May 25, 1917.

THE COLLIERY GUARDIAN.

989

SUBSIDENCE RESULTING FROM
MINING.*

By L. A. Young and H. H. Stoek.

{Continued from page 947.)

THEORIES OF SUBSIDENCE.

In order to study the reactions which may exist in
the rocks overlying a mineral deposit, it will he
necessary to make certain assumptions in order to
arrive at some definite conclusions. For example, it
must be assumed that the rock is uniformly of a
known strength, that it is free from structural weak-
nesses, and that it exists in masses or beds whose
extent, thickness, depth, and dip are known.

The principles of mechanics may be applied to
various types of mine openings, notably:—(1) The
long, narrow excavation which may be driven through
massive or bedded rocks, or along the strike or the
dip of bedded rocks, as tunnels, drifts, cross cuts, and
entries. (2) Excavations of greater width, as rooms
or stopes. (3) Excavations of great lateral extent, as
those of a longwall coal mine, or sections of a pillar-
and-room mine after the pillars have been drawn. In
these various types of openings the fact must be recog-
nised that maximum pressure may not always be due
to a thrust acting vertically downward.

In order to simplify the problem, it may be sug-
gested that the rock and mineral overlying and sur-
rounding the excavation be considered as forming one
of the following:—(1) A beam of rock lying horizon-
tally or inclined and extending from pillar to pillar
or column to column; (2) a cantilever supported by a
pier of rock or mineral; (3) an arch or series of arches
of equal or unequal spans ; (4) a column or pier, either
vertical or inclined, supporting (1), (2), or (3); (5) a
dome of the earth’s crust.

It should be noted further that when the roof is con-
sidered as acting as a beam, it may be supported by
piers of mineral, of non-coherent filling, of timber, or
of masonry, resting upon a more or less yielding floor.
With these explanatory statements, the various
theories of subsidence that have been formulated will
be considered.

Belgian-French Theories.

Belgian engineers were among the first to make a
scientific study of earth movements due to mining
operations. In 1825 a Commission investigating the
cause of surface cracks about the city of Liege,
expressed the opinion that a distance of 300 ft.
between the mine workings and the surface is more
than sufficient to protect the surface. Further dis-
turbance of the surface raised the same questions in
1839. Another Commission of mining engineers con-
cluded that there would be no danger to buildings or
wells from mining operations at a depth of 300 ft.

Although credit for formulating the first theory of
subsidence is usually given to the Belgian engineer,
J. Gonot, it is claimed by L. Thiriart that the funda-
mental idea of the theory of the normal was first pre-
sented by the French engineer, Toillez, in 1838. Gonot
studied surface subsidence in the vicinity of Liege in
1839, and formulated a theory which was published in
1858. He claimed that following the removal of coal
the overlying strata would sink, and the angle of frac-
ture would be perpendicular to the plane of the coal
bed. (Fig. 6.) This theory was later referred to as
the “ law of the normal.” Mining operators in
general and many engineers criticised this theory, and,
while many later writers accepted the principle as it
applied to horizontal and slightly dipping beds,
various qualifications were suggested in regard to the
angle of fracture of steeply inclined beds. Gonot also
held that the break extends through to the surface,
irrespective of the depth of mining. He based this
theory on observations he had made on subsidence at
Liege. The Belgian engineer, Rucloux, who was
appointed with Wellekens to investigate subsidence
about Liege in 1858, called attention to the fact that
Gonot’s theory undoubtedly could not be applied to
vertical and highly - inclined beds. While many
criticisms were offered, no new theory was presented.
The Commission held that the observed facts were
sufficient to establish the principle that with solid beds
of an ordinary thickness and at moderate depths
exploitation by contiguous openings and successive
fillings up to a considerable extent may be made with-
out affecting the surface. Where the depths are slight,
or when for one reason or another the beds lose their
solidity, subsidence may be prevented by preserving
pillars. The subsidences which are produced on
account of the underground work generally follow
vertical lines, but may deviate from these lines accord-
ing to the direction of the beds, more often toward
the lower side, and often also toward the upper side.

In 1868 four engineers were commissioned by the
Prussian Government to collect information on the
question of the “ influence that mine workings may
have on surface building ” in the coal fields of various
countries. They found that at that time the majority
of Belgian engineers believed that when the coal is
entirely removed the most careful packing gives no
guarantee against damage to surface building; that
the packing only lessens the sinking; and that the sur-
face may be protected by leaving pillars. In order to
make this method effective, only half the area of the
coal seams must be removed.

In 1871 the Belgian engineer, G. Dumont, who had
been appointed to make an investigation of conditions
in and about Liege, made a careful study of the pro-
blem, and submitted a report, in which he supported
the fundamental idea of the “ law of the normal,” but
limited its applicability to beds dipping not more than
68 degs. from the horizontal. This conclusion was
based in part upon upwards of 1,000 levels at various
parts of the town. He called attention to the direc-
tion and amount of the forces acting on the block of
rock overlying the excavation. The broken p:eces

* From University of Illinois Engineering Experiment
Station Bulletin No. 91.

must fall into the excavation, and on highly-inclined
seams, according to Gonot’s theory, the masses of
broken rock would have to move toward the excava-
tion on an angle less than the sliding angle. If a-b,
in fig. 7, represents the weight of the rock A-B, and
this force is resolved into the forces a-d and a-c, it is
evident that, as the bed becomes steeper, the force
corresponding to a-d will become less, and the force
corresponding to a-c greater. The tendency, then, will
be to create a cavity vertically above the excavation,
rather than in a direction perpendicular to the plane
of the bed.

Dumont held that the inclination of the strata
lessens the depth of the subsidence, but increases the
area damaged. Timbering hinders the beds forming
the roof of a seam from breaking, and therefore pre-
vents the increase in their volume, which takes place
when they break. It thus increases rather than
diminishes the subsidence at the surface.

The period during which the movement of the sur-
face may continue is uncertain. In Belgium it
extends generally over 10 to 12 years, but in certain
instances has been known to continue 20 and even 50
years. The draining of old workings or the flooding
of a mine may bring about fresh movements a long
time after the original movement has ceased.

Fig. 6.—Diagram Illustrating

the Law of the Normal.

Vertical.

HorizpnUil

Fig. 8.—Line of Break
between Normal and

Fig. 7.—Forces acting on Rock
in an Inclined Plane.

Callon supported Gonot’s theory, but with some
reservations. He believed that when the coal bed is
overlaid with unconformable beds, the angle of frac-
ture will extend through each bed perpendicular to its
plane of bedding. He held that the amount of sur-
face subsidence would depend on the compressibility of
the material which fell into the excavation. In hard
rocks a cavity narrowing upwards would be formed,
while in soft rocks the cavity would be funnel-shaped.

The Colliery Owners’ Association of Liege published
a reply to Dumont in 1875. The validity of Gonot’s
theory for beds of low dip was admitted, but his claim
that the fracture would be normal to highly-inclined
seams was disputed. They argued that the fracture
over the workings would take place in a series of
breaks approximately perpendicular to the bedding
plane of each stratum, but that the force of gravity
would cause the material to fall from the outcrop side
of the excavation, causing the line of fracture to lie
between the vertical and the perpendicular to the
vein; while on the lower side of the excavation, each
bed would tend to support the bed above, and there
would be an overhanging of slabs of rock toward the
excavation. Thus the line of fracture would be
between the vertical and the normal to the bedding
planes. (Fig. 8.) They also called attention to
Coulomb’s measurement of the angle of fracture by
crushing. The combination of this force producing
crushing with that tending to break the bed by bend-
ing induces fracture along a line intermediate between
the two directions, and such line goes further from the
normal as the inclination of the strata increases. On
the whole, the Colliery Owners’ Association thought
the Dumont theory was unsatisfactory, and often of
no practical use, and that the only rule to follow was
the examination of the special facts in each particular
case.

Haton de la Goupilliere (1884) held views similar to
those of Callon. , He pointed out the effect of the
fallen material, which tends to check subsidence, and,
-in fact, may stop it at a certain level. With longwall
mining and filling he thought the movement would be
almost independent of the depth. He held that it
would be impossible to have the “ law of the normal ”
completely verified in practice.

The continued subsidence of the surface at Liege and
the disagreement among engineers as to the theories
of subsidence induced H. Fayol to make observations
of elevations at mines and to conduct laboratory
experiments. He first summarised the contradictory
opinions of the time as follow: —

(1)	Upon the extension of the movement upwards:
(a) The movement is transmitted to the surface what-
ever may be the depth'of the workings; (b) the sur-
face is not affected when the workings exceed a cer-
tain depth.

(2)	Upon the amplitude of the movements: (a) Sub-
sidence extends to the surface without sensible dimi-
nution ; (b) movements become more and more feeble
as they extend upwards.

(3)	' Upon the relative positions of the surface sub-
sidence and of the mining excavation: (a) Subsidence
always takes place vertically above the workings; (b)
subsidence is limited to an area bounded by lines
drawn from the perimeter of the workings and perpen-

dicular to the beds; (c) subsidence cannot be referred
to the excavation either by vertical lines or lines
normal to the beds, but only by lines drawn at an angle
of 45 degs. to the horizon, by the angle of repose of the
ground, or by some other similar angle.

(4)	Upon the influence of gobbing: (a,) The use of
packing protects the surface effectually; (b) packing
simply reduces the effect of subsidence; (c) subsidence
is greater with stowing than without it.

Fayol conducted a long series of investigations and
experiments, and came to the conclusion that the move-
ments of the ground are limited by a kind of dome,
which has for its base the area of the excavation, and
that their amplitude diminishes by degrees as they
extend further away from the centre of the area. This
rule agrees with all the facts observed; absence of sub-
sidence, more or less important subsidences, move-
ments limited to the vertical above the perimeter of
the excavations, those limited to the normal or to
other inclinations, and so on. It has the disadvantage
of being indefinite; but in a question which embraces
so many elements, many of which are unknown or not
well known, such as the nature of the rocks, the thick-
ness of the beds, irregularities in geological structure,
the action of water, etc., we cannot hope to arrive at
absolutely accurate formulse.

According to Fayol, the disturbance of the strata is
greatest over the centre of the area excavated, and it
diminishes in amount toward the perimeter of the
excavated area. As the vertical distance
above the excavation increases, the amount
of the movement decreases, and, if the
workings are at great depth, there will be
a depth beyond which the movement will
cease. When graphically represented, the
limits of the movement are depicted by a
dome; outside of this dome there can be no
disturbance whatever. However, Fayol
called attention to the possibility of move-
ment if there should be a series of these
domes in close proximity to each other, and
to the effect of dip, rock structure, etc.,
upon the practical application of this
theory. As a result of his experiments and
observations, he concluded :

(1) If excavations were stowed in a
thoroughly tight and efficient manner with
incompressible materials, there would be
no subsidence, but ordinary stowing is not
done under these conditions, because the
materials employed are all - more or less
compressible, and the excavations are
never perfectly filled up. When the
roof settles, the stowing resists feebly at first, after
which the resistance rapidly increases, and finally
arrests the downward movement.

(2) The amplitude of the subsidence diminishes in
proportion to the depth of the workings below the sur-
face, the diminution being proportional to the increase
of depth.

Leon Thiriart, in 1912, directed attention to the
theory of Banneux, and which he called the “ law of
the tangent,” which resembles that of Hausse. The
bending moment is considered for each bed succes-
sively, beginning with the one immediately overlying
the coal. By elaborate calculation-; based on observa-
tions of subsidence, formulae are derived by which a
table showing the angle of break for various dips has
been compiled. (To be

MINING INDUSTRY AND MILITARY SERVICE.

The managing director of a colliery with an output of
160,000 tons per annum came before the West Glamorgan
appeal tribunal at Swansea, the military representative sub-
mitting that he was not indispensable. It was stated, on
his behalf, that new electrical plant was being installed,
and it could not be proceeded with unless he were retained.
The tribunal adjourned their decision.

The Pontypool tribunal has declined to continue its
sittings to hear cases of married men, and takes this action
as a protest against the failure of the Government to “comb
out” single men from the collieries, from controlled works,
and Government departments. Communication was made
to the War Office, but no reply having been received
beyond an official acknowledgment of the letter, the
members, with the exception of the chairman, vacated their
seats on Friday of last week. One of them, Mr. Bythway,
referred to the action of other local tribunals—Swansea and
Penarth—in adjourning their proceedings because single
men were sheltered at the expense of married, and said that
in the Eastern Valleys, and particularly at the northern
end, they could find hundreds of single young men who
should be dealt with before Pontypool tribunal was asked
to break up homes and businesses, and to send into the
Army men who were not fit for general service. With
great reluctance, he said, that tribunal had sent married
men into the Army, breaking up their homes; and now they
were asked to send more married men. Another speaker
stated that they knew in the district married men employed
at the collieries and controlled works who could scarcely
get enough money to keep their homes going; that, in fact,
the Miners’ Federation had recently made a grant to some
of the married men because they had lost so much time.
This being so, quite a large number of the active young
men could be taken into the Army without any decrease in
the output. When married men’s cases were called on,
Mr. Bythway said he should withdraw as a protest, and he
invited his colleagues to follow him—which they did. The
chairman announced that he could not proceed without a
quorum; and added that the action was a protest against
the failure of the Government to call up single men.

At Blyth, Mr. Storey, of the Bedlington Coal Company
Limited, appealed on behalf of a staithsman, aged 41 years,
and classed Bl. He stated that the company had already
lost one staithsman, and that it had all along been under-
stood that no more would be taken. There were three
staithsmen, but two were over military age. The military
representative replied that it was their duty to get all avail-
able men into the Army whose services at home could be
dispensed with. He suggested that the various collieries
shipping at Blyth might co-operate, and have the whole of
the work done with fewer men. Mr. Storey remarked that,
under present circumstances, the conference suggested
would have no beneficial results. Exemption for two
months was granted.