THE COLLIERY GUARDIAN

AND

JOURNAL OF THE COAL AND IRON TRADES.

Vol. CX.

FRIDAY, NOVEMBER 5, 1915.

No. 2862.

The Stresses in the Mine Roof.*

By R. DAWSON HALL.

The stresses in the simplest structures are often those
we"'find most difficult to analyse. The most complex
condition in mine stresses is found in simple tunnels
where the roof, the sides, and the floor are a monolith.
The functions of the parts are like the parts themselves
not distinct and spe’cialised, and the problems to be
solved are like those in a metal structure with riveted
joints or a redundancy of bars. This unity between roof,
sides, and floor, which to the coal miner is a difficult
conception, really deserves a scientific appellation, and
perhaps holoid (from holos, whole, and eidos, form) will
serve the purpose as well as any other.

In a simple tunnel the roof, the sides, and the floor
form integral parts of one and the same structure, and
the distortion of one cannot be conceived without a con-
sequent strain in the others. Thus when the roof of the
tunnel droops by reason of its weight, the upper parts
of the sides are drawn in, because they are integrally
connected with the roof, and must approach each other
whenever, by the sagging of the roof, the distance
between any two points in it is diminished. (See fig. 1.)
The sides in their turn operate on the floor of the holoid
structure, producing a tensile stress. The writer has
always been impressed with the value of soap as a means
of illustrating the action of mine stresses. With that
idea in mind, a cake of naphtha soap measuring 4f in.
by 2| in. by 1| in. was taken, and a tunnel was made
through it 1| in. long, 2| in. wide, and l|in. high.
(See fig. 2.) A load was then placed at the mid-span
of the tunnel. Eventually, the upper bar, or “ roof,”
broke at the centre line, and along both “ ribs ” of the
tunnel, the breaks being approximately vertical and pro-
ceeding, as might be expected, on the ribs from the
“ surface ” downward, and at the centre line from the
tunnel upward, the failure being from bending moment,
not shear.

This is interesting, because it shows that breakage
at the ribs is not necessarily evidence of shear. It may
be only a demonstration of a holoid structure. It is the
form of failure whenever coal is blasted down, and not
an infrequent form of roof demolition. The test on the
soap tunnel further showed that as soon as rupture
takes place in the roof of the tunnel, there must inevit-
ably come a thrust on the ribs. The tension draws them
together till rupture occurs, and then the two roof units,
in endeavouring to revolve, crowd each other and push
on the opposing walls. (See fig. 3.)

When a holoid structure, by reason of the weakness of
the floor or because of a lack of adhesion between the
ribs and the floor, ceases to engage the floor in its move-
ments, then its shape as a structural element roughly
resembles the Greek letter tt and for want of a better
name we might term the. new element a pyoid structure.
(See fig. 4.) By reversing the soap tunnel after the
roof has been caved, the weakness of the pyoid structure
is made clear. As soon as pressure is brought on the
new roof (formerly the floor of the tunnel), the two ribs
are seen to recede markedly, and if the floor were intact
this would result in a well-developed stress in that
element of the holoid structure. (See figs. 5 and 6,
showing progressive demolition.)

Probably it is well here to express a belief in the
importance of the .holoid. The general notion is that
all the beds shear horizontally along the lines of
stratification, and that it is a mistake to consider the
mine or even the roof as a monolith. It is true that
most of the accidents in mines are due to the lack of
unity in the roof. Nevertheless, it is interesting to
note how firmly roof and coal are usually “ burned ” to
one another. Even when undermined and sheared on
both sides, the coal often fails to fall, being supported by
the ventical shearing strength of the one side still
attached, and by the adhesion to the roof. The writer

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

is hardly prepared to state when holoid structure ceases
to exist, and, of course, the time and conditions will
vary with the materials under consideration.

It is obvious that with the holoid structure, the ribs
being drawn together by the movement of the roof, they
must tend more or less to be split vertically and in
longwall they will then fall down on the advancing
undercut. In certain sub-bituminous mines the writer
has noted a tendency toward what he thought was a
vertical shear parallel -to the headings. This developed
rapidly after the work was opened, especially at great
depth. Whether this was only a vertical shear seems
doubtful. It may have been due -to the holoid character
of the structure, the ribs receiving no relief by a
horizontal shear between ribs and roof. Instead the

FIG 1

Fl 6.3

TH-

FIG.6

roof pulled off the edge of the pillar as the former bent
under the load. It was interesting to note that these
lines of fracture did not coincide with the normal
cleavage of the coal.

This rending along vertical planes eventually throws
back the real rib lines far into the pillar. Where the
draw slate and roof proper leave one another, we have
probably a plate structure superposing one which is
holoid or pyroid in character, and in the longwall the
breaks back of the face which brings coal and roof down
together, or which tend so to do if the latter is not duly
propped, are failures of the semi-holoid or semi-pyoid,
and not of the plate structure above. (See figs. 9
and 10.)	..............

The breaking of even the holoid roof, is not necessarily
a sudden, unheralded event, such as one might antici-
pate from a cursory consideration of the problem. It is
clear that the action of the . moments cannot destroy the
roof without revolving in a degree the elements into
which the roof is broken, and any revolution inevitably
binds these elements against one another so that they
are less able to fall. Either a recession of -the ribs or-
a further demolition of the revolving elements must take
place or the roof will not fall. One form of demolition
which frequently occurs in shallow workings is vertical
shear along the cracks already made by the bending-
moment stresses. But horizontal shears may make it
possible for the roof masses to revolve and yet fit the
space they occupied by a counter revolution of the
strata past each other. Or.again, the whole mass may
be broken up by the rubbing of the opposing faces of the
elements as they try to fall.

It is this last action which is in evidence in coal
brought down by a shot when it is broken considerably

in falling, and that vertical shear is not an important
cause of the fall of coal is shown by the fact that there
is a distinct tendency for the coal to roll away from
the side ribs.

It is necessary now to consider the plate structure in
which the roof is considered as a vast plate, a monolith
in itself but resting without adhesion on'its. supports.
Whenever there is a mined area the roof is depressed,
and being elastic it tends to rise on the surrounding
supports, resting its weight on the edges of the sur-
rounding ribs of the excavation. This area of quasi-
elevation is followed by another area of depression
surrounding the central depression and the area
of quasi-elevation. Thus the roof plate is bent into a
series of waves around the central area of disturbance
just as the surface of the water is rippled round the
point where a stone has fallen and disturbed its
equilibrium. (See fig. 11.)

Of course, the elevations are only relative, not actual,
and naturally, like all undulations, as they recede from
the point of disturbance they die down. But it is essen-
tial to remember that while the holoid structure is to a
large extent a closed force chain, this is not nearly so
true of the plate, the stresses in which are less localised
and circumscribed. This structure we may dub as
cumoid (from taa, a wave). The remarkable
feature about such a structure is that it develops points
of great stress far away from the disturbing cause, and
it may break over the pillar instead of in the opening.

It is the peculiarity of the cumoid structure that the
stresses it involves may be greater farther from the point
of disturbance than at some nearer point. But, like the
holoid structure and the pyoid, it puts the greater burden
on the pillar’s edge. The centre of the pillar between
two large open spaces may be relieved from much of the
normal pressure because of the bending of the cumoid
roof over the pillar. (See fig. 13.)

There is some evidence that in actual operations in
some sections of the country the roof soon breaks by
horizontal shear .into two or more separa te cumoid struc-
tures, of which, of course, one is free of external load,
while the others, though below other cumoids, may or
may not be loaded. If the stiffness of the upper
cumoid, -or cumoids, exceeds that of the lower, the load-
ing may be relieved from the open spaces, and the upper
cumoids may restrain the lateral, and therefore the
vertical movement of the lower cumoids, ‘ thus adding to
their resistive strength. The late F. C. Keighley called
attention to. the fact that when the lower roof broke or
was preparing to break in the mined spaces of the
Connellsville region, it frequently weakened the lower
roof in the rooms and headings near by, despite the

Cumoid

Semiho/oid^

Fl 6.9

C urr/mri

FIG.12

Cumoid

FI6.10



Area of
^depression

Cumoid

’ /TensionHember

/Area of (hast- elevation
dtrea of Excavation

Fl6.il

Stiff Cumoid

Weak Cumoid'

strong support afforded by large pillars. This caused
in the narrow places many falls, which had to be loaded
out. It Would seem, therefore, that the breaking of the
lower roof or its initial stressing tears the lower roof
from the upper and from the ribs, converting it into a
cumoid structure which is too weak to stand the strains
to which it is exposed. In some cases, however, these
primary failures may be due to substitution of a pyoid
for a holoid structure. For it must not be forgotten
that where the bottom, ribs, and roof are one, and
indivisible, the floor is an element of strength, and pre-
vents the roof from breaking. Just as the lower flange
in a rail helps the ball of the rail to support the weight,-