Simplified Model for Frost Heave-Induced Deformation in Prestressed Anchorage Systems

Engineering accidents caused by frost heave-induced deformation in prestressed anchor cable support structures are frequent in the paramos freeze-thawing region, and accurately predicting the impact of frost heave deformation on support structures has become an urgent engineering problem. This study established a one-dimensional freezing heat transfer model for deep excavation slope soil based on Stefan phase change theory, determined that the freezing front position exhibits a square root relationship with time, and constructed a simplified calculation model for frost heave-induced deformation in prestressed anchor cable support structures. The model adopts the generalized Pasternak two-parameter foundation model, describes the concentrated action effect of anchor cable tension through Dirac function, establishes a fourth-order differential governing equation, and transforms the complex pile-anchor-soil interaction into solvable linear equation systems using the finite difference method. A quantitative calculation method for frost heave coefficient was established based on the Gardner soil–water characteristic curve model, dividing 25 calculation regions according to 1 °C gradient, with fitting accuracy R² reaching 0.982. A three-dimensional numerical verification model was constructed through open system unidirectional freezing tests, with optimized determination of water supply soil column height of 4.0 m and moisture content increment of 0.86%. Verification results show that the model predicted freezing depth of 1.7 m compared to measured 1.69 m with an error of only 0.59%, the simulation of pile horizontal displacement during overwintering period showed high consistency with monitoring data, errors at all monitoring points were less than 15%, and anchor cable tension calculation errors ranged from 10.61% to 17.58%. The simplified model significantly outperformed traditional analytical methods in prediction accuracy, with horizontal displacement predictions 37.08% and 22% higher than Pasternak solution and Winkler solution respectively, and bending moment and shear force prediction deviations controlled within 6.33%. Sensitivity analysis determined optimal design parameters: anchor cable spacing of 3.0 m, prestress of 300kN, and anchor length of 15 m. The study found that frost heave rate and structural response exhibit a nonlinear relationship, and when the frost heave rate increased from 3 to 11%, the Maximum displacement increased sharply from 0.72 to 2.26 cm, demonstrating obvious threshold effects. This study successfully transformed complex three-dimensional frost heave problems into analytically solvable mathematical models, significantly improving prediction accuracy while maintaining computational efficiency, providing quantitative basis and reliable theoretical tools for optimization design of cold region support structures.