1Numerical Modelling of SurfaceSubsidence Associated with Block CaveMining Using a FEM/DEM ApproachAlex Vyazmensky Ph.D.https://sites.google.com/site/alexvyazmensky/http://kz.linkedin.com/in/vyazmensky
Presentation Outline• Problem Statement: Block Caving Mining and Associated Surface Subsidence• Research Objectives• Modelling Methodology• Conceptual Study of Factors Controlling Surface SubsidenceDevelopment• Caving Induced Instability in Natural and Man-made Slopes 2
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.
Subsidence Examples 5Northparkes mine, Australia San-Salvador mine, Chile
Research Objectives and Strategy 7RESEARCH OBJECTIVES NUMERICAL RESEARCH OUTCOME ANALYSIS new FEM/DEM-DFN introduce new methodology formethodology 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
Toolbox for Subsidence Analysis 9Current approaches to assessing surface subsidence associated with block cavingmining 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 providean opportunity to improve understanding of subsidence phenomena andincrease accuracy in subsidence predictions.
Continuum ModellingModelling Numerical Rock Mass Representation Rock Mass Failure RealizationApproach MethodContinuum FDM, FEM continuous medium flexural deformations, plastic yieldFLAC3D ABAQUSConnors, 2006 Beck, 2007 10
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 movementsPFC 3D 3DECGilbride et al, 2005 Brummer et al, 2005 11
New Numerical Modelling Approach 12Most natural rocks subjected to engineering analysis are brittle; failure in such rocksis a result of brittle fracture initiation and propagation.Continuum and discontinuum modelling approaches provide approximations ofbrittle fracturing to some degree, none of them however offer realistic representationof 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 asthe principal modeling tool. The code allows the caving process to be simulated as abrittle fracture driven continuum-discontinuum transition with thedevelopment 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 fragmentationExamples: caving blasting toppling initiation
FEM/DEM Modelling Examples 13Rock bridge failure Step-path drive open pit wall failureLink to animation Link to animation
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
Rock Mass Representation in FEM/DEM 15Possible 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
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
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 " " tan1 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 (( 6015D 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
Subsidence Simulation Example - Crater Formation 21 Evolution of vertical displacements (0.1 – 1m) 50m20° Link to animation 70° surface subsidence, m
Conceptual Study of Factors Governing Subsidence Development 22
Conceptual Study Strategy Factors affecting surface subsidence development Stress Block Geological ExtractionJoint 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
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
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 mass70° movement developing rock 20° mass failure 70°
Conceptual Study Example: Effect of Joint Orientation 36Evolution of zone of major (≥10cm) vertical (YY) and horizontal (XX) surfacedeformations 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 mannerOre 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
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 verticalExtent 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%
Conceptual Study Example: Effect of Joint Orientation 38Resultant surface profiles 0 Lowest • Rotation of the joint -10 point pattern shifts centre ofVertical 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°
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 (cavingfar-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
Conceptual Study Example: Effect of Joint Orientation - Conclusions 40• Well defined, persistent, vertical to steeply dipping joints govern the direction ofcave propagation and the mechanism of near surface rock mass mobilization.• The shallower the dip of these joints the more inclined from vertical is the cavepropagation direction and the more asymmetrical are the surface deformations.• In cases where multiple well defined and persistent steeply dipping sets arepresent the steepest set will generally have the predominant influence.• Major subsidence asymmetryis observed in the dip directionof the sub-vertical/steeply dipping set,where joints are inclined towardsthe cave, the rock mass fails 53° 74°through block-flexural andblock toppling and detachment and sliding of major rock segments.• Depending on joint inclination the joint persistence may have a very significanteffect on surface subsidence induced by block caving.
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 caving0° 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°
Conceptual Study Example: Effect of Fault Location and Inclination 43• Steeply dipping faults, daylighting into the cave and located within an area ofimminent caving are likely to be caved and are unlikely to play any major role in theresultant subsidence.• Faults partially intersecting the caving area may create favourable conditions forfailure of the entire hanging wall.• Depending on rock mass fabric faults located in the vicinity of the caving zone mayhave 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 thesurface.• Inclination of the fault partially intersecting the caving area controls the extent ofsurface subsidence deformations. Low dipping faults will extend and steeply dippingfault will decrease the area of surface subsidence.
Example of Surface Subsidence Simulation 44 CAVE ARREST, CROWN PILLAR FAILURE and RESULTANT SUBSIDENCE 50m Link to animation
Conceptual Study of Block Caving Induced Step-path 52 Driven Failure in Large Open Pit Slope SLOPE IS STABLE WITHOUT CAVINGCONCEPTUAL MODEL embedded animationNumerical Analysis of Block Caving Induced Instabilityin Large Open Pit Slopes: A Finite Element / DiscreteElement Approach 750m rock bridges persistent joints daylighting into the cave 400m block cave
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 RB600750m RB300 60o 50o400m 300m 300m
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, mVertical 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
55 100 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 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 -15Fig. Error! No text of specified style in document..1 Variation of vertical stress inthe crown pillar (50m below pit bottom) for models M1-M5
Case Study - Palabora mine 57 Note limited extend A of the failure beyond pit rim ~160° Lateral release ASurface subsidence infrastructur Mine
Case Study - Palabora mine 58DFN based analysis (section A-A)
Case Study - Palabora mine 59 98 m approximate f ailure approximate f ailure crest location crest location
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.
Publications 61“Role of Rock Mass Fabric and Faulting in the Development of Block Caving Induced SurfaceSubsidence”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 FiniteElement / 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 surfacesubsidence 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 blockcaving 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 aFEM/DEM approach" PhD thesis SFU08 PDF