Some minerals, such as coal and potash, are extracted from stratified sedimentary rocks, usually by underground mining. To safely calculate the excavations, geotechnical studies are required in order to ensure that the openings made do not collapse. The dimensions of the excavations are frequently calculated by using a numerical tool such as the elastoplastic finite element software Phase2 (Rocscience Inc.). However, for being an analysis tool, Phase2 does not directly provide the most appropriate dimensions for an excavation project. It should be used only to confirm if a previously developed project is adequate or not. We hereby propose a different method of design for dimensioning underground excavations in stratified rocks. We have assessed the use of an analytical method to calculate the optimal width of an underground excavation. Using Mathcad software (Mathsoft Inc.), we employed mathematical models to design theoretical mining projects for strata with three different types of behavior:
embedded beams on rigid supports,
simply supported beams on rigid supports, and
beams on flexible supports. We compared the solutions from the three models with one another and with the respective results obtained with Phase2.
The correlation for each pair of analytical-numerical results proved that the analytical method is more efficient for designing excavations. While the analytical method readily provides the adequate width of the excavations, the numerical method requires a trial-and-error approach, which is a slow process, in which the dimensions of the excavation are varied until the necessary level of stability is achieved. Therefore, a logical and effective strategy for the design of an excavation should include the use of an analytical tool to calculate its dimensions followed by the use of a numerical tool to verify these dimensions.
