More is different: On the emergence of collective phenomena in fractured rocks

Abstract

Fractures widely exist in crustal rocks and form complex networks dominating the bulk behaviour of geological media. Thus, understanding how fracture networks affect subsurface processes/phenomena is highly relevant to many rock engineering applications. However, the large-scale behaviour of a fractured rock mass consisting of numerous fractures and rocks cannot be predicted by simple applications of the knowledge of individual fractures and/or rocks, due to upscaling complexities involving the hierarchy of scales, heterogeneities, and physical mechanisms as well as the possible emergence of qualitatively different macroscopic properties. In other words, macroscopic phenomena in fractured rocks arise from the many-body effects (i.e. collective behaviour) of numerous interacting fractures and rocks, such that the emergent properties at the fracture system scale are much richer than those of individual components. Hence, more is different! This paper gives a discussion on the mechanism of emergence in fractured media from a combined statistical physics and rock mechanics perspective, and further presents a multiscale conceptual framework to link microscopic responses of single fractures/rocks to macroscopic behaviour of rock masses consisting of many fractures and rocks. This framework can serve as a useful tool to bridge experimentally-established constitutive relationships of fracture/rock samples at the laboratory scale to phenomenologically-observed macroscopic properties of fractured rock masses at the site scale.