Permeability

Permeability, as the name implies (ability to permeate), is a measure of how easily a fluid can flow through a porous medium. In geotechnical engineering, the porous medium is soils and the fluid is water at ambient temperature. Generally, coarser the soil grains, larger the voids and larger the permeability. Therefore, gravels are more permeable than silts. Hydraulic conductivity is another term used for permeability.

 Just as with porosity, the packing, shape, and sorting of granular materials control their permeability. Although a rock may be highly porous, if the voids are not interconnected, then fluids within the closed, isolated pores cannot move. The degree to which pores within the material are interconnected is known as effective porosity. Rocks such as pumice and shale can have high porosity, yet can be nearly impermeable due to the poorly interconnected voids. In contrast, well-sorted sandstone closely replicates the example of a box of marbles cited above. The roundedsand grains provide ample, unrestricted void spaces that are free from smaller grains and are very well linked. Consequently, sandstones of this type have both high porosity and high permeability.

The range of values for permeability in geologic materials is extremely large. The most conductive materials have permeability values that are millions of times greater than the least permeable. Permeability is often directional in nature. The characteristics of the interstices of certain materials may cause the permeability to be significantly greater in one direction. Secondary porosity features, like fractures, frequently have significant impact on the permeability of the material. In addition to the characteristics of the host material, the viscosity and pressure of the fluid also affect the rate at which the fluid will flow.

Units

The SI unit for permeability is m2. A traditional unit for permeability is the darcy (D), or more commonly the millidarcy (mD) (1 darcy  10−12m2). The unit of cm2 is also sometimes used (1 m2= 104 cm2).

DARCY’S LAW

Assumptions made defining Darcy’ law.

1 The flow is laminar that is, flow of fluids is described as laminar if a fluid

Particles flow follows a definite path and does not cross the path of other particles.

2 Water & soil are incompressible that is, continuity equation is assumed to be valid

3 The soil is saturated

4 The flow is steady state that is, flow condition do not change with time.

Darcy law

In 1856, modern studies of groundwater began when French scientist and engineer, H.P.G. Darcy (1803-1858) was commissioned to develop a water-purification system for the city of Dijon, France. He constructed the first experimental apparatus to study the flow characteristics of water through the soil medium. From his experiments, he derived the equation that governs the laminar (non-turbulent) flow of fluids in homogeneous porous media which became to be known as Darcy’s law.

Schematic diagram depicting Darcy’s experiment

The schematic diagram representing Darcy’s experiment is depicted in Figure By measuring the value of the rate of flow, Q for various values of the length of the sample, L, and pressure of water at top and bottom the sample, h1 and h2, Darcy found that Q is proportional to (h1 – h2)/L or the hydraulic gradient, i, that is,

Q=kh1−h2

LA=k

∆ hL

A

Q=kiA

The loss of head of _h units is affected as the water flows from h1 to h2. The hydraulic gradient defined as loss of head per unit length of flow may be expressed as,

i=∆ hL

k is coefficient of permeability or hydraulic conductivity with units of velocity, such as mm/sec or m/sec. Thus the theory of seepage flow in porous media is based on a generalization of Darcy's Law which is stated as, “Velocity of flow in porous soil media is proportional to the hydraulic gradient” where, flow is assumed to be laminar. That is,

v= k i

Where, k is coefficient of permeability, v is velocity of flow and i is the hydraulic gradient.

Factors affecting permeability

The coefficient of permeability as used by geotechnical engineer is the approach or superficial velocity of the permeant flowing through soil medium under unit hydraulic gradient hence it depends on the characteristics of permeant, as well as those of the soil.

Considering the flow through a porous medium as similar to a flow through a bundle of straight capillary tubes, the relationship showing the dependency of soil permeability on various characteristic parameters of soil and permeant was developed by Taylor as given below,

k=D2 ρμ

e3

(1+e)C

This equation reflects the influence of permeant and the soil characteristics on permeability.

In the above equation D is the effective diameter of the soil particles, r is the unit weight of fluid, μ is the viscosity of fluid and C is the shape factor. Therefore, with the help of above equation, factors affecting permeability can be listed as follows,

Soil characteristics

i. Grain-size

• Shape and size of the soil particles.

• Permeability varies with the square of particle diameter.

• Smaller the grain-size the smaller the voids and thus the lower the permeability.

• A relationship between permeability and grain-size is more appropriate in case

of sands and silts.

• Allen Hazen proposed the following empirical equation, 2

10 k(cm / s) = C D , C is a constant that varies from 1.0 to 1.5 and D10 is the effective size, in mm

ii. Void ratio

• Increase in the porosity leads to an increase in the permeability.

• It causes an increase in the percentage of cross-sectional area available for flow.

iii. Composition

• The influence of soil composition on permeability is generally insignificant in

the case of gravels, sands, and silts, unless mica and organic matter are present.

• Soil composition has major influence in the case of clays.

• Permeability depends on the thickness of water held to the soil particles, which

is a function of the cation exchange capacity.

iv. Soil structural

• Fine-grained soils with a flocculated structure have a higher coefficient of

permeability than those with a dispersed structure.

• Remoulding of a natural soil reduces the permeability

• Permeability parallel to stratification is much more than that perpendicular to

stratification

v. Degree of saturation

• Higher the degree of saturation, higher is the permeability.

• In the case of certain sands the permeability may increase three-fold when the

degree of saturation increases from 80% to 100%.

vi. Presence of entrapped air and other foreign matter.

• Entrapped air reduces the permeability of a soil.

• Organic foreign matter may choke flow channels thus decreasing the

Permeability Hence, it is important to simulate field conditions in order make realistic estimate of the permeability of a natural soil deposit, particularly when the aim is to determine field permeability in the laboratory.

LABORATORY DETERMINATION OF PERMEABILITY

Permeability of a coarse grained soil can be determined by a constant head permeability test (AS1289.6.7.1-2001; ASTM D2434), and in a fine grained soil, falling head permeability test (AS1289.6.7.2-2001; ASTM D5856) works the best. In a constant head permeability test (Fig. 7.6), the total head loss (hL) across a cylindrical soil specimen of length L and cross sectional area A, is maintained constant throughout the test, and at steady state, the flow rate (Q) is measured.

Therefore, the discharge velocity (v) is given by:

v = Q/A

The hydraulic gradient (i) across the soil specimen is hL/L. Applying Darcy’s law,

Q/A = k hL/L

Therefore, k is given by:

k= QLhL A

CONSTANT HEAD PERMEABILITY TEST

SCOPE

The permeability test is a measure of the rate of the flow of water through soil. In this test, water is forced by a known constant pressure through a soil specimen of known dimensions and the rate of flow is determined. This test is used primarily to determine the suitability of sands and gravels for drainage purposes, and is made only on remolded samples. The test is limited to materials which have a coefficient of permeability of approximately 300 mm/day or greater. The “Constant Head” type of test is used on samples that represent materials to be used as backfill for abutments, as permeable material for underdrains, as sand drains, as sand blanket for sand drain areas, and similar materials.

OBJECTIVE

To determine the coefficient of permeability of a soil using constant head method.

NEED AND SCOPE OF PERMEABILITY

The knowledge of this property is much useful in solving problems involving yield

of water bearing strata, seepage through earthen dams, stability of earthen dams,

and embankments of canal bank affected by seepage, settlement etc.

  PLANNING AND ORGANIZATION

1.      Preparation of the soil sample for the test

2.      Finding the discharge through the specimen under a particular head of

water.     

DEFINITION OF COEFFICIENT OF PERMEABILITY

The rate of flow under laminar flow conditions through a unit cross sectional are of

porous medium under unit hydraulic gradient is defined as coefficient of

permeability. 

EQUIPMENT

1. Permeameter mould of non-corrodible material having a capacity of 1000 ml,

2. The mould shall be fitted with a detachable base plate and removable extension

counter.

3. Compacting equipment: 50 mm diameter circular face, weight 2.76 kg and

height of fall 310 mm as specified in I.S 2720 part VII 1965.

4. Drainage bade: A bade with a porous disc, 12 mm thick which has the

permeability 10 times the expected permeability of soil.

5. Drainage cap: A porous disc of 12 mm thick having a fitting for connection to

water inlet or outlet.

6. Constant head tank: A suitable water reservoir capable of supplying water to the

permeameter under constant head.

7. Graduated glass cylinder to receive the discharge.

8. Stop watch to note the time.

9. A meter scale to measure the head differences and length of specimen.

 PREPARATION OF SPECIMEN FOR TESTING

A. UNDISTURBED SOIL SAMPLE

1. Note down the sample number, bore hole number and its depth at which the

sample was taken.

2. Remove the protective cover (paraffin wax) from the sampling tube.

3. Place the sampling tube in the sample extraction frame, and push the plunger to

get a cylindrical form sample not longer than 35 mm in diameter and having height

equal to that of mould.

4. The specimen shall be placed centrally over the porous disc to the drainage base.

5. The angular space shall be filled with an impervious material such as cement

slurry or wax, to provide sealing between the soil specimen and the mould against

leakage from the sides.

6. The drainage cap shall then be fixed over the top of the mould.

7. Now the specimen is ready for the test. 

DISTURBED SOIL SAMPLE

1. A 2.5 kg sample shall be taken from a thoroughly mixed air dried or oven dried

material.

2. The initial moisture content of the 2.5 kg sample shall be determined. Then the

soil shall be placed in the air tight container.

3. Add required quantity of water to get the desired moisture content.

4. Mix the soil thoroughly.

5. Weigh the empty permeameter mould.

6. After greasing the inside slightly, clamp it between the compaction base plate

and extension collar.

7. Place the assembly on a solid base and fill it with sample and compact it.

8. After completion of a compaction the collar and excess soil are removed.

9. Find the weight of mould with sample.

10. Place the mould with sample in the permeameter, with drainage base and cap

having discs that are properly saturated.

 TEST PROCEDURE

1. Fill the reservoir to the outlet level with water. Place the perforated plate on the specimen and place the mold and specimen on the “U” shaped hanger to give a head of water. Level the mold with the aid of the nuts on the three vertical studs, and introduce water to the top of the specimen. It may be necessary to use less head if there is an exceptional high rate of flow, “K” of 60 or 90 m/day, (0.07- 0.1 cm/sec) or if there is any indication of piping or of passing of fines from the sample during the test.

2. Allow percolation for some time to ensure a high degree of saturation and uniformity of test results.3. Establish steady flow of water. Allow water to run into the intake reservoir at a rate slightly faster than the rate of flow through the specimen. Waste the excess through the intake overflow tube into the sink. The outlet reservoir must be full to the point of overflow before the test is begun. The excess water from the outlet reservoir during the test is the amount that has flowed through the specimen.

4. Determine the quantity of flow (Q) by means of either a graduated container or by weighing, and determine the elapsed time (t) for the quantity of flow. Record these determinations

5. Repeat three times for the same interval.

  OBSERVATION AND RECORDING

The flow is very low at the beginning, gradually increases and then stands

constant. Constant head permeability test is suitable for cohesionless soils. For

cohesive soils falling head method is suitable.

COMPUTATION

Coefficient of permeability for a constant head test is given by

Details of sample

Diameter of specimen                              6.4cm

Length of specimen (L)                             17cm

Area of specimen (A)                           32.17cm2

Initial dry mass of soil + pan (M1) 1675.0g

Final dry mass of soil + pan (M2) 865.6g

Dry mass of the soil specimen (M) 809.4g

Volume of soil specimen (V) 846.9cm3

Dry density of soil (δd) 1.48 g/cm3

Experiment No. 1 2 3

Length of specimen L(cm) 17 17 17Area of specimen A(cm2) 32.17 32.17 32.17

Time t (sec) 84 55 48

Discharge volume q(cm3) 750 750 750

Height of water h(cm) 30 50 60

k= QLAht

(cm/sec) 0.149 0.137 0.130

Average permeability (k) = 0.1386 cm/sec

Coefficient of permeability in different soils