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Fig. 6. Theoretical size of the areas in which the compressive shear strength of the rock is exceeded by the concentrated stresses. For the values of the effective compressive principal stress and coef- ficient of friction shown, the contours in each figure define the size of the initial failure zone for a given value of tp and AP = 0.

Figure 6 Theoretical size of the areas in which the compressive shear strength of the rock is exceeded by the concentrated stresses. For the values of the effective compressive principal stress and coef- ficient of friction shown, the contours in each figure define the size of the initial failure zone for a given value of tp and AP = 0.

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Fig. 3. Representative breakout shapes in granite from the Monti- cello 2 well near Monticello, South Carolina.
Fig. 3. Representative breakout shapes in granite from the Monti- cello 2 well near Monticello, South Carolina.
Fig. 4. Representative breakout shapes in tuff from wells drilled at the Nevada Test Site. (a}{c) Well USW-G1, where the breakouts are concentrated in a flow breccia unit. (d}{f) Well USW-G2, where the breakouts are in the Bullfrog (Figure 4d) and Trom (Figure 4c); Figure 4f is units of the Crater Flat Tuff.
Fig. 4. Representative breakout shapes in tuff from wells drilled at the Nevada Test Site. (a}{c) Well USW-G1, where the breakouts are concentrated in a flow breccia unit. (d}{f) Well USW-G2, where the breakouts are in the Bullfrog (Figure 4d) and Trom (Figure 4c); Figure 4f is units of the Crater Flat Tuff.
Fig. 5. (a) Orientation of potential shear failure surfaces adjacent to a well bore for S,*=45 MPa, S,* =30 MPa, AP=0, and p= 1.0. (b) Area in which failure is expected for tg = 12.5 MPa. The 6,, @,, and r, are described in the text.
Fig. 5. (a) Orientation of potential shear failure surfaces adjacent to a well bore for S,*=45 MPa, S,* =30 MPa, AP=0, and p= 1.0. (b) Area in which failure is expected for tg = 12.5 MPa. The 6,, @,, and r, are described in the text.
where o, is the radial stress, og is the circumferential stress, t,, is the tangential shear stress, R is the radius of the hole, r is For a cylindrical hole in a thick, homogeneous, isotropic elastic plate subjected to effective minimum and maximum principal stresses (S,* and S,*), the following equations apply (Kirsch, 1898; Jaeger, 1961]:
where o, is the radial stress, og is the circumferential stress, t,, is the tangential shear stress, R is the radius of the hole, r is For a cylindrical hole in a thick, homogeneous, isotropic elastic plate subjected to effective minimum and maximum principal stresses (S,* and S,*), the following equations apply (Kirsch, 1898; Jaeger, 1961]:
TABLE 1. Comparison of Observed and Theoretical Breakout Size Auburn, New York It is straightforward to extend the theory presented above to consider the general problem of the initial size of breakouts in terms of the rocks’ cohesive strength and coefficient of fric- tion and the magnitude of the horizontal principal stresses. For simplicity, we assume here that S,* < 3S,*, which is almost always the case in situ [see Brace and Kohlstedt, 1980], and that there is no excess fluid pressure in the well bore (AP = 0). A more complete analysis is presented in the appen-
TABLE 1. Comparison of Observed and Theoretical Breakout Size Auburn, New York It is straightforward to extend the theory presented above to consider the general problem of the initial size of breakouts in terms of the rocks’ cohesive strength and coefficient of fric- tion and the magnitude of the horizontal principal stresses. For simplicity, we assume here that S,* < 3S,*, which is almost always the case in situ [see Brace and Kohlstedt, 1980], and that there is no excess fluid pressure in the well bore (AP = 0). A more complete analysis is presented in the appen-
Fig. 7. Relationship between the ratio of the horizontal principal stresses and the maximum depth and width of breakouts. The curves correspond to breakouts with various values of @,, the half width, where » = 0.6 and AP = 0. The example data from Auburn, New York, are explained in the text.
Fig. 7. Relationship between the ratio of the horizontal principal stresses and the maximum depth and width of breakouts. The curves correspond to breakouts with various values of @,, the half width, where » = 0.6 and AP = 0. The example data from Auburn, New York, are explained in the text.
dix. By substituting (1)}{3) into (4), we can express the cohesive strength at the point the breakout intersects the well bore To(R, 9,), and the cohesive strength at the breakout’s deepest point, t,(r,, 2/2), as
dix. By substituting (1)}{3) into (4), we can express the cohesive strength at the point the breakout intersects the well bore To(R, 9,), and the cohesive strength at the breakout’s deepest point, t,(r,, 2/2), as
Figure 7 graphically shows S,*/S,*, which is independent of T), as a function of r,/R and @, (where ¢, = 1/2 — 0,, see Figure 5b) for 4 = 0.6. As expected, extremely little spalling will occur when the two effective horizontal stresses are about equal. Although the breakouts get deeper and wider as S,*/S,* increases, even for large stress ratios, the well bore radius increases by only about 15% when 49, is as large as 50°. It is clear, then, that although this simple theory of the initial formation of a breakout can explain the broad, flat-bottomed
Figure 7 graphically shows S,*/S,*, which is independent of T), as a function of r,/R and @, (where ¢, = 1/2 — 0,, see Figure 5b) for 4 = 0.6. As expected, extremely little spalling will occur when the two effective horizontal stresses are about equal. Although the breakouts get deeper and wider as S,*/S,* increases, even for large stress ratios, the well bore radius increases by only about 15% when 49, is as large as 50°. It is clear, then, that although this simple theory of the initial formation of a breakout can explain the broad, flat-bottomed
Fig. 8. The effect of excess well bore fluid pressure AP on the size of well bore breakouts. As in Figure 2, the contours define the size of the initial failure zone for tg = 10 MPa when S,,* = 22.0 MPa, S,* = 11.0 MPa, and p = 0.6. (a) No excess well bore pressure (AP = 0). (5) Excess pressure in well bore of 2.5 MPa (AP = 2.5 MPa). (c) Well bore pressure which is 2.5 MPa less than the formation pore pressure (AP = —2.5 MPa).
Fig. 8. The effect of excess well bore fluid pressure AP on the size of well bore breakouts. As in Figure 2, the contours define the size of the initial failure zone for tg = 10 MPa when S,,* = 22.0 MPa, S,* = 11.0 MPa, and p = 0.6. (a) No excess well bore pressure (AP = 0). (5) Excess pressure in well bore of 2.5 MPa (AP = 2.5 MPa). (c) Well bore pressure which is 2.5 MPa less than the formation pore pressure (AP = —2.5 MPa).
Fig. 9. Successive stages of breakout extension based on bound- ary element calculations of redistributed stresses around a broken out well bore [after Mastin, 1984].
Fig. 9. Successive stages of breakout extension based on bound- ary element calculations of redistributed stresses around a broken out well bore [after Mastin, 1984].
If og — a, is positive, take the positive sign for a,, bz, c,, and d, and the negative sign for e and f. If a, — a, is negative, take the negative sign for a2, b3, c,, and d, and the positive sign for e and f. Using formulae (9}+{11) become
If og — a, is positive, take the positive sign for a,, bz, c,, and d, and the negative sign for e and f. If a, — a, is negative, take the negative sign for a2, b3, c,, and d, and the positive sign for e and f. Using formulae (9}+{11) become
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Civil EngineeringBorehole GeophysicsFracture MechanicStress Concentration
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