ground motions and liquefaction the loading part of the equation

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

= Ih

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

width

Risk curve – Cost vs

Cost











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

2 m

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

(N1)60-cs = 60

H = {4, 9, 14 m}

20 m

4.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

0.1 1 10 100 1000

Closest Distance, R (km)

Mag

nitu

de

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

(ru)

ave


Sufficiency

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

PGA PGA

Ia Ia

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

(m/s)

CAV5

Cumulative absolute velocity5 cm/sec2 threshold

Accelerogram

|a(t)|

|a(t)| after threshold

Integral

Little scatter = efficient

Little dependence on M or R = sufficient

CAV5


CAV5

Predictability – attenuation relationship developed from database of CA earthquakes

Standard error

ln PGA = 0.620

ln Ia = 1.070

ln CAV5 = 0.708

Low

High

Medium-low

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

dPGArG PGAuru

IM

N

iiuu i

IM

u IMIMrrPr1

* |*

IM

log IM

IM hazard curve

ru

log ru

ru hazard curve IM

P[ru>r*u|IM]

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

ru|IM fragility curves

0

1

Discrete form


M

log m

log R

ln Y

M = M*

R = R*

ln Y

Influence of predictability

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

Y = Y*


M

log m

log R

ln Y

M = M*

R = R*

ln Y


Y = Y*

How does uncertainty in attenuation

relationship affect IM?


log m

log R

ln Y

M = M*

R = R*

ln Y


Y = Y*

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

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

IM

IM

Poor predictability

Goodpredictability

IM

IM

IM

P[EDP>EDP* | IM]

1.0

0.0


IM

ru proportional to sum of thick

red lines

IM

IM

IM

P[EDP>EDP* | IM]

1.0

0.0



red lines

Fragility curve with less uncertainty (in

prediction of EDP|IM)

IM

IM

IM

P[EDP>EDP* | IM]

1.0

0.0


red lines


IM

IM

IM

P[EDP>EDP* | IM]

1.0

0.0


red lines


Reduction in EDP

Increasing efficiency of IM leads to reduction in EDP


CAV5

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



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

Documents