Calculation Model for Surface Settlement of Prestressed Anchor Support Structures in Deep Foundation Pits Under Freeze–Thaw Damage

To address the challenges of soil damage and structural deformation caused by freeze–thaw cycles in deep foundation pit engineering in seasonal frozen regions, this study developed a surface settlement calculation model for deep foundation pits with prestressed anchor cable support considering freeze–thaw damage effects. First, by introducing the freeze–thaw damage variable α, the damage evolution equation and soil damage constitutive relationship were established. Subsequently, the freeze–thaw damage mechanism was integrated into the pile-soil interaction model, the global stiffness matrix was modified, and a pile displacement calculation model was developed. Finally, the principle of the ground loss method was extended to settlement analysis of deep foundation pits in seasonal frozen regions. Field monitoring revealed the two-stage evolution pattern of foundation pit surface settlement. During the fluctuation period, the total settlement variation was controlled within 15 mm, while the maximum settlement growth rate reached 265.52%. During the subsequent attenuation and stabilization period, the cumulative settlement increased by only 5-10 mm, and the daily settlement rate decreased to below 0.05 mm/d. Meanwhile, the spatial–temporal evolution of settlement exhibited three-stage characteristics, and surface settlement showed a significant lag response of 10–15 days to temperature changes. Model validation results showed that the maximum settlement values from theoretical calculation, finite element simulation, and field monitoring were 19.28 mm, 22.34 mm, and 20.22 mm, respectively. The differences between the theoretical model and the monitored values and simulated values were 9.6% and 4.5%, respectively, which adequately validated the reliability and engineering applicability of the model. This research effectively filled the gap in traditional soil damage theory under freeze–thaw cycles and provided scientific theoretical foundation and practical calculation tools for foundation pit engineering design in seasonal frozen regions.