Environmental Engineering Reference
In-Depth Information
The use of a wavy plane through a soil mass can bias the
final outcome toward a preconceived notion.
The stress state variables for a multiphase system must rely
on accepted principles of statics and continuum mechanics
where spatial variation is brought into the analysis through
the use of stress field representations applied to the phases of
an REV. When stress field equations are written for the overall
element and the various phases of a multiphase system, the
area of contact and other soil properties do not appear in the
designation of stress state variables.
values with respect to space (i.e., depth and laterally). Soil
behavior can then be visualized in terms of the magnitudes
of the stress state variables and potential changes in the
stress state variables. The components of stress revert to
effective stress states σ
u w as the soil becomes satu-
rated. The effect of in situ stress history is often assessed on
the basis of laboratory oedometer measurements. Possible
final (or future) stress state profiles are often assumed on
the basis of engineering experience or computed based on
other theoretical considerations.
The total vertical stress under geostatic conditions is a
function of the density or the total unit weight of the soil.
The magnitude and distribution of the total normal stress
are also affected by the application of external loads such
as buildings or the removal of soil through excavation.
Let us consider geostatic conditions where the ground sur-
face is horizontal and the vertical and horizontal planes do
not have shear stresses (Lambe and Whitman, 1979). The net
normal stresses in the vertical and horizontal directions are
related to the density of soil. The net vertical stress σ v
3.4 REPRESENTATION OF STRESS STATES
Stress state variables become part of the mathematical
equations used in the engineering design process. The
stress state conditions are required for three dimensions
of the Cartesian coordinate system. In some cases it
might be possible to reduce engineering formulations to a
two-dimensional or one-dimensional formulation.
It is necessary to be able to take the components of the
stress state variables and determine how each stress com-
ponent can be computed under field conditions (i.e., in situ
stress states) on a practical engineering project. The ques-
tion being addressed can be stated as follows, “How can the
magnitude and distribution of total stresses and pore fluid
stresses be determined in the field?”
u a
is called the overburden pressure, which can be computed
as follows (Fig. 3.12):
y 1
σ v
u a =
ρ (y) gdy
u a
(3.27)
y 2
where:
3.4.1 In Situ Designation of Stress Components
The magnitude and distribution of the stress components
in the field need to be computed as part of a geotechnical
engineering analysis. The distribution of the components of
stress allows the computation of in situ profiles for net nor-
mal stress σ
σ v
u a
=
vertical net normal stress,
u a
=
pore-air pressure,
dy
=
incremental distance in the vertical direction,
ρ (y)
=
density of the soil as a function of depth,
u w . Procedures
are necessary for the assessment of each of the stress com-
ponents. The stress components can then be used to compute
the stress state variable distributions with space.
Totals stresses in three orthogonal directions need to be
computed as well as the pore-water and pore-air pressure
u a and matric suction u a
y 1 =
ground surface elevation,
y 2 =
elevation under consideration, and
g
=
gravitational acceleration.
The vertical net normal stress distribution with respect
to depth is a straight line as long as the soil density is a
z 1
Horizontal ground surface
s v u a
s h
u a
z 2
s h u a = K 0 ( s v u a )
s v
u a =
r g ( z 1
z 2 )
(a)
(b)
Figure 3.12 In situ net normal stress profile under geostatic conditions: (a) vertical net normal
stress; (b) horizontal net normal stress.
 
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