Search

In countries of low to moderate seismicity, such as Switzerland, unreinforced masonry (URM) is mainly used in residential buildings due to its good insulation capacity and fire resistance along with a fair compressive strength. URM walls however show a limited horizontal in-plane deformation capacity, which can lead to an unfavorable seismic response. To predict this response, at least the walls' effective stiffness, shear force and drift capacity are required. While mechanics-based models for the force capacity are well established, such approaches are largely lacking for the effective stiffness and the drift capacity. The mostly empirical code equations for the two latter parameters lead to unsatisfactory and, in the case of drift capacities, often unconservative predictions when compared to tests. To address the issue, this thesis introduces an analytical model describing the monotonic force-displacement response of in-plane loaded URM walls. Based on a Timoshenko beam, the influence of diagonal shear and horizontal flexural cracking is captured by mechanical models, leading to an analytical description of the pre-peak force-displacement response. The shear force capacity is determined using local stress criteria and the ultimate drift capacity is estimated with a plastic zone approach evaluating a crushed region of high curvatures at the wall toe at ultimate failure. A comparison with experiments indicates that the model yields reliable predictions of stiffness, strength and drift capacity. Moreover, the monotonic model is extended to capture the full cyclic response including stiffness degradation and residual displacements. Furthermore, an existing numerical mesoscale approach is used to conduct parametric studies. The wall is modelled with solid elements, capturing brick crushing, and interface elements, simulating sliding and flexural uplift in the bed-joints. A study of the load history influence shows that for walls failing in shear, the drift capacity can reduce to half from monotonic to reversed-cyclic loading. The second study simulates different test setups used in the literature to impose double-fixed support conditions. While there appears to be hardly any difference between the force and the mixed-controlled mode, simulating the double-fixed wall as a cantilever with half its original height leads in many cases to a strong overestimation of force and drift capacities. The final investigation concerns a change in axial force during horizontal loading. The force and drift capacities of walls under changing normal force appear to be very similar to those of walls under a constant normal force that corresponds to the changing axial load towards ultimate failure. In addition, a database of shear-compression tests is extended and analysed for trends in stiffness and drift capacity. Both, the initial and the effective stiffness increase with increasing axial load, while the ratio of effective-to-initial stiffness is rather constant and lies around 0.75. As for the drift capacity, an upward trend with increasing shear span ratio and a downward trend with increasing axial load are observed. Concluding, simple mechanics-based formulations for the effective stiffness, the force and the drift capacity to be used in design are proposed. A validation with the database shows that the new formulations are more accurate in predicting effective stiffness and drift capacity than currently used code equations.

A correction to this paper has been published: https://doi.org/10.1617/s11527-021-01653-6

The performance of shear-compression stone masonry walls with regard to their interaction with plaster is investigated by means of numerical simulations. A 3D finite element model based on the simplified micro-modelling technique is developed for the masonry-plaster system and verified against test results. The walls are simulated by using the commercial finite element software Abaqus. A constitutive law specifically formulated for brittle materials is used for the stone blocks and a material model taking into account the evolution of their properties under cyclic loading is used for the mortar joints. The model is the extension of a model previously developed for unreinforced mortar-brick masonry walls. In its extension to stone masonry, a modelling technique is introduced in order to capture the interaction between the masonry wall and the plaster. In the comparison with the test results the model shows itself capable of capturing two main phenomena that govern the masonry-plaster system: i) the cracking of the plaster and ii) its detachment from the masonry wall.

Code design of unreinforced masonry (URM) buildings is based on elastic analysis, which requires as input parameter the effective stiffness and the ultimate drift capacity of the in-plane force-displacement response of URM walls. Eurocode 8, for example, estimates the effective stiffness as 50% of the gross sectional elastic stiffness. Code provisions for the drift capacities are usually empirical equations relating a base drift value to the failure mode and a slenderness ratio. However, comparisons with experimental results have shown that neither approach yields accurate predictions. In this paper, 61 full-scale shear-compression tests of modern URM walls of different masonry typologies from the literature are investigated. It shows that both the initial and the effective stiffness increase with increasing axial load ratio and that the effective-to-initial stiffness ratios are approximately 75% rather than the used 50%. An empirical model for the computation of the effective-to-initial stiffness ratio is suggested based on a recently developed analytical approach, which attributes the loss in stiffness to diagonal cracking and brick crushing. As for the drift capacity, the experimental evidence supports the fact that it reduces with increasing axial load and increases with increasing shear span ratio. A recently developed analytical model for the prediction of the ultimate drift capacity for both shear and flexure controlled URM walls is presented. It considers the effect of kinematic and static boundary conditions on the drift capacity. A comparison to test results shows that the proposed models yield better estimates than current code provisions.

In the seismic design of unreinforced masonry walls, the elastic modulus E and shear modulus G are essential parameters for the calculation of the in-plane wall stiffness. Current codes provide empirical estimates of the elastic modulus and furthermore a ratio of shear to elastic modulus G/E. This ratio, however, is not based on scientific evidence and consensus concerning the value and influencing parameters is lacking. This article develops a closed-form formulation for the G/E ratio of masonry walls with running bond pattern. The formulation is derived by using an analytical homogenization tech-nique already employed in the literature and modified here to consider the finite thick-ness of the wall. The resulting formulation is based on the geometry of the units, the thickness of the joints and the elastic moduli of units and joints. The resulting analytical expression for the G/E ratio is used to assess the influence of various parameters and validated by comparing it to finite element simulations.

In der Erdbebenüberprüfung von unbewehrten Mauerwerksscheiben stellen der Elastizitäts- und Schubmodul (E und G) essentielle Parameter für die Berechnung der Wandsteifigkeit in der Ebene dar. Heutige Normen beinhalten empirische Schätzungen des Elastizitätsmoduls sowie des Verhältnisses zwischen G und E. Dieses Verhältnis basiert jedoch nicht auf einem mechanischen Fundament und bis heute mangelt es an einem wissenschaftlichen Konsensus was seine Größe und beeinflussenden Faktoren angeht. In diesem Artikel wird eine geschlossene Formulierung für das G zu E Verhältnis von Mauerwerksscheiben im Läuferverband vorgestellt. Die Gleichung wird unter Benutzung von analytischen Homogenisierungstechniken, die bereits aus der Literatur bekannt sind und abgewandelt werden um eine endliche Wanddicke zu berücksichtigen, hergeleitet. Die resultierende Formulierung basiert auf der Ziegelgeometrie, der Fugendicke, den Elastizitätsmoduli von Ziegeln und Lagerfugen sowie den Querdehnzahlen von Ziegeln und Mörtel. Sie wird mittels Finite-Elemente-Simulationen validiert und schlussendlich dazu verwendet, den Einfluss verschiedener Parameter auf das G zu E Verhältnis zu studieren.