In the Netherlands, subsidence due to different causes is linked to damage to the ubiquitous masonry structures. Finite element (FE) analyses can be used to assess the response of the structures subjected to settlements. This paper presents the comparison between three-dimensional FE modelling strategies to investigate the response of an unreinforced masonry building on a strip foundation. The aim is to investigate whether different modelling approaches demonstrate consistent results. The soil-structure system is modelled employing two strategies: a coupled model, in which the structure is tied to the soil volume, and an uncoupled approach that divides the soil and structure into two sub-systems. Two displacement fields, imposed at the bottom of the soil volume, idealize various shapes of the subsidence troughs, with increasing intensity measured by their distortion. Non-linear interfaces are used to simulate the soil-foundation interaction, and their stiffness values vary based on the type of model. The displacements, interface stresses and crack patterns of the selected modelling strategies are consistent. The interface types do not influence the response of the façade, whereas the shape of the settlement does play a key role. The uncoupled models exhibit, on average, slightly higher values of damage than coupled models for a given imposed distortion. The two modelling strategies require almost the same computational time and show similar convergence. Because of the limited contribution of small soil volumes in uncoupled models, the superstructure sub-system can be directly utilized to assess the response of structures undergoing vertical displacements, thereby reducing the modelling burden.

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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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Historical quay walls, constructed in unreinforced masonry, play a crucial role in the infrastructure of many Dutch cities. Designed originally as gravity retaining walls, these structures are increasingly subjected to traffic loads due to vehicles operating on roads built on their backfill. This study conducts a preliminary numerical evaluation of a strengthening technique aimed at prolonging the service life of such quay walls, focusing on a specific case in Amsterdam. The strengthening method involves drilling tubular steel piles through the existing masonry to anchor into a stable soil layer, with the piles bonded to the masonry using low-shrinkage casting concrete. The assessment models the interaction between the strengthening technique and the existing quay structures, including a detailed simulation of the installation process, identified as critical for proper simulation of the structural behaviour. While the technique significantly enhances the quay's force capacity, an improvement in displacement capacity was not evident, highlighting the need for further investigation.

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This paper introduces novel analysis procedures for the structural assessment of masonry earth retaining structures subjected to traffic loading. Given their substantial presence, particularly in transportation networks of historical cities, and the challenges posed by ageing, deterioration, and exposure to loads beyond their original design considerations, this research highlights the necessity of accounting for potential load redistribution mechanisms during their assessment. This can prevent overly conservative interventions that may not be necessary and also contravene sustainability and heritage preservation principles. Four distinct analysis procedures – 2D monotonic, 3D monotonic, 3D static moving load and 3D dynamic moving load – are developed, each progressively more refined than its predecessor in capturing potential load redistribution mechanisms in masonry earth retaining structures. These mechanisms may develop due to the dynamic loading conditions of the vehicular passage, the 3D structural configuration of retaining structures, and non-linear material behaviour. By comparing the structural capacity evaluated using the four procedures, contributions from different sources of load redistribution can be separately quantified, aiding in the reduction of conservatism inherent in less refined assessment procedures. The application of the developed procedures and consequent quantification of load redistribution is demonstrated through a case study of an existing masonry retaining structure in Amsterdam, the Netherlands.

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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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Canals delimited by masonry quay walls are integral elements of many cities in the Netherlands. Historically built to enable the efficient transportation of goods, today such infrastructure also gives the cities their historical and monumental character. In recent years, many quay walls in the Netherlands have shown substantial deformation and damage, and in few cases even collapse. Historical quay walls, which are constructed in thick multi-wythe unreinforced brick masonry and are supported on a system of timber piles, nowadays sustain traffic loads larger than the one they were designed for. Instances of collapse and severe damage has given rise to a need for research assessing the safety of these structures, which are not appropriately covered by any normative or standardised guidelines. This paper presents a novel methodology to numerically assess the performance of masonry walls in historical quays under the dynamic effect of traffic loads. Application of the proposed methodology to a case study in Amsterdam, the Netherlands, is presented.@en

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 quay walls constructed in unreinforced masonry are integral elements of many cities. Originally designed as gravity retaining walls, they are nowadays often subjected to the action of traffic loads as a result of vehicles travelling on roads constructed on their backfill. This paper presents a numerical analysis procedure for carrying out the structural assessment of quay walls under traffic loads. The procedure simulates the non-linear dynamic response of the quay wall under the effect of the passage of a vehicle. Non-linear dynamic calculations are performed not only to be representative of the actual nature of loading but also to produce realistic estimations of structural safety, load redistribution capacities and displacements. Adopting a tier-based approach, the computational burden typically associated with such simulations is significantly reduced. This is obtained by adopting simplifications which allow for the modelling the 3D soil block comprising the backfill of the quay wall only in the first tier of the procedure. To demonstrate the implementation of the procedure, a detailed application to an existing quay wall in Amsterdam, the Netherlands, is presented. Different foundation damage scenarios are also considered. Though the procedure is presented in this paper for a specific typology of quay walls, it has conceptual and methodological value. With appropriate modifications it can be used for the structural assessment of other earth retaining structures as well, under the effect of vehicular traffic on their backfills.@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

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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The probability of light damage to unprepared, unreinforced masonry structures exposed to induced seismicity due to gas extraction in the north of the Netherlands is still under investigation. Repeated light seismic excitations caused by frequent, light and nearby earthquakes have been linked to economical losses and societal unrest in particular, with extensive damage claims. Moreover, the damaging potential of the seismic events has been related to the condition of the structure, especially if damage corresponding to settlement causes is already present. A comprehensive testing campaign oriented towards the initiation and progression of light damage of replicated clay brick masonry has been conducted at Delft University of Technology. Based on these tests, calibrated finite element models have been produced. This article uses the calibrated non-linear time-history models to simulate the effect of earthquake ground motion on a variety of initial conditions, wall geometry, material properties, and number, type and intensity of earthquakes. The results are then used to regress a relationship between damage and these parameters. This is subsequently employed to run a MonteCarlo simulation and produce fragility curves where the probability of exceeding specific damage values for various initial damage levels is presented against the seismic hazard. The vulnerability or fragility curves show that visible damage, with cracks wider than 0.1 mm, appears, with a 10% exceedance probability, at 13 mm/s of peak ground velocity; but, if the masonry had already undergone some light, yet imperceptible damage, a PGV of 6 mm/s was sufficient to aggravate it into visible cracks. To attain a 1% probability of exceeding light damage however, for which the masonry would need more invasive repair, it was observed that PGVs larger than 15 mm/s were required. These fragility curves were finally compared to graphs from other authors and found to capture well the variability in the range assigned to light damage.

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Recent, light earthquakes induced by the extraction of gas in the north of the Netherlands have been linked to light, mostly aesthetic damage of the traditional masonry structures in the region; this is also connected to economic losses and societal unrest. To be able to accurately assess the light damage, detailed finite element models are necessary and need to include realistic soil movement, wave propagation, and soil-structure interaction boundaries. Moreover, the minute deformation of the soil, including the rocking and translational components of seismic ground motion, has shown to be influential to light damage. Consequently, this study has pursued the definition of efficient soil-structure interaction boundaries to implement in finite element models of buildings. A methodology, following the sub-structure method for the seismic Soil-Structure-Interaction (SSI) is defined and presented. The soil-structure-system is divided into three sub-systems: the far-field soil, the near-field soil and the superstructure. First, a 3 km deep and 8 km wide, plane-strain model of the soil is employed to study the behaviour of the soil at the surface due to deep, simplified seismic events. The soil model is linear-elastic since only light seismic excitations are considered. Next, a smaller, 30 × 300 m (shallow) soil model with a building on top, is given boundary elements calibrated to replicate the behaviour observed at the surface in the larger model. Finally, 2D models of masonry façades set on the intermediate soil model are used to reduce the soil-structure interaction to representative interface elements. The models are matched in terms of dynamic behaviour, strains, cracking, and displacements, and the behaviour is compared to existing ground motion data for the Zeerijp and Westerwijtwerd earthquakes. It is demonstrated that the equivalent interface allows efficient modelling of seismic excitations considering a detailed soil-structure interaction for complex, smeared non-linear, time-history analyses of wall models to assess (light) damage in probabilistic studies. Models with this equivalent interface show greater damage than comparison models without it.

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In the region of Groningen (NL), human-induced earthquakes initiated by gas extraction are causing structural damage. In that area, the building stock is mainly composed of unrein- forced masonry (URM) buildings with light and flexible timber floors and roofs. Thus, an ex- perimental campaign was arranged for assessing the in-plane response of these diaphragms, and a retrofitting method was developed, consisting of an overlay of plywood panels screwed to the existing sheathing around their perimeter. This light, reversible stiffening measure showed a great increase in the in-plane strength, stiffness, and energy dissipation of the floors. Subsequently, an analytical model was developed, showing very good agreement with experimental results, and enabling the design of retrofitting interventions with this technique. Starting from the formulated model, a user-supplied subroutine was implemented in the finite element software DIANA FEA, allowing to represent the in-plane response of the diaphragms, including their energy dissipation. Finally, the impact of this retrofitting intervention on a case study of an existing building was evaluated by means of nonlinear time-history analyses. The results of numerical analyses show that the user-supplied subroutine accurately describes the in-plane behaviour of the retrofitted timber floors. Besides, the proposed retrofitting tech- nique greatly increases the global seismic performance of the building, compared with both its as-built configuration and to stiffer and less reversible strengthening measures.@en

The north of the Netherlands is prone to frequent, light earthquakes linked to economical losses and societal unrest due to the induced seismicity in the region. These light earthquakes produce correspondingly low values of in-plane drift on the typical masonry structures of the region, many of which are built with cavity walls composed of an inner, load-bearing calcium-silicate masonry leaf, and an outer, exposed fired-clay masonry veneer. To assess the resulting damage from the lighter earthquakes, it is thus necessary to understand the difference in behaviour of the inner and the outer masonry leaves when exposed to the same drift values. Experimental tests of replicated, full-scale calcium-silicate brick walls and spandrels are detailed herein and compared to previously tested clay masonry samples. A purposely developed, scalar damage parameter is used to assess the width, number and length of the cracks to objectively quantify damage. High resolution digital image correlation is used to accurately monitor the initiation and propagation of cracks. The experiments reveal that calcium-silicate samples exhibit slightly greater damage than clay samples when subjected to the same in-plane drift. From the tests, drift values for light damage or ‘damage state one’ are set between 0.15 and 0.65‰ for the type of wall tested. Moreover, in these tests, cracks in calcium-silicate samples were significantly more likely to split brick units, whereas cracks in the type of clay samples employed, always followed the masonry joints. This fundamental difference in the light-damage behaviour between the two materials is of importance when considering the perception of damage, the strategies and cost of the repairs, and the strategies for strengthening of masonry structures with cavity walls resembling the type of masonry tested herein.

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Induced seismicity in the north of the Netherlands has recently exposed unprepared, unreinforced masonry structures to considerable earthquake hazard. While the ultimate-limit state capacity of the structures is vital to assess the individual's risk, their behaviour during more frequent, lighter earthquakes leading to ‘light damage’, has shown to be strongly linked to economical losses and societal unrest. To study the effect of these repeated light earthquakes, the behaviour of masonry structures, typical of the region, needs to be investigated when subjected to multiple small cycles. In particular, insight into the potential aggravation of the light damage is sought. Hence, shear walls of replicated clay brick masonry have been tested in the laboratory and exposed to a high number of low in-plane drift cycles. The experiments show, under inspection with high-resolution Digital Image Correlation, how stair-case, diagonal cracks initially distribute in multiple cracks running in joints at the centre of the walls, but later localise into a single, visible, wider crack. The tests are used to establish an interval over which light damage can be expected for these types of walls. Furthermore, this initial distribution of strains in ‘bands’ and subsequent localisation, previously observed only with computational finite element models and which could not be verified experimentally, is compared and reproduced with improved models both at the composite continuum scale (macro-model) and the brick-to-brick micro scale. The models are calibrated based on the quasi-static, cyclic experimental results and later used for extrapolation in dynamic nonlinear settings to assess the influence of natural ground motion excitations.

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In recent years, gas extraction in the northern part of the Netherlands has been causing low-magnitude, induced, shallow earthquakes. Besides safety, the prediction and evaluation of ‘light’ damage due to these induced ground motions is important, as it is related to economic and serviceability losses, and societal unrest. An experimental and numerical campaign is ongoing at Delft University of Technology, aiming to improve the knowledge of the underlying physics of crack initiation and propagation in unreinforced masonry (URM) structures typical in the Netherlands. A damage scale and damage parameter are defined herein in order to objectively quantify cracking damage as a function of the number, length, and width of cracks in masonry walls. The cracking mechanisms are studied for URM walls and spandrels subjected to in-plane loading. Displacements, strains, and loads under which cracking starts and propagates are evaluated and correlations are sought. The Digital Image Correlation measuring system is used to accurately detect crack formation and the evolution of the cracking pattern. This is also utilised to validate and calibrate non-linear finite element models. From the experiments, drift values are obtained for the light damage state of the masonry walls. A range between 0.3‰ and 1.1‰ is set as belonging to light damage. Moreover, a damage accumulation or material degradation was observed during cyclic testing. Additionally, fracture-mechanics based, micro and macro finite element models are capable of reproducing the repetitive behaviour of the tests.

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