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- 1. 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
- 2. DATE:10th Nov, 2010 CET Hall
- 3. www.cesnitsilchar.wordpress.com Fanpage MISSION 2015::NIT Silchar www.twitter.com/cesnitsilchar
- 4. 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
- 5. 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)
- 6. 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.
- 7. 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
- 8. )(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.
- 9. 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
- 10. 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
- 11. 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
- 12. 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.
- 13. 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.
- 14. PDF of CRRPDF of CRR 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.
- 15. PDF of CRRPDF of CRR [ ] 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 CyclicResistanceRatio(CRR) 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.
- 16. 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.
- 17. 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 CyclicResistanceRatio(CRR) 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
- 18. 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.
- 19. 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 CorrectedBlow Count , (N1)60 ProbabilityLiquefaction Depth = 8m G.W.T. = 2m FC = 5%
- 20. 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(b) Influence of fines content on liquefaction probability. 0% 20% 40% 60% 80% 100% 0 10 20 30 40 CorrectedBlow Count , (N1)60 ProbabilityLiquefaction FC= 5% Depth = 8m G.W.T. = 2 m FC = 5~35% FC = 35%
- 21. 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(c) Influence of ground water table on liquefaction probability. 0% 20% 40% 60% 80% 100% 0 10 20 30 40 CorrectedBlow Count, (N1)60 ProbabilityLiquefaction G.W.T. = 0 m G.W.T. = 6 m Depth = 8m G.W.T.= 0~6m FC = 5%
- 22. 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 ==
- 23. Application ExampleApplication Example 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%
- 24. Application ExampleApplication Example 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.
- 25. 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

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