CYCLIC STRENGTH OF STRATIFIED SOIL SAMPLES
J.-M. KONRAD,
Dept. of Civil Engineering, Université Laval, Québec, Canada, G1K 7P4
S. DUBEAU,
Dept. of Geology and Geological Engineering, Université Laval, Québec,
Canada, G1K 7P4
Abstract
This paper presents the results of a laboratory testing program on the influence of
stratification on cyclic strength of soil samples. Reference undrained cyclic triaxial tests
were conducted on fine Ottawa sand samples and a much finer silica silt sample. Both
samples were prepared by pluviation under water. Undrained cyclic triaxial tests
conducted on stratified sand-silt samples revealed that layering induced a much lower
cyclic resistance than that developed in either of the materials. Differential pore pressure
generation in each soil unit suggest that water migration occurred from the sand layer to
the silt layer and caused this strength reduction. The experimental data have significant
implication for field conditions, especially for submarine slopes.
Keywords: Sand, silt, layered, cyclic strength, saturated
1. Introduction
Saturated sands subjected to undrained cyclic loading are known to develop excess pore
pressures, leading ultimately to failure by liquefaction. The investigation of this
phenomenon in the laboratory may be done using triaxial tests. Results from
consolidated isotropically undrained (CIU) cyclic triaxial tests show that the pore
pressure increases progressively until it reaches a value equal to the total stress acting
upon the sand. Thus, there is a momentary condition of zero effective stress, referred to
as liquefaction. The number of cycles required to reach liquefaction, NL, decreases with
increasing density (decreasing void ratio) and with increasing applied cyclic shear
stress. The relationships between void ratio, cyclic stress amplitude and number of
cycles to liquefaction define the cyclic strength of a given sand placed with a given
method (wet compaction, pluviation in air or water, etc...).
While the cyclic strength curves of various sands with and without fines have been
extensively studied, few experimental data on layered samples are available in the
literature. Piezocone testing reveal that uniform sand deposits are seldom encountered in
nature. Often, sand deposits are layered with several soil units ranging from coarse- to
fine-grained. This is typical of sedimentary environments where as the conditions
change, so does the nature of the sediments deposited.
Layering in apparently uniform sand deposits may also be induced by changes in
density where a loose sublayer may be sandwiched between denser layers.
47
48
Konrad and Dubeau
Recent studies by Kokusho et al., 1998, Kokusho and Kojima, 2002 have established by
means of shake table tests that liquefaction of layered sand is associated with the
presence of a thin water film beneath a less pervious sublayer due to the local migration
of pore water, indicating thus a greater susceptibility to flow sliding during earthquakes.
This paper presents the results of cyclic CIU tests on a reference Ottawa sand as well as
on layered sand-silt samples and discusses in detail the role of pore pressure build-up in
each soil unit. The implication for field conditions, especially for submarine slopes
where stratification is often significant, is highlighted.
2. Material tested
Two materials have been used in this study. The finer material was silt composed of
silica dust whereas the coarser one was Ottawa sand, a well-known uniform reference
sand. The silt was SILEX regular silica produced by INDUSMIN and purchased from
the Wilkinson Foundry, Toronto, Canada. It is 99.5% silica with trace amounts of iron,
aluminum, and calcium oxides. The minimum and maximum void ratios for the sand
were respectively of 0.5 and 0.8.
The grain size distribution of both materials is shown on figure 1.
3. Specimen preparation
The objectives of this experimental study were to obtain the cyclic strength
characteristics of layered sand-silt samples using CIU cyclic triaxial tests. Sample
preparation of 100% silt samples presents some challenges, which are even increased if
the samples are layered. In order to achieve reproducible void ratio states, it was decided
to proceed with a preparation technique known as water pluviation for both materials.
This technique had also the advantage of producing fully saturated samples, an
indispensable condition for liquefaction studies.
3.1 SAND SAMPLES
Six sand samples were prepared using fine Ottawa sand. Appropriate amounts of dry
clean sand were deposited in bottles in which distilled deaerated water was added. Any
air bubbles in the soil sample were removed.
Sand was subsequently deposited into a mould filled with deaired water to produce
100.0 mm high samples with a diameter of 100.6 mm. Each sample was prepared to a
different void ratio by hitting the mould with a hammer once the content of a bottle had
been deposited (loose samples) or by placing it on a vibrating plate (denser samples).
The set-up time of these samples was approximately 30 minutes.
Cyclic strength of stratified soil samples
49
100
Sand
80
Percent passing
Silt
60
40
20
0
1
0.1
0.01
0.001
Grain size (mm)
Figure 1. Grain size distribution for silt and sand.
3.2 SILT SAMPLES
Only one silt specimen was prepared to evaluate its pore pressure evolution during
cyclic loading. The method of preparation of this sample was the same as that used for
the sand specimens. Since the sedimentation time depends on the size and weight of the
particles, the sedimentation time for a 2-cm thick silt sample exceeded 48 hours. The silt
sample required more than a week of preparation since it was composed of five
individual layers.
3.3 STRATIFIED SAMPLES
Three different sand-silt stratified samples were prepared with the pluviation technique.
The first stratified sample was composed of a 4-cm thick sand layer, overlain by a 2-cm
thick silt layer and another 4-cm thick sand layer. Prior to the silt deposition, the sand
layer was densified to the desired density. The upper sand layer was also densified to
the same target density. This procedure will affect the density condition in the silt layer
and required therefore careful measurements of the moisture content in each soil unit
after cyclic triaxial testing.
Since the pore pressure values are measured at the base of the specimen, the 2-cm thick
silt layer was placed above a 2-cm thick sand layer and an 8-cm thick sand layer as
illustrated schematically in table 1.
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Konrad and Dubeau
Table 1. Test conditions.
Reference Sand
1
Stratified Samples
2
3
Void Ratio (e)
0.53 to 0.60
Silt → from 0.76 to 0.79
Sand → from 0.57 to 0.59
Global void ratio of 0.61
Cyclic Stress Ratio
0.125 to 0.25
0.125
4. Testing procedure and Experimental program
All the samples were isotropically consolidated to an effective confining stress of 100
kPa, using a cell pressure of 500 kPa and a backpressure of 400 kPa.
Samples were tested in compression and extension. The loading system used a
Bellofram cylinder connected to an electric-to-pneumatic transducer and a function
generator which provided a sinusoidal loads at a frequency of 0.2 Hz. Automatic data
acquisition was done with the GEN2000 software. Pore pressure at the base of the
sample, axial load, confining pressure, and axial strain were monitored with time.
The testing program consisted of three test series. Series 1 included six tests to
characterise the cyclic strength of the reference sand under different density and cyclic
stress conditions. Four samples with a void ratio of 0.57 were subjected to different
cyclic stress ratios, σd/2 σ’c, of 0.25, 0.20, 0.175 and 0.125, respectively. Two tests were
conducted on samples with void ratio’s of 0.55 and 0.53 and CSR values of respectively
0.25 and 0.18.
Series 2 was done on a 100% silt sample placed at a void ratio of 0.85 and subjected to a
cyclic stress ratio of 0.166.
In Series 3, three layered sand-silt-sand samples were subjected to approximately the
same cyclic stress ratio of 0.15 ¹ 0.02. The position of the 2-cm thick silt layer was
respectively 2, 4, and 8 cm above the base platen where the pore pressure is measured.
5. Test results
5.1 REFERENCE SAND
Figure 2 shows the results from a typical cyclic triaxial test on the reference sand placed
at a void ratio of 057. The basic data are generally summarized in three different plots:
Cyclic strength of stratified soil samples
51
a) Axial strain vs. number of cycles
b) Pore pressure vs. number of cycles
c) Stress path in a Cambridge diagram
∆u (kPa)
∆u (kPa)
Axial strain ε (%)
Axial strain (%)
The applied cyclic deviator stress was +/-25 kPa, i.e. a CSR value of 0.125. As
anticipated, there is a progressive build-up of pore pressure while the cyclic axial strain
’
remains less than 0.2 %. Figure 2 indicates that when the pore pressure ratio, ∆u/ σ χ,
reaches 0.80 after 410 cycles, compressive and extensive axial strains increase
significantly with each subsequent cycle. The pore pressure ratio reaches a value of
100% after 420 cycles. As illustrated on Figure 2c, the effective stress path passes
through the origin, the effective stress is thus momentarily equal to zero, and the sample
has liquefied.
Number of cycles
Number of cycles
Deviatoric stress
Figure 2. Typical results for reference sand
(e = 0.57, CSR = 0.125).
Mean effective stress p’ (kPa)
Figure 3a summarizes the experimental results for the reference sand in terms of cyclic
strength characteristics where the number of cycles to liquefaction failure is related to
both the cyclic stress ratio and the void ratio.
Figure 3b shows the same results in a plot of void ratio versus the number of cycles to
failure with equal CSR values. Lines corresponding to particular CSR values have been
plot on the graph for values of 0.25, 0.20, 0.175 and 0.15.
This graph is useful to interpolate cyclic strength values for different combinations of
CSR and void ratio values. Test Series 1 confirms that the cyclic strength of a saturated
uniform fine sand increases with decreasing cyclic shear stress and decreasing void
ratio.
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Konrad and Dubeau
5.2 SILT SAMPLE
Figure 4 presents the data for the silt sample which was placed at a void ratio of 0.85
and subjected to a cyclic stress ratio of 0.166. Similarly to the sand samples, pore
pressure build-up occurred while the axial strain remains close to zero until liquefaction
0.30
σd/2σ’3
0.25
0.20
e = 0.53
e = 0.55
0.15
e = 0.57
0.10
0
100
200
300
400
Cycles
0.60
Legend
σd/2σ’3 = 0.25
σd/2σ’3 = 0.20
σd/2σ’3 = 0.18
σd/2σ’3 = 0.15
Void ratio
0.58
0.56
σd/2σ’3 = 0.15
0.54
σd/2σ’3 = 0.175
σd/2σ’3 = 0.25
σd/2σ’3 = 0.20
0.52
0
100
200
300
400
Cycles
Figure 3. Test results for reference sand.
is reached after 90 cycles. Once liquefied, dynamic effects develop and the pore
pressure ratio exceeds 100 % in the compressive strain domain. This translate also in the
fact that the effective stress path in compressive does not move along the MohrCoulomb failure envelope as do the sands.
Cyclic strength of stratified soil samples
53
Work by Singh (1996) showed that the cyclic strength characteristics of compacted
saturated silt displayed similar trends to those of sands, i.e. increasing cyclic strength
∆u (kPa)
Axial strain ε (% )
Number of cycles
1XPEHURIF\FOHV
D
3
N
T
V
V
H
U
W
V
F
L
U
R
W
D
L
Figure 4. Typical results for reference silt
(e = 0.85, CSR = 0.166).
Y
H
'
Mean effective stress p’ (kPa)
with decreasing CSR and void ratio values. Since only one test was done on silt, the
trend of pore pressure build-up for different CSR and void ratio values was indicated on
Figure 5.
5.4 STATIFIED SAMPLE
All three samples have been tested at a constant cyclic stress ratio of 0.125. Figure 6
summarizes the results for a sample in which the 2-cm thick silt layer was placed at mid
height of the sample, sandwiched between two sand layers (sample 3). Water content
measurements after the test was completed indicated that the void ratio in the sand
layers was 0.57 and that of the silt layer was 0.78. The overall void ratio of the layer
sample was thus 0.61. Liquefaction was observed after 42 cycles. Pore pressure buildup occurred with axial strains of less than 0.2%. Graph 6a indicates that the sample was
subjected to a slight increase in mean extensive axial strain, which is different from the
tests carried out on 100% sand or 100% silt where the mean axial strain remained
constant until the onset of liquefaction. Figure 6c shows that, once the stratified sample
is liquefied, the effective stress path follows the Mohr-Coulomb failure envelope in both
compression and extension.
Figure 7 summarizes the results for the stratified samples and compares their cyclic
strength to that of the reference sand placed at the same void ratio and subjected to the
54
Konrad and Dubeau
same cyclic stress ratio. The latter cyclic strength was determined using the results
plotted in Figure 3b. As indicated in Table 1, the void ratio of the sand layer was
slightly different in each stratified samples. For the sample with the silt layer closest to
the base plate (sample 1), the void ratio of the sand was 0.58 and for the sample with the
silt layer closest to the top plate (sample 2), it was 0.59. The void ratio of the silt layer
was also slightly different in each sample. It was 0.76, 0.79 and o.78 for sample 1, 2
and 3, respectively.
1
Reference silt
e = 0.85
CSR = 0.166
e↓
CS R ↓
∆u/σ’c
0.8
0.6
0.4
0.2
0
40
80
120
160
200
Number of cycles
Figure 5. Influence of void ratio and cyclic stress on pore pressure build-up in silt.
The data presented in Figure 7 show three different values of void ratio for the stratified
sample, one for the sand layer, one for the silt layer and one for the overall sample.
When the number of cycle to reach liquefaction failure in the stratified sand-silt samples
are compared to the number of cycles required to reach failure in the reference sand
placed at the same density and subjected to the same cyclic stress ratio, a significant
reduction of the cyclic strength was observed for all three stratified samples. The cyclic
strength reduction appears to be relatively the same in all three cases and about 50
cycles.
∆u (kPa)
Axial strain ε (%)
Cyclic strength of stratified soil samples
55
Number of cycles
Number of cycles
r
Figure 6. Typical results for stratified
samples.
Deviatoric stress q (kPa)
Mean effective stress p’ (kPa)
0.90
2
0.80
Void ratio (e)
1
3
0.70
100 % sand
0.60
↑ Cyclic strength reduction
0.50
0
25
50
75
100
Number of cycles to failure
Figure 7. Test results for stratified samples 1,2,and 3.
125
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Konrad and Dubeau
6. Discussion
The results presented above clearly demonstrated that saturated stratified samples with
layers of different properties leading to different responses under cyclic loading
experience a significant reduction in their cyclic strength. In order to gain some insight
into this phenomenon, let us examine the pore pressure response of each layer and let us
consider sample 3 as an example. Figure 8 shows the evolution of normalised pore
pressure with the number of cycles of a 100% sand sample at a void ratio of 0.57 and
that of a silt sample at a void ratio of 0.78. The latter values are based on the trends
presented on Figure 5 since no data are available for the silt at a void ratio of 0.78.
However, it is safe to assume that the rate of pore pressure build-up will be less than that
observed in the silt sample placed at a higher void ratio of 0.85. The important aspect to
stress is the fact that, at any given number of cycles, the pore pressures in the silt are
definitively smaller than those in the sand layer. This differential pore pressure
generation causes water to migrate from the sand layers to the silt layer. The undrained
test is thus no longer a truly undrained test, especially for the silt layer.
Recent work by Vaid and Eliadorani (1998) has shown that partially drained conditions
may render sand unstable that would otherwise be stable in a completely undrained
state. It was demonstrated that extremely small water content changes caused by water
injection contributed to sand instability.
The cyclic tests presented herein on stratified samples indicate that the presence of
layers with different pore pressure responses to undrained cyclic loading cause also a
condition of local volume change near the layer interfaces, resulting in a drastic
reduction in cyclic strength.
1
0.8
Sand
e = 0.57
∆u/σ’c
0.6
Silt
e = 0.78
0.4
0.2
0
0
20
40
60
80
100
Number of cycles
Figure 8. Differential pore pressure build-up in sand and silt
Cyclic strength of stratified soil samples
57
7. Conclusion
A laboratory study was conducted to investigate the behaviour of stratified sand-silt
samples subjected to cyclic triaxial-compression-extension stresses. The cyclic strength
of these stratified sand-silt samples was considerably decreased when compared to that
of a 100% sand sample at the same void ratio and subjected to identical undrained cyclic
loads. The data suggest that differential pore pressure build-up in the sand and in the silt
layer sandwiched between the sand layers causes water to migrate from the sand
towards the silt. This then results in small expansive volumetric deformations which
accelerate the liquefaction process.
The implication of this finding is important for the stability of underwater slopes
displaying layering. Depending on the properties of each layer, flow liquefaction may
be triggered despite the fact that each individual layer may have a sufficiently high
cyclic strength. It also means that an earthquake of a smaller magnitude than expected
could trigger liquefaction in a stratified deposit.
8. Acknowledgements
This research was supported by the NSERC Canada (Natural Sciences an Engineering
Research Council) via COSTA-Canada project. The technical assistance of François
Gilbert is gratefully acknowledged.
9. References
Kokusho, T. and Kojima, T. , 2002. Mechanism for postliquefaction water film generation in layered sand.
Journal of geotechnical and geoenvironmental engineering, Vol. 18, No 2, 129-137.
Kokusho, T., Watanabe, K., Sawano, T. 1998. Effect of water film on lateral flow failure of liquefied sand.
CD publication,
Proc. 11th European Conf. Earthquake Engineering, Paris, France.
ECEE/T2/kokeow.pdf.
Singh, S. 1996. Liquefaction characteristics of silts. Geotechnical and geological engineering, 14, 1-19.
Vaid, Y.P., and Eliadorani, A., 1998. Instability and liquefaction of granular soils under undrained and
partially drained states. Canadian geotechnical J., Vol. 35, No 6, 1053-1062.