Constitutive Modeling of Peat in Dynamic Simulations
Peat is a highly compressible organic material with unique properties that differ from inorganic mineral soils, which poses a challenge in their constitutive modeling. The main specific challenge addressed in this dissertation include matching dynamic properties (i.e., modulus reduction and damping behavior). Constitutive models used in 1D site response typically use modulus reduction and damping curves as input parameters, and usually introduce a misfit of the desired behavior, particularly at high strains. This is problematic for peat because large strains are expected to develop during cyclic loading due to the peat softness.
Nonlinear one dimensional ground response models generally present a compromise between fitting the backbone curve or the hysteretic damping curve. Fitting the damping curve depends on unloading and reloading rules. Most of the models use Masing rules or extended Masing to correct the overdamping at high strains resulting from using Masing rules. Frequency dependent Rayleigh damping is used to introduce damping at low strains. I present a new formulation of unloading and reloading rules completely departing from Masing rules. The main idea is to rotate the axis of the stress strain curve and change the point of reference to calculate the stress at the next time step. The small strain damping is made hysteretic by increasing the initial departure tangent modulus when unloading, in a way consistent with what has been observed in laboratory tests. The unloading-reloading rule is implemented in a nonlinear code and is able to match any backbone and hysteretic damping without Rayleigh damping.
Dynamic curves are typically not used in 2D or 3D models because their inclusion in a plasticity framework is complicated due to their dependence on confining pressure, which can change during earthquake loading (e.g. when excess pore pressure develops under undrained loading). Hence, the damping behavior is not an input of current 3D constitutive models. In order to facilitate the inclusion of dynamic curves in constitutive models, I present a new concept that plots modulus reduction and damping curves against stress ratio instead of shear strain. This results in pressure-independent modulus reduction and damping curves for three empirical relationships commonly-used to derive modulus reduction and damping curves. This finding is useful for implementation in one-dimensional effective stress ground response analysis codes for undrained loading conditions, and in advanced plasticity models.
I then extend the developed unloading-reloading rule and include it in a 3D constitutive model that uses modulus reduction and damping curves that are plotted against stress ratio by using the aforementioned concept. The formulation of the model allows to match dynamic properties (i.e., modulus reduction and damping curves), in 1D and 2D site response. At large strains the strength is controlled by a bounding surface algorithm following the formulation from Dafalias and Manzari (2004). The volumetric response is controlled by a dilation surface that introduces plastic volumetric strains based on deviatoric plastic strains. Most of the input parameters are well-known engineering properties easily measured in laboratory tests. Default values are defined for the input parameters that are not easily measured. I present the implementation of the model in FLAC and some typical predictions of the model through simulations of cyclic triaxial and simple shear tests. Finally, I present the calibration of the model for Sherman Island peat based on laboratory tests, and the performance of the model in 1D site response simulations.