the foundation.
Solution:
1 Since the head of water in the gravel is greater than the depth of clay above, it follows that the GWT may be assumed to be at the ground surface.Thus,Head of water in clay = 8 mHead of water in gravel = 10 m⇒Head of water lost in clay = 2 mq = AkiConsider a unit area of 1 m2 then:
2 Height of clay left above gravel after excavation = 8 − 2 = 6 mUpward pressure from water on base of clay = 10 × 9.81 = 98.1 kPaDownward pressure of clay = 6 × 19 = 114 kPa.It is clear that the downward pressure exceeds the upward pressure and thus, on the face of it, the foundation will not be lifted by the buoyant effect of the upward‐acting water pressure, i.e. it is safe. We can quantify how ‘safe’ the foundation is against buoyancy by introducing the term factor of safety, F:Downward pressure after construction = 114 + 100 = 214 kPai.e. the factor of safety against buoyant uplift is higher after construction.We can also assess the safety against buoyancy using the limit state design approach defined in Eurocode 7 (see Chapter 6). The solution to Example 2.6 when assessed in accordance with Eurocode 7 is available for download from the companion website.
Units of pressure
The pascal is the stress value of one newton per square metre, 1.0 N/m2, and is given the symbol Pa. In the example above, pressure has been expressed in kilopascals, kPa. Pressure could have equally been expressed in kN/m2 as the two terms are synonymous.
2.12 Design of soil filters
As seen above, water seeping out of the soil can lead to piping and therefore drainage should be provided in such situations to ensure ground stability. To prevent soil particles being washed into the drainage system, soil filters can be provided as the interface between base material and drain. The design procedure for a filter is largely empirical, but it must comprise granular material fine enough to prevent soil particles being washed through it and yet coarse enough to allow the passage of water.
The following formulae are used in the specification of the filter material, based initially on the work of Terzaghi and developed through the experimental research of Sherard et al. (1984a, b):
The first equation ensures that the filter layer has a permeability several times higher than that of the soil it is designed to protect. The requirement of the second equation is to prevent piping within the filter. The ratio D15 (filter)/D85 (base) is known as the piping ratio.
The required thickness of a filter layer depends upon the flow conditions and can be estimated with the use of Darcy's law of flow. The filter material should be well graded, with a grading curve more or less parallel to the soil. All material should pass the 75 mm size sieve and not more than 5% should pass the 0.063 mm size sieve (see Example 2.7 and Fig. 2.14).
Protective filters are usually constructed in layers, each of which is coarser than the one below it, and for this reason they are often referred to as reversed filters. Even when there is no risk of piping, filters are often used to prevent erosion of foundation materials and they are extremely important in earth dams.
Example 2.7 Filter material limits
Determine the approximate limits for a filter material suitable for the material shown in Fig. 2.14.
Solution:
From the particle size distribution curve:
Using Terzaghi's method:
This method gives two points on the 15% summation line. Two lines can be drawn through these points roughly parallel to the grading curve of the soil, and the space between them is the range of material suitable as a filter (Fig. 2.14).
2.13 Capillarity and unsaturated soils
The behaviour of unsaturated soils is a relatively specialised subject area and readers interested in gaining a good understanding of the topic are referred to the publications by Fredlund et al. (2012) and Ng and Menzies (2007). Simple coverage of some of the key aspects involved are offered in the following sections.
2.13.1 Surface tension
Surface tension is the property of water that permits the surface molecules to carry a tensile force. Water molecules attract each other, and within a mass of water, these forces balance out. At the surface, however, the molecules are only attracted inwards and towards each other, which creates surface tension. Surface tension causes the surface of a body of water to attempt to contract into a minimum area: hence, a drop of water is spherical.
The phenomenon is easily understood if we imagine the surface of water to be covered with a thin molecular skin capable of carrying tension. Such a skin, of course, cannot exist on the surface of a liquid, but the analogy can explain surface tension effects without going into the relevant molecular theories.
Fig. 2.15 Capillary effects.
Surface tension is given the symbol T and can be defined as the force in Newtons per millimetre length that the water surface can carry. T varies slightly with temperature, but this variation is small, and an
