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SUMMARYThe paper describes a new assumed stress triangular element for Reissner-Mindlin plates, called TIP3, with three nodes and three degrees of freedom per node. The kinematics is constructed by means of the so-called linked interpolation ruled by technically significant degrees of freedom (i.e. one transversal displacement and two rotations per node) without using additional bubble modes. The static representation starts from a moment-shear uncoupled polynomial approximation and is constrained to satisfy some equilibrium conditions in order to reduce the stress parameters to a minimum number. The resulting element is locking free, presents correct rank and passes the bending patch test even for very thin plates. The good performances of the element are demonstrated by several comparisons with other triangular plate elements available in the literature.

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Rock pillars can be defined as the in-situ rock between two or more underground openings. However, one aspect that is seldom considered in analysis of hard rock pillars, and indirectly in synthetic rock mass models to determine rock mass strength, is the actual stress level and stress path imposed on the pillar due to the excavation sequence and the location of the pillars within the mine lay out. In this paper we propose to use numerical stress analysis to determine how stresses vary across the excavated pillars in a typical room-and-pillar mine lay out, and thus generate a spatially variable determination of pillar stability. Because of the computational difficulty associated with hybrid modelling of realistic discrete fracture networks, synthetic rock mass modelling is commonly carried out using a 2D approach. By comparing 3D and 2D results for selected cross-sections across, we believe the results of the analysis will provide the opportunity to better constrain the stability implications of a 2D approach to pillar design and synthetic rock mass modelling.