Essentials of material behaviour - The Mechanics of Soils and Foundations - page 27

Figure 3.4 States of stress in triaxial and shear tests.

strains depend on a number of factors but principally on the angle θ between the

directions of the planes in Figs. 3.4(a) and (b).
The volumetric strain

ε

v describes the change in size of an element while the shear

s describes the change in its shape. The value 2 3 in Eq. (3.5) is required for
consistency. During an increment of straining the work done per unit volume of soil
δ

strain ε

W must be invariant (i.e. independent of the choice of parameters). In terms of axial
and radial stresses and strains

= σ a ε σ r δε δ +

W 2 (3.7)

a r

and also

q δε p δε δ W = + (3.8)

s v

You should substitute Eqs. (3.3) to (3.6) into Eq. (3.8) and demonstrate that this
reduces to Eq. (3.7). When considering the behaviour of soils in triaxial tests I will