Ground Motions and Liquefaction The Loading Part of the Equation

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Ground Motions and Liquefaction – The Loading Part of the EquationGround Motions and Liquefaction – The Loading Part of the Equation

Steve Kramer

Roy Mayfield

Bob Mitchell

University of Washington

Seattle, Washington USA

Evaluation of Liquefaction PotentialEvaluation of Liquefaction Potential

DemandCapacity

LoadingResistance

CSRCRRFS

SPTCPTVs

Peak accelerationMagnitude

= 0.65 rdPGA

g ’vo

vo 1MSF

Intensity Measure (IM):

• PGA & M (simplified method)

• Ih (Arias intensity method)

Vector measure

Scalar measure

Arias intensity

Most research

Performance-Based Earthquake EngineeringPerformance-Based Earthquake Engineering

Covers range of hazard (ground motion) levels

Includes effects of ground motions

Accounts for uncertainty in parameters, relationships

dIMEDPdGEDPDMdGDMDVG IMDV

Intensity measure

Engineering demand

parameterDamage measure

Decision variable

Repair cost

Crack width

Interstory drift

Sa(To)

Seismic hazard

curve – PGA vs Sa(To)

Fragility curve – interstory drift given

Sa(To)

Fragility curve – crack width

given interstory drift

Fragility curve – repair cost given crack

Risk curve – Cost vs

dIMEDPG IMEDP

dPGArG PGAuru

For liquefaction,EDP = ru

IM = PGA

Intensity MeasuresIntensity 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

(N1)60-cs = {5, 15, 25 }

(N1)60-cs = 60

H = {4, 9, 14 m}

0.1 1 10 100 1000

Closest Distance, R (km)

Distance

9 profiles

22 earthquakes

>450 motions

~300 candidate IMs

Efficiency

EDP = depth-averaged excess pore pressure ratio, (ru)ave

PGA (cm/sec2) Arias intensity (m/sec)

High scatter = low efficiency

Lower scatter = higher efficiency

Sufficiency

EDP = depth-averaged excess pore pressure ratio, (ru)avg

PGA PGA

Strong trends – insufficient w/r/t magnitude

Weaker trends – more sufficient w/r/t distance

A New Intensity Measure for LiquefactionA New Intensity Measure for Liquefaction

Cumulative absolute velocity5 cm/sec2 threshold

Accelerogram

|a(t)|

|a(t)| after threshold

Integral

Little scatter = efficient

Little dependence on M or R = sufficient

Predictability – attenuation relationship developed from database of CA earthquakes

Standard error

ln PGA = 0.620

ln Ia = 1.070

ln CAV5 = 0.708

Medium-low

Implications for Performance-Based Liquefaction Hazard EvaluationImplications for Performance-Based Liquefaction Hazard Evaluation

dPGArG PGAuru

iiuu i

u IMIMrrPr1

log IM

IM hazard curve

log ru

ru hazard curve IM

P[ru>r*u|IM]

(ru)1(ru)2 (ru)3

ru|IM fragility curves

Discrete form

M = M*

R = R*

Influence of predictability

P[Y > Y*| M=M*, R=R*]

Y = Y*

M = M*

R = R*

Y = Y*

How does uncertainty in attenuation

relationship affect IM?

M = M*

R = R*

Y = Y*

P[Y > Y*| M=M*, R=R*]

Reducing uncertainty in attenuation relationship reduces P[Y > Y* | M,R], which reduces IM.

Poor predictability

Goodpredictability

P[EDP>EDP* | IM]

ru proportional to sum of thick

red lines

P[EDP>EDP* | IM]

red lines

Fragility curve with less uncertainty (in

prediction of EDP|IM)

P[EDP>EDP* | IM]

red lines

P[EDP>EDP* | IM]

red lines

Reduction in EDP

Increasing efficiency of IM leads to reduction in EDP

Frequency domain characteristics

Relationship between IM and spectral acceleration

Depends on period at which spectral acceleration is computed

20 Chi-Chi motions

0.1g < PGA < 0.3g

11 km < R < 26 km

Highest correlation at

high frequencies for PGA and Ia

Highest correlation at lower frequencies

for CAV5

CAV5 efficiency w/r/t Chi-Chi motions

Same 20 motions

Soil profile consistent with Berth 4 at Port of Taichung

Same 20 motions

Scaled three times:

(1) to produce surface PGA = 0.1g (5% probability of liquefaction) in equivalent linear analysis

(2) to produce surface Ia = 0.265 m/sec

(3) to produce surface CAV5 = 5.39 m/sec

Same 20 motions

Scaled three times:

Applied as input motions to three sets of nonlinear, effective stress analyses

Same 20 motions

Scaled set of 20 motions three times:

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

Same 20 motions

Scaled three times:

Applied as input motions to nonlinear, effective stress analyses

Pore pressure ratio profiles computed

Upper 20 m(N1)60 ~ 15FC ~ 15%

PGA Arias intensity CAV5

Dispersion in ru lowest for CAV5, highest for PGA

Chi-Chi values

below CA values

Chi-Chi values slightly below CA values

Attenuation relationship – M7.6, reverse

Chi-Chi values well below California values

SummarySummary

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.

Ground Motions and Liquefaction The Loading Part of the Equation

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