Geoscience Reference
In-Depth Information
The Mohr-Coulomb failure envelope in the p-q diagram is a straight line. The
relation with the friction angle
and the cohesion c is M = 6sin
/(3-sin
) and a/c
= 6cos
/(3-sin
). The friction angle
can therefore be found from
sin
= 3 M /(6+ M )
(7.12)
The yielding of soft soils is more diverse than can be represented by a simple
failure criterion. Yielding is defined as a distinct point where the stress-strain curve
deflects. These yield points can be investigated in a triaxial cell under different
loading conditions, such as isotropic loading (D), one-dimensional compression
(C), constant mean stress (E) and undrained triaxial (U). Some corresponding
effective stress paths are shown in Fig 7.6b. A yield and a failure surface are used
in sophisticated constitutive models, such as in the double sliding theory or the
critical state theory, the backbone of the CamClay model (see Chapter 9).
E UNDRAINED STRENGTH
The condition of undrained loading and corresponding undrained strength is of
great practical importance in the case of clays and silts, and for saturated sands
under rapid loading (earthquake). Soil may fail when induced pore pressures have
not been consolidated. During undrained loading shear related volume changes are
counterbalanced by additional induced pore pressures that may be positive
(contraction) or negative (dilation), affecting actual strength (Fig 7.7).
total
stress
total
stress
pore
pressure
pore
pressure
undrained
dilatant
strength
undrained
dilatant
strength
drained
strength
drained
strength
+
+
undrained
contractant
strength
undrained
contractant
strength
effective
stress
effective
stress
Figure 7.7 Total and effective stress paths in normally consolidated clay under undrained
simple shear
For treatment of undrained stability problems in a total stress analysis, simplified
expressions for undrained shear strength are used, symbolised by s u in stead of |
s |
from equation (7.2). Values of s u can be obtained by triaxial CU tests.
Distinction can be made for active (compression) and passive (extension) states.
In active loading the shear stresses increase in the same direction as those imposed
during consolidation, and generally high undrained strengths are measured (e.g. in
triaxial compression tests). In passive loading the shear stresses are reversed
 
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