Environmental Engineering Reference
In-Depth Information
TABLE 3.26
Parameters of Deformation
Parameter
a
Reference
Definition
Normal Application
Elastic Moduli (ST)
Expression
Young's modulus
Relates stress to strain
E
σ
/
ε
Rock masses, sands,
strong granular
cohesive soils
E
2(1
Shear modulus
Figure 3.69
Relates shear strain to shear
G
Not commonly
v
)
force (modulus of rigidity)
used statically
E
3(1
Bulk modulus
Figure 3.69
Ratio of all-around pressure to
B
Not commonly
2
v
)
change in volume per unit
used statically
volume (modulus describing
incompressibility)
v
)
(1
E
(1
Constrained
Figure 3.69
Deformation occurring in
D
Structure of large
v
)(1
2
v
)
modulus
confined compression
areal extent under-
lain by relatively
thin compressible
soil deposit
Dynamic Elastic Parameters — See
Table 3.27
Moduli From The Stress-Strain Curve
Initial tangent
Figure 3.70
Initial portion of curve
E
i
σ
/
ε
Usually taken as E for
modulus
geologic materials
∆σ
∆
Secant modulus
Figure 3.70
σ
and
ε
taken between
E
se
Define E for a partic-
two particular points
ular stress limit
σ
d
d
Tangent modulus
Figure 3.70
Modulus at specific point.
E
t
The lowest value for
Often taken at point of
E usually reported
maximum curvature before
rupture
Other Moduli
Compression
Figure 3.87
Lateral deformation caused
E
c
E
α
In situ
measures of
E
modulus
by applied stress from
(tons/ft
3
)
for materials
pressure meter
difficult to sample
Modulus of subgrade
Figure 3.90
A unit of pressure to produce
k
s
p
/
y
Beam or plate on an
reaction
a unit of deflection
elastic subgrade
problems
a
Unless noted, units are tsf, kg/cm
2
, kN/m
2
.
Other Moduli
These include the compression modulus, as determined by pressuremeter testing, which
varies in its relationship to Young's modulus with soil type and the modulus of subgrade
reaction, measured by plate load test.
Plastic Deformation
Compression in Clays
Compression in clay soils is essentially plastic deformation defined in terms of consolida-
tion, i.e., the decrease in volume occurring under applied stress caused primarily by the
expulsion of water from the interstices (see
Section 3.5.4)
.
Most soils exhibit primary and
