Selecting Advanced Constitutive Models: An Overview

"Numerical modelling is becoming universal in rock engineering practice. Most applications focus on the prediction of failure loads of 2D problems, where the numerical models are useful extensions to analytical methods and experience-based design criteria. For 3D problems and problems where the assessment of serviceability indicators – displacements, ground-structure response, etc. – are of importance, the selection of the constitutive models themselves and the implications of the selection of material parameters may have a very heavy impact on the reliability of the model outcome and its predictive capability.This paper overviews basic common aspects of constitutive equations used in practical rock engineering and summarizes some challenges that are frequently observed when reviewing numerical models performed for routine problems in rock engineering. INTRODUCTIONNumerical methodsFrom a philosophical perspective models, either analytical or numerical, are idealizations of a perceived reality. For us engineers, models are just tools we use to guide our judgement and understanding of the problem in hand. When dealing with problems in rock engineering, we resort to a wide range of techniques:1. Closed form solutions like confinement-convergence methods for circular tunnels: these methods satisfy equilibrium and compatibility requirements at the cost of a crude simplification of the material behavior and geometry;2. Limit analysis methods, like bearing capacity formulas: lower bound methods satisfy equilibrium but sacrifice compatibility, and upper bound methods do the opposite. Material behavior must be simple, geometry admits limited freedom;3. Limit equilibrium methods, like method of slices for slope stability: they satisfy restricted forms of equilibrium, do not satisfy compatibility requirements, require simple material behavior but have a much greater flexibility on geometry;4. Numerical methods, where a mesh is employed to discretize the problem geometry: when properly formulated, these methods satisfy equilibrium and compatibility requirements and give reasonable approximations to the behavior of very complex geometries and construction sequences. Very little restrictions remain on geometry and material behavior, but the cost of calibrating the material parameters can be very high."