This report details the data verification process for the information utilized in the publica- tion ”Empirical fragility and ROC curves for masonry buildings subjected to settlements” [3]. The data are stored in the 4TU.ResearchData repository [4]. Data collection and anal- ysis took place between 2020 and 2021, with the final version being published in 2023. A thorough check was conducted before and after the publication of the manuscript to ensure data quality. While the first check was conducted by the Authors of [3] during the initial data collection, this report focuses on the second check, carried out after the pub- lication. In this document, the adopted methodology for the data verification is detailed and the results of the procedure are presented.

This report begins with Section 2, which outlines the methodology used for the data verification, whereas Section 3 summarises the results. Section 4 offers a discussion and conclusions. Finally, appendix A contains the calculations that support the verification checks.@en

In this study, 2D and 3D modelling strategies are used to represent the behaviour of historical masonry buildings on strip foundations undergoing settlements. The application focuses on a two-story building, typical of the Dutch architectural heritage. An improved 2D modelling is presented: It includes the effect of the lateral walls to replicate the response of the detailed 3D models. The masonry strip foundation is modelled and supported by a no-tension interface, which represents the soil-foundation interaction. Two settlement configurations, hogging and sagging, are applied to the models, and their intensity is characterized using their angular distortion. The improved 2D model that includes the stiffness and weight of the lateral walls agrees in terms of displacements, stress and damage with the detailed 3D models. Conversely, the simplified 2D façade models without lateral walls exhibit different cracking, and damage from 2 to 7 times lower at an applied angular distortion of 2‰ (1/500). The improved 2D model requires less computational and modelling burden, resulting in analyses from 9 to 40 times faster than the 3D models. The results prove the importance of identifying and including the 3D effects that affect the response of structures subjected to settlements.

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This study aims to investigate the damage response of unreinforced masonry (URM) façades resting on strip foundations and subjected to ground settlements via numerical models. The models depict the non-linear constitutive behaviour of both the masonry, via smeared cracking, and of the soil-foundation interaction, via nonlinear interface elements. The influence of building features, such as the masonry material, the length over height (L/H) ratio of the geometry, the wall thickness, the number and size of openings and different types of strip foundations (i.e. reinforced concrete and unreinforced) is examined. A sensitivity study additionally investigates the influence of the interface stiffness and its constitutive model. A Gaussian curve is used to replicate the shape of the ground settlements; These simulate the loss of support underneath the foundation due to urban subsidence. Eight settlement shapes are applied in the FE models, including both symmetric and asymmetric profiles, while the angular distortion is used to measure their intensity. A new aspect is that the extent of the induced damage to the façade is assessed objectively using a damage parameter that represents the number, length and width of cracks in a single scalar value. The method distinguishes between the applied settlement profile at the bottom of the interface and the retrieved settlement profile measured on the façade. The analyses indicate that for a value of the angular distortion equal to 2 ‰ (or 1/500), computed from the resulting deformations of the façades, 60% of the models exhibit serviceability damage associated with cracks of about 5 mm width. Accordingly, the limit values available in the literature are observed to be too optimistic and not conservative in relation to the analyses presented in this study. A key outcome is that facades with an L/H smaller or equal to 1 do not exhibit cracks wider than 1 mm. Façades on reinforced concrete foundations were observed to be less susceptible to settlement damage, compared to unreinforced ones.

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This paper presents an improved 2D modelling strategy which aims to represent the behavior of historical unreinforced masonry buildings on shallow foundations subjected to ground settlements. The application is presented with reference to a two-storey building, typical of the Dutch built heritage. The novelty comprises the inclusion of the effect of the lateral house-to-house separation walls of such old buildings. Additionally, the masonry strip foundation is modelled and supported by a boundary interface representing the interaction between the soil and the foundation. Two realistic hogging and sagging settlement configurations are applied to the model and their intensity is characterized using the angular distortion of the settlement shape. The response in terms of damage and deformations of the proposed modelling strategy is compared with the ones of five selected approaches based on the state of the art. For all the selected models, the damage severity is quantified objectively by means of a scalar parameter, which is computed considering the cracks’ number, length, and width.

The results of the proposed 2D model agree in terms of displacements, crack patterns and damage with the 3D models. On the contrary, the façade models that do not include the effect of the lateral walls do not exhibit the same cracking and damage, resulting in lower damage and deformations for the same applied angular distortion. Accordingly, the proposed modelling strategy requires less modelling complexity and the analyses are 9 to 28 times faster to run with respect to the 3D models. The efficient and accurate model allows performing a wide number of analyses to easily investigate the role of the various building’s features.@en

Historical masonry façades are sensitive to various damaging processes. A recent study, looking at the initiation and progression of cracks in masonry, in the range of 0.1 to 5 mm in width and thus corresponding to light damage [1], has allowed for the calibration of finite-element models that include a material model capable of accurately replicating this damage and which is populated with material properties corresponding to existing structures [6]. The models, which also include a soil-structure interaction boundary designed to account for the effect of the soil during earthquake vibrations [7], have been used to determine the fragility of masonry buildings via the proxy of 2D walls [2]. In the study presented herein, the finite element models are employed to replicate the geometry of (historical) masonry facades to determine their sensitivity to light damage as a consequence of the two damaging processes observed to be most common for this type of façade, namely (differential) settlements and (earthquake) vibrations [3]. The masonry façades were first pre-damaged via settlement distortions which generate just-visible cracks in the order of 0.1 mm to 1 mm in width. Then, an acceleration time history corresponding to two different Dutch earthquake events and two recordings of traffic-induced building vibrations [9] were separately applied at the base of the models. In this manner, the effect of existing damage could be assessed in regards to the aggravation generated by vibrations. The settlement part of the study revealed that long façades were more vulnerable to applied soil distortions, for instance. Then, subsequent vibrations further increased damage for intensities measured with a peak ground velocity (PGV) larger than 2 mm/s while the control set of virgin or uncracked façades remained undamaged at this PGV. At 32 mm/s, many pre-damaged façades also exceeded the light damage range. At equal PGV, the traffic vibrations, with a larger number of effective cycles, resulted in increased damage aggravation in comparison to the earthquake recordings.

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In the Netherlands, the potential damage to the building stock due to subsidence phenomena has recently received increased awareness. However, evaluating and predicting damage to buildings in subsiding areas is a complex task that requires associating the vulnerability of exposed structures with the intensity of the subsidence hazard. Considering the widespread presence of subsidence-related damage to the built heritage, the focus of this study is to provide empirical-based insights to assess and forecast subsidence damage to masonry buildings. A rich dataset with manual levelling measurements was collected comprising 386 surveyed masonry buildings, mainly low-rise (terraced) houses built before 1950. Of the total set of buildings, 122 cases rest on shallow foundations and 264 on piled foundations. For each building, the recorded damage is related to the settlement, calculated from the bed-joint levelling measurements, using four different intensity parameters, namely differential settlement, rotation, relative rotation and deflection ratio. These four parameters are appraised in their capacity to effectively predict the intensity of the damage. The Receiver Operating Characteristic (ROC) method is used to evaluate the relative efficacy of the selected hazard parameters. The rotation, the relative rotation (angular distortion) and the deflection ratio are observed as the most accurate when predicting the intensity of damage, while the differential settlement appears less accurate. Additionally, the dataset was used to generate empirical fragility curves where the probability of damage is described as a function of the aforementioned parameters. Thresholds were set to distinguish between the light damage and the functional and structural damage state. At a relative rotation of 1/500 masonry buildings on shallow foundations were observed to reach or exceed light damage with a probability of 13%, and functional and structural damage with 5%. The availability of the bed joint levelling measurements made it possible to classify eight recurrent settlement profiles, including both symmetric and asymmetric profiles, associated with both the overall deformation and the rigid rotations of the surveyed buildings.@en

This paper demonstrates the use of non-linear finite element modelling to investigate the response of structures subjected to different shapes of subsidence-related ground settlements. The approach is presented with reference to a two-storey unreinforced masonry façade resting on a shallow foundation. Eight realistic settlement shapes, based on field and literature data, are applied in the model with increasing intensity. The intensity of the subsidence profiles is characterized using their (angular) distortion. The extent of the induced damage on the façade is objectively and directly quantified by a damage parameter, based on the number of cracks, their length and opening. The performance of different settlement indicators and corresponding limiting values, typically employed in the state of the art, is in this paper discussed in relation to the damage modelling strategy; these are observed to be dependent on the shape of the settlement profiles. The aim of this paper is thus to provide insight into the extent to which the vulnerability of masonry buildings depends on the shape of the subsidence pattern and may serve as a warning not to use (deterministic) damage indicators such as angular distortion without considering the settlement shape.@en

This study presents a novel framework in which numerical modelling contributes to the performance of district-scale, subsidence-induced damage assessment in cities where ground settlements affect entire quarters. Therein, the implementation of expeditious procedures offers geotechnical engineers the possibility of contributing beyond the typical site scale. For this purpose, several “typified” hydro-geomechanical-loading (HGL) models, which represent (simplified) scenarios of masonry buildings undergoing settlements, were set up to account for different predisposing or triggering factors (i.e., soil heterogeneity, loading conditions, and groundwater variations) of settlement occurrence in built-up areas. These models exploit multi-source, wide-area input datasets encompassing the hydro-mechanical properties of geomaterials, in situ investigations and measurements (e.g., groundwater levels in wells), and innovative remote sensing data (i.e., DInSAR techniques). With reference to a district in Rotterdam City (the Netherlands), which was built on “soft soils”, the numerical simulations of different scenarios (i) provide an overview of the comparative role of predisposing or triggering factors on settlement occurrence and (ii) allow assessments of the expected induced damage to masonry buildings over 30 years with the exploitation of fragility curves. Considering the widespread diffusion of such geohazards, the proposed approach could help prioritise (rather expensive) maintenance work to the built heritage within sustainable strategies for subsidence risk mitigation.

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This paper presents an integrated analysis based on the use of multi-source wide-area datasets consisting of hydro-mechanical properties of geomaterials, in-situ investigations/measurements (e.g. groundwater levels in wells) and innovative space-borne data (i.e. DInSAR techniques) to support numerical analyses aimed at assessing and predicting the settlements affecting built-up areas in variable soil conditions. To this aim, an expeditious procedure was developed and tested with reference to a district in Rotterdam City (The Netherlands) affected by subsidence phenomena due to the presence of heterogeneous settling strata mainly composed by peat and organic soils. The results obtained allowed investigating the role of predisposing factors of the settlement occurrence and assessing the induced damage on buildings. Considering the widespread diffusion of such geohazards, the followed procedure could help the in-charge authorities to carry out activities at urban scale aimed at identifying the areas most affected by subsidence risk and to select the most suitable and sustainable mitigation strategies.@en