Page 176 - Rock Mechanics For Underground Mining

PRE-MINING STATE OF STRESS

A second determinant of the mechanical acceptability of an in situ stress measure-
ment is derived from the requirement for conditions of static equilibrium on pervasive
planes of weakness in the rock mass. Application of this criterion is best illustrated
◦
◦
by example. Suppose a fault plane has the orientation 295 /50 (dip direction/dip),
and that the measured in situ stress field is defined by:
1 , magnitude 15 MPa, dips 35 towards 085 ;
◦
◦
2 , magnitude 10 MPa, dips 43 towards 217 ;
◦
◦
◦
◦
3 , magnitude 8 MPa, dips 27 towards 335 .
The groundwater pressure at the measurement horizon is 2.8 MPa, and the angle of
friction for the fault surface 25 . These data can be used to determine the normal and
◦
resultant shear stress components acting on the fault, and thus to calculate the angle
of friction on the fault surface required to maintain equilibrium.
The given data are applied in the following way. When plotted on a stereonet, the
direction angles ( , , ) between the principal axes and the pole to the fault plane
◦
are measured directly from the stereonet as (24 , 71 , 104 ). These yield direction
◦
◦
cosines(l 1 ,l 2 ,l 3 )of(0.914, 0.326, −0.242)ofthefaultnormalrelativetotheprincipal
stress axes. The effective principal stresses are given by

= 12.2MPa
1

= 7.2MPa
2

= 5.2MPa
3
Working now in terms of effective stresses, the resultant stress is given by
2
2
2
2
2

R = l + l + l 3 2 1/2 = 11.46 MPa
1
2
3
2
1
and the normal stress by
2
2
2

= l + l + l = 11.26 MPa

n 1 1 2 2 3 3
The resultant shear stress is
2

= R − n 2 1/2 = 2.08 MPa

The angle of friction mobilised by the given state of stress on the plane is
−1
mob = tan (2.08/11.26) = 10.5 ◦
Since mob is less than the measured angle of friction for the fault, it is concluded that
the in situ state of stress is compatible with the orientation and strength properties of
the fault. It is to be noted also that a similar conclusion could be reached by some
simple constructions on the stereonet. Clearly, the same procedures would be followed
for any major structural feature transgressing the rock mass.
For the example considered, the measured state of stress was consistent with static
equilibrium on the plane of weakness. In cases where the field stresses apparently
violate the equilibrium condition, it is necessary to consider carefully all data related to
158