The modelling of layered rocks using a numerical homogenisation technique and an artificial neural network

A method of creating a constitutive model of layered rocks based on an artificial neural network (ANN) is reported in this work. The ANN gives an implicit constitutive function ∑ⁿ⁺¹=F(∑ⁿ,ΔE ), relating the new state of homogenized stresses ∑ⁿ⁺¹ with the old state ∑ⁿ and with the increment of homogenized strains ΔE. The first step is to repeatedly run a strain- controlled homogenisation on an uni-dimensional finite element model of a periodic cell with elastic-plastic models (Drucker-Prager) of the components. Paths are created in (∑, E) space, from which, a set of patterns is formed to train the ANN. A description of how to prepare this data and a discussion on ANN training issues are presented. Finally, the procedure based on trained ANN is put into a finite-element code (ZSoil.PC) as a user-delivered constitutive function. The approach is verified by comparing the results of the developed model basing on ANN with a direct (single-scale) analysis, which showed acceptable accuracy.