Experimental Verification of Capillary Force and Water Retention between Uneven-Sized Spheres

The recently established theoretical results of the solid-water characteristic curve (SWCC) and capillary force characteristic curve (CFCC) are experimentally verified for mechanical and hydrologic interaction between uneven-sized spherical particles under partially saturated conditions. It is shown that the theoretical framework, based on the minimization of the free energy of the liquid meniscus between the two uneven-sized particles, can predict both water retention and capillary force accurately for spherical particles ranging in radius from 165?to?252?μm. The experimental technique is novel and the results at such scale are valuable for the understanding of gas-solid-liquid interaction among granular media, since there is very limited experimental data available in the literature. The comparisons between the theoretical and experimental predictions of the SWCC and CFCC indicate that the agreements are generally very good, confirming the validity of the theory.     

Hysteresis of Matric Suction and Capillary Stress in Monodisperse Disk-Shaped Particles

The dependences of matric suction and capillary stress on the degree of saturation in monodisperse disk-shaped particles are established for the full range of the degree of saturation. A thermodynamic free energy approach is employed to obtain both the soil–water characteristic curve (SWCC) and the capillary stress characteristic curve (CSCC) for both wetting and drying processes. It is shown that the thermodynamic energy stability concept can lead to the establishment of hysteresis in both the SWCC and CSCC without explicit involvement of the contact angle and ink-bottle hysteresis. The air-entry pressure value and capillary condensation pressure value are quantified and their functional dependencies on the average pore sizes are established. For particle sizes ranging between 0.001 and 1?mm, the air-entry and capillary condensation pressures decrease from several hundred kPa to several kPa and capillary forces are found to range between tens and hundreds of micronewtons.     

Effective Stress from Force Balance on Submerged Granular Particles

A new equation for effective stress is derived from a physically based approach of force balance on submerged granular particles. The Euler cut principle and the Euler’s first law of mechanics are used to analyze the interparticle contact stress in a fluid saturated porous media. The analysis starts from basic principles and provides a detailed derivation of the formulas. Tensor algebra together with Coulomb’s friction law, the mean value theorem and area weighted averaging techniques are used to simplify the mathematical formulation leading to effective stress. A new mathematical constraint, requiring spatially averaged interparticle contact stress to be orders of magnitude larger than spatially averaged pore pressure, is presented for the widely used Terzaghi’s effective stress equation.     

Water Flow in Unsaturated Soils in Microgravity Environment

In this study, two types of soils with varying soil water potentials were used for evaluating the effect of gravity on water flow through unsaturated soils. Experiments were conducted in both 1- and 0-g environments. Water content distributions were evaluated as a function of distance from the source of water intake and time. The experimental results indicated that the capillary potential and the advective forces due to interfacial tension gradients are overshadowed by the gravitational potential in a 1-g environment. The fast water movement in the 0-g condition is attributed to the capillary potential as well as to the advective forces that developed. In addition, microstructural changes have contributed to water flow in the 0-g condition. Depending on soil type, the magnitude of such an effect (i.e., water movement) varies from three- to four-fold. To analyze the experimental results, a one-dimensional model, based on Darcy’s law and the conservation of mass equations, was developed and solved numerically by the finite difference method. A nondimensional Bond number was extracted from the resulting flow equation and used as a basis for incorporating the gravitational component of the flow process into the formulation. The numerical results compare quite well in some instances with the experimental results. In other cases, significant departures are noted. The departure was attributed to the significant changes in microstructure of soil samples under the 0-g condition. Consequently, the requisite water retention and hydraulic conductivity functions used in the model may not apply in outer space.     

Hysteresis of Capillary Stress in Unsaturated Granular Soil

Constitutive relationships among water content, matric suction, and capillary stress in unsaturated granular soils are modeled using a theoretical approach based on the changing geometry of interparticle pore water menisci. A series of equations is developed to describe the net force among particles attributable to the combined effects of negative pore water pressure and surface tension for spherical grains arranged in simple-cubic or tetrahedral packing order. The contact angle at the liquid–solid interface is considered as a variable to evaluate hysteretic behavior in the soil–water characteristic curve, the effective stress parameter χ, and capillary stress. Varying the contact angle from 0 to 40° to simulate drying and wetting processes, respectively, is shown to have an appreciable impact on hysteresis in the constitutive behavior of the modeled soils. A boundary between regimes of positive and negative pore water pressure is identified as a function of water content and contact angle. Results from the analysis are of practical importance in understanding the behavior of unsaturated soils undergoing natural wetting and drying processes, such as infiltration, drainage, and evaporation.     

Examination of the Response of Regularly Packed Specimens of Spherical Particles Using Physical Tests and Discrete Element Simulations

Significant insight into the response of granular materials can be gained by coupling accurately controlled physical tests with complementary discrete element simulations. This paper discusses a series of triaxial and plane strain laboratory compression tests on steel spheres with face-centered-cubic and rhombic packings, as well as discrete element simulations of these tests. The tests were performed on specimens of uniform-sized steel balls and on specimens of steel balls with specified distributions of ball diameters. The packing configurations are ideal and differ considerably from real sand specimens, however, studies of such idealized granular materials can yield considerable insight into the response of granular materials and the capability of discrete element simulations to capture the response. The differences in response for the two packing configurations considered illustrate the importance of fabric. The numerical simulations captured the observed laboratory response well if the particle configurations, particle sizes, and boundary conditions were accurately represented. However, the postpeak response is more difficult to capture, and it is shown to be sensitive to the coefficient of friction assumed along the specimen boundaries. The simulations of the tests on the nonuniform-sized specimens demonstrated a clear correlation between strength and coordination number.