Stress Measurements - Rock Mechanics Based on an Anisotropic Jointed Rock Model - page 532

If the maximum principal stress is horizontal, the fracture initiated by the breakdown
pressure will be oriented approximately parallel to the borehole axis, that is vertically
(Hubbert & Willis 1957). Under the assumptions mentioned before, in this case fracture
occurs when the tangential tensile stress induced by the hydraulic pressure exceeds the
sum of the minimum tangential stress at the borehole wall and the tensile strength

σ t

of the rock mass. Then the minimum and maximum horizontal stresses σ H are

oriented normal and parallel to the fracture, respectively, (Fig. 16.15, right) and are
equal to the maximum and minimum principal normal stresses. In this case,

σ h and

σ h and σ H

are related to the shut-in pressure p s and the breakdown pressure p b as follows:

σ h = σ 3 = p s , (16.18)

σ H = σ 1 = σ t + 3p s - p b . (16.19)

The vertical stress σ V then is the intermediate principal stress and is calculated from the

rock mass unit weight γ and height h of overburden:

σ V = σ 2 = γ · h . (16.20)

After crack generation, the rock's tensile strength is zero. In the refrac cycles the maxi-
mum horizontal stress σ H can therefore be calculated from Equation (16.19) setting

σ t = 0 and replacing p b by the reopening pressure p r (Bredehoeft et al. 1976):

σ H = 3p s - p r . (16.21)

From Equations (16.19) and (16.21) σ t can be deduced as

σ t = σ b - p r . (16.22)

With the aid of (16.18), (16.20) and (16.21) the following magnitudes of stress compo-
nents were derived for the test whose results are represented in Fig. 16.16:

σ V = γ · h = 25 · 94 kPa = 2.35 MPa ,

σ h = p s = 2.11 MPa ,

σ H1 = 3p s - p r1 = 3.83 MPa ,

σ H2 = 3p s - p r2 = 3.67 MPa .

The maximum horizontal stress σ H was calculated as the arithmetic mean of σ H1 and

σ H2 resulting in σ H = 3.75 MPa (Fig. 16.16, below).

Tensile strength estimated from breakdown pressure p b and reopening pressures p r1 and
p r2 yielded: