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Consolidation 1
Introduction
It is possible to use a seepage solution to perform a consolidation analysis, since the Terzaghi consolidation equation is fundamentally identical to the seepage governing differential equation. Moreover, since closed form solutions are available for the consolidation equation, it is also possible to check the transient capability of the model by comparing hand-computed results for a one-dimensional consolidation problem with modeled results.
2
Feature Feature highligh ts
GeoStudio feature highlights include: •
Transient 1D flow
•
Comparison with closed form solution
3
Geometry Geometry and boundary conditi ons
In accordance with the Terzaghi theory of consolidation, the dimensionless dimensionless time factor T and the real time t can be related as follows: 2
t =
H T C v
where: H
=
maximum drainage path,
T
=
non-dimensional time factor, and
C v
=
coefficient of consolidation.
Using the above equation and commonly available graphical charts, (see Lambe and Whitman, 1969, p. 408), the time t required to reach a certain degree of consolidation can be computed for a given time factor T. The geometry for the model is very simple and is shown below. It consists of a 1D column, one meter in height with 20 divisions along the vertical region edge. An initial condition analysis is solved as steady state, in which a pressure head of 100m is placed at the top. In the transient consolidation analysis, analysis, a pressure of zero condition condition (Head = elevation) is specified specified along the top edge. There is no no flow at the base of sides of the column.
SEEP/W Example File: Consolidation.doc (pdf) (gsz)
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GEO-SLOPE International Ltd, Calgary, Alberta, Canada
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1.1 1.0
H=1m
0.9 0.8 0.7
n o 0.6 i t a v e 0.5 l E 0.4 0.3 0.2 0.1 0.0 0.45
0.55
0.65
0.75
0.85
0.95
1.05
Distance 4
Material pro perties
We know in this example that the Cv = 5e-4 m2/sec and that the Mv = 0.01 / kPa with a saturated hydraulic conductivity of 4.9e-5 m/sec. The hydraulic conductivity is calculated using
k
=
Cvγ w mw
Since this is a fully saturated problem, we can apply the Saturated Only material model, as shown below.
SEEP/W Example File: Consolidation.doc (pdf) (gsz)
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5
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Discussion of results
The graph below shows the drawdown curves at various saved times. The form of the curves is the same as commonly published graphical solutions for Terzaghi's equation.
PWP dissipation 1.0
0.8
) m (
0 sec 180 sec 360 sec 540 sec 720 sec 900 sec 1080 sec 1260 sec 1440 sec 1620 sec 1800 sec
0.6
Y
0.4
0.2
0.0 0
200
400
600
800
1000
Pore-Water Press ure (kPa)
SEEP/W Example File: Consolidation.doc (pdf) (gsz)
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GEO-SLOPE International Ltd, Calgary, Alberta, Canada
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The table below presents the resulting excess head at mid-height and at the bottom of the layer, as determined by hand-calculation and by SEEP/W. A close agreement can be observed between the SEEP/W solution and the closed-form solution. Comparis on o f Terzaghi and SEEP/W resul ts T
t (sec)
Head at Mid Height
Head at Botto m
Terzaghi
SEEP/W
Terzaghi
SEEP/W
0.05
100
88
89.20
99
97.93
0.10
200
74
76.88
95
92.93
0.15
300
64
66.48
86
86.02
0.20
400
55
58.08
77
78.34
0.30
600
42
45.98
60
64.01
0.40
800
33
36.74
47
51.85
0.50
1000
26
29.49
37
41.87
0.60
1200
20
23.73
29
33.81
0.70
1400
15
19.12
22
27.32
SEEP/W Example File: Consolidation.doc (pdf) (gsz)
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