1379
Technical Committee 202 /
Comité technique 202
interest. As the construction of the motorway takes some month
it is not necessary to describe the curvature of the time-
dependent deformation, which is observed during the first
period.
According to figure 4, the deformation characteristics after
approximately 100 days may be described by a creep law given
by Buisman 1939. This law was originally developed to
describe the creep following consolidation of clays after a
stepwise increase in effective stresses. In addition it is suitable
to describe the deformation characteristic of the dump mainly
made up of unsaturated coarse-grained sandy soils. The creep
law demands two model parameters, a reference time (defined
as the time when the deformation starts) and the magnitude of
creep deformation. The deformation rate characterized by the
slope in a semi-logarithmic time vs. deformation plot as given
in figure 4 is described by the parameter C
K
in analogy to the
parameter C
B
given in the original work of Buisman 1936 (“K”
represents the German word “Kippe” meaning “dump”).
In figure 5, the parameter C
K
derived from the time
dependent deformation curve of the survey points along the
alignment of the planned A 44 autobahn is plotted. C
K
was
evaluated from the slope of the deformation characteristics for a
period of 1 year after the completion of dumping until mid
2011.
4000
4500
5000
5500
6000
6500
7000
Station [m]
0.00
0.05
0.10
0.15
0.20
analyzed from 365 days on after
completion of the dumping process
Parameter C
K
[%]
south
north
dumping process
Figure 5. Parameter C
K
along the A 44 autobahn route
The plot in figure 5 gives a very uniform distribution of the
parameter C
K
in between the station 4500 m and 6800 m of the
A 44 route. C
K
varies in between 0.075 % and 0.125 % with a
mean value of roughly 0.1 %. Only some points around 6700 m
give smaller values of C
K
. Analyses of the data show that the
depth of the dump along the observed survey points has no
effect on the parameter C
K
. Nevertheless the depth of the dump
within the area that can be observed until now changes from in
the south 135 m to 155 m in the north.
In the future the dumping process will advance another 3 km
to the north creating depths of dump up to 185 m. The shown
geodetic measurements provide data for determining time
dependent deformations. Therefore, special care is required in
the evaluation of geodetic data on a continuous basis to verify
that the values of C
K
will change in the northern region because
of an increasing depth of dump. In the event the dumping
concept described in chapter 2 is carried out until the dump
beneath the A 44 alignment is completed, the measured C
K
of
0.1 % will provide valuable information for the prediction of
deformations.
3.2
Effect of initial density on the time-dependent behaviour
The stress and time-dependent deformation behaviour of the
soils was investigated using one-dimensional compression tests.
Four different soils representing the majority of the curves
plotted in figure 3 were chosen. In different test series the effect
of varying initial density and loading rate on the time-dependent
compression were examined in detail. Additionally, soaking at
different stresses was evaluated.
All tests were carried out by increasing the stress stepwise
while observing the axial deformation of the sample. Within the
first few seconds after the stress was applied, comparatively
large strains were measured. The following strains reduce
rapidly with elapsed time. This characteristic can be described
by drawing a straight line in a diagram plotting strain versus
natural logarithmic time (see figure 6). The slope of the straight
line can be expressed by the Buisman constant C
B
(Buisman
1936).
time t
= C
B
·ln(t/t
0
)
strain
[%]
logarithmic
(base 2,718)
t
0
0
t0
ti
t
0
t
i
t
i
time t
strain
[%]
stepwise increase
of stress
Figure 6. Time-dependent deformation after a stepwise stress increase
Figure 7 illustrates the values of C
B
determined for a silty
fine sand with a content of fines of 15 mass-%. The samples had
heights of 2 cm and 10 cm with respective diameters of 10 cm
and 30 cm. Different initial densities with density indices I
D
= 0
to 0.8 were examined. The initial water content was about 10 %
for all tests. The tests show a clear dependence of the Buisman
constant on the initial compaction index and governing stress.
C
B
increases clearly with increasing stress. On comparing the
results for different relative densities it can be seen that the C
B
value decreases with increasing density. On analysing all tests
carried out on 4 soils samples, no significant influence of the
soil type was recognized. Only a slightly higher C
B
value was
determined for the silty sand (see figure 7) having a fines
content of 15 mass-% opposed to the other investigated soils for
which the fines content varies between 3 and 6 mass-%.
0
250 500 750 1000 1250 1500 1750 2000 2250 2500
Parameter C
B
[%]
Stress
z
[kN/m ]
2
0.00
0.02
0.04
0.06
0.08
0.10
Dimensions of the soil sample
height = 2 cm
diameter = 10 cm
height = 10 cm
diameter = 30 cm
Initial relative density I
D
I
D
≈ 0,2
I
D
≈ 0,4
I
D
≈ 0,6
I
D
≈ 0,8
I
D
≈ 0,0
Figure 7. Influence of the initial relative density I
D
on the Parameter C
B
for a fine sand from the Garzweiler dump (silt and clay = 15 mass-%)
4
PREDICTION OF TIME-DEPENDENT
DEFORMATIONS
To predict the future time-dependent deformation of the
dump especially regarding the areas along the A 44 route that
are not yet filled up, the validation of a model based on a soil
mechanic theory was necessary. As a reference date for the
model used, the completion of dumping was set to the 1.1.2017.
The information seen in figure 8 was calculated using two basic
equations describing the stress and time-dependent deformation.
This simple model only allows the calculation of a one-
dimensional deformation. On expanding the model for
predicting more complex dumping processes (e.g. simulating
unloading and reloading) within a three-dimensional geometry,
