Essentials of material behaviour - The Mechanics of Soils and Foundations - page 28

generally use the parameters q , p , ε s and ε v and for shear tests I will generally use the

τ n , σ n , parameters γ and ε

n .

3.3 Strength
The strength of a material describes the ultimate state of stress that it can sustain before
it fails. (For soils that can suffer very large strains we will have to define failure very
carefully, but this will be considered in detail later.) People talk about tensile strength,
compressive strength, shear strength, and so on, as though they were all different, but
these should really all be related to some fundamental characteristic strength.
The link between these different strengths is the maximum shear stress, or the size
of the largest Mohr circle that the material can sustain. Figure 3.5(a) and (b) shows
uniaxial tensile and compression tests and the corresponding Mohr circle of stress; the
test samples fail when the Mohr circle reaches the limiting size given by the radius τ f .

Figure 3.5(c) shows a vertical cut and the shear and normal effective stresses on some
inclined planes are τ n , and σ n ; failure will occur when the Mohr circle reaches its

limiting size.
We can say that materials that have strength can sustain shear stresses and the
strength is the maximum shear stress that can be sustained. Only materials with
strength can have slopes because shear stresses are required to maintain a slope.
A material that cannot sustain a slope, like stationary water, has no strength, there are
no shear stresses in it and the Mohr circle reduces to a point as shown in Fig. 3.5(d).
There are two fundamentally different failure criteria to consider. The first illus-
trated, in Fig. 3.6(a), is called cohesion and it says that the material will fail when the
Mohr circle of stress touches an envelope given by

τ = c (3.9)

where c is the cohesion. The second, illustrated in Fig. 3.6(b), is called friction and
it says that the material will fail when the Mohr circle of effective stress touches an
envelope given by

τ = σ µ = σ tan φ

(3.10)

φ is the angle of friction. You probably did
experiments at school to measure the coefficients of friction of different materials.
There is a third criterion of failure called the Mohr-Coulomb criterion and it is
simply the sum of cohesion and friction. It is illustrated in Fig. 3.6(c) and it says that
the material will fail when the Mohr circle touches a line given by

where µ is the coefficient of friction and

τ = c + σ tan φ

(3.11)

The development of the Mohr-Coulomb criterion from Coulomb's original research
is described by Heyman (1972). All three criteria are used to describe the strength of
soils under different conditions of drainage and strain and these will be discussed in
later chapters.