ABSTRACT
Three-dimensional excavations include caverns such as hydroelectric machine halls for civil engineering purposes and stopes in hardrock mines. Stopes are regions in mines where ore is excavated. In hardrock mines, stopes range from relatively large brick-shaped excavations to thin, tabular zones that may be flat lying, gently to steeply dipping, or vertical. Stopes differ from shafts, tunnels, and entries. The latter excavations are long relative to cross-sectional dimensions and are amenable to two-dimensional analysis (plane strain, plane stress, axial symmetry). Cavern and stope design usually requires a three-dimensional analysis of stress. The purpose of an analysis is the same in any case: determination ofmagnitudes and locations of peak tensile and compressive stresses. From these data, stress concentration factors may be obtained for use in design safety factor calculations:
Fc = Co σc
= Co KcS1
Ft = To σt
= To KtS1
(7.1)
where Co, σc, Kc, To, σt , Kt , and S1 are unconfined compressive strength, peak compressive stress, compressive stress concentration factor, tensile strength, peak tension, tensile stress concentration factor, and major principal stress before excavation. When compressive stress is considered positive, then a positive stress concentration factor implies a peak compressive stress; a negative stress concentration factor implies tension. A safety factor greater than one at a point of peak stress, assures that all other points at the excavation wall are also safe with respect to compression or tension or both.
