Presentation on theme: "SLOPE STABILITY ANALYSIS"— Presentation transcript:
1SLOPE STABILITY ANALYSIS Tuncer B. EdilUniversity of Wisconsin-Madison
2LECTURE OUTLINE Common Features of Slope Stability Analysis Methods Water Forces on SoilInfinite Slope AnalysisFinite Slopes: Plane, Circular and Noncircular Failure Surfaces
3COMMON 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: safetyShape 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
4INFINITE SLOPE ANALYSIS Translational failures along a single plane failure surface parallel to slope surfaceThe 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 materialsEquilibrium of forces on a slice of the sliding mass along the failure surface is considered
6INFINITE 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.
7WATER FORCES ON SOILWater fills voids and increase weight which increases driving forcesWater also exerts pore pressures which decrease effective stress and therefore strengthThere are mathematically two equivalent ways of taking water forces into account in stability analyses
8EQUIVALENT 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 mass2. Seepage force + submerged unit weight Fs = i wV; ’ consider soil element as particle skeleton with water external to it
16ORDINARY METHOD OF SLICES Assumes that resultant of side forces on each slice are collinear and act parallel to failure surface and therefore cancel each otherF = [cn ln + (Wn cosn - un ln) tann] / Wn sinnUndrained analysis: F = [cn ln] / Wn sinn
18BISHOP’S SIMPLIFIED METHOD Assumes that resultant of side forces on each slice act in horizontal direction and therefore vertical side force components cancel each otherF = [cn bn + (Wn - un bn) tann](1/m) / Wn sinnm = cosn + (sinn tann)/FUndrained analysis: F = [cn ln] / Wn sinn
21SPENCER’S METHODAssumes 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 solutionThis method is more exact than Bishop’s
23WEDGE METHODFailure surface consists of two or more planes and applicable to slope containing several planes of interfaces and weak layersForce equilibrium is satisfiedAssumes that resultant of side forces on each slice either acts horizontally or at varying angles from horizontal (typically up to 15o)
25WEDGE ANALYSISEquilibrium of Forces in each slice is considered to adjust the inter-slice forces and balance them resulting in a correct solution.
26JANBU’S SIMPLIFIED METHOD A method of slices applicable to circular and noncircular failure surfacesF = fo [cn bn + (Wn - un bn) tann](1/ cosnm)} / Wn tannfo is a correction factor that varies with depth to length ratio of sliding mass and type of soil (c, or c = 0)
28MORGENSTERN-PRICE METHOD No assumption is made regarding inclination or point of application of resultants and these are determined as part of the solutionRequires computers for solving the basic equationExact but not practical
29REFERENCESJ.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.
30Slide 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.