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The critical state is an important concept for saturated and partially saturated granular materials as the strength and volume become constant and unique under continuous shear. By incorporating the water bridge effect, the mechanical behaviours of wet granular matters can be studied by the discrete element method (DEM). A series of DEM simulations are performed following the conventional triaxial loading path for dry and wet granular materials, and different suction values are applied at various confining stress levels. Unique critical state behaviours have been observed in both macroscopic and microscopic scales. It shows that the confining stress level plays an important role in the critical state behaviour of wet granular materials. The critical stress ratio for a wet material is not a constant value at different stress levels, and it is found that both the critical stress ratio and void ratio in wet granular matters are also much higher with a low confining stress. A framework is proposed by considering both the contact stress and the capillary stress effects to model the critical state lines. At large strain, the coordination number, the mean inter-particle force and fabric anisotropies evolve to constant critical state values for both dry and wet materials. The macro-parameters formulating the critical state stress ratio are found to be associated with the critical state anisotropies in solid skeleton and water phase fabrics, respectively.

Wet granular materials are three-dimensionally simulated by the discrete element method with water bridges incorporated between particles. The water bridges are simplified as toroidal shapes, and the matric suction is constantly maintained in the material. A comparison with experimental tests in the literature indicates that the toroidal shape approximation may be one of the best choices with high practicability and decent accuracy. Mechanical behaviours of wet granular materials are studied by triaxial tests. Effects of particle size distributions and void ratios are investigated systematically in this study. The hydraulic limit of the pendular state is also discussed. It gives the capillary cohesion function which is not only determined by the degree of saturation but also positively correlated to relative density and particle size polydispersity and inversely proportional to mean particle size. Furthermore, the capillary strengthening effect is also analysed microscopically in aid of the Stress–Force–Fabric relationship, mainly in fabric anisotropy, coordination number and stress transmission pattern, which revealed the micro-mechanisms of the additional effective stress induced by capillary effect.

This paper explores 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–fo...

Capillarity in wet granular materials induces cohesion and increases the material strength due to the attractive forces acting on capillary bridges. In the funicular state, water bridges may be not only formed between two grains but also binding three or more particles, which breaks the axial symmetry of the liquid bridge. This work presents a fundamental study on capillary forces and rupture behaviours of funicular water bridges between three spherical bodies at equilibrium (or static) configurations. Funicular water clusters are numerically solved by an energy minimization approach. Experimental comparisons are made by measuring capillary forces and these confirm the validity of the numerical solutions. Evolutions of capillary forces and rupture distances are investigated systematically by moving two spheres away from the centre. The fixed water volume condition and the constant mean curvature condition are studied respectively. Comparisons are made between the un-coalesced pendular liquid rings and the coalesced funicular bridge. For a same fixed total water volume, the capillary force is weakened by water bridge coalescence to a funicular bridge when the spheres are packed together, but the situation may vary for different contact angles and inter-particle distances. For the constant mean curvature condition, water bridge coalescence does not alter capillary force significantly when particles are packed closely, but the discrepancy is larger by increasing the gap. Funicular water bridge rupture criteria are also proposed based on the studied configurations. It is observed that in general the transmission from pendular to funicular state extends the rupture distance when it has a relatively high water volume or low air-water pressure difference.