Chapter 6Chapter 6

Slope Stability ConceptsSlope Stability Concepts* Only cover 6.1~6.10* Only cover 6.1~6.10

IntroductionIntroduction

• Limit equilibrium approach• Classical closed-form solutions• Popular method of slices• Derivation of several procedures• Computer programs

– Limit equilibrium– Finite element methods

Mode of Failure

Homework #2Homework #2Use OMS, Bishop and Use OMS, Bishop and JanbuJanbu methodmethod

30

If 0.1<D/L<0.15 a combined rotational and translational failure

Main items required to evaluate the Main items required to evaluate the stability of a slopestability of a slope

• Shear strength• Slope geometry• Pore pressures or seepage forces• Loadings and environmental conditions

Stability analysisStability analysis

• Develop a subsoil model of the slope and foundation soils

• Select appropriate shear strengths- Su or c, phi

• Slope geometry - given– Existing natural slope, embankment , cut slope

• Take care the change in effective stress caused by pore water pressures

6.3 factor of safety concepts6.3 factor of safety concepts

• F.S. is to account for uncertainty and thus guard against ignorance about the reliability of the items that enter the analysis

• F.S. constitutes an empirical tool whereby deformation stability performance are limited to tolerable amounts within economic restraints.

Planar failure surfaces

Mobilized strength

However, one must realize that However, one must realize that ……

• Mobilized strength, ratio of forces, or ratio of moments will not give identical FS values for c-phi soils.

• Typical slope designFS > 1.5 for long term conditionFS > 1.2 for heavy rain conditionFS > 1.1 for earthquake condition

6.4 Pore water pressures6.4 Pore water pressures

• Phreatic surface– open standpipe, most common

• Piezometric data – field piezometer, flow net, FEM, FDM solution

• Pore water pressure ratio, ru=u / sigma v– The ratio between u and the total vertical stress

• Piezometric surface– For back-analysis of failed slopes; different from a phretic

surface; a search for the critical surface is not possible.

• Constant pore water pressure– Specify to a particular soil layer

E.Q. 6.3Sloping straight-line phretic surface case

Convex phretic surface – overestimate the pore water pressure

The overestimation is small and will only affect a few slices within the sliding mass.

This conservatism is not expected to significantly affect the FOS.

Specified to a single, unique failure surface

Back-analysis for known p.w.p.

hw=hDifferent from fig.6.5

Example

6.4.4 Negative pore pressures6.4.4 Negative pore pressures

• Take the advantage of the apparent cohesive strength due to matrix suction in unsaturated zone.

• Increasing the total cohesion• Increase the shear strength of the soil• Not recommended because it affects only

the frictional component and may not generate reliable values of strength

6.5 Block analysis6.5 Block analysis

Sliding Sliding –– shear strength of the fill is greater that that of shear strength of the fill is greater that that of the foundation soilsthe foundation soils

6.6 Infinite slope analysis6.6 Infinite slope analysisSee Eq. 6-11 on page 344 for F.S.

See Eq. 6-15~6-17 on page 345 for F.S.

6.7 Planar surface analysis6.7 Planar surface analysisSee mobilized shear strength in Eq. 6-20 andthe relationship in Eq. 6.21

See Table 6.3 for try-and-error method for Fc=Fphi

6.8 Circular surface analysis6.8 Circular surface analysisPhi u=0 methodPhi u=0 method

Neglected

Example Example -- Phi u=0 method Phi u=0 method

Friction circle method Phi u > 0Friction circle method Phi u > 0See procedure on page. 352See procedure on page. 352

Not often used today.Not often used today.

Rf = R Sin(phi m)

Graphical solution exampleGraphical solution example

6.9 Method of slices6.9 Method of slices

General system of forcesGeneral system of forces

Statically indeterminate: 6nStatically indeterminate: 6n--2 > 4n 2 > 4n

At the midpoint of slice

Assumptions : to reduce the number of unknowns

• See page 356~357 for each limit equilibrium method

No good for noncircular surfaces (p.363)

For EQ.6-43

• 6.9.1 OMS• 6.9.2 Simplified Janbu Method• 6.9.3 Simplified Bishop Method• 6.9.4 GLE method – an extension of

Spencer’s procedures• 6.9.5 Janbu’s Generalized Procedures of

slices (GPS)

6.9.6 example 6.9.6 example

OMS method

Unreasonable thrust line

better

Erratic; not good

6.9.7 Control of negative normal 6.9.7 Control of negative normal effective stresseseffective stresses

• Sometime lead to numerical difficulties• Usually encountered in the cases of:

– High pore water pressures– Thin slices with a low self-weight and high

cohesion– Steep slice-base angles

• Curing: Modification of the excessive pwp• If it does not works, then …

3 options3 options

3 options3 options

6.9.8 Comparison of LEM6.9.8 Comparison of LEM

• difference in FS using different LEM• 15% ?• 30% ?• 5% ?

Example for Comparison of LEMExample for Comparison of LEMby by FredlundFredlund and and KrahnKrahn (1977)(1977)

Satisfy complete static equilibrium

6.10 Selection and use of limit 6.10 Selection and use of limit equilibrium methodsequilibrium methods6.10.1 Essential first four steps6.10.1 Essential first four steps

• Attempt to visual the probable shape of slip surface/surfaces.

• First-time slides? Or existing slip surfaces?• Strength parameters, back-analysis, lab

and field tests, p.w.p., groundwater conditions.

• Effective or total stress analysis?

6.10.2 selection of analysis method6.10.2 selection of analysis method

• LONG UNIFORM SLOPES – infinite slope EQ• Shallow, long planar failure surfaces – simplified

Janbu method• Planar failure surfaces – a block analysis, GLE

method• Arc-circle surface – stability charts, simplified

Bishop method• Arbitrary shape – a generalized procedure of slices;

prelim. Study - Janbu’s simplified procedures(w/ointerslice forces; accurate studies- Janbu’s GPS method, Spencer’s procedures, Morgenstern-Price method or Sarma’s method

Inherent Inherent weaknessweakness of the limit of the limit equilibrium methodsequilibrium methods

• See P.379~P.380• Incipient早期的 failure • Constant FOS• Neglect stress-strain relationship

6.10.3 Considerations6.10.3 Considerations

• See p.380• Crack, open joints, fill with water • Sensitivity analyses• Great care for curvy strength envelope• Progressive failure• Delayed failure

P.397