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57 Basic constitutive laws
a.
ELASTIC
Stress Strength Stress
F
E E
k
Strain Strain
CONCEPTUAL IDEALIZED ROCK REALISTIC ROCK
b.
POROELASTIC
Stress Fast
Fluid E undr Stiffness
Fluid “squirt” Sonic lab
“squirt”
Slow Seismic
h
F
E dr
k “Maxwell” Strain Hz
CONCEPTUAL IDEALIZED ROCK FREQUENCY RESPONSE
c.
ELASTIC-PLASTIC
Stress Perfect Stress
k plasticity
F
m
Frictional sliding Strain Strain
CONCEPTUAL IDEALIZED ROCK REALISTIC ROCK
d.
VISCOELASTIC
k 1 Stress h high Stress h high
k 2
h low
F
h h low
Strain Time
Standard linear solid
CONCEPTUAL IDEALIZED ROCK REALISTIC ROCK
Figure 3.1. Schematic illustration of elastic, poroelastic, elastic–plastic and viscoelastic
constitutive laws. In the left panels, analogous physical models are shown, in the center, idealized
stress–strain curves, and in right panels, schematic diagrams representing more realistic rock
behavior are shown.
