Soil Water Permeability and Flow

2.1 Subsurface water

This is the term used to define all water found beneath the Earth's surface. The main source of subsurface water is rainfall, which percolates downwards to fill up the voids and interstices. Water can penetrate to a considerable depth, estimated to be as much as 12000 metres, but at depths greater than this, due to the large pressures involved, the interstices have been closed by plastic flow of the rocks. Below this level water cannot exist in a free state, although it is often found in chemical combination with the rock minerals, so that the upper limit of plastic flow within the rock determines the lower limit of subsurface water.

Subsurface water can be split into two distinct zones: saturation zone and aeration zone.

2.1.1 Saturation zone

This is the depth throughout which all the fissures, etc., are filled with water under hydrostatic pressure. The upper level of this water is known as the water table, phreatic surface or ground water level, and water within this zone is called phreatic water or ground water.

The water table tends to follow in a more gentle manner the topographical features of the surface above (Fig. 2.1). At ground water level the hydrostatic pressure is zero, so another definition of water table is the level to which water will eventually rise in an unlined borehole.

Water table

Water table

Tendency of the water table to follow the earth's surface.

The water table is not constant but rises and falls with variations of rainfall, atmospheric pressure, temperature, etc., whilst coastal regions are affected by tides.

When the water table reaches the surface, springs, lakes, swamps, and similar features can be formed.

2.1.2 Aeration zone

Sometimes referred to as the vadose zone, this zone occurs between the water table and the surface, and can be split into three sections.

Capillary fringe

Owing to capillarity, water is drawn up above the water table into the interstices of the soil or rock. Water held in this manner is in a state of suction or negative pressure; its height depends upon the material, and in general the finer the voids the greater the capillary rise. In silts the rise can be as high as two and a half metres and in clays can reach twice that amount, as illustrated later in Section 2.19 which deals with capillarity.

Intermediate belt

As rainwater percolates downward to the water table a certain amount is held in the soil by the action of surface tension, capillarity, adsorption, chemical action, etc. The water retained in this manner is termed held water and is deep enough not to be affected by plants.

Soil belt

This zone is constantly affected by evaporation and plant transpiration. Moist soil in contact with the atmosphere either evaporates water or condenses water

Ground surface

Soil water

Soil belt

Aeration zone

Intermediate water

Intermediate belt

Capillary fringe

Capillary water

Water table

Saturation Ground water zone

Rock flow zone

Internal water

Fig. 2.2 Diagram illustrating types of subsurface water.

into itself until its vapour pressure is equal to atmospheric pressure. Soil water in atmospheric equilibrium is called hygroscopic water, whilst the moisture content (which depends upon relative humidity) is known as the hygroscopic water content.

The various zones are illustrated in Fig. 2.2.

2.2 Flow of water through soils

The voids of a soil (and of most rocks) are connected together and form continuous passageways for the movement of water brought about by rainfall infiltration, transpiration of plants, unbalance of chemical energy, variation of intensity of dissolved salts, etc.

When rainfall falls on the soil surface, some of the water infiltrates the surface and percolates downward through the soil. This downward flow results from a gravitational force acting on the water. During flow, some of the water is held in the voids in the aeration zone and the remainder reaches the ground water table and the saturation zone. In the aeration zone, flow is said to be unsaturated. Below the water table, flow is said to be saturated.

2.2.1 Saturated flow

The water within the voids of a soil is under pressure. This water, known as pore water, may be static or flowing. Water in saturated soil will flow in response to variations in hydrostatic head within the soil mass. These variations may be natural or induced by excavation or construction.

2.2.2 Hydraulic or hydrostatic head

The head of water acting at a point in a submerged soil mass is known as the hydrostatic head and is expressed by Bernoulli's equation:

Hydrostatic head = Velocity head + Pressure head + Elevation head v2 p h = + —+ z 2g 7w

In seepage problems atmospheric pressure is taken as zero and the velocity is so small that the velocity head becomes negligible; the hydrostatic head is therefore taken as:

Excess hydrostatic head

Water flows from points of high to points of low head. Hence flow will occur between two points if the hydrostatic head at one is less than the hydrostatic head at the other, and in flowing between the points the water experiences a head loss equal to the difference in head between them. This difference is known as the excess hydrostatic head.

2.2.3 Seepage velocity

The conduits of a soil are irregular and of small diameter - an average value of the diameter is Djo/5. Any flow quantities calculated by the theory of pipe flow must be in error and it is necessary to think in terms of an average velocity through a given area of soil rather than specific velocities through particular conduits.

If Q is the quantity of flow passing through an area A in time t, then the average velocity (v) is:

This average velocity is sometimes referred to as the seepage velocity. In further work the term velocity will infer average velocity.

2.3 Darcy's law of saturated flow

In 1856 Darcy showed experimentally that a fluid's velocity of flow through a porous medium was directly related to the hydraulic gradient causing the flow, i.e.

where C = a constant involving the properties of both the fluid and the porous material.

2.4 Coefficient of permeability (k)

In soils we are generally concerned with water flow: the constant C is determined from tests in which the permeant is water. The particular value of the constant C obtained from these tests is known as the coefficient of permeability and is given the symbol k.

It is important to realise that when a soil is said to have a certain coefficient of permeability this value only applies to water (at 20°C). If heavy oil is used as the permeant the value of C would be considerably less than k.

Temperature causes variation in k, but in most soils work this is insignificant.

Provided that the hydraulic gradient is less than 1.0, as is the case in most seepage problems, the flow of water through a soil is linear and Darcy's law applies, i.e.

where i = hydraulic gradient (the head loss per unit length), or v = Ci v = ki or

From this latter expression a definition of k is apparent: the coefficient of permeability is the rate of flow of water per unit area of soil when under a unit hydraulic gradient.

BS1377 specifies that the dimensions for k should be m/s and these dimensions are used in this chapter.

Whilst suitable for coarse grained soils, Swartzendruber (1961) showed that Darcy's law is not truly applicable to cohesive soils due to the departure from Newtonian flow (perfect fluid flow) and he therefore proposed a modified flow equation for such soils. Many workers maintain that these variations from Darcy's law are related to the adsorbed water in the soil system, with its much higher viscosity than free water, and also to the soil structure, which can cause small flows along the sides of the voids in the opposite direction to the main flow. Absorbed water is discussed in Section 2.19. Although these effects are not always negligible, the unmodified form of Darcy's law is invariably used in seepage problems as it has the great advantage of simplicity. It may be that, as work in this field proceeds, some form of modification may be adopted.

2.5 Determination of k in the laboratory

The constant head permeameter

The test is described in BS 1377: Part 5 and the apparatus is shown in Fig. 2.3. Water flows through the soil under a head which is kept constant by means of the over-flow arrangement. The head loss, h, between two points along the length of the sample, distance 1 apart, is measured by means of a manometer (in practice there are more than just two manometer tappings).

Fig. 2.3 The constant head permeameter.

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