S OIL M OISTURE –P ERMEABILITY AND C APILLARITY
5.6 FACTORS AFFECTING PERMEABILITY
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SOIL MOISTURE–PERMEABILITY AND CAPILLARITY 131 through a circular capillary tube. The flow through a porous medium is considered similar to a flow through a bundle of straight capillary tubes. The equation is :
k = D e
e C
s2 3
. . 1
( ). γ
µ + ...(Eq. 5.31)
in which,
k = Darcy’s coefficient of permeability Ds = effective particle-size
γ = unit weight of permeant µ = viscosity of permeant e = void ratio
C = shape factor
This equation helps one in analysing the variables affecting permeability. The charac-teristics of the permeant are considered first and those of the soil next.
5.6.1 Permeant Fluid Properties
Equation 5.31 indicates that the permeability is influenced by both the viscosity and the unit weight of the permeant fluid. In the field of soil mechanics, the engineer will have occasion to deal with only water as the common permeant fluid. The unit weight of water does not signifi-cantly vary, but its viscosity does vary signifisignifi-cantly with temperature. It is easy to understand that the permeability is directly proportional to the unit weight and inversely proportional to the viscosity of the permeant fluid.
It is common practice to determine the permeability at a convenient temperature in the laboratory and reduce the results to a standard temperature; this standard temperature is 27°C as per I.S. Code of practice. (IS : 2720 Part XVII-1966 and its revised versions). This is done by using the following equation :
k27 = kT. µT
µ27 ...(Eq. 5.32)
where kT and µT are the permeability of soil and the viscosity of water at the test temperature of t°C and, k27 and µ27 are the permeability and viscosity at the standard temperature, i.e., 27°C.
According to Muskat (1937), these two permeant characteristics, that is, viscosity and unit weight, can be eliminated as variables by defining a more general permeability, K, as follows :
K = k.µ
γ ...(Eq. 5.33)
where
K = specific, absolute, or physical permeability µ = viscosity of the permeant
γ = unit weight of the permeant k = Darcy’s coefficient of permeability.
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Since k has the units L/T, K has the units L2. K is also expressed in Darcy’s; 1 darcy being equal to 0.987 × 10–8 cm2. K has the same value for a particular soil, for all fluids and at all temperatures as long as the void ratio and structure of the soil remain unaltered.
Viscosity and unit weight are considered to be the only variables of the permeant fluid that influence the permeability of pervious soils; however, other permeant characteristics can have a major influence on the permeability of relatively impervious soils. The effects of viscosity and unit weight may be eliminated by expressing the permeability in terms of the absolute permeability. It has been found by Michaels and Lin (1954) that the values of absolute permeability of Kaolinite varies significantly with the nature of the permeant fluid, when the comparisons are made at the same void ratio. Further, they found that the variation was large when the kaolinite was moulded in the fluid which was to be used as the permeant than when water was used as the moulding fluid and initial permeant, each succeeding permeant displacing the preceding one. These differences in permeability at the same void ratio have been attributed to the changes in the soil fabric resulting from a sample preparation in the different fluids.
The effect of the soil fabric will be discussed in next sub-section.
5.6.2 Soil Characteristics
The following soil characteristics have influence on permeability : 1. Grain-size
2. Void ratio 3. Composition
4. Fabric or structural arrangement of particles 5. Degree of saturation
6. Presence of entrapped air and other foreign matter.
Equation 5.31 indicates directly only grain-size and void ratio as having influence on permeability. The other characteristics are considered indirectly or just ignored. Unfortunately, the effects of one of these are difficult to isolate in view of the fact that these are closely interrelated; for example, fabric usually depends on grain-size, void ratio and composition.
Grain-size
Equation 5.31 suggests that the permeability varies with the square of particle diameter. It is logical that the smaller the grain-size the smaller the voids and thus the lower the permeabil-ity. A relationship between permeability and grain-size is more appropriate in case of sands and silts than that of other soils since the grains are more nearly equidimensional and fabric changes are not significant.
As already stated in sub-section 5.5.6, Allen Hazen proposed, k = 100 D102 where D10 is in cm and k is in cm/s.
Void Ratio
Equation 5.31 indicates that a plot of k versus e3/(1 + e) should be a straight line. This is more true of coarse grained soils since the shape factor C does not change appreciably with the void ratio for these soils.
Other theoretical equations have suggested that k versus e2/(1 + e) or k versus e2 should be a straight line. It is interesting to note that, as indicated in Fig. 5.9, a plot of log k versus e approximates a straight line for many soils within a wide range of permeability values.
SOIL MOISTURE–PERMEABILITY AND CAPILLARITY 133 This suggests a simple method for the permeability of a soil at any void ratio when values of permeability are known at two or more void ratios. Once the line is drawn, the per-meability at any void ratio may be read directly.
Increase in the porosity leads to an increase in the permeability of a soil for two distinct reasons. Firstly, it causes an increase in the percentage of cross-sectional area available for flow. Secondly, it causes an increase in the dimension of the pores, which increases the aver-age velocity, through an increase in the hydraulic mean radius, which enters the derivation of Eq. 5.31, and which, in turn, is dependent on the void ratio.
Composition
The influence of soil composition on permeability is generally of little significance in the case of gravels, sands, and silts, unless mica and organic matter are present. However, this is of major importance in the case of clays. Montmorillonite has the least permeability; in fact, with sodium as the exchangeable ion, it has the lowest permeability (less than 10–7 cm/s, even at a very high void ratio of 15). Therefore, sodium montmorillonite is used by the engineer as an additive to other soils to make them impermeable. Kaolinite is a hundred times more perme-able than montmorillonite.
Fabric or Structural Arrangement of Particles
The fabric or structural arrangement of particles is an important soil characteristic influenc-ing permeability, especially of fine-grained soils. At the same void ratio, it is logical to expect a soil in the most flocculated state will have the highest permeability, and the one in the most dispersed state will have the lowest permeability. Remoulding of a natural soil invariably reduces the permeability. Stratification or macrostructure also has great influence; the per-meability parallel to stratification is much more than that perpendicular to stratification, as will be shown in a later section.
100 200 300 400 500 1000
0.4 0.5 0.6 0.7
Permeability (k × 10 mm/s) (log scale) (b)
5
Voidratio,e
0 0.1 0.2 0.3 0.4 0.5
Void ratio function (a) 1000
800
600
400
200
e/(1 +e)
3e/(1+e)
3 e/(1
+e)
2
e/(1+e)
2
e
2
e
2
Permeability(k×10mm/s)5
Fig. 5.9 Permeability-void ratio relationships
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Degree of Saturation
The higher the degree of saturation, the higher the permeability. In the case of certain sands the permeability may increase three-fold when the degree of saturation increases from 80% to 100%.
Presence of Entrapped Air and Other Foreign Matter
Entrapped air has pronounced effect on permeability. It reduces the permeability of a soil.
Organic foreign matter also has the tendency to move towards flow channels and choke them, thus decreasing the permeability. Natural soil deposits in the field may have some entrapped air or gas for several reasons. In the laboratory, air-free distilled water may be used a vacuum applied to achieve a high degree of saturation. However, this may not lead to a realistic esti-mate of the permeability of a natural soil deposit.
The importance of duplicating or simulating field conditions is emphasised by the pre-ceding discussion on the factors affecting permeability, when the aim is to determine field permeability in the laboratory.