The fully-coupled model for rock engineering systems

Abstract

This paper introduces the fully-coupled model (FCM). The model is developed from rock engineering systems (RES) concepts and graph theory. The basic device used in the RES approach is the interaction matrix: for any rock mechanics or rock engineering problem, the relevant state variables of the system are listed along the leading diagonal of the matrix—and the relations between each pair of variables, i.e. the binary mechanisms, are identified in the off-diagonal boxes. The interaction matrix can contain any number of state variables, depending on the engineering objective and level of analysis required. The FCM considers the interaction matrix as a mechanism network. Graph theory is used to assess the contributions of all the mechanisms in all the pathways, a key feature being the identification of mechanism feedback loops and their stability. The (uncoupled) binary interaction matrix is thus transformed into a (fully-coupled) global interaction matrix. The system outputs for any problem being modelled are then obtained from the system inputs via the global interaction matrix. Advantages of the FCM in the context of rock engineering are that the primary state variables of the system, the binary interactions, all the mechanism pathways, each step in the coupling process, and the consequential evolution of the matrix values can be clearly identified. The FCM has been developed initially with linear mechanisms. Five numerical examples of the linear FCM are given: simultaneous equations, spring structures, a pressurized thick cylinder, a six-variable dam system and a nine-variable pressure tunnel system. Using these examples, we demonstrate that the output resulting from any input perturbations can be rapidly assessed with the FCM. We also indicate how the FCM can be extended to include non-linear mechanisms.