Crack Patterns Turned Into Numbers: A Probabilistic Way to Diagnose Masonry Damage

Engineers assessing old masonry buildings have long relied on expert judgement to interpret the cracks that snake across their walls. A new study published in Built Heritage proposes a way to replace that subjectivity with numbers: a phenomenological probabilistic model that converts measurable crack characteristics into a quantitative indicator of a structure’s condition, calibrated against laboratory experiments and demonstrated on a real building.

The research, conducted by Oksana Kichaieva and Dietmar Adam, addresses a persistent gap in engineering practice. Assessments of historic buildings are still largely based on qualitative defect analysis, which does not provide a unified quantitative interpretation of the condition of individual structural elements or of the building as a whole. The authors argue that for many historic structures, particularly those protected from invasive inspection, observable crack patterns are the only quantitative indicators of structural condition available to an inspector.

The model rests on three parameters: crack width, crack length and crack density, defined as the total crack length per unit area of the surveyed surface. These are treated as random variables and linked to the relative loading level of a wall, expressed as the dimensionless ratio N/Nu, where N is the applied load and Nu is the ultimate failure load. The aim is an inverse problem: instead of predicting damage from loading, the method identifies the loading stage from the cracks that are actually observed.

The experimental foundation comes from earlier laboratory tests on three masonry wall specimens, each 1.68 by 1.52 metres with a thickness of 250 millimetres, built from solid calcium-silicate bricks with a compressive strength of roughly 15 megapascals and laid in M10 mortar. The specimens simulated a deep beam wall with window openings, and differential foundation settlement was reproduced by locally weakening the supports in three different configurations. Loading was applied incrementally, with crack width, length and density recorded at each stage.

Those experiments revealed a staged failure process. Cracks initiate in stress-concentration zones near openings, then widen, propagate along the height of the wall, and finally coalesce into extended failure zones. The crack parameters showed a pronounced nonlinear relationship with the loading level, and the support configuration mattered: the earliest crack initiation appeared in the specimen weakened over two edge sections, followed by the specimen with the largest weakened section, while the latest cracking occurred in the specimen with the smallest weakened zone. Four stages were identified: no cracking below the crack initiation load, crack initiation at that load, damage development between initiation and ultimate load, and structural failure at the ultimate load.

To build the model, the three crack parameters are normalised and combined into a generalised condition index using principal component analysis. The weighting coefficients are the squares of the components of the first eigenvector of the correlation matrix, so they are nonnegative and sum to one, and can be read as the relative contribution of each parameter to the dominant pattern of variability. Because the crack parameters are governed by a common physical damage process, the authors interpret the first principal component as an integral characteristic of the structural condition. For the case study building, the first eigenvalue accounted for approximately 63 percent of the total variability, and the crack width and crack length, which were strongly correlated at 0.895, dominated the index, while crack density contributed little.

Uncertainty is handled with the Monte Carlo method. Random realisations of the three parameters are generated according to calibrated probability distributions, respecting their correlation structure and physical constraints such as nonnegativity, and the condition index is computed for each realisation. The study employed 105 realisations to ensure statistical stability. The resulting distribution of the index is then compared with reference distributions corresponding to different structural loading stages, and probabilities of exceeding each reference state are calculated. Notably, these probabilities are not failure probabilities in the classical reliability sense; they express the position of the current condition relative to reference ranges, and the authors stress that they may take intermediate values and should not be read as the frequency of a rare event.

The model was applied to a fire station building previously inspected by one of the authors. The three-story structure combines masonry walls with an incomplete reinforced-concrete frame, rests on different foundation types with varying depths, and lacks monolithic tie beams or systematic masonry reinforcement. During its 23 years of service, numerous cracks developed in the external walls, predominantly because of differential foundation settlements. The statistical characterisation was based on measurements of 35 cracks in the surveyed external load-bearing walls. The distributions of crack width and crack length proved bimodal and were represented as mixtures of two normal components, each verified with a Pearson goodness-of-fit test, while crack density was adequately described by a normal distribution constrained to nonnegative values.

The results placed the building’s condition between the second and third loading stages, that is, between crack initiation and active damage development, which the authors report is consistent with the observed damage pattern. The probabilities of exceeding the reference states decreased consistently from 0.968 for the state below crack initiation to 0.103 for the ultimate state, indicating that the probability of the building having reached failure is low. The mean of the condition index was 0.113 with a standard deviation of 0.086. The authors note that the identified condition is consistent with the observed damage pattern and adequately reflects the actual state of the structure.

The approach has clear limits. It is intended for masonry buildings composed of small-unit elements in which walls are the primary load-bearing components, and it excludes cracks in nonload-bearing elements such as partitions, whose development follows different mechanisms. The weighting coefficients must be calibrated individually for each structure, results depend on the quality and completeness of inspection data, and visual crack identification remains partly subjective. The validation presented relied on a single building, and the authors call for further testing across a wider range of structures with different ages, damage mechanisms and conservation conditions. Even so, the model offers heritage managers a decision-support tool that requires no invasive testing, works under field conditions, and is independent of a building’s service life, potentially helping to plan repair, strengthening and preservation measures while minimising intervention in historic fabric.

Subject of Research: A phenomenological probabilistic model for diagnosing the condition of masonry structures from crack-pattern parameters

Article Title: Phenomenological model for the damage diagnosis of masonry structures based on crack parameters

Article References: Kichaieva, O., & Adam, D. (2026). Phenomenological model for the damage diagnosis of masonry structures based on crack parameters. Built Heritage, 10(1), Article 64. https://doi.org/10.1186/s43238-026-00303-6

Image Credits: AI Generated

DOI: 10.1186/s43238-026-00303-6

Keywords: masonry structures, crack patterns, structural health assessment, probabilistic model, Monte Carlo simulation, principal component analysis, heritage buildings, nondestructive testing, differential settlement, condition index, load-bearing walls, fire station case study