U.S.-Taiwan Workshop on Soil Liquefaction U.S.-Taiwan Workshop on Soil Liquefaction A Practical Reliability- A Practical Reliability- Based Method for Assessing Based Method for Assessing Soil Liquefaction Potential Soil Liquefaction Potential Jin-Hung Hwang Jin-Hung Hwang National Central National Central University, Taiwan University, Taiwan
25
Embed
A Practical Reliability-Based Method for Assessing Soil Liquefaction Potential
Lecture Topic: A Practical Reliability-Based Method for Assessing Soil Liquefaction Potential
By Prof. Jin-Hung Hwang of National Central University, Taiwan.
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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
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