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In this article we will discuss about the:- 1. Meaning of Permeability 2. Darcy’s Law for Determining the Permeability of Soils 3. Coefficient 4. Factors 5. Determination.
Meaning of Permeability:
The velocity of water flowing through a soil mass between any two points depends directly on the hydraulic gradient or the head loss per unit length between the two points. The property of the soil that permits the flow of water through its voids with ease is known as permeability. Quantitatively, permeability is defined as the velocity of flowing water under unit hydraulic gradient. In other words, permeability indicates the ease with which water flows through the soil. Units of permeability are the same as those of velocity, that is, cm/s or m/day.
Permeability of soil controls the rate at which saturated soils undergo compression below foundations under external loads. Knowledge of permeability of soil is required in determining the discharge or yield designing of the well and hydraulic structures and through earth dams. Permeability is also required in designing filters used to prevent piping failure in earth dams; it also controls the stability of hydraulic structures.
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A soil mass is called pervious when water can easily flow through it, and thus, pervious soils such as sand and gravel have high permeability. As permeability decreases, the soil becomes less pervious, as in the case of silts. In highly impervious or impermeable soils, such as clays, very little water flows per unit time and such soils have very low values of permeability.
Soils are classified as pervious, semi-pervious, and impervious based on the value of permeability, as shown in Table 9.1.
Darcy’s Law for Determining the Permeability of Soils:
The law governing the flow of water through saturated soils was first demonstrated experimentally by Darcy in 1856 and is known as Darcy’s law. It states that for laminar flow conditions in a saturated soil, the rate of flow of water is directly proportional to the hydraulic gradient.
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Consider any two points A and B in a saturated soil mass, shown in Fig. 9.1. Let h1 be the piezometric or pressure head at point A, h2 be the piezometric or pressure head at point B, and L be the distance between point the two points and v be the velocity of flow between points A and B. Then –
where i is the hydraulic gradient (head loss per unit length) given by –
Here v is the velocity of flowing water and k is a constant of proportionality, known as coefficient of permeability or simply permeability. Equation (9.1) is the mathematical expression of Darcy’s law. Since hydraulic gradient (i = Δh/1) has no units, permeability has the same units as that of velocity. It is usually expressed in cm/s or m/day.
From Darcy’s law, it is clear that when the hydraulic gradient i = 1 in Eq. (9.1), then v = k. This means that permeability of soil may also be defined as the velocity of flow under unit hydraulic gradient. We know that the rate of flow or discharge –
q = v.A
Substituting the value of v from Darcy’s law we get –
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q = kiA …(9.3)
where A is the area of cross-section of the soil, including the area of voids and area of solids, perpendicular to the direction of flow. Darcy’s law has important applications in the field of soil mechanics. Terzaghi used Darcy’s law in deriving the consolidation equation to determine the rate of compression of saturated soils under loads with time.
The yield of wells and the seepage loss through the body of earth dams or below hydraulic structures are estimated using Darcy’s law. The stability of hydraulic structures is checked using flow net, which is another application of Darcy’s law. Finally, the design of filters on the downstream side of earth dams is done using the permeability value obtained through Darcy’s law. Groundwater flows through the soil under the influence of gravity. The rate of flow through the soil increases with the increase in permeability and the head causing flow.
Coefficient of Absolute Permeability:
The coefficient of permeability k, as used in Darcy’s law, depends not only on the properties of the soil but also on the viscosity and density of the permeant (water). To express permeability independent of properties of the flowing fluid (i.e., permeant), a new term known as coefficient of absolute permeability (ka) is used. The coefficient of absolute permeability is thus independent of the properties of the permeant and is defined as –
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ka = K µ/γw …(9.4)
The units for the coefficient of absolute permeability can be obtained by substituting the units on the right-hand side of Eq. (9.4). That is, –
Thus, the coefficient of absolute permeability has units of m2, cm2, or mm2. Another unit used is darcy.
1 darcy = 0.987 mm2
The coefficient of absolute permeability is constant for a given soil, irrespective of the temperature, density, and viscosity of the flowing fluid.
Factors Affecting Permeability of Soils:
Following are the various factors that affect the permeability of soils:
1. Grain size.
2. Void ratio.
3. Particle shape.
4. Soil structure and fabric.
5. Pore fluid properties.
6. Adsorbed water (in clay).
7. Soil stratification.
8. Saturation degree.
9. Impurities and foreign matter.
10. Pore size distribution and flow path tortuosity.
The effect of each of the above factors on permeability is discussed below:
Permeability of soils increases with the increase in the grain size of soils. This is because pore size increases with the increase in particle size, thus increasing the area available for flow of water. Thus, permeability of coarse-grained soils is several times more than that of fine-grained soils. The increasing order of permeability for different soils is clay < silt < sand < gravel.
Allen Hazen showed that for loose uniform sands, permeability is given by the relation –
k = C.D102 …(9.5)
where D10 is the effective size of soil in centimeters (particle size corresponding to 10% cumulative finer) and C is a constant of proportionality (= 100 – 150). The range of permeability for different types of soils is shown in Table 9.2.
Permeability of soils increases considerably with the increase in the void ratio of soils that the relationship between permeability and void ratio is –
k ∝ e3/1+ e …(9.6)
All soils are found to have an approximately linear relationship with e2 or e3/(1 + e) and log10k.
Permeability is found to be less for soils with angular particles than for soils with rounded particles at the same void ratio. This is because permeability is inversely proportional to specific surface, and angular particles have higher specific surface than rounded particles.
Permeability is more for soils with a flocculent structure than those with an oriented fabric, for the same soil type. This is because the void ratio is more for soils with a flocculent structure that has an edge-to-face particle arrangement.
Permeability is influenced by the density and viscosity of water or any other fluid flowing through soils. It increases with the increase in density marginally and decreases with the increase in viscosity significantly. An increase in temperature of the permeant (pore fluid) increases the density marginally and decreases the viscosity significantly. Thus, increase in temperature of the pore fluid increases the permeability of the soil.
Fine-grained soils contain a layer of water strongly attached to the particle surface that is known as adsorbed water. Adsorbed water is not free to move under gravity and hence reduces the effective void space available for fluid flow. Hence, permeability of clays decreases with the increase in the thickness of the adsorbed water layer and vice versa.
The specific surface and cation exchange capacity of the soil as well as the electrolyte concentration of the pore fluid and the valence of the exchangeable cations are important among several variables that affect the thickness of the adsorbed water layer.
In the case of transported soils that occur in several layers, permeability in the horizontal direction parallel to the stratification is many times that in the vertical direction perpendicular to the stratification. An exception to this is the case of loess deposits, which show more permeability in the vertical direction than in the horizontal direction.
Permeability of the soil is directly proportional to the degree of saturation of the soil. In one way increase in the degree of saturation increases the area of flow and hence increases the permeability. Also, partially saturated soils contain air pockets that are formed due to entrapped air or due to air liberated from the percolating water. These air pockets create additional obstruction to the flow of water and hence, the permeability of partially saturated soils is considerably less than that of fully saturated soils.
9. Impurities and Foreign Matter:
Any impurities/foreign matter accumulated in the soil plugs the voids and reduces the area available for fluid flow and hence decreases the permeability of the soil.
10. Pore Size Distribution and Flow Path Tortuosity:
The size of voids in a soil mass is not uniform but varies at different points. In addition to grain size variations, the pore size distribution in soil depends on the conditions during soil formation. The distribution of voids or pores in a soil mass determines the change in direction that the water has to undergo when flowing through the soil, known as tortuosity of flow path. The higher the tortuosity of flow path, the more the changes in direction that the water has to undergo when flowing in the forward direction, causing more head loss and hence a decrease in permeability.
Determination of Permeability:
The following are the different methods for the determination of permeability of soil:
1. Laboratory Methods:
i. Constant head permeability test.
ii. Variable head permeability test.
iii. Capillarity permeability test.
iv. Consolidation test.
2. Field Methods:
i. Pumping-out tests.
Constant head permeability test is suitable for coarse-grained soils. Variable head permeability test, also called falling head permeability test is suitable for both coarse-grained and fine-grained soils. The falling head permeameter avoids the need to collect and measure discharge through the soil sample. Permeability of partially saturated soils can be determined using capillarity permeability test. Permeability is determined indirectly from the coefficient of consolidation from the consolidation test results.
When water flows through the soil sample, the finer particles are carried by the flowing water due to the pressure exerted. These finer particles are likely to reach the bottom of the soil sample and form a thin layer, slightly reducing the permeability. To avoid the effect of this filter skin on the accuracy of permeability measurement, the head loss should be measured in the middle third height of the soil sample.
The error in the measurement of permeability due to leakage between the side walls of the permeameter and the soil sample will be small and negligible as long as the average particle size of the soil is about 1/10 – 1/15 of the diameter of the permeameter mold.
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