Deformation behaviour of railway embankment ... - Liikennevirasto

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2 INTRODUCTION TO THE MECHANICAL BEHAVIOUR OF GRANULAR
MATERIALS
2.1 Stresses in engineering materials
The stress state acting on a given infinitesimal cubic soil element can be defined by its
normal and shear stress components oriented according to a cartesian reference system,
as illustrated in Figure 2.1:1.
Figure 2.1:1 Stress components on a cubic soil element.
The stress components are often given in a matrix form. Stress is a tensor which can be
represented by a matrix in Cartesian coordinates:
σ
τ
xx
yx
zx
τ
τ
xy
yy
zy
τ
σ
xz
σ = τ σ τ . (Eq. 2.1:1)
yz
zz
The indices refer to the coordinate system x, y, z. The first index specifies the direction
in which the stress component acts, and the second identifies the orientation of the
surface upon which it is acting.
We can use equilibrium of moments to study the relationship between τ xy and τ yx .
Assuming a unit thickness, the horizontal and vertical faces are of area dx and dy
respectively (Figure 2.1:2).