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 team, led by Yanglong Chen and Chaojun Ouyang of the Chinese Academy of Sciences, compiled a database of 32,714 landslide records drawn from public inventories around the world, including thousands of landslides triggered by the 2008 Wenchuan earthquake in China and the 2015 Gorkha earthquake in Nepal. The collection spans rainfall-triggered rock slopes in Hong Kong, hurricane-induced soil slides in Puerto Rico, coseismic failures in Greece and the Nepal Himalaya, and many other settings. Each record contains geometric descriptors such as landslide volume, source area, vertical drop height, slope angle, and various width measurements, along with the observed runout distance. The sheer scale of the database is itself a milestone, but its heterogeneity is what makes it scientifically interesting and computationally challenging.

That heterogeneity takes several forms. Different data sources cover different regions, report different subsets of variables, and describe vastly different numbers of events. Rainfall-triggered landslides account for 17,637 cases in the compiled dataset, earthquake-triggered events for 14,391, while landslides triggered by combined factors number only 67. Rock landslides dominate with 27,824 samples, compared with 4,533 soil landslides and just 285 mixed-material events. Because some inventories report volume but not slope angle, and others record source width but not total area, every possible combination of input factors corresponds to a different subset of usable samples. A model trained on one configuration may therefore be evaluated on data that differ systematically from the data behind another configuration, confounding any comparison of which factors truly matter.

The researchers argue that this is precisely where most previous machine learning studies of landslide runout have fallen short. Work has typically emphasized predictive accuracy for a single landslide type or region, treating model selection as a secondary concern. But different algorithms trained on the same data can latch onto different relationships, and when similarly performing models disagree about which factors drive runout, the popular SHAP interpretation technique, which attributes predictions to individual input variables, will produce different answers depending on which model happens to be chosen. In other words, factor importance inferred from a single model may reflect the quirks of that algorithm rather than any stable property of the underlying physics.

To break this dependence, the team built a selective ensemble framework. Six base learners representing distinct modeling paradigms were trained under identical preprocessing, factor configurations, and data splits: a multilayer perceptron, Random Forest, Support Vector Regression, XGBoost, and two attention-based deep learning architectures for tabular data, TabNet and FT-Transformer. Performance was assessed with five-fold cross-validation, and only models whose relative performance fell within five percent of the best learner, or three percent for very small sample groups, were admitted to the ensemble. The selected models were then combined using non-negative least squares, a constrained optimization that assigns each model a non-negative weight, preventing predictions from canceling one another and keeping every contributor’s influence directly interpretable. Crucially, the ensemble is retained only if its cross-validation performance exceeds that of the best individual model; otherwise the framework falls back to the single best learner. This combination of screening, constrained aggregation, and a validation-based fallback rule is what allows the method to reduce model-selection variability without blindly averaging everything together.

The results are striking. When the vertical drop height H was included among the predictors, the ensemble achieved coefficients of determination between roughly 0.65 and 0.98 across the seven landslide types analyzed, with earthquake-triggered rock landslides reaching an R-squared of 0.96533 on independent test sets and soil landslides 0.95341. For four of the seven types, optimal performance was achieved with only two input variables, height and volume, echoing a familiar lesson from empirical runout formulas: a small number of well-chosen geometric factors often outperforms a crowded feature list, especially when adding variables shrinks the usable sample size. The ensemble matched or exceeded the best individual model in most cases, and its cross-validation performance was never lower, confirming improved stability rather than merely marginal accuracy gains.

The framework was also used to quantify what happens when a key factor becomes unavailable. Vertical height is often difficult to estimate accurately before a landslide occurs, so the team compared models with and without it. The consequences varied dramatically by landslide type. Rainfall-triggered landslides suffered the largest performance collapse, with R-squared falling from about 0.944 to roughly 0.377 when height was removed and remaining factors re-screened. Earthquake-triggered landslides were far more resilient, dropping only from 0.965 to 0.914, because substitute variables such as source height could partially compensate. This sensitivity analysis turns an abstract question about factor importance into a practical guideline: for some landslide types, investing in better pre-event height estimates pays enormous dividends, while for others, existing topographic proxies are nearly sufficient.

The ensemble-level SHAP analysis then revealed how the same physical factors behave differently depending on the triggering mechanism and material. Vertical height emerged as the dominant or near-dominant factor in nearly every category, showing a consistent nonlinear signature: its contribution is negative at low values, rises rapidly as height increases, and then plateaus, indicating diminishing marginal returns on elevation difference. Volume, by contrast, behaved in a trigger-dependent way. For rainfall-triggered rock landslides its contribution generally decreased with increasing volume, while for earthquake-triggered rock landslides it increased, a contrast the authors interpret cautiously given the strong correlations among volume, source area, and source width in the rainfall subset. Slope angle showed the starkest divergence: its contribution declined with steeper angles for rainfall-triggered and soil landslides, consistent with the idea that steep rain-fed slopes store and infiltrate less water, but it turned sharply positive above roughly 50 degrees for earthquake-triggered rock slopes, where seismic shaking can destabilize near-vertical faces directly.

The authors are careful to frame these patterns as statistical associations learned by the models rather than proof of physical causation, noting that correlated predictors share attribution and that data-processing differences among source inventories introduce uncertainties that cannot be fully eliminated. They also acknowledge gaps: multiple factor-triggered landslides remain severely underrepresented, and type-specific variables such as rainfall intensity are inconsistently documented across databases. Even so, the study delivers a template that other hazard domains could adopt. By screening diverse learners under uniform conditions, combining only the competitive ones with transparent weights, and interpreting factors at the ensemble level, the framework converts an unruly, heterogeneous compilation of 32,714 landslides into a stable basis for deciding which variables matter, for which landslide types, and at what cost in data availability. For regional-scale risk assessment, where thousands of potential failures must be screened quickly and cheaply, that combination of robustness, interpretability, and modest data requirements may prove as consequential as any single accuracy record.

Subject of Research: Machine learning prediction of landslide runout distance using a multi-source heterogeneous dataset and a selective ensemble framework with SHAP-based factor evaluation

Article Title: A selective ensemble framework for reliable factor evaluation and landslide runout prediction under data heterogeneity

Article References: Chen, Y., Ouyang, C., Zhao, B., Yang, W., & Wang, F. (2026). A selective ensemble framework for reliable factor evaluation and landslide runout prediction under data heterogeneity. Results in Engineering, 32, Article 113218. https://doi.org/10.1016/j.rineng.2026.113218

Image Credits: AI Generated

DOI: 10.1016/j.rineng.2026.113218

Keywords: landslide runout, machine learning, selective ensemble, SHAP, data heterogeneity, hazard assessment, Wenchuan earthquake, Gorkha earthquake, XGBoost, Random Forest, vertical drop height, regional risk mapping