Civil Engineering Reference
In-Depth Information
see how the state of a soil initially on the wet side or the dry side moves towards the
critical state line during shearing.
It is essential to emphasize that at the critical state soil continues to distort (i.e.
suffer shear strains) without any change of shear stress or normal stress or voids ratio
(i.e. it is distorting at constant state) and the strains are associated with turbulent
flow. The essential features of the critical states are that, during shearing, all soils will
ultimately reach their critical states (provided that the flow remains turbulent) and
the critical states are independent of the initial states. Thus, in Fig. 9.1, the critical
shear stresses
τ
f
are the same for the soils initially on either the wet or the dry sides of
critical, because they have the same normal effective stress
σ
f
and the voids ratios
e
f
at the critical states will also be the same. Later we will see how we can explain fully
the behaviour of soils from knowledge of their initial and ultimate states.
The existence of unique critical states for soils is, at first sight, surprising, but it is
quite logical. Firstly, during continuous shear straining any soil must ultimately reach
a constant state because, if it did not, it would continue to compress and strengthen or
dilate and weaken indefinitely, which is, of course, impossible. During shearing from
the initial to the critical states there will be relatively large strains and the soil will be
essentially reworked or reconstituted by the shear straining. Thus the soil will forget
its initial state and it is reasonable to suppose that the new, reconstituted, soil will
achieve unique states independent of the initial states.
Since the critical state is independent of the initial state, the parameters
φ
c
,
e
and
C
c
in Eqs. (9.2) and (9.3) depend only on the nature of the grains of the soil: they are
material parameters. Relationships between these, and other, material parameters and
soil classifications are discussed in Chapter 18.
The critical state lines illustrated in Fig. 9.4 are a very good idealization for the
critical states of most clays and sands. For coarse-grained soils volume changes during
first loading and during shearing are often accompanied by fracture of the soil grains,
and it is often necessary to apply large stresses (greater than 1000 kPa) to identify the
full range of behaviour.
9.4 Undrained strength
The critical state strength of soil given by Eq. (9.2) relates the ultimate shearing resis-
tance to the corresponding normal effective stress. This can be used to determine soil
strength provided that the pore pressure is known so that
σ
(
u
) can be calculated.
Pore pressures in the ground will generally only be determinable for cases of drained
loading and the strength for undrained loading - the undrained strength - must be
calculated differently.
Figures 9.5(a) and (b) show the critical state line for soil and are the same as
Figs. 9.4(a) and (b). Figure 9.5(c) combines these and shows the corresponding relation-
ship between the critical state shear stress and the voids ratio: this shows the strength
decreasing with increasing voids ratio. In saturated soil the voids ratio is simply related
to the water content by Eq. (5.6) so Fig. 9.5(c) shows that there is a unique relation-
ship between critical state strength and water content. It is common experience that
the strength of soil decreases as the water content increases.
If a sample of saturated soil is taken from the ground and tested, or if it is tested in
the ground, without any change in water content the strength measured will represent
=
σ
−
