Environmental Engineering Reference
In-Depth Information
assumed to be 400 kPa at the bottom boundary, decreasing
to 20 kPa at ground surface. The vertical edge boundaries
were assumed to be no-flow boundaries. An evaporation flux
rate of 10 mm/day was applied to the uncovered ground
surface outside the flexible slab. The soil properties used in
the seepage analysis are shown in Table 16.9.
The left and right stress-deformation boundary conditions
are free to move vertically while the bottom boundary is
fixed. The initial vertical total stress state was determined
from the total unit weight multiplied by the depth
below ground surface. The soil properties used in the
stress-deformation analysis are shown in Table 16.10.
The calculated differential deflections are presented in
Table 16.11. A differential deflection of 5.33mm was pre-
dicted after five days of evaporation when the ground surface
cover was flexible. When modeling a concrete slab with a
modulus of elasticity of 20MPa there was a decrease in
the differential deflection to 4.94 mm. Increasing the elastic
modulus of the concrete slab resulted in a small decrease
in deflection for the concrete slab. A modulus of 100 GPa
for the concrete slab decreases the differential deflection to
about 4.27mm after 5 days of drying.
The initial modeling of the concrete slab for edge drop did
not allow for separation between the soil and the concrete
slab. It is possible, however, for the soil to separate from
the concrete giving rise to an air gap. The length of the air
gap is known as the moisture variation distance
e
m
. A trial-
and-error procedure was used to compute the length of the
air gap separation between the soil and the concrete slab.
16.9.1 Comparing Ground Displacements for Edge
Drop Example Using Flexible or Stiff Concrete Slab
The combined seepage and stress-deformation analysis was
performed for conditions of a flexible slab on the ground
surface as well as the case of a more rigid concrete slab.
Figure 16.53 shows a comparison of the vertical displace-
ments along the ground surface when modeling a flexible
slab and a concrete slab with a modulus of elasticity of 100
GPa. The vertical displacements along the ground surface
were used to compute the differential deflection at the base
of the concrete slab, as shown in Fig. 16.53.
16.9.2 Methodology Used to Determine Separation
Distance between Slab and Underlying Soil
for Edge-Drop Case
The potential separation between the concrete slab and the
underlying soil can be modeled based on a variety of assump-
tions related to the interaction between the soil and the con-
crete slab. A stress-deformation analysis was performed using
the changes in matric suction from a seepage analysis as input
to the analysis.
Let us first assume that the slab is flexible and the ver-
tical displacement along the ground surface is computed.
The analysis is then repeated taking the elastic properties
of the concrete slab into consideration. The concrete slab is
assumed to remain in contact with the soil at all points. The
vertical displacements and vertical stresses can be computed
along the ground surface.
There will be a point along the bottom of the concrete slab
where tensile stresses start to develop. A distance of sepa-
ration can be assumed and then a check can be made to see
if any of the vertical stresses go into tension (Fig. 16.54).
The stress analysis can again be performed and the results
again examined for tensile stresses. This trial-and-error pro-
cess can be repeated until the analysis shows that there are
no tensile stresses between the soil and the concrete slab.
In this way, the length of the gap between the soil and the
concrete slab becomes a “review” boundary condition. The
soil-concrete slab separation distance can be assumed to be
equivalent to the moisture variation distance
e
m
.
The results of the analysis with no separation between the
soil and the concrete slab (Fig. 16.53) can be compared with
the results where separation was allowed between the soil and
the slab (Fig. 16.55). The results show that tensile stresses
existed over a distance of approximately 0.6m from the edge
of the slab. The effect of allowing a separation of 0.01m
between the soil and the slab is shown in Fig. 16.55. The
results in Fig. 16.55 illustrate the difference in the deformed
shape of the concrete slab depending upon the assumption
Table 16.9 Assumed Soil Properties for 2D Edge-Drop
Seepage Analysis
Soil Properties
Values
10
−
8
m/s
Coefficient of permeability at
saturation,
k
s
1
×
Volumetric water content at saturation,
θ
s
0.45
Parameters for SWCC (Fredlund and
Xing, 1994) and permeability function
(Leong and Rahardjo, 1997a)
a
f
=
300 kPa,
n
f
=
1
.
5,
m
f
=
1,
p
=
1
Table 16.10 Assumed Soil Properties for 2D
Edge-Drop Stress Analysis
................
Soil Properties
Values
17.2 kN/m
2
Total unit weight,
γ
Initial void ratio,
e
0
1.0
Swelling index,
C
s
0.15
Swelling index,
C
m
0.13
Poisson's ratio,
μ
0.4
Coefficient of earth pressure at rest,
K
0
0.33
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