This is the diameter around a source at which the effect of the loss factor commences. Inside the circle of diameter $D_x$, the temperature changes according to the peak value of the losses. Outside this circle, it changes with the average losses. The characteristic diameter is a function of the diffusivity of the medium and the length of the loss cycle. In the majority of cases, the soil diffusivity $\delta_{soil}$ will not be known. In these cases, a value of 0.5*10-6 m$^2$/s can be used. This value is based on a soil thermal resistivity of 1.0 K.m/W and a soil moisture content of about 7% of dry weight.
The calculation of the characteristic (or fictitious) diameter for sinusoidal load is based on the IEEE paper 'Ampacity calculation for deeply installed cables' by E. Dorison et al, dated 2010. Three different methods can be chosen:
$60000K_x \sqrt{\frac{\tau}{3600} \delta_{soil}}$ | Method by Neher McGrath |
$\frac{k_H}{\sqrt{n_{cycle}} {\rho_4}^{0.4}}$ | Method by Heinhold |
$D_e e^{\frac{1}{\frac{q_x D_e}{2000}} |\frac{\operatorname{k0}\left(\frac{q_x D_e}{2000}\right)}{\operatorname{k1}\left(\frac{q_x D_e}{2000}\right)}|}$ | Method by Dorison |