Development of extended STZ model for granular soils subjected to combined static loading and vibration

Abstract

The “shear-transformation zone” (STZ), which may be referred to as a weak domain in granular material, is the main source of plastic deformations in non-cohesive soils such as sand or gravel. To theoretically investigate the vibration-induced shear resistance reduction (ViSRR) of granular materials, this paper proposes an extended STZ model that considers the coupling effect between vibration and quasi-static loadings. The framework of the model consists of three components: (1) the motion of STZs including the transition, creation and destruction of STZs; (2) the relation between the motion of small-scale STZs and the observable, macroscopic plastic strain; and (3) the evolution law of a “configurational temperature” that reflects the energy that drives the motion of STZs. The conventional STZ model developed for amorphous materials is enhanced to accommodate both volumetric and shear deformations in the spatial stress state. Specifically, in addition to considering plastic shear strains induced by the change in STZ orientation as the result of the transition, as in conventional STZ models, the extended STZ model correlates plastic volumetric strains with the change in STZ amount resulted from creation and destruction.

Experimental and modelling investigation of vibration‐induced fluidization in sheared granular soils

“…The extended STZ model takes into account shear‐induced volume change of granular materials subjected to combined quasi‐static loading and vibration. In granular materials, a STZ (weak spot) can be visualized as a weak particle loop with at least four grains as shown in Figure 7 (see Xie et al 56 …”

“…The processes of transition, creation, and destruction are collectively called the motion of STZ, which is driven by the evolution of internal energy in the granular system. Hence, the extended STZ model 56 has three groups of governing functions: (1) the motion of STZ, (2) the evolution law for the configurational temperature as an indicator of internal energy and the driving power associated with the motion of STZ and (3) the relationship between the motion of STZ and the corresponding plastic strains.…”

“…First, the motion of STZ can be described by 56 $$$$\begin{eqnarray} {\tau _0}{\dot{H}_{ij}} = \Lambda {R_{ij}} - {R^*}{H_{ij}} + {\left({\frac{{{\Lambda ^{eq}}}}{\Lambda } - 1} \right)}{\tilde{\Gamma }_{im}}{H_{mj}} \end{eqnarray}$$$$with $$$$\begin{eqnarray} \def\eqcellsep{&}\begin{array}{*{20}{c}}{H_{ij}} = \frac{1}{{{N_g}}}\sum \limits _{\alpha = 1}^N {h_i^\alpha } h_j^\alpha ,&{{{\tilde{\Gamma }}_{ij}} = \Gamma {\delta _{ij}} + \lambda {d_{ij}}} \end{array} \end{eqnarray}$$$$in which $$ H_{ij}$$ is the STZ tensor used to reflect the spatial distribution of STZ with $$ h_i^\alpha$$ being the unit orientation vector of the αth STZ; N and $$ N_{g}$$ are the total number of STZ and the total number of particles in a REV, respectively; τ 0 is a time scale and is assumed to be inversely proportional to the loading rate $$ {\dot{\varepsilon }_1}$$ (axial strain rate in traditional triaxial compression tests), that is, …”

“…In other words, an original STZ model is unable to describe any plastic volumetric change of granular materials, such as shear‐induced dilation or contraction, or vibration‐induced compression. Recently, by correlating the creation and destruction of STZ with the plastic volumetric strain, an extended STZ model was developed to describe the behaviour of granular soils subjected to combined quasi‐static shearing and vibration 56 …”

“…This paper focuses on the experimental exploration of vibration‐induced fluidization (ViF) of granular material using a modified triaxial apparatus, as well as a theoretical investigation adopting the extended STZ model 56 . The paper is organized as follows: First, we briefly describe the specially designed testing system, which is based on a conventional triaxial apparatus.…”