Design of Coal Pillars on Soft
Clay Floors
©2012 Dr. B. C. Paul
Note – The material presented here relies heavily on notes and support
materials compiled by Dr. Paul Chugh for use with his Rock Mechanics course
at SIUC.
Coal Pillars are Normally Designed
Using a Tributary Area Formula
Overburden Load
SF = Average OB Load/ Coal strength
Remaining Coal Pillar
After entries mined out.
Having that coal pillar mash to
Pieces could ruin your whole day!
But What If The Failure Comes
From the Pillar Punching Into the
Floor
Such as happens
When weak underclays
Are present.
Factors of Safety
• If Pillar Strength Controls
– Safety Factor = Uniaxial Compressive Strength
(adjusted for pillar size)/ Average Compressive Load
on Pillar
• If Plastic Floor Failure Controls
– Safety Factor = Ultimate Bearing Capacity (adjusted
for pillar size) / Average Compressive Load on Pillar
• The calculation is essentially the same except
that the Ultimate Bearing Capacity of the Floor
before plastic failure replaces the crush strength
of the coal pillar
The Key Ultimate Bearing Capacity
• UBC = Nm*Unconfined Shear Strength of
the Floor
Overburden
Load
Model is Based on this set-up
Coal Pillar
Squishy Fireclay Floor
Respectable Rock
Underneath
The Terms of the Equation
• The Unconfined Shear Strength can be
estimated from plate load tests conducted in a
mine
– Luck has also be had in estimating Unconfined Shear
Strength from the % moisture in the clay
• (Hint – this means that getting a fireclay floor wet can cause
you to be screwed).
• Nm is a bearing constant derived from a mixture
plastic failure theory and empirical
measurements
– Nm is a multi-step pain in the tail section to calculate
(unless you can pawn the work off on a spreadsheet)
Meet the Soft Clay Floor
Spreadsheet
(Inspired by the Vesic Method)
Soft Floor Pillar Sizing
Unconfined Shear Strength Floor (S1)
Moisture Cont (MC)
Unconfined Shear Strength of Rock below Clay Floor (S2)
Angle of Internal Friction (Ø)
Weak Layer Thickness (H)
Pillar Width (B)
Pillar Length (L)
Entry Width
Cross Cut Width
Depth
60
10
500
Speck estimate of S1
S1  (2070  167 * MC ) * .15
0
5
160
160
20
20
450
K
8.333333
β
8
Nq
1
Nc
5.14
Ec
1.194553
Nc*
6.14
Nm
11.36024
681.6145
InSitu psi
Stress Ratio
Extraction Ratio
Floor Stress
Safety Factor
Safety Factor
Safety Factor
495
1.265625
20.98765
626.4844
1.087999
0.924799
0.761599
As typical
Yellow fields are for
Your input
ft
ft
ft
ft
ft
ft
K

S2
S1
Green is a calculated
Field
B*L
2 * ( B  L) * H
 tan( )
Nq  e
2
* tan (
 
 )
4 2
If (  0)thenNc  5.14elseNc  ( Nq  1) * cot( )
Ec  1 
Red is answers you
Probably want to know
B Nq
*
L Nc
Nc*  Ec * Nc
K * Nc * *( Nc *    1)(( K  1) * Nc*  (1  K ) * Nc *    1)
2
Nm 
UBC
60
( K * ( K  1) * Nc *  K    1)(( Nc *   ) * Nc *    1)  ( K * Nc *    1)( Nc * 1)
UBC  Nm * S1
%
short term
long term
wetted safety Factor
The Green Fields are Inhabited by
Constants Used to Get Nm
K
8.333333
β
8
Nq
1
Nc
5.14
Ec
1.194553
Nc*
6.14
K

S2
S1
B*L
2 * ( B  L) * H
 tan( )
Nq  e
2
* tan (
 
 )
4 2
If (  0)thenNc  5.14elseNc  ( Nq  1) * cot( )
Ec  1 
B Nq
*
L Nc
Nc*  Ec * Nc
The formulas used to calculate the values in green are shown.
You could read papers on how they were developed and what
They mean – or your could call Sr. Design an application of
Your rock mechanics class and pretend you don’t want to know
(or maybe who’s pretending).
Your Essential Inputs
Unconfined Shear Strength Floor (S1)
Moisture Cont (MC)
Unconfined Shear Strength of Rock below Clay Floor (S2)
Angle of Internal Friction (Ø)
Weak Layer Thickness (H)
Pillar Width (B)
Pillar Length (L)
Entry Width
Cross Cut Width
Depth
60 psi
10 %
500 psi
Speck estimate
S1 
0
5
160
160
20
20
450
ft
ft
ft
ft
ft
ft
Your Rock Mechanics Properties are Unconfined Shear Strengths angles of internal
Friction and moisture content
Making life more simple – The Angle of Internal Friction for Plastic Clay is usually
Treated as 0. Speck developed a respectable correlation of the Unconfined Shear
Strength of the Floor with its moisture content
The Spreadsheet has Specks
Estimator of Shear Strength Right
Next to Where You Must Input
Shear Strength
Speck estimate of S1
60
S1  (2070  167 * MC ) * .15
For this class you can estimate S2 to be 1100 psi and MC to be 12% where the
Clay floor has not been wetted.
The Rest of the Inputs Come From
Your Conditions and Your Pillar Design
Unconfined Shear Strength Floor (S1)
Moisture Cont (MC)
Unconfined Shear Strength of Rock below Clay Floor (S2)
Angle of Internal Friction (Ø)
Weak Layer Thickness (H)
Pillar Width (B)
Pillar Length (L)
Entry Width
Cross Cut Width
Depth
60 psi
10 %
1100 psi
Speck estima
S1
0
5
160
160
20
20
450
ft
ft
ft
ft
ft
ft
You need to enter your Fireclay thickness – assume once thickness goes past
1.3 feet that clay floor designs will take over for pillar sizing.
You need to know your Depth
The pillar dimensions and entry widths come from your own designs.
The Outputs
UBC
793.1628
InSitu psi
Stress Ratio
Extraction Ratio
Floor Stress
Safety Factor
Safety Factor
Safety Factor
495
1.2
16.66667
594
1.335291
1.134997
0.934704
UBC  Nm * S1
%
short term
long term
wetted safety Factor
The Spreadsheet Calculates the Ultimate Bearing Capacity of the Floor
It Also Calculates the Extraction Ratio and Stress on the Floor
From This the Spreadsheet
Estimates Your Factor of Safety
UBC
793.1628
InSitu psi
Stress Ratio
Extraction Ratio
Floor Stress
Safety Factor
Safety Factor
Safety Factor
495
1.2
16.66667
594
1.335291
1.134997
0.934704
UBC  Nm * S1
%
short term
long term
wetted safety Factor
The short term factor of safety is what can be achieved with undegraded floor.
For a panel where you will mine in and then abandon a 1.2 short term factor
Of safety is acceptable.
On a long term basis – such as might be encountered if one wanted to know that
Floor failure would not cause subsidence one would consider a long term
Safety factor (the floor is assumed to pick up moisture as result of exposure to
The air and some minor water incident to mining operations). The reduction is
An empirical value based on observations by Dr. Paul Chugh for the Illinois basin.
The Last Safety Factor
• The Last Safety Factor reduces strength for a
clay floor basically getting into constant covered
water contact for 24 hours
– Again it is based on an average measured by Dr. Paul
Chugh
• What could cause such wet floor conditions
– A mine flood that you failed to pump out in time
– Exposing the clay floor to a water bearing formation
with significant water present
– Exposing a clay floor to bleed water from backfill