A practical method for determining the elastic modulus of frozen soils

Elastic modulus of frozen soil is an important mechanical parameter for the design and construction of buildings and infrastructures in seasonal frozen soil and permafrost regions. To explore a reasonable approach for determining the elastic modulus of frozen soil, this study selects frozen silty sand, frozen silty clay, and frozen loess as representatives, and investigates the variations of 10 deformation moduli with confining pressure. The moduli are the initial tangent modulus (E_0qf), secant moduli (E_0.2qf - E_0.5qf) measured up to 20 %, 30 %, 40 %, 50 % of failure stress, and secant moduli (E_0.1εf - E_0.5εf) measured up to 10 %, 20 %, 30 %, 40 %, 50 % of failure strain. A linear model is proposed to describe the moduli variations with confining pressure, and the performance of the model is evaluated based on 12 indicators. The results show that the change of each modulus with confining pressure is influenced by the yielding mode of the test specimen. The moduli decrease with increasing confining pressure when the specimen yields in a shear mode, and increase with the confining pressure further increase once the specimen yields in compressibility mode. Under the same yielding mode, there exist linear relationships between the deformation moduli and confining pressure. It is interesting to find that the relationship between E_0qf - E_0.5qf and confining pressure is affected by soil type, while the linear relationship between E_0.1εf - E_0.5εf and confining pressure is independent of the soil type tested. Moreover, the linear relationships between E_0.1εf - E_0.5εf and confining pressure are more significant than those between E_0qf - E_0.5qf and confining pressure. Using E_0.2εf - E_0.5εf as the elastic modulus can effectively reduce the discreteness of the index, thus reduce the quantity of the experiments for determining the elastic modulus, and facilitate to determine more realistic frozen soil deformation in engineering calculation. From this point of view, this study provides a practical method for determining the elastic modulus of frozen soils.