The main motive for this research was to study the behaviour of quay walls when there is an uneven pile foundation present. This means that the number of piles varies in the thickness of the quay wall along the length. The inspiration came from the failure of the Grimburgwal (Amsterdam, the Netherlands) that collapsed in 2020, which had a length of 65 meters, according to Korff et al. (2021). Korff et al. (2021) reported that the main failure mechanisms that are considered in the case of the Grimburgwal, is the deformation of the piles due to horizontal bending, in the section where there were only two instead of three rows of piles present in the thickness of the wall.

A 2D model with a length of 22.5 meters in the longitudinal direction (along the length of the quay) wall is used in this research, to study the influence of the uneven pile foundation in the thickness of the wall. The quay wall’s out-of-plane behaviour is not considered. The masonry and timber floor are modelled with linear plane stress elements. An interface condition is used to model the interaction between masonry and the timber floor. The longitudinal support beams and kespen are modelled as one element. The piles are modelled as equivalent translational springs that are evenly distributed in the longitudinal direction. In the central area, one spring represents two piles in the cross-section, while the rest of the springs represent three piles. After the application of the deadweight of masonry and timber, a uniform distributed load was used on top of the model to cause settlement of the piles and wall. The dilatation joint was modelled with a nonlinear interface with a high dummy stiffness and no tension, and with a gap of one millimeter.

If the length of the section with two rows of piles is increased, the capacity of the wall reduces. The cracks at the bottom of the masonry, still do not increase significantly if the length of the length of the section with two rows of piles is increased, but it does take less load to generate the same cracks. The boundary conditions also play a large role in the distribution of forces, since it is seen that the piles near the dilatation joint are less critical than the piles near the constrained edge. In the end, this model does give information on how the forces in the piles distribute and how the piles settle, before both brittle and ductile failure of the piles occurs and cracking within the model. However, it should be kept in mind that the model that is considered is a 2D model, whereas the problem of a quay wall is a 3D problem, so the results are not expected to be accurate.

Glass is gaining more and more popularity as a structural material and has become a big share of the building industry. Unfortunately, the building industry is the largest polluter in terms of industrial waste and is responsible for 40% of Europe’s energy demand (CIB, 1999), and glass is also playing a significant role in this number. One strategy to reduce the amount of pollution from a product or industry is by making it circular (PBL, 2019). Meaning the amount of waste is minimized and the energy needed to produce new material is also decreased. In the Netherlands, buildings have to be completely circular from
2050 (Rijksoverheid, 2016). In order for glass to contribute to this goal, elements have to be able to be reused or recycled, taking demountability into account during the design of a structure.
One way of creating such a demountable joint, is by making use of portal frames, which require a rigid connection between the columns and beams. Currently, this connection is designed using either mechanical connections or adhesives. Rigid mechanical connections are visually not aesthetically pleasing and cause impurities right at the points where stresses are highest. This makes the joint more sensitive to failure. Rigid adhesive connections are very prone to execution and design errors, and are uncertain regarding their long-term strength. Currently, there is no efficient way to properly remove adhesives, making them non-demountable joints. This research will therefore design a demountable and rigid joint using contact pressure, taking inspiration from traditional Japanese joinery. To develop this joint, first, theory is studied, followed by the design and lastly by experimental testing.

From literature, the Kanawa and Gooseneck joints are selected, because they have the capacity to take up both shear and a bending moment. These joints are then further optimized to determine the optimal geometry for a rigid glass joint. This means a geometry that minimizes tensile stresses in the glass, decreasing the chance an existing flaw will tear and cause the material to fail. This optimization is done using analytical and numerical analyses, followed by full-scale experiments. To determine the optimal force transfer the geometries were first schematized, and the relevant parameters were determined
for later variation. From hand calculations, it follows that the optimal geometry finds a balance between the stresses resulting from normal force and the stresses resulting from the eccentricity of the internal line of force.

Using a parametric Grasshopper model, the geometries are further optimized by varying dimensions and curvature. Several designs are imported into DIANA FEA and Abaqus to acquire numerical values for the expected stresses of these set parameters. The models are set up as two 2D glass panes with a polymer interlayer in between them. In DIANA FEA a lot of difficulties arose with the combination of complex geometry and multiple contact surfaces. Therefore all designs were mitigated to Abaqus, because this software is more suitable for complex contact surfaces. Comparing the heavily simplified hand
calculations to the FEA, there was a constant increase of peak stresses with a factor of 4.

The Gooseneck design was manufactured using a CNC milling machine and afterwards, its edge was polished, resulting in optimal edge quality. Due to the nature of the geometry, the Kanawa design had to be manufactured using a waterjet. There was a large difference between the accuracy of the two production methods, resulting in the Kanawa joint having a lot more space between the glass plates. This strongly influences the placement of the interlayer materials, but also the stiffness of the joint during the experiments.

Before these models could be validated using experiments, a suitable interlayer to place between the edges of the glass panes was researched. POM, PVC, Surlyn, PA6 and PU85 are deemed suitable and are examined. Eventually, only PU85 could be fitted between the glass panes, which seemed to have the least favourable mechanical properties. The angle of the geometry was too small for most materials to bend them into, even after heating the plastics. The other issue lay with the tight tolerances of the polished glass panes. These had to be additionally polished by hand and the PU85 was treated with
silicone spray, in order for the whole joint to fit. The disadvantage was that this manual polishing damaged the edge quality, increasing the probability of failure at a lower strength.

Experiments were then conducted to validate earlier analytical and numerical calculations, using full-scale single-pane annealed glass. The joints were tested in pure tension and a bending moment, using polarizing filters to visualize the stress trajectories. For the Gooseneck model, the stress trajectories and expected stiffness corresponded well with the models. The samples failed at an average force of 6.0 kN. The model predicted peak stresses of 300 N/mm2 and stiffness of 2.8 N/m at this point, the experiments displayed a stiffness of 3.0 N/m. This means the model turned out to be 5.7% less stiff than the
experiments.

The stress trajectories coincided less clearly with the model for the Kanawa tension model. The samples failed at an average force of 4.1 kN. The expected peak stresses at this point were 150 N/mm2 and the stiffness 0.73 N/m based on the model. The experiments showed a stiffness of 1.1 N/m. The model underestimates the stiffness of the experiments by 33%.

Interestingly, because the tolerances in the Kanawa joint were larger, there was more movement possible in this joint. This influenced the force transfer and therefore resulted in different peak stresses than expected. The Gooseneck model turned out to be almost 3 times as stiff as the Kanawa model. This has two likely reasons. First of all, the geometry of the Kanawa joint is not designed to take up pure tension in the direction that it was tested. Therefore, the geometry itself was a lot less stiff than that of the Gooseneck joint. Secondly, the tolerances were of large influence. Because the Kanawa samples were produced using a waterjet, with quite large tolerances, there was a lot of movement possible in the joint. This meant little force was necessary to displace the joint, resulting in a lower stiffness.

The Kanawa design was tested under a bending moment, because the force transfer is very different compared to pure tension for this design. The full beam had dimensions of 2400mmx 400mmx 10 mm. Locations of peak stresses were similar to the models. The samples failed at an average of 4.0 kN, which corresponds with a moment of 1.1 kNm. The force-displacement graph of the experiments was not linear, but showed varying stiffness with plateaus where the stiffness was around 0. Most likely, this was caused by a combination of the plastic deformation of the PU85 and movement and/or sliding in the
machine itself. It was attempted to calibrate the model to the experiments, by increasing the stiffness of the interlayer. This did not result in sufficient stiffness, which implies the stiffness originates from another element in the setup. The rotational stiffness was 611 kNm/rad, which is 9.1% of the stiffness compared to a solid beam of the same dimensions.

This means the designed joint is not fully rigid, but this exploratory study shows there is great potential for such a system. Further optimizing the geometry and finding a more suitable interlayer could result in a rigid and demountable glass joint, as part of a portal frame.

Masonry structures occupy a significant share of the current building stock due to widespread material availability and cost-effectiveness. Regions with high seismicity, like the Himalayas, have typically developed local seismic culture over the centuries. This has led to improved construction techniques providing an enhanced seismic performance, as evident from post-earthquake surveys. Bhatar is a building typology found in the Himalayas, featuring embedded horizontal timber bands in masonry walls, enhancing the box-behaviour and in turn avoiding their premature out-of-plane failure.
This work aims to quantify the improvement of the out-of-plane performance of masonry walls due to the presence of horizontal timber bands. Numerical analyses were conducted in DIANA FEA software starting from the few experimental results available in literature on this typology. These were used to calibrate the properties of masonry, which was represented as a homogeneous isotropic continuum, with nonlinearities considered by means of a total strain rotating crack model.
Firstly, a U-shaped masonry wall having the same geometry and boundary conditions as the experimental tests was simulated using 3D modelling approach. Non-linear static analyses were performed exploring two different strategies, with minor variations in analysis parameters. Very good agreement was obtained with the results from literature for both strategies with one able to simulate local cracks better, while the other was able to simulate global failure mechanism better. The calibrated numerical model was then employed to conduct sensitivity analyses for precompression load and aspect ratio.
Further refinements to the calibrated model were done. The influence of the frictional behaviour between timber and masonry was explored through discretely modelled interface elements. The timber-to-timber connection was modelled as a hinge. The improvement in the behaviour of the wall due to timber bands connected throughout the frontal wall was also evaluated.
Finally, the calibrated numerical model was employed for the pushover analysis of a full-scale structure representing the geometry of a typical Bhatar house. The results from the numerical analysis were used for seismic assessment using Capacity Spectrum Method. The assessment demonstrated the capability of a Bhatar structure to resist ground acceleration specified for the highest earthquake category defined by Indian Standard Criteria for Earthquake Resistant Design of Structures. Contrarily, an unreinforced masonry structure did not possess the required ductility to resist such an earthquake.
Inclusion of timber bands at corners of a U-shaped masonry wall resulted in an increase of lateral resistance by 40%. Walls with timber bands connected throughout the front wall presented a further increase of 35% in the force capacity. The corresponding improvement in force capacity for a full-scale Bhatar house was even more remarkable at 109% compared to an identical unreinforced house. There was also a noticeable increase in the ductility.
This work constitutes a further step towards a better understanding of the behaviour of Himalayan masonry structures under earthquakes, promoting better seismic risk reduction strategies. This improved understanding into the role of timber in greater seismic resilience of masonry structures also informs better maintenance, conservation and preservation of heritage and historical masonry structures in the Himalayas.

Masonry arch bridges have been around for centuries and are, in the Netherlands, mostly located in historical city centres. As the axle loads of vehicles passing these bridges have increased over the years, the need to re-evaluate the structural safety of these bridges has increases. To do so, different techniques have been developed. However, assumptions had to be made due to limited computational power and lack of knowledge regarding the actual behaviour of masonry. Over the years, the computational power has increased, making it possible to perform more advanced analysis and describe the behaviour of complex materials. Despite this increase, a conservative approach is still used to determine the safety of masonry arch bridges. When it is not sure whether the bridge is safe enough, the bridge is immediately strengthened or a weight restriction is applied, without calculations of the bridges actual capacity. As these interventions could be costly or cause issues with the supply of goods to the city, it is needed to find a better approach and understanding of the actual behaviour of masonry arch bridges. Therefore this study addresses the following research question:
What is the role of constitutive models on simulating the structural behaviour of masonry arch bridges?
In order to formulate an answer to the question, the behaviour of masonry, masonry arch bridges and soils have been investigated first. The investigation shows which function each part of a masonry arch bridge fulfils and which failure modes are expected to occur. When a masonry arch bridge is loaded, the backfill spreads the load and transfers this to the masonry arch. Due to this load, the arch will deform. This deformation is, however, restricted by the backfill. This interaction between the backfill and the masonry arch makes the behaviour of these types of structures a complex structural-geotechnical problem.
For masonry arch bridges, the most common failure mode is the formation of a four hinge mechanism, therefore this study focusses on modelling the behaviour of the masonry arch. Alongside the behaviour of the materials, the development in numerical tools is investigated as well. Doing so, it can be determined what assumptions have been made in the past and what the shortcomings of the approaches are. With the combined knowledge, it is possible to select different material models that can be used for masonry arch bridges. Three different models were created, two macro models and a micro model. The two macro models are both total-strain based models, where one is described by an isotropic - and one with an anisotropic material model, the so called “Total strain crack” and “Engineering masonry” model, respectively. The macro models consider the masonry as a continuum, whereas the micro model distinguishes between units and joints.
To validate the numerical models, test results are needed. As the study focuses on modelling the masonry arch, the different models are first compared to the results of a test on just a masonry arch. The chosen test was performed at the University of Minho in Portugal; a masonry arch was created and, in a displacement control manner, loaded until failure. Prior to performing the tests, the materials were first tested and their properties accurately reported, which is very useful when making a numerical model. After creating and comparing the results of the models and tests, it was found that the Engineering masonry and micro model show a similar shape of the force-displacement curve, while the isotropic “total strain crack” model does not. The engineering masonry and micro model are able to show the brittle failure of the arch, which was also obtained with the tests. However, this failure occurred when only two hinges were formed, where, in the test, a four hinge mechanism was formed. The numerical results do show that cracks are starting to form, however, this does not mean that it also is a hinge. Besides that, the test results show that there is still some redistribution of forces after the peak load. This is not possible when four hinges are already formed. It is expected that the, by the researchers defined, hinges are not actually hinges, but, are the points where cracks start to form. Despite this difference in hinge formation, the resulting force-displacement curves of the models are very close to those of the tests, therefore it can be stated that the used models are suitable to represent the behaviour of masonry arches.
After validating the effectiveness of the masonry material models, the modelling of the problem was extended by adding backfill. Again test results were needed to determine whether the models are also suitable to simulate the extended problem. This test was performed at the University of Salford in the United Kingdom and has been used by Wittenveen+Bos to validate other numerical programs in the past. The bridge was tested in a specially designed chamber, in such a way that plain strain conditions hold, and the load was applied at quarter span in a displacement controlled manner. The results were obtained by loading the arch beyond the peak load, with the applied force being reduced while the displacement continued to increase, which was, according to the research, when a four hinge mechanism was formed.
A negative consequence of plain strain conditions is that the engineering masonry material model was not available to be used, therefore only the “total strain crack” model and the micro model were compared. The initial results of the numerical model resulted in local failure of the soil just below the point load, which did not occur in reality. In order to eliminate this local failure, a small area below the load had to be given linear elastic properties. Although this local failure now doesn’t happen, the results still show that plastic strains develop in the backfill, as well as cracks in the masonry arch. A parametric study was conducted to determine the sensitivity of the models to small changes in material properties. This study showed that the models are most sensitive to changes in soil properties, specifically the internal friction angle. For the micro model, it even appeared that only changes in the soil properties affect the behaviour of the structure, meaning that the sliding failure in the backfill is the governing failure mechanism. In the isotropic “total strain crack” model, a lower tensile strength caused the behaviour of the structure to change drastically. It is found that this is due to Poisson’s ratio and the isotropic nature of the material model. The compressive stresses cause small lateral strains which, due to Poisson’s ratio, cause longitudinal strains. Due to the isotropic nature of the material model, a low tensile strength is assigned in this longitudinal direction, causing the arch to form an unrealistic crack or failure pattern. While in reality the tensile strength in this longitudinal direction, the brick tensile strength, is larger compared to the assigned the brick-mortar bond strength.
Eventually, it could be concluded that it is possible to model the behaviour of masonry arch bridges with great detail. However, in this study the behaviour of the backfill governed the behaviour of the structure, making it difficult to state which modelling approach should be used for the masonry arch. What can be said, is that a micro modelling approach is currently preferred. The study shows that this model is capable of mimicking the behaviour of just a masonry arch, and is less sensitive to changes is masonry properties when backfill is added compared to the isotropic “total strain crack” material model. The anisotropic “engineering masonry” model would be a good alternative, but cannot be used in plain strain conditions, yet. Further research is needed to investigate other modelling options, as a three-dimensional model. However, to fully understand the behaviour, more tests are needed. These tests should not only be focussed on the behaviour of the arch, but also on the behaviour of the backfill; and these material properties should be tested and reported extensively.

Masonry is one of the most common building materials globally due to its ease of construction, price, durability and fire resistance. Its heterogeneity and orthotropic nature make its mechanical behaviour rather complex, highlighting the importance of an appropriate constitutive model to describe such behaviour accurately. In literature, most of the existing constitutive models for masonry fall in one of the two following categories: macro-models or micro-models. The micro-models (also called block-based models), which explicitly describe masonry's geometrical and material heterogeneities, exhibit higher accuracy but require higher numerical efforts when simulating masonry's mechanical behaviour. The macro-models (also called continuum models), which model masonry as homogeneous material and smear out the damage over the continua, are less accurate but offer a good compromise between accuracy and numerical efficiency. They are therefore used more often to simulate masonry structures. However, most of the macro-models are not capturing well the damage localization occurring along the mortar joints and the energy dissipation in the bricks and mortars. To increase the applicability of continuum models, the components' damage localization and energy dissipation should be improved. This thesis presents a homogenized constitutive model for applications on masonry structures under in-plane loading. The developed homogenized material model for masonry includes the description of shearing, tensile cracking, crushing and splitting. Inspired by the micro-mechanical models of Zucchini and Lourenço, four models were developed in this thesis to describe the different types of in-plane failure of masonry, naming: tensile failure of bed joints, horizontal shear sliding of bed joints, tensile cracking of unit, diagonal tensile cracking failure, masonry crushing failure. The first model is derived for the masonry’s pure shear behaviour, where the shear sliding failure is introduced. The second one is derived for the horizontal tensile behaviour, where the vertical tensile cracking of brick units and the vertical joints is proposed. The third one is derived for the vertical compression behaviour, where masonry crushing failure is adopted. The fourth one is coupling the failure mechanisms described in the previous three models with a novel algorithm. Additionally, the diagonal tension cracking failure and the horizontal tensile cracking of horizontal joints are incorporated in the fourth and final material model. To derive these models, first, a representative volume element (RVE) was selected for running bond wall, where the bricks are staggered by half-length of brick from the adjoining courses above and below. Each RVE consists of two-quarters of bricks connected through a bed joint, and each one is connected to a head joint on one side. For each of the models, the active internal stresses of each component (brick, bed, head or cross joint) are calculated through the compatibility and equilibrium equations resulting from the assumed deformed mechanisms. Different damage state variables are introduced for every component in the damage model, where exponential softening is assumed for tension and shear. Additionally, a Ducker-Prager yield criterion with bi-parabolic hardening is used in combination with an explicit Euler-forward algorithm to describe the elastoplastic behaviour of the material in compression. As a result, the material model’s constitutive law is obtained with the homogenization procedures after coupling the damage and plastic model together by a specific algorithm originally introduced by Zucchini and Lourenço. The constitutive equations for model 1 (shear), model 2 (tension), model 3 (compression) and model 4 (coupled) were coded successfully in MATLAB. The components’ shearing, tensile cracking, crushing and splitting failures are correctly modelled analytically with an algorithm, which can be applied to simplify the micro-mechanical model. Besides, constitutive laws of models 1 and 2 were also implemented successfully in the finite element software DIANA version 10.4 (check). The ability of the model to capture the failure of the components in shear, tensile cracking or crushing was examined through simple analytical applications. Moreover, the model was compared against experimental results from tests performed on masonry wallets under compressive loading; the model was able to predict the strength of the specimens satisfactorily. Therefore, this alternative constitutive material model can adequately simulate masonry’s behaviours with a simpler algorithm than the previous model. Meanwhile, the component’s elastic and elastoplastic behaviours can be simulated in more detail in this model, as the case that the horizontal joint is first damaged in shear and compressive splitting effects are additionally included.

This research investigates if confining rubble stone masonry by timber bands and columns increases resistance against earthquake loads, by performing a number of numerical analyses in the finite element software program Diana. In order to establish a reliable model, the input parameters are investigated by means of a literature study and sensitivity study. Additionally, the numerical model is validated by comparing the results to an analytical study. From the analytical study it is determined that the failure mechanisms are correctly estimated by the numerical analysis. However, differences between the values of ultimate strength and ductility were observed. The effect of the confinement is investigated by a pushover analysis on a shear wall with two different masonry tensile strengths: ft = 0.01 N/mm2 and ft = 0.03 N/mm2. These values are selected to show how such a small difference in tensile strength results in a different failure mechanism of the wall, and therefore results in a vastly different displacement capacity and ultimate strength. Additionally, a shear wall with and without a window opening is studied. If the building is constructed with extremely low-strength masonry (ft = 0.01 N/mm2), the timber frame confinement will increase the resistance of the wall (with or without window opening) against the pushover load. If the building is constructed with masonry having a tensile strength of 0.03 N/mm2 or higher, the confinement has a negative impact on the ductility of the closed wall. For the wall with window opening the confinement triples its ultimate strength. Weather a strong or a ductile structure is more desirable, depends on the demand with respect to the seismic spectrum. If the ground motion demands a strong structure, it is advised to confine the masonry with a timber frame consisting of four timber bands, and columns at each wall junction. The design of the timber frame as recommended by the Nepali building codes is determined to not be sufficient and must be altered in order to provide this positive impact on the structure’s resistance. Firstly, the columns must be placed at both sides of the band, instead of on the inner side only, to avoid eccentric loads on the bands. Secondly, the cross-sectional dimensions of the bands and columns must be increased avoid failure of the connections and splitting of the timber. Taking these aspects into account, a new design for the confinement method is presented in this study. The limitations of the conclusions of this research follow from the investigation of a single, in-plane wall only. One of the goals of the use of bands is to improve the box behaviour, for which the out-of-plane performance must be investigated. Moreover, an analysis on a three-dimensional structure is needed to fully answer the research question. In a three-dimensional study, the closed walls and walls with opening give a combined response to the load, therefore, the advantages and disadvantages of the confinement are combined as well.

Each year, the province of Groningen experiences many induced earthquakes due gas extraction, which has been ongoing since 1963. The earthquakes cause damage to the buildings situated in the Groningen area, and they constitute a potential danger for the safety of the residents. These buildings are typically unreinforced masonry structures which are designed without knowledge of the presence of seismic activity in this area.

It is therefore essential develop and use assessment methods that are on one end reliable and accurate, but on the other hand allow to perform a large number of assessments of the vulnerability of the buildings in a short time. In other words, the assessment of all the buildings requires a quick and reliable assessment method. Such an assessment method should offer a strong understanding of the occurring failure mechanism during an earthquake, an acceptable prediction of the ground acceleration at which the collapse of the building may occur (maximum base shear force) and the displacement capacity of unreinforced masonry (URM) building.

The NPR9998 recommends four seismic assessment approaches, which differ in complexity and assessment time needed to be performed. The most comprehensive and time-consuming assessment method is the NLTHA (nonlinear time history analysis), which includes both the dynamic and nonlinear effects. In practice, this method is used only in special cases, such as in the case of monumental buildings. A simpler approach is the NLPO (nonlinear pushover) analysis, which is static and considers the nonlinear properties of the structure. An NLPO is less time consuming than an NLTHA, even when the finite element method (FEM) is considered.

A more simplified approach is the Simple Lateral Mechanism Analysis (SLaMA). This method is a simplified mechanism-based analytical approach. If the SLaMA method predicts realistically conservative global capacities, it could serve as an effective alternative assessment method for URM buildings, and especially to the NLPO FEM analysis. This study focusses on the comparison between the SLaMA method and the NLPO FEM analysis. Therefore, this study aims to answer the following research question:

Could the SLaMA method be a realistically conservative and effective alternative to the NLPO FEM analysis in making a seismic assessment for two-storey unreinforced masonry buildings?

In conclusion, the SLaMA method could be a realistically conservative and effective alternative to the NLPO FEM analysis in predicting the maximum base shear force. The displacement capacity predicted using the SLaMA method is validated only for buildings with RC floors. This predicted SLaMA method was realistically conservative compared with the ultimate displacement achieved using the NLPO FEM analysis. The SLaMA method is overall suitable for obtaining a quick understanding of the behaviour of an URM building. However, it requires a proper evaluation of the analyses to identify properly the type and the location of the failure mechanisms. For this reason, this method could be valuable to be applied before using a more complex assessment method.

The seismic assessment of unreinforced masonry structures in Groningen is still ongoing. The assessment is vital to determine whether a building must be strengthened or not. Different assessment approaches have been followed in recent years. First, the Non Linear Time-History analyses (NLTHA) were initially the only approach used for the seismic assessment. They are still overall the most accurate type of assessment, but they are also the most time-consuming one. Nowadays, NLPO analyses are more frequently used. This assessment procedure presents some limitations of application and may be less accurate for complex structures but it requires less computational time. The NLPO analyses can be performed by means of different tools, such as analyses based on the finite element method (FEM), equivalent frame (EF) or macro-element based analyses and, eventually, also analytical mechanism based analyses. The SLaMA method belongs to this last category: this method is an analytical approach already tested and validated in New Zealand for RC structures.
This research aims to answer the following research question:
• How is the in-plane behaviour of single-storey URM wall facades affected in simplified calculation methods compared to FEM when geometrical irregularities are present?
The walls have been modelled in 2D with three different methods: FEM, EF and SLaMA. Material properties and modelling assumptions were maintained as consistent as possible within the three different methods. For researching the influence of the geometrical irregularities on the accuracy of EF and SLaMA when compared to FEM, the variation of geometrical irregularities, each quantified by an index value, have been studied. The influence of these indices on the accuracy of the calculation methods has been researched with a sensitivity analysis.
The objective has been pursued by looking into single-floor URM façades, and the conclusions of this research can be applied to this typology of walls in Groningen made of solid clay brick masonry (pre 1945). The study focuses specifically on the base shear capacity of the walls.
The differences observed when comparing the in-plane behaviour of a wall analysed with 3MURI and DIANA are not significantly affected by the presence of geometrical irregularities. The ratio between the base shear capacity computed with the two approaches and the predicted failure mechanisms remains consistent for all geometrical irregularities defined in this report.
Similarly, the differences observed when comparing the in-plane behaviour of a wall analysed with SLaMA and DIANA are not largely affected by the presence of geometrical irregularities, since the base shear computed according to SLaMA is consistently lower than that obtained with DIANA. However, the base shear capacity obtained with SLaMA showed large variations between 0.34 and 0.75 with respect to DIANA when implementing geometrical irregularities. The largest variation is obtained when more than a single pier is considered, due to the inability of SLaMA to define the re-distribution of the vertical axial forces in the piers, nor correct boundary conditions at the top of the piers since the constraining action of the spandrel appear underestimate. This affected also the prediction of the failure modes, which differed for the two methods. However, in most of cases flexural failure mode was obtained, and the study should be extended to consider also geometries and loading conditions that cause also the shear failure of the walls.

Since the 60’s the Nederlandse Aardolie Maatschappij (NAM) has been extracting gas from the province of Groningen in the Netherlands. This resulted into seismic activity. However, the buildings in Groningen are not designed to withstand any seismic loading. The assessment of the seismic behavior of the building stock of Groningen is required to verify whether a structure causes any life safety risk during an earthquake. In this thesis two main objectives are studied. Firstly, it is studied whether the simplified analysis approaches: Simplified Lateral Mechanism Analysis (SLaMA), as described in the NPR9998-2018, and the Equivalent Frame Method (EFM) as implemented into the software package 3Muri are able to describe the seismic behavior of an Unreinforced Masonry (URM) terraced house. Secondly, the influence of the geometry of the piers in a facade is assessed. Both the objectives are studied by means of two case studies. The first case study represents a typical but idealized URM structure of a terraced house from which the seismic capacity was determined in the TU Delft lab by cyclic pushover tests. The second case study concerns a specific two-storey URM terraced house located in Groningen. The case studies are characterized by large daylight openings, slender piers and a low lateral capacity into the x-direction.

Drying shrinkage can cause structural damage to concrete industrial floors. Shrinkage is caused by evaporation of moisture from the drying material. In the design- and construction-standards, this complex process is not described on a fundamental level. Using finite element modelling to simulate the flow of Moisture through the concrete, it is possible to simulate drying shrinkage. The research question of this thesis is: ‘How can a parametric FEM model efficiently simulate drying shrinkage in industrial concrete floors?’. Verification of the produced model is performed. The outcome is compared to shrinkage
measurements of concrete prisms. The theoretical framework presented in this thesis is based on the fact that the relative pore humidity is changing during drying. In a finite element model, the changing relative pore humidity (pore-RH) over time is calculated. Drying is caused by internal diffusion of moisture, which is driven by differences in concentration. The moisture flow is modelled using the transient heat equation. The resulting pore-RH values are used to determine the hydrostatic capillary pressure based on the equations of Kelvin and Laplace. The material response of cement paste subjected to the capillary pressure is calculated using Bentz law. At last, the models of Pickett and Neville are used to include the restraining effect of aggregates and determine the absolute deformation of concrete subjected to drying. The initial conditions of the material are determined based on HYMOSTRUC cement simulation and Powers’ volumetric model. The results of the presented theoretical framework are reasonable. Usage of the framework and the heat equation for modelling drying in FEM, proved to be successful. A significant uncertainty is found in the restraining effect of aggregates. The theoretical model is based on material modelling of drying cement paste. However, the deformation of concrete is only
16%~23% of the total deformation of cement paste. Recommended is to further research the (local) effect of aggregates on drying shrinkage. Drying shrinkage has been calculated according to the construction standards and compared to the measured drying shrinkage of the concrete prisms. From this, it can be concluded that calculations by structural engineers on drying shrinkage are preferably done according to the ‘Model code 2010’.

Masonry is one of the most commonly used construction materials for residential buildings and historic buildings around the world. Some of these buildings are located at seismic zones, while unreinforced masonry structures are vulnerable to seismic loads. To assess the existing masonry buildings and to design new masonry structures, nonlinear seismic simulations are conducted with macro modelling or micro modelling approach. The macro modelling approach, which smears out the details of the bricks and joints as a homogenous material, can efficiently and robustly model complete masonry structures. A commonly used orthotropic constitutive model is the Engineering Masonry Model of the DIANA FEA, which is based on the Total Strain Method that eliminates the mapping-back process in conventional elastoplastic constitutive models. The micro modelling approach, which explicitly models the bricks and joints, can better represent the mechanical behaviours of masonry. However, most of the constitutive models used in micro modelling are based on elastoplasticity that usually causes numerical difficulties due to its mapping-back process. The lack of a robust constitutive model has severely hindered the application of this accurate analysis approach.

So, this thesis proposes a sub-increment based iterative constitutive model for interface elements, based on Multi-surface Plasticity Criterion. This model aims to enhance the robustness and accuracy of the constitutive model used for micro modelling. It eliminates the conventional mapping-back process in elastoplastic constitutive models by introducing the ideas of sequential uni-axial loading algorithm and an extra damage iterative calculation algorithm. These algorithms are robust even when the stress state is at the corners of the yield surface. The model also introduces the concept of sub-increments to consider the path dependency in plastic process. All the formulations of this constitutive model are derived based on a simple mechanical model. Formulas and examples are provided for obtaining the input parameters from material tests. The proposed constitutive model is tested on a single integration point level and found to be stable and reliable. It is further applied on the component level, by modelling three masonry walls of different dimensions and boundary conditions, under cyclic loading. For the verification of these wall models, the numerical results are compared with the experimental results in terms of force-displacement curve and crack pattern. Finally, the thesis presents a brief study on parameter sensitivity to provide guidelines for the level of accuracy needed for each input parameter, in order to get satisfactory numerical results.

The constitutive model is found to be robust for all the wall analyses conducted, without encountering divergence. The comparison between numerical results and experimental results shows that this constitutive model can cover the majority of shear and flexural failure mechanisms and mimic the crack patterns well. It is capable of modelling shear failure with high accuracy. It can also model flexural failure well with a few parameters calibrated. The fact that the model is little sensitive to parameters that are hard to be measured from experiments, such as tensile strength and tensile fracture energy, ensures its feasibility in engineering practices.

The increased seismicity due to the exploitation of natural gas in the Groningen region has put many residential buildings in the region at risk of sustaining seismic induced damages. This has prompted many studies on the seismic behavior of the residential buildings, particularly the ones built from unreinforced masonry (URM). One experimental study has been conducted at TU Delft on a two-story CS element structure simulating a terraced house unit. Several numerical studies have also been carried out in the interest of assessing the viability of numerical models for engineering purposes. This research project will examine the viability of several modeling approaches for practical use in analyzing CS element structures. The assessment will be conducted by performing numerical analyses on several models and comparing the results from each analysis with the experimental results. The performance of each model is assessed in terms of hysteretic behavior, interstory drift, cracking patterns and failure mechanisms. Two modeling approaches will be considered in this research project, the continuum element-based macro-modeling approach and the block-based micro-modeling approach with each modeling approach having several variations with different constitutive models. Shell finite elements will be used for all numerical models. In addition to the numerical analyses on the numerical models, several additional analyses will also be conducted on the macro-models. A sensitivity study on the macro-models will be carried out to examine how changes in the considered material parameters affect the results of the numerical analyses on the macro-models. The effects of the inclusion of interface elements in the wall-pier connections of the macro-models will also be investigated in this report. All numerical analyses are carried out using the structural analysis software package DIANA 10.3. The constitutive elements considered for the numerical models will be limited to those already available in the software package.

This research describes the demand of a Displacement-based approach for the assessment of out-of plane behaviour of one-way vertically-spanning unreinforced masonry (URM) walls of terraced and detached houses in the Groningen Province. One of the most vulnerable components of a typical Dutch unreinforced masonry building subjected to earthquake excitation is the face-loaded walls. As the Dutch masonry walls are quite slender, this matter is of significant importance. Up to now, codes and standards evaluate the structural integrity of unreinforced masonry face-loaded walls with either force-based or displacement-based approaches. The latter present beneficial advantages, since the rocking mechanism of an out-of-plane wall is considered to be an instability problem. Particularly, for the definition of the demand (in terms of mid-height displacement for an out-of-plane unreinforced masonry wall) for the Groningen Case, it will be based on the design response outlined in New Zealand Society for Earthquake Engineering Standard (NZSEE) for the Seismic Assessment of Unreinforced Masonry Buildings. Nonetheless, a new rendition of the Shape Factor Coefficient Ci(Tp) and Height Coefficient CHi is necessary, in order to relate the design response with the genuine characteristics of Groningen seismicity. The Shape Factor or Part Coefficient indicates the interaction between the seismic responses of the structural parts and the building, while the Height Coefficient indicates the amplification of the peak ground accelaration through the height of building. The procedure towards the description of the out-of-plane seismic demand is analysed by three parts. In the first part, a series of Nonlinear Time History (NLTH) analyses are performed in single degree of freedom (SDOF) systems. In total, seven SDOF systems are modelled in Opensees. Each of them represents the equivalent SDOF system, according to Eurocode 8, of the considered structures for this research. The SDOF system characteristics as well as the ground motion records for five areas in the Groningen Province are provided from in-house studies of BAM Advies en Engineering. The ground motion records are related to the Draft NPR 9998:2017. Furthermore, two hysteresis rules for the structures are included in the Opensees Models. Hysteretic Rule 1 accounts for low-to-moderate energy dissipation, while Hysteretic Rule 2 for moderate energy dissipation. The hysteretic rules are in accordance with hysteretic behaviour of URM piers under in-plane loading. The geometry, loading conditions and mechanical properties of the piers are chosen to represent the piers in typical Dutch terraced and detached houses. These piers were tested at the Stevin Laboratory of the Delft University of Technology, which provided the data of the tests. Two specific in-plane wall specimens (COMP-2 and COMP-3) are used in this work. The Opensees parameters describing the aforementioned hysteretic rules, are calibrated according to the cyclic tests of these specimens. Next, the NLTH analyses are performed. The deliverables are the Floor Response Spectra (FRS) of each equivalent structure, per hysteretic rule, area and direction. Generally, a response spectrum is a plot that indicates the maximum response of linear oscillators with varying natural frequency or period. The oscillators are excited under the same vibration. Analogously, a FRS indicates the maximum seismic accelaration that the structural parts attract, if they are placed on the respective floor. Since a significant amount of FRS is provided from the NLTH analyses of the 1D Models, the production of Design Floor Accelaration Spectra per area is aimed. Design Floor Accelaration Spectra are “smooth” spectra that can be described by equations and act as an upper bound envelope for all the FRS produced per area. For their derivation, the Newmark-Hall method is applied to the mean Floor Response Spectra of all the structures per area. Consequently, a Design Spectrum per area is produced along with the equations that describe the Shape Factor Coefficient Ci(Tp). The Design Floor Accelaration Spectra efficiently describe the demand expressed in the response spectra of the 1D Models. Nevertheless, in some of the FRS, narrow high amplified spectra are observed with spectral values greater than the design plateau value. These cases are related to stiff structures that did not show proper plastic behaviour in direction X (“weak” direction of the structures governed by openings and rocking piers) and to all the structures in direction Y (“strong” direction of the structures governed by large shear walls), where they remain elastic, with the FRS to be bell shaped curves, highly amplified in a narrow period range around the fundamental period. This raises the necessity of examining if out-of-plane walls can potentially be subjected to these greater accelarations indicated by the narrow high amplified spectra. Therefore, the incorporation of a set of out-of-plane walls in the Opensees Models is decided, in order to compare their actual NLTH out-of-plane responses with their design responses ph. For the definition of the design response, the produced Shape Factor Coefficient Ci(Tp) for the Groningen Case is used. Hence, the second part of this research deals with the extended 1D Models, which are described as two degree of freedom mass-spring systems (2DOF systems). In the extended 1D Models, the nonlinear springs are in series and portray the hysteresis of the buildings and the out-of-plane walls. The hysteretic behaviour of the out-of-plane walls in the Opensees Models are calibrated to the experimental test of one-way spanning, double-clamped out-of-plane wall specimen COMP-7, performed at the Stevin Laboratory of the Delft University of Technology. Twelve wall configurations are considered, as a result of the 4 boundary conditions in the edges of one-way spanning walls presented in NZSEE Norm and 3 considered overburden loads (5 kN, 15 kN and 30 kN). The sensitivity studies in Opensees indicate that the design responses are larger than the NLTH responses for the non-failing walls and predict the failure when it is indicated in the NLTH responses. As a result, the Shape Factor Coefficient Ci(Tp) satisfies also the cases in which the FRS present higher values than the design plateau value. In the third part of the research, NLTH analyses are carried out in a 3D Model that resembles four two storey terraced houses with rigid diaphragms. The finite element method (FEM) software that is used for the NLTH analyses is ANSR-II and the Macro-element based modelling approach is adopted. ANSR-II allows the definition of nonlinear membrane elements to model the structural components. For shear walls and spandrels, specific in-plane backbone curves and hysteresis profiles are provided, being in agreement with the provisions of NZSEE Norm and Draft NPR 9998:2017. Regarding the in-plane rocking piers, no hysteresis is involved. However, the rocking capacity is in accordance with the Norms mentioned above. Triaxial excitations of the 3D Model with 11 sets of ground motions per area are performed in ANSR-II, following the requirements of Annex F of Draft NPR 9998:2017. From the NLTH analyses, the Floor Response Spectra are produced for each of the two floors of the 3D Model. These FRS are compared with the Design Floor Accelaration Spectra derived from the simplified 1D Models. A good predictabilty of the Response Spectra from the Design Spectra is found. Moreover, the Height Coefficient CHi is obtained as the ratio of the Peak Floor Accelaration (PFA) over the Peak Ground Accelaration (PGA). Linear regression analysis related to PFA/PGA ratios in the two floor levels of the structure is implemented per direction and area. The output is the linear equation describing the height effect as a function of height h. This equation has the same format with the one describing the Height Coefficient in NZSEE Norm, hence they are directly comparable. Similar to the 1D Models and for analogous purposes, sensitivity studies of one-way vertically-spanning out-of-plane walls in ANSR-II are conducted. The variation of the walls is retained the same. The out of plane walls in the 3D Model are modelled as beam elements that can rock out of their plane. The behaviour of these beam elements under dynamic excitation in ANSR-II is described by elastic loading and unloading, so no hysteresis is introduced. That is a major difference compared with the Opensees Models. In spite of that, the behaviour of the out-of-plane beam elements in ANSR-II is based on the rigid bodies assumption and rocking mechanism of an out-of-plane wall according to Nonlinear Kinematic Analysis (NLKA). In fact, a good agreement is observed between the capacity curves of the considered out-of-plane walls in ANSR-II and the capacity curves derived from the NLKA method. The results of the sensitivity studies in ANSR-II lead to same conclusions as the ones derived from the sensitivity studies in Opensees Models. That enhances the ability of the Shape Factor Coefficient Ci(Tp) and the Height Coefficient CHi to provide the appropriate design response. As an overall conclusion, it is stated that the Shape Factor Coefficient Ci(Tp) and the Height Coefficient CHi produced in this thesis, can be used for the definition of the displacement demand of one-way spanning out of-plane walls for the Groningen Case, using the displacement-based methodology described in NZSEE Norm. The deliverables serve all the possible factors and parameters that distinguish the characteristics of the Dutch scenario. As the number of the Opensees Models is already satisfying, it is recommended to carry out NLTH analyses in more 3D Models. It is believed that this would further raise the consistency of the deliverables.

The growing need to understand the behaviour of un-reinforced masonry URM), subjected to
repeated light man-made earthquakes caused by the extraction of gas in the north-eastern part
of The Netherlands has resulted in intense research to determine the exact process of crack
initiation and propagation. The historical masonry buildings and Dutch terraced houses in
Groningen are prone to light damages which become severe upon repeated lateral earthquake
loading. Although there are material models that describe the behavior of modern brick
masonry, they do not accurately represent the mechanical properties of 19th century clay brick
masonry. This led to a large-scale research into the mechanical behavior of un-reinforced
masonry and an orthotropic continuum macro-model called the Engineering Masonry Model
(EMM) was proposed. The existing tension constitutive model in EMM assumes a secant
unloading-reloading branch which does not consider the strength degradation of URM under
repeated loading. Since tension mode-I fracture results in cracking of URM, it is important
to study the effects of repeated loading on the propagation of the crack and its effects on the
capacity of the structure.
This thesis presents a degradation model to represent the strength deterioration of URM
observed during repeated loading. The constitutive model formulated in this thesis is based on
hyperbolic functions along with a secant slope for the unloading-reloading branch. To justify
the model assumptions, a single linear 4-node element is analysed with the new model and the
effect of varying different components of the constitutive equations is established. The window
bank spandrel sample modeled as a 4-point bending test is analysed using the new model for 10,
30 and 100 repetitions. It is shown that the hyperbolic model can predict accurately the stress
reduction within each repetition displacement set and also represent the crack width widening
and crack propagation accurately when compared to the experimental results. The new model
is tested on a wall with a window opening sample and the results closely matched that of the
experiment. Finally, recommendations are provided for further development of the hyperbolic
model and calibration of the material properties.

In the recent years, increasing induced seismic activities have been observed in the northern part of the Netherlands due to gas extraction. These seismic events may cause severe damages to the building stock in this area, which is mainly composed of unreinforced masonry (URM) buildings not designed to withstand seismic loads. An extensive experimental campaign has been carried out at the Stevin II laboratory of Delft University of Technology to characterize the seismic responses of these URM structures. In this framework, a quasi-static cyclic pushover test on a full-scale masonry assemblage has been performed. In this treatise, the seismic behavior of the tested masonry assemblage is modeled and analyzed via finite element analyses. The validation against the experimental results is achieved through nonlinear pushover analyses on a well-built model of the assemblage. Moreover, as the pushover method used in the aforementioned studies is based on static loading, its accuracy and applicability on studying the seismic behavior for this type of masonry structure need to be evaluated. The evaluation is achieved by performing a series of nonlinear time-history analyses on the model to obtain accurate seismic response of the structure. The applied horizontal ground motion is representative of the earthquakes in the Groningen province and the incremental dynamic analysis method (IDA) is employed.
The nonlinear pushover analyses reproduce the test results properly, showing similar maximum base shear forces and asymmetric capacity curves. In both experimental and numerical analyses, cracks start to form at the top and bottom of the masonry piers due to rocking mechanism and the failure of the structure is governed by damages of the wide piers. Moreover, a sensitivity study based on the monotonic pushover analysis shows that the post-peak behavior of the model is directly related to the masonry compressive strength. The incremental dynamic analysis provides similar base shear capacity and failure mechanisms as the nonlinear pushover analysis. However, the maximum displacement is smaller in both loading directions and a more distributed crack pattern is observed. Overall, for the studied masonry house, the pushover method is capable of properly estimating the base shear capacity but the deformation capacity might be overestimated.

The out-of-plane behavior of unreinforced masonry walls subjected to lateral loading is a complex structural problem. This thesis focuses on the stability of URM walls in a building system under seismic loads that are comparable to those found in the Groningen scenario. The investigation is carried out by addressing both the physical and the geometrical nonlinear nature of the rocking mechanism.

Existing sophisticated numerical micro- and macro models have already proven to be capable of simulating typical masonry behaviour. However, assessing the global response of masonry buildings using brick-to-brick micro modelling or even simplified macro modelling, in which masonry is regarded as a continuum material, takes such an amount of time that these methods cannot be considered as cost-effective. For the last two decades it has been recognized that, for the global structural behaviour of masonry buildings, simplifications have to be made. The idealization of a masonry wall as an assemblage of numerically integrated (or fibre) beam elements could considerably reduce the computational burden and therefore this study addresses the following research question:
To what extent are numerically integrated beam elements applicable for assessing the global response of masonry structures?
Whereas existing equivalent frame methods are usually based on lumped plasticity models, the approach discussed here considers the entire member (e.g pier or spandrel) as an inelastic element in which the sectional response is evaluated via a fibre discretization in which each fibre (or integration point over the depth) may follow a material uniaxial nonlinear stress-strain relation. Initially the shear response is kept linear, automatically idealizing the structural response as purely flexural. The proposed model will be hereinafter named FFM (Fibre Flexure Model). Additionally, an extension of the FFM has been proposed, describing the shearing behaviour by means of a structural nodal interface element. Adopting the nodal interface element, placed between two nodes of adjacent beam elements, the axial and bending behaviour is described with the fibre-section discretization and the shear behaviour is modelled via an equivalent Coulomb-type criterion describing the shear force limit. The proposed model will be hereinafter named FF-LSM (Fibre Flexure – Lumped Shear model) because it lumps shearing nonlinearities in one single interface element located in the centre of the structural component, whereas flexural and crushing behaviour is evaluated via smeared crack beam elements.
To validate the numerical models, two different types of benchmarks have been investigated, respectively representing the behaviour of either a single structural component (masonry pier) or a composite façade. All numerical models have been subjected to static nonlinear (pushover) analyses and results have been compared with experimental and numerical data through the use of a reference continuum model.
First, it has been demonstrated that the FFM, idealizing the structural response as purely flexural, is capable of simulating the rocking failure mode of unreinforced masonry walls, whereas it fails to simulate typical masonry shearing modes such as diagonal cracking and sliding. The use of the model for squat members that are characterized by shear failure leads to significant overpredictions, making the model not applicable for the analysis of masonry structures containing relatively squat structural components, having shear span to depth ratios less than approximately 1.
Second, the shortcoming of the FFM regarding the shearing failure mode has been overcome by combining the numerically integrated beam elements with a structural nodal interface element describing the shear behaviour. The FF-LSM including the nodal interface is able to correctly predict the shear capacity of both slender and squat walls, although the observed level of accuracy depends largely on the adopted shear failure criterion. Various shear force criteria (Coulomb friction based) have been considered: the Mann and Muller (1982) criterion, the correction proposed by Magenes and Calvi (1997) and the modification according to Abrams (1992). Generally it was observed that the criteria developed by Abrams (1992) was the most accurate and that especially for a decreasing shear ratio the criterion developed by Magenes and Calvi (1997) appeared to be less precise.
Third, analysing a composite façade, with respect to the reference continuum model the FFM and FF-LSM significantly reduce the number of elements, nodes and integration points, consequently minimizing the computational effort and maximizing the computational robustness. In comparison with the corresponding continuum model the computational time decreases by a factor of approximately 10. Despite the limitations of the FFM regarding the shearing failure mode, the model shows an acceptable accuracy in terms of initial stiffness, stiffness reduction and peak strength. Adopting the FF-LSM the numerical model predictions were significantly enhanced and both flexural and shearing failure modes (in piers and spandrels) were detected correctly. Therefore, the result of the investigation has proved to be very promising as with the FF-LSM an acceptable balance between computational cost and accuracy is found, applicable to the global analysis of two dimensional masonry structures constituting slender as well as squat walls. As many problems in engineering practice require solutions in three-dimensional space, a fully three-dimensional extension of the FF-LSM is highly recommended.