taken for the surface tension of water is 0.000 075 N/mm (0.075 N/m).
The fact that surface tension exists can be shown in a simple laboratory experiment in which an open‐ended glass capillary tube is placed in a basin of water subjected to atmospheric pressure; the rise of water within the tube is then observed. It is seen that the water wets the glass and the column of water within the tube reaches a definite height above the liquid in the basin.
The surface of the column forms a meniscus such that the curved surface of the liquid is at an angle α to the walls of the tube (Fig. 2.15a). The arrangement of the apparatus is shown in Fig. 2.15b.
The base of the column is at the same level as the water in the basin and, as the system is open, the pressure must be atmospheric. The pressure on the top surface of the column is also atmospheric. There are no externally applied forces that keep the column in position, which shows that there must be a tensile force acting within the surface film of the water.
Let
Height of water column = hc
Radius of tube = r
Unit weight of water = γw
If we take atmospheric pressure as datum, i.e. the air pressure = 0, we can equate the vertical forces acting at the top of the column:
(2.23)
(2.24)
Hence, as expected, we see that u is negative which indicates that the water within the column is in a state of suction. The maximum value of this negative pressure is γwhc and occurs at the top of the column. The pressure distribution along the length of the tube 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 hc can be obtained by substituting u = − γwhc in the above expression to yield:
(2.25)
From the two expressions, we see that the magnitudes of both −u and hc 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 πr2hcγw).
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 hc 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 hc = 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, hc,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 hc,max, is governed by the minimum size of the voids. Within the range hc,min to hc,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 hc,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, ua, and the water pressure, uw.
(2.27)
If ua 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
