Stress–Force–Fabric Relationship for Unsaturated Granular Materials in Pendular States

Abstract

In this paper, we explore the particle-scale origin of the additional shear strength of unsaturated granular materials in pendular states induced by the capillary effect by applying the Stress-ForceFabric (SFF) relationship theory into unsaturated granular material stress analysis. The work is based on Discrete Element simulations with the particle interaction model modified to incorporate the capillary effect. By decomposing the total stress tensor into a contact stress tensor originating from contact forces and a capillary stress tensor due to capillary effect, the directional statistics of particlescale information have been examined. The observations have been used to support the choice of the appropriate analytical approximations for the directional distributions associated with the solid skeleton and water bridges respectively. The SFF relationship for unsaturated granular materials is hence formulated, which has been shown matching with the material stress state in good accuracy and used to interpret the material strength in terms of the relevant micro-parameters. Macro and micro observations are carried out on both relatively dense and loose samples in triaxial shearing path to the critical state. The capillary force remains nearly isotropic during triaxial shearing. Anisotropy in the water bridge probability density, however, develops alongside the anisotropy in contact normal density, which gets smaller when the suction level gets lower and the water content becomes higher.The anisotropy effect in the water phase is much smaller than the solid skeleton and it coupling effect with the solid phase makes the fabric anisotropy in wet materials smaller than that of the dry ones.Combining with the SFF function, it can be clarified that the increased solid coordination numbers and mean contact forces by water bridge effect are more important factors for the suction induced shear strength.

A micro–macro investigation of the capillary strengthening effect in wet granular materials

“…A complete contact model comprising the capillary effect and the mechanical force induced by the particle contact has been adopted for the DEM simulation. The Hertz-Mindlin model [18,37] is employed to represent the mechanical force induced by inter-particle deformation and the capillary force is calculated by the suction controlled water bridge model introduced in [57] and [62]. The toroidal shape approximation is adopted for the liquid bridge shape in which the meridian profile of the water bridge surface is described as a circular arc, which is same to the method I in [12].…”

“…For given values of suction, particle size, inter-particle distance and contact angle, the water bridge geometry is solved iteratively by the process introduced in [62]. The capillary force can then be obtained by the 'gorge method' [20] as the sum of the pressure difference acting on the section of the bridge neck and the surface tension acting on the air-water interface:…”

“…Scholtès et al [48] interpreted the stress tensor as the sum of the contact stress tensor and capillary stress tensor by the homogenization techniques. This definition is followed by Wang et al [62] and it can be expressed as:…”

“…Its tensorial form is then expressed in [26,27]. Based on the capillary stress tensor definition [48], which is a homogenization technique over the liquid bridge effect, a Stress-Force-Fabric (SFF) relationship for wet granu-lar materials has been introduced [57,62]. This SFF relationship explicitly formulates the macro stress tensor by the micro parameters associated with mean particle interactions and anisotropies in the solid phase and water phase, which can be a fundamental theory to analyse the micro-mechanisms of the capillary effect.…”

“…-To validate the capillary bridge model in [57] and [62] by comparing with experiment data and other solutions in the literature. -To clarify the limit of the pendular regime assumption for different granular assemblies.…”