Page 528 - Rock Mechanics For Underground Mining

MINING-INDUCED SURFACE SUBSIDENCE

where w( , ) is a weighting factor introduced to take account of variations in thick-
ness of extraction or the effect of convergence control measures, and
2
2 1/2
r = [(x − ) + (y − ) ]
By writing dA = d d , the subsidence due to an area of extraction, A, can be
found by integrating equation 16.13 to give

%%
2
2 1/2
s(x, y) = w( , ) f {[(x − ) + (y − ) ] } d d
A
Brauner (1973) discusses a range of influence functions used mainly in Germany
and eastern Europe. They are generally trigonometric or exponential functions of the
form

p(r) = k 1 Sf (B,r, k 2 )

where S is the subsidence at the panel centre, B = h tan is the critical radius of
extraction, and k 1 , k 2 are constants. One of the most widely used functions is

2
r
nS max
p(r) = exp − n
B 2 B
where n is a parameter which characterises the strata properties.
It is apparent that by integration over a large area A, a profile function can be derived
from an influence function. Thus the two types of function are not mathematically
distinct. Profile functions appear to have the advantage of greater simplicity, but
influence functions are more adaptable and can be more useful for irregularly shaped
mining panels.
Peng(1992) provides a detailed account of the use of influence functions of the
exponential type for subsidence analysis in the USA. Lin et al. (1992) used asym-
metrical influence functions involving both trigonometric and exponential terms with
variable functional parameters to derive solutions giving good fits to NCB data for
seams having inclinations of up to 30 . Sheorey et al. (2000) modified the conventional
◦
influence function method to take account of asymmetrical subsidence, multi-seam
mining involving extraction below existing goafs, the effect of hydraulic stowing,
and to allow more accurately for the effects of the edges of the extraction zones.
They applied their approach to a number of cases in India, including cases involving
inclined seams, complex extraction shapes and multi-seam mining.

16.5.3 Trough subsidence analysed as elastic deformation
If in mining deep tabular deposits, fracture or plastic deformation of the rock mass
is restricted to a relatively small zone surrounding the excavation, it may be assumed
that most of the superincumbent strata deforms elastically, at least to a reasonable
approximation. As a further idealisation, the problem of excavating a thin seam may
be represented as one of a crack in an elastic medium. The problem is then one of
determining the stresses and, through the stress–strain equations of elasticity, the
strains and hence the displacements, induced by the creation of the crack or slit in a
previously stressed semi-infinite elastic body.
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