Civil Engineering Reference
In-Depth Information
Essentials of material behaviour
Before reading this chapter, read the note at the beginning of Chapter 2.
3.1 Stress-strain behaviour, stiffness and strength
In Chapter 2, I considered the states of stress and strain in loaded and deforming
material. The analyses that were developed for stresses and strains, using Mohr circles,
are not dependent on the material and they are equally applicable for steel, concrete or
soil. In order to analyse any kind of structure, or any kind of solid or fluid continuum,
it is necessary to have relationships between stresses and strains. These are called
constitutive relationships and they take a number of different forms depending on the
nature of the material and on the loading.
Figure 3.1 shows an idealized relationship between stress and strain and it is simi-
lar to the stress-strain curves for common engineering materials like metals, plastics,
ceramics and engineering soils. For soils and other granular materials, it is neces-
sary to deal with something called effective stress to take account of pore pressures
in the fluid in the voids between the grains. (In simple terms effective stresses can be
thought of as the stresses effective in the soil grains.) Effective stress will be covered in
Chapter 6 where it will be shown that all soil behaviour, including stiffness and
strength, is governed by an effective stress which is denoted by a prime (as in
σ
).
As this topic is about soil I will use effective stresses from now on.
Stiffness is the gradient of the stress-strain line. If this is linear the gradient is easy
to determine but, if it is curved, the stiffness at a point such as A in Fig. 3.2 may be
quoted as a tangent or as a secant and given by
σ
d
d
tangent stiffness
=
(3.1)
ε
=
σ
ε
secant stiffness
(3.2)
The stiffness of a material largely determines the strains and displacements in struc-
tures, or in the ground, as they are loaded or unloaded. Another term often used in soil
mechanics to describe the relationship between stress and strain is 'compressibility',
but this is basically the reciprocal of stiffness. Often there is a marked change in the
gradient of a stress-strain curve at a yield point, as shown in Fig. 3.1. This is associated
