Artificial ground freezing is a widely used, reliable method for excavation in water-bearing ground. The questions posed in the thermal design of ground freezing projects require solving moving boundary (Stefan) problems. Approximate analytical solutions, such as the ones by St¨
ander1 and Sanger and Sayles,2 have been
developed for thermal engineering design and are used by practitioners across the industry. For instance, Sanger
& Sayles’ solution is widely used for the single-freeze-pipe problem, but it has proven to be of limited accuracy.3
In the present paper, an adjustment to this formula is proposed based on the re-evaluation of their empirical
assumption that the ratio between the temperature penetration depth and the phase-change radius equals a
constant value of 3 regardless the conditions. A sensitivity study is performed using a verified numerical model as
a benchmark to study several problems with different initial and boundary conditions (initial, phase change and
freeze pipe temperatures) and thermal properties of the ground (water content, thermal conductivity and heat
capacity). This is done for the freezing times of 10 and 365 days, in order to consider the potential change of the
ratio with the freezing time. In this way, a calibrated formula is proposed to find appropriate values of this ratio
and a suitable adjustment to Sanger & Sayles’ solution is determined. Adjusting Sanger & Sayles’ solution in this
manner, a significantly higher and more consistent accuracy is achieved for different boundary and initial
conditions. This accuracy improvement was checked for real conditions from an engineering project, which
shows that the adjustment can be useful for thermal problems in engineering design of ground freezing.
