文档介绍：Mechanical Behaviors of Rocks
General relationship between stress and strain for rock deformation
Yield stress
elastic
plastic
failure
strain
stress
Where is stress, strain and E the Young’s modulus or elastic modulus
Hooke’s law
Linear elasticity
E= / =tan
= E
Sketch shown viscous flow layers The flow speed is the function of y
Linear viscous law(Newtonian viscous law)
Shear stress is proportional to speed gradient
Viscosity (Pa·s)
Flow speed
The variation of flow speed along the y direction, called
speed gradient
Shear stress, or frictional force between the
adjacent flow layers
Shear strain rate
dy
du
--shear strain
Another express for Newtonian viscous law
Shear stress is proportional to shear strain-rate
--viscosity of material
For longitudinal deformation:
= d/dt
d/dt
Stress
Strain-rate
Viscosity of some materials
materials
viscosity
Air (20◦ C)
water (20 ◦ C)
Pitch (50 ◦ C)
Glacial ice
Rock salt (20◦ C)
Glass (20◦ C)
Limestone (20◦ C)
Lava (1100 ◦ C)
(1200 ◦ C)
(1300 ◦ C)
Lithosphere
Asthenosphere
Mechanical behavior of materials
A Ideal elastic strain
B Ideal viscous strain
C Ideal elastoviscous
strain at constant
Stress: an instantaneous
elastic strain is
followed by viscous
strain for a stress of
longer duration
D Ideal elastoplastic strain: elastic strain at low values of stress is replaced by viscous strain above the yield stress
Simple Rheological Models
E: Young’s Modulus
h: Viscosity (Pa s-1)
dashpot
spring