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<p>The evolution of temperature distributions plays a critical role in governing freeze–thaw phase transitions and the associated alterations in the mechanical properties of seasonally frozen soils. Conventional subsurface temperature measurements are constrained by sparse spatial sampling, structural disturbance, and limited continuous-imaging capability, which restrict noninvasive characterization of frozen soil temperature fields. To overcome these limitations, the present study developed a semi-open capacitance testing apparatus for seasonally frozen soils, grounded in the principles of capacitance tomography. Calibration experiments were conducted to examine the relationship between capacitance and temperature under varying moisture contents and dry densities, with a focus on analyzing capacitance responses throughout the freeze–thaw cycle. The findings reveal that the capacitance of seasonally frozen soils exhibits a characteristic nonlinear “S”-shaped increase as temperature rises, with the most pronounced changes occurring between − 4 and 4&#xa0;°C. This behavior is primarily attributed to variations in unfrozen water content and equivalent permittivity resulting from ice-water phase transitions. A capacitance–temperature model for seasonally frozen soils was formulated based on a Boltzmann-type function, with model parameters estimated via an orthogonal distance regression algorithm. This approach demonstrated superior fitting accuracy compared to the Levenberg–Marquardt algorithm. Additionally, by integrating multi-electrode capacitance measurements with a linear interpolation algorithm, the study achieved visualization of the temperature field within seasonally frozen soils and identified the temperature-sensitive range under unidirectional freezing conditions. The results show that capacitance responses capture the top-down evolution of the frozen soil temperature field, localize the 0&#xa0;°C ice front, and track migration of the − 4 to 4&#xa0;°C sensitive interval. The proposed method provides a nondestructive tool for monitoring seasonally frozen soil temperature fields, identifying freeze–thaw dynamics, and supporting early warning for cold region engineering safety.</p>

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Construction of a seasonal frozen soil capacitance-temperature model based on capacitance tomography and research into the evolution of the temperature field

  • 期刊论文

  • 发表日期：

    2026年8月1日

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  • Tianhua Liu,
  • Miao Wang,
  • Mingwei Hai

摘要

The evolution of temperature distributions plays a critical role in governing freeze–thaw phase transitions and the associated alterations in the mechanical properties of seasonally frozen soils. Conventional subsurface temperature measurements are constrained by sparse spatial sampling, structural disturbance, and limited continuous-imaging capability, which restrict noninvasive characterization of frozen soil temperature fields. To overcome these limitations, the present study developed a semi-open capacitance testing apparatus for seasonally frozen soils, grounded in the principles of capacitance tomography. Calibration experiments were conducted to examine the relationship between capacitance and temperature under varying moisture contents and dry densities, with a focus on analyzing capacitance responses throughout the freeze–thaw cycle. The findings reveal that the capacitance of seasonally frozen soils exhibits a characteristic nonlinear “S”-shaped increase as temperature rises, with the most pronounced changes occurring between − 4 and 4 °C. This behavior is primarily attributed to variations in unfrozen water content and equivalent permittivity resulting from ice-water phase transitions. A capacitance–temperature model for seasonally frozen soils was formulated based on a Boltzmann-type function, with model parameters estimated via an orthogonal distance regression algorithm. This approach demonstrated superior fitting accuracy compared to the Levenberg–Marquardt algorithm. Additionally, by integrating multi-electrode capacitance measurements with a linear interpolation algorithm, the study achieved visualization of the temperature field within seasonally frozen soils and identified the temperature-sensitive range under unidirectional freezing conditions. The results show that capacitance responses capture the top-down evolution of the frozen soil temperature field, localize the 0 °C ice front, and track migration of the − 4 to 4 °C sensitive interval. The proposed method provides a nondestructive tool for monitoring seasonally frozen soil temperature fields, identifying freeze–thaw dynamics, and supporting early warning for cold region engineering safety.