summary presentation of my PhD research work at SFU (2005-2008)

1. 1
Numerical Modelling of Surface
Subsidence Associated with Block Cave
Mining Using a FEM/DEM Approach
Alex Vyazmensky Ph.D.
https://sites.google.com/site/alexvyazmensky/
http://kz.linkedin.com/in/vyazmensky

2. Presentation Outline
• Problem Statement: Block Caving Mining and Associated
Surface Subsidence
• Research Objectives
• Modelling Methodology
• Conceptual Study of Factors Controlling Surface Subsidence
Development
• Caving Induced Instability in Natural and Man-made Slopes
2

3. Problem Statement
3

4. Block Caving and Associated Subsidence 4
Block cave mining is characterized by caving and
extraction of a massive volume of ore which
translates into a formation of major surface
depression or subsidence zone directly above
and in the vicinity of the mining operations.
The ability to predict surface subsidence
associated with block caving mining is
important for mine planning, operational hazard
assessment and evaluation of environmental
and socio-economic impacts.
Owing to problems of scale and lack of access, the
fundamental understanding of the complex rock
mass response leading to subsidence
development is limited as are current subsidence
prediction capabilities.
Current knowledge of subsidence phenomena can
be improved by employing numerical modelling
techniques in order to enhance our
understanding of the basic factors governing
(modified after Sandvik Tamrock block caving animation)
subsidence development; essential if the required
advances in subsidence prediction capability are
to be achieved.

5. Subsidence Examples 5
Northparkes mine, Australia
San-Salvador mine, Chile

6. Research Strategy
6

7. Research Objectives and Strategy 7
RESEARCH OBJECTIVES NUMERICAL RESEARCH OUTCOME
ANALYSIS
new FEM/DEM-DFN
introduce new
methodology for
methodology for numerical
numerical analysis of
analysis of surface
surface subsidence
subsidence associated
associated with block
with block cave mining
cave mining
identification of
conceptual study of characteristic
improve understanding of
factors controlling subsidence
block caving subsidence
surface subsidence development
phenomenon
development mechanisms,
comparative analysis
and ranking of factors
conceptual study of
controlling surface
caving induced
investigate block caving subsidence
instability in natural
induced failure development
slopes
mechanisms leading to
slope instability in large assessment of critical
engineered slopes case study of partial deformation thresholds
failure of northern pit leading to slope
wall at Palabora mine instability

8. Modelling Methodology
8

9. Toolbox for Subsidence Analysis 9
Current approaches to assessing surface subsidence associated with block caving
mining includes empirical, analytical and numerical methods:
• Empirically based block caving subsidence estimates include “rules of thumb”
and experience based design charts linking angle of brake, rock mass rating
and other parameters.
• Analytical methods include limit equilibrium solutions for specific failure
mechanisms (e.g. progressive sub-level caving of an inclined orebody).
• Different modelling approaches exist, based on the concept that the
deformation of a rock mass subjected to applied external loads can be
considered as being either continuous or discontinuous. The main differences
between the various analysis techniques lie in the modelling of the fractured
rock mass and its subsequent deformation.
Numerical techniques being inherently more flexible and sophisticated provide
an opportunity to improve understanding of subsidence phenomena and
increase accuracy in subsidence predictions.

10. Continuum Modelling
Modelling Numerical Rock Mass Representation Rock Mass Failure Realization
Approach Method
Continuum FDM, FEM continuous medium flexural deformations, plastic yield
FLAC3D ABAQUS
Connors, 2006
Beck, 2007
10

11. Discontinuum Modelling
Modelling Numerical Rock Mass Representation Rock Mass Failure Realization
Approach Method
Discontinuum DEM assembly of deformable or blocks movements and/or
rigid blocks blocks deformations
assembly of rigid bonded bond breakage, particle
particles movements
PFC 3D 3DEC
Gilbride et al, 2005 Brummer et al, 2005 11

12. New Numerical Modelling Approach 12
Most natural rocks subjected to engineering analysis are brittle; failure in such rocks
is a result of brittle fracture initiation and propagation.
Continuum and discontinuum modelling approaches provide approximations of
brittle fracturing to some degree, none of them however offer realistic representation
of the actual brittle fracturing phenomena which involves fracture growth,
propagation and material fragmentation.
A state-of-the-art combined continuum-discrete element code ELFEN is employed as
the principal modeling tool. The code allows the caving process to be simulated as a
brittle fracture driven continuum-discontinuum transition with the
development of new fractures and discrete blocks.
Modelling Numerical Rock Mass Rock Mass Failure Realization
Approach Method Representation
Hybrid FEM/DEM continuous degradation of continuum into discrete
Continuum- medium deformable blocks through fracturing and
Discontinuum fragmentation
Examples: caving
blasting toppling
initiation

13. FEM/DEM Modelling Examples 13
Rock bridge failure Step-path drive open pit wall failure
Link to animation
Link to animation

14. Modelling Strategy for Subsidence Analysis 14
Modelling Options:
• Back analysis of selected case studies.
Given the complexity of modeling mine scale problems and generally
variable quality of geological/geotechnical data available - a number of
simplifications and assumptions will be necessary. There is a risk of
“oversimplifying” the problem.
• Conceptual analysis.
Aiming to develop fundamental understanding of mechanisms
controlling subsidence development on smaller scale conceptual models.
Apply new knowledge to the analysis of a case study.
modelling studies done to date were largely oriented towards
providing site specific subsidence predictions.
CURRENT RESEARCH FOCUSED ON CONCEPTUAL ANALYSIS

15. Rock Mass Representation in FEM/DEM 15
Possible Approaches to Rock Mass Representation in FEM/DEM Modeling Context:
• jointed intact rock mass system is represented as a continuum with reduced
intact rock properties to account for presence of discontinuities;
Equivalent
• rock mass properties can be deduced from one of the rock mass classification
Continuum
systems such as RMR, Q or GSI;
• this approach does not consider kinematic controls of the failure.
• rock mass is represented as an assembly of discontinuities and intact rock
regions;
• intact rock properties can be established based on laboratory tests and the
Discrete Network pattern of discontinuities can be determined from field mapping/borehole
logging data or stochastic modeling;
• not feasible to consider high density of fractures for models larger than
pillar/bench scale
• necessary simplification for analysis of large scale problems;
• resolution of fractures should be sufficient to capture failure kinematics;
Mixed
Approach
• rock mass properties can be deduced from one of the rock mass classification
systems and then calibrated against known response.
selected for current analysis

16. Modelling Methodology - Typical Model Setup 16
FracMan DFN model Constraint
3D model 2D trace plane Properties Constrain:
calibration
criteria:
fractures Caveability Laubscher’s
exported caveability chart
into
ELFEN Cave Conceptual
development model of caving
2D ELFEN model progression by Duplancic &
Brady (1999)
Subsidence Mining
limits experience
ore
block
model
response
evaluation
ore block is undercut and fully extracted

17. RMC Based Equivalent Continuum Properties 17
RMC Estimates of Rock Mass Strength and Deformability Reference
System Characteristics
Serafim &
E m  10( RMR 10) / 40 (GPa) Pereira
RMR   5  RMR / 2 (1983)
c  5RMR (kPa) Bieniawski
(1989)
1
Em  10  Qc 3 (GPa)
J J 
" "  tan1  r  w 
J
 a 1 

Q  RQD 1 c  Barton
" c"  
 J  SRF  100  (MPa)
 (2002)
 n 
where:
Qc  Q( c / 100) - normalized Q;
c – uniaxial compressive strength (MPa)
 1 D / 2 
Em  Ei  0.02  (( 6015D  GSI ) / 11) 
(MPa)
 1 e 
  a sin
'



6amb s  mb 3n '

a 1


 
 2 1  a 2  a   6amb s  mb 3n
'

a 1


Hoek et al.
(2002)
c' 
 '

 ci 1  2a  s  1  a  mb 3n s  mb 3n
'
a 1
(MPa)
GSI



1  a 2  a  1   6amb s  mb 3' n a 1



1  a 2  a  Hoek &
Diederichs
(2006)
where:
Ei – intact rock Young’s modulus;
D - disturbance factor;
a, s, mb – material constant;
 3n   3 max /  c ,  3 max - upper limit of confining stress
' '

18. RMC Based Equivalent Continuum Properties 18
(a) Deformability modulus (b) Friction angle
60 60 56.6
RMR 56.2 55 57
52.7
GSI - tunnel (-200m) 52.8
50 50
45 45 45
Deformability modulus, GPa Q 45
43.9
Friction angle, degrees
40 40 45
40
26 37.4
31.2 35
30 30
30
31.6
20 20
18.4
17.7 17.8
RMR
11.17
10 10 GSI - tunnel (-200m)
10.0
Q
0 0
50 60 70 80 50 60 70 80
RMR RMR
(c) Cohesion (d) Tensile Strength
52 / 80 43.4 / 80 21.7 / 80
20 15
RMR RMR
18 GSI - tunnel (-200m)
GSI - tunnel (-200m)
Q 12.5
16 Q
15.1 Q - 50% cut-of f
14
Tensile strength, MPa
10 Q - 90% cut-of f
Cohesion, MPa
12
10
6.3
8
5 3.9
6 4.3
4.7 4.9
4 2.9
2 1.3 1.8 1.25
2 1.6 1.4 0.8 1.6
0.35 0.4 0.65 0.39
0.3 0.33
0 0 0.17
0.25 0.13 0.31 0.33
50 60 70 80 50 60 70 80
RMR RMR

19. Q 6.2 (70% c.o.) RMR 70
Rating
Q 6.2
RMR70
Deformabilit
y modulus,
17.7
31.6
E, GPa
Cohesion,
4.7
0.35
ci, MPa
Friction, I
45
40
degrees
Rock Mass Properties
RMC Based Equivalent Continuum Properties
Tensile
strength, t,
1.18
0.33
MPA
(70% c.o.)
19

20. Subsidence Simulation Example - Caving Initiation 20
block undercutting
HR=10
HR=20 HR=30
HR=40 HR=50

21. Subsidence Simulation Example - Crater Formation 21
Evolution of vertical displacements (0.1 – 1m)
50m
20°
Link to animation
70°
surface
subsidence,
m

22. Conceptual Study of Factors Governing
Subsidence Development
22

23. Conceptual Study Strategy
Factors affecting surface subsidence
development
Stress Block Geological Extraction
Joint Orientation & Faults Rock Ratio, K Depth Domains volume
Persistence Mass
Strength
Series of conceptual numerical experiments
investigating relative significance of the above factors
Influence Matrix
Identification of characteristic Ranking factors in terms of their
subsidence mechanisms influence on subsidence footprint
Worst case scenarios
23

24. Conceptual Study Example: Effect of Joint Orientation 24
0°
90° Direction of
cave
propagation
towards the
surface,
location of
10° the cave
breakthroug
h and the
80° mechanisms
of near
surface rock
mass failure
are strongly
controlled by
20° the joint
orientation
70°
Vyazmensky et al, MassMin2008

25. 25
10%

26. 26
20%

27. 27
30%

28. 28
40%

29. 29
50%

30. 30
60%

31. 31
70%

32. 32
80%

33. 33
90%

34. Conceptual Study Example: Effect of Joint Orientation 34
ore extraction
35% ore extraction 50% ore extraction 60% ore extraction Joint orientation
0°
controls not only
the cave
propagation
direction but
also plays
0°
a significant
90° 50m
role in a manner
0°
the rock mass is
90° mobilized by the
5°
caving
10°
80°
Legend:
10°
80°
9° rotational failure;
translational failure
20° active rock mass
70° movement
developing rock
20° mass failure
70°

35. Conceptual Study Example: Effect of Joint Orientation 35
• In order to quantify the
extent of major surface
subsidence deformations
10cm displacement
angle delineating threshold is adopted.
major (≥10cm) It is assumed that this
surface threshold limits the zone
displacements of major surface
disturbances
• Combination of
vertical and horizontal
sets results in nearly
symmetrical subsidence
profile
• Subsidence asymmetry
is strongly controlled by
the inclination of
sub-vertical and
sub-horizontal sets.
• Major subsidence
asymmetry is observed in
the dip direction of the
sub-vertical set, in this
area rock mass fails
through flexural and
block toppling and
detachment and sliding
of major rock segments
AV © 2008

36. Conceptual Study Example: Effect of Joint Orientation 36
Evolution of zone of major (≥10cm) vertical (YY) and horizontal (XX) surface
deformations with continuous ore extraction
100 100
90 90
80 0° 80 10°
Ore extraction, %
Ore extraction, %
70 70
60 90° 60 80°
50 50
40 40
30 BC - 30
J1 - YY
20 YY 20
BC -
10 10 J1 - XX
XX
0 0
-250 -200 -150 -100 -50 0 50 100 150 200 250 -250 -200 -150 -100 -50 0 50 100 150 200 250
Extent of 10cm surface deformations, m Extent of 10cm surface deformations, m
100
90
• Major subsidence deformations
80 develop in a relatively rapid manner
Ore extraction, %
70
20° related to a quick mobilization of
60
50 70° massive rock mass segments
40
30
20
J2 - YY • About 90% of maximum surface
10 J2 - XX displacements are achieved by 50%
0
-250 -200 -150 -100 -50 0 50 100 150 200 250
ore extraction
Extent of 10cm surface deformations, m

37. Conceptual Study Example: Effect of Joint Orientation 37
350 350 350
Total extent of 10cm vertical
350 350 350
normalized by Base Case, %
Total extent of 10cm vertical
Extent of of major vertical (≥10 cm) surface displacements
Total extent of 10cm horiz. 10cm horiz.
surface displacements, m
surface displacements, m
Total extent of 10cm vertical
normalizednormalized by Base Case, %
Total extent of 10cm vertical
Total extent of 10cm horiz.
surface displacements, m
surface displacements, m
300 300 300
surface displacements
268 300 300 300
surface displacements
268
250 234 250 250 235
250 207 234 250 250 218 235
207 218
200
350 200
350 200
350
200 200 200
Total extent of 10cm vertical
by Base Case, %
Total extent of 10cm vertical
Total extent of
surface displacements, m
surface displacements, m
150
300 150
300 150
300
surface displacements
150 268 150 150
235
129%
100
250 234 100
250 100
250 218
129%
113%
108%
100 100 100
100%
207
100%
113%
108%
100%
100%
50
200 50
200 50
200
50 50 50
0
150 0
150 0
150
0 0 0
BC J1 J2 BC J1
129%
100 BC J1 J2 100 100 BC J1
113%
108%
100%
100%
50 50 50
Extent of 10cm surface vertical dispacements in Extent of 10cm surface horiz
Extent of 10cm surface vertical dispacements in
relation to block centre, m Extent of 10cm surface horizo
relation to block
0 0 0
-250 -200 -150 -100 -50 block centre, m
relation to 0 50 100 150 200 250 -250 -200 -150 -100 -50 block
relation to 0
-250 -200 -150 -100BC-50 J1 0 50 100 150 200
J2 250 -250 -200 -150 -100BC -50 J1 0
-112 100% BC -118 100% B
-112 100% BC -118 100% BC
Extent of 10cm surface vertical dispacements in Extent of 10cm surface horizo
J1
-123 110% J1 -123 104%
-123 relation to block centre, m
110% J1 -123 relation to block
104% J1
-250 -200 -150 -100 -50
-161 0 J2 50 100 150 200 250 -250 -200 -150 -100 -50
-201 0 J2
144% 170% J2
-161 144% J2 -201 170%
-112 100% BC BC100% 95 95 -118 100% BC BC
BC 100% BC
-123 110% J1 J1 117% 111 -123 J1 J1
104%J1
J1 117% 111
-161 144% J2 J2 113% 107 -201 170% J2 J2
J2 113% 107 J2
95 BC
-300 -200 -100 BC 0 100%100 200 300 -300 -200 -100 0
-300 -200 -100 0 100 200 300 -300 -200 -100 0
Extent of 10cm surface vertical displacements in
J1 117% 111 J1
Extent of 10cm surface horiz
Extent of 10cm surface vertical displacements in
relation to block centre, normalized by Base Case, % relation to10cm surface horizo
Extent of block centre, norm
relation to block centre, normalized by Base Case, %
J2 113% 107 relation to block centre, norm
J2
-300 -200 -100 0 100 200 300 -300 -200 -100 0
Change in joint orientation causes an increase in the total
Extent of 10cm surface vertical displacements in major surface
Extent of 10cm surface horizo
relation to block centre, normalized by Base Case, % relation to block centre, norm
deformations extent of up to 30%

38. Conceptual Study Example: Effect of Joint Orientation 38
Resultant surface profiles
0
Lowest
• Rotation of the joint
-10 point pattern shifts centre of
Vertical displacements, m
-20
coordinates surface depression;
Base case 0, -55
-30 • Depth of the subsidence
J1
-40 10, -50 crater is related to the
J2 9.4, -44.5 extent of the rock mass
-50
mobilized by the failure,
-60 - larger extent of
-70 rock mass mobilization
results in shallower
-80
crater
-350 -250 -150 -50 50 150 250 350
Distance from block centre, m
0° 10° 20°
90° 80° 70°

39. Conceptual Study Example: Effect of Joint Orientation 39
From the point of view mine infrastructure placement it is
important to appreciate the amount of surface displacements at
some distances from the area of the imminent failure (caving
far-field displacements boundary and immediate vicinity).
Distance from block centre, m
-300 -250 -200 -150 150 200 250 300
Vertical displacements, m
0
J2
-0.05
The least amount of surface displacements is
-0.1 exhibited by the Base Case model (90°/0°), so
that only minor horizontal displacements of
-0.15 about 1cm are observed 100m from the caving
-0.2 boundaries (150m from block centre).
-0.25 The largest amount of displacements are
J2
-0.3
observed for J2 (70°/20°) model, where 1cm
-0.38
horizontal displacements are noted as far as
0.9
200m westwards from the caving boundaries.
Surface displacements in the far-field are
Horizontal displacements, m
0.3
J2
0.25 generally mirror the trends observed for major
surface deformations, showing strong
0.2 asymmetry in the dip direction of the sub-
0.15
vertical/gently dipping set.
0.1
J2
J1
BC
0.05
J2
J2
BC
J1
BC
J1
0
-300 -250 -200 -150 150 200 250 300
Distance from block centre, m

40. Conceptual Study Example: Effect of Joint Orientation - Conclusions 40
• Well defined, persistent, vertical to steeply dipping joints govern the direction of
cave propagation and the mechanism of near surface rock mass mobilization.
• The shallower the dip of these joints the more inclined from vertical is the cave
propagation direction and the more asymmetrical are the surface deformations.
• In cases where multiple well defined and persistent steeply dipping sets are
present the steepest set will generally have the predominant influence.
• Major subsidence asymmetry
is observed in the dip direction
of the sub-vertical/steeply dipping set,
where joints are inclined towards
the cave, the rock mass fails 53° 74°
through block-flexural and
block toppling and detachment and sliding of major rock segments.
• Depending on joint inclination the joint persistence may have a very significant
effect on surface subsidence induced by block caving.

41. Subsidence Simulation Example - Influence of fault 41
Geometry Evolution of vertical displacements (0.1 – 1m)
60°
100m
Subsidence crater development
Link to animation
50m
AV © 2008

42. Effect of Fault Location 42
former fault position
-300 -250 -200 -150 -100 -50 0 50 100 150 200 250 300
60°
fault location prior
to caving
0° 50m
Legend:
73° angle
90° of fracture
initiation
10cm displ. contours
vertical
73° 73° horizontal
60°
0° 100m
90°
61° 76°
60°
0° 150m
90°
73° 74°

43. Conceptual Study Example: Effect of Fault Location and Inclination 43
• Steeply dipping faults, daylighting into the cave and located within an area of
imminent caving are likely to be caved and are unlikely to play any major role in the
resultant subsidence.
• Faults partially intersecting the caving area may create favourable conditions for
failure of the entire hanging wall.
• Depending on rock mass fabric faults located in the vicinity of the caving zone may
have minimal influence or decrease the extent of the area of subsidence deformations.
• A topographical step in the surface profile is formed where the fault daylights at the
surface.
• Inclination of the fault partially intersecting the caving area controls the extent of
surface subsidence deformations. Low dipping faults will extend and steeply dipping
fault will decrease the area of surface subsidence.

44. Example of Surface Subsidence Simulation 44
CAVE ARREST, CROWN PILLAR FAILURE and RESULTANT SUBSIDENCE
50m
Link to animation

45. Conceptual Study Results Synthesis 45

46. Conceptual Study Results Synthesis 46

47. Conceptual Study Results Synthesis 47

48. Conceptual Study Results Synthesis 48

49. Conceptual Study of Factors Governing
Subsidence Development
49

50. Block Caving and Natural Slopes: caving close to slope toe 50
potential slope instability
induced displacements field
cave propagation
AV © 2007
block caving induced
Simplified applied displacements modeling approach slope failure
AV © 2007
200m
200m
200m
AV © 2007
200m

51. Block Caving and Natural Slopes: caving within slope 51
CONCEPTUAL MODEL Animation
surface inclination
15 degrees
AV © 2007 Questa mine
AV © 2007
simulated failure pattern resembles the deformations observed in similar
settings at Questa mine

52. Conceptual Study of Block Caving Induced Step-path
52
Driven Failure in Large Open Pit Slope
SLOPE IS STABLE WITHOUT CAVING
CONCEPTUAL MODEL
embedded animation
Numerical Analysis of Block Caving Induced Instability
in Large Open Pit Slopes: A Finite Element / Discrete
Element Approach
750m rock
bridges
persistent joints
daylighting into
the cave
400m
block
cave

53. Conceptual Study of Block Caving Induced Step-path
53
Driven Failure in Large Open Pit Slope
75m Fracturing
regions
10 excavation stages History point
history point
RB600
750m
RB300
60o 50o
400m
300m 300m

54. Conceptual Study of Block Caving Induced Step-path
54
Driven Failure in Large Open Pit Slope
ΔXY displ. at surface outcrop, m
15 0
Norm. shear stress XY, MPa
RB600
10 -0.05
RB300
5 differential XY displ. at -0.1
surface outcrop
0 -0.15
20 22 24 26 28 30 32 34 36
-5 simulation time, num.sec -0.2
0 0
Crown pillar thickness, m
Vertical stress YY, MPa
50
end of pit excavation
σyy (50m below pit bottom)
100
-5 crown pillar thickness, m
150
200
250
-10
300
350
-15 400
RB600 failure RB300 failure

55. 55
100 0
crown pillar:
destressing, %
Crown pillar destressing, %
Remaining crown pillar
80 thickness, % -20
thickness , %
60 last rock -40
bridge failure
first rock
40 -60
bridge failure
20 -80
0 -100
2 4 6 8 10
% rock bridges

56. 56
Simulation time, num.sec
0
20 22 24 26 28 30 32 34 36
Vertical stress YY, MPa
four rock
bridges
M1 M2 M3 two rock bridges
-5 three rock
M4 M5
bridges
-10
-15
Fig. Error! No text of specified style in document..1 Variation of vertical stress in
the crown pillar (50m below pit bottom) for models M1-M5

57. Case Study - Palabora mine 57
Note limited extend
A of the failure
beyond pit rim
~160°
Lateral
release
A
Surface subsidence
infrastructur
Mine

58. Case Study - Palabora mine 58
DFN based analysis (section A-A)

59. Case Study - Palabora mine 59
98 m
approximate f ailure approximate f ailure
crest location crest location

60. Key contributions 60
• A new FEM/DEM-DFN modelling approach was developed and successfully
applied to block caving subsidence and caving - large open pit interaction
analysis. This methodology allows physically realistic simulation of the entire
caving process from caving initiation to final subsidence deformations.
• Limitations of the rock mass classifications properties output were
highlighted and a procedure for calibration of rock mass classifications based
properties for FEM/DEM-DFN subsidence analysis was devised.
• Through a comprehensive conceptual numerical modelling analysis major
advances were gained in our understanding of the general principles of block
caving induced subsidence development and the role of major contributing
factors.
• The principles of step-path failure development in large open-pit - caving
mining environment were investigated using a proposed “total interaction”
approach to modelling data interpretation.
• Applicability of the FEM/DEM-DFN modelling for practical engineering
analysis was demonstrated in the preliminary simulation of the Palabora mine
failure.

61. Publications 61
“Role of Rock Mass Fabric and Faulting in the Development of Block Caving Induced Surface
Subsidence”
Vyazmensky A., Elmo D., Stead D.
Rock Mechanics and Rock Engineering Journal. Volume 43, Issue 5 (2010), 533 - 556.
“Numerical Analysis of Block Caving Induced Instability in Large Open Pit Slopes: A Finite
Element / Discrete Element Approach”
Vyazmensky A., Stead D., Elmo D., Moss, A.
Rock Mechanics and Rock Engineering Journal. Volume 43, Number 1 / February (2010), 21 - 39.
“Numerical analysis of the influence of geological structures on the development of surface
subsidence associated with block caving mining”
A. Vyazmensky, D. Elmo, D. Stead & J. Rance. MassMin 2008. Lulea, Sweden. 857-866. (2008).
“Combined finite-discrete element modelling of surface subsidence associated with block
caving mining”
Vyazmensky A., Elmo D., Stead D. & Rance J.
Proceedings of 1st Canada-U.S. Rock Mechanics Symposium. Vancouver, Canada. 467-475. (2007).
"Numerical modeling of surface subsidence associated with block cave mining using a
FEM/DEM approach" PhD thesis SFU'08 PDF

62. Acknowledgements 62
SFU Resource Geotechnics Research Group
Rio Tinto
Rockfield Technology Ltd.
Golder Associates Ltd.