## Behaviour of soils under shear

Before discussing this important subject the following definitions must be established.

• Overburden: The overburden pressure at a point in a soil mass is simply the weight of the material above it. The effective overburden is the pressure from this material less the pore water pressure due to the height of water extending from the point up to the water table.

• Normally consolidated clay: Clay which, at no time in its history, has been subjected to pressures greater than its existing overburden pressure.

• Overconsolidated clay: Clay which, during its history, has been subjected to pressures greater than its existing overburden pressure. One cause of overconsolidation is the erosion of material that once existed above the clay layer. Boulder clays are overconsolidated, as the many tons of pressure exerted by the mass of ice above them has been removed.

• Preconsolidation pressure: The maximum value of pressure exerted on an overconsolidated clay before the pressure was relieved.

• Overconsolidation ratio: The ratio of the value of the effective preconsolidation pressure to the value of the presently existing effective overburden pressure. A normally consolidated clay has an OCR = 1.0 whilst an over-consolidated clay has an OCR> 1.0.

3.13.1 Type of soil

### Sands and other granular materials

Unless drainage is deliberately prevented, a shear test on a sand will be a drained one as the high value of permeability makes consolidation and drainage virtually instantaneous.

A sand can be tested either dry or saturated. If dry there will be no pore water pressures and the intergranular pressure will equal the applied stress; if the sand is saturated, the pore water pressure will be zero due to the quick drainage, and the intergranular pressure will again equal the applied stress.

A dense sand tends to dilate (increase in volume) during shear whereas a loose sand tends to decrease in volume, and if the movement of pore water is restricted the shear strength of the sand will be affected: a dense sand will have negative pore pressures induced in it, causing an increase in shear strength, while a loose sand will have positive pore pressures induced with a corresponding reduction in strength. A practical application of this effect occurs when a pile is driven into sand, the load on the sand being applied so suddenly that, for a moment, the water it contains has no time to drain away. The density at which there is no increase or decrease in shear strength when the sand is maintained at constant volume is called the critical density of the sand.

Saturated cohesive soils

These soils are defined as saturated clays and silts in either their natural or a remoulded state.

### Unsaturated cohesive soils

Until the late 1980s, it was felt that both the value of the shear strength and the volume change characteristics of an unsaturated soil could be considered as functions of a single effective stress, in a similar manner to that for a saturated soil.

This theory has now been discarded as it has been found that the strength and volume changes in an unsaturated soil are governed by the two forms of the different stress paths that the soil experienced in reaching its relevant final pattern of applied stresses (see Sections 12.7.1 and 12.7.2).

Shear testing of unsaturated soils is presently a very open subject and is discussed in Section 12.8.

3.13.2 Undrained shear

The shear strength of a soil, if expressed in terms of total stress, corresponds to Coulomb's Law, i.e

Tf = cu + a tan <j>u where cu = unit cohesion of the soil, with respect to total stress <f>u = angle of shearing resistance of soil, with respect to total stress a = total normal stress on plane of failure.

For saturated cohesive soils tested in undrained shear it is generally found that rf has a constant value being independent of the value of the cell pressure <73 (see Fig. 3.29). The main exception to this finding is a fissured clay.

Hence, we can say that (j>n = 0 when a saturated cohesive soil is subjected to undrained shear. Hence:

Because of this, the term cu is referred to as the undrained shear strength of the soil. As will be seen later, the value of cu is used in slope stability analyses

Fig. 3.29 Strength envelope for a saturated cohesive soil subjected to an undrained shear test.

when it can be assumed that cf>u = 0 and the value of cu can be obtained on site by the simple and economical unconfined compression set.

If we wish to think of the results of an undrained test in terms of effective stress we should consider the nature of the test. In the standard compression undrained triaxial test, the soil sample is placed in the triaxial cell, the drainage connection is removed, the cell pressure is applied and the sample is immediately sheared by increasing the axial stress. Any pore water pressures generated throughout the test are not allowed to dissipate.

If, for a particular undrained shear test carried out at a cell pressure pc, the pore water pressure generated at failure is u then the effective stresses at failure are:

Remembering that, in a saturated soil, the pore pressure parameter B = 1.0 it is seen that if the test is repeated using a cell pressure of pc + Apc the value of the undrained strength of the soil will be exactly as that obtained from the first test because the increase in the cell pressure, Apc, will induce an increase in pore water pressure, Au, of the same magnitude (Au = Apc). The effective stress circle at failure will therefore be the same as for the first test (Fig. 3.29), the soil acting as if it were purely cohesive. It is therefore seen that there can only be one effective stress circle at failure, independent of the cell pressure value, in an undrained shear test on a saturated soil.

### 3.13.3 Drained and consolidated undrained shear

The triaxial forms of these shear tests have already been described. It is generally accepted that, for all practical purposes, the values obtained for the drained parameters, c' and <j>', from either test are virtually the same.

The c' value for normally consolidated clays is negligible and can be taken as zero in virtually every situation. A normally consolidated clay therefore has an effective stress strength envelope similar to that shown in Fig. 3.30 and, under drained conditions, will behave as if it were a frictional material.

The effective stress envelope for an overconsolidated clay is shown in Fig. 3.31. Unless unusually high cell pressures are used in the triaxial test the soil will be sheared with a cell pressure less than its preconsolidation pressure value. The resulting strength envelope is slightly curved with a cohesive intercept c'. As the curvature is very slight it is approximated to a straight line inclined at <t>' to the normal stress axis.

In Fig. 3.31 the point A represents the value of cell pressure that is equal to the preconsolidation pressure. At cell pressures higher than this the strength envelope is the same as for a normally consolidated clay, the value of 4>' being increased slightly. If this line is projected backwards it will pass through the origin.

Owing to the removal of stresses during sampling, even normally consolidated clays will have a slight degree of overconsolidation and may give a small c' value, usually so small that it is difficult to measure and has little importance.

The shearing characteristics of silts are similar to those of normally consolidated clays.

The behaviour of saturated normally consolidated and overconsolidated clays in undrained shear is illustrated in Fig. 3.32 which illustrates the variations of both deviator stress and pore water pressure during shear.

Fig. 3.30 Strength envelope for a normally consolidated clay subjected to a drained shear test.

Fig. 3.31 Strength envelope for an overconsolidated soil subjected to a drained shear test.

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