Fractional order creep model of thawing sandstone incorporating nuclear magnetic resonance phase transition damage.

Creep instability induced by the thawing of frozen walls has emerged as a critical challenge threatening the long-term safety of deep shafts penetrating water-rich Cretaceous weakly cemented strata. Existing creep models are predominantly based on macro-phenomenological fitting, which lacks a physical characterization of the microscopic driving mechanisms during ice-water phase transitions. Here, we conducted constant load-variable temperature triaxial creep tests coupled with synchronous Nuclear Magnetic Resonance (NMR) monitoring to define a microscopic damage parameter based on the evolution of unfrozen water content. By integrating this parameter into a fractional-order creep framework, we developed a cross-scale mechanical model capable of describing the entire thawing process. Our results indicate that within the active phase transition zone (- 6 °C to - 2 °C), the unfrozen water content surges from 1.24 to 6.23%, leading to a 3-to4-fold increase in the steady-state creep rate. By introducing microscopic state variables, the proposed model effectively achieves the theoretical decoupling of geometric damage triggered by pore ice melting from mechanical damage caused by the intrinsic weakening of the rock skeleton. Validation analysis demonstrates that the model calculations for the attenuation, steady-state, and accelerated creep stages achieve an agreement of over 90% with experimental data. This study reveals a cross-scale cascading mechanism of accelerated failure in thawing rocks: microscopic phase transitions induce a dynamic attenuation of long-term rock strength. When this dynamic strength threshold falls below the constant external load, it triggers mesoscopic crack connectivity and macroscopic instability. These findings provide a quantitative theoretical foundation for the early warning of long-term stability during the thawing period of deep shafts in cold regions.