ground motions and liquefaction the loading part of the equation
DESCRIPTION
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 measureTRANSCRIPT
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
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
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
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
Intensity MeasuresIntensity Measures
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
Intensity MeasuresIntensity Measures
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
A New Intensity Measure for LiquefactionA New Intensity Measure for Liquefaction
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
Implications for Performance-Based Liquefaction Hazard EvaluationImplications for Performance-Based Liquefaction Hazard Evaluation
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*
Implications for Performance-Based Liquefaction Hazard EvaluationImplications for Performance-Based Liquefaction Hazard Evaluation
M
log m
log R
ln Y
M = M*
R = R*
ln Y
Influence of predictability
Y = Y*
How does uncertainty in attenuation
relationship affect IM?
Implications for Performance-Based Liquefaction Hazard EvaluationImplications for Performance-Based Liquefaction Hazard Evaluation
log m
log R
ln Y
M = M*
R = R*
ln Y
Influence of predictability
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
Implications for Performance-Based Liquefaction Hazard EvaluationImplications for Performance-Based Liquefaction Hazard Evaluation
IM
ru proportional to sum of thick
red lines
IM
IM
IM
P[EDP>EDP* | IM]
1.0
0.0
Implications for Performance-Based Liquefaction Hazard EvaluationImplications for Performance-Based Liquefaction Hazard Evaluation
ru proportional to sum of thick
red lines
Fragility curve with less uncertainty (in
prediction of EDP|IM)
IM
IM
IM
P[EDP>EDP* | IM]
1.0
0.0
ru proportional to sum of thick
red lines
Implications for Performance-Based Liquefaction Hazard EvaluationImplications for Performance-Based Liquefaction Hazard Evaluation
IM
IM
IM
P[EDP>EDP* | IM]
1.0
0.0
ru proportional to sum of thick
red lines
Implications for Performance-Based Liquefaction Hazard EvaluationImplications for Performance-Based Liquefaction Hazard Evaluation
Reduction in EDP
Increasing efficiency of IM leads to reduction in EDP
A New Intensity Measure for LiquefactionA New Intensity Measure for Liquefaction
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
A New Intensity Measure for LiquefactionA New Intensity Measure for Liquefaction
CAV5 efficiency w/r/t Chi-Chi motions
Same 20 motions
A New Intensity Measure for LiquefactionA 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 LiquefactionA 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:
(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
A New Intensity Measure for LiquefactionA 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:
(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
Applied as input motions to three sets of nonlinear, effective stress analyses
A New Intensity Measure for LiquefactionA 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:
(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
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 LiquefactionA New Intensity Measure for Liquefaction
Same 20 motions
Soil profile consistent with Berth 4 at Port of Taichung
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
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
A New Intensity Measure for LiquefactionA New Intensity Measure for Liquefaction
Dispersion in ru lowest for CAV5, highest for PGA
A New Intensity Measure for LiquefactionA New Intensity Measure for Liquefaction
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.