SLOPE STABILITY SLOPE STABILITY ANALYSISANALYSIS

Tuncer B. Edil

University of Wisconsin-Madison

LECTURE OUTLINELECTURE OUTLINE

Common Features of Slope Stability Analysis Methods

Water Forces on Soil Infinite Slope Analysis Finite Slopes: Plane, Circular and

Noncircular Failure Surfaces

COMMON FEATURES OF COMMON FEATURES OF SLOPE STABILITY SLOPE STABILITY

ANALYSIS METHODSANALYSIS METHODS Safety Factor: F = S/Sm where S = shear

strength and Sm = mobilized shear resistance. F = 1: failure, F > 1: safety

Shape and location of failure is not known a priori but assumed (trial and error to find minimum F)

Static equilibrium (equilibrium of forces and moments on a sliding mass)

Two-dimensional analysis

INFINITE SLOPE ANALYSISINFINITE SLOPE ANALYSIS

Translational failures along a single plane failure surface parallel to slope surface

The ratio of depth to failure surface to length of failure zone is relatively small (<10%)

Applies to surface raveling in granular materials or slab slides in cohesive materials

Equilibrium of forces on a slice of the sliding mass along the failure surface is considered

INFINITE SLOPEINFINITE SLOPE

hp

d

sat

c

N

T

W’

hp

INFINITE SLOPE ANALYSISINFINITE SLOPE ANALYSIS F = f(c’, ’, , , d, u) F = (c’/ d) seccosec + (tan’/tan)(1-ru sec2)

where ru = u/d (different ru for seepage parallel to slope face,

seepage emerging, seepage downward, etc)

For Granular Soil: F = (tan’/tan)(1-ru sec2) Dry Granular Soil (ru = 0): F = (tan’/tan)

For Cohesive Soil: F decreases with increasing depth to failure plane; if c is sufficiently large, dc for F = 1 may be large and infinite slope failure may not apply.

WATER FORCES ON SOILWATER FORCES ON SOIL

Water fills voids and increase weight which increases driving forces

Water also exerts pore pressures which decrease effective stress and therefore strength

There are mathematically two equivalent ways of taking water forces into account in stability analyses

EQUIVALENT METHODS EQUIVALENT METHODS FOR WATER FORCESFOR WATER FORCES

1. Boundary water force + total unit weight u = hpw; sat consider soil element (particles and water filled pores) as single solid mass

2. Seepage force + submerged unit weight Fs = i wV; ’ consider soil element as particle skeleton with water external to it

BOUNDARY WATER FORCEBOUNDARY WATER FORCE

SEEPAGE FORCESEEPAGE FORCE

Hydraulic Gradient, i = sin ; Seepage Force,Fs = i w VolumeEffective Weight, W’ = ’ Volume; ’ = - w

FINITE SLOPES: FINITE SLOPES: PLANE PLANE FAILURE SURFACEFAILURE SURFACE

Translational Block Slides along single plane of weakness or geological interface

F = c’L + (W cos uL) tan’ / W sin + Fw

BLOCK SLIDESBLOCK SLIDES

BLOCK SLIDESBLOCK SLIDES

FINITE SLOPES: FINITE SLOPES: CIRCULAR CIRCULAR FAILURE SURFACEFAILURE SURFACE

Rotational Slides - Method of Slices Applies to slopes containing cohesive soils Ordinary Method of Slices (Fellenius’ Method) Bishop’s Simplified Method Spenser’s Method

ORDINARY METHOD OF ORDINARY METHOD OF SLICESSLICES

Assumes that resultant of side forces on each slice are collinear and act parallel to failure surface and therefore cancel each other

F = [cn ln + (Wn cosn - un ln) tann] / Wn sinn

Undrained analysis: F = [cn ln] / Wn sinn

SIDE FORCES IN ORDINARY SIDE FORCES IN ORDINARY METHOD OF SLICESMETHOD OF SLICES

BISHOP’S SIMPLIFIED BISHOP’S SIMPLIFIED METHODMETHOD

Assumes that resultant of side forces on each slice act in horizontal direction and therefore vertical side force components cancel each other

F = [cn bn + (Wn - un bn) tann](1/m) / Wn sinn

m = cosn + (sinn tann)/F

Undrained analysis: F = [cn ln] / Wn sinn

CHART FOR mCHART FOR m

SIDE FORCES IN SIDE FORCES IN BISHOP’S METHODBISHOP’S METHOD

SPENCER’S METHODSPENCER’S METHOD

Assumes that the point of application of resultant of side forces on each slice is at mid-height of each slice but no assumption is made regarding inclination of resultants; inclination is determined as part of the solution

This method is more exact than Bishop’s

FINITE SLOPES: FINITE SLOPES: NONCIRCULAR NONCIRCULAR FAILURE SURFACEFAILURE SURFACE

Wedge Method Janbu’s Simplified Method Morgenstern-Price Method

WEDGE METHODWEDGE METHOD

Failure surface consists of two or more planes and applicable to slope containing several planes of interfaces and weak layers

Force equilibrium is satisfied Assumes that resultant of side forces on

each slice either acts horizontally or at varying angles from horizontal (typically up to 15o)

WEDGE METHODWEDGE METHOD

Layer B

Layer A4

3

21

m

WEDGE ANALYSIS

Equilibrium of Forces in each slice is considered to adjust the inter-slice forces and balance them resulting in a correct solution.

JANBU’S SIMPLIFIED JANBU’S SIMPLIFIED METHODMETHOD

A method of slices applicable to circular and noncircular failure surfaces

F = fo [cn bn + (Wn - un bn) tann](1/ cosnm)} / Wn tann

fo is a correction factor that varies with depth to length ratio of sliding mass and type of soil (c, or c = 0)

Factor, f o

Ratio, d/L

c, soil

c = 0

L

d

MORGENSTERN-PRICE MORGENSTERN-PRICE METHODMETHOD

No assumption is made regarding inclination or point of application of resultants and these are determined as part of the solution

Requires computers for solving the basic equation

Exact but not practical

REFERENCESREFERENCES

J.M. Duncan, A.L. Buchignani and M. De Wet (1987), An Engineering Manual for Slope Stability Studies, Virginia Tech Department of Civil Engineering, Blacksburg, Virginia.

L.W. Abramson, T.S. Lee, S. Sharma and G.M. Boyce (1996), Slope Stability and Stabilization Methods, Wiley, N.Y.

Das, B. M., Principles of Geotechnical Engineering, 3rd Ed., PWS Publishing Co., Boston, MA, 1994.

Soil Mechanics Design Manual, NAVFAC DM-7.1, Department of the Navy, 1982.

Slide 21..- La Conchita, California-a small seaside community along Highway 101 north of Santa Barbara. This landslide and debris flow occurred in the spring of 1995. Many people were evacuated because of the slide and the houses nearest the slide were completely destroyed. Fortunately, no one was killed or injured. Photograph by R.L. Schuster, U.S. Geological Survey.