Modified soils as Functionally Graded Materials: numerical modelling with finite element method and artificial neural networks

Various modifications of mechanical properties of soils are widely used in engineering. In this paper we limit our consideration to cohesiveless soils, and focus our attention on the common mechanism of injecting a liquid phase that fills the pores as reinforcing medium. After some time, needed for the solidification of the filling liquid, the hydro-mechanical properties of the soil change. In this way, the resulting medium can be considered as a composite with a solidified matrix and inclusions that reflect the granular composition of the initial granular soil. However, during the injection of a reinforcing medium, the initial granular structure of the soil changes. The properties of the modified soil (especially when it is modified in situ) vary gradually from those of a perfectly bounded composite to those of an intact soil. This transformation shows some regularities due to the technique of injection or mixing. The border of the domain of the modified soil is never sharp and an external layer is always developing. Therefore, the resulting composite can be considered as a functionally graded material. This gradation is not intentional, it results from the modification technique and it plays an important role on the bearing capacity of the composite. In this paper both hydrofobisation and reinforcing with cementitious materials are considered as a possible field of application of the proposed numerical approach. The main purpose of this work is to predict the resulting hydro-mechanical properties of soils as a function of the distance from the source of injection. This aspect is very important, since existing estimations of the injection-pails diameter or of the size of the hydrofobised area are mostly phenomenological. In our approach, the calculated hydro-mechanical properties of the modified soil are expressed in terms of the known properties of the initial materials. We present our numerical model of the static, non-linear effective behaviour of the modified soil considered as a Functionally Graded Material (FGM). As it is known, the geometry and material composition of a “representative volume” (suitably defined for the case of FGM) are functions of a global variable x; therefore effective material coefficients defined for some small neighbourhood surrounding x are also functions of the global variable. In solving the boundary value problem (BVP) formulated for FGM, the spatial variation of its macro properties must be taken into consideration. In our approach, when the geometry of the microstructure is complex, Finite Element Method (FEM) and Artificial Neural Networks (ANN) are jointly applied to describe the dependence of the effective material parameters on the physical characteristics of the micro components. We use ANNs to approximate the functional dependence of the composite properties on its microstructure. For different representative volumes we compute the effective material properties by using virtual testing of composites as in [1] and [2].