How to Determine the Permeability of Soil ?

The following article will guide you about how to determine the permeability of soil.

Constant Head Permeability Test:

Permeability of coarse-grained soils having high permeability is determined in the laboratory by the constant head permeability test. The principle of the test is to measure the volume of water flowing through a soil specimen in a given time and determine the permeability from the discharge using Darcy’s law.

Figure 9.3 shows the schematic diagram for the constant head permeability test. The equipment for the test, known as permeameter, consists of a cylindrical mold, a drainage cap with an inlet valve and an air release valve, and a drainage base plate with an outlet pipe. The mold is 10 cm in diameter and 12.73 cm in internal height. The base plate has a recess at the center in which the bottom porous disc is placed. A filter paper is placed over the bottom porous disc.

The soil is compacted into the permeameter mold at the required density and water content. Alternately, an undisturbed soil sample from the soil sampler is cut into the permeameter mold, taking care to avoid leakage through the side walls. A filter paper is placed over the top surface of the soil specimen and the top porous disc is placed on the filter paper. The porous disc is specially manufactured with sand and cement, with voids to permit the flow of water.

A constant head water tank is connected to the drainage cap of the permeameter. The overflow pipe of the water tank ensures constant water level in the tank so that constant head is maintained for water flowing through the soil specimen. The permeameter mold is connected to a bottom water tank with an overflow pipe. The difference between the water levels in the constant head water tank and the bottom tank is the head causing the flow of water through the soil specimen.

Before commencement of the test, the soil specimen should be completely saturated so that Darcy’s law is valid.

To ensure complete saturation of the soil specimen, the air in the soil specimen is removed by the following methods:

i. Allowing water to flow upward by attaching the constant head reservoir to the drainage base for sufficient time and opening the air release valve.

ii. Applying a vacuum pressure of about 70 cm of mercury through the drainage cap for about 15 min after closing the drainage valve.

After the soil sample has been completely saturated, the constant head reservoirs are connected to the drainage cap of the permeameter mold. Water is allowed to flow through the soil sample for sufficient time till a steady state is established.

When the steady state is established, water is collected from the bottom tank in a graduated measuring jar for a convenient time period, which is measured using a stopwatch. If q is the volume of water collected in a time interval “t,” discharge through the soil sample is –

Q = q/t

As per Darcy’s law, this discharge is –

Q = q/t = kiA …(9.7)

where k is the coefficient of permeability of the soil sample, i is the hydraulic gradient (= h/l),h is the head causing flow (difference in the water levels between the constant head reservoir and the bottom tank), I is the length of flow (length of soil sample), and A is the total cross-sectional area of soil. Substituting these in Eq. (9.7), we get –

q/t = k (h/l) A Þ k = ql/hAt …(9.8)

The test is repeated several times and the average of the several permeability determinations is taken as the perme­ability of the soil.

The constant head permeability test is suitable only for coarse-grained soils, for which a significant volume of water can be collected in a reasonable time interval.

Falling Head Permeability Test:

For soils of low permeability, the quantity of water collected in the graduated jar of the constant head permeability test is very small and cannot be measured accurately. For such soils, the variable head permeability test is used. As per Lambe (1969), the variable head permeability test is also more convenient for cohesionless soils than the constant head test because of simpler instrumentation.

The permeameter used in the falling head test is the same as that used for the constant head test, having a 10-cm diameter, 12.73-cm height, and 1000-mL capacity. A vertical graduated standpipe of known cross-sectional area a is fitted to the top of the permeameter. The permeameter mold has a drainage base with a recess for a porous disc and a drainage cap with inlet and air release valves, as shown in Fig. 9.4.

After placing the bottom porous disc, the soil sample is compacted into the permeameter mold and the top porous disc is placed on the compacted soil. The purpose of using the bottom porous disc is to prevent washing and escape of soil particles during downward flow, while the top porous disc helps in the distribution of inlet water over the entire cross-sectional area of the soil sample. The porous disc and water tubes should be de-aired before placing the sample.

Before conducting the test, removal of entrapped air and full saturation of soil sample must be done. This is achieved by applying vacuum through the drainage cap, after closing the drainage valve in the drainage base and the air release valve in the drainage cap. The vacuum pressure is slowly increased to 70 cm of mercury and maintained for about 15 min. The soil sample is saturated by allowing the de-aired water to flow upward from the drainage base under vacuum. When the soil sample is saturated, both the top and the bottom outlets are closed.

The standpipe is filled with water to the required height. After a steady state of flow has been established, the time required for the water level in the standpipe to fall from height h₁ to height h₂ is noted. The head is measured with reference to the water level in the bottom tank. When the head of water in the standpipe is “h,” let the head drop by dh, during an infinitesimally small time dt. If the discharge through the soil sample is q, which is constant, then –

Volume of water entering the soil sample = –a × dh

where a is the cross-sectional area of the standpipe. Now –

Volume of water leaving the soil sample = q × dt

–a × dh = q × dt = (kiA) dt = k. (h/l)Adt

Þ (Ak/al) dt = –dh/h

Integrating both sides between limits t₁ and t₂ and h₁ and h₂, we have –

The coefficient of permeability is reported at 27°C. The falling head permeability test is suitable for fine-grained soils, for example, fine sand, silt, clay, etc. If the room temperature is different from 27°C, the permeability, k_T, deter­mined at room temperature T°C should be converted to that at 27°C using

k₂₇°_C = k_T (µ_T/µ₂₇) …(9.10)

The elapsed time required for the fall of head from h₁ to √h₁h₂ and from √h₁h₂ to h₂ must be compared, which should be the same. If these times do not agree within 2% – 3%, the standpipe shall be refilled with water and the test is conducted again.

Capillary Permeability Test:

The permeability of partially saturated soils can be determined using the capillarity permeability test, which is also known as “horizontal capillarity” test. The test is also used to find “capillary head or soil suction” in soils.

Figure 9.6 shows the test setup in the horizontal capillarity test. The apparatus consists of a transparent tube, 4 cm in diameter and 35 cm in length, made of Lucite or glass. The soil sample is placed in the tube and screens are fixed at both ends. One end of the transparent tube is connected to the high-level and low-level water reservoirs, as shown in Fig. 9.6. The other end is open to atmosphere through an air vent pipe. The air vent pipe is connected to the screens at the open end with a spring.

The valve A connected to the high-level reservoir is closed. When the valve B connected to the low-level reser­voir is opened, capillary action in the soil occurs and it draws water into the soil. The wet surface of the soil sample starts advancing toward the open end. Let h_c be the capillary head in the soil (which is negative), x be the distance of advancement of the wet surface at any instant. The total head causing flow is increased because of the negative head (h_c) and is given by –

H = h₁ + h_c

The velocity of flow through the soil sample is given by Darcy’s law –

v = ki Þ v = k_u . [(h₁ + h₂)/x] …(9.11)

where k_u is the permeability of a partially saturated soil. The wet surface moves with a seepage velocity (v_s) given by –

v_s = v/n_u = 1/n_u . k_u . [(h₁ + h_c)/x]

where n_u is the porosity of the saturated portion of the soil = S.n, S is the degree of saturation, and n is the porosity of the fully saturated soil. Hence –

v_s = k_u/Sn . [(h₁ + h_c)/x]

The rate of advancement of the wet surface with time may also be expressed as dx/dt. But the rate of advancement of the wet surface is equal to the velocity of water. Therefore, –

Integrating both sides, we get –

Equation (9.12) contains two unknown h_c and k_u. The valve A is now opened and the advancement of the wet surface due to the flow of water from the high-level reservoir is monitored. The advancement of the wet surface from x₂ to x₃ from instant t₂ to t₃ under head h₂ is measured.

A similar treatment will give the following equation:

The unsaturated coefficient of permeability k_u and the capillary head h_c can be determined by solving Eqs. (9.12) and (9.13) simultaneously. For accurate results, the capillary head h_c should be maintained constant along the vertical wetting surface by revolving the tube slowly about its longitudinal axis.

Consolidation Test:

Permeability of a soil may also be obtained indirectly from the results of a consolidation test using Eq. (9.14). It should be, however, noted that the permeability so obtained is an average for the clay layer and has limited appli­cability to similar/identical pressure and drainage conditions.

k = c_v m_v γ_w …(9.14)