An Alternative Solution For the In Situ Stress State Inferred From Borehole Stress Relief Data

Il a ete demontre que l'analyse traditionnelle de gauges de deformation dans les sondages qui sert de base afin de deduire la tension in situ d'une longue perforation cylindrique dans de la roche elastique lineaire est fausse. Heureusement, une erreur secondaire annule l'erreur primaire, ainsi minimisant les consequences pratique, du moins dans de la roche isotrope. Une version de l'analyse corrigee est donnee.

Gezeigt wird, dass die herkommliche Analyse von Deformationsmessungen von vergebohrten land-zylindrischen Bohrlochern in Bohrkernen als Methode zur Berechnung von in situ Sapnnungsverhaltnissen im elastischem Gestein schon an der Basis fehlerhaft ist. Gezeigt wird auch, wie aber ein sekundarer Berechnungsfehler der fehlerhaften Grundannahme entgegenwirkt und somit die praktischen Konsequenzen der fehlerhaften Analylse, jedenfalls auf isotropisches Gestein bezogen, auf ein Minimum reduziert. Schliesslich wird eine berichtete Version der Analyse gegeben.

The stress relief over core method is a frequently used technique for obtaining data from which the in situ state of stress is inferred. Gages used in a pilot hole respond to changes in displacement and strain at the borehole wall during over core drilling. The U.S. Bureau of Mines (USBM) borehole deformation gage is an example of a gage that responds to displacements only. The CSIRO gage is an example of a gage that responds to strains. A nominal 150 mm (6 in.) diameter overcore hole provides the requisite stress relief for these gages. The USBM gage requires measurements in three nonparallel holes while the CSIRO gage requires only one hole for the determination of the three-dimensional stress state in situ.

These gages and similar devices depend on the same theoretical solution to the problem of determining the state of stress about a long cylindrical hole drilled in initially stressed elastic rock. The initial stress state is, of course, the in situ stress to be determined. The solution to this problem, and therefore the data reduction formula for isotropic rock, was first obtained by Hiramatsu and Oka (1962). Subsequent equipment development and theoretical refinements have extended the technology to solid and hollow inclusion gages and to anisotropic rock (Fairhurst, 1964, 1968; Panek, 1966; Leeman, 1964, 1967, 1968; Merrill, 1967; Moody, 1968; Hirmatasu and Oka, 1968; Bonnechere, 1969; Oka and Bain, 1970; Niwa and Hirashima, 1971; Rocha and Silverio, 1969, 1974; Martinetti and Ribacchi, 1974; Bonnechere and Cornet, 1977; Ribacchi, 1977; Herget, Miles and Zawadski, 1977; Hirashima and Koga, 1977; Duncan Fama and Pender, 1980; Morgan, 1982; van Heerden, 1983; Amadei, 1983; Borsetto, Martinetti and Ribacchi, 1984; Rahn, 1984; Kanagawa and others, 1986).

One of the early theoretical refinements was the recognition that the present or post-hole stress about a borehole is composed of contributions from (i) the pre-hole or initial stress state σ° and (ii) the stress change a' caused by introductionof the hole. In the elastic case σ = σ° + σ ¹. The stress change a' is computed on the basis of a plane analysis in the sense that derivatives in the direction of the hole axis are zero. The initial stress is arbitrary. Strains ε⁰ and ε¹ are associated with σ⁰ and σ¹ through the stress strain relations (Hooke's law). Displacements u⁰ and u¹ are obtained by integration of the strain displacement equations. Overcoring of the gage relieves the stress σ; a gage thus responds to total strains and displacements ε and u. The strains ε = ε⁰ + ε¹ and are generally not plane in the sense that derivatives in the direction of the hole axis are not zero.

However, the original solution by Hiramatsu and Oka (1962) is based on the plane assumption. They solved the problem of determining the stress distribution about an infinitely long circular hole loaded by a set of prescribed stresses at infinity. The medium is isotropic and linearly elastic. Independence of all quantities with respect to the direction of the hole axis is explicitly assumed. Their solution therefore tacitly implies that the displacements and strains associated with the pre-hole stresses also do not vary in the direction of the hole. Alternatively, they view the loads as being applied only after the pilot hole is drilled. Subsequent refinements including the more recent extension to anisotropic rock by Amadei (1983), for example, are also based on the plane assumption in whole or in part.