Frozen soil is a common foundation material in cold region engineering. Therefore, the control and prediction of cumulative plastic strain for frozen soil materials are essential for the construction and long-term stability of actual foundation engineering under complex dynamic loadings. To investigate the influence of complex cyclic stress paths on frozen soil, a series of complex cyclic stress paths were conducted using the frozen hollow cylinder apparatus (FHCA-300).These cyclic stress paths included the triaxial cyclic stress path (TCSP), directional cyclic stress path (DCSP), circular-shaped cyclic stress path (CCSP), elliptical-shaped cyclic stress path (ECSP), and heart-shaped cyclic stress path (HCSP).The results indicated that the cumulative plastic strain under the five cyclic stress paths at three temperatures (-1.5,-6,and-15 degrees C) can be ranked as follows: DCSP>ECSP>HCSP>CCSP>TCSP. The cyclic stress paths are quantified based on the combined effects of the maximum shear stress (q(max)) and the principal stress axis angle (a). A developed model predicting cumulative plastic strain, considering complex cyclic stress paths, is introduced and demonstrates excellent predictive performance. The study's findings can offer insights into foundation engineering's deformation characteristics and settlement predictions under diverse complex dynamic loadings

To investigate the mechanical characteristics of frozen silty clay under complex stress paths, using the true triaxial instrument for permafrost, tests were carried out under triaxial compressive and plane strain stress states using the true triaxial instrument for permafrost to analyze deformation characteristics and strength evolution law under different stress paths and minor principal stresses (sigma(3)) and establish strength criterion under plane strain conditions. PFC3D numerical simulation results were compared to test results and meso-crack evolution law was discussed. The results showed that stress-strain curves were characterized by strain hardening. Destructive strength showed a gradual increase with the increase of sigma(3) and the values obtained from plane strain tests were higher than those of triaxial compression tests. Volume strains basically showed shear shrinkage characteristics and all sigma(3) directions were expansion deformation. Strength at damage under plane strain state was approximated based on generalized Mises and Lade-Duncan plane strain strength criterion using generalized plane strain strength criterion. Stress-strain curves obtained from numerical simulation tests in PFC3D basically agreed well with those obtained from indoor test results. The number of tensile and shear cracks in the developed numerical model under various stress paths were increased with generalized shear strain.

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.