The simulation and discretisation of random fields for probabilistic finite element analysis of soils using meshes of arbitrary triangular elements

This paper presents a new methodology to discretise random fields for reliability assessment by the Random Finite Element Method. The methodology maps a random field to an arbitrary triangular finite element mesh by local averaging. Derivations for the variance reduction and covariance between local averages of triangular areas using numeric integration are presented. The new methodology is compared against a published reliability assessment of a drained slope. The results matched expectations that not accounting for spatial variability will, in the case analysed, significantly underestimate reliability. A method to generate random fields using a form of Cholesky decomposition appropriate even for singular covariance matrices is presented and analysed. Finally, the derivations for the discretisation of random fields onto triangular meshes are presented for three dimensional tetrahedral elements.