Mesoscopic modelling of masonry using GFEM: a comparison of strong and weak discontinuity models

Abstract

These days, durability and sustainability are gaining more and more interest. High energy and material costs force us to optimise the energy use in buildings and the use and re-use of building materials. An obvious way to re-use building materials is renovation in buildings. Since in a renovation project the function of the building is not always kept, changes must be made in order to make the new function of the building possible. These changes can be both on the architectural (e.g. changes in division) as on the constructive level (e.g. change of loading conditions). This leads to new mechanical conditions which often incluse a raise of vertical loads due to higher floor loads, increase of slenderness of the wall due to new intermediate floors and the introduction of eccentric loading due to new intermediate floors. In order to preserve the existing load carrying structure, the construction must be recalculated with these new loading conditions. Most old and historical buildings are constructed using masonry. The recalculation of masonry structures subjected to the new loading conditions shows multiple problems. First of all, the actual material parameters describing the behaviour of masonry are not the same as the initial parameters. Over the years, strength and stiffness of masonry change, altering the overall behaviour of a wall. It is well known that masonry structures can suddenly collapse(1). Secondly, the current masonry codes are based on new brick materials and mortars. In older buildings, the quality of brick and mortar differs from values nowadays. Finally, the masonry wall may already be damaged or there might be irregularities in the wall (e.g.windows openings). Consequently, advanced computational modelling techniques are often necessary to compute a realistic value of the ultimate collapse load of a masonry structure. Three major groups of finite element modelling approaches exist: microscopic, mesoscopic and macroscopic (2). The former approach models each masonry constituent (the units, the mortar and the unit-mortar interface) in high detail, thus leading to many degrees of freedom and high computation times. In the macroscopic approach the joints and bricks are homogenized to one orthotropic material. The main advantage of this method is that not much computational effort is needed to calculate large structures. However, the obtained crack path is less detailed. These drawbacks can be alleviated by the use of mesoscopic models. In this approach, joints and bricks are modelled by separate entities, but in less detail than the microscopic approach. Classically, the joints are incorporated by interface elements, situated on the boundaries of the continuum brick elements (2)(3). When a critical state is reached in a joint, a strong discontinuity(i.e. a jump in the displacement field) is introduced in the interface. An alternative way to incorporate strong discontinuities is the partition of unity method(4)(5)(6). Withn this method, nodes are locally enhanced to enrich the solution with discontinuous models. This concept was applied to masonry by De Proft et al.(7) and will be extended in this paper by the incorporation of weak discontinuities. A weak discontinuity introduces a jump in the strain field, allowing for failure to localise in a zone with finite width(8)(9). The thickness of this failure is in this case linked to the joint thickness. The main advantages of the weak discontinuity approach are the ability to perform the constitutive modelling in the general stress and strain spaces.