河海大学殷宗泽高等土力学1(英文)Constitutive Law of Soil

Shear stress and strain on a given plane and Complicate stress state Octahedral shear stress
oct
1 3


1
1 2 2 2 3 2 3 1 2
cylindrical cell
base
cylindrical sample
v
r

Then — deviator stress 1 3
through piston apply
Strain components Nhomakorabeaa
– Complicated stress state
Earth dam, underground structure, harbor, excavation, etc. Extensive Hooke’s law （linear assumption）
C13 C 23
C12 C 22 C32
C13 x C 23 y C33 xy
— reflect shear dilation
C31 C 32 — reflect average normal stress inducing shear strain
p 1 1 2 3 3
p — average normal stress, or global stress
1 3
1 3
p = constant
a
p = constant
a
v
v
Shear compression
Shear dilation
• Shear dilation
Elastic model — C13 C 23 = 0
C 31 C 32 = 0
Plastic model can reflect these effects
(4) Softening and hardening


direct shear test
peak strength
residual strength
p e

may drop into pore space, and the relative position between the two particles can not be recovered.
Deformation can not be recovered

Stress – strain curve of the after cycle is different from the before one.
3
sample metal Dike, dam, retaining wall,
Cell pressure —— 3 Axial stress —— 1
1
3
no deformation in longitudinal direction
(4) True triaxial test
1
2 3 , then q 1 3
oct G oct
q
s
3G
energy of shear deformation
W s q s
• Shear strain induced by global stress p
Triaxial test
a
is induced by p change.
3 1
3 200kPa
3 100kPa
a
• Effect of intersection in stress-strain matrix
x C11 t C 21 C xy 31
a


Mohr circle goes left. When the Mohr circle tangent to the failure line, the deviator strain is very large. The deviator strain
a
is due to existence of initial shear stress.


triaxial shear test
residual deviator stress
a
hardening
Softening
3 1
a
3 1
(5) influence of stress path & stress history
Stress space — the space consists of stress component axes
•
induced by p
p v
Macroscopic — compress Microscopic — slip between grains p
p
loading unloading
p
vp
ve
v
vp
• vp induced by Shear stress
Perform triaxial test with p = constant 1 3 increase, but 3 decrease
Constitutive Law of Soil
Yin Zong-ze 殷宗泽
What is constitutive law?
Stress-strain relationship Stress-strain-strength relationship Stress-strain-time relationship Stress-strain-temperature relationship
Dilation —— dense sand, overconsolidated clay Compression —— loose sand, normal consolidated clay
Shear compressive
Shear dilative
For triaxial test
v a 2 r
2
a compress
a

additional stress
E r a
r
expand
(3) Plane strain test
1
Sample is enclosed in a rubber membrane, and is put in the cylindrical cell.
stress strength strain


T t
f


1. Stress-strain Tests
(1) Compression test
– Simple stress condition
Settlement of building——one dimensional problem Confined compression test, (oedometer test) p s h p
3
2
Apply 1
2
3
Measure
1 2 3
(5) Torsional shear test（hollowed）
M
z
r
ring column shape
x 0
d 2 d1
d1 d2

r1
r2

Isolative body


r2
v a 2 r 0 r 0.5 a
v 0 r 0.5 a
1 r a 2
a
r
Shear dilative
Shear compressive
(3) Plastic shear strain
• Expression of shear strain
1
M ·
z
N
2
3
Principal stress space
x
y
geometric space
A point in stress space represents a stress state at a point in soil body
2. Deformation Characteristics of Soils
(1) Non-linear and non-elastic


metal soil


Plastic strain — irrecoverable strain,
due to adjustment of position of grains. One particle may slip over another particle,
Extensive shear stress
1 q 2
1 2
2
2 3 3 1
2
2
3 oct 2
Extensive shear strain 2 1 2 2 2 1 2 2 3 3 1 oct s 3 2 If
cc
lg p
(2) Conventional triaxial test
piston shaft organic glass rubber membrane
3
1
cap
First — cell pressure 3
surrounding pressure confining pressure