2.6.2 Borehole tests

      Where bedrock level is very deep or where the permeabilities of different strata are required, borehole permeability tests can be used. (See Chapter 7 for details on borehole construction.)

      In borehole permeability testing, open or closed systems can be used and procedures for all borehole hydraulic testing are given in BS EN ISO 22282:2012 (BSI, 2012).

       Open system

      A casing, perforated for a metre or so at its end, is driven into the ground. At intervals during the driving, the rate of flow of water placed under either a constant or a falling head within the borehole is determined. From this rate, together with knowledge of the hydraulic gradient and the cross‐sectional area through which the water flows from the borehole into the adjacent soil, a measure of the soil's permeability can be determined.

       Closed system

      Whereas an open system simply uses a hydraulic head of water in the borehole to cause water to flow into the soil at the perforated section, a closed system uses a pump to introduce water into the soil or rock under pressure and involves the use of one or more packers.

       Packer test

      This test is performed in a partly unlined borehole and can apply to both open and closed systems. The unlined section is the part that is placed under test and, since loose sands and gravels would collapse in on themselves, the test is predominantly used for measuring the permeability of a section of fissured rock mass. An inflatable rubber membrane known as a packer, wrapped around a vertical, perforated hydraulic pipe, is lowered to the depth in the borehole at which the rock is to be tested. The pipe extends below the base of the packer. The packer is inflated to form a watertight seal above the point to be tested. Water is then pumped through the pipe at a controlled pressure and the volume of water injected into the rock over a period of time is measured and used to establish the permeability of the rock.

      A variation on this single packer test is to have a packer both above and beneath the section to be tested. Such an arrangement is known as a double packer test.

2.7 Approximation of coefficient of permeability

      It is obvious that a soil's coefficient of permeability depends upon its porosity, which is itself related to the particle size distribution curve of the soil (a gravel is much more permeable than a clay). It would therefore seem possible to approximate the permeability of a soil given its particle size distribution, and typical ranges of k for different soil types are given below. In addition, k can be approximated for a clean sand thus:

      where D₁₀ = effective size in mm.

      Wise (1992) offered approximations for other soils based on pore size distribution but it should be remembered that no formula is as good as an actual permeability test.

       Typical ranges of coefficient of permeability

       Gravel >10−1 m/s

       Sands 10−1–10−5 m/s

       Fine sands, coarse silts 10−5–10−7 m/s

       Silts 10−7–10−9 m/s

       Clays <10−9 m/s

      Example 2.4 Approximation of k

      Calculate an approximate value for the coefficient of permeability for the soil in Example 1.2.

       Solution:

2.8 General differential equation of flow

Figure 2.7 shows an elemental cube, of dimensions d_x, d_y, and d_z, in an orthotropic soil with an excess hydraulic head h acting at its centre (an orthotropic soil is a soil whose material properties are different in all directions).

      Let the coefficients of permeability in the coordinate directions x, y, and z be k_x, k_y, and k_z, respectively. Consider the component of flow in the x direction.

      The component of the hydraulic gradient, i_x, at the centre of the element will be:

      (2.9)

      (Note that it is of negative sign as there is a head loss in the direction of flow).

      The rate of change of the hydraulic gradient i_x along the length of the element in the x direction will be:

      (2.10)

      Hence, the gradient at the face of the element nearest the origin

      (2.11)

      From Darcy's law:

(2.12)

Fig. 2.7 Element in an orthotropic soil.

      The gradient at the face furthest from the origin is:

      (2.13)

      Therefore,

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