## Consolidation settlement

This effect occurs in clays where the value of permeability prevents the initial excess pore water pressures from draining away immediately. The design loading used to calculate consolidation settlement must be consistent with this effect.

A large wheel load rolling along a roadway resting on a clay will cause an immediate settlement that is in theory completely recoverable once the wheel has passed, but if the same load is applied permanently there will in addition be consolidation. Judgement is necessary in deciding what portion of the superimposed loading carried by a structure will be sustained long enough to cause consolidation, and this involves a quite different procedure from that used in a bearing capacity analysis which must allow for total dead and superimposed loadings.

### 9.3.1 One-dimensional consolidation

The pore water in a saturated clay will commence to drain away soon after immediate settlement has taken place, the removal of this water leading to the volume change is known as consolidation (Fig. 9.1b). The element contracts both horizontally and vertically under the actions of A<t'3 and Acri, which gradually increase in magnitude as the excess pore water pressure, Au, decreases. Eventually, when Au = 0, then A<t'3 = Aer3 and Aa\ = Aa\, and at this stage consolidation ceases, although secondary consolidation may still be apparent.

If it can be arranged for the lateral expansion due to the change in shape to equal the lateral compression consequent upon the change in volume and for these changes to occur together, then there will be no immediate settlement and the resulting compression will be one-dimensional with all the strain occurring in the vertical direction. Settlement by one-dimensional strain is by no means uncommon in practice, and most natural soil deposits have experienced one-dimensional settlement during the process of deposition and consolidation.

The consolidation of a clay layer supporting a foundation whose dimensions are much greater than the layer's thickness is essentially one-dimensional as lateral strain effects are negligible save at the edges.

### 9.3.2 The consolidation test

The apparatus generally used in the laboratory to determine the primary compression characteristics of a soil is known as the consolidation test apparatus (or oedometer) and is illustrated in Fig. 9.6a.

The soil sample (generally 75 mm diameter and 20 mm thick) is encased in a steel cutting ring. Porous discs, saturated with air-free water, are placed on top of and below the sample which is then inserted in the oedometer.

A vertical load is then applied and the resulting compression measured by means of a dial gauge, or transducers, at intervals of time, readings being

(a) Consolidation apparatus (b) Typical test results

Fig. 9.6 The consolidation test. The deformation gauge may be replaced by a transducer.

(a) Consolidation apparatus (b) Typical test results

Fig. 9.6 The consolidation test. The deformation gauge may be replaced by a transducer.

taken until the sample has achieved full consolidation (usually for a period of 24 hours). Further load increments are then applied and the procedure repeated, until the full stress range expected in situ has been covered by the test (Fig. 9.6b).

The test sample is generally flooded with water soon after the application of the first load increment in order to prevent pore suction.

After the sample has consolidated under its final load increment the pressure is released in stages at 24 hour intervals and the sample allowed to expand. In this way an expansion to time curve can also be obtained.

After the loading has been completely removed the final thickness of the sample can be obtained, from which it is possible to calculate the void ratio of the soil for each stage of consolidation under the load increments. The graph of void ratio to consolidation pressure can then be drawn, such a curve generally being referred to as an e-p curve (Fig. 9.7a).

It should be noted that the values of p refer to effective stress, for after consolidation the excess pore pressures become zero and the applied stress increment is equal to the effective stress increment.

If the sample is recompressed after the initial cycle of compression and expansion, the e-p curve for the whole operation is similar to the curves shown in Fig. 9.7b; the recompression curve is flatter than the original compression

(a) Typical e-p curve (b) Effect of expansion

### Fig. 9.7 Void ratio to effective pressure curves.

curve, primary compression being made up of (i) a reversible part and (ii) an irreversible part. Once the consolidation pressure is extended beyond the original consolidation pressure value (the preconsolidation pressure), the e p curve follows the trend of the original compression curve.

All types of soil, whether sand, silt or clay, have the form of compression curves illustrated in Fig. 9.7. The curves shown can be produced quite quickly in the laboratory for teaching purposes, using a dry sand sample, but consolidation problems are mainly concerned with clays and the oedometer is therefore only used to test these types of soil.

### 9.3.3 Volumetric change

The volume change per unit of original volume constitutes the volumetric change. If a mass of soil of volume V! is compressed to a volume V2, the assumption is made that the change in volume has been caused by a reduction in the volume of the voids.

Vi 1+ei

1 + e, where ei = void ratio at pi e2 = void ratio at p2.

The slope of the e-p curve is given the symbol 'a', then: Pi - P2

The slope of the e-p curve is seen to decrease with increase in pressure; in other words, a is not a constant but will vary depending upon the pressure. Settlement problems are usually only concerned with a range of pressure (that between the initial pressure and the final pressure), and over this range a is taken as constant by assuming that the e-p curve between these two pressure values is a straight line.

9.3.4 The Rowe oedometer

An alternative form to the consolidation cell shown in Fig. 9.6 was described by Rowe and Barden (1966) and is listed in BS 1377: Part 6.

The oedometer is hydraulically operated and a various range of cell sizes are available so that test specimens as large as 500 mm diameter and 250 mm thick can be tested. The machine is particularly useful for testing samples from clay deposits where macrofabric effects are significant.

A constant pressure system applies a hydraulic pressure, via a convoluted rubber jack made from rubber some 2 mm thick, on to the top of the test specimen. Vertical settlement is measured at the centre of the sample by means of a hollow brass spindle, 10 mm diameter, attached to the jack and passing out through the centre of the top plate to a suitable dial gauge or transducer.

Drainage of the sample can be made to vary according to the nature of the test and can be either vertical or radial, the latter being arranged to be either inwards or outwards. The expelled water exits via the spindle and it is possible to measure pore water pressures during the test, as well as applying a back pressure to the specimen if required. The apparatus can also be used for permeability tests, as described in BS 1377.

### 9.3.5 Coefficient of volume compressibility mv

This value, which is sometimes called the coefficient of volume decrease, represents the compression of a soil, per unit of original thickness, due to a unit increase in pressure, i.e.

mv = Volumetric change/Unit of pressure increase If Hi = original thickness and H2 = final thickness:

Vi-V2 Hi-H2

Volumetric change = ——-= ——- (as area is constant)

Volumetric change

■ ■ mv = TT"^ T = T~,— m /MN 1 + ei dp 1 + ei

For most practical engineering problems mv values can be calculated for a pressure increment of 100kN/m2 in excess of the present effective overburden pressure at the sample depth.

Once the coefficient of volume decrease has been obtained we know the compression/unit thickness/unit pressure increase. It is therefore an easy matter to predict the total consolidation settlement of a clay layer of thickness H:

Total settlement = pc = mv dp H

### Typical values of mv are given in Table 9.3.

In the laboratory consolidation test the compression of the sample is one-dimensional as there is lateral confinement, the initial excess pore water pressure induced in a saturated clay on loading being equal to the magnitude

Soil |
mv (m2/MN) |

Peat |

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