Environmental Engineering Reference
In-Depth Information
According to
loading condition
z
σ
z
ε
z
τ
xz
x
ζ
zx
ζ
zx
y
Uniaxial loading
Simple shear
(a)
(b)
σ
o
Isotropic
compression
Confined
compression
(c)
(d)
FIGURE 3.69
Various types of elastic moduli: (a) Young's modulus —
E
σ
z
/
z
σ
/
;
x
y
v
x
; (b) shear modulus
—
G
zx
/
zx
E
/2(1
V
); (c) bulk modulus —
B
σ
0
/ 3
x
E
/ 3(1
2
V
); (d) constrained modulus
D
σ
z
/
2
v
). (From Lambe, T. W. and Whitman, R. V.,
Soil Mechanics,
Wiley, New York,
1969. Reprinted by permission of John Wiley & Sons, Inc.)
z
E
(1
v
) / (1
v
) (1
TABLE 3.27
Dynamic Elastic Parameters
Parameter
Expression
Compression-wave velocity
V
p
{[K
(4/3)
G
]/
ρ
)
1/2
m/s (
Section 2.3.2
)
Shear-wave velocity
V
s
(
G
/
ρ
)
1/2
m/s (
Section 2.3.2
)
Mass density of materials
ρ
γ
/
g
kg/m
3
(determined by gamma probe,
Section 2.3.6
)
Dynamic Poisson's ratio
v
(
V
2
p
/2
V
2
s
1)/(
V
2
p
/
V
2
s
1)
Appropriate values
Igneous rocks — 0.25
Sedimentary rocks — 0.33
Soils —
see
Section 11.3.2
Dynamic Young's modulus
a
E
d
p
(3
V
2
p
4
V
2
3
)/(
V
2
p
/
V
2
s
1) or
E
d
2p
V
2
s
(1
m)
Dynamic shear modulus
a
G
d
pV
2
s
E
d
/2(1
v)
Dynamic bulk modulus
a
K
p
(
V
2
p
4
V
2
s
/3)
E
d
/3(1
2
v
)
Note
:
Units are tsf, kg/cm
2
, kN/m
2
.
secondary consolidation and, in some soils, the latter phenomenon, which is not well
understood, can be of very significant magnitude. A substantial time delay in compression
occurs in clay soils under a given applied stress that increases generally as the plasticity of
the clay increases.
Compression in Sands
Sands and other cohesionless granular materials undergo a decrease in void volume under
applied stress, caused primarily by the rearrangement of grains
(Section 3.5.4).
Small elastic
