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**SLOPE STABILITY ANALYSIS**

Tuncer B. Edil University of Wisconsin-Madison

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**LECTURE OUTLINE Common Features of Slope Stability Analysis Methods**

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

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**COMMON FEATURES OF SLOPE STABILITY ANALYSIS 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

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**INFINITE 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

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INFINITE SLOPE hp d sat c N T hp W’

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**INFINITE 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.

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WATER 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

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**EQUIVALENT METHODS FOR 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

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BOUNDARY WATER FORCE

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

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**FINITE SLOPES: PLANE FAILURE SURFACE**

Translational Block Slides along single plane of weakness or geological interface F = c’L + (W cos uL) tan’ / W sin + Fw

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BLOCK SLIDES

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BLOCK SLIDES

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**FINITE SLOPES: CIRCULAR FAILURE 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

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**ORDINARY METHOD OF SLICES**

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

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**SIDE FORCES IN ORDINARY METHOD OF SLICES**

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**BISHOP’S SIMPLIFIED METHOD**

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

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CHART FOR m

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**SIDE FORCES IN BISHOP’S METHOD**

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SPENCER’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

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**FINITE SLOPES: NONCIRCULAR FAILURE SURFACE**

Wedge Method Janbu’s Simplified Method Morgenstern-Price Method

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WEDGE 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)

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WEDGE METHOD

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

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**JANBU’S SIMPLIFIED METHOD**

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)

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**MORGENSTERN-PRICE METHOD**

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

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REFERENCES 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.

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Slide La Conchita, California-a small seaside community along Highway 101 north of Santa Barbara. This landslide and debris flow occurred in the spring of 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.

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