Using Shear Strength Reduction Method for 2D and 3D · PDF fileUsing Shear Strength Reduction...

Using Shear Strength Reduction Method for 2D and 3D Slope Stability Analysis

Thamer Yacoub, Ph.D. P.Eng.President, Rocscience Inc.

Toronto, CanadaAnnual Kansas City Geotechnical Conference 2016

OutlineSlope stability analysis using Limit Equilibrium Method (LEM) vs. Shear Strength Reduction Method (SSR)Advantages and disadvantages of LEM and SSRShear Strength Reduction outlineApplications Soil modelsMSE wall Slope with supports 3D effect on slope stability analysis

Recommendations and Conclusion

“Developments in the characterization of complex rock slope deformation and failure using numerical modelling techniques” D. Stead, E. Eberhardt, J.S. Coggan

Slope failure analysis

“Developments in the characterization of complex rock slope deformation and failure using numerical modelling techniques” D. Stead, E. Eberhardt, J.S. Coggan

Limit Equilibrium Analysis

Most common slope analysis methodExtensive experienceRelatively simple formulation (easy to understand)Quick analysis Useful for evaluating sensitivity of failure to input parametersMinimal material input parameters

Pros


Based on assumption soil mass can be divided into slicesArbitrary assumptions to ensure static determinacyNeglects stress‐strain behaviourDoes not provide information on deformationsFinding lowest factor of safety can be very challenging

Cons

Non‐Circular Search Methods

Global Search MethodsCuckoo Search (Slide 7)Simulated Annealing

Local Search MethodsAuto Refine SearchBlock SearchPath SearchMonte Carlo Optimization


Search Method (Local and Global methods)


Search Method (Local and Global methods)

1.28

1.03

4.80

0.45



Auto Refine Search: FS = 2.74 Cuckoo: FS = 1.51

1.5061.5061.5061.506

Limit Equilibrium AnalysisActive‐Passive wedgeMethod: Spencer FS: 1.54

Limit Equilibrium AnalysisActive‐Passive wedgeMethod: Non‐Vertical Sarma FS: 1.67

RS2 FS: 1.67

Shear Strength Reduction Method (SSR)

Overview of SSR MethodConventional Finite Element (FE) analysisElasto‐plastic constitutive relationship Elastic‐perfectly plastic –most common assumption Produces results similar to LE

Overview of SSR MethodBishop, “The Use of the Slip Circle in the Stability Analysis of Slopes”, Geotechnique, 1955

Overview of SSR MethodGeometric interpretation of strength envelope reduction

0

10

20

30

40

50

60

70

0 20 40 60 80 100

Original MCReduced MC

F

Overview of SSR MethodReduction of Mohr‐Coulomb (MC) shear strength envelopeOriginal MC equation

Reduced (factored) MC equation

FFc tan''

tan'' c

Generalized Hoek‐Brown StrengthReduction of GHB shear strength envelope

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

-0.05 0.05 0.15 0.25 0.35

n

Shear envelope for

original GHB criterion

Envelope after reduction by F

F

Reduction of GHB shear strength envelope New parameters are calculated from fitted curve

Can be used for other non‐linear strength envelopes

Reduce strength of slope materialsin FEM model by factor

Compute FEM model

If analysis converges to solution, reduce factor and re-compute

If solution does not converge end calculations (slope has failed)

Factor of safety = factor initiating failure

SSR‐FEM Slope Stability Analysis

Stopping Criteria for SSRDefinition of failureNon‐convergence of solution (Zienkiewicz, 1971) Shear strength parameters reduced until non‐convergence or numerical instabilities occur

Bulging of slope line (Snitbhan and Chen, 1976) Failure is described by horizontal displacements of slope surface

Shear strains Computed shear strains used to estimate FOS

Definition of Non‐ConvergenceNon‐convergence of solution within specified number of iterationsNo stress distribution satisfies failure criterion (global equilibrium)Rapid increase in nodal displacements

0.5

0.6

0.7

0.8

0.9

1.0

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

Str

eng

th R

edu

ctio

n F

acto

r

Maximum Total Displacement [m]

Importing LEM filesAssumptions when importing LEM files (Slide to RS2)Elastic Moduli set to 50000 kPa or 106 psf (soil)Poisson’s ratio set to 0.4

0.00

0.25

0.50

0.75

1.00

1.25

1.50

Fact

or o

f Saf

ety

SSRLE

Poisson’s ratio = 0.4(Varying E)

Poisson’s ratio = 0.2(Varying E) Dilation angle > 0

Importing LEM filesAssumptions when importing LEM files (Slide to RS2)Mohr‐Coulomb tensile strength = cohesionPerfectly plastic materials Peak strength parameters = Residual strength parameters

Initial stresses hydrostatic

1v

hK

Importing LEM filesAssumptions when importing LEM files (Slide to RS2)3000 elementsSix‐noded triangles Linear strain element or higher order elements

Uniform meshPins (not rollers) for boundaries

Hinges vs. RollersRollers:

Rollers

Hinges vs. RollersHinges

Hinges

Homogeneous slopeFE mesh (6‐noded triangular elements)

Homogeneous slopeContours of maximum shear strain

Critical SRF: 1.24

MaximumShear Strain

0.00e+0003.50e-0037.00e-0031.05e-0021.40e-0021.75e-0022.10e-0022.45e-0022.80e-0023.15e-0023.50e-0023.85e-0024.20e-0024.55e-0024.90e-0025.25e-0025.60e-0025.95e-0026.30e-0026.65e-0027.00e-002

LEM‐FS (spencer)=1.24

SSR‐FS=1.24

Homogeneous slopeContours of total displacement with deformed mesh

SSR‐FS=1.24

Multi‐Material Examples

SSR = 1.01LE = 1.01

SSR = 1.27LE = 1.30

Slopes with supports

LEM vs SSR Reinforcement Forces

T1

T2

T3

LEM reinforcement forcesLoad distribution along reinforcement is prescribedMagnitude of force included in LE calculations depends on location of bolt‐slip surface intersection

Piles for Slope Stabilization

Failure Surface

Stable Soil

Installed Piles

Concept Applied soil displacement from ground to slip surface representing the allowed soil displacement tolerance based on design criteria Depth and angle of slip surface intersection will determine the magnitude of axial and lateral displacement

Slip surface

“Design of micropiles for slope stabilization” by Dr. Erik Loehr, University of Missouri

Predicting pile resistance

Estimate profile of soil movement Resolve soil movement into axial and lateral components Predict axial and lateral resistance

Use “p‐y” analyses for lateral load transferUse “t‐z” analyses for axial load transfer

Select appropriate axial and lateral resistance (consider compatibility and serviceability)

Pile Model

Soil Lateral Resistance (p)

Sliding Surface

Pile BendingStiffness (EI)

Lateral Componentof moving soil

Stable Soil(no soil movement)

Transition (Sliding) Zone

δ lat

z

Input Profile of Lateral Soil Movement

p‐y analyses for lateral resistance

0

10

20

30

40

50

60

0.0 1.0 2.0 3.0 4.0 5.0

Dep

th (f

t)

Pile Deformation (cm)

0

10

20

30

40

50

60

‐80 ‐40 0 40 80Mobilized Shear Force (kN)

slide

rock

clay

0

10

20

30

40

50

60

‐1500 ‐750 0 750 1500

Mobilized Bending Mom. (kN-cm)

Lateral resistance

Cap BearingSoil Shear Resistance (t)

Sliding Surface

Pile AxialStiffness (EA)

Axial Componentof moving soil

Stable Soil(no soil movement)

Transition (Sliding) Zone

δ axial

z

Input Profile of Axial Soil Movement

Soil EndBearing (Q)

t‐z analyses for axial resistance

0

10

20

30

40

50

60

0 20 40 60 80 100 120 140 160D

epth

(m)

Mobilized Axial Load (kN)

clay

rock

Slide

Mobilization of axial resistance

Concept Applied uniform soil displacement Enter a Soil Displacement and a Sliding Depth Can be used for RSPile and for Slide

Axially Loaded Piles (Settlement, Axial Force)

Axially Loaded Piles (Settlement, Axial Force)

Sliding Depth

Axial Force at the Sliding Depth is the Axial Resistance Against Sliding

Laterally Loaded Piles (Deflection, Moment and Shear)

Laterally Loaded Piles (Deflection, Moment and Shear)

Shear Force at the Sliding Depth is the Lateral Resistance Against Sliding

Sliding Depth

Pile Resistance Against Sliding

Repeat process for a number of sliding depths to develop resistance functions

Max Allowable Displacement

Ultimate Displacement

Support Forces

0

983.017

0

1039.84

0

983.017

0

1039.84

SSR Analysis of Reinforced Slopes Important commonly cited advantage of SSR is ability to predict reinforcement loads at failureSolution depends on: Reinforcement stiffness, Post‐failure strength, and Failure mechanism

LEM vs SSR Reinforcement ForcesSSR reinforcement forces Final load distribution depends on: Strength parameters including post‐yield behaviour of soil and reinforcement Deformation characteristics (stress‐strain behaviour) of soil and reinforcement Applied loads

ExampleSlope reinforced with multiple geotextile layers

ResultsExample SSR factor of safety similar to LE results Zero post‐yield assumption gives factor of safety different from LE Elastic‐perfectly plastic post‐yield assumption gives factor of safety similar to LE

Results

Bishop circular failure surface

Zero Residual Strength Support Perfectly Plastic Support

ResultsFactor of Safety

Method Factor of Safety

LE‐Spencer (non‐circular) 1.65

SSR (elastic‐perfectly plastic) 1.65

SSR(zero post‐failure strength) 1.54

ResultsExample Total displacement contours (for deformed mesh)

SRF=1.00SRF=1.60SRF=1.62SRF=1.75

SRF=1.50

Results ‘Complex’ distribution of loads along geotextile layers

Reinforced Slope – Case I

Reduction Factor = 1.0

Reinforced Slope Critical SSR = 1.0


Reinforced Slope


Reinforced Slope – Case II


Reinforced Slope Critical SSR = 0.86


Reinforced Slope


Open‐Pit Slope Example

Open Pit Stability

Zone IIIHoek‐Brown material

UCS = 75 MPam = 0.3, s = 0.00016, a = 0.5

Zone IHoek‐Brown material

UCS = 70 MPam = 0.25, s = 0.00015, a =0.5

Zone IIMohr‐Coulomb material

c = 0 MPa, = 12o

Open Pit Stability

Open Pit StabilityShear strains at Strength Reduction Factor = 1.00

Open Pit StabilityCritical Strength Reduction Factor = 1.39

Lowest failure surface FS = 1.19

Open Pit StabilityCritical Strength Reduction Factor = 1.39

Failure surface form Spencer method

FS: 1.43

SSR Failure MechanismActive wedge

Passive wedge

Shear strength reduction in 3D slope stability using RS3

Three‐dimensional effect of Boundary Conditions

B

Compare the factor of safety as we increase B/H ratio12.5 m

H = 5 m7.5 m

5 m

30 m

5 m

Fixed xyz

Fixed xyz Restrained x

Restrained x

Three‐dimensional effect of Boundary Conditions

1.3

1.5

1.7

1.9

2.1

0 2 4 6 8 10 12

Factor of Safety

B/H Ratio

Zhang K. et al.RS3 2.0RS2B

H

Zhang K. et al. (2011). Simulation analysis on three‐dimensional slope failure under different conditions.

Three‐dimensional effect of Turning Corner10 m

9 m10 m

3 m

26 m

θ

10 m

Θ = 90 degTurning Corner Angle

Three‐dimensional effect of Turning Corner

θ = 180 degFS = 1.20

θ = 135 degFS = 1.24

θ = 90 degFS = 1.27

θ = 225 degFS = 1.21

θ = 270 degFS = 1.22

Concave

Convex

θ = 90 deg (Curve)FS = 1.29

Supports in SSR slope stability analysis

Pile Spacing, D’

Pile Spacing on Slope StabilityDiameter of pile, D = 0.8 m D’ = distance from one pile centre to the next pile centre

Pile Spacing, D’

Diameter of Pile, D = 0.8 m

Pile Spacing on Slope StabilityFactor of Safety is directly proportional to pile spacing

Pile Spacing Factor of Safety

No Piles 1.29

2D 1.46

3D 1.42

4D 1.38

6D 1.34

Total Slope Displacement Model

Embedded Length

Embedded Length of Pile on Slope StabilityEmbedded Length of pile is directly proportional to factor of safety

Embedded Length of Pile on Slope StabilityFactor of safety is directly proportional to embedded length

Embedded Length (m) Factor of SafetyNo support 1.18

1 1.30

2 1.53

10 1.57

Total Slope Displacement Model

Total Slope Displacement ModelSlice result

Staggered Pile Support System

6DIncrease distance of second pile row by 1D for each model

1D

6D

Total Slope Displacement ModelInfluence of Piles on Slope Displacement

Staggered Pile Support System Factor of Safety decreases slightly with increasing distance between staggered pile support rows For each pile row the spacing between piles is set at 6D

Distance Between Pile Rows Factor of SafetyOne Row of Piles 1.34

1D 1.472D 1.474D 1.466D 1.458D 1.42

For one row of piles at 2D, FS=1.55

3D Effects on Slope Stability Analysis using SSRRS3 Full 3D Analysis

3D Effect on Slope Stability Analysis using SSRRS3 2.0 is able to capture full 3D effects on slope stability analysis using SSR

Find the critical slip surface location and shape

3D Effect on Slope Stability Analysis using SSRRS3 2.0 is able to capture full 3D effects on slope stability analysis using SSR

Find the critical slip surface location and shape

It is logical to estimate the failure surface to be at the nose where the two surface connect

Maximum Shear Strain Contours

Two Critical Failure Surfaces on Either Side of the Embankment Corner

FS = 1.11

Total Displacement Contours

Maximum Displacement at Embankment Corner

FS = 1.11

Total Displacement ContoursRS3: FS = 1.11 Slide3D Spherical Search: FS = 1.09

In Slide3D, the spherical global failure surface is similar to the failure surface obtained in RS3 2.0

D Spherical Search: FS = 1.09

Total Displacement ContoursRS3: FS = 1.11

In Slide3D, the spherical global failure surface is similar to the failure surface obtained in RS3 2.0

Maximum Shear Strain Contours

Critical Slip Surface Assumed at Embankment Corner

FS = 1.29

Specify an SSR Region

Total Displacement Contours

Critical Slip Surface Assumed at Embankment Corner

FS = 1.29

Specify an SSR Region

Total Displacement ContoursRS3: FS = 1.29 Slide3D: FS = 1.33

If we analyze a region around the embankment corner, we obtain a higher factor of safety in both programs

2D VerificationFS = 0.99

In the 2D analysis, a slice along the nose is also not the critical slope section

FS = 1.22

Cut Sections

Concluding Remarks

Disadvantages of SSR Analysis

Computational speed/time can be an issueRequires more material input parameters deformation properties, elasto‐plastic stress‐strain behaviour

Requires more numerical modelling expertise than is commonly taught to geotechnical engineers Inexperience with method

Disadvantages of SSR Analysis

Definition of instability of solution Definition of convergence can be result of numerical instability (and not physical instability)

Sensitivity/probablistic analysis is time consuming

Advantages of SSR Analysis

Accounts for various material stress‐strain behavioursDoes not assume failure mechanism shape or location of failure surface

Provides information on deformations at working stress levelsReveals progress of failure development of failure mechanism


Able to capture slope failure driven by stressesProvides information on deformations, bending moments and axial loads of support elements at failureHighly reliable and robust – performs well under wide range of conditionsVery flexible – accommodates range of inputs used in limit‐equilibrium analysis

Thank you….

Using Shear Strength Reduction Method for 2D and 3D · PDF fileUsing Shear Strength Reduction...

Documents

Transcript of Using Shear Strength Reduction Method for 2D and 3D · PDF fileUsing Shear Strength Reduction...