A constitutive model for size dependent behaviour of soils

Localisation of deformation in the form of shear bands during material failure leads to the breakdown of the assumption of homogenous deformation, due to considerable variation of strain across the shear band. Classical continuum models based on the assumption of homogeneous deformation is therefore invalid in such cases. In addition, these models also ignore the effects of inclination, thickness and evolution of shear band in constitutive equations. In this sense, traditional continuum models are unable to capture correctly localised failure of soils. On the other hand, existing enrichment approaches such as non-local and gradient dependent regularizations and the discretization-based enhancements, although having reached a mature state of developments, are usually mixed with the numerical methods for solving boundary value problems. As a consequence, the analysis of localised failure and size effects always have to depend on the analysis of boundary value problems. These existing approaches are also complicated to be implemented in a numerical code, and/or computationally expensive for wide applications in engineering design. The research in this paper follows a new line of developments in which a length scale is embedded directly in the constitutive structure once localisation takes place, and hence will naturally describe the localisation induced size effects at the material level. The formulation is established and preliminary results illustrated to demonstrate the promising features of the new approach.