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
dy
ud ?
?? ?
? — 粘度，其单位为帕 ? 秒（ Pa ? s ）
u? — 流速
dy
ud ?
— u
?
在 y 轴方向的变化率，称为速度梯度
?
— 剪应力
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
?? — 剪应变速率
?? ?? ????
?
?
???
??
?
?
??
?
??
dt
d
dy
du
dt
d
dt
du
dy
d
dy
ud
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
材料 粘度 (Pa.s)
空气 (20 ℃ )
水 (20 ℃ )
沥青 (50 ℃ )
冰川冰
岩盐 (20 ℃ )
玻璃 (20 ℃ )
灰岩 (20 ℃ )
熔岩 (1 100 ℃ )
(1 200 ℃ )
(1 300 ℃ )
岩石圈
软流圈
1.8
?
10
- 5
1.00
?
10
- 3
10
6
10
13
3
?
10
15
10
18
~10
21
10
21
4
?
10
3
3
?
10
2
30
10
22
~10
23
10
19
~10
20
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
?,Viscosity (Pa s-1)
dashpot
spring
Yield
point
Strain-time relationship for visco-
elastic materials
?
?
Triaxial experiment
A- compression,B- extension
Confining
pressure
Confining
pressure
Rock Testing Apparatus (Triaxial Cell)
Two typical relaxation curves
岩石 抗压强度 (MPa) 抗张强度 (MPa) 抗剪强度 (MPa)
花岗岩
大理岩
石灰岩
砂岩
玄武岩
页岩
148 （ 37 ∽ 379 ）
102 （ 31 ∽ 262 ）
96 （ 6 ∽ 360 ）
74 （ 11 ∽ 252 ）
275 （ 200 ∽ 350 ）
20 ∽ 80
3 ∽ 5
3 ∽ 9
3 ∽ 6
1 ∽ 3
—
—
15 ∽ 30
10 ∽ 30
10 ∽ 20
5 ∽ 15
10
2
Strength of some rocks under normal
temperatures and normal pressures
Granite
Marble
Limestone
Sandstone
Basalt
Shale
Rocks Tensile strength(MPa)Compressive Strength(MPa) Shear strength(Mpa)
Effect of Confining Pressure on Rock
Strength
Strain Before Failure,Pc and Rock Type
Effect of Pore Pressure (a)
Effect of confining pressure
(b) And effect of water
content (c)
a
b
c
Effect of Temperature on Strength & Ductility
Effects of Temperature on Rock & Mineral Strength
SUMMARY OF EFFECTS
If you increase:
? Pore Pressure – lower strength,decrease ductility
? Confining Pressure – raise strength,increase ductility
? Temperature – lower strength,increase ductility
? Major changes in the amount of strain before failure
for different rock types