Executive Summary : | Rate-dependent mechanical response of sand, subjected to loading of medium to high strain rate range, is of interest for several geotechnical applications, e.g. explosions and air blasts, mine blasts, projectile penetration, dynamic compaction, installation of deep-sea anchors, pile driving and rapid load testing of piles etc. Rate effect in sand is generally manifested by an apparent enhancement of soil strength and stiffness, and noticed to vary significantly based on the initial density state of the sand, applied confining pressure, considered strain rate range, drainage condition and sand morphology. In order to effectively model such boundary value problems pertaining to geotechnical engineering and involving loading of medium to high strain rate range, a visco-plastic constitutive response is often employed to mimic the rate-dependent mechanical response of sand. In this regard, Perzyna type overstress formulation is often employed, where the flow rule has been modified explicitly by adopting a power law type relation that governs the evolution of incremental visco-plastic strain. Though the overstress type visco-plastic constitutive framework was originally proposed for metals with possibility of only visco-plastic shear deformation, it has often been adopted in the past to predict the rate-dependent behavior of sand. Such overstress models are primarily based on the critical state concept and can be governed by both volumetric and shear strain hardening. However, direct adaptation of overstress type formulation often results to poor prediction of volumetric response of sand under varying strain rate due to lack of separate control over the volumetric and shear strain-rate hardening part. On contrary to the overstress formulation, consistency type visco-plastic formulation can be seen as an extension of the classical plasticity theory with the concept of a single yield surface. In case of metals, the evolution of such yield surface is governed by both accumulated visco-plastic shear strain and its rate. However, the consistency formulation is generalized enough and has the potential to incorporate more than one internal hardening variable, i.e. both visco-plastic shear and volumetric strains, and their rates in an uncoupled form. Inclusion of multiple internal variables within the constitutive formulation in an uncoupled form becomes imperative for capturing the rate-dependent behaviour of sand addressing influence of initial density and confinement level. The proposed study envisions to devise a generalized mathematical framework for predicting the rate-dependent shearing response of sand following the consistency type visco-plastic formulation. A stress update algorithm will be proposed for numerical implementation of the constitutive model and in this regard, a MATLAB code will be developed. The developed code will be used for carrying out validation of the model against existing experimental data from literature. |