Failure mechanisms in open pit mining applications often involve a combination of weak rock mass and adverse structure. Major structure is typically included explicitly with less persistent fabric included using general anisotropy or ubiquitous joint constitutive models in both continuum and discontinuum applications. Implicit strength anisotropy in these constitutive models, however, is not equivalent to explicit jointed rock mass. This paper uses a conceptual slope example to illustrate that constitutive models incorporating ubiquitous joints exhibit an inherent strengthening which is considered a function of mesh density, mesh orientation, anisotropy orientation, and lateral constraint. The implication is an overestimate of the predicted stability margin by 5 – 10% or higher when key variables are compounded. Key observations are summarized with the intent to provide the reader with a guide to using ubiquitous joint models.
Numerical simulation of anisotropic rock mass behavior has been the topic of rock engineering research for decades (Huang et al. 2022; Leng et al. 2021; Lu et al. 2020; Sainsbury et al. 2017). Unlike homogeneous engineered materials such as concrete, metal, plastic, etc., rock mass is a geologically formed heterogeneous and anisotropic material with a mechanical behavior controlled by a combination of intact rock mass properties and natural or induced directional weakness embedded through joints, bedding, foliation, and other discontinuities.
General anisotropy or ubiquitous joint (UJ) constitutive models allow for the implicit representation of discontinuities in continuum numerical models. Structural features are represented as preferential orientations of weakness in the rock mass as opposed to the explicit modeling of structure used in discontinuum models, which are limited in their applicability in large scale mining projects due to high computational costs. A detailed overview of UJ models can be found in Sainsbury et al. (2013).
UJ constitutive models are widely implemented in mining projects involving rock slopes, providing an efficient method of modelling anisotropic rock mass behavior in both two-dimensional (2D) and three-dimensional (3D) applications (RocScience, 2023; Itasca, 2019). Many uncertainties remain however over its use in practical applications to inform design and operational decisions due to the common misconception that UJ models are indeed equivalent to discrete joints. Sainsbury et al. (2017) highlighted that UJ models do not consider the effects of joint spacing, length, stiffness, block interlocking, internal moments and bending rigidity of rock layers which results in misrepresentation of yielding and deformation response when compared to the more accurate discontinuum models. Carvalho et al. (2019) demonstrated that the implementation of UJ constitutive models can lead to unexpected stress and deformation behavior. Lu et al. (2020) demonstrated that the factor of safety is sensitive to the size of discretized mesh elements, until a certain threshold of element size is reached, and relatively insensitive to dilation and boundary extent.
