3.4 Multi-seam subsidence prediction methods
3.4.3 Methods based on influence function
Sheorey et al. (2000)
Sheorey et al. (2000) modified the influence function method based on the
observations in the Indian coalfields. They used an influence function as
follow: Kz = 0.5352 R2 1 + cosπ.r R (3.3)
where Kz, r and R are the same as in Equation 2.8. Sheorey et al. (2000)
noted that there is a need for panel edge adjustment as the observed subsi-
dence and predicted subsidence by IFM over the edge of the extracted panels
are different. In addition, they noted that the location of the maximum sub-
sidence always occurs closer to the start of the panel in the Indian Coalfields,
which creates asymmetric subsidence trough. On this basis, they suggested
consideration of two correction factors as Wz for panel edge adjustment and
Qz for asymmetric shape of the subsidence trough as:
Wz = 0.5 tanh 5db 1.5N EW × H − 2.4 + 0.5 (3.4) and
Qz = 0.9 − 0.1 tanh0.5(d − 0.4demax)
(3.5)
where N EW is the non-effective width-to-depth ratio, which has been mea-
sured for different Indian coalfields (Sheorey et al., 2000) and can be used
to estimate the critical width of the extractions, db is the distance from an
tance from an extraction element to the start line of the panel and dmax is
the distance between the start and end line of the extraction. The subsidence
profile can then be calculated by integrating the following equation over the
extraction area
ds0 = QzWzds (3.6)
where ds is the elemental subsidence at a surface point calculated by the
conventional IFM and ds0 is the elemental subsidence at the surface point by
the modified method.
Sheorey et al. (2000) suggested some changes to the explained influence
function in order to account for the effect of multi-seam extractions. Based
on trial and errors for the Indian coalfields, they reported that reduction of
the original value of N EW by 40% and increase in the subsidence factor by
17% would result in reasonable multi-seam subsidence predictions. In their
methodology, these changes should only be applied to the overlapping parts
of the panels in the two mining seams and the overburden layers but not the
interburden thickness. This is because, the interburden layers remains intact
after the first mining activity and should be assigned the original values of
N EW and subsidence factor. This modification can be done by taking a
weighted average of N EW and subsidence factor values as:
N EW0 = 0.6N EW (H − TIB) + N EW × TIB
H (3.7)
and
SF0 = 1.17SF (H − TIB) + SF × TIB
where N EW0 and SF0 are the modified values of N EW and SF for overlap-
ping elements of the multi-seam panels and TIB is the interburden thickness.
Sheorey et al. (2000) applied their modified method for prediction of multi-
seam subsidence in a few cases in India and reported improved correlation
between the predicted and observed subsidence profiles.
Generalised Influence Function Method (GIFM)
Ren et al. (2010a) suggested inputting tabular weighting factors into the IFM
instead of calculating the factors based on the mathematical expression of the
influence function. They called this new method the Generalised Influence
Function Method (GIFM). The tabulated data can be modified case to case
and by trialling different weighting factors to reach the best agreement with
the observed subsidence. There is only one condition for the tabulated data
as the sum of the weighting factors for all the rings should equal unity:
n
X
i=1
S(i) = 1 (3.9)
where S(i) is the weighting factor of ith ring and n is the total number of
rings. In this case only, it is guaranteed that the maximum subsidence after
extracting an area would be reached.
The GIFM for its ability to adapt to different shapes of subsidence curves
has more flexibility than the conventional IFM. Mathematical definition of
the influence function can be used to calculate the initial weighting factors
Table 3.2: Weighting factors resulted from using GIFM as reported by Ren et al. (2014) for 10 rings (i = 1 to 10).
S(i) 1 2 3 4 5 6 7 8 9 10 ΣS(i)
GIFM 0.034 0.091 0.132 0.156 0.164 0.158 0.115 0.095 0.045 0.01 ΣS(i)
be reached, e.g. giving more weight to the centre zones to achieve deeper
subsidence directly above the extracted parts. Ren et al. (2014) used this
method to calculate the multi-seam subsidence in a case in Australia and
reported improved correlation between the observations and the predicted
results. The weighting factors that they used are noted in Table 3.2.
Comprehensive and Integrated Subsidence Prediction Model for Multi- ple Seam Mining (CISPM-MS)
Luo and Qiu (2012b) developed an influence function that allows dividing
the overburden into finite number of layers with equal thickness. In this
method, the subsidence at one layer in the overburden layers causes the
subsidence of the immediate layer above it, until this movement reaches the
ground surface. The subsidence at each level can then be calculated by
integrating the influence function defined for the proper horizontal interval.
The influence function to calculate the subsidence at a point on the surface
of the ith layer (i = 1 is the immediate roof layer and i = n is the ground
surface) can be defined by
fs(x0, zi) =
S(x + x0, zi−1).ai
Ri
e−π(Rix0)2 (3.10)
panel and ziis the vertical distance from the coal seam and the top surface of
the ith layer. Thus, to find the final subsidence at a point (on ground surface
or underground) the respective influence function can be integrated within
the suitable computing area as follow
S(x, zi) = ai Ri Z Wi−di2−x di1−x S(x + x0, zi−1).e −π(x0 Ri) 2 dx0 (3.11)
where i = 1, 2, ..., n and ai, Ri, di1 and di2 are the ith layer’s final subsidence
parameters as respectively subsidence factor, radius of subsidence influence
and the offset distance of the inflection points on the left and right sides of
the extracted panel (Luo and Qiu, 2012a).
Luo and Qiu (2012a) modified this approach for consideration of multi-
seam extractions and introduced a tool for multiple-seam subsidence predic-
tions, called CISPM-MS. This modified method has the ability to account
for presence of pillars in the multi-seam workings. Their work mostly fo-
cuses on the pillar stability at an upper layer, interaction of the multi-seam
workings and subsurface subsidence evaluation. In addition, Luo and Qiu
(2012a) introduced a pillar strength reduction factor that is related to an
undermining activity and then proposed considering a safety factor for sta-
bility of existing pillars in an upper seam. They calibrated the empirical
equations in their methodology by means of the numerical simulation of the
problem with the software FLAC3D. The ability of their proposed method in
studying the multi-seam interactions and evaluating the pillar stability were
demonstrated with a case study in the USA, where an active room and pillar
pillar extraction being carried out over large areas in the lower level.