Strain hardening index model of artificial frozen soil based on fractional derivative

Artificial frozen soil can be regarded as the blending of ideal solid and ideal fluid in a certain proportion. Its mechanical properties neither comply with the Hooke’s law nor the Newton’s viscosity law, but obey certain relationship between them. Fractional derivative can well describe this blending phenomenon. Uniaxial compression tests were performed on the expansive soils of Hefei under different freezing temperatures, and the influence law of freezing temperature on stress and strain were obtained. The fractional derivative was introduced into the exponential model, and the improved exponential model was the fractional exponential model of stress-strain under uniaxial compression of artificial frozen soil. By taking natural logarithms on both sides of the improved model, the stress-strain linear equations at different temperatures were obtained, and the fractional derivative model parameters were determined by solving the established equations. To further verify the applicability of the established model, a set of triaxial shear tests of frozen silty clay in Nanjing were quoted and the influence of confining pressure was taken into account in the fractional order coefficient. The stress-strain fractional order exponential model was improved to take the influence of confining pressure into account. Comparing the calculated results of the improved stress strain exponential equation of artificial frozen soil with the experimental results, the results show that the calculated results are in good agreement with the experimental results and can accurately predict the changing trend of the shear stress strain curves under uniaxial compression and triaxial compression. The improved fractional derivative model has few parameters and definite physical meaning, which is convenient for engineering application. The current model is only applicable to the strain hardening type. In order to further describe the mechanical properties of the strain softening type, the further study is to establish a fractional exponential model of the strain softening type by considering the damage in the model. At the same time, how to reflect the influence of the structure and anisotropy of frozen soil on the stress-strain in the model will also be investigated.