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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, ID
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, ID or relative density, of the soil:
(1.27)
The theoretical maximum possible density of a granular soil must occur when e = emin, i.e. when ID = 1.0. Similarly, the minimum possible density occurs when e = emax and ID = 0. In practical terms this means that a loose granular soil will have an ID value close to zero whilst a dense granular soil will have an ID value close to 1.0.
1.7.6 Summary of soil physical relations
A summary of the relationships established in Section 1.7 is given below:
Exercises
Exercise 1.1
The results of a sieve analysis on a soil were:
| Sieve size (mm) | Mass retained (g) |
| 50 | 0 |
| 37.5 | 15.5 |
| 20 | 17.0 |
| 14 | 10.0 |
| 10 | 11.0 |
| 6.3 | 33.0 |
| 3.35 | 114.5 |
| 1.18 | 63.3 |
| 0.6 | 18.2 |
| 0.15 | 17.0 |
| 0.063 | 10.5 |
The total mass of the sample was 311 g. Plot the particle size distribution curve and, from the inspection of this curve, determine the effective size and uniformity coefficient. Classify the soil.
Answer D10 = 0.7 mm; D60 = 5.2 mm. Cu = 7.4. 70% gravel, 30% sand. Well graded sandy GRAVEL.
Exercise 1.2
Plot the particle size distribution curve for the following sieve analysis, given the sieve sizes and the mass retained on each. Classify the soil.
Sample mass = 642 g.
Retained on 425 μm sieve – 11 g, 300 μm sieve – 28 g, 212 μm sieve – 77 g, 150 μm sieve − 173 g, 63 μm sieve – 321 g.
Answer By inspection of grading curve soil is a uniform SAND. This is confirmed from the value of Cu = 2.3.
