Smith's Elements of Soil Mechanics. Ian Smith

is shown in Fig. 2.15c. It is seen that the water pressure gradually increases with loss of elevation to a value of 0 at the base of the column.

      An expression for the height h_c can be obtained by substituting u = − γ_wh_c in the above expression to yield:

      (2.25)

      From the two expressions, we see that the magnitudes of both −u and h_c increase as r decreases.

      A further interesting point is that, if we assume that the weight of the capillary tube is negligible, then the only vertical forces acting are the downward weight of the water column supported by the surface tension at the top and the reaction at the base support of the tube. The tube must therefore be in compression. The compressive force acting on the walls of the tube will be constant along the length of the water column and of magnitude 2πT cos α (or πr²h_cγ_w).

      It may be noted that for pure water in contact with clean glass which it wets, the value of angle α is zero. In this case, the radius of the meniscus is equal to the radius of the tube and the derived formulae can be simplified by removing the term cos α.

      With the use of the expression for h_c we can obtain an estimate of the theoretical capillary rise that will occur in a clay deposit. The average void size in a clay is about 3 μm and, taking α = 0, the formula gives h_c = 5.0 m. This possibly explains why the voids exposed when a sample of a clay deposit is split apart are often moist. However, capillary rises of this magnitude seldom occur in practice as the upward velocity of the water flow through a clay in the capillary fringe is extremely small and is often further restricted by adsorbed water films, which considerably reduce the free diameter of the voids.

      2.13.2 Capillary effects in soil

      The region within which water is drawn above the water table by capillarity is known as the capillary fringe. A soil mass, of course, is not a capillary tube system, but a study of theoretical capillarity enables the determination of a qualitative view of the behaviour of water in the capillary fringe of a soil deposit. Water in this fringe can be regarded as being in a state of negative pressure, i.e. at pressure values below atmospheric. A diagram of a capillary fringe is shown in Fig. 2.15d.

      The minimum height of the fringe, h_c,min, is governed by the maximum size of the voids within the soil. Up to this height above the water table the soil will be sufficiently close to full saturation to be considered as such.

      The maximum height of the fringe h_c,max, is governed by the minimum size of the voids. Within the range h_c,min to h_c,max, the soil can be only partially saturated.

      We saw in Section 2.1.2 that Terzaghi and Peck (1948) give an approximate relationship between h_c,max and grain size for a granular soil:

      (2.26)

Owing to the irregular nature of the conduits in a soil mass, it is not possible, even approximately, to calculate water content distributions above the water table from the theory of capillarity. This is a problem of importance in highway engineering and is best approached by the concept of soil suction.

      2.13.3 Soil suction

      The capacity of a soil above the groundwater table to retain water within its structure is related to the prevailing suction and to the soil properties within the whole matrix of the soil, e.g. void and soil particle sizes, amount of held water, etc. For this reason, it is often referred to as matrix or matric suction.

      It is generally accepted that the amount of matric suction, s, present in an unsaturated soil is the difference between the values of the air pressure, u_a, and the water pressure, u_w.

      (2.27)

      If u_a is constant, then the variation in the suction value of an unsaturated soil depends upon the value of the pore water pressure within it. This value is itself related to the degree of saturation of the soil.

      2.13.4 The water retention curve

If a slight suction is applied to a saturated soil, no net outflow of water from the pores is caused. However, as the suction is increased, water starts to flow out of the larger pores within the soil matrix. As the suction is increased further, more water flows from the smaller pores until at some limit, corresponding to a very high suction, only the very narrow pores contain water. Additionally, the thickness of the adsorbed water envelopes around the soil particles reduces as the suction increases. Increasing suction is thus associated with decreasing soil wetness or water content. The amount of water remaining in the soil is a function of the pore sizes and volumes, and hence a function of the matric suction. This function can be determined experimentally and may be represented graphically as the water retention curve, such as the examples shown in Fig. 2.16.

Fig. 2.16 Example wetting and drying water retention curves.

The amount of water in the pores for a particular value of suction will depend on whether the soil is wetting or drying. This gives rise to the phenomenon known as hysteresis, and the shape of the water retention curve for each process is shown in Fig. 2.16. A full descriptive text on water retention curves and hysteresis is given by Fredlund et al. (2012).

      2.13.5 Measurement of soil suction

      From a geotechnical point of view, there are two components of soil suction as follows:

      1 matric suction: that part of the water retention energy created by the soil matrix;

      2 osmotic suction: that part of the water retention energy created by the presence of dissolved salts in the soil water.

      It should be noted that these two forms of soil suction are completely independent and have no effect on each other.

      The total suction exhibited by a soil is obviously the summation of the matric and the osmotic suctions.

      If a soil is granular and free of salt, there is no osmotic suction and the matric and total suctions are equal. However, clays contain salts and these salts cause a reduction in the vapour pressure. This results in an increase in the total suction, and this increase is the energy needed to transfer water into the vapour phase (i.e. the osmotic suction).

      There are several types of equipment available which can be used to measure soil suction values. Amongst them are psychrometers, porous blocks, filter papers, suction plates, pressure plates, and tensiometers, the last being the most popular for in situ measurements. A useful survey was prepared by Ridley (2015).

       The psychrometer method

      A psychrometer is used to measure humidity and is therefore suitable to measure total soil suction, i.e. the summation of the matric and the osmotic components. The equipment and its operation have been described by Fredlund et al. (2012).

      A