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.

Under the effect of wave loads, continuous and cyclic principal stress rotation (PSR) occurs, with constant principal stress values in foundation soil units. The stability of coastal engineering structures in permafrost regions is inevitably subjected to the persistent impact of wave loads, which poses a significant challenge to their durability. Consequently, a series of experimental studies were carried out using a frozen hollow cylinder apparatus (FHCA) to investigate the influence of crucial three-dimensional stress state parameters, including the coefficient of intermediate principal stress (b), mean principal stress (p), and principal stress rotation radius (R), on the deformation characteristics and dynamic property evolution of frozen soils. The results indicated that under continuous principal stress rotation, the mean principal stress p has a limited impact on the deformation behavior and mechanical property evolution of the frozen soil. In contrast, b and R significantly influence the mechanical properties of frozen soil. When b and R at low values, the continuous rotation of principal stress causes axial strain to develop positively, decreases the mechanical property parameter damping ratio, increases the elastic modulus, and densified the sample. However, with the increase in b and R beyond a threshold, the repeated principal stress rotation causes the axial strain to develop negatively, increases the damping ratio continuously, decreases elastic modulus, and leads to significant softening of the frozen soil with an increase in rotation cycles.

The fatigue and damage characteristics of frozen soil under cyclic loading are highly dependent on the three-dimensional (3D) stress state, due to the anisotropic properties of the ground. Measuring and researching the deformation behavior and fatigue failure characteristics of frozen soil under complex 3D cyclic stress states are significant for the stability assessment of frozen soil when it is subjected to earthquakes and vehicular traffic. In this paper, a hollow cylindrical apparatus was used to simulate a cyclic stress state with constant values of principal stress direction angle (alpha), coefficient of intermediate principal stress(b), and amplitude of the first principal stress under -6degree celsius conditions. The influences of 3D stress parameters (alpha and b) on the deformation behavior, damage evolution, and fatigue failure characteristics of frozen silty clay were systematically investigated. The results indicated that the deformation of the samples was dominated by axial strain, when alpha < 15 degrees and b = 0. Furthermore, as the value b increased, both the accumulated axial strain and accumulated torsional shear strain exhibited a decreasing-then-increasing trend. When 30 degrees <=alpha <= 60 degrees, the deformation feature is primarily dominated by torsional shear direction. With the increase of the value b, the accumulated torsional shear strain increased rapidly, while the axial strain gradually decreases, and then in turn to compressive elongation deformation. The increase of 3D stress parameters leads to a decrease in accumulated torsional shear strain, absolute value of accumulated axial strain, number of cycles, and accumulated torsional shear dissipated energy density at the failure of frozen soil. This indicated that under cyclic stress conditions, the increase of 3D stress characteristic parameters accelerates the damage evolution and fatigue failure process of frozen soil samples. Essentially, the increase of 3D stress parameters accelerates the damage of soil particle and ice lens structures in horizontally layered and the growth of micro-crack of frozen soil, thereby reducing the transverse shear resistance of frozen soil samples.

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.