Smith's Elements of Soil Mechanics. Ian Smith
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difference in manometer = 50 mm
Distance between manometer tappings = 100 mm
Diameter of test sample = 100 mm
Determine the coefficient of permeability in m/s.
Solution:
2.5.2 The falling head permeameter
A sketch of the falling head permeameter is shown in Fig. 2.5. In this test, which is suitable for silts and some clays, the flow of water through the sample is measured at the inlet. The height, h1, in the standpipe is measured and the valve is then opened as a stop clock is started. After a measured time, t, the height to which the water level has fallen, h2, is determined.
Fig. 2.5 The falling head permeameter.
k is given by the formula:
where
A = cross‐sectional area of sample
a = cross‐sectional area of standpipe
l = length of sample.
As just mentioned, during the test, the water in the standpipe falls from a height h1 to a final height h2.
Let h be the height at some time, t.
Consider a small time interval, dt, and let the change in the level of h during this time be −dh (negative as it is a drop in elevation).
The quantity of flow through the sample in time dt = −adh and is given the symbol dQ. Now
Integrating between the test limits:
(2.7)
Example 2.2 Falling head permeameter
An undisturbed soil sample was tested in a falling head permeameter. The results were:
Initial head of water in standpipe = 1500 mm
Final head of water in standpipe = 283 mm
Duration of test = 20 minutes
Sample length = 150 mm
Sample diameter = 100 mm
Stand‐pipe diameter = 5 mm
Determine the permeability of the soil in m/s.
Solution:
2.5.3 The hydraulic consolidation cell (Rowe cell)
The Rowe cell (described in Chapter 12) was developed for carrying out consolidation tests. The apparatus can also be used for determining the permeability of a soil, though it is fairly rare to see this equipment in a commercial soils laboratory.
2.6 Determination of permeability in the field
2.6.1 Field pumping test
Laboratory tests can only determine k for the small sample of soil tested. To establish the permeability of a whole aquifer, a field pumping test is carried out. The test can be used to measure the average k value of a stratum of soil below the water table and is effective up to depths of about 45 m. Details of pumping test procedures are given in BS EN ISO 22282‐4:2012 (BSI, 2012) and BS ISO 14686:2003 (BSI, 2003).
A casing of about 400 mm diameter is driven to bedrock or to impervious stratum. Observation wells of at least 35 mm diameter are put down on radial lines from the casing, and both the casing and the observation wells are perforated to allow easy entrance of water. The test consists of pumping water out from the central casing at a measured rate, q and observing the resulting drawdown in groundwater level by means of the observation wells.
At least four observation wells, arranged in two rows at right angles to each other should be used although it may be necessary to install extra wells if the initial ones give irregular results. If there is a risk of fine soil particles clogging the observation wells then the wells should be surrounded by a suitably graded filter material (the design of filters is discussed later in this chapter) or a geofabric filter.
It may be that the site boundary conditions, e.g. a river, canal or a steep sloping surface of impermeable subsurface rock, a fault or a dyke, do not allow the two rows of observation wells to be placed at right angles. In such circumstances, the two rows of wells should be placed parallel to each other and at right angles to the offending boundary.
The minimum distance between the observation wells and the pumping well should be 10 times the radius of the pumping well and at least one of the observation wells in each row should be at a radial distance greater than twice the thickness of the ground being tested.
Fig. 2.6 Field pumping test.
In addition to the observation wells, an additional standpipe inside the pumping well is desirable so that a reliable record of the drawdown of the well itself can be obtained. Figure 2.6 illustrates conditions during pumping.
Consider an intermediate distance r from the centre of the pumping well and let the height of the GWL above the impermeable layer during pumping be h.
and 2πrh = area of the walls of an imaginary cylinder of radius r and height h.
Now,
i.e.
and, integrating between test limits:
i.e.
(2.8)
Pumping tests can be expensive as they require the installation of both the pumping and the observation wells as well as suitable pumping and support equipment. Care must be taken in the design of a suitable test programme and,