Power Law for Elastic Moduli of Unsaturated Soil

Elastic moduli (Young’s modulus and shear modulus) are material properties that describe a material’s elastic stress-strain relation, and are therefore two of the most important properties in geotechnical engineering design and analysis. For soils, in addition to their well-known dependence on stress, these moduli depend on volumetric water content and/or matric suction, particularly for silty and clayey soils. This study proposes a simple power law to describe the dependence of these two moduli on volumetric water content for all types of soils. A series of uniaxial compression tests are conducted on various compacted soils under varying volumetric water content. Young’s moduli are measured and used to test the validity of the proposed power-law relationship. Additional validation and comparative analyses are conducted using other compacted soils studied by previous investigators and empirical models for shear modulus from the literature. It is shown that the proposed power law agrees well with the other models, but is much simpler because the other models use both matric suction and volumetric water content as independent variables and involve more fitting parameters. A practical three-point testing procedure is provided to determine the single fitting parameter that defines the power law for any type of soil. The procedure involves measuring elastic moduli at three states of water content: dry, wet (nearly saturated), and the middle points. Test results for 16 soils demonstrate that the proposed three-point testing procedure can accurately capture the dependence of Young’s moduli for all types of soils from sandy to silty to clayey soils ($R^2>95\%$ for most soils). The proposed power law provides a simple and practical way to describe changes in elastic moduli of soils under variably saturated conditions.