##### Document Text Contents

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Chapter 1. Charge Calculations for Tunneling

ROGER HOLMBERG

INTRODUCTION

The driving of drifts is a very important aspect of

underground mining. It is not unusual for the percent-

age of rock broken during development in a mine using

sublevel caving, for example, to be as much as 25% of

the total. If one also considers the amount broken for

transport, ventilation, and exploration drifts, one can

easily understand that the planning and excavation of

drifts play a major part in the total economics of the

mine (Fig. 1) .

Increasing mechanization in mining demands larger

tunnel areas for transport and mining equipment. With

modern machines the hard work involved in using hand-

held pushers is gone, and a better environment is

achieved. More rational methods could be used, but

much of the experience the working man acquired by

working close to the rock face (such as utilizing the

natural weak planes in the rock when he placed the drill-

ing holes) has unfortunately been lost. By having sepa-

rate shifts for drilling, loading, and hauling, more atten-

tion has to be placed upon a well-designed drilling

pattern.

Some reduction in the number of holes required can

be achieved with mechanized drilling because of the

larger holes that can be produced. On the other hand,

it is probably not possible to achieve the same precision

as with pneumatic pushers, and it is difficult to utilize the

larger holes because these cause more damage to the re-

maining rock. Recently, however, the precision has be-

come very good with the parallel booms and automatic

devices for setting the lookout angle (Fig. 2). A larger

arch of the drift roof requires a more carefully executed

blasting procedure than before in order to prevent rock

fall and to insure a sufficiently long stand-up time.

In this chapter, empirical relationships that can be

used to design an economic and optimal drift blasting

design will be presented. The principles of the calcula-

tion method are based upon the earlier work of Lange-

fors and Kihlstrom ( 1963) and Gustafsson (1973).

COMPARISON OF EXPLOSIVES

To provide for the use of various explosives it is

necessary to have a basis of comparison. Several meth-

ods have been developed to charactxize the strength of

an explosive. Some examples are comparison of values

given by ( 1 ) calculated explosion energies; (2) the bal-

listic mortar test; (3 ) the Trauzl lead block test; (4) the

brisance test; (5) the weight strength concept; and

( 6 ) the underwater test. However, most of these meth-

ods should be used carefully when stating the breaking

Fig. 1. Development for sublevel

caving.

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1582 UNDERGROUND MINING METHODS HANDBOOK

CHARGE CALCULATION AND DESIGN OF

DRILLING PATTERN

Tunnel blasting is a much more complicated opera-

tion than bench blasting because the only available free

surface toward which initial breakage can occur is the

tunnel face. Because of the high constriction there will

be a need for a much higher specific charge. Fig. 4 pre-

sents a good guide for explosive consumption for vary-

ing tunnel sizes.

Environmental aspects influence the choice of explo-

sive by requiring the avoidance of high concentrations of

toxic fumes. The small burdens used in the cut demand

an explosive agent which is sufficiently insensitive so that

flashover from hole to hole is impossible, and which has

a sufficiently high detonation velocity to prevent occur-

rence of channel effects when the coupling ratio is less

than one. With the mechanized drilling equipment used

today larger holes than the charge demands are normally

drilled. Channel effects can occur if an air space is pres-

ent between the charge and the borehole wall. If the

detonation velocity is not high enough (less than about

3000 m/s), the expanding detonation gases drive for-

ward the air in the channel as a compressed layer with

a high temperature and a high pressure. The shock front

in the air compresses the explosive in front of the deto-

nation front, destroys the hot spots, or increases the den-

sity to such a degree that the detonation could stop or

result in a low energy release. The explosive used in the

lifters must also withstand water. In the contour holes

special column charges should be used to minimize

damage to the remaining rock.

To simplify the charge calculations let us divide the

tunnel face into five separate sections A through E.

Each one has to be treated in its own special way during

the calculation. A is the cut section; B involves the

stoping holes breaking horizontally and upward; C is the

stoping holes breaking downward; D is the contour

holes; and E is the lifters (Fig. 5 ) .

The most important operation in the blasting pro-

cedure is creating an opening in the rock face to serve

as another free surface. If this stage fails the round will

definitely not be a success.

In the cut the holes are arranged in such a way that

the delay sequence permits the opening to gradually in-

crease in size until the stoping holes can take over. The

Fig. 5. Sections A-E represent the types of holes used

under different blasting conditions.

holes can be drilled in a series of wedges (V-cut), as a

fan, or in a parallel geometry usually centered around

an empty hole.

The choice of the cut has to be made with respect

to the type of available drilling equipment, the tunnel

width, and the desired advance. With V-cuts and fan

cuts where angled holes are drilled, the advance is strictly

dependent upon the width of the tunnel. In the last dec-

ade the parallel cut (four-section cut) with one or two

centered large empty diameter holes has been used to a

very large extent. The obvious advantages to using this

cut are that no attention has to be paid to the tunnel

width, and the cut is much easier to drill with machines

as there is no need to change the angle of the boom.

The principle behind a parallel cut is that small di-

ameter holes are drilled with great precision around a

larger hole (4 65 to 4 175 mm). The larger empty hole

serves as a free face for the smaller holes, and the open-

ing is enlarged gradually until the stoping holes take

over. The predominant type of parallel hole cut is

the four-section cut which is used in the following

t Specific charge kg/m3

H = 0.15 + 34.1 4 - 39.4 (m) (2)

where 4 is the empty hole diameter in meters.

The advance I is

I = 0.95 H (m) (3)

calculation.

Advance

The advance is restricted by the diameter of the

empty hole and the hole deviation for the smaller diame-

ter holes. Good economics demand maximum utiliza-

tion of the full hole depth. Drifting is getting very ex-

pensive if the advance becomes much less than 95% of

the hole depth. Fig. 6 illustrates the required hole depth

as a function of the empty hole diameter when a 95%

advance is desired with a four-section cut (Fig. 6).

The equation for hole depth (H) can be expressed as

- 7

2 5 5 0 7'5 loo ~ r e a -m2

Fig. 4. Specific charge as a function of the tunnel area.

Eqs. 2 and 3 are valid only for a drilling deviation

not exceeding 2%.

Sometimes two empty holes are used instead of one

in the cut, for example, if the drilling equipment can not

handle a larger diameter. Eq. 2 is still valid if 4 is com-

puted according to the following:

Page 4

H

t

Hole depth at

95% advance m

BLASTING

Vl 1 Burden m

I C

0.1 a 2 0 Empty hole m

Fig. 6. Hole depth as a function of empty hole diameter

for a four-section cut.

do denotes the hole diameters of the two empty holes.

The general geometry for the cut and cut spreader holes

is outlined in Fig. 7.

Burden in the First Quadrangle

The distance between the empty hole and the drill

holes in the first quadrangle should not exceed 1.7 times

the diameter of the empty hole if satisfactory breakage

and cleaning are to take place. Breakage conditions dif-

fer very much depending upon explosive type, structure

of the rock, and distance between the charged hole and

the empty hole.

As illustrated in Fig. 8, there is no advantage in

using a burden greater than 2 4 as long as the aperture

angle is too small for the heavy charge. Plastic defor-

mation would be the only effect of the blast. Even if the

distance is smaller than 2 4, too great a charge concen-

tration would cause a misfunction of the cut due to rock

impact and sintering which prevents the necessary swell.

If the maximum accepted hole deviation is of the magni-

FOUR SECTION CUT

%

- - - - - - - - - - - - - 0

Fig. 7. Four-section cut: V 4 represents the practical burden

for quadrangle i.

I the holes meet

0:1

*

0.2 d3 0 Empty

hole m

Fig. 8. Blasting result for different relations between the

practical burden and the empty hole diameter. Hole

deviation is less than 1% (Langefors and Kihlstrom,

1963).

tude 0.5 to 1 % , then the practical burden (V,) for the

spreader holes in the cut must be less than the maximum

burden ( V = 1.7 4) .

We use

v,= 1.54. (m) (5)

When the deviation exceeds 1 %, V, has to be re-

duced even further. The following formula should then

be used.

V, = 1.7 4 - ( a H + B) (m) (6)

where the last term represents the maximum drill de-

viation (F), a is the angular deviation (m/m), H is the

hole depth (m) , and /3 denotes the collaring deviation in

meters. In practice drilling precision is normally good

enough to allow the use of Eq. 5.

Charge Concentration in the First Quadrangle

Langefors and Kihlstrom (1963) have verified the

following relationship between charge concentration ( I ) ,

the maximum distance between the holes (V), and the

diameter of the empty hole 4, for a borehole with a

diameter of 0.032 m.

I = 1 . ( V ) (V - 4/21 (kg/m) (7)

To utilize the explosive in the best manner, a burden

of V, = 1.5 4 for a deviation of 0.5 to 1 % should be

used.

One must remember that Eq. 7 is valid only for a

drill-hole diameter of 0.032 m. If larger holes are going

to be used in the round an increased charge concentra-

tion per meter of borehole has to be used. To keep the

breakage at the same level it is necessary to increase the

concentration approximately in proportion to the di-

ameter. Thus if a drill-hole diameter of d is used instead

of d, = 0.032 m, the charge concentration is determined

by

d

I = - I , .

dl

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1584 UNDERGROUND MINING METHODS HANDBOOK

Obviously, when the diameter is increased this means

that the coupling ratio and the borehole pressure de-

crease. It is important to carefully select the proper ex-

plosive in order to minimize the risk of channel effects

and incomplete detonation.

Considering the rock material and type of explosive,

Eq. 7 can now be rewritten in terms of a general hole

diameter d:

where saxso denotes the weight strength relative to

ANFO, and c is defined as the rock constant.

Often the possible values for charge concentration

are rather limited due to the restricted assortment from

the explosives manufacturer. This means that the charge

concentration is given, and the burden is calculated from

Eq. 9 instead. This can easily be done by using a pro-

grammable pocket calculator and an iterative procedure.

Rock Constant

Factor c is an empirical measure of the amount of

explosive needed for loosening one cubic meter of rock.

The field experiments by which the c values were deter-

mined took place with a bench-blasting geometry. It

turns out that the rock constant determined in this way

also gives a good approximation for the rock properties

in tunneling. In trial blasts it was found that c fluctuated

very little. Blasting in brittle crystalline granite gave a

c factor equal to 0.2. In practically all other rock ma-

terials, from sandstone to more homogeneous granite, a

c value of 0.3 to 0.4 kg/m3 was found. Under Swedish

conditions c = 0.4 is predominant in blasting operations.

The Second Quadrangle

After the first quadrangle has been calculated, a new

geometry applies when solving the burdens for the fol-

lowing quadrangles. Blasting tosalds a circular hole

naturally demands a higher charge concentration than

blasting towards a straight face due to a higher constric-

tion and a less effective stress wave reflection.

If there is a rectangular opening of width B, and the

burden V is known (Fig. 9 ) , the charge concentration

( I ) relative to ANFO is given by

32.3 d c V

I =

~ A N F O [sin (atn(B/2V)

(kg/m). (10)

If instead we start from the assumption that the

charge concentration for the actual explosive and the

rectangular opening width B are known, then the bur-

Fig. 9. Geometry for blasting towards

a straight face.

Fig. 10. Influence of the hole devia-

tion.

den V can be expressed explicitly with good accuracy as

a function of B and I.

When calculating the burden for the new quadrangle,

the effect of the faulty drilling F (defined in Eq. 6 ) must

be included. This is done by treating the holes in the

f ist quadrangle as if they were placed at the most un-

favorable location (Fig. 10).

From Fig. 10 one can see that the free surface B that

should be used in Eq. 11 differs from the hole distance

B' in the first quadrangle.

B = V 2 ( v , -F) (m) . (12)

By substitution, the burden for the new quadrant is

v = 10.5 . 10-2 1 / ( ~ 1 - 7 ) IsaNm (m). (13)

Of course this value has to be reduced by the drill-

hole deviation to obtain the practical burden.

v ,=v-F (m). (14)

There are a few restrictions that must be put on V,.

It must satisfy the following:

V, 6 2B (15)

if plastic deformation is not to occur. If it does not,

using Eqs. 10 and 15, the charge concentration should be

reduced to

or

1 = 5 4 0 d ~ B / s ~ , , ~ (kg/m). (17)

If the restriction for plastic deformation cannot be

satisfied, it is usually better to choose an explosive with a

lower weight strength in order to optimize the breakage.

The aperture angle should also be less than 1.6 rad

(90"). If not the cut will lose its character of a four-

section cut. This means

V, > 0.5 B. (18)

Gustafsson (1973) suggests that the burden for each

quadrangle be V, = 0.7 B'.

A rule of thumb for the number of quadrangles in

the cut is that the side length of the last quadrangle B'

should not be less than the square root of the advance.

Page 6

BLASTING 1585

The algorithm for the calculation of the remaining quad-

rangles is the same as for the second quadrangle.

Holes in the quadrangles should be loaded so that a

hole length (h) of ten times the hole diameter is left

unloaded.

h = l O d (m). (20)

Lifters

The burden for the lifters in a round are in principle

calculated with the same formula as for bench blasting.

The bench height is simply replaced by the advance, and

a higher fixation factor is used due to the gravitational

effect and to a greater time interval between the holes.

The maximum burden can be found using

where f is the fixation factor, E IV denotes the relation

between the spacing (E) and the burden (V), and E is

the corrected rock constant. A fixation factor f of 1.45

and an E I V ratio equal to 1 are used for lifters.

When locating the lifters, one must remember to con-

sider the lookout angle (see Fig. 11). The magnitude of

the angle is dependent upon available drilling equipment

and hole depth. For an advance of about 3 m a lookout

angle equal to 0.05 rad (3") (corresponding to -5

cmIm) should be enough to provide room for drilling

the next round.

Hole spacing should be equal to V. However, it will

vary depending upon the tunnel width.

The number of lifters N is given by

tunnel width f 2 H sin y

N = integer of v + 2).

The spacing EL for the holes (with the exception of

the comer holes) is evaluated by

tunnel width + 2 H sin y

EL =

N - 1

(m). (23)

The practical spacing EL. for the corner holes is

equal to

EL* = EL - H sin y (m). (24)

The practical burden VL should be reduced by the

bottom lookout angle and the drill hole deviation.

V L = V - H s i n y - F (m). (25)

The length of the bottom charge (h,) needed for

loosening the toe is

Fig. 11. Blasting geometry for lifters.

The length of the column charge (h,) is given by

and the concentration of this charge can be reduced to

70% of the concentration in the bottom charge. How-

ever, this is not always done because it is time-consuming

work. Generally the same concentration is used in both

the bottom and in the column. For lifters an unloaded

hole length of 10 d is usually used at the collar.

If Eq. 20 is going to be used, the following condition

has to be fulfilled:

Otherwise the maximum burden has to be succes-

sively reduced by lowering the charge concentration.

Then the practical spacing EL and burden V, can be

evaluated.

Fixation Factor

In the formulas, different fixation factors f are used

for calculating the burden in different situations. For

example, in bench blasting with vertical hole positioned

in a row with a fixed bottom, f = 1. If the holes are in-

clined it becomes easier to loosen the toe. To account

for this a lower fixation factor (f < 1) is used for an

inclined hole. This results in a larger burden. In tun-

neling a number of holes are blasted with the same delay

number. Sometimes the holes have to loosen the burden

upward and sometimes downward. Different fixation

factors are used to include the effects of multiple holes

and of gravity.

Stoping Holes

The method for calculating the stoping holes in sec-

tions B and C (Fig. 5) does not differ much from the

calculation of the lifters. For stoping holes breaking

horizontally and upward in section B, a fixation factor f

of 1.45 and an E I V ratio equal to 1.25 are used. The

fixation factor for stoping holes breaking downward is

reduced to 1.2, and EIV should be 1.25. The column

charge concentration for both types of stoping holes

should be equal to 50% of the concentration for the

bottom charge.

Contour Holes

If smooth blasting is not necessary, the burden and

spacing of the contour holes are calculated according to

what has been said previously about the lifters, with the

following exceptions: ( 1 ) fixation factor f = 1.2; (2)

E IV ratio should be 1.25; and (3) charge concentration

for the column charge is 50% of the bottom charge

concentration.

The blast-damaged roof and walls in a drift often

need an excessive amount of support. In low strength

rock, a long stand-up time usually can be achieved by

more careful contour blasting. A 3-m long borehole

with ANFO (1.5 kgIm) is capable of producing a

damaged zone of about 1.5-m radius.

With smooth blasting this damage zone is reduced to

a minimum. Our experience shows that the spacing is a

linear function of hole diameter (Persson, 1973).

where the constant k is in the range of 15 to 16. An

E IV ratio of 0.8 should be used. For a 41-mm hole

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1586 UIVDERGROUND MINING METHODS HANDBOOK

kg lm ANFO eauivalent

0-21 -/I7 mm GURlT

I / . 11 mm GURlT

J

2 0 40 60 Diameter mm

Fig. 12. Minimum required charge concentration for

smooth blasting and recommended practical hole diam-

eter for NABlT and GURlT charges.

diam the spacing will be about 0.6 m and the burden

about 0.8 m.

The minimum charge concentration per meter of

borehole is also a function of the hole diameter. For

hole diameters up to 0.15 m the relationship

applies. In smooth blasting the total hole length must be

charged to avoid ripping. In Fig. 12, 1 is plotted as a

function of d.

Rock Damage

The sudden expansion caused by an explosion in a

borehole generates a stress wave that propagates into the

rock mass. For an elastic material the generated stress is

directly proportional to density, particle velocity, and

wave propagation velocity.

Close to the charge the strain will reach a magnitude

where permanent damage is produced. Whether this

damage will have any significant influence on the

stand-up condition for a tunnel depends upon the char-

acter of the damage, the exposure time, the influence of

ground water, and the orientation of the joint planes

with respect to the contour and the static load.

For a long time, the damage criteria for structures

built in the vicinity of a blasting site have been based

upon the peak particle velocity. At SveDeFo (Swedish

Detonic Research Foundation) the same criteria have

been found to apply for estimating damage in the re-

maining rock (Persson, Holmberg, and Persson, 1977;

Holmberg and Persson, 1978; Holmberg, 1978).

The empirical equation is

where v is the particle velocity (mm/s); Q is the charge

weight ( kg ) ; and R denotes the distance (m). It is valid

for calculating the particle velocity at such distances

where the charge can be treated as being spherical. For

short distances the discrepancy between the calculated

and the measured values is unacceptable.

By performing an integration over the charge length

it was found possible to get the particle velocity as a

function of distance, charge length, and charge concen-

tration per meter of borehole. In Fig. 13 the calculation

for a 3-m long charge is given.

When the particle velocity exceeds some value be-

tween 700 and 1000 mm/s (Fig. 13), cracks are induced

or enlarged in a granite rock mass. A concentration of

Fig. 13. Peak particle velocity as a function of distance

and charge concentration for a 3-m long charge.

1 kg/m means that damage occurs in a zone of radius

1.0 to 1.4 m around the charge.

In field experiments for gneiss, pegmatite, and ,;an-

ite (tensile strength = 5 to 15 MPa), a very good agree-

ment between the calculated and measured values was

found. Reports about damage zones also agree well with

the calculated distances for similar charges if the 700 to

1000 mm/s criterion is used. This is valid for charge

concentrations in the range 0.2 to 75 kg/m.

In the field experiments accelerometers have been

used together with FM-tape and transient recorders.

Numerical integration provided the particle velocities.

The closest distance from the charges located in 25 to

250-mm holes to the accelerometers has been in the

range 1.5 to 13 m.

Measurements close to tunnel contours have indi-

cated that charges in the row next to the contour often

cause higher particle velocities and more damage than

the smooth blasted row. If a smooth blasting result

should not be ruined by the rest of the holes it is a good

idea to reduce the charge concentration in the row next

to the contour. Fig. 13 provides a guide for estimating

the charge concentration. A concentration of 0.2 kg/m

in the contour results in a damage zone of 0.3 m. If the

burden was 0.8, one can see that the charge concentra-

tion for the inner row should be limited to about 1 kg/m

if the damage zone of 0.3 m is not to be exceeded

(Fig. 14).

Fig. 14. A well-designed round where the charge concen-

trations in the holes close to the contour are adjusted

so that the damage zone from each hole coincides.

Page 8

BLASTING 1587

EXAMPLE OF CHARGE CALCULATION

Conditions

Hole diameter = 45 mm.

Empty hole, 4 = 102 mm.

Tunnel width = 4.5 m.

Abutment height = 4.0 m.

Height of arch = 0.5 m.

Smooth blasting in the roof.

Lookout for contour holes y = 0.05 rad ( 3 " ) .

Angular deviation a = 10 mm/m.

Collar deviation p = 20 mm.

Explosive: a water gel explosive is used with car-

tridge dimensions of 4 25 x 600, + 32 x 600, 4 38 x 600

mm.

Heat of explosion = 4.5 MJ/kg.

Gas volume at STP = 0.85 m3/kg.

Density = 1200 kg/m3.

Rock constant c = 0.4.

Calculation

Weight strength relative to LFB (Eq. 1 ) .

and

sANFO = 0.92/0.84 = 1.09

Charge concentration 4 mm I kg lm

25 0.59

32 0.97

3 8 1.36

Advance

Using an empty hole diameter 4 = 102 mm, Eq. 2

results in a hole depth of 3.2 m, and the advance is

3.0 m.

Cut

First Quadrangle

Maximum burden V = 1.74=0.17m

Practical burden V, = 0.12 m (Eq. 6 )

Charge concentration I = 0.58 kg/m (Eq. 9 )

1 for the smallest cartridge is 0.59 kg/m which is

sufficient for clean blasting the opening.

Unloaded hole length = 10d = 0.45 m (Eq. 19).

Hole distance in quadrangle B' = = 0.17 m.

No. of 25 x 600 cartridges = (3.2 - 0.45) 10.6 =

4.5.

Second Quadrangle

The rectangular opening to blast toward is B = \/Z

(0.12 - 0.05) = 0.10 m (Eq. 12).

Maximum burden for 425 cartridges V = 0.17 m

(El. 1 1 ) .

Maximum burden for 432 cartridges V = 0.21 m

(Eq. 1 1 ) .

Maximum burden for 438 cartridges V = 0.25 m

(Eq. 1 1 ) .

Eq. 15 says the practical burden must not exceed 2B.

This implies that the 432 x 600 cartridges are the

most suitable ones in this quadrangle.

Practical burden V2 = 0.16 m (Eq. 14)

Unloaded hole length h = 0.45 m 0%. 19)

Hole distance in quadrangle B' = a (0.16 + 0.17/

2 ) = 0.35 m.

No. of 432 x 600 cartridges = 4.5.

Third Quadrangle

B = f l (0.16 + 0.17/2 - 0.05) = 0.28 m.

Use 438 x 600 cartridges with charge concentration

I = 1.36 kg/m.

Maximum burden V = 0.42 m.

Practical burden V3 = 0.37 m.

Unloaded hole length h = 0.45 m.

Hole distance in quadrangle B' = a (0.37 + 0.35/

2 ) = 0.77 m.

No. of 438 x 600 cartridges = 4.5.

Fourth Quadrangle

B = \a (0.37 + 0.35/2 - 0.05) = 0.70 m.

Maximum burden V = 0.67 m.

Practical burden V, = 0.62 m.

Unloaded hole length h = 0.45 m.

B' = a (0.62 + 0.77/2) = 1.42 m.

No. of 438 x 600 cartridges = 4.5.

The side length of this quadrangle is 1.42 m which is

comparable to the square root of the advance.

Therefore there is no need for more quadrangles.

Lifters

Use 438 x 600 cartridges with a charge concentration

of 1 = 1.36 kg/m.

Maximum burden V = 1.36 m (Eq. 20)

No. of lifters N = 5 (Eq. 22)

Spacing E, = 1.21 m (Eq. 23)

Spacing, corner holes E', = 1.04 m (Eq. 24)

Practical burden V, = 1.14 m (Eq. 25)

Length of bottom charge h, = 1.43 m (Eq. 26)

Length of column charge h, = 1.32 m (Eq. 27)

This charge concentration shall be 70% of the bot-

tom charge concentration; 0.70 X 1.36 = 0.95 kg/m.

Use 2.5 cartridges 438 x 600 as the bottom charge

and 2 cartridges 432 x 600 as the column charge.

Contour Holes, Roof

Smooth blasting with 425 x 600 cartridges is speci-

fied.

Spacing E = 0.68 m (Eq. 29) .

Burden V = E/0.8 = 0.84 m.

Due to lookout and deviation the practical bur-

den becomes V, = 0.84 - 3.2 sin 3" - 0.05 = 0.62 m.

The minimum charge concentration for this smooth

blasting is 1 = 90 d2 = 0.18 kg/m (Eq. 30).

The charge concentration for the 425 X 600 car-

tridges is 0.59 kg/m which is considerably more than

what is really needed.

No. of holes; integer of (4.7/0.68 + 2 ) = 8.

5 cartridges per hole are used.

Contour Holes, Wall

The abutment height is 4.0 m and from the calcula-

tion it is known that the lifters should have a burden of

1.14 m, and the roof holes should have a burden of

0.62 m. This implies that there are 4.0 - 1.14 - 0.62 =

2.24 m left in the contour along which to position the

wall holes.

By using a fixation factor f = 1.2, and an E/V-ratio

equal to 1.25, Eq. 20 results in a maximum burden

V = 1.33 m.

Practical burden V,, = 1.33 - 3.2 sin 3" - 0.05 =

1.12 m.

No. of holes = integer of (2.24/ (1.33 X 1.25) + 2 )

= 3.

Page 9

UNDERGROUND MINING METHODS HANDBOOK

Spacing = 2.24/2 = 1.1 2 m.

Length of bottom charge h, = 1.40 m.

Length of column charge h, = 1.35 m.

2.5 cartridges $38 x 600 are used as the bottom

charge, and 2 cartridges $32 x 600 are used in the

column.

Stoping

The side of the fourth quadrangle in the cut is

1.42 m, and the practical burden V , for the wall holes

was determined to be 1.12 m. As the tunnel width is

4.5 m a distance of 4.5 - 1.42 - 2 X 1.12 = 0.84 m is

available for placing horizontal stoping holes.

Maximum burden ( f = 1.45) V = 1.21 m.

Practical burden V H = 1.21 - 0.05 = 1.16 m.

Instead the burden VH = 0.85 m is used, due to the

tunnel geometry.

The height of the fourth quadrangle was 1.42 m, and

this will of course determine the spacing for the two

holes, which becomes 1.42 m.

For stoping downwards:

~ax imLmburden V = 1.33 m.

Practical burden V , = 1.28 m.

The maximum height of the tunnel is specified to be

4.5 m. If we subtract the height of the fourth quadrangle

( 1.42 m) , the burdens for the lifters (1.14 m) and the

roof holes (0.62 m), there is 1.32 m left for a stoping

hole. This is just a little more than the practical burden,

but if the stoping holes are placed at 1.28 m above the

cut, the remaining 0.04 m will in all probability be re-

moved by the overcharged contour. Furthermore, the

formulas used in the calculation have a safety margin

that can tolerate small deviations.

Three holes for stoping downward are positioned

above the fourth quadrangle (see Fig. 15). The charge

distribution for the stoping holes is the same as for the

wall holes.

A summary of explosive consumption is given in

Table 2.

ACKNOWLEDGMENT

This work was done as a part of the rock-blasting

research program of the Swedish Detonic Research

Foundation supported by Swedish industry and the

National Swedish Board for Technical Development.

Fig. 15. Calculated drilling pattern; MS stands for rn-sec

caps (4 no. = 100 rn-sec) and HS stands for half sec

caps (1 No. = 0.5 sec).

The author gratefully acknowledges professional dis-

cussions with present and former colleagues at SveDeFo

and Nitro Consult whose experiences in the art of charge

calculations helped in the formulation of this chapter.

REFERENCES AND BIBLIOGRAPHY

Gustafsson, R., 1973, Swedish Blasting Technique, Gothen-

burg, Sweden.

Holmberg, R., 1975, "Computer Calculations of Drilling

Patterns for Surface and Underground Blastings," Design

Methods in Rock Mechanics, C. Fairhurst and S. Crouch,

eds., 16th Symposium on Rock Mechanics, University of

Minnesota, Minneapolis.

Holmberg, R., and Hustrulid, W., 1981, "Swedish Cautious

Blast Excavations at the CSM/ONWI Test Site in Colo-

rado," 7th Conference of Explosives and Blasting Tech-

nique, Phoenix.

Holmberg, R., and Mahi, K., 1982, "Case Examples of Blast-

ing Damage and Its Influence on Slope Stability," Stability

in Surface Mining, Vol. 3, AIME, New York.

Holmberg, R., and Persson, P.-A., 1979, "Design of Tunnel

Perimeter Blasthole Patterns to Prevent Rock Damage,"

Proceedings, Tunnelling '79, M.J. Jones, ed., Institution of

Mining and Metallurgy, London.

Holmberg, R., 1978, "Measurements and Limitations of

Table 2. Summary of Explosive Consumptlon

No. of Cartridges

Hole No. of Charge per Total

Type Holes 425 432 438 mm Hole, kg kg

1st quad. 4 4.5 1.59 6.37

2nd quad. 4 4.5 2.62 10.48

3rd +4th quad. 8 4.5 3.67 29.36

Lifters 5 2.0 2.5 3.20 16.00

Roof 8 5.0 1.77 14.16

Wall 6 2.0 2.5 3.20 19.20

Stoping 5 2.0 2.5 3.20 16.00

Total charge weight = 11 1.6 kg

Cross sectional area = 19.5 m2

Advance = 3.0 m

Specific charge = 1.9 kg/m3

Total No. of holes = 40

Hole depth = 3.2 m

Specific drilling = 2.2 m/m3

Chapter 1. Charge Calculations for Tunneling

ROGER HOLMBERG

INTRODUCTION

The driving of drifts is a very important aspect of

underground mining. It is not unusual for the percent-

age of rock broken during development in a mine using

sublevel caving, for example, to be as much as 25% of

the total. If one also considers the amount broken for

transport, ventilation, and exploration drifts, one can

easily understand that the planning and excavation of

drifts play a major part in the total economics of the

mine (Fig. 1) .

Increasing mechanization in mining demands larger

tunnel areas for transport and mining equipment. With

modern machines the hard work involved in using hand-

held pushers is gone, and a better environment is

achieved. More rational methods could be used, but

much of the experience the working man acquired by

working close to the rock face (such as utilizing the

natural weak planes in the rock when he placed the drill-

ing holes) has unfortunately been lost. By having sepa-

rate shifts for drilling, loading, and hauling, more atten-

tion has to be placed upon a well-designed drilling

pattern.

Some reduction in the number of holes required can

be achieved with mechanized drilling because of the

larger holes that can be produced. On the other hand,

it is probably not possible to achieve the same precision

as with pneumatic pushers, and it is difficult to utilize the

larger holes because these cause more damage to the re-

maining rock. Recently, however, the precision has be-

come very good with the parallel booms and automatic

devices for setting the lookout angle (Fig. 2). A larger

arch of the drift roof requires a more carefully executed

blasting procedure than before in order to prevent rock

fall and to insure a sufficiently long stand-up time.

In this chapter, empirical relationships that can be

used to design an economic and optimal drift blasting

design will be presented. The principles of the calcula-

tion method are based upon the earlier work of Lange-

fors and Kihlstrom ( 1963) and Gustafsson (1973).

COMPARISON OF EXPLOSIVES

To provide for the use of various explosives it is

necessary to have a basis of comparison. Several meth-

ods have been developed to charactxize the strength of

an explosive. Some examples are comparison of values

given by ( 1 ) calculated explosion energies; (2) the bal-

listic mortar test; (3 ) the Trauzl lead block test; (4) the

brisance test; (5) the weight strength concept; and

( 6 ) the underwater test. However, most of these meth-

ods should be used carefully when stating the breaking

Fig. 1. Development for sublevel

caving.

Page 3

1582 UNDERGROUND MINING METHODS HANDBOOK

CHARGE CALCULATION AND DESIGN OF

DRILLING PATTERN

Tunnel blasting is a much more complicated opera-

tion than bench blasting because the only available free

surface toward which initial breakage can occur is the

tunnel face. Because of the high constriction there will

be a need for a much higher specific charge. Fig. 4 pre-

sents a good guide for explosive consumption for vary-

ing tunnel sizes.

Environmental aspects influence the choice of explo-

sive by requiring the avoidance of high concentrations of

toxic fumes. The small burdens used in the cut demand

an explosive agent which is sufficiently insensitive so that

flashover from hole to hole is impossible, and which has

a sufficiently high detonation velocity to prevent occur-

rence of channel effects when the coupling ratio is less

than one. With the mechanized drilling equipment used

today larger holes than the charge demands are normally

drilled. Channel effects can occur if an air space is pres-

ent between the charge and the borehole wall. If the

detonation velocity is not high enough (less than about

3000 m/s), the expanding detonation gases drive for-

ward the air in the channel as a compressed layer with

a high temperature and a high pressure. The shock front

in the air compresses the explosive in front of the deto-

nation front, destroys the hot spots, or increases the den-

sity to such a degree that the detonation could stop or

result in a low energy release. The explosive used in the

lifters must also withstand water. In the contour holes

special column charges should be used to minimize

damage to the remaining rock.

To simplify the charge calculations let us divide the

tunnel face into five separate sections A through E.

Each one has to be treated in its own special way during

the calculation. A is the cut section; B involves the

stoping holes breaking horizontally and upward; C is the

stoping holes breaking downward; D is the contour

holes; and E is the lifters (Fig. 5 ) .

The most important operation in the blasting pro-

cedure is creating an opening in the rock face to serve

as another free surface. If this stage fails the round will

definitely not be a success.

In the cut the holes are arranged in such a way that

the delay sequence permits the opening to gradually in-

crease in size until the stoping holes can take over. The

Fig. 5. Sections A-E represent the types of holes used

under different blasting conditions.

holes can be drilled in a series of wedges (V-cut), as a

fan, or in a parallel geometry usually centered around

an empty hole.

The choice of the cut has to be made with respect

to the type of available drilling equipment, the tunnel

width, and the desired advance. With V-cuts and fan

cuts where angled holes are drilled, the advance is strictly

dependent upon the width of the tunnel. In the last dec-

ade the parallel cut (four-section cut) with one or two

centered large empty diameter holes has been used to a

very large extent. The obvious advantages to using this

cut are that no attention has to be paid to the tunnel

width, and the cut is much easier to drill with machines

as there is no need to change the angle of the boom.

The principle behind a parallel cut is that small di-

ameter holes are drilled with great precision around a

larger hole (4 65 to 4 175 mm). The larger empty hole

serves as a free face for the smaller holes, and the open-

ing is enlarged gradually until the stoping holes take

over. The predominant type of parallel hole cut is

the four-section cut which is used in the following

t Specific charge kg/m3

H = 0.15 + 34.1 4 - 39.4 (m) (2)

where 4 is the empty hole diameter in meters.

The advance I is

I = 0.95 H (m) (3)

calculation.

Advance

The advance is restricted by the diameter of the

empty hole and the hole deviation for the smaller diame-

ter holes. Good economics demand maximum utiliza-

tion of the full hole depth. Drifting is getting very ex-

pensive if the advance becomes much less than 95% of

the hole depth. Fig. 6 illustrates the required hole depth

as a function of the empty hole diameter when a 95%

advance is desired with a four-section cut (Fig. 6).

The equation for hole depth (H) can be expressed as

- 7

2 5 5 0 7'5 loo ~ r e a -m2

Fig. 4. Specific charge as a function of the tunnel area.

Eqs. 2 and 3 are valid only for a drilling deviation

not exceeding 2%.

Sometimes two empty holes are used instead of one

in the cut, for example, if the drilling equipment can not

handle a larger diameter. Eq. 2 is still valid if 4 is com-

puted according to the following:

Page 4

H

t

Hole depth at

95% advance m

BLASTING

Vl 1 Burden m

I C

0.1 a 2 0 Empty hole m

Fig. 6. Hole depth as a function of empty hole diameter

for a four-section cut.

do denotes the hole diameters of the two empty holes.

The general geometry for the cut and cut spreader holes

is outlined in Fig. 7.

Burden in the First Quadrangle

The distance between the empty hole and the drill

holes in the first quadrangle should not exceed 1.7 times

the diameter of the empty hole if satisfactory breakage

and cleaning are to take place. Breakage conditions dif-

fer very much depending upon explosive type, structure

of the rock, and distance between the charged hole and

the empty hole.

As illustrated in Fig. 8, there is no advantage in

using a burden greater than 2 4 as long as the aperture

angle is too small for the heavy charge. Plastic defor-

mation would be the only effect of the blast. Even if the

distance is smaller than 2 4, too great a charge concen-

tration would cause a misfunction of the cut due to rock

impact and sintering which prevents the necessary swell.

If the maximum accepted hole deviation is of the magni-

FOUR SECTION CUT

%

- - - - - - - - - - - - - 0

Fig. 7. Four-section cut: V 4 represents the practical burden

for quadrangle i.

I the holes meet

0:1

*

0.2 d3 0 Empty

hole m

Fig. 8. Blasting result for different relations between the

practical burden and the empty hole diameter. Hole

deviation is less than 1% (Langefors and Kihlstrom,

1963).

tude 0.5 to 1 % , then the practical burden (V,) for the

spreader holes in the cut must be less than the maximum

burden ( V = 1.7 4) .

We use

v,= 1.54. (m) (5)

When the deviation exceeds 1 %, V, has to be re-

duced even further. The following formula should then

be used.

V, = 1.7 4 - ( a H + B) (m) (6)

where the last term represents the maximum drill de-

viation (F), a is the angular deviation (m/m), H is the

hole depth (m) , and /3 denotes the collaring deviation in

meters. In practice drilling precision is normally good

enough to allow the use of Eq. 5.

Charge Concentration in the First Quadrangle

Langefors and Kihlstrom (1963) have verified the

following relationship between charge concentration ( I ) ,

the maximum distance between the holes (V), and the

diameter of the empty hole 4, for a borehole with a

diameter of 0.032 m.

I = 1 . ( V ) (V - 4/21 (kg/m) (7)

To utilize the explosive in the best manner, a burden

of V, = 1.5 4 for a deviation of 0.5 to 1 % should be

used.

One must remember that Eq. 7 is valid only for a

drill-hole diameter of 0.032 m. If larger holes are going

to be used in the round an increased charge concentra-

tion per meter of borehole has to be used. To keep the

breakage at the same level it is necessary to increase the

concentration approximately in proportion to the di-

ameter. Thus if a drill-hole diameter of d is used instead

of d, = 0.032 m, the charge concentration is determined

by

d

I = - I , .

dl

Page 5

1584 UNDERGROUND MINING METHODS HANDBOOK

Obviously, when the diameter is increased this means

that the coupling ratio and the borehole pressure de-

crease. It is important to carefully select the proper ex-

plosive in order to minimize the risk of channel effects

and incomplete detonation.

Considering the rock material and type of explosive,

Eq. 7 can now be rewritten in terms of a general hole

diameter d:

where saxso denotes the weight strength relative to

ANFO, and c is defined as the rock constant.

Often the possible values for charge concentration

are rather limited due to the restricted assortment from

the explosives manufacturer. This means that the charge

concentration is given, and the burden is calculated from

Eq. 9 instead. This can easily be done by using a pro-

grammable pocket calculator and an iterative procedure.

Rock Constant

Factor c is an empirical measure of the amount of

explosive needed for loosening one cubic meter of rock.

The field experiments by which the c values were deter-

mined took place with a bench-blasting geometry. It

turns out that the rock constant determined in this way

also gives a good approximation for the rock properties

in tunneling. In trial blasts it was found that c fluctuated

very little. Blasting in brittle crystalline granite gave a

c factor equal to 0.2. In practically all other rock ma-

terials, from sandstone to more homogeneous granite, a

c value of 0.3 to 0.4 kg/m3 was found. Under Swedish

conditions c = 0.4 is predominant in blasting operations.

The Second Quadrangle

After the first quadrangle has been calculated, a new

geometry applies when solving the burdens for the fol-

lowing quadrangles. Blasting tosalds a circular hole

naturally demands a higher charge concentration than

blasting towards a straight face due to a higher constric-

tion and a less effective stress wave reflection.

If there is a rectangular opening of width B, and the

burden V is known (Fig. 9 ) , the charge concentration

( I ) relative to ANFO is given by

32.3 d c V

I =

~ A N F O [sin (atn(B/2V)

(kg/m). (10)

If instead we start from the assumption that the

charge concentration for the actual explosive and the

rectangular opening width B are known, then the bur-

Fig. 9. Geometry for blasting towards

a straight face.

Fig. 10. Influence of the hole devia-

tion.

den V can be expressed explicitly with good accuracy as

a function of B and I.

When calculating the burden for the new quadrangle,

the effect of the faulty drilling F (defined in Eq. 6 ) must

be included. This is done by treating the holes in the

f ist quadrangle as if they were placed at the most un-

favorable location (Fig. 10).

From Fig. 10 one can see that the free surface B that

should be used in Eq. 11 differs from the hole distance

B' in the first quadrangle.

B = V 2 ( v , -F) (m) . (12)

By substitution, the burden for the new quadrant is

v = 10.5 . 10-2 1 / ( ~ 1 - 7 ) IsaNm (m). (13)

Of course this value has to be reduced by the drill-

hole deviation to obtain the practical burden.

v ,=v-F (m). (14)

There are a few restrictions that must be put on V,.

It must satisfy the following:

V, 6 2B (15)

if plastic deformation is not to occur. If it does not,

using Eqs. 10 and 15, the charge concentration should be

reduced to

or

1 = 5 4 0 d ~ B / s ~ , , ~ (kg/m). (17)

If the restriction for plastic deformation cannot be

satisfied, it is usually better to choose an explosive with a

lower weight strength in order to optimize the breakage.

The aperture angle should also be less than 1.6 rad

(90"). If not the cut will lose its character of a four-

section cut. This means

V, > 0.5 B. (18)

Gustafsson (1973) suggests that the burden for each

quadrangle be V, = 0.7 B'.

A rule of thumb for the number of quadrangles in

the cut is that the side length of the last quadrangle B'

should not be less than the square root of the advance.

Page 6

BLASTING 1585

The algorithm for the calculation of the remaining quad-

rangles is the same as for the second quadrangle.

Holes in the quadrangles should be loaded so that a

hole length (h) of ten times the hole diameter is left

unloaded.

h = l O d (m). (20)

Lifters

The burden for the lifters in a round are in principle

calculated with the same formula as for bench blasting.

The bench height is simply replaced by the advance, and

a higher fixation factor is used due to the gravitational

effect and to a greater time interval between the holes.

The maximum burden can be found using

where f is the fixation factor, E IV denotes the relation

between the spacing (E) and the burden (V), and E is

the corrected rock constant. A fixation factor f of 1.45

and an E I V ratio equal to 1 are used for lifters.

When locating the lifters, one must remember to con-

sider the lookout angle (see Fig. 11). The magnitude of

the angle is dependent upon available drilling equipment

and hole depth. For an advance of about 3 m a lookout

angle equal to 0.05 rad (3") (corresponding to -5

cmIm) should be enough to provide room for drilling

the next round.

Hole spacing should be equal to V. However, it will

vary depending upon the tunnel width.

The number of lifters N is given by

tunnel width f 2 H sin y

N = integer of v + 2).

The spacing EL for the holes (with the exception of

the comer holes) is evaluated by

tunnel width + 2 H sin y

EL =

N - 1

(m). (23)

The practical spacing EL. for the corner holes is

equal to

EL* = EL - H sin y (m). (24)

The practical burden VL should be reduced by the

bottom lookout angle and the drill hole deviation.

V L = V - H s i n y - F (m). (25)

The length of the bottom charge (h,) needed for

loosening the toe is

Fig. 11. Blasting geometry for lifters.

The length of the column charge (h,) is given by

and the concentration of this charge can be reduced to

70% of the concentration in the bottom charge. How-

ever, this is not always done because it is time-consuming

work. Generally the same concentration is used in both

the bottom and in the column. For lifters an unloaded

hole length of 10 d is usually used at the collar.

If Eq. 20 is going to be used, the following condition

has to be fulfilled:

Otherwise the maximum burden has to be succes-

sively reduced by lowering the charge concentration.

Then the practical spacing EL and burden V, can be

evaluated.

Fixation Factor

In the formulas, different fixation factors f are used

for calculating the burden in different situations. For

example, in bench blasting with vertical hole positioned

in a row with a fixed bottom, f = 1. If the holes are in-

clined it becomes easier to loosen the toe. To account

for this a lower fixation factor (f < 1) is used for an

inclined hole. This results in a larger burden. In tun-

neling a number of holes are blasted with the same delay

number. Sometimes the holes have to loosen the burden

upward and sometimes downward. Different fixation

factors are used to include the effects of multiple holes

and of gravity.

Stoping Holes

The method for calculating the stoping holes in sec-

tions B and C (Fig. 5) does not differ much from the

calculation of the lifters. For stoping holes breaking

horizontally and upward in section B, a fixation factor f

of 1.45 and an E I V ratio equal to 1.25 are used. The

fixation factor for stoping holes breaking downward is

reduced to 1.2, and EIV should be 1.25. The column

charge concentration for both types of stoping holes

should be equal to 50% of the concentration for the

bottom charge.

Contour Holes

If smooth blasting is not necessary, the burden and

spacing of the contour holes are calculated according to

what has been said previously about the lifters, with the

following exceptions: ( 1 ) fixation factor f = 1.2; (2)

E IV ratio should be 1.25; and (3) charge concentration

for the column charge is 50% of the bottom charge

concentration.

The blast-damaged roof and walls in a drift often

need an excessive amount of support. In low strength

rock, a long stand-up time usually can be achieved by

more careful contour blasting. A 3-m long borehole

with ANFO (1.5 kgIm) is capable of producing a

damaged zone of about 1.5-m radius.

With smooth blasting this damage zone is reduced to

a minimum. Our experience shows that the spacing is a

linear function of hole diameter (Persson, 1973).

where the constant k is in the range of 15 to 16. An

E IV ratio of 0.8 should be used. For a 41-mm hole

Page 7

1586 UIVDERGROUND MINING METHODS HANDBOOK

kg lm ANFO eauivalent

0-21 -/I7 mm GURlT

I / . 11 mm GURlT

J

2 0 40 60 Diameter mm

Fig. 12. Minimum required charge concentration for

smooth blasting and recommended practical hole diam-

eter for NABlT and GURlT charges.

diam the spacing will be about 0.6 m and the burden

about 0.8 m.

The minimum charge concentration per meter of

borehole is also a function of the hole diameter. For

hole diameters up to 0.15 m the relationship

applies. In smooth blasting the total hole length must be

charged to avoid ripping. In Fig. 12, 1 is plotted as a

function of d.

Rock Damage

The sudden expansion caused by an explosion in a

borehole generates a stress wave that propagates into the

rock mass. For an elastic material the generated stress is

directly proportional to density, particle velocity, and

wave propagation velocity.

Close to the charge the strain will reach a magnitude

where permanent damage is produced. Whether this

damage will have any significant influence on the

stand-up condition for a tunnel depends upon the char-

acter of the damage, the exposure time, the influence of

ground water, and the orientation of the joint planes

with respect to the contour and the static load.

For a long time, the damage criteria for structures

built in the vicinity of a blasting site have been based

upon the peak particle velocity. At SveDeFo (Swedish

Detonic Research Foundation) the same criteria have

been found to apply for estimating damage in the re-

maining rock (Persson, Holmberg, and Persson, 1977;

Holmberg and Persson, 1978; Holmberg, 1978).

The empirical equation is

where v is the particle velocity (mm/s); Q is the charge

weight ( kg ) ; and R denotes the distance (m). It is valid

for calculating the particle velocity at such distances

where the charge can be treated as being spherical. For

short distances the discrepancy between the calculated

and the measured values is unacceptable.

By performing an integration over the charge length

it was found possible to get the particle velocity as a

function of distance, charge length, and charge concen-

tration per meter of borehole. In Fig. 13 the calculation

for a 3-m long charge is given.

When the particle velocity exceeds some value be-

tween 700 and 1000 mm/s (Fig. 13), cracks are induced

or enlarged in a granite rock mass. A concentration of

Fig. 13. Peak particle velocity as a function of distance

and charge concentration for a 3-m long charge.

1 kg/m means that damage occurs in a zone of radius

1.0 to 1.4 m around the charge.

In field experiments for gneiss, pegmatite, and ,;an-

ite (tensile strength = 5 to 15 MPa), a very good agree-

ment between the calculated and measured values was

found. Reports about damage zones also agree well with

the calculated distances for similar charges if the 700 to

1000 mm/s criterion is used. This is valid for charge

concentrations in the range 0.2 to 75 kg/m.

In the field experiments accelerometers have been

used together with FM-tape and transient recorders.

Numerical integration provided the particle velocities.

The closest distance from the charges located in 25 to

250-mm holes to the accelerometers has been in the

range 1.5 to 13 m.

Measurements close to tunnel contours have indi-

cated that charges in the row next to the contour often

cause higher particle velocities and more damage than

the smooth blasted row. If a smooth blasting result

should not be ruined by the rest of the holes it is a good

idea to reduce the charge concentration in the row next

to the contour. Fig. 13 provides a guide for estimating

the charge concentration. A concentration of 0.2 kg/m

in the contour results in a damage zone of 0.3 m. If the

burden was 0.8, one can see that the charge concentra-

tion for the inner row should be limited to about 1 kg/m

if the damage zone of 0.3 m is not to be exceeded

(Fig. 14).

Fig. 14. A well-designed round where the charge concen-

trations in the holes close to the contour are adjusted

so that the damage zone from each hole coincides.

Page 8

BLASTING 1587

EXAMPLE OF CHARGE CALCULATION

Conditions

Hole diameter = 45 mm.

Empty hole, 4 = 102 mm.

Tunnel width = 4.5 m.

Abutment height = 4.0 m.

Height of arch = 0.5 m.

Smooth blasting in the roof.

Lookout for contour holes y = 0.05 rad ( 3 " ) .

Angular deviation a = 10 mm/m.

Collar deviation p = 20 mm.

Explosive: a water gel explosive is used with car-

tridge dimensions of 4 25 x 600, + 32 x 600, 4 38 x 600

mm.

Heat of explosion = 4.5 MJ/kg.

Gas volume at STP = 0.85 m3/kg.

Density = 1200 kg/m3.

Rock constant c = 0.4.

Calculation

Weight strength relative to LFB (Eq. 1 ) .

and

sANFO = 0.92/0.84 = 1.09

Charge concentration 4 mm I kg lm

25 0.59

32 0.97

3 8 1.36

Advance

Using an empty hole diameter 4 = 102 mm, Eq. 2

results in a hole depth of 3.2 m, and the advance is

3.0 m.

Cut

First Quadrangle

Maximum burden V = 1.74=0.17m

Practical burden V, = 0.12 m (Eq. 6 )

Charge concentration I = 0.58 kg/m (Eq. 9 )

1 for the smallest cartridge is 0.59 kg/m which is

sufficient for clean blasting the opening.

Unloaded hole length = 10d = 0.45 m (Eq. 19).

Hole distance in quadrangle B' = = 0.17 m.

No. of 25 x 600 cartridges = (3.2 - 0.45) 10.6 =

4.5.

Second Quadrangle

The rectangular opening to blast toward is B = \/Z

(0.12 - 0.05) = 0.10 m (Eq. 12).

Maximum burden for 425 cartridges V = 0.17 m

(El. 1 1 ) .

Maximum burden for 432 cartridges V = 0.21 m

(Eq. 1 1 ) .

Maximum burden for 438 cartridges V = 0.25 m

(Eq. 1 1 ) .

Eq. 15 says the practical burden must not exceed 2B.

This implies that the 432 x 600 cartridges are the

most suitable ones in this quadrangle.

Practical burden V2 = 0.16 m (Eq. 14)

Unloaded hole length h = 0.45 m 0%. 19)

Hole distance in quadrangle B' = a (0.16 + 0.17/

2 ) = 0.35 m.

No. of 432 x 600 cartridges = 4.5.

Third Quadrangle

B = f l (0.16 + 0.17/2 - 0.05) = 0.28 m.

Use 438 x 600 cartridges with charge concentration

I = 1.36 kg/m.

Maximum burden V = 0.42 m.

Practical burden V3 = 0.37 m.

Unloaded hole length h = 0.45 m.

Hole distance in quadrangle B' = a (0.37 + 0.35/

2 ) = 0.77 m.

No. of 438 x 600 cartridges = 4.5.

Fourth Quadrangle

B = \a (0.37 + 0.35/2 - 0.05) = 0.70 m.

Maximum burden V = 0.67 m.

Practical burden V, = 0.62 m.

Unloaded hole length h = 0.45 m.

B' = a (0.62 + 0.77/2) = 1.42 m.

No. of 438 x 600 cartridges = 4.5.

The side length of this quadrangle is 1.42 m which is

comparable to the square root of the advance.

Therefore there is no need for more quadrangles.

Lifters

Use 438 x 600 cartridges with a charge concentration

of 1 = 1.36 kg/m.

Maximum burden V = 1.36 m (Eq. 20)

No. of lifters N = 5 (Eq. 22)

Spacing E, = 1.21 m (Eq. 23)

Spacing, corner holes E', = 1.04 m (Eq. 24)

Practical burden V, = 1.14 m (Eq. 25)

Length of bottom charge h, = 1.43 m (Eq. 26)

Length of column charge h, = 1.32 m (Eq. 27)

This charge concentration shall be 70% of the bot-

tom charge concentration; 0.70 X 1.36 = 0.95 kg/m.

Use 2.5 cartridges 438 x 600 as the bottom charge

and 2 cartridges 432 x 600 as the column charge.

Contour Holes, Roof

Smooth blasting with 425 x 600 cartridges is speci-

fied.

Spacing E = 0.68 m (Eq. 29) .

Burden V = E/0.8 = 0.84 m.

Due to lookout and deviation the practical bur-

den becomes V, = 0.84 - 3.2 sin 3" - 0.05 = 0.62 m.

The minimum charge concentration for this smooth

blasting is 1 = 90 d2 = 0.18 kg/m (Eq. 30).

The charge concentration for the 425 X 600 car-

tridges is 0.59 kg/m which is considerably more than

what is really needed.

No. of holes; integer of (4.7/0.68 + 2 ) = 8.

5 cartridges per hole are used.

Contour Holes, Wall

The abutment height is 4.0 m and from the calcula-

tion it is known that the lifters should have a burden of

1.14 m, and the roof holes should have a burden of

0.62 m. This implies that there are 4.0 - 1.14 - 0.62 =

2.24 m left in the contour along which to position the

wall holes.

By using a fixation factor f = 1.2, and an E/V-ratio

equal to 1.25, Eq. 20 results in a maximum burden

V = 1.33 m.

Practical burden V,, = 1.33 - 3.2 sin 3" - 0.05 =

1.12 m.

No. of holes = integer of (2.24/ (1.33 X 1.25) + 2 )

= 3.

Page 9

UNDERGROUND MINING METHODS HANDBOOK

Spacing = 2.24/2 = 1.1 2 m.

Length of bottom charge h, = 1.40 m.

Length of column charge h, = 1.35 m.

2.5 cartridges $38 x 600 are used as the bottom

charge, and 2 cartridges $32 x 600 are used in the

column.

Stoping

The side of the fourth quadrangle in the cut is

1.42 m, and the practical burden V , for the wall holes

was determined to be 1.12 m. As the tunnel width is

4.5 m a distance of 4.5 - 1.42 - 2 X 1.12 = 0.84 m is

available for placing horizontal stoping holes.

Maximum burden ( f = 1.45) V = 1.21 m.

Practical burden V H = 1.21 - 0.05 = 1.16 m.

Instead the burden VH = 0.85 m is used, due to the

tunnel geometry.

The height of the fourth quadrangle was 1.42 m, and

this will of course determine the spacing for the two

holes, which becomes 1.42 m.

For stoping downwards:

~ax imLmburden V = 1.33 m.

Practical burden V , = 1.28 m.

The maximum height of the tunnel is specified to be

4.5 m. If we subtract the height of the fourth quadrangle

( 1.42 m) , the burdens for the lifters (1.14 m) and the

roof holes (0.62 m), there is 1.32 m left for a stoping

hole. This is just a little more than the practical burden,

but if the stoping holes are placed at 1.28 m above the

cut, the remaining 0.04 m will in all probability be re-

moved by the overcharged contour. Furthermore, the

formulas used in the calculation have a safety margin

that can tolerate small deviations.

Three holes for stoping downward are positioned

above the fourth quadrangle (see Fig. 15). The charge

distribution for the stoping holes is the same as for the

wall holes.

A summary of explosive consumption is given in

Table 2.

ACKNOWLEDGMENT

This work was done as a part of the rock-blasting

research program of the Swedish Detonic Research

Foundation supported by Swedish industry and the

National Swedish Board for Technical Development.

Fig. 15. Calculated drilling pattern; MS stands for rn-sec

caps (4 no. = 100 rn-sec) and HS stands for half sec

caps (1 No. = 0.5 sec).

The author gratefully acknowledges professional dis-

cussions with present and former colleagues at SveDeFo

and Nitro Consult whose experiences in the art of charge

calculations helped in the formulation of this chapter.

REFERENCES AND BIBLIOGRAPHY

Gustafsson, R., 1973, Swedish Blasting Technique, Gothen-

burg, Sweden.

Holmberg, R., 1975, "Computer Calculations of Drilling

Patterns for Surface and Underground Blastings," Design

Methods in Rock Mechanics, C. Fairhurst and S. Crouch,

eds., 16th Symposium on Rock Mechanics, University of

Minnesota, Minneapolis.

Holmberg, R., and Hustrulid, W., 1981, "Swedish Cautious

Blast Excavations at the CSM/ONWI Test Site in Colo-

rado," 7th Conference of Explosives and Blasting Tech-

nique, Phoenix.

Holmberg, R., and Mahi, K., 1982, "Case Examples of Blast-

ing Damage and Its Influence on Slope Stability," Stability

in Surface Mining, Vol. 3, AIME, New York.

Holmberg, R., and Persson, P.-A., 1979, "Design of Tunnel

Perimeter Blasthole Patterns to Prevent Rock Damage,"

Proceedings, Tunnelling '79, M.J. Jones, ed., Institution of

Mining and Metallurgy, London.

Holmberg, R., 1978, "Measurements and Limitations of

Table 2. Summary of Explosive Consumptlon

No. of Cartridges

Hole No. of Charge per Total

Type Holes 425 432 438 mm Hole, kg kg

1st quad. 4 4.5 1.59 6.37

2nd quad. 4 4.5 2.62 10.48

3rd +4th quad. 8 4.5 3.67 29.36

Lifters 5 2.0 2.5 3.20 16.00

Roof 8 5.0 1.77 14.16

Wall 6 2.0 2.5 3.20 19.20

Stoping 5 2.0 2.5 3.20 16.00

Total charge weight = 11 1.6 kg

Cross sectional area = 19.5 m2

Advance = 3.0 m

Specific charge = 1.9 kg/m3

Total No. of holes = 40

Hole depth = 3.2 m

Specific drilling = 2.2 m/m3