Teaching and Training Material Drill & Blast

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Australian Drilling Industry Training Committee Ltd

DRAFT

Calculations & Terms

used in

Drill & Blast Operations

library National Centre for Vocational Education Resea h

level 11. 33 King William SI. Adelaide SA 5000 Decembe~199~-----------------------+~

Calculations & Terminology for Drill & Blast Operations

This document was developed by:

The Australian Drilling Industry Training Committee Ltd P.O. Box 1545 Macquarie Centre NSW 2113 Phone: (02) 9887 1077 Fax: (02) 9888 2078

Project Manager Virginia Hilliard Chief Executive Officer Australian Drilling Industry Training Committee Ltd P.O. Box 1545 Macquarie Centre NSW 2113 Phone: (02) 9887 1077 Fax: (02) 9888 2078

Project Officer:. Lee Fletcher

We gratefully acknowledge the contribution made by Coldwell Drilling Co, Rockhampton, Qld.

--~-~----- .

. '(1s1dd I -' c;, i::;jrc;:JiJb3 lsf1oif5:)oV 101 9'tr~9J 'sno!Js't-1 f

c rr:::;i!~:\J') 2I'1i){ se . t t Isv9J . I. . ~."~= ['2 9C.,c!".~.~ Copyrigh;l: Commonwealth of Australia, 1999

.. __ .. _.- .. .. ---Galculatiens-&-rerminology for Drill & Blast Operations was developed with funding from the Workplace English Language and Literacy Program through

the Department of Employment, Training and Youth Affairs.

Contents

Section 1- Quick Reference Metric Summary Chart

Conversion factors

Examples using Common Formulae .......................................................... .

Complex Formulae

Section 2 - Carrying Out Calculations Area

Triangle Trapezium Cylinder Annulus

Volume & Capacity

Volume Cylinder Rectangular Prism Blast Pattern Blast Hole

Density & Specific Gravity

Up-Hole Velocity

Angles

Charts Inclined Blast Hole Sine, Cosine & Tangent

Page

2

4

5

6

10

13

14

17

18

19

20

Blast Design Parameters ... ............ .................................... ... ...... ... ......... 22 Bench height Blast hole diam~ter Burden Spacing Sub-grade drilling Stemming Blast hole angle Powder factor Relative Weight Strength Relative Bulk Strength Intra-Row & Inter-Row Delay

Contents (continued)

Page

Scaling of Blast Parameters ...................................................................... 27

Geometrical Formulae

. Density of Rock Type

Wet Hole Calculations

28

29

30

Scaled DistancesNibration Control ............................. , ... ... ... ... ... ... ... ... ...... 30

Unit of Measure Conversion .... ...... ... ......... ... ... ... ...... ... ... ...... ... ... ... ...... ... . 32

Blast Hole Loading Densities Chart .................. .................. ...... ...... ...... ...... 34

Section 3 - Blast Hole Terminology

Abbreviations

Definitions

Section 4 - Test Yourself Answers

36

37

42

Section 1

Quick Reference

Calculations & Terms used in Drill & Blast Operations 1

2

Metric Summary Chart

Length Units of length are: millimetres (mm)

centimetres (cm) metres (m) kilometres (km)

1m 1000mm = 10mm 100cm 1000m

= 1cm = 1.0m = 1km

CapacityNolume Units of liquids: millilitres (ml)

Litres (I) Kilolitres (kl) Megalitre (MI)

Units of solids: . cubic cm (cm3) Cubic metres (m3)

1000ml = 1 litre 1 000 litres = 1 kl

= 1m3 1000KI = 1MI

Mass Units of mass/weight: milligrams (mg)

grams (g) kilograms (kg) tonnes (t) .

1000mg 1000g 1000kg

Pressure

= 19 = 1kg = 1 tonne

The unit of measurement is a Pascal. It is too small to be of use by itself.

1000Pa 1000 kPa

= 1 kilo pascal or 1 kPa = 1 Megapascal or 1 Mpa

Calculations & Terms used in Drill & Blast Operations

Area Units of area:

1 hectare

square mm (mm2) square cm (cm2) square m (m2) hectares (ha)

= 10,OOOm2

100mm2 10,OOOcm2

= (eg. a square 100m x 100m) :: 1cm2 = 1m2

Metric Units For simple estimation purposes we can use our own body as reference to measure things.

Check your own body measurements and write them in the boxes below.

Body measurements

Width of little nail/finger (is about 1cm)

Width of palm of hand ( is about 10cm)

Hand span from tip of little finger to tip of thumb (is about 20cm)

Outstretched arm from nose to fingertip ( is about 1 metre)

A long stride (is about 1 metre)

Calculations & Tel7Tls used in Drill & Blast Operations 3

Conversion Factors

Length Inches (in)

Feet (ft)

Mass

Pounds (Ibs)

Imperial ton(2,2401bs)

US ton (2,000lbs)

Volume

US gallons (Usgal)

US gallons (Usgal)

Imperial gallons (gal)

Cubic metres (m3 )

Barrel

Flow Rate

Cubic ft per min (cfm)

x 25.4 = millimetres (mm)

x 0.305 = metres (m)

x 0.454 = kilograms (kg)

x 0.98 = metric tonne (T)

x 0.909 = metric tonne (T)

x 0.833 = imperial gallons

x 3.785 = litres (L)

x 4.54 = Htres (L)

x 1,000 = litres (l)

x 158.8 = litres (l)

x 28.3 = litres per min (Umin)

Cubic metres per min (m3/min) x 1,000 = litres per min (Umin)

Litres per sec (Usec) x 790 = imperial gal per hr (GPH)

Cubic metres per day (m3/day) x 220 = imp gal per day (GPD)

Density

Pounds per US gal (Ib/gal) x 0.12 = specific gravity (SG)

4 Calculations & Tenns used in Drill & Blast Operations

Examples using Common Formulae

Formula Example Perimeter of rectangle (add sides) P (perimeter) = 2(1 + b) Find perimeter of rectangle

3.7 m long & 2.2 m wide.

I I P = 2 (I + b)

= 2 (3.7 + 2.2) = 2 x 5.7 = 11.8 m

Area of rectangle (multiply 2 . sides) A (area) = I x b Find area of rectangle 6

A = Ib metres long and 2.3 metres

I I wide.

A =Ib = 6x 2.3 = 13.8 m2

Circumference of a circle C = 21tr or C = 1td Find the circumference of a

0 circle with a diameter of 20 (1t = 3.142) cm. C = 1td = 3.142 x 20 = 62.83 cm

Area of circle

0 A = 1tr2 Find the area of a circle with a

radius of 10 cm. A = 1t~

= 3.142 x 10 x 10 = 314.16 m2

Volume of rectangular prism V (volume) = I xb x h Find volume of a rectangular

0 0 = Ibh prism 47 mm long, 30 mm wide & 15 mm high. V.= Ibh = 47 x 30 x 15 = 21150 mm3

Volume of cylinder V = base area x length Find the volume of a cylinder

= 1t~ x I (length) with diameter of 4 m & height of3 m. If diameter is 4m then r = 2.

V = n~h = n2x2x3

Volume = 37.70 m3


Area

Complex Formulae

Legend

p = perimeter A = Area h = height r= radius d= diameter e = length of diagonals

Right angled triangle - Pythagoras c2 formula

p = a+b+c

c2 = a2 + b2

b c b = "c2 _a2

A = ab indicates right 2 angle a

or

y. axb

Equilateral Triangle

p = 3a

h = a"3 = 0.866a a 2

A = a2 "3 = 0.433a2 4 a

indicates rig hi angle

6 Calculations & Terms used in Drill & Blast Operations

Trapezoid

A = Y:z h (a + b)

Trapezium

P = a+b+c+d

A = Sum of areas of two major triangles

Ellipse

p = D (a + b) approx

or D [1.5(a + b) - "abj

A = Dab

b

Calculations & Tenns used In Drill & Blast Operations

a

7

Volume of Solids

Legend

A = total area V = volume

Cube

a a

Parallelopiped

A = 2(ab + bc + ac) v = abc

a

Sphere

A = 4ltr = 12.566r

v = 4 ltr = 4.189r

Cone(eg stock pile)

8 Calculations & Tenns used in Orill & Blast Operations

Section 2

How to carry out calculations

Calculations & Tenns used in Drill & B/ast Operations 9

Area

Area of a Triangle

A = %Ix h

10cm = % x 12 x 10

= 60 cm2 ( 2 because it is area)

12cm

Test Yourself

Find the area of these triangles

a) h = 24cm, I = 30cm

b) h = 8.24cm, I = 3.4cm

Area of a Trapezium

A = Yo h (a + b)

15cm A = Yo x 7(1 Oem + 15cm)

\j7cm 7 = Yo x 7 x 25 (Always do sum in brackets first) = 87.5cm2 ( 2 because it is area)

10cm

Test Yourself

Find the area of this trapezium.

a = 30m, b = 45m, h = 8m


Surface Area of a Cylinder If we could cut a cylinder down one side and unroll it, it would be a rectangle. h

The circumference of the circle must be equal to the length of the rectangle, and the height of the cylinder must be equal to the breadth.

circumference -0 (11 = 3.142)

Circumference ...... 4--

21Tr

RadiUS-) If the radius of the cylinder ( r ) was 2 cm, then the length of the rectangle is

r = 2 C = 2m

= 2x3.142x2 = 12.6 cm

If the height of the cylinder was 5 cm, then the breadth of the rectangle will be 5 cm. Hence, the surface area of the cylinder (ie. area of the rectangle) is

Area = Ixb = 12.6 x 5 = 63 cm2

The ends of the cylinder are circles. Area of a circle is 11 f. For both ends the area is 2 11 f. Therefore, total surface area of a cylinder is

A = 211fh + 211f or A = 211r (h + r)

Test Yourself

A cylinder has a base diameter of 40cms and height of 60cms. Find

a) the surface area of the cylinder (rectangle). Use your calculator.

b) The total surface area of the cylinder

Calculations & Tenns used In Drill & Blas,t Operations 11

..... Annulus-- ... - .-- ....... -.-

The annulus is the space between two circles.

Area of annulus = area of outside circle - area of inside circle

Find the area of the annulus. The radius of outside circle is 1 m; radius of inside circle is SOcm.

A (outside circle) = 1tx1mx1m

= 3.14m2

A (inside circle) = 1t x O.Sm x O.Sm

= 2.01m2

Area of annulus = 3.14-2.01m2

= 1.13m2 (1t = 3.142)

Test Yourself

Find the area of the annulus in m2 when using 100mm drill pipe in a 250mm diameter hole.

A (outside circle) = =

=

A (inside circle) =

=

=

Area of annulus =

=


Volume The basic measurement of volume is the cubic metre (m3 ).

1m 1m

1m

..1 ............. _ ... _-1---7 / ./~.

/ v = Length x Width x Depth (L x W x D)

We get the volume of the tank this way: v = 1m x 1m x 1m

Example A tank has these dimensions: L = 1.1 metres; W = 0.8 metres; D = 0.4 metres

V=LxWxD

= 1.1xO.BxO.4

= 0.3/i2m

Capacity

Directly related to volume is capacity, which is the amount of fluid a tank can hold.

A litre is the amount of liquid that will fit in a container 10cm by 10cm by 10cm.

As well as expressing the volume of the tank in m3 , we can express the volume in Iitres.

Remember, 1 m3 = 1000 Iitres, so

Liquid volume = 0.352 x 1000

= 3521itres

Test Yourself

A rectangular mud pit is L = 1.2m, W = 0.8m, D = 0.6m

What is the volume of the pit in m3 ?

What is the liquid volume?

Calaulations & Terms used in Drill & Blast Operations 13

Volume of Cylinder

A cylinder is an object that has circular ends. It can be solid or hollow, eg pipes

The area of a circle is 1l~ (11 "=3.142) To calculate the volume of a cylinder we multiply the circular base area by the height of the cylinder. length _-+I

Volume of cylinder = base area x length

= 1l~ x I (length) ~ " circular base

For example;

What is the volume of a pipe with a length of 8 m and diameter of 0.3 m?

Formula is V = llrZ h

Radius: r = diameter 2

= 0.3 m 2

= 0.15 m

Area of base: = 1l~

= 3.142xO.15mxO.15m

= 0.0707 m2

So, volume: = 0.0707 m2 x 8 m

= 0.566 m3 or 566 litres

Test Yours"elf

What is the volume of a cylinder with a diameter of 4m and a height of 3m?


Volume of a Rectangular Prism.

Formula

Iv =Ixbxh

, = Ibh

example: Find the volume of a rectangular prism 47m long, 30m wide and 15m high.

J , ............. _,_." .. -""""" .. "." .... . /

,/

Test Yourself

v = Ibh

= 47x30x15

= 21150m3 (or21150cubicmetres)

Find the volume of a rectangular prism with these dimensions:

2.5m wide, 8.5m long, 3.2m high

Calculations & Tenns used in Drill & Blast Operations 15

Volume of a Blast Pattern

Volume of pit

Volume in Iitres

= length x width x vertical height = m30rfe

= m3 x 1000

'real' blast hole average dimensions

Example: Dimensions of a blast hole are:

I = 6m; w = 3m; vh = 1m.

Volume of hole = (6 x 3 x 1) m3

- 18m3

Volume in litres = 18 x 1000l

= 18,000l or 18Kl

Volume of a Blast Hole

Formula

Example: What is the volume of a hole with a depth of 8m and diameter of 0.3m?

785 x 0.3 x 0.3 x 8

= 565.2 l

Test Yourself


Density

Formula

Density = Mass Volume

Example:

A 20L drum is full of liquid. The weight of the liquid is 25kg. What is the density of the liquid in kg/m3?

Density =

=

=

Mass Volume

25kg 20L

1.25kg/L

Specific Gravity (S.G.) Density of water is taken to be 1 kg/L.

This formula is used to detern:tine whether explosive will sink in water.

Specific gravity = weight of explosive weight of same volume of water

If volume is greater than 1, explosive will sink. If volume of explosive is less than 1, explosive will float.

Example 1: If we have 1 litre of salt water weighing 1.2kg, the S.G.= 1.2 + 1 = 1.2.

Volume of cylinder = package of explosive

D =

L =

Calculate V =

Weight =


Up-Hole Velocity (UHV) The velocity (speed) of air flowing up the annulus is a critical factor in lifting and clearing cuttings from a drill hole.

The size of the annulus will determine up-hole velocity when using a consistent volume of delivered air. This means that UHV will be higher in a small annulus and lower in a large annulus.

The recommended UHV for blast hole air drilling is:

1,500 to 2,100 metres per minute (mpm) 5,000 to 7,000 feet per minute (fpm)

Formula

U.H.V. (m/min) =

or

2 x cfm x 28.3 02_d2

2 x Umin 02 - d2 (ins)

cfm = cubic feet per minute Lpm = Litres per minute 0 2 = hole diameter in inches d2 = drill rod or pipe diameter

in inches

Example: A drilling project requires a number of 6" diameter holes to a depth of 20 metres. Our available rig is equipped with 4" diameter drill pipe and a compressor which delivers 650 c.f.m (18,400 Umin) of air.

U.H.V. =

=

=

Test Yourself

18

2 x 18,400 36-16

36,790 20

1,840 m/min

Calculations & Tenns used in Drill & Blast Operations

Measuring Angles Angles are used to measure how far something has turned/rotated.

o CD 360' 90' 180'

360 degrees is one complete revolution.

Angles have 2 arms. The arms meet at the point called the vertex.

Acute angle

A

C

C

Obtuse angle B A ~-----

We use a protractor to measure angles. It covers a range of 180'.

270'

SA and BC are arms

B is the vertex

L is the symbol for angle

) indicates angle

The centre point of the base line of the protractor goes on the vertex of the angle.

Example,

This angle measures 135.

TestVourself

Write down the size of the angle in the following.


Inclined Blastholes

v = Vertical distance including vertical sub-grade (metres) D = Deviation from the vertical to the nearest 0.1m V

L = Length from the vertical to the nearest 0.1 m D

Angle from Vertical 5 10 15 20 25 30 35 40

V D L D L D L D L D L D L D L D L

5 0.4 5.0 O.g 5.1 1.3 5.2 1.8 5.3 2.3 . 5.5 2.9 5.8 3.5 6.1 4.2 6.5 6 0.5 6.0 1.1 6.1 1.6 6.2 2.2 6.4 2;8 6.6 3.5 6.9 4.2 7.3 5.0 7.8 8 0.7 8.0 1.4 8.1 2.1 8.3 2.9 8.5 3.7 8.8 4.6 9.2 5.6 9.8 6.7 10.4 10 0.9 10.0 1.8 10.2 2.7 10.4 3.6 10.6 4.7 11.10 5.8 11.5 7.0 12.2 8.4 13.1 12 1.1 12.0 2.1 12.2 3.2 12.4 4.4 12.8 5.6 13.2 6.9 13.9 8.4 14.6 10.1 15.7 14 1.2 14.1 2.5 14.2 3.7 14.5 5.1 14.9 6.5 15.4 8.1 16.2 9.8 17.1 11.8 18.3 15 1.3 15.1 2.6 15.2 4.0 15.5 5.5 16.0 I 7.0 16.6 8.7 17.3 10.5 18.3 12.6 19.6 16 1.4 16.1 2.8 16.2 4.3 16.6 2.8 17.0 7.5 17.7 9.2 18.5 11.2 19.5 13.4 20.9 i 18 1.6 18.1 3.2 18.3 4.8 18.6 6.6 19.2 8.4 19.9 10.4 20.8 12.6 22.0 15.1 23.5 ' 20 1.8 20.1 3.5 20.3 5.4 20.7 7.3 21.3 9.3 22.1 11.6 23.1 14.0 24.4 16.8 26.1 22 1.9 22.1 3.9 22.3 5.9 22.8 8.0 23.4 10.3 24.3 12.7 25.4 15.4 26.9 18;5 28.7 24 2.1 24.1 4.2 24.4 6.4 24.8 8.7 25.5 11.2 26.5 13.9 27.7 16.8 29.3 20.1 31.3 25 2.2 25.1 4.4 25.4 6.7 25.9 9.7 26.6 11.7 27.6 144 28.9 17.5 30.5 21.0 32.6

(Contributed by Coldwell Drilling Co)


Anole (Dearees) Sine Cosine Tangent 0.0 0.000 1.000 0.000 2.5 0.044 0.999 0.044 5.0 0.087 0.996 0.087 7.5 0.131 0.991 0.132 10.0 0.174 0.985 0.176 12.5 0.216 0.976 0.222 15.0 0.259 0.966 0.268 17.5 0.301 0.954 0.315 20.0 0.342 0.940 0.364 22.5 0.383 0.924 0.414 25.0 0.423 0.906 0.466 27.5 0.462 0.887 0.521 30.0 0.500 0.866 0.577 32.5 0.537 0.843 0.637 35.0 0.574 0.819 0.700 37.5 0.609 0.793 0.767 40.0 0.643 0.766 0.839 42.5 0 .. 676 0.737 0.916 45.0 0.707 0.707 1.000 47.5 0.737 0.676 1.091 50.0 0.766 0.643 1.192 52.5 0.793 0.609 1.303 55.0 0.819 0.574 1.428 57.5 0.843 0.537 1.570 60.0 0.866 0.500 1.732 62.5 .. 0.887 0.462 1.921 65.0 0.906 0.423 2.145 67.5 0.924 0.383 2.414 70.0 0.940 0.342 2.747 72.5 0.954 0.301 3.172 75.0 0.966 0.259 3.732 77.5 0.976 0.216 4.511 80.0 0.985 0.174 5.671 82.5 0.991 0.131 7.596 85.0 0.996 0.087 11.430 87.5 0.999 0.044 22.904 90.0 1.000 0.000 inf

tan 0 = o~ adj c050 = a~ hyp

Hypotenuse djacent

5in0 = Op% hyp

Opposite

hyp2 = adj2 + Opp2

(Contributed by Coldwell Drilling Co) Calculations & Terms used in Drill & Blast Operations 21

Blast Design Parameters

The following 'rules of thumb", derived from years of practical experience, are more appropriate for developing an initial blast design. The 'rules of thumb' apply to looses Iy poured ANFO at a density of 0.8 g/cm3 in a rock of average strength.

Bench Height

Chosen on the basis of local ground conditions, safety regulations and the size and type of the loading equipment.

Rule of Thumb

8ench height (H) = 60 x blast hole diameter (mm)

Blast Hole Diameter (d)

Generally dictated by the available equipment but should be selected so that the bench height (H) is in the range of 60d to 140d.

Rule of Thumb

d (mm) = (8 - 15) H (m)

{Where d = blast hole diameter (mm) and H = bench height (m) }

Burden (B)

The burden is the distance between two drilled rows of blast holes. Generally iUs in the range of 24d to 36d. A value of 30d should be chosen initially.

Rule of Thumb

8 (m) = (20 to 35 ) d (m)

Spacing (S)

20 Hard massive rock 27 Average rock 35 Softer well-jointed rock

The spacing (m) is the distance between two blast holes within the same row.

Spacing too close, causes premature splitting, crushing and cratering between blast holes. Spacing too large, causes inadequate fracturing between blast holes resulting in poor fragmentation of the rock mass.

Should initially be 1.158 (gives an equilateral triangle pattern).


Rule of Thumb

S (m) = (1 to 1.8) B (m)

Subgrade Drilling (SO)

1 hard massive rock 1.15 (equilateral triangle) 1.8 soft jointed rock

Subgrade drilling (sub-drill) is the distance drilled below floor level to ensure that the full face of the rock is removed.

stemming

Explosive charge length

Generally in the range of 8d to 12d. A value of 10d is usually chosen initially.

Rule of Thumb

SO (m) = (0.1 tq 0.5) B (m)

Stemming (ST)

0.1 easy toe 0.3 average toe 0.5 hard toe

Stemming is an inert material which is used to fill the zone from the top of the explosive charge to the collar of the blast hole. This material confines the explosive gasses and reduces airblast.

Rule of Thumb

ST = (0.7 to 1.0) B

Blast Hole Angle

0.7 hard massive rock/good stem material 1.0 easy to blast rock, cautious blasting

Should be selected so that blast holes are parallel to the face (where possible).


Powder Factor

Powder factor is defined as the mass of explosive divided by the volume of rock expressed in kg/m3.

Powder factor = Mass of Explosive Volume of Rock

= Explosives Mass Per Metre (1) x Charge Length (2)

(1) Exp Mass per metre = 1L x Jf. x P 4 1000

d = diameter (mm)

Burden x Spacing x Bench Height

p = density of explosive (g/cm3) (2) Exp Charge Length = Blast hole length (3) - Stemming length

(3) Note that blast holes drilled on an angle are longer than blast holes drilled vertically (for the same Bench Height and Subdrill) and need to be accounted for.

Soft well structured rock usually requires powder factors of about 0.10 kgfT of ANFO while in hard massive rocks the powder factor ranges up to 0.40 kgrT.

Relative Weight Strength (RWS)

RWS is a percentage approximation of the strength of an explosive compared kg for kg to ANFO. ANFO = 100%. Explosive)t RWS = 125% (1.25) is supposed to be 25% stronger than ANFO on a kg for kg basis.

Relative Bulk Strength (RBS)

RBS is a percentage approximation of the strength of an explosive compared volume to volume (ie litre for litre) to ANFO. ANFO = 100%.

Intra - Row Delay

Generally in the range of 2 to 5 ms/m of spacing. A value of 3 ms/m should be chosen initially.

Inter - Row Delay

Generally in the range of 10 to 20 ms/m of burden. A value of 15ms/m should be chosen initially.


Example:

A blast pattern is required with Burden x Spacing = 2.7m x 3.0m.

Hole diameter 089mm

Subgrade drilling 0.5m

Hole depth 8m

No. of holes 50

Stemming 2.5m

Explosive = ANFO SG = 0.85.kg/L

1) What is the volume of rock expected out of the blast?

Volume of blast = 8 x S x H+ x No.Holes

= 2.7 x 3.0 x B.O x 50

= 64.8m3 x 50

= 3240m3

Total Hole Depth = Depth + Subdrill

= 8.0"+ O.5rn

= 8.5m

2) How much explosive required?

Explosive Charge Length =

=

=

Total hole depth - Stemming Length

8.5m-2.5m

6.0m

Explosive charge per metre (volume of cylinder)

Volume of hole/per m = 1t r2 x h (where h = 1) = 5.29 kg/m

Therefore, explosive Charge Weight Calculations & Terms used in Drill & Blast Operations

= Charge length x Charge/m 25

= 6.0m x.5.29 kg/m

= 31.74kg

No. of holes = 50

:. Total Explosive Weight for entire blast = 50 x 31.74 kg

= 1587.0 kg

3) What is the powder factor? Powder factor =

=

=

26

Explosive Weight Blast Volume

1587 kg 3240 m3

.......... Kg/m3

Calculations & Te,!"s used in Drill & Blast Operations

Scaling of Blast Parameters Wherever there is a change in blast hole diameter (d) or explosive type, a new blast geometry needs to be developed. As the parameters of blast design are increased, there is a law of diminishing returns applying to fragmentation and muckpile looseness. (This applies unless there is a substantial increase in explosives Energy Factor or the fragmentation is almost completely defined by rock jointing Istructure.) For this reason, blast pattern expansion is generally not proportional to increases in explosive energy or blast hole diameter.

The new geometry should be calculated using a scaling factor:

where:

K = -p-

c

RBEE is the relative bulk effective energy and subscripts c and p refer to the current and proposed system respectively.

K is then used to calculate the new burden distance (Bp) and new blast hole spacing (Sp) using the relationship:

Where:

K" [Be X Scl

N varies between about 0.8 and 1.0. A value of 0.8 is recommended for introductory blasts. Initially, Sp : bp should be 1.15.


Geometrical Formulae

Circumference of a circle = 1t0

Area of a circle = Y. 1t 0 2 or 1t r2

Area of rectangle = length x width

Area of triangle = % base x height

Surface of sphere = 41tr2

Volume of cone = 1/12 1t 02H or 1t r2h 3

Volume of wedge = % area of base x height

Volume of cylinder = Y. 1t D2H or 1t r2 h

Volume of Rock Blasted (m3) Per metre of hole = BxS Per hole = BxSxH Per blast = B x S x H x Holes

Mass of Rock (t) Mass = volume x density

Relative Weight Strength RWS = Q exp/Q anfo (Where Q = Available energy)

Relative Bulk Strength RBS = (RWS exp/RWS anfo) x (p exp/p anfo) (Where p = Relative Oensity)

Powder Factor Pfa = Mass of explosives Volume of rock

Energy Factor Ef = Pta x RWS


Density of Rock Type

Material Relative Weight Density Solid Broken

- tmO mOlt T/m o mOlt

Basalt 2.8 -3.0 3.0 0.33 1.96 0.51

Coal - Anthracite 1.3-1.8 1.6 0.63 1.05 0.96

Coal - Bituminous 1.2-1.5 1.41 0.71 0.92 1.09

Diabase 2.6 -3.0 2.8 0.36 1.83 0.55

Diorite 2~8 - 3.0 3.0 0.33 1.96 0.51

Dolomite 2.8 - 2.9 2.9 0.35 1.90 0.53

Gniess 2.6-2 .. 9 2.9 0.35 1.90 0.53

Granite 2.6 -2.9 2.8 0.36 1.83 0.55

Gypsum 2.3-3.3 2.8 0.36 1.83 0.55

Haematite 4.5-'5.3 4.8 0.21 3.14 0.32

Limestone 2.6-2.9 2.7 0.37 1.76 0.57

Limonite 3.6-4.0 3.8 0.26 2.48 0.40

Magnesite 3.0-3.2 3.2 0.31 2.09 0.48

Magnetite 4.9-5.2 5.0 0.20 3.27 0.31

Marble 2.1-2.9 2.5 0.40 1.63 0.61

Quartzite 2.0-2.8 2.6 0.38 1.70 0.59

Sandstone 2.0-2.8 2.4 0.42 1.57 0.64

Shale 2.4-2.8 2.6 0.38 1.70 0.59

Silica Sand 2.2 -2.8 2.6 0.38 1.70 0.59

Slate 2.5-2.8 2.7 0.37 1.76 0.57


Wet Hole Calculations

Number of cartridges to build out of water

NE = Hf x 1000 LE

HF = Ho X D2 D2_d2

Number of cartridges needed

Final height of water (m)

Length of cartridge (mm)

Ho = Original height of water (m)

D = Diameter of borehole (mm) ~ Indicates annulus volume

D = Diameter of cartridge (mm~

Scaled DistancesNibration Control

For a given distance the mass of explosives per delay (> Bms) can be calculated as follows:

(D), or Ds

If the mass of explosives per delay and the distance is known, the scaled distance can be calculated as a check to see of it is within limits:

DS = D DME

Where:

Me = Mass of explosive (kg) per delay (> Bms)

D = Distance to property of concern (m)

Ds = Scaled distance (m)

30 Calculations & Tenns used in Drilf & Blast Operations

(1) The United States Bureau of Mines (USBM) gives Ds = 31m

(2) The office of Surface Mining (US) recommends

Ds = 74m ifD is smaller than 150m

= 82m if Dis 150 to 1,500m

= 96m if D is greater than 1,500m

Based on the USBM standard the following are recommended.

Distance to structure Mass of explosives Distance to structure Mass of explosives or property of (kg) per delay (> or property of (kg) per delay (>

concern Sms) concern Sms) 10 0.1 300 100 20 0.4 50 250 30 1.0 750 600 50 2.5 1000 1000 75 6.0 . 1500 2500

100 10.0 2000 4000 150 25.0 3000 10000

Calculations & Terms used in Drill & Blast Opera~ions 31

Unit of Measure Conversion

Take the measure of the unit to be converted and multiply with the figure on the opposite side to get the measure in the opposite unit.

Example: 1.0 metre = 3.5 acres =

1 3.281 = 3.281 feet 3.5.0.405 = 1.418 hectares

Length 25.400 millimetres 1

0.914 metres 1 0.305 metres 1 0.025 metres 1 1.609 kilometres 1 1.152 statute miles 1

Area 6.452 sq. centimetres 1 0.836 sq. metres 1 0.093 sq. metres 1 0.405 hectares 1

Volume 16.387 cu. centimetres 1

0.765 cu. metres 1 0.028 cu. metres 1 0.568 Iitres 1 4.546 lfires 1 3.785 litres 1

Mass/Weight 28.350 grams 1

0.454 kilograms 1 1.000 kilograms 1 2.240 pounds 1 9.810 kN 1 1.016 tons (metric) 1 0.102 tons 1

Density/Powder Factor 0.016 gm/cu. cm 1 0.593 kg/cu. metre 1

16.016 kg/cu. metre 1

32

0.039 inches 1.094 yards 3.281 feet

39.372 inches 0.621 statute miles 0.868 nautical miles

0.155 sq. inches 1.196 sq. yards

10.764 sq. feet 2.471 acres

0.061 cu. inches 1.308 cu. yards

35.315 cu. feet 1.761 pints 0.220 imperial galls 0.264 U.S. gallons

0.035 ounces . 2.205 pounds 0.001 tons (metric) 0.446 103 (imperial) 0.102kgf 0.984 tons (imperial) 9.810 kN

62.438 pounds/cu. ft 1.686 pounds/cu. yd 0.062 pounds/cu. ft


Pressure 1,013 bar 0,069 bar 0,010 bar 0,102 m water head 10,194 m water head 2,307 ft water head

Flow Rate 0.076 litres/second

Viscosity 1.000 Ns/m<

1.000.000 m2/s 47.847 Ns/m2

0.093 m2/s

Temperature

ut

1 0.987 atmospheres 1 14.500 Ibs/sq. inch 1 100.000 kPa (kNm2) 1 9.810 kPa 1 0.098 bar 1 0.434 Ibs/sq. inch

1 I 13.200 gallons/minute

1 0.001 centipoise (cP) 1 0.000,001 centistoke (cSt) 1 0.021 Ibf s/tr 1 . 10.760 tr/s

0.738 ft-Ibf 1.341 horse ower

- To convert degrees Celsius to degrees Fahrenheit, multiply by 9/5 and add 32.

- To convert degrees Fahrenheit to degrees Celsius, subtract 32 and multiply by 5/9.


2.49 2.80 3.11 3.73 4.35 3.27 3.68 4.09 4.90 5.72 6.54 3.66 4.12 4.58 5.50 6.41 7.33 4.08 4.59 5.10 6.12 7.14 8.17 4.60 5.17 5.07

13.08 13.85 15.42 16.33 18.15 19.96 20.87 21.78 22.68 23.23 23.59 24.50 16.88 17.87 19.86 21.84 22.83 23.83 24.82 25.42 25.81 26.81 18.18 19.24 21.38 23.52 24.59 25.66 26.73 21.15 22.40 24.88 27.37 28.62 29.86 31.11

12.36 14.56 15.59 17.32 20.78 24.25 27.71 29.44

16.47 18.53 20.59 24.71 28.83 32.95 35.01 19.79 22.27 24.74 29.69 34.64 39.58 42.06

86.73

(Contributed by Coldwell Drilling Co)


Section 4

Drill & Blast Terminology


Abbreviations

36

AN ANFO B C cm

CN DRC E

EE EP FO g g/m Gpa KgF KJ L1L MJ mm

MMU Mpa ms

MSC PETN PS RBEE RF RQD RWEE RWS s

S SG t TLD TNT VOD

Ammonium Nitrate Ammonium Nitrate - Fuel Oil Burden Centigrade Centimetre Calcium Nitrate Detonating relay Connector Young's Modulus Effective Energy Emulsion Phase Fuel Oil grams grams per metre Gigapascal Kilograms force Kilojoule Lead in Line Megajoule millimetre Mobile Manufacturing Unit Megapascal millisecond Millisecond Connector Pentaerythritol Tetranitrate Polystyrene Relative Effective Energy Radio Frequency Rock Quality Designation Relative Weight Effective Energy Relative Weight Strength second Spacing Specific Gravity Tonne Trunkline Delay Trinitrotoluene Velocity of Detonation


Definitions

Capped fuse

Circuit

Crimper

Delay detonator

Detonating cord

Detonator

Downline

Exploder

Fuse lighter

Igniter cord

Leadwires

Misfire

Safety fuse

Signal tube

Trunkline

A length of safety fuse with a plain detonator crimped to one end

Insulated electric wires connecting electric detonators together

A special tool to securely attach a plain detonator to safety fuse

'A detonator which fires at a specified time after initiation

A continuous core of detonating explosive powder covered by an outer jacket

A small, sensitive high explosives charge inside a protective shell

The link which transmits an initiation signal inside a blasthole

A portable source of electrical energy used to fire electric detonators

A pyrotechnic device used to initiate safety fuse

An incendiary cord used to ignite safety fuse

The wires which are permanently attached to an electric detonator

An explosive which has not completely fired after initiation

A continuous core of black powder covered by braided yarns

A hollow plastic tube which transmits energy by a shock wave

The link which transmits an initiation signal to blasthole collars

Calculations & Tenns used In Drill & Blast Operations 37

Burden

Collar

Drilling pattern

Equilateral triangle

Grade

Inclination

Spacing

Stemming

Sub-drill

S:B ratio

Toe

Blast Geometry

AN

Classification

Day box

Division

Expense box

Exudation

38

Distance between a free face and an explosive charge 9ie when it fires)

Top or upper section of a blasthole (ie at or near the bench top)

General layout of blasthole collar positions (eg square or rectangular grid)

A triangle that has all sides of equal length

Design floor level 9ie top of next bench down) in an openOcut mine or quarry

Angle usually measured in degrees from a vertical line

Distance between adjacent blasthole collars (ie usually in the same row)

Inert material (eg crushed rock) put into blasthole collars to contain explosion gases

Length of blasthole drilled below the design grade level (also called sub-grade)

Blasthole spacing divided by blasthole burden distance

Bottom or lower section of a blasthole

Ammonium Nitrate

Separation of explosives according to their hazard characteristics

A container used to store daily reqUirements of explosives on the job

One of the five official groups into which explosives are divided

Another term for day box

proplets of NG liquid on the outer wrapper of packaged explosives


HE High explosives goften used to mean detonator-sensitive explosives)

IMCO (IMO) Intergovernmental Maritime Organization

Magazine A special storage place used for keeping explosives or detonators

Magazine shoes Special overshoes (galoshes) for wearing inside magazines

NG Nitrglycerine

Receptacle Licensed container to store or transport small amounts of explosives

Recrystallisation Salt crystals formed by evaporation of salty liquids from explosives

Safety distance The separation distance required arour'ld explosives magazines

Signal Tube Initiation ,Systems

Bridging Linking together of separate sections of a blast initiation system

Burden Measured distance between an explosive charge and a free face

Burning front Gap between firing a downline and explosion of the charge around it

Control row Line of initiation which controls sequencing and timing in a blast

Cut-off Failure caused by physical damage or disruption during the blast

Dummying A method to establish correct delay timing for odd blasthole patterns.

Echelon A diagonal line between the collars of a staggered blasthole pattern

Free face Open area available for charged blastholes to fire (ie break) towards

Hookup Connection of the individual components of the initiation system


Incoming initiation signal or component coming in from another location

Leading hole The blasthole which is deSigned to fire first (ie lead) during a blast

Outgoing Initiation signal or component going out towards another location

Shrapnel Tiny fast-moving fragments produced by detonating explosives

Spacing Measured distance between adjacent blastholes in the same row

Explosives Properties

ANFO

Approved

Blasting agent

Bulk strength

Critical diameter

Dead pressing

Detonation

DPD (Dynamic Pressure Desensitisation)

Emulsion

GMB (Glass MicroBalioon)

Oxidiser

Primer

40

A mixture of Ammonium Nitrate (AN) and distillate Fuel Oil (FO). usually mixed together in the ratio of 94:6 (by weight) Approved by the relevant Explosives/Dangerous Goods & Mines Department

Explosives which cannot be initiated by a #8 strength detonator

Energy yield per unit volume of explosive

The minimum diameter at which an explosive will reliably detonate

Compression of an explosives charge to a density at which it is so insensitive that it cannot be initiated or sustain a stable detonation

An explosive chemical reaction which involves a supersonic "shock wave"

The effect of an intense shock wave passing through an explosive charge. resulting in the destruction of the explosives sensitising agent. rendering it insensitive to detonation

A super-fine mixture of oxidisers (eg AN solution) and fuels (eg Fuel Oil) stabilised by surface-active "emulsifiers Extremely small hollow glass spheres used to sensitise some emulsion explosives

An ingredient that provides oxygen in an explosive

A high explosives unit designed to initiate the main explosives charge

Calculations & Tenns used in DriJl & Blast Operations

REE (Relative Effective Energy) VOD (Velocity of Detonation)

Weight strength

Energy available to do useful work (compared to ANFO as 100%)

The speed at which the detonation wave travels through a confined explosive column

Energy output per unit weight of explosive


42 Calculations & Tel7l7S used in Drill & Blast Operations

Section 4

Test Yourself Answers


Area of a Triangle (Page 10) Find the area of these triangles

a) h = 24cm, = 30cm A = Yo I x h, .. A = 360cm2

b) h = B.24cm, = 3.4cm A = 14.008cm2

Area of a Trapezium (Page 10) Find the area of this trapezium: A = 30m, h = Bm

A = =

=

=

Yo h (a + b) Yo x B (30 + 45) Yo x B x 75 300cm2

Surface Area of Cylin,der (Page 11) A cylinder has a base diameter of 40cms and height of 60cms. Find a) the surface area of the cylinder (rectangle) b) the total surface area of the cylinder

a) IfD = 40, r = 20

A = 21tr x h

= 2 x 1t X 20 x 60

= 7539.B224 (frolT] calculator)

Area = 7540cm2 (to nearest cm2)

b) A = 21tr (h + r)

= 2 x 1t X 20 x (60 + 20)

= 2 x 1t X 20 x BO

= 10053.096

Area = 10053cm2 (to nearest cm2)


Annulus (Page 12)

Find the area of the annulus in m2 when using 100mm drill pipe in a 250mm diameter hole.

A (outside circle) = 1t r = 3.142 x 0.1252

= 0.049m2

A (inside circle) = 1tr = 3.142 x 0.052

= 0.0079m2

Area of annulus = 0.049 - 0.0079

= 0.0411m2

Capacity (Page 13)

A rectangular mud pit is L = 1.2m, W = 0.8m, 0 = 0.6m

What is the volume of the pit in m3?

V (m3) = 1.2 x 0.8 x 0.6

= 0.576m3

Liquid V. = 0.576 x 1000

= 576 L

Volume of Cylinder (Page 14)

What is the volume of a cylinder with a diameter of 4 m and a height of 3 m?

V = 1t r h (r = 2 m) Area of base = 1t r

= 3.142 x 2 x 2

= 12.6m2

So volume = 12.6m2 x 3

= 37.8m3 or 37,800 litres


Volume of Rectangular Prism (Page 15)

Find the volume of a rectangular prism with these dimensions:

2.5m wide, 8.5m long, 3.2m high

V = Ixbxh

= 8.5 x 2.5 x 3.2

= 68m3 or 68 cubic metres

Volume of a Blast Hole (Page 16)

Up-Hole Velocity (Page 18)

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