Civil Engineering Reference
In-Depth Information
Peak states
10.1 Introduction
Figure 10.1 shows the states of soil samples at the same effective stress
σ
but at different
voids ratios and overconsolidation ratios: at N the soil is normally consolidated, at W
it is lightly overconsolidated or loose and the state is on the wet side of the critical state,
and D
1
and D
2
are two states on the dry side where the soil is heavily overconsolidated
or dense. For samples W and N on the wet side of critical the state parameter
S
v
(see Sec. 9.9) is positive and for samples D
1
and D
2
the state parameter is negative.
Figure 10.2 shows the behaviour of these samples during drained shear tests and is
similar to Fig. 9.1. At the critical states at C the samples have the same shear stress
τ
f
, the same normal stress
σ
f
and the same voids ratio
e
f
, but at the peak states the
shear stresses and voids ratios are different. The idealized behaviour described in this
chapter is based on experimental data given by Atkinson and Bransby (1978) and by
Muir Wood (1991).
Peak states from shear tests on samples with different values of normal effective
stress, overconsolidation ratio and voids ratio generally fall within the region OAB
in Fig. 10.3 which is above the critical state line, and at first sight there is no clear
relationship for the peak states as there was for the critical states. There are three ways
of examining the peak states: the first is to make use of the Mohr-Coulomb equation,
the second is to fit a curved line to the peak state points and the third is to include
a contribution to strength from dilation. I am going to consider each of these three
methods. They are simply different ways to describe the same peak strengths; although
the equations are different the soil behaviour remains the same.
10.2 Mohr-Coulomb line for peak strength in
shear tests
Figure 10.4 shows peak states of two sets of samples which reached their peak states
at voids ratios
e
1
and
e
2
. These can be represented by the Mohr-Coulomb equation
written with effective stresses
τ
p
=
c
pe
+
σ
p
tan
φ
p
(10.1)
