Discrete Element Bonded-Block Models for Detailed Analysis of Masonry

Abstract

A detailed modelling approach to represent masonry at the meso-scale is proposed, based on the discrete element method, considering the nonlinear behavior of the joints and the units. The fracture of units is represented by the bonded-block concept, in which a random network of potential cracks is created, allowing the progressive development of failure mechanisms. For simplicity, only the 2D case is presented, but the extension to 3D is straightforward. A key component of the proposed model is a framework for a joint or interface constitutive model, including the post-peak softening range, taking into account the experimental fracture energies. In this model, the softening curves in tension or shear are defined by piecewise linear segments, calibrated to reproduce the most common masonry constitutive models. The essential issues involved in the application of bonded-block models to masonry are examined, namely the block shape, either Voronoi polygons or triangles; size; deformability; and the influence of the main constitutive parameters. Uniaxial compression tests are analyzed in detail. The simulation of a well-known experiment of a brick panel under shear shows the good performance of the proposed approach. The investigation results demonstrate the model’s capabilities and provide guidelines for its application.

Application of Bonded-Block Models to Rock Failure Analysis

“…The scope of bonded-block models has extended outside rock mechanics to include the fracture of other geomaterials and structures, for example, in the detailed analysis of lab tests on masonry specimens, prisms and wallettes [54][55][56]. Concrete fracture has also been approached with bonded-block models [57] and related numerical techniques employing polygonal or polyhedral elements [58].…”

“…In explicit time-stepping solution algorithms, unreasonably high stiffness parameters penalize computational efficiency. Intermediate solutions are possible, for example, by assigning 90-95% of the deformability to the blocks, which gives approximately the same results without excessive run times [56]. In most bonded-block models, the inner blocks are assumed to be either rigid or elastic.…”

“…For systems with deformable inner blocks, only a fraction of the deformation is assigned to the joints; therefore, the stiffnesses values will be proportionally higher. Comparisons of rigid-block models with deformable-block models in which the block material was assigned 50% and 95% of the total deformation have been presented [56]. The deformableblock model generally leads to a more realistic deformation pattern, but at a computational cost.…”

“…These micro-properties can be calibrated to obtain the intended global strength. More elaborate models add a post-peak-softening regime in tension and shear, which allow the consideration of fracture energies [37,38,55,56]. Research on fracture modeling has shown the importance of size effects due to the numerical element size.…”

A solution for the frictional resistance in macro-block limit analysis of non-periodic masonry

“…Rigid and/or deformable blocks may be used depending on the research question and the expected outcomes from the numerical model, also considering a compromise between computational cost and accuracy. As shown by various studies in the literature, DEM offers a wide range of solutions to simulate regular and irregular, discontinuous medium subjected to quasi-static, dynamic, or coupled thermo-mechanical loadings from mesoscale to macro-scale [26,[30][31][32][33].…”