Page 171 - Rock Mechanics For Underground Mining

METHODS OF IN SITU STRESS DETERMINATION

pressure, substitution of the expressions for

, nn ,
n (equations 5.3) into the
expression for A (equation 5.4) yields
1
A = p ll {(1 − cos 2 ) − 2 cos 2
[(1 + ) − (1 − ) cos 2 ]}
2
1
+ p mm {(1 − cos 2 ) + 2 cos 2
[(1 + ) − (1 − ) cos 2 ]}
2
1
+ p nn (1 + cos 2 ) − p lm 2 sin 2
{(1 + ) − (1 − ) cos 2 }
2
+ p mn 2 sin 2 cos
− p nl 2 sin 2 sin
(5.8)
or

C 1 p u + C 2 p mm + C 3 p nn + C 4 p lm + C 5 p mn + C 6 p nl = A (5.9)
Equation 5.9 confirms that the state of stress in any position/orientation in the hole
boundary is linearly related to the field stress components, by a set of coefficients
which are simply determined from the geometry of the measurement system. Thus if
six independent observations of A are made at various locations defined by angles
and , a set of six simultaneous equations is established:

[C][p] = [ ] (5.10)
The terms of the coefficient matrix [C] in this equation are determined from
and
for each boundary stress observation, using equation 5.8.
In the design of a measurement programme, the boundary stress measurement
positions and orientations must be selected carefully, to ensure that equations 5.10 are
both linearly independent and well conditioned. The criterion for a poorly conditioned
setofequationsisthatthedeterminantofthe[C]matrixisnumericallysmallcompared
with any individual term in the matrix.

5.3.4 Hydraulic fracturing
Ashortcoming of the methodsof stress measurement describedpreviously is that close
access to the measurement site is required for operating personnel. For example, hole
depths of about 10 m or less are required for effective use of most triaxial strain cells.
Virtually the only method which permits remote determination of the state of stress is
the hydraulic fracturing technique, by which stress measurements can be conducted
in deep boreholes such as exploration holes drilled from the surface.
The principles of the technique are illustrated in Figure 5.7. A section of a borehole
is isolated between inflatable packers, and the section is pressurised with water, as
shown in Figure 5.7a. When the pressure is increased, the state of stress around
the borehole boundary due to the field stresses is modified by superposition of
hydraulically-induced stresses. If the field principal stresses in the plane perpen-
dicular to the hole axis are not equal, application of sufficient pressure induces tensile
circumferential stress over limited sectors of the boundary. When the tensile stress ex-
ceeds the rock material tensile strength, fractures initiate and propagate perpendicular
to the hole boundary and parallel to the major principal stress, as indicated in Figure
5.7b. Simultaneously, the fluid pressure falls in the test section. After relaxation of
the pressure and its subsequent re-application, the peak borehole pressure achieved is
less than the initial boundary fracturing pressure by an amount corresponding to the
tensile strength of the rock material.
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