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.
Exercise 1.3
A BS cone penetrometer test carried out on a sample of boulder clay gave the following results:
| Cone penetration (mm) | 15.9 | 17.1 | 19.4 | 20.9 | 22.8 |
| Water content (%) | 32.0 | 32.8 | 34.5 | 35.7 | 37.0 |
Determine the liquid limit of the soil.
Answer wL = 35%
Exercise 1.4
A liquid and plastic limit test gave the following results:
| Test no. | 1 | 2 | 3 | 4 | PL | PL |
| Wet mass (g) | 33.20 | 32.10 | 28.20 | 31.00 | 11.83 | 15.04 |
| Dry mass (g) | 28.20 | 26.50 | 22.40 | 23.90 | 11.25 | 14.07 |
| Tin (g) | 7.02 | 7.04 | 7.10 | 7.02 | 7.04 | 7.25 |
| Penetration (mm) | 14.5 | 17.0 | 20.9 | 22.7 | – | – |
Determine the plasticity index of the soil and classify the soil.
Answer 22, CI
If the natural water content was 28%, determine the liquidity index in the field.
Answer 0.64
Exercise 1.5
A sand sample has a porosity of 35% and the specific gravity of the particles is 2.73. What is its dry density and void ratio?
Answer e = 0.54, ρd = 1.77 Mg/m3
Exercise 1.6
A sample of silty clay was found to have a volume of 14.88 ml, whilst its mass at natural water content was 28.81 g and the particle specific gravity was 2.7. Calculate the void ratio and degree of saturation if, after oven drying, the sample had a mass of 24.83 g.
Answer e = 0.618, Sr = 70%
Exercise 1.7
A sample of moist sand was cut from a natural deposit by means of a sampling cylinder. The volume of the cylinder was 478 ml and the mass of the soil was 884 g before drying, and 830 g after drying. The volume of the dried sample, when rammed tight into a graduated cylinder, was 418 ml and its volume, when poured loosely into the same cylinder, was 616 ml. If the particle specific gravity was 2.67, determine the density index and the degree of saturation of the deposit.
Answer ID = 69%, Sr = 32%
Exercise 1.8
In order to determine the density of a clay soil, an undisturbed sample was taken in a sampling tube of volume 0.001 664 m3.
The following data were obtained:
Mass of tube (empty) = 1.864 kg
Mass of tube and clay sample = 5.018 kg
Mass