Craig's Soil Mechanics 7th Edition
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Craig's Soil Mechanics 7th Edition

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however, are the
same. From Figure 4.8(e) it is apparent that the difference between maximum and
ultimate stress decreases with increasing effective normal stress; therefore, if the
maximum shear stress is plotted against effective normal stress for each individual
test, the plotted points will lie on an envelope which is slightly curved, as shown in
Figure 4.8(g). The value of �0max for each test can then be represented by a secant
parameter, the value decreasing with increasing effective normal stress until it
becomes equal to �0cv. The reduction in the difference between maximum and
ultimate shear stress with increasing normal stress is mainly due to the correspond-
ing decrease in ultimate void ratio. The lower the ultimate void ratio the less scope
there is for dilation. In addition, at high stress levels some fracturing or crushing of
particles may occur with the consequence that there will be less particle interlocking
to be overcome. Crushing thus causes the suppression of dilatancy and contributes
to the reduced value of �0max.
In practice, the routine laboratory testing of sands is not feasible because of the

problem of obtaining undisturbed specimens and setting them up, still undisturbed, in
the test apparatus. If required, tests can be undertaken on specimens reconstituted in
the apparatus at appropriate densities but the in-situ structure is then unlikely to be
reproduced. Guidance on appropriate values of the parameters �0max and �

cv is given in

certain codes of practice. In the case of dense sands it has been shown that the value of
�0max under conditions of plane strain can be 4

� or 5� higher than the corresponding
value obtained by conventional triaxial tests. The increase in the case of loose sands
is negligible.


Liquefaction is a phenomenon in which loose saturated sand loses a large percentage
of its shear strength and develops characteristics similar to those of a liquid. It is
usually induced by cyclic loading of relatively high frequency, resulting in undrained
conditions in the sand. Cyclic loading may be caused, for example, by vibrations from
machinery and, more seriously, by earth tremors.
Loose sand tends to compact under cyclic loading. The decrease in volume causes an

increase in pore water pressure which cannot dissipate under undrained conditions.
Indeed, there may be a cumulative increase in pore water pressure under successive
cycles of loading. If the pore water pressure becomes equal to the maximum total stress
component, normally the overburden pressure, the value of effective stress will be zero,
i.e. interparticle forces will be zero, and the sand will exist in a liquid state with
negligible shear strength. Even if the effective stress does not fall to zero the reduction
in shear strength may be sufficient to cause failure.
Liquefaction may develop at any depth in a sand deposit where a critical combin-

ation of in-situ density and cyclic deformation occurs. The higher the void ratio of the
sand and the lower the confining pressure the more readily liquefaction will occur. The
larger the strains produced by the cyclic loading the lower the number of cycles
required for liquefaction.

Shear strength of sands 105


Isotropic consolidation

If a saturated clay specimen is allowed to consolidate in the triaxial apparatus under
a sequence of equal all-round pressures, sufficient time being allowed between
successive increments to ensure that consolidation is complete, the relationship
between void ratio (e) and effective stress (�03) can be obtained. Consolidation in
the triaxial apparatus under equal all-round pressure is referred to as isotropic
The relationship between void ratio and effective stress depends on the stress history

of the clay. If the present effective stress is the maximum to which the clay has ever
been subjected, the clay is said to be normally consolidated. If, on the other hand, the
effective stress at some time in the past has been greater than the present value, the clay
is said to be overconsolidated. The maximum value of effective stress in the past divided
by the present value is defined as the overconsolidation ratio (OCR). A normally
consolidated clay thus has an overconsolidation ratio of unity; an overconsolidated
clay has an overconsolidation ratio greater than unity. Overconsolidation is usually
the result of geological factors, for example, the erosion of overburden, the melting of
ice sheets after glaciation and the permanent rise of the water table. Overconsolidation
can also be due to higher stresses previously applied to a specimen in the triaxial
The characteristic relationship between e and �03 is shown in Figure 4.9. AB is the

curve for a clay in the normally consolidated condition. If after consolidation to
point B the effective stress is reduced, the clay will swell or expand and the relation-
ship will be represented by the curve BC. During consolidation from A to B, changes
in soil structure continuously take place but the clay does not revert to its original
structure during swelling. A clay existing at a state represented by point C is now in
the overconsolidated condition, the overconsolidation ratio being the effective stress

Figure 4.9 Isotropic consolidation.

106 Shear strength

at point B divided by that at point C. If the effective stress is again increased the
consolidation curve is CD, known as the recompression curve, eventually becoming
the continuation of the normal consolidation curve AB. It should be realized that a
state represented by a point to the right of the normal consolidation curve is

Undrained strength

In principle, the unconsolidated–undrained triaxial test enables the undrained strength
of the clay in its in-situ condition to be determined, the void ratio of the specimen at
the start of the test being unchanged from the in-situ value at the depth of sampling. In
practice, however, the effects of sampling and preparation result in a small increase in
void ratio. Experimental evidence (e.g. Duncan and Seed [10]) has shown that the
in-situ undrained strength of saturated clays is significantly anisotropic, the strength
depending on the direction of the major principal stress relative to the in-situ orienta-
tion of the specimen. Thus, undrained strength is not a unique parameter.
When a specimen of saturated clay is placed on the pedestal of the triaxial cell the

initial pore water pressure is negative due to capillary tension, total stresses being
zero and effective stresses positive. After the application of all-round pressure the
effective stresses in the specimen remain unchanged because, for a fully saturated soil
under undrained conditions, any increase in all-round pressure results in an equal
increase in pore water pressure (see Section 4.7). Assuming all specimens to have the
same void ratio and composition, a number of unconsolidated–undrained tests, each
at a different value of all-round pressure, should result, therefore, in equal values of
principal stress difference at failure. The results are expressed in terms of total stress
as shown in Figure 4.10, the failure envelope being horizontal, i.e. �u ¼ 0, and the
shear strength is given by �f ¼ cu. It should be noted that if the values of pore water
pressure at failure were measured in a series of tests then in principle only one
effective stress circle, shown dotted in Figure 4.10, would be obtained. The circle
representing an unconfined compression test would lie to the left of the effective stress
circle in Figure 4.10 because of the negative pore water pressure in the specimen. The
unconfined strength of a clay is due to a combination of friction and pore water
If the best common tangent to the Mohr circles obtained from a series of tests is not

horizontal then the inference is