Chapter 7 Slope Stability 7.1 General For the analysis of the stability of slopes of arbitrary shape and composition various approximate methods have been developed. Most of these assume a circular slip surface. Limiting equilibrium methods are normally used in the analysis of slope stability in which it is considered that failure is on the point of occurring along an assumed or a known failure surface. In the traditional approach the shear strength required to maintain a condition of limiting equilibrium is compared with the available shear strength of the soil, giving the average (lumped) factor of safety along the failure surface. In slope stability analysis we determine the Factor of Safety as a ratio of resisting forces to driving forces F s = Resisting / Driving Theoretically, any slope with a Factor of Safety less than one will fail and any slope with a factor of safety greater than one will not. Design focuses on the soil parameters and geometry that will provide the maximum factor of safety. Sometimes, the analysis of an existing slope will be what is called a parametric study that is establishing a factor of safety and performing an analysis that back calculates the strength parameters. The engineer will then determine his/her confidence level as to whether or not the soil has that strength through experience, lab, and/or field data. W T T N Stable condition T>T Inner friction angle Stability factor 7.2 Sandy Soil Slope 7.3 Clay Soil Slope Fellenius, Taylor, Bishop, Morgenstern-Price, Spencer, Janbu, among others N f W R O B C A (1) Sweden Arc Method For equilibrium the shear strength which must be mobilized along the failure surface is expressed as Example 1 A slope is excavated to a depth of 8m in a deep layer of saturated clay of unit weight 19 kN/m3: the relevant shear strength parameters are cu=65 kN/m2 and U=0. Determine the factor of safety for the trial failure surface specified in Figure 9.4. Check that no loss of overall stability will occur according to the limit state approach. Solution: a b c d i ii O C R A B H (2) Slice Arc Method For any slice the inclination of the base to the horizontal is and the height, measured on the centreline, is h. The analysis is based on the use of a lumped factor of safety (F ), defined as the ratio of the available shear strength (f ) to the shear strength (m) which must be mobilized to maintain a condition of limiting equilibrium. c d b a lili XiXi PiPi X i+1 P i+1 NiNi TiTi WiWi Example 2 H=6m =55 =18.6kN/m 3 =12 c =16.7kPa Solution h i b i sin i cos i W i O O O 1 O 2 O 3 (m) (m) W i kN/m 1(o)1(o) W i sin i W i cos i (3) Taylor Method 7.4 Discussion Slopes in overconsolidated fissured clays require special consideration. A number of cases are on record in which failures in this type of clay have occurred long after dissipation of excess pore water pressure had been completed. Analysis of these failures showed that the average shear strength at failure was well below the peak value.