Failure Surfaces for Common Brickwork Settings Used in Historical Masonry Structures

ABSTRACT

The need to preserve and protect the historical masonry structures has been the emergence of researches directed towards the analytical modeling of failure in masonry. However, since masonry is a composite material made of units (brick, blocks, etc.) and mortar, the fracturing mechanism in masonry is a complex phenomenon due to its components’ distinct material properties. Masonry is also a material which exhibits distinct directional properties because the mortar joints act as planes of weakness. An accurate analysis of masonry structures in a macro-modeling (or composite) perspective requires a material description for all stress states. Uniaxial behavior of masonry is dictated by the tensile cracking and compressive crushing mechanisms, while in-plane mechanical behavior of masonry panels under biaxial loading is a more complex phenomenon. Due to the orthotropic nature of masonry, its failure cannot be defined simply in terms of a criterion based on the principal stresses at any point; therefore, the influence of a third variable, must be also considered. One suitable graphical representation of the failure surface for in-plane behavior of masonry panels could be in terms of the full stress components (σ_x, σ_y, τ_xy) whereas the material axes are assumed to be defined by the bed joints direction (y direction). Another possible representation can be obtained in terms of principal stresses and an angle, θ, which measures the angle between the principal stress axes and the material axes. Clearly, different diagrams in the principal stress planes are found according to different values of θ. This study focusing on a series of masonry models with the roman brick setting (Wright 2009) aimed to develop a complete (σ₁, σ₂, θ) failure surface for all principal stress combinations. Employing micro-modeling approach, the Distinct Element Method was used to numerically model the brickwork unit discrete medium, in which both geometric and physical nonlinearities of the intact bricks and brick-mortar discontinuities are taken into account. For two other types of brickwork settings used in ancient buildings (such as historical vaulted constructions in Tabriz Bazaar) so called Herringbone arrangements (Brunskill 1997), a graphical representation of the failure surface in terms of the full stress vector (σ_x, σ_y, τ_xy) was also obtained.

KEYWORDS:

• bed joints
• biaxial stress
• brickwork arrangement
• Distinct Element Method
• failure surface