GLE/CEE 330: Soil Mechanics Infinite Slope Analysis Geological Engineering University of Wisconsin-Madison

Learning Objectives Discuss when infinite slope analysis may be appropriate Learn basic analysis approach Describe example problems for total stress analysis (undrained) and effective stress analysis (drained)

Common Features of Slope Analysis Methods Safety factor analysis: available shear strength of soil equilibrium shear stress Shape and location of failure surface is not known a priori but assumed (trial and error to find minimum FS) Limit equilibrium analysis (static equilibrium) Two-dimensional analysis

Infinite Slope Analysis Translational failure along single failure plane with failure surface parallel to slope surface. Ground water table parallel to slope surface Ratio of depth to failure surface to length of failure zone is small (<10%) Applies to surface raveling in granular materials or slab slides in cohesive materials (Translational Slides) Assumed Failure Surface

= angle of failure (and slope) surface D = depth of failure surface zw = height of GWT above failure surface W/b = Weight of element (per unit width) N/b = Normal force on failure surface T/b = Shear force on failure surface SL/b and EL/b = Shear and normal forces on left SR/b and ER/b = Shear and normal forces on right (same as left) Can also account for seepage force

Effective Stress Analysis (ESA) For dry granular soil (zw = 0, c’ = 0): For saturated granular soil (zw = D, c’ = 0): Total Stress Analysis (TSA) FS decreases with depth

Example 1

Example 2 Water has two effects: 1) increases driving forces because unit weight increases 2) decreases resisting forces because effective stress decreases