Cn (SPT) y Potencial

Computers and Geotechnics 38 (2011) 393–406

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Computers and Geotechnics

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Comparison of SPT-N-based analysis methods in evaluation of liquefactionpotential during the 1999 Chi-chi earthquake in Taiwan

Muhsiung Chang a,⇑, Chih-ping Kuo b, Shih-hui Shau c, Ron-eeh Hsu d

a National Yunlin University of Science & Technology, Taiwan, ROCb National Taiwan University of Science & Technology, Taiwan, ROCc Da-Ho Construction Group, Taiwan, ROCd National Pei-Men Senior A & I Vocational School, Taiwan, ROC

a r t i c l e i n f o

Article history:Received 27 August 2010Received in revised form 15 January 2011Accepted 15 January 2011Available online 4 February 2011

Keywords:Liquefaction assessmentSPT-N-based methodSensitivity studyMethod comparisonChi-chi earthquake

0266-352X/$ - see front matter � 2011 Elsevier Ltd Adoi:10.1016/j.compgeo.2011.01.003

⇑ Corresponding author. Tel.: +886 5 534 2601; faxE-mail address: [email protected] (M. Cha

a b s t r a c t

SPT-N-based methods have been adopted for liquefaction assessment of soils during earthquakes for dec-ades. However, there has not been a consistent way of assessing the accuracy and applicability of thesemethods. The Chi-chi earthquake of 1999, which has been the most serious ground shaking in Taiwanwithin the century, caused extensive liquefactions in mid-west alluvial deposits of the island. This paperassesses the prediction accuracy of several SPT-N-based methods using liquefaction and non-liquefactionincidents observed during the earthquake. A sensitivity study on commonly adopted parameters showsthat the SPT blow count and peak ground acceleration are most sensitive in computing liquefactionpotential. By comparing the error in predicting liquefaction and non-liquefaction incidents, this studyconcludes that Tokimatsu and Yoshimi’s method is more accurate than the other methods. However,the differences between prediction errors of various methods are minimal, indicating all of the methodsexamined are applicable for the 1999 earthquake in Taiwan.

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1. General

Evaluation of liquefaction potential of a saturated sandy depositduring an earthquake requires knowledge of the intensity andduration of cyclic shear stresses of shaking as well as the cyclicshear resistance of deposit materials. Generally, cyclic shear stres-ses could be assessed through a simplified manner [1–4], or basedupon results of a site response analysis [5]. The cyclic shear resis-tance of soils could be evaluated in the laboratory, such as throughcyclic triaxial or cyclic simple shear testing, or based upon empir-ical relationships between liquefaction case histories and on-sitematerial parameters (e.g., SPT-N, CPT-qc, or Vs values) through var-ious field testing programs.

The majority of liquefaction assessment methods available todate are simplified-empirical; namely, the cyclic shear stress dueto shaking is estimated by a simplified procedure, and the cyclicresistance of soils is based on an empirical approach. A review ofthese methods can be found in a summary report by National Cen-ter for Earthquake Engineering Research (NCEER) of the UnitedStates [6] and the paper by Liam Finn [7]. The vast worldwide data-base, allows the SPT-N-based approach to become a dominantmethodology in the simplified-empirical category. Although thisapproach has been applied for many years, the ways of assessing

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the accuracy and applicability of the related methods have notreached a consensus.

Lee et al. [8] carried out a study on 21 simplified-empiricalmethods, using 100 liquefaction incidents due to earthquakes fromaround the world with a magnitude greater than 6.1. They foundthat the method by Seed et al. [4] is the most accurate in predictingliquefaction, followed by Tokimatsu and Yoshimi (T–Y) method [9]as the second. The new version of Japan Road Association (JRA)method [10] ranks tenth, and the original JRA method [11] appearsto be the least accurate in prediction.

Hwang and Chen [12] indicates that the original JRA method[11], which has been adopted in the seismic design codes for build-ings in Taiwan [13], overestimates liquefaction resistance of sandysoils with SPT-N values that are greater than 20. By examining re-sults of laboratory and field testing as well as liquefaction case his-tories, the authors recommend the T–Y method [9] to be adoptedfor the current codes in Taiwan [14] for optimal results.

Based on a study on liquefaction damages at Yuanlin Town dur-ing the 1999 Chi-chi Earthquake, Su and Wang [15] indicatesSeed’s method, as modified and suggested by the NCEER/NSFWorkshops [6], would provide most consistent predictions in com-parison to observations from the earthquake.

Hwang and Yang [16] conducted a systematic evaluation onSPT-N-based methods using 302 liquefaction and non-liquefactioncases from the 1999 Chi-chi Earthquake. The success rate and theat-least safety factor error (Fm) are adopted as indices for this

394 M. Chang et al. / Computers and Geotechnics 38 (2011) 393–406

evaluation. According to the results, Seed’s method [14] yields thehighest success rate and the lowest Fm (i.e., most accurate), whilethe T–Y method [9] and the new version of JRA method [10] arethe next accurate. On the other hand, the original JRA method[11] is the least accurate in prediction. The evaluation above isbased on a critical depth with a minimum corrected blow count(N1,60). The correlation between the ‘‘one-point’’ estimation andthe observed surface manifestations of liquefaction could thus bedoubtful.

The Chi-chi earthquake of 1999, with a magnitude (Mw) of 7.6,has been the most serious earthquake within the century whichcaused extensive liquefaction damages in the mid-west alluvialdeposits of Taiwan [30]. With more than 1500 borehole logs col-lected from the deposits in this study, the liquefaction and non-liq-uefaction incidents of the earthquake provide an excellentopportunity to examine the accuracy and applicability of variousSPT-N-based approaches for use in Taiwan.

The paper therefore aims to address this issue, by first conduct-ing a sensitivity study on the factors commonly adopted in N-basedmethods, then evaluating the prediction accuracy of the methodsby using liquefaction and non-liquefaction incidents of theearthquake.

However, the analysis methods for liquefaction assessment dis-cussed are primarily for design purposes, which involve variousdegrees of idealization and simplification. Accordingly, analysis re-sults of the methods might vary from observations in the field,which generally reflects the simplifications adopted in each ofthe methods. In order to provide a basis for selection of designmethods, this study compared the relative accuracy or degree ofconservatism of the methods in predicting the observations ofthe 1999 earthquake.

2. SPT-N-based liquefaction analysis approaches

Analysis methods considered in this study include: (1) Seed’smethod – modified and suggested by NCEER/NSF Workshop [6];(2) Tokimatsu and Yoshimi’s (T–Y) method [9]; (3) a new versionof Japan Road Association (JRA) method [10]; and (4) the ChineseCode for Seismic Design of Buildings (CSDB) method [17]. Eachmethod is briefly reviewed as follows.

Two analysis procedures have been recently proposed by Idrissand Boulanger [36] and Cetin et al. [37] to revise the original Seed’smethod [1,4,6]. However, these two procedures appear to disagreein regards to the rd (stress reduction factor, or model mass partic-ipation factor) and Kr (correction factor for effective overburdenpressure) relationships, which are adopted in the evaluation ofin situ CSR for the triggering correlations from back analysis of fieldperformance case histories [38]. Since more verification would beneeded for the new procedures, to settle the conflict in the pro-posed rd and Kr relationships, this paper would only evaluate theprediction accuracy of the commonly-adopted analysis proceduresin the industry today.

2.1. Seed’s method

This method was first proposed by Seed and Idriss in 1971, thenmodified by the authors and other colleagues in subsequent years[1–4]. In 1996 and 1998, this method was further synthesized andupdated in the workshops held by NCEER and NSF [6]. The updatedversion is used in the current study. An analysis flowchart of thismethod is shown in Fig. 1, indicating two separate procedures toestimate the cyclic stress ratio (CSR) due to shaking and the cyclicresistance ratio (CRR) of soils. The effects of earthquake magnitude(Mw), fines content (FC), and effective overburden pressure r0v

� �are

incorporated in the CRR estimation. The stress reduction factor (rd)

for the CSR estimation uses the original average relationship sug-gested by Seed and Idriss [1] and endorsed by NCEER/NSF work-shops [6]. The earthquake magnitude scaling factor (MSF), asshown in the figure, adopts the revised version by Idriss duringthe 1995 Seed’s Memorial Lecture, as suggested by NCEER/NSFworkshops as a lower bound for MSF values [6].

2.2. Tokimatsu and Yoshimi (T–Y) method

Tokimatsu and Yoshimi [9] proposed a similar approach toSeed’s method, by estimating CSR and CRR separately prior to thecomputation of the factor of safety against liquefaction (FL). How-ever, the T–Y method is different from Seed’s method in developingthe CRR relationships. The CRR boundary curves of soils are estab-lished based on the results of laboratory testing on high qualityundisturbed (frozen) samples from Niigata, Japan, where severeliquefactions had occurred in 1964 [18]. The cyclic strength of soilsin laboratory is determined based on a given cyclic strain at 15stress cycles, and the cyclic strain is correlated to the level of sever-ity in liquefaction damages observed during 70 case histories in Ja-pan and 20 cases in other parts of the world. The assessmentflowchart of T–Y method is presented in Fig. 2, showing the earth-quake magnitude (M) is accounted for in the CSR estimation. Asmentioned, the CRR curves take into account the level of severityof liquefaction damages, which is reflected by the coefficient, Cs.According to the authors, a Cs-range of 80–90 (i.e., a cyclic shearstrain c = 5.5–1.5%) is normally adopted. For extensive liquefaction,however, a Cs value of 75 (i.e., a cyclic shear strain c ; 10%) issuggested.

2.3. New JRA (NJRA) method

The original JRA method was promulgated in 1990 [11] by syn-thesizing studies of several parties [19–21]. The CRR curves of thismethod are based on the results of laboratory evaluation of in situsamples, where the cyclic resistance is determined with a numberof liquefaction stress cycle (Nl) of 20. After the Hyogoken-NambuEarthquake of Japan in 1995, this method has been considerablyrevised [10]. In view of the findings from the earthquake, a set ofscreening criteria has been added prior to the assessment proce-dure. The cyclic resistance of gravelly soils, as evidenced in theearthquake, is also considered based on limited laboratory resultsof frozen samples. Although the earthquake magnitude is not in-cluded in the CSR formulation, two types of earthquake are ac-counted for in assessing the cyclic resistance of soils. Type Iquakes occurs along the subduction zone boundaries, and Type IIquakes occurs under the intraplate of continents. Fig. 3 indicatesthe analysis flowchart of the revised method. It is noted that themaximum values of the CSR and CRR are computed in the process,unlike the majority of SPT-N-based approaches, where only aver-age values are employed.

2.4. Chinese building code (CSDB) method

The Chinese liquefaction assessment procedure was establishedin the Code for Seismic Design of Buildings (CSDB) of China in 1974(Doc. No. TJ11-74). This procedure adopts a critical SPT N-value,Ncr, which is a function of seismic intensity, groundwater depth,and the depth of interest, indicating that a lower limit is requiredfor the soil to prevent liquefaction. After the Haichen (1975) andTongshan (1976) earthquakes, this assessment procedure has beenmodified by considering the attenuation effect of ground shaking,as shown in the building code of 1989 (Doc. No. GBJ11-89). In2001, the building code (Doc. No. GB50011-2001 [17]) was slightlyupdated by adjusting the assessment procedure and adopting de-sign earthquake groups to account for both the characteristic

Horizontal peak

ground acceleration,

amax

EQ magnitude,

M

SPT N-value,

N

Effective overburden

pressure, o’( kg/cm2)

Fines content,

FC (%)

⎟⎠⎞⎜

⎝⎛

+=

727.0'

7.172,1

ERNN

oσ ⎪⎩

⎪⎨⎧

+−=Δ

41.0

5

0

FC

FCN f

)10(

)105(

)5(

FC

FC

FC

≤<≤

<

Stress reduction factor

zrd 015.01−=

Equiv. average cyclic stress ratio, CSR

dv

v

Lo

rg

aM

')1(1.0

'max

σσ

στ −=⎟⎟⎠

⎞⎜⎜⎝

⎛

Cyclic resistance ratio, CRR

a=0.45, Cr=0.57, n=14, Cs=80~90,

Cs=75 for extensive liquefaction situation

⎥⎥⎦

⎤

⎢⎢⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛+=⎟⎟⎠

⎞⎜⎜⎝

⎛n

s

aar

Ro C

NNaC

16

100

16

'στ

Factor of safety against liquefaction

LoRoL CSR

CRRF ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛==

'/

' στ

στ

fa NNN Δ+= 72,1

Fig. 2. Analysis flow chart of 1983 T–Y method.

Horizontal peak

ground acceleration,

amax

EQ magnitude,

Mw

SPT N-value,

N

Effective overburden

pressure, v’( kPa)

Fines content,

FC (%)

Equiv. average cyclic stress ratio

dv

v rg

aCSR

'65.0 max

σσ=

Cyclic resistance ratio, CRR7.5

x=N1,60,FC, a=0.048, b=-0.1248, c=-4.721E-3,

d=9.578E-3, e=6.136E-4, f=-3.285E-4,

g=-1.673E-5, h=3.714E-6

432

32

5.7 1 hxfxdxbx

gxexcxaCRR

+++++++=

Factor of safety against liquefaction

LoRoL CSR

CRRF ⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛==

'/

' στ

στ

60,1,60,1 NN FC βα +=

Stress reduction factor, rd

zrd 00765.01−=zrd 0267.0174.1 −=

zrd 008.0744.0 −=

mz 15.9≤mz 2315.9 ≤<

mz 3023 ≤<

⎟⎠⎞⎜

⎝⎛=

6060

ERNN

'100

vNC

σ=

6060,1 NCN N= ⎪⎩

⎪⎨⎧

−=0.5

)]/190(76.1exp[

02FCα

)35(

)355(

)5(

FC

FC

FC

≤<<

≤

⎪⎩

⎪⎨⎧

+=2.1

)1000/(99.0

0.15.1FCβ

)35(

)355(

)5(

FC

FC

FC

≤<<

≤

56.2

24.210

wMMSF =

Cyclic resistance ratio

5.7CRRMSFCRR ×=

Fig. 1. Analysis flow chart of 2001 Seed’s method.

M. Chang et al. / Computers and Geotechnics 38 (2011) 393–406 395

period and the ground motion acceleration in determining Ncr.Fig. 4 shows the analysis flowchart of the updated version. The Chi-nese building code method is significantly different from the afore-

mentioned methods in its analysis philosophy. The seismicintensity and the earthquake group are exclusively defined and ap-plied for use in China only.

Screening criteria for further assessment(1) Groundwater depth 10m, with saturated sand located 20m below ground surface; (2) Fines contents (FC) 35%, or FC>35% and PI 15%; and (3) Effective grain size D50 10mm and D10 1mm.

Design horizontal

EQ coefficient, khc

SPT N-value,

N

Effective overburden

pressure, o’ ( kg/cm2)

Fines content,

FC (%)

Mean grain size,

D50 (mm)

⎟⎠⎞⎜

⎝⎛

+=

727.0'

7.172,1

ERNN

oσ⎪⎩

⎪⎨⎧

−+=

1)20/(

50/)40(

1

1

FC

FCc)60(

)6010(

)100(

FC

FC

FC

≤<≤<≤

⎩⎨⎧

−=

18/)10(

02 FC

c)10(

)100(

FC

FC

≤<≤Sand:

Gravel: 272,11 cNcNa +=

[] )2/(log36.01 501072,1 DNNa −=

⎪⎪⎩

⎪⎪⎨

⎧

−×+=

− 5.46 )14(106.17.1

0882.0

7.10882.0

aa

a

L

NN

N

R

)14(

)14(

a

a

N

N

≤

<

EQ Type I:

EQ Type II:

0.1=wc

⎪⎩

⎪⎨⎧

+=0.2

67.03.3

0.1

Lw Rc

)4.0(

)4.01.0(

)1.0(

L

L

L

R

R

R

≤<≤

<

khc replaced by

g

amax

Stress reduction factor

zrd 015.01−=

Equiv. max. cyclic stress ratio

'v

vhdkrLCSR

σσ==

Cyclic resistance ratio

LwRcRCRR ==

Factor of safety against liquefaction

L

R

CSR

CRRFL ==

Fig. 3. Analysis flow chart of 1996 JRA method.

396 M. Chang et al. / Computers and Geotechnics 38 (2011) 393–406

3. Liquefaction potential assessment by Iwasaki’s depth-weighted technique

Liquefaction analysis calculates factors of safety against lique-faction at separate depths of a borehole. To address the severityof liquefaction for the entire borehole in the ground, the computedfactors of safety and the associated depth intervals need to be con-sidered. Several techniques on assessing liquefaction potential forthe entire borehole depth have been proposed [10,17,20,21]. Thefollowing parametric study utilizes Iwasaki’s depth-weighted aver-age technique [21], and the associated liquefaction potential index(PL) is computed for the sensitivity study among various factors.

4. Parametric study of liquefaction analysis methods

4.1. Analysis conditions

The sensitivities of computation of the PL ratio due to variousanalysis parameters are determined for the liquefaction assess-ment methods considered. As shown in Table 1, a set of commonparameters adopted in the SPT-N-based assessment methods are

examined, which includes: depth to groundwater level (GWT),maximum ground acceleration (amax), SPT blow count (N), finescontent (FC), stress reduction coefficient (rd), earthquake magni-tude (M), overburden pressure correction factor (CN), and hammerenergy ratio (ER).

As a basis for comparison, the following values of parametersare assumed: GWT = 1.5 m, amax = 0.25 g, FC = 15%, M = 7.5,ER = 73.5%, as well as a unit weight cm = csat = 21.1 kN/m3 and aneffective grain size D50 = 1.5 mm. Three types of SPT N-profile ofsoil deposit are postulated, namely: constant distribution, line-arly-increasing distribution, and linearly-decreasing distributionswith depth, all with an average blow count of 10. In addition, TypeI earthquake is assumed in the NJRA method. As for the CSDBmethod, the following values are adopted: clay fraction CF = 10%,seismic intensity I = 8, and earthquake groups 1–3.

Since SPT blow count would be affected by the overburdenpressure at the depth of testing, the SPT blow count is adjustedto a common (effective) vertical stress by a correction factor CN.Several CN–r0o relationships have been proposed, as shown inFig. 5, which could be broadly represented by CN ¼ 1� k log r0o,with k value ranging from 0.7 to 1.4. A higher k value indicates agreater gradient in the CN–r0o relationship; implying more of an

Design earthquake

group Seismic intensity

(I, amax)

SPT N-

basic value (N0)

Groundwater

depth (dw)

Soil depth

(ds)

Clay fraction

(CF, %)

SPT N-

value (N)

SPT N-critical value (Ncr)

Ncr = N0 [0.9 + 0.1(ds-dw)] (3/CF)0.5, for ds 15m

Ncr = N0 [2.4 - 0.1ds] (3/CF)0.5, for 15m ds 20m

Factor of safety against liquefaction

crL N

N

CSR

CRRF ==

Screening criteria for further assessment for sands or silts (except loess)(1) Geologic age younger than Pleistocene Epoch; (2) Clay fraction (CF) less than 10, 13, and 16 (%), for seismic intensity (I) less than

7, 8, and 9, respectively; (3) For overlaying non-liquefaction soil thickness (du) and groundwater depth (dw),

satisfying: du (d0+db-2m), dw (d0+db-3m), or (du+dw) (1.5d0+2db-4.5m), where db=building embedment, d0=liquefaction characteristic depth.

Fig. 4. Analysis flow chart of 2001 CSDB method.

Table 1Parameters adopted in the liquefaction analysis methods.

Analysisparameter

Analysis methods

Seeda T–Yb NJRAc CSDBd

GWT Yes Yes Yes Yesamax Yes Yes Yes Yese

SPT-N Yes Yes Yes YesFC Yes Yes Yes n/af

rd For z 5 9.15 m, rd ¼ 1� 0:015z rd ¼ 1� 0:015z n/ard ¼ 1� 0:00765zFor9.15 m < z 5 23 m,rd ¼ 1:174� 0:0267z

M 102:24

M2:56Yes n/ag n/ag

CNffiffiffiffiffiPar00

q 1:7r00þ0:7

1:7r00þ0:7

n/a h

ER (%) 60 72 72 60Cs n/a 80–90 Use 75

for extensiveliquefaction

n/a n/a

Note: n/a = not applicable.a NCEER modified Seed’s method (Youd et al., 2001).b Tokimatsu and Yoshimi’s method (1983).c The new version of Japan Roadway Association’s method (JRA, 1996).d Code for Seismic Design of Buildings, China (CD/PROC 2001).e Based on the relationship between the seismic intensity (I) and the peak ground

acceleration (amax).f Considered by the content of clay particles (<5 lm).g Considered by the type of earthquakes.h Considered the soil thickness (ds) and groundwater depth (dw) in computation

of the critical SPT-N value, Ncr.

oN 'log1C σλ−=

0.0

1.0

2.0

3.0

4.0

5.0

0.0 0.4 0.8 1.2 1.6

Effe

ctiv

e O

verb

urde

n Pr

essu

re (k

g/cm

2 )

Peck et.al. (1974)

Seed (1976)

Tokimatsu et.al. (1983)

Liao & Whitman (1986)

Seed et.al. (1979) Dr = 40~60%

Seed et.al. (1979) Dr = 60~80%

Lambda = 1.4

Lambda = 0.7

Fig. 5. Distribution of overburden pressure correction factor.

M. Chang et al. / Computers and Geotechnics 38 (2011) 393–406 397

amplification of the SPT N-value at a shallower depth and more of areduction at a greater depth. The above expression for CN is an as-sumed simplified format intended for the parametric study of sen-sitivity of CN on the computed liquefaction. In the later part of thispaper, the respective expression of CN for each of the analysismethods is adopted for the liquefaction assessment of the studyarea during the 1999 earthquake.

Stress reduction factor (or model mass participation factor), rd,is adopted to consider the soil profile as a deformable body in esti-mating CSR. The relationship of the stress reduction factor and thedepth has been developed by several parties, but the results arescattered significantly [1,21,22,36–38]. This study assumes ageneral expression of the stress reduction factor as rd = 1 �mz.The slope m is assumed to vary from 0.005 to 0.030, as shown inFig. 6, covering approximately the ranges Seed and Idriss [1] andother researchers [1,21,22,36–38] had proposed. A higher m-valueindicates a greater gradient in the stress reduction curve; implyinga greater reduction in CSR with depth. Similarly, the aboveexpression for rd is an assumed simplified form for the purposesof parametric study of the sensitivity of rd on the computed lique-faction. In the later part of this paper, however, the specific expres-sion of rd for each of the liquefaction analysis methods is used forthe liquefaction assessment of the study area during the 1999earthquake.

0

10

20

30

40

50

60

70

80

90

100

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Dep

th, z

(ft)

Seed & Idiss (lower limit)

Seed & Idiss (upper limit)

m = 0.005

m = 0.010

Iwasaki et al. (m = 0.015)

m = 0.020

m = 0.025

m = 0.030

)/3048.0(1 ftmeterzmd ⋅⋅−=γ

Fig. 6. Distribution of stress reduction factor.

398 M. Chang et al. / Computers and Geotechnics 38 (2011) 393–406

4.2. Findings of parametric study

Results of the sensitivity study are summarized in Table 2. Forall the parameters examined, SPT blow count (N) and peak groundacceleration (amax) appear to be most sensitive in the computedliquefaction potential. Hammer energy ratio (ER), earthquake mag-nitude (M), fines content (FC), and groundwater depth (GWT) arealso fairly sensitive. Stress reduction factor (rd) and overburdenpressure correction factor (CN) are the least sensitive of the param-eters studied.

The Chinese building code (CSDB) method shows significantsensitivity in the computed liquefaction potential due to SPT blowcount (N) and hammer energy ratio (ER). In comparison, otheranalysis methods in this study are not as sensitive; implying theprediction accuracy of the CSDB method relies greatly upon thesetwo parameters.

With exception to the CSDB method, Seed’s method appearsmost sensitive in the computed liquefaction potential due to SPTblow count (N), hammer energy ratio (ER), and earthquake magni-tude (M); while NJRA method is least sensitive.

It is important to note the effect of the groundwater level on thecomputed liquefaction potential. An increase in the groundwaterlevel would decrease the effective stress of soil, which would, inturn, enhance the computed seismic force (i.e., CSR) at the depthof interest. On the other hand, as a result of the increase in ground-water level, a decrease in the effective stress of soil would amplifythe overburden pressure correction factor (CN) in order to accom-modate the underestimated SPT N-value due to rising groundwa-

Table 2Results of relative sensitivity study.

Parameter Parameter value Variations in computed liquefactionpotential index ratio, DPL/PL fordifferent liquefaction assessmentmethods

Range Reference Seed(%)

T–Y(%)

NJRA(%)

CSDB(%)

SPT-N 3–15 10 ±153 ±91 ±87 ±192–325ER 50–100% 73.5% ±76 ±50 ±40 ±91–129k, for CN 0.7–1.4 1.0 ±5 ±3 ±1 –FC 0–40% 15% ±55 ±56 ±32 –GWT 0.5–5 m 1.5 m ±50 ±57 ±46 ±33–39amax 0.15–0.35 g 0.25 g ±98 ±102 ±86 ±40–49m, for rd 0.005–0.030 0.015 ±28 ±24 ±17 –M 6.0–8.0 7.5 ±72 ±45 – –Cs 75–95 85 – ±53 – –

ter, and causing the cyclic resistance of soil (CRR) to remain thesame. As pointed out by Youd et al. [6], the effective stress adoptedfor CN should be the overburden pressure at the time of drilling andtesting, implying that the corrected N-value (N1) and the cyclicresistance (CRR) of soil should be determined at the time of testingand remains constant afterwards, even if the groundwater levelmight be fluctuating over time.

An example of the misinterpretation of the CRR and the associ-ated factor of safety against liquefaction (FL) is indicated by Linet al. [23] and shown in Fig. 7a. In the example, an increase ingroundwater level causes amplification of CN factor and increasesN1 and CRR of soil, resulting in an adverse increase of FL at shal-lower depths. If N1 is decided at the time of testing and remainsconstant afterwards (i.e., N1 irrelevant to groundwater fluctuation),then the increase in groundwater level would only enhance CSR,and therefore decrease the FL, as shown in Fig. 7b.

5. The 1999 Chi-chi earthquake

Liquefaction and non-liquefaction incidents of the 1999 earth-quake are used to compare the prediction accuracy by variousSPT-N-based methods. Since the CSDB method adopts a signifi-cantly different analysis philosophy, this method is excluded fromthe comparison. Accordingly, only Seed’s method [6], the T–Ymethod [9], and the NJRA method [10] are considered in the fol-lowing study.

5.1. The earthquake and liquefaction damages

On September 21, 1999, a severe earthquake, with a magnitude(Mw) of 7.6, hit central Taiwan, resulting in more than 2300 peoplekilled, 8700 people wounded, and numerous structures damaged[24]. The epicenter of the quake is in Chi-chi Town, Nantou County,at a depth of about 7 km along the Chelungpu Fault, as shown inFig. 8. The quake is triggered by a rupture of the thrust fault (fromeast to west) with a length of about 85 km. Based on the definitionby Bolt [32], the duration of the main shock is approximately 40 s,which is considered long enough to contribute to the extensive liq-uefaction incidents during the earthquake. Fig. 9 [33] indicates anexample of the acceleration-time histories recorded at YuanlinTown, which had the most wide-spread liquefaction area duringthe earthquake. Due to the nature and location of the faulting,the east–west component of the shaking is the greatest in alldirections.

(a) N1 Relevant to GWT Fluctuation0123456789

1011121314151617181920

FL

Dep

th (m

)

GWT=0,N=15

GWT=1,N=15

GWT=2,N=15

GWT=3,N=15

GWT=4,N=15

GWT=5,N=15

GWT=0,N=20

GWT=1,N=20

GWT=2,N=20

GWT=3,N=20

GWT=4,N=20

GWT=5,N=20

(b) N1 Irrelevant to GWT Fluctuation0123456789

1011121314151617181920

0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0

FL

Dep

th (m

)

GWT=0,N=15

GWT=1,N=15

GWT=2,N=15

GWT=3,N=15

GWT=4,N=15

GWT=5,N=15

GWT=0,N=20

GWT=1,N=20

GWT=2,N=20

GWT=3,N=20

GWT=4,N=20

GWT=5,N=20

Fig. 7. Potential flaws in FL computation due to erroneous N1 estimation.

500 100Km

Taichung

Changhua

Yunlin

Chiai

Miaoli

Liquefaction Site

Chuoswei River

(downstream)

ChelungpuFault

StudyArea

Nantou

Epicenter

Fig. 8. Locations of liquefaction sites and the causative fault.

M. Chang et al. / Computers and Geotechnics 38 (2011) 393–406 399

Most liquefaction analysis methods employ the earthquakemagnitude as an index to account for the number of stress cycles,or the duration of shaking. To verify the representative stress cyclesof the 1999 earthquake, a weighting procedure proposed by Seedet al. [34] and described by Lee and Chan [35] was conducted. Theresults indicate the equivalent number of stress cycles was approx-imately 21 for the magnitude 7.6 earthquake. Compared with therelationship proposed by Seed [2], the estimated number of stresscycles falls within the range of one-standard deviation (i.e., 8–25),with an average of 16 cycles. Accordingly, the assumption of thenumber of stress cycles adopted in most of liquefaction analysismethods is generally valid for the case of the 1999 earthquake.

Locations of the liquefaction sites are indicated in Fig. 8, withthe most serious damage at Yuanlin Town and nearby townships

of Changhua County, which is located at the northern part of theChuoswei River alluvial fan. The study area encompasses the entirealluvial fan, where most of the shallower sediments consist of sat-urated loose sands or silts (SM or ML) interbedded with clayey lay-ers of low plasticity (CL) [29,39].

Thirty-four strong motion stations have been installed in thestudy area by the Central Weather Bureau of Taiwan prior to theearthquake [24,30], with their locations shown in Fig. 10. The re-corded peak ground accelerations (PGAs; E–W direction) of theearthquake are adopted in the current study. Due to a fairly evendistribution of the stations across the study area, the PGAs at eachof the borehole locations are considered appropriate and deter-mined by interpolation based on the 34 recorded data for liquefac-tion analysis of the 1999 earthquake. Fig. 10 shows the PGAcontours adopted in this study.

5.2. Borehole data and analysis conditions

A total of 1571 borehole logs have been collected for this study.Some of the logs are neglected due to the lack of essential informa-tion or reliability of results. The remaining 1084 borehole logs,with locations shown in Fig. 11, are deemed effective and adoptedin the analyses. According to different screening criteria, the actualborehole numbers adopted in the assessment methods are slightlyvaried, as shown in Table 3.

The adopted boreholes are assigned as either liquefaction ornon-liquefaction boreholes prior to the subsequent analyses. Asin usual practices, boreholes with observed surface manifestationsof liquefaction (e.g., sand boils, lateral spreads, and tilted, settled orfloated structures, etc.) in the vicinity of the boreholes during the1999 earthquake are assigned as liquefaction boreholes, whilethose without surface manifestations are assigned as non-liquefac-tion boreholes. It is noted that liquefaction often occurs at depthwhich may or may not extend up to the ground surface due to sev-eral reasons. In accordance, the observed surface manifestationsare indicative of soil liquefaction, while no surface manifestationsare implying either non-liquefaction or liquefaction sites. For in-stance, Youd and Carter [40] indicate no liquefaction phenomenonwas observed in the vicinity of the instrument sites at Treasure Is-

Fig. 9. Acceleration-time histories recorded at Yuanlin Station (TCU120), ChanghuaCounty during the 1999 earthquake [33].

160000 170000 180000 190000 200000 210000 2200002600000

2610000

2620000

2630000

2640000

2650000

2660000

2670000

2680000

0 10000 20000 30000 40000 (m)

: PGA contours (gal) : Strong motion stations

N

S

EW

Fig. 10. Recorded peak ground acceleration (PGA; amax,EW) contours and 34 strongmotion stations in the study area during the 1999 earthquake.

160000 170000 180000 190000 200000 210000 2200002600000

2610000

2620000

2630000

2640000

2650000

2660000

2670000

N

S

EW

20 Kilometers100

Fig. 11. Locations of analysis boreholes in the study area.

400 M. Chang et al. / Computers and Geotechnics 38 (2011) 393–406

land and Alameda Navy Air Station, California, during the 1989Loma Prieta Earthquake. However, a sudden shift of frequency con-tents to longer periods and a decrease in acceleration amplitudesafter some time period in the actual motions, as compared withthose in the predicted motions (without soil softening), clearlyindicate that soil liquefactions had occurred at the sites. Since nodetailed ground response analysis has been conducted for boreholecategory classification purposes in this study, some falsely-as-signed non-liquefaction boreholes may exist. The potential impactof the falsely-assigned borehole categories is further discussed inSection 6.4.3 of this paper.

An earthquake with a magnitude of 7.6 is adopted in the anal-yses by Seed’s and T–Y’s methods. For the NJRA method, however,a Type I Earthquake is assumed in order to be comparable to the1999 earthquake condition. In consideration of the level of lique-faction damages, this study adopts Cs = 83 for the T–Y method,which is consistent with an earthquake magnitude of 7.6, per sug-gestions by Wu [25]. Based on limited on-site data [23,26,39], anenergy ratio of 73.5% is assumed for the current study, which isconsistent with the value adopted by NCREE/Taiwan for the SPThammers used in the island. In analysis, the unit weight of soil ateach of the material strata is based on the borehole data obtainedat the time of drilling.

Due to lack of real time monitoring data, this study assumes thegroundwater levels recorded in the borehole logs to form an aver-age groundwater datum for the area. To account for seasonal fluc-tuations [27] and the timing of the earthquake, an additional 3 m isassumed on top of the average datum as the groundwater levelduring the 1999 earthquake. The datum and its additional 3 massumption is limited by the condition that the groundwater levelshould be at least 1 m below the ground surface.

6. Comparison of accuracy in predicting liquefaction and non-liquefaction of soils

The accuracy of liquefaction analysis could be evaluated in dif-ferent ways. The factor of safety against liquefaction (FL) could becomputed at any given (or critical) depth and compared with thesurface manifestations observed during an earthquake [16,28].However, the use of a single depth to compute the safety factor

Table 3Number of boreholes for analysis.

Case Numbers of boreholes

Collected Analyzed

Seed’smethod

T–Y’smethod

NJRA’smethod

Liquefaction 69 66 67 67Non-liquefaction 1015 920 927 930Sum 1084 986 994 997

M. Chang et al. / Computers and Geotechnics 38 (2011) 393–406 401

would normally be very difficult to relate to surface observations.An improved method would be to use a section or an entire depthinterval to compute a depth-weighted average safety factor, or liq-uefaction potential index (PL), as suggested by Iwasaki et al. [21].However, the accuracy in liquefaction prediction would be affectedby the depth-weighting function assumed.

Another method of comparison is to examine the details ofcomputation for CRR and CSR, which would provide a picture onsituations where the values are relatively overestimated or under-estimated among the various SPT-N-based methods.

6.1. Basis of comparison

Although SPT-N-based methods generally include computationsof CRR and CSR, the analysis philosophy and computation details ofthe methods are slightly different. As stated previously, Seed’smethod considers the effect of the earthquake magnitude as an in-verse modification in the cyclic strength of soil (Fig. 1). Conversely,the T–Y method accounts for the earthquake magnitude directly inthe cyclic stress formulation (Fig. 2).

To form a basis of comparison, this study adopts the analysisframework by Seed [1,6] and converts the CRR and CSR estimationsof the other two methods into the same platform; i.e., CRRave,M andCSRave,M=7.5, where CRRave,M is the adjusted average cyclic resistanceratio of the ground for an earthquake magnitude other than 7.5,and CSRave,M=7.5 is the average cyclic stress ratio of an earthquakeshaking with a magnitude of 7.5. For an earthquake magnitudeother than 7.5, the original CRR7.5 prediction in all of the methods

CR

R

CR

R

FC =

0

0.1

0.2

0.3

0.4

0.5

0

0.1

0.2

0.3

0.4

0.5

0 10 20(N1(N1)60

FC = 5%

0 10 20 30 40 50

Seed´s method

T & Y´s method

NJRA´s method

Fig. 12. CRRav–N1,60 curves for liquefaction analysis of the 1999

is corrected based on the relation: CRRM = MSF � CRR7.5, where MSFis a magnitude scaling factor suggested by Idriss [6]. For CSR pre-dictions, however, the values are adjusted corresponding to apre-assumed earthquake magnitude of 7.5. In the NJRA method,both CRR and CSR refer to peak values, and a coefficient of 0.65,which conforms to the coefficient used in the Seed’s method, is fur-ther applied to the CRR and CSR in the above procedures.

6.2. Comparisons of CRR predictions

Under the same basis of comparison, results of the CRR predic-tions by the three methods for the soils in the study area during the1999 earthquake (M = 7.6) are shown in Fig. 12. The CRR curves areplotted for a normalized blow count, N1,60, with different fines con-tents (FC). As shown in the figure, predictions in CRR by the threemethods vary in different ranges of N1,60 and FC. To facilitate com-parison, Table 4 is prepared with corresponding orders in CRRshown in each of the ranges of N1,60 and FC.

As indicated in the table, Seed’s method normally provides thehighest CRR predictions at higher blow counts (e.g., N1,60 > 10) andgives the lowest CRR values at lower blow counts (e.g., N1,60 < 10),as shown by the bold letter ‘‘S’’ in the table. The T–Y method ap-pears to compute the highest CRR for FC = 15% and N1,60 < 10,and the lowest CRR for FC ; 35% and N1,60 = 10, as shown by thebold letter ‘‘T’’ in the table. Except for a blow count of less thanor equal to 2, the NJRA method would result in the greatest CRRprediction for FC < 5% and N1,60 < 15, and the smallest CRR predic-tion for FC ; 15% and N1,60 > 10, as shown by the bold letter ‘‘N’’in the table. A higher CRR would tend to provide a higher FL, hencea lower PL estimation, and vice versa.

6.3. Comparison of CSR predictions

Results of the CSR predictions by the three methods for the 1999earthquake are shown in Table 5. Generally, cyclic shear stressesare higher at liquefaction sites than those at non-liquefaction sites.The cyclic stress ratio, however, appears to be slightly increasingwith depth, at both liquefaction and non-liquefaction sites. Thecomputed CSRs are similar for the three methods considered. Dueto a more conservative assumption on the stress reduction

(N1)60

CR

R

FC = 35%

0 10 20 30 40 50

Seed´s method

T & Y´s method

NJRA´s method

15%

0

0.1

0.2

0.3

0.4

0.5

30 40 50

Seed´s method

T & Y´s method

NJRA´s method

)60

earthquake (CRR converted per Seed’s analysis framework).

Table 4Comparison of CRRs by various analysis methods for the 1999 earthquake (CRR converted per Seed’s analysis framework).

FC (%) SPT-N1,60

0–2 2–8 8–10 10–12 12–15 15–24 >24

(a) Emphasis on the ‘‘highest’’ cyclic resistance ratio (CRRav)55 S > T � N N > T > S N > T > S N > T > S N > S > T S > N > T S > T > N�15 T > S > N T > N > S T > N > S T > S > N S > T > N S > T > N S � T > N�35 T > N � S T > N � S S > T � N S > T � N S > T � N S > N > T N > S > TRemark: The bold symbol (S, T, N) indicates the method with the ‘‘highest’’ computed CRR value.

(b) Emphasis on the ‘‘lowest’’ cyclic resistance ratio (CRRav)55 S > T � N N > T > S N > T > S N > T > S N > S > T S > N > T S > T > N�15 T > S > N T > N > S T > N > S T > S > N S > T > N S > T > N S � T > N�35 T > N � S T > N � S S > T � N S > T � N S > T � N S > N > T N > S > TRemark: The bold symbol (S, T, N) indicates the method with the ‘‘lowest’’ computed CRR value.

Note: S = NCEER modified Seed’s method (Youd et al., 2001).T = Tokimatsu and Yoshimi’s method (1983).N = The new version of Japan Roadway Association’s method (JRA, 1996).

Table 5Comparison of CSRs by various analysis methods for the 1999 earthquake (CSR converted per Seed’s analysis framework).

Depth (m) CSRSeed CSRT–Ya CSRNJRA,max CSRNJRA,ave

b

Liquefactionboreholes

Non-liquefactionboreholes

Liquefactionboreholes

Non-liquefactionboreholes

Liquefactionboreholes

Non-liquefactionboreholes

Liquefactionboreholes

Non-liquefactionboreholes

0–3.75 m 0.14–0.26 0.02–0.40 0.13–0.25 0.02–0.40 0.20–0.39 0.04–0.48 0.13–0.26 0.03–0.31Average 0.19 0.09 0.17 0.09 0.28 0.14 0.18 0.093.75–6.75 m 0.16–0.24 0.03–0.42 0.16–0.22 0.02–0.40 0.23–0.35 0.04–0.50 0.16–0.23 0.03–0.33Average 0.21 0.11 0.20 0.10 0.31 0.16 0.20 0.106.75–9.75 m 0.20–0.24 0.04–0.37 0.19–0.23 0.03–0.35 0.29–0.35 0.05–0.50 0.19–0.23 0.03–0.33Average 0.23 0.12 0.21 0.11 0.32 0.17 0.21 0.11>9.75 m 0.15–0.24 0.03–0.42 0.16–0.23 0.03–0.42 0.25–0.35 0.05–0.50 0.16–0.23 0.03–0.33Average 0.20 0.10 0.20 0.10 0.31 0.17 0.20 0.11

a Assume M = 7.5.b Assume CSRNJRA,ave = 0.1(M � 1)CSR NJRA,max = 0.1(7.5 � 1)CSR NJRA,max = 0.65CSR NJRA,max.

402 M. Chang et al. / Computers and Geotechnics 38 (2011) 393–406

coefficient (rd), however, T–Y and NJRA methods provide some-what smaller predictions than the Seed’s method.

6.4. Comparison of liquefaction and non-liquefaction predictions

6.4.1. Predictions vs. observationsThe comparisons stated previously provide a general view on

the situations where CRR or CSR might be overestimated or under-estimated for the N-based methods considered. However, the accu-racy of predictions by the various methods has not yet beenverified.

The assessment methods compute CRR and CSR, and hence thefactor of safety against liquefaction, at any given depth of a bore-hole. Without knowing the exact location of liquefaction, this studypostulates four potential depth intervals of liquefaction (i.e.,0–3.75 m, 3.75–6.75 m, 6.75–9.75 m, and >9.75 m), and computesthe CRR and CSR accordingly for the depth points within theintervals. Results of the analyses for a certain depth interval aresubsequently compared with observations from the earthquake.Fig. 13 shows typical results of the analyses for a depth interval be-tween 3.75 m and 6.75 m.

Several post-quake explorations have been carried out at Yuan-lin Town, and the results reveal a potentially liquefiable layer ofsilty fine to medium sand, with a thickness of about 3 m, locatedwithin the top 9 m of the profile [29,39]. Tests on erupted andcored samples also indicate that the liquefiable soils contain signif-icant amounts of non-plastic fines (FC = 10–45%) [30,39].

In view of the high fines content of liquefied soils, the compar-ison of predictions and observations indicates that the locations ofliquefaction boreholes appear to be better matched with the

computed CRR curves of Seed’s method at a depth interval of6.75–9.75 m. Similarly, better matched cases for the T–Y methodare located at depth intervals of 3.75–6.75 m (Fig. 13) and 6.75–9.75 m, and that for the NJRA method is located at a depth intervalof 6.75–9.75 m.

6.4.2. Prediction errorsIn order to quantify the above comparison of the analyses

methods, this study considers a measurement of the error esti-mates in analysis and adopts the terms: ‘‘prediction error ratiosfor liquefaction and non-liquefaction sites (eL and eNL),’’ whichare illustrated and defined in Fig. 14. Since SPT-N-based analysisschemes generally divide the CSR–N1,60 space into liquefactionand non-liquefaction regions by a CRR curve, predictions wouldbe correct if a liquefaction site is determined by a liquefaction pre-diction, and a non-liquefaction site is determined by a non-lique-faction prediction. Conversely, if a site has a known liquefactionor non-liquefaction condition, but is defined by the other side ofthe predicted condition, then the prediction would be incorrect.It is noted that there is no scale to measure how accurate is a cor-rect prediction. However, a measurement on how far the predic-tion deviates from a correct (CRR) boundary would be exists foran incorrect prediction. Accordingly, this study adopts the conceptof measuring prediction inaccuracy for comparing the accuracy inprediction by various liquefaction assessment methods.

Results of prediction error ratios for liquefaction and non-lique-faction sites are shown in Tables 6 and 7, respectively. Forliquefaction cases (Table 6), the minimum average prediction errorratios (eL,av,min) appear to be located at the depth interval of3.75–6.75 m, for all of the assessment methods studied. However,

(N1)60

NJRA’s Method, 3.75-6.75m

0

0.1

0.2

0.3

0.4

0.5

0

0.1

0.2

0.3

0.4

0.5

0

0.1

0.2

0.3

0.4

0.5

0 10 20 30 40 50

CRR, FC = 5%

CRR, FC = 15%

CRR, FC = 35%Liquefaction cases

Non-liquefaction cases

(N1)60

T & Y’s Method, 3.75-6.75m

0 10 20 30 40 50

CRR, FC = 5%CRR, FC = 15%

CRR, FC = 35%Liquefaction cases

Non-liquefaction cases

(N1)60

CSR

CSR

CSR

Seed’s Method, 3.75-6.75m

0 10 20 30 40 50

CRR, FC = 5%CRR, FC = 15%

CRR, FC = 35%Liquefaction cases

Non-liquefaction cases

Fig. 13. Comparison of predictions vs. observations for analysis at a depth interval: 3.75–6.75 m during the 1999 earthquake (M = 7.6).

Prediction Error Ratio for Non-Liquefaction Site, εNL:

B

BBNL CRR

CRRCSR −=ε

Prediction Error Ratio for Liquefaction Site, εL:

A

AAL CRR

CSRCRR −=ε

Liquefaction Site:

Non-Liquefaction Site:

AB

Falsely-Assigned Liquefaction Site:

A

B

CRR Curve Liquefaction

Region

Non- Liquefaction

Region

CSRB

CRRB

CSRA

CRRA

CSR &

CRR

SPT-NNA NB

Fig. 14. Schematic illustration on prediction error ratios.

M. Chang et al. / Computers and Geotechnics 38 (2011) 393–406 403

the smallest percentage of cases with erroneous predictions (PL,err,-

min) would be at the depth interval of 6.75–9.75 m. In considerationof the prediction error and population of the cases for the wholedepth range, the NJRA method yields the smallest sum of theweighted average prediction error ratio (min.REL,av; i.e., most accu-rate), the T–Y method next, and Seed’s method the greatest (max.-REL,av; i.e., least accurate) for the liquefaction cases.

For non-liquefaction cases (Table 7), the minimum average pre-diction error ratios (eNL,av,min) are located at the same depth interval(3.75–6.75 m) as the liquefaction cases. However, the minimumpercentage of cases with erroneous predictions (PNL,err) is locatedat the top depth interval (0–3.75 m) for all of the analysis methods.Considering the prediction error and population of the cases for thewhole depth range for non-liquefaction cases, the sum of theweighted average prediction error ratios (RENL,av) is the smallestfor the T–Y method (i.e., most accurate), next smallest for Seed’smethod, and greatest for the NJRA method (i.e., least accurate).

The above discussion appears to be inconclusive because lique-faction and non-liquefaction cases are not considered at the same

time. An overall sum of weighted average prediction error ratios(OPER) is subsequently defined and computed for all the assessmentmethods to combine both cases together and account for the pop-ulation in each of the cases. As shown in Table 8, the OPER rankingindicates that the T–Y method would be most accurate (i.e., thesmallest OPER) in predicting both liquefaction and non-liquefactioncases with Seed’s method following in accuracy, while the NJRAmethod would be least accurate in prediction (i.e., the greatestOPER).

The aforementioned OPER ranking is based upon the computa-tion of liquefaction and non-liquefaction cases for the entire depthrange of borehole, which could be obscured by the involvement ofnon-critical depth intervals consisting of higher percentages ofcases with erroneous predictions or higher prediction error ratios.The ranking of prediction accuracy is consequently improved byusing the critical depth interval.

In consideration of the depth interval that would provide min-imum average prediction error ratios (eL,av,min or eNL,av,min) for lique-faction and non-liquefaction cases (Tables 6 and 7), a critical depthrange of 3.75–6.75 m is selected. This critical depth interval ap-pears to be consistent with the location of the potential liquefiablelayer identified during on-site explorations after the earthquake[29,39]. Based on the critical depth range, the OPER ranking is com-puted as indicated in Table 9. This shows that the T–Y method pro-vides the most accurate prediction and the NJRA method nextaccurate, whereas Seed’s method yields the least accuracy.

From a safe (or conservative) design standpoint, an erroneousprediction at a liquefaction site (i.e., a non-liquefaction prediction)would be the primary concern. As determined through the valuesof REL,av or EL,av shown in Tables 8 and 9 for the whole depth rangeor the critical depth interval, the NJRA method yields the mostaccurate (or safest) prediction and the T–Y method would yieldthe second most accurate prediction, whereas Seed’s methodwould be the least accurate.

6.4.3. Potential impact due to falsely-assigned borehole categoryAs discussed in Section 5.2, the analysis boreholes are pre-as-

signed as liquefaction or non-liquefaction ones based on the condi-tion of surface manifestations in the vicinity of the boreholesduring the 1999 earthquake. Since surface manifestations may

Table 6Prediction errors for ‘‘liquefaction’’ cases (whole depth range) in the 1999 earthquake (M = 7.6).

Method Depth interval (m) Depth case analyzed Percentage of caseswith erroneouspredictions PL,err (%)

Average predictionerror ratio eL,av

Weighted averageprediction errorratioa EL,av (%)

Sum of weightedaverage predictionerror ratio REL,av (%)

Ranking

Seed 0–3.75 56 57.1 0.264 15.06 36.0 33.75–6.75 51 37.3 0.186 6.936.75–9.75 23 4.4 0.321 1.40>9.75 169 53.3 0.237 12.64

T–Y 0–3.75 58 56.9 0.210 11.95 27.0 23.75–6.75 51 31.4 0.166 5.206.75–9.75 23 4.4 0.267 1.16>9.75 175 33.1 0.261 8.66

NJRA 0–3.75 64 51.6 0.296 15.27 25.4 13.75–6.75 52 15.4 0.141 2.166.75–9.75 22 4.6 0.205 0.93>9.75 172 20.9 0.337 7.05

Note: Bold numbers indicate the minimum values in all depth intervals.a EL,av = PL,err � eL,av � 100.

Table 7Prediction errors for ‘‘non-liquefaction’’ cases (whole depth range) in the 1999 earthquake (M = 7.6).

Method Depthinterval(m)

Depth caseanalyzed

Percentage of cases witherroneous predictions PNL,err

(%)

Average predictionerror ratio eNL,av

Weighted averageprediction error ratioa ENL,av

(%)

Sum of weighted averageprediction error ratio RENL,av (%)

Ranking

Seed 0–3.75 643 7.0 0.377 2.65 13.1 23.75–6.75 1100 12.5 0.293 3.666.75–9.75 783 11.1 0.334 3.72>9.75 2613 9.1 0.332 3.03

T–Y 0–3.75 655 5.1 0.453 2.30 12.3 13.75–6.75 1112 8.7 0.331 2.886.75–9.75 801 9.7 0.361 3.51>9.75 2756 9.3 0.384 3.58

NJRA 0–3.75 811 5.2 0.473 2.46 14.0 33.75–6.75 1240 9.9 0.365 3.606.75–9.75 920 10.1 0.396 3.99>9.75 3014 10.1 0.390 3.95

Bold numbers indicate the minimum values in all depth intervals.a ENL,av = PNL,err � eNL,av � 100.

Table 8Prediction errors for ‘‘liquefaction and non-liquefaction’’ cases (whole depth range) in the 1999 earthquake (M = 7.6).

Method Liquefaction cases Non-liquefaction cases Overall sum of weighted averageprediction error ratio OPER (%)

Ranking

Sum of weighted averageprediction error ratio REL,av

(%)

Ratio of analyzedborehole numbersBL

Sum of weighted averageprediction error ratio RENL,av

(%)

Ratio of analyzedborehole numbersBNL

Seed 36.0 66/986 13.1 920/986 14.6 2T–Y 27.0 67/994 12.3 927/994 13.3 1NJRA 25.4 67/997 14.0 930/997 14.8 3

Note: OPER = REL,av � BL + RENL,av � BNL.

404 M. Chang et al. / Computers and Geotechnics 38 (2011) 393–406

not fully reflect the occurrence of soil liquefaction underneath theground, as shown by Youd and Carter [40], the above criterion forassigning borehole categories could result in two unwanted situa-tions: (i) a falsely-assigned liquefaction borehole, and (ii) a falsely-assigned non-liquefaction borehole. A falsely-assigned liquefactionborehole is unlikely because the observed liquefaction phenomenaon the ground surface cannot produce without the causes otherthan soil liquefaction under the ground. Conversely, a falsely-as-signed non-liquefaction borehole is likely due to the fact that theextent of soil liquefaction could be hindered by thick overlyingstrata.

Since detailed ground response analysis, as the ones shown byYoud and Carter [40], has not been performed for all of the non-liq-uefaction boreholes, the actual number of falsely-assigned non-liq-

uefaction boreholes cannot be certain. In viewing that most of theobserved liquefaction sites during the 1999 earthquake are clus-tered in few townships, which account for a small portion of bore-hole population as compared with the entire borehole database,the actual number of falsely-assigned non-liquefaction boreholeshould be limited in this study.

As shown in Fig. 14, the falsely-assigned non-liquefaction bore-hole (XO) could fall on both sides of the CRR boundary curve. For XO

above the CRR curve, the prediction error ratio (eNL), and theweighted prediction error ratio (ENL) as well, will be computedfor the falsely-assigned non-liquefaction boreholes, which will re-sult in a slightly-overestimated overall weighted prediction errorratio (OPER). For XO below the CRR curve, however, the predictionerror ratio (eL), and the weighted prediction error ratio (EL) as well,

Table 9Prediction errors for ‘‘liquefaction and non-liquefaction’’ cases (critical depth interval: 3.75–6.75 m) in the 1999 earthquake (M = 7.6).

Method Liquefaction cases Non-liquefaction cases Overall weighted averageprediction error ratio OPER (%)

Ranking

Weighted averageprediction error ratio EL,av

(%)

Ratio of analyzedborehole numbers BL

Weighted averageprediction error ratio ENL,av

(%)

Ratio of analyzedborehole numbers BNL

Seed 6.93 66/986 3.66 920/986 3.88 3T–Y 5.20 67/994 2.88 927/994 3.04 1NJRA 2.16 67/997 3.60 930/997 3.50 2

Note: OPER = EL,av � BL + ENL,av � BNL.

M. Chang et al. / Computers and Geotechnics 38 (2011) 393–406 405

will not be computed as they should be for the actually liquefied(but falsely-assigned) boreholes, which will result in a slightly-underestimated overall weighted prediction error ratio (OPER).

It is noted that similar degrees of over or under estimations onthe OPER computation would exist among various liquefactionassessment methods considered in this study. In addition, the overand under estimations of OPER due to falsely-assigned non-liquefac-tion boreholes would be partially self-compensated, which rendersthe final OPER computation (including liquefaction and non-lique-faction cases) essentially unchanged.

In consideration of the above discussions, the falsely-assignednon-liquefaction boreholes should have a minimal influence onthe overall prediction error computations, and the major findingsof this study should remain unchanged.

7. Concluding remarks

This study examines the computation sensitivity and predictionaccuracy of several SPT-N-based methods, using liquefaction andnon-liquefaction incidents of the 1999 Chi-chi Earthquake inTaiwan. The major findings of the study are listed as follows:

(1) Sensitivity studies on parameters adopted in the N-basedmethods show that the SPT blow count (N) and peak groundacceleration (amax) are most sensitive in the computed lique-faction potential. Hammer energy ratio (ER), earthquakemagnitude (M), fines content (FC), and groundwater depth(GWT) follow in sensitivity. Stress reduction factor (rd) andoverburden pressure correction factor (CN) appear leastsensitive.

(2) By converting CRR and CSR estimations into the same analy-sis framework by Seed [1,6], Seed’s method provides thehighest CRR predictions at higher blow counts (e.g.,N1,60 > 10) and yields the lowest CRR values at lower blowcounts (e.g., N1,60 < 10). The T–Y method appears to computethe highest CRR for FC = 15% and N1,60 < 10, and lowest CRRfor FC ; 35% and N1,60 = 10. The NJRA method would begreatest in CRR for FC < 5% and N1,60 < 15, and least in CRRfor FC ; 15% and N1,60 > 10. For CSR predictions, T–Y andNJRA methods provide somewhat smaller predictions thanthe Seed’s method.

(3) By comparing predictions and observations during theearthquake, locations of liquefaction boreholes appear bettermatched with the computed CRR curves by Seed’s method ata depth interval of 6.75–9.75 m. Similarly, better matchedcases for the T–Y method are at depth intervals of3.75–6.75 m and 6.75–9.75 m, and for the NJRA method adepth interval of 6.75–9.75 m.

(4) In liquefaction and non-liquefaction cases, the minimumaverage prediction error ratios (eL,av,min and eNL,av,min) arecomputed at a depth interval of 3.75–6.75 m, for all theN-based assessment methods studied. This critical depthinterval appears to be consistent with the location of poten-tially liquefiable layers identified on-site.

(5) Based on computations of liquefaction and non-liquefactioncases for the entire depth range of a borehole, the OPER (over-all weighted average prediction error ratio) ranking showsthat the T–Y method would yield the most accurate (i.e.,the smallest OPER) prediction and Seed’s method the secondmost accurate prediction, while the NJRA method yieldsthe least accurate prediction (i.e., the greatest OPER).

(6) For the critical depth interval of 3.75–6.75 m, the OPER rank-ing shows the T–Y method remains most accurate and theNJRA method following in accuracy, whereas Seed’s methodis the least accurate in predicting both liquefaction and non-liquefaction cases.

(7) Prediction error ratios for the N-based methods consideredin this study are usually similar and negligible, indicatingthat all of the methods are generally applicable for the1999 earthquake of Taiwan.

As mentioned previously, the analysis methods considered inthis study are primarily for design purposes. Differences betweenthe analysis results and the observations during the earthquake re-flect the simplifications adopted in each method. Although themethods studied herein provide similar degrees of accuracy in pre-dicting the liquefaction incidents during the 1999 earthquake, themethods are by no means accurate enough for predicting soil liq-uefaction in all cases. Peck [31] has raised a relevant viewpointregarding the issue of science and practice in liquefaction evalua-tion in his remark, ‘‘engineering science and engineering practiceare not identical.’’ An analysis method that is considered to be rea-sonably adequate for applications should have sufficient field evi-dence and verifications.

Acknowledgement

Financial support from the National Council for Research inEarthquake Engineering of Taiwan (NSC89-2711-3-319-200-28,NSC90-2711-3-319-200-12, NSC91-2711-3-319-200-08) are grate-fully appreciated.

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