Numerical simulation of unstable suction transients in unsaturated soils: the role of wetting collapse

Abstract

Fluid injection is one of the major triggering factors of instability in unsaturated soils. Robust simulation tools are therefore required to examine hydrologic transients in such a class of inelastic materials. In this paper, the governing equations imposing the balance of mass and momentum in deformable unsaturated porous media are inspected from an analytical perspective. Our main goal is to examine the role of volume collapse on the stability of suction transients. Distinct scenarios are considered in terms of material behavior, distinguishing the case of elastoplastic and viscoplastic materials. It shows that in elastoplastic materials the mathematical ill-posedness of the partial differential equations leads to a diffusive instability of the pore pressure field, signaled by the loss of stress controllability under water injection. By contrast, the introduction of viscosity restores the mathematical well-posedness and ensures the positive diffusivity. Numerical implications of these findings have been explored through simulations of water injection with a 1D finite element solver. It shows that an increase of the soil hydraulic sensitivity (i.e., a marked deterioration of the yield stress upon suction removal) can deteriorate the diffusive stability and prevent the computation of suction changes across a collapsible soil layer. While the incorporation of minor amounts of viscosity can restore numerical stability by suppressing the constitutive singularity. Such numerical results have been corroborated by the computation of local stability indicators based on controllability theory, which proved to be robust diagnostic tools to identify the culprit of runaway instability emerging from coupled hydro-mechanical processes.

Viscoplastic modelling of rainfall-driven slow-moving landslides: application to California Coast Ranges

“…y  = tan ,  is material friction angle at yield. Although inelastic strains due to suction loss may play a key role in shallow landslide deformation processes (Li et al, 2021;Chen and Buscarnera, 2021), thus requiring specific constitutive laws (e.g., Alonso et al, 1990), unsaturated effects have not been taken into account in this study, in that for most landslides in the selected studied area the shear zones are below the phreatic level and, thus, fully saturated. In addition, the plastic shear strain p  is determined by the viscoplastic flow rule (Perzyna, 1963;1966):…”

Dynamics of Creeping Landslides Controlled by Inelastic Hydro-Mechanical Couplings

“…However, this model too did not fully resolve the effect of inelastic mechanisms mediated by the stress-strain nonlinearity, in that excess porewater pressure dissipation was modeled via poroelastic protocols based on a constant diffusion coefficient. This assumption conflicts with the notion that inelastic deformation can lead to major alterations of the shear zone diffusivity (Rice, 1975;di Prisco et al, 2015;Chen and Buscarnera, 2021). These coupled effects render the process inherently poroplastic, which implies that a stressstrain constitutive law is necessary to quantify the timescale of excess pore-water pressure dissipation within the shear zone, as well as the magnitude and rate of landslide motion resulting from inelastic deformation.…”

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

“…Many hydromechanical models in the unsaturated range have been developed to model porous media subjected to drying and wetting process 46–56 . Some of these models 57–59 extend the modified Cam‐Clay (MCC) model 60,61 or the Barcelona Basic Model (BBM) 62 to account for the mechanical behavior of partially saturated materials.…”

“…Many hydromechanical models in the unsaturated range have been developed to model porous media subjected to drying and wetting process. [46][47][48][49][50][51][52][53][54][55][56] Some of these models [57][58][59] extend the modified Cam-Clay (MCC) model 60,61 or the Barcelona Basic Model (BBM) 62 to account for the mechanical behavior of partially saturated materials. Various authors have further extended these plasticity models to account for the effects of evolving anisotropy.…”