Reduction of Numerical Model in Some Geotechnical Problems

The concept of equivalence of the realistic, initial reference model and the simplified, reduced model is proposed. In reduced models, the action of the soil on the structure is replaced by the action of a layer with prescribed properties, defined by a set of parameters. The main difficulty here is to find the parameter values required by the simplified theory. The subject of this work is to find the dependence of the parameters of the reduced model on the parameters of the full model, including realistic soil behavior, in order to ensure the equivalence of both models. We show the potential of the method by presenting two examples: Winkler and Pasternak's model of a plate on the ground. We assume that both models are equivalent if they give identical results (displacements) at a finite number of observation points. An artificial neural network (ANN) is built in order to approximate and record the dependence of the parameters of the reduced model (at the network output) from the parameters of the full model (given at the network input). The complex network acts as a formula that assigns the parameters of the reduced model to a realistic description of the soil structure that is used for finite element method (FEM) modeling. The formalism we propose is quite general and can be applied to many engineering problems. The presented procedure is entirely numerical; it allows to calculate the parameters of the reduced model without resorting to symbolic calculations or additional theoretical considerations.