Probabilistic criterion of failure for cohesionless frictional materials

On the assumption that the internal friction coefficient is a random variable, a probabilistic approach is followed to explain the role of the intermediate principal stress on failure in cohesionless granular materials. A probabilistic failure criterion has been developed o the basis of Coulomb\u2019s assumption concerning the limiting state at any plane of potential sliding in conjunction with an extension of the weakest link concept. The corresponding conical surfaces of expected strengths in the principal stress space have the cross sections on the deviatoric planes and their shape has been found to depend on the statistical dispersion