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,


***Undergraduate Student, Dept. of Civil Engineering, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Selangor,


****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])

Koo Kean Yong, Lim Jun Xian, Yang Chong Li, Lee Min Lee, Yasuo Tanaka, and Zhao JianJun

− 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–( )-----------------------------------------------------×=


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.



Fig. 1. Distribution of Residual Soils in Peninsular Malaysia

Fig. 2. Particle Size Distribution Curves for Tropical Residual Soils Fig. 3. Compaction Curves


Vol. 21, No. 5 / July 2017 − 1739 −

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



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


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



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


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)



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


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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