Geonumerics in Rock Engineering
Dr. Debasis DebProfessor
Department of Mining Engineering
IIT Kharagpur – 721 302
E-mail: [email protected], [email protected]
IIT Kharagpur
Research Interests
Rock Mechanics
Ground Control
Mine Design
Analytical and numerical methods in design of geo-structures
Extended Finite Element Methods in bolt mechanics and support design
Mesh-free numerical methods in geomechanics
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IIT Kharagpur
Structural Defects in Rocks
Fault in RockFolds in Rock
Jointed Rock Mass
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IIT Kharagpur
Rock Failure
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Frost wedging in joints, fastest
movement and rock can become air born, results in talus
A bedding or joint plane in a
rock slope
IIT Kharagpur
Stability Analysis of Underground Mine
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Shaft X-cut to-183 mRL ore drive
Shaft X-cut to -230 mRL ore drive
Decline X-cut to -243 mRL ore drive
Sectional view of the ore body
Ore body and shafts inside the solid model
IIT Kharagpur
Model: Stope Pillars in a Moderate to Hard Rocks
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Stopes, crown, trough and rib pillars
Zoomed view of ore body
Shaft
Solid model of the study area
IIT Kharagpur
A Snap Shot of Stress Pattern
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Major principal stress around the stoping area
IIT Kharagpur
Stability Analysis of Open Stopes in Hard Rocks
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A schematic diagram of
sub-level open stope
ANSYS Solid Model having
multiple ore bodies
Trough Pillar
Draw Point
IIT Kharagpur
Model: Open Stopes in Hard Rocks
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Top
rocks/soil
Ore body
Abandoned
surface mine
162 m
230 m
219 m
Top
rocks/soil
Ore body
Abandoned
surface mine
162 m
230 m
219 m
Chromite ore
Sub grade
ore
Sepentinite
Gabbro
+30 mRL
0 mRL
-30 mRL
-130 mRL
Chromite ore
Sub grade
ore
Sepentinite
Gabbro
+30 mRL
0 mRL
-30 mRL
-130 mRL
-60 mRL
-90 mRL
The In-situ Model Different Ore/Rock Types
IIT Kharagpur
The Stope/Excavation Model
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Trough
Trough drive
10m Rib pillar
Trough pillar
0 mRL
-30 mRL
Trough
Trough drive
10m Rib pillar
Trough pillar
0 mRL
-30 mRL
Finite element mesh of stopes
IIT Kharagpur
Stress Distribution
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C
D
D’
C’
Tensile
zone
C
D
D’
C’
Tensile
zone
Minor Principal Stress distribution
-0.8000
-0.6000
-0.4000
-0.2000
0.0000
0.2000
0.4000
-150 -100 -50 0 50 100 150
Distance from mid of pillar(m)
Min
imu
m p
rin
cip
al str
ess(M
Pa)
Middle of pillar
Stress along C-C’
at 0 mRL
Stress along D-D’
at -30 mRL
-0.8000
-0.6000
-0.4000
-0.2000
0.0000
0.2000
0.4000
-150 -100 -50 0 50 100 150
Distance from mid of pillar(m)
Min
imu
m p
rin
cip
al str
ess(M
Pa)
Middle of pillar
Stress along C-C’
at 0 mRL
Stress along D-D’
at -30 mRL
Minor principal stress distribution at 0 mRL and -30 mRL across the rib pillar
IIT Kharagpur
Weak and Gently Dipping Ore Body
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Longitudinal model section
Plan of the region showing
geotechnical borehole locations
Enlarged view of raise and rib pillar located from 4th level to 2nd level.
IIT Kharagpur
3D Solid and Mesh Model
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Figure 19. 3D model showing ore body, HW, FW and loading conditions
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Sequence of Excavation
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Backfilled Backfilled
Stope 1Stope 2
Rib pillar
New slice
Backfilled Backfilled
Stope 1Stope 2
Rib pillar
New slice
Backfilled Backfilled
Rib pillar
Backfilled Backfilled
Rib pillar
New slice
Stope-1 Stope-2
Backfilled Backfilled
Rib pillar
Backfilled Backfilled
Rib pillar
New slice
Stope-1 Stope-2
Backfilled Backfilled
Stope 1 Stope 2
Backfilled Backfilled
Stope 1 Stope 2
Backfilled Backfilled
Stope 1 Stope 2
Backfilled Backfilled
Stope 3 Stope 4
Backfilled Backfilled
Stope 1 Stope 2
Backfilled Backfilled
Stope 3 Stope 4
Figure 20b. Stage 1 of mining activities Figure 20c. Stage 2 of mining activities
IIT Kharagpur
Principal Stress around the Stoping Area
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Mining stage-3 Mining stage-4
Mining stage-1 Mining stage-2
IIT Kharagpur
Future Directions and Developments
Numerical Modelling in Geotechnical Engineering
o Numerical Analysis of Jointed Rock Mass
o Numerical Analysis of Reinforcement
o Mesh-free Methods for Dynamic Fracture Process
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IIT Kharagpur
Numerical Methods for Jointed Rock Mass
Continuum methodso Finite Difference Method (FDM)
o Finite Element Method (FEM)
o Boundary Element Method (BEM)
o Smoothed Particle Hydrodynamics (SPH)
Discontinuum methodsDiscrete Element Method (DEM)
Discrete Fracture Network (DFN) methods
Hybrid continuum/discontinuum modelsHybrid FEM-DEM
Hybrid SPH-FEM
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IIT Kharagpur
Uniaxial Loading: Rock Sample with a Joint
Analytical solution:
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n
Joint
plane
n
Joint
plane
-140
-120
-100
-80
-60
-40
-20
0
0 10 20 30 40 50 60 70 80 90
Maxim
um
diffe
rntia
l str
ess
1-
3 (M
Pa)
Angle, (deg)
Analytical
XFEM
fracture strength of
rock
Slip of joint plane
Analytical Model X-FEM Model
single joint plane in rock sample Analytical solution and X-FEM results
3
1 3
2 tan
1 tan cot sin 2
j j
j
c
IIT Kharagpur
A Joint Plane Intersecting a Tunnel
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A
Joint plane
Enhanced node
0.00
0.05
0.10
0.15
0.20
0.25
0.30
1.0 1.5 2.0 2.5 3.0 3.5 4.0Distance along the joint plane ( )
Analytical solution
XFEM-solution
/ nτ σ
/r a
The variation of the ratio along the joint plane
IIT Kharagpur
Performance Analysis of Reinforcement:Fully Grouted Rock Bolts
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Block building using rock bolts Highway slope
Drilling process for installing bolt
Tunnel in Rock Mass Reinforced
IIT Kharagpur
Bolt Mechanism
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Axial load
Shear load
Anchor length
Bolt
Nut
Face plate
ResinRebar
Nut with hemispherical seating
Face plate
Thread bar
Cement grout
Axial load
Shear load
Anchor lengthPickup length
Neutral point
Bolt
Excavation Face
Axial load
Shear load
Anchor lengthPickup length
Neutral point
Bolt
Excavation Face
Conventional wisdom on load distribution along a bolt
Recent concept of load distribution along a bolt
Rebar type rock bolt Threaded type rock bolt
IIT Kharagpur
Direct Shear Test
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0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
Sh
ear
forc
e o
n join
t (k
N)
Shear displacement (mm)
Experimental result (Spang & Egger, 1990)
Simulation result (Spang & Egger, 1990)
Proposed doubly enriched finite elements result
joint
bolt
n
A maximum shear load of 31.4 kN, 30 kN and 31.25 kN are obtained from experimental, simulation and proposed DEFE method for shear displacement of 20 mm, 12.5 mm and 18.9 mm respectively.
IIT Kharagpur
Mesh Free Methods for Dynamic Fracture: Smoothed Particle Hydrodynamics (SPH)
Failure under uniaxial Compression:
Tensile Failure:
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0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
0
0.5
1
1.5
2
2.5
3
3.5
0
2
4
6
8
10
12
14
16
x 106
0
0.5
1
1.5
Associative Law Non-associative Law
Maximum Tensile Stress
Effective Plastic Strain
IIT Kharagpur
Slope Failure Analysis
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Effective Plastic Strain
0
2
4
6
8
Effective Plastic Strain
0
1
2
3
4
Effective Plastic Strain
0
5
10
15
x 10-3Bench Width = 6 m Bench Width = 8 m
Bench Width = 10 m
IIT Kharagpur
Failure of Jointed Rocks
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0
0.5
1
1.5
2
2.5
x 10-3
0
0.2
0.4
0.6
0.8
1
x 10-3
Accumulated plastic strain in the presence of multiple intersecting joint planes
Accumulated plastic strain in the presence of single joint plane
Wedge failure in jointed rock mass after rectangular opening
IIT Kharagpur
Rock Blasting
Without joint plane
With joint plane
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IIT Kharagpur
Digital Image Correlation: Data acquisition System
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UTM
Rock sample
Web camera
Magnetic
camera stand
Upper platen of UTM
Visualization and
recording system
Speckled face
Load cell
Computer
Data
logger
Camera
Upper
platen
Lower platen
IIT Kharagpur
Thank you
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