## What Is Z In Soil Mechanics

Permeable

(b) Triangular

(a) Square

(b) Triangular

### Fig. 10.19 Popular arrangements of sand drains.

Spacing of drains: depends upon the type of soil in which they are placed. Spacings vary between 1.5 and 4.5 m. Sand drains are effective if the spacing, a, is less than the thickness of the consolidating layer, 2H. Arrangement of grid: sand drains are laid out in either square (Fig. 10.19a) or triangular (Fig. 10.19b) patterns. For triangular arrangements the grid forms a series of equilateral triangles the sides of which are equal to the drain spacing. Barron (1948) maintains that triangular spacing is more economical. In his paper he solved the consolidation theory for sand drains. Depth of sand drains: dictated by subsoil conditions. Sand drains have been installed to depths of up to 45 m.

Type of sand used: should be clean and able to carry away water yet not permit the fine particles of soil to be washed in.

Drainage blanket: after drains are installed a blanket of gravel and sand from 0.33 to 1.0 m thick, is spread over the entire area to provide lateral drainage at the base of the fill.

Overfill or surcharge: often used in conjunction with sand drains. It consists of extra fill material placed above the permanent fill to accelerate consolidation. Once piezometer measurements indicate that consolidation has become slow this surcharge is removed.

Strain effects: although there is lateral drainage, lateral strain effects are assumed to be negligible. Hence the consolidation of a soil layer in which sand drains are placed is still obtained from the expression:

pc = mvdp 2H Consolidation theory

The three-dimensional consolidation equation is:

where ch = coefficient of consolidation for horizontal drainage (when it can be measured: otherwise use cv).

The various co-ordinate directions of the equation are shown in Fig. 10.20. The equation can be solved by finite differences.

Fig. 10.20 Coordinate directions. Equivalent radius

The effect of each sand drain extends to the end of its equivalent radius, which differs for square and triangular arrangements (see Fig. 10.19).

For a square system:

Area of square enclosed by grid = a2 Area of equivalent circle of radius R = a2

For a triangular system:

A hexagon is formed by bisecting the various grid lines joining adjacent drains (Fig. 10.21). A typical hexagon is shown in the figure from which it is seen that the base of triangle ABC, i.e. the line AB, = a/2. Now

Fig. 10.20 Coordinate directions. Equivalent radius

The effect of each sand drain extends to the end of its equivalent radius, which differs for square and triangular arrangements (see Fig. 10.19).

For a square system:

Area of square enclosed by grid = a2 Area of equivalent circle of radius R = a2

For a triangular system:

A hexagon is formed by bisecting the various grid lines joining adjacent drains (Fig. 10.21). A typical hexagon is shown in the figure from which it is seen that the base of triangle ABC, i.e. the line AB, = a/2. Now

hence:

So that:

Radius of the equivalent circle, R = 0.525a Determination of consolidation rates from curves

Barron has produced curves which give the relationship between the degree of consolidation due to radial flow only, Ur, and the corresponding radial time factor, Tr.

T _ Cbt r~4R2 where t = time considered.

These curves are reproduced in Fig. 10.22 and it can be seen that they involve the use of factor n. This factor is simply the ratio of the equivalent radius to the sand drain radius.

To determine U (for both radial and vertical drainage) for a particular time, t, the procedure becomes:

(i) Determine Uz from the normal consolidation curves of Uz against Tz (Fig. 10.4):

Tz = where H = vertical drainage path

(ii) Determine Ur from Barron's curves of Ur against Tr.

(iii) Determine resultant percentage consolidation, U, from:

Time factor, Tr

Fig. 10.22 Radial consolidation rates (after Barron, 1948).

Time factor, Tr

Fig. 10.22 Radial consolidation rates (after Barron, 1948).

### Smear effects

The curves in Fig. 10.22 are for idealised drains, perfectly installed, clean and working correctly. Wells are often installed by driving cased holes and then backfilling as the casing is withdrawn, a procedure that causes distortion and remoulding in the adjacent soil. In varved clays (clays with sandwich type layers of silt and sand within them) the finer and more impervious layers are dragged down and smear over the more pervious layers to create a zone of reduced permeability around the perimeter of the drain. This smeared zone reduces the rate of consolidation, and in situ measurements to check on the estimated settlement rate are necessary on all but the smallest of jobs.

### Effectiveness of sand drains

Sand drains are particularly suitable for soft clays but have little effect on soils with small primary but large secondary effects, such as peat. See Lake (1963).

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