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Mining Science and Technology Vol.20 No.6810

it just indicates the equilibrium of various forces ondestruction. A difficulty with all these equilibrium

methods is that, in turn, these necessitate the assump-

tions relating to side force directions between theslices, yet the concept of the side forces is entirely

artificial and is not well established till date[1]

. Thus,discrete element method, which conducts analyzing

the rock slopes having joints through an aspect on the

behavior of particle size, was used in this study toevaluate the stability of these external overburden

dumps[4-7]

. The Discrete Element Method (DEM) de-scribed the mechanical behavior of these assemblies

of discs (2D) and spheres (3D) representing the

geo-materials by shape for the considered externaloverburden mine dumps. The method is based on theuse of an explicit numerical scheme in which the in-

teractions between or amongst the particles aremonitored following contact-by-contact, and the mo-

tion of the particles are modeled particle-by-particle.Results were compared with the ones derived from

the existing limit equilibrium method, after analyzing

an aspect of final failure surface that originated fromthe movement of the dump surfaces.

2 Limit equilibrium method

Limit equilibrium method has been widely used toanalyze dump or embankment slope stability in the

past, worldwide. In the present study, in order to

evaluate the interrelation between the behavior of the

joint faces and the stability of the overburden dumpslopes; the material properties derived from the safety

factor obtained from the limit equilibrium methodwere used in this study. The Eq.(1) was used to

evaluate the safety factor of a dry slope where tension

crack does not exist. The basic material properties ofoverburden were used for the analysis, and the calcu-

lations were carried out to derive the safety factorvalues of 1.67, 1.17, 0.95, and 0.92 by changing the

gradient of the joint surfaces while other parameters

kept on the same.

( )2

cos tan

sin

cos

1cot cot

2

P

P

P

P f

CA WFoS

W

A H ec

W H

+-=

=

=

(1)

where FoS is the safety factor; C and the cohe-

sion and the friction angle of joint respectively;A and

W the contact area and the weight of the moving

ground block respectively; P and f the angle of

joint planes and the slope face angle respectively; all

expressed in consistent units.The interrelation between safety factor and the

gradient of discontinuity evaluated through the limit

equilibrium method in the present study have beenproduced in Table 1. It may be observed from the

table that keeping the other parameters like the cohe-sion, friction angle, the slope angle and the height of

the slope fixed the factor of safety decreases withincrease in the angle of the joint.

Table 1 Calculated parameter P for obtaining the safety factors with other parameters for the considered slope

Density (kg/m3) Cohesion (kPa) Friction angle () Slope angle () Height (m) Angle of joint plane () Factor of safety

2000 2 20 45 35 15 1.67

2000 2 20 45 35 22 1.17

2000 2 20 45 35 29 0.95

2000 2 20 45 35 35 0.92

3 Discrete element method

In the DEM, the interaction of the particles istreated as a dynamic process with states of equilib-

rium developing whenever the internal forces balance

each other. The contact forces and displacements of astressed assembly of particles are found by tracing themovements of the individual particles. Movements

result from the propagation, through the particle sys-tem, of disturbances caused by the specified walls

and the particle motion and/or body forces. This is adynamic process in which the speed of propagation

depends on the physical properties of each of these

discrete systems.

The dynamic behavior is represented numericallyby an explicit time stepping algorithm, using a cen-tral-difference scheme to integrate the accelerations

and the velocities. The DEM is based upon the idea

that the time step chosen may be so small that, during

a single time step, disturbances cannot propagate

from any particle further than its immediateneighbors. Then, at all times, the forces acting on any

particle are determined exclusively by its interactions

with the neighboring particles with which it is incontact. Since the speed at which a disturbance can

propagate is a function of the physical properties ofthe discrete system, the time step can be chosen ac-

cordingly to satisfy the above constraint. The use of

an explicit, as opposed to an implicit, numericalscheme makes it possible to simulate the nonlinearinteraction of a large number of particles without ex-cessive memory requirements or the need for an it-

erative procedure.The calculations performed in the DEM alternate

between the application of Newtons second law to

the particles and a force-displacement law at the con-


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RADHAKANTA Koner et al Discrete element approach for mine dump stability analysis 811

tacts. The Newtons second law is used to determinethe motion of each particle arising from these con-

tacts and body forces acting upon it; while the

force-displacement law is used to update the contactforces arising from the relative motion at each of

these contacts. The presence of walls in PFC2D re-quires only the force-displacement law to account for

behaviour of the ball-wall contacts. The Newtons

second law is not applied to the walls, since the wallmotion is specified as boundary of the model i.e.,

fixed (Fig. 1).

Fig. 1 Calculation cycle followed in PFC2D

4 Evaluation of the model properties for

simulation

The laboratory results of solids such as rocks, canbe simulated with the numerical tests on synthetic

materials. The PFC2D input parameters could bevaried until the behavior of the numerical samplematches that of the physical sample. The correspond-

ing parameters may then be used in a PFC2D simula-

tion for a larger problem containing the same solidmaterial as in the sample.

Biaxial tests simulated by confining a rectangularsample (comprised of a compacted particle assembly)

within the defined four walls of the numerical model.The top and bottom walls simulate loading platens;whereas the left and right walls simulate the con-

finement experienced by the sample sides.

The sample is loaded in a strain-controlled fashionby specifying the velocities of the top and bottom

walls. During all stages of the test, the velocities ofthe left and right walls are controlled automatically

by a numerical servo-mechanism that maintains aconstant confining stress within the sample. Thestresses and strains experienced by the sample are

determined in a macro-fashion by summing all theforces acting upon it, and relative the distance be-

tween the appropriate walls. Material response is

computed by tracking the various stress and strainhistories.

The complete set of micromechanical parameters

that characterizes a contact-bonded material are givenby:

/

c

n s

c

c

E

k k

-

wherecE is the Youngs modulus at each parti-

cle-particle of the contact;sn

kk / the ratio of parti-

cle normal to shear stiffness; the particle friction

coefficient (that applies when the contact bond has

broken); and c and c the normal and shear

strengths, respectively, of the material lying between

any two particles joined by a contact bond.

In order to determine the basic material propertiesof overburden dump geo-materials, which are equiva-

lent to those of limit equilibrium method, for using inthe discrete element method, the material calibrationshould be carried out as depicted in Fig. 2

[4-5].

-

-

c

c

sn

c

t

kk

E

c

E

/

Fig. 2 Calibration of micromechanical properties from the

physical mechanical properties of solids

Similar to the numerical biaxial test; the direct

shear tests were also simulated to convert the me-chanical properties of the overburden dump geo-ma-

terials into the micromechanical properties for the

numerical analysis[6-10]

. The procedure of simulationis shown in Figs. 1 to 4. The derived input propertiesare presented in Tables 2 to 4.

Fig. 3 Flowchart of the method adopted for predictingdisplacement profiles using the discrete element method


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Mining Science and Technology Vol.20 No.6812

K

(a) Test model (b) Simulation

Fig. 4 Numerical biaxial the test model and simulation

Table 2 Original and artificial properties of the dump mass

Parameter Original property Artificial property

UCS (MPa) 96 100

Youngs modulus (GPa) 73 7

Poissons ratio 0.26 0.25

Table 3 Micromechanical properties used for dump mass

Item Density (kg/m3) 2300

Kn 1x108

Ball Stiffness (N/m)Ks 1x10

8

Pb_rad (m) 1.0

Pb_ks (GPa/m) 1.5

Pb_kn (GPa/m) 1.5

Pb_nstrength (MPa) 2

Parallel bond

Pb_ssterngth (MPa) 2

Table 4 Micromechical properties used fordiscontinuity plane (joint)

Items Value

Friction coefficient 0.0

N_bond (N) 1000.0

S_bond (N) 1000.0

Spacing 0.1

5 Model geometry

Fig. 5 shows the geometry of the overburden dump

slope model investigated for the present study. Ana-lyzed range of dump mass geometry is 95 m60 m,

the height of slope is 30 m and gradient of slope is45. The sides of the model were fixed to the X-axis

and the lower part was fixed in bothX- and Y-axes as

the boundary conditions imposed for the analysis.

P

(a) 30 m high dump slope with both side (b) Joint inserted at the distinct element model (15)

roller boundary and rigid at the base

Fig. 5 Numerical dump slope geometry

6 Results and discussion

Discrete element analyses were carried out usingthe simulated material properties for each of thesafety factor as input data; results have been shown in

Fig. 6. In each figure, a red line showed the critical

discontinuity surface by joint. The effect of disconti-nuity surface (joint) did show small displacement

responses for the first and the second models with thesafety factors of 1.67 and 1.17 respectively. So, this

represents the safer sides of these dumps in view of

the stability conditions (Figs. 6a and 6b). But gradualsliding movement occurred along the slopes of joint

faces for the third and the fourth cases with the safetyfactors of 0.95 and 0.92 respectively (Figs. 6c and 6d).In these mine dumps, the sliding occurred along the

discontinuity surface (more prominent in the Fig. 6d,

discontinuity surface oriented at 35 dip direction).

There were also some potential irregular failuresurfaces developed (as shown in Fig. 7, the line join-

ing the cracks distinguished by the red line), that only

gave hints about the imminent failure. These mayserve as indicators and proper precautionary measures

may be taken up based on these observations.

7 Conclusions

In this study, the behavior of the external mineoverburden dump slopes interlocked with the discon-tinuity surfaces was analyzed using the PFC2D tool,

which implements one of the discrete element meth-

ods. To describe the basic behaviours, microme-chanical material properties were derived from labo-

ratory test models. Four mine external overburden


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RADHAKANTA Koner et al Discrete element approach for mine dump stability analysis 813

dump slope models were analyzed which wereequivalent to the limit equilibrium models with dif-

ferent safety factors of 1.67, 1.17, 0.95, and 0.92.

(a) Angle 15 and displacement of 0.2 m (b) Angle 22 and displacement of 0.4 m

(c) Angle 29 and displacement of 2.57 m (d) Angle 35 and displacement of 3.27 m

Fig. 6 DEM analysis for different joint set dip angles and displacements

Fig. 7 Line of potential failure surface and the unstableblock region at the dump slope

The safety factors of 1.67 and 1.17 obtained in

DEM models did not show any failure behavioraround the slope faces or discontinuity planes, while

those for 0.95 and 0.92 showed sliding along the dis-

continuity planes and slope faces. Consequently, onecan estimate the safety factor as well as estimate the

failure behavior on the joint planes and slope faces by

the use of the distinct element methods; of which thelater cannot be analysed in the equilibrium analysismethods. Similar to the fact that, at any real mineexternal overburden dump, the failure surface(s) is

(are) usually not regular has been established using

this analysis where the output also is observed to bethe irregular potential failure surface in the dump

slope.

References

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Application of numerical methods for assessment ofslope stability.Mine Tech, 2008, 29(1): 3-10.

[4] Koner R, Chakravarty D. Stability study of the mineoverburden dumps slope: a micromechanical approach.

Studia Geotechnica et Mechanica, 2010, XXXII(1): 35-58.

[5] Preh A, Poisel R, Krastanov J. Investigation of the fail-

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[8] Yin S H, Wu A X. Experimental study of preferentialsolute transportation during dump leaching. Journal ofChina University of Mining & Technology, 2006, 16(4):

416-420.[9] Ataei M, Bodaghabadi S. Comprehensive analysis of

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