S4
•
Stresses Changes Due to Surface Loads (
Δσ
v
)
o
Stresses within a soil mass will change as a result of surface loads.
The change in total
stress spreads and diminishes with distance from the load.
Equations and charts are
available to calculate both the vertical and horizontal stress change (
Δσ
v
and
Δσ
h
).
o
If for some reason the complete total stress at a point is required, then add the
geostatic stress,
σ
v
or
σ
h
, to the loadinduced stress change,
Δσ
v
or
Δσ
h
.
o
We are normally most interested in vertical stress increases due to surface
compression loads.
(As a rule, we assume that soil cannot withstand tension stresses.)
o
Often we need to know
Δσ
v
to determine
how much a structure will settle.
(remember the CEG4011 consolidation test??)
o
To find
Δσ
v
must first define :
o
size and shape of building foundation
o
loads supported by building foundation
o
location of interest within soil mass
o
Most solutions are based on elasticity theory
assuming a
homogeneous, isotropic, elastic,
halfspace.
o
Note that soil is seldom homogeneous, only approximately isotropic, and elastic only at
small loads (<1020% of the failure stress).
But, we have no simple alternatives, and
experimental results agree reasonably well. The above assumptions are only a first
order approximation, but this approximation is often adequate.
o
With the above assumptions, the vertical stress increase is independent of the elastic
constants: Young’s Modulus (E) and Poisson’s Ratio (
v
h
or
ε
Δ
ε
Δ
=
ν
μ
).
However, the
horizontal stress is not.
o
Before looking at the various stress calculation methods, using your intuition what do
you think will cause the greater stress increase at point P in the example below?
(These footings have the same average contact pressure, q.)
σ
V
due to soil self weight
(geostatic)
Δσ
V
due to building
(surcharge)
P
Clay
Sand
10 ft x 10 ft
20 ft
5000 tons
50 tons
P
100 ft x 100 ft
P
C
L
C
L
q = ?
Δσ
vA
= ?
Δσ
vB
= ?
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•
Pyramid Approximation For Surface Loads:
The “2:1 method “ used for “back of the
envelope” solutions (seen on the PE exam).
o
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 Fall '08
 Staff
 Boussinesq, ∆σv

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