Engineering Rock Mechanics

394

Use these values together with the Hoek-Brown criterion,

• =-+ rn-++,
  cc e3 cc E-

to determine the maximal vertical stress the pillars can sustain (1)
at their faces and (2) at their centres. Assume that the ratio of hori-
zontal to average vertical stress is 0.075 at the centre of each pillar.
Use the tributary area theory to estimate the average vertical stress
in the pillar, and hence determine the factor of safety of the pillars.

A20.9 If we consult a table of RMR parameters (see Appendix C), we
can assign the following values to the rock mass of the pillars:

Parameter Comments Rating

Compressive strength measured as 100 MPa 4

Groundwater conditions described as generally dry

Spacing described as 'moderate' 10

12

RQD value associated with a spacing of, say, 0.4 m

will be close to 100%

Discontinuity condition persistence of bedding planes will be high (0),

aperture is zero (6), smooth to touch (l),

no infilling (6), slight weathering (5)

20

18

Total 64

The Hoek-Brown criterion,

requires us to know both m and s but, for the case where we are

examining the face of a pillar, we can assume a3 = 0 and hence use the

reduced form of

C1 = ffc&

Substituting the relation s = exp [(RMR - 100) /9] into this equation we

obtain

a1 =ac/m=acexp( Rh4R 18 - 100

from which, with a, = 100 MPa and RMR = 64, we find 01 = 13.5 MPa.

This is the maximal vertical stress that the rock at the face of the pillar

can sustain.

For the case when we are examining the centre of the pillar, where

triaxial conditions exist, the laboratory triaxial test data can be used

to determine a value for the parameter m. As the laboratory test took

place on a specimen of intact rock, we know that s = 1. Consequently,

rearranging the Hoek-Brown criterion of

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