Article · Scientific Reports · April 28, 2026
Estimation of the shear modulus of unsaturated soils using the capillary model
Zhiming Wang, Qian Zhai, Yiyao Zhu, Harianto Budi Rahardjo, Alfrendo Satyanaga, Guoliang Dai
Abstract
The shear modulus is a fundamental parameter for evaluating soil deformation and stiffness. It is influenced by various factors, including void ratio, confining pressure, soil type, and soil suction (or degree of saturation). Similar to the coefficient of permeability of unsaturated soils, the shear modulus of unsaturated soils can vary significantly with changes in soil suction. Numerous empirical models have been proposed to describe the shear modulus of unsaturated soils. However, many existing models adopt either soil suction or degree of saturation (or water content) as a single independent variable for shear modulus estimation. Based on the analysis presented in this study, it is observed that a single variable-either soil suction or degree of saturation-cannot adequately represent the pore structure characteristics of different soil types, such as sands, silts, and clays. In contrast, the soil-water characteristic curve (SWCC), which defines the relationship between retained water content and soil suction, inherently reflects the pore structure of soils. Therefore, incorporation of the SWCC is necessary for the estimation of the shear modulus of unsaturated soils. In this paper, a capillary-model-based method is proposed to estimate the small-strain shear modulus of unsaturated soils. The proposed model is validated using experimental data for various soil types obtained from the published literature. The results demonstrate that the model can be applied to estimate the shear modulus of unsaturated soils under both drying and wetting conditions.
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