Figure 5 - uploaded by Paulo B. Lourenco
Content may be subject to copyright.
Source publication
Two dimensional nonlinear finite element analysis based on experimental test data has been carried out to model deformation characteristics, such as load–displacement envelope diagrams and failure modes of historical stone masonry shear walls subjected to combined axial compression and lateral shear loading. An experimental research work was carrie...
Contexts in source publication
Context 1
... type 1 (dry-stack stone masonry), the finite element mesh was generated using a Figure 5a shows division of units in x and y directions, interface around the unit and fake thickness of joints. Figure 5b shows a possible potential crack at the middle of the stone unit. ...
Context 2
... type 1 (dry-stack stone masonry), the finite element mesh was generated using a Figure 5a shows division of units in x and y directions, interface around the unit and fake thickness of joints. Figure 5b shows a possible potential crack at the middle of the stone unit. ...
Context 3
... type 1 (dry-stack stone masonry), the finite element mesh was generated using a Figure 5a shows division of units in x and y directions, interface around the unit and fake thickness of joints. Figure 5b shows a possible potential crack at the middle of the stone unit. ...
Similar publications
The response of unreinforced masonry structures under horizontal actions like earthquakes or wind has a unique behaviour differs significantly from the response of other structural systems such as reinforced concrete. This unique behaviour is caused mainly by the high stiffness, brittle material behaviour, and the deformability of the slab system....
Numerous modern seismic codes including Eurocode 8 provide rules to avoid possible adverse impact of the presence of masonry infills in concrete buildings or unbraced steel or composite structures. These adverse effects include damage of columns in contact with strong infills, reduction of the clear column height because of partial contact with mas...
Citations
... A useful methodology in this regard is numerical modeling [17][18][19][20]. In fact, the construction of accurate finite element models (FEMs) makes it possible to simulate various stress conditions that may occur on a structure [21][22][23][24]. Finite element modeling has produced countless outstanding results over the years; therefore, regarding the case of masonry structures, we can distinguish three main approaches of constructing an FE model [25]: ...
This study analyzes the thermo-mechanical behavior of a brick vault and the effect of a fire on its dynamic characteristics. Based on the results of an experimental test of a real barrel vault with a net span of 161 cm and a net rise of 46.5 cm, an accurate numerical model to simulate the behavior of the brick-and-mortar structure under thermo-mechanical stresses has been implemented. The comparison of the evolution of the displacement in the keystone and the temperatures at various points of the vault allows us to affirm that the adopted micro-modeling approach presents a good accuracy and a feasible computational effort. Finally, this study shows, from a numerical point of view, how the variation in the structure’s eigenfrequencies can be predicted for extreme situations, such as fire damage. This aspect can be critical to develop effective intervention and prevention strategies, which can be useful for the preservation of our valuable cultural and historic resources.
... In simplified micro-modelling (Fig. 1b), mortar is considered as zero-thickness interface elements, characterising the cohesion between masonry units and mortar itself. This approach has been widely utilised in simulating the behaviour of regular brick/block masonry structures [9] and was applied to irregular stone masonry walls recently [10]. However, using zero-thickness interface elements instead of original mortar implies that each masonry unit is enlarged and the fracture within mortar is ignored artificially. ...
Rubble stones are commonly found in many civil engineering components, such as foundations, walls. In general, rubble stone masonry walls are composed of irregular-shaped stone units and mortar. They are usually subjected to vertical and horizontal loads simultaneously and exhibit high degree of nonlinearity and discontinuity in service conditions. The combined finite-discrete element method (FDEM) was employed to investigate the mechanical behaviour of rubble stone masonry walls in this study. In order to overcome the disadvantages in both macro- and simplified micro-modelling, a detailed micro-modelling approach was utilised, i.e. stone, mortar and stone-mortar interface were considered explicitly, providing close approximation to physical structures. Stone units and mortar were discretised into linear triangular elements with finite element formulation incorporated in, and therefore, accurate estimate on structural deformation and contact forces can be obtained. Damage of rubble stone masonry was evaluated through cohesive fracture models. Numerical examples were validated, and further parametric discussions were performed. Influence of stone unit pattern, ratio of stone and strength of mortar on the failure behaviour of rubble stone masonry walls was revealed. A very good agreement between FDEM results and experimental data was observed. It was found that the higher the ratio of stone, the better the bearing capacity, and uniform-shaped stone units with regular distribution were recommended. In addition, use of mortar with both tensile and shear strengths higher than 0.2 MPa was suggested.
... Upon exceeding the tensile strength, the normal stress is set to zero, and the shear strength is lost, showing a relatively brittle material behaviour ). Since the Mohr -Coulomb criterion for the brick-to-brick contacts was assumed, the joint stiffness was simulated as a combination of unit and mortar stiffness, according to Equation 1 ( Senthivel and Paulo 2009) and Equation 2 (Senthivel and Paulo 2009); ...
... According to Refs. [28,[55][56][57][58][59]61], a macro-modelling simplified approach was used (Fig. 2), where masonry is considered a homogeneous anisotropic continuum. Stone, mortar joints and interfaces are represented by single continuous elements (masonry as a one-phase material). ...
... Due to the efficiency of modeling the complex geometry and nonlinear material behaviors that are intrinsic to masonry structure, the finite element method is commonly adopted. Ideally speaking, the masonry element (e.g., piers and spandrels) should be discretized by finite elements, respectively, for the brick/block units and mortar joints, which leads to the so-called micro-modeling approach [10,11]. When the mortar joint (of physical thickness) is modeled by a zero-thickness interface element, the so-called simplified micromodeling approach is arrived [12]. ...
... Due to the efficiency of modeling the complex geometry and nonlinear material behaviors that are intrinsic to masonry structure, the finite element method is commonly adopted. Ideally speaking, the masonry element (e.g., piers and spandrels) should be discretized by finite elements, respectively, for the brick/block units and mortar joints, which leads to the so-called micro-modeling approach [10,11]. When the mortar joint (of physical thickness) is modeled by a zero-thickness interface element, the so-called simplified micro-modeling approach is arrived [12]. ...
Situated on the northern bank of the Qiantang River estuary, the ancient seawall serves not only as a national cultural relic but also as an active agent in flood and tide prevention. This seawall features a trapezoidal cross-section and is constructed with layered stone blocks and a sticky rice mortar. To investigate the load-bearing and deformation attributes of this ancient structure, a scaled-down specimen with a ratio of 1:4 was created. Monotonic and cyclic vertical loadings were then applied to the wall’s top surface. During these loading procedures, measurements of the loading force, seawall displacement, and front and side deformation fields were taken. Experimental findings reveal that the seawall tends to lean towards the soil-retaining side under vertical loading. After ten loading cycles, the vertical rigidity of the wall was reduced by 10%. Upon application of a uniformly distributed vertical load of 1.6 MPa at the top of the wall, significant cracks began to materialize in the blocks at the base of the seawall. When the loading at the top increased to 2 MPa, a vertical crack that cut through the mortar layer at the wall’s center was observed. By comparing it to a three-dimensional finite element model, the load-bearing and deformation characteristics of the ancient seawall observed in the experiments were confirmed, which could contribute to the scientifically informed conservation and protection of the seawall.
... The multi-surface criterion was composed of three constitutive laws in tension, shear and compression, respectively. They were tension cut-off, shear slipping and compression cap criteria ( Figure 3a) [62,63]. Table 2 presents the adopted material -7 -parameters. ...
... E u is the elastic stiffness of units E j is the elastic stiffness of joints ℎ is the thickness of joints considering the difference of elastic stiffness between units and joints [62]. ...
... Post-peak stress-strain curve was described by exponential softening based on the tensile fracture energy (Gft) (Figure 3b). [59,62]. In this analysis, discrete cracking was considered in units as shown in Figure 4a. ...
The paper discusses the mechanical behaviour of masonry composed of fired solid bricks and earth mortar. Such masonry is a typical construction technique in South and Southeast Asia. As its mechanical behaviour is complex due to high anisotropy attributed to noticeable difference in stiffness and strength between bricks and earth mortar, it is still considered challenging to comprehend the mechanical behaviour of such masonry. Taking into account this background, the present research addresses the formulation of the mechanical behaviour of brick masonry in earth mortar. Numerical analysis was performed to reproduce uniaxial compression and diagonal compression tests, referring to empirical evidences on interface behaviour between bricks and earth mortar. Meso-scale analysis was performed, applying a multi-surface failure criterion composed of cracking, shearing and crushing to unit-joint interfaces. The analysis showed very similar stress-strain relations and failure patterns to the tests. The simulation of the uniaxial compression test presented that the distributions of compressive stress shifted along with the progress of cracks. In the reproduction of the diagonal compression test, vertical stress was irregularly distributed after diagonal stepwise cracks appeared. Two comparative studies were conducted to examine the shear performance of brick masonry in earth mortar. First, sensitivity analysis indicated the noticeable influences of compressive strength, friction angle and facture energy of unit-joint interfaces. Second, macro-scale analysis was conducted, using a homogeneous material model. The observed diagonal crack patterns were similar to the test. The paper contributes to the understanding of the mechanical behaviour of brick masonry in earth mortar.
... The modeling approach is based on the assumption that the constituent elements of the masonry structure (stones and mortar) consist of a skeleton of aggregates of various dimensions in direct contact with cohesive connections that enable the aggregates to withstand tensile forces. Unlike FE-based micro-modeling approaches, which require complex cohesive contact models and face convergence issues under cycling loading and large displacement [26], particle models are capable of predicting complex macroscopic failure phenomena with simple constitutive models by directly taking into account the physical particle interactions and material randomness associated with the grain structure of the wall's components: stone units, mortar, and reinforcement elements. Additionally, particle models are suitable for large displacement analysis and cyclic loading and can generate complex numerical models that are representative of rubble stone masonry. ...
The structural rehabilitation of historic/traditional rubble masonry wall constructions requires consolidation and retrofitting solutions to be employed in order to withstand dynamic loads, high vertical loads, and differential settlements. One of these strengthening techniques is based on the use of steel bar connectors perpendicular to the wall, considered individually or integrated into more complex strengthening techniques. The aim of this study is to evaluate numerically the strengthening effect of transverse steel connectors on rubble masonry walls. With this purpose, a 2D particle-reinforced model (2D-PMR) was devised and applied to model uniaxial compression tests. The results presented show that predictions calculated using the proposed 2D-PMR model are very close to known experimental results, particularly in the corresponding failure modes, the increase of the maximum uniaxial compression value, and ductility. Parametric studies are also conducted by varying the diameter of the steel bars and the level of strengthening to assess the influence of the bar-bond effect and lateral plates. The presented parametric numerical studies show that (i) a two-level strengthening solution guarantees a similar response to the three-level strengthening solution adopted in the experiments; (ii) it is not relevant to apply a grout injection during the application process of the steel connectors if lateral plates are adopted; and (iii) the 2D-PMR model can be used in the definition of the steel bar diameter and properties; as shown, a smaller (8 mm) bar diameter predicts a similar strengthening effect to the (12 mm) bar size adopted in the experiments. Given the performance of the proposed 2D-PMR model, further work is underway that will allow the 2D-PMR model to numerically assess other reinforcement techniques, namely, reinforced micro-concrete layers and textile reinforced mortar.
... Even for meso-scale modeling, where nonlinear behavior is represented by interfaces, its use in the seismic assessment of the whole structure is not feasible due to its complexity and computational cost. Therefore, meso-and micro-scale models are preferred in research where detailed damage assessments are examined [28][29][30]. The macro modeling approach is, thus, generally preferred in such large analyses, and the homogenization methods [31] are emphasized. ...
Failure under seismic action generally occurs in the form of out-of-plane collapses of walls before reaching their in-plane strength in historical stone masonry buildings. Consistent finite element (FE) macro modeling has emerged as a need for use in seismic assessments of these walls. This paper presents the numerical model calibration of U-shaped multi-leaf stone masonry wall specimens tested under ambient vibrations and out-of-plane (OOP) load reversals. The uncertain elastic parameters were obtained by manual calibration of the numerical models based on ambient vibration test (AVT) data of the specimens. To obtain nonlinear calibration parameters, static pushover analyses were performed on FE models simulating quasi-static tests. The calibrated numerical models matched well with the experimental results in terms of load-drift response and damage distribution. As a result, the modulus of elasticity and tensile and compressive degrading strength parameters of masonry walls were proposed. A parametric study was conducted to examine the effects of different materials and geometric properties (tensile strength, aspect ratio, slenderness ratio, and geometric scale) on the OOP behavior of stone masonry walls. A quite different strain distribution was obtained in the case of a large aspect ratio, while it was determined that the geometric scale had no effect on the strain distribution. Tensile strength was the dominant parameter affecting the load-drift response of the models. Within the presented work, a practical tool for out-of-plane seismic assessment has been proposed for the structures covered in this paper.
... However, it is interesting to note that while a vast amount of literature exists on the numerical modelling of the in-plane response of brick masonry walls, the same cannot be said about rubble stone masonry walls, especially works which aimed at capturing shearcompression experiments. A seminal work in this context was carried out by Senthivel and Lourenço [37] who modelled the shearcompression tests performed by Vasconcelos and Lourenço [12], adopting a 2-D finite element method (FEM) based micro-modelling strategy. In the adopted modelling strategy, the stones were modelled elastic and all non-linearity was lumped in interface elements representing the mortar joints as well as the stone-mortar interface using plasticity theory based micro modelling techniques. ...
... The same experiments were simulated also by Tarque et al. [38] again using a FEM based micro-modelling technique adopting the well-known concrete damaged plasticity [39,40] formulation for mortar joints and modelling the stones as rigid bodies. Tarque et al. [38] modelled also the mortar joints using continuum elements in contrast to Senthivel and Lourenço [37] who modelled the same using zero thickness interface elements. The experiments performed by Milosevic et al. [30] on rubble stone masonry piers were also numerically modelled. ...
... This was done by Ponte et al. [41] who used a macro-modelling approach, modelling rubble stone masonry as a homogenous material represented by the Total Strain Crack Model which uses an isotropic Rankine yield surface and is based on a fixed stress-strain law concept. However, an interesting aspect to note is that while both experimental studies i.e. [12,30] were performed applying a cyclic shear loading/displacement history, all numerical studies simulating them i.e. [37,41,42] modelled the applied loading as monotonic. ...
An applied element method-based modelling strategy to model rubble stone masonry is presented for the first time. The strategy represents rubble stone masonry as rigid blocks connected by deformable interface springs where non-linear material properties are lumped. Cyclic in-plane shear-compression experiments on rubble stone masonry piers representative of Portuguese historical constructions are reproduced with good accuracy. The robustness of the strategy is then investigated further by performing a parametric study and comparing results with existing literature on the subject. The numerical procedure marks a significant improvement in terms of computational burden with respect to conventionally used finite element-based strategies, making it attractive for performing non-linear dynamic seismic safety assessment of large structures.
... The tangential stiffness Kt can be calculated directly from the normal stiffness using the theory of elasticity. Considering the Poisson's ratio equal to 0.2, Kt results around 0.4 times as large as Kn (Senthivel and Lourenço 2009). However, a range of possible values may be found considering FEM and DEM analyses Ptaszkowska and Oliveira 2014;Tóth, Orbán, and Bagi 2009;Dimitri and Tornabene 2015;Giamundo et al. 2016;Lourenço 1996;Dimitri, De Lorenzis, and Zavarise 2011;Senthivel and Lourenço 2009). ...
... Considering the Poisson's ratio equal to 0.2, Kt results around 0.4 times as large as Kn (Senthivel and Lourenço 2009). However, a range of possible values may be found considering FEM and DEM analyses Ptaszkowska and Oliveira 2014;Tóth, Orbán, and Bagi 2009;Dimitri and Tornabene 2015;Giamundo et al. 2016;Lourenço 1996;Dimitri, De Lorenzis, and Zavarise 2011;Senthivel and Lourenço 2009). In this regard, interface stiffness was assessed by means of a sensitivity analysis varying the normal stiffness and the ratio with the tangential one. ...
Masonry is a heterogeneous material that consists of units and joints displaying a complex mechanical behaviour. In the present chapter, the experimental behaviour of masonry is briefly reviewed considering an advanced mechanical characterization of components (namely, units and mortar) and of masonry as a composite. Moving to vaulted structures, although a certain consensus has been reached in the masonry community regarding their static behaviour, ongoing research is still investigating their dynamic one. In this respect, the present chapter describes two paradigmatic case studies for two- and three-dimensional elements. First, the shaking table tests performed on a scaled dry‐joint arch undergoing windowed sine pulses is presented. A feature tracking‐based measuring technique, employed to evaluate the displacement of selected points, was used to analyse the failure mechanisms. Secondly, a scaled dry‐joint cross vault and a full‐scale mortared cross vault tested on the shaking table are presented. Finally, two engineering applications related to the safety assessment of vaulted structures are examined.KeywordsHistorical masonry arches and vaultsExperimental campaignsQuasi-static testsShaking table testsReduced scale vaultFull scale vault
