Civil Engineering Reference
In-Depth Information
Stiffness of soil
13.1 Introduction
Stiffness relates increments of stress and increments of strain. A knowledge of soil
stiffness is required to calculate ground movements and to obtain solutions to problems
of soil-structure interaction, such as loads on retaining walls. Often simple analyses
are carried out assuming that soil is linear and elastic and solutions for foundations
will be considered in Chapter 22. However, it is recognized that soil strains are often
significantly inelastic and more complicated elasto-plastic models such as Cam clay
(see Chapter 12) have been developed to model the stress-strain behaviour of soil.
The stress-strain behaviour of soil is actually more complex than that given by the
simple Cam clay model, particularly at small strains and for states inside the state
boundary surface where, in the simple theory, the strains are elastic. A detailed treat-
ment of soil stiffness is beyond the scope of this topic. What I am going to do in this
chapter is simply describe the essential features of the stress-strain behaviour of soil
as an introduction to further studies.
13.2 Cam clay and soil stiffness
In Chapter 12 the basic ideas of the classical theories of elasticity and plasticity were
combined with the basic soil mechanics theories of friction and logarithmic compres-
sion into a general model known as Cam clay. A set of non-linear constitutive equations
was obtained in terms of the intrinsic soil parameters
λ
,
M
,
,
κ
and
g
, together with
parameters describing the current state and the loading history.
The basic equations for Cam clay for states on the state boundary surface (Eqs. 12.16
and 12.17) contain elastic and plastic components of straining, while for states inside
the state boundary surface the basic equations (Eqs. 11.3 and 11.4) contain only elastic
strains. It turns out that the ordinary Cam clay equations are reasonably good for states
on the state boundary surface but the basic Cam clay theories are rather poor for states
inside the state boundary surface where soil behaviour is not elastic and recoverable.
The consequences of this for geotechnical design are illustrated in Fig. 13.1. This
shows two soils subjected to exactly the same loading paths A
D.
The soil which starts from A is lightly overconsolidated; it yields at Y when the
state reaches the state boundary surface and then it moves along Y
→
B and C
→
B on the state
boundary surface with elastic and plastic strains. The soil which starts fromC is heavily
→
