Page 163 - Rock Mechanics For Underground Mining

FACTORS INFLUENCING THE IN SITU STATE OF STRESS

horizontal stresses are reduced by amounts less than the reduction in vertical stress;
i.e.

p xf , p yf > p zf

or the ratios of the stresses p xf /p zf , p yf /p zf are greater than unity. For a point at
shallow current depth h c , it can be shown that, for h e h c , is possible for the ratios
of the horizontal stresses to the vertical stress to achieve very high values indeed.
From this analysis, it can also be deduced that the horizontal/vertical stress ratio
decreases as the current depth h c increases, approaching the pre-erosion value when
h c is significantly greater than h e .

5.2.3 Residual stress
Residual stresses exist in a finite body when its interior is subject to a state of stress in
the absence of applied surface tractions. The phenomenon has long been recognised
in the mechanics of materials. For example, Love (1944) describes the generation
of residual stresses in a cast-iron body on cooling, due to the exterior cooling more
rapidly than the interior. Timoshenko and Goodier (1970) also discuss the develop-
ment of residual (or initial) stresses in common engineering materials. In general,
residual stresses may be related to physical or chemical processes occurring non-
homogeneously in restricted volumes of material. For example, non-uniform cooling
of a rock mass, or the presence in a rock mass subject to uniform cooling, of contigu-
ous lithological units with different coefficients of thermal expansion, will produce
states of stress which are locally ‘locked-in’.
Processes other than cooling that produce residual stresses may involve local min-
eralogical changes in the rock medium. Local recrystallisation in a rock mass may
be accompanied by volumetric strain. Changes in the water content of a mineral
aggregation, by absorption or exudation and elimination of chemically or physically
associated water, can result in strains and residual stresses similar in principle to those
associated with spatially non-uniform cooling.
A comprehensive understanding of the thermal history and subtle geologic evo-
lution of the members of a rock formation is not considered a practical possibility.
The problem of residual stresses therefore remains an inhibiting factor in predicting
the ambient state of stress in a rock mass, from either basic mechanics or detailed
geological investigations. The inverse process may be a more tractable proposition;
i.e. anomalous or non-homogeneous states of stress in a formation may be related to
the features or properties of the rock mass which reflect the spatial non-uniformity of
its thermal, chemical or petrological history.

5.2.4 Inclusions
Inclusions in a rock mass are lithological units that post-date the formation of the host
rock mass. Common inclusions are extrusive features such as dykes and sills, and
veins of such minerals as quartz and fluorspar. The existence of a vertical, subplanar
inclusion in a rock mass may have influenced the current in situ state of stress in
two ways. First, if the inclusion were emplaced under pressure against the horizontal
passive resistance of the surrounding rock, a high-stress component would operate
perpendicular to the plane of inclusion. A second possible influence of an inclusion
is related to the relative values of the deformation moduli of the inclusion and the
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