Road cut slope stability analysis for static and dynamic (pseudo-static analysis) loading conditions

Leta Meko; Yadeta C. Chemeda; Bikila Meko

doi:10.1515/geo-2022-0561

Article Open Access

Road cut slope stability analysis for static and dynamic (pseudo-static analysis) loading conditions

Leta Meko , Yadeta C. Chemeda and Bikila Meko

Published/Copyright: November 13, 2023

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From the journal Open Geosciences Volume 15 Issue 1

Abstract

Slope instability has been identified as one of the most natural and man-made disasters that can lead to the life of humans in danger and enormous loss of capital. The roads which pass on the hilly and mountainous terrains are frequently affected by slope failures since hilly and mountainous areas are characterized by variable topographical, geological, hydrological, and land-use conditions. Slope stability analysis was carried out using FEM (plaxis 2D) and LEM (slide software). The stability analysis covers both static and dynamic (in pseudo-static analysis) loading conditions on soil and rock material along selected critical slope sections. Two soil-critical slope sections and two rock-critical slope sections are analyzed in this study. The strength reduction method and method of the slice with Mohr–Coulomb model were used in FEM and LEM, respectively. The slope stability analysis was carried out for both dry and wet states of the soil and rock material along the critical slope sections (i.e., static dry, dynamic dry, static wet, and dynamic wet). The analysis result shows that the total displacement of the slope along soil critical slope section one is (0.58703, 0.58755, 2.35, and 2.38 m), along soil critical slope section two is (0.6574, 0.6621, 1.2841, and 1.2872 m), along rock-critical slope section one is (4.8624, 4.8672, 17.8463, and 17.8512 m) and total displacement along rock-critical slope section two is (3.8365, 3.8391, 11.437, and 11.6275 m) during static dry, dynamic dry, static wet, and dynamic wet loading conditions, respectively. In general, the result shows soil critical slope sections one and two are stable in dry conditions and unstable in wet conditions. Rock-critical slope sections are stable during the dry and wet states of the slope.

Keywords: slope stability; slope failure; critical slope section; pseudo-static analysis

1 Introduction

Slope stability problems and associated disastrous event have been faced throughout history when human or nature has disrupted the easily damaged balance of natural rock and soil slopes [1,2]. Slope instability has been identified as one of the most natural disasters that can lead to the life of humans in danger and enormous loss of capital [3]. Although improvement in identification, prediction, and mitigation measures is advanced, the slope stability problem still triggers economic and environmental crises in mountainous regions [4,5]. This is partly due to the complicity of the factors that causes slope failure and our inadequate knowledge of surface and sub-surface condition. The roads that pass on the hilly and mountainous terrains are frequently affected by slope failures since hilly and mountainous areas are characterized by variable topographical, geological, and hydrological, and land-use conditions [5]. This is because, the road crosses on hilly and mountainous terrains experience both deep and shallow excavations in the construction stage, which disturb the inherent nature of rock and soil slopes [6].

In addition, several factors affect the failure of rock or soil slopes. Earthquakes, high groundwater pressure (after heavy rains), geological factors, and human activity can cause large rocks or earth blocks or even large stone slabs to fall on the lower side of the road [7]. As both natural and human activities are responsible for the failure of slopes, it is difficult to prevent the problem entirely. However, the level of damage can be significantly reduced by assessing the stability condition and adopting different preventive measures [8]. Different mechanisms of slope failure and respective conditions of failure are explained in Table 1.

Table 1

Common types of rock and soil slope failures [1,9,10]

Mechanisms of failure	Conditions of failure
Planar failure	Rock slope failure occurs under gravity when rock blocks rest on an inclined failure like a joint that daylight into free space
Wedge failure	Occurs when two discontinuities striking obliquely into the rock slope face and slide of wedges take place along the line of intersection of two such a plane
Topples	Tops are a force exerted by gravity and the force of adjacent elements moving apart or a rock slab forward
Slides	A translation or rotational movement that occurs along the zone of weakness which separates the slide material from the underlying stable material
Falls	Sudden movement on steep slopes formed due to undercutting, differential weathering, and stream wearing down.
Earth flow	It occurs on liquefiable soils especially when dynamic force occurs in saturated materials
Debris flow	It is a fast mass movement of loose soil, rock, and organic matter that erodes soft soils at high altitudes and is stimulated by heavy rainfall or rapid ice flow

There are various remedial measures used to reduce the impact of slope failures, and these can be grouped into four general classes (i.e., geometric modification, drainage control, slope reinforcement, and retaining structure) [11,12,13]. It must be noted that, to design safe and economical slopes, assess the stability of existing slopes, and adopt suitable remedial measures on it, understanding the cause of failure, mode of failure, and methods of stability analysis approaches are necessary.

Therefore, to assess the instability of the slope, everyone requires to know comprehensive information about the rainfall, engineering property of the slope material, engineering geology, and seismicity, of the area. Slope stability analysis is often carried out to ensure that the analyzed slope can be made safe and the probability of slope failure is minimized [14,15]. Among several methods, the Limit equilibrium method and finite element method are the most widely used and accepted for analyzing slope stability problems [16]. Therefore, the current study is entirely focused on Limit equilibrium and finite element method slope stability analysis.

For analysis purposes in this study, plaxis 2D and Slide software have been utilized to analyze the stability of the slope along the road cut slopes in the study area. The minimum factor of safety has been computed or calculated by the software’s using several parameters and for analysis; values were adopted from the soil and rock investigation reports.

Many naturally occurring factors conspire to fail a slope [8,17]. These factors include the geometry of the slope, shear strength parameters of soil or rock material, layering, surface drainage characteristics, and groundwater conditions [8] as shown in Table 2. Depending on the cause of failure, geometry, materials involved, and rate of movement, slope failures can take place in various types of movements [18]. Many factors affect slope stability. A change in any one or the combination of these factors can alter the steady-state condition of the slope, decreasing its stability and leading to slope failure. When the slope is in a critical state of stability, the destabilization can be generated by a relatively sudden triggering event of natural (such as an earthquake and soil saturation) and human events (undercutting slope for construction purposes) [14,19]. The most important factor controlling slope stability is explained in Table 2 [8,12].

Table 2

Factors affecting the stability of a slope [20,21]

Factors affecting slope stability	Descriptions
The geometry of the slope	The angle of the slope, slope profiles, and height of the slope
Rock discontinuities	Fault, Joint, bedding plane properties
Soil and rock properties	Index and strength properties (Grain size, density, Atterberg limit, UCS, and shear strength parameters)
Groundwater and rainfall	Groundwater conditions, rainfall, drainage pattern, and permeability
Excavation and human activities	Cutting, drilling, and other human activities
Dynamic forces	Seismic activity and blasting

1.1 Objective of the study

Identification of the critical road cut slopes along the road section.
Determination of the Geotechnical and Engineering geological properties of the soil and rock mass along critical slope section.
Analysis and discussion of slope stability of critical slope sections along the road section during dry and wet conditions under both static and dynamic (pseudostatic analysis) loading conditions.

1.2 Study area

The study area is located in the west Shoa Zone of the Oromia region of Ethiopia which is specifically around Guder as shown on the map given in Figure 1. Guder is a town located 12 km west of Ambo and 131.3 km from the capital of Addis Ababa. The area is mostly covered by sandy soil and highly weathered and fractured vesicular basaltic rock. The rainy period of the year lasts for 9.1 months, from February 5 to November 8, with a sliding 31-day rainfall of at least 0.5 in. The month with the most rain in Guder is August, with an average rainfall of 11.1 in. The rainless period of the year lasts for 2.9 months, from November 8 to February 5, and the area falls in zones of low risk (zone 1) in earthquake activity with an acceleration of 0.03–0.06 g (EBCS-2015) (Table 3).

Figure 1

Map of the study area.

Table 3

Location and elevation of selected critical slope sections

Section	Easting	Northing	Elevation (m)
SCSS1	36°22′51″	99°17′04″	2,160
SCSS2	36°23′31″	99°16′86″	2,169
RCSS3	36°24′32″	99°14′46″	2,145
RCSS4	36°18′48″	99°21′32″	2,182

Note: SCSS is the soil-critical slope section; RCSS is rock-critical slope section.

2 Material and method

The data collected for this study consist of both qualitative data and quantitative data. Successive field investigations are carried out to obtain information about the slope sections. During the field investigation information on location, geological structures of the site, discontinuity, and geometry of the critical slope sections were identified. Data collection was made through observation, and measuring (location, geometry, and discontinuity data). Representative soil (disturbed) and rock (irregular shape) samples are taken from selected critical slope sections for the laboratory investigation to get the index and strength parameters of the materials.

Laboratory test results are used to classify the soil and know the specific gravity of the soil, the natural water content of the soil, rock density to calculate rock unit weight and shear strength parameter of the soil and rock. Secondary data such as groundwater table of the site, geological data, earthquake data, stiffness parameters of the soil, and rocks are obtained from correlations and pieces of literature. Rock data software is used to determine strength and stiffness parameters. The zone and acceleration coefficient of earthquake for the study area were adopted from the seismic risk map of Ethiopia and Ethiopian building codes of standard (EBCS-2015). The rainfall data of the study area were collected from the Ambo Meteorological Agency.

Slope stability analysis susceptible to different types of faults can be performed with different techniques. The choice of a suitable technique is, therefore, a very important factor in the slope stability evaluation process. In this research work, slope stability analysis is carried out by LEM and FEM, from conventional and numerical slope stability analysis methods, respectively.

Method of slices is used in LEM that, the soil above the surface of sliding is divided into several vertical parallel slices, and each slice is treated separately [16,22]. Also, the SSR method is used in FEM in which the soil strength parameters are reduced until the slope becomes unstable and FS is determined as a ratio of the initial strength parameter to the critical strength parameter [4,16,23,24]. As it is known that earth materials like rocks and soils may behave in-elastically under very low stresses and that they have very different compressive and tensile strengths, the Mohr–Coloumb failure criteria are used for slope stability analysis.

Conditions for which stability analysis was made: In this research work, the factor of safety and deformation of the cut slope was determined for dry and wet conditions.

Dry condition: Dry condition is the condition by considering that the slope section is completely dry, stability analysis for this condition is performed under both static and pseudo-static state. This condition defines that the water within the slope, if any, will not contribute to any kind of destructive water forces within the slope and may not contribute towards the instability of the slope.

Wet condition: This condition is when the slope is saturated to some degree with water. This situation may occur during very heavy sustained rain in the area. The groundwater will be fully recharged, and the slope material will be saturated. Under such a situation, the water forces developed within the slope material will be destructive and will induce total instability conditions in the slope. For this condition, stability analysis is performed in both static and pseudo-static situations.

2.1 Software application

Finite element-based plaxis 2D and limit equilibrium-based slide softwares are used for this research work. First, the project setting such as failure direction, units, and analysis methods adjusted when using slide software. Then, adding the external boundary and the material is defined for the added boundary. Finally, loads are applied step by step as the condition of the stability analysis. According to (Plaxis 2D, 2013), the continuum must be discretized into small pieces or elements to describe the behavior or actions of individual pieces and reconnect them to represent the behavior of the continuum as a whole. The first step in FEM is defining the problem domain which includes defining the geometrical model, material model, and also applying boundary conditions. Triangular area elements were used to discretize soils in plaxis 2D to form a mesh that connects with nodes to transfer forces and displacements between them. The element stiffness functions are formed after the problem domain is defined and discretized into finite elements. The element stiffness matrix is gathered and assembled to form a global continuum equation containing the material and geometric data. The unknown nodal displacements are solved from the global equations by applying known boundary conditions. The values between nodes are obtained from interpolated shape functions. The remaining parameter forces, stresses, and strains are obtained by post-processing using determined nodal displacements in the element and global equations. Input parameters are identified from different field investigations, field tests, laboratory tests, and correlations given in equations (1)–(8).

2.1.1 Field investigation

During field investigation weathering conditions and discontinuity, characteristics were identified in the critical slope section. Data collected from field investigation parameters such as textural classification, geological strength index (GSI), intact rock coefficient (mi), and disturbance factor (D) were determined through correlation and slope material conditions. The uniaxial compressive strength of rock is determined from the Schmidt rebound hammer test at the site during field investigation.

The rebound number is taken from the Schmidt rebound hammer test and converted to UCS using a correlation formula and correlation chart. At the end of the field investigation, soil samples are taken for laboratory investigation to determine the index and strength parameters of slope material depending on the material variation of the critical slope section. Four soil samples are taken from two different critical sections for the determination of index and strength parameters. Rock samples are taken from different four critical sections to determine the rock density in the laboratory. The sampling of soils was taken 1m horizontally from the face of the slope.

The amount, as well as the sample location, is decided based on the standards (ASTM, 2014 and EBCS, 2015).

2.1.2 Laboratory tests

Shear strength parameters and unit weight of the soil which composes the slope soil mass is the most important input parameter to be determined from the direct shear test to perform the stability analysis of the slope under consideration. In addition to that, the Atterberg limit test and grain size distribution test of the soils were performed to give a general classification of the soil. The unit weight of the rock is determined using the buoyancy technique in the laboratory. Two samples were taken from each critical slope section and a buoyancy technique was used for the samples from each critical slope section, and finally, the average of three values was taken for the stability analysis. The parameters given in Table 4 are obtained from laboratory tests and correlations. Laboratory tests are carried out as per ASTM standards.

Table 4

Soil and rock parameters used as input in numerical analysis

Slope section	Layer	Classification	γsat. (kN/m³)	γdry (kN/m³)	C (kPa)	ϕ	V	E (MPa)	ψ
Soil slope Section 1	Layer 1	Sand with silt and gravel (SW-SM)	19.2	15.3	11.3	30.4	0.181	20,400	0.4
	Layer 2	Sand with silt (SW-SM)	18.6	16.2	13.5	32.2	0.208	8,500	2.2
	Layer 3	Highly weathered vesicular basalt	25.2	24.5	209	40.6	0.322	1267.08	10.7
Soil slope Section 2	Layer 1	Well-graded sand (SW)	18.1	15.8	5.3	38.4	0.301	44,800	8.4
	Layer 2	Sand with gravel (SW)	17.2	14.8	8.5	35.2	0.253	26,000	5.2
	Layer 3	Highly weathered vesicular basalt	26	25.5	377	50.8	0.487	3705.76	20.8
Rock slope Section 1	Layer 1	Highly weathered and fractured vesicular basaltic rock	25.8	24.2	265	39.78	0.31	2392.00	9.78
Rock slope Section 2	Layer 1	Highly weathered and fractured vesicular basaltic rock	26	24.4	206	36.36	0.292	3706.00	6.36

Note: γsat. is saturated unit weight, γdry is dry unit weight, c is cohesion, ϕ is internal friction angle, v is void ratio, E is the modulus of elasticity, and ψ is the dilatancy.

Here, γsat, γdry, c, ϕ, V, E, and ψ are saturated unit weight, dry unit weight, cohesion, internal friction angle, void ratio, modulus of elasticity and dilatancy, respectively.

2.1.3 Material definition

The strength parameters and stiffness parameters for soil and rock are determined from a field test, laboratory tests, as well as correlations as discussed in Section 3. For this research work, Mohr–Coulomb elastic perfectly plastic model is used, and rock layers were modeled using Hoek’s Brown equivalent Mohr–Coulomb model. Parameters used as input in plaxis 2D and slide software are arranged as shown in Table 4.

2.2 Correlation for rock mass properties and soil stiffness parameters:

Modulus of elasticity and poisons ratio are the important soil stiffness parameters used for deformation analysis in numerical modeling of the slope section. Suitable values of these parameters were obtained from numerical correlations and literature. The corrected SPT N value to an average energy ratio of 60% is calculated using equation (1) as recommended by Wolff (1989). The modulus of elasticity of the soil is correlated with SPT N value as proposed by Begemann (1974) as cited by Das (2002). The drained poisons ratio of granular soils is obtained from equation (5) as suggested by Kulhawy and Mayne (1990) as cited by Das (2002). These correlations are selected as the study area is highly dominated by highly weathered rock and sandy soil.

(1) ϕ = 27.1 + 0.3 N 60 − 0.00054 N 60 2 ,

(2) E = 1 , 200 ( N + 6 ) kN m 2 .

For N < 15 and sandy gravel.

(3) E = 4 , 000 + 1 , 200 ( N − 6 ) kN m 2 .

For N > 15 and sandy gravel soil.

(4) E P a = 5 N 60

For sand with fines.

(5) vd = 0.1 + 0.3 ϕ − 25 20 .

For ϕ < 45

(6) ψ = ϕ − 30 .

Slope stability analysis involves an examination of the shear strength of the rock mass on the sliding surface which is expressed in terms of the Mohr–Coulomb failure criterion.

The shear strength parameters of rock mass are determined from rocdata software using the generalized Hoeke-Brown strength criterion in terms of the major and minor principal stresses. The Hoek-Brown failure criterion is an empirical formulation for estimating the confinement strength relationship of a rock mass [13]. Uniaxial compressive strength (UCS), the geological strength index (GSI), intact rock coefficient (mi), disturbance factor (D), slope height, and unit weight of the rock are used as input for the software.

(7) E = 1 − D 2 2 UCS 100 10 GSI − 10 40 ,

where UCS < 100 MPa and E is in GPa.

(8) ν = − 0.002 GSI − 0.003 mi + 0.457

Hoek–Brown failure criterion can allow the determination of rock mass modulus of deformation used for numerical analysis of slope stability using equation (7) [13]. Poisson’s ratio of the rock mass is one of the most important rock parameters used for calculating the deformation of rock slopes. The value of Poisson’s ratio for rock mass is estimated by correlating it with the internal friction angle as shown in equation (8).

2.3 Slope modeling

This will provide the insight to remove insignificant features from the geometry eventually saving some computational time as well as unwanted complexity. During FE geometric modeling the selection of model extent influences the accuracy of the result. In this research work, four critical slope sections of the slope were used for plaxis 2D modeling. The soil critical slope sections one and two are modeled for slope angles of 35 and 40, respectively. The slope length for both slope sections is 50 m. Here, slope length is the inclined face of the slope where an overland flow travels along its flow path before arriving at a point of concentrated flow or deposition. The angle and length of the slope are measured from the site using a compass and tape meter, respectively, during the site visit. The extent of the horizontal boundary and vertical boundary of the slope is taken within the tolerable limit of displacement. The sample slope model for soil critical slope section one is shown in Figure 2.

Figure 2

Sample slope modeling for soil critical slope section one.

3 Result and discussion

3.1 Deformation

The deformation analysis was made for two soil-critical slope sections and two rock-critical slope sections under both static and dynamic loading conditions in the dry and wet states of the slope. During deformation analysis, staged construction was used for static loading conditions, and a total multiplier is used for dynamic analysis for all critical slope sections. The result shows that the slope material is highly deformed during the wet conditions of the slope or when the groundwater table is high.

The displacement of the slope is increased slowly from static dry condition to dynamic dry condition and increased rapidly from static dry condition to static and dynamic wet condition since the factor highly affecting the displacement of the slope is the rise of the groundwater table or high amount of moisture content within the slope material. The total displacement of soil critical slope section one is 0.58703, 0.58755, 2.35, and 2.38 m during static dry, dynamic dry, static wet, and dynamic wet conditions, respectively. Total displacements for all critical slope sections are shown in Figures 3 and 4.

Figure 3

Total displacement under different loading conditions for soil critical slope sections one and two.

Figure 4

Total displacement under different loading conditions for soil critical slope sections one and two.

A large amount of displacement is recorded on the critical rock slope sections during both static wet and dynamic wet conditions. It must be recognized that the deformation is only static (i.e. not resulted from dynamic vibration) in this loading condition. The simulations showed that the groundwater table position with the application of seismic activity affects a large amount of displacement. However, the effect of the rise of the groundwater table was a more dominant factor affecting a large amount of displacement than seismic earthquake activity when they were applied to the slope section separately.

3.2 Factor of safety

Theoretically, all slopes with a factor of safety greater than unity are safe. However, many design standards recommend the use of FoS greater than one. Because, with time, there are certain processes or events (rainfall, weathering, earthquake, etc.) that tend to destabilize the slope reducing temporarily or permanently the factor of safety of the slope. At some point, one of those factors will result in reducing the factor of safety to less one, and subsequently, the slope fails or a landslide occurs.

The two soil slope sections are marginally stable during the static dry and dynamic dry conditions and unstable during static wet and dynamic wet loading conditions. The factor of safety of the slope is decreased from its initial static dry condition by 0.077, 24.65, and 24.8% on average during dynamic dry, static wet, and dynamic wet conditions, respectively. The result of FoS for soil slope sections and rock slope sections from Both LEM and FEM is summarized in Table 5. Bishop method, Janbu, and Generalized limit Equilibrium method are used from the limit equilibrium method of analysis. The total displacement of all critical slope sections during static dry, dynamic dry, static wet, and dynamic wet is summarized in Figures 3 and 4. The result from the FEM simulation is given in Figures 8–11.

Table 5

Factor of safety calculated from both LEM and FEM

Slope section	Critical slope section	Loading condition	FoS from LE methods			FoS from FE method
Slope section	Critical slope section	Loading condition	Bishop	Janbu	GLE	FoS from FE method
Soil slope section	SCSS1	Static dry	1.429	1.337	1.428	1.403
		Static wet	1.024	0.905	1.035	1.402
		Dynamic dry	1.278	1.195	1.279	1.467
		Dynamic wet	0.987	0.888	0.996	0.976
	SCSS2	Static dry	1.216	1.147	1.300	1.205
		Static wet	0.832	0.722	0.847	0.975
		Dynamic dry	1.093	1.027	1.083	1.204
		Dynamic wet	0.742	0.631	0.758	0.974
Rock critical slope section	RCSS1	Static dry	2.466	1.282	2.472	2.526
		Static wet	1.961	1.970	1.966	1.861
		Dynamic dry	2.361	2.325	2.364	2.524
		Dynamic wet	1.820	1.788	1.823	1.857
	RCSS2	Static dry	1.797	1.943	2.001	2.07
		Static wet	1.326	1.407	1.468	1.512
		Dynamic dry	1.703	1.775	1.775	2.069
		Dynamic wet	1.250	1.282	1.300	1.467

The rock-critical slope sections are stable for all loading conditions and slope states. A factor of safety of both rock critical slope sections is reduced from its initial static dry condition during dynamic dry, static wet, and dynamic wet analyses. The factor of safety of the rock slope sections is reduced from the initial static condition by 0.15, 18.4, and 19.6% on average during dynamic dry, static wet, and dynamic wet conditions, respectively. Accordingly, factor of safety of the slope sections decreases in the order of static dry, dynamic dry, static wet, and dynamic wet, respectively, as the highly affecting factor of instability of the slope is the rise of the groundwater table from both FEM and LEM.

Two main concepts that should be considered when comparing LEM and FEM are, first LEM is based on plasticity, we directly solve the factor of safety of a trial slip surface, and then, we need to check other trial surfaces to find the slip surface with the lowest factor of safety. Second, FEM is indirectly solving for a factor of safety by the non-convergence of the model through the SSR process which will lead to a large strain and the contours of this strain identify the slip surface (no trial slip surface to assume and no searching).

The analyzed slope model for soil critical slope section one using slide and plaxis 2D software for wet and dry states of the slope under both static and dynamic(pseudo-static analysis) loading conditions are given in Figures 5–12.

Figure 5

Factor of safety for soil critical slope section one from LEM (slide) during static dry loading condition.

Figure 6

Factor of safety for soil critical slope section one from LEM (slide) during static wet loading condition.

Figure 7

Factor of safety for soil critical slope section one from LEM (slide) during dynamic dry loading condition.

Figure 8

Factor of safety for soil critical slope section one from LEM (slide) during dynamic wet loading condition.

Figure 9

Factor of safety for soil critical slope section one from FEM (plaxis 2D) during static dry loading condition.

Figure 10

Factor of safety for soil critical slope section one from FEM (plaxis 2D) during static wet loading condition.

Figure 11

Factor of safety for soil critical slope section one from FEM (plaxis 2D) during dynamic dry loading condition.

Figure 12

Factor of safety for soil critical slope section one from FEM (plaxis 2D) during dynamic wet loading condition.

4 Conclusions

Soil slope sections of the study area of this research work are dominated by sandy soil and the rock sections are highly weathered rock. The slope stability analysis was carried out using the finite element method (plaxis 2D) and limit equilibrium method (slide) for dry and wet slope states under both static and dynamic (pseudo-static) loading conditions. Mohr–Columb material model and strength reduction method were used in finite element analysis. The method of slice was used in the limit equilibrium method. The following conclusions are made from the stability analysis:

The two soil critical slope sections are stable during the dry state (static dry and dynamic dry) and unstable during the wet state (static wet and dynamic wet) when there is high rainfall infiltration.
The two rock-critical slope section is stable in dry and wet states of the slope for both static and dynamic loading condition.

The result from this study shows that as the moisture content and seismicity of the slope section increase, the stability of the slope decreases.

Funding information: There was no external funding for the study.
Conflict of interest: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Ethical approval: This article does not contain any studies involving human or animal subjects.

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Received: 2022-04-17

Revised: 2023-07-12

Accepted: 2023-09-30

Published Online: 2023-11-13

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/geo-2022-0561

Keywords for this article

slope stability; slope failure; critical slope section; pseudo-static analysis

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