Kinematic model and drawbody in underground mining process

F. Vivanco1, C. Fuentes2, V. Apablaza2 & , F. Melo1

1Universidad de Santiago de Chile, CIMAT2IM2, Codelco, Chile

Outline

• Goal: Develop a simple tool to help in optimizing ore recovery reducing dilution in undergroundmines.

• Approach: Kinematic model, laboratory scaleexperiment validation.

Underground mining - blockcaving

• Large scale production. Low cost methodapplicable in weak ore, unsafe to mine with othertechniques (1000M ton., cost US$ 1000M, profit US$6000M).

• Conditions. Massive ore bodies, large dimensions, rock mass breaking into manageable size block.

Courtesy of C. Fuentes

• Problems. Lots pre-ore recovery, ore dilution1,2

extraction, surface disturbance.

Block caving

• Description. Gravity+rock stresses fracturing rock mass. Minimal drilling and blasting.

1tonnes waste rock mined/tonnes ore mined2tonnes waste rock mined/tonnes ore+waste mined

Block design andoperation optimization

DRAWBODY

LOOSENING ZONE

DRAWPOINT

Concepts

Drawbody models

• Bergmark-Roos

2

20

0

20 )(

21)(),(

rr

tartr r

ρρ

θθθ

=

−=

Drawbody models

0

2

20 )(

ρρ

θ

=

−= frrvv D

r

• Plasticity1

1Velocity distribution is obtained from stress distribution in static material

Drawbody volume

max

3 3 2 20 max max max

30 max

(1 cos )6

(1 cos )6D

G D D D

Gr r

r r r r r r

r

π θ

π θ>>

⎡ ⎤Ω = − − + +⎣ ⎦

→ Ω = −

• Bergmark-Roos

23 3

0 max

3 3max

0 2

cos 2cos 1( )3 1 cos

2 sin 13 ( / 2 ) 1 2

G GD

G

DG

G G

r r

r r

θ θπθ

π π θπ θ θ

⎡ ⎤− +Ω = − ⎢ ⎥−⎣ ⎦

⎡ ⎤ ⎡ ⎤−Ω = −⎢ ⎥ ⎢ ⎥−⎣ ⎦ ⎣ ⎦

• Plasticity

Kinematic model

Nedderman and Tüzun, Powder Technol. 22, 243 (1979)

2

2y y y

x P P

v v vv D D

x y x∂ ∂ ∂

= − ⇒ =∂ ∂ ∂

1z zP

v vD rz r r r

∂ ⎡ ∂ ⎤∂ ⎛ ⎞= ⎜ ⎟⎢ ⎥∂ ∂ ∂⎝ ⎠⎣ ⎦

• Velocity distribution in rectangular hopper.

• Stationary conditions.

• Loose packing state.

• Dilation when dense packing systems start to flow.

Single drawpoint extraction

• Particles streamline

( ), , ,dx f x y D Qdt

=

( ), , ,dy g x y D Qdt

=

• Condition for drawbody

( )0 0, ,R x y D Qt=

R

• Extraction: simultaneousor alternating

• Open question: How drawpoint interact?

• Drawpoints distribution isbased on common belief.

• Description simplified by linearity of kinematicmodel.

Drawpoints interaction

Drawpoints interaction

• Simultaneous extraction )(0 i

LQ Lxvv

i

i−=∑

Drawpoints interaction

• Alternating extraction

Experiment & model

• Pure kinematic model

• Good agreement close tothe aperture.

• Theoretical prediction fails athigher vertical positions.

• Area of deflection is equal toextracted material (constantdensity hypothesis.) Notfulfilled in experiments.

• Dilatancy effect must be considered.

F. Melo et al, to be published in IJRMMS (2006).

Experiment & model

• Kinematic model + dilatancy

DILATION

2

2( ) ( , )n n

nT T

v vD v f v d vy x

∂ ∂= +

∂ ∂

0( , ) exp( )n

TT

v vf v dd d

α= − −

Summary• Model in use (B-R) presents unphysical increase of density.• More physical models, Kinematic and plasticity, are suitable to

describe drawbody and loosening shape.• Simple kinematic model captures characteristics found in

single drawpoint extraction.• Interactions of drawpoint can be described by kinematic

model.• Divergence between kinematic model and experiments can be

surpassed introducing a dilatancy term.• Kinematic model can be used as a simple tool to optimize

draw spacing and draw strategy in underground mining.• We believe even in the worst case it is enough to characterize

a single drawpoint experimentally and use linear superpositionto get insights on flows interactions.

Ongoing research• Lab. scale ore stock experiment.

C. Fuentes, G.Bravo & D. Opazo

Ongoing research

• Full scale ore stock experiment.

• 1100M ton. Stock capacity• 500K ton. Production, 3 months duration.• Local measure accessibility