Environmental Engineering Reference
In-Depth Information
C
m
=
volume change index with respect to matric suc-
tion, and
14.8.2 Reanalysis of Previous Examples Using
Incremental Elastic Analysis
The example problem involving the prediction of total heave
in a 2-m layer of expansive clay is reanalyzed to demon-
strate the use of a one-dimensional, finite element numerical
model to compute total heave. The results are compared to
the nonlinear, longhand solution presented in Fig. 14.38. The
example problem assumes that the pore-water pressures in
the soil will increase with time to establish a new equilib-
rium pore-water pressure profile.
The longhand analysis used only three layers and com-
puted a total heave of 117 mm. Figure 14.60 shows the
results of the finite element numerical solution when the
2-m layer of expansive clay is divided into varying num-
bers of layers. The finite element numerical model shows
that the total heave is computed to be 117.3mm when 25
one-dimensional finite elements are used. Further refine-
ment in the number of finite elements shows little additional
improvement in the solution.
The prediction of heave using the one-dimensional solu-
tion requires that the elastic modulus with respect to matric
e
0
=
initial void ratio.
Equation 14.80 can be used to compute vertical displace-
ment due to net normal stress changes and/or matric suction
changes. A finite element numerical model can be used to
solve the stress-deformation equations provided appropri-
ate head (or pore-water pressure) boundary conditions are
specified.
Equation 14.80 is nonlinear since the elastic moduli are
functions of the stress state variables. An incremental,
marching-forward procedure can be used as shown in
Fig. 14.59. Both total load changes and matric suction
changes need to be divided into increments and applied in
incremental steps. The elastic moduli are assumed to remain
constant within each incremental step. A new modulus is
selected at the beginning of the application of each new
increment of load (or matric suction). The displacements
computed for each incremental step of loading are accu-
mulated to give the total displacement or heave.
Final stress state
Accumulated error
in predicted strain
5
th
stress step
m
1
4
th
Initial stress state
3
rd
2
nd
1
st
0
Stress state variables,
σ
-
u
a
or
u
a
-
u
w
Figure 14.59
Incremental elasticity procedure for calculating amount of heave when a soil is
wetted.
120
115
0.45 mm or 0.5% total heave
25 layers, total heave = 117.30 mm
110
100 layers, total heave = 117.75 mm
105
100
0
20
25
40
60
80
100
Number of layers
Figure 14.60
Total heave calculated using varying numbers of soil layer in calculations.
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