A tensor-type capillary stress, instead of a scalar suction, has been proposed to serve as a stress-like state variable to capture the effects of capillarity in the mechanics of unsaturated granular soils. However, the influence of water content on the evolution of capillary stress in such soils remains insufficiently understood. This study performs numerical simulations of unsaturated granular soils in the pendular regime using the Discrete Element Method (DEM) involving a volume-controlled capillary bridge model. In these simulations, water content is maintained constant by redistributing the water from ruptured capillary bridges to adjacent ones. The evolution of capillary stress with varying water contents during triaxial and biaxial loading conditions is systematically examined. The DEM simulation results show that, under both loading conditions, the mean component of the capillary stress generally decreases, while its deviatoricity gradually develops. These changes are observed to become less significant as the initial degree of saturation increases. At low saturation levels, capillary bridges between non-contacting particle pairs rupture due to soil deformations, and the water from these ruptured bridges redistributes to existing contacts. This redistribution leads to an anisotropic distribution of pore water aligned with the contact network. At higher saturation levels, non-contacting capillary bridges persist due to their ability to sustain large relative displacements between particles, allowing the spatial distribution of pore fluids to remain less constrained by the solid contact network. Additionally, at higher water contents, relative sliding and particle rearrangement are the primary factors influencing the directional distribution of capillary bridges.

The current study adopts a micromechanical approach to explore the nature of stress transmission in wet granular materials. First, we derive the discrete form of the capillary stress tensor obtained from homogenization to show the virial nature of capillarity through the application of point -wise capillary forces in Discrete Element Modeling (DEM). Furthermore, the non -spherical character of the capillary stress tensor is highlighted through a series of DEM triaxial simulations. Contrary to common thinking, the capillary stress tensor has indeed both mean and deviatoric components due to the underlying micromechanical aspects. Relevant key dimensionless parameters are identified to evaluate the relative magnitude of the capillary stress to the externally applied and contact (intergranular) stresses, thus determining the specific conditions under which the contribution of the deviatoric part becomes considerable. In addition, a DEM simulation of a simple shear test is performed to confirm the anisotropy (non -sphericity) of capillary stress tensor. Finally, the effective nature of the contact stress in the sense of Terzaghi for the constitutive behavior of wet granular materials is investigated via a DEM stress probing analysis. Results suggest that a single contact stress variable - germane to an effective stress - cannot relate to strain for the constitutive law in triphasic condition.

While the shear behavior of granular soils is directly related to the microstructure of contacts which often leads to the coaxiality between Cauchy stress and Satake fabric tensors, it is generally accepted by the geomechanics and geotechnical engineering community that the capillary effects are isotropic. At low saturation levels, however, the pore fluid tends to form interparticle menisci that can also manifest an anisotropic structure, which may result in the development of anisotropic capillarity in wetted granular media. To study the interplay between the solid grain contacts and the liquid bridges at the micro-scales, this study adopts a coupled discrete element method that utilizes a linear contact model combined with a capillary model, and explores their effects by conducting a series of numerical experiments. The distributions of contact and capillary force orientations during the experiment are further investigated to better understand how their alignments affect the global response of the granular assembly subjected to a deviatoric loading. The results indicate that the global shear stress response is not only affected by the contact fabric but also by the network of liquid bridges, and we also observe that the particles may lose contact while the pendular menisci may not be destroyed during the elastic unloading.