# Permeability (Falling Head Test) Calculator IS 2720

## Permeability (Falling Head Test) Calculation

cm
cm
cm

Test-I
cm
cm
Second
Test-II
cm
cm
Second
Test-III
cm
cm
Second

#### Avg. Permeability

3.59
Permeability

$=\frac{\mathrm{K1\left(TestI\right)+K2\left(TestII\right)+K3\left(TestIII\right)}}{3}$

$=\frac{\mathrm{3.97+3.19+3.60}}{3}$

$={\mathrm{3.59 %}}^{}$

#### Result of Test-I

3.97
Permeability (K)

$=2.303×\frac{a\mathrm{\left(L\right)}}{A\left(tf-ti\right)}×{\mathrm{log}}_{10}\left(\frac{h1}{h2}\right)$

$=2.303×\frac{\mathrm{706.86}\mathrm{\left(10\right)}}{\mathrm{314.16}\left(\mathrm{30}\right)}×{\mathrm{log}}_{10}\left(\frac{\mathrm{10}}{\mathrm{20}}\right)$

$={\mathrm{3.97}}^{}$

#### Result of Test-II

3.19
Permeability (K)

$=2.303×\frac{a\mathrm{\left(L\right)}}{A\left(tf-ti\right)}×{\mathrm{log}}_{10}\left(\frac{h1}{h2}\right)$

$=2.303×\frac{\mathrm{706.86}\mathrm{\left(10\right)}}{\mathrm{314.16}\left(\mathrm{50}\right)}×{\mathrm{log}}_{10}\left(\frac{\mathrm{30}}{\mathrm{40}}\right)$

$={\mathrm{3.19}}^{}$

#### Result of Test-III

3.60
Permeability (K)

$=2.303×\frac{a\mathrm{\left(L\right)}}{A\left(tf-ti\right)}×{\mathrm{log}}_{10}\left(\frac{h1}{h2}\right)$

$=2.303×\frac{\mathrm{706.86}\mathrm{\left(10\right)}}{\mathrm{314.16}\left(\mathrm{40}\right)}×{\mathrm{log}}_{10}\left(\frac{\mathrm{20}}{\mathrm{30}}\right)$

$={\mathrm{3.60}}^{}$

## What is Falling Head permeability Test?

For a falling head test arrangement, the specimen shall be connected through the top inlet to selected stand-pipe. The bottom outlet shall be opened and thetime interval required for the water level to fall from a known initial head to a known final head as measured above the centre of the outlet shall be recorded. The stand-pipe shall be refilled with water and the test repeated till three successive observations give nearly same time interval; the time intervals being recorded for the drop in head from the same initial to final values, as in the first determination. Alternatively, after selecting the suitable initial and final heads hl and hi respectively, time intervals shall be noted for the head to fall from ${h}_{1}$ to $\sqrt{{h}_{1}{h}_{2}}$ and similarly from $\sqrt{{h}_{1}{h}_{2}}$ to ${h}_{2}$ . The time intervals should be the same; otherwise the observation shall be repeated after refilling the stand-pipe.

Test Setup

##### Apparatus
• The mould assembly (including drainage base and drainage cap) shall conform to IS : 11209-1985.
• The compaction rammer shall conform to IS : 9198-1979.
• Set of Stand Pipes - Glass stand pipes for falling head (variable head) test arrangement, varying in diameter from 5 to 20 mm, suitably mounted on stand or otherwise fixed on wall.
• Constant Head Tank - A suitable water reservoir capable of supplying water to the permeater under constant head for constant head test arrangement.
• Vacuum Pump
• Miscellaneous Apparatus - Such as IS sieves, mixing pan, graduated cylinder, metre scale, stop watch, 75-micron wire gauge, thermometer and a source of de-aired water.

##### Record of Observation
• The dimensions of specimen, length L and diameter D, are measured and recorded in Appendix B. Area a of stand-pipe is recorded. The temperatureT, of water is also measured and recorded.

• During the test, observations are made of initial time ${t}_{1}$ , final time ${t}_{f}$ , initial head ${h}_{1}$ , final head ${h}_{2}$ in stand-pipe and are recorded in co1 2 to 5 of Appendix B respectively. h1/h2 and ${\mathrm{log}}_{10}\left(h1/h2\right)$ are calculated and recorded in co1 6 and 7 of Appendix B respectively. The permeability kris calculated and recorded in co1 8 of Appendix B. Remarks, if any, are entered in co1 9 of Appendix B.

• At the end of the test, the weight of wet soil specimen ${w}_{t}$ is measured and recorded. Then the sample is dried in the oven for 24 hours and the dry weight ${w}_{s}$ is measured and recorded. The water content, W is computed and noted. Void ratio, e, and degree of saturation Sare calculated using specific gravity G, of the specimen and water content, W.

$Permeability Falling Head \left(K\right) =2.303×\frac{a\mathrm{\left(L\right)}}{A\left(tf-ti\right)}×{\mathrm{log}}_{10}\left(\frac{h1}{h2}\right)$
Where,
• a is Area of Tube
• A is Area of Soil Specimen
• L is Length of Soil specimen
• tf−ti is Time Interval (T)

## Preparation of Test Specimen

##### Disturbed Soil Sample
• A 2.5-kg sample shall be taken from a thoroughly mixed air-dried or oven-dried material which has been obtained in accordance with IS : 2720 (Part l)-1983.
• The moisture content of the 2.5-kg sample shall be determined as described in IS : 2720 (Part 2)-1973. The sample shall be placed in an airtight container. The quantity of water to be added to the stored sample to give the desired moisture content shall be computed and spread evenly over the sample, and after thoroughly mixing, the material shall again be placed in the storage container. The moisture content of the sample shall again be determined and the entire process repeated until the actual moisture content is within 0.5 percent of that desired.
• The permeameter mould shall be weighed empty to the nearest gram. After greasing lightly the inside of the mould, it shall be clamped between the compaction base plate and the extension collar. The assembly shall be kept on a solid base.
• The dry density for remoulding of soil samples shall be either the field density or the value of the maximum dry density estimated by thecompaction tests [see IS : 2720 (Part 7)-1980 and IS:2720 (Part 8)-19831 or any other density at which the permeability is desired. The moisture content used for compaction should be the optimum moisture content or the field moisture as the case may be. The compactive effort may be varied to simulate field conditions. Static compaction may also be used where necessary. After completion of compaction, the collar, if attached, shall be removed and excess soil trimmed level with the top of the mould. The base shall be detached and the mould full of the compacted specimen shall be weighed.
• The mould with the specimen inside shall be assembled to the drainageand cap having porous discs. The porous discs shall be saturated before assembling the mould.

##### Undisturbed Soil Sample
• For testing undisturbed soils, undisturbed specimen shall be trimmed in the form a cylinder not larger than about 85 mm in diameter and having a height equal to that of the mould. The specimen shall be placed centrally over the porous disc of the drainage base fixed to the mould. The annular space between the mould and the specimen shall be filled with ‘an impervious material such as cement slurry, or a mixture of 10’percent dry powdered bentonite and 90 percent fine sand by weight to provide sealing between the soil specimen and the mould against leakage from the sides. When using the cement slurry, the mould shall be kept on a flat surface other than the porous discs. The mixture shall be compacted using a small tamping rod. The drainage cap shall then be fixed over the top of the mould.

##### Saturation
• In the case oQsoils of medium to high permeability, the specimen shall be subjected to sufficient head, flow or immersion so as to obtain full saturation. Soils of low permeability require flow under a high head for periods ranging from a day to a week depending upon the permeability and the head. Alternatively, in the case of soils of low permeability, the specimen shall be subjected to a gradually increasing vacuum with bottom outlet closed so as to remove to form the soil voids. The vacuum shall be increased to at least 70 cm of mercury which shall be maintained for 15 minutes or more depending upon the soil type. The evacuation shall be followed by a very slow saturation of the specimen with de-aired water from the bottom upwards under full vacuum. When the specimen is saturated, both the top and bottom outlets shall be closed.

## Presentation of Results

The permeability values at temperatures T and are reported as numbers with units as cm/s. The state of the sample is also reported in terms of water content, void ratio and degree of saturation.