Minerals Beneficiation - Rock Mechanics - Application of Probability Theory to Factor of Safety

The theory of probability with respect to the failure of structures is discussed. It is shown that the probability of safety, probability of failure, and factor of safety are directly related to each other and that as standard deviation approaches zero, the probability curves approach a unit step function which can be interpreted as the conventional factor of safety. The factor of safety is numerically the ratio of the load to the strength of the material at a particular point or plane in an engineering structure. Mathematically, it can be illustrated as a unit step function undefined at the point where the factor of safety is one (Fig. 1). The uncertainty of variation of soil and rock strengths require factors of safety much higher than those used in other engineering structures. The factors of safety used are generally determined from past experiences with similar structures. However, the factors thus determined do not have any theoretical meaning or do not indicate any relationship to actual safety.' It seems, therefore, logical to develop a system with a sound theoretical basis to obtain a more suitable factor of safety for structures. An application of elementary theory of probability indicates that it is possible to relate this number to theoretical and practical engineering facts.