Principles and the Uncertainty Principles of the Probabilistic Strength of Materials and Their Applications to Seismology

Abstract

The principles of Fracture-Statistics Mechanics are presented using two functional equations, namely one for the cumulative probability of fracture, and another for the local probability of fracture. These two functional equations are independent and they become compatible only when the volume considered is very small. The determination of the specific-risk function can be made by means of integral equations, without having to specify the analytical expression for this function. This two principles give two principles of uncertainty. Some applications to seismology are given where it is shown that the possibilities of predicting the instant of occurrence and the magnitude of an earthquake are null. Only the probability of occurrence of an earthquake of a given magnitude in a given place can be known. The instant of occurrence, the magnitude and the location are aleatory.