Page 178 - Rock Mechanics For Underground Mining

PRE-MINING STATE OF STRESS

by the expression

k = 0.3 + 1500/z

where z is the depth below the ground surface in metres.
At shallow depth, values of k vary widely and are frequently much greater than
unity. At increasing depth, the variability of the ratio decreases and the upper bound
tends towards unity. Some of the variability in the stress ratio at shallow depths and
low stress levels may be due to experimental error. However, the convergence of the
ratio to a value of unity at depth is consistent with the principle of time-dependent
elimination of shear stress in rock masses. The postulate of regression to a lithostatic
state by viscoplastic flow is commonly referred to as Heim’s Rule (Talobre, 1957).
The final observation arising from inspection of Figures 5.11a and b is a confirma-
tion of the assertion made at the beginning of this chapter. The virgin state of stress
in a rock mass is not amenable to calculation by any known method, but must be
determined experimentally. In jointed and fractured rock masses, a highly variable
stress distribution is to be expected, and indeed has been confirmed by several investi-
gations of the state of stress in such settings. For example, Bock (1986) described the
effect of horizontal jointing on the state in a granite, confirming that each extensive
joint defined a boundary of a distinct stress domain. In the analysis of results from
a jointed block test, Brown et al. (1986) found that large variations in state of stress
occurred in the different domains of the block generated by the joints transgressing
it. Richardson et al. (1986) reported a high degree of spatial variation of the stress
tensor in foliated gneiss, related to rock fabric, and proposed methods of deriving a
representative solution of the field stress tensor from the individual point observa-
tions. In some investigations in Swedish bedrock granite, Carlsson and Christiansson
(1986) observed that the local state of stress is clearly related to the locally dominant
geological structure.
These observations of the influence of rock structure on rock stress suggest that
a satisfactory determination of a representative solution of the in situ state of stress
is probably not possible with a small number of random stress measurements. The
solution is to develop a site-specific strategy to sample the stress tensor at a number
of points in the mass, taking account of the rock structure. It may then be necessary to
averagetheresultsobtained,inawayconsistentwiththedistributionofmeasurements,
to obtain a site representative value.
The natural state of stress near the earth’s surface is of world-wide interest, from
the points of view of both industrial application and fundamental understanding of
the geomechanics of the lithosphere. For example, industrially the topic is of interest
in mining and petroleum engineering and hazardous waste isolation. On a larger
scale, the topic is of interest in tectonophysics, crustal geomechanics and earthquake
seismology. From observations of the natural state of stress in many separate domains
of the lithosphere, ‘world stress maps’ have been assembled to show the relation
between the principal stress directions and the megascopic structure of the earth’s
crust. An example is shown in Figure 5.12, due to Reinecker et al. (2003). The map
is a section of the world map showing measurements of horizontal principal stresses
in and around the Australasian plate.
The value of such a map in mining rock mechanics is that it presents some high
level information on orientations of the horizontal components of the pre-mining
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