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ENCE 361ENCE 361Soil MechanicsSoil Mechanics

Slope StabilityFellenius Method

Types of Slope Types of Slope FailureFailure

Types of Slope FailureTypes of Slope Failure

Methods of Failure Analysis for Methods of Failure Analysis for Rotational FailureRotational Failure

Swedish Slip Circle Method

Methods of Slices Fellenius Method

(Ordinary Method) Bishop Method

(Simplified) Spencer Morganstern-Price GLE

Chart Solutions Based on Methods of Slices Taylor Bishop-Morganstern Barnes

Non-circular failure surfaces

Overview of Rotational Failure Overview of Rotational Failure CriteriaCriteria

Stability of a Slope in ClayStability of a Slope in Clay(Swedish Slip Circle Method)(Swedish Slip Circle Method)

Factors of SafetyFactors of Safety

Fellenius MethodFellenius MethodDeveloped by Wolmar Fellenius as a result of

slope failures in sensitive clays in SwedenFirst method of slices to be widely accepted

and usedReduces the force resolution of the slope to a

statically determinate structureSimplest method of slices; also produces the

lowest factor of safety (most conservative)

Assumptions for Fellenius Assumptions for Fellenius MethodMethod

Side forces (shear and compressional) are not significant

Included ForcesWeight of the slice,

including weight of water Resisting Shear forces at

base of slice, both those from the cohesion of the soil and those from effective stress

Governing Equation for Fellenius Governing Equation for Fellenius MethodMethod

M resistingM causingResisting moments are

generated by the shear strength of the soil at the failure surface

Causing moments are generated by the weight of the soil, including the weight of the water

Moments for Fellenius MethodMoments for Fellenius Method

M causingr W t sinM resistingr c'lW cos tan

FSM resistingM causing

FS c'lW cos tanW t sin

Fellenius MethodFellenius MethodWater Table InclusionWater Table Inclusion

FS c'lW cos tanW t sin

These weights do not include bouyancy calculations

These weights include bouyancy calculations

Example of Fellenius MethodExample of Fellenius Method

Parameters for ExampleParameters for ExampleSoil Parameters Unit Weight = 125 pcf Cohesion = 60 psf Internal Friction Angle

= 32Slope Slope = arctan (1/1.5) =

33.7 Height of slope = 20'

Circle Parameters Radius of Failure

Circle = 30' Centre of failure circle

is 30' above elevation of toe

Centre of failure circle is 4.5' to the right of the toe of the slope

Determination of Circle Centre Determination of Circle Centre and Radiusand Radius

Basic VariablesBasic Variables

b1, ft. H, ft. sin alpha1 4.5 1.6 900 -1.72 -0.032 3.2 4.2 1680 2.87 0.052A 1.8 5.8 1305 8.05 0.143 5 7.4 4625 14.48 0.254 5 9 5625 24.83 0.425 5 9.3 5812.5 35.45 0.586 4.4 8.4 4620 47.73 0.746A 0.6 6.7 502.5 55.08 0.827 3.2 3.8 1520 60.46 0.87

Slice Number

Wdry, lbs.

Alpha, deg.

Dry Slope ComputationsDry Slope Computations

Factor of Safety = 17592.01/12282.95 = 1.43

b1, ft. H, ft. sin alpha1 4.5 1.6 900 -1.72 -0.03 -27 405.18 562.13 967.312 3.2 4.2 1680 2.87 0.05 84 288.36 1048.47 1336.832A 1.8 5.8 1305 8.05 0.14 182.7 163.61 807.42 971.033 5 7.4 4625 14.48 0.25 1156.25 464.76 2798.25 3263.014 5 9 5625 24.83 0.42 2362.5 495.85 3189.85 3685.75 5 9.3 5812.5 35.45 0.58 3371.25 552.41 2958.73 3511.146 4.4 8.4 4620 47.73 0.74 3418.8 588.75 1941.75 2530.56A 0.6 6.7 502.5 55.08 0.82 412.05 94.35 179.72 274.077 3.2 3.8 1520 60.46 0.87 1322.4 584.12 468.3 1052.42Sums 12282.95 17592.01

Slice Number

Wdry, lbs.

Alpha, deg.

W sin alpha

Cohesion Term

Friction Term (Dry)

Resisting Moment (Dry)

Wet Slope ComputationsWet Slope Computations

Factor of Safety = 15257.09/12282.95 = 1.24

H, ft.

1 4.5 1.6 900 -1.72 -0.03 -27 405.18 562.13 967.31 0 900 562.13 967.312 3.2 4.2 1680 2.87 0.05 84 288.36 1048.47 1336.83 0 1680 1048.47 1336.832A 1.8 5.8 1305 8.05 0.14 182.7 163.61 807.42 971.03 0.45 1255 776.49 940.13 5 7.4 4625 14.48 0.25 1156.25 464.76 2798.25 3263.01 3.37 3575 2162.97 2627.734 5 9 5625 24.83 0.42 2362.5 495.85 3189.85 3685.7 4.65 4175 2367.58 2863.435 5 9.3 5812.5 35.45 0.58 3371.25 552.41 2958.73 3511.14 4.01 4562.5 2322.44 2874.856 4.4 8.4 4620 47.73 0.74 3418.8 588.75 1941.75 2530.5 1.82 4120 1731.6 2320.356A 0.6 6.7 502.5 55.08 0.82 412.05 94.35 179.72 274.07 0 502.5 179.72 274.077 3.2 3.8 1520 60.46 0.87 1322.4 584.12 468.3 1052.42 0 1520 468.3 1052.42Sums 12282.95 17592.01 15257.09

Slice Number b1, ft. Wdry, lbs. Alpha, deg. sin alpha W sin alpha Cohesion Term

Friction Term (Dry)

Resisting Moment (Dry)

Phreatic Surface, ft.

Wet effective weight

Friction Term (Wet)

Resisting Moment (Wet)

Wet efficive weight of slope = total weight of slope weight of waterThe weight of the water = (distance from lower end of slice to water table)

(width of the slice)(unit weight of water)

Modified Bishop MethodModified Bishop Method

Same as Fellenius Method except that it includes normal forces along sides of slices

Problem becomes statically indeterminate as a result of this and requires an iterative solution

Results tend to result in higher factors of safety than the Fellenius method

Equations for Bishop's MethodEquations for Bishop's Method

Procedure for Bishop's MethodProcedure for Bishop's Method

Example Using Bishop's MethodExample Using Bishop's Method

Example Using Bishop's MethodExample Using Bishop's Method

Use of Computer SoftwareUse of Computer SoftwareAutomates many of the processes that are

required for slope analysisEliminates the need for iterative solutionsEnables running multiple cases and varying

parameters without difficultySlope-W software (from Geo-Slope) available

from website

Example CaseExample CaseNo Water No Water

TableTable

Setup of Geometry and Soil Properties

1

21

2 3

4 5678

9

1011

1213

14

15

16 17

18

19 20

Fellenius Fellenius MethodMethod

Dry CaseDry Case

Slide ForcesSlide ForcesFellenius MethodFellenius Method

Slice 4 - Ordinary Method

3203.3

1451.4

2651.1

Bishop MethodBishop MethodDry CaseDry Case

Bishop SliceBishop SliceSlice 4 - Bishop Method

3203.3

1472.2

2874.8

1523.41830.5

Slope-W SetupSlope-W SetupWet CaseWet Case

1

21

2 3

4 5678

9

1011

1213

14

15

16 17

18

19 20

Bishop Bishop SolutionSolution

Wet CaseWet Case

Fellenius Fellenius SolutionSolution

Wet CaseWet Case

Comparison of ResultsComparison of Results

Dry 1.43 1.42 - 1.5Wet 1.24 1.15 1.3 1.3

Factors of Safety

Fellenius (Spreadsheet)

Fellenius (Slope-W)

Bishop (NAVFAC)

Bishop (Slope-W)

Fellenius Method in Slope-W used different centre of radius of failure

Questions?Questions?