(as illustrated in Example 4.3).

Figure 4.12 Correction factor for undrained strength measured by the vane test. (After
Bjerrum [5].)

Table 4.1 Undrained strength classification

Stiffness state Undrained strength (kN/m2)

Hard >300
Very stiff 150–300
Stiff 75–150
Firm 40–75
Soft 20–40
Very soft <20

110 Shear strength

Tangent parameters c0 and �0 apply only to a relatively small stress range. The tangent
value of �0 is likely to be lower than the critical-state value. Caution is required in the
use of the c0 parameter, especially at low stress levels where it would represent a
significant proportion of shear strength. If the critical-state value of �0cv is required
for a heavily overconsolidated clay then, if possible, tests should be performed at stress
levels that are high enough to define the critical-state envelope, i.e. specimens should
be consolidated at all-round pressures in excess of the preconsolidation value. Alterna-
tively, an estimated value of �0cv can be obtained from tests on normally consolidated
specimens reconsolidated from a slurry.
Effective stress parameters can also be obtained by means of drained triaxial tests

(or direct shear tests). Clays under drained conditions behave as frictional materials.
The rate of strain must be slow enough to ensure full dissipation of excess pore water
pressure at any time during application of the principal stress difference. Total and
effective stresses will thus be equal throughout the test. The rate of strain must again
be related to the permeability of the clay. The volume change taking place during the
application of the principal stress difference must be measured in the drained test so
that the corrected cross-sectional area of the specimen can be calculated.
Typical test results for specimens of normally consolidated and overconsolidated

clays are shown in Figure 4.14. In consolidated–undrained tests, axial stress and pore
water pressure are plotted against axial strain. For normally consolidated clays, axial
stress reaches an ultimate value at relatively large strain, accompanied by increase in
pore water pressure to a steady value. For overconsolidated clays, axial stress increases
to a peak value and then decreases with subsequent increase in strain. However, it is not
usually possible to reach the ultimate stress due to excessive specimen deformation. Pore
water pressure increases initially and then decreases, the higher the overconsolidation
ratio the greater the decrease. Pore water pressure may become negative in the case of
heavily overconsolidated clays as shown by the dotted line in Figure 4.14(b). In drained
tests, axial stress and volume change are plotted against axial strain. For normally
consolidated clays an ultimate value of stress is again reached at relatively high strain.
A decrease in volume takes place during shearing and the clay hardens. For over-
consolidated clays a peak value of axial stress is reached at relatively low strain.

OC

NC

φcv
σ′

τ

′

Figure 4.13 Failure envelopes for normally consolidated (NC) and overconsolidated (OC) clays.

Shear strength of saturated clays 111

Subsequently, axial stress decreases with increasing strain but, again, it is not usually
possible to reach the ultimate stress in the triaxial apparatus. After an initial decrease,
the volume of an overconsolidated clay increases prior to and after peak stress and the
clay softens. For overconsolidated clays the decrease from peak stress towards the
ultimate value becomes less pronounced as the overconsolidation ratio decreases.
In practical situations, if the stress in a particular soil element becomes equal to the

peak shear strength, any further increase in strain will result in a reduction in strength.
Consequently, additional stress will be transferred to adjacent elements, perhaps
resulting in peak strength being also reached in these elements. A sequence of pro-
gressive failure could thus be set in train within a soil mass. Therefore, unless it is
certain that strains throughout the soil mass will remain less than that corresponding
to peak strength, it is necessary to use the critical-state strength in design.

Figure 4.14 Typical results from consolidated–undrained and drained triaxial tests.

112 Shear strength

Stress paths

The successive states of stress in a test specimen or an in-situ element of soil can be
represented by a series of Mohr circles or, in a less confusing way, by a series of stress
points. The curve or straight line connecting the relevant stress points is called the
stress path, giving a clear representation of the successive states of stress. Stress paths
may be drawn in terms of either effective or total stresses. The horizontal distance
between the effective and total stress paths is the value of pore water pressure at the
stresses in question. In general, the horizontal distance between the two stress paths is
the sum of the pore water pressure due to the change in total stress and the static pore
water pressure. In the normal triaxial test procedure the static pore water pressure (us)
is zero. However, if a triaxial test is performed under back pressure, the static pore
water pressure is equal to the back pressure. The static pore water pressure of an in-situ
element is the pressure governed by the water table level.
The effective and total stress paths (denoted by ESP and TSP, respectively) for the

triaxial tests represented in Figure 4.14 are shown in Figure 4.15, the coordinates being
1⁄2 (�

0
1��03) and 1⁄2 (�01þ�03) or the total stress equivalents. The effective stress paths

terminate on the modified failure envelope. All the total stress paths and the effective
stress paths for the drained tests are straight lines at a slope of 45�. The detailed shape
of the effective stress paths for the consolidated–undrained tests depends on the clay
in question. The effective and total stress paths for the drained tests coincide, provided
no back pressure has been applied. The dotted line in Figure 4.15(c) is the effective
stress path for a heavily overconsolidated clay in which the pore water pressure at
failure (uf) is negative.

The hydraulic triaxial apparatus

This apparatus, developed by Bishop and Wesley [4], is shown diagrammatically in
Figure 4.16. The chamber containing the soil specimen is similar to a conventional
triaxial cell; however, the pedestal is connected by a ram to a piston in a lower
pressure chamber, the vertical movement of the ram being guided by a linear
bearing. Rolling seals are used to accommodate the movement of the ram in both
chambers. Axial load is applied to the specimen by increasing the pressure in the
lower chamber. Standard constant pressure systems can be used but preferably with
a motorized drive arrangement to control the rate of pressure increase. Although the
axial load on the specimen can be calculated from a knowledge of the pressures in
the two chambers, the mass of the ram and apparatus dimensions, it is preferable to
measure the load directly by means of a load cell above the specimen. A cross-arm
mounted on the ram passes through the slots in the side of the apparatus (the
section of the apparatus containing the linear bearing being open to atmosphere);
vertical rods attached to the ends of the cross-arm operate against dial gauges (or
transducers), enabling the change in length of the specimen to be measured. The
slots in the side of the apparatus also accommodate the pore pressure and drainage
connections from the pedestal. The potential of the apparatus can be fully exploited
by means of an automatic system controlled by a computer. The apparatus enables
a wide range of stress paths, reproducing in-situ stress changes, to be imposed on the
specimen.

Shear strength of saturated clays 113

Example 4.1

The following results were obtained from direct shear tests on specimens of a sand