effective stresses
3.6 Laboratory exercise: particle size distribution and other classification tests 61
angular sub-angular subrounded rounded well rounded Figure 3.16. Particle shapes.
spherical diameter 6 µm (radius r = 3 µm) will have settled below a depth of 100 mm below the surface of the water. This is the size of particles at the bound-ary between medium silt and fine silt, and thus at this time all particles of medium silt size and above will have settled past our sampling depth:
t = zr
V = 9ηzr
2gr2(ρs− ρw)
= 9× 0.891 × 10−3× 0.1
2× 9.81 × (3 × 10−6)2× (2.65 − 1) × 103 = 2752 s = 45 m 52 s
3.6.3 Particle shape
Both these techniques – sieving and sedimentation – are describing the soil particles with reference to a simple model of equivalent spheres. It will probably be helpful, if the individual particles can be inspected with the naked eye or with a readily available optical microscope, to give some indication of the shape of the particles.
Some indication of the scale of descriptors from angular to well rounded is hinted at in Fig.3.16.
As a pedagogic laboratory exercise, it is good training for students to grasp the idea of combining objective quantitative measurements (for example, proportions retained on particular sieves) – which could be repeated by others with the expec-tation of achieving essentially the same numerical results – with descriptions (for example, particle shape or colour or general soil consistency) – which are more qual-itative but nevertheless must be immediately clear to someone who is not actually present (Think, when we talk of horses, that you see them printing their proud hoofs i’the receiving earth...).
3.6.4 Sand: relative density
In Table3.2typical values for the densities of “dense” and “loose” soils were given.
The terms “dense” and “loose” are rather vague terms which can be made slightly more objective if they are somehow tied to the range of densities for which a
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62 Density
particular sandy or gravelly soil can exist. More or less standard laboratory tests4 can be used to characterise this range – discovering a maximum density or mini-mum void ratio and a minimini-mum density or maximini-mum void ratio for the particular soil in its dry state.
A standard vibratory procedure is used to discover the minimum void ratio, emi n, of the soil. A series of repeated inversions of a large tube containing a sample of the sandy soil is used to estimate the maximum void ratio, emax. The maximum and minimum void ratios determined in this way do not actually define the actual extremes of packing; they merely provide a useful index for the soil. In reality, the absolute lowest value of void ratio must be zero when the stresses have been in-creased so enormously that all the particles have broken and there are no longer any visible voids. And there is a maximum void ratio – a very loose packing – for which the particles are not really in proper stationary contact, and the material is not able to transmit stress from one side to the other.
However, given these index or reference values of void ratio, if the soil is pre-pared or found to exist at any other void ratio, e, then a relative density, Dr, can be defined:
Dr = emax− e emax− emi n
(3.38) This range of void ratios depends on the range of particle sizes and the typical parti-cle shapes. For example, angular partiparti-cles are able to exist in rather looser packings than rounded particles. Well-graded soils – soils such as the glacial till shown in Fig.
3.9 with a wide range of particle sizes – tend to have low void ratios because for any size of particles there exist smaller particles which are happy to sit in the spaces that would exist around the larger particles. The most efficient packing of particles would be linked with a self-similar fractal distribution of particle sizes in which the arrangement of particles has the same general appearance no matter at what scale the soil is observed. Then the proportion of particles within a range of sizes having the same ratio would be the same, so that if d1/d2= d3/d4then the proportion in the size range d2to d1would be the same as that in the size range d4to d3, and so on.
Classification tests of this type are valuable in providing information which is expected to correlate, broadly, with stiffness and strength properties of the soil that may be relevant for calculation of the performance of geotechnical structures of which that soil forms part.
3.7 Summary
Here is a concise list of the key messages from this chapter, which are also encapsu-lated in the mind map (Fig.3.17).
1. Soils are composed of mineral particles separated by voids which may be par-tially or wholly filled with liquid.
4 Kolbuszewski, J.J. (1948) An experimental study of the maximum and minimum porosities of sands.
Proc. 2nd Int. Conf. on Soil mechanics and foundation engineering, Rotterdam 1 158–165.
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Figure 3.17. Mind map: density.
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64 Density
2. Many aspects of the behaviour of soils are strongly influenced by the density of packing of the mineral particles: it is necessary to define density or volumetric variables to characterise the packing.
3. Ratios of volumes are used to define void ratio, e, specific volume,v and poros-ity, n. The volumetric proportion of the voids filled with water is the degree of saturation, Sr.
4. Water content,w, is a ratio of masses and is straightforward to measure.
5. Determination of density requires some means of estimating the volume of a soil sample.
6. For a given amount of compaction energy, there is an optimum moisture con-tent which produces the maximum density or minimum specific volume.
7. Soil particles originate from weathering of rocks and subsequent transport.
8. The sizes of particles that may be found in natural or man-made soils cover a very wide range.
9. The distribution of sizes of coarser particles can be found by sieving; the distri-bution of sizes of finer particles can be found by sedimentation.
10. Significant electrostatic forces between packets of clay molecules encourage open structures with high void ratios.
11. The larger inert grains of sands and gravels interact through interparticle con-tact forces.