1. Modeling Dynamic Break
in
Underground Metal Mining
Christopher Preston, Troy Williams, Ian Lipchak

2. Underground Blasting Attributes
• Ring blasting can be complex - constrained by orebody shape, drift size and sublevel height
• Mass blasts can be large and multi-level in scope – fragmentation is qualitatively appraised as broken
material is mucked from draw point to ore pass via scooptram and operator (Bucket Count)
• Void space (via slots) must be created to accommodate broken muck from rings to be blasted – limits
number of rings per blast – timing must take into account the expected percentage of free face moved
prior to firing successive rings
• Powder factors are not easily calculated for oblique orientations of holes – powder factors used in
underground blasting operations can be twice those used in surface mining operations
• Energy distributions from explosive loads tend to be concentrated in the collars and diluted near toes due
to confined nature of drilling from drifts – challenging to get a uniform energy distribution throughout a
ring – let alone a multi-ring blast
• Free face not visible – very difficult to determine actual burden distance from one ring to the next (after
blasting) – location of blast holes is important in order to provide consistent fragmentation ring to ring
• Priming location is extremely important – priming point usually dictates the direction of blast motion – it is
not wise to prime in collar area or near any free face since blast motion would be directed to closest void
space (which should be the slot)

3. Underground Mining Objectives
• Safety - always the top priority
• Development and production blasting design must be done in such a way to mitigate damage to support
structures – perimeter control in drifting is essential – avoid stress throw back into country rock
• Blasting is focused on achieving 100% recovery ideally with no dilution – fragmentation specification is
designed to match material handling equipment
• Conservation of blasting energy throughout rings is important – need to avoid the concentration of energy
that produces fines and to ensure that enough energy is available to break toes to eliminate oversize
• Observance of in-situ structure is critically important especially for ground control
• Future of underground mining is to go deeper – problems to be solved include;
• Ventilation, working in hot humid surroundings along with autonomous material handling equipment
– facilitated using battery operated haulage equipment
• Use of advanced methodologies for rock mechanics and ground control with benefits of innovative
monitoring equipment and methodologies consistent with deep mining
• Innovative computer modeling for blasting design in high stress environments
• New role for underground blasting operations – acting as primary crushers for the future

4. Common Drilling and Loading Problems

5. Drilling and Loading Concerns – Open Stope Slot and Slash
• Left figure - plan section of a ring drilled and short loaded due to blocked holes -
belief that the next ring will take care of the problem
• Middle figure - primitive radial break used to look at ‘hot’ and ‘cold’ energy zones
• Gyroing holes - extremely important to detail problems with drilling so that
practices can be improved
In order to improve a process – it must be measured first

6. Blast Hole Location in a Blind Raise
Pleiades Star Cluster

7. The Powder Factor Dilemma – Using Explosive Weight
• 𝑷𝑭 =
𝑾 𝑬𝒙𝒑𝒍𝒐𝒔𝒊𝒗𝒆
𝑽 𝒐𝒓𝒆,𝑾 𝒐𝒓𝒆
Volume for a quadrilateral with no sides
parallel can be determined using CAD,
however the break subtended by the two
blast holes in unclear
Based on parallel hole configurations for
square, rectangular or staggered patterns
Use of isosurfaces for ‘planner’ break

8. The Concept of Dynamic Break
Regions defined by radial break
(From a Dynamic Process)
Courtesy Geotechnical Engineering and Blasting (2014)
100%
0%
Radial Break Distance
Probability Min Max
?

9. Characterising Dynamic Modulus by Experiment
P
(m/s)
S
(m/s)
PR Density
g/cc
FI YM
GPa
BM
GPa
SM
GPa
CV
m/s
4030 2262 0.27 3 .35 39 28 15 425
Values for Norite

10. Defining a Dynamic Break Model
Rectangular Volume
𝑽 = 𝑩𝑺𝑳
Cylindrical Volume
𝑽 = 𝝅𝑹 𝟐
𝑳
Prolate Ellipsoid Volume
𝑽 =
𝟒
𝟑
𝝅 ×
𝟏
𝟐
𝑳 × 𝑹 𝟐
L = Column Length = 30.5 m
B = Ring Burden = 2.4 m
S = Toe Spacing = 2.7 m
W = Charge Weight = 203 kg ANFO at 0.85, or 299 kg Emulsion at 1.25 g/cc
R to be calculated for equivalent volumes

11. Calculating Powder Factor in Terms of Radial Break
Break Radius in Terms of Common Geometric Shapes
Geometrical Shape
Volume
(m3)
Radial Break
(m)
Powder Factor
(kg/tonne)
Rectangular
𝑽 = 𝑩 × 𝑺 × 𝑳
198
1.03
(ANFO)
1.51
(Emulsion)
Cylindrical
𝑽 = 𝝅 × 𝑹 𝒄𝒚𝒍𝒊𝒏𝒅𝒆𝒓
𝟐
𝑳
𝑹 𝒄𝒚𝒍𝒊𝒏𝒅𝒆𝒓=
B × S
π
=1.44
Prolate Ellipsoidal
𝑽 =
𝟒
𝟑
𝝅 ×
𝟏
𝟐
𝑳 × 𝑩 𝟐
R 𝐞𝐥𝐥𝐢𝐩𝐬𝐞=
𝟑 × 𝐒
𝟐 × 𝛑
=1.77

12. V of Bbreak
(m3)
ρexp
(gm/cm3)
Eexp
(cal/gm)
VOD∅
(m/s)
VODideal
(m/s)
Etotal.ANFO
(MJ/m3)
EFbreak.ANFO
(MJ)
198 0.85 880 3375 4500 101 24
198 0.85 880 4500 4500 178 43
ANFO
Energy Association in Blast Design
V of Bbreak
(m3)
ρexp
(gm/cm3)
Eexp
(cal/gm)
VOD∅
(m/s)
VODideal
(m/s)
Etotal.emulsion
(MJ/m3)
EFbreak.emulsion
(MJ)
198 1.17 690 4125 5500 111 27
198 1.17 690 5500 5500 198 47
EMULSION

13. Measuring the Dynamic Effects of Blasting on In Situ Stresses
𝑺𝑫 = 𝒅/𝑾^(𝟏/𝟐) = 𝟑𝟓
𝑫𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 = 𝟕. 𝟐 𝒎𝒊𝒄𝒓𝒐𝒏𝒔
𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 − 𝟎. 𝟖𝟓𝟎 𝒌𝑯𝒛
𝑺𝑫 = 𝒅/𝑾^(𝟏/𝟐) = 𝟏𝟓
𝑫𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 = 𝟓. 𝟖 𝒎𝒊𝒄𝒓𝒐𝒏𝒔
𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 − 𝟐. 𝟖𝟓𝟎 𝒌𝑯𝒛
Dynamic/Static Probe

14. Measuring the Static Effects of Blasting on In Situ Stresses
• Young’s Modulus - 103 GPa
• Poisson’s Ratio - 0.10
• Stress < 138 KPa over 12 days
• After 15 weeks monitoring - cumulative stress < 69 MPa
• Stress rotations > 90 degrees over the same time period
attributed to blasting

15. Isosurface Representation
Of
Break

16. Isosurface Attributes
• 3D surface of constant value
• Model break/damage
• Advantage
• Indicates volumes with poor energy
concentration
• Disadvantage
• Doesn’t indicate charge concentration

17. Voxel Attributes
• Represent values in 3D grids
• Used to approximate volumes and
meshes
• Relatively simple
• Stable Boolean operations
• Can store attributes
• P and S Wave Velocities
• Dynamic Young’s Modulus
• Dynamic Poisson’s Ratio
• Grade Percent
• Density
• Used to construct isosurfaces

18. CMS – Cavity Monitoring Survey/System
• 3D scan of blast cavity
• Accurate representation of blast
cavity
• Compared with original for
dilution estimate and blasting
performance

19. Comparison - CMS and Isosurfaces
• How does the CMS compare to
the isosurface?
• Meshes converted to voxel
representation
• Symmetric differences
• % Match
• Estimate and display/visualize
common volumes
• Estimate and display/visualize
volume differences

20. Scalar Field Definition
• Mathematical function
that maps a value to
every coordinate in space
• Classifies CMS based on
shape to single value
• Field functions use
explosive, rock and blast
hole geometry

21. Scalar Field Best Fit
• Scalar field values
calculated for each voxel
• Search for best fit field
isosurface to CMS

22. Recommendations for Future Work
• Compare scalar field predicted shape with CMS
• Calibration – combine isovalues from individual CMS (average)
• Tie break and damage zone model to planned blast isosurface
• Tie break and damage zone model to field model
• Tie energy (MJ/m^3) to field model
• Tie timing to break and field models
• Explore more functions for scalar fields

23. END