Analytical solution of energy redistribution in rectangular openings upon in-situ rock mass alteration

This paper aims at deriving analytical expressions of mining-induced energy redistribution around rectangular openings that involve local alteration of rock mass properties. As energy combines the effects of strains and stresses simultaneously, this research work is intended to complement existing approaches that rely on stress-based stability criteria. The energy density on the boundaries and its distribution within the domain, obtained analytically through direct derivation, is compared to numerical solutions obtained by Finite Element simulation for a given hypothetical field case. The analytical and numerical solutions show a good agreement and reflect the importance of analytical solutions especially in the vicinity of severe geometrical singularities. Our parametric study shows that the initial stress coefficient and opening span-height ratio have great influence on the variation of strain energy density. We found that the energy density concentrates on the excavation corners and that the energy density concentration index value on the opening side boundary decreases when the span-height ratio decreases. Areas of energy reduction appear on the excavation boundaries, which transform from the top centers to the side centers as the initial stress coefficient increases. Our study indicates that both energy density concentration and reduction areas need to be considered in excavation design. The derived expressions of mining-induced energy redistribution can be considered as a tool to assess the stability of rock masses and predict failure conditions such as rock burst and mine seismicity around non-circular shaped openings.