poulos_liquefaction.pdf

Assessment of soil liquefaction incorporating earthquake characteristics

D.S. Liyanapathiranaa,*, H.G. Poulosb

aDepartment of Civil, Mining and Environmental Engineering, University of Wollongong, Wollongong, NSW 2522, AustraliabCoffey Geosciences Pty Ltd, Department of Civil Engineering, University of Sydney, Sydney, NSW 2006, Australia

Accepted 18 November 2003

Abstract

This paper investigates the effect of nature of the earthquake on the assessment of liquefaction potential of a soil deposit during earthquake

loading. Here, the nature of the earthquake is included via the parameter V ; the pseudo-velocity, that is the gross area under the acceleration

record of the earthquake at any depth below the ground surface. By analysing a number of earthquake records from different parts of the

world, a simple method has been outlined to assess the liquefaction potential of a soil deposit based on the pseudo-velocity. For many

earthquakes occurred in the past, acceleration records are available or can be computed at the ground level or some other depth below the

ground surface. Therefore, this method is a useful tool at the preliminary design stage to determine the liquefaction potential before going

into a detailed analysis. Validation of the method is carried out using a database of case histories consisting of standard penetration test

values, acceleration records at the ground surface and field observations of liquefaction/non-liquefaction. It can be seen that the proposed

method has the ability to predict soil liquefaction potential accurately, despite its simplicity.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Soil liquefaction; Nature of the earthquake; Pore pressure generation; Cyclic shear stress; Pore pressure dissipation; Liquefaction potential index

1. Introduction

When saturated sand deposits are subjected to earth-

quake-induced shaking, pore water pressures are built-up

leading to liquefaction or loss of soil strength. Major

earthquakes that have occurred during past years, such as

the 1964 Alaska, 1964 Niigata, 1989 LomaPrieta and the

1995 HyogokenNambu have demonstrated the damaging

effects of soil liquefaction. Therefore, it is necessary to

obtain a proper understanding of the effect of parameters

such as soil properties and the nature of the earthquake on

the severity of the soil liquefaction.

Most major earthquakes occur around the boundaries of

the tectonic plates such as those that exist in California,

USA. The Australian continent is in the middle of one of the

worlds largest tectonic plates, and therefore, Australia is

subjected to relatively low earthquake activity. However,

the 1989 Newcastle earthquake, which caused 13 deaths,

increased the awareness of the need to properly assess the

possible consequences of earthquakes in areas subjected to

intraplate events.

Although Australian earthquakes can have acceleration

levels as high as those in Californian earthquakes, evidence

of liquefaction has not been reported. The major difference

between Californian and Australian earthquakes is that, in

Australian earthquakes, the predominant frequency is high

and any large acceleration levels last for a very brief

duration, while in Californian earthquakes, the predominant

frequency is lower and high acceleration levels exist during a

significant proportion of the longer duration of the earth-

quake. Hence this gives a clear indication about the

significance of the nature of the earthquake on the

liquefaction.

Although ground response analyses based on the finite

element method provide a better assessment of liquefaction

of a soil deposit by taking into account the nature of the

earthquake and the pore pressure dissipation [13,16,17,21,

27,29,30,40,42], they are often costly and time-consuming.

In addition, constitutive models used in those programs

need large number of parameters to determine the pore

pressure generation in soil due to earthquake loading.

Therefore, simplified methods in assessing soil liquefaction

are popular among practicing engineers. These procedures

are very useful at the preliminary design stages to assess

0267-7261/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.soildyn.2003.11.010

Soil Dynamics and Earthquake Engineering 24 (2004) 867875

www.elsevier.com/locate/soildyn

* Corresponding author.

E-mail address: [email protected] (D.S. Liyanapathirana).
http://www.elsevier.com/locate/soildyn

the liquefaction risk. If the liquefaction risk is high, then a

detailed finite element analysis can be carried out to obtain

the pore pressure distribution and ground displacement

along the depth of the soil deposit, which is necessary in

subsequent design of deep foundations.

In simplified methods, the earthquake loading parameter

is generally represented either by the cyclic shear stress

generated due to the earthquake or by the amount of

energy released due to the earthquake. The presently

available simplified methods can be divided into three

main categories: (1) methods based on the cyclic shear

stress generated in the soil, (2) energy based methods and

(3) probabilistic methods.

In the cyclic shear stress approach, the cyclic stress ratio

(CSR) generated at any depth of the soil deposit due to the

earthquake loading can be obtained using the simplified

equations [19,33,37,48] and CSR depends on the maximum

acceleration at the ground surface. If CSR exceeds the

cyclic resistance ratio (CRR) at any depth of the soil deposit,

soil liquefaction occurs at that depth.

Over the past 25 years, numerous studies have been

carried out to correlate the CRR to the standard penetration

test (SPT) data [34,37,38,41], cone penetration test (CPT)

data [31,33,35,43], electrical probe measurements [3] and

shear wave velocity measurements [1,8,9,20,32,38,44,46].

In energy based methods, pore water pressure increment is

related to the energy dissipated during the earthquake loading

[5,7,12,23,24,28,45,47]. In contrast, energy based methods

proposed by Egan and Rosidi [10] and Kayan and Mitchell

[22] used the Arias intensity [2] to represent the energy

content of the earthquake. Based on case studies of field

behaviour during earthquakes, Arias intensity at any depth

below the ground surface is associated with the liquefaction

resistance at that depth, as measured by the SPT or CPT.

Although probabilistic methods [6,11,14,20,25] have

been developed to obtain the probability of occurrence of

liquefaction as a function of earthquake load and soil

parameters, the usefulness of these methods depends on the

soundness of the assumed mechanistic models and on the

feasibility of quantifying uncertainty of model parameters.

Therefore, these methods are not very popular among

practicing geotechnical engineers.

Although a large number of simplified methods in

assessing soil liquefaction are available, the cyclic shear

stress method is the standard practice in most parts of the

world. However, this method does not take into account the

effect of the nature of the earthquake on the degree of soil

liquefaction. The degree of liquefaction is assessed based on

the maximum shear stress generated at any depth below the

ground surface, which is calculated based on the maximum

acceleration of the earthquake at the ground surface.

This paper investigates the significance of the nature of

the earthquake on the liquefaction potential of a soil deposit,

and a simplified procedure is outlined to incorporate the

nature of the earthquake into the assessment of liquefaction

potential of a soil deposit.

2. Liquefaction potential

Here the liquefaction potential is assessed using the

liquefaction potential index IL defined by Iwasaki et al. [18])

based on the cyclic stress method proposed by Seed and

Idris [37]. This term gives an indication of the degree of

severity of an earthquake. Although, the factor of safety

against liquefaction is a widely used term in assessing the

degree of liquefaction, it gives an indication about the

liquefaction potential only at a particular depth. When

comparing liquefaction potential of different soil deposits,

the factor of safety at various depths within the deposit

should be compared, and this can be facilitated by using IL;

as it is the integrated value of several factor of safety values

along the soil deposit as shown below

IL 20

0FWzdz 1

where F 1 2 FL for FL # 1:0 and F 0 for FL .1:0:Wz 10 2 0:5z and z is the depth in meters.

FL is the factor of safety against liquefaction and

defined as

FL CRR

CSR2

where CRR is the in situ cyclic undrained shear strength of

the soil mobilised for the equivalent number of stress cycles

developed due to the earthquake, and CSR is the average

shear stress level developed in the ground due to earthquake

loading at the depth under consideration. According to the

simplified method, the average shear stress developed at a

depth z below the ground surface is given by

CSR 0:65 amaxg

rdgsz 3

where gs is the unit weight of soil, amax is the peakhorizontal acceleration at the ground surface, rd is the stress

reduction coefficient, z is the depth below ground surface in

meters and g is the acceleration due to gravity. The

coefficient rd is less than unity and Seed and Idriss [37],

Iwasaki et al. [19] Liao and Whitman [48], T.F. Blake [48],

and I.M. Idriss [1] have suggested values for rd:

By analysing liquefied and non-liquefied sites during

earthquakes Iwasaki et al. [18] proposed a simplified

classification system as shown in Table 1, to assess soil

liquefaction at a particular site based on the liquefaction

potential index given by Eq. (1).

Table 1

Liquefaction risk assessment [18]

Liquefaction risk

IL 0 Very low0 , IL # 5 Low

5 , IL # 15 High

15 , IL Very high

D.S. Liyanapathirana, H.G. Poulos / Soil Dynamics and Earthquake Engineering 24 (2004) 867875868

3. Ground response analysis

When using the simplified method of calculating shear

stresses induced in ground due to earthquake loading, CSR

at any depth below the ground surface is calculated based on

the maximum ground acceleration, neglecting the nature of

the earthquake. In this present study, CSR is calculated

using a one-dimensional finite element model based on the

effective stress approach, which effectively captures the

nature of the earthquake.

The equations of the motion are integrated directly using

the constant average acceleration method [4]. Soil beha-

viour has been modeled using a hyperbolic stressstrain

relationship, which reflects hysteretic behaviour of sands. In

addition to the hysteretic damping, viscous damping is

also included. According to Seed and Idriss [36], viscous

damping should be on the order of 20% of the critical

damping under the amplitude of motions likely to develop

during earthquakes. This term takes into account the energy

dissipation due to visco-elastic properties of the soil. Here,

critical damping is calculated based on the initial maximum

values of shear modulus G0 and shear strength t0 of the soil,and is kept constant throughout the analysis.

The initial maximum values for shear modulus G0 and

shear strength t0 of the soil are estimated using therelationships given by Hardin and Drnevich [15] as shown

below

G0 14:762:973 2 e2

1 e

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi47 900

1 2K03

s0v0

skPa

4

t0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1 K02

sinf0 2

21 2 K0

2

2ss0v0 kPa 5

where e is the void ratio of the soil, K0 is the coefficient of

earth pressure at rest, f0 is the effective angle of shearingresistance and s0v0 is the initial effective overburden pressurein kPa.

With the generation of pore water pressure due to an

earthquake, the effective vertical stress of the soil is reduced

during and after the seismic event. Consequently, the loss of

soil strength and stiffness can be incorporated into the

analysis through substituting the current value of effective

stress in Eqs. (4) and (5).

Generation of pore water pressure during earth-

quake shaking has been calculated using the equivalent

cycle method proposed by Seed et al. [40] and Martin

and Seed [26]. Pore pressure dissipation due to consolida-

tion of the soil has also been incorporated into the analysis.

The earthquake motion induces periods of high stress

intensity followed by periods of little activity. Therefore,

the number of equivalent cycles of the earthquake, Neq [39],

is calculated by dividing the total duration of the earthquake

into number of periods for which, the rate of application of

stress cycles are calculated separately.

4. Calculation of liquefaction potential index

The steps involved in computing the liquefaction

potential index of a soil deposit can be summarised as

follows:

1. Using the finite element model stresses developed in the

soil, and hence Ss at each depth, which is 65% of

maximum shear stress, can be computed.

2. Before calculating IL in Eq. (1), FL within the first 20 m

of the soil deposit should be calculated. Now Ss is known.

Since Neq is known, R in Eq. (2) can be obtained from the

cyclic liquefaction strength curve of the particular soil

considered.

3. Once FL is known, F can be obtained based on the value

of FL as described in Section 2. By integrating FWzalong the upper 20 m of the soil deposit, the liquefaction

potential index, IL; of the soil deposit can be obtained

from Eq. (1).

5. Effect of nature of the earthquake on liquefaction

potential

To study the effect of the nature of the earthquake on the

liquefaction potential, acceleration records of 15 earthquakes

scaled to different acceleration levels of 0.1, 0.15, and 0.2 g,

that have occurred during the past 60 years in different parts

of the world have been analysed. Here, a parameter, the

pseudo-velocity V ; is introduced, which takes into account

the nature of the earthquake, where V is given by

V td

0laccl dt 6

where td is the duration of the earthquake and acc is the

acceleration at time t:

Table 2 summarises the V values obtained for earth-

quakes used for this study, scaled to a maximum accelera-

tion of 0.1g. All Australian earthquakes have lower V values

compared to inter-plate earthquakes such as San Fernando,

Northridge, Taft, Pasadena and El-Centro. According to the

V values recorded in Table 3, all Australian earthquakes

except the two Newcastle earthquakes, scaled to 0.1g, have

values of V less than 0.7.

Table 2

Values of parameters used for the analysis

Input parameters

Density rS 1900 kg/m3Coefficient of earth pressure at rest K0 0.6Poissons ratio e 0.6Pore pressure parameter a 1.3Friction angle f0 408Relative density (Dr %) 55

D.S. Liyanapathirana, H.G. Poulos / Soil Dynamics and Earthquake Engineering 24 (2004) 867875 869

The liquefaction potential index IL has been computed

for the soil deposit with properties as given in Table 3, when

subjected to the earthquakes listed in Table 2, scaled to

acceleration levels 0.1, 0.15 and 0.2g. Pore pressure

dissipation is found to be significant only for clean sands

and sand mixed with gravels with permeability greater than

1024 m/s. Therefore, the soil is assumed to be undrained. G0and t0 are modelled using Eqs. (4) and (5). Pore pressuregeneration is calculated based on the liquefaction strength

curves given by Seed et al. [40].

Pseudo velocity is a parameter, which varies along

the depth of soil deposit for a particular earthquake.

Therefore, when relating IL with V ; a reference depth

should be selected. Here, 15 m below the ground surface has

been taken as the reference depth and V at 15 m depth is

referred as Vref :

Fig. 1 shows the variation in IL with Vref ; when relative

density is 55%. It can be seen that although all earthquake

records are scaled to the same acceleration level, the

calculated liquefaction potential index increases with

increasing Vref : Therefore, it can be concluded that the

nature of the earthquake has a significant influence on the

liquefaction potential and it is not the maximum acceleration

level at the ground surface that controls the soil liquefaction.

According to Fig. 1, there is a critical value for Vref ;

beyond which, IL starts to increase with Vref : If the

variation in maximum excess pore pressure generated in

the soil deposit is studied, it can be seen that beyond the

critical Vref ; the maximum pore pressure ratio is 1.0, and

when Vref is less than the critical Vref ; the maximum pore

pressure ratio generated in the deposit has a linear variation

with Vref : This is illustrated in Fig. 2 for the sand at relative

density of 55%.

If the analysis is repeated for several relative densities,

it can be seen that each relative density has a different

critical Vref : Fig. 3 shows the IL corresponding to different

Vref ; when Dr varies from 45 to 90%. A chart such as this is

very useful in assessing IL for a soil deposit if the

acceleration record at z 15 m and relative density of thesoil are known.

According to Figs. 1 and 2, it is clear that the liquefaction

potential is very low when Vref is relatively low. Australian

earthquakes have relatively low Vref values, and conse-

quently, it can be concluded that the risk of liquefaction of

sand deposits in Australia may be significantly lower than

the same deposit in the USA, Japan and other areas

subjected to inter-plate seismic events.

For many earthquakes, acceleration records are available

at the ground surface. Therefore, to relate the Vref to Vsurfaceat the ground surface, the ratio of Vz=Vsurface; along the depth

for a 30 m soil deposit are given in Fig. 4, for the earthquake

records given in Table 2. The average line given for

Vz=Vsurface can be used to relate Vsurface to V at any depth

below the ground surface. The analysis is repeated by

varying the profile of shear modulus along depth, density of

the soil and the relative density of the soil. It can be seen that

the distribution of Vz=Vsurface with depth does not change

significantly with those parameters.

Fig. 1. Variation in liquefaction potential index with Vref :

Table 3

V values for the earthquakes used for the study

Name of earthquake V (max. acc. 0.1g)

New Zealand-1973 2.36

New Zealand-1991 1.07

San Fernando 3.05

Northridge 2.89

Oolong 0.44

Taft 3.95

Gunjung 1.53

Tenant Creek 0.32

Meckering 0.66

Cadoux 0.19

Newcastle-1989 2.29

Newcastle-1994 2.13

Pasadena 7.33

Melendy Ranche 0.51

El-Centro 4.11


5.1. Maximum pore pressure ratio based on ILfor non-liquefying soil

Fig. 5 shows the variation in IL with maximum pore

pressure ratio, rp; generated in the soil deposit for several

relative densities. It can be seen that there is a reasonably

unique relationship between IL and the maximum pore

pressure ratio, irrespective of the relative density of the soil.

This chart shows three regions. If rp , 0:65; IL is zero andhence the liquefaction risk is very low. If rp 1:0; IL . 5and the liquefaction risk is high. If 0:65 # rp , 1:0; 0 ,IL # 5 and the liquefaction risk is low. In this region, IL andrp are linearly related as follows:

IL 14rp 2 9 0:65 # rp , 1:0 7

Fig. 2. Variation in max. pore pressure developed in the deposit with Vref :

Fig. 3. Variation in liqueaction potential with critical Vref : and relative density (Dr%).

Fig. 4. Variation of V along depth/V at the ground surface.


When the liquefaction risk is low, the above equation can

be used to estimate the maximum pore pressure ratio

generated in the soil deposit. Charts like this are very useful

for preliminary design when there is a lack of detailed site

information.

5.2. Depth of liquefied zone based on IL

Fig. 6 shows the variation of depth of liquefied region/

depth of soil deposit HL=H for different IL: These resultswere obtained using the earthquake records given in Table 2

and by varying the relative density of the soil from 45 to 90%.

It can be seen that irrespective of the relative density, HL=H

has a reasonably unique relationship with IL: According to

Fig. 6, with the increase in IL; HL=H increases. There is

a rapid increase in liquefied depth when the 5 , IL , 15:When IL reaches 15, according to Table 1, the liquefaction

risk is very high and the depth of liquefied region is about

45% of the total depth of the soil deposit.

6. Summary of practical procedure

The proposed practical procedure for assessing the

liquefaction potential of a soil deposit can be summarized

as follows:

1. First calculate Vsurface for the soil deposit Eq. (3), based

on the acceleration record at the ground level.

2. According to Fig. 4, on average, Vref < 0:5 Vsurface at15 m.

Fig. 5. Variation of IL with maximum pore pressure rario, rp:

Fig. 6. Variation of depth of liquefaied zone with the IL:


3. Based on the relative density of the soil and the Vref ; ILfor the deposit can be obtained from Fig. 3.

4. If IL is less than 5, soil liquefaction risk is low or very

low. If required, the maximum pore pressure generated in

the soil deposit can be assessed using Fig. 5.

5. If IL is greater than 5, soil liquefaction risk is assumed to

be high and it may be necessary to develop mitigation

measures.

7. Application of the method to case histories

The method presented in the paper has been applied to 23

liquefied and non-liquefied sites due to 1964 Niigata, 1971

San Fernando, 1976 Tangshan, 1978 Miyagi-Oki, 1979

Imperial Valley, 1981 Westmoreland, 1987 Elmore Ranch,

1987 Superstition Hills and 1989 Loma Prieta earthquakes

as shown in Table 4. The SPT values for these sites have

been obtained from the data given by Berrill and Davis [5]

and Egan and Rosidi [10].

The approximate values of relative densities for these

sites were calculated based on the SPT data. For these

earthquakes, acceleration records are available at the

surface level and thus, to relate the Vref at 15 m below the

surface to Vsurface; Fig. 4 has been used.

According to Fig. 5, when IL is 5, the maximum pore

pressure ratio in the soil deposit becomes one. That means

the boundary between the liquefied and non-liquefied sites

should be represented by the IL 5 line shown in Fig. 3.Fig. 7 shows the Vref vs. Dr for the data given in Table 4.

Also the IL 5 line given in Fig. 3 is plotted. It can be seenthat this line quite satisfactorily separates the liquefied and

non-liquefied sites.

Table 4

Summary of earthquake characteristics

Earthquake Site PGA (g) SPT Dr % Vz0 Vz15m Liquefaction? Reference

Loma Prieta 1989 Mission Pointe (Sunnyvale) 0.22 16 63 4.04 1.5 No [10]

Port of Oakland (Fill) 0.29 12 54 7.0 2.7 Yes [10]

Port of Oakland (Native A) 0.29 14 58 7.0 2.7 Yes [10]

Port of Oakland (Native B) 0.29 30 80 7.0 2.7 Yes [10]

Coyote Creek (Milpitas) 0.17 10 50 5.3 1.8 No [10]

Coyote Creek (Agnew) 0.14 10 50 4.9 1.6 No [10]

Treasure Island 0.16 6 37 5.44 1.9 Yes [10]

Superstition Hills 1987 Imperial Wildlife (surface) 0.21 8 43 7.96 3.25 Yes [10]

Imperial Valley 1979 McKim Ranch (El Centro #4) 0.49 10 50 6.02 2.25 Yes [10]

McKim Ranch (El Centro #4) 0.49 21 70 6.02 2.25 No [10]

Radio Tower (Brawley) 0.22 7 40 4.9 1.7 Yes [10]

Radio Tower (Brawley) 0.22 14 58 4.9 1.7 No [10]

River Park 0.17 4.7 34 8.23 3.5 Yes [5]

River Park 0.17 8.8 47 8.23 3.5 Yes [5]

San Fernando 1971 Juvenile Hall 0.26 2.1 16 5.09 1.7 Yes [5]

Westmoreland 1981 Radio Tower (Brawley) 0.16 7.0 40 2.75 1.3 Yes [10]

Radio Tower (Brawley) 0.16 14.0 58 2.75 1.3 No [10]

Elmore Ranch 1987 Imperial Wildlife (surface) 0.13 8.0 43 3.71 1.5 No [10]

Miyagi-Oki 1978 Ishinomaki 0.32 5.5 35 13.83 6.5 Yes [10]

Niigata 1964 Niigata 0.13 6.9 40 6.0 2.3 Yes [10]

Niigata 0.13 13.8 58 6.0 2.3 No [10]

Tangshan 1976 Weigezhuang 0.14 15.2 60 10.0 4.5 Yes [5]

Lujiatuo 0.14 4.4 33 10.0 4.5 Yes [5]

Fig. 7. Validation of the method using case history data.


8. Conclusions

A simple method is presented for the preliminary

assessment of liquefaction potential incorporating the

effects of pore pressure dissipation and the nature of the

earthquake. The pseudo-velocity Vref ; which is the gross

area under the input acceleration record at 15 m below the

ground surface, is introduced to represent the nature of the

earthquake. By analysing 15 earthquake records at different

maximum acceleration levels, it has been shown that

although the maximum acceleration levels of the earth-

quakes are the same, the liquefaction risk is low when Vref is

relatively low.

Using data collected at liquefied and non-liquefied sites

during past earthquakes, it has been shown that the IL 5line plotted in the Vref vs. Dr space separates the liquefied

and non-liquefied sites. This indicates that the pseudo

velocity can be a useful and reliable measure of earthquake

severity in the field.

Acknowledgements

This work is part of a project on Pile Design for

Seismically Active Areas funded by the Australian

Research Council, and it has been carried out within the

Centre for Geotechnical Research, The University of

Sydney. This support is gratefully acknowledged.

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Assessment of soil liquefaction incorporating earthquake characteristicsIntroductionLiquefaction potentialGround response analysisCalculation of liquefaction potential indexEffect of nature of the earthquake on liquefaction potentialMaximum pore pressure ratio based on &f;I&m.inf;&rm;L&/rm;&/m.inf;&/f; &?show $262#;for non&hyphen;liquefying soilDepth of liquefied zone based on &f;I&m.inf;&rm;L&/rm;&/m.inf;&/f;Summary of practical procedureApplication of the method to case historiesConclusionsAcknowledgementsReferences

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