Smith's Elements of Soil Mechanics. Ian Smith

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Smith's Elements of Soil Mechanics - Ian  Smith


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      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.

Schematic illustration of pycnometer used in the determination of particle density. (a) Pycnometer filled with water only. (b) Pycnometer filled with soil and water.

      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:

equation equation equation equation equation equation

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

equation

      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)equation

      (1.12)equation

equation

      As an example, consider water at 20 °C:

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

      Hence the unit weight of water, γw = 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.

       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:

equation

      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.

equation

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

      (1.13)equation

       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)equation

       Saturated unit weight,


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