Determination of dynamic shear stress and strain thresholds in frozen coarse-grained materials: experimental and M-K statistical analysis

The dynamic features of frozen coarse-grained materials (FCGMs) are crucial for geotechnical engineering in cold regions. This study investigated the dynamic responses of FCGMs through stress-controlled triaxial cyclic tests. An improved Hardin model was proposed to describe stress–strain relationships. The variations in backbone curves, dynamic shear modulus, and damping ratio with various confining pressures, temperatures, and frequencies were investigated. Mathematical expressions were developed to describe the attenuation of dynamic shear modulus and the growth of damping ratio, considering the effects of temperature and loading frequency. The results indicated that both the dynamic shear stress and the maximum dynamic shear modulus increased significantly with decreasing temperature and increasing confining pressure. The Mann-Kendall (M-K) method was employed to identify the threshold dynamic shear stress and strain. It was found that the threshold dynamic shear stress increased with higher confining pressure and loading frequency, but decreased with rising temperature. When the shear modulus changes abruptly, the corresponding threshold dynamic shear strain of FCGMs is about 0.25%, where the dynamic shear modulus G_d is about 88% of the maximum dynamic shear modulus G_dmax. This study provides a new approach to determine the threshold dynamic shear stress and strain, reducing observation errors. Besides, this paper offers valuable insights into the dynamic characteristics of frozen soils in cold regions.