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A heterogeneous quasi-brittle granular material can withstand certain levelsof internal damage before global failure. This robustness depends not just onthe bond strengths but also on the topology and redundancy of the bondedcontact network, through which forces and damage propagate. Despite extensivestudies on quasi-brittle failure, there still lacks a unified framework thatcan quantify the interdependent evolution of robustness, damage and forcetransmission. Here we develop a framework to do so. It is data-driven,multiscale and relies solely on the contact strengths and topology of thecontact network for material properties. Using data derived from discreteelement simulations of concrete specimens under uniaxial tension, we uncoverevidence of an optimized force transmission, characterized by two noveltransmission patterns that predict and explain damage propagation from themicrostructural to the macroscopic level. The first comprises the optimizedflow routes: shortest possible paths that can transmit the global transmissioncapacity. These paths reliably predict tensile force chains. The second are theforce bottlenecks. These provide an early and accurate prediction of theultimate pattern, location and interaction of macrocracks. A two-prongedcooperative mechanism among bottlenecks, enabled by redundancies intransmission pathways, underlies robustness in the pre-failure regime.Bottlenecks take turns in accommodating damage, while member contacts spreadthe forces to confine damage to low capacity contacts which leave behind a webof strong contacts to support and curtail the failure of tensile force chainsin the region. This cooperative behavior, while serving to minimize theinevitable reduction in global transmission capacity, progressively heightensthe interdependency among these contacts and elicits the opposite effect.

Interdependent evolution of robustness, force transmission and damage in  a heterogeneous quasi-brittle granular material: from suppressed to cascading  failure