Smith's Elements of Soil Mechanics. Ian Smith

      Recall, when soil is saturated, S_r = 1. Therefore,

      (1.15)

       Dry unit weight, γd

      (1.16)

       Effective, or buoyant, unit weight, γ'

      When a soil is below the water table, part of its weight is balanced by the buoyant effect of the water. This upthrust equals the weight of the volume of the water displaced.

      Hence, considering unit volume:

      (1.17)

      The effective unit weight is also referred to as the buoyant unit weight or the submerged unit weight.

      Note: The two terms weight density and unit weight are synonymous, and both are in common use. Both terms are used throughout this book.

       Additional expressions for densities

      As with the unit weights, similar expressions can be obtained for densities:

      (1.18)

      (1.19)

      (1.20)

      (1.21)

       Relationship between density and unit weight values

      In the previous expressions, G_s, e, S_r and the number 1 are all dimensionless.

      Hence, a particular unit weight = γ_w times a constant.

      The corresponding density = ρ_w times the same constant.

Example 1.8 Dry unit weight

      A sample of wet soil was extruded from a sampling tube of diameter 100 mm in a soil testing laboratory. The length of extruded sample was 200 mm. The mass of the wet soil was 3.15 kg. Following a water content determination, the mass of the dry soil was found to be 2.82 kg.

      Determine the bulk density, water content, dry density and dry unit weight of the soil.

       Solution:

       Relationship between w, γd and γ

(1.22)

(1.23)

(1.24)

Rearranging (1.24) and substituting into (1.22) gives:

And substituting into (1.23) gives:

      Thus, to find the dry unit weight from the bulk unit weight, divide the latter by (1 + w) where w is the water content expressed as a decimal.

       Relationship between e, w and Gsfor a saturated soil

      i.e.

      (1.25)

       Relationship between e, w and Gs for a partially saturated soil

      i.e.

      (1.26)

      Example 1.9 Physical properties determination

      In a bulk density determination, a sample of clay with a mass of 683 g was coated with wax. The combined mass of the clay and the wax was 690.6 g. The volume of the clay and the wax was found, by immersion in water, to be 350 ml.

      The sample was then broken open and water content and particle specific gravity tests gave respectively 17% and 2.73.

      The specific gravity of the wax was 0.89. Determine the bulk density, unit weight, void ratio and degree of saturation of the soil.

       Solution:

      Now,

      Now,

      1.7.5 Density index, I_D

      A granular soil generally has a large range into which the value of its void ratio may be fitted. If the soil is vibrated and compacted the particles are pressed close together and a minimum value of void ratio is obtained, but if the soil is loosely poured a maximum value of void ratio will result.

These maximum and minimum values can be obtained from laboratory tests and it is often convenient to relate them to the naturally occurring void ratio of the soil. This relationship is expressed as the density index, I_D or relative density, of the soil:

      (1.27)

      The