Environmental Engineering Reference
In-Depth Information
Strip load,
q
per unit area
σ
y
=
ql
σ
y
σ
y
b
Width of load
(a)
1.2
1.0
0.8
Influence factors for strip footing
Boussinesq
Numerical model
Poisson's ratio = 0.333
0.6
0.4
0.2
0.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
b
/
y
(b)
Figure 14.64
Calculation of influence factors for total stresses below a strip footing: (a) defini-
tion of influence factors; (b) comparison of numerical modeling solution to closed-form Bousinesq
theory.
specific testing conditions using a best-fit
regression
where:
analysis on measured data.
Some mathematical equations are shown that describe the
void ratio constitutive surfaces associated with an unsatu-
rated, swelling soil. Terzaghi (1943) and Casagrande (1936)
noted that the virgin compression curve of the void ratio ver-
sus logarithm of effective stress (i.e.,
σ
σ
=
designation of the stress state and
a
,
b
=
constants (i.e., fitting parameters).
Fredlund (1979) suggested that the void ratio constitutive
surface for an unsaturated soil could be linear over a wide
range of stress changes using the logarithm of the stress state
variables. The void ratio under any set of stress conditions
is written as follows:
u
w
) is essentially
a straight line. The equation for the virgin compression por-
tion of void ratio can be written as follows for a saturated
soil:
−
C
c
log
σ
σ
p
σ
−
u
a
u
a
−
u
w
e
=
e
0
−
C
t
log
u
a
)
0
−
C
m
log
(14.88)
(σ
−
(u
a
−
u
w
)
0
e
=
e
0
−
(14.86)
Similarly, the water content under any set of stress con-
ditions is written as follows:
where:
σ
−
u
a
u
a
−
u
w
e
0
=
initial void ratio,
=
w
0
−
D
t
u
a
)
0
−
D
m
log
w
log
(σ
−
(u
a
−
u
w
)
0
(14.89)
C
c
=
volume change index for the virgin compression
curve, and
where:
σ
p
=
preconsolidation pressure.
e
0
=
initial void ratio,
A similar equation can be written for the rebound curve
(i.e., unloading-reloading curve) that takes on the following
form:
C
t
=
volume change index with respect to net
normal stress,
C
m
=
volume change index with respect to matric
suction,
e
=
a
+
b
log
(σ )
(14.87)
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