Displacements from relief of In situ stress by a cylindrical hole

Abstract

The holographic in situ stressmeter is an instrument which records the displacement field on a barehole wall induced by the drilling of a small, stress-relieving sidehole. The data is in the form of double-exposure holograms; the patterns of interference fringes on these holograms may be analyzed to yield the state of stress at a location on the borehole wall. A set of at least three of these holograms, properly spaced around the borehole at a given depth, can in turn be analyzed to reveal the far-field state of stress. Previous work with this instrument has modelled the borehole wall as a thin flat elastic plate through which a hole is drilled. This model, while adequate, was not capable of fitting the observed fringe data within two radii of the sidehole in every case. Several previous holograms were obtained, generally from locations in the borehole which had low levels of borehole wall stress, which could not be modelled satisfactorily. This work improves the model by using the analytic approach of Youngdahl and Sternberg for the displacements on the free surface of a half space with a through-going hole subjected to a plane state of stress at infinity. This model relaxes the assumption inherent in the thin plate model that the body is in a state of plane stress everywhere in its interior. To test the effectiveness of this model, we re-analyzed holograms obtained from field deployment of the holographic in situ stressmeter. The new analysis gives approximately the same result as the old model; however, the errors corresponding to this solution are significantly reduced. We believe that the Youngdahl and Sternberg model may also be applied in other situations. The in situ state of stress of a rock wall could be determined by drilling a stress-relieving hole, measuring the resulting displacements or strains, and analyzing the data with the technique described in this paper.