Charge Calculations for Tunneling (HOLMBERG)

Chapter 1. Charge Calculations for Tunneling

ROGERHOLMBERG INTRODUCTION The driving of drifts is a very important aspect of underground mining. It is not unusual for the percentage 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 handheld 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 drilling holes) has unfortunately been lost. By having separate shifts for drilling, loading, and hauling, more attention 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,

Fig. 1. Development for sublevel

caving.

it is probably not possible to achieve the same precision as with pneumatic pushers, and it is difficultto utilize the larger holes because these cause more damage to the remaining rock. Recently, however, the precision has become 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 calculation method are based upon the earlier work of Langefors 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 methods have been developed to charactxize the strength of an explosive. Some examples are comparison of values given by ( 1 ) calculated explosion energies; ( 2 ) the ballistic 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 methods should be used carefully when stating the breaking

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1582

CHARGE CALCULATION AND DESIGN OF DRILLING PATTERN Tunnel blasting is a much more complicated operation 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 presents a good guide for explosive consumption for varying tunnel sizes. Environmental aspects influence the choice of explosive 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 occurrence 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 present 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 forward 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 detonation front, destroys the hot spots, or increases the density 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 procedure 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 increase in size until the stoping holes can take over. The

t

Specific charge kg/m3

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 decade 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 diameter 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 opening 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 calculation. Advance The advance is restricted by the diameter of the empty hole and the hole deviation for the smaller diameter holes. Good economics demand maximum utilization of the full hole depth. Drifting is getting very expensive 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 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)

25

7

50

7'5

loo ~ r e a-m2

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

(3)

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 computed according to the following:

BLASTING

t

H Hole depth at 95% advance

I

1Burden Vl

m

0.1

m

C

a2

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 differ 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 deformation would be the only effect of the blast. Even if the distance is smaller than 2 4, too great a charge concentration 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-

%

-

SECTION -FOUR - - - - -CUT - -

- -

-0

I

the holes meet 0.2 d3

0:1

*

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 reduced 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 deviation (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 . (

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

V

) (V - 4/21

(kg/m)

(7)

T o 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 concentration 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 diameter. 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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Obviously, when the diameter is increased this means that the coupling ratio and the borehole pressure decrease. It is important to carefully select the proper explosive 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 programmable pocket calculator and an iterative procedure.

Fig. 10. Influence of the hole deviation. den V can be expressed explicitly with good accuracy as a function of B and I.

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 determined 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 materials, 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 following quadrangles. Blasting tosalds a circular hole naturally demands a higher charge concentration than blasting towards a straight face due to a higher constriction 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= (kg/m). (10) ~ A N F O[sin (atn(B/2V) 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-

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 fist quadrangle as if they were placed at the most unfavorable 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 drillhole 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 foursection cut. This means V, > 0.5 B. (18)

Fig. 9. Geometry for blasting towards a straight face.

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.

BLASTING The algorithm for the calculation of the remaining quadrangles 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=lOd (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 I V 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 consider 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 = (m). (23) N-1 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. VL=V-Hsiny-F (m). (25) The length of the bottom charge (h,) needed for loosening the toe is

+

Fig. 11. Blasting geometry for lifters.

1585

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. However, 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 successively 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 inclined 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 tunneling 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 sections 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 E I V 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 I V 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 I V ratio of 0.8 should be used. For a 41-mm hole

UIVDERGROUND MINING METHODS HANDBOOK

1586

k g l m ANFO eauivalent

0-21

mm GURlT

7I / -

I/.

20

11 mm GURlT J

40

60 Diameter

mm

Fig. 12. Minimum required charge concentration for smooth blasting and recommended practical hole diameter 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 character 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 remaining 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 ( k g ) ; 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 concentration per meter of borehole. In Fig. 13 the calculation for a 3-m long charge is given. When the particle velocity exceeds some value between 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 ,;anite (tensile strength = 5 to 15 MPa), a very good agreement 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 indicated 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 concentration 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 concentrations in the holes close to the contour are adjusted so that the damage zone from each hole coincides.

BLASTING 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 cartridge 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 k g l m 25 0.59 32 0.97 38 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). = 0.17 m. Hole distance in quadrangle B' = 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' = (0.16 0.17/ 2 ) = 0.35 m. No. of 432 x 600 cartridges = 4.5.

a

+

1587

Third Quadrangle B = fl(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' = (0.37 0.35/ 2 ) = 0.77 m. No. of 438 x 600 cartridges = 4.5.

+

a

+

Fourth Quadrangle B= (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' = (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.

\a

+

a

+

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. 2 3 ) 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 bottom 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 specified. Spacing E = 0.68 m (Eq. 2 9 ) . Burden V = E/0.8 = 0.84 m. Due to lookout and deviation the practical burden 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. 3 0 ) . The charge concentration for the 425 X 600 cartridges 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 calculation 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.

+

UNDERGROUND MINING METHODS HANDBOOK Spacing = 2.24/2 = 1.12 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 V H= 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: ~ a x i m L m b u r d e nV = 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 removed 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 discussions 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, Gothenburg, 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 Colorado," 7th Conference of Explosives and Blasting Technique, Phoenix. Holmberg, R., and Mahi, K., 1982, "Case Examples of Blasting 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 Type

No. of Holes

1st quad. 2nd quad. 3rd +4th quad. Lifters Roof Wall Stoping

4 4 8 5 8 6 5

425

432

438 mm

4.5 4.5 2.0

4.5 2.5

2.0 2.0

2.5 2.5

5.0

Total charge weight Cross sectional area Advance Specific charge Total No. of holes Hole depth Specific drilling

=

111.6 kg

= 19.5 m2 = 3.0 m

1.9 kg/m3 40 3.2 m = 2.2 m/m3 = = =

Charge per Hole, kg

Total kg

1.59 2.62 3.67 3.20 1.77 3.20 3.20

6.37 10.48 29.36 16.00 14.16 19.20 16.00

Rock Damage in Remaining Rock," Rock Mechanics Meeting, Stockholm. Holmberg, R., and Persson, P.A., 1978, 'The Swedish Approach to Contour Blasting," 4th Conference on Explosives and Blasting Technique, New Orleans, LA, Feb. Johansson, C.H., and Persson, P.A., 1970, Detonics o f High Explosives, Academic Press, London. Langefors, U., and Kihlstrom, B., 1963, The Modern Technique of Rock Blasting, Almqvist and Wiksell, Stockholm. Naarttijhi, T., et a]., 1980, "Field Experiments with Cau-

tious Blasting," TULEA, 1980:26, University of Lulea, Sweden. Persson, P.A., 1973, "The Influence of Blasting on the Remaining Rock," Report DS 1973: 15, Swedish Detonic Research Foundation. Persson, P.A., Holmberg, R., and Persson, G., 1977, "Careful Blasting of Slopes in Open Pit Mines," Report DS 1977 :4, Swedish Detonic Research Foundation. Svanholm, B.O., Persson, P.A., and Larsson, B., 1977, "Smooth Blasting for Reliable Underground Openings," Rockstore 77, Session 1, Sweden, Sep.