Non-linear elastic formulation for clays

Abstract

Clays, as one of the most important materials in soil mechanics, have been widely investigated and experimental research has shown that clays are diffi cult materials to model. For instance, they have a highly non-linear response even at small deformations which makes the determination of a yielding point a diffi cult task. Another aspect to be considered when modelling clays is that experimental work has shown that the clays’ stiffness is pressure dependent, which is of great importance when modelling soil deformations around tunnels. Such behaviour investigations led to the formulation of many models ranging from simple to complex. While simple models are preferred due to the simple approach and few parameters needed, they cannot represent those different characteristics of clay behaviour. On the other hand, more sophisticated models (normally including multi-surfaces) tend to have many parameters. In some cases these models violate the laws of nature as some of them are semi-empirical, relying on graphical methods and different ad hoc assumptions. Alternatively, thermodynamics based models are able to model successfully different aspects of granular materials, but many models were developed just for sands. Within this framework, the formulation of a pair of potentials has to be postulated: the free energy and the dissipation function, the fi rst of which encapsulates the elastic response of the material. Although the elastic regime is rather complicated to determine for clays, developing a correct non-linear formulation allows to model the stiffness dependency on the effective stresses. This research aims to present a new model for clays which will be able to model both non-linear elastic, plastic response and which would omit the need to defi ne a yield surface. This could lead to a great simplifi cation for both laboratory and computational analysis. In this paper the focus will be given on formulating the stress-dependency of the elastic stiffness.