Smith's Elements of Soil Mechanics. Ian Smith

      Particle density is determined in the laboratory through a well‐established and reliable testing procedure (described in BS EN ISO 17892‐3:2015, BSI, 2015). A mass of dry soil is mixed with distilled water in a standard glass vessel known as a pycnometer to separate all the particles and to enable all the air to be removed from the soil. In the test the difference in the volumes of water required to fill the pycnometer, both with and without the soil present, is determined. The particle density is equal to the dry mass of the soil divided by that volume difference.

For sands and fine soils, a sample of the soil (minimum 10 g) is oven dried, weighed and placed into the pycnometer of minimum volume 50 ml along with distilled water at room temperature (Fig. 1.13). Coarse soils can be tested in a larger pycnometer or the gravel portion can be mechanically broken down to pass a 4 mm sieve and placed in the smaller pycnometer. Formerly, in the UK, a 1 l gas jar was used for coarse soils – see earlier editions of this book for details of the gas jar procedure.

The pycnometer and contents are shaken steadily but vigorously to remove all air bubbles. The glass stopper is then removed, the jar topped up carefully to full capacity with further distilled water and the stopper replaced to seal the vessel without trapping any air inside. The stopper has a capillary tube through it, which permits the water to flow out its top as it is inserted into pycnometer. From various weighings that are made, the particle density of the soil can be calculated (see Example 1.7).

Fig. 1.13 Pycnometer used in the determination of particle density. (a) Pycnometer filled with water only. (b) Pycnometer filled with soil and water.

Example 1.7 Particle density

      The mass of an empty pycnometer, together with its glass stopper, was 178.0 g. When completely filled with water and the stopper fitted the mass was 228.2 g. An oven dried sample of soil was placed in the pycnometer and the total mass, including the stopper, was 191.2 g. Water was added to the soil and, after a suitable period of shaking, was topped up until the vessel was brim full. The stopper was fitted and the total mass was found to be 236.4 g.

      Determine the particle density of the soil.

       Solution:

      The particle density can be quickly found from a formula thus:

      where

       ms = mass of dry soil (g)

       m1 = mass of pycnometer + water (g)

       m2 = mass of pycnometer + water + soil (g)

      1.7.4 Density and unit weight

      The amount of material in a given volume, V, may be expressed in two ways:

      the amount of mass, M, in the volume, or the amount of weight, W, in the volume.

      If we consider unit volume, the two systems give the mass density and the weight density of the material respectively. The mass density is usually simply referred to as density and the weight density is routinely referred to as the unit weight:

      (1.11)

      (1.12)

      As an example, consider water at 20 °C:

      Density of water, ρ_w = 1000 kg/m³ = 1.0 Mg/m³

      Hence the unit weight of water, γ_w = 1.0 × 9.81 = 9.81 kN/m³.

      Soil densities are usually expressed in Mg/m³ to the nearest 0.01.

      Soil weights are usually expressed in kN/m³.

In soils work, it is generally more convenient to measure the density of a soil through test (e.g. Example 1.8) then to perform the geotechnical analysis using the unit weight, or weight density, derived from the density value.

       Density of soil

       Bulk density

      The bulk density of a soil is a frequently requested, easily determined, geotechnical property. By sampling a soil using a sampler (e.g. a steel tube) of known volume, V, the mass, M can easily be measured on laboratory scales and the bulk density determined:

      The bulk density is the density of the wet soil, as it considers the mass of water in the soil as well as the soil particles.

       Dry density

      The dry density is the density of the soil particles within the same volume, V as the bulk density.

      The dry density can be determined from the bulk density and the water content (in %):

      (1.13)

       Unit weight, or weight density, of soil

      As mentioned, the unit weight of a material is its weight per unit volume. In soils work the most important unit weights are:

       Bulk unit weight, γ

      This is the natural in situ unit weight of the soil. Referring to Fig. 1.12 and Section 1.7.3:

      (1.14)

       Saturated unit weight,