Multi⁃field coupling analysis of slope displacement with frame⁃anchor supporting in seasonal frozen zone

In order to explore the temperature，moisture，stress field and internal force of the anchor rod under the ac⁃ tion of freeze⁃thaw load， a new hydro⁃thermal⁃mechanical coupling equation is established based on the traditional hydro⁃thermal⁃mechanical coupling equation and considering the conditions of drainage and water replenish⁃ ment.Through the COMSOL software PDE and the solid mechanics module interface，the coupled solution of tempera⁃ ture，moisture and stress fields is realized. The established slope multi⁃field coupling calculation model can well reflect the changing laws of various physical quantities during the freezing and thawing process. Combined with outdoor tests，the monitoring and calculation values of soil temperature，displacement，unfrozen water，and internal force of anchor rods during the freezing and thawing period are compared and analyzed.The result shows that during the freezing period，the unfrozen water content is dis⁃tributed from small to large along the surface. The maximum im⁃ pact depth of surface temperature changes on soil temperature is about 2. 5 m. During the thawing period， there are two thawing zones that are nearly parallel to the ground surface，which cause the unfrozen water content to be dis⁃ tributed from the ground surface downwards from large to small and then from small to large.From the stress distribu⁃ tion cloud diagram，it is known that before the support，the slope has no trend of concentrated development of shear stress during the freezing period and is in a stable state.During the melting period，the melting of the soil causes obvi⁃ ous shear stress concentration on the top of slope and the foot of slope，and the slope is in an unstable state.After the support，the concentration of shear stress dissipates，indicating that the support effect is good.During the entire freezing and thawing period，the axial force of the anchor rod increases the most during the freezing period.During the melting period，the axial force drops sharply but is still larger than the initial time，indicating that the slope is permanently de⁃ formed.The influence of frost heave deformation on the internal force of the anchor rod cannot be ignored，and the at⁃ tention should be paid to slope engineering in the areas with similar soil climate.