January 22, 1915.

THE COLLIERY GUARDIAN.

187

THE LIMITS OF MIKING UNDER
HEAVY WASH *

Throughout the northern anthracite field of Pennsyl-
vania glacial and alluvial deposits of sand, grave], and
clay exist in varying quantities. These deposits of
sand, &c., overlying the coal measures attain a maximum
depth of more than 300 ft., and are usually saturated to
such an extent as to render them semi-fluid. It is this
condition of fluidity that limits the mining of coal
seams cropping in or in close proximity to these
deposits. The dangers incident to mining under deep
deposits of sand have long been realised by operators in
the northern anthracite field, and much has been done
to prove the contour o± the rock and vein croppings
underlying these water-bearing deposits of sand and
gravel.

To safeguard the mine workings against possible
danger, some of the mining companies have formulated
rules for minimum thickness of rock to be maintained
under water-bearing wash. These rules are variable.
Some companies work to 100 ft. of rock over the vein
when the depth of wash exceeds 100 ft., and for less
than 100 ft. of wash the thickness of rock is maintained
the same as the depth of wash to and including 40 ft.;
others work to a uniform thickness of rock, varying
from 20 to 100 feet, for all depths of wash. Then again,
with the progress of mining and the more definite and
closer proving of the rock contour, the minimum rock
thick) esses previously established are reduced and the
workings carried closer to the overlying sand deposits.

A number of accidents have occurred, due to mine
workings striking into deposits of sand, &c.

Datum 400 00

SCALE OF FEET

JOO

Before

or

<K
oc

25 Tun’l

W. Kidney

15Tun’i N
JW Hillman

a

Wash
) D of









Bio. 1.—Section showing Conditions
Cave-in.

Fig. 2.—Section showing Conditions After
Cave-in.

Datum 400.00

SCALE OF FEET

Wash

JOO

z

X

m
IO

15 Tun’l N
<W.Hillman

25 Tun’l
,W.Kidney

<x

CE

O'
£K

o p of Rock
rrrfnrtr rjrnj rntrnrrm	1

CAVE

Figs. 1 and 2 illustrate an accident which occurred at
the Sugar Notch Mine on June 10, 1914. In this case
the material carried into the mine consisted principally
of sand and clay in a semi-fluid state, from a swamp
in which the cave occurred. Approximately 20,000
cu. yds. of solid material was carried into the mine,
which filled or partly filled several thousand feet of
gangways and tunnels and required months to clean up.
Fig. 1 illustrates the conditions as they were considered
to exist before the accident. The face of breast 15 at
the time of the cave was at A, or at an elevation of
+ 590’0. It was intended to drive this breast to an
elevation of +600’0, as the elevation of the top of rock
immediately over this breast was thought to be +630 0.
The elevation of the surface directly above is +657’0.
Fig. 2 illustrates the conditions after the accident. The
top of rock at the point of cave is at elevation +600’0,
winch is only 10ft. above the face of the breast at the
time of the accident.

At the Exeter Colliery, near West Pittston, in proving
the top of rock in advance of mining in the Pittston
vein, a pot or gorge was developed. This erosion has a
maximum depth of 110 ft. and a width on top of about
200 ft. The depth from the surface to the bottom of
the pot or gorge is 127 ft. Two holes 100 ft. apart and
at right angles to the holes proving a width of 200 ft.
show the same depth of erosion, so it appears that it
may be an eroded gorge, but if a pot, it is probably
elliptical in shape. An indication that the erosion is a
gorge is given by considering the rock measures. The
top of rock immediately north of the erosion is
apparently the bottom rock of the Checker vein and at
the location of the deep erosion there is apparently a
broken anticlinal, which would give cause for the deeper
erosion. The proving of top of rock in this locality was
being done with holes spaced 200 ft. centres when the
deep erosion was discovered.

A very interesting proving of rock erosion at the
Stearns Colliery, near Nanticoke, indicates the presence
of a deep gorge with a width on top of about 100 ft.
and a depth of one side of 95 ft. and on the other
side of 45 ft. The bottom of the gorge is 105 ft. below

* From a paper read before the American Institute of
Mining Engineers.

the surface. The gorge as developed indicates, in con-
sideration of provings of the top of rock on sections
to the east and west, that it is a contraction in the
eroded channel, and like the so-called pot hole over the
Pittston vein at the Exeter colliery is probably nothing
more than an eroded gorge. These possible conditions
exemplify the importance of contouring the top of rock
in provings of lock erosions.

In developing the top of rock under sand deposits by
drilling, it is advisable to construct sections on the lines
of drilling and also contour maps of the top ( f rock.
Such sections and contour maps are of great value in
proving the possible existence of gorges or abrupt
erosions, and at the same time are of further value in
determining the most desirable locations of di ill holes
and the lines of working limits for definite rock cover.

DEPTH TO TOP OF VEIN (d I

210

270

300

180

240

150

120

30

90

60

10

E

65

D

THICKNESS OF ROCK COVER(dl FOR 24 F00T CHAMBERS

70	75

45	50

20	25	30	35

Fig. 3.

Numerous tests of various stones have proved that
sandstones take permanent sets for the smallest loads,
whereas granite and limestones are nearly perfectly
elastic. It has also been proved by tests on various
stones that the modulus of elasticity in compression is
practically the same as in cross bending, but no fixed
relation has been determined of the compressive, tensile,
or shearing strength of the various kinds of stone. The
shearing strength of sandstones and slates per square
inch is generally slightly in excess of the modulus of
rupture, and the compressive strength of various stones
is variable and of comparatively little consequence here,
as the compressive strength of even the lightest sand-
stones ranges from 4,0001b. to 6,0001b. per square inch.
The moduli of rupture of various kinds of stone as
given by a number of authorities are shown in the
following table :—

Table I.—Moduli of Rupture of Stones.

	Maxi- Mini- Aver-	A  mum. mum. age.	Aurnonty.	
Blue stone flagging		4,511..	.. 360...2,700...Baker.
Slate 		9,000..	.1,800... 5,400... Baker.
Slate 		11,230.	..7,425... — ...Arsenal tests, 1902.
Slate 		—	— ...8,480... Merriman.
Granite 		2,700..	. 900... 1,800...Baker.
Granite 		—.	. — ...1,754...Merrill.
Granite 		— ..	. — ...2,610...Arsenal tests.  1907.  . — ...1,667...Arsenal tests.  1905.
Granite 		— ..	
Granite 		—	.. — ...1,365... Bauschinger.
Granite 		—	.. — ...1,194...Bauschinger.
Glass 		3,500	— ... — ...Church.
Glass 		4,132..	. — .. — .. Fairbairn.
Sandstone 		— ..	.. — ...1,576... Technology Quarterly . — ...1,200... Merriman.
Sandstone 		—	
Sandstone 		1,273..	. 655 .. — .. Arsenal tests, 1895.
Sandstone 		2,243..	.1,500 .. — ...Arsenal tests,
Sandstone 		2,340..	1895.  . 576...1,260...Baker.
Sandstone (variegated)	—	. — ... 469...Bauschinger.
Sandstone (variegated)	—	— ... 718...Bauschinger.
Sandstone (variegated)	—	. — ...1,109... Bauschinger.
Sandstone (variegated)  Sandstone (carboni-	— ...	. — ... 341...Bauschinger.
ferous) 		—	. — ... 483 Bauschinger.
Sandstone (slaty)		—	. — ... 249... Bauschinger.
Sandstone (slatv)		—	. — . 135... Bauschinger.
Sandstone (green)			. — ... 156... Bauschinger.
Sandstone (cretaceous)	—	. — ... 597 Bauschinger.
Sandstone (cretaceous)	—	— ... 967...Bauschinger.
Grey stone 		2,200/.	. — ... — ...Kent.
Light stone		1,170..	. — ... — ...Kent.
Stone		—	. — ...2,000...Merriman.
Quartz conglomerate	—	— ... 651 ..Merriman.

From the results of tests as given in this table, the
average moduli of rupture for the various stones can be,
considered as follows :—

Pounds per
square inch.

Blue stone flagging.............. 2,700

Slate ........................... 7,736

Granite.......................... 1,681

Glass (maximum).................. 3,866

Sandstone ......................... 806

Blue stone flagging...	1,500	...	—	...	200

Granite................ 1,200	...	200	...	150

Limestone ............... 800	...	150	...	125

Sandstone ............... 700	...	150	...	75

It is to be observed, in the case of sandstone, that a
safe tensile strength of 75 lb. and a shearing strength
of 1501b. per square inch are given. Now, in con-
sideration of the fact that the modulus of rupture i%
invariably in excess of the tensile strength, also thatr.
the resistance to shear slightly exceeds the moqkilus off

rupture, a value of 100 lb. per square inch for the
modulus of rupture of sandstone would be consistent.
This assumed value of 100 lb. per square inch as the
modulus of rupture for sandstone beams compared with
the average modulus as derived from Table I. gives a
safety factor which, although slightly less than the
factors generally used for stone in building construc-
tion, seems to be sufficient for the conditions of this
problem.

When sandstones and slates, which generally overlie
the coal veins, are considered as beams or slabs spanning
mine openings for the support of overlying strata or
other superimposed load, their transverse strength is of
first importance. The ability of such material to serve
as a beam depends upon its tensile strength, since that
is always less than its compressive strength.

In the formula for flexure 2? = Mm, we can compute
6

the value of p, the greatest normal stress in any outer
element, when all other quantities are known. This
value of p is theoretically correct provided the elastic
limit of the material has not been exceeded. This
formula has also been used for the rupture of beams by
flexure by calling the value of p thus obtained the
modulus of rupture B. The value of B may be found
to differ considerably from the unit tensile strength of
some materials and is frequently much larger, having a
value between the ultimate tensile and the ultimate
compressive strength. This might be expected, since,
even supposing the relative extension of the fibres to be
proportional to their distances from the neutral axis as
the load increases towards rupture, the corresponding
stresses, not being proportional to these strains beyond
the elastic limit, no longer vary directly as the distances
from the neutral axis, and the neutral axis does not
necessarily pass through the centre of gravity of the
section. It is evident that the modulus of rupture does
not express the actual stress in the extreme fibre of the
beam, but is a quantity useful only as a basis of
comparison.

The manner of failure under test depends upon the
kind of material. Stones and brittle materials fail by
the fibres breaking in tension, whereas timber and the
more plastic materials fail by crushing. Stone and
plain concrete beams of deep section fail sometimes by
shearing on a diagonal plane near the point of support.

In deriving a formula for computing the breaking
load of a slab of stone from the formula — Mm, let
e

W represent the distributed loading plus the weight of
the beam itself in pounds ; let 5, d and L represent the
breadth, depth and span respectively in inches; let B
equal the modulus of rupture in pounds per square inch.

The maximum bending moment for a constrained or
WL

prismatic beam is equal to —By substituting in

the formula for flexure	we obtain the

271/72

formula W =	— R. Likewise the maximum moment

L

WL

at the centre of such a beam being equal to -57-, the

24

formula becomes W = R.

1j

So it is evident that failure of flexure would theoreti-
cally take place at the points of support and not at the
centre of the span.

25d2

In applying the formula W =	- R to the case of a

slab spanning a breast or other mine opening, the
weight of the overlying material will be taken at 108 lb.
per cubic foot, and the depth of the opening below the
surface will be designated by d' in feet.

We will then have W =	which would he the

12

loading of the slab with a breadth of 1 ft. Substituting
2bd2

this value of W in the equation W = —y- B and

simplifying, we obtain

d2B = |L2d'.

By taking the width of the opening, L, as 24 ft. and
100 lb. per square inch as the value of B, the formula
becomes d = 17’63 Vd7, which becomes d = 1’47 d' for
values of d in feet. __For 120 lb. per cubic foot this
becomes d = 1’55 d', so, for convenience in use and
without appreciable error, this is taken as d — 1'50 Vd'.
From this formula Table III. has been prepared, which

Safe unit stresses for various stones have been given by
many authorities, and in the next table is given the
stresses in pounds per square inch, recommended by
W. J. Douglas, as illustrative of possibly a fair average;
of such values.

Table II.—Safe Unit Stresses for Stone.

Compression Shear Tension
pounds per pounds per pounds per
square inch, square inch, square inch.

Table BT—Minimum Thickness of Rock for Various Depths below the

Surface, over Chambers 24 Ft. Wide  

Depth	Thickness ot Rock	Depth	Thickness of Rock
d',	d,	d',	d,
Feet	Feet	Feet	Feet
10	4 74	160	18 97
20	6 71	170	19 55
30	8 21	180	20 13
40	9 48	190	20 67
50	10 61	200	21 21
60	11 62	210	21 74
70	12 55	220	22 25
80	13 41	230	22 75
90	14 23	240	23 23
100	15 00	250	23 72
110	15 73	260	24 18
120	16 43	270	24 65
130	17 10	280	25 10
140	17 75	290	25 54
150	18 37	300	25 98

gives the thicknesses of rock for depths ranging from
10 to 300 ft. and 24 ft. width of chambers.

In the use of the formula derived for determining the
minimum safe thickness of rock over mine openings for
various depths below the surface, consideration must be
given to a number of conditions, the more important of
which are: