Environmental Engineering Reference
In-Depth Information
Influencing Factors
Magnitude and form of deformation in geologic materials are influenced by material
properties;
in situ
stress conditions; the level, direction, and rate of application of applied
stress; temperature of environment; and time interval under stress.
Deformation in Practice
Foundations
undergo settlement or heave; bending occurs in mats, continuous footings,
and piles from differential deflection.
Flexible retaining structures
undergo bending; deflections may result in significant back-
slope subsidence.
Tunnels
, particularly in rock masses, result in arching, which affects loads on support
systems; in soils, deformations may result in ground surface subsidence.
Pavements
undergo settlement or heave, and bending.
Elastic Body Characteristics
Elastic Media
In an elastic medium, strain is instantly and totally recoverable. Stress is directly propor-
tional to strain as related by Hooke's law, expressed by
Young's modulus E
(or
modulus of
elasticity
) as
E
σ
/
ε
(in tsf, kPa)
(3.56)
Poisson's ratio
ν
is the inverse ratio between strain in the direction of applied stress
E
σ
and
the induced strain
ε
L
in a perpendicular direction:
v
ε
L
/
ε
ε
L
/
E
σ
(3.57)
Young's modulus and Poisson's ratio are referred to as the elastic constants.
Dependent Factors for Elasticity
For a body to exhibit elastic characteristics defined by only a single value of
E
and
v
it must
be isotropic, homogeneous, and continuous.
Isotropic:
Particles are oriented so that the ratio of stress to strain is the same regardless
of the direction of applied stress, i.e., the elastic properties in every direction through any
point are identical.
Homogeneity:
The body has identical properties at every point in identical directions.
Continuity:
Refers to structure; if a mass is continuous it is free of planes of weakness or
breaks.
Validity for Geologic Materials
Sound, intact, massive rock
approaches an elastic material under most stress levels prior to
rupture.
Generally,
most rocks
are, to some extent, anisotropic, nonhomogeneous, and discontin-
uous, and are termed as quasielastic, semielastic, or nonelastic. In intact rock specimens,
deformation varies with the rock type as shown in
Table 3.24
with regard to mineral hard-
ness, grain bonding, and fabric (see
Section 5.2).
Nonintact rock or rock masses are basi-
cally discontinuous, usually undergoing plastic deformation as fractures close, then elastic
deformation, often followed by plastic deformation.
