Rock Mechanics.pdf - Mining and Blasting

Figure 16.6 (a) Rectangular block
geometry, and (b) assumed distribution
of water pressure with depth, for
limiting equilibrium analysis of chimney
caving.
MINING-INDUCED SURFACE SUBSIDENCE
An example of wide applicability is that shown in Figure 16.6a. A block of width
a and base length b has one pair of sides oriented in the direction of the strike of the
orebody and the other pair in the dip direction. The dip is , the maximum height
of the block is h, and the water table is a distance d below the horizontal ground
surface. The groundwater pressure is assumed to be zero at the water table, to have an
initially hydrostatic rate of increase with depth, to be zero at the stope hanging wall
and to have an infinite rate of decrease with increasing depth at this point. The skewed
parabolic water pressure distribution shown in Figure 16.6b satisfies these boundary
conditions. For this distribution, the maximum water pressure is z ′ w/2, and the total
water pressure force generated over a depth z ′ = z − d, isz ′2 w/3.
In this case, it is necessary to evaluate the shear resistance developed on each of
the four vertical faces (Figure 16.7). The total shear resistance is then given by
Q = 2QBCGF + QDCGH + QABFE
(16.5)
Consider the side face BCGF when 0 ≤ d ≤ h − b sin , i.e. groundwater level intersects
the up-dip face DCGH. If Coulomb’s shear strength criterion is used, equation
16.3 applies. This gives
b cos z
QBCGF =
0 0
(c ′ + k z tan ′ )dz −
(z − d)2
w tan
3
′
dx
From Figure 16.7, z = h − x tan . Substitution for z and integrating gives
QBCGF = Q1 − w tan ′
b cos h
3
2 − hb sin + b2
3 sin2
−d[2h − b sin − d]
where
490
Q1 =
b cos
2
c(2h − b sin ) + k tan ′
h 2 − bh sin + b2 sin 2
3