Various Viscosity Types of Geomaterials in Shear and Their Mathematical Expression

Abstract

ABSTRACT The viscous properties, or loading-rate effects on the stress-strain behaviour, of unbound and bound soils, in particular unbound granular materials, are summarised. The viscous properties were evaluated by stepwise changing the strain rate, e ˙ , and performing sustained loading during otherwise monotonic loading (ML) at a constant e ˙ and also by performing ML tests at different constant values of e ˙ . Four basic viscosity types, Isotach, Combined, TESRA (or Viscous Evanescent) and Positive & Negative (P & N), which were recently found are described. The Isotach type is the most classical one and, in the case of ML, the current viscous stress component is a function of instantaneous irreversible strain, eir and its rate, e ˙ ir . So, the strength during ML at a constant e ˙ increases with e ˙ . With the other three types, the viscous stress increment that has developed at a given moment, denoted as Δσv, decays with eir towards different residual values during subsequent ML. With the TESRAtype, Δσv decays eventually totally and the strength during ML at constant e ˙ is essentially independent of e ˙ . With the Combined type, Δσv decays with eir like the TESRA type, but it does not decay totally. So, the strength during ML at constant e ˙ increases with e ˙ like the Isotach type. With the P & N type, found latest, a positive value of Δσv decays towards a negative value. So, the strength during ML at constant e ˙ decreases with an increase in e ˙ . The viscosity type tends to change with eir: e.g., from Isotach toward TESRA and from TESRA toward P & N. A general mathematical expression that can describe these four viscosity types and transitions among them is proposed. Numerical simulations of typical drained triaxial compression tests of geomaterials based on a non-linear three-component model incorporating the general expression of the viscous stress are presented. The viscosity type is controlled by at least, grading characteristics and particle shape.