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Influence of sample conditions on shear wave velocity measurements in a
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DOI: 10.1080/1064119X.2020.1711833
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Influence of sample conditions on shear wave
velocity measurements in a sedimentary stiff clay
Paulina A. Janusz, Kenny K. Sørensen, Ole R. Clausen & Katrine J. Andresen
To cite this article: Paulina A. Janusz, Kenny K. Sørensen, Ole R. Clausen & Katrine J. Andresen
(2020): Influence of sample conditions on shear wave velocity measurements in a sedimentary stiff
clay, Marine Georesources & Geotechnology, DOI: 10.1080/1064119X.2020.1711833
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MARINE GEORESOURCES & GEOTECHNOLOGY
https://doi.org/10.1080/1064119X.2020.1711833
Influence of sample conditions on shear wave velocity measurements
in a sedimentary stiff clay
Paulina A. Janusza, Kenny K. Sørensena
, Ole R. Clausenb
and Katrine J. Andresenb
a
Department of Engineering, Aarhus University, Aarhus, Denmark; bDepartment of Geoscience, Aarhus University, Aarhus, Denmark
ABSTRACT
ARTICLE HISTORY
The study presented in this paper aims to investigate the prospects of using bender elements in
the offshore industry for determining shear wave velocity of fragmented, fragile and brittle clay
samples and cuttings. The result from the study shows that the laboratory-measured S-wave velocities of intact samples of Søvind Marl, a sedimentary stiff Palaeogene clay, in general, are lower
than those determined from in-situ seismic cone penetration testing. The reason may be unavoidable volume-constant distortion and changes to effective stress conditions experienced by the natural clay upon sampling and subsequent sample preparation. Correlation between the size of the
samples and velocity is not noticed. In contrast, the S-wave velocities for natural samples that
were remoulded and then reconstructed are observed to be comparable with the in-situ seismic
measurements, however, the results are found to be dependent on sample density. The influence
of cross-talk, near-field, and boundary effects on the results is assessed.
Received 13 June 2019
Accepted 30 December 2019
Introduction
Prediction of shear wave (S-wave) velocity in offshore sediments in the overburden and reservoir rocks is crucial in
the oil industry for instance in seismic modelling, AVO
(Amplitude Versus Offset) analysis (Lee 2006) and in the oil
well drilling process. It also plays an important role in marine geotechnical engineering because of the direct relation
between shear wave velocity and the dynamic shear modulus. The dynamic shear modulus of shallow depth offshore
sediments is a controlling factor in e.g. the response of offshore wind turbines towers or oil platforms to wave loading.
However, information about S-wave velocity is usually not
sufficient. In-situ determination of S-wave velocity in offshore conditions is usually very expensive and technically
complex (e.g. petrophysical well-logging, seismic surveys,
seismic Cone Penetration Tests S-CPT), in addition, indirect
measurements are difficult to interpret. For some deep seismic applications, shear wave velocity is still often estimated
using only empirical relations with compression wave (Pwave) velocity (Castagna et al. 1985). In shallow depth geotechnical engineering, even more uncertain correlations
based on soil index parameters such as soil type, density
and porosity are used (Yi and Yi 2016; L’Heureux and Long
2016). Laboratory measurements can provide more precise
information; however, the availability of soil and rock cores
is limited mainly because of the cost of offshore core drilling. In the hydrocarbon industry cores are usually retrieved
only from reservoir units. For shallower units, often only
drill cuttings or disturbed or fragmented soil and rock samples are accessible. This is a problem since well-preserved
CONTACT Kenny K. Sørensen
kks@eng.au.dk
Bender elements; clay
sediments; offshore
constructions; shear
wave velocity
intact samples are essential to obtain reliable results from
the on-sample measurements. Especially the interval between
50–100 m below the seafloor is critical since indirect measurements like petrophysical well-logging are not commonly
performed, and intact samples from coring or from shallow
depth geotechnical boreholes are sparse. Often, only very
disturbed drill cuttings are accessible.
One of the simple methods of measuring the shear wave
velocity in the laboratory is bender element testing which has
been used in geotechnical research for many decades to determine the soil properties such as small strain dynamic shear
modulus (G0) (Black et al. 2009; Lee and Santamarina 2005).
The bender element method is a simple, non-destructive, inexpensive and quick procedure that is generally used to determine shear wave velocity for relatively big, intact samples. In
this study, the possibilities of estimating S-wave velocity in a
situation of material shortage are investigated. This situation is
common in the offshore industry, where often only disturbed
drill cuttings, fragile heavily fractured rocks or completely
remoulded or broken-down soil and rock samples are available.
In this study, the shear wave velocity was measured for both
intact small clay samples and reconstructed samples and then
compared to the results of in-situ Seismic Cone Penetration
Testing (S-CPT) for verification.
Materials and methods
Bender element principle
Bender elements are piezoelectric bimorph transducers
which are characterized by a capability of conversion of
Department of Engineering, Aarhus University, Aarhus, Denmark
ß 2020 Informa UK Limited, trading as Taylor & Francis Group
KEYWORDS
2
P. A. JANUSZ ET AL.
Figure 1. a) Bender element’s schematic cross-section. b) Series element. c)
Parallel element. After Lee and Santamarina (2005).
electrical energy into mechanical deflection and vice versa.
The typical experimental setup consists of two thin bender
elements: one, used as a transmitter which when excited
with a small voltage generates a bending motion that propagates as a wave through the medium. The second bender
element detects vibrations and transforms it into a voltage
output (Black et al. 2009; Chee-Ming 2010).
The generation of motion is possible due to the bender
element’s layered internal structure (Figure 1). In the centre,
there is a conductive metal shim, surrounded by two piezoceramic sheets and two conductive outer electrodes. While
one piezoelectric layer contracts, another one expands.
Two connection configurations are possible (Figure 1):
series, where the polarities of the piezoelectrical layers are
opposite to each other, and the element is connected only at
the outer electrodes and parallel, where two piezoelectrical
layers have the same poling direction, and the element is
connected both at the outer electrodes and metal shim.
It is generally recommended to use a parallel bender element as the transmitter and a series element as the receiver to
attain optimal signal quality (Lee and Santamarina 2005).
Shear wave velocity Vs can be calculated by dividing the
tip-to-tip distance Ltt between bender elements by travel
time t of the S-wave determined from the bender element
test (Black et al. 2009).
One of the main reasons for the popularity of the bender
element tests is the simplicity of the procedure which is fast,
inexpensive and non-destructive. However, the output signal
can be strongly affected among others by electromagnetic
coupling, near-field (Lee and Santamarina 2005) or boundary effects (Ingale et al. 2017).
Electromagnetic coupling between source and receiver
(cross-talk) is a common issue related to bender element
testing, especially in wet and conductive materials. It is
manifested by the apparently almost instantaneous arrival of
the transmitted wave. The amplitude of that early component is relatively high, and it can significantly affect the
determination of travel time (Lee and Santamarina 2005;
Rio 2006). Different methods to remove or reduce the crosstalk effect are discussed among others in Lee and
Santamarina (2005), Zhu et al. (2011) and Rio (2006).
Figure 2 shows how grounding of the receiving element
effectively removes cross-talk in a test on an intact subsample. Figure 2a shows the signal before the receiving
element was grounded. A closer look at the received signal
from the grounded receiver is shown in Figure 2b (notice
that the y-axis scale has been adjusted). Although grounding
effectively removes most of the cross-talk, some are still seen
to remain, but the interpretation is now possible.
Many authors report the significant influence of nearfield effects on the determination of shear wave velocity
(Black et al. 2009; Arroyo et al. 2003). The phenomenon of
near-field effect is caused by very complex processes near
the source of wavefield (Arroyo et al. 2003), usually, it is
understood as a distortion of the transmitted signal due to
unknown early wave components (Ingale et al. 2017).
With reducing sample size, the influence of boundary effects
increases on the received wave. Distortion of the signal due to
the interference of shear wave with side reflections, refractions,
and converted waves may make identification of S-wave travel
time impossible.
Experimental setup
Both intact and reconstructed samples were tested under unconfined conditions to ensure that testing could be performed using
a fast and simple procedure. Bender element testing was performed by placing the sample between a stainless-steel pedestal
and a top cap with embedded bender elements protruding into
the sample at either end, as shown from the photos in Figure 3.
Bender elements
Bender elements were manufactured in-house. Only series elements were used in this study for simplicity. Standard 0.51 mm
thick brass-reinforced extension actuators T200-H4-503X
(Piezo Systems) were used. A coaxial cable (RG174/U) was soldered to each element. To ensure waterproofing and protection
of the electrical circuit, the soldering points were encapsulated
in a thin epoxy coating (LOCTITE EA 3430) before a thin
polyurethane coat was added to the element. The bender elements were cast into stainless-steel rings using a 2-part epoxy
(Figure 3). Only the bottom end of the element was fixated in
the ring to allow for greater free length and deflection of the
element. The protrusion of the element above the ring, which
equals the embedment depth of the element into the sample,
was chosen to be around 4 mm to minimize sample disturbance. The measured sizes of used bender elements and their
protrusion above the ring are given in the Table 1. To improve
the quality and strength of the transmitted signal, bigger (X0)
series elements were used as the transmitter as compared to
the receiver (X2 or X5).
Shear wave velocity measurement
A Function Generator (Aim-TTi TG1010A 10 MHz DDS
Function Generator) (Figure 4) was used to excite the
MARINE GEORESOURCES & GEOTECHNOLOGY
3
Figure 2. Examples of the output signals disturbed by cross-talk, near-field, and boundary effects. a) Intact subsample si1_2 before the receiver was grounded. b)
Intact subsample si1_2 after the receiver was grounded (different scale).
transmitter with multiple sine pulses with a peak-to-peak
amplitude of 10 or 20 V. The transmitted signal was amplified by a factor of 10 by a power amplifier (High Voltage
Linear Amplifier P200, FLC Electronics x10). Both transmitted and received electrical signals were digitalised and
recorded on an oscilloscope (Pico Technology, PicoScope
4224, 16 bit), and were preliminarily examined using
PicoScope 6 software. Then, the results were exported and
analysed using self-prepared Matlab scripts.
the signal was not good enough to perform cross-correlation. Therefore, it was decided to use a time-domain to
determine travel time. Figure 5 shows three signals with a
different number of pulses recorded for the transmitted frequency of 5.5 kHz. For each signal, the last transmitted peak
and the last major received peak before the signal starts to
show damping (marked using dots) are matched together
and used to calculate shear wave velocity. Output signals for
a different number of pulses were plotted together to find a
consistent solution independent of the number of pulses.
Signal interpretation
The travel time determination is usually the source of the
greatest uncertainties in the bender element method.
Techniques of finding shear wave travel time in the frequency
domain (e.g. cross-correlation) are claimed to be more reliable
while time-domain methods (e.g. visual picking) are more subjective and but certainly more straightforward. Even though
different methods have their advantages and disadvantages,
final outcomes are usually comparable (Chee-Ming 2010).
Because some of the received signals were greatly affected
by cross-talk, near-field and boundary effects, the quality of
Material
Søvind Marl samples were retrieved from a test field near
the town Randers (Figure 6). The geological profile at the
site consists of about 4 m of postglacial clay till underlaid by
Søvind Marl clay formation extending at least to 15 m below
the ground (Simonsen and Sørensen 2018).
Søvind Marl is a highly plastic, stiff and very low permeable, light grey to almost white marl or calcareous clay,
deposited in middle and late Eocene within a deep shelf
marine environment. It is fine-grained (less than 0.01 mm)
4
P. A. JANUSZ ET AL.
Table 1. Measured sizes of bender elements used in the study.
Name
Type
Free length [mm]
Width [mm]
Thickness [mm]
Protrusion [mm]
Figure 3. a) Reconstructed sample placed between stainless-steel pedestal and
stainless-steel top cap. b) Bender element in the stainless-steel ring in the top cap.
with a clay fraction of 65–70% that mainly consists of
smectite (60%) and to a lesser extent also illite and chlorine.
Samples appear fissured with the presence of slickensides.
Even though it is in general highly calcareous, the CaC03
content is found to vary from 0 to 70%. Both thick layers of
white marl with high CaC03 content and thinner, dark
green, almost CaC03 free clay can be found, a few glauconite-rich horizons also appear in the profile (Simonsen and
Sørensen 2018; Simonsen 2018).
After deposition, the Søvind Marl formation was covered
by a thick sequence of younger strata which in certain areas
have been eroded or dislocated during Quaternary (Figure
6). Due to the removal of the load from eroded layers and
the weight of numerous glaciers, the formation is heavily
overconsolidated. The overconsolidation ratio is estimated to
be in the order of 10 to 20 based on the geological loading
history, but significant swelling of the clay after unloading is
likely to have disturbed the intact structure to such a degree
that it can be considered lightly overconsolidated rather
than heavily overconsolidated (Simonsen and Sørensen
2018; Simonsen 2018).
The properties and composition of Søvind Marl are
changing quite significantly across the profile even on the
centimetre scale, especially when it comes to carbonate content, which is also reflected in the water content, plasticity
index, stiffness and shear strength (Simonsen 2018).
In Table 2 representative geotechnical properties determined from samples from the test field are listed. More general information about Søvind Marl, its geology, and
geotechnical properties can be found in Grønbech et al.
(2015) and Heilmann-Clausen et al. (1985).
Sample preparation
Intact samples
Three different intact samples (si1, si2, and si3) of Søvind Marl
from two different depths intervals were studied (Table 3). The
X0
X2
X5
Y3
Y4
Series
10.8
8.0
1.7
3.4
Series
7.7
6.3
1.6
3.9
Series
7.4
6.4
1.4
3.8
Parallel
7.4
6.3
1.7
3.6
Parallel
7.4
5.6
1.3
3.8
Figure 4. Bender element experimental setup.
variability of the tested samples was clearly visible; samples si1
and si2 were dark green clay, quite easy to break, while si3 was
more brownish and plastic. Moreover, si2 appeared much
more fissured than si1, even though both samples were from
the same depth interval. To investigate the applicability of the
bender element method in a situation of low material availability, the size of the quasi-cylindrical samples was reduced after
every measurement, both in height and in diameter.
Reconstructed samples
To estimate the shear wave velocity for very disturbed
material, a quite innovative technique of reconstructing samples from a destroyed material was used. A similar method
has been used before by Mehrabi Mazidi et al. (2012) to
estimate the uniaxial compressive strength of cuttings.
Based on a preliminary laboratory study the optimal procedure of producing reconstructed specimens was found.
The material from previously tested intact samples (Table 2)
was oven-dried at 110 C, then crushed until achieving grain
sizes less than 0.5 mm. This was found to ensure visual
homogeneity of the subsample and at the same time, the
preparation did not take too much time. The crushed material was then compressed in 3–5 layers in a thick-walled
stainless-steel compression cell to the desired density by
applying a static load using a stiff load frame. The load was
applied in small incremental steps to ensure homogenous
compaction of the specimens. Subsamples were compressed
until they reached the measured natural dry density of the
intact material (Table 2) or to higher density if they were
initially too fragile to perform the bender element test.
Available equipment made it possible to build small,
cylindrical subsamples with a diameter of 31.5 mm and
height up to 35 mm, which however gave height to diameter
ratio below the recommended ratio of 2.
To measure shear wave velocity using bender elements,
piezoelectric transducers should have a good connection
MARINE GEORESOURCES & GEOTECHNOLOGY
5
Figure 5. Example of determination of the S-wave travel time.
with the sample interface to transmit vibrations effectively.
To ensure a good connection for dry reconstructed specimens, especially with low density, it was decided to add a
small amount of extra material which would fill in the small
gap between the bender element and the sides of the groves
made in the test specimens. Two materials were tested:
ordinary gypsum and Polyfilla.
In-situ seismic S-CPT testing
The results of laboratory measurements were compared to
shear wave velocities derived from in-situ Seismic Cone
Penetration testing (S-CPT) performed by the Danish geotechnical engineering contractor Geo at the test site (Figure 6). The
seismic signals were recorded using a seismic module consisting of two accelerometers located 0.5 m from each other
behind the electric cone (A.P. van den Berg’s Icone Seismic
Module). At each time step, the seismic module was pushed
1 m into the soil, and the seismic wave was generated by hitting a wooden beam placed at ground level using a hammer
from respectively left and right side. The difference in the
arrival time of the wave recorded on two accelerometers was
used to calculate the value of shear wave velocity. For each
depth, 6 measurements were carried out (respectively 3 from
the left and 3 from the right side) and then stacked to enhance
quality. Figure 7 shows an example of measured seismic signals
for different depths. In the shallow part, the signal is seen to
be noisier, but the interpretation is still possible with support
from signals captured at larger depth.
Results and discussion
Tables 4 and 5 give an overview of the sample dimensions
and the measurement results from the performed bender
element tests on intact and reconstructed samples respectively. Subsample with irregular shape is marked with in
Table 4 and subsamples with added gypsum (G) and
Polyfilla (P) respectively are shown in Table 5.
The shear wave velocities shown in Tables 4 and 5 are
weighted averages of several measurements. The weights
correspond to the uncertainties of the single tests (including
i.e. uncertainty of determination of the sample height, the
protrusion length of the elements and their location, as well
as the precision of finding the positions of the peaks).
Presented shear wave velocities were determined for each
subsample at the natural frequencies given in the tables. The
natural frequency of the specimen is the frequency at which
the amplitude is the highest and the signal is the clearest
(Black et al. 2009). It is accepted that at the natural frequency, obtained results are the most reliable as the transmitted shear wave will not be subjected to transformation.
The ratio between the tip-to-tip length Ltt (height reduced
by the protrusion length of the bender elements) and wavelength k is also stated. According to the common recommendation, it should be higher than 2 to reduce the impact
of near-field effects (Arroyo et al. 2003)
Comparison of the in-situ and laboratory measurements
Figure 8 compares the shear wave velocities of intact and
reconstructed subsamples determined from the bender element test to the shear wave profile from Seismic Cone
Penetration Testing. All plotted subsamples were prepared
from one of three original samples (si1, si2, and si3). For
visualisation reasons, points are plotted at different depths,
however, each sample was retrieved from a specific but
unknown depth within the respective intervals (grey shading) on the plot. The position of the subsample located
6
P. A. JANUSZ ET AL.
furthest to the right (marked using a frame with dashed
line) is incorrect, its S-wave velocity is much higher, however, for visualisation reasons, it was moved to the left.
Figure 6. Map of Denmark (Jutland and Funen) with a marked test site near
the town of Randers (red circle). Areas, where Eocene clays are just below
Quaternary, are marked using grey bands. After Simonsen and Sørensen (2018).
Table 2. Some geotechnical parameters measured for Søvind Marl samples
from the test site. After Simonsen and Sørensen (2018).
Property
Clay fraction
Smectite content
Calcite content
Natural water content
Liquid limit
Plasticity index
Unit weight
Undrained shear strength/effective cohesion cu/c0
Angle of shearing resistance /0
Coefficient of permeability k
CPT cone tip resistance qnet
Value
65–70%
60%
8–30%
44–62%
160–220%
110–177%
17–19 kN/m3
70/25 kPa
20
210–11 m/s
1–3 MPa
The uncertainty of the results is shown as an error bar.
The uncertainty includes both the variations of the results
between different tests and uncertainties of individual measurements. The uncertainty in the shear wave velocities varies
from 3 to 20 m/s with an average of 7 m/s.
The shear wave velocity for the intact subsamples is generally much lower than the S-wave velocity from the in-situ seismic survey. The main reasons for the observed discrepancy are
believed to be an unavoidable disturbance of the intact samples
due to volume constant distortion during sample preparation
and lack of in-situ confinement pressure. It is possible to perform bender element test for confined samples using a triaxial
cell, however, this would be much more time consuming and
furthermore require modifications to the standard setup to
accommodate the smaller samples.
If the only reason for the discrepancy is a change of pressure conditions, the results from the bender element test can
be corrected accordingly and used as a proxy of in-situ shear
wave velocity. However, many more measurements are
needed to find such a relation.
The intact subsamples from the shallower interval (si3) are
characterized by a higher velocity (Figure 8) than from the
deeper one (si1 and si2), although the seismic velocity is generally expected to increase with depth in homogeneous sediment
due to increasing overburden and hence density. The reason
may be that the impact of the confining pressure removal in
connection to sampling has been more pronounced for the
deeper samples. However, geological factors can explain part of
the difference in velocity as well—as sample si1 and si2 had
more fissures and were more fragile than si3.
Søvind Marl is characterized by significant horizontal and
vertical variability. In the shown 16 m interval (Figure 8), shear
wave velocity is changing from about 110 to 190 m/s. Søvind
Marl can vary even on the scale of centimeters. Because seismic measurement was performed for every 1 m, small-scale
variations cannot be distinguished, that is why reliable laboratory tests are needed. But for the same reason, even if the
obtained results can be corrected for the effect of pressure,
their verification using the in-situ seismic profile may be difficult due to the difference of resolution and sampling error.
Reconstructed subsamples
The difference between shear wave velocity for dry and saturated rocks or soils is usually low (Mavko 2005), however,
in this study, reconstructed, pseudo-dry specimens were
almost always characterized by significantly higher velocity
than wet intact subsamples (Figure 8). Only in one case,
when the reconstructed subsample had a very low density
(s2_2_r1), the result was found to be comparable to those
obtained for intact samples. It is suspected that the
Table 3. Properties and characteristics of Søvind Marl intact samples tested in this study.
Name
Depth interval [m]
Water content [%]
Wet density [g/cm3]
Dry density [g/cm3]
Characteristic
si1
si2
si3
14–14.7
47
2.23 ± 0.37
1.52 ± 0.25
Dark green, fissured
14–14.7
50
1.75 ± 0.05
1.16 ± 0.04
Dark green, highly fissured
8–8.7
45
1.71 ± 0.13
1.19 ± 0.09
Brown-green, plastic
MARINE GEORESOURCES & GEOTECHNOLOGY
7
Figure 7. Examples of measured seismic signals for different depths.
explanation for the disparity may be a result of suctioninduced stress which has changed the properties of the dry,
compressed subsamples. However, this has not been possible
to confirm.
The obtained shear wave velocities of the reconstructed
specimens generally fit the in-situ seismic results well
(Figure 8), which seems promising. Figure 9 shows results
for all tested subsamples expressed as a normalized shear
velocity which is the S-wave velocity from the bender element test divided by the velocity from the in-situ seismic profile for the corresponding interval.
In Figure 9a normalized shear wave velocity was juxtaposed
with density. Some of the reconstructed subsamples almost
exactly reflect the seismic measurement (points close to 1 on
vertical scale). However, the best fit is not necessarily for the
subsamples compressed exactly to the dry density of the corresponding intact material. For example, the dry density of sample si2 is 1.16 g/cm3 (Table 2), however, the reconstructed
subsample with a density of 1.3 g/cm3 is the closest to the seismic measurement. For practical reasons, it is positive that subsamples with higher density show results which are a closer
match to the in-situ seismic measurements because specimens
with a density below 1.3 g/cm3 are very fragile and break easily.
It was expected to see a clear positive correlation between
density and the S-wave velocity (Figure 9a), however, the
relation is clear only for samples with added gypsum. Many
other factors can be crucial here, among other variations in
the properties of the compressed material, amount and type
of filler used or moisture content of the specimen.
Influence of the size and shape
It has been suggested that to reduce the impact of the nearfield effect, the ratio between the tip-to-tip distance Ltt and
wavelength k of a transmitted signal should at least be
higher than 2 but lower than 4 (Arroyo et al. 2003). An
aspect ratio (height/diameter) of the sample of at least 2 has
been recommended by many authors to minimize the
boundary effects (Ingale et al. 2017). In addition, because of
complicated wave propagation in irregular samples, tested
specimens should be ideally cylindrical.
However, because of the scarcity of the undisturbed samples from drilling in the offshore industry, the intact specimens which fulfil all listed requirements may be unavailable.
That is why quite small and slightly irregular intact samples
which were sometimes below or on the verge of the recommended size (Table 4) were tested in this study. In addition,
very often retrieved samples are prone to breakage, which
makes it difficult to prepare ideally cylindrical specimens.
Therefore, Søvind Marl with its fissured character was a
good example of determining the likely challenges. Indeed,
the prepared samples had very often rough, irregular boundaries and broke easily while their size was reduced
(Figure 10).
The reconstructed subsamples were even smaller than the
intact ones, mainly due to technical limitations, however, it
reflected the real conditions where availability of suitable
material may be very low. In addition, the preparation of
bigger specimens is relatively time-consuming while the
intention in this study is to provide a simple and fast
method of estimating shear wave velocity.
Normalized shear wave velocities for intact subsamples
are plotted against their size in Figure 9b. Because both
diameter and height were changed, the size is expressed as a
ratio of height to diameter. In theory, if the same travel
path is maintained, the change of shape or diameter of the
sample should not affect the arrival time. In addition, a
change of height for almost homogenous samples should
8
P. A. JANUSZ ET AL.
Table 4. Overview of all measured quasi-cylindrical intact subsamples including their sizes and the measurement results.
No
Name
Height [mm]
Diameter [mm]
Natural
frequency [kHz]
Shear wave
velocity [m/s]
Ltt
k
1
2
3
4
5
6
7
13
14
15
19
20
21
22
23
24
25
si1_1
si1_2
si1_3
si1_4
si1_5
si1_6
si1_7
si2_1
si2_2
si2_3
si3_1
si3_2
si3_3
si3_4
si3_5
si3_6
si3_7
60.2
50.6
39.1
39.1
39.1
39.1
39.1
44.6
44.6
44.6
59.2
50.4
43.6
31.8
31.8
31.8
31.8
70.0
70.0
70.0
65.4
59.3
51.2
42.5
70.0
49.4
41.0
70.0
70.0
70.0
70.0
57.3
47.8
37.3
5.5
5.5
5.5
5.5
5.5
5.5
5.5
5.7
6.0
4.8
5.3
5.3
5.5
5.3
5.8
6.8
5.7
89.30
80.44
70.55
77.92
114.04
83.60
69.28
64.72
87.38
88.05
103.06
98.20
105.74
111.91
112.76
73.33
75.64
3.26
2.96
2.48
2.25
1.54
2.10
2.53
3.28
2.56
2.03
2.67
2.33
1.89
1.16
1.27
2.28
1.85
Table 5. List of all measured quasi-cylindrical reconstructed subsamples including their sizes and the measurement results. P ¼ Polyfilla; G ¼ Gypsum.
No
Name
Height
[mm]
Density
[g/cm3]
Filing
material
Natural
frequency [kHz]
Shear wave
velocity [m/s]
Ltt
k
8
9
10
11
12
16
17
18
26
si1_7_r1
si1_7_r2
si1_7_r3
si1_6_r1
si1_7_r4
si2_2_r1
si2_2_r2
si2_2_r3
si3_5_r1
30.4
30.2
30.0
30.2
29.9
35.8
34.3
29.6
34.3
1.43
1.44
1.46
1.48
1.50
1.21
1.31
1.51
1.30
P
P
P
P
P
G
G
G
G
31
26
23
28
28
6
26
30
23
174.06
194.42
149.45
209.51
210.58
77.33
185.73
302.68
155.74
4.13
3.07
3.36
3.07
3.01
2.15
3.77
2.20
3.98
Figure 8. Shear wave velocity determined from the bender element test for intact and reconstructed subsamples compared to the results from the in-situ seismic survey.
MARINE GEORESOURCES & GEOTECHNOLOGY
9
Figure 9. Results for all tested subsamples expressed as a normalized shear wave velocity a) plotted against density; b) plotted against height/diameter ratio.
Figure 10. a) Søvind Marl intact subsample. When the size of the subsample was reduced, specimen b) broke easily, c) as well as during drying. d)
Reconstructed subsamples.
not influence the outcome significantly. In reality, any
irregularity of the shape or size reduction magnifies the
undesired effects in the near-field and generates unexpected reflections that affect the determination of travel
time. Indeed, Figure 9b shows that the results for the
same sample with a variation in the ratio of height to
diameter not consistent. Any clear correlation between
size and velocity cannot be seen, however, some subsamples show weak trends, for example, for specimens no. 1,
2 and 3 which have the same diameter but respectively
lower height, velocity is seen to decrease almost linearly.
However, many other factors can effectively mask the
eventual influence of the size which is something that
needs further attention.
Other factors affecting the measurements
Generally, both the natural frequency of the sample and the
shear wave velocity are expected to increase with increasing
stiffness of the sample. Table 5 shows a clear relationship
between the shear wave velocity and the natural frequency
for the reconstructed samples, while similar consistency is
not found for the intact samples, as seen in Table 4. The
natural frequency of the reconstructed samples is generally
found to be 23 to 31 kHz (apart from sample si2_2_r1 which
is seen to display a much lower natural frequency), while
much lower natural frequencies are found for the intact
samples. The lack of consistency for the more irregular
shaped intact samples compared to the reconstructed samples is a likely result of boundary effects which will have an
10
P. A. JANUSZ ET AL.
increased influence on the received signals due to the irregularities in dimensions.
Some above-mentioned issues like variation of properties
of the Søvind Marl, change of the size of the subsamples or
signal disturbances are mainly responsible for the inconsistency of the results visible in Figure 9. However, another
important factor may be the deterioration of the quality of
the connection between the bender element and the sample’s
interface. In addition, the drying of intact wet subsamples
may change their strength and elastic properties (Tovar and
Julio 2011). For reconstructed subsamples also amount and
type of the filling material can be the issue. However, it was
found that when filling material was gypsum the effect was
minimal when measurements were performed after at least
3 hours after the bender elements were placed in the sample.
On the other hand, tests for subsamples with added Polyfilla
performed later than 3 hours were rejected because of high
disturbance of the signal.
Wrong identification of natural frequency may also affect
the results, in the performed experiments a difference of up
to 16% with a mean of 14 % was found, when a different
frequency than the natural frequency was chosen. Moreover,
the S-wave velocity for one sample was not found to be the
same when a different number of pulses was used. In this
study, the velocity was found to differ by up to 4% when a
signal with a different number of pulses was chosen, but the
mean uncertainty is only about 1%, hence this is of minor
importance. The reason for this can be a dispersion or more
complex boundary reflections that may interfere with the
“true” signal.
The above-mentioned factors have led to the accuracy of
the results being less than optimal. However, in some applications where shear velocity is derived using uncertain
empirical relations, a large number of simple and fast but
low precision measurements would be useful to better estimate the S-wave velocity.
Applicability for drill cuttings and other heavily
disturbed samples
The preliminary aim of the project was to investigate the
possibility of applying the presented method of sample
reconstruction to drill cuttings to estimate the shear wave
velocity in the depth intervals where cores are not available.
However, even though cuttings samples must be stored
(Danish Energy Agency 2009), their amount and weight
may not be sufficient to conduct a proper analysis.
Moreover, because stored wet samples are contaminated by
drilling mud, dry samples should be washed (Danish Energy
Agency 2009). Nevertheless, it is suspected that the remains
of drilling mud would change their properties. The possibility of using the presented method for drill cuttings has not
been completely excluded. However, it seems more promising and applicable to perform the bender element test to
estimate shear wave velocity for intact uncontaminated samples or for reconstructed samples if the specimen is highly
disturbed but the procedure can be time-consuming, and
the choice of proper density is decisive to find the correct velocity.
Conclusion
The study shows that the bender element method can provide a simple, fast and cheap procedure to estimate shear
wave velocity even in the case of scarcity of good-quality
samples. Generally, there is an agreement between S-wave
velocity from the in-situ Seismic Cone Penetration Testing
and laboratory measurements of the reconstructed samples
using bender elements. Moreover, it is suspected that the
laboratory results for the intact samples can be corrected for
the change of pressure conditions and also used as a proxy
of in-situ S-wave velocity. However, the signal interpretation
for very small or fractured specimens which were mostly
used in this study was impeded because of near-field and
boundary effects. A correlation between the size of the samples and the velocity has not been found.
The study shows the direction for further investigations
and highlight problems that should be focused on. More
research is necessary to understand better the obtained
results and their significance.
Acknowledgments
Geo is acknowledged for carrying out and providing results from the
in-situ Seismic Cone Penetration Testing at the test site, in addition to
providing intact samples.
Funding
This work was supported by the Danish Hydrocarbon Research and
Technology Centre (DHRTC) under Grant no. RIS-16 2918.
ORCID
Kenny K. Sørensen
http://orcid.org/0000-0001-9400-7753
http://orcid.org/0000-0002-6825-9065
Ole R. Clausen
http://orcid.org/0000-0001-8029-3234
Katrine J. Andresen
References
Arroyo, M., D. Muir Wood, and P. Greening. 2003. Source Near-Field
Effects and Pulse Tests in Soil Samples. Geotechnique 53 (3):
337–345. doi:10.1680/geot.2003.53.3.337.
Black, J., S. Stanier, and S. Clarke. 2009. Shear Wave Velocity
Measurement of Kaolin during Undrained Unconsolidated Triaxial
Compression. In Halifax, Proceedings of the 62nd Canadian
Geotechnical Conference.
Castagna, J. P., M. L. Batzle, and R. L. Eastwood. 1985. Relationships
between Compressional-Wave and Shear-Wave Velocities in Clastic
Silicate Rocks. Geophysics 50 (4): 571–581. doi:10.1190/1.1441933.
Chee-Ming, C. 2010. Bender Element Test in Soil Specimens:
Identifying the Shear Wave Arrival Time. Geotechnical and
Geological Engineering 15: 1–8.
Danish Energy Agency. 2009. Guidelines for Drilling. Denmark: Danish
Energy Agency.
Grønbech, G., B. N. Nielsen, L. B. Ibsen, and P. Stockmarr. 2015.
Geotechnical Properties of Søvind Marl—a Plastic Eocene Clay.
Canadian Geotechnical Journal 52 (4): 469–478. doi:10.1139/cgj-20140066.
MARINE GEORESOURCES & GEOTECHNOLOGY
Heilmann-Clausen, C., O. Nielsen, and F. Gersner. 1985.
Lithostratigraphy and Depositional Environments in the Upper
Paleocene and Eocene of Denmark. Bulletin of the Geological Society
of Denmark 33: 287–323.
Ingale, R., A. Patel, and A. Mandal. 2017. Performance Analysis of
Piezoceramic Elements in Soil: A Review. Sensors and Actuators A:
Physical 262: 46–63. doi:10.1016/j.sna.2017.05.025.
L’Heureux, J.-S., and M. Long. 2016. Correlations between Shear Wave
Velocity and Geotechnical Parameters in Norwegian Clays. In 17th
Nordic Geotechnical Meeting (NGM 2016). Reykjavik, Iceland.
Lee, J.-S., and J. Santamarina. 2005. Bender Elements: Performance
and Signal Interpretation. Journal of Geotechnical and
Geoenvironmental Engineering 131 (9): 1063–1070. doi:10.1061/
(ASCE)1090-0241(2005)131:9(1063).
Lee, M. W. 2006. A Simple Method of Predicting S-Wave Velocity.
Geophysics 71 (6): F161–F164. doi:10.1190/1.2357833.
Mavko, G. 2005. Conceptual Overview of Rock and Fluid Factors That
Impact Seismic Velocity and Impedance. Stanford, CA: Stanford
Rock Physics Laboratory.
Mehrabi Mazidi, S., M. Haftani, B. Bohloli, and A. Cheshomi. 2012.
Measurement of Uniaxial Compressive Strength of Rocks Using
Reconstructed Cores. Journal of Petroleum Science and Engineering
86–87: 39–43. doi:10.1016/j.petrol.2012.03.015.
View publication stats
11
Rio, J. F. M. E. 2006. Advances in Laboratory Geophysics Using
Bender Elements. Doctoral Thesis, London: University College
London, Department of Civil & Environmental Engineering.
Simonsen, T. R. 2018. Pore Water Pressure Response and Heave of
Palaeogene Clays in Connection with Deep Excavation and Pile
Driving. Doctoral Thesis, Aarhus: Department of Engineering,
Aarhus University.
Simonsen, T. R., and K. K. Sørensen. 2018. Performance of Vibrating
Wire Piezometers in Very Low Permeable Clay. In 10th
International Symposium on Field Measurements in Geomechanics
(FMGM2018). Rio de Janeiro, Brazil.
Tovar, R., and C. Julio. 2011. Effect of Drying and Wetting Cycles on
the Shear Strength of Argillaceous Rocks. In Proceedings of the 5th
International Conference on Unsaturated Soils, 1471–1476. London.
Yi, F., and F. P. Yi. 2016. Estimation of Shear Wave Velocity Based on
SPT Profile Data. In 5th International Conference on Geotechnical
and Geophysical Site Characterisation. Jupiters Gold Coast,
Queensland, Australia.
Zhu, J., Y.-T. Tsai, and S.-H. Kee. 2011. Monitoring Early Age
Property of Cement and Concrete Using Piezoceramic Bender
Elements. Smart Materials and Structures 20 (11): 115014–115017.
doi:10.1088/0964-1726/20/11/115014.