# APPENDIX 2 - Volumetric Relations in Soil Materials

(Source Skaven-Haug 1972)

Solid matter

The solids in soil materials range from organic substances in pure plant material to mineral matter in pure sands, clays or silts. At the same time the specific gravity of the solids, Ds, varies from Do in pure plant material to Dm in mineral matter. For the majority of soil materials, containing both organic and mineral matter in the solids, the numerical value of Ds is an expression of the ratio organic matter/mineral matter.

The specific gravity Do for pure organic matter is not constant. It varies with habitat, species present and degree of decomposition. The principal constituents, cellulose and lignin, have specific gravities of 1.52 and 1.46 t/m3 respectively. Literature on the subject gives a specific gravity of 1.53 for fresh spruce and pine while values for other materials lie between 1.47 and 1.52. As a practical estimate

Do = 1.50 t/m3
Also the specific gravity Dm for pure mineral matter is not constant. It can vary from 2.3 t/m3 for gypsum to 5.2 t/m3 for hematite for example. In mineral soils a large number of minerals are present, and the mean specific gravity varies between much narrower limits. A collection of data from many soil mechanics laboratories shows a variation between 2.65 and 2.85, and generally speaking the lower value is found in coarse and uniform sand, with values rising the more finely divided the material becomes. For Norwegian sand and clay sediments the specific gravity lies between the following limits which for practical purposes we also choose:
Dm = 2.7 t/m3 ± 2% for sand
Dm = 2.8 t/m3 ± 3% for clay
The dry specific gravity Dd is the weight of solids per unit of volume, t/m3 For groups of materials with approximately constant specific gravity for their solids, Dd is a serviceable expression for both weight and volume ratios. This measure is used in international soil mechanics as a characteristic of the quantity of mineral matter. The Norwegian Bog Association has for many years used the corresponding measure g/dm3 in dry peat in its investigations of bogs and Dd can be regarded as a suitable measure of solidity compaction in peat and bark material.

For the large group of soil materials with varying specific gravity of solids Ds, Dd is not suitable as a basis for comparison.

Water

The amount of water that the soil material contains, or in certain circumstances can contain, depends on the physical properties of the material. The water content is therefore used as a basis of comparison of soil parameters and as an expression of their quality. The water content may be expressed as the ratios:

weight of water/weight of dry matter (w)
weight of water/total weight (wtot)
volume of water/total volume (wv)
All three ratios are in use, and this has sometimes caused confusion. As explained above the weight expressions are not always reliable as a basis for comparison.

The weight ratio w has been adopted in international soil mechanics and is in general use in technology. For groups of materials with approximately the same Ds, w is a serviceable basis of comparison. For materials with variable Ds, w is not a good parameter for reference. This can be illustrated by an extreme example. A cubic metre of saturated Norwegian clay contains 0.5 m3 of water, and has w = 0.36 = 36 percent. Peat (agricultural peat in bales) with the same water content, 0.5 m3, has w = 5.0 = 500 percent.

The weight ratio wtot been used for a long time in peat terminology, and for peat with approximately the same weight of dry matter it gives a serviceable basis for comparison. One advantage is that wtot is always less than 100 percent.

The volume ratio wv is determined by weighing a known volume, before and after drying. Volume determinations cause extra work, but they make it possible to determine both wv and Dd. When Ds is known, the weight and volume relationships can be calculated in the 3-phase system of water, solids and air.

Some technical calculations need quantities of water and thus of wv. Artificial drying of materials and the, determination of thermal parameters is an example. Since wv is also a good basis for comparison, independent of the kind of material, its use should be widely advocated.

Air

Except for agricultural literature the air content of soil is rarely used. This is probably because of its insignificant weight, so that it must be stated as a volume. The air content of soil is often directly indicative of certain properties, such as low specific gravity, low thermal conductivity, and a large capacity for absorbing water.

Formulae

Weight and volume ratios can be derived from the unit volume (Fig. 36). Here is a survey of formulae that are suitable for practical use:

 Symbols w ratio of weight of water/dry matter wtot ratio of weight of water/total weight wv ratio of volume of water/total volume D bulk density of wet material Dd specific weight of dry material (dry density) Ds specific gravity of solids sv ratio of volume solids/total volume n porosity sr degree of saturation Do specific gravity of organic matter Dm specific gravity of mineral matter ov ratio of volume of organic matter/total volume mv ratio of volume of mineral matter/total volume lv ratio of volume of air/total volume o ratio of weight of organic matter/dry matter m ratio of weight of mineral matter/dry matter a ratio of weight of ash/dry matter

For practical purposes the weight of air is regarded as zero, and the specific gravity of water as unity. The numerical values of the volume and weight of water are thus equal, and the factor 1 is omitted from the formulae. Ratios of weight, proportions of volume, porosity and degree of saturation are dimensionless quantities, which if multiplied by 100 give percentages. Specific gravities are reckoned in tons per cubic metre (t/m3).

 wv = (D x w) ÷ (w + 1) (1) Dd = D ÷ (w + 1) (2) wv = Dd x w (3) Dd = D - wv (4) wv = D x wtot (5) Dd = D (1 - wtot) (6) wv = (Dd x wtot) ÷ (1 - wtot) (7) sv = Dd ÷ Ds (8) lv = (1 - wv) - sv (9) sr = wv ÷ n = (wv x Ds) ÷ (Ds - Dd) (10)

If the volumes are measured and Ds is known, the volume ratios in the 3-phase system, solids, water and air, can be found. If the material is saturated with water we have only two phases, solids and water, and the relations are simpler.

Then sv = 1 - wv

If the volumes are measured, Ds can be calculated. We shall come back to this later.

The relation between wtot and wv, equation (7), is shown in Figure 36 for a number of organic materials with Ds = 1.55 t/m3 and known values for Dd. The highest two curves are related to slightly decomposed sphagnum peat in bogs. The curve for which Dd = 0.10 t/m3 corresponds to the same peat in agricultural bales for protection against frost under railway tracks. The bottom curve, with Dd = 0.25 t/m3 relates to bales of bark under roads and railways. For bark matting in situ with measured wtot = 0.72, we may read off, in round figures, wv = 0.65, lv = 0.19 and sv = 0.16.

Fig. 36. Relationship of weight and volume ratios for a range of organic materials with known specific gravities

Fig. 37. Cubic unit of a soil material with four phases: organic substance, mineral substance, water and air

Proportions of organic and mineral substances

The dry material may contain both organic and mineral matter, and Ds is then the mean specific gravity. It remains to determine the quantitative relations between organic and mineral substances.

By considering Figure 37 and setting up weight and volume equations we get:

 ov = Dd(Dm - Ds) ÷ Ds(Dm - Do) (11) ov + mv = sv mv = Dd(Ds - Do) ÷ Ds(Dm - Do) (12)

In the same way we have the following mutual relations for weight:

 o = Do(Dm - Ds) ÷ Ds(Dm - Do) (13) o + v = 1 m = Dm(Ds - Do) ÷ Ds(Dm - Do) (14)

We now have a complete survey of the volume and weight relations in the 4-phase system, organic matter, mineral matter, water and air. We can easily measure Dd and Do, and Dm may be regarded as known. It remains to determine the key value Ds.

The Specific Gravity of Solid Matter

There are several methods of determining Ds.

 a. The pycnometer method can in principle be used for all soil materials, but is time-consuming, especially when it comes to removing the last vestiges of air in organic matter, and is not suitable for routine investigations. b. For cohesive soils saturated with water, e.g. silt, clay and mud, commensurable volumes can easily be prepared and Ds can be calculated. The measurement of volume can also be carried out by weighing in air and when submerged in water. This method is suitable for routine investigations, but is limited to the above mentioned saturated materials. c. The weight ratio can be found by chemical means, and then Ds calculated from formula (13). A distinction is made between direct and indirect methods. The direct methods consist of removing the organic matter and weighing what is left. The best method is by ignition, which will be described later. Indirect methods are based on the assumption that a particular element is contained in the organic substance in a constant proportion, so that the organic substance can be calculated for this element by means of a conversion factor. These methods, like the direct ones, are not fully accurate, but must be regarded as the most reliable for soil materials with only moderate contents of organic matter.