36
Int. J, Rock Mech. Min. Sci. Vol. 3, pp. 129-153. Pergamon Press Ltd. 1966. Printed in Great Britain SUBLEVEL CAVING* I. JANELIDand R. KvhPm Department of Mining and Mine Surveying, Royal Institute of Technology, Stockholm, Sweden (Received 1 November 1965) A~traet--The following article contains a summary of the results obtained by theoretical calculations, model experiments and large-scale tests concerned with sublevel caving problems. 1. PRINCIPLES AND APPLICATION OF SUBLEVEL CAVING IN METALLIFEROUS MINING THERE is a wide selection of various underground mining methods which can be adapted to the local conditions and to the particular requirements of the orebody concerned and of the surrounding areas. If optimum results as regards production are to be achieved, a number of interrelated problems arise. These must normally be solved by research and development in a certain sequence if they are to be fitted into a joint process. In the area of mining engineering and of most other industries one certain technical detail or detailed process may be of decisive importance for the whole subsequent structure and organization. We shall therefore first of all give a list of details and components which constitute a portion of the conditions of metalliferous mining by present-day mining methods. Table 1 shows diagrammatically the plan which we have followed in principle in our research and development work for a number of years. One must never lose sight of the influence which one certain detail or individual process may have for all subsequent operations. TABLE 1. LIST OF RESEARCH AND DEVELOPMENT PROJECTS IN HAND AT PRESENT Development project Examples Operation, active factors, etc. Technical details Drill bits, rock drills, detonators, A.N.F.O. explosive Drilling, blasting Drifting, loading, haulage Development workings, sublevel caving, backfilling methods Cut-off grade, loading limit Ore losses, admixture of barren rock Cleaning, dressing, planning, organization, capital investment Profitable production unit Simple operations Combined operations Ore mining Factors which affect the results Result * This work has been carried out within the framework of the programme Mine Research of the Swedish Mining Association. The research problems were investigated at the Mining Department of the Royal Institute of Technology, Stockholm with the collaboration of various Swedish mining companies, especially LKAB Kiruna. 129 I

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Page 1: Sublevel Caving Paper

Int. J, Rock Mech. Min. Sci. Vol. 3, pp. 129-153. Pergamon Press Ltd. 1966. Printed in Great Britain

SUBLEVEL CAVING* I. JANELID and R. KvhPm

Department of Mining and Mine Surveying, Royal Institute of Technology, Stockholm, Sweden

(Received 1 November 1965)

A~traet--The following article contains a summary of the results obtained by theoretical calculations, model experiments and large-scale tests concerned with sublevel caving problems.

1. PRINCIPLES AND APPLICATION OF SUBLEVEL CAVING IN METALLIFEROUS MINING

THERE is a wide selection of various underground mining methods which can be adapted to the local conditions and to the particular requirements of the orebody concerned and of the surrounding areas. If optimum results as regards production are to be achieved, a number of interrelated problems arise. These must normally be solved by research and development in a certain sequence if they are to be fitted into a joint process.

In the area of mining engineering and of most other industries one certain technical detail or detailed process may be of decisive importance for the whole subsequent structure and organization. We shall therefore first of all give a list of details and components which constitute a portion of the conditions of metalliferous mining by present-day mining methods.

Table 1 shows diagrammatically the plan which we have followed in principle in our research and development work for a number of years. One must never lose sight of the influence which one certain detail or individual process may have for all subsequent operations.

TABLE 1. LIST OF RESEARCH AND DEVELOPMENT PROJECTS IN HAND AT PRESENT

Development project Examples Operation, active factors, etc.

Technical details Drill bits, rock drills, detonators, A.N.F.O. explosive Drilling, blasting Drifting, loading, haulage Development workings, sublevel caving, backfilling methods Cut-off grade, loading limit Ore losses, admixture of barren rock Cleaning, dressing, planning, organization, capital investment Profitable production unit

Simple operations Combined operations Ore mining

Factors which affect the results

Result

* This work has been carried out within the framework of the programme Mine Research of the Swedish Mining Association. The research problems were investigated at the Mining Department of the Royal Institute of Technology, Stockholm with the collaboration of various Swedish mining companies, especially LKAB Kiruna.

129 I

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130 I. JANEL1D AND R. KVAPIL

One detail, quite minute in itself, may become decisive for a whole row of subsequent operations. The T.C. drill bit, for example, has been a direct decisive factor for the following functional relations: rock drills--long straight holes--mining methods. Another such detail is the short-delay method of firing which has influenced the following processes: Large rounds, problems of large lumps, ground vibrations, stope organization, etc. The subjects 'simple operations', 'combined operations', 'metalliferous mining' etc. can be discussed on similar lines.

The research and development work in this area will shortly have reached a point where long and nearly straight holes can be drilled in any desired direction. It will be possible for large rounds to be charged and fired with adequate regard to safety. The driving of rise is now a safe and highly mechanized operation and in the very near future all tunnelling or drifting will probably be extensively mechanized, in some cases with machines drilling out the complete section.

The operations mentioned above are, however, only a means to an end when more or less irregular ore bodies are to be mined which used to be done by conventional methods applying drilling, blasting and loading in suitable workings.

The diagrammatic scheme of the table indicates the necessity of taking into consideration in mine planning such items as ore losses, dilution by barren rock, cut-off grade, sorting etc. if a profitable production is to be achieved.

Underground mining in Sweden produces annually about 40 million tonnes of ore and rock, the principal mining systems being sublevel caving, sublevel stoping, block caving, open stopes and pillars, and shrinkage stoping. As far as quantity is concerned, sublevel caving is now the most important method with about 25 million tonnes per annum out of which Kiruna alone accounts for 19 million tonnes per annum.

Past experience has shown that metalliferous mining in any of these methods is very advantageous from the point of view of mechanization when long holes are drilled. Long- hole mining can be divided into two main groups, i.e. mining systems without backfilling when the ore conditions and the rock strength permit, and caving systems when a system without backfilling is impracticable. The second group with its main representative, the sublevel caving method, is very complicated as far as control is concerned, but it has many advantages as regards safety and mechanization.

These possibilities of development and future prospects were borne in mind when systematic theoretical calculations were carried out during the last few years, together with model and large-scale tests, in order to establish the factors which determine or influence especially two items, i.e. the ore yield and the admixture of barren rock. If these two prob- lems can be solved satisfactorily, most orebodies of vertical extent can be mined very effectively with respect to safety, mechanization and capacity by the new modified form of sublevel caving which will be described in this article.

Before we proceed to the theoretical part dealing with the gravity flow of the blasted material, the location of the sublevel headings, drilling, loading, etc. we shall describe the sublevel caving operations in Sweden at the present stage of development based on a number of illustrations.

Figure 1 shows the location of the sublevet headings and the principal operations required consisting of drifting, drilling of the sublevel holes and ore loading.

Drifting is a fairly substantial part of sublevel caving and whilst in earlier times pre- ference was given to air-leg mounted rock drills, the mines are now changing over to various types of drill rigs. In smaller headings of say 2.2 m × 2.5 m one of the rigs used is the

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SUBLEVEL CAVING 131

" L

~ - ~ <)

:iii

i~! !i: 'i

ii,ili i~

i::z i i11. ~;I-

ii!ii :!ii, i i,il

ii.i~ i ~li,:i I ! !:

i i

i I i iil ii I !~i I!

i ! i

[i: i

I l l II 'i

FIG. 1. Diagrammatic plan of sublevel caving in Kiruna: l - -dr i f t ing ; 2 - - r ing drilling (roof of slice); 3---charging of explosive; 4 - -o re loading.

so-called Tunnler 200 (Fig. 2) with from 1 to 3 drills on a chain-feed cradle and in larger headings drill rigs with hydraulically operated feed cradles may be used.

Most production drilling, i.e. the sublevel drilling, is now done by hydraulically operated drill rigs with one or two rock drills, operated by one man. These rigs ensure a high capacity and also a sufficiently accurate hole direction which is of great importance as we shall see later. Figure 3 shows a drill rig type Simba 11 on rails designed for medium-size headings and with one hydraulically operated set. The Kiruna mine with its larger headings of 3.5 m x 5 m uses drill rigs on pneumatic tyres with two rock drills, type Simba 22, as shown in Fig. 4. This rig is operated by one man and has a capacity of 255 m drilled per shift which corresponds to 2400 tonnes ore per man and shift. The explosive used to blast

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132 I. JANEL1D AND R. KVAPIL

in the sublevel is of the ammonium nitrate or slurry type. The charging capacity of one charging set (Fig. 5) for A.N. explosive is 1000 kg/hr. Dynamite cartridges can also be charged in long holes by means of a charging robot illustrated in Fig. 6 which has a capacity of 400-800 kg/hr.

The ore is loaded from large sublevel headings in mines like Kiruna by JOy loaders 18 HR and 19 HR into shuttle cars or into so-called Kiruna dumpcars with diesel drive (see Fig. 7). Shovel loaders of various types are also being used for direct transport into an ore chute. Figure 8 shows such a 'Scoopmobil' in operation.

Most of the loading in small drifts is done by rocker shovels in combination with various haulage cars. With a compressed-air-driven car type U3N of 2 m a capacity (see Fig. 9) in combination with the shovel loader type LM 65H one man has reached an output of 300 tonnes per shift over a haulage distance of 50 m.

In several mines the loading and haulage operations in narrow headings are carried out by a trackless method as dump cars type T2G (Auto-Loader) of 0.75 m a capacity are used (see Fig. 10).

This brief description of the mining methods and of the mechanical equipment used indicates that mechanization as well as a simplification of the whole process is feasible.

If we possess exact and detailed information about the gravity flow of the blasted rock in the sublevel and if we carry out an exact planning and control especially of the drilling and loading operations, we can turn the modified sublevel caving method into an effective, cheap and above all a safe mining method.

2. F U N D A M E N T A L LAWS F O R THE GRAVITY F L O W OF GR ANULAR MATER IAL

A most important factor in sublevel caving is the gravity flow of the lumpy material, i.e. of the blasted ore and of the barren rock.

The basic deductions from the laws of gravity flow can be explained most simply by the motion of granular material in a bunker.

In the case of free discharge through the outlet at the bottom of the bunker a certain zone of the bunker contents will be set in motion. This zone within which the granular material is moving is called the active zone A. The remaining part of the bunker contents is immobile and forms a passive zone P (see Fig. I l).

I'1: : ! : fl 1/ IiIi 1 A

1

F~c. 11. Gravity flow of granular material.

The movement of the particles in the active zone is effected by gravity so that we can designate the active zone as the gravity flow of the granular material. The centre line of the gravity flow is vertical in case the conditions of the granular material remain unchanged.

The motion of the particles in a gravity flow obeys certain laws. Let us consider a certain point N which lies at the height hn, above the vertical axis

of the discharge opening (see Fig. 12). For the sake of clarity, the point N lies in the hori- zontal plane formed by the interface n of materials of different colour.

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.-FIG. 2. ‘Tunnler 200’.

facing page 132 KM.

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FIG. 3. Drill rig ‘Simba It’ on rails with 2 hydraulically positioned feed screw cradles.

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FIG. 4. Drill rig ‘Simba 22’ on pneumatic tyres with 2 hydraulically positioned feed screw cradles.

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FIG

. 5.

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rm.

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. 6.

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.

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FIG

. 7.

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ith JOY

18 H

R

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a

KIRUNA

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.

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FIG. 9. Transport by U3N car of 2 rn:j capacity driven by compressed air.

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FIG. 10. Loading and haulage into an ore chute by dumpcar (‘Auto-loader’) T2G of 0.75 n9 capacity.

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SUBLEVEL CAVING 133

When the outlet is opened the material begins to flow and the point N drops towards the discharge. The original straight plane of the interface n deflects downwards due to the discharge of the material (see Fig. 13).

At the moment when point N reaches the plane of the discharge opening, a certain amount (volume VN) of granular material has left the bunker (see Fig. 14). This volume VN did not run off at random but came from a certain zone which in form looks very similar to an elongated ellipsoid of revolution. For this reason this zone is called an ellipsoid of motion. In Fig. 15(b) this ellipsoid of motion is marked Eiv. We can distinguish between its semi-major axis aN and its semi-minor axis bN.

/:..:/:~....::/[~,, ~ .:,-/. . . . . .

FIG. 12. Run-off process. FIG. 13. Run-off process. FIG. 14. Run-off process.

......... EN '~N . . . . . . . . .

_Jl . . .

F1G. 15. Zones of motion during run-off of granular material.

The volume of the ellipsoid of motion Eiv approximately corresponds to that of the discharged material VN. We have thus the relationship of

EN ~, VN. (1)

The plane of the interface n, which was originally horizontal, deflects downwards to approach the limit marked in Fig. 15(a) with the points 1 and 2 (see also Fig. 14). The funnel-shaped deflexion of the boundary n forms a cone Klv as indicated in Fig. 15(c). The circular base of the cone Klv has the diameter of line 12, the height of the cone is hN and its apex corresponds to the point N in the discharge opening [see Figs. 15(a)and 15(c)]. The volume of the discharge cone KN approximately corresponds to the volume V / of the discharged material and, of course, also to the volume of the ellipsoid of motion E~v.

The relationship between the volumes of the ellipsoid of motion Ex, of the discharge cone KN and the volume of material discharged V/can thus be described by

Ely ~ Ku ~ Vx. (2)

If the volume V~v and the height of the ellipsoid of motion are known, the semi-minor axis biv of Fig. 15(b) can be calculated from the formula

/IN

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134 I. JANELID AND R. K V A P I L

The characteristics of the shape of the ellipsoid of motion are determined by its eccen- tricity ~a- where

1 eU ~- - x/(a~ -- b2N). ( 4 )

aN

The terms ax and b2v in equation (4) correspond to those of Fig. 15(b). The Characteristics of the shape of the ellipsoid of motion, i.e. its eccentricity, are not

constant, but depend very much on the particle size of the material. Smaller particles of material correspond to a slimmer ellipsoid of motion and to a greater eccentricity. Larger particles extend the ellipsoid in width and its eccentricity becomes less. This is shown schematically in Figs. 16(a, b, c).

0 l,~0 ! ~

FIG. 16 (a-c). Form of ellipsoid of motion as a function of particle size.

For the same material the eccentricity depends on a number of factors such as the size of the discharge opening (enlargement of the discharge opening increases the eccentricity), the height of the ellipsoid of motion (a greater height increases the eccentricity), the velocity of discharge (a faster rate of discharge increases the eccentricity) etc.

If, for a certain material, the eccentricity E~v and the height h2v under certain conditions are known, we can calculate the semi-minor axis from the following formula:

hN b~ = 5 - V(1 - ~ ) . (5)

The run-off of granular material (without cohesion) causes no cavity due to the ellipsoid of motion and the surrounding material subsides evenly. This loosens the material some- what. This process also follows a regular pattern, especially in that it takes place in a zone resembling an ellipsoid of revolution. This ellipsoid is characterized by its size reaching a certain limit as the material runs off from the ellipsoid of motion E2v. Outside this limit which is formed by the outer contours of this ellipsoid the granular material remains stationary. This ellipsoid of motion is therefore called the limit ellipsoid Ea as indicated in Fig. 17.

i

FIG. 17. T h e e l l ipso id o f m o t i o n E~v a n d i t s l imi t e l l i p so id Ec.

Let us now assume that the limit ellipsoid Ea resembles the ellipsoid of motion/iN.

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SUBLEVEL CAVING 135

The loosening of the granular material brought about in the limit ellipsoid can be described by the loosening factor a where

Ec a - - E o - - E l y (6)

and Ec and EN are the volumes of the corresponding ellipsoids. The value of the loosening factor for broken material varies from 1.066 to 1.100. The volume of the limit ellipsoid Ec (caused by the loosening process) stands in a certain

ratio to the volume of the ellipsoid E~v. This ratio can be expressed by the formula

Ec ~ EN (7) a - - I

where ~ is the loosening factor from equation (6). Most of the granular materials tend towards the lower figure of 1.066 for the loosening

factor. If we apply this figure to equation (7) we obtain

Eo ~ 15 EN. (8)

This means that the volume of the limit ellipsoid Eo is about 15 times greater than the volume of the ellipsoid of motion EN.

The approximate height ho of the limit ellipsoid can be taken as

ho ~ 2"5 h~v. (9)

The contours of the limit ellipsoid form the boundary between the zone of motion (inside the limit ellipsoid) and the remaining stationary material (outside the limit ellipsoid). Should the discharge of the material be stopped, the loosening will gradually become less on account of the progressive consolidation of the granular material.

The limit ellipsoid continues to develop in proportion to the continued discharge of the material from the outlet. This brings about the kinetic flow. We are mainly concerned with the problems relating to the lower part of the kinetic flow over a certain height hiv. It is important to establish here the width d of the kinetic flow at a certain height hN at a moment when the material from the ellipsoid E~v (with the height h~v) has already run off through the outlet. The schedule for the calculation can be seen in Fig. 18.

The width of the kinetic flow at the height hN (at the moment in question) is given by the points of intersection 1 and 2 in which the contours of the limit ellipsoid intersect the originally horizontal plane of the interface n [see Figs. 14 and 15(a) and (c)]. The points 1 and 2 at the same time represent the edge of the base of the discharge cone Klv [see Fig. 15(c)]. Figure 18 indicates that d = line ]'2.

p0

• -~ ..-..-- ~.~ ......

FIG. 18. Width d of gravity flow at certain height above run-off opening.

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136 1. J A N E L I D A N D R . K V A P I L

The relationship between EN, K N and E a enables us to calculate the width of the kinetic flow d -- 2r for the height h~v from the following formula

r ~ ~ / [ ( h c - - hN) hN(1 - - ~2)]. (10)

The terms h~ and h~v in formula (10) correspond to those in Figs. 17 and 18. The path of the particles in a gravity flow is not straight but a little curved as drawn

schematically in Fig. 19. The particles along the centre line of the kinetic flow are, however, an exception. The curvature of the paths is, however, so little that we can regard them asstraight lines.

I

/ i ' ,' l

FIr. 19. Trajectory of particles in gravity flow.

The velocity of travel of the particles in the gravity flow is not uniform, but is distributed as follows:

The velocity is greater at shorter distances of the particle from the discharge opening and from the centre line of the gravity flow. (The rule is that the velocity of a particle in the centre line of the flow at a certain height h above the opening is inversely proportional to the ratio h /e where e is the diameter or the width of the discharge opening.)

Inversely, the velocity of travel of a particle is reduced as the distance from the discharge opening and from the centre line of the gravity flow increases. There is no motion at the boundary of the limit ellipsoid Ea.

This pattern of the velocity distribution can be clearly seen in the individual phases of a tested model shown in Fig. 20.

~ Z

- - ,-w £¢,

E~ ~vr

~vf

......... ~Y

FI~. 21. Ellipsoid of like velocity Ev~.

This model was used to produce a constant gr~tvlty flow of the granular material which was then photographed at various times of exposure. The relation between the velocity of travel of the particles and the time of exposure makes the moving particles of the model filling appear on the film as lines. An increasing time of exposure allows smaller velocities of

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FIG

. 20

. Z

ones

of

inc

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city

of

mot

ion

in t

he s

ame

grav

ity

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.

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SUBLEVEL CAVING 137

travel of the particles to be recorded on the film. If the time of exposure is shortened, all those particles are practically 'cut off' which have a velocity of travel below that correspond- ing to the ratio between time of exposure and velocity. These particles appear to be motion- less on the photograph. The individual phase of Fig. 20 were obtained at times of exposure of V1 > 1:2 > I:3 . . . . The differing times of exposure make it possible to differentiate between the zones of the different velocities in that each shorter time of exposure determines the zone of the next higher velocity.

For the sake of clarity Fig. 21 shows a summary of the velocity distribution schematically on the basis of a vertical section through the centre line of the limit ellipsoid Ea. The velocity of the particles at any point of the ellipsoid Ea is represented with V1 along the X-axis.

The schematic spatial representation of the velocity distribution of the particles in the ellipsoid E a according to Fig. 21 shows that the velocity is zero on the periphery of the limit ellipsoid E¢. A given velocity such as 1:1 (Fig. 21) describes by its path in the plane Z Y a figure resembling an ellipsoid. In the spatial representation we can talk of an ellipsoid of like velocities which is marked in Fig. 21 as Evl .

Figure 22 shows that a particle at the apex of the ellipsoid has travelled after a certain time from point I to point I ' . This particle has therefore moved in a certain time a certain distance w.

FIG. 22

The original height of the ellipsoid of like velocity Ev has been reduced from h to hi because hi = h -- w (Fig. 22).

As the apex particle moves from I to I ' , all other particles lying at the contours of the ellipsoid of like velocity E v travel with the same velocity, as can be seen when we compare in Fig. 22 the apex particle I, for example, with the particle 1.

During this process the centre of the ellipsoid E v also shifts from O to O1. (It should be noted that the centre O of the ellipsoid does not signify any particular particle, but merely an imaginary point where the semi-major and semi-minor axes of the ellipsoid intersect.) This means that in the same time during which the particles have travelled the distance w, the ellipsoid of like velocity has shrunk by w and its centre has travelled the distance f . According to Fig. 22 an approximate solution can be expressed by

h-- w f = A O - - AO1 ~, h/2 2 - - w/2. (ll)

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138 1. J A N E L I D A N D R. KVAP1L

We can therefore state that the subsidence of the centre O of the ellipsoid of like velocity E v is about equal to half the distance travelled in the same time by the particles at the contours of the ellipsoid E v .

The laws in connexion with the gravity flow of granular materials do not undergo any basic changes even when the gravity flow is prevented for various reasons from developing fully and symmetrically to the vertical axis. Such cases arise, for example, if the discharge opening lies not in the centre of the bunker bottom, but in the side wall. Under such con- ditions the ellipsoid of motion is, figuratively speaking, cut off by the bunker wall. This is illustrated by Fig. 23 where this is indicated diagrammatically. The ellipsoid of motion Ex and the limit ellipsoid Ec are designated in this illustration in the same way as in Fig. 17. The centre line O of the gravity flow (Fig. 23) deviates from the perpendicular by a certain angle r I. This deviation becomes greater as the friction along this wall becomes greater, i.e. the greater the roughness of the wall surface.

As regards the velocity distribution in the gravity flow the statements made earlier apply in the same way for these cases (Fig. 23).

~ -~ E G

FIG. 23. The ellipsoid of motion E~. and its limit ellipsoid E~, when granular material runs off through opening in the vertical bunker wall.

3. GRAVITY FLOW AND DETERMINATION OF THE PARAMETERS IN SUBLEVEL

CAVING The gravity flow of the material in sublevel caving corresponds in principle to the case

of Fig. 23 because the gravity flow in the sublevel caving is, figuratively speaking, cut off by the wall of the slice.

We have here a condition shown diagrammatically in Fig. 24 which represents a vertical section through the slice along the longitudinal axis of the extraction drift.

,I

:v :i::

c~

r///,,~/ / //~/l, ' // " "

FIG. 24. Diagrammatic vertical section through longitudinal axis of extraction drift in sublevel caving.

The legends of Fig. 24 are as follows: H--he ight of extraction drift M--blasted ore G --waste

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S U B L E V E L C A V I N G 139

S - -height of slice V - - b u r d e n

- -gradient of slice, called negative when ct > 90 °, vertical when ct ----- 90 ° and positive when ~ < 90 °.

Other dimensions are indicated in Fig. 25 which shows a diagrammatic view of the slice wall and corresponds to the section along I-I' in Fig. 24.

' ) g "i

i $

. . . . . . . . . . . . .

I_ P IBM_ P j B_3

FIG. 25. Diagrammatic view of the slice wall in the plane of the section I-1' of Fig. 24.

The legends of Fig. 25 are: B - - w i d t h of extraction drift P - -width of pillars between extraction drifts A - -width of slice h~,--thickness of roof.

The other symbols are the same as in Fig. 24. The sublevel caving method is characterized by a gravity flow of lumpy material because

both the blasted ore and the waste may contain large lumps of over 400 mm. To optimize the production of clean ore and to minimize contamination by waste as well

as ore losses, it is necessary to determine the opt imum parameters of the slice. This is mainly a matter of determining the height of slice S, the burden V, the width of

slice A, the slice gradient a, the width B and height H of the extraction drifts and the width P of the pillars between drifts.

The determination of the parameters is closely allied to the laws of gravity flow or, in other words, the correct parameters of the slice should in the opt imum case correspond to the laws of gravity flow.

3.1 Form of gravity flow We are mainly interested in the form of the gravity flow of the broken ore. The form of

the gravity flow over a certain height h' can be expressed in simplified form by the ratio of the outflow width e to the inflow width d (Fig. 26). The gravity flow is narrower (more parallel) as the ratio e/d approximates 1.0. At a ratio e/d ---- 1 the gravity flow is completely parallel. I f the ratio e/d becomes less than 1, the gravity flow is transformed and is reduced at the lower end.

FI~. 26. Inflow width d and outflow width e of gravity flow.

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140 I. JANELID AND R. KVAPIL

The form of the gravity flow depends on many factors and we can regard its form as a function of these factors. As the gravity flow corresponds to the limit ellipsoid we can say that the form of the gravity flow is a function of the eccentricity of the limit ellipsoid, i.e.

e/d - f ( , ) .

The factors which are at work in this function are still concealed in this formulation and it is therefore preferable to state the form of the gravity flow in a simplified symbolic function as

e/d f (K, h, c, l,) (12)

where K -- properties of the lumpy material, including loosening phenomena which can be expressed (in the simplified form) by the particle size

h ~: height of gravity flow c - size of extraction area, here given as the extraction width t, - velocity of travel of material in the gravity flow, given by the extraction velocity.

The effect of the factor K, i.e. of the particle size of the material is characterized by smaller particle sizes resulting in a narrower (more parallel) gravity flow which as they become smaller approaches the ratio e/d -- 1. As the particle size becomes larger, the inflow width d increasingly exceeds the outflow width e and the ratio e/d drops below 1. If we wish to express the effect of the particle size on the eccentricity of the ellipsoid of motion (Fig. 16) we find that the eccentricity is inversely proportional to the particle size.

The height h of the gravity flow has the effect of making the form of the gravity flow more narrow (as regards parallelity) as the height h becomes greater, and vice versa.

The extraction width c has the effect of making the form of the gravity flow more narrow (more parallel) as the extraction width increases.

The effect of the extraction velocity is characterized by a more narrow (parallel) gravity flow at higher extraction velocities, because the latter affect the spread of the loosening process.

In the same plane of section as in Fig. 24 we can represent the gravity flow in sublevel caving with a vertical slice in the way shown diagrammatically in Fig. 27.

.L__L.~~ FIG. 27. Pattern of distribution of zones EN, Et; and KN governing motion in vertical section perpendicular

vertical slice wall.

The symbols EN, Eo, KN, hx and bN are the same as in Fig. 15. The height of the ellipsoid of motion EN can be taken, with a slight simplification, as

twice the slice height, i.e. hN ~ 2 S. The contours of the limit ellipsoid are also the boun- daries for the gravity flow. The width r of the gravity flow at the height hN is given by

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SUBLEVEL CAVING 141

formula (10). As the approximate height of the limit ellipsoid ha ~ 2.5 h~v from formula (9) and as we have assumed that h~v ~ 2 S the width of the gravity flow can be expressed as

r ~ V [ ( 5 s - 2 s ) 2 s (l - ,2)]

where S is the slice height. The unknown quantity is the eccentricity E because this depends mainly on the particle size.

The blasted ore (and also the waste) can be a very complex and variegated mixture of factors, so that it is not possible to state exact figures for the eccentricity of these lumpy materials. The eccentricity is also governed by a number of other factors such as the effect of the particle forms, the mechanical properties of the material of the particles, the effect of moisture content, of the roughness of the walls, of consolidation properties and, in an inverse sense, of the effect of loosening phenomena and external forces. These problems suffer an additional complication in that even a proportion of 5 to 7 per cent of fine material can modify the properties of the lumpy material significantly.

The volume of the ellipsoid of motion depends on the eccentricity. As the eccentricity depends mainly on the particle size, a diagram has been plotted in Fig. 28 which indicates the approximate principal relations between volume V of the ellipsoid of motion, the particle size K and the height h of the ellipsoid of motion. In this diagram the graph (1) applies to fine and the graph (2) to lumpy materials.

When planning a sublevel caving operation we can take in first approximation rough values of the eccentricity for blasted hard ore from the diagram of Fig. 29 as a function of the height hu ~ 2 S. The eccentricity figures read from this diagram can be applied both for the calculation of the width r of the kinetic flow, and for the approximate deter- mination of the semi-minor axis bu of the ellipsoid of motion EN, see Fig. 27. The approxi- mate width of the semi-minor axis can be calculated from equation (5).

The exact values of the eccentricity and, resulting therefrom, of the flow width r and of the semi-minor axis b~v, can only be determined by large-scale tests. These tests can be organized in various ways. One way is that of distributing marked tracers over the plane n (Fig. 27). All that need be done during the test is to establish the volume of ore loaded up to the moment when the tracers have arrived at the extraction drift from point N (Fig. 27) [see also the case in Fig. 15]. Designating this loaded volume of ore as lie we can calculate the semi-minor axis of the ellipsoid of motion from the formula

/ i 2 (13 bu = N/t2_09 ~/tN]

where hiv ~ 2 S corresponds to the symbol in Fig. 27. As the semi-major axis of the ellipsoid of motion a s = hN/2 ~ S, we can calculate the

eccentricity from formula (4). These tests can also be carried out successfully away from a slice. A large-scale test is a good means of determining the exact form of the gravity flow in the plane of the section according to Fig. 27 if the run-off width m is measured at the same time.

Figure 30 illustrates diagrammatically the form of the gravity flow in the plane of the wall of the slice, i.e. in a vertical section along I - l ' in Fig. 27. In principle the condition of the gravity flow corresponds to the case of Fig. 15 and the values for r, bN and E can be determined in accordance with the explanation given to Fig. 27. The same formula and the same diagram can be applied as in Fig. 29 and we can therefore determine in a large-scale test the exact figures of the desired quantities and the run-off width e.

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142 h JANELID AND R. KVAPIL

v (~

FIG. 28. Approximate relation between height h and volume V of ellipsoid of motion.

0 9 9 ,

09"/' ~- - - 0.96 . . . .

095

0 9 3

0 9 2

0 9 0 I0 20 30

h=2S

FIG. 29. Rough approximation of eccentricity.

4 0

FIG. 30. Pattern of distribution of zones E~., E¢: and K,~ governing motion in verti- cal section in plane of vertical slice wall.

The run-off width e (Fig. 30) is an important factor which governs the shape of the gravity flow. In practice the run-offwidth e depends on the extraction width c.

The extraction width c is given by the operating reach of the loader and by the loading system. The gravity flow approaches more closely a parallel form if the operating reach of the loader is wider and the loading system covers the width of the extraction drift more fully.

The extraction width c of a loader is narrower than the width of the extraction drift. I f the loader is always stationed at the same spot, for example, in the middle (Fig. 31) or near the side (Fig. 32) of the extraction drift, the gravity flow will be considerably reduced in the lower regions, the waste will soon arrive in the extraction drift and the relatively small run-off width may easily cause undesirable arching of the lumpy material.

FIG. 3 I. Ore run-off during extraction by loader in middle of extraction drift.

FIG. 32. Ore run-off during extraction by loader along sidewall of extraction drift.

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SUBLEVEL CAVING 143

The theoretically best conditions are created when the operating reach of the loader equals the width of the drift. This can be achieved with a loader of smaller reach by letting the machine deal with the ore in stages across the whole width of the slope in the extraction drift. An advantageous system is that of I, 11I, 1I (Fig. 33) where 1, II, III are the positions of the loader.

Such a loading system ensures that the extraction width c as well as the run-off width e are equal to the drift width B, i.e. c -- e = B. The shape of the gravity flow is good in this case because it approximates a parallel form and because the contact of the ore with the waste being high up prevents the latter from reaching the extraction drift prematurely.

FIG. 33. Ore run-offduring extraction by loader according to the system 1, IIl, il over the full width B of the extraction drift.

The width B of the extraction drift should therefore, not only promote a good shape of the gravity flow, but also induce an even run-off of the lumpy ore. When planning the width of the drift we must therefore take into consideration the particle size of the blasted ore by using the following formula for the approximate width

B > ~,,/[5(5D) z k] (14)

where D = diameter of largest lumps of the blasted ore and k ~ factor of composition of the mixture of lumpy material, determined by means of the nomogram of Fig. 34.

It can be seen from the nomogram that the factor k depends on the percentage of lumps (region I), on the percentage of medium ranges (region II) and on the percentage of fine, damp constituents such as powder- and earth-like constituents, etc. (region IV). The key of the nomogram is indicated in the illustration by dotted arrows.

Correct ore extraction demands, not only an optimum run-off and extraction width, but also a good thickness m of the gravity flow (Fig. 27). The dimension m will, of course, depend on how far the loader can dig into the slope.

If we apply Rankine's theory on the distribution of the trajectories of the maximum principal stresses, we can establish the optimum depth of penetration of the loader into the slope. The trajectories of the principal stresses in the slope (Fig. 35) are inclined against the

90° -- 4' where 4' is the natural angle of repose. The theoretically best depth x vertical by 2

is given by the points I and 2. Point 1 indicates in Fig. 35 the end of the slope and point 2 is given by the intersection between the trajectory of the principal stresses, which originates from the upper edge of the extraction drift (point 3), and the floor level.

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144

IV

15 #0 5

I. JANELID A N D R. KVAPIL

PIG. 34. Nomogram for approximate calculation of factor k.

/1// / / / /1// / / / / / / / / / [ / / / / / / / / / / / / / / / / / / /~// , . .,9 02-~ ~."

I S i G I / l l l / / l l / l l / l l l ~ l / l l f l , ~ i i l l l / l l l i / 7 1 i l i l l l l l l l l l l l / l l l / l " / i / / / / / / l I i l l l l l

I I

FIG. 35. Theoretically best digging depth of loader in ore pile of extraction drift.

In conformity with the legends of Fig. 35 we can calculate the theoretically best depth from the formula

90 <' ¢ x ~ H c o t ¢ - H t a n - . (15)

2

The digging depth xp applied in practice is usually smaller than the theoretically best depth

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SU BLEVEL CAVING 145

x and we should note that the results will be the better, the more the applied digging depth xp of the loader approaches the opt imum depth x [from formula (15)].

3.2 Burden From a theoretical point of view the burden will be governed by many factors. In prin-

ciple we can express the burden by a symbolic function of these factors, bearing in mind

FIo. 36. Schedule of calculation.

that the effect of the individual factors may differ considerably within this function. There is also a certain mutual interference between the individual factors.

The burden V can therefore be written down in the form of the symbolic function

V = f ( K , h, c, v, S, x, m, B, a) (16)

where the first four factors K, h, c and v are the same as in formula (12) and the others are as follows :

S ---- height of slice x ~ digging depth of loader, also with respect to the height of the extraction drift

(Fig. 35) m = run-off width according to Fig. 27 B -- width of extraction drift a = gradient of the slice. The problem is the determination of the opt imum burden V for a certain height of slice S.

The proper burden should in the opt imum case correspond to the gravity flow of the blasted ore in the way shown diagrammatically in Fig. 36.

The opt imum burden (see Fig. 36) for a vertical slice can be calculated approximately from the formula

V _> blv ---- ? ~/(1 - - c 2) (17a)

or, since hN/2 ~ S, from the formula

V -> S V(1 - - ,z). (17b)

An extremely large burden is a disadvantage because this would soon start near the top a considerable contamination by waste which quickly arrives at the extraction drift and may also cause large ore losses. Too small a burden is also bad because this very soon leads to considerable contamination by waste from the sides.

As regards the quantity of pure ore, the greatest theoretically possible amount to be won from a slice is 50 per cent of the total amount of blasted ore. The rest will become mixed with the waste.

K

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146 I. JANELID AND R. KVAPIL

3.3 Height o f slice The height of the slice can also be expressed by a symbolic function of the effective factors

such as S ~ f ( K , h, c, t,, V, x, m, B, P, ct) (18)

where P is the width of the pillars between the extraction drifts (Fig. 25) and the other legends are the same as in formula (16).

The approximate height of a vertical slice can be calculated from the formula

V S ~ (19)

where V is the burden. The optimum height of slice and that of the burden have to meet other additional tech-

nical and economical requirements.

3.4 Location of extraction drifts The problem in locating the extraction drifts is to decide which drift pattern is better,

the checkered arrangement or the vertical arrangement, and what are the best dimensions, especially as regards B, P, A and S.

A good location of the extraction drift depends on the form of the gravity flow and on the chance of mining the ore remnants between the extraction drifts.

The condition of the ore remnants R is shown diagrammatically in Fig. 37 for a vertical pattern and in Fig. 38 for a checkered pattern of drifts.

! R

i i

, 0

FIG. 37. Posi t ion o f ore r emnan t s R with vertical ~arrangement of extract ion drifts.

i

E 2 ~ t t

FIG. 38. Posit ion of ore r emnan t s R with checkered a r rangement of extraction drifts.

When the ore is drawn off at the bot tom extraction drift the material moves fastest along the centre line of a gravity flow which coincides with the axis e f the extraction drift. The difference between the vertical and the checkered arrangement of the extraction drift can be clearly seen from the phases (a)-(b)-(c) in Figs. 39 and Fig. 40.

The third phase of the extraction (phase c) shows that the waste G has already reached the extraction drift in the case of a vertical drift arrangement when it is still far away from the drift in the case of a checkered arrangement, see Fig. 40(c). When the waste has reached the extraction drift, as shown in Fig. 39(c) no more pure ore can be extracted because there is an increasing contamination of ore by waste. Figures 39 and 40 show clearly that this happens earlier with a vertical than with a checkered drift pattern. The checkered arrangement is preferred for these reasons because a great quantity of pure ore can be extracted.

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S U B L E V E L C A V I N G 1 4 7

The approximate height of slice S can, if the burden has been fixed, be calculated from formula (19) and the approximate width of the extraction drift B from the formula (14). The approximate width of the slice (Fig. 25) should be smaller than or at most the same as the width of the gravity flow d (Fig. 30). In conformity with the formula (10) and applying

(a) k~o

: , : i f - t

I

(t~) k ~ o .,5i55

z

I

(c) ~1..o , Jl.,.,

N I i

FIG. 39 (a--c). Ore run-off with vertical arrangement of extraction drifts.

(a) i..,,.1~. 0

1

'" ".'Z~:,."

,J, 4:;i

• i M

i

FIG. 40 (a-c). Ore run-off with checkered arrange- ment of extraction drifts.

the calculations according to Fig. 30 we can calculate roughly the width of the slice from the formula

A -< 2 a / [ ( 5 S - - 2 S ) 2 S ( 1 -- E2)]

where S is the height of slice from the formula (19). The width of the intermediate pillars P (Fig. 25) is then found from

P = A - - B

(20)

where A can be calculated from formula (20) and B from formula (14). Under good conditions for the ore extraction, i.e. adequate width of extraction drift and

ore extraction over the full width of the drift, the relationship between drift width B, inter- mediate pillar width P and the slice width A may be approximately

A ~ B ~ P .

In this case the gravity flow is nearly parallel and its width cannot be much greater than that of the extraction drift. Such a case is illustrated diagrammatically in Fig. 41.

FIc. 41

3.5 Gradient of slice The slice gradient a (see Fig. 24) is also a function of a number of factors. If we introduce

merely the most important of them, we can write down the symbolic function of the slice gradient in the following form

= f ( K M / K ~ , S, V, v, R) (21)

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148 I. JANELID AND R. KVAPIL

where KM = particle size of ore Ke = particle size of waste S = height of slice V = burden v velocity of travel of material in gravity flow as given by the extraction velocity R -- roughness of slice walls.

The slice gradient a is to have the effect of preventing as much as possible the inter- mixing of waste or, inversely, the intermixing of ore into waste.

A material of fine particle size can, as a result of the gravitational force, fill the lower- lying cavities and gaps in a material of coarse particle size, i.e. fine ore lying over lumpy waste or vice versa. The slice gradient should be chosen such that the optimum conditions are obtained in this respect.

A principal decision as regards the best slice gradient, whether it is to be positive, vertical or negative, can be obtained from the ratio of ore particle size to waste particle size. Table 2 can be consulted for this purpose.

TABLE 2

Ratio of particle sizes Slice gradient

K,~t/Kc > 1 Positive, ~ < 90' K.v/Kc : 1 Vertical, a = 90 ~ KM/Kc < 1 Negative, a > 90 ~

The particle size ratio K~vl/Kc can be modified in practice because the size distribution of the ore in the slice depends on the blasting operations.

The earlier formulae provide, as has been mentioned before, merely approximate figures for the parameters of sublevel caving which we can apply in planning the mining system.

The precise optimum values of the parameters of sublevel caving, including all detailed effective factors, can only be found on the basis of tests under natural conditions. The proper execution of such tests is facilitated by an application of the knowledge of the principles of gravity flow described in detail in Sections 2 and 3 of this article. The execution of tests under natural conditions is advantageous because the optimum parameters of sub- level caving can thereby be determined, not only as they are affected by purely technical factors, but by operational and economical factors as well.

4. FRONT CAVING

On the basis of experimental investigations and practical experience it has been found that the contamination of the blasted ore by waste will be the more comprehensive and rapid as the contact areas between blasted ore and waste in the slice become greater and more curved.

A modified subtevel caving called front caving has been worked out for thick ore deposits, the characteristic feature being that the blasted ore in the slice forms a continuous front so that the contact area with the waste is very small.

As the height F of the slice front can be twice as much in front caving as that of a con- ventional slice height S, the middle sublevel of extraction drifts can be eliminated in the

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S U B L E V E L C A V I N G 149

case of front caving. The arrangement of the drifts in front caving is shown diagrammatically in Fig. 42.

Extraction of the ore from the upper drifts, sublevel I, leaves between the extraction drifts the ore remnants marked in Fig. 42 by R.

The principle of the gravity flow in front caving is the same as in sublevel caving. We can, therefore, calculate the approximate burden V in front caving from formula (17b).

The approximate front height can be calculated from formula

2V F < ~/(i ~- e2)" (22)

With respect to the drift arrangement in front caving, the checkered pattern (Fig. 42) is again to be preferred to the vertical pattern.

The ore extraction from the drifts of the lower sublevel lI (Fig. 42) can take place in front caving either simultaneously or in stages. The process of simultaneous extraction is illustrated in its individual phases a to e of a tested model in Fig. 43, and the process of extraction in stages in Fig. 44.

Simultaneous ore extraction yields the best results, but may encounter certain difficulties for practical mining reasons, one of them being that it requires the simultaneous operation of several loaders. If such an operation is possible, the simultaneous ore extraction can not only result in a considerable improvement of the ore yield, but also in a very high production capacity. If the distance between the individual extraction stages of the successive extraction drifts becomes shorter, ore extraction in stages may gradually approximate the simultaneous extraction.

The approximate height hR of the ore remnants between the extraction drifts of the upper sublevel I (Fig. 42) can be calculated from the formula

hR ~ hN P/2r (23)

where P = width of pillars between the extraction drifts (Fig. 42) h~v = an arbitrary height above the extraction drift of the lower sublevel r = half the width of the gravity flow (Fig. 18) calculated from formula (10)

by applying formula (8).

Figure 42 shows clearly that the ore remnants become smaller as the width P of the intermediate pillars becomes less. Any chosen width must of course meet the conditions of ample load-bearing capacity.

J i I

FIG. 42. Arrangement of extraction drifts in front caving.

Page 31: Sublevel Caving Paper

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Page 32: Sublevel Caving Paper

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Page 33: Sublevel Caving Paper

FIG. 47. Stress distribution with checkered arrangement of extraction drifts (photoelastic stress model).

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SUBLEVEL CAVING 151

The precise optimum values of the parameters of front caving can, as with sublevel caving, be established only on the basis of large-scale tests.

Two more illustrations will help to give a better idea of the distinction between front caving and sublevel caving. Figure 45 shows diagrammatically the location of the extrac- tion drifts and a view of the direction of the slice walls I, 1I and III. In Fig. 46 we have shown diagrammatically the arrangement of the extraction drifts and a view in the direction of the front wall in front caving.

The contact area of blasted ore with waste in sublevel caving is two to five times greater than in front caving, because the blasted ore is extracted in sublevel caving separately from single burdens of differing arrangement. In some cases this difference may in practice be much greater.

Front caving may have considerable advantages compared with sublevel caving. At practically the same panel height the middle sublevel of extraction drifts can be saved in front caving. Furthermore, the continuous ore extraction over the full width of the front wall and the small contact area in front caving, not only yield a larger quantity of pure ore, but they also diminish the contamination and the ore remnants.

5. STRESS STATE IN SUBLEVEL CAVING The stress distribution and the stress state in the orebody of the slice has been investigated

by models. By means of photoelastic stress investigations we indicated the characteristics of the

stress distribution which is shown in the photograph of Fig. 47 in the form of isochromatic lines of a photoelastic stress model. The model represents a checkered arrangement of the extraction drifts at a predominantly vertical action of the pressure. The models were made of gelatin and the photographs were taken in monochromatic and circular-polarized light.

The highest stress concentration (Fig. 47) occurs at the corners of the extraction drifts and at the junctions of the oblique corners between the upper and lower extraction drifts. This characteristic pattern of the stress concentration causes in case of critical loads a typical destruction of the orebody in the slice. This destruction can be seen clearly from the form of the cracks in a plaster-of-Paris model in Fig. 48, where a checkered arrange- ment of extraction drifts has been modelled. For the sake of a theoretical comparison Fig. 49 shows a photograph of a tested model of plaster-of-Paris with a vertical arrangement of drifts, again loaded until fracture occurred. When the extraction drifts are in a checkered arrangement, a critical load destroys the whole orebody of the slice (see Fig. 25). In the case of a vertical arrangement (Fig. 49), on the other hand, the pillars between the extrac- tion drifts remain whole.

The load-bearing capacity is smaller with a checkered drift arrangement than with a vertical arrangement.

This difference in load-bearing capacity becomes the larger, the smaller the thickness of roof hF (Fig. 25) and the greater the width B of the extraction drifts.

Laboratory investigations have shown that this difference is considerably diminished even at critical loads if the thickness of the roof exceeds the width of the extraction drift by at least 20 per cent, i.e.

hp >-- 1.2 B (24)

where he = thickness of roof above extraction drift (see Figs. 24 and 25) B = width of extraction drift (Fig. 25).

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152 1. JANELID AND R. KVAPIL

If, for example, the width of the extraction drift B ~ 6 m, the necessary thickness of the roof hE = 1.2 × 6 = 7-2 m, and if the height of the extraction drift H ~ 3.7 m, the mini- mum required height of slice is

S > H - k - h E = 3 . 7 - - k 7 . 2 - - 10"9~ l l m .

The lowest sublevels of the iron ore mine Kiruna, where B ~ 6.0 m and H ~ 3.7 m, begin with a height of slice S ~ 13.0 m.

The question whether sublevel caving is practicable even at greater depths below ground level has often been discussed. Both theoretical and practical points of view indicate a positive answer. A few Swedish metalliferous mines operate sublevel caving already today at depths of over 700 m below ground level.

The case of Fig. 50 will illustrate the point more clearly. In this case the sublevel is in the virgin state, i.e. no ore has been mined as yet. The plane of break 1, 2 in the hanging and 3, 4 in the foot wall practically forms a large notch 1, 2, 3, 4 with the horizontal plane of the ore (Fig. 50). The stress pattern has, therefore, the same characteristics as that of a notch under similar conditions. The lines t which indicate the direction of the maximum principal stresses therefore follow in principle a pattern as shown diagrammatically in Fig. 50.

, , l , l t

FIG. 50. No t ch effect and stress state in sublevel caving.

In the unworked sublevel of the slice (shaded area in Fig. 50) the stress state is characterized by the horizontal compressive forces in most cases being greater than the vertical forces. This is indicated in Fig. 50 by thick arrows. It is as if the upper part of the ore stratum is subjected to lateral compression. The predominating horizontal pressures are in this case due to the effect of the notch 1, 2, 3, 4. The highest stress concentration occurs at the cor- ners 3 and 2 (especially 2) of the notch. This stress state causes no, or at least very few, difficulties in practice during development work, i.e. when the drifts are being driven hori- zontally and perpendicularly to the longitudinal axis of the deposit from hanging to foot wall. As soon as the first burden has been mined, the stress state immediately changes. This is shown diagrammatically in Fig. 51. The removal of the first burden interrupts the con- tinuity of the orebody and the stress concentration is shifted from the corner 2 ('Fig. 50) to the corner 6 (Fig. 51). This removes the effect of the horizontal pressures from the overlying strata on the slice front and the whole process of the stress concentration takes place below the working zone of the sublevel (shaded area in Fig. 51). The compressive forces marked in Fig. 51 by thick arrows run underneath the lowest notch outlines and must therefore pass around the corners 6, 7 and 3. The additional notch effect of the corners 6 and 7 (Fig. 51) is very beneficial for the work in the mining zone of the slice. The working zone of the sublevel is stress-relieved by it because the weight of the waste from the destroyed hanging (and sometimes from destroyed foot wall) can under practical conditions

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SUBLEVEL CAVING 153

F~G. 51. Changes in stress state when mining the first slice.

never a t ta in the or iginal figure o f the rock pressure o f a virgin rock mass. This character is t ic in terp lay o f forces can create sui table condi t ions for sublevel caving even at greater mining depths be low g round level.

The formulae quoted above for the app rox ima te ca lcula t ion o f the pa ramete r s o f sublevel caving or f ront caving can be app l ied for min ing descending f rom foot wall to hanging or vice versa.

REFERENCES I. JANELID |. Mining Engineering and its Development in Swedish Mines, Almqvist & Wiksells, Uppsala (1961). 2. JANELID I. Research and Development in Swedish Mining, Jubilee paper "Leoben Miners' Day 1962" (1962). 3. JANELID I. Development trends of drilling and blasting in Swedish metalliferous mines, Berg- undHiittenm.

Monatshefte No. 2, 25-35 (1963). 4. JANELID I. State and development trends of the loading and haulage operations in Swedish metalliferous

Mines, Berg- und Hiittenm. Monatshefte No. 4, 153-161 (1964). 5. KVAPIL R. Theory of the Flow of Granular and Coarse Materials in Hoppers, SNTL Prague (1955); Theory

of Motion of Free-Flowing Material, Verlag Technik, Berlin (1959); Motion of Free-Flowing Materials in Bunkers, Gosgortekhizdat, Moscow (1960).

6. KVAPIL R. Gravity flow of granular materials in hoppers and bins, Int. J. Rock Mech. Min. Sci. 2, 2541 (1965); 2, 277-304 (1965).

7. KVAPIL R. Problems of stress distribution in pillars and roofs of rooms, Tech. Digest No. 5, 3-12 (1961). 8. KVAPIL R. Problems of gravity flow of free-flowing materials, Aufbereitungs-Technik Nos. 3, 4, 10, 12

(1964).