1509
Technical Committee 203 /
Comité technique 203
influenced by the cyclic loading. The creep rate increased with
increasing permanent shear strain at the end of the cyclic
loading and increasing shear stress ratio,
.
Table 1 Mean parameters for the two test series.
Parameter
Samples 2007/08 Samples 2011
Water content, w
i
(%)
39.5
32
Clay content (%)
38
36
Plasticity index, Ip (%)
11
8
Liquid limit, w
l
(%)
31
24.5
Plastic limit, w
p
(%)
20
16.5
s
u
(Fall Cone) (kPa)
34
17
Sensitivity (Fall cone)
100
140
OCR
~1.5
Uncertain
Gmax/
vc
’ for
c
=0
236
252 (one test)
Gmax/
vc
’ for
c
>0
236
220
The test results were compiled in two different types of contour
diagrams. The first type defines average and cyclic shear strains
as functions of average and cyclic shear stresses, both
normalized with undrained shear strength. The diagrams were
established for different number of cycles and load periods. This
type of diagram is illustrated by an example for 100 cycles and
a load period of 0.1 s in Figure 3. (The average shear strain is
defined as the average shear strain in a cycle, and the permanent
shear strain is defined as the shear strain at the end of a cycle.
For the test conditions that are relevant herein, the average and
the permanent shear strains can be assumed to be the same).
Andersen, 2009, gives a more detailed description of definitions
and this type of diagram.
cy
~=0.12%
a
~=4.5%
cy=15%
a=15%
Figure 3 Contour diagram for N=100 and load period of 0.1 s for
determining cyclic stresses and strains.
The second type of contour diagram is a time-to-failure diagram
shown Figure 4 that relates the time to creep failure to the
permanent shear strain at the end of cyclic loading and the
normalized average shear stress (=degree of mobilization).
Figure 4 Time-to-failure diagram. Green dashed lines show to degrees
of mobilisation 0.6 and 0.7 that were used in calculations.
5 VIBRATION AMPLITUDE TO CAUSE LOCAL
FAILURE
The vibration velocity necessary for local failure of the soil in
the zone near the rock-clay border that are subjected to the
largest vibrations are estimated with help of equation (1) and the
two contour diagrams described above. The following example
illustrates the procedure.
We assume the soil density and initial shear wave velocity
to be 1800 kg/m
3
, and 80 m/s, respectively, giving an initial
shear modulus,
of 11.5 MPa. These values are typical for
soft Norwegian quick clays.
As the first step the permanent shear strain that will almost
cause creep failure is read off from the time-to-failure diagram
in Figure 4. (Permanent shear strains are the shear strains at the
start of creep and are termed
start
in Figure 4). Permanent
strains of 2.5% and 1.5% are close to causing failure for
mobilization degrees (
a
/s
u
) of 0.6 and 0.7 (corresponding to
factors of safety of 1.7 and 1.4 for infinitely long slopes).
In the next step we want use the contour diagram in Figure 3
to estimate cyclic shear strains,
cy
. This diagram is based on
averages strains,
a
(that are almost the same as permanent
strains). However the average strains used in Figure 3 include
the shear strains during consolidation,
c
. Therefore the shear
strain during consolidation has to be added to the permanent
shear strains determined from Figure 4. The shear strain during
consolidation can be determined from the average shear strains
along the horizontal axis in Figure 3. The resulting average
strains to be used in Figure 3 thus become 4.5% and 6% for
mobilization degrees of 0.6 and 0.7, respectively. The strains
are shown in Table 2.
Table 2 Shear strains that would cause creep-failure in laboratory.
Mobilization degree
0.6 0.7
Permanent strain at end of cyclic loading,
p
[%]
(from
Figure 4
)
2.5 1.5
Consolidation shear strain,
c
[%]
2.0 4.5
Resulting average strain,
a
[%]
(to be used in Figure 3)
4.5 6.0
The duration of a typical blast vibration time history is about 3
seconds and contains three to five cycles at the highest strain
level, which is relevant to pore pressure build-up. During a blast
operation there are three to five blasts, thus the number of
cycles, N, are estimated to 15-25. Since the dominant
frequencies of blasting vibrations in the soil are in the range 15-
