Sensitivity analysis of temperature changes for determining thermal properties of partially frozen soil with a dual probe heat pulse sensor

Abstract

Determining thermal conductivity (λ) and volumetric heat capacity (C) of partially frozen soils with a dual probe heat pulse (DPHP) sensor is challenging because an applied heat pulse melts ice surrounding the heater probe. Examining DPHP temperature changes with a commonly-used analytical solution that only accounts for heat conduction leads to inaccurate λ and C estimates for partially frozen soils at temperatures between −5 °C and 0 °C. In order to determine λ and C accurately and simultaneously, it is necessary to understand how various properties of partially frozen soil influence the temperature changes produced by DPHP sensors. The objective of this study is to determine the sensitivity of DPHP temperature changes to soil conditions and soil thermal properties. A numerical solution for radial heat conduction with soil freezing and thawing is developed. A series of simulations are performed, in which various errors are imposed onto a selected model parameter while other model parameters are held constant, and sensitivity coefficient values (φ) of the time of maximum probe temperature (tm) and of the maximum probe temperature rise (Tm) for each parameter are calculated. Temperature changes at the measurement probe are quite sensitive to initial soil temperature (φ values for tm and for Tm are −0.99 and 0.99, respectively), λ (φ value for tm is −0.93), and parameters determining the shape of the soil freezing characteristic (FC) curve, i.e., saturated water content θs (φ values for tm and for Tm are 0.59 and −0.73, respectively) and n (φ values for tm and for Tm are −2.7 and 2.4, respectively). Temperature changes are not very sensitive to C (φ values for tm and for Tm are 0.034 and −0.15, respectively). Although previous investigations tried to determine C by inverse analysis, this sensitivity analysis shows that the influence of C on temperature response to a heat pulse is masked by that of the FC. Thus, λ and FC parameters are the best candidate parameters to be determined by inverse analysis of DPHP data. This new result will guide further testing of DPHP sensors in partially frozen soils.