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with
max is the dilation angle at failure, D r the relative
density, p' the mean normal effective stress at failure, Q a parameter accounting for
mineralogy (quartz: 10, limestone: 8, anthracite: 7, chalk: 5.5), and I R =
I
D
(
Q
ln
p
'
)
1
.
R
r
1 ). For the projection of triaxial test results to plane symmetrical
situations other empirical formulas are suggested, such as
d
v /(0.3 d
pl =
tr (1+0.163 D r ).
Cam-Clay model for clay
Soil behaviour reveals irreversible strain and strain hardening, and plastic
yielding is not synonymous with the maximum stress, as is assumed in the Mohr-
Coulomb model. To cover these aspects, the soil mechanics group at Cambridge
developed the Cam-Clay model (Schofield and Wroth). The Cam-Clay model is a
linear-elastic plastic strain-hardening/softening model. It is based on Critical State
theory, characterised by the critical state line (CSL), where soil elements can
experience unlimited deformations without any changes in stress or volume. The
model is able to describe deformation and failure especially for normally
consolidated soft soils in applications involving loading conditions such as
embankment or foundation. The adopted associated flow rule limits the simulation
of undrained behaviour of sand and clay.
The state of a soil sample is characterised by three parameters: effective mean
stress p' , deviatoric shear stress q , and specific volume v (note: v = 1 + e ). The
change of state can be described by the isotropic compression line (loading) and
swelling lines (unloading), both straight lines in the v -ln p space, characterised by
the compression index
, respectively. 41 The critical state line
corresponds to the failure stress and is parallel to isotropic compression line in the
v -ln p space. The critical-state parameter M is related to the internal friction angle
, the swelling index
. 42 Since the original Cam-Clay model led to too high K 0 values, the Modified
Cam-Clay model adopts an ellipse for the yield cap. 43
The cap supports a constant volume constraint at the critical state. The parameter
<
defines the critical state line at unit pressure. In Fig 9.2 two cases are worked out,
one for hardening (the preconsolidation pressure increases during loading) and one
for softening (the preconsolidation pressure decreases). These cases are also
referred to as the wet and dry side, because the wet side (hardening), in the higher-
pressure zone, causes the clay to compact resulting is wet clay (pore water
expelled), while the dry side (softening), in the lower pressure zone
(overconsolidated) the clay swells resulting in dry clay (water sucked in). The latter
case is more difficult to model in numerical codes. Originally, cohesion is not
included in the Cam-Clay model; new versions do.
41 and show similarity to a amd b , mentioned in Chapter 6
42 M = 6sin / (3sin) for triaxial tests
43
The original Cam-Clay model has a logarithmic yield cap.
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