Stress concentration due to underground excavation in cross-anisotropic and nonhomogeneous elastic halfspace

Abstract

Materials occurring in nature are seldom isotropic and even less frequently homogeneous. The displacements and stresses in surface loaded cross-anisotropic and nonhomogeneous elastic halfspaces are significantly different from those in an isotropic and homogeneous halfspace. A similar effect is expected when prestressed halfspaces of a similar description are to be pierced with openings of various shapes located at various depths. The object of this paper is to assess this effect quantitatively. Both deep and shallow underground openings of circular, long elliptical and tall elliptical shapes are analysed. The medium containing these openings is discretized by a combination of finite and infinite elements to simulate near-field and far-field, respectively. The stress concentration factors at selected locations are calculated to demonstrate the effect of cross-anisotropy and nonhomogeneity of the media. The variation of surface displacements due to shallow excavation is also plotted. The popular belief that the effect of elastic anisotropy is no larger than the variation in rock strength is re-examined in light of the numerical results of this study.