Factor of Safety
A “factor of safety” index can be defined for any relevant problem parameter by taking the ratio of the calculated parameter value under given conditions to the critical value of the parameter at which the onset of an unacceptable outcome manifests itself. A relevant problem parameter could be a dimensionless group that governs the problem at hand (e.g., a stability number). Examples of (dimensional) parameters for slope stability include slope height, water level, applied load, and strength property.
Unacceptable outcome relates to “safety” (and is usually taken as shear failure), but other possibilities, such as displacement above a given threshold, convergence beyond an acceptable level (such as in a tunnel excavation), toppling failure, slope raveling (cyclic freezing/thawing, weathering), etc. can also be considered.
By convention, a factor of safety index larger than one indicates stable conditions. Thus, factor of safety index is taken as the actual over the critical parameter value if the parameter value above critical is acceptable (e.g., material cohesion), and as the inverse of this ratio otherwise (e.g., slope height). Note that, with the exception of simple cases, the calculated factor of safety index will not in general be linearly related to the selected problem parameter for which it is defined. Also, different measures will give different values of factor of safety for the same problem. Factor of safety index is most valuable when used on a comparative basis, in analyses using the same index definition (e.g., use of the index may produce the following statement: this slope with wider benches has a higher index than that with higher benches).
The effort involved in computing the factor of safety index (once the definition is established) consists of identifying actual as well as critical parameter values. In the most general case, the actual parameter value is evaluated by direct resolution of field and constitutive equations governing the problem, and this often is done using a numerical method. On the other hand, an inverse boundary value problem needs to be solved to estimate the critical value of the parameter. In principle, this can be achieved using a trial-and-error technique, whereby numerical simulations are performed for a range of parameter values until the critical value is found. We refer to this general approach as the “parameter reduction technique.” Any appropriate geo-mechanical software (e.g., finite difference, finite element, and distinct element method) can be used to perform this task for problems involving various levels of complexity (e.g., geometry, material constitutive law, discrete fracture network, slope reinforcement, support systems, mechanical structures, etc.).
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