Comparative study of numerical formulations developed for constitutive modeling of static and dynamic behavior of saturated sands: A newly proposed hardening law

Abstract

 Constitutive modeling of static behaviors of loose and dense sands  Constitutive modeling of cyclic behaviors of loose and dense sands  Modeling of cyclic behavior with the proposed hardening lawIn this study, both static and dynamic constitutive behaviors of saturated sands are modeled using the Generalized Plasticity Theory. Analyses performed using a yield surface and a potential surface in the model are compared with the results obtained without any surface definition. The need for including such mathematical functions, which makes a distinction between the elastic and plastic behavior of sands is questioned here. In this paper, firstly the unit vectors for loading and plastic flow directions are defined and the static and dynamic response of sands are calculated. Then, yield and potential surfaces are derived by integrating these unit vectors and the constitutive relations are presented for the two formulations in terms of a number of triaxial test simulations on saturated loose sands (see Figure A). In the second part of the study, a new hardening law is proposed within the generalized plasticity formulation using the surface definitions. The plastic loading modulus is also updated with a newly proposed kinematic interpolation rule and the liquefaction behavior of loose sands is remodeled. Figure A. Monotonic pore pressure results for various relative density sands simulated in this study Purpose: The main purpose of this research is understanding the static and dynamic behaviors of saturated sands through theoretical frameworks of constitutive models. Theory and Methods:Theoretical approach taken in this study is the generalized plasticity model. The model is formulated in two ways where in one there is no yield or a potential surface defined in the theory and in the other such surface definitions are made and plastic strains as well as the stress-strain relationship of sandy soils are evaluated accordingly in static and dynamic simulations. A new hardening law is proposed and such calculations are done based upon this new method within the generalized plasticity framework. Results:First, drained and undrained static triaxial tests were simulated. Then, dynamic behavior of loose sand was modeled without surface definitions, and all the results were found to be fairly matching with experiments. A new hardening rule was also proposed and the liquefaction of loose sands was modeled. The results were tested with undrained cyclic triaxial tests. While the results were particularly consistent with experiments in stresscontrolled triaxial tests, contractive behavior was not equally comparable with the test results. The reason is that the plastic hardening modulus, which is compatible with the newly developed hardening law, could not capture the behavior with the same accuracy in extension. On the contrary, liquefaction and cyclic mobility behavior of loose sand could be qualitatively and quantitatively modeled with acceptable accuracy. Conclusion:This study reveals that in modeling the constitutive behavior o...