It is particularly important to study the strength of unsaturated loess, and its accurate determination is crucial to the stability analysis of soil slope and foundation and calculation of earth pressure. In order to reveal the control mechanism of physical parameters on the shear strength of unsaturated loess, the intact and remolded loess were used as the research object; sandy silt, quartz flour, and quartz sand were used as contrast; the systematic direct shear tests of unsaturated loess, sandy silt, and quartz sand under different conditions of water content, dry density, and clay content were carried out. The results show that the cohesion, internal friction angle, and shear strength of unsaturated loess piecewise functionally decrease with the increase of water content, its shear strength increases linearly with the increase of dry density, and its internal friction angle shows an upward quadratic function relation with the increase of clay content. The law results of comparing sandy silt, quartz flour, and quartz sand with loess considering water content and dry density are the same; therefore, the equation of shear strength of unsaturated loess is proposed for practical engineering reference, and by the first derivative analysis of the equation, it is feasible to determine the control proportion of the three parameters on the shear strength of unsaturated loess. A stage‐like difference between the three control proportions is observed, depending on the combination variations of water content and clay content.

In order to study the effects of dry density and initial water content on the permeability characteristics of loess, the saturated permeability tests of undisturbed loess and remolded loess were carried out in Lanzhou New Area. The anisotropy of undisturbed loess under two factors is analyzed and compared, and the permeability difference between undisturbed loess and remolded loess is also analyzed. The results show that the structure of loess has an important impact on the permeability characteristics, and the dry density is an important structural parameter. The natural structure of undisturbed loess has obvious anisotropy. Under different pore conditions and water contents, it will show the anisotropic behavior of permeability. The influence of water content on permeability is mainly reflected in the influence on the properties of cement between soil particle skeletons. Under different dry density conditions, the influence of water content on permeability is different. When the pore structure is relatively compact, the influence of water content is more obvious. In practical engineering, these two factors need to be comprehensively considered in order to accurately describe the permeability distribution of loess. This study can provide some theoretical guidance for the construction of relevant loess projects.

To investigate the distinctive characteristics of deformation and internal force variations in frame beam anchor structure supporting frozen soil slopes during freezing-induced frost heave, a comprehensive three-dimensional finite element model was developed. This model, utilizing the Winkler elastic foundation beam theory, is engineered to examine frost heave occurrences in frame anchor structures during freezing periods. The frame beam is modeled as a homogeneous elastic Euler-Bernoulli continuous beam, while the frozen soil behind the slope is represented through simplified pre-compressed soil springs. Simultaneously, based on the heat conduction differential equation during the phase coexistence of solid and liquid in the freezing-expansion process, the freezing expansion distribution force acting on the frame beam is obtained. By employing MATLAB programming and leveraging existing engineering cases, customized calculation programs were developed and compared against numerical simulation outcomes. The findings underscore the efficacy of the proposed method in accurately portraying the free frost heave displacement of frozen soil on slopes. Lateral displacements and bending moments obtained through this approach are consistently aligned with the results of numerical simulations. Moreover, the proposed calculation method offers a swift means of assessing frost heave displacement and the stress state of frame anchor structures, requiring only a minimal set of parameters. The research outcomes not only present a comprehensive insight into the three-dimensional dynamics between frozen soil and frame anchor support structures but also provide invaluable scientific guidance for designing frame anchor slope structures in cold regions.