Underground roof rock beams crossed by vertical joints, are analysed numerically. Various joint patterns and joint material compliances, are considered. Their effect, for small deflections, is related to the mechanical response of the roof rock beams; i.e. the joint contact length and extreme strain at the abutments and midspan, the midspan deflection, and the shape of the thrust line. Finally, these values are correlated to the analytical ones which correspond to the simpler voussoir beam idealizations.


The behaviour of an underground roof composed of stratified, jointed and competent rock has been studied initially by Fayol (1885); he noted experimentally that the lowest stratum of the roof was not loaded by the upper ones. Subsequent researchers, starting with Evans (1941), studied the behaviour of such a single bed roof and provided graphs, tables and algorithms for the prediction of its behaviour. Wright (1974) created a design procedure for the control of layered, bolted or unbolted, underground, undermined roofs, based on finite element and laboratory experiment results. Sterling (1980) captured the salient features of the work of Evans and other researchers and by experimenting on his apparatus provided a coherent picture of the deformation and failure modes of roof rock. This was noted by Brady and Brown (1985), who suggested an explicit account to be taken of the presence and compressibility of cross joints in estimating the elastic modulus. Therefore, it is considered necessary to investigate on the behaviour of such roofs and on the divergence of their response from the pertinent analytic formulae for the idealised model. Evaluation of the response of the various roof beam geometric configurations is achieved with the distinct element code UDECTM (1999), under plane strain conditions. These rock roofs contain vertical joints of varying frequency of occurrence and material compliance.

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