1.0  Factor of Safety and Probability of Failure

In the traditional allowable stress design (ASD) approach (AASHTO, 2002) safety is achieved with a single factor of safety (FS) applied to the resistance to obtain an allowable stress (or load).  Since the FS is an all-inclusive entity, it is difficult to identify the portion of the FS value that applies to the structural or geotechnical design.  For example, in the design of drilled shafts a FS=2.5 is commonly used.  In this case, is the FS equally distributed on the structural and geotechnical designs as 1.25 in an additive manner or is it distributed in some other combination?  It is difficult to answer this question with certainty.   This uncertainty occurs because each component (structural and geotechnical) of the substructure design has different load and resistance statistics, i.e., mean value, coefficient of variation, and distribution, e.g., normal or non-normal.  Generally, structural loads are normally distributed while geotechnical resistances are log-normally distributed.

One has to be careful in recognizing that some loads in substructure design may be induced by the geomaterials themselves, e.g., downdrag, which is added to structural loads.  Downdrag load, depending on the method used to determine it, may be distributed in a non-normal pattern resulting in an overall non-normal distribution of the total load on the substructure element.  Due to these considerations, it is difficult to quantify the probability of failure, P_f, for a substructure element in the ASD framework.  The AASHTO-LRFD provides a solution to this problem by explicitly identifying a reliability index, β, which in essence is an alternative quantification of the probability of failure, P_f.

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