Of cuts and cracks: data analytics on constrained graphs for early prediction of failure in cementitious materials

¹ School of Mathematics and Statistics, The University of Melbourne, Australia
² School of Earth Sciences, The University of Melbourne, Australia
³ Faculty of Civil and Environmental Engineering, Gdańsk University of Technology, Poland

^* e-mail: atordesi@unimelb.edu.au

Published online: 30 June 2017

Abstract

Using data from discrete element simulations, we develop a data analytics approach using network flow theory to study force transmission and failure in a ‘dog-bone’ concrete specimen submitted to uniaxial tension. With this approach, we establish the extent to which the bottlenecks, i.e., a subset of contacts that impedes flow and are prone to becoming overloaded, can predict the location of the ultimate macro-crack. At the heart of this analysis is a capacity function that quantifies, in relative terms, the maximum force that can be transmitted through the different contacts or edges in the network. Here we set this function to be solely governed by the size of the contact area between the deformable spherical grains. During all the initial stages of the loading history, when no bonds are broken, we find the bottlenecks coincide consistently with, and therefore predict, the location of the crack that later forms in the failure regime after peak force. When bonds do start to break, they are spread throughout the specimen: in, near, and far from, the bottlenecks. In one stage leading up to peak force, bonds collectively break in the lower portion of the specimen, momentarily shifting the bottlenecks to this location. Just before and around peak force, however, the bottlenecks return to their original location and remain there until the macro-crack emerges right along the bottlenecks.