U.S.-Taiwan Workshop on Soil LiquefactionU.S.-Taiwan Workshop on Soil Liquefaction

A Practical Reliability-Based Method for A Practical Reliability-Based Method for Assessing Soil Liquefaction PotentialAssessing Soil Liquefaction Potential

Jin-Hung HwangJin-Hung Hwang

National Central University, TaiwanNational Central University, Taiwan

Jin-Hung HwangJin-Hung Hwang

National Central University, TaiwanNational Central University, Taiwan

DATE:10th Nov, 2010CET Hall

www.cesnitsilchar.wordpress.com Fanpage MISSION 2015::NIT Silchar www.twitter.com/cesnitsilchar

OutlineOutlineOutlineOutline

Previous studiesPrevious studies

Reliability modelReliability model

Probability density function of CSRProbability density function of CSR

Probability density function of CRRProbability density function of CRR

Liquefaction probability and safety factorLiquefaction probability and safety factor

Summary and discussionSummary and discussion

Previous studiesPrevious studies

Reliability modelReliability model

Probability density function of CSRProbability density function of CSR

Probability density function of CRRProbability density function of CRR

Liquefaction probability and safety factorLiquefaction probability and safety factor

Summary and discussionSummary and discussion

Previous StudiesPrevious StudiesPrevious StudiesPrevious Studies

Haldar and Tang (1975),Haldar and Tang (1975),

Fardis and Veneziano (1982),Fardis and Veneziano (1982),

Chameau and Clough (1983),Chameau and Clough (1983),

Liao Liao et alet al. (1988),. (1988),

Youd and Nobel (1997),Youd and Nobel (1997),

Toprak Toprak et alet al. (1999) ,. (1999) ,

Juang Juang et alet al. (2000a,2000b). (2000a,2000b)

Haldar and Tang (1975),Haldar and Tang (1975),

Fardis and Veneziano (1982),Fardis and Veneziano (1982),

Chameau and Clough (1983),Chameau and Clough (1983),

Liao Liao et alet al. (1988),. (1988),

Youd and Nobel (1997),Youd and Nobel (1997),

Toprak Toprak et alet al. (1999) ,. (1999) ,

Juang Juang et alet al. (2000a,2000b). (2000a,2000b)

Some commentsSome comments Soil parameters and data should be updated. Soil parameters and data should be updated. Probabilistic cyclic strength curves without the Probabilistic cyclic strength curves without the

statistics.statistics. Juang’s work is a notable advancement, however Juang’s work is a notable advancement, however

ANN is a little unfamiliar to engineers.ANN is a little unfamiliar to engineers.

Some commentsSome comments Soil parameters and data should be updated. Soil parameters and data should be updated. Probabilistic cyclic strength curves without the Probabilistic cyclic strength curves without the

statistics.statistics. Juang’s work is a notable advancement, however Juang’s work is a notable advancement, however

ANN is a little unfamiliar to engineers.ANN is a little unfamiliar to engineers.

Reliability ModelReliability ModelReliability ModelReliability Model Based on Seed’85 methodBased on Seed’85 method Assume CSR and CRR are normal distributionAssume CSR and CRR are normal distribution

Based on Seed’85 methodBased on Seed’85 method Assume CSR and CRR are normal distributionAssume CSR and CRR are normal distribution

)(0.1

22

f

SR

sR

P

)(0.1

22

f

SR

sR

P

τ L τ R

fR(R)fL(L)

S, RPr

obab

ility

Den

sity

μ Z

fz(z)

Z

Z > 0 , non-liquefyZ < 0 , liquefy

liquefaction probability , Pf

σ zσ z

β σ z

Fig.1 Probability density distribution for the liquefaction performance function.

Assume CSR and CRR are log-normal distributionsAssume CSR and CRR are log-normal distributions Assume CSR and CRR are log-normal distributionsAssume CSR and CRR are log-normal distributions

)(0.1

)1)(1ln(

1

1ln

2/122

2/1

2

2

2ln

2ln

lnln

f

SR

R

S

S

R

S

SR

Z

Z

P

Flow chart of calculationFlow chart of calculation Flow chart of calculationFlow chart of calculation

Liquefaction probability

CRR statistics

Geological data

Attenuation formulato compute

Earthquake magnitude andhypocentral distance

Earthquake data

M

CSR statistics

581.0

/65.0 max5.7

CSR

dv

v MSFrg

ACSR

604.0

])(000507.0)(06008.063.2exp[ 2601601

CRR

CRR NN

)(1 fP

841.00168.000009.0

10

0.1

10

2

FCFCK

FCIf

K

FCIf

S

S 60'601

1NN

v

Fines content) (FCfKS

SPT

60N

Effectiveoverburden stress

)/( 2cmkgv

Magnitudescaling factor

11.1)5.7

( M

MSF

Reliability index

2/122

2/1

2

2

2ln

2ln

lnln

)1)(1ln(

1

1ln

CSRCRR

CRR

CSR

CSR

CRR

CSRCRR

CSRCRR

Z

Z

R

maxA

Information requiredInformation required Mean values and variance coefficients of Mean values and variance coefficients of

CSR and CRRCSR and CRR

Information requiredInformation required Mean values and variance coefficients of Mean values and variance coefficients of

CSR and CRRCSR and CRR

Table 2 Mean values and variance coefficients of CSR and CRRTable 2 Mean values and variance coefficients of CSR and CRR

)(65.0 max'

MMSFrg

Ad

v

v

])(000507.0)(06008.063.2exp[ 2601601 NN

Mean value Variance coefficient

CSR 0.581

CRR 0.604

PDF of CSRPDF of CSRPDF of CSRPDF of CSR

2

)ln(

)ln(

)ln(

maxmax

))ln(

(2

1exp

2

1)(

)(/)(65.0

CSR

CSR

CSR

CSR

dv

v

CSR

CSRCSRf

AaMMSFzrg

ACSR

0.0

1.0

2.0

3.0

4.0

5.0

0 0.2 0.4 0.6 0.8 1

Cyclic Stress Ratio (CSR )

Prob

abili

ty D

ensity

depth = 10mG.W.T. = 5.3m

σ v = 20.3 t/m2

σ ' v = 15.3 t/m2

r d = 0.899 PGA = 0.28g

μ ln(CSR) = -1.757

σ ln(CSR) = 0.677

Fig.2 Calculated probability density function of a soil at a depth of 10 m.

PDF of CRRPDF of CRRPDF of CRRPDF of CRR

3

2601260110 )()()1/1ln(

exp

cscsL NNPCSR

Table 1 Parameters in the logistic modelTable 1 Parameters in the logistic model

Parameter β0 β1 β2 β3

Regressed result 10.4 -0.2283 -0.001927 3.8

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50

Corrected Blow Count, (N1)60

Cyc

lic

Res

ista

nce

Rat

io (C

RR

)

0.7 0.3P L = 0.99 0.9 0.5 0.1 0.01

Fig.3 Probabilistic cyclic resistance curves

regressed by the logistic model.

PDF of CRRPDF of CRRPDF of CRRPDF of CRR

2

1

))(1(

)()(

b

b

CRRa

CRRabCRRf

0

2

4

6

8

10

12

0.0 0.2 0.4 0.6 0.8 1.0

Cyclic Resistance Ratio, CRR

Prob

abili

ty D

ensity

(N1)60 = 5

(N1)60 = 30

The greater (N1)60 , the greater δ CRR

Fig.4 Probability density function of the soil cyclic resistance ratio.

PDF of CRRPDF of CRRPDF of CRRPDF of CRR

3

2601260110 )()(exp

b

NNa cscs

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50

Corrected Blow Count, (N1)60

Cyc

lic

Res

ista

nce

Rat

io (C

RR

)

Median value (P L =0.5)

P L =0.6

Mean value

Fig.5 Mean and median curves compared with the probabilistic curve of PL=0.6.

Liquefaction Probability and Safety FactorLiquefaction Probability and Safety FactorLiquefaction Probability and Safety FactorLiquefaction Probability and Safety Factor

)(0.1

7758.0

)ln(013.0

)1)(1ln(

11

ln

2/122

2/1

2

2

f

SR

R

S

S

R

P

FS

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6

Safety Factor , FS

Liq

uefa

ctio

n Pr

obab

ility

, P L

δ = 0.0

δ = 1.0

assume δ CSR = δ CRR

Fig.7 Relations of liquefaction probability with the safety factor for different variance coefficients.

Compared with the safety factor defined by Compared with the safety factor defined by the Seed’85 methodthe Seed’85 method

Compared with the safety factor defined by Compared with the safety factor defined by the Seed’85 methodthe Seed’85 method

Fig.8 Comparison of the probabilistic CRR curves with the empirical curve proposed by Seed’85 method.

0.0

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50

Corrected Blow Count, (N1)60

Cyc

lic

Res

ista

nce

Rat

io (

CR

R)

P L = 0.6 0.5 0.2

Seed'85 Method

(N1)60=14, PL =0.44, Cr=1.18

(N1)60=20, PL =0.35, Cr=1.31

(N1)60=28, PL =0.22, Cr=1.55

(N1)60=29, PL =0.30, Cr=1.38

(N1)60=30, PL =0.57, Cr=1.03

(N 1)60=8, PL =0.32, Cr=1.35

Compared with Juang’s resultCompared with Juang’s result Compared with Juang’s resultCompared with Juang’s result

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6

Safety Factor , FSSeed

Liq

uefa

ctio

n Pr

obab

ility

, P L

Juang et al. (2002)

Cr = 1.18

Cr = 1.30

Cr = 1.55

Fig.9 Relation of liquefaction probability with the safety factor calculated by Seed’85 method.

Parameter StudyParameter StudyParameter StudyParameter Study Influences of and Influences of and

the ground water table on the liquefaction the ground water table on the liquefaction probabilityprobability

Influences of and Influences of and the ground water table on the liquefaction the ground water table on the liquefaction probabilityprobability

(%), ,)( 601 FCContentFinesN

fP

Fig.10(a) Variation of liquefaction probability with (N1)60.

0%

20%

40%

60%

80%

100%

0 10 20 30 40

Corrected Blow Count, (N1)60

Prob

abili

ty L

ique

fact

ion

Depth = 8mG.W.T. = 2mFC = 5%

Parameter StudyParameter StudyParameter StudyParameter Study Influences of and Influences of and

the ground water table on the liquefaction the ground water table on the liquefaction probabilityprobability

Influences of and Influences of and the ground water table on the liquefaction the ground water table on the liquefaction probabilityprobability

(%), ,)( 601 FCContentFinesN

fP

Fig.10(b) Influence of fines content on liquefaction probability.

0%

20%

40%

60%

80%

100%

0 10 20 30 40

Corrected Blow Count, (N1)60

Prob

abili

ty L

ique

fact

ion

FC= 5%

Depth = 8mG.W.T. = 2 mFC = 5~35%

FC = 35%

Parameter StudyParameter StudyParameter StudyParameter Study Influences of and Influences of and

the ground water table on the liquefaction the ground water table on the liquefaction probabilityprobability

Influences of and Influences of and the ground water table on the liquefaction the ground water table on the liquefaction probabilityprobability

(%), ,)( 601 FCContentFinesN

fP

Fig.10(c) Influence of ground water table on liquefaction probability.

0%

20%

40%

60%

80%

100%

0 10 20 30 40

Corrected Blow Count, (N1)60

Prob

abili

ty L

ique

fact

ion

G.W.T. = 0 m

G.W.T. = 6 m

Depth = 8mG.W.T.= 0~6mFC = 5%

Application ExampleApplication ExampleApplication ExampleApplication Example Active Hsinhwa fault (12km rupture)Active Hsinhwa fault (12km rupture) 1946 Tainan earthquake1946 Tainan earthquake Caused extensive liquefactionCaused extensive liquefaction Design earthquakeDesign earthquake Result of liquefaction analysis Result of liquefaction analysis

Active Hsinhwa fault (12km rupture)Active Hsinhwa fault (12km rupture) 1946 Tainan earthquake1946 Tainan earthquake Caused extensive liquefactionCaused extensive liquefaction Design earthquakeDesign earthquake Result of liquefaction analysis Result of liquefaction analysis

gPGAM L 28.0 ,8.6

Application ExampleApplication ExampleApplication ExampleApplication ExampleTable 3 Result of liquefaction analysis for the site near the Hsinhwa faultTable 3 Result of liquefaction analysis for the site near the Hsinhwa fault

LP

depth(m)

Unit weight(t/m3)

SPT-NFC(%)

Soil classificationF.S.

(Seed)PL (%)

1.3 1.97 3 73 CL-ML - -

2.8 2.02 6 69 CL-ML - -

4.3 2.00 7 75 CL-ML - -

5.8 1.89 15 82 ML - -

7.3 1.93 6 99 ML - -

8.8 2.01 6 91 CL-ML - -

10.3 1.98 17 33 SM 1.2 35%

11.8 1.95 23 29 SM 1.4 19%

13.3 1.87 18 33 SM 1.2 35%

14.8 1.96 13 14 SM 0.8 62%

16.3 1.95 9 99 CL - -

18.8 2.04 33 25 SM 2.0 6%

19.3 2.19 33 20 SM 1.9 9%

Application ExampleApplication ExampleApplication ExampleApplication Example

0

5

10

15

20

0 1 2 3

Safety factor , FS

dept

h (m

)

0

5

10

15

20

0 0.5 1

Liquefaction probability , P f

dept

h (m

)

0

5

10

15

20

0 10 20 30

SPT-N

dept

h (m

)

Simplified profile

20

dept

h(m

)

ML

CL

SM

SM

15

10

5

0

PGA = 0.28g ML = 6.8

0

5

10

15

20

0 50 100

FC (%)

dept

h (m

)

CL

PGA = 0.28g ML = 6.8

Seed85 method

Fig.11 Result of liquefaction analysis for the site near the Hsinhwa fault.

Summary and DiscussionSummary and DiscussionSummary and DiscussionSummary and Discussion A simple and practical reliability method A simple and practical reliability method

for liquefaction analysis was proposedfor liquefaction analysis was proposed The liquefaction probability is just a The liquefaction probability is just a

probability under a given earthquake eventprobability under a given earthquake event It needs to combine the probability of It needs to combine the probability of

earthquake occurrenceearthquake occurrence

A simple and practical reliability method A simple and practical reliability method for liquefaction analysis was proposedfor liquefaction analysis was proposed

The liquefaction probability is just a The liquefaction probability is just a probability under a given earthquake eventprobability under a given earthquake event

It needs to combine the probability of It needs to combine the probability of earthquake occurrenceearthquake occurrence