A Practical Reliability-Based Method for Assessing Soil Liquefaction Potential

U.S.-Taiwan Workshop on Soil LiquefactionU.S.-Taiwan Workshop on Soil Liquefaction
A Practical Reliability-Based Method forA Practical Reliability-Based Method for
Assessing Soil Liquefaction PotentialAssessing Soil Liquefaction Potential
Jin-Hung HwangJin-Hung Hwang
National Central University, TaiwanNational Central University, Taiwan

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

OutlineOutline
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
 Haldar and Tang (1975),Haldar and Tang (1975),
Fardis and Veneziano (1982),Fardis and Veneziano (1982),
Chameau and Clough (1983),Chameau and Clough (1983),
LiaoLiao et alet al. (1988),. (1988),
Youd and Nobel (1997),Youd and Nobel (1997),
ToprakToprak et alet al. (1999) ,. (1999) ,
JuangJuang 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 theProbabilistic cyclic strength curves without the
statistics.statistics.
 Juang’s work is a notable advancement, howeverJuang’s work is a notable advancement, however
ANN is a little unfamiliar to engineers.ANN is a little unfamiliar to engineers.

Reliability ModelReliability Model
 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
β
σσ
µµ
β
Φ−=
+
−
=
f
SR
sR
P

)(0.1
22
β
σσ
µµ
β
Φ−=
+
−
=
f
SR
sR
P
τ L τ R
fR
(R)fL
(L)
S, R
ProbabilityDensity
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
[ ]
)(0.1
)1)(1ln(
1
1
ln
2/122
2/1
2
2
2
ln
2
ln
lnln
β
δδ
δ
δ
µ
µ
σσ
µµ
σ
µ
β
Φ−=
++














+
+
=
+
−
==
f
SR
R
S
S
R
S
SR
Z
Z
P

 Flow chart of calculationFlow chart of calculation
Liquefaction probability
CRR statistics
Geological data
Attenuation formula
to compute
Earthquake magnitude and
hypocentral distance
Earthquake data
M
CSR statistics
581.0
/65.0 max
5.7
=
×
′
×=
CSR
d
v
v
MSFr
g
A
CSR
δ
σ
σ
604.0
])(000507.0)(06008.063.2exp[ 2
601601
=
++−=
CRR
CRR NN
δ
µ
)(1 βφ−=fP
841.00168.000009.0
10
0.1
10
2
++−=
>
=
≤
FCFCK
FCIf
K
FCIf
S
S( ) 60
'601
1
NN
v
×=
σ
Fines content
)(FCfKS =
SPT
60N
Effective
overburden stress
)/( 2
cmkgvσ′
Magnitude
scaling factor
11.1
)
5.7
( −
=
M
MSF
Reliability index
[ ] 2/122
2/1
2
2
2
ln
2
ln
lnln
)1)(1ln(
1
1
ln
++














+
+
=
+
−
==
CSRCRR
CRR
CSR
CSR
CRR
CSRCRR
CSRCRR
Z
Z
δδ
δ
δ
µ
µ
σσ
µµ
σ
µ
β
R
maxA

 Information requiredInformation required
 Mean values and variance coefficients ofMean 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
'
MMSFr
g
A
d
v
v
⋅⋅⋅⋅
σ
σ
])(000507.0)(06008.063.2exp[ 2
601601 NN ++−
Mean value Variance coefficient
CSR 0.581
CRR 0.604

PDF of CSRPDF of CSR







 −
−
⋅
=
⋅=
′
=
2
)ln(
)ln(
)ln(
max
max
)
)ln(
(
2
1
exp
2
1
)(
)(/)(65.0
CSR
CSR
CSR
CSR
d
v
v
CSR
CSR
CSRf
AaMMSFzr
g
A
CSR
σ
µ
σπ
σ
σ
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 )
ProbabilityDensity
depth = 10m
G.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 CRR





 −−−−−
=
3
2
601260110 )()()1/1ln(
exp
β
βββ cscsL NNP
CSR
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, (N 1)60
CyclicResistanceRatio(CRR)
0.7 0.3
P L = 0.99 0.9 0.5 0.1 0.01
Fig.3 Probabilistic cyclic resistance curves
regressed by the logistic model.

2
1
))(1(
)(
)( b
b
CRRa
CRRab
CRRf
+
−=
−
0
2
4
6
8
10
12
0.0 0.2 0.4 0.6 0.8 1.0
Cyclic Resistance Ratio, CRR
ProbabilityDensity
(N 1)60 = 5
(N1)60 = 30
The greater (N 1)60 , the greater δ CRR
Fig.4 Probability density function of the soil cyclic resistance ratio.

[ ]
3
2
601260110 )()(exp
β
βββ
−=
−−−=
b
NNa cscs
0.0
0.2
0.4
0.6
0.8
1.0
0 10 20 30 40 50
Corrected Blow Count , (N 1)60
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 Factor
[ ]
)(0.1
7758.0
)ln(
013.0
)1)(1ln(
1
1
ln
2/122
2/1
2
2
β
δδ
δ
δ
µ
µ
β
Φ−=
+−=
++














+
+
=
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
LiquefactionProbability,PL
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 byCompared 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
CorrectedBlow Count , (N1)60
PL = 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
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6
Safety Factor , FS Seed
LiquefactionProbability,PL
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 Study
 Influences of andInfluences of and
the ground water table on the liquefactionthe 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
ProbabilityLiquefaction
Depth = 8m
G.W.T. = 2m
FC = 5%

fP
Fig.10(b) Influence of fines content on liquefaction probability.
0%
20%
40%
60%
80%
100%
0 10 20 30 40
FC= 5%
Depth = 8m
G.W.T. = 2 m
FC = 5~35%
FC = 35%

fP
Fig.10(c) Influence of ground water table on liquefaction probability.
0%
20%
40%
60%
80%
100%
0 10 20 30 40
CorrectedBlow Count, (N1)60
G.W.T. = 0 m
G.W.T. = 6 m
Depth = 8m
G.W.T.= 0~6m
FC = 5%

Application 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 analysisResult of liquefaction analysis
gPGAML 28.0,8.6 ==

Table 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-N
FC
(%)
Soil classification
F.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%

0
5
10
15
20
0 1 2 3
Safety factor , FS
depth(m)
0
5
10
15
20
0 0.5 1
Liquefaction probability , P f
depth(m)
0
5
10
15
20
0 10 20 30
SPT-N
depth(m)
Simplified profile
20
depth(m)
ML
CL
SM
SM
15
10
5
0
PGA = 0.28g
ML = 6.8
0
5
10
15
20
0 50 100
FC (%)
depth(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 Discussion
 A simple and practical reliability methodA simple and practical reliability method
for liquefaction analysis was proposedfor liquefaction analysis was proposed
 The liquefaction probability is just aThe liquefaction probability is just a
probability under a given earthquake eventprobability under a given earthquake event
 It needs to combine the probability ofIt needs to combine the probability of
earthquake occurrenceearthquake occurrence

A Practical Reliability-Based Method for Assessing Soil Liquefaction Potential

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