A Practical Method in Evaluating Liquefaction Potential of Soils

7/30/2019 A Practical Method in Evaluating Liquefaction Potential of Soils

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A Practical Method in Evaluating Liquefaction Potential of Soils

Yie-Ruey Chen, Shun-Chieh Hsieh and Pai-Lung Shan-KungDepartment of Land Management and Development, Chang Jung Christian University

Tainan, Taiwan, China

ABSTRACT

Based on existing methods eight common parameters affecting the soilliquefaction are considered and weighted through the principalcomponent analysis. To reduce the dimensionality of the data set, four

principal components are obtained by projecting the multivariate datavectors on the space spanned by the eigenvectors. Using the availablefield liquefaction and non liquefaction data, the influence of various

parameters in evaluation model is quantified by golden section search.

The field data gathered from the Chi-Chi earthquake of Taiwan in 1999is also used to perform the verification of evaluation model. The resultsreveal that the proposed method is simple and effective.

KEY WORDS: Soil liquefaction; principal component analysis;golden section search

INTRODUCTION

Due to the liquefaction of soils, there were many ground failures with

the occurrence of earthquake. Lots of damages such as landslide,ground deformation, and sand boiling were observed during the Chi-Chiearthquake of Taiwan in 1999 and numerous earthquakes in the past.Concerning the engineering practice for the land development, theestablishment of appropriate evaluation method to estimate theliquefaction potential of soils could be an important task. Thus, the

assessment of liquefaction potential of soils would be the importanttopic in the last few decades.

Simplified method is one of the most often used for evaluation ofliquefaction potential of soils (Seed, 1979; Seed and Idriss, 1982;Tokimatsu and Yoshimi, 1983; Shibata and Teparaksa, 1988,Tokimatsu and Uchida, 1990; Robertson et al., 1992; Stark and Olson,1995; Olsen, 1997). Associated with engineering practical application,data obtained from the laboratory and field tests are adopted to develop

the simplified methods. Basically, the data treatment in existingsimplified methods can be divided into two groups: The first groupincludes the calculation of equivalent shear stress by means of themagnitude of earthquake and peak ground acceleration. The secondgroup relates the evaluation of liquefaction resistance of soils through

the field observations and the empirical relations. The factor of safetyfor the resistance of liquefaction can be obtained from the ratio of

resistance to the shear stress. Owing to the difficulty in obtaining a

testing undisturbed samples of cohesionless soil, many engineers preto adopt the methods of the second group. However, most of tmethods of the second group ignore some important influencing facto

Zhang (1998a) investigates the feasibility of using Fibonacci search

assess liquefaction potential from actual standard penetration test (SPfield data. The factors considered are: earthquake magnitude (M), S

blow count (N), depth of soil (Ds), depth of water (Dw) and epicentdistance (L). The most important factors have been identified earthquake magnitude and the SPT blow count. Zhang (1998b) alinvestigates the feasibility of using Fibonacci search to asse

liquefaction potential from actual cone penetration test (CPT) field daThe factors considered are: earthquake magnitude (M), peak grouacceleration (amax), CPT tip resistance (qc), soil mean grain size (D5and effective overburden pressure ( ). The most important factor h

been identified as the CPT tip resistance and its influence is much mothan that of earthquake magnitude. Moreover, the weight of soil megrain size is higher than that of earthquake magnitude. Since neithnormalization of the SPT blow count or CPT tip resistance n

calculation of the seismic shear stress ratio is required, the methods asimpler than the conventional methods. However, two different sets five factors are selected in each paper of Zhang and the correlationthem is unknown. Moreover, in the proposed methods the factors a

graded according to some standard without explanation and that tgrading standard for earthquake magnitude is different in those tw

papers may be confused.

Whenever concerning about the factors which any liquefactievaluation desired, Seed and Idriss (1982) indicated that three group

soil properties, environmental factors and earthquake characterist

should be taken into account. However, the relation is complicatbetween parameters selected from the above three categories constructed the evaluation model. In addition, parameters and thsignificance adopted in the existing evaluation methods of sliquefaction vary. Therefore, the evaluation results may be different t

high degree. In this paper, parameters affecting liquefaction aconsidered as many as possible to reduce the uncertainty. Based eight parameters that are widely perceived to be the major factors

liquefaction potential of soils, four principal components weidentified through principal component analysis as new parameters

Proceedings of The Thirteenth (2003) International Offshore and Polar Engineering Conference

Honolulu, Hawaii, USA, May 2530, 2003

Copyright 2003 by The International Society of Offshore and Polar Engineers

ISBN 1880653-605 (Set); ISSN 10986189 (Set)

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be used in evaluation model. Using the available field liquefaction andnon liquefaction data, the influence of various parameters in evaluationmodel is quantified by golden section search. The field data gathered

from the Chi-Chi earthquake of Taiwan in 1999 is also used to performthe verification of evaluation model. The results reveal that the

proposed method is simple and effective.

PRINCIPAL COMPONENT ANALYSIS

The parameters causing the liquefaction of soils generally have thenature of co-linear in statistic analysis. That is, there are correlations to

a high degree between those parameters. Principal component analysis(PCA) involves a mathematical procedure that transforms a number of(possibly) correlated variables into a (smaller) number of uncorrelated

variables called principal components. The first principal componentaccounts for as much of the variability in the data as possible, and eachsucceeding component accounts for as much of the remainingvariability as possible (Sharma 1996). Such a variable reduction canreduce the computational overhead of the subsequent processing stages.

The first column in Table1 represents existing evaluation methods asfollows: (1) Seed et al. 1985; (2) Japan Railway Association 1990; (3)TokimatsuYoshimi 1983; (4) China simplified method 1989; (5)Shibata & Teparaksa 1988; (6) Tokimatsu & Uchida 1990; (7) NewJapan Railway Association 1996; (8). Zhang 1998a; (9) Zhang 1998b.

Parameters as shown in Table 1 and their significance adopted in theexisting evaluation methods of soil liquefaction vary. Based on thosemethods and availability of the parameters, eight common parameters:

earthquake magnitude (M), peak ground acceleration (amax), CPT tipresistance (qc), soil fines content (FC), depth of soil (Ds), depth of water

(Dw), soil mean grain size (D50), and effective overburden pressure ( )are considered to produce a new set of components by multiplying each

of the original parameters by a weight, and adding the results. Theweights in the transformations are collectively known as theeigenvectors.

Table 1. Parameters adopted in the existing evaluation methods of soilliquefaction

Note: K, lateral earth pressure coefficient; V, shear wave velocity.

In this paper, 180 data sets (90 sets for model construction and 90 setsfor verification) presented by Stark and Olson (1995) have been used to

perform principal component analysis. The correlation matrix for

original variables is presented in Table 2. This is of considerableinterest in that it indicates the degree to which the original variableswere inter-correlated.

A set of variance derived from the eigenvalues and explained by eachnew variable is shown in table 3. Since there are eight variables, a totalof eight new variables can be extracted. Each new variable is a linearcombination of the original variables. The first new variable accountsfor 50.236% of the total variance of the original data. The second newvariable accounts for 18.017% of the total variance that has not been

accounted for by the first new variable. The third new variable accoufor 11.614% of the total variance that has not been accounted for by tfirst two new variables, and so on. The eight new variables a

uncorrelated. Since the relatively high cumulative variance 87.084%the data is accounted for by the first four new variables, we can use onthese four principal components in further analysis of the data insteadthe eight original variables.

Table 2. Correlation matrix for the selected parameters

M amax qc FC Ds Dw D50 M 1.000 -0.540 -0.055 -0.666 -0.397 -0.605 0.340 -0.56

amax -0.540 1.000 0.080 0.454 0.313 0.625 -0.202 0.50

qc -0.055 0.080 1.000 -0.097 0.223 0.228 0.245 0.27

FC -0.666 0.454 -0.097 1.000 0.399 0.577 -0.573 0.53

Ds -0.397 0.313 0.223 0.399 1.000 0.455 -0.336 0.9Dw -0.605 0.625 0.228 0.577 0.455 1.000 -0.163 0.76

D50 0.340 -0.202 0.245 -0.573 -0.336 -0.163 1.000 -0.29

-0.569 0.506 0.272 0.531 0.912 0.768 -0.294 1.00

Table 3. Variance explained by each component

Component Eigenvalue % of Variance Cumulative %

1 4.019 50.236 50.236

2 1.441 18.017 68.2533 0.929 11.614 79.8674 0.577 7.217 87.0845 0.455 5.692 92.776

6 0.348 4.345 97.1217 0.225 2.812 99.9348 5.300E-03 6.626E-02 100.000

The simple correlation between the original and the new variables, al

called loadings, give an indication of the extent to which the originvariables are influential or important in forming new variables. A tabof componentloadings of original variables is shown in Table 4.

Table 4. Table of componentloadings

Principal components1 2 3 4

M -0.715 -0.144 0.451 -0.112amax 0.856 0.161 -2.576E-02 -6.288E-02qc 5.735E-02 0.157 0.155 0.962FC 0.551 0.170 -0.705 -3.213E-02Ds 0.159 0.944 -0.210 9.976E-02

Dw 0.798 0.381 -9.166E-02 0.165D50 -1.761E-02 -0.199 0.890 0.186

0.479 0.840 -0.177 0.155

Table 5 shows the values of the new variables that are called principcomponents scores. The higher the loading the more influential tvariable is in forming the principal component scores and vice verFor example, high correlations of 0.302, 0.532 and 0.38 between tfirst principal component and magnitude of earthquake, peak grou

acceleration and water table depth, respectively, indicate that magnituof earthquake, peak ground acceleration and water table depth are veinfluential in forming the first principal component.

qc N FC Dw D50 Ds K L M amax V

1 2 3 4 5 6 7 8 9

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Table 5.Coefficient matrix of principal components scores

Principal components1 2 3 4

M -0.302 0.247 0.242 -0.173amax 0.532 -0.098 0.281 -0.228

qc -0.088 -0.147 -0.168 1.043FC 0.132 -0.198 -0.469 0.112Ds -0.246 0.711 0.065 -0.126Dw 0.380 0.024 0.173 0.009D50 0.270 0.013 0.727 -0.057

0.004 0.512 0.134 -0.079

GOLDEN SECTION SEARCH

Golden Section search is one of search methods for unconstrainedoptimization and is a direct search method which relies only onevaluating function at a sequence of points and comparing values toreach the optimal point. This simple and efficient method is based onthe fact that (Walsh 1975)

618034.0G

Glimr

1n

n

n=

+

(1)

where r is well-known Golden Ratio and Gn and Gn+1 are successiveterms of the Fibonacci sequence.

Let g(x) be a function of a continuous variable x defined on the closedinterval [0, Ln]. The points of evaluation in Golden Section search are

x1 = r2 Ln, x2 = r Ln. (2)

The Golden Section search to minimize the function g(x) on the interval[0, Ln] proceeds as follows:1. Evaluate g(x1) and g(x2), where x1 and x2 are given by equation [2].2. If g(x2) > g(x1), discard the interval (x2, Ln]. The remaining interval

is of length r Ln and x1 = r (r Ln) = r2 Ln is one of the points of

evaluation on it. The other evaluation point is x = r2

(r Ln) = r3

Ln.

On the other hand, if g(x1) > g(x2), discard the interval [0, x1). Theremaining interval is again of length of rLn and x2 is one of the

points of evaluation on it. The other point of evaluation is x = x1 + r(r Ln) = 2r

2 Ln.3. Repeat steps 1 and 2 for the successive remaining intervals of

lengths rLn, r2Ln, r

3Ln, , until the desired accuracy in optimalpoint is attained. If the minimum value of function with an error ofnot more than in optimal point is to be found, then n steps arerequired, where n is the smallest integer satisfying

Ln(0.618034)n .

The above procedure can be applied for multivariate case, if only thefunction is considered as a function of one variable while the othervariables are regarded as constants.

CONSTRUCTION OF ASSESSMENT MODEL OF

LIQUEFACTION POTENTIAL

Before conducting Golden Section search, the variables are graded tosimplify the calculation. The grading index P(*) of varied variables is

defined as 0, 1, 2 and 3 for different level of liquefaction from noliquefaction, low probability, moderate to high probability inliquefaction. Principal components F1, F2, F3 and F4 are graded

according to the standard shown in Table 6. For grade 0, liquefaction

wont happen. For grade 4, liquefaction must happen. In between, itdivided into three parts that are called grade 1 and 2 as shown in Fig1~4.

Table 6. Grading standard for values of principal components

Grade F1 F2 F3 F4

0 >2.42 >2.12 -0.74 ~ -0.95 > 0.991

0.46 ~ 2.42 0.72 ~ 2.12-0.74 ~ 1.24 &

-1.31 ~ -0.95-0.01 ~ 0.9

2-1.77 ~ 0.46 -1.77 ~ 0.72

1.24 ~ 2.64&-2.66 ~ -1.31 -1.06 ~ -0.0

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-1

-0.50

0.51

1.52

2.53

3.54

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0 50 100 150 200Liquefaction Nonliquefaction

Fig. 4Grading diagram for principal component 4

The index of liquefaction potential (ILP) is defined as follows:

ILP = C1 P(F1) + C2 P(F2) + C3 P(F3) + C4 P(F4), (3)

where coefficients C1, C2, C3, and C4 are defined on the set of datapoints. Let ILP

L,I

Land (I

L)site

be critical value of liquefaction, predictedliquefaction index and in situ liquefaction index, respectively. A binary

value of 1 is given for the sites that liquefied, i.e., when ILP ILPL, IL= 1. A value of 0 is given for the sites that did not liquefied, i.e., whenILP < ILPL, IL = 0. Then, the objective function g (i.e. the number of

prediction errors) can be established as follows:

( )=

=n

1iisiteLL

IIg (4)

where n is the total number of data points.

Using the Golden Section search procedure described before, theassessment model of liquefaction potential can be obtained as follows:

ILP = 60 P(F1) + 17 P(F2) + 9 P(F3) + 52 P(F4), (5)

and ILPL = 198. The minimum value of g is 28, where ILP of 6liquefaction site is less than 198, ILP of 22 non-liquefaction site isgreater than 198. The predicted results of 90 case records aresummarized in Figs 5~8. In total, there are just 28 errors, giving 84.44%success rate. Therefore, the proposed method is effective.

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-1

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0

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1

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2

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50 75 100 125 150 175 200 225 250 275 300 325 350

Index of liquefaction potential

Principalcomponent1

Liquefaction Nonliquefaction

Fig. 5 Relationship between principal component 1 and ILP

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-1

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0

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1

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2

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3

50 75 100 125 150 175 200 225 250 275 300 325 350 3


Principalcomponent2



-3

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-2

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-1

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0

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1

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2

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3

50 75 100 125 150 175 200 225 250


Principalcomponent3



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4

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50 75 100 125 150 175 200 225 250 275 300 325 350 3


Principalcomponent4



VERIFICATION OF THE ASSESSMENT MODEL

In this paper, another 90 sets of 180 data sets presented by Sta

and Olson have been used to verify the method and there are ju30 errors. The success rate in verification which is 83.33%is

little less than that in model construction. However, it indicatthat the proposed model can predict the potential of liquefacti

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up to 80% success rate and it is stable. In practice, the proposedmethod is simpler than the existing methods in data acquisition,

analysis, grading and field work.

The 54 sets of field data gathered from the Chi-Chi earthquake ofTaiwan in 1999 are also used to perform the verification of evaluationmodel and give 80% success rate. The following reasons may affect theaccuracy of assessment for the latter case:1. The maximum ground acceleration in data set may not be correct.2. The factors considered which are not specified in field test are

transformed from calculation.3. The grading is not fine enough.

Compared with conventional liquefaction prediction method, theproposed method has some advantages as follows:

1. The feasible assessment model is constructed by using adequatedata points and it is stable for different set of data points.

2. The data for analysis and calculation are easy to obtain. Moreover,the model is simple and can be applied in liquefaction assessment of

large area.3. The factors for model calculation result from principal component

analysis, so more correlation is considered and man-made error isreduced by standard operation procedures.

4. The proposed method can avoid theoretical assumptions andlaboratory experimental error.

5.Safety indicator associated with liquefaction can be easilyobtained by dividing ILPby ILPL.

CONCLUSIONS

Liquefaction is related with environmental factors, soil properties and

earthquake characteristics, so, it is very complicated. If parametersaffecting liquefaction are considered as many as possible, the analysis

procedure would be very difficult. Therefore a simple evaluation

method is required for practical use. This paper investigates theuncertainty of the existing methods, and employs principal componentanalysis to transform a number of correlated variables into a smallernumber of uncorrelated variables. Then Golden Section search isapplied to determine the coefficient of assessment model. Comparedwith the existing methods, the proposed method is stricter in factor

selection. However, it is still a simplified method since assessment canbe done by substituting the field data point into the model directly. Withits effectiveness and feasibility, the proposed method can be easilyapplied in practice.

ACKNOWLEDGEMENTS

Part of studies presented in this paper was conducted under ROC

National Science Council contract number NSC90-2211-E-309-008.

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A Practical Method in Evaluating Liquefaction Potential of Soils