Civil Engineering Reference
In-Depth Information
Figure 1.4
Compression and distortion.
where
is the shear strain. The simplest
theory for stiffness is the theory of elasticity in which
K
and
G
are constants and apply
equally to loading and unloading.
Strength is the limiting shear stress that the material can sustain as it suffers large
shear strains. The two most common theories for strength are to say that the material
is cohesive and the limiting shear stress is a constant for the material given by
ε
=
V
/
V
0
is the volumetric strain and
γ
v
τ
f
=
s
(1.2)
or to say that the material is frictional so that the strength is proportional to the
confining pressure given by
τ
f
=
σµ
=
σ
tan
φ
(1.3)
where
is a friction angle. Later we will find that both
of these theories apply to soils, but in different circumstances.
Values for the stiffness parameters
K
and
G
and the strength parameters
s
and
µ
is a coefficient of friction and
φ
µ
(or
) will obviously depend on the material, but they may also depend on other things
such as temperature and rate of loading. For example, if the strength depends on the
rate of strain the material is said to be viscous. The first part of this topic, up to
Chapter 15, deals largely with the basic theories for the strength and stiffness of soils
and other granular materials.
φ
