Ground Motions and Liquefaction – The Loading Part of the Equation Steve Kramer Roy Mayfield Bob Mitchell University of Washington Seattle, Washington USA

Evaluation of Liquefaction Potential SPT CPT Vs Most research = 0.65 rd PGA g s’vo svo 1 MSF = Ih Peak acceleration Magnitude Arias intensity Intensity Measure (IM): PGA & M (simplified method) Ih (Arias intensity method) Vector measure Scalar measure

Engineering demand parameter Performance-Based Earthquake Engineering Covers range of hazard (ground motion) levels Includes effects of ground motions Accounts for uncertainty in parameters, relationships Engineering demand parameter Decision variable Damage measure Intensity measure Repair cost Crack width Interstory drift Sa(To)

Performance-Based Earthquake Engineering Covers range of hazard (ground motion) levels Includes effects of ground motions Accounts for uncertainty in parameters, relationships Risk curve – lCost vs Cost Fragility curve – repair cost given crack width Fragility curve – crack width given interstory drift Fragility curve – interstory drift given Sa(To) Seismic hazard curve – lPGA vs Sa(To)

Performance-Based Earthquake Engineering Covers range of hazard (ground motion) levels Includes effects of ground motions Accounts for uncertainty in parameters, relationships For liquefaction, EDP = ru IM = PGA

Intensity Measures Desirable characteristics of an IM Efficient – should be closely correlated to EDP of interest Sufficient – should not require additional information to predict EDP Predictable – should be accurately predictable 2 m (N1)60-cs = {5, 15, 25 } (N1)60-cs = 60 H = {4, 9, 14 m} 20 m Magnitude Distance 9 profiles 22 earthquakes >450 motions ~300 candidate IMs

Intensity Measures Efficiency EDP = depth-averaged excess pore pressure ratio, (ru)ave High scatter = low efficiency Lower scatter = higher efficiency (ru)ave PGA (cm/sec2) Arias intensity (m/sec)

Intensity Measures Sufficiency EDP = depth-averaged excess pore pressure ratio, (ru)avg Strong trends – insufficient w/r/t magnitude Weaker trends – more sufficient w/r/t distance PGA PGA Ia Ia

A New Intensity Measure for Liquefaction (m/s) A New Intensity Measure for Liquefaction Little scatter = efficient CAV5 Cumulative absolute velocity 5 cm/sec2 threshold Accelerogram |a(t)| Little dependence on M or R = sufficient |a(t)| after threshold Integral CAV5

A New Intensity Measure for Liquefaction CAV5 Predictability – attenuation relationship developed from database of CA earthquakes Low Standard error sln PGA = 0.620 High sln Ia = 1.070 Medium-low sln CAV5 = 0.708

Implications for Performance-Based Liquefaction Hazard Evaluation Discrete form ru log lru ru hazard curve IM log lIM IM hazard curve IM P[ru>r*u|IM] (ru)1 (ru)2 (ru)3 ru|IM fragility curves 1

Implications for Performance-Based Liquefaction Hazard Evaluation Influence of predictability log lm ln Y P[Y > Y*| M=M*, R=R*] Y = Y* ln Y R = R* M = M* log R M

How does uncertainty in attenuation relationship affect lIM? Implications for Performance-Based Liquefaction Hazard Evaluation Influence of predictability log lm How does uncertainty in attenuation relationship affect lIM? ln Y Y = Y* ln Y R = R* M = M* log R M

Implications for Performance-Based Liquefaction Hazard Evaluation Influence of predictability log lm Reducing uncertainty in attenuation relationship reduces P[Y > Y* | M,R], which reduces lIM. ln Y P[Y > Y*| M=M*, R=R*] IM lIM Poor predictability Y = Y* ln Y Good predictability M = M* R = R* log R

lru proportional to sum of thick red lines Implications for Performance-Based Liquefaction Hazard Evaluation P[EDP>EDP* | IM] 1.0 lru proportional to sum of thick red lines 0.0 IM lIM DlIM IM

lIM Implications for Performance-Based Liquefaction Hazard Evaluation P[EDP>EDP* | IM] Fragility curve with less uncertainty (in prediction of EDP|IM) 1.0 lru proportional to sum of thick red lines 0.0 IM lIM IM

lru proportional to sum of thick red lines Implications for Performance-Based Liquefaction Hazard Evaluation P[EDP>EDP* | IM] 1.0 lru proportional to sum of thick red lines 0.0 IM lIM IM

lru proportional to sum of thick red lines Implications for Performance-Based Liquefaction Hazard Evaluation P[EDP>EDP* | IM] 1.0 Increasing efficiency of IM leads to reduction in lEDP Reduction in lEDP lru proportional to sum of thick red lines 0.0 IM lIM IM

A New Intensity Measure for Liquefaction CAV5 Frequency domain characteristics Relationship between IM and spectral acceleration Depends on period at which spectral acceleration is computed Highest correlation at high frequencies for PGA and Ia Highest correlation at lower frequencies for CAV5 20 Chi-Chi motions 0.1g < PGA < 0.3g 11 km < R < 26 km

A New Intensity Measure for Liquefaction CAV5 efficiency w/r/t Chi-Chi motions Same 20 motions

A New Intensity Measure for Liquefaction CAV5 efficiency w/r/t Chi-Chi motions Same 20 motions Soil profile consistent with Berth 4 at Port of Taichung

A New Intensity Measure for Liquefaction CAV5 efficiency w/r/t Chi-Chi motions Same 20 motions Soil profile consistent with Berth 4 at Port of Taichung Scaled three times: to produce surface PGA = 0.1g (5% probability of liquefaction) in equivalent linear analysis to produce surface Ia = 0.265 m/sec to produce surface CAV5 = 5.39 m/sec

A New Intensity Measure for Liquefaction CAV5 efficiency w/r/t Chi-Chi motions Same 20 motions Soil profile consistent with Berth 4 at Port of Taichung Scaled three times: to produce surface PGA = 0.1g (5% probability of liquefaction) in equivalent linear analysis to produce surface Ia = 0.265 m/sec to produce surface CAV5 = 5.39 m/sec Applied as input motions to three sets of nonlinear, effective stress analyses

A New Intensity Measure for Liquefaction CAV5 efficiency w/r/t Chi-Chi motions Same 20 motions Soil profile consistent with Berth 4 at Port of Taichung Scaled set of 20 motions three times: to produce surface PGA = 0.1g (5% probability of liquefaction) in equivalent linear analysis to produce surface Ia = 0.265 m/sec to produce surface CAV5 = 5.39 m/sec Applied each set of scaled motions as input motions to three sets of nonlinear, effective stress analyses Three sets of pore pressure ratio profiles computed

A New Intensity Measure for Liquefaction Same 20 motions Soil profile consistent with Berth 4 at Port of Taichung Scaled three times: to produce surface PGA = 0.1g (5% probability of liquefaction) in equivalent linear analysis to produce surface Ia = 0.265 m/sec to produce surface CAV5 = 5.39 m/sec Applied as input motions to nonlinear, effective stress analyses Pore pressure ratio profiles computed PGA Arias intensity CAV5 Upper 20 m (N1)60 ~ 15 FC ~ 15%

A New Intensity Measure for Liquefaction Dispersion in ru lowest for CAV5, highest for PGA

A New Intensity Measure for Liquefaction Chi-Chi values well below California values Chi-Chi values below CA values Chi-Chi values slightly below CA values Attenuation relationship – M7.6, reverse

Summary Tremendous advances have been made in liquefaction hazard evaluation over the past 40 yrs Performance-based earthquake engineering will place additional demand on liquefaction hazard evaluators Most research efforts have focused on liquefaction resistance, but progress can also be made on loading side of equation Optimum characterization of loading requires parameter that is efficient, sufficient, and predictable CAV5 appears to have combination of efficiency, sufficiency, and predictability that is better than that of parameters more commonly used for liquefaction hazard evaluation. CAV5-based liquefaction hazard evaluation procedures should be investigated.