Assessment of the Slope Stability Under Geological Conditions Using FDAHP-TOPSIS (A Case Study for Sungun Open Pit Mine)

Journal of Soft Computing in Civil Engineering 5-4 (2021) 21-40
How to cite this article: Niromand M, Mikaeil R, Advay M. Assessment of the slope stability under geological conditions using
FDAHP-TOPSIS (A Case Study for Sungun Open Pit Mine). J Soft Comput Civ Eng 2021;5(4):21–40.
https://doi.org/10.22115/scce.2021.290413.1337
2588-2872/ © 2021 The Authors. Published by Pouyan Press.
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Journal of Soft Computing in Civil Engineering
Journal homepage: www.jsoftcivil.com
Assessment of the Slope Stability Under Geological Conditions
Using FDAHP-TOPSIS (A Case Study for Sungun Open Pit Mine)
Morteza Niromand1
, Reza Mikaeil2*
, Mehran Advay3
1. Ph.D. Student, Department of Mining, Ahar Branch, Islamic Azad University, Ahar, Iran
2. Associate Professor, Faculty of Environment, Urmia University of Technology, Urmia, Iran
3. Assistant Professor, Department of Mining, Ahar Branch, Islamic Azad University, Ahar, Iran
Corresponding author: reza.mikaeil@uut.ac.ir
https://doi.org/10.22115/SCCE.2021.290413.1337
ARTICLE INFO ABSTRACT
Article history:
Received: 13 June 2021
Revised: 19 September 2021
Accepted: 29 October 2021
Determining the degree of slope stability is one of the most
important steps in the design of open pit mines that are affected by
other mining activities. So that the collapse of a part of the wall will
lead to irreparable human and compensatory damages. Slope
stability is affected by natural factors such as lithology, tectonic
regime, rock mass conditions, climatic conditions and design
factors including slope angle, slope height, pattern and blasting
method. In the present study, using a combination of fuzzy
approach and multi-criteria decision models, the stability and
ranking of the slope stability has been investigated. For this
purpose, the stability of 28 slopes of 8 large open pit mines was
evaluated. In the first step of the research, after identifying the
parameters affecting the slope stability and recording their values
for the studied mines, the degree of importance of these parameters
were determined by experts using the Fuzzy Delphi Analytical
Hierarchy Process. Then the slopes were evaluated and ranked
using the technique of order preference similarity to the ideal
solution technique. The slope A23 with similarity index 0.742 was
selected as the most desirable alternative and the slope A15 with
similarity index 0.335 as the most undesirable alternative in terms
of slope stability. Meanwhile, Sungun copper mine with a similarity
index of 0.399 was ranked 12th in the second half of the slope
stability classification table. The results showed that, the matching
of research results and field observations shows the applicability of
the model in the initial evaluation of slopes to determine its
stability.
Keywords:
Slope stability;
Sungun copper mine;
FDAHP;
TOPSIS.

22 M. Niromand et al./ Journal of Soft Computing in Civil Engineering 5-4 (2021) 21-40
1. Introduction
Assessing the slope stability plays an important role in design, planning and mining costs. For
example, increasing the angle of slope will reduce waste disposal or increase mineral extraction,
resulting in higher profits and shorter payback periods. A high angle of slope also reduces the
safety factor and increases the cost of failure. Factors influencing failure include lithology,
tectonic regime, rock mass conditions, climatic conditions and design factors including slope
angle, slope height, pattern and blasting method. Fractures in rocks occur at discontinuous
surfaces, including joints and faults, and in the form of plates, wedges, overturns, and two
blocks, and spoon or circular fractures in rocks. Intensity of weathering or earthen slopes occurs.
Instability in open pit mines occurs mainly in the form of gradual or sudden falls. Sudden failure
or collapse, which usually has warning signs, is one of the most dangerous types of falls and
usually causes a lot of damages Including causing (irreparable) casualties and extensive direct
financial damages (especially damage to the devices, which sometimes causes the devices to go
completely out of service), mixing minerals with tailings that in most cases, it will cause a large
volume of mineral loss, stop or reduce production in the mine, which will be directly related to
the volume of the fall (Angoran mine fall is a good example in this regard), impose additional
costs to remove the volume of fallow soil , Incurring ancillary costs for cleaning and repairing
the stairs or stairs on which the collapse has taken place (need to redesign the end walls) can be
mentioned. The use of rating systems and models is one of the common and basic methods to
evaluate the stability of a slope.
Hack, R., et al., developed A new approach to rock slope stability–a probability classification
(SSPC) [1]. Taherynia, et al. 2014 studied the slope instability and risk analysis of road slopes in
Lashotor Pass, Iran [2]. Fereidooni, et al. 2015 investigated a modified rock mass classification
system for rock slope stability analysis in the Q-system [3]. Azarafza, et al., 2017, studied the
rock slope stability by slope mass rating (SMR) in the gas flare site in Assalouyeh, South of Iran
[4]. Baghbanan, et al. 2017, studied Numerical probabilistic analysis for slope stability in
fractured rock masses using DFN-DEM approach [5]. Haghshenas et al. (2017), used fuzzy and
classical MCDM techniques to rank the slope stabilization methods in a rock-fill reservoir dam
[6]. Azarafza et al. (2017), studied the discontinuous rock slope stability using block theory and
numerical modeling for the South Pars Gas Complex, Assalouyeh, Iran [7]. Sujatha, and
Thirukumaran, 2018, studied the rock slope stability assessment by using geomechanical
classification and its application for specific slopes along Kodaikkanal-Palani Hill Road, Western
Ghats, India [8]. Zhang et al. (2018), developed a risk assessment model of expansive soil slope
stability based on Fuzzy-AHP method and its engineering application [9]. Chen et al. (2018),
studied the bedding rock slope based on random seismic response and dynamic fuzzy reliability
analysis based on pseudo excitation method [10]. Zhou et al. (2018), investigated the slope
stability under uncertain circumstances[11]. Xu et al. (2019), evaluated the rock slope stability
by using the hierarchically weighted rough-set genetic algorithm in the freeze–thaw
mountains[12]. Zhou et al. (2019): investigated the highway slope stability based on hierarchical
fuzzy comprehensive evaluation method [13]. Moayedi et al. (2019), Monitored and evaluated
the slope stability by using novel remote sensing based on fuzzy logic [14]. Wang et al. (2019),
studied the characterization of rock slope stability using key blocks within the framework of

M. Niromand et al./ Journal of Soft Computing in Civil Engineering 5-4 (2021) 21-40 23
GeoSMA-3D [15]. Azarafza et al. (2020), investigated the discontinuous rock slope stability
analysis under blocky structural sliding by using fuzzy key-block analysis method [16]. Xia et al.
(2020), studied the slope stability analysis based on group decision theory and fuzzy
comprehensive evaluation[17]. Chen et al. (2021), investigated the application of group decision-
making AHP of confidence index and cloud model for rock slope stability evaluation [18]. Zhao
et al. (2021) developed a new stability forecasting model for goaf slope based on the AHP–
TOPSIS theory [19]. Spanidis et al. (2021) used a Fuzzy-AHP for planning the risk management
of natural hazards in surface mining projects[20].
One of the most important goals of this research is to investigating and evaluating the application
of decision models in important engineering topics such as slope stability analysis according to
the characteristics of the rock mass. Comparing the stability of sloping walls of large mines with
each other and with Sungun copper mine is one of the important innovations of this research.
2. Research significance
In the present study, a decision model has been proposed to rank the evaluated slopes and select
the walls prone to instability by combining Fuzzy Delphi Analytical Hierarchy Process (FDAHP)
and Technique of Order Preference Similarity to the Ideal Solution (TOPSIS). For this purpose,
28 slopes of 8 mines were studied. Finally, in order to evaluate the accuracy of the model, the
results were evaluated with the actual behaviors of the slopes. Investigating the stability of slops
with FDAHP and TOPSIS is one of the important innovations of this research.
To present the model in the first step, the degree of importance of the criteria was determined
based on the opinions of experts. At this stage, first a questionnaire form was sent to experts in
the field of slope stability and after collecting the questionnaire forms, the degree of importance
of each criterion was calculated using FDAHP. Finally, the slopes were ranked using the
TOPSIS. The results of model were compared with the actual behavior of the studied slopes. The
flowchart of study is shown in Figure 1.
Fig. 1. Flowchart of research.

3. Methods
3.1. FDAHP method
Fuzzy theory and fuzzy sets were first introduced by Zadeh in a treatise entitled "Fuzzy Sets" in
1965 to analyze complex systems[21]. In the theory of classical collections, the membership of
members in a collection is determined as binary sentences based on a binary condition that a
member either belongs to the collection or not, and the boundaries of a collection are quite clear
and sharp, and therefore they are clearly defined. In fuzzy theory, the relative degrees of
membership of the members in the set are allowed and the boundaries are blurred and soft. Fuzzy
sets are generalizations of the characteristic {0,1} to all numbers in the range [0,1][22]. In fact,
in fuzzy sets, unlike classical sets, elements are not divided into two categories: member and
non-member; rather, according to the defined functions, the membership of different elements in
fuzzy sets varies between zero and one.
In the following, some researches related to this method are briefly described. Hosseini et al.
(2009) presented a new classification system for assessing permeability using the FDAHP
method [23]. Mikael et al. (2013) also classified the ability of cutting building blocks using the
FDAHP method [24]. Que et al. (2016) also assessed the risk of water pollution in a coal mine
located in China by the combined method of FDAHP and gray dependence analysis[25]. The
results of the mentioned researches show the capability of FDAHP method in classifications
related to different issues. Based on the results of research conducted with this method, it is clear
that it can be used in analyzes and classifications related to mining engineering issues. The
reason for the compatibility of this method and the results of its applications, which are very
compatible with real conditions, shows this combined method has all the advantages of AHP
methods, fuzzy theory and Delphi method, and the disadvantages of each of these methods, when
combined will be minimized. On the other hand, the use of aggregation of the advantages of the
above three methods in the form of the combined FDAHP method causes not only the results of
its application for the simulated data to have acceptable results. However, the results of the
mentioned method are significantly similar to the real conditions and its results can be used for
executive and operational applications. Therefore, in order to implement the above method in
classifying the stability of sloping walls, first it is necessary to determine the importance of
effective criteria based on the opinions of experts.
After forming the pairwise comparison matrices, the results were used to form a fuzzy pairwise
comparison matrix. In forming this matrix, the triangular membership function and as a result,
triangular fuzzy numbers have been used. Calculations related to this method include the
following steps:
Calculation of fuzzy numbers: To calculate fuzzy numbers (αij), the opinions obtained from the
survey of experts are directly considered. In this study, fuzzy numbers were calculated based on
the triangular membership function. Figure (2) shows the calculation of fuzzy numbers by the
triangular method. According to Figure (2) in the Delphi fuzzy method, a fuzzy number can be
calculated using equations (1) to (4):

Fig. 2. Triangular membership function in Delphi fuzzy method [26].
𝑎𝑖𝑗 = (𝛼𝑖𝑗, 𝛿𝑖𝑗, 𝛾𝑖𝑗) (1)
𝑎𝑖𝑗 = 𝑀𝑖𝑛(𝛽𝑖𝑗𝑘) , 𝑘 = 1,2, … , 𝑛 (2)
𝛿𝑖𝑗 = (∏ 𝛽𝑖𝑗𝑘
𝑛
𝑘=1 )
1
𝑛
, 𝑘 = 1,2, … , 𝑛 (3)
𝛾𝑖𝑗 = 𝑀𝑎𝑥(𝛽𝑖𝑗𝑘) , 𝑘 = 1,2, … , 𝑛 (4)
In the above relations, γij and αij represent the upper limit and the lower limit of expert opinions,
respectively. The parameter βijk also indicates the relative importance of the parameter i relative
to the parameter j from the kth' s point of view [26].
Formation of fuzzy pairwise comparison matrix: In this step, using the fuzzy numbers obtained
from the previous step, a fuzzy pairwise comparison matrix between different parameters is
formed using Equation (5):
(5)
𝐴 = [𝑎𝑖𝑗] = [
1
1/𝑎12
⋮
1/𝑎1𝑛
𝑎12
1
⋮
1/𝑎2𝑛
…
…
⋮
…
𝑎1𝑛
𝑎2𝑛
⋮
1
]
𝑎
̃𝑖𝑗 × 𝑎
̃𝑖𝑗 ≈ 1 , ∀𝑖, 𝑗 = 1,2, … , 𝑛
𝐴
̃ =
[
(1,1,1) (𝛼12, 𝛿12, 𝛾12) (𝛼13, 𝛿13, 𝛾13)
(1
𝛾12
⁄ , 1
𝛿12
⁄ , 1
𝛼12
⁄ ) (1,1,1) (𝛼23, 𝛿23, 𝛾23)
(1
𝛾13
⁄ , 1
𝛿13
⁄ , 1
𝛼13
⁄ ) (1
𝛾23
⁄ , 1
𝛿23
⁄ , 1
𝛼23
⁄ ) (1,1,1) ]
At this stage, the fuzzy weight belonging to each parameter can be determined using Eqs. (6) and
(7) [26]:
𝑍
̃𝑖 = [𝑎
̃𝑖𝑗⨂ … ⨂𝑎
̃𝑖𝑛]
1
𝑛
(6)
𝑊
̃𝑖 = 𝑍
̃𝑖⨂(𝑍
̃𝑖⨁ … ⨁𝑍
̃𝑛) (7)
In the above relations, is the multiplication sign of fuzzy numbers and ⨁ is the sum of fuzzy
numbers. Finally, the parameter W ̃i, which is a linear vector, represents the fuzzy weight of the
parameter i-m.

De-fuzzy weighting of fuzzy numbers: After finding the fuzzy weights related to each of the
parameters, all numbers are converted to non-fuzzy using Eq. (8) [26]:
𝑊
̃𝑖 = (∏ 𝜔𝑗
3
𝑖=1 )
1
3
(8)
3.2. TOPSIS technique
The method of similarity to the ideal option was proposed by Yoon and Hwang in 1981. In this
method, the options are ranked based on the similarity to the ideal solution, so that the more
similar an option is to the ideal solution, the higher it ranks. If there are n criteria and m options
in a multi-criteria decision problem, in order to select the best option using the similarity method
to the ideal solution, the steps of the method are as follows [27]:
Step 1- define the decision matrix
According to the number of criteria and the number of options and the evaluation of all options
for different criteria, the decision matrix is formed as follows:











mn
m
n
x
x
x
x
X





1
1
11
Where ij
x
is the function of option i ( m
i ,...,
2
,
1
 ) in relation to criterion j ( n
j ,...,
2
,
1
 )
Step 2 - Unscaling the decision matrix
In this step, we tried to convert criteria with different dimensions into dimensionless criteria and
the R matrix is defined as follows:











mn
m
n
r
r
r
r
R





1
1
11
There are several methods for scaling, but usually we use the following equation:



m
i
ij
ij
ij
x
x
r
1
2
(9)
If the distance between the measured values is not large, the following equations can be used to
scale the positive and negative criteria, respectively:
}
min{
}
max{
}
min{
ij
ij
ij
ij
ij
x
x
x
x
r



(10)

}
min{
}
max{
}
max{
ij
ij
ij
ij
ij
x
x
x
x
r



(11)
Step 3- Determine the weight vector of the criteria
At this stage, according to the coefficients of importance of different criteria in decision making,
the weight vector of the criteria is defined as follows:
 
n
w
w
w
W 
2
1

The elements of the vector W are the coefficient of importance of the relevant criteria.
Step 4- Determine the weighted unmatched decision matrix
Weighted unmeasured decision matrix is obtained by multiplying the unmeasured decision
matrix by the weight vector of the criteria:
.
,
,
1
;
,
,
1 m
i
n
j
r
w
v ij
j
ij 
 


(12)
Step 5 - Find the positive-ideal and negative-ideal solution
The positive-ideal with and negative -ideal is shown as follows:
 





 n
j v
v
v
v
A ,
...
,
,
...
,
, 2
1
(13)
 





 n
j v
v
v
v
A ,
...
,
,
...
,
, 2
1
(14)
Where
*
j
v
is the best value of j among all the options and

j
v
is the worst value of the criterion j
of all the options. The options in
*
A and

A represent the better and the worse, respectively.
Step 6- Calculate the distance from the ideal and anti-ideal solution
In this step, for each option, the distance from the positive-ideal solution and the distance from
the negative-ideal solution are calculated from the following relations, respectively:
 




n
j
j
ij
i V
V
S
1
2
*
*
(15)
 






n
j
j
ij
i V
V
S
1
2
(16)
Step 7- Calculate the similarity index
In the last step, the similarity index is calculated from the following equation:




i
i
i
i
S
S
S
C *
*
(17)

The value of the similarity index varies between zero and one. The closer the option is to the
ideal, the closer the value of its similarity index will be to one. It is quite clear that if an option
matches the ideal option, then its distance to the ideal solution is equal to zero and its similarity
index is equal to one, and if an option matches the counter-ideal solution, then its distance to the
counter-ideal solution is equal to zero. Its similarity index will be equal to zero. Therefore, to
rank the options based on the value of the similarity index, the option that has the most similarity
index is in the first rank and the option that has the lowest similarity index is in the last rank.
4. Data collection and analysis
In rock engineering system, in order to develop a rank system, selecting the most effective
parameters are the most important issues. In rank system, as a very important and basic rule, the
number of parameters that are used should be small. Therefore, using all of parameters in the
rank system is inconvenient from the practical and engineering point of view. Thus, in the rank
system, for selecting the final main parameters, the two assumptions have been considered: (a)
the number of parameters that are used should be small, and (b) equivalent parameters should be
avoided. Considering these two assumption, 18 parameters such as Rock Type (C1), Rainfall
(C2), Intact Rock Strength-UCS (C3), RQD (C4), Weathering (C5), Tectonic Regime (C6),
Groundwater Conditions (C7), Number of Major Discontinuity Sets (C8), Discontinuity
Persistence (C9), Discontinuity Spacing (C10), Discontinuity Orientation (C11), Discontinuity
Aperture (C12), Discontinuity Roughness (C13), Discontinuity Filling (C14), Slope (pit-wall)
Angle (C15), Slope (pit-wall) Height (C16), Blasting Method (C17), Convexity/Concavity
(C18), that have been chosen for assessing the rank system. In this study, data related to 28
slopes from 8 open pit mines in the world have been used to assess and rank sustainability. Table
1 shows the sloping walls studied in this study. Completion of information about each wall is
done either in the field or by reading pre-recorded reports [28].
Table 1
The studied slopes.
Case No. Name Case No. Name
A1 Sarcheshmeh-Iran- East wall A15 Aznalcollar- Spain- South wall
A2 Sarcheshmeh-Iran- North wall A16 Aznalcollar- Spain- West wall
A3 Sarcheshmeh-Iran- South wall A17 Aznalcollar- Spain- North wall
A4 Sarcheshmeh-Iran- West wall A18 Cadia Hill- Australia- Northeast wall
A5 Angoran-Iran- Southeast wall A19 Cadia Hill- Australia- East wall
A6 Sangan-Iran-Baghak wall A20 Cadia Hill- Australia- West wall
A7 Sangan-Iran- Anomaly A A21 Cadia Hill- Australia- North wall
A8 Chuquicamata- Chile- Northwest wall A22 Cadia Hill- Australia- South wall
A9 Chuquicamata- Chile- South wall A23 Aitik- Sweden- East wall
A10 Chuquicamata- Chile- West wall A24 Aitik- Sweden- Northeast wall
A11 Chuquicamata- Chile- North wall A25 Aitik- Sweden- Northwest wall
A12 Chuquicamata- Chile- East wall A26 Aitik- Sweden- Southeast wall
A13 Aznalcollar- Spain- Southeast wall A27 Aitik- Sweden- Southwest wall
A14 Aznalcollar- Spain- Southwest wall A28 Sungun- Iran- Southwest wall
A1 to A28: Considered alternatives (large open pit)

4.1. Case study
One of the most important goals of this research is to compare the stability of Sungun copper
mine wall with other large mines in the world. In fact, the stability of this mine along with other
large mines whose stability status has been evaluated can be a specific way to assess the stability
of large mines according to the characteristics of the rock mass. This mine is one of the largest
open pit mines in Iran. Sungun copper mine is one of the most important copper mines in Iran
and the Middle East which is located in 105 km northeast of Tabriz, 75 km northwest of Ahar
and 28 km north of Varzaghan, in the vicinity of the Republic of Azerbaijan and the Republic
of Armenia. Its longitude is 46 degrees and 43 minutes east, and the latitude is 38 degrees and
42 minutes north, and the average height of the region is 2000 m from sea level (maximum
2700 m) which is located on the global copper belt. This mine is located on the Arasbaran
mountain range (Gharadagh) in the form of a penetrated mass. This mountain range with 80
km width is a part of the Alpine-Himalayan orogenic belt. The probable reserve of this mine is
more than one billion tons, the extractable reserve (given the discoveries made) is about 796
million tons, and the total amount of the definitive, probable and possible reserves in the
surrounding area of Varzaghan Sungun mine is about 1.7 billion tons of copper ore at a grade
of 0.61%. Figure 3, shows the location and view of Sungun copper mine.
Fig. 3. The location of Sungun Copper Mine.
Field studies were conducted to evaluate the stability of this mine. Figure 4 and 5 show the
geological map and the discontinuity characteristics of the mine levels. The Sungun copper
deposit is in the northwestern part of a NW-SE trending Cenozoic magmatic belt (Sahand-
Bazman) where porphyry copper deposits are located [29].
The Sungun porphyry (reportedly Miocene in age, based largely on regional geological
relationships) has intruded a sequence of Cretaceous limestone and calcareous sedimentary
units following collision of the Persian sub-continent with Europe and closure of the Neotethys
in the Oligocene – Miocene. The intrusion and related post-mineralization dykes are a product
of magmatic activity, the location of which is controlled by regional fault zones which strike
WNW and are compartmentalized by a series of transfer faults which strike NNE-to-NE.

Fig. 4. Geological map of Sungun copper deposit [29].
The structure and regional tectonics can be used to constrain the chronology of alteration and
mineralization at Sungun. The following points are suggested;
1. ~20–15 Ma, intrusion of the Sungun porphyry,
2. Propylitic alteration (predominantly meteoric fluids driven by thermal perturbation),
3. Locally developed silica (± kaolinite) acidic alteration as a result of exsolution of magmatic
fluids,
4. locally developed sericite + pyrite ± quartz alteration which is fault controlled and found
associated with WNW, NW and NE striking faults as well as a number of shallowly west
dipping faults,
5. Intrusion of DK1a dykes (possibly synchronously with the sericitic alteration, which is also
controlled by locally active faults.
6. 14–10 Ma, quartz + sulphide (including copper) vein mineralization with a NW preferred
orientation.
7. Post mineralization, emplacement of NW and WNW striking dykes.
8. < 10 Ma, Late fault movement.
Stages 1 to 5 can be constrained to the period when there was a southwestward shortening as a
result of the collision of Persian terranes with Europe. Stages 6 and 7 occurred during south
eastward shortening from about 14 Ma as a result of plate reorganization at that time. Stage 8
may have occurred during several tectonic events in the Pliocene and Quaternary, including
Quaternary tecto magmatic activity that resulted in the extrusion of sequences of intermediate
tephra and volcanic [29].

a B
Fig. 5. a) View of a joint located at level of 2250 with a slope of 70 degrees, extension 25, in the direction
of slope 295, which is severely crushed. b) View of a joint located at the level of 2287.5 with a slope of
80 degrees, extension 150, direction of the slope of 240 and an average opening of about 1-2 cm.
Table 2 shows field study information taken from the southwestern wall of the Sungun copper
mine.
Table 2
Field study information recorded from the southwest wall of Sungun copper mine, Iran.
NO Parameters SW Sungun
C1 Rock Type (Major) Quartz Monzonite (SP) & Diorite (Dk-1)
C2 Rainfall (mm/year) 300-450
C3 Intact Rock Strength-UCS (MPa) 30-80
C4 RQD (%) 50-75
C5 Weathering W3
C6 Tectonic Regime Strong
C7 Groundwater Conditions Damp
C8 Number of Major Discontinuity Sets 1
C9 Discontinuity Persistence (m) 10-30
C10 Discontinuity Spacing (m) 0.06-2
C11 Discontinuity Orientation Favorable
C12 Discontinuity Aperture (mm) 0.5-1
C13 Discontinuity Roughness (JRC) Smooth
C14 Discontinuity Filling Hard Filling
C15 Slope (pit-wall) Angle (deg) 30-40
C16 Slope (pit-wall) Height (m) 450
C17 Blasting Method Modified production
C18 Convexity/Concavity Concave
C1 to C18: Considered criteria (Geotechnical and geomechanical properties)

Table 3 shows the quantitative characteristics affecting the stability of the studied slopes. During
this research, it was tried to evaluate all the characteristics affecting the stability capability
quantitatively or qualitatively.
Table 3
Characteristics of sloping walls of studied mines.
Name C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18
A1 80 135 60 45 90 60 100 3 12.5 5.3 40 3 90 60 35 390 40 60
A2 80 135 70 55 90 60 100 3 6.5 350 90 3 90 60 35 420 40 60
A3 80 135 55 45 90 60 60 4 10 350 60 3 80 40 35 620 40 60
A4 80 135 55 45 90 60 60 4 10 300 40 3 80 50 35 800 40 60
A5 40 497 73 41 90 60 100 4 20 75 40 3 40 50 30 170 40 60
A6 60 155 105 45 85 75 100 1 7.5 125 40 0.55 90 50 41 50 40 60
A7 60 155 90 40 60 75 60 3 15 85 40 0.55 40 50 45 65 40 60
A8 80 35 59 48 60 60 100 3 5 200 40 0.55 40 60 32 210 40 60
A9 80 35 52 59 40 60 100 4 2.75 325 60 0.55 90 60 31 700 40 60
A10 80 35 48 23 60 60 60 5 5.75 325 15 3 60 50 32 750 40 60
A11 80 35 67 44 40 60 100 5 5.75 400 60 0.55 60 60 31 750 40 60
A12 60 35 85 46 60 60 100 6 7.75 240 10 3 80 50 42 780 40 60
A13 80 650 55 60 100 40 100 3 3 225 80 0.1 80 60 34 240 40 60
A14 40 650 24 25 100 40 60 4 10 165 15 3 60 60 34 210 40 60
A15 40 650 20 25 60 40 60 4 10 90 40 3 60 40 34 210 40 60
A16 40 650 35 40 60 40 60 5 15 115 40 3 40 40 32 210 40 60
A17 60 650 35 40 100 40 60 3 7.5 60 60 0.55 60 60 32 240 40 60
A18 95 800 87 60 100 60 100 3 6.5 415 60 0.55 90 40 58 500 80 90
A19 95 800 53 56 100 60 100 2 4.5 375 60 3 90 40 58 500 80 60
A20 95 800 50 60 100 60 100 3 4.5 105 40 0.55 90 40 46 500 80 60
A21 95 800 89 68 100 60 100 3 3 175 80 3 100 40 58 500 80 60
A22 60 800 46 65 90 60 60 4 5.5 75 40 3 80 40 52 500 80 90
A23 95 680 133 78 60 60 60 4 2.25 350 80 0.55 80 80 42 125 60 90
A24 60 680 75 80 60 60 60 5 9.5 150 40 3 80 80 47 230 60 90
A25 95 680 138 82 100 60 100 5 3 325 60 0.55 90 40 51 250 60 90
A26 95 680 124 78 60 60 100 4 2.5 325 80 0.1 90 40 49 325 60 60
A27 95 680 138 85 60 60 100 4 3.5 150 60 0.55 90 40 53 325 60 90
A28 95 375 75 30 60 60 100 1 20 100 90 0.75 40 80 35 475 60 90
C1 to C18: Considered criteria, A1 to A28: Considered alternatives
5. Results
The first step in data analysis is to determine the degree of importance of the criteria for creating
a new classification system. The importance of each of the mentioned criteria was determined
based on the opinions of experts and specialists. At this stage, first the questionnaire form was
completed by experts and then the degree of importance of each criterion was calculated using
the FDAHP method. Table (4) shows an example of a questionnaire.

Table 4
Sample of the questionnaire, answered by the first expert.
Parameters affecting the slope
stability
Importance of each parameter
Very Strength Strength Moderate Weak Very weak
Rock Type (Major) 
Rainfall (mm/year) 
Intact Rock Strength-UCS (MPa) 
RQD (%) 
Weathering 
Tectonic Regime 
Groundwater Conditions 
Number of Major Discontinuity Sets 
Discontinuity Persistence (m) 
Discontinuity Spacing (m) 
Discontinuity Orientation 
Discontinuity Aperture (mm) 
Discontinuity Roughness (JRC) 
Discontinuity Filling 
Slope (pit-wall) Angle (deg) 
Slope (pit-wall) Height (m) 
Blasting Method 
Convexity/Concavity 
Then, the pairwise comparison matrix was formed based on the opinions of experts using the
Saaty’ s scale [30]. At this stage, the elements of each level were paired and compared to their
other existing elements at a higher level and paired comparison matrices were formed. Allocation
of numerical scores related to pairwise comparison of the importance of two indicators was done
based on Table (5).
Table 5
Quantitative and qualitative classification for pairwise comparison of criteria.
Definition Intensity of Importance
Extreme importance 9
Very strong or demonstrated importance 7
Strong importance 5
Moderate importance 3
Equal Importance 1
Weak, Moderate plus, Strong plus and
Very, very strong
2, 4, 6 and
8
The pairwise comparison matrix is an n × n matrix in which n is the number of elements
compared. For each n × n pairwise comparison matrix, the elements on the diameter are equal to
one and do not need to be evaluated, but in other matrix components they must be determined
based on pairwise comparisons. Symmetries with respect to diameter are inversely proportional
to each other. The pairwise matrix based on the opinion of the first expert is listed in Table (6).

Table 6
Pairwise matrix based on the opinion of the first expert.
C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18
C1 1.00 9.00 1.00 3.00 5.00 7.00 7.00 5.00 5.00 3.00 3.00 5.00 5.00 7.00 1.00 1.00 3.00 7.00
C2 0.11 1.00 0.11 0.14 0.20 0.33 0.33 0.20 0.20 0.14 0.14 0.20 0.20 0.33 0.11 0.11 0.14 0.33
C3 1.00 9.00 1.00 3.00 5.00 7.00 7.00 5.00 5.00 3.00 3.00 5.00 5.00 7.00 1.00 1.00 3.00 7.00
C4 0.33 7.00 0.33 1.00 3.00 5.00 5.00 3.00 3.00 1.00 1.00 3.00 3.00 5.00 0.33 0.33 1.00 5.00
C5 0.20 5.00 0.20 0.33 1.00 3.00 3.00 1.00 1.00 0.33 0.33 1.00 1.00 3.00 0.20 0.20 0.33 3.00
C6 0.14 3.00 0.14 0.20 0.33 1.00 1.00 0.33 0.33 0.20 0.20 0.33 0.33 1.00 0.14 0.14 0.20 1.00
C7 0.14 3.00 0.14 0.20 0.33 1.00 1.00 0.33 0.33 0.20 0.20 0.33 0.33 1.00 0.14 0.14 0.20 1.00
C8 0.20 5.00 0.20 0.33 1.00 3.00 3.00 1.00 1.00 0.33 0.33 1.00 1.00 3.00 0.20 0.20 0.33 3.00
C9 0.20 5.00 0.20 0.33 1.00 3.00 3.00 1.00 1.00 0.33 0.33 1.00 1.00 3.00 0.20 0.20 0.33 3.00
C10 0.33 7.00 0.33 1.00 3.00 5.00 5.00 3.00 3.00 1.00 1.00 3.00 3.00 5.00 0.33 0.33 1.00 5.00
C11 0.33 7.00 0.33 1.00 3.00 5.00 5.00 3.00 3.00 1.00 1.00 3.00 3.00 5.00 0.33 0.33 1.00 5.00
C12 0.20 5.00 0.20 0.33 1.00 3.00 3.00 1.00 1.00 0.33 0.33 1.00 1.00 3.00 0.20 0.20 0.33 3.00
C13 0.20 5.00 0.20 0.33 1.00 3.00 3.00 1.00 1.00 0.33 0.33 1.00 1.00 3.00 0.20 0.20 0.33 3.00
C14 0.14 3.00 0.14 0.20 0.33 1.00 1.00 0.33 0.33 0.20 0.20 0.33 0.33 1.00 0.14 0.14 0.20 1.00
C15 1.00 9.00 1.00 3.00 5.00 7.00 7.00 5.00 5.00 3.00 3.00 5.00 5.00 7.00 1.00 1.00 3.00 7.00
C16 1.00 9.00 1.00 3.00 5.00 7.00 7.00 5.00 5.00 3.00 3.00 5.00 5.00 7.00 1.00 1.00 3.00 7.00
C17 0.33 7.00 0.33 1.00 3.00 5.00 5.00 3.00 3.00 1.00 1.00 3.00 3.00 5.00 0.33 0.33 1.00 5.00
C18 0.14 3.00 0.14 0.20 0.33 1.00 1.00 0.33 0.33 0.20 0.20 0.33 0.33 1.00 0.14 0.14 0.20 1.00
C1 to C18: Considered criteria , A1 to A28: Considered alternatives
Table 7 shows the degree of importance of the criteria affecting the stability of sloping walls
using Delphi fuzzy hierarchical analysis.
Table 7
The degree of importance of the parameters affecting the slope stability.
Criteria Weight Criteria Weight
C1 0.140 C10 0.033
C2 0.051 C11 0.035
C3 0.123 C12 0.039
C4 0.064 C13 0.027
C5 0.047 C14 0.038
C6 0.045 C15 0.058
C7 0.018 C16 0.078
C8 0.022 C17 0.090
C9 0.033 C18 0.059
C1 to C18: Considered criteria
In the next step, the studied slopes are evaluated and ranked according to the various steps
described in the similarity model to the ideal solution. The computational steps performed for
this purpose are given below.
Step 1. define unscaled decision matrix
The decision matrix is scaled according to the values in Table 4 according to Eq. 5. Table 8
shows the unscaled decision matrix.
Step 2. define a weighted unscaled decision matrix
According to the weight vector determined for the problem criteria, a weighted unscaled matrix
was formed. Table 9 shows the unmeasured weighted matrix.

Table 8
Unscaled matrix.
A1 0.159 0.149 0.145 0.154 0.257 0.0041 0.263 0.163 0.047 0.1959 0.213 0.195 0.218 0.134 0.224 0.211 0.141 0.165
A2 0.159 0.149 0.169 0.1882 0.133 0.2697 0.263 0.176 0.047 0.1959 0.213 0.195 0.218 0.302 0.224 0.211 0.141 0.165
A3 0.159 0.198 0.133 0.154 0.205 0.2697 0.263 0.259 0.047 0.1959 0.213 0.195 0.131 0.201 0.199 0.141 0.141 0.165
A4 0.159 0.198 0.133 0.154 0.205 0.2312 0.263 0.334 0.047 0.1959 0.213 0.195 0.131 0.134 0.199 0.176 0.141 0.165
A5 0.136 0.198 0.177 0.1403 0.411 0.0578 0.263 0.071 0.174 0.0979 0.213 0.195 0.218 0.134 0.099 0.176 0.141 0.165
A6 0.186 0.05 0.254 0.154 0.154 0.0963 0.048 0.021 0.054 0.1469 0.201 0.244 0.218 0.134 0.224 0.176 0.141 0.165
A7 0.204 0.149 0.218 0.1369 0.308 0.0655 0.048 0.027 0.054 0.1469 0.142 0.244 0.131 0.134 0.099 0.176 0.141 0.165
A8 0.145 0.149 0.143 0.1642 0.103 0.1541 0.048 0.088 0.012 0.1959 0.142 0.195 0.218 0.134 0.099 0.211 0.141 0.165
A9 0.141 0.198 0.126 0.2019 0.056 0.2504 0.048 0.293 0.012 0.1959 0.095 0.195 0.218 0.201 0.224 0.211 0.141 0.165
A10 0.145 0.248 0.116 0.0787 0.118 0.2504 0.263 0.314 0.012 0.1959 0.142 0.195 0.131 0.05 0.149 0.176 0.141 0.165
A11 0.141 0.248 0.162 0.1505 0.118 0.3082 0.048 0.314 0.012 0.1959 0.095 0.195 0.218 0.201 0.149 0.211 0.141 0.165
A12 0.19 0.297 0.206 0.1574 0.159 0.1849 0.263 0.326 0.012 0.1469 0.142 0.195 0.218 0.034 0.199 0.176 0.141 0.165
A13 0.154 0.149 0.133 0.2053 0.062 0.1734 0.009 0.1 0.228 0.1959 0.237 0.13 0.218 0.269 0.199 0.211 0.141 0.165
A14 0.154 0.198 0.058 0.0855 0.205 0.1271 0.263 0.088 0.228 0.0979 0.237 0.13 0.131 0.05 0.149 0.211 0.141 0.165
A15 0.154 0.198 0.048 0.0855 0.205 0.0694 0.263 0.088 0.228 0.0979 0.142 0.13 0.131 0.134 0.149 0.141 0.141 0.165
A16 0.145 0.248 0.085 0.1369 0.308 0.0886 0.263 0.088 0.228 0.0979 0.142 0.13 0.131 0.134 0.099 0.141 0.141 0.165
A17 0.145 0.149 0.085 0.1369 0.154 0.0462 0.048 0.1 0.228 0.1469 0.237 0.13 0.131 0.201 0.149 0.211 0.141 0.165
A18 0.263 0.149 0.21 0.2053 0.133 0.3198 0.048 0.209 0.28 0.2326 0.237 0.195 0.218 0.201 0.224 0.141 0.281 0.247
A19 0.263 0.099 0.128 0.1916 0.092 0.289 0.263 0.209 0.28 0.2326 0.237 0.195 0.218 0.201 0.224 0.141 0.281 0.165
A20 0.208 0.149 0.121 0.2053 0.092 0.0809 0.048 0.209 0.28 0.2326 0.237 0.195 0.218 0.134 0.224 0.141 0.281 0.165
A21 0.263 0.149 0.215 0.2327 0.062 0.1349 0.263 0.209 0.28 0.2326 0.237 0.195 0.218 0.269 0.249 0.141 0.281 0.165
A22 0.236 0.198 0.111 0.2224 0.113 0.0578 0.263 0.209 0.28 0.1469 0.213 0.195 0.131 0.134 0.199 0.141 0.281 0.247
A23 0.19 0.198 0.322 0.2669 0.046 0.2697 0.048 0.052 0.238 0.2326 0.142 0.195 0.131 0.269 0.199 0.282 0.211 0.247
A24 0.213 0.248 0.181 0.2737 0.195 0.1156 0.263 0.096 0.238 0.1469 0.142 0.195 0.131 0.134 0.199 0.282 0.211 0.247
A25 0.231 0.248 0.334 0.2806 0.062 0.2504 0.048 0.105 0.238 0.2326 0.237 0.195 0.218 0.201 0.224 0.141 0.211 0.247
A26 0.222 0.198 0.3 0.2669 0.051 0.2504 0.009 0.136 0.238 0.2326 0.142 0.195 0.218 0.269 0.224 0.141 0.211 0.165
A27 0.24 0.198 0.334 0.2908 0.072 0.1156 0.048 0.136 0.238 0.2326 0.142 0.195 0.218 0.201 0.224 0.141 0.211 0.247
A28 0.159 0.05 0.181 0.1026 0.411 0.0771 0.066 0.199 0.131 0.2326 0.142 0.195 0.218 0.302 0.099 0.282 0.211 0.247
Table 9
Weighted unscaled matrix.
A1 0.009 0.003 0.018 0.0099 0.008 0.0001 0.01 0.013 0.002 0.0274 0.01 0.009 0.004 0.005 0.006 0.008 0.013 0.01
A2 0.009 0.003 0.021 0.012 0.004 0.0089 0.01 0.014 0.002 0.0274 0.01 0.009 0.004 0.011 0.006 0.008 0.013 0.01
A3 0.009 0.004 0.016 0.0099 0.007 0.0089 0.01 0.02 0.002 0.0274 0.01 0.009 0.002 0.007 0.005 0.005 0.013 0.01
A4 0.009 0.004 0.016 0.0099 0.007 0.0076 0.01 0.026 0.002 0.0274 0.01 0.009 0.002 0.005 0.005 0.007 0.013 0.01
A5 0.008 0.004 0.022 0.009 0.014 0.0019 0.01 0.006 0.009 0.0137 0.01 0.009 0.004 0.005 0.003 0.007 0.013 0.01
A6 0.011 0.001 0.031 0.0099 0.005 0.0032 0.002 0.002 0.003 0.0206 0.009 0.011 0.004 0.005 0.006 0.007 0.013 0.01
A7 0.012 0.003 0.027 0.0088 0.01 0.0022 0.002 0.002 0.003 0.0206 0.007 0.011 0.002 0.005 0.003 0.007 0.013 0.01
A8 0.008 0.003 0.018 0.0105 0.003 0.0051 0.002 0.007 6E-04 0.0274 0.007 0.009 0.004 0.005 0.003 0.008 0.013 0.01
A9 0.008 0.004 0.015 0.0129 0.002 0.0083 0.002 0.023 6E-04 0.0274 0.004 0.009 0.004 0.007 0.006 0.008 0.013 0.01
A10 0.008 0.005 0.014 0.005 0.004 0.0083 0.01 0.024 6E-04 0.0274 0.007 0.009 0.002 0.002 0.004 0.007 0.013 0.01
A11 0.008 0.005 0.02 0.0096 0.004 0.0102 0.002 0.024 6E-04 0.0274 0.004 0.009 0.004 0.007 0.004 0.008 0.013 0.01
A12 0.011 0.007 0.025 0.0101 0.005 0.0061 0.01 0.025 6E-04 0.0206 0.007 0.009 0.004 0.001 0.005 0.007 0.013 0.01
A13 0.009 0.003 0.016 0.0131 0.002 0.0057 3E-04 0.008 0.012 0.0274 0.011 0.006 0.004 0.009 0.005 0.008 0.013 0.01
A14 0.009 0.004 0.007 0.0055 0.007 0.0042 0.01 0.007 0.012 0.0137 0.011 0.006 0.002 0.002 0.004 0.008 0.013 0.01
A15 0.009 0.004 0.006 0.0055 0.007 0.0023 0.01 0.007 0.012 0.0137 0.007 0.006 0.002 0.005 0.004 0.005 0.013 0.01
A16 0.008 0.005 0.01 0.0088 0.01 0.0029 0.01 0.007 0.012 0.0137 0.007 0.006 0.002 0.005 0.003 0.005 0.013 0.01
A17 0.008 0.003 0.01 0.0088 0.005 0.0015 0.002 0.008 0.012 0.0206 0.011 0.006 0.002 0.007 0.004 0.008 0.013 0.01
A18 0.015 0.003 0.026 0.0131 0.004 0.0106 0.002 0.016 0.014 0.0326 0.011 0.009 0.004 0.007 0.006 0.005 0.025 0.015
A19 0.015 0.002 0.016 0.0123 0.003 0.0095 0.01 0.016 0.014 0.0326 0.011 0.009 0.004 0.007 0.006 0.005 0.025 0.01
A20 0.012 0.003 0.015 0.0131 0.003 0.0027 0.002 0.016 0.014 0.0326 0.011 0.009 0.004 0.005 0.006 0.005 0.025 0.01
A21 0.015 0.003 0.026 0.0149 0.002 0.0045 0.01 0.016 0.014 0.0326 0.011 0.009 0.004 0.009 0.007 0.005 0.025 0.01
A22 0.014 0.004 0.014 0.0142 0.004 0.0019 0.01 0.016 0.014 0.0206 0.01 0.009 0.002 0.005 0.005 0.005 0.025 0.015
A23 0.011 0.004 0.04 0.0171 0.002 0.0089 0.002 0.004 0.012 0.0326 0.007 0.009 0.002 0.009 0.005 0.011 0.019 0.015
A24 0.012 0.005 0.022 0.0175 0.006 0.0038 0.01 0.008 0.012 0.0206 0.007 0.009 0.002 0.005 0.005 0.011 0.019 0.015
A25 0.013 0.005 0.041 0.018 0.002 0.0083 0.002 0.008 0.012 0.0326 0.011 0.009 0.004 0.007 0.006 0.005 0.019 0.015
A26 0.013 0.004 0.037 0.0171 0.002 0.0083 3E-04 0.011 0.012 0.0326 0.007 0.009 0.004 0.009 0.006 0.005 0.019 0.01
A27 0.014 0.004 0.041 0.0186 0.002 0.0038 0.002 0.011 0.012 0.0326 0.007 0.009 0.004 0.007 0.006 0.005 0.019 0.015
A28 0.009 0.001 0.022 0.0066 0.014 0.0025 0.003 0.015 0.007 0.0326 0.007 0.009 0.004 0.011 0.003 0.011 0.019 0.015

Step 3. Find the positive-ideal and negative-ideal solution
In this step, the values of positive-ideal and negative-ideal solutions for the problem criteria were
calculated and entered in Table 10.
Table 10
Positive-ideal and negative-ideal values for the problem criteria.
a+ 0.008 0.001 0.041 0.0186 0.002 0.011 0.01 0.002 6E-4 0.0326 0.011 0.011 0.004 0.011 0.007 0.011 0.025 0.015
a- 0.015 0.007 0.006 0.005 0.014 0.0001 3E-4 0.026 0.214 0.013 0.004 0.006 0.002 0.001 0.003 0.005 0.013 0.01
C1 to C18: Considered criteria , a+: the positive-ideal solution, a-: the negative-ideal solution
Step 4. Find the distance from the positive-ideal and negative-ideal solution
In this step, the distance values from the positive-ideal and negative -ideal solutions were
determined for the studied options (Table 11).
Step 5. Determine the similarity index
According to the relationship, 13 similarity index values were determined. Table 11 shows the
similarity indices for the 28 slopes, respectively.
Table 11
Values of distance from positive-ideal, negative -ideal solution and similarity index for the studied slopes.
Case No. S- S+ c Rank
A1 0.0303 0.034 0.4703 15
A2 0.0348 0.029 0.5449 8
A3 0.029 0.037 0.4418 19
A4 0.0276 0.04 0.408 23
A5 0.0305 0.037 0.45 17
A6 0.0407 0.027 0.6049 5
A7 0.0359 0.031 0.5368 9
A8 0.0337 0.032 0.5099 11
A9 0.0294 0.039 0.4311 21
A10 0.0278 0.042 0.3961 24
A11 0.0299 0.038 0.442 18
A12 0.0297 0.038 0.4403 20
A13 0.0323 0.034 0.4856 14
A14 0.0253 0.047 0.3495 27
A15 0.0243 0.048 0.3353 28
A16 0.0244 0.045 0.3526 26
A17 0.0254 0.042 0.3775 25
A18 0.0375 0.029 0.563 7
A19 0.0343 0.035 0.4965 13
A20 0.0312 0.037 0.458 16
A21 0.0391 0.028 0.5828 6
A22 0.0271 0.039 0.4109 22
A23 0.0505 0.018 0.7421 1
A24 0.0334 0.03 0.5305 10
A25 0.0495 0.02 0.7155 2
A26 0.0453 0.022 0.6716 4
A27 0.0478 0.022 0.6852 3
A28 0.0327 0.033 0.4992 12
S-: Distance from negative -ideal solution,
S+: Distance from positive-ideal solution,
c: Similarity index

According to the results in Table 11, 4 slopes of the Spanish Asnalquier mine are in the bottom
rows of the table with similarity indices less than 0.4. In contrast, the two eastern and
northwestern slopes of the Itik mine in Sweden with indices above 0.7 were in the first and
second ranks, respectively. Other options were ranked in the middle according to the value of the
similarity index.
6. Discussion
In order to evaluate the accuracy of the research results, field reports were collected from all
studied mines and then a comparison was made between their actual behavior and the predicted
categories. The results of these studies are given in Table 12 and Figure 6.
Table 12
Actual behavior of studied slopes.
Case Slope behavior (Actual) Rank Case Slope behavior (Actual) Rank
A1 Stable 15 A15 Overall failure 28
A2 Stable 8 A16 Overall failure 26
A3 Stable 19 A17 Failure in the set of benches 25
A4 Stable 23 A18 Stable 7
A5 Overall failure 17 A19 Stable 13
A6 Failure in the set of benches 5 A20 Stable 16
A14 Overall failure 27 A28 Stable 12
A1 to A28: Considered alternatives
Fig. 6. Ranking of studied slopes according to similarity index.
0
5
10
15
20
25
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28

The results of this study and its comparison with the actual behavior of slopes in all studied
mines have shown the proper performance of the ranking system. So that the reports received
from the slopes in the bottom rows of the table (slopes studied in the mine of Asnalquier, Spain),
indicate the instability of the slopes in this mine and the total collapse of the walls. On the other
hand, objective reports from the walls in the upper rows of the table indicate the stability of the
walls. Also, with the examinations performed in some of the recorded reports, it was observed
that in some of the slopes located in the middle ranks of the table, slight instability occurred in
parts of the slope. So that the slopes located in the middle ranks can be prone to instability and
the category of minor instabilities.
7. Conclusion
Slope stability is one of the most important challenges in large open pit mines. The occurrence of
accidents may be accompanied by the occurrence of limited or large displacements, which in
both cases, in addition to irreparable loss of life, cause problems or damages to structures located
on the slope or lower parts. Instability of slopes may occur under natural conditions solely due to
the weight of the unstable mass, or may be due to factors such as earthquakes, heavy and
prolonged rains, or floods. Of course, in natural conditions, the presence of other factors such as
erosion of the wall due to water or wind flow, gradual rise of groundwater level or even human
activities, including the application of loading and unloading on the wall can make it unstable.
Intensify. In the present study, we have tried to evaluate and rank 28 slopes from 8 large open pit
mines in the world according to all identifiable influential factors on the slope stability. For this
purpose, the TOPSIS and FDAHP with 18 criteria were used to rank the studied slopes. The
slope: A23 with similarity index 0.742 was selected as the most desirable alternative and the
slope: A15 with similarity index 0.335 as the most undesirable alternative in terms of slope
stability. According to the results, 3 walls of Asnalquier mine in Spain are in the last 3 ranks of
the ranking table with similarity index less than 0.4, in contrast to the 2 eastern and northwestern
walls of Itik mine in Sweden with index Those above 0.7 were ranked first and second,
respectively. In order to evaluate the accuracy of the research results, field reports were collected
from all studied mines and then a comparison was made between their actual behavior and the
predicted categories. The results showed that the slopes located in the bottom rows have a
general collapse and the slopes located in the upper rows of the table are completely stable.
Observations also show that the slopes located in the middle categories have slight falls in parts
of the wall, which can be evaluated in the class of fair instability. Meanwhile, Songun copper
mine with a similarity index of 0.399 was ranked 12th in the second half of the slope stability
classification table. This indicates the acceptable stability of this mine compared to other mines
in the half table. Finally, the results showed that, the matching of research results and field
observations shows the applicability of the model in the initial evaluation of slopes to determine
its stability.
Acknowledgments
The comments received from and the enlightening discussions with our anonymous reviewers
improved the paper and are appreciated.

Funding
This research received no external funding.
Conflicts of interest
The authors declare no conflict of interest.
Authors contribution statement
Morteza Niromand: Conceptualization; Data curation; Formal analysis; Reza Mikaeil and
Mehran Advay: Project administration; and Writing, review & editing.
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