Dilation and Post-peak Behaviour Inputs for Practical Engineering Analysis

Numerical models used by engineers to simulate rockmass behaviour are often limited by poor or incomplete representations of post-yield behaviour. Although conventional plasticity theory is often capable of predicting stress distributions around excavations, it is more difficult to fully capture the complex displacement patterns that are observed in situ. This is largely because conventional material models fail to capture the confinement and damage accumulation dependencies of post-yield dilatancy. Even with these mechanistic limitations in mind, simple constitutive models can be used for practical applications, although no reliable methodology for parameter selection exists. This study aims to remedy this deficiency. In this work, existing models for dilatancy based on laboratory testing data are considered and their limitations are discussed. The most accurate of these models add complexity to the analyses and also require additional input parameters beyond those which are typically obtained from laboratory testing. While the concept of a constant dilation angle during yield is not physically valid, it may be, in some cases, a sufficient model for ground response prediction. It is of interest, for practical engineering analyses, to understand the conditions where this additional complexity is required and where simplified models may be adequate. For the case of circular excavations in a uniform stress field, plastic zone displacements for mobilized and constant dilation angle models are compared and parametric sensitivities are discussed. Many material parameter combinations representative of relatively ductile rockmasses are tested, and it is shown that for most of these cases, the results obtained using a mobilized dilation angle can be well approximated through the use of an appropriate best-fit constant dilation angle. Through a statistical analysis of the data, a practical methodology for the selection of a constant dilation angle for use in simpler continuum numerical models is proposed. Further analysis under more general conditions performed using finite-difference models shows that the methodology can be applied to non-circular excavation geometries (errors are only significant near corners), general strain softening behaviour, and non-hydrostatic stress conditions where the stress anisotropy is moderate. An example of the methodology is presented in the context of extensometer data from a deep mine shaft, and the success of the methodology in providing a reasonable dilation angle estimate is demonstrated.