12 An Introduction to the Mechanics of Soils

1
???????12? An Introduction to the Mechanics
of Soils

• ?? ??
• ahirooka_at_civil.kyutech.ac.jp
• http//geo.civil.kyutech.ac.jp

2
?????????-1

• Elastic and Plastic Deformations

• Stress-strain curves for an ideal soil-like
  material for uniaxial compression
• Strain hardening
• Strain softening

3
?????????-2

• Yielding, Hardening and Plastic Flow

YaYc yield curve FaFc failure
envelope YaYc FaFc geometrically similar or not
YaYc ? GaGc Strain Hardening change of yeild
curve ? Hardening law plastic strain
4
?????????-3
The state of the material can be on or within the
yield surface but cannot lie outside it.
for a strain hardening material
yield surface
5
?????????-4
unloading path A?E
loading path A?B A?C A?D
Paths for loading and unloading
Softening material
Hardening material
6

• Flow rule of plasticity theory
• Plastic potential
• Normality condition

plastic potential yield curve ? associated flow
rule ? normality condition
7

• 1.8 Ideal Elastic Behavior

? Hookes law
the behavior of isotropic elastic material
E Youngs modulus n Poissons ratio
reversible recoverable ?conservative
8
on the principal stress (strain) plane
(s2 s3 , de2 de3)
for the special case of axial symmetry
K bulk modulus G shear modulus
9
for plane strain
(de2 0)
Kps bulk modulus appropriate for plane
strain Gps shear modulus appropriate for
plane strain
10
for the special case of axial symmetry des
dependent only on dq increment of shear
stress ? increment of shear strain dev
dependent only on dp increment of normal
stress ? increment of volumetric strain
for plane strain deg dependent only on
dt dev dependent only on ds
11
? plasticity theory (1.7)
the relationship between two ratios ? the
value of Poissons ratio independent of
Youngs modulus
12

• 1.9 Elasto-Plastic Behavior

total strains elastic component plastic
component
13
(No Transcript)
14
(No Transcript)
15

• 1.10 Equilibrium and Compatibility

a complete solution for stresses and displacement
of a soil structure ? necessary to satisfy
conditions of equilibrium and compatibility
for plane strain
in the xz plane
g the unit weight of the soil
16
in terms of effective stresses
no seepage pore pressure are hydrostatic
17
the compatibility condition
and hence
valid for drained and undrained loading
18

• 1.11 Relationships between Stress and Strain for
  Plane Strain

the stress-strain relationship for plane strain
19
(No Transcript)
20
(No Transcript)
21
An Introduction to the Mechanics of Soils

• 2.1 Introduction

the mechanical behavior of small elements of soil
? a number of mathematical models
a stress strain relationship valid for all
cases of loading and unloading
elastic behavior ? plastic behavior ? the state
boundary surface (a yield surface)
the critical state model
22

• 2.2 Drained and Undrained Loading

loading unloading
pore pressure response ? excess pore pressure
generated
consolidation effective stress change
volume change
drained loading
the rate of loading ? the rate of consolidation
undrained loading