Constitutive Model of Soil Based on a Dynamical Systems Approach

A soil when sheared ultimately reaches a steady-state condition at which it deforms at a constant shear stress, effective normal stress, and void ratio. Various systems in nature dynamically evolve similarly from some initial condition, to a final steady-state condition. Such systems have been studied using dynamical systems theory. This technical note uses this theory to model monotonic shear of soil as a dynamical system. The principle proposed is simple—the rates of change of the shear stress, effective normal stress, and void ratio are proportional to the applied values of the shear and effective normal stress with the proportionality values decaying with strain until ultimately these proportionality values become zero at the steady-state condition. It provides a well-formed qualitative principle that fits closely the stress-strain-void ratio curves of undrained shear tests on uncemented, resedimented clays at various over consolidated ratios (OCRs), and drained shear tests on sands and silts at various relative densities, for various stress paths including compression, extension from standard triaxial, and true-triaxial tests. For the undrained shear of resedimented clay, these proportionalities and their decay rates vary smoothly with OCR. For drained shear of sand and silt, the model parameters show orderly variation with relative density. Its value lies in that a well-formed qualitative principle derived from the steady-state condition provides an alternate approach to current complex elastoplastic models based on critical state theory.