Geoscience Reference
In-Depth Information
7
TRIAXIAL STRESS AND STRAIN
A
CONTINUUM MECHANICS
In mechanics the principles of equilibrium and compatibility are considered, i.e.
forces and displacements (or stresses and strains), and their connection through
constitutive laws. Equilibrium requires directional balance of forces and rotational
balance of moments, and compatibility requires displacements without loss or gain
of material (connected material remains connected during deformation). A one-
dimensional relation of stress and strain is shown in Fig 5.1. Concepts for stresses
and strains can be developed quite precisely, but constitutive models, which define
their mutual relation, are based on rather empirical laws. Soil stiffness increases
with regard to volumetric compression (characterised by the bulk modulus
K
) and
decreases with regard to shear strain (characterised by the shear modulus
G
). It is
therefore common in soil mechanics to distinguish between isotropic (volumetric)
and deviatoric (shear) stresses and strains. A specific material behaviour, important
in soil mechanics, is the yield point, i.e. the stress where the elastic response
changes to plastic straining, usually marked by an abrupt change in the slope of the
stress-strain curve. Deviatoric stress may show a peak (curve A in Fig 7.1b), for
sands due to high density, interlocking, cementation, etc., and for clays due to
overconsolidation, interlocking, etc.
i
compression
distortion
A
contractancy
i
A
K
B
G
B
dilatancy
v
(a) (b)
Figure 7.1 Stress-strain behaviour for compression and distortion
Soil is even more complex. Except for cemented soils, it cannot sustain tension.
Saturated soils undergo volumetric changes when pore water is squeezed out or
sucked in. Sometimes a loose granular structure may collapse into a denser one
(contraction), or dense sand becomes loose (dilatancy). Some soils exhibit brittle
failure; others more plastic. Microscopic elements (organic matter) may influence
soil stiffness and strength significantly (peat, organic clay).
Several so-called constitutive models exist, which approximate the soil
behaviour during triaxial (multi-dimensional) loading. This is the field of
continuum mechanics. Such models try to link the three-dimensional (effective)
stress state to the corresponding strain state by a specific set of parameters. Here, a
distinction must be made between stiffness (deformation) and strength (failure).
For sand or clay one may use the Mohr-Coulomb model or the CamClay model
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