ORI GIN AL PA PER

Shaking table tests to investigate the influence of variousfactors on the liquefaction resistance of sands

Renjitha Mary Varghese • G. Madhavi Latha

Received: 22 February 2013 / Accepted: 9 March 2014 / Published online: 21 March 2014� Springer Science+Business Media Dordrecht 2014

Abstract This paper presents the shaking table studies to investigate the factors that

influence the liquefaction resistance of sand. A uniaxial shaking table with a perspex model

container was used for the model tests, and saturated sand beds were prepared using wet

pluviation method. The models were subjected to horizontal base shaking, and the varia-

tion of pore water pressure was measured. Three series of tests varying the acceleration and

frequency of base shaking and density of the soil were carried out on sand beds simulating

free field condition. Liquefaction was visualized in some model tests, which was also

established through pore water pressure ratios. Effective stress was calculated at the point

of pore water pressure measurement, and the number of cycles required to liquefy the sand

bed were estimated and matched with visual observations. It was observed that there was a

gradual variation in pore water pressure with change in base acceleration at a given

frequency of shaking. The variation in pore water pressure is not significant for the range of

frequency used in the tests. The frequency of base shaking at which the sand starts to

liquefy when the sand bed is subjected to any specific base acceleration depends on the

density of sand, and it was observed that the sand does not liquefy at any other frequency

less than this. A substantial improvement in liquefaction resistance of the sand was

observed with the increase in soil density, inferring that soil densification is a simple

technique that can be applied to increase the liquefaction resistance.

Keywords Shaking table � Liquefaction � Acceleration � Frequency �Density of sand � Model tests

R. M. Varghese � G. Madhavi Latha (&)Department of Civil Engineering, Indian Institute of Science, Bangalore 560012, Indiae-mail: madhavi@civil.iisc.ernet.in

R. M. Varghesee-mail: renjitha@civil.iisc.ernet.in

123

Nat Hazards (2014) 73:1337–1351DOI 10.1007/s11069-014-1142-3

1 Introduction

Liquefaction of cohesionless soils is one of the potential research areas of recent times

because the awareness toward the liquefaction-related damages during seismic events and

the need for mitigation of liquefaction hazards has been increased worldwide. The reasons

for liquefaction are explained by many researchers (Castro 1975; Martin et al. 1975;

Ishihara et al. 1975; Seed 1979; Vaid and Chern 1983; Seed et al. 1985; Poulos et al. 1985).

Liquefaction is associated with the pore water pressure development in the soil due to the

reduction in the volume during undrained loading condition. Development of pore water

pressure starts with the rearrangement of soil grains in loose saturated cohesionless soils

when earthquake waves pass through them. The soil grains try to rearrange themselves to

take a denser form, and pore water gets pressurized during this process because of loss in

the grain contacts. The increment in the pore water pressure is directly proportional to the

decrement in the effective stress of the soil. Apparently the decrease in grain-to-grain

contact or effective stress causes decrease in shear strength of the cohesionless soil and

finally leads to liquefaction or complete loss of shear strength. Liquefaction response of

soil mainly depends on the initial stress and other state parameters of the soil apart from the

ground motion parameters of the seismic shaking (Lee and Seed 1967; Castro and Poulos

1977; Vaid and Finn 1978; Vaid et al. 1985).

Liquefaction of soils has been successfully investigated by several researchers using

reduced scale models in shaking table and centrifuge. Hushmand et al. (1988) and Dobry

et al. (1995) carried out centrifuge tests on saturated sand deposits to understand the time

histories of accelerations and pore pressures during cyclic shaking in centrifuge models.

Use of shaking table tests to understand liquefaction of soils has been demonstrated by

several researchers (Ye et al. 2013; Ha et al. 2011). Sasaki et al. (1992) carried out shaking

table tests to understand the ground displacements during liquefaction and concluded that

the displacements are due to large shear strains in sand which is softened by the generation

of excess pore pressures. Mohajeri and Towhata (2003) and Towhata et al. (2006) carried

out 1-g shaking table tests on soil models prepared in laminar box to study the rate-

dependent behavior of liquefied soils. Kokusho (1999) carried out shaking table tests to

understand the effect of drainage conditions on the liquefaction-induced deformations.

Ueng et al. (2010) used a biaxial laminar shear box mounted on shaking table to study the

settlements in saturated clean deposits of sand and related the volumetric strain in liquefied

sand to the relative density for various shaking durations and earthquake magnitudes.

Maheshwari et al. (2012) reported increase in liquefaction resistance of reinforced sand

through shaking table tests and concluded that the type and amount of reinforcement in the

soil layer has influence on its liquefaction potential.

The low stress levels in 1-g model tests are always argued about and the applicability of

results from these tests for real conditions is questioned. To overcome this difficulty, few

researchers proposed procedures to maintain similitude between shaking table tests and

field conditions. Toyota et al. (2004) carried out 1-g shaking table tests on Toyoura sand to

study the effect of shaking acceleration and frequency on the liquefaction response. These

tests were carried out with reduced density to account for the reduced stress levels in 1-g

model tests. Iai (1989) derived a similitude for the shaking table tests on saturated soil-

structure-fluid model in 1 g gravitational field using e basic equations of equilibrium and

constitutive laws of soil.

There are still several gaps in understanding the influence of various factors that

influence the liquefaction behavior of sand. This paper presents the results of 1-g free field

liquefaction studies on sand through uniaxial shaking table tests. The effect of acceleration

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and frequency of base shaking and relative density of sand on the liquefaction potential and

pore water pressure development are studied through systematic series of shaking table

tests.

2 Testing material

The shaking table tests are performed on poorly graded sand. Figure 1 shows the grain size

distribution curve of the test material. The grain size distribution curve is falling within the

range of gradation for liquefiable sand given by Xenaki and Athanasopoulos (2003). Other

properties of the sand are given in Table 1.

The scanning electron microscopy image in Fig. 2 shows that the test sand particles are

sub-angular in shape. Angularity of particles reduces the liquefaction susceptibility of the

sand because of stable interlocking of grains.

3 Experimental setup and model preparation

Experiments are carried out on a uniaxial shaking table having a pay load of capacity one

tonne. A transparent perspex model container of size 1,200 9 500 9 800 mm was

mounted over the shaking table for preparing the sand bed. It was verified that the natural

frequency of the whole setup does not coincide with the natural frequency of the soil

sample to avoid resonance. Natural frequency of the shaking table used in this study is

100 Hz. Natural frequency of the sand bed in the study is estimated as 30 Hz from the

shear wave velocity of the sand bed (Kramer 2009), which is in turn estimated as 72 m/s

from the void ratio and initial mean effective confining pressure (Hardin and Richart 1963).

In any liquefaction analysis, sample preparation is the major issue because the density

and water content of the sand should be maintained uniform throughout the sample, which

is not an easy task. Different sample preparation methods are available in literature to

evaluate liquefaction resistance of cohesionless soil. They include the following: (1) dry

pluviation method, (2) wet pluviation method, (3) moist tamping method, (4) sedimenta-

tion method. Mulilis et al. (1977) described the effect of sample preparation on sand

liquefaction and concluded that the liquefaction response of a soil specimen significantly

depends on the method of sample preparation. For the present study, wet pluviation method

was adopted for sample preparation. As per literature, wet pluviation method simulates the

natural sand deposition compared to other methods. A 600-mm-thick sand bed was pre-

pared inside the perspex box mounted on the shaking table. Precalculated amount of water

exactly equal to the saturated water content (27 %) of the soil was poured in the perspex

box before pouring the sand. Sand was poured loosely into the water using a conical

hopper. An inverted solid cone with a 60� angle was attached at the end of the funnel to get

the uniform distribution of loose soil. Vaid and Negussey (1988) proved that the sample

prepared by pluviation under water will be homogeneous, and it is almost independent of

height of fall. Figure 3 shows the sequence of stages in sample preparation.

Miniature pore water pressure transducer of range 0–20 kPa with minimal self-weight

of 1.2 gms was used to monitor the pore water pressure variation during the test. Pore

water pressure transducer was kept exactly at mid-height along the central line of the sand

bed so that it is free from any of the boundary effects, and the thread and cable arrangement

ensures the relative movement of the sensor along with the table while shaking. Figure 4

shows the experimental setup before shaking.

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4 Testing and methodology

Saturated sand bed with uniform relative density was prepared in the model container to

measure the response of soil to different seismic shaking conditions. Shaking table along

with the model container was subjected to displacement-controlled sinusoidal base shak-

ing. Acceleration amplitude and frequency of the shaking were varied in different tests.

Three series of shaking table tests were carried to understand the effects of base accel-

eration, frequency and density of sand bed on the pore water pressure development and

liquefaction response of sand bed. Table 2 gives the test matrix used for this study. The

letter symbols A, F and D in the test notation represent the test series to study the effect of

acceleration, frequency and density, respectively. In test series A, frequency of shaking and

relative density of sand bed were kept uniform as 1 Hz and 43 %, respectively, while

varying the acceleration of shaking from 0.1 g to 0.15 g. In series F, acceleration of

shaking and relative density of sand bed were kept uniform as 0.1 g and 43 %, respec-

tively, while varying the frequency of shaking from 1 to 4 Hz. Test series D was intended

Fig. 1 Grain size distribution curve of sand used for tests

Table 1 Properties of sand usedfor shaking table tests

Property Value

Maximum dry unit weight (kN/m3) 17.67

Minimum dry unit weight (kN/m3) 14.23

Specific gravity 2.65

Maximum void ratio 0.862

Minimum void ratio 0.5

Coefficient of uniformity (Cu) 2.857

Coefficient of curvature (Cc) 1.35

D10 0.23

Particle shape Sub-angular

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to study the effect of density of the sand bed in which the acceleration and frequency were

kept as 0.15 g and 1 Hz uniformly, and relative density was varied between 43 and 67 %.

Light stirring and vibration was used for achieving higher initial densities. Water content in

Fig. 2 SEM image of the testing material

Fig. 3 Stages of sample preparation. a Place the perspex box on shaking table. b Fill the box withcalculated water for saturation. c Fix the sensor at position. d Hang the conical hopper. e Adjust the height offall for sand pluviation. f Prepared sand bed of required density

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this bed corresponds to the saturated water content of the sand. Test series with multiple

notations denote overlapping tests across the series.

Variation of pore water pressure at the midpoint of the sand bed was monitored with the

number of shaking cycles for each test. Initiation of liquefaction is identified with respect

to pore water pressure ratio, which is defined as the ratio between excess pore water

pressure developed during dynamic loading (Du) to the initial effective vertical stress (rv0).

The soil bed is said to be liquefied when the pore water pressure ratio reaches one, where

the effective vertical stress becomes zero. Number of cycles for liquefaction was deter-

mined from the data, by calculating the pore water pressure ratio at every cycle and the

number of cycles required for the pore water pressure ratio to reach a value of unity.

5 Results and discussion

5.1 Effect of acceleration on sand liquefaction

It is observed that for the given soil, the liquefaction was initiated at 0.15 g acceleration

amplitude at a frequency of 1 Hz, and the number of cycles required for liquefaction was

six. It was clearly observed that the response of sand is substantially affected by the small

variations in acceleration amplitude. Flow liquefaction with complete loss of shear strength

was visually observed in the sand bed at 0.15 g acceleration and 1 Hz frequency. For all

the acceleration amplitudes less than this, there was limited liquefaction, exhibited by

increase in pore pressure ratio and decrease in effective stress.

Figures 5 and 6 show the variations of pore pressure ratio and effective stress,

respectively, with varying acceleration amplitude. It can be seen that for the test sample

subjected to 0.15 g acceleration at 1 Hz frequency, pore pressure ratio reached 1.0 in six

cycles and the effective stress dropped to zero at this point, concurring with the visual

observation of flow liquefaction of sand at the end of six cycles of shaking. For all other

accelerations, pore pressure ratio increased with number of cycles, but it was much less

than 1.0. It is also observed that the order of increase in pore pressure ratio or decrease in

effective stress is in the order of increase in acceleration amplitude. For example, maxi-

mum pore pressure ratio was 0.13 for acceleration amplitude of 0.12 g, whereas it was 0.2

for 0.13 g, 0.27 for 0.14 g and 1.0 for 0.15 g. Figure 7 shows the sand bed liquefied in the

test with base acceleration of 0.15 g.

Fig. 4 Prepared sand bed before liquefaction

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Reduction in time to reach the peak pore water pressure was observed as the acceler-

ation value increases. Figure 8 indicates the increase in maximum pore water pressure with

respect to acceleration. It can be seen that the influence of acceleration amplitude on the

pore pressure development is highly nonlinear. The influence is less significant at lower

acceleration amplitudes, and at higher accelerations, even a small change in the amplitude

can cause drastic build-up of pore water pressure, demonstrating the quick loss of strength

during liquefaction.

Seed et al. (1976) presented the variation of pore pressure ratio with the number of

cycles during the process of liquefaction and showed a typical band for this variation. The

pore pressures measured in the present study for the case of liquefied sand bed (0.15 g and

1 Hz input base motion) is compared against the plot presented by Seed et al. (1976), and it

is found that the pore water pressure generation is following the presented trend as the

variation of pore pressure ratio with the number of cycles is falling within the boundary.

Here, N represents the number of cycles and Nl represents the number of cycles for

liquefaction. De Alba et al. (1975) also observed that the rate of pore pressure development

Table 2 Test matrix

Variable Test Relative density (%) Acceleration(g) Frequency (Hz)

Acceleration AFT1 43 0.1 1

AT2 43 0.12 1

AT3 43 0.13 1

AT4 43 0.14 1

ADT5 43 0.15 1

Frequency FT1 43 0.1 2

FT2 43 0.1 3

FT3 43 0.1 4

Density DT1 58 0.15 1

DT2 67 0.15 1

Fig. 5 Variation in porepressure ratio for sand bedsubjected to differentaccelerations at 1 Hz frequency

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depends on Nl. and presented an equation to calculate the pore pressure ratio at any cycle of

loading during liquefaction as:

Pore water pressure ratio; ru ¼1

2

� �þ 1

p

� �sin�1 2

N

Nl

� �ð1=aÞ�1

" #ð1Þ

where N is the number of cycles, Nl is the number of cycles for liquefaction and a is a

coefficient that depends on the soil properties and test conditions and usually taken as 0.7

for cohesionless soils. Figure 9 shows the rate of pore water pressure development during

the experiments in present study compared with the range presented by Seed et al. (1976)

and the calculated values using the equation given by De Alba et al. (1975).

Fig. 6 Variation in effective stress for sand bed subjected to different accelerations at 1 Hz frequency

Fig. 7 Sand bed subjected to flow liquefaction (Base acceleration 0.15 g, frequency 1 Hz)

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In this series of tests, cyclic resistance ratio (CRR) of sand beds was same for all the

tests, because the density and water content were same. However, these sand beds were

subjected to different levels of cyclic stresses, because of change in ground motion

accelerations, which varies the cyclic stress ratio (CSR) of the sand beds. Hence, the pore

water pressures developed in the sand beds were different in different tests. Liquefaction

was initiated in the sample, when the CSR was equal to CRR (Kramer 2009), which

happened when the acceleration of shaking was 0.15 g.

Fig. 8 Variation in maximum pore water pressure with different accelerations at 1 Hz

Fig. 9 Rate of pore water pressure generation during the test with 0.15 g and 1 Hz

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5.2 Effect of frequency on sand liquefaction

To study the effect of dynamic loading frequency on sand liquefaction, sand beds are

subjected to base shaking of different frequencies, keeping the acceleration and relative

density of sand same. These tests are carried out at an acceleration amplitude of 0.1 g with

relative density of sand as 43 %, changing the frequency of shaking from 1 Hz to 4 Hz.

Variation of pore pressure ratio in these tests is shown in Fig. 10. From Fig. 10, it can be

observed that the pore pressure ratio is not altered significantly with frequency for fre-

quency range 1–3 Hz. Sand bed is not liquefied completely in these tests. However, for the

test with 4 Hz frequency, in which the sand bed was subjected to flow liquefaction in 19

cycles of shaking, pore pressure ratio increased drastically and reached a value of unity

when sand is liquefied.

Figure 11 gives reduction in effective stress due to pore water pressure development for

different frequencies. It is clear that the drop in effective stress is not significant at lower

frequency levels. Only for a frequency of 4 Hz, the effective stress dropped down to zero,

and hence, this frequency can be termed as threshold frequency for liquefaction for the

given sand at acceleration amplitude of 0.1 g. The maximum pore water pressure devel-

opment can be seen only in threshold frequency for a given acceleration amplitude. This

can be further confirmed from Fig. 12 in which the variation of pore water pressure with

the frequency of base shaking is presented. Up to the threshold frequency, the maximum

pore water pressure developed remained almost the same and it increased drastically for

the threshold frequency.

Figure 13 presents the rate of pore water pressure development for the test with 0.1 g

and 4 Hz where the soil was liquefied and the comparison of the same with the band

presented by Seed et al. (1976) and the calculated variation as per De Alba et al. (1975). It

is observed that initially the measured response is little different from the predictions given

in the literature as the pore water pressure ratio with the number of cycles is falling outside

the given band. Also significant variation in the measured rate of pore water pressure

generation and calculated response as per De Alba et al. (1975) was observed up to a pore

water pressure ratio of 0.7. But at later stages, the experimental trend coincided with the

expected path.

5.3 Effect of relative density of sand on liquefaction

To understand the effect of density of sand on its liquefaction potential, tests were carried

out on sand beds with relative density of the sand varying from 43 to 67 %, keeping the

acceleration amplitude and frequency of base shaking as 0.15 g and 1 Hz, respectively.

Results from these tests are shown in Figs. 14 and 15. It was observed that the sand bed got

completely liquefied for the relative densities of 43 and 58 %, where as it did not liquefy

when the relative density was 67 %.

When pore pressure ratios are compared (Fig. 14), in case of sand bed with relative

density of 67 %, the maximum pore pressure ratio achieved was only 0.3, much less than

the unity, showing that the soil needs extremely higher cyclic loading to liquefy. Figure 15

shows that even though there was not much difference in initial vertical effective stress, the

pore water pressure development is considerably affected by the density of the sand bed.

This can be explained clearly using state parameter of soil at different densities. State

parameter represents the difference in void ratios of sand in present state and the sand in

critical state. Loose sands have void ratio close to the critical void ratio compared to the

dense sands, and hence, less amount of cyclic shaking is enough to bring them to a

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liquefied state, whereas denser sands have lesser void ratio and more shaking is required to

initiate liquefaction in these samples. Liquefaction resistance of the soil increases with

density. Hence, soil densification is the simplest method to improve the liquefaction

resistance of the soils. The cyclic loading parameters used for this series of tests represent a

seismic event of moderate magnitude. Using densification techniques, such as vibroflota-

tion, heavy tamping and blasting, the relative density can be improved further to withstand

seismic events of much higher magnitudes.

In this series of tests, sand beds were subjected to same level of cyclic stresses, because

the ground motion accelerations are same. Hence, the cyclic stress ratio (CSR) of the sand

beds was same. However, cyclic resistance ratio (CRR) of sand beds was different for

Fig. 10 Variation in pore water pressure ratio for sand bed subjected to different frequencies of shaking at0.1 g

Fig. 11 Variation in effectivestress for sand bed subjected todifferent frequencies of shakingat 0.1 g

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different models, because the density is different. Hence, the pore water pressures

developed in the sand beds were different in different tests. Sand beds of lower relative

densities (43 and 58 %) got liquefied, because the CSR value exceeded the CRR values,

and the sand bed of 67 % relative density could stay without liquefying because of higher

CRR value.

Change in the geometry of test bed will have some influence on the values of ground

shaking parameters that initiate liquefaction in the sand bed in scaled tests. Also, 1-g

shaking table studies suffer from scale effects on stress intensities. Hence, the results from

these studies cannot be directly extrapolated for estimating the ground motion parameters

Fig. 12 Variation in maximum pore water pressure for sand bed subjected to different frequencies ofshaking at 0.1 g

Fig. 13 Rate of pore waterpressure generation during thetest 0.1 g and 4 Hz

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that could initiate liquefaction in field. However, qualitative conclusions drawn from this

study are valid for understanding the initiation of liquefaction in saturated sand beds.

6 Conclusions

The following conclusions are drawn from the present study.

• Saturated sands subjected to base shaking get liquefied. The number of cycles needed to

liquefy the soils depends on the acceleration amplitude, frequency of base shaking and

relative density of sand.

Fig. 14 Variation in pore waterpressure ratio of sand bed withdifferent relative densities

Fig. 15 Variation in effective stress of sand with different relative densities

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• Acceleration amplitude is the most important cyclic loading parameter that controls

liquefaction. Higher the acceleration, less number of cycles needed for liquefaction and

higher the pore water pressure developed at any stage.

• There is a threshold frequency for the given sand to achieve initial flow liquefaction at

any given acceleration amplitude. As the frequency increases, the liquefaction

resistance of the sand decreases.

• Pore pressures developed in the model tests depended both on the cyclic stress induced

by the shaking and the cyclic resistance of the sand bed. Liquefaction is initiated when

the cyclic stress ratio exceeded the cyclic resistance ratio.

• Density of sand plays a major role in its liquefaction response. Loose soils, whose state

parameter is less, liquefy faster. Denser sands need higher cyclic loads for liquefaction.

Limited liquefaction of denser sand is achieved at lower cyclic loads, where the pore

pressures increase to certain extent but the pore pressure ratio can never reach unity and

the effective stress does not drop to zero.

• Soil densification is the simplest and effective technique for improving the liquefaction

resistance of sands. Increase in relative density of sand from 58 to 67 % showed drastic

improvement in the liquefaction resistance of the sand used in present study.

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