A nonlinear elastic-viscoplastic constitutive relationship for earth materials

Abstract

A constructive equation is developed for earth materials which allows for cohesion and friction between the particles and presumes isothermal behavior. The theory is restricted to deformation for which displacement gradients are small but where physical nonlinearity is permitted. The earth medium under consideration is treated as an isotropic and homogeneous continuum with average phenomenological properties. The constitutive relationship takes into account nonlinear pressure-volume relation, nonlinear shear resistance-shear deformation relaxation, effect of pressure on shear resistance, effect of deformation-rate on shear resistance, plastic failure and fracture. The above mentioned physical nonlinearities are incorporated into a mathematical model and then translated to a general tensorial relationship satisfying the invariance principles of the theory of constitutive equations and the requirements of isotropy. Some simple states of deformation are examined and are shown to agree with the actual behavior of various soils.