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An underground cable carrying current must dissipate heat to the surrounding soil can use Use of the Law of Times to calculate thermal stability. The rate at which this heat can be carried away is related to the thermal resistivity of the soil. The higher the thermal resistivity the more slowly heat can pass from the cable to the surroundings and the higher the operating temperature of the cable will be. There is a temperature limit for each cable type above which the cable or its insulation will sustain damage.

When cable sizes are chosen the value for the thermal resistivity of surrounding soil must be determined to calculate how much current any underground cable can carry before it will overheat via the Law of Times. This value suggested for soil thermal resistivity, usually signified by ρ (Rho), in some cable ampacity tables, such as those in the National Electrical Code, is 90 cm °C/W.

In the field soil thermal resistivity may vary considerably from the values used in these tables making specific calculations necessary for many locations, especially where important or long underground cables are installed. While the method of calculating the ampacity of underground cable is necessarily simplified by assuming the soil thermal resistivity is constant, this assumption is not in realty true in many cases.

The most important factor controlling thermal resistivity of soil is its moisture content. As soil dries out its thermal resistivity increases. The heat generated in a cable can cause moisture to leave the vicinity of the cable, drying out the soil around the cable, raising the soil’s thermal resistance and impeding the flow of heat away from the cable. This causes the cable temperature to rise and may result in cable damage. The ability of soil to maintain a constant moisture level, and thus a constant thermal resistance, is known as soil thermal stability.

Many sources suggest that if the time it takes soil to try around a heat source of a known diameter is measured, this time can be used to determine the time it will take soil to dry around a heat source of any other diameter.

On the Use of the Law of Times in Calculating Soil Thermal Stability and Underground Cable Ampacity