


































Energy and Earth Science 
Vol. 4, No. 2, 2021 

www.scholink.org/ojs/index.php/ees 

ISSN 2578-1359 (Print)   ISSN 2578-1367 (Online) 

1 
 

Original Paper 

Evaluation of the Influence of In Situ Stress on the Stability of 

Mine Pit Walls: A Case Study of Songwe Mine 

Dyson Moses
1*

, Hideki Shimada
1
, Takashi Sasaoka

1
, Akihiro Hamanaka

1
, Tumelo K. M Dintwe

1
,
 
Joan 

A. Onyango
1
 & Cho Thae Oo

1
 

1
 Rock Engineering and Mining Machinery Laboratory, Department of Earth Resources Engineering, 

Kyushu University, Fukuoka, Japan 

*
 Dyson Moses, Rock Engineering and Mining Machinery Laboratory, Department of Earth Resources 

Engineering, Kyushu University, Fukuoka 819-0395, Japan 

 

Received: April 15, 2021         Accepted: April 22, 2021       Online Published: May 25, 2021 

doi:10.22158/ees.v4n2p1             URL: http://dx.doi.org/10.22158/ees.v4n2p1 

 

Abstract 

The investigation of the influence of in situ stress in Open Pit Mine (OPM) projects has not been 

accorded a deserved attention despite being a fundamental concern in the design of underground 

excavations. Hence, its long-term potential adverse impacts on pit slope performance are overly 

undermined. Nevertheless, in mines located in tectonically active settings with a potential high 

horizontal stress regime like the Songwe mine, the impact could be considerable. Thus, Using FLAC3D 

5.0 software, based on Finite Difference Method (FDM) code, we assessed the role of stress regimes as 

a potential triggering factor for slope instability in Songwe mine. The results of the evaluated shearing 

contours and quantified strain rate and displacement values reveal that high horizontal stress can 

reduce the stability performance of the pit-wall in spite of the minimal change in Factor of Safety (FoS). 

Since mining projects have a long life span, it would be recommendable to consider “in situ 

stress-stability analyses” for OPM operations that would be planned to extend to greater depths and 

those located in tectonically active regions. 

Keywords 

In situ stress, dilation angle, finite difference method, flow rule 

 

 

 

 

 



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1. Introduction 

For decades, the investigation of the influence of in situ stress has been conventionally limited to 

underground mining studies. In underground mining the analyses focus on failures such as squeezing, 

spalling and rock bursting which could impact mine safety and production. Despite being a 

fundamental concern in the design of underground excavations, in situ stresses for open pit projects are 

still not regarded as influential. However, Stacey (2007) highlighted the significance of investigating 

the role of in situ stress in OPM on slope instability since excavation creates stress imbalance. As the 

demand for mineral resources increases to cater for the world booming population, surface mining 

operations are advancing to greater depths. Open pit mining operations are generally cost-effective 

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 (Sjoberg, 1996). However, slope instability is a major challenge to OPM operations. 

Llano-Serna, et al. (2016) quantify that roughly, two open pit failures occur worldwide annually. The 

instability of the slopes documented by far is governed by the slope geometry, rock mass strength, 

geological structures, shock loading, and hydraulic conditions. Stress regimes are hardly factored in 

among potential triggering factors for mine pit-wall instability. 

A study by Sjoberg (1996) on the Bingham Canyon mine, currently at 850m depth, concluded that the 

large scale failures involving up to 2 metric tonnes of material were due to a combined effect of 

pre-existing discontinuities and excessive water pressure leading to plane shear failure and rotational 

shear failure respectively. However, though not considered among the factors (Sjoberg, 1996) reported 

that the stress state in the mine was characterised by horizontal stresses being higher than the vertical 

stress with a k-ratio of greater than 1.1. In South Africa, the Sandsloot open pit mine is a typical 

example of an active tectonic environment that encountered instability. The tectonism is characterised 

by three major joint sets, which relate to the emplacement of the Potgietersrus Limb. The mine in the 

area experienced slope failure that prompted a comprehensive study to establish the triggers. Without 

any reference to in situ stress among controlling factors, Bye and Bell (2001) attributed the principal 

cause of the slope instability at the mine to the steep dipping and persistent joints.  

At Buzhaoba mine in China, the failure that occurred was loosely attributed to tectonic stress as a 

dominating factor (Chen et al., 2019). According to the analysis, the principal stress direction that was 

theorised and simulated at 123º showed that as the excavation progressed to a deeper horizon, the 

cumulative effects of stress were exhibited through rock mass deformation and instability along the 

direction of the principal stress. In the case of Songwe mine, it is sited within the active tectonic setting 

of the Malawi Rift System (MRS) that is part of the main East African Rift System (EARS). Therefore, 

this work builds on the hypothesis that high in situ stresses, especially in tectonically active 

environments, could have a critical influence in OPMs. Accordingly, this contribution is aimed at 

evaluating the accruing influence of in situ stress and its role as a potential triggering factor for slope 

instability. 



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1.1 Location and Geology of the Study Area 

Songwe mine is expected to perch at Songwe Hill situated in Phalombe district southern Malawi 

(Figure 1a) .The Hill has a North-South diameter of 800m and measures 450m East to West. In terms 

of regional geology, the area is underlain by crystalline rocks of Precambrian to lower Palaeozoic age 

referred to as the Malawi Basement Complex which are intruded into by alkaline intrusive bodies 

(Garson & Smith, 1965; British Geological Survey, 2009). The emplacement of these alkaline 

intrusions occurred during the Late Jurassic—Early Cretaceous period which affected an area 

approximately 300-400 km in diameter in the south of Malawi and in Mozambique (Figure 1a). 

The local geology of the study area is principally composed of; carbonatite and fenite surrounded by a 

massive intrusion of syenite (Figure 1b). Carbonatite, which is the ore hosting rock, occurs in three 

categories namely: coarse-grained calcite carbonatite (sovite); fine-grained carbonatite (alvikite); and 

Fe-rich ferroan calcite carbonatite (Broom-Fendley et al., 2017; Broom-Fendley et al., 2017b; Simandl 

& Paradis, 2018). Fenites form an aureole around the carbonatite intrusion. Large blocks of 

encapsulating fenite show evidence of being in situ, hence the carbonatite intrusion never reached the 

surface beyond roofing fenite (Broom-Fendley et al., 2017). Structurally, the site is within the active 

tectonic environment of the Malawi Rift System (MRS) that is part of the main East African Rift 

System (EARS). Therefore, faulting and the development of joints may not be an uncommon 

phenomenon. However, the structural disruption at the carbonatite complex is not vividly reflected on a 

large scale except for a major fault on the eastern side of the hill that runs NW to SE. The subtle 

evidence of structural deformation is revealed in sharp lithological breaks across the hill. 

 

 

Figure 1. Location and Geology of Study Area (Modified after Broom-Fendley et al., 2017) 

 

 

 

 



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2. Method 

2.1 Numerical Methods 

Numerical methods are capable of simulating natural failure process and representing deformation and 

displacement of the failing rock mass (Diederichs et al., 2007; Matsui & San, 1992; Hammah et al., 

2004; Dawson et al., 1999). Analysis based on a numerical approach involves dividing the rock mass 

into elements assigned with the idealised stress-strain relation and properties that describe how the 

material behaves. The most commonly applied numerical methods in slope stability analysis are 

divided into three categories: (i) continuum methods, (ii) discrete methods, and (iii) hybrid 

continuum/discrete methods. In this study, a continuum code based on the finite difference method 

(FDM) using FLAC
3D

 5.0 software (Itasca, 2012) was applied in simulating the potential slope 

instability.  

The FDM approach was preferred because the constitutive models are treated with no modification to 

the solution algorithm as such the modeling is justifiably more accurate for plastic collapse loads and 

plastic flow (Itasca, 2012). The analysis was performed in elasto-plastic state in finding the solution 

with the Mohr-Coulomb constitutive model and failure criterion. The Shear Strength Reduction (SSR) 

technique embedded in the FDM code achieved the determination of slope performance. The SSR 

involves a methodical iterative search of the Factor of Safety (FoS) value that stretches the slope to the 

limits of failure. The roller boundary conditions were assigned in the x- and y-direction thereby fixing 

the boundary planes in the x- and y-direction respectively, pinned boundary condition (i.e., constrained 

in the x-, y- and z-directions) was applied at the bottom of the model and the top of the model was left 

unconstrained. 

2.2 Model Construction 

The hill dimensions guided the numerical model of the pit. The OPM at the site is anticipated to cover 

almost the whole stretch of the hill. The overall dimensions of the final pit are expected to be 

approximately 650 m North to South and 400 m East to West. Regarding pit height, it is planned that 

the deepest level will be 300 m when measured from the highest Reduced Level (RL) of the pit on the 

southern side of the pit (Figure 2). Accordingly, the simulation model stretches 1000 m in length, 400 

m in height, and the width measures 400 m. The 100 m addition in length on both ends was to make 

sure that the boundary conditions do not influence the solution when stepping. Monitoring points were 

added at the mid-section of the pit to observe displacements and induced stresses on the pit walls. The 

excavation of the stack benches (dimension 15 m height and 7.5 m width) was done in three sequential 

stages.  

Three conceptual cases were generated with respect to pit height. In the first scenario, shear strain 

behaviour on the pit-slope was investigated at the current planned depth of 250 m. The planned depth is 

within the bounds of proven ore reserve hence the geological confidence is high. The second scenario 

is for 280 m depth and the third case is based on the ultimate depth of 300 m. At this depth, the 

geological confidence is relatively low since less than 10% of the drilled holes reached 300 m. The 



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analysis was performed at the trial steep overall angle of 45º (Moses et al., 2020) in the non-associated 

flow rule (ψ=0°) and associated flow rule (ψ≠0°). The two flow rules are conducted to comprehend 

both the worst-case and idealistic scenario of rock mass deformation. The material properties used in 

this study are presented in Table 1. Rock density , uniaxial compressive strength (UCS), Young’s 

modulus (E), tensile stress , friction angle , cohesion (c), Poisson ratio (v) and dilation angle (ψ) 

were obtained from laboratory rock strength tests conducted except for Syenite lithological unit, which 

were sourced from literature. 

 

Table 1. Mechanical Properties of the Rock Units 

Rock Type 
UCS 

(MPa) 

 

(g/m
3
) 

E 

(GPa) 

 

(MPa) 

 

(Deg) 

C 

(MPa) 

Ψ 

(Deg) 
V 

Carbonatite  83.2 2.78 45.30 8.6 35 0.32 2.3 0.28 

Fenite 118.6 2.70 44.40 10.4 36 0.30 3.5 0.29 

Phonolite 150.4 2.88 64.30 11.5 37 0.45 3.5 0.29 

Syenite* 70.0 2.55 53.40 3.37 30 0.28 - 0.25 

Note. *Based on empirical values (Katz et al., 2000; Croll et al., 2014). 

 

 

 

 

 

 

 

 

 

 



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(a) cross section of Songwe open pit mine 

 

 
 

(b) Model extents 

Figure 2. Cross Section of the Mine and Numerical Model 

 

3. Result and Discussion 

In evaluating the stability of excavation, the Factor of Safety (FoS) is utilised as an index to determine 

the performance of the excavated sections. In this study, the evaluation of the safety of the pit slope is 

based on the Mohr-Coulomb failure criterion as presented in the equation in Figure 3, which is a 

classic approach in geotechnical studies (Labuz & Zang, 2012). The application of the criterion in 

FDM utilises the Shear Strength Reduction (SSR) technique that entails a systematic iterative search 

for a value that stretches the slope to the limits of failure. When FoS, derived as a ratio between supply 

(shear strength) and demand (shear stress), is ≥ 1 the excavated face is described as stable and if < 1 it 

is unstable.   

 

400 m 

1000 m 

400 m 



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Figure 3. Mohr Coulomb Failure Criterion Relation 

Note. Where:  is the shear strength; C is cohesion; is internal friction angle;  is normal 

stress. 

 

3.1 Pit Wall Stability 

In most mining engineering projects, analyses are performed without incorporating dilation angle as a 

parameter since the interest is in the worst-case scenario. However, we considered both the 

non-associative flow rule (ψ=0°) and the associative flow rule (ψ≠0°) because dilatancy is one of the 

crucial phenomena of geo-materials during shear distortion of elements in a material. The results of the 

analysis are shown in Figure 4. The simulation outcome indicates that the pit walls are satisfactorily 

stable at 250 m pit height. The values of FoS are well above the threshold of 1.2 as recommended by 

(Adams, 2015; Read & Stacey, 2010; Sullivan, 2013) for OPM. However, the performance of the pit 

walls falls under the threshold implying unreliable stability as the excavation extends to a deeper 

horizon.  

The comparative analysis of the non-associated flow rule (ψ=0°) and associated flow rule (ψ≠0°) 

illustrates that taking into account ψ improves the stability performance of the pit wall slopes. The 

dilation angle of the rock mass appears to increase the shear strength of the rock mass under shearing 

conditions. This increase in strength can be ascribed to the rearrangement of the constituent mineral 

grains in the rock mass as shearing occurs. In an intact rock state, the mineral grains are interlocked and 

as such, they do not have the freedom to move. When stressed, the contiguous mineral grains gravitate 

towards each other, which ultimately produces a bulk expansion of the material due to occlusion. The 

findings concur with the pioneering empirical formulas by Bolton and Reynolds on the effect of 

dilation angle (Logani, 1973). We can observe that the consideration of ψ is vital to yield accurate and 

realistic slope stability besides the fact that engineering considers the worst-case scenario. 

 



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250m 280m 300m
1.10

1.15

1.20

1.25

1.30

F
ac

to
r 

o
f 

S
af

et
y

 (
F

o
S

)

Pit Height (m)

  Non-associative flow rule (ψ=0°)

 Associative flow rule (ψ≠0°)

 

Figure 4. Pit Stability Condition at Different Excavation Depth 

 

To appreciate the influence of dilation angle on slope performance in details, we undertook a 

parametric analysis by varying the values of dilation angle. The averaged dilation angle was changed 

within the range of 0°-20°. The findings of the parametric analysis are given in Figure 5. The results 

affirm that the dilation angle enhances the stability of the excavated faces. Higher values of dilation 

angle yielded relatively larger stability values when compared to the conventional non-associative flow 

rule. This phenomenon underscores the positive correlation of the associated flow rule of ψ in 

increasing the shear strength of the rock mass on excavated slopes under shearing conditions. Having 

appreciated the stability conditions under a unit stress condition (k=1), the study explores further for 

varied stress conditions, and the results of the analysis are based on the non-associated flow rule 

(ψ=0°). 

 

0° 3° 6.5° 10° 13.5° 17°
1.10

1.15

1.20

1.25

1.30

1.35

F
ac

to
r 

o
f 

S
af

et
y

 (
F

o
S

)

Averaged Dilation Angle (deg)

 250m Pit height

 280m Pit height

 300m Pit height

 

Figure 5. Parametric Analysis of the Influence of Dilation Angle on the Stability of Pit Walls 

 



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3.2 Influence of In-situ Stress in Open Pit Mine 

The pre-mining initial stress state is an important aspect in numerical modeling for equilibrium 

stepping and determination of mining induced stress. To understand the influence of the in-situ stress 

state during rock excavation, the virgin stresses were analysed. In this research project, due to 

unavailability of site-specific data, which is technically complex and expensive to collect, the 

pre-mining stresses were approximated from mean South African regional stress compilation in OPMs; 

Impala, Parabola, and Rustenburg mines grouped as A, B, and C respectively, Carolusberg and 

Klerksdorp mine which portray identical directional pattern to Malawi (Figure 6).  

Thus, different stress ratios ( ) were considered to appreciate the influence they could have 

on the stability of the pit walls. Based on the regional data, it can be observed that the mean ratio 

between vertical stress and major horizontal stress can be tested up to k=2.5 in open-pit mines. The 

initial run of the simulation was based on the in situ stress ratio of k=1 and then varied at 0.5 intervals. 

The results of the analysis are displayed in Figure 7. The outcome shows that the stability of the pit, as 

adjudged quantitatively from FoS, could negligibly be affected even under high-stress conditions. As 

observed from Figure 7, the factor of safety remains the same under different stress regimes except 

when the pit start to extend to deeper levels at 280 m and 300 m pit height which recorded a marginal 

decrease from 1.16 to 1.15 and 1.12 to 1.11 at k=1 with the increase in stress ratio respectively.  

Since the determination of stability is quantitative, this phenomenon explains why in situ stress is 

conventionally considered in underground mines. However, a qualitative evaluation of the stability 

state through shearing contour analysis reveals that the pit wall stability conditions would be different 

under high-stress regimes that could potentially influence the long-term performance of the slope. 

Although the factor of safety experiences minimal reduction, it is evident that the pit wall shearing 

becomes intense and the straining of the walls becomes effusive under high-stress ratio conditions. In 

this situation, it should be appreciated that with the passage of time, the pit walls could potentially 

fatigue under high in situ stress. In addition, if the depth extend further, the minimal accrual could 

translate into a significant value of FoS. Thus, as a “first check” in the evaluation of the stability of a 

pit slope, we apply the strain-based approach to failure prediction and determine if further attention 

regarding monitoring could be necessary to incorporate the Trigger Action Response Plan (TARP) for 

instability in different stress regimes. 

 



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Kmean vs Depth

0

500

1000

1500

2000

2500

3000

3500

0 1 2 3 4 5 6

Kmean

D
e

p
th

(m
)

All A,B and C data

Impala Plats.

Rustenburg Plats.

Carletonville

Klerksdorp

N.C.Gay 1975

 

 

(a) Mean stress ratios for representative OPM (b) Location of data representative mines 

Figure 6. The Averaged Ratio of Vertical Stress and Maximum Horizontal Stress 

 

3.3 The Strain Criteria Approach to Failure Prediction 

The essence of pit wall stability analysis is to evade or inhibit failures by adopting an optimal mine 

design. Therefore, the strain-based approach, as applied in this study, could provide guidance regarding 

strain thresholds for pit wall performance in diverse stress conditions. Strain is the ability of a stressed 

material, in the presence of a stress field, to deform. Generally, rock mass succumbs to the application 

of stress which is due to the rearrangement of the natural in situ stress field when the slope is excavated. 

The extent of straining is consequent to the slope geometry and slope construction and in situ stress 

conditions. The strain-based approach to assessing pit slope stability utilises the fundamental principles 

of the strain formula after Brix & Newcomer (2003) given as.  

 

where: =the maximum deformation of the pit wall, H=the total height of the wall and ε=the strain 

in percentage.  

Based on over 12 case studies, Brox & Newcomen (2003), Newcomen & Dick (2016) and Zavodni in 

Hastrulid (2001) developed the strain percentage criteria for the principal failure modes in various rock 

mass classes. The threshold strain levels for rock mass were established to have a lower bound strain at 

collapse of 0.1% and upper bound strain to collapse of 3% (Newcomen & Dick, 2016; Coetsee et al., 

2020). The results of the stability performance of pit wall, based on strain approach, against failure 

under different stress regimes are given in Figure 8. It can be observed that the peak strain rate 

increases with stress regimes. That is, as the k-ratio increases, the straining correspondingly increases.  

 



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Shear 

contours 

  

Shear 

contours 

  

k-ratio = 1 k-ratio = 1.5 

Shear 

contours 

  

Shear 

contours 

  

k-ratio = 2 k-ratio = 2.5 

(a) Shearing pattern of pit walls at 250 m pit height 

Shear 

contours 

  

Shear 

contours 

  

k-ratio = 1 k-ratio = 1.5 

Shear 

contours 

  

Shear 

contours 

  

 k-ratio = 2  k-ratio = 2.5 

(b) Shearing pattern of pit walls at 280 m pit height 

Shear 

contours 

 

 

Shear 

contours 

 

 

 k-ratio=1 

 

 

 k-ratio=1.5 

FoS=1.23 

FoS=1.23 

FoS=1.23 

FoS=1.23 

FoS=1.15 
FoS=1.15 

FoS=1.16 FoS=1.15 

FoS=1.12 FoS=1.11 



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Shear 

contours 

 

 

Shear 

contours 

 

 

 k-ratio=2  k-ratio=2.5 

(c) Shearing pattern of pit walls at 300 m pit height 

Figure 7. Shearing Pattern under Different Stress Conditions 

 

This trend is in tandem with the qualitative shearing conditions of the pit wall previously presented in 

Figure 7. However, the percentage of strain in this study demonstrates that the pit walls would be 

almost 60% below the lower bound strain to collapse in all the simulated cases. The highest strain rate 

of almost 0.04% is recorded at 300 m height with the highest possible in situ stress condition of k=2.5. 

Thus, at this rate of straining the pit walls stability performance would still be guaranteed though 

relatively high. The pit height is also an important determinant of straining on pit slopes. The outcome 

shows that as the pit extends to a deeper horizon, the strain rate congruently increases. At the Ultimate 

Pit Limit (UPL) of 300 m, the strain values are comparatively high against 280 m and 250 m pit heights. 

For example, at the stress condition of k=2.5, the strain values are 0.029% at 250 m, 0.032% at 280 m 

and 0.036% at 300 m pit height. 

 

K=1 K=1.5 K=2 K=2.5
0.00

0.01

0.02

0.03

0.04

S
tr

ai
n

 (
%

)

Stress Ratio (σ_h⁄σ_v)

 300m Pit height 250m Pit height

 280m Pit height

 
Figure 8. Peak Strain of Pit Walls against Potential Failure under Different Stress Regimes 

 

 

 

FoS=1.11 FoS=1.11 



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3.4 Displacement Pattern 

To check the criticality of the stability state, in connection to the strain analysis, the extent of 

displacement was evaluated under different stress conditions. The results of total displacement with 

respect to k-ratio are depicted in Figure 9. It can be observed that the pattern of displacement is in 

harmony with the strain state such that an increase in stress ratio led to increase in the extent of total 

displacement. At 250 m pit height, the peak displacement values are 19 mm, 57 mm, 74 mm, and 107 

mm at k=1, k=1.5, k=2 and, k=2.5 respectively.  

 

Contours 

 

 

 

Contours 

 

 

k-ratio = 1 k-ratio = 1.5 

Contours 

 
 

Contours 

 
 

k-ratio = 2 k-ratio = 2.5 

(a) Pit wall displacements at 250 m pit height 

Contours 

 

 

 

Contours 

 

 

k-ratio = 1 k-ratio = 1.5 

Contours 

 
 

Contours 

  

 k-ratio = 2  k-ratio = 2.5 

(b) Pit wall displacements at 280 m pit height 

 



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Contours 

  

Contours 

 

 

 k-ratio=1  k-ratio=1.5 

Contours 

 

 

 

Contours 

 

 

 k-ratio=2  k-ratio=2.5 

(c) Pit wall displacements at 300 m pit height 

Figure 9. Pit Wall Displacement under Different Stress Conditions 

 

As excavation progressed, the extent of displacement gradually increased. That is, at 280 m pit height, 

the displacement values recorded are 19 mm, 58 mm, 83 mm and 109 mm in the order of increasing 

stress ratio. And at the currently planned UPL the displacements are 21 mm, 59 mm, 83 mm, and 149 

mm at k=1, k=1.5, k=2, and k=2.5 respectively. The deformations around the pit are generally induced 

by relaxation on the excavated pit sections. Corollary, increase in maximum initial horizontal stress 

appear to counter the gravity loading effect, hence lateral material movement becomes more dormant to 

vertical movements. From the displacement trends, we can observe that in situ stress condition is 

indispensable for consideration in OPM as they could have a long-run compounding effect on pit wall 

performance.  

 

4. Conclusion 

The significance of investigating the role of in situ stress in OPM cannot be over-emphasised as surface 

mining operations are advancing to greater depths with the safety of mines being among paramount 

concerns. In this contribution, the influence of in situ stress and its role as a potential triggering factor 

of slope instability was assessed. The evaluation of the shearing contours and quantified strain rate and 

displacement values demonstrate that high horizontal stress regimes can reduce the stability 

performance of the pit-wall. Even though the quantitative outcome based on FoS gives a guised 

impression of no significant impact as values of stability remain almost constant, this scenario could 

have adverse impacts on the long-term stability performance of the pit slope since mining projects 

extend for years. This calls for a perspective transformation of the conventional approach of confining 

in situ stress impact in solely underground excavations. Therefore, this work suggests that “in situ 

stress-stability analysis” is a worth consideration for OPM operations that would be planned to extend 



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to greater depths, and those located in tectonically active settings. 

 

Acknowledgement 

The authors express their sincere gratitude to Mkango Resources Company for providing the required 

geotechnical data for the study to be conducted. 

 

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