Stresses Around a Wellbore Due to Internal Pressure and Unequal Principal Geostatic Stresses

Abstract

A three-dimensional photoelastic study was made to determine the stress state around the wall and bottom of a well bore due to fluid pressure with~n the wellbore and unequal principal geostatzc stresses.Models simulating the well bore were made from a phthalic anhydride-cured epoxy resin. The froz~n stress technique of three-dimensional photoelastzcity was used to determine the stresses within the model. Two separate problems were solved:(1) hydrostatic pressure on all sides of the model with the exception of the inside of the hole, and (2) uniaxial compression perpendicular to the center line of the hole.The results are presented in the form of contour curves for each stress component. The curves cover a region which extends several hole radii from the bottom and wall of the hole. By proper use of these results, the state of stress may be calculated for any point on the wall or bottom of ~he hole, as well as for any point within the materzal that surrounds the hole. A systematic method is given for calculating these stress components for any combination of fluid pressure within the wellbore and system of unequal principal geost~tic stresse~, provided one of the principal geostatzc stresses zs parallel with the well bore.The results show that stresses around the wall and bottom of a wellbore, induced by an unequal system of principal geostatic stresses, are appr~ ciably different from those induced by geostatzc stresses that are hydrostatic. For unequal principal geostatic stresses, the experimentally determined stresses on the wall of the hole several radii from the bottom are in good agreement with the stresses calculated by elastic theory.

The relation of geology to stress changes caused by underground excavation in crystalline rocks at Idaho Springs, Colorado

“…Elastic stress data from ... model differed only slightly in magnitude from the stresses indicated by Galle and Wilhoit (1962). The shape of the applied loading curve is almost exactly the same as that obtained from the acrylic model, except that the percentage concentration of the applied stress ahead of the ad-vancing tunnel is slightly lower and this region of stress concentration is not as extensive.…”

“…The directions of the principal stress changes r~mained essentially fixed (table 7; figs. 16A, 1 n Stresses estimated from photoelastic studies by Galle and Wilhoit (1962), in a smaller but similarly loaded plastic block ahead of a 3.18-cm-(1.25 in.) diameter bore, are in good agreement with the stresses monitored by the probe for a 1.50-tunnel-diameter interval between the probe and the tunnel face ( fig.…”

“…According to elastic theory and the experiments of Galle and Wilhoit (1962), the stress concentration ahead of an advancing tunnel in an elastic material should be confined to a zone within, at most, 2 diameters ahead of the advancing tunnel. It can be seen in figures l6B, I9B, and 22B that the experimental data correspond reasonably well to those obtained by the photoelastic techniques employed by Galle and Wilhoit for approximately 1 diameter ahead of the model-tunnel face( fig.…”

“…Our field evidence agrees approximately with an onset of stress increase at about 2-5 tunnel diameters ahead of a modeltunnel face. The model used by Galle and Wilhoit (1962) may have been of too limited an extent to show this stress peak because their models extended only 2.25 diameters ahead of their model-tunnel face ( fig. 24).…”

Stiffness of geomaterials at very small strains

“…In particular, effects from removal of deviatoric and total stresses, termed`block sampling' by Baligh et al (1987), will lead to some disturbance. Also, shear distortion as a result of base heave may cause damage as the borehole is made (Galle & Wilhoit, 1962;Lefebvre & Poulin, 1979). A number of investigators have shown that sampling disturbance of soft clays leads to a reduction in mean effective stress (Hight, 1986;Clayton et al, 1992).…”