The structural state of several cast iron lighthouses in the Netherlands has been deteriorating, as cracks have formed in the cast iron plates of the columns. Current assessment methods of such large cast iron plate structures require a very detailed finite element model, which is time consuming to create and analyse. In this thesis, the use of an orthotropic continuum damage model, the Engineering Masonry Model (EMM) of DIANA FEA in this case, for the structural analysis of cast iron plate structures is explored. The thesis focuses on a specific case: the lighthouse the ‘Lange Jaap’, located in Den Helder, the Netherlands.

First, to obtain the required input parameters for an orthotropic continuum damage model,
detailed models of small plate structures are created. Different loading conditions are applied, and the resulting force-displacement curves are analysed to derive constitutive laws for the structural analysis. Next, a sensitivity study of the size effect of the structure is performed, which resulted in some changes in the failure modes for some of the loading types. This resulted in quite a difference in strength and ultimate strain between the small and large structures. For each load case, a unit structure size should be defined, which should have the same failure modes as those expected to occur in the large structure the study focuses on. After obtaining the input parameters, they are verified and calibrated by using them in equivalent EMM models of the small plate structures.

The final, calibrated input parameters were used in an orthotropic continuum damage model for the cast iron plate structure of lighthouse the Lange Jaap and it was concluded that very similar results were obtained as from a detailed model, when all strains were in the linear-elastic regime. As the obtained values of the bed- and head-joint tensile strengths that were quite low, the tensile stresses exceeded the tensile strength of the material quite quickly in the model of the lighthouse. Once plastic deformations occurred, cracks started to form and the analysis of the model quickly became unstable, so the results were no longer accurate. This shows that, after the calibration of the parameters, the linear-elastic behaviour of the structure is accurately captured in the model, while the plastic behaviour is not.

It is concluded that, by using an orthotropic continuum damage model, the complexity of a structural analysis of a cast iron plate structure is reduced in the following way: reduced total modelling time, reduced complexity of geometry and reduced running time of analysis. The last point is achieved by using regular curved shell elements instead of structural solids, which is the result of the simplification in geometry. Using an orthotropic continuum damage model for similar structures is a very suitable modelling method for studies in which many finite element analyses have to be made for a structure, where small changes are made in every analysis. For the lighthouse structure, a study of the effectiveness of different strengthening solutions for the columns is a very good example. ... Read more

In the 1960s a large natural gas field was discovered in the Dutch province of Groningen, in the northern part of the Netherlands. Due to gas extraction, localised earthquakes started occurring in the 1990s. In this part of the country large numbers of buildings are constructed using unreinforced masonry (URM). Damage due to seismic activity in the region poses a threat to the structural integrity of existing masonry structures, as these buildings were never designed to withstand seismic loading. Among others, an intervention method that was considered was retrofitting with bed joint reinforced repointing. This is an attractive solution, as it is already often used in strengthening of masonry structures against settlement-induced damage, especially for heritage structures, as it does not affect the aesthetics of the structure. Furthermore, since this reinforcing technique is already applied to limit damage due to ground settlements, it is an attractive potential solution to counter damage due to seismic loading, as it does not require additional funding. However, not much research is available on the performance of existing masonry structures retrofitted with bed joint reinforced repointing, considering both the effect of ground settlements and seismic loading conditions. To investigate the added benefit of bed joint reinforcement, used to counteract seismic-induced damage, nonlinear finite element analyses, of a case study of a typical masonry farmhouse in the Groningen region, were performed. The masonry farmhouse was modelled as a façade, meaning no out-of-plane failure could occur. In this research, an orthotropic continuum model called the engineering masonry model (EMM) was adopted. The used numerical modelling approach was first validated against in-plane experimental tests of unstrengthened and strengthened masonry walls, performed at TU Delft previously. For the façade, various cases were analysed: an unstrengthened façade, strengthened façades, using various peak ground velocities and a partially reinforced masonry façade. The results were analysed in terms of crack widths, crack patterns and damage values, which were developed previously by others. The numerical results showed that limited damage is caused by an earthquake with the expected seismic load (PGV of 64mm/s). It was found that retrofitting with bed joint reinforced repointing after the settlement had already occurred, did not greatly increase the structural performance of this type of farmhouse façade, as most of the damage was already formed at the end of the settlement loading phase. Since the damage due to seismic loading is so small, it was therefore not recommended to strengthen this type of façade with bed joint reinforcement purely against seismic-induced damage, as the added benefit is small. However, since this strengthening technique is often applied already for strengthening against only ground settlements, it could provide a minor benefit during seismic loading, as a side effect. Amplification of the seismic load by a factor 1.5 showed only a limited increase in damage in the strengthened façade, compared to the numerical model using the expected load, while the reinforcement was significantly more activated. However, damage quickly ramped up when the seismic load is amplified by a factor 2. In this numerical model failure of the masonry façade is even observed. The numerical results of the façade with partially reinforced masonry showed a significant reduction in damage, since the bed joint reinforcement now also resisted the action of settlement loading, which is one of the most sensitive parameters of the considered façade. Since this numerical model simulates the case in which the bed joint reinforcement is applied during the construction phase, it was concluded that use of bed joint reinforcement would be beneficial for future masonry constructions. ... Read more

Masonry structures subjected to a lateral load, such as earthquakes and wind, can be prone to out-of-plane failure. It is known that geometrical properties and boundary conditions have a large influence on the out-of-plane bending capacity of walls. In this thesis, a numerical study is performed to evaluate the influence of the bond pattern on the two-way out-of-plane bending capacity of unreinforced brick masonry walls. A nonlinear finite element analysis with a 3D block-based model has been adopted to simulate the texture of the wall in detail. The study builds on the work of Chang et al., which was validated against the experimental benchmarks by Griffith et al. The numerical model can accurately estimate the initial stiffness and out-of-plane bending capacity, but the model is less accurate post-peak.
It is assumed that the material properties of the mortar in the bed joints are the same as the one of the head and collar joints. The masonry wall was first subjected to self-weight and a vertical pre-compression of 0.1 MPa. Afterwards, a monotonic out-of-plane pressure placed on the face of the masonry wall is applied. The numerical model takes both physical and geometrical nonlinearity into account.
In the first phase, different modelling assumptions were checked and a sensitivity study was performed. Prior to the study must the compressive behaviour of the brick be determined, as the bricks are elastic without a limit, thus nonlinear effects like crushing are not modelled. The resulting check determined that the minimum principal stress did not exceed the compressive strength of the brick.
A mesh sensitivity study has also been performed as a change in mesh size was needed. In the model of Chang, the face of the brick was divided over its length into two parts called a halfbrick (Hbrick). The bond patterns require a division of the face into 4 parts, a quarterbrick (Qbrick) or an octogonalbrick (Obrick) which maintains the aspect ratio of the Hbrick. Eventually, the Qbrick mesh is the best option as convergence issues arose for the Obrick.
Additionally, experiments have shown that cracks can propagate through the bricks, while this is not possible with a smeared cracking model. To simulate this effect a discrete cracking model within the brick was introduced. The possible locations of the cracks can easily be assumed in a masonry wall, to be in line with a mortar joint in the course above or below it. The change to the discrete cracking model did not influence the out-of-plane two-way bending capacity, while convergence issues arose, and it was subsequently not used.
Finally, in the experiment by Griffith et al., clamps are installed over the height of the end of the return walls. These clamps prevent any horizontal translations and rotations in the horizontal plane. These clamps are represented by tyings in the numerical model. In this study are these tyings removed and is the length of the return wall parametrised. A masonry wall without any return walls is fully one-way bending and to a length of 360 mm does the masonry wall show a transition between one-way to two-way bending. A return wall of at least 480 mm long is sufficiently long to achieve two-way bending.
A parametric study was performed considering five single wythe and three double wythe bond patterns: stretcher bond, quarter bat bond, lateral bond, half Flemish bond, stack bond, chain bond, English bond and Flemish bond. The double wythe masonry wall has been assembled by adding an outer shell to the single wythe wall and by decreasing the pre-compression to 0.0478 MPa to maintain the same vertical force as the single wythe bonds.
The highest out-of-plane bending capacity for the single wythe bond patterns is the half Flemish bond with 4.9 kPa with a spread of 5.4% and for the double wythe bond patterns it is the Flemish bond with 18.7 kPa with 7.2%. The spread between the highest and lowest out-of-plane bending capacity is small. All the walls, except the one in stacked bonded masonry, show a crack pattern in the form of a cross. The slopes of the diagonal cracks with respect to the horizontal bed joint line have also been studied and relates as follows: a shallow slope in the crack pattern coincides with a higher two-way out-of-plane bending capacity. While a steeper slope or the absence of a cross-shaped pattern coincides with a lower out-of-plane bending capacity. On the contrary, the initial stiffness of the masonry wall does not relate to the out-of-plane bending capacity.
To further confirm these findings, research is needed concerning different masonry types, considering relative properties between bricks and mortar joints, different properties between bed, head and collar joints, and spatial variability of properties. ... Read more

Unreinforced Masonry, a popular construction material with a rich historical legacy, has been resilient through centuries, despite its susceptibility to failure through various loading conditions such as seismic forces. Understanding the mechanical behaviour of masonry, particularly the cohesion and frictional mechanisms at interfaces between bricks and mortar, is crucial for assessing its structural reliability.
This thesis presents an experimental study characterising masonry frictional interfaces using a tribometer test, a novel approach in masonry research. The study aims to investigate the frictional behaviour of brick-mortar interfaces under varying precompression levels and test frequencies (3 Hz and 0.2 Hz). A novel sampling method was implemented, wherein the required specimens were extracted from a bonded masonry couplet specimen. The couplets were bond wrenched and then subjected to a mechanical extraction. Bond wrenching, through tension, separates the couplets, thereby isolating frictional response from the influence of cohesion by decoupling cohesion between the unit and joint. A tribometer was chosen for the investigation of frictional parameters, tribometers are typically employed with metal surfaces and rarely applied to masonry. Consequently, experiments were conducted using a reciprocating tribometer, featuring a novel specimen extraction procedure and a modified setup. The novel extraction involved mechanically altering a parent brick couplet to extract compatible specimens. Customised holders were procured and used to accommodate the prepared specimen. The obtained specimens were then, fastened into the appropriate sample holders. Tests were performed on the specimen with displacement, tangential force, normal force and time being recorded. Three key parameters, the mean Coefficient of Friction (CoF), the Energy Coefficient of Friction (ECoF), and tangential contact stiffness were analysed from the collected data. The above mentioned parameters were evaluated through two approaches, (i) Mean Curve approach and (ii) Cycle approach. A mean curve is the averaged curve of the measured hysteresis loop, which encompasses the overall behaviour exhibited by the hysteresis loop.
The experimental results revealed a dependency between the coefficient of friction and the applied pre-compression level, showing a non-Coulomb behaviour; this is in contradiction with assumptions of several models used for the analyses of masonry structures. Initially, experiments were conducted at a higher frequency (3 Hz) and followed by experiments at a lower frequency (0.2 Hz), and the results in both cases revealed a non-Coulomb friction behaviour characterised by a nonlinear connecting trend between kinetic and static friction region. The connecting trend between the kinetic and static region demonstrated a reduction in the degree of non-linearityan enhanced symmetry in the hysteresis profile as the precompression levels increased. The mean curve and the cycle approach yielded identical estimates for the coefficients of friction (CoF) and effective coefficients of friction (ECoF).
The evolution of Coefficient of friction (CoF), did not exhibit any clear systematic time dependency, while Energy Coefficient of friction (ECoF) showed a systematic decrease over time. The ECoF related the energy dissipated by friction across each cycle to a hypothetical Coulomb energy dissipation. Therefore the ECoF captures the energy dissipation due to friction during one cycle, while the CoF captured the static friction region. The energy dissipation across different precompression levels were also studied and it was observed that the energy dissipation increased for increasing precompression levels.
Tangential Contact stiffness refers to the tangential force required to effect a unit displacement in the tangential direction. The contact stiffness was calculated from the slope of the region of the hysteresis loop associated with displacement reversal. Contact stiffness was observed to increase with increasing precompression levels. This observation was also validated by the theoretical model which illustrates a proportionality between the applied normal load (precompression) and tangential contact stiffness.
Additionally, the study highlights the impact of frequency on the observed frictional behaviour, noting more prominent static and kinematic components at lower frequencies due to reduced inertial forces. A preliminary study using the LuGre model was used to plot the analytically derived frictional force-velocity relationship, to briefly study the impact of sliding velocity on frictional force. It was deduced that the velocity had an influence over the frictional force at the interface.
In conclusion, the findings provide valuable insights into the frictional characteristics of masonry interfaces under varying loading conditions. The results also shed light on the practical aspects of testing methods and offer considerations for further research in the field of masonry engineering.
... Read more

The preservation of historical heritage buildings frequently requires the assessment of brick masonry structures. These structures exhibit complex behaviour due to the arrangement of units and the interaction between bricks and mortar. This study aims to compare two modelling techniques for simulating masonry's compressive response and understanding which technique performs better.

This study employs two block-based modelling techniques: a simplified brick-to-brick model and a detailed brick-to-brick model. The block-based modelling technique was selected to capture the intricate structural details and crack patterns of masonry specimens. Wallet specimens were evaluated to understand the compressive behaviour of masonry.

Two experimental benchmarks were chosen to validate the selected modelling approach. First, experimental results by Thamboo (2020), also modelled with a simplified brick-to-brick model by Zahra et al. (2021), were considered. However, to obtain numerical results comparable to the experimental ones, unrealistic input parameters had to be assumed (i.e., very low value of elastic modulus for the bricks); consequently, this benchmark was ultimately deemed unreliable. Hence, a second benchmark from Jafari (2021) was chosen which did not present such issues.

Considering the effect of confinement was crucial to obtain results in agreement with experiments. The detailed brick-to-brick model, explicitly modelling each brick-and-mortar joint with solid elements and accounting for mortar confinement, proved to be the only modelling approach able to simulate the second experimental benchmark. The simplified modelling technique, considering mortar joints as zero-thickness interfaces between solid elements representing the bricks, consistently underestimated the peak loads as mortar confinement was not included. This may explain why unrealistic input parameters were used by Zahra et al. (2021) to simulate the first benchmark. In general, the post-peak behaviour was difficult to simulate.

A sensitivity study was performed by varying the boundary conditions, Poisson’s ratio of mortar and integration scheme. The study on boundary conditions was performed on both the simplified and detailed models whereas the study on Poisson’s ratio and integration scheme was performed on the detailed model. The boundary conditions did not have a significant influence on the global behaviour of the specimen in the detailed or simplified models. Small variation in compressive strength and crack pattern were observed, but the effect on post-peak behaviour could not be evaluated due to numerical instability. The Poisson’s ratio of mortar was found to have a significant influence on the peak compressive strength of the masonry specimen. A higher Poisson's ratio resulted in a greater value in the peak compressive strength of masonry. A higher value of Poisson’s ratio increases the amount of confinement in mortar layers resulting in higher values of compressive strength of masonry. A high integration scheme (3×3×3) and a regular integration scheme (2×2×2) effectively captured crack propagation. On the contrary, a reduced integration scheme (1×1×1) could not do so effectively. The reason can be attributed to the higher number of integration points in the former cases which allows for better propagation of cracks.

These investigations provide precious insight into the choice of modelling techniques for simulating the compressive behaviour of brick masonry. The detailed modelling technique can be implemented to study the compressive behaviour of masonry specimens if mortar confinement is accounted for. However, further effort is necessary to reduce numerical instability to simulate the post-peak response. This can be adopted further to study the influence of, for example, bond pattern, specimen thickness (e.g., multi- vs single-wythe masonry) and specimen shape (e.g. wallets, prism, core) on the compressive behaviour of masonry. ... Read more

The gas production in the Groningen gas field of the Netherlands has caused a significant amount of shallowhuman induced earthquakes. Among various building typologies, Groningen is home to many Dutch historical churches constructed by unreinforced masonry which has shown to be highly vulnerable to these earthquakes. From the perspective of conservation and prevention of loss of our historical and cultural heritage, the structural assessment of these churches and their monitoring is of importance. The assessment of the seismic performance of historic churches is a challenging task because of their unique design, governed by macro element behaviour and nonlinear material behaviour. An accurate and reliable earthquake resistant assessment with appropriate numerical modelling of the structure and proper assumptions of all the uncertainties is crucial. The structural monitoring cannot be applied to all historical churches. By selecting representative case studies, indepth study regarding both numerical modelling and structural monitoring are possible. This information can then serve engineers and professionals to evaluate similar structures. The research gap lies in accurate modelling of historical churches to achieve reliable and faster results by linear dynamic modelling. The fundamental modes, eigenfrequencies and modal shapes, geometry and material properties, boundary conditions, connections between structural elements and loading variations are studied using 3D models with shell elements of the casestudy. Although, the models described cannot closely represent the real structure. Firstly, a regular thickness has been assigned to masonry walls and piers despite their irregularities. Secondly, the material properties have been estimated from similar structures in Groningen, and may not represent the actual material characteristics of this case study. Thirdly, the cavity ties has been disregarded because they have been assumed to be corroded (no actual information was available). Finally, the concrete slab at the entrance of the church is disconnected to the foundation, which was an approximation from the drawings but could not be verified. For the casestudy prior structural retrofitting (models 15); Numerical Model 3 with eliminated foundation and timber flooring and a rigid base at the ground level is expected to give the best approximation of dynamic response of the church. The fundamental frequency in X direction of the casestudy prior structural retrofitting can be approximated between 2.30Hz to 2.75Hz and the fundamental frequency in Y direction between 3.0Hz to 3.45Hz. The fundamental global modes in this model show maximum deformation in the timber roof of the mainstructure and tip of the belltower in globalnd Y directions. This indicates weakness of the casestudy prior structural retrofitting. The Old Church has undergone structural retrofitting in July 2018, to prevent further seismic damage on the structure. From the survey of the casestudy and the retrofitting measures, the recent findings (eg., cavity walls, installation of steel frame, steel and timber columns) are incorporated into the finite element model of the casestudy and various modelling variations are presented in models 6 to 10. From comparing the results of these models post structural modifications, Numerical Model8 (or Model9 which has almost similar results) with degraded material properties of masonry and timber diaphragms, a shallow masonry step foundation and a rigid base at the foundation level are predicted as the closest approximation of the dynamic properties of the church. The fundamental frequency of the casestudy post structural retrofitting can be predicted to lie between 1.5Hz2.6Hz in global X direction and between 1.1Hz1.65 Hz in global Y direction. It can be observed that the implemented measures make the church stiffer and the weakness of the structure post structural retrofitting is localised at masonry facade walls of the belltower, cavity wall between the belltower and mainstructure, tip of the belltower, lateral walls and timber roofing of the mainstructure. This research on simulating a numerical model that closely represents the dynamic properties of the Old Church in Garrelsweer for achieving reliable, computationally effective and faster results. This can be used as a basis to compare the results of ambient vibration testing and operational modal analysis, and a relevant guide to study how the numerical models can be defined for modelling similar structures. ... Read more

The city of Amsterdam has a large number of old quay walls with rotten foundation piles. These foundation piles need to be identified and measures need to be taken. The urban quay walls are supported by two types of foundation: pinewood piles, which are easily affected by bacterial decay and spruce piles. To understand the mechanical behaviour of quay walls better, it is needed to know the type of wood used for each pile foundation along the 200 km of quay walls currently showing signs of damage. For that reason, specialized diving teams are hired to identify the rotten piles and foundation defects, to know which foundation piles need replacement. Since the area is very large and diving inspections are costly and lengthy in time, there is a need to correlate the foundation defect to the masonry damage above the water level. The masonry above the water level could give lots of information about the condition of the foundation, due to cracks or deformations in the masonry. This research could help to relate foundation defects with damage patterns in the masonry. Understanding this relation helps to identify foundation defects at an earlier stage and helps the municipality to prioritize the replacement of foundation piles. The thesis aims to find indicators above the water line to identify foundation problems by studying the crack patterns in a typical unreinforced masonry quay in Amsterdam. From the point of view of the masonry structures, failure of foundation piles results in a settlement deformation causing cracking. This research will support the current work by Sweco in helping to find foundation defects from above the waterline via masonry damage patterns in quay walls. This will be achieved by performing a parametric study, bases on 2D nonlinear finite element analyses, varying the extent of the pile defects, the material properties of the masonry and lateral boundary conditions for a selected representative base case. To simulate the damage in masonry, a smeared crack approach was used. The foundation defects were simulated by applying a settlement deformation to the quay wall. A Gaussian settlement deformation profile was imposed and the ratio between the length of the profile and the length of the quay wall was varied to simulate the failure of single or multiple piles. To capture the influence of the material properties of masonry (especially related to tension failure), three types of masonry were defined: weak, average and strong. The influence of the boundary conditions at the edges was checked by performing analyses with horizontally free lateral sides and with horizontally fixed lateral side. This is done to simulate the effect of arching in the structure. Eventually, the influence of the location of the foundation defect was analyzed by comparing a symmetric Gaussian settlement deformation with an asymmetric settlement. The analyses show correlations between the vertical displacement at the top of the structure and the length of the settlement profile. As expected, this can be interpreted with the fact that if several piles are damaged simultaneously, a larger portion of the quay wall is cracking. The material properties of the masonry influence the development of crack patterns. The stronger is the masonry, meaning increasing the values of Young’s modulus, tensile strength and fracture energy, the larger is the settlement displacement needed to obtain the same crack pattern. The lateral constraints contribute mostly to the development of the horizontal crack since no horizontal cracks appeared in situations without these constraints. Since the influence of additional loads is not considered in the analysis and the model is modelled in 2D it is recommended to analyze the influence of both in further studies. It is also recommended to validate the model against field measurements since no verification has been done. ... Read more

Gas-induced earthquakes are a major problem in the north of the Netherlands due to many unreinforced masonry (URM) buildings being located in this area. To improve the seismic performance of the URM buildings, existing structures must be retrofitted and if the aesthetic of the building is important, the implemented retrofitting technique must not alter the appearance of the property. An experimental campaign was conducted at Delft University of Technology to investigate whether bed joint reinforcement (BJR) can be used for seismic retrofitting of URM walls. In this thesis, the influence of BJR, diagonal anchors and reinforcement layout on the in-plane seismic behavior of the retrofitted wall is studied. To achieve this goal several nonlinear static analyses using DIANA software were performed. First, the case experimentally tested is adopted as a benchmark and a validation of the numerical model is performed. Afterwards, the validated numerical model is adopted to perform a parametric study considering different reinforcement layouts. The numerical study showed that BJR was able to improve the seismic performance of the retrofitted wall. The Peak-load was increased slightly (13%) in the retrofitted wall compared with the URM wall. BJR acts in tension to restrains the crack opening so, the maximum crack width is another affected factor: a difference of -110% in maximum crack width was observed after retrofitting. Finally, the crack pattern and failure mechanism of the structure was changed due to BJR. The sensitivity analysis showed that the results were sensitive to variation in tensile fracture energy and modulus of elasticity, while tensile strength, compressive strength, and compressive fracture energy were the other variations that did not affect the results considerably. According to an extensive parametric study, it was concluded that double BJR was slightly more effective than single BJR. By applying only 4 layers of double BJR almost the same peak-load and maximum crack width were obtained comparing the results of the retrofitted wall with the original layout (with 12 BJR layers). The location of the BJR, however, was the governing concern. In the URM wall cracks mostly developed diagonally from the window corners and by applying horizontal bars below and above the window opening, the diagonal cracks were restricted and failure modes of the wall changed. The absence of single BJR next to the opening (in piers) might lead to the shear mechanism of the piers. The number of BJR is a function of the opening’s dimension. According to a proposed reinforcement layout it is believed that the mentioned 4 layers of double BJR (above and below the opening) and 3 layers of single BJR (next to the opening) were a wise choice for retrofitting of the wall. Furthermore, diagonal anchors could be ignored as they did not affect the performance of the wall. Conservatively, a layer of double BJR far above and below the window level could be applied. In this way reinforcement was decreased by 30%, however, the results were comparable with the retrofitted wall with original reinforcement layout. ... Read more

The fracture energy for hardwood was modeled using finite element modeling (FEM) software DIANA. The results of the model was compared to the fracture energy experimental research performed by Boerenveen (2019). The fracture energy results obtained by the model are similar to the results obtained from the experimental research. An model fracture energy over tested fracture energy ratio of 1.02 was found. ... Read more

Unreinforced masonry (URM) buildings are vulnerable when subjected to out-of-plane dynamic loading, especially under as earthquakes. Within the masonry building, the wall spanning in the direction perpendicular to the seismic loading is the most critical component. Damage to these walls (out-of-plane failure) frequently leads to the partial or global collapse in the URM building structures, especially if the wall is a load-bearing wall. Boundary conditions and overburden load drastically influence the response of out-of-plane loaded walls. Two-way spanning walls that are restrained on three or four sides show a larger force capacity compares to one-way spanning walls, which are only restrained at top and bottom. Nevertheless, the studies on the behavior of two-way spanning walls are limited. This thesis aims to understand the two-way bending behavior of unreinforced masonry walls subjected to out-of-plane loading employing numerical analysis. A three-dimensional model using a shell element is adopted. Cracking is modeled with a continuum damage approach by comparing the isotropic model, namely the rotating smeared cracking approach (TSRC), and an orthotropic model, namely the engineering masonry model (EMM). The effect of the top boundary condition on the response of the two-way spanning walls is examined by considering case studies: four sides restrained wall with overburden load, and three sides restrained wall without overburden load. Both the walls are vertically connected with the pier (or return wall) with an alternate row of headers providing full moment restraint. The description concerning the seismic behavior of the two-way spanning wall made based upon the analysis carried out incorporating different loadings types like the uniform, mode proportional loading, time history, and cyclic loading. The orthotropic material model is better in evaluating the response of the two-way spanning wall as compared to the isotropic material model if the proper support condition is specified. The difference in response using either material model is visible at the onset of cracking. The response of the two-way spanning wall under monotonic increasing load using EMM demonstrates walls have a displacement capacity to sustaining a relatively constant load, whereas the TSRC fails to capture this behavior. Due to high non-linearity because of cracking in the elements, the solution becomes non-convergent, and a solid statement regarding the ultimate displacement capacity of the wall can not be made. However, based on the results from static analysis using EMM, a two-way spanning wall have sufficient displacement capacity well over the wall thickness. The displacement capacity signifies the wall can deform in the out-of-plane direction without failure and is beneficial, especially during an earthquake event. In two-way spanning walls, both the peak load and initial stiffness of the walls is enhanced by higher pre-compression and top lateral support. It is found both experimentally and numerically, as precompression increases flexural and shear resistance capacity of the wall to resist the out-of-plane load. Furthermore, in the wall restrained on three sides, the crack pattern is initiated at the main-wall and pier connection, representing the head-joint cracking, leading to changing the behavior from two-way to one-way. While in the wall restrained on four sides, the cracking is initiated at the top and bottom support, therefore the wall can sustain the load both via horizontal bending along the vertical edge. Furthermore, the influence of top rotation fixity on the crack pattern in four sides restrained wall demonstrates the change in crack pattern without significant difference in the force-displacement plot. Therefore, it is vital to know the proper boundary condition in the wall to help in identifying the weakest link and suggest the necessary strengthening location. To predict the dynamic behavior of the two-way spanning wall by alternative load application is studies using static, non-linear time history, and cyclic analysis. The analysis of the wall with uniform monotonic increasing load fails to capture the post-crack behavior. Whereas, under the application of mode-proportional loading and using the material properties as stated in the case study, the initial stiffness and peak load is significantly lower, because of the applied load pattern. Therefore, the material properties are calibrated to match the initial stiffness and peak load but fail to provide information regarding peak load and ultimate displacement capacity. Using the original material properties, the outcome of the non-linear time history (NLTH) gives reasonable prediction in response up to the pre-crack run as compared to the case study. The four sides restrained wall shows very stiff response with very few cracks initiations to dissipate energy in the wall while rapid degradation in the three sides restrained wall is found, which attributed to the brittle response with wall top reaching the larger out-of-plane displacement. Due to non-linearity (follows from cracking), irrespective of the material model, the outcomes of NLTH analysis fails to capture the crack and post-crack behavior. Therefore, the material model needs improvement in tension and cohesion softening to better account for non-linearity in the time-history analysis. Due to the limitation of the NLTH analysis, cyclic analysis with increasing magnitude of load cycles was carried out to replicate the dynamic response. The outcomes give a fair indication of material degradation (based on energy dissipation) and crack formation but fail to capture the displacement capacity. Furthermore, the contribution of mode-II fracture energy in the overall energy degradation is significant for three sides restrained wall but not in four sides restrained wall. Due to top support, and increased shear strength capacity of the wall due to pre-compression load. Analyzing the two-way spanning wall under different loading shows the asymmetric response in the positive (toward pier) and negative (away from pier) displacement directions (with a 36% difference in force capacity). This asymmetry is arisen due to the presence of the return wall at the vertical junction. Finally, the combination of static (with uniform load) and cyclic analysis provides a reliable indication of wall force degradation of the two-way spanning wall. It can be used as a substitute for NLTH analysis. However, no solid statement regarding displacement capacity can be made based on the non-convergence in the numerical analysis. Furthermore, the crack pattern observes under different loading shows the damage is primarily influenced by boundary conditions rather than the type of loading. Based on the outcome of the thesis work, further studies are needed to improve the convergent behavior of the numerical analyses to gain information on the displacement capacity of two-way spanning walls subject to out-of-plane loading. Additionally, it becomes interesting to explore the use of micro-modeling to understand the crack propagation in the masonry wall, and to exploring different anisotropic model such as the Rankine-Hill model, or to
explore the implementation of strain rate dependent constitutive model (mainly used for impact loading) to understand the dynamic behavior in NLTH analysis. ... Read more

The increasing seismic activity observed in the last few years in the northern part of the Netherlands (Groningen region) due to geo-resources exploitation raised the need of assessing the current building stock, which is mainly made of low-rise unreinforced masonry structures.
In this thesis the performance of the equivalent frame modelling approach in predicting the nonlinear response of unreinforced masonry structure is evaluated. The model is applied in the case of typical Dutch modern terraced houses made of calcium silicate element masonry.
In order to evaluate the performances of the EF model, the quasi-static cyclic pushover tests on a masonry assembled structures is simulated. The model calibration and validation make use of the experimental results obtained during the large-scale tests on components and assembled structure performed at TU Delft in 2016/2017. A model sensitivity study is performed to investigate the effect of different modelling choices on the global structural response.
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