INTRODUCTION:

Slope either occurs naturally or is engineered by humans. Slope stability problems have been faced throughout history whenever the delicate balance of nature has been disturbed by any kind of internal or external forces. The forces with in nature like of internal or external forces. The forces with in nature like heavy rainfall leading to erosion and landslides constituent and important example of internal disruptive forces while the external forces mainly human activities such as excavation and filling of slopes have also cause the slide.

Analytical methods of slope stability and monitoring methods are improved lately. Through these methods and recent developments, the slope stability analysis process is more accurate, because experience and engineering judgment, which are still considered as primary important part of analysis, are well combined with rational methods, in order to improve the accuracy level, which should be achieved by systematic monitoring, continuing testing and complex analysis. Despite the fact that all the methods used can comply the soil behavior, it is important to know that these half empirical methods. Given that, the real soil conditions are different, we shall relay more in site investigations data.

Stability of natural slopes and man-made slopes such as road/railway embankment, hydraulically constructed dams, earth dams etc.is a major issue in geotechnical engineering. Traditional methods used for slope stability analysis is ‘limit equilibrium method', in which a single value of factor of safety is calculated to predict the stability of slope. Afterwards, some researchers developed finite element methods as a powerful technique in analyzing the slope stability problems. But the problem of slope stability is related to risk and reliability. Thus a single factor of safety cannot be relied on for taking safety measures against failure. Reliability analysis of slopes involves the calculation of reliability index for a slope or alternatively probability of failure of a slope In both the above given approaches the very important part is the search of critical slip surface i.e. critical deterministic slip surface or critical probabilistic slip surface which is a constraint optimization problem. Various optimization techniques have their advantages in solving slope stability problems. With the advancement of computers it becomes easy to implement any of these methods.

This paper aims to deal with the comparison of factors of safety assessed by using limit equilibrium method (LSM) analysis is performed by using PLAXIS 2D. The Finite Element method (FEM) analysis is performed by using PLAXIS 2D

1.1 The limit Equilibrium Methods (LSM):

1. Simplified Bishop Method

2. Janbu’s simplified method

3. Swedish circle method

Table 1: Characteristics of Commonly Used Methods of Limit Equilibrium Analysis (Modified after Duncan and Wright, 2005)

Procedure	Use
Swedish Circle (ø = 0) Method	Swedish Circle (ø = 0) Method Applicable to slopes where ø = 0 (i.e., untrained analyses of slopes in saturated clays).
Logarithmic Spiral Method	Suitable for homogeneous slopes. Useful for developing slope stability charts and used some in software for design of Reinforced slopes.
Friction Circle Method	Suitable for total or effective stress types of Analysis in homogeneous soils with ø > 0.
Ordinary Method of slices	Applicable to non-homogeneous slopes and c-ø soils where slip surface can be approximated by a circle. Very convenient for hand calculations. Inaccurate for effective stress analyses with high pore Water pressures.
Simplified Bishop Method	Applicable to non-homogeneous slopes and c-ø soils where slip surface can be approximated by a circle. More accurate than Ordinary Method of slices, especially for analyses with high pore water pressures. Calculations feasible by hand or Spreadsheet.
Janbu’s Simplified Method	Applicable to non-circular slip surfaces. Also for shallow, long planar failure
Spencer’s Method	An accurate procedure applicable to virtually all slope geometries and soil profiles. The simplest complete equilibrium procedure for computing factor of safety.
Morgenstern and Price’s Method	An accurate procedure applicable to virtually all slope geometries and soil profiles. Rigorous, well established Complete equilibrium procedure.
Sharma's Method	Suitable for more complex problems particularly where non-vertical slice boundaries are significant. A convenient complete equilibrium procedure for computing the seismic coefficient required Producing a given factor of safety.

1.2 Scope of the project work:

· By using PLAXIS 2D we can find factor of safety of such slope embankment are found out before construction work.

· To provide safe slopes to embankments to be constructed.

· To prevent the landslide before it occurs.

2. Methodology:

2.1 PLAXIS 2D

PLAXIS 2D is powerful and user friendly finite element package intended for two- dimensional analysis of deformation and stability in geotechnical engineering and rock mechanics. PLAXIS is used worldwide by top engineering companies and institutions in the civil and geotechnical engineering industry. Applications range from excavations, embankment and foundations to tunneling, mining and reservoir geo mechanics.

2.2 Material Model:

The Mohr–Coulomb model was used for this analysis. This model involves five parameters, namely Young’s modulus, E, Poisson’s ratio, ν, the cohesion, c, the friction angle, φ, and the dilatancy angle, ψ. In this case dilatancy angle was assumed to be zero, since it is close to zero for clay and for sands with a friction angle less than 380.

2.3 Geotechnical Model:

The geotechnical model adopted in this analysis is illustrated in Figure 1. The soil is classified as unsaturated sand and comprises of the properties in Table 5, kept constant throughout all analyses.

Figure1: Simple Homogeneous Soil Slope

The slope considered has an embankment batter of 1:1.5, producing a slope angle equal to 33.7˚. No water table has been considered

Figure 2: Image of a Road Embankment

2.4 Material Properties:

The properties of the unsaturated sand material are presented in Table 3. These properties are adequate for the Mohr-Coulomb approach.

Table 3: Unsaturated Sand Material Properties - Simple Homogeneous Soil Slope

	Unit Weight (kN/m3)	Elastic Modulus (MPa)	Poisson’s Ratio	Cohesion (kPa)	Friction Angle (˚)
Unsaturated Sand	17	13	0.3	1	30

3. PLAXIS Analysis:

· Upon starting PLAXIS the projects title and models units and dimensions is to be set.

· The model is drawn using the inbuilt CAD interface.

· The material properties need to be created and assigned. PLAXIS requires the advanced properties of E and ν of the soil as well as the standard Mohr-Coulomb.

· The restraints are then set as standard fixities.

· The mesh is generated. A medium mesh is being used to help improve accuracy.

· In the calculation phase, the stability of the embankment needs to be simulated,

· The results are then viewed showing deformation, total displacement, FOS etc.

Figure 3: Measurement of slope

3.1 Geometry:

The generation of a finite element model begins with the creation of a geometry model, which is a representation of the problem of interest. A geometry model consists of generated by the program. In addition to these basic components, structural objects or special conditions can be assigned to the geometry model to simulate tunnel linings, walls, plates, soil-structure interaction or loadings.

Figure 4: Geometry model of road embankment 3.2 Material data sets for soil and interfaces

The material properties and model parameters for soil clusters are entered in material data sets (fig 5).The material properties of interfaces are related to the soil properties and are entered in the same data sets as the soil properties. A data set for soil and interfaces generally represents a certain soil layer and can be assigned to the corresponding clusters in the geometry model. The name of the data set is shown in the cluster properties window. Interfaces that are present in or along that cluster obtain the same material data et.

Figure 5: Soil and interface material set window

3.3 Material model:

Mohr-coulomb model

This well-known model is used as a first approximation of soil behavior in general. The model involves five parameters, namely Young’s modulus, E, Poisson’s ratio, v, the cohesion, c, the friction angle, ᶲ, and the dilatancy angle, Ψ.

3.4 Type of material behavior - Material type:

In principle, all model parameters in PLAXIS are meant to represent the effective soil response, i.e. the relation between the stresses and strains associated with the soil skeleton. An important feature of soil is the presence of pore water. Pore pressures significantly influence the soil response.

3.5 Untrained behavior:

This setting is used for a full development of excess pore pressures. Flow of pore water can sometimes be neglected due to a low permeability (clays) and/or a high rate of loading. All clusters that are specified as untrained will indeed behave untrained, even if the cluster or a part of the cluster is located above the phreatic level. Note that effective stiffness parameters should be entered, i.e. E' and ν' and not Eu and ν u.

Figure 6: Soil and interface material set window parameters

3.6. Mesh generation:

The generation of the mesh is started by clicking on the mesh generation button in the tool bar or by selecting the Generate option from the Mesh sub-menu. The generation is also activated directly after the selection of a refinement option from the Mesh submenu. We use medium mesh.

3.7 Initial conditions:

Once the geometry model has been created and the finite element mesh has been generated, the initial stress state and the initial configuration must be specified. This is done in the initial conditions part of the input program. The initial

Figure 7: Mesh Generated

Conditions consist of INPUT PRE-PROCESSING two different modes: One mode for the generation of initial water pressures (water conditions mode) and one mode for the specification of the initial geometry configuration and the generation of the initial effective stress field (geometry configuration mode).

3.8 Prelatic levels:

Pore pressures and external water pressures can be generated on the basis of phreatic levels. A phreatic level represents a series of points where the water pressure is just zero. Using the input of a phreatic level, the water pressure will increase linearly with depth according to the specified water weight (i.e. the pressure variation is assumed to be hydrostatic).

Figure 8: Active pore pressure

Figure 9: Deformed Mesh

4. Numerical study:

After the generation of a finite element model, the actual finite element calculations can be executed. Therefore it is necessary to define which types of calculations are to be performed and which types of loadings or construction stages are to be activated during the calculations. This is done in the Calculations program. PLAXIS allows for a different types of finite element calculations. Groundwater flow was discussed in the previous chapter on the Input program, since a groundwater flow calculation is generally used to generate a water pressure distribution for use as input data for a deformation analysis. The Calculations program considers only deformation analyses and distinguishes between a Plastic calculation, a Consolidation analysis, Phi-c reduction (safety analysis) and a Dynamic calculation.

4. 1Plastic calculation:

A Plastic calculation should be selected to carry out an elastic-plastic deformation analysis in which it is not necessary to take the decay of excess pore pressures with time into account. If the Updated Mesh option in the advanced general settings window has not been selected, the calculation is performed according to the small deformation theory. The stiffness matrix in a normal plastic calculation is based on the original unreformed geometry. This type of calculations is appropriate in most practical geotechnical applications.

4.2 Consolidation analysis:

A Consolidation analysis should be selected when it is necessary to analyze the development or dissipation of excess pore pressures in water-saturated clay-type soils as a function of time. PLAXIS allows for true elastic-plastic consolidation analyses. In general, a consolidation analysis without additional loading is performed after an untrained plastic calculation. It is also possible to apply loads during a consolidation analysis. However, care should be taken when a failure situation is approached, since the iteration process may not converge in such situations.

4.3 Phi-c reduction (safety analysis):

A safety analysis in PLAXIS can be executed by reducing the strength parameters of the soil. This process is termed Phi-c reduction and is available as a separate type of calculation. Phi-c reduction should be selected when it is desired to calculate a global safety factor for the situation at hand. A safety analysis can be performed after each individual calculation phase and thus for each construction stage. However, note that a phi-c reduction phase cannot be used as a starting condition for another calculation phase because it ends in a state of failure. When performing a safety analysis, no loads can be increased simultaneously. In fact, Phi-c reduction is a special type of plastic calculation. The input of a time increment is generally not relevant in this case.

Figure 10: Connectivity

Figure 11: Effective stresses

5. RESULT AND DISCUSSION:

Table 4: Simplified bishop method

Slice No.	Slice Width (∆X)	Slice Ht.	VOL.	Wt.	α	C	W Sinα	u	(C.∆x+ (W- u.)×Tan ∅	mα		Col10 Col11
Slice No.	Slice Width (∆X)	Slice Ht.	VOL.	Wt.	α	C	W Sinα	u	(C.∆x+ (W- u.)×Tan ∅	Trial1 F=2.0	Trial2 F=1.85	Trial1 F=2.0	Trial2 F=1.8 5
1	1.5	0.6684	1.002 6	17.04 4	9	1	2.66	0	11.34	0.94	1.037	12.63	10.93
2	1.5	1.7357	2.59	44.03	4	1	3.071	0	26.28	1.017	1.019	25.84	25.78
3	1.5	2.41	3.615	61.45	17	1	17.96	0	36.34	1.040	1.049	34.92	34.64
4	1.5	2.74	4.11	69.97	33	1	38.05	0	41.20	0.995	1.0126	40.20	40.68
5	1.84	1.7	3.128	53.17	53	1	42.46	0	32.20	0.83	0.8578	38.79	37.57
							∑=10 4.201					∑=152 .38	∑=149 .6

152.38

F (1) TRIAL = ---------------- = 1.46

104.201

149.6

F (2) TRIAL = -------------- = 1.43

104.201

Factor of Safety =1.46

Table 5: JANBU’S Simplified method

Slice No.	Slice Width(∆X)	Slice Height	Volume	Weight	α	C	ARC Length (L)	P	WTanα
1	1.5	0.6684	1.0026	17.044	9	1	1.52	16.084	2.69
2	1.5	1.7357	2.59	44.03	4	1	1.51	42.87	3.07
3	1.5	2.41	3.615	61.45	17	1	1.49	57.057	18.78
4	1.5	2.74	4.11	69.97	33	1	1.88	65.62	45..37
5	1.84	1.7	3.128	53.17	56	1	3.29	57.84	78.84
						1	∑C×L=9.69	∑P=239.471	∑=148.75

Table 6: Swedish Circle Method

Slice No.	Slice Width (∆X)	Slice Height	Volume	Weight	α	T = WSinα	N = WCosα
1	1.5	0.6684	1.0026	17.044	0	0	0
2	1.5	1.7357	2.59	44.03	4	3.071	43.92
3	1.5	2.41	3.615	61.45	17	17.96	58.46
4	1.5	2.74	4.11	69.97	33	38.053	58.59
5	1.84	1.7	3.128	53.17	53	42.46	32.002
						∑T=101.54	∑N=192.972

Figure 12: Displacement Vs Multiplier Graph Factory of Safety = 1.104

Table 6: Comparison of factor of safety of all methods

Sr. No.	Analysis method	Fos
1.	Plaxis 2d	1.104
2.	Simplified bishop Method	1.460
3.	Janbu’s simplified Method	1.309
4.	Swedish circle method	1.192

By analyze the slope stability such as FEM method (PLAXIS 2D) is (FOS=1.104) it is 21% reduce as compare to Janbu’s simplified method (FOS=1.309), Bishop simplified (FOS=1.406) increase 15% w.r.to Janbu’s simplified method and Swedish circle method (FOS=1.192) It’s educe 12% w.r.to Janbu’s simplified method. Thus we have to conclude Janbu’s simplified method are more accurate because it will consider shear stresses.

6. CONCLUSION:

Based on slope stability analysis that applying on finite element with PLAXIS 2D and limit equilibrium methods the conclusion can be summed up as follows.

1. The slope can be stabilizing by using limit equilibrium methods i.e Janbu’s simplified method. In this method factor of safety is more precise as compared to other limit equilibrium because the shear stresses considered.

2. By analyze the slope stability such as FEM method (PLAXIS 2D) is (FOS=1.104) it is 21% reduce as compare to Janbu’s simplified method (FOS=1.309), Bishop simplified (FOS=1.406) increase 15% w.r.to Janbu’s simplified method and Swedish circle method (FOS=1.192) It’s educe 12% w.r.to Janbu’s simplified method.

3. Thus we have to conclude Janbu’s simplified method is more accurate because it will consider shear stresses.

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Received on 18.08.2023 Modified on 14.11.2023

Research J. Science and Tech. 2024; 16(1):29-38.

DOI: 10.52711/2349-2988.2024.00006