Site investigation for groundwater lowering
6.6 Determination of permeability
6.6.4 Laboratory testing: particle size analysis
There are a number of empirical methods available to allow the permeability of granular soils to be estimated from analyses of particle size distributions (PSDs) of samples. An American water works and sanitary engineer from New England, Allen Hazen (1892; 1900) was the first to propose an empirical correlation for the permeability of a sand from its PSD curve. Probably due
to the great simplicity of his ‘rule’, Hazen is still widely used by many of today’s geotechnical practitioners, often without due regard to the limitations that Hazen himself stated. His objective was to determine guidelines for suit-able sand gradings for water supply filtration. He determined that the D10 particle size (called the ‘effective grain size’) and D60/D10(the ‘uniformity coefficient’) were both important factors.
Hazen included allowances for variations in the temperature of water.
However, the temperature of the groundwater in the United Kingdom varies little between about 5 and 15⬚C; so Hazen’s rule used to estimate permeability k may be stated as:
k:C(D10)2 (6.1)
where C is a calibration factor and D10is the 10 per cent particle size taken from the particle size distribution curves (Fig. 6.6).
Hazen stated in his work that his rule was applicable over the range of D10particle size from 0.1 mm to 3.0 mm and for soils having a uniformity coefficient less than five. He also stated that (when k is in m/s and D10is in mm) his calibration factor C could vary between about 0.007 and 0.014.
In practice, presumably for reasons of simplicity, C is normally taken to be 0.01. It cannot be stressed too strongly that, even within its range of appli-cation, Hazen’s rule gives approximate permeability estimates only.
Since Hazen many others – particularly Slichter, Terzaghi, Kozeny and Rose (all reported in Loudon 1952) and Masch and Denny (reported in Trenter 1999) – have developed expressions for estimating permeability
Figure 6.6 Application of Hazen’s rule.
values from grain size distributions of sands. Unlike Hazen, who did not seek to address in situ soils, some have taken account of porosity, angular-ity of the grains and specific surface of the grains. None claim to be relevant to soils other than ‘a wide range of sands’.
Loudon (1952) thoroughly reviewed various published formulae and sup-plemented his review with his own laboratory investigations. He concluded that the error in prediction using Hazen’s rule could be of the order of plus or minus 200 per cent but that Kozeny’s formula – which is similar to that of Terzaghi, though more complicated – was to be preferred to the various others. Loudon stated that an accuracy of about plus or minus 20 per cent can be expected from Kozeny’s formula.
He also proposed that his own formula, based on Kozeny, should be used for reasons of simplicity.
log10(kS2):a;bn (6.2)
where k is the permeability expressed in cm/s, n is porosity of the granular soil (a dimensionless ratio, expressed as a fraction not as a percentage), S is specific surface of grains (surface area per unit volume of grains) expressed in (cm2)/(cm3), and a and b are calibration factors with values of 1.365 and 5.15 respectively.
Whilst the porosity of a sample can be determined in the laboratory, it is virtually impossible to determine the porosity of a sample in situ. This is a limitation on the usefulness of Loudon and other similar works and an explanation for the somewhat erratic results that they sometimes give.
They take little or no account of density and heterogeneity of soils. Standard penetration test N values do give an indication of relative density of granu-lar soils and so may afford some tentative indication of porosity. Refer to Appendix 6A for further information concerning Loudon’s method.
In the 1950s in America the late Professor Byron Prugh researched and developed an empirical method for estimating permeability based on the use of particle size data together with in situ density field measurements. He checked his predictions against field measurements of permeability. Prugh’s approach represents a return to the pragmatic co-ordination of academic and field observations.
Prugh plotted (Fig. 6.7) curves for various uniformity coefficients (D60/D10).
The D50 grain sizes are plotted on the horizontal axis to a log scale.
Permeability is plotted on the vertical axis, also to a log scale. Three separate sets of uniformity coefficient curves were compiled for:
(a) dense soils
(b) medium dense soils (c) loose soils.
To use Prugh’s curves first determine whether the soil sample is dense, medium dense or loose (based on standard penetration test N values from
reproduced by kind permission of CIRIA).
borehole logs); then project upwards from the D50grain size of the sample onto the appropriate uniformity coefficient curve; from the uniformity coefficient curve project horizontally to read off the permeability value.
Prugh’s data indicate that as the uniformity coefficient increases (i.e. the sample becomes less and less a single-size material), the permeability decreases noticeably. The significance of the Prugh curves, apart from their usefulness, is that of helping greatly the understanding of the inter-relationship of vari-ous factors (other than D10used in Hazen’s rule) affecting soil permeability.
His work has been published by Powers (1992) and in CIRIA Reports (Preene et al. 2000). Like others, Prugh did not claim his method to be rel-evant to soils other than ‘a wide range of sands.’
Irrespective of which method is used to estimate permeability, these approaches all use data from samples recovered from boreholes, rather than tested in situ. This can lead to inaccuracies in permeability assessment, including:
1 Any soil structure or fabric present in the in situ soil will be destroyed during sampling and test specimen preparation. Permeability estimates Figure 6.7 Continued.
based on the PSD curve of the resulting homogenized sample are likely to be unrepresentative of the in situ permeability. If a clean sand deposit contains laminations of silt or clay, these will become mixed into the mass of the sample during preparation and the PSD curve will indicate a clayey or silty sand. Under-estimates of permeability will result if the Hazen or Prugh methods are applied to these samples.
2 The samples used for particle size testing may be unrepresentative.
When bulk or disturbed samples are recovered from below the water level in a borehole there is a risk that finer particles will be washed from the sample. This is known as ‘loss of fines’. Samples affected in this way will give over-estimates of permeability if the Hazen or Prugh methods are used. Loss of fines is particularly prevalent in samples taken from the drilling tools during light cable percussion boring. This can be minimized by placing the whole contents (water and soil) into a tank or tray and allowing the fines to settle before decanting clean water. Unfortunately, in practice this is rarely done. Loss of fines is usually less severe for tube samples such as SPT or U100 samples; these methods may give more representative samples in fine sands.