Two-Part hooke model (TPHM): Theory, validation and applications

Abstract

Hooke’s law was discovered by Robert Hooke (1635-1703) and states that during elastic deformation of a solid body the strain is linearly proportional to the stress. While Hooke’s law was initially developed based on experimental observations for relatively homogeneous materials, natural rocks generally contain small-scale deformation heterogeneities (such as the existence of micro-cracks). To address this issue, this chapter introduces the two-part Hooke model that was developed by conceptually dividing a natural rock into hard and soft parts that are subject to different degrees of mechanical deformation under a given stress. Remarkable consistency between the model and observations from different sources, for both rock matrix and fractures, has been achieved. The usefulness of the model in dealing with several engineering problems is also demonstrated, including coal-permeability changes caused by swelling under different stress conditions, coupled hydro-mechanical processes associated with CO2 geological sequestration in a fractured formation, and evolution of the excavation damage zone related to nuclear waste disposal in a shale formation.