teaching and training material drill & blast
DESCRIPTION
Calculations & Termsused inDrill & Blast Operations in open cut and underground miningTRANSCRIPT
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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~-----------------------+~
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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.
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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
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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
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Section 1
Quick Reference
Calculations & Terms used in Drill & Blast Operations 1
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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
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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
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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
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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
Calculations & Terms used in Drill & Blast Operations 5
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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
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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
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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
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Section 2
How to carry out calculations
Calculations & Tenns used in Drill & B/ast Operations 9
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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
10 Calculations & Terms used in Drill & Blast Operations
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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
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..... 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 =
=
12 Calculations & Tenns used in Drill & Blast Operations
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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
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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?
14 Calculations & Tenns used in Drill & Blast Operations
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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
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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
16 Calculations & Tenns used in Drill & Blast Operations
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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 =
Calculations & Tenns used in Drill & Blast Operations 17
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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
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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.
Calculations & Tenns used in Drill & Blast Operations 19
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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)
Calculations & Terms used in Drill & Blast Operations 20
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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
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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).
22 Calculations & Terms used in Drill & Blast Operations
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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).
Calculations & Terms used in Drill & Blast Operations 23
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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.
24 Calculations & Terms used in Drill & Blast Operations
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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
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= 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
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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.
Calculations & Terms used in Drill & Blast Operations 27
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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
28 Calculations & Tenns used in Drill & Blast Operations
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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
Calculations & Terms used in Drill & Blast Operations 29
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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
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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
Calculations & Terms used in Drill & Blast Operations
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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.
Calculations & Terms used in Drill & Blast Operations 33
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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)
Calculations & Terms used in Drill & Blast Operations 34
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Section 4
Drill & Blast Terminology
Calculations & Terms used in Drill & Blast Operations 35
-
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
Calculations & Terms used in Drill & Blast Operations
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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
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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
Calculations & Terms used in Drill & Blast Operations
-
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
Calculations & Terms used in Drill & Blast Operations 39
-
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
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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
Calculations & Tenns used in Drill & Blast Operations 41
-
42 Calculations & Tel7l7S used in Drill & Blast Operations
-
Section 4
Test Yourself Answers
Calculations & Tenns used in Drill & Blast Operations 43
-
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)
44 Calculations & Terms used in Drill & Blast Operations
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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
Calculations & Terms used in Drill & Blast Operations 45
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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)
\
46 Calculations & Tenns used in Drill & Blast Operations