Civil Engineering Reference
In-Depth Information
Figure 10.11
Comparison between linear Mohr-Coulomb and curved power law failure criteria
for peak strengths.
the test points. Figure 10.11(b) shows different points
d
,
e
and
f
which are close to the
same power law curve as that in Fig. 10.11(a) with a linear Mohr-Coulomb envelope
drawn as the best fit to the test points.
Neither of the linear Mohr-Coulomb envelopes passes through the origin or the
critical state point. Although both Mohr-Coulomb envelopes are close to the test
points which they represent they have different parameters
c
p
and
φ
p
. These are not,
after all, material parameters because they depend on the range of effective stress over
which the peak strengths were measured.
The linear Mohr-Coulomb failure criterion is the one which is nearly always
used in current geotechnical engineering practice, mainly because it has been the
basis of soil mechanics for a very long time. However, the curved power law
envelope passes through the origin and through the critical state point which is
required for uncemented soils. Peak strengths measured in triaxial tests over a wide
range of effective stresses are close to curved power law envelopes. On the present
evidence the curved power law envelope is to be preferred to the linear Mohr-
Coulomb envelope. Notice that the Mohr-Coulomb envelope is above the curved
power law envelope, and so it is unconservative, for stresses outside the range of the
tests.
10.5 Peak states and dilation
If you examine Fig. 10.2 you will notice that the samples D
1
and D
2
which have peak
strengths also dilate during shearing; their volume increases. You will also notice that
the rate of dilation given by the gradient (
) of the volumetric strain curve in
Fig. 10.2(b) is maximum at the point of peak shear stress. When the soil is at its peak
strength the shear stresses are both overcoming friction and expanding the sample
against the normal effective stresses.
Figure 10.12(a) shows a sample of soil which was originally on the dry side of critical
at its peak state in a shear test. The effective stresses are
δε
v
/
δγ
τ
and
σ
and there are small
increments of displacement
δ
h
and
δ
v
. As given in Chapter 2 the angle of dilation
ψ
is
