If you can assume isotropic distribution of moisture, iso-volume and no dissolution phenomena, the heat capacity per unit mass of the total soil is simply the mass-averaged sum of the components in the soil.

Stick to mass and revert to volume if you can.

The heat capacities of soils can be calculated from the sum of its components.

The main soil forming minerals have similar heat capacities. Exceptions are water and organic materials (Data: Bachmann, 2005):

Quarz: 0,76 J g-1 K-1 at 10°C

Clay minerals: 0,76 J g-1 K-1 at 10°C

Organic: 1,93 J g-1 K-1 at 10°C

Water: 4,19 J g-1 K-1 at 10°C

Ice: 2,04 J g-1 K-1 at 0°C

Quarz: 0,8 J g-1 K-1 at 55-60°C

Kaolinit: 0,94 J g-1 K-1 at 55-60°C

CaCO: 0,85 J g-1 K-1 at 55-60°C

Because of this the SIA (1996) suggests a way of calculating the heat capacity of wet soils. They use an average value of the heat capacity of soil forming minerals and:

·        the temperature

·        the water content

·        the dry density

of the soil.

This is an approach. But I developed a similar approach in my thesis and it worked quite good.

Calculation of heat capacity is carried out by using the following formula (SIA 1996):

Cs = 1,64 * Temp [°C] + 704

Cp = (100 * Cs + 4190 * w) / (100 + w)

Cv = Cp * TRD

Cp = specific Heat capacity of the wet soil [J * kg-1 * K-1]

Cs = specific heat capacity of the dry soil [J * kg-1 * K-1]

Cv = volumetric heat capacity [J * kg-1 * m-3]

TRD = dry density of the soil [kg * m-3]

w = water content [mass-%]

This formula should work for unfrozen soils. I took the formula not directly from the SIA but from http://www.lbeg.niedersachsen.de/download/1220 (page 30, in German) please check it before working with it.

Many data to thermal properties of soils are given in Farouki (1986) http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA111734 and in the papers of Campbell et al.

https://www.researchgate.net/profile/Gaylon_Campbell?_sg=DSMoX2JrtMOEuDUNNxcsJG4OXw75BaZ5BlK71QELwh4NvBbynCx_FBgvEmib9mp9FyNCIyh3vlccFZ2N0BTBBg.Pue5GiHpkiLjCWFKmCHQFG3CWvfogG7jVPJG3GNF-aFMgtb9u8Pr_Dk6iC-Ayc7g

Literature:

Bachmann, J. (2005): Thermisches Verhalten der Böden, Kap. 2.6.4., In: Blume, H.P., P. Felix- Henningsen, W.R. Fischer, H.-G. Frede, R. Horn und K. Stahr (Hrsg.). Handbuch der Bodenkunde, 22. Erg. Lfg. 8/0532 S. Ecomed Verlag, Landsberg/Lech.

SIA – SCHWEIZER INGENIEUR UND ARCHITEKTENVEREIN (1996): Grundlagen zur Nutzung der untiefen Erdwärme für Heizsysteme. – SIA Dokumentation D 0136, Schweizer Ingenieur- und Architektenverein; Zürich.