Mechanisms of creep in shale from nanoscale to specimen scale

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The last several decades have seen a surge of papers dealing with analytical and semi‐analytical solutions to the problem of one‐dimensional consolidation of soils. But rarely has any of these contributions focused on the time scales arising from combined primary and secondary compression. Primary compression has always been attributed to the dissipation of excess pore pressure as fluid is expelled from the soil skeleton to the drainage boundaries. However, there have been several schools of thought when it comes to the process governing the secondary compression. In this paper, we attribute the secondary compression to any of the following processes occurring either individually or in combination: (a) rate‐dependent (viscoplastic) constitutive response of the soil skeleton; (b) existence of a secondary pore scale system that expels fluid from the smaller‐scale pores to the larger‐scale pores; and (c) delayed compression due to creep following Bjerrum's concept of secondary consolidation. Contributions of the present work include closed‐form analytical solutions to the problem of combined primary and secondary compression of soils in one dimension, as well as a quantitative analysis of the time scales involved in such coupled hydromechanical processes.

“…The plastic modulus

\cal H

can be made to be a nonlinear function of deformation to closely match real soil behavior, 76 but for now we shall assume it to be constant. In terms of the effective vertical stress

\sigma _{\rm v}^{\prime }

, the viscoplastic vertical strain rate is given by the Perzyna over‐stress model 77–79 as

\begin{equation} \dot{\varepsilon }{}^{\rm vp}_{\rm v} = \frac{f}{\eta }{\rm sign}(\sigma ^{\prime }_{\rm v})\,, \end{equation}

where

\eta

is the dashpot coefficient and

f

is the yield function given by

\begin{equation} f = \sigma ^{\prime }_{\rm v} - \sigma _{\rm Y}\,. \end{equation}

…”

Section: Elasto–viscoplastic Consolidationmentioning

confidence: 99%

Section: Elasto-viscoplastic Consolidationmentioning

confidence: 99%

Time scales in the primary and secondary compression of soils

Liu

Borja

2022

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“…[38] and adopted by Refs. [36, 43, 49] that is,

\begin{equation} {\dot{p}}_{\text{c}}=-\frac{{\dot{\varepsilon}}_{\text{v}}^{\text{p}}}{{C}_{\text{c}}-{C}_{\text{r}}}{p}_{\text{c}}, \end{equation}

where

{C}_{\text{c}}

is the compression index, and

{\dot{\varepsilon}}_{\text{v}}^{\text{p}}

is the rate of volumetric plastic strain. Equations (14) ∼ (16), together with the KKT conditions, can be solved iteratively by the return mapping algorithm at discrete time steps.…”

Section: Constitutive Laws For Saturation‐dependent Anisotropy In Fro...mentioning

confidence: 99%

Freezing‐induced stiffness and strength anisotropy in freezing clayey soil: Theory, numerical modeling, and experimental validation

Yin

Andò

Viggiani

et al. 2022

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This paper presents a combined experimental‐modeling effort to interpret the coupled thermo‐hydro‐mechanical behaviors of the freezing soil, where an unconfined, fully saturated clay is frozen due to a temperature gradient. By leveraging the rich experimental data from the microCT images and the measurements taken during the freezing process, we examine not only how the growth of ice induces volumetric changes of the soil in the fully saturated specimen but also how the presence and propagation of the freezing fringe front may evolve the anisotropy of the effective media of the soil–ice mixture that cannot be otherwise captured phenomenologically in the isotropic saturation‐dependent critical state models for plasticity. The resultant model is not only helpful for providing a qualitative description of how freezing affects the volumetric responses of the clayey material, but also provide a mean to generate more precise predictions for the heaving due to the freezing of the ground.

“…Many rocks exhibit anisotropy in both their mechanical deformation and fluid flow behaviors 1–7 . Failure to consider this aspect could lead to large errors in the prediction of their hydro‐mechanical responses 8–11 .…”

Section: Introductionmentioning

confidence: 99%

“…Many rocks exhibit anisotropy in both their mechanical deformation and fluid flow behaviors. [1][2][3][4][5][6][7] Failure to consider this aspect could lead to large errors in the prediction of their hydro-mechanical responses. [8][9][10][11] Mechanical anisotropy in rocks mainly arises from the presence of cleavage, micro-cracks, and bedding planes.…”

Section: Introductionmentioning

confidence: 99%

Evolution of anisotropy with saturation and its implications for the elastoplastic responses of clay rocks

Borja

2021

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Many clay rocks have distinct bedding planes. Experimental studies have shown that their mechanical properties evolve with the degree of saturation (DOS), often with higher stiffness and strength after drying. For transversely isotropic rocks, the effects of saturation can differ between the bed-normal (BN) and bedparallel (BP) directions, which gives rise to saturation-dependent stiffness and strength anisotropy. Accurate prediction of the mechanical behavior of clay rocks under partially saturated conditions requires numerical models that can capture the evolving elastic and plastic anisotropy with DOS. In this study, we present an anisotropy framework for coupled solid deformation-fluid flow in unsaturated elastoplastic media. We incorporate saturation-dependent strength anisotropy into an anisotropic modified Cam-Clay (MCC) model and consider the evolving anisotropy in both the elastic and plastic responses. The model was calibrated using experimental data from triaxial tests to demonstrate its capability in capturing strength anisotropy at various levels of saturation. Through numerical simulations, we demonstrate the role of evolving stiffness and strength anisotropy in the mechanical behavior of clay rocks. Plane strain simulations of triaxial compression tests were also conducted to demonstrate the impacts of material anisotropy and DOS on the mechanical and fluid flow responses.