Civil Engineering Reference
In-Depth Information
Figure 3.17
Behaviour during a cycle of loading on and under yield surface.
up to failure. We will develop such a constitutive equation for soil in Chapter 12 when
we have obtained equations for the yield surface and for the successive yield curves
for soil.
3.11 Time and rate effects
In developing constitutive equations for materials we have, so far, considered only
relationships between changes of effective stress and changes of strain. This means
that no strains occur at constant load (except at failure). In addition it was assumed
that the relationships between stresses and strains were independent of the rate of
loading or the rate of straining. In soils there are a number of time and rate effects
mainly due to drainage of water and, to a limited extent, due to creep and viscosity in
the soil skeleton.
Time-dependent straining due to drainage of water is known as consolidation and
it is a coupling of deformations due to effective stress with seepage. Theories for
consolidation will be considered in Chapter 15.
The theory of viscosity relates stresses in moving materials (usually fluids) to the
velocity of flow, so that the shear stresses in water flowing in a pipe are related to the
velocity of the flow. In solid materials such as steel, concrete or soil, the strength or
stiffness may be governed by the rate of loading or by the rate of straining. It turns out
that the important mechanical properties of most soils, except peats and organic soils,
are not significantly influenced by the rate of loading, and usually we will not have to
worry about viscous effects in soil mechanics.
Materials under constant stress generally continue to strain, but at a rate that
diminishes with time; this is known as creep. The basic relationship for creep is
c
δε
=
C
α
ln
(
t
/
t
0
)
(3.32)
where
C
α
is a creep parameter that depends on a number of factors, including
the magnitudes of the (constant) stresses, and
t
0
is time from which the creep
