Study on dynamic characteristics and non-constant fractional dynamic creep model for frozen silty clay

The long-term dynamic characteristics of frozen soil are important theoretical basis for the dynamic stability evaluation of geoengineering in cold regions. Compared to unfrozen soil, the dynamic creep behaviour is more complicated owing to its rheological property. In this study, triaxial tests under cyclic loads with different constant stress amplitudes and confining pressures for frozen silty clay (FSC) are carried out. The long-term dynamic creep process and deformation mechanism under different dynamic stress amplitudes were investigated. The test results show that with the cyclic numbers increasing, the dynamic elastic modulus and the hysteretic loop area decrease because of the damage accumulation in the samples. Also the dynamic strength decreases with an increase in failure cyclic numbers under different confining pressures. Based on the fractional calculus theory, replacing the Newton's dashpot in the traditional Maxwell model with fractional Abel's dashpot, a fractional dynamic creep model is established. Considering the melting and crushing of the ice inclusion, the slip effect in frozen soil is increasingly significant, the viscosity coefficient of dashpot element is decreasing with an increase in loading time. In the proposed model, a non-constant dashpot element is introduced to clarify the constitutive relation of the FSC in the accelerated creep stage. The comparison results confirm that the proposed constitutive model is valid and suitable for reflecting the long-term dynamic creep behaviours of the FSC.