Engineering Rock Mechanics

54 In situ rock stress

With the I axis parallel to the strike of the plane and the n axis normal
to the plane, the m axis is the line of maximum dip of the plane. The
trend and plunge of each of the axes are then as follows:

QI = 205" (Y, = 295" a, = 115"

= 0" Pm = 50" Pn = 40"

The matrix R, computed as shown in A4.8, is

-0.906 -0.423 O.OO0

0.272 -0.583 0.766

-0.324 0.694 0.643

1 8.70 1.01 -0.441

1.01 13.06 2.65.

and the matrix a,,, is

1-0.44 2.65 11.231

As a result, the matrix qmn = Ru,,,,RT or

10.26 0.94 -2.24

-2.24 0.32 13.94

If we use the matrix a,,, resulting from the high-precision orientation

[ 8.71 0.88 -0.541 [ 10.16 0.93 -2.121

=R 0.88 13.04 2.69 RT = 0.93 8.76 0.29 MPa.

It is clear from these calculations that, although the stress invariants

vary little between the two sets of input orientations, the same is not

true for the values of the stress components calculated for the fault

orientation. For example, the shear stress in the plane, tmn, is different

by about 10% using the different precisions, i.e. 0.32 MPa to 0.29 MPa.

Also, in practice it is likely that the stress field would be perturbed

by the presence of the fault and so would differ from this theoretically

computed stress state.

data of A4.8 to compute the stresses on the fault, we obtain

-0.54 2.69 11.24 -2.12 0.29 14.07