**6.5.1 Factor of Safety**

In conventional limit equilibrium methods, the factor of safety is defined as the ratio of resisting movements to the overturning movement. It can also be defined as the ratio of actual shear strength to the assumed value of reduced shear strength leading to failure. When the uncertainty and the consequences of failure are both small, it is acceptable to use small factor of safety, of the order of 1.3 or even smaller in some circumstances. However, when the uncertainties or the consequences of failure increase, larger factor of safety is necessary. Large uncertainties coupled with large consequences of failure represent an unacceptable condition irrespective of the calculated value of the factor of safety. Typical minimum acceptable value of factor of safety is about 1.3 for end of construction and multistage loading, 1.5 for normal long-term loading conditions, and 1.1 to 1.3 for rapid drawdown in cases where it represents an infrequent loading condition (ref). In cases where rapid drawdown represents a frequent loading condition, as in pumped storage projects, the factor of safety should be higher. The use of a factor of safety greater than 1.5 for static analyses is recommended. Fractured or jointed cemented slope could be analyzed using peak strength parameters which are derived from high quality samples of unfractured material (Hoek and Bray 1981).

The shear strength reduction technique has two advantages over the conventional approach. The critical failure surface is found automatically and it is not necessary to specify the shape of the failure surface. In general, the failure mode of slopes is more complex than simple circles or segmented surfaces. Further, numerical methods automatically satisfy the translational and the rotational equilibrium conditions, whereas, not all the limit equilibrium methods satisfy these conditions. To perform slope stability analysis with the shear strength technique, simulations are run for a series of increasing trial factor of safety, F, actual shear strength properties cohesion (c) and internal friction angle () are reduced for each trial using equations (1) and (2). If multiple materials are present, reductions are made simultaneously for all materials. The trial factor of safety is gradually increased until the slope fails. At failure, the safety factor equals the trial safety factor.

….(1)

…..(2)