Development of a 3-D confinement-dependent dilation model for brittle rocks; part 2, formulation and parameterization based on the Cartesian plastic strain increments ratios approach

Abstract

Experiences from deep mining have seen an increase in operational and safety challenges related to excessive rock mass bulking due to brittle fracturing and spalling. These have exposed limitations in available constitutive models used to assess post-peak deformation potential, as required for excavation support design. Despite the spalling process being driven by extensional fracturing in the low-confined rock near the excavation boundary, the yield and dilation models available in commercial numerical modelling software are dominated by shear-based models (e.g., Mohr-Coulomb, Hoek-Brown, etc.) more suitable for shear fracturing under intermediate to high confinement. In the context of plasticity theory , this corresponds to important limitations that arise from the assumptions inherent in the development of dilation models (also referred to as flow rules). Flow rules determine the relative incremental plastic straining of the yielding rock under a specific stress state and at a specific plastic straining history. The commonly-used flow rules in rock engineering have been shaped by experiences in soil mechanics and weak rock, and consequently, ignore the fact that stress-induced brittle fracturing has a strong directional component and is sensitive to 3-D confinement. In particular, the influence of the intermediate principal stress , σ 2 , on the directionality and magnitude of dilation is not accounted for. Another limitation is that many advanced dilation models require numerous empirical parameters that do not have clear physical meaning. This conflicts with the of practitioners being able to intuitively understand the influence and sensitivity of important controlling parameters on modelled deformation response . In the Part 1 companion paper to this, we presented the theoretical framework for deriving a non-potential flow rule using the concept of Cartesian-based Plastic Strain Increments Ratios (PSIRs). We demonstrated the advantages of using PSIRs for understanding the 3-D dilation/contraction behaviour of rock in relation to the underlying 3-D confinement-dependent fracturing processes. In this Part 2 paper, we first conduct a thorough review of existing dilation models and their formulation to investigate mathematical models that can be used to effectively represent both pre- and post-peak dilative behaviour in brittle rocks. We then further investigate the true dilative characteristics of brittle rock using triaxial compression test data for Lac du Bonnet Pink Granite . This data and analysis are further used to validate and parameterize the model developed. Next, we derive a σ 2 -independent dilation model based on the PSIR concept and use this to then develop a 3-D σ 2 -dependent dilation model, both of which are first-of-their-kind. The derivations also outline how the PSIR approach allows for optimization of the number of input parameters required for the dilation model, each with physical meaning. Finally, the advantages over existing dilation models used in practice is demonstrated and discussed with respect to the importance of σ 2 - and strain history-dependency in relation to 3-D brittle fracturing and bulking processes.