Plane-stress and shell macromodels are often preferred to analyze masonry structures because of their numerical efficiency. However, they often misestimate the hysteretic behavior of the structures. Additionally, due to the nature of smeared cracks, the cracks may be diffused. This article proposes a new orthotropic model, which focuses on the cyclic, nonlinear behavior of brick masonry structures. The model adopts a total-strain based rotating crack approach. It describes tensile and compressive failure in the rotating principal directions, while including indirectly shear failure through an internal iterative algorithm. Two distinctions are made regarding the tensile postpeak and unloading/reloading behavior based on the crack orientation at crack initiation: a steep softening branch and secant unloading are adopted when the crack angle corresponds to in-plane flexural failure, and a softening branch and bilinear unloading are adopted when the crack angle corresponds to diagonal shear failure. Bilinear unloading/reloading is adopted in compression, resulting in a cyclic behavior resembling shear. The constitutive model was implemented in a finite element software and validated against experimental results. The numerical simulations reproduced well the experimental outcomes in terms of envelope load-displacement curve and hysteretic behavior, while simultaneously they resulted in localized damage, representative of the experimental crack patterns.

This paper presents a benchmark exercise for the seismic assessment of unreinforced masonry (URM) buildings as a follow-up of a blind prediction test organized in the context of the European Conference of Earthquake Engineering Series. The blind prediction exercise was aimed at better defining the open issues in current procedures for modeling and performing seismic analysis of URM buildings, by highlighting the uncertainty that can influence the results. This work presents an overview of the approaches used by different research teams and the scope of predictions. The benchmark structure was a three-story building with traditional European architecture from which two Cases were considered: A) stone masonry walls and flexible horizontal diaphragms and B) brick masonry walls and rigid horizontal diaphragms. A wide range of approaches was used by the participating teams concerning modeling strategies, methods of analysis and criteria for the attainment of limit states, which are here addressed as potential sources for the dispersion of predictions. The results were compared in terms of capacity curves, predicted failure mechanisms compatible with the fulfillment of limit states of near collapse and damage limitation, and related minimum values of peak ground acceleration (PGA). The results show an overall good agreement for damage patterns and collapse mechanisms in both benchmark structures, presenting some differences in the type of failure mode and its extent. However, the scatter of predicted capacity curves and critical PGAs is very high, especially for the Case with brick masonry and rigid diaphragms, indicating that clearer procedures in the building codes are required for professionals.

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

This paper proposes a sub-step based iterative constitutive model for line interface elements used to analyse masonry structures loaded in-plane. Based on a total deformation theory, the model adopts characteristics of multi-surface plasticity, including a Coulomb friction failure surface for shear, with tension and compression cut-off and softening for all three domains. The model is driven by two damage parameters, one for compression and one that couples tension and shear. The sub-stepping technique is demonstrated to be numerically stable and is used as an alternative to the traditional return-mapping algorithms, which are prone to convergence issues and instability. The proposed model has been validated against experimental tests performed on masonry walls subjected to cyclic, in-plane loading. The numerical simulations adequately identify the failure mode, the hysteretic behaviour and the crack pattern. When toe crushing is governing, the results appear to be sensitive to the assumed masonry compressive strength. It is shown that calibration of the lumped compressive strength makes possible to fully describe the damage evolution in walls that exhibit a mix of flexural crack-crush failure and shear failure. Overall, the model is demonstrated to be an efficient and robust tool for analysing the cyclic, in-plane behaviour of masonry walls.