Shaking Table Test on Dynamic Behaviours of Tropical ...
Transcript of Shaking Table Test on Dynamic Behaviours of Tropical ...
KSCE Journal of Civil Engineering (2017) 21(5):1735-1746
Copyright ⓒ2017 Korean Society of Civil Engineers
DOI 10.1007/s12205-016-1856-8
− 1735 −
pISSN 1226-7988, eISSN 1976-3808
www.springer.com/12205
Geotechnical Engineering
Shaking Table Test on Dynamic Behaviours of Tropical Residual Soils in Malaysia
Koo Kean Yong*, Lim Jun Xian**, Yang Chong Li***, Lee Min Lee****,
Yasuo Tanaka*****, and Zhao JianJun******
Received April 18, 2016/Revised July 28, 2016/Accepted September 8, 2016/Published Online November 11, 2016
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Abstract
Studies on dynamic behaviours of tropical residual soils are still very limited in the current available literature. This paper mainlyaims to investigate the dynamic properties (shear modulus and damping ratio) of two selected tropical residual soils (sandy silt andsilty sand) in Malaysia under different overburden pressures. A series of shaking table tests were performed by applying 13combinations of input shaking frequencies and lateral displacements. The measured acceleration data were subjected to baselinecorrections and filtering processes. The results showed that the shaking table setup was capable of facilitating a considerably largestrain level of deformation. The shear modulus increases proportionally with the confining pressure. Under the same confiningpressure, shear modulus attenuates with the increase of strain amplitude. The shear modulus of sandy silt was consistently larger thanthat of silty sand. The damping ratios of the tested soils approximately range between 1% and 12%.
Keywords: dynamic behaviours, deformation, shear modulus, damping ratio, tropical residual soil, shaking table
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1. Introduction
According to McCarthy (1993), residual soils are those that
formed from rock or accumulation of organic material and
remain at the place where they were formed. The development of
residual soils depends on the interaction of three natural variables
including chemical compositions of the rock, environmental/
climate conditions, and time. Climate, among others, is usually
regarded as the most influential factor in soil formation. It
governs the amount of precipitation and temperature in a region.
High rainfall and temperature generally increase the propensity
for weathering by increasing the susceptibility of rocks to
chemical reactions. Therefore, warm and humid climatic regions
generally have more weathered rock with higher rates of
weathering. Under the tropical climate, Malaysia receives
sunlight and abundant rainfall throughout the year which results
in massive chemical weathering of rocks. Residual soils which
are products of intensive in-situ weathering of parent rocks cover
more than three-quarters of the land area in Peninsular Malaysia
(Taha et al., 2000). Residual soil in Malaysia is widely known to
consist of varying fine to coarse contents. The soil is generally in
unsaturated state because of the deep water table in the residual
soil profile. There are deep weathering profiles and intense
formations of tropical residual soils in the country. The major
compositions of the residual soil in Malaysia are made up of sand,
silt and clay and combined in varying proportions depending on the
geological setting of the soil (Nithiaraj et al., 1996). As residual
soils are derived from weathering of the parent bedrock in-situ, the
distribution of tropical residual soils is directly related to the
distribution of the various rock formations in Malaysia. The
behaviour of a soil mass is dependent on three fundamental
properties of the soil, namely its physical properties, chemical
properties, and composition of the soil. Owing to the nature of
chemical weathering in the humid tropics, almost all rock
formations are overlain by a thick layer of residual soils. Their
physical properties are prominent criteria to be considered by
TECHNICAL NOTE
*Undergraduate Student, Dept. of Civil Engineering, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Selangor,
Malaysia (E-mail: [email protected])
**Graduate Student, Dept. of Civil Engineering, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Selangor,
Malaysia (E-mail: [email protected])
***Undergraduate Student, Dept. of Civil Engineering, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Selangor,
Malaysia (E-mail: [email protected])
****Associate Professor, Dept. of Civil Engineering, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Selangor,
Malaysia; State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology), Chengdu, China
(Corresponding Author, E-mail: [email protected])
*****Professor, Dept. of Civil Engineering, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Selangor, Malaysia (E-
mail: [email protected])
******Professor, State Key Laboratory of Geohazard Prevention and Geoenvironment Protection (Chengdu University of Technology), Chengdu, China (E-
mail: [email protected])
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− 1736 − KSCE Journal of Civil Engineering
engineers during a planning stage of various engineering
construction works.
In general, the differences of tropical residual soils between
one place and another can be distinguished by the rate and mode
of weathering. The residual soil in Malaysia consists of thick
(about 10-30 m) laterite soils with varying grain sizes. Borden et
al. (1996) who studied on Piedmont residual soil in United State
found that their soils vary from silty sand to silt with a high
plasticity. Leong et al. (2003) studied the residual soil from Jurong
formation in Singapore and found that their soils range from silt to
clay with a low plasticity. It can thus be concluded that the residual
soil in different regions may have different physical and engineering
properties attributed to their weathering effects. At present,
extensive studies of unsaturated shear strength and hydraulic
properties of tropical residual soils can be traced from the current
literature database (Rahardjo et al., 2004; Ng and Xu, 2012; Toll,
2012). There are also a wide variance of researches on various
geotechnical problems related to residual soils such as deep
foundation in residual soil, use of residual soil as a compact liner,
and rainfall induced landslides in residual soil etc. (Rahardjo et al.,
2005; Taha and Kabir, 2004; Cunha et al., 2002). However, there
are still very limited researches on dynamic behaviours of residual
soil. In recent years, Malaysia had experienced several moderate
seismic events despite of the fact that the country is not located on a
seismic active zone. One of these events had struck Sabah, a state at
the northeast of the Borneo Island on 5 June 2015 with a moment
magnitude of 6.0 and killed 18 people. These unexpected
earthquake incidents have proven that the chances of Malaysia
being hit by an earthquake cannot be completely ruled out.
Consequently, increasing attentions have been drawn into the
studies of soil dynamic behaviours in Malaysia.
In general, dynamic loads imposed on soil are produced by
earthquakes, blasting, wind loading or machine vibrations. Different
types of dynamic loads generate different levels of strain. Since
soil dynamic properties are strain level dependent, the effect of
strain level is essential for selecting an appropriate testing
method to determine the soil dynamic properties. Wave propagation
represents the elastic properties of soil when strain level is less
than 10−4, while larger strain level manifests changes in deformation
modulus, damping ratio, pore-water pressure or volume (Prasad,
2009). Therefore, various idealized models and analytical
techniques, either in-situ or laboratory tests, have been established to
improve the results of dynamic soil properties at different strain
levels. Several researchers have explored the complex behaviours of
soil dynamics. Senetakis et al. (2012) studied the dynamic
properties of dry sand/rubber (SRM) and gravel/rubber (GRM)
mixtures; He and Cui (2014) investigated the dynamic responses
of thawing soil around the tunnel by numerical simulations and
compared the behaviours between thawing soil and undisturbed
soil; Shahrour et al. (2010) studied seismic responses of tunnels
in soft soils by applying elasto-plastic finite element analysis.
They described soil behaviours by using an advanced elasto-
plastic cyclic constitutive relation. Kim et al. (2007) conducted a
series of cyclic loading tri-axial tests on sand. They found that
the shear modulus increased linearly with the confining pressure
on a log-log scale. In addition, various analytical and empirical
equations have been established to estimate dynamic responses
of soils. For instances, based on the data obtained on dry and
saturated sands and cohesive soil, empirical equations have been
proposed for determining the shear modulus of soils (Hardin and
Black, 1968; Hardin and Drnevich, 1972; Hardin, 1978). In light
of the wide-ranging and unique physical properties of residual
soils, more dynamic testing should be conducted in order to
enrich the current database and used as valuable input data for
numerical modelling of various geotechnical problems.
The important mechanical properties associated with soil
dynamics are shear modulus (G) and damping ratio (D). Shear
modulus is defined as the ratio between shear stress amplitude
and shear strain amplitude. It can be obtained from a hysteresis
loop. A material will experience a significant horizontal deformation
when the shear stress is sufficiently high. Shear modulus represents
the rigidity characteristics of a material. Hardin and Drnevich
(1972) reported that the shear modulus of clean sand is affected
by several parameters including shear strain amplitude, effective
stress level, and void ratio. For clay, Idriss et al. (1978) summarized
that an increase in pore-water pressure will lead to a decrease in
shear modulus. Bolton and Oztoprak (2013) proposed an equation
for estimating elastic (maximum) shear modulus of sandy soil
covering different levels of strain:
(1)
where,
A(γ) = 5520 for γ = 0. 001%
m(γ) = 0.51 for γ = 0. 001%
e = Void ratio
Pa= Reference pressure of 100 kPa
P' = Effective pressure (kPa)
Energy dissipation commences when soil deposits are subjected
to dynamic loading. The amount of energy dissipated can be
obtained from the hysteresis loop of a stress-strain curve. It is
usually manifested as a damping ratio which is the ratio of
damping coefficient over the critical damping coefficient. The
increase in damping ratio is corresponding to the increase in
cyclic shear strain. GovindaRaju (2005) performed cyclic tri-
axial tests and found that the frequency of cyclic loading did not
significantly affect the shear modulus notwithstanding a significant
influence on the damping ratio. Numerous researchers found that
the damping ratio increases with increasing frequency vibration.
However, Maxwell model showed an opposite result (Prasad,
2009). The rate of excess pore-water pressure generation increases
with respect to increment of frequency and magnitude of loading
(Dash and Sitharam, 2009). For an idealized hysteresis loop, the
damping ratio is governed by the following equation (Dietz and
Muir Wood, 2007):
(2)
G0
A γ( ) Pa
×
1 e+( )3---------------------
P′Pa
-----⎝ ⎠⎛ ⎞
m γ( )
×=
D1
4π------
Loop Area
τmax
τmin–( ) γmax γmin–( )-----------------------------------------------------×=
Shaking Table Test on Dynamic Behaviours of Tropical Residual Soils in Malaysia
Vol. 21, No. 5 / July 2017 − 1737 −
where, τmax
= Maximum shear stress (kPa)
τmin = Minimum shear stress (kPa)
γmax = Maximum shear strain
γmin = Minimum shear strain
In general, dynamic properties of soil can be measured or
evaluated by means of either element test or model test. Model
tests are essential to investigate the effects of various parameters
on the failure mechanisms of a prototype which are often
complex and hard to comprehend. The model tests can be
performed by two main methods, i.e. those performed under the
gravitational field of earth and those performed under higher
gravitational accelerations (Kramer, 1996). 1g shaking table test
is a model test performed under the gravitational field of earth.
1g shaking table test has been regarded as a valuable model test
in investigating liquefaction, soil-structure interaction and
ground settlement problem. An actual soil prototype can be
prepared and compacted easily for a 1g shaking table model test.
In contrast to the model test, the soils of an element test are
usually resorted to smaller particle sizes during preparation
stage. Numerous works have been conducted in the interest of
comprehending failure mechanisms and dynamic properties by
using shaking table test. Dietz and Muir Wood (2007) investigated
the dynamic performances of shear stacks by filling in sand
samples and compared the dynamic responses with the idealized
responses that predicted by Hardin and Drnevich (1972) using
the hyperbolic stress-strain relationship. The dimensions of the
shear stack were 1.2 m long, 0.55 m wide and 0.8 m deep. The
use of shear stack enabled simulations of free-field conditions
and good results of soil dynamic properties at low stress levels.
Prasad et al. (2004) examined the ground behaviours by using a
1-D manual shaking table with laminar shear box. They
concluded that the 1-D manual shaking table is adequate to
provide satisfactory performances to investigate ground
amplification, liquefaction, cyclic mobility phenomenon, etc.
Matsuo (1990) utilized acceleration and pore-water pressure
measurements to examine the cyclic stress strain behaviours of
soil on a shaking table. He adopted a reduced scale embankment
model sat on saturated sandy ground. Kokusho (2003) provided
a good explanation on the use of the shaking table to investigate
soil liquefaction. Brennan et al. (2005) reviewed numerous key
aspects of signal processing techniques in dynamic centrifuge
test. Shear modulus and damping degradation curves for dry
sand, saturated sand, soft clay and a waste material were
evaluated in dynamic centrifuge tests under different testing
conditions to form a comprehensive database of soil dynamic
properties.
The intention of the present study is to investigate the soil
dynamic behaviours under different confining pressures replicating
the field conditions. Therefore, the 1g shaking table model test is
chosen in light of the sample preparation and application of the
present research. However, it is agreed that different types of
dynamic soil testing may be required in order to cover a wide
range of strain. As such, several dynamic soil testing apparatus
are currently developed in the authors’ laboratory with the hope
of enriching the dynamic properties database of tropical residual
soil in the near future.
Despite of the fact that extensive studies have been carried out
pertaining to the topic of soil dynamic behaviours, very limited
studies have focused on tropical residual soils. Recent series of
earthquake incidents in Malaysia has accelerated the adoption of
Euro-Code 8 (Earthquake Design) for building designs in
Malaysia. Thus, it would be advantageous to study the dynamic
properties of ground materials in Malaysia which are mainly
formed by tropical residual soil. The present study aims to
examine and compare the dynamic properties of tropical residual
soils extracted from two selected locations in Malaysia by using
shaking table tests.
2. Testing Materials
2.1 Soil Specimens
In this study, two types of tropical residual soil were
collected from two different locations in Peninsular Malaysia.
Soil A is collected from Shah Alam, Selangor (central region of
Peninsular Malaysia) whereas soil B is collected from Simpang
Renggam, Johor (southern region of Peninsular Malaysia)
(refer to Fig. 1) The soil from Site A is deposits of highly
weathered Kenny Hill Formation (sedimentary rock) while the
soil from Site B is of Gemas Formation (sandstone, siltstone
and shale). Fig. 1 shows the distributions of tropical residual
soil in Peninsular Malaysia (Ooi, 1982). The soil can be
categorized into two general types based on their parent rocks,
i.e. residual granite soil and residual sedimentary rock soil. The
tropical residual soils can be found in a widespread of geotechnical
engineering applications e.g. slopes, embankments, excavation,
dam foundations, tunnelling works etc. These sampling sites were
selected to investigate and compare the dynamic behaviours
of tropical residual soils that are characterized by different
weathering profiles, physical properties and geological
formations. The soil samples were extracted from the
respective sites at depths between 1 m and 2.5 m below the
ground surface. Soil preparation processes including removal
of unwanted substances, air drying and soil clog disaggregation
(using rubber mallet) were performed before storing the soil
samples into containers.
The soil particle size distributions are presented in Fig. 2.
Physical properties of the soil specimens were identified in
accordance with British Standard. Based on the British Standard
Soil Classification System, the residual soil of Site A is classified
as silty sand, while the residual soil of Site B as sandy silt.
Laboratory standard proctor compaction tests were performed to
determine the compaction curves of the two soil specimens
(Fig. 3). The maximum dry density (MDD) of Soil A was 1970
kg/m3 corresponding to the optimum moisture content (OMC) of
11.8%. For Soil B, the MDD was 1664 kg/m3 corresponding to
the OMC of 20.4%. The plasticity indexes of soil A and soil B
were 4.6 and 18, respectively.
Koo Kean Yong, Lim Jun Xian, Yang Chong Li, Lee Min Lee, Yasuo Tanaka, and Zhao JianJun
− 1738 − KSCE Journal of Civil Engineering
Fig. 1. Distribution of Residual Soils in Peninsular Malaysia
Fig. 2. Particle Size Distribution Curves for Tropical Residual Soils Fig. 3. Compaction Curves
Shaking Table Test on Dynamic Behaviours of Tropical Residual Soils in Malaysia
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2.2 Shaking Table System
A shaking table system was set up in the laboratory for
dynamic testing purposes. The shaking table was capable of
producing one-dimensional motion generated by a mega-torque
motor or actuator manufactured by NSK Co. Ltd. The capacity
of this motor in terms of frequencies and linear displacements
were initially found to be in the range of 0.1-20 Hz and 0.1-50
units of displacement, respectively. A height-adjustable steel
base frame was used to form the base platform of the shaking
table. The shaking table platform has a square dimension of 1.8
m. The entire table was lifted by 5 bar of pressurized air during
the testing. Under this configuration, the shaking table was
capable of supporting a sample load of about 3 tonnes. For
heavier loading, a higher pressurized air shall be supplied to the
bottom of the table.
Three laminar shear stacks were used to form a shear box
having dimensions of 1.5 m (Length) × 0.7 m (Width) × 0.21 m
(Height). Each shear stack was equipped with 4 stiff rings to
provide an unrestrained lateral displacement and to facilitate a
simple shear deformation.
Figure 4 shows the components of the shaking table system
that consists of a shaking table platform, a mega-torque motor,
an ESA NSK type motor driver unit, a control box and control
software. The operation of the mega-torque motor was controlled
by the driver unit via computer software, namely MotCtlProg
(3DA-GateCtrl). This software allowed manual inputs of
frequencies and displacements. Upon data imputations, signals
were sent to the driver unit and mega-torque motor through the
control box which was used to stabilize the signals.
2.3 Instrumentation & Data Acquisition System
Accelerometers were used to measure the horizontal acceleration
of soil samples when subjected to cyclic motions. Lateral
displacements of the soil model were derived from the acceleration
data captured at different elevations. This was done by performing
double integration on the measured acceleration with respect to
time. The derived lateral displacements were subsequently used
to compute shear strain. As for the computation of shear stress, it
was evaluated based on the shear force induced by the surcharge
loading together with the contact area of soil samples. Hysteresis
loop was plotted by using the measured shear strain and shear
stress in order to obtain the shear modulus and damping ratio of
soil.
Figure 5 shows the locations of eight accelerometers installed
on the testing samples. Five of them were manufactured by
Kyowa Electronic Instruments Co., Ltd. (KYOWA) while the
remaining were the products of Tokyo Sokki Kenkyujo Co., Ltd.
(TML). Accelerometers were embedded near the centre region
of the compacted soil model to avoid the effect of stress
concentration. One accelerometer was placed on the base of the
shaking table to measure the base acceleration. Six accelerometers
were embedded in the soil model to measure the accelerations at
the height of 0.07 m, 0.105 m and 0.21 m, respectively. Additional
one accelerometer was installed on the surcharge load. Fig. 4. Shaking Table System
Fig. 5. Data Acquisition System
Koo Kean Yong, Lim Jun Xian, Yang Chong Li, Lee Min Lee, Yasuo Tanaka, and Zhao JianJun
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The accelerometers within the soil body were equipped with
flat plastic plates to provide a smooth contact surface between
the soil matrix and the accelerometer sensors. Soil compactions
around the embedded accelerometers were carried out with extra
care by tamping carefully and uniformly.
The accelerometers were connected to a data logger (Model
DRA-30A) with a maximum scanning rate of 1 ms. Data logger
was connected to a computer which was operated with DRA-
730AD software to enable capturing and retrieval of data from
the logger. Fig. 5 shows the schematic diagram of the data
acquisition system used for the shaking table tests.
3. Testing Setup
3.1 Membrane Fabrication
Soil samples were contained by a geo-membrane during the
shaking table tests in order to simulate the desired boundary
condition of the in-situ soil. This would enhance the accuracy of
the testing results and prevent damages on the aluminium
laminar shear stacks. However, the geo-membrane was not
available in the commercial markets due to the requirements of
the custom size. Therefore, the geo-membrane was fabricated
manually by using High Ammonia Latex Concentrate.
The geo-membrane was made to perfectly fit to the size of
laminar shear box with a nominal thickness of 3 mm. A mould of
similar size to the laminar shear box was first fabricated. Painting
and trimming processes were carried out to ensure smooth
surfaces of the mould. Instead of painting the latex concentrate
directly onto the mould, the geo-membrane was fabricated part
by part to ensure a uniform thickness of the membrane. The side
and bottom membranes were fabricated separately and assembled
together on the mould by applying a thin layer of latex concentrate
between the overlapping surfaces. The fabricated membranes
were left air-dried for 1 week before demoulding. During the
demoulding process, the membranes were pulled out carefully
with the aids of flour.
3.2 Sample Preparation
Prior to compacting the soils into the shear box, the masses of
soils and water needed were computed based on the MDD and
OMC obtained from the compaction test. The target dry density
was set at 95% of MDD.
Wood tampers with a contact area of 0.1 m × 0.1 m area were
coated with a thin layer of latex membrane. These tampers were
employed to compact the soil in 6 layers into the 0.21 m high
shear box. Each of the layers was about 0.035 m, and the soil and
water needed was predetermined. Markings were made on the
membrane as reference levels for compaction. The surface of
each compacted layer was scratched or gridded to ensure good
bonding between two soil layers.
3.3 Surcharge Loadings
In this research, different confining pressures (0, 5 kPa and 10
kPa) were pragmatically achieved by applying a surcharge on the
top of soil model. In order to achieve confining pressure of
10 kPa, physical load weighed about 1 tonne was required. A
higher confining pressure was not feasible with the current setup
as it was constrained by the available space, performance
capacity of the shaking table, and safety precaution for stacking
up a heavier physical load on the testing specimen. A new testing
setup is currently developed in the laboratory with a smaller
sample that allows supplies of air pressure to the confined model
to generate a higher confining pressure. Fig. 6 depicts the set-up
for shaking table test in the present study. The applications of
these different surcharges were performed by stacking packed
aggregate bags of 30 kg each into a prefabricated 1.4 m (length)
× 0.6 m (width) × 1.0 m (height) wooden container. A panel of
plywood was placed at the interface between the surcharge
container and the soil specimens to ensure a uniform load
distribution on the soil specimen. The plywood was roughened
by nailing uniformly and placed onto the soil surface in a grid-
like arrangement. Each of the nails protruded a depth of about 5
mm into the soil to produce a shearing surface when shaking. In
Fig. 6. Set-up for Shaking Table Testing
Table 1. Testing Frequencies & Amplitudes
NumberFrequency
(Hz)Amplitude
(displacement unit)
1 0.1 0.5
2 0.1 2
3 0.5 2
4 1 1
5 1 2
6 1 5
7 20 0.1
8 20 0.3
9 2 0.5
10 2 1
11 2 2
12 5 0.5
13 5 1
Shaking Table Test on Dynamic Behaviours of Tropical Residual Soils in Malaysia
Vol. 21, No. 5 / July 2017 − 1741 −
addition, the soil surface was covered by a layer of membrane to
reduce loss of soil moisture.
3.4 Testing Programs
A series of shaking tests with 13 combinations of input lateral
displacements and shaking frequencies (Table 1) were performed
in this study to evaluate the dynamic behaviours of the soil under
different shaking motions. The 13 shaking combinations were
designed to cover both high frequency-small displacement and
low frequency-large displacement shaking situations. Each
shaking motion was introduced to the soil specimen for about
10 s. For simplicity, a motion having 5Hz and 1 unit of displacement
is denoted as F5D1 in the following discussions. With two types
of soil specimens (Soil A and Soil B) and three overburden
pressure conditions (0, 5 and 10 kPa), this study yielded a total of
78 tests.
4. Evaluation of Dynamic Properties- Data Pro-cessing & Analysis
Through a series of measurement and analysis, secant shear
modulus (G) and damping ratio (D) of the tested soil specimens
can be reasonably evaluated. As mentioned earlier, velocity and
displacement can be numerically obtained through single and
double integrations of acceleration time-series records, respectively.
However, the unadjusted acceleration data showed distortions
and shifts of the baseline while displacement time-series showed
unphysical residual displacement at the end of shaking. Boore
and Bommer (2005) also reported similar observations in their
raw experimental data. It was anticipated that the sensor-to-
surface placement condition and noise are the principal causes to
these flaws. Therefore, reasonable baseline correction schemes
have to be reviewed prior to application of the data. After some
exploratory studies, it was decided to refer to the well-known
correction scheme proposed by Boore (2001). Baseline correction
has been found to be effective in eliminating long-period or low-
frequency noise, as can be observed in Fig. 7. However, it was
Fig. 7. Fourier Amplitudes of Acceleration Data for Soil B under 5
kPa Surcharge Loading without any Input Shaking Motion
(Noise): (a) Before Baseline Correction, (b) After Baseline
Correction
Fig. 8. Fourier Amplitude after Baseline Correction for Soil B under
5 kPa Surcharge Loading with Shaking Motions of F5D1
Fig. 9. Acceleration, Velocity and Displacement Time-history after
Baseline Correction and Filtering for Soil A with Shaking
Motions of F5D1
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− 1742 − KSCE Journal of Civil Engineering
found that high-frequency noise combined with the signal.
Fourier amplitude spectrum in Fig. 8 showed the need of
applying filtering in the process of analysing. Although the
shaking frequency was set to 5 Hz, frequencies of higher than 5
Hz were still observed in the testing result. Therefore, Butterworth’s
low-pass (high-cut) filtering technique was used to remove the
higher-frequency noise (Boore and Bommer, 2005).
Figure 9 shows the acceleration, velocity and displacement
time-history at 0.07 m high of the testing specimen upon
applying the baseline correction and filtering. Similarly, the
adjusted data were obtained for other accelerometers at different
locations. From the observations on the mode of specimen
displacement under the shaking motions, it was decided to
compute the hysteresis loop using the interval between the
specimen base and the point at 0.07 m high. The displacements
were normalized progressively in order to examine the amount
of displacement from the centre of movement. The normalization
was first done by polynomial fitting to the neighbouring three
maximum and minimum data points. The average trend line
between peak and trough polynomial functions could then be
obtained. Finally, localised displacement records were individually
subtracted from that average function. As such, the computation
of strain became possible and reasonable. Fig. 10 depicts a
displacement-time series plot before and after applying
normalization. The shear strain was subsequently obtained
based on the relative displacements computed at the two selected
points. Fig. 11 depicts the lateral displacement profile of selected
time frame at two elevations: CH1 at the base and CH3 at 7 cm
above the base. From the figure, simple shear deformation could
fairly be observed. Therefore, the use of 0.21 m high specimen
was justifiable. The shear stress was computed by considering
the inertia actions (stresses or forces) of overlying soil layers.
The inertia shear stress of each soil layer is the integral product
of soil density and average acceleration (Kazama et al., 1996).
For the testing with surcharge loading, the shear stress on the
plane was computed from the summation of inertia shear stresses
of the soil layers and the inertia shear stress induced by the
Fig. 10. Displacement Time-Series Plot before and after Applying
Normalization for Soil A with Shaking Motions of F5D1
Fig. 11. Displacement Profile of Compacted Soil Model
Fig. 12. Hysteresis Loops for Soil A with Shaking Motion of F5D1:
(a) 0 kPa, (b) 5 kPa, (c) 10 kPa
Fig. 13. Hysteresis Loops for Soil A with Shaking Motion of F5D0.5:
(a) 0 kPa, (b) 5 kPa, (c) 10 kPa
Fig. 14. Hysteresis Loops for Soil B with Shaking Motion of F5D1:
(a) 0 kPa, (b) 5 kPa, (c) 10 kPa
Fig. 15. Hysteresis Loops for Soil B with Shaking Motion of F5D0.5:
(a) 0 kPa, (b) 5 kPa, (c) 10 kPa
Shaking Table Test on Dynamic Behaviours of Tropical Residual Soils in Malaysia
Vol. 21, No. 5 / July 2017 − 1743 −
surcharge loading.
From the computed shear strain and shear stress, several
hysteresis loops were produced. Fig. 12 to Fig. 15 depicts the
stress-strain relationships of the tropical residual soils A and B.
For the reasons of results presentation and interpretation, only
two input motions (F5D0.5 and F5D1) were selected. It can be
seen that a higher shaking displacement could facilitate a greater
shaking magnitude and a larger loop area under the same
confining pressure. Subsequently, the secant shear modulus and
damping ratio were computed. Furthermore, the relationship
between normalized shear modulus and shear strain, namely
normalized G-γ relationship, is shown in Fig. 16 and Fig. 17 for
soil A and soil B.
5. Results and Discussions
Small (0.01%) to medium (0.5%) strain is generally encountered
in the deformation analysis of soils around geotechnical structural
system (Bolton and Oztoprak, 2013). Fig. 16 and Fig. 17 shows
the relationship between normalized shear modulus and shear
strain amplitude for soil A and soil B under three different levels
of confining pressure. It was found that the strain amplitudes
were in the range of 0.3% to 1.8%. Pragmatically, Equivalent
Linear Model (ELM) can be used if large strain (>1%) is not
encountered in an analysis (Santos and Correia, 2000). Equivalent
Linear Model (ELM) is considered as an approximation of the
more complicated non-linear behaviour of soil (Kramer, 2014).
Two equivalent linear parameters, known as secant shear
modulus and damping ratio, can be obtained from hysteresis
loop based on the equivalent linear model. After dynamic
shaking test and data processing, a number of hysteresis loops
can be obtained experimentally. By using the ELM, two dynamic
properties (secant shear modulus and damping ratio) can be
evaluated. Considering that most of the strain amplitudes obtained
from the present study were close to 1% and the simplicity of the
ELM, it was decided to adopt the ELM for the computation of
soil dynamic properties (i.e. secant shear modulus and damping
ratio). From a previous study on a smaller soil sample using the
similar testing setup, it was found that the strain amplitude was in
the range between 0.1% and 1%. This comparison reflected the
fact that the ranges of strains between the former and the present
study were fairly close to each other. As compared with the
normal strain level for a cyclic tri-axial test which is usually
below 0.01%, the use of shaking table apparatus in the present
study could facilitate greater strain amplitudes.
In this study, a representative line for tropical residual soil was
unable to be constructed owing to limited number of data points
available. However, experimentally obtained data points can be
compared with proposed line from the existing database, which
was founded on a large amount of data points from various types
of laboratory tests. Although many empirical equations have
been developed (Hardin and Black, 1968; Vardanega and Bolton,
2013; Bolton and Oztoprak, 2013), the database was largely
based on saturated sand or/and clay, rather than the more
complicated tropical residual soils that consist of mixtures of
sand, silt and clay in an unsaturated condition. Herein, experimental
data points were normalized with respect to the maximum
(elastic) shear modulus before they were introduced into the G-γ
curve lines as proposed by Bolton and Oztoprak (2013). This
reliable degradation curve is statistically based on the curve-
fitting technique. It is worth noting that the maximum shear
modulus was computed at a small strain level (0.001%) in Eq.
(1). In fact, a seismic test is widely regarded as a more common
and reliable way to evaluate the maximum shear modulus. It can
be seen from Fig. 16 and Fig. 17 that the experimental results do
not lay within the proposed zone of degradation curves. It was
realized that the proposed normalized G-γ relationship was
fundamentally based on test results having higher confinement
pressures (between 100 kPa and 200 kPa) for sand. Comparing
results from current study with the established degradation
relationship, it can be concluded that the obtained shear modulus
were apparently lower than those of proposed lines (of saturated
Fig. 16. Relationship between Normalized Shear Modulus and
Shear Strain for Soil A
Fig. 17. Relationship between Normalized Shear Modulus and
Shear Strain for Soil B
Fig. 18. Relationship between Shear Modulus and Shear Strain for
Soil A (F5D0.5 and F5D1 only)
Koo Kean Yong, Lim Jun Xian, Yang Chong Li, Lee Min Lee, Yasuo Tanaka, and Zhao JianJun
− 1744 − KSCE Journal of Civil Engineering
sandy soil). This tendency (overestimation for tropical residual
soils if using proposed curves for sandy soils) had also been
reported by Leong et al. (2003) using cyclic tri-axial test. For a
clearer presentation, only input motions of F5D0.5 and F5D1
were presented on the G-γ plots as plotted in Fig. 18 and Fig. 19
under three different confining pressures (0, 5 kPa and 10 kPa).
G-γ plots of other shaking motions showed a similar trend.
In general, the shear strain amplitude increases with the
increasing confining pressure. This finding can be clearly seen in
the hysteresis loops, as shown in Fig. 12 to Fig. 15. In addition, it
was found that the area of loop is getting larger from low to high
confining pressures. This implied that more energy was stored
when a higher magnitude of shaking was applied. Damping
ratios were computed from the hysteresis loops. The values
ranged approximately from 1% to 12% and proportional to the
applied surcharge loading.
The relationships between shear modulus and confining pressure
(0 kPa, 5 kPa and 10 kPa) are plotted in Fig. 20 to provide a
better insight to the influence of confining pressure on the shear
modulus. As can be seen from Fig. 20, shear modulus increased
with confining pressure for the two studied soils. This result is
favourable and can be regarded as an important finding for
tropical residual soil tested using shaking table under low
confining pressures. Seed et al. (1986) reported that the influence
of confining stress on D-γ relationship (for dry sand) is only
significant for very low stresses (<25 kPa). In addition, it was
observed that the shear modulus of soil B (sandy silt) was
consistently larger than that of soil A (silty sand). This was
possibly due to the fact that soil B has higher plasticity index and
experienced smaller levels of strain. Soil density could be a
factor that may affect the shear modulus of soil. In addition, soil
stiffness can be affected by strain amplitude, void ratio, mean
principal effective stress, plasticity index (PI), Over-consolidation
Ratio (OCR) and number of loading cycles (Kramer, 2014). It is
well-known that secant shear modulus will attenuate with the
increase of shear strain amplitude. From the perspective of
inherent soil properties, sand is largely affected by void ratio and
confining stress whereas clay is influenced by plasticity index
and over-consolidation ratio. In this study, it is apparent that soil
A showed a greater strain amplitude than that of soil B. Vucetic
and Dobry (1991) discussed modulus reduction curves for fine-
grained soils having different plasticity. Under a same level of
strain, a higher plasticity index could give rise to a greater secant
shear modulus. Since tropical residual soil is known to be a
mixture of varying proportions of sand, silt or clay, it is also
advantageous to interpret dynamic properties with respect to its
plasticity index. Soil A (PI = 4.6) has a much lower shear
modulus than soil B (PI = 18). Such comparison agrees with the
established literature findings.
Experimental results were fitted into the relationships of
damping ratio versus strain (D-γ), as proposed by Ishibashi and
Zhang (1993). These relationships are shown in Fig. 21 and
Fig. 22, respectively. Low and high plasticity index (i.e. PI = 0
and PI > 70) were introduced to define lower and upper bound
D-γ curves. From the D-γ relationship, there is no obvious trend
Fig. 19. Relationship between Shear Modulus and Shear Strain for
Soil B (F5D0.5 and F5D1 only)
Fig. 20. Relationship between Shear Modulus and Confining Pres-
sure for Soil A and Soil B
Fig. 21. Relationship between Damping Ratio and Strain for Soil A
Fig. 22. Relationship between Damping Ratio and Strain for Soil B
Shaking Table Test on Dynamic Behaviours of Tropical Residual Soils in Malaysia
Vol. 21, No. 5 / July 2017 − 1745 −
can be defined for soils having different fine contents. It should
be noted that the fine contents for soil A and soil B were 30%
and 57%, respectively. Mean damping ratio was correlated with
three different levels of confining pressure as plotted in Fig. 23.
It was found that a greater confining pressure can induce a higher
damping ratio for the two studied soils. This result is somewhat
inconsistent with some previous literature findings. Ishibashi and
Zhang (1993) reported that a higher confining pressure tends to
yield a smaller damping ratio at a small strain level (0.1%). The
disagreement may be due to limited number of data points and
large strain (1%) deformation obtained in the present study.
The void ratio for soil A is 0.416 whereas soil B has a void
ratio of 0.676. There seems to be no obvious correlation between
the void ratio and damping ratio. This could be caused by limited
data points in the present experiment. In this research, the
number of cycles was not intended to be taken as the main
parameter. In other words, during the test, the duration of
shaking was not set with correspond to different levels of
shaking frequency. It was also practically difficult to examine the
number of cycles due to the large dimension of the compacted
soil model.
6. Conclusions
A series of shaking table tests were performed on two selected
tropical residual soils that varied by their grain sizes (silty sand
and sandy silt) and geological formations. Followings are the
conclusions that can be drawn from this study:
1. The shaking table setup used in the present study is able to
facilitate a considerably large strain level. This is particu-
larly useful for investigating the soil dynamic behaviours in
Malaysia which is subjected to low frequency and large dis-
placement far-field seismic activities. (Balendra and Li,
2008). In order to evaluate shear modulus at a low-strain
level, other relevant tests (i.e. cyclic tri-axial test or resonant
column test) should be conducted.
2. The shear modulus increases proportionally with the confin-
ing pressure. Under the same confining pressure, shear mod-
ulus attenuates with the increase of strain amplitude. It is
found that damping ratio increases with confining pressure.
This finding is somewhat incompatible with some estab-
lished literature findings.
3. The shear modulus of sandy silt is consistently larger than
that of silty sand. This can be explained by the effect of plas-
ticity index and strain amplitude.
Acknowledgements
The authors would like to acknowledge the financial supports
from the State Key Laboratory of Geo-hazard Prevention and
Geo-environment Protection (Chengdu University of Technology)
(SKLGP2014K002), and the Fundamental Research Grant Scheme
(FRGS), Malaysia (Grant No. FRGS/2/2014/TK02/UTAR/02/1).
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