The document describes a numerical model of the failure of a cemented backfill pillar under simulated retreat mining. The pillar is modeled using FLAC, a numerical modeling code. The model geometry, material properties, and boundary conditions are defined. Excavation is simulated by incrementally removing constraints along the left boundary in 6 m blast heights. The model remains in equilibrium for the first three blast heights but begins to collapse at 24 m, with total collapse occurring by 30 m. Displacement vectors and plasticity indicators are plotted at each stage to analyze deformation and failure.

1. By
ASHUTOSH KUMAR
ROLL NO. 15CE64R08
GEOTECHNICAL ENGINEERING
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2. PROBLEM STATEMENT
The failure mode of cemented backfill pillars are represented as a Mohr-
Coulomb material. The pillar is three-dimensional in geometry,
measuring 75 m in height by 27 m
in length and 15 m in width. The material properties of the fill are as
follows:
density (ρ) 2100 kg/m3
bulk modulus (K) 110 MPa
shear modulus (G) 37MPa
cohesion (c) 0.1 MPa
friction angle (φ) 35◦
tensile strength ( c/tanφ ) 0.14
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3. MODELING PROCEDURE
The analysis is made along a two-dimensional longitudinal section through the pillar
center. A sliding interface is used along one of the ore body-sand fill contacts to
allow downward settling of the sand during collapse.
The boundary at the fill-ore contact, which is to be excavated, is given a roller
boundary, and the right-hand boundary is fixed in the x- and y-directions; the top is
free (Figure 3.1).
The modeling sequence is as follows.
First, the gravity stresses are allowed to develop in the Sand fill , and forces
equilibrate across the interface. This is done elastically so that the fill will not yield.
At equilibrium, displacements are reset, cohesion is set to the proper value, and
vertical retreat mining is simulated by removing the x-direction fix along the left-
face boundary in small increments that simulate the blast height (6 m). Both
x-displacement and x-velocity histories are used to evaluate whether the system is
coming to equilibrium at each step. Excavation is continued until active collapse of
the pillar occurs.
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4. 4

5. FLAC CODE
 ;Project Record Tree export
 ;... State: init.sav ....
 config
 ;Mining Example Problem
 ;Stability of cemented sand pillars
 gri 17,25
 Mohr-Coulomb model, 30:1 sand:cement ratio, no tension cutoff
 m mo
 ;sand
 prop s=37e6 bu=110e6 de=2100 coh=1e10 fri=35 tens=1.43e10
 ;rock
 prop s=2.292e10 b=3.056e10 d=2700 fric 35 coh 1e7 i 17 j 1 25
 ;pillar 75m high by 15m wide
 gen 0,0 0,75 17,75 17,0
 ;create interface
 mod null i=16
 ini x add -1 i=17
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6. • ;declare interface
 int 1 as from 16,26 to 16,1 bs from 17,26 to 17,1
 int 1 coh=0 fric=0 kn=1e9 ks=1e9 tbond=0
 set grav=9.8
 ;boundary conditions
 fix y j=1
 fix x i=1
 fix x i=18
 his unbal
 his syy i=8 j=1
 ;step to initial gravity equilibrium
 solve
 save init.sav
 ;... State: step1.sav ....
 ;large strain mode on
 set large
 ;turn down cohesion and tension
 prop coh=0.1e6 tens=0.14e6
 ;turn up friction for interface
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7. • int 1 fric=35
 ;fix y at right face boundary
 fix y i=18
 reset displacements
 ini xdis=0 ydis=0
 his xdis i=1 j=3
 his xdis i=1 j=5
 his xdis i=1 j=7
 his xdis i=1 j=9
 his xdis i=1 j=11
 his xdis i=1 j=13
 his xdis i=1 j=15
 his xdis i=1 j=17
 his xdis i=1 j=19
 set sratio 1e-4
 ;simulate vertical retreat mining in adjacent slope by
 ;freeing xfix on node points
 ; 6 m blast height
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8. free x i=1 j=4,5
solve
save step1.sav
;... State: step2.sav ....
; 12 m blast height
ini xdis=0 ydis=0
free x i=1 j=6,7
solve
save step2.sav
;... State: step2del.sav ....
;delete zones that failed in tension
model null i 1 j 4 6
solve
save step2del.sav
;... State: step3.sav ....
; 18 m blast height
ini xdis=0 ydis=0
free x i=1 j=8,9
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9. model null i 1 j 7
solve
save step3.sav
;... State: step4.sav ....
;... State: step3.sav ....
; 18 m blast height
ini xdis=0 ydis=0
free x i=1 j=8,9
model null i 1 j 7
solve
save step3.sav
;... State: step4.sav ....
; 24 m blast height
; these final steps will require a greater number of timesteps
; to determine potential instability and deformation pattern
ini xdis=0 ydis=0
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10. free x i=1 j=10,11
model null i 1 j 8
solve
save step4.sav
;... State: step5.sav ....
; 30 m blast height
ini xdis=0 ydis=0
free x i=1 j=12,13
step 4000
save step5.sav
;*** plot commands ****
;plot name: Displacement Vector
plot hold bound displacement
;plot name: Plasticity Indicator
plot hold bound plasticity
;plot name: History of x-displacement
plot hold history 7 line
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11.  ; 30 m blast height
 ini xdis=0 ydis=0
 free x i=1 j=12,13
 step 4000
 save step5.sav
 ;*** plot commands ****
 ;plot name: Displacement Vector
 plot hold bound displacement
 ;plot name: Plasticity Indicator
 plot hold bound plasticity
 ;plot name: History of x-displacement
 plot hold history 7 line
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12. OUTPUT:
Displacement vectors in the model at
6m
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13. Displacement vectors in the
model at 12m
Here a small localized
displacement is visible.
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14. Displacement vectors in the
model at 18m
Here clearly the lines are on
On verge of failure.
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15. Displacement vectors in the
model at 24m
Here, collapse of the
Pillar begins to occur.
The failure is shown by
The large downward
Movement.
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16. Displacement vectors in the
model at 30m
Here, the pillar is totally
collapses. The zones nearest
to the left- face boundary fail
in tension.
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17. The deformed boundary and plasticity states at
collapse of the pillar
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18. Result
The model comes to equilibrium for the first three blast heights (6 m, 12 m and 18
m).Shown displacement vector at different blast heights from fig 3.2 to fig. 3.7 .
Note that after excavation of the 12 m blast height, the zones nearest to the left-face
boundary fail in tension. These zones are deleted in order to remove elements that will
produce a bad zone geometry as the excavation continues. The model is still in equilibrium
after these zones are deleted; first three stages (6 m, 12 m and 18 m blast heights), the
model can be brought to equilibrium after each excavation is made by using the SOLVE
command.
At the fourth blast height (24 m), collapse of the pillar begins to occur. Finally the
deformed boundary and plasticity states at collapse of the pillar is shown at output.
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19. THANK
YOU…19