Page 531 - Rock Mechanics For Underground Mining

CONTINUOUS SUBSIDENCE DUE TO THE MINING OF TABULAR OREBODIES

material having a non-linear elastic modulus which increases with increasing stress.
Salamon (1991) presented a set of numerical results which reproduce many of the
elements of the subsidence behaviour associated with longwall coal mining.

16.5.4 Numerical methods
The results presented in the previous section suggest that the theory of elasticity for
transversely isotropic materials may be used to give reasonably good estimates of
subsidence profiles in some circumstances. The use of numerical methods could be
expected to eliminate the influence of some of the simplifying assumptions made in
Berry’s original analysis. It might also be expected that numerical methods could be
used to model non-linear and post-yield material properties, specific geological fea-
tures and the broken material in the goaf, and to allow more completely for the effects
of the in situ stresses and incomplete closure. Accordingly, over the last 25 years, a
wide range of approaches have been developed for the numerical modelling the sur-
face subsidence caused by longwall mining in both coal and hard rock applications.
These approaches have used, variously, the electrical resistance analogue method,
the boundary element method particularly the form known as the displacement dis-
continuity method (Crouch and Starfield, 1983, G¨urtunca and Bhattacharyya, 1988),
the distinct element method, linear and non-linear forms of the finite element method
(Holla and Sagar, 1996, Yao et al., 1993) and the finite difference method (Alejano
et al., 1999). Most of these numerical modelling approaches have treated the super-
incumbent rock masses as transversely isotropic materials and have allowed for the
dips of the seam and the superincumbent strata. Some have included non-linearities
such as tensile cut-off and Hoek-Brown strength criteria and many have treated the
goaf as a non-linearly compressible material. Most numerical modelling approaches
have been validated by reference to subsidence monitoring data, often that from the
extensive UK data base.
The illustrative example of the use of numerical modelling to be presented here
is that due of Alejano et al. (1999). They used the two-dimensional finite difference
code FLAC2D to model initially the subsidence associated with a horizontal seam
under conditions typically experienced in the Midlands coalfields of the UK with the
results being validated against National Coal Board data. In this case, a hydrostatic
in situ stress field was applied. The approach was then used for inclined seams and
further validated against model tests and field data for seams with inclinations of up to
30 . Finally, the method was applied to steeply inclined and sub-vertical seams having
◦
◦
◦
dips in the range 45 –90 . Rock mass behaviour was modelled using the following
assumptions:
transversely isotropic elastic pre-failure behaviour;

non-linear (Hoek-Brown) anisotropic yield in which yield may occur along joints

or the stratification or through the material; and
isotropic non-linear elastic post-failure behaviour using models developed for the

compressibility of rock fill.
Figures 16.25 and 16.26 show some of the results obtained by Alejano et al. (1999)
compared with National Coal Board (1975) data for typical flat seam conditions in
the UK Midlands. Figure 16.25 shows the subsidence profiles for a range of width to
depth (w/h) ratios for a constant mining depth of h = 300 m. Figure 16.26 shows
the subsidence with respect to the rib side for longwalls of varying depth but with a
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