A microscale-based model for small-strain stiffness in unsaturated granular geomaterials

Stiffness at very small strains G₀ is commonly assessed by way of laboratory and field methods, and used to design a wide range of infrastructure. When stiffness is inferred from field measurements, its value depends on the soil suction and state of saturation at the time of the measurement, and models are needed to infer G₀ at varying suction and degree of saturation. When stiffness is measured on saturated specimens in the laboratory, models are needed to extrapolate the laboratory ‘saturated’ stiffness to the field ‘unsaturated’ stiffness. This paper presents an experimental investigation of G₀ of unsaturated sand using the hanging water column method and the bender element technique. Experimental results revealed that wave propagation velocity and, hence, stiffness is not controlled by the product ‘suction times the degree of saturation’. A microscale-based model was formulated to interpret the experimental results, and to elucidate the mechanisms underlying different patterns of G₀ in unsaturated materials observed in the literature. According to the proposed model, the evolution of G₀ is controlled by the evolution of the suction/degree of saturation-induced intergranular stress during drying–wetting cycles. The breadth of the water retention curve and the magnitude of the intergranular stress due to the presence of the menisci were found to be responsible for the different patterns of G₀.