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Analytical formulation for the deformability assessment of rock masses with filled discontinuities

The estimation of the deformation modulus of a rock mass is a fundamental factor in the design of civil works such as tunnels and dams. However, it is one of the parameters that entails highest difficulty when evaluating the rock mass. In this paper, a new analytical model is presented to assess rock mass deformability, with the aim of improving the estimation of the properties and their implementation in numerical models. The model presented is analytical, anisotropic and based on the equivalent continuum approach, and considers: the geometry of the rock mass for orientation, spacing and thickness of the discontinuities, the presence of fill; and, finally, the deformational properties of the intact rock and the discontinuities. The resultant model was adapted for the specific case of filled discontinuities using both the linear elastic model and the Hertz-Mindlin law. The assessment presented includes: the implementation of the model, the analysis of various theoretical scenarios, the estimation of deformabilities for multiple cases, a numerical validation using the Distinct Element Method, and a discussion of the scale effect. The results are compared with some empirical formulations for the deformability assessment of rock masses. This comparison underlines the importance of separately considering all the factors that define the rock mass, as well as the necessity of heeding the anisotropy caused by the orientation of the discontinuity sets.

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