The load transferred from the adjacent goaf areas is dependent upon the depth of cover to satisfy subsidence compatibilty.

For sub-critical subsidence conditions the following expression is used to calculate the load supported by a pillar:

Where :

w = width of longwall face (m)

h = depth below surface (m)

g = average density of overburden (kg/m^{3})

f = average angle of shear (o)

p = pillar width (m)

B = bord (heading) width (m)

For critical and super critical mining subsidence situations, the goaf load trinagle will reach the surface boundary, for this situation the load on the pillar equation becomes,

The respective average pillar stress for these two conditions are given by:

Worked Example

A single line of square chain pillars separate two longwall panels. A 2.8m thick coal seam is being mined at a depth of 400 metres below the surface and the longwall face is 170 metres wide. Given that:

Average angle of shear f = 31˚

Width of the roadways/bords = 5.5 m

Overburden density g = 2500 kg/m3

Calculate the following:

The size of the pillars

Factor of Safety of the pillars when both sides of the pillars have been mined

Solution

Data given:

w = 170 metres

h = 400 metres

f = 31˚

b = 5.5 metres

g = 2.5 tonnes/m3

m = 2.8 metres

p = ? metres

**1. Calculate the size of the pillars which complies to the CMRA**

The CMRA recommends that the width of a pillar should be estimated as 1/10 of the depth.

Therefore,

Pillar width = 1/10 x 400

= 40 x 40 metres.

**2. Factor of Safety of the pillars when the panels on both sides of the pillars have been mined.**

w/h = 170/400

= 0.425

2 tan 31˚ = 1.20

Therefore, w/h < 2 tan f, thus it is sub-critical subsidence.

Pillar Strength = [ 7.4 x (40)0.46 ] / [ (2.8)0.66 ]

= 20.467 Mpa

Load on the Pillar = 9.81 x 2.5[(40+170).400 – (1702cot31˚)/4].(40 + 5.5)/402

= 50.197 MPa

FOS of the pillar = Load on the Pillar / Pillar Strength

= 20.467 / 50.197

= 0.4

For a factor of safety of less than 1.0 a pillar is likely to collapse, therefore this pillar will collapse after the longwall has passed on both sides of the pillar.