8th World Conference on
Applied Sciences, Engineering & Management
26-28 Sep 2019, SDIT-Mangalore, India
05-07 Dec 2019, Kyushu University, Japan
Slope Angle Optimisation for Songwe Open Pit Mine
DYSON N MOSES 1,2, HİDEKİ SHİMADA 1 ,TAKASHİ SASAOKA 1, AKİHİRO HAMANAKA 1, SUGENG
WAHYUDİ 1
1
Department of Earth Resources Engineering, Faculty of Engineering, Kyushu University, Fukuoka 819-0395,
Japan
2
Department of Geography and Earth Sciences, Faculty of Science, University of Malawi, P.O Box 280, Zomba,
Malawi
Email: dysonmoses@gmail.com
Abstract: Open pit mining is generally regarded as a cost-effective mining method permitting a high grade of
mechanisation and large production volumes and where feasible extract mineral deposits of a very low grade
which could not be mined economically using underground methods. However, slope instability is a major
challenge to open pit mining operations. As open pit mines are being planned to greater depth, slope angles need
to be carefully planned and designed with respect to the ultimate height of the pit to ensure economical and safe
mining operations. In this study, finite element (FE) code, in Phase2, is used to numerically model and analyse
the stability of the Songwe mine at different angles. The stability assessment is based on shear strength reduction
(SSR) analysis to determine the safety factor. The results of finite element analysis (FEA) show that overall slope
angle of 410 with safety factor of 1.27 is optimal for mining operations at the mine with a minimal risk of slope
material displacement in the event of failure.
Keywords: Carbonatite, Finite element code, Slope angle optimisation, Slope stability, Songwe
Introduction:
The carbonatite complex hosting rare earth elements
(REE) at Songwe Hill in Malawi prominently extrudes
to the surface of the earth. The massive style of
mineralisation at this conical hill will inevitably be
extracted using surface mining method. Open pit
mining is generally touted as a cost-effective mining
method allowing a high grade of mechanisation and
large production volumes and where feasible extract
mineral deposits of a very low grade which could not
be mined economically using underground methods
[1] However, slope instability is a major challenge to
open pit mining operations. The instability leading to
failure of slopes are triggered as a result of downward
movements of material due to gravity as shear stresses
exceed the shear strength. This is resultant to
perturbations on the delicate balance of natural or
manmade slopes induced by anthropogenic activities
and/or nature. Zaruba & Mencl (1982) stress that it is
of primary significance to recognise the conditions
that cause slopes to become unstable and the factors
that trigger the movement in order to solve slope
stability problems [2].
The rate of displacement of the rock mass surrounding
the open pit renders the recovery of ore uneconomical
if the pit was being actively mined [1]. But failure
mechanisms in hard rock slopes, which involve high
stress regime, are much more complex since
progressive failure in hard rock slopes involves
initiation and progression of failure along existing
weakness planes, and even in intact rock. As open pit
mines are being planned to greater depth, slope angles
need to be carefully planned and designed with respect
to the ultimate height of the pit to ensure economical
and safe mining operations. Thus, this contribution is
aimed at assessing pit slope stability on carbonatite
complex under high stress conditions for optimal
design of overall slope angle.
Location and Geology:
Songwe hill is located within the Chilwa Alkaline
Province (CAP) in Phalombe district southern Malawi
(Figure 1). Surface mapping and drill cores from the
three phases show that the principal geological units
of the carbonatite complex include: carbonatite, fenite
and fenite breccia. Minor geological units consist of
veins of apatite and fluorite-rick rock and phonolite.
These alkaline bodies intrude into the basement
granulite and gneiss. Broom-Fendley presented new
petrographic and geochemical observations following
thin sections [3].
Carbonatite
The carbonatite, which is the ore hosting rock, is best
exposed on the north and north-eastern slopes with
relatively smaller extent along the north western slope.
There are essentially three REE mineralised
carbonatites namely: coarse grained calcite
carbonatite (soviet); fine grained carbonatite
(alvikite); and Fe-rich ferroan calcite carbonatite.
Mkango resources, the company developing the
deposit, adopted the shorthand C1, C2 and C3
respectively to distinguish the different types of
carbonatites.
Fenite
Fenites at Songwe form an aureole around the
carbonatite intrusion. Large blocks of fenite show
WCSEM 2019XXX Copyright © 2019 BASHA RESEARCH CENTRE. All rights reserved
DYSON N MOSES
evidence of being in situ and interpreted as fractured
blocks from the margins, or the roof of the carbonatite.
It is postulated that the carbonatite intrusion never
reached the surface since the fenite is continuous with
only rare carbonatite veinlets [3]. In terms of the
texture, the fenites display a coarse-grained
equigranular igneous texture, strongly suggesting an
igneous protolith. The fenitisation at Songwe is
predominantly potassic with a composition of
orthoclase and minor aegirine.
Figure 1: Location and geology of study area [3]
Methodology:
The study is based on FE numerical modelling. Phase2
was used owing on its capability to compute
displacement and/or deformation behaviour in
continuum. The modelling was based on shear
strength reduction (SSR) method to determine
potential instability (Figure 2).
Shear Strength Reduction Method
The SSR technique of FE slope stability analysis
involves a systematic iterative search for a strength
reduction factor (SRF) value that stretches the slope to
limits of failure. Lately, the SSR method based on the
FEM is widely used to analyse slope stability. The
trend is attributed to the apparent advantages of the
FEM over the popular traditional LEM which uses
factor of safety (FOS) in the analysis. As highlighted
by many developers and authors [4-6] the key
advantages of SSR are:
1. No assumptions are made in advance about the
shape or location of the failure surface. Thus,
failure occurs “naturally” through the zones
within the soil or rock mass in which the shear
strength is unable to resist the shear stress leading
to non-convergence
2. It accounts for various material stress-strain
behaviours
3. Provides information on deformation at working
levels and is capable to monitor propagation of
failure up to and including overall shear failure.
4. Provides information on deformations, bending
moments and axial loads of support elements at
failure
For these facts, SSR is regarded as highly reliable and
robust in performing under wide range of conditions.
The SSR technique applies the constitutive law of
Mohr-Coulomb strength for slope materials. The
Mohr-Coulomb strength envelope is most widely
applied as a failure criterion in geotechnical
engineering. A unique feature of this linear failure
model is the fact that it can be simply and explicitly
expressed in both principal stress and shear-normal
stress. In SSR approach, the Mohr-Coulomb material
is factored or reduced to determine the safety factor as
presented in equation (1).
𝜏 𝑐
𝑡𝑎𝑛𝜑
= +𝜎
… … … … … … … … (1)
𝐹 𝐹
𝐹
Where: 𝜏 is shear stress; C is cohesion; 𝜑 is internal
friction angle; 𝜎 is normal stress and
F is strength reduction factor or slope safety
factor
The equation can be re-written as equation (2).
𝜏
= 𝑐 ′ + 𝜎 tan 𝜑′ … … … … . . (2)
𝐹
𝑐
tan 𝜑
Where 𝑐 ′ =
and
𝜑 ′ = 𝑎𝑟𝑐𝑡𝑎𝑛 (
)
are
𝐹
𝐹
factored Mohr-Coulomb shear strength parameters.
Figure 2: Research method and design
Note: UCS → Uniaxial compressive strength, TBS →
Brazilian tensile strength, TCS → Triaxial
compressive strength.
Critical Shear Reduction Factor
The process of systematically finding the critical shear
reduction factor (CSRF) or critical safety factor (F)
that stretches a previously stable slope (F≥1.0) to the
Proceedings of the 8th World Conference on Applied Sciences, Engineering and Management
26-28 September 2019, SDIT-Mangalore, India and 05-07 December 2019, Kyushu University, Japan
ISBN 13: 978-81-930222-3-8, pp xxx-xxx
Slope Angle Optimisation for Songwe Open Pit Mine
verge of failure was done through iterative steps until
the model fails to converge.
Numerical Modelling:
To evaluate the optimal angle of stability for the
Songwe mine design, a number of numerical models
were run in Phase2. The model design is presented in
Figure 3. The continuum approach was adopted to
understand the behaviour of the rock pit walls using
FE code. Table 1 and 2 presents the mechanical
properties of the rock materials and model calibration
respectively.
Figure 3: Numerical model dimensions
the meshing type applied is graded mesh determined
at 350 nodes of meshing intensity with a gradation
factor of 0.1. The meshing quality was adopted having
demonstrated a reliable stability of solutions.
Results and Discussion:
To evaluate the stability condition of the pit design, a
series of models were constructed at different angles
and observe the safety factor. The testing commenced
with the steeper slope angle of 500 and then ‘the
change slope angle editing tool’ was used to optimise
the open pit design to make the slope as steep as
possible while maintaining acceptable safety factor.
At the ultimated proposed final mine depth of -350 m,
the slope angle 500 with a steep bench angle 780 yields
the CSRF of 1.04 (Figure 4) which indicates that the
slope is close to failure and the design is thus
unacceptable since safe operations could be
compromised. By changing the angle to less steeper
slope the safety factor improved to up to 1.31 at 40 0
with a steep bench angle of 600 (Figures 5-7). In a hard
rock condition with a rock mass rating (RMR) of 71, a
CSRF of ≧1.25 could be considered safe for mining
operations [9-13]. By plotting the slope angle versus
CSRF, the optimum slope angle for the mine design is
found to be 410 with a CSRF of 1.27 (Figure 8)
Table 1: Model mechanical properties
γ
[g/m3]
Carbonatite 2.78
Fenite
2.70
Rock type
E
[GPa]
45.30
44.40
UCS
σt
φ
C
V
[MPa]
[MPa] [deg] [MPa]
83.2 0.28 8.60
35
0.18
118.6 0.29 10.40 36
0.18
Table 2: Parametric settings
Parameter
Setting(s)
Number of iterations
500
Tolerance of stress analysis
0.005
Mesh type and density
6 nodded triangle, 350 nodes
Boundary conditions
Restrain XY for bottom boundary
Free XY for top boundary
Restrain X for y-axis boundaries
Model Calibration
In order to ensure that results realised from the
numerical modelling are realistic and reliable,
calibration of the FE models was undertaken. The
calibration was based on the sensitivity test carried out
as a pre-validation process of the FEA. The tests
established key parametric settings that proved to
affect the FEA results namely; tolerance of stress
analysis and mesh quality.
The tolerance value defines the point at which the
finite element solution is considered to have
converged [7]. After a sensitivity test, it was noted that
at 0.005 the solutions are less sensitive, giving
accurate and reliable results while optimizing
computation time.
Mesh density can also highly influence the accuracy
of the results if not properly set up [7, 8]. In this study,
Figure 4: Overall slope stability at 500 with steep
bench angle 780
Figure 5: Overall slope stability at 450 with steep
bench angle 690
Proceedings of the 8th World Conference on Applied Sciences, Engineering and Management
26-28 September 2019, SDIT-Mangalore, India and 05-07 December 2019, Kyushu University, Japan
ISBN 13: 978-81-930222-3-8, pp xxx-xxx
DYSON N MOSES
optimized slope angle of 410, material movement is
simulated to be confined within 1.10 m.
Figure 6: Overall slope stability at 420 with steep
bench angle 640
Figure 9: Material displacement risk on the slope
face at 500
Figure 7: Overall slope stability at 400 with steep
bench angle 600
Figure 10: Material displacement risk on the slope
face at 450
2,5
CSRF
2
1,5
1
Excavation stage 1
Excavation stage 2
Excavation stage 3
0,5
0
38 39 40 41 42 43 44 45 46 47 48 49 50 51
Slope Angle (deg)
Figure 8: Slope stability for excavation stages 1, 2
and 3
Deformation Behavior
Excavation during mining operations create an
imbalance of forces especially on the cut face. The
deformation behavior on a cut rock slope in an openpit mine may be due to inelastic as well as elastic
deformation due to excavation. The displacement risk
evaluation on the pit slope face was carried out under
gravitational loading. The outcome shows high risk
displacement contours at 500 which gradually reduces
to minimal risk at 400 (Figures 9-12). The material
displacement risk on the pit slopes echo the results of
the stability condition with respect to CSRF.
Furthermore, in the event of slope failure, the loss of
cohesion is more pronounced at steeper angle leading
to a longer sliding and/or falling distance (Figure13).
Slope face material sliding distance would increase
from 1.13 m at 400 to 2.02 at 500. At the proposed
Figure 11: Material displacement risk on the slope
face at 420
Figure 12: Material displacement risk on the slope
face at 400
Proceedings of the 8th World Conference on Applied Sciences, Engineering and Management
26-28 September 2019, SDIT-Mangalore, India and 05-07 December 2019, Kyushu University, Japan
ISBN 13: 978-81-930222-3-8, pp xxx-xxx
Slope Angle Optimisation for Songwe Open Pit Mine
Figure 13: Extent of displacement at slope angles
400, 420, 450 and 500
Conclusion:
Slope stability conditions of open pit mine depends
principally on the stress conditions in the pit slopes,
the geological structures, the rock mass strength and
the pit geometry. In this study, attention was accorded
to pit geometry with respect to slope angle. The results
of FEA for Songwe REE designed mine shows that an
overall slope angle (OSA) of 400 is the most stable
state. However, based on safety factor criterion, the
slope angle can be optimally steepened enough to 410
while maintaining acceptable safety factor.
On displacement, when shear stress exceeds shear
strength, steeper slope angle of 500 demonstrated
unacceptable high risk of slope material displacement
than the gentle slopes at 410. Additionally, steeper
angles would lead to a longer sliding and/or falling
distance of simulated failed material than gentle slopes
after loss of cohesion.
Mechanics and Foundation Engineering, pp. 5970
[7] Rockscience, "rocscience.com," 04 09 2019. [O
nline]. Available: https://www.rocscience.com.
[8] Ghavidel, A., Mousavi, R. S and Rashki, M.,
(2017) "The Effect of FEM Mesh Density on the
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[9] Stacey, T. R., (2001) "Best practice rock
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Braamfontein, South Africa
[10] Read, J and Stacey, P., (2009) “Guidelines for
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Publishing
[11] Contreras, L. F., (2015) "An economic risk
evaluation approach for pit slope optimization,"
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Mining and Metallurgy, pp. 607-622
[12] Golestanifar, M., Ahangari, K., Goshtasbi, K.,
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optimization," The Southern African Institute of
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[13] Adams, B. M., (2015) "Slope Stability
Acceptance Criteria for Opencast Mine Design,"
Adams Geotechnical Limited, New Zealand
References:
[1] Sjoberg, J., (1996) "Large Scale Slope Stability
in Open Pit Mining," Division of Rock
Mechanics; Lulea University of Technology,
Sweden
[2] Zaruba, Q and Mencl, V., (1982) “Landlides and
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[3] Broom-Fendley, S., Brady, A. E., Horstwood, M.
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[4] Hammah, R. E., Curran, J. H., Yacoub T. and B.
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Colloquium. Schuber, Canada
[5] Diederichs, M. S., Lato, M., Hammah, R. and
Quinn, P., (2007) "Shear Strength Reduction
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United Arab Emirates University, London
[6] Matsui, T. and San, K.-C. (1992) "Finite Element
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Proceedings of the 8th World Conference on Applied Sciences, Engineering and Management
26-28 September 2019, SDIT-Mangalore, India and 05-07 December 2019, Kyushu University, Japan
ISBN 13: 978-81-930222-3-8, pp xxx-xxx