather than eliminating it. Only the braced frame remained on the ductility axis throughout, converting the failure mode into a stable, energy-dissipating one. The connection component of the index thus serves as an indicative retrofit-screening signal, flagging interventions that leave a residual brittle pathway even when headline performance metrics look satisfactory.

Transferability—the acid test for any index claiming generality—was examined on six external cases lying outside the calibration set, four bare and two retrofitted. In every labelled case, the mechanism reported by the experimental or analytical source landed on the leading ternary axis of the index. The classical scalars, by contrast, tracked damage severity faithfully but could not name the mechanism in any of them. This separation between knowing how much and knowing what kind is, in the authors’ framing, the essential contribution of the work.

The practical implications extend well beyond the laboratory. Post-earthquake reconnaissance following recent sequences in Türkiye has repeatedly documented the lethal consequences of brittle joint failures in non-ductile frames, and retrofit campaigns guided only by severity-based indices may inadvertently favor interventions that mask rather than remove the underlying vulnerability. A screening tool that can be applied identically across bare, jacketed, and braced configurations, using response quantities measurable from instrumentation or extracted from a calibrated simulation, offers engineers a common currency for comparing retrofit options on the dimension that matters most in a collapsing building: which mechanism will win.

The authors are careful to delineate the scope of their framework. It applies to regular planar systems under single-direction motion, and the frozen weight set is anchored to joint-panel thresholds specific to the calibration series used. Extending the approach to three-dimensional response, torsionally irregular buildings, and bidirectional ground motion remains open. The data supporting the study are available from the corresponding author upon reasonable request, and the authors report no external funding or competing interests. Even within these bounds, however, the Mechanism Evolution Index represents a meaningful conceptual advance: a damage measure that evolves alongside the structure, tracing not just the accumulation of harm but the shifting identity of the mechanism inflicting it.

As cities with vast stocks of pre-modern-code concrete buildings confront escalating seismic risk, the difference between a retrofit that redirects failure into a ductile pathway and one that merely postpones a brittle one is not an academic distinction—it is a matter of life and death. By giving engineers a single bounded number paired with an interpretable mechanism diagnosis, the Istanbul Technical University team has provided a tool that could make that distinction visible before the next earthquake makes it tragically apparent.

Subject of Research: A mechanism evolution index for the seismic assessment of retrofitted non-ductile reinforced concrete frames

Article Title: A mechanism evolution index for the seismic assessment of retrofitted non-ductile RC frames

Article References: Oyguc, R., & Oyguc, E. (2026). A mechanism evolution index for the seismic assessment of retrofitted non-ductile RC frames. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02679-3

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02679-3

Keywords: seismic retrofitting, reinforced concrete, damage index, ductility, CFRP, buckling-restrained brace, OpenSees, non-ductile frames, beam-column joints, shake table testing, earthquake engineering, structural assessment