Modeling Dynamic Breakin

Underground Metal Mining

Christopher Preston, Troy Williams, Ian Lipchak

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)

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

Common Drilling and Loading Problems

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

Blast Hole Location in a Blind Raise

Pleiades Star Cluster

The Powder Factor Dilemma – Using Explosive Weight

• 𝑷𝑭 =𝑾𝑬𝒙𝒑𝒍𝒐𝒔𝒊𝒗𝒆

𝑽𝒐𝒓𝒆,𝑾𝒐𝒓𝒆

Volume for a quadrilateral with no sidesparallel can be determined using CAD,however the break subtended by the twoblast holes in unclear

Based on parallel hole configurations forsquare, rectangular or staggered patterns

Use of isosurfaces for ‘planner’ break

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

?

Characterising Dynamic Modulus by Experiment

P(m/s)

S(m/s)

PR Densityg/cc

FI YMGPa

BMGPa

SMGPa

CVm/s

4030 2262 0.27 3 .35 39 28 15 425

Values for Norite

Defining a Dynamic Break Model

Rectangular Volume𝑽 = 𝑩𝑺𝑳

Cylindrical Volume𝑽 = 𝝅𝑹𝟐𝑳

Prolate Ellipsoid Volume

𝑽 =𝟒

𝟑𝝅 ×

𝟏

𝟐𝑳 × 𝑹𝟐

L = Column Length = 30.5 mB = Ring Burden = 2.4 mS = Toe Spacing = 2.7 mW = Charge Weight = 203 kg ANFO at 0.85, or 299 kg Emulsion at 1.25 g/cc R to be calculated for equivalent volumes

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 × 𝑹𝒄𝒚𝒍𝒊𝒏𝒅𝒆𝒓𝟐𝑳

𝑹𝒄𝒚𝒍𝒊𝒏𝒅𝒆𝒓= B × S

π=1.44

Prolate Ellipsoidal

𝑽 =𝟒

𝟑𝝅 ×

𝟏

𝟐𝑳 × 𝑩𝟐

R𝐞𝐥𝐥𝐢𝐩𝐬𝐞= 𝟑 × 𝐒

𝟐 × 𝛑=1.77

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

Measuring the Dynamic Effects of Blasting on In Situ Stresses

𝑺𝑫 = 𝒅/𝑾^(𝟏/𝟐) = 𝟑𝟓𝑫𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 = 𝟕. 𝟐 𝒎𝒊𝒄𝒓𝒐𝒏𝒔𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 − 𝟎. 𝟖𝟓𝟎 𝒌𝑯𝒛

𝑺𝑫 = 𝒅/𝑾^(𝟏/𝟐) = 𝟏𝟓𝑫𝒊𝒔𝒑𝒍𝒂𝒄𝒆𝒎𝒆𝒏𝒕 = 𝟓. 𝟖 𝒎𝒊𝒄𝒓𝒐𝒏𝒔𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 − 𝟐. 𝟖𝟓𝟎 𝒌𝑯𝒛

Dynamic/Static Probe

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

Isosurface RepresentationOf

Break

Isosurface Attributes

• 3D surface of constant value

• Model break/damage

• Advantage• Indicates volumes with poor energy

concentration

• Disadvantage• Doesn’t indicate charge concentration

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

CMS – Cavity Monitoring Survey/System

• 3D scan of blast cavity

• Accurate representation of blast cavity

• Compared with original for dilution estimate and blasting performance

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

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

Scalar Field Best Fit

• Scalar field values calculated for each voxel

• Search for best fit field isosurface to CMS

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

END