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

2. Evaluation of Liquefaction Potential
SPT
CPT Vs
Most research
= 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

3. 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)

4. 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)

5. 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

6. 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

7. 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)

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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

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

21. 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

22. 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 = m/sec
to produce surface CAV5 = 5.39 m/sec

23. 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 = m/sec
to produce surface CAV5 = 5.39 m/sec
Applied as input motions to three sets of nonlinear, effective stress analyses

24. 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 = 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

25. 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 = 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%

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

27. 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

28. 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.