Undisturbed Ground Temperature Model: Xing[LINK]

Approach[LINK]

This model uses the correlation developed by Xing, 2014 to predict undisturbed ground temperature. The correlation parameters for 4000+ international locations can be found in Xing, 2014. The parameters were first determined by creating and validating a finite difference numerical model which used local weather data for boundary conditions. From the numerical model, the correlation parameters were determined to provide for this simplified design model.

$$T(z,t)={\overline{T}}_s-\sum _{n=1}^2\Delta {\overline{T}}_{s,n}\cdot e^{-z\cdot \sqrt{\frac{n\pi }{\alpha \tau }}}\cdot cos[\frac{2\pi n}{\tau }(t-{\theta }_n)-z\sqrt{\frac{n\pi }{\alpha \tau }}]$$

$T(z,t)$ is the undisturbed ground temperature as a function of time and depth

${\overline{T}}_s$ is the average annual soil surface temperature, in deg C

$\Delta {\overline{T}}_{s,n}$ is the n-th amplitude of the soil temperature change throughout the year, in deg C

${\theta }_n$ is the n-th phase shift, or day of minimum surface temperature

$\alpha$ is the themal diffusivity of the ground

$\tau$ is time constant, 365.

References[LINK]

Xing, L. 2014. Estimations of Undisturbed Ground Temperatures using Numerical and Analytical Modeling. Ph.D. Diss. Oklahoma State University, Stillwater, OK.