This document discusses the design of pillars in underground coal mining. It notes that pillar failure can be either gradual or sudden, with sudden failures causing disasters. Statutory guidelines for pillar dimensions are provided but have limitations as mine depths increase. The author proposes modifications to the standard formula for calculating rock load on pillars to account for dynamic loads during pillar extraction, with a dynamic load factor. Two common formulas for estimating pillar strength are examined, with the author noting limitations and making suggestions to better account for depth and pillar width factors. Overall, the author aims to provide a more scientifically-based approach to pillar design for stability during formation and extraction.

1. Author: Tikeshwar Mahto,
Dy.Director of Mines Safety, Bilaspur
Region(India).
+917898033693
tikeshwarmahto@yahoo.co.in
DESIGN OF PILLARS, A CRITICAL ASPECT FOR STRATA CONTROL IN UNDERGROUND PILLAR
MINING - A Case Study.
INTRODUCTION:
One of the hazards of pillar mining is the possibility of collapse of pillars in course of time. The mode of pillar
failure might be either gradual or sudden. Gradual failure occurs in the form of pillar spalling and slabbing and
such failure can be controlled. Sudden failure is not necessarily by deterioration of the pillars. Once the
process has started, it cannot be controlled. Gradual failures do not generally cause deaths or injuries, but
sudden collapses have been resulted in disasters. In 1960, in South African Coal brook North colliery, an area
of over 2.5 sq.km, standing on pillars had suddenly collapsed killing 437 persons. Sudden collapses of pillars
have invariably been associated with severe air- blasts. Lists of the disasters due to pillar collapses in Indian
mines are given below
Sl.No. Name of Mine Date of occurance No. of persons killed.
1. Chanda Colliery(Jharia coal field) 31-08-1915 10
2. Bhowrah Colliery(Jharia coal field) 05-02-1916 24
3. Rawanwara colliery(M.P.) 14-04-1923 15
4. West Chirmiri Colliery(M.P.) 11-04-1968 14
5. GDK.NO.-8A Incline(SCCL) 2003 16
6. VK-7(SCCL) 2006 4
Hence, natural support has a very important role in controlling overlying strata, while extracting coal from
underground mines. Artificial supports erected after creation of voids to ensure stability during the formation
and extraction of pillars, and during the period between such formation and extraction are merely for
immediate roof.
Because artificial supports are designed for resisting strata loads upto a certain height of roof rock. Artificial
supports by props, cogs etc.cannot prevent premature collapse; they can prevent falls of immediate roof only.
Therefore, the premature collapses can be controlled by natural supports only. Natural supports mean supports
or resistances offered by natural sources, like strength of pillar, strength of overlying strata, strength of
underlying floor etc. Hence, scientific base is necessary for proper design of natural supports to ensure stability
of workings and also for minimizing loss of valuable property inside the collapsed strata.

2. In this paper author is sharing his experience for proper design of pillars to ensure stability of workings during
the formation and extraction of pillars. The author is working in underground coal mines since last eight years
and has observed from very close about the conditions and behavior of standing pillars while extraction.
STATUTORY BACK-UP:
CMR-1957 has made some guidelines for design of pillars in underground working to ensure safety of men,
machinery and coal (a national property). Following are the directives regarding the above subjects made by
the statutes
Reg. -99 Development Work;
The dimensions of pillars and galleries, and the shape of pillars, formed in any seam or section shall be such
as to ensure stability during the formation and extraction of pillars, and during the period between such
formation and extraction. No gallery in a seam or section shall exceed 3m in height or 4.8m in width at any
place without prior permission of RIM.
The pillars formed in any seam or section shall normally be rectangular in shape. The distance between the
centres of any two adjacent pillars left in seam or section shall not be less than that specified in the appended
table as corresponding to the depth of the seam or section from the surface at that point and the width of the
galleries in the workings
The distance between centres of adjacent pillars shall not be less
than
Depth of seam from surface Where the Where the Where the Where the width
Width of width of width of of the galleries
the galleries the galleries the galleries does not
does not does not does not exceed
exceed 3.0m exceed 3.6m exceed 4.2m 4.8m
(1) (2) (3) (4) (5)
Not exceeding 60m
Exceeding 60m but not
exceeding 90m
Exceeding 90m but not
exceeding 150m
Exceeding 150m but not
exceeding 240m
Exceeding 240m but not
exceeding 360m
Exceeding 360m
Meter Meter Meter Meter
12.0 15.0 18.0 19.5
13.5 16.5 19.5 21.0
16.5 19.5 22.5 25.5
22.5 25.5 30.5 34.5
28.5 34.5 39.5 45.0
39.0 42.0 45.0 48.0

3. 6. In the case of all workings, where in the opinion of the RIM, the dimensions of the pillars or galleries are
such as to render it likely that crushing of pillars or the premature collapse of any part of the workings will
occur either before or during the extraction of pillars, he may by an order in writing, require such modification
of the dimensions aforesaid in respect of any further working as he may specify.
LIMITATIONS OF THE ABOVE MENTIONED STATUTORY BACK-UP REGARDING PILLAR
DESIGN:
Dimensions of pillar given above as per the Reg.-99 are based on the experience and past working conditions
only. It has some limitations and drawbacks. It has no scientific base and it can be used upto a depth of 360m
only. Mine workings are going deeper and deeper, and in future there will be no alternative except deep
mining. Hence, for deep mining design of natural supports is very essential for the safety point of view and for
this there is need of scientific approach towards rock load estimation and strength of the load bearing pillars.
ROCK LOAD CALCULATION FOR DESIGNING PILLARS:
For pillar design, rock load is calculated by ` Tributary –Area Method ` which is shown in figure given below;
Fig.1 Plan view of Bord and Pillar System
Where in the Fig. 1,
W= is the length of square pillar corner to corner ;
b = the width of the gallery (bord).
Here rock load (P) on the pillars calculated by the tributary – area method is as follows,
P = µH( W + b/W )2
t/m2
, where `µ` is the density of overlying rock in `t/m3`
and H is the depth of
working in meters .The rock load calculated above in `t/m2`
can be converted into `Mpa` (mega Pascal) in the
following ways;
P = µH{(W+b)/W}2
*103
Kg/m2
[ 1 tonne = 1000 Kgs ]

4. Or, P = µH{(W+b)/W}2
* 103
* 10 N/m2
[ 1 Kgf. = 10 N ]
Or, P = µH{(W+b)/W}2
*104
Pa [ 1 N/m2
= 1 Pascal & 1 Mpa = 106
Pascal ]
Or, P = µH{(W+b)/W}2
* 10-2
Mpa . Taking µ = 2.5 t/m3
(approximately),
Hence, P = 0.025 H{(W+b)/W}2
Mpa …………………………(1)
Author’
s observation :
From the Fig.1 and equation (1), it is clear that the pillar is designed as natural support based on strata load
coming on the pillars during development stage only. There is no consideration of dynamic loads( shock
bumping etc.) transferring on pillars during final extraction of pillars , which should be the main criteria for
pillars design in bord and pillar mining . Because in Reg-99(1), it is clearly mentioned that`` the dimensions of
pillars and galleries, and the shape of pillars, formed in any seam or section shall be such as to ensure stability
during the formation and extraction of pillars, and during the period between such formation and extraction`` .
Hence, for load calculation to design pillars, the effect of dynamic loading during extraction of pillars should
also be considered for more stability of underground workings. The dynamic loads transferring on pillars at
the time of final extraction are different in magnitude for different method of extraction . In case of sand
stowing it is negligible, but in case of caving it is disastrous ,which leads overriding of pillars and premature
collapse of workings. History of disasters due to premature collapse is very dreadful. In recent past, the author
has seen two major disasters due to premature collapse in SCCL, in which about 20 persons were killed. The
author has done some case study and suggested a modified formula for load calculation in pillars design.
Author’s suggestion:
As the author has explained in detail that the dynamic loading is a major contributing factor for premature
collapse of pillars and workings, so there must be a dynamic load factor in calculation of rock load while,
designing pillars for final extraction. Also, before designing pillars, there must be a pre-plan of method of
working i.e. whether the pillars shall be extracted by sand stowing method or by caving method .Because the
dynamic load factor shall be different for both the method of workings. For the sand stowing it will be around
unity(1),because there will be less effect of settled goaf stowed with sand on the unextracted pillars, but in the
caving method dynamic loading is very-very disastrous . Sometimes it is more than the static load calculated
by the Tributary-area method, which may create the condition of premature collapse of workings. Although, in
caving method of workings there is provision of `Breaker line supports`, but practically it is very difficult to
limit the effect of dynamic loading on surrounding pillars by using breaker line supports, particularly in strong
and massive strata . The static and dynamic loading of pillars has been shown in Fig.2 given below. The arrow
shows the static load due to overburden and the curve line shows the dynamic load due to hanging goaf. In
Fig.2 , W = width of the pillar , b = width of the gallery and h = height of the gallery(or pillar height )

5. Modification of formula suggested by the author for load calculation on pillar:
From the equation (1) and Fig.2 , the formula for load calculation can be written in the following way;
P = 0.025KH(W+b/W)2
Mpa ……………………………..(2)
Where , P = load on pillar( in Mpa) ,
K = a dynamic load factor,
H = depth of cover (in meter),
W = size of square pillar (in meter), and
b = width of gallery (in meter).
Here , K = 1 for sand stowing method and for the caving method it will be more than unity(1). The value of
K can be taken in range of 1.3- 1.6 . For easily cavable strata K = 1.3 and for strong and massive strata
K = 1.6 . The assumed values of dynamic load factor (K) are not actual. The author has assumed these values
for the convenience and simplicity.
STRENGTH OF PILLAR FOR DESIGNING NATURAL SUPPORT IN UNDERGROUND COAL
MINES;.
Estimation of strength of pillars is a critical part of the pillar design . There is no straight forward formula for
calculating strength of the pillars. Based on experience and the conditions of geological formation, some
empirical formulae have been developed by scientists, which are explained below in detail about their merits
and demerits.
Salomon & Munroe formula:
They have developed formula for calculating strength of pillar based on size of the pillar and height of
extraction , which is given below ;
Dynamic
load curves
Hanging
Goaf
Static
Load

6. S = 1320*(W)0.46
/(h)0.66
Psi …………………………….(3)
Where , S = strength of pillar (in Psi),
W = equivalent width of pillar (in ft.),
= 4A/P
= 4(W1*W2)/2(W1+W2)
= 2W1*W2/W1+W2; where W1 & W2 are length and width of rectangular
Pillar (in ft.)
h = height of extraction (in ft.)
The strength of the pillar can be changed from Psi to Mpa , by taking width of pillar and height of extraction
in meters in the following ways;
S = 1320(3.28W)0.46
/(3.28h)0.66
*145 Mpa [1Mpa = 145 Psi ]
[ 1 meter = 3.28 ft.]
Or , S = 1320(W)0.46
/(3.28)0.66
*145(3.28)0.20
Mpa
Or ,S = 7.18 (W)0.46
/h0.66
Mpa …………………………….(4)
Where , W and `h` are in meters.
Author’s observations;
From the equation (4) , the strength of pillar can be calculated by knowing width of pillar and height of
extraction only. There is no consideration of depth of working and geological intrusions into the pillars i.e. the
pillars having same width and height of extraction shall have same strength irrespective of depth of workings.
Also in Salomon & Munroe formula, less weightage has been given to the width of the pillar, which estimates
less than the actual strength of the pillar. The author thinks that it is not suitable for Indian conditions. Because
Indian statute has strictly restricted the height of extraction to 3m, but there is no any restriction for higher
limit of the width of pillar. Therefore, in author’s view , width of pillar(W) should be given more weightage
for calculating actual strength of pillars.
CMRI formula developed by Dr. P. R. Sheorey for calculating strength of pillar:
In Dr. Sheorey,
s formula, major factor for calculating strength of the pillar is depth of working(H). There is far
difference in strength values calculated by Salomon - Munroe and Dr. Sheorey. In Salomon - Munroe’
s
formula, there is no depth factor , but in Dr. Sheorey,
s formula strength of pillar varies as the
depth of cover(H) increases .The author has made comparative studies in detail, and also given some
suggestion for modification in strength formula, which will be discussed later.
Dr. Sheorey,
s formula for strength calculation is given below;
S=0.27pc* h-0.36
+(H/250 +1)(W/h -1) Mpa………………………………….(5)
Where, S = strength of pillar (in Mpa)
pc = compressive strength of sample of 25mm cube (23.8 Mpa);
h = height of extraction (in meter);
H = depth of cover(in meter) , and
W = equivalent width of pillar (in meter)
= 4A/P
= 2W1*W2/W1+W2 (for rectangular pillar )

7. The author’s observations and suggestion:
In Dr. Sheorey,
s formula of strength calculation, there are two parts. First part is function of compressive
strength of the sample piece and height of extraction and second part is function of depth of cover and size of
the pillar. In this formula, if we assume size of pillar (W) and height of extraction (h) as constants for any
depth, the strength of pillar of particular dimensions will be directly proportional to the depth of cover (H) as
shown in Fig.4, i.e. more the depth of cover, more will be strength of pillar. In author’s view, there is
contradiction between the assumptions of two scientists mentioned ` above. The author has critically diagnosed
about the above mentioned systems of pillar design, which are as follows;
Assuming, width of pillar (W) and height of extraction (h) as constants for any depth and expanding this
formula, we get;
S = (0.27pc*h-0.36
+ W/h -1) + H(W/h – 1)/250
As per assumption W, h, pc are all constants, therefore
(0.27pc*h-0.36
+ W/h- 1) = a constant ( C1 ), and also (W/h- 1)/250 =an another constant (C2)
Hence, putting these constants in equation (5) we get
S = C1 +C2*H …………………………………(6)
From the equation (6), we can infer that it is an equation of straight line in S and H i.e. the strength of pillar
is directly proportional to the depth of cover for a particular size of pillar and height of extraction.
In other words, it can also be inferred that the strength of a coal seam will vary proportionally to the depth of
cover, which is not possible. Because, the strength of any material is its internal property and, it will not
change in great extent by changing only external conditions (like pressure and temperature due to increase in
depth).
In author’s view, the strength of coal seam will change with the depth of cover, but in small extent due to
metamorphism of coal under heat and pressure. Strength of coal generally varies with the age of formation and
compactness. Moreover, compactness depends upon internal granular structure (i.e. cohesiveness) of rock
mass.
In author’s view, both the scientists (Salomon- Munroe & Dr. Sheorey) have assumed only external conditions
for calculating strength of pillar. They have not considered about internal conditions (weaknesses). Internal
weakness means any geological disturbance like clay band, joints, slip, fault, fold etc. embedded into the seam.
The author has observed that in same mine (GDK.NO.-10 Incline) and in same seam (NO.3 Seam); a coal
pillar developed at 150m depth is stronger than the pillar developed at 350m depth. The above-mentioned
seam is not having any internal weakness at 150m depth, but the same seam after 230m depth is intruded with
1.0m clay& shale band at 4.0 m height from the floor. Therefore, in the mine pillars have been developed after
leaving 1.5m coal in floor due to strata control problem, which has positioned the clay & shale band just below
the roof. Due to this band inter granular cohesive bond of the coal seam got weakened. Hence, when strata
weighting occurs, the coal pillars start spalling from its sides. Due to sides spalling effective area of the pillar
decreases, and load on the pillar (P/A) increases, which may cause premature collapse of the workings. All
these can be understood by the pictorial representation shown in Fig.3.

8. Strata Load
Floor reaction
Coal pillar having no internal weakness Coal pillar having internal weakness
(Clay & Shale band)
Shape of pillar after sides spalling
Fig. 3
From the Fig.3, it is clear that, in case of coal pillar having discontinuities like clay & shale band shown in the
figure as example, the total strata load is not transferring to the floor. Only a fraction of it is transferred to the
floor of the seam and greater portion of the load is diverted towards sides of the pillar due to discontinuity of
rock mass as shown in the Fig.3, which causes sides spalling and weakening the pillars. On the other hand, in
case of the pillar developed in uniform and undisturbed seam maximum strata load is transferred to the floor of
the seam, which indicates strongness of the pillar. Length of arrow in the figure shows the magnitude of the
load.
Strata Load
Floor
reaction
Clay &
Shale
band
Clay &
Shale
band

9. Comparative studies between Salomon – Munroe and Dr. Sheorey,
s hypothesis for pillar design:
Assumptions :
Width of the pillar : 40m,
Height of extraction : 2.8m
From equation (6),Dr, Sheorey,
s strength formula is S = C1 + C2*H ,where C1 and C2 are constants for a
particular width of pillar (W) and height of extraction (h).
Here S = strength of the pillar,
C1 = (0.27pc*h-0.36
+ W/h -1),
C2 = (W/h– 1)/250.
Assuming width of pillar (W) and height of extraction (h) constants for any depth of cover (H) for calculating
strength of pillar and factor of safety(FOS) for a particular width of pillar and height of extraction.
Hence, W = 40m, h = 2.8m, pc = 23.8(assumed by Dr. Sheorey ).
Therefore, C1 = 0.27pc*h-0.36
+W/h -1
= 0.27*23.8*(2.8)-0.36
+40/2.8 -1
= 17.72. and
C2 = (W/h – 1)/250
= (40/2.8 -1)/250
= 0.053
Thus, Dr. Sheorey,
s formula for strength of the pillar can be expressed in the following way;
S = 17.72 + 0.053H Mpa ……………………………..(7)
and Salomon – Munroe formula for strength of pillar is;
S = 7.18W0.46
/h0.66
Mpa
And factor of safety (FOS) = strength /load
= S/P
Where, P(load) = 0.025H(W+b/W)2
Mpa
Quantitative comparison of strength of pillar and factor of safety of pillar design, taking width of pillar(W)
and height of extraction (h) as constants for any depth of working is tabulated below;

10. Depth
of
cover
(H) in
mtr.
Width
of
pillar
(W) in
mtr.
Height of
extraction
(h)
Width of
gallery(
b) in
mtr.
Load on
pillar(P)
in Mpa.
Strength
of
pillar(S1)
in Mpa ,
by
Dr.Sheore
y
Strength of
pillar(S2) in
Mpa, by -
Salomon-
Munroe
Factor
of safety
(FOS1)
by
Dr.Sheo
rey
Factor of
safety
(FOS2)
By
Salomon-
Munroe
100 40 2.8 4 3.02 23.02 19.86 7.61 6.56
200 40 2.8 4 6.05 28.32 19.86 4.68 3.28
300 40 2.8 4 9.07 33.62 19.86 3.70 2.19
400 40 2.8 4 12.10 38.92 19.86 3.22 1.64
500 40 2.8 4 15.12 44.22 19.86 2.92 1.31
600 40 2.8 4 18.15 49.52 19.86 2.73 1.09
700 40 2.8 4 21.17 54.82 19.86 2.59 0.94
800 40 2.8 4 24.20 60.12 19.86 2.48 0.82
900 40 2.8 4 27.22 65.42 19.86 2.40 0.73
1000 40 2.8 4 30.25 70.72 19.86 2.34 0.66
1100 40 2.8 4 33.27 76.02 19.86 2.28 0.60
1200 40 2.8 4 36.30 81.32 19.86 2.24 0.55
1300 40 2.8 4 39.32 86.62 19.86 2.20 0.50
1400 40 2.8 4 42.35 91.92 19.86 2.17 0.47
100m
200m
300m
1200m
1300m
1400m
Surface
Coal Seam
Square Coal
Pillars
(40m width)
Depth

11. Graphical representation of strengths of pillar by using Dr. Sheorey and Salomon – Munroe formulae has been
sown in Fig.4 given below, in which width of the pillar and height of extraction have been fixed for the depth
of the cover from 100m- 1200m.
Graphical comparision of Dr. Sheorey and Salomon- Munroe
0
20
40
60
80
100 300 500 700 900 1100
Depth of cover (H) in meter
Strengthofpillar(S)inMpa
S1(Strength of
pillar by Dr.
Sheorey)
S2(Strength of
pillar by
Salomon-
Munrou)
Fig.4
From the above table and Fig.4, according to Dr. Sheorey, strength of a 40m square pillar is increasing with
the depth of cover and it is about 81 Mpa at the depth of 1200m, which is impossible. On the other hand,
according to Salomon – Munroe, strength of a pillar (keeping size of pillar constant) is not changing with the
depth of cover.
Also in Fig.5, a graph has been drawn between factor of safety and depth of cover(H), in which as per Dr.
Sheorey,
s assumption factor of safety of a 40m square pillar is 2.24 at depth of 1200m. It means a 40m square
pillar is sufficient for the stability point of view at 1200m depth. Contrarily, according to Salomon- Munroe,
there is no meaning of a 40m square pillar at depth of 1200m. These are the main aspects, the author wants to
summarize in this article.

12. Comparision of factorof safety of pillar by using formula of Dr. Sheorey and Salomon-
Munroe
0
1
2
3
4
5
6
7
8
100 300 500 700 900 1100 1300 1500
Depth of cover(H) in mtr.
Factorofsafety(FOS)
Factor of safety(FOS1) by
Dr.Sheorey
Factor of safety (FOS2) by
Salomon- Munroe
Fig.5
Modification of strength formula suggested by the author:
The author has designed the formula for calculation of strength of the pillar based on Salomon- Munroe and
Dr. Sheorey,
s assumptions. Some inherent factors have been considered for representing all types of coal at
various depths.
Assumptions :
W : width of pillar (in mtr.) ,
h : height of extraction( in mtr.),
S : strength of pillar (in Mpa ).
As we have discussed earlier that more the width of pillar, more will be the strength, but more the height of
extraction, lesser will be its strength.

13. So, the strength of pillar will be designed on the basis of these assumptions and then factors for internal
weakness and ranking of coal will be considered. The author has assumed that the relationship among strength,
width of pillar and height of extraction will be same for sample piece and standing pillars for determining
values of some unknown factors. For this purpose sample pieces from strong portion of the coal seam shall be
collected, as shown in Fig.6 and their uniaxial compressive strengths will be determined in the laboratory.
Now Strength of sample piece(s) α (w)m
, and also
Strength of sample piece(s) α 1/(h)n
Where `m` and `n` are exponent to width of sample piece (w) and height of sample piece (h) respectively.
Hence, combining the above two equations, we get;
s α (w)m
/(h)n
;
or , s = K1 *wm
/hn
Mpa ……………………………….(8)
And strength of whole pillar can be formulated from equation (8) by assuming same factors (m), (n) and a
factor (K) the constant of proportionality for the standing pillars. Here another factors K2 (factor for internal
weaknesses) and K3 (factor for ranking or grade of coal ) shall be considered for representing all types of coal
deposits.
It has been observed that the constant of proportionality (k) for the sample piece and standing pillar varies
inversely to the shape factor (w/h ratio).
W2
h2
h2
h1
W1
W1
W1
W1
Fig. 6
W2

14. Thus, for the sample piece, K1 α 1/(w/h);
And , for the standing pillar K α 1/(W/h).
Thus comparing above two equations we get,
K/K1 = (w/h)sample piece/(W/h)standing pillar
Or, K = K1 * (w/h) sample piece/ (W/h) standing pillar
Or, K = K1 *(w/h)/(W/h).
Thus, the strength of pillar (S) = KK2K3*Wm
/hn
Mpa ……………………………(9)
Where, K = proportionality constant. As per Salomon- Munroe’
s assumption K= 1320(or, 7.18 in SI system)
and, m= 0.46, n= 0.66.;
K2 = a factor for internal weaknesses (i.e. any geological disturbance or discontinuity embedded in
working section of coal Seam);
K3 = a factor for ranking (grade) of coal which depends upon the age of coal formation
. and depth of working;
W = width of pillar in meter, and
h = height of extraction in meter.
Determination of values of constants K1, K2, K3, m, and `n` :
From equation (6), the strength of a sample piece is;
S = K1* (w)m
/ (h)n
Mpa.
Taking two sample pieces from Fig.6, having same width but different height (or length), whose compressive
strengths are S1 and S2 respectively.
Therefore, S1 = K1* (w1)m
/(h1)n
Mpa , and ………………………… (10)
S2 = K1*(w1)m
/(h2)n
Mpa . ………………………….(11)
Dividing the above two equations we get;
S1/S2 = (h2)n
/(h1)n
= (h2/h1)n
Taking logarithm both sides, we get;
Loge(S1/S2) = Loge(h2/h1)n
,
Or , Loge(S1/S2) = n* Loge(h2/h1) ,
Or, n = Loge(S1/S2)/ Loge(h2/h1) ………………………………………..(12)
Here , h1 and h2 are known and S1 , S2 can be known by the compressive strength test of sample pieces .
Hence, value of `n` can be determined by putting values of h1, h2 , S1 and S2 in equation (12).

15. Again taking two samples from Fig.6, having different widths (w1 and w2) but same height (or length), whose
compressive strengths are S2 and S3 respectively;
Thus, S2 = K1* (w1)m
/(h2)n
, ……………………………….(13)
and S3 = K1* (w2)/(h2)n
. …………………………………….(14)
Dividing the above two equations we get;
S2 /S3 = (w1)m
/(w2)m
,
Or, S2/S3 = (w1/w2)m .
Again , taking logarithm both sides ;
Loge(S2/S3) = Loge(w1/w2)m
Or, Loge(S2/S3) = m* Loge(w1/w2),
Or, m = Loge(S2/S3)/Loge(w1/w2). ……………………………..(15)
We know the values of w1, w2 from sample pieces and corresponding values of S2 , S3 can be known by
compressive strength test of sample pieces. Hence, value of `m` can be determined by putting the values of
w1, w2 , S2 and S3 in equation (15).
Now, the value of `K1` can be determined from equation (10);
S1 = K1* (w1)m
/(h1)n
Mpa. ;
Or, K1 = S1*(h1)n
/(w1)m
……………………………………(16)
Here, values of S1, w1 , h1, m, and `n` are known.
Values of K2 and K3 can be assumed by observation of seam section in bore hole samples or in cross-
measure drift covering whole seam thickness and assessment for ranking (or grade) of coal seam.
Here K2 = a factor for internal weakness ( any disturbance or discontinuity like fault, fold, clay & shale band,
joints etc.embedded into the working section of coal seam),
and
K3 = a factor for ranking (grade) of coal.
Values of K2 can be assumed less than one(1) for the seam having internal weaknesses and one(1) for the
seam having no intrusion. Also for K3 , it is one(1) for lower rank of coal and 1.2 - 1.5 for higher rank of
coal.
Thus, K2 = 0.7-0.8 for the coal seam having internal intrusions, and
= 1.0 for the coal seam having no internal intrusion.
K3 = 1.0 for the lower rank of coal , and
= 1.2- 1.5 for higher rank of coal .

16. The above values of K2 and K3 are not actual. It has been assumed by the author for simplicity.
Conclusion;
The author’s approach can be verified in the field for determining satisfactory values of the factors, which
have been used by the author in this paper. The author’s approach is based on the practical experience and
study of disasters due to pillar failure.
Therefore, if it is applied in the field, it will certainly be a handy tool for mining engineers to control strata and
make the underground workings safe and technically viable.
Declaration:
All the statements and comments made by the author are personal and not necessarily to the organisation.
References:
 Kejriwal, B.K., Professor,ISM-Dhanbad, Safety in Mines
 Coal Mines Regulation, 1957
Signature of the author
Date 11.08.15
(Tikrshwar Mahto)
Director Director of Mines Safety,
Bilaspur Region(India).
+917898033693
tikeshwarmahto@yahoo.co.in