A. AHMED (1) and N.G. SHRIVE (2)
(1) PhD Candidate, Department of Civil Engineering, University of Calgary, Calgary, Alberta, Canada T2N 1N4
(2) Professor Emeritus, Department of Civil Engineering, University of Calgary, Calgary, Alberta, Canada T2N 1N4
ABSTRACT
Hilsdorf’s “lateral tensile splitting theory”, proposing that unit/mortar stiffness differences induce lateral tensile stresses which drive fracture, remains the consensus describing masonry fracture in the literature. This is the case despite finite-element analyses demonstrating that the lateral tensile stresses induced by this effect are only 1/50 of unit tensile strengths. Masonry fracture ought to be understood via fracture mechanics, wherein material flaws are considered to drive fracture; the influence of masonryspecific phenomena, such as lateral tensile splitting stresses, should be determined by considering their effect on material flaws. Historically, compressive fracture mechanics has been limited by the analytical complexity of the ensuing differential equations. However, a recent theoretical development – fractal voids – has greatly simplified compressive fracture analysis. Herein, an application of fractal voids to the analysis of masonry fracture in uniaxial compression is presented. Firstly, the development of the fractal void approach is situated within earlier compressive fracture literature. The fractal void surface, and the mathematical implications, are then elucidated. A two-dimensional fracture mechanics analysis is then used to understand the influence of masonry’s heterogeneity on its fracture. Lateral tensile splitting stresses are found to minimally influence fracture, increasing tensile stresses on circular voids by only 12%. Lateral tensile stresses are also found insufficient to induce tensile fracture at line cracks; the stress intensity factor induced by tensile stresses for a 24mm crack were comparable to those induced by distant compressive loading on a 0.5mm radius fractal void. A rational approach to accounting for variable material properties and void distribution metrics is also presented.
KEYWORDS: fracture, compression, fractal, voids.