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Improved Liquefaction Hazard Evaluation through PLHA
Steven L. KramerUniversity of Washington
Three primary questions to answer:
Is the soil susceptible to liquefaction?
oil Liquefaction
If so, is the anticipated loading strong enough to initiate liquefaction?
If so, what will be the effects of liquefaction?
Susceptibility Initiation EffectsYes Yes
No
No hazard
No
No hazard
Lateral spreadingFlow slidingSettlement
Three primary questions to answer:
Is the soil susceptible to liquefaction?
oil Liquefaction
If so, is the anticipated loading strong enough to initiate liquefaction?
If so, what will be the effects of liquefaction?
Susceptibility Initiation EffectsYes Yes
No
No hazard
No
No hazard
Evaluation of liquefaction potential
Current procedures produce inconsistent liquefaction potential
Inferred damage levels are inconsistent
Inferred loss levels are inconsistent
Inferred risk is inconsistent
Probabilistic performance-based approach can solve this problem
Full-blown probabilistic analyses (PLHA) are time-consuming
Approximate procedures are available
Using mapped parameters, engineers can obtain benefits of fully probabilistic approach using conventional calculations
quefaction Potential
DemandCapacity
LoadingResistance
CSRCRRFS
SPTCPTVs
valuation of Liquefaction Potential
Simplified Method
Youd et al.Youd et al. Cetin-SeedCetin-Seed
DemandCapacity
LoadingResistance
CSRCRRFS
SPTCPTVs
= 0.65 rdPGA
g ’vo
vo 1MSF
Peak accelerationMagnitude
Intensity Measure (IM):
• PGA
• M
valuation of Liquefaction Potential
Simplified Method
Measure of amplitude of motion
Measure of duration (number of loading cycles)
Conventional Evaluation of Liquefaction Potential
1. Determine 475-yr (or 2,475-yr) PGA
2. Determine corresponding Mw from deaggregation
3. Compute CSR = 0.65 rdPGA
g ’vo
vo 1MSF
4. Based on (N1)60, compute CRR
5. Compute FSL = CRR / CSR
Conventional criterion:
FSmin = 1.1 – 1.3
Probabilistic representation of ground motion hazard is combined with deterministic representation of liquefaction resistance
Probabilistic representation of ground motion hazard is combined with deterministic representation of liquefaction resistance
One PGA
One Mw
One CSR
otball Defense
11 playersDifferent sizesDifferent speedsDifferent consequences
Free safetySmallReally fastMakes tackles all over field
otball Defense
Middle linebackerBigFastMakes tackles in middle of field
otball Defense
Defensive tackleHugeSlowLittle range, but hits really hard
otball Defense
rrent Liquefaction Procedures
Only block one player
Smaller, more frequent
Bigger, more rare
iquefaction pproach to
play calling
mproved Liquefaction Procedure
Probabilistic Liquefaction Hazard Analysis (PLHA)
Coupled probabilistic liquefaction potential procedure with PSHA
mproved Liquefaction Procedure
Probabilistic Liquefaction Hazard Analysis (PLHA)
Coupled probabilistic liquefaction potential procedure with PSHA
Application of PEER PBEE framework
Mean annual rate of non-exceedance of FSL
Sum over all peak accelerations
Sum over all magnitudes
*
mproved Liquefaction Procedure
Probabilistic Liquefaction Hazard Analysis (PLHA)
Coupled probabilistic liquefaction potential procedure with PSHA
Application of PEER PBEE framework
log
FS
Short TRWeak motionsHigh FSL
Long TRStrong motionsLow FSL
mproved Liquefaction Procedure
Probabilistic Liquefaction Hazard Analysis (PLHA)
Coupled probabilistic liquefaction potential procedure with PSHA
Application of PEER PBEE framework
log
FS
TR,L
Return period of liquefaction
Illustration of procedure
Idealized soil profile
erformance-Based Liquefaction Evaluation
Liquefiable in weak motions
Liquefiable in strong motions
Element at 6 m depth: (N1)60 = 18
P k l ti ( )
0.0 0.2 0.4 0.6 0.8 1.0
Mea
n an
nual
rate
of e
xcee
danc
e,
amax
(yr-1
)
0.0001
0.001
0.01
Seismic environments
erformance-Based Liquefaction Evaluation
But we also need Mwto evaluate
liquefaction potential
USGS National Hazard Mapping ProgramUSGS National Hazard Mapping Program
Selection of magnitude
• Multiple magnitudes contribute to PGA at a given return period
erformance-Based Liquefaction Evaluation
Selection of magnitude
• Multiple magnitudes contribute to PGA at a given return period
• Contributions are different at different return periods
108 yrs 975 yrs
475 yrs
224 yrs 2475 yrs
4975 yrs
USGS Seattle DeaggregationUSGS Seattle Deaggregation
erformance-Based Liquefaction Evaluation
erformance-Based Liquefaction Evaluation
Selection of magnitude
• Multiple magnitudes contribute to PGA at a given return period
• Contributions are different at different return periods
ak down hazard curve into mponents associated with different gnitudes – sum is equal to Total ve
ak down hazard curve into mponents associated with different gnitudes – sum is equal to Total ve
erformance-Based Liquefaction Evaluation
Location Lat. (N) Long. (W) 475-yr amax 2,475-yr amax
Butte, MT 46.003 112.533 0.120 0.225
Charleston, SC 32.776 79.931 0.189 0.734
Eureka, CA 40.802 124.162 0.658 1.023
Memphis, TN 35.149 90.048 0.214 0.655
Portland, OR 45.523 122.675 0.204 0.398
Salt Lake City, UT 40.755 111.898 0.298 0.679
San Francisco, CA 37.775 122.418 0.468 0.675
San Jose, CA 37.339 121.893 0.449 0.618
Santa Monica, CA 34.015 118.492 0.432 0.710
Seattle, WA 47.530 122.300 0.332 0.620
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Ann
ual r
ate
of e
xcee
danc
e,
0.0001
0.001
0.01ButteCharlestonEurekaMemphisPortlandSalt Lake CitySan FranciscoSan JoseSanta MonicaSeattle
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Ann
ual r
ate
of e
xcee
danc
e,
0.0001
0.001
0.01ButteCharlestonEurekaMemphisPortlandSalt Lake CitySan FranciscoSan JoseSanta MonicaSeattle
Assume idealized site is located in 10 different U.S. cities
erformance-Based Liquefaction Evaluation
Deterministic analysis – using mean magnitudes
Higher PGA475 leads to:Higher PGA475 leads to: Lower FSL
Higher Nreq
Lower FSL
Higher Nreq
erformance-Based Liquefaction Evaluation
Performance-based analysis
Hazard curves for FSL, Nreq for element at 6 m depthHazard curves for FSL, Nreq for element at 6 m depth
erformance-Based Liquefaction Evaluation
Performance-based analysis
Hazard curves for FSL, Nreq for element at 6 m depthHazard curves for FSL, Nreq for element at 6 m depth
0021
erformance-Based Liquefaction Evaluation
Performance-based analysis
0021
Hazard curves for FSL, Nreq for element at 6 m depthHazard curves for FSL, Nreq for element at 6 m depth
erformance-Based Liquefaction Evaluation
Performance-based analysis
Hazard curves for FSL, Nreq for element at 6 m depthHazard curves for FSL, Nreq for element at 6 m depth
erformance-Based Liquefaction Evaluation
Performance-based analysis
Hazard curves for FSL, Nreq for element at 6 m depthHazard curves for FSL, Nreq for element at 6 m depth
n compute deterministic Nreques associated with nventional criterion for adequate uefaction resistance (FSL > 1.2 ng PGA475 and mean magnitude
n compute deterministic Nreques associated with nventional criterion for adequate uefaction resistance (FSL > 1.2 ng PGA475 and mean magnitude
n then use liquefaction hazard rves for Nreq to compute return riod for liquefaction (N < Nreq)
n then use liquefaction hazard rves for Nreq to compute return riod for liquefaction (N < Nreq)
vel of agreement will provide ight into consistency of
uefaction hazards as evaluated ng conventional approach
vel of agreement will provide ight into consistency of
uefaction hazards as evaluated ng conventional approach
erformance-Based Liquefaction Evaluation
Performance-based analysis
n compute deterministic Nreques associated with nventional criterion for adequate uefaction resistance (FSL > 1.2 ng PGA475 and mean magnitude
n compute deterministic Nreques associated with nventional criterion for adequate uefaction resistance (FSL > 1.2 ng PGA475 and mean magnitude
n then use liquefaction hazard rves for Nreq to compute return riod for liquefaction (N < Nreq)
n then use liquefaction hazard rves for Nreq to compute return riod for liquefaction (N < Nreq)
vel of agreement will provide ight into consistency of
uefaction hazards as evaluated ng conventional approach
vel of agreement will provide ight into consistency of
uefaction hazards as evaluated ng conventional approach
onsistent application of conventional procedures for evaluation of liquefaction t ti l l d t i i t t t l li f ti h d
onsistent application of conventional procedures for evaluation of liquefaction t ti l l d t i i t t t l li f ti h d
erformance-Based Liquefaction Evaluationerformance-Based Liquefaction Evaluation
Location Lat. (N) Long. (W) 475-yr amax 2,475-yr amax
Butte, MT 46.003 112.533 0.120 0.225
Charleston, SC 32.776 79.931 0.189 0.734
Eureka, CA 40.802 124.162 0.658 1.023
Memphis, TN 35.149 90.048 0.214 0.655
Portland, OR 45.523 122.675 0.204 0.398
Salt Lake City, UT 40.755 111.898 0.298 0.679
San Francisco, CA 37.775 122.418 0.468 0.675
San Jose, CA 37.339 121.893 0.449 0.618
Santa Monica, CA 34.015 118.492 0.432 0.710
Seattle, WA 47.530 122.300 0.332 0.620
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Ann
ual r
ate
of e
xcee
danc
e,
0.0001
0.001
0.01ButteCharlestonEurekaMemphisPortlandSalt Lake CitySan FranciscoSan JoseSanta MonicaSeattle
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Ann
ual r
ate
of e
xcee
danc
e,
0.0001
0.001
0.01ButteCharlestonEurekaMemphisPortlandSalt Lake CitySan FranciscoSan JoseSanta MonicaSeattle
Assume idealized site is located in 10 different U.S. cities
Equal PGA475
erformance-Based Liquefaction Evaluationerformance-Based Liquefaction Evaluation
Deterministic analysis – using mean magnitudes
Assume idealized site is located in 10 different U.S. cities
Similar FSLSimilar FSL Similar NreqSimilar Nreq
erformance-Based Liquefaction Evaluation
n compute deterministic Nreques associated with nventional criterion for adequate uefaction resistance (FSL > 1.2 ng PGA475 and mean magnitude
n compute deterministic Nreques associated with nventional criterion for adequate uefaction resistance (FSL > 1.2 ng PGA475 and mean magnitude
n then use liquefaction hazard rves for Nreq to compute return riod for liquefaction (N < Nreq)
n then use liquefaction hazard rves for Nreq to compute return riod for liquefaction (N < Nreq)
vel of agreement will provide ight into consistency of
uefaction hazards as evaluated ng conventional approach
vel of agreement will provide ight into consistency of
uefaction hazards as evaluated ng conventional approach
onsistent application of conventional procedures for evaluation of liquefaction t ti l l d t i i t t t l li f ti h d
onsistent application of conventional procedures for evaluation of liquefaction t ti l l d t i i t t t l li f ti h d
erformance-Based Liquefaction Evaluation
N reqdet N PB
req NCRRNCRR
PBreq
reqdet
Location
Butte, MT 6.6 7.3 0.95Charleston, SC 15.9 12.1 1.32Eureka, CA 34.9 34.8 1.01Memphis, TN 19.4 15.7 1.31Portland, OR 17.9 18.8 0.94Salt Lk. City, UT 22.5 21.1 1.11San Fran., CA 31.8 31.5 1.02San Jose, CA 28.3 29.6 0.91Santa Mon., CA 27.3 27.5 0.99Seattle, WA 23.5 24.2 0.95
Relative factors of safety
erformance-Based Liquefaction Evaluation
N reqdet N PB
req NCRRNCRR
PBreq
reqdet
Location
Butte, MT 6.6 7.3 0.95Charleston, SC 15.9 12.1 1.32Eureka, CA 34.9 34.8 1.01Memphis, TN 19.4 15.7 1.31Portland, OR 17.9 18.8 0.94Salt Lk. City, UT 22.5 21.1 1.11San Fran., CA 31.8 31.5 1.02San Jose, CA 28.3 29.6 0.91Santa Mon., CA 27.3 27.5 0.99Seattle, WA 23.5 24.2 0.95
Relative factors of safety< 1.0 = unconservative
> 1.0 = conservative
Relative FS in Charleston is 45% higher than in San Jose
Relative FS in Charleston is 45% higher than in San Jose
onsistent application of conventional procedures for evaluation of liquefaction t ti l l d t i i t t t l li f ti h d
onsistent application of conventional procedures for evaluation of liquefaction t ti l l d t i i t t t l li f ti h d
erformance-Based Liquefaction Evaluation
Relative factors of safety
These are big differences
Geotechs spend a lot of time tweaking various components
Magnitude scaling factor, MSF
Depth reduction factor, rd
Overburden stress factor, K
Fines content correction
Effects of tweaks have much smaller effect than those shown here
erformance-Based Liquefaction Evaluation
So what can we do to improve consistency?
Base liquefaction criteria on return period of liquefaction
Consistent return period will lead to consistent probability of liquefaction
Can handle liquefaction potential in different ways
0.33gMw=6.6
0.10gMw=6.0
0.07gMw=5.9
0.12gMw=6.4
0.08gMw=5.9
0.22gMw=6.4
0.30gMw=6.8
0.25g
0.27gMw=8.4
0.26gMw=8.4
erformance-Based Liquefaction Evaluation
So what can we do to improve consistency?
Base liquefaction criteria on return period
Consistent return period will lead to consistent probability of liquefaction
Can be expressed in terms of Nreq for a specified return period
ulations performed on across state (247 pts)
ach point, PB calcs dered 100 PGA levels 0 magnitudes
of 247 deterministic 94,000 probabilistic
ulations performed on across state (247 pts)
ach point, PB calcs dered 100 PGA levels 0 magnitudes
of 247 deterministic 94,000 probabilistic
erformance-Based Liquefaction Evaluation
Contours of Nreq for FSL = 1.2 in 6-m-deep element based on conventional analysis with 475-yr PGA and mean Mw
Nreq ~ 22 for SeattleNreq ~ 22 for Seattle
erformance-Based Liquefaction Evaluation
Contours of Nreq for FSL = 1.2 in 6-m-deep element based on conventional analysis with 475-yr PGA and mean Mw
Nreq ~ 22 for Seattle
From Nreq hazard curve, corresponding return period is 400 yrs.
Nreq ~ 22 for Seattle
From Nreq hazard curve, corresponding return period is 400 yrs.
erformance-Based Liquefaction Evaluation
Contours of Nreq for FSL = 1.2 in 6-m-deep element based on conventional analysis with 475-yr PGA and mean Mw
Nreq ~ 22 for Seattle
From Nreq hazard curve, corresponding return period is 400 yrs
To obtain uniform hazard across state, use hazard curves to determine 400-yr Nreq values everywhere
Nreq ~ 22 for Seattle
From Nreq hazard curve, corresponding return period is 400 yrs
To obtain uniform hazard across state, use hazard curves to determine 400-yr Nreq values everywhere
erformance-Based Liquefaction Evaluation
Contours of Nreq based on performance-based analysis with 400-yr return period
Nreq ~ 22 for SeattleNreq ~ 22 for Seattle
erformance-Based Liquefaction Evaluation
Nreq ~ 22 for Seattle
Nreq values east of Seattle are very nearly the same as deterministic values
Nreq ~ 22 for Seattle
Nreq values east of Seattle are very nearly the same as deterministic values
Contours of Nreq based on performance-based analysis with 400-yr return period
erformance-Based Liquefaction Evaluation
Nreq ~ 22 for Seattle
Nreq values east of Seattle are very nearly the same as deterministic values
Nreq values west of Seattle are lower
Nreq ~ 22 for Seattle
Nreq values east of Seattle are very nearly the same as deterministic values
Nreq values west of Seattle are lower
Contours of Nreq based on performance-based analysis with 400-yr return period
erformance-Based Liquefaction Evaluation
Contours of difference in Nreq for conventional and performance-based analyses
erformance-Based Liquefaction Evaluation
Contours of relative factor of safety inherent in use of conventional analyses
Coastal sites are effectively being required to design for 40% - 50% higher FS than required to obtain same hazard as Seattle
Coastal sites are effectively being required to design for 40% - 50% higher FS than required to obtain same hazard as Seattle
erformance-Based Liquefaction Evaluation
Contours of relative factor of safety inherent in use of conventional analyses
Coastal sites are effectively being required to design for 40% - 50% higher FS than required to obtain same hazard as Seattle
Risk-consistent design using conventional analyses should use
Coastal sites are effectively being required to design for 40% - 50% higher FS than required to obtain same hazard as Seattle
Risk-consistent design using conventional analyses should use
erformance-Based Liquefaction Evaluation
Contours of Nreq based on performance-based analysis with 400-yr return period
Results correspond to 6 m deep element in reference profile. How can they be used for different depths in different profiles,
i.e. for site-specific liquefaction hazard evaluations?
Results correspond to 6 m deep element in reference profile. How can they be used for different depths in different profiles,
i.e. for site-specific liquefaction hazard evaluations?
erformance-Based Liquefaction Evaluation
ite-specific correction
32.13)(85.1605.0)/'ln(70.3ln53.29)004.01(
exp1
60,1 Lavow PFCpMFCNCRR
Cetin equation
LettingThe image part with relationship ID rId6 was not found in the file.
we can write
)(85.16)/'ln(70.3ln53.29ln32.13 1,60,1 Lavowcs PpMCSRN
253.085.16)/'ln(70.3ln53.29
'65.0ln32.13 max
,60,1
avowd
vo
vocs pMr
gaN
Substituting for CSR and using PL = 0.6 (equivalent to standard curve)
erformance-Based Liquefaction Evaluation
ite-specific correction
Defining these terms for a reference site condition,
253.085.16)/'ln(70.3ln53.29'
65.0ln32.13 max,,60,1
refavowrefd
refvo
vorefcs pMr
ga
N
Then the site-specific required penetration resistance can be defined as
N1,60,cs,req = N1,60,cs,ref + N
So N = N1,60,cs,req - N1,60,cs,ref
avodvovo pr /'ln703ln3213'/ln3213
253.085.16)/'ln(70.3ln53.29
'65.0ln32.13 max
avowd
vo
vo pMrg
a
253.085.16)/'ln(70.3ln53.29'
65.0ln32.13 max
refavowrefd
refvo
vo pMrg
a- Response-related termResponse-related term
Initial stress-related termsInitial stress-related terms
Site- and profile-specific blowcount adjustment
drrefd
d
refvo
vo
refvovo
vovo NNrr
)(ln32.13
)'('ln70.3
)'/('/ln32.13N
erformance-Based Liquefaction Evaluation
Then
= N + Nrd
Function of:densitygroundwater leveldepth
Function of:depthshear wave velocitypeak accelerationearthquake magnitude
erformance-Based Liquefaction Evaluation
drrefd
d
refvo
vo
refvovo
vovo NNrr
)(ln32.13
)'('ln70.3
)'/('/ln32.13N
Then
= N + Nrd
Function of:densitygroundwater leveldepth
Function of:depthshear wave velocitypeak accelerationearthquake magnitude
erformance-Based Liquefaction Evaluation
Correction of stress-related terms
erformance-Based Liquefaction Evaluation
Correction of rd-related terms
erformance-Based Liquefaction Evaluation
mparison of Nreq values – chart-based approximate procedure vs. full PB analysis
Site-specific FSL
erformance-Based Liquefaction Evaluation
mparison of Nreq values – chart-based approximate procedure vs. full PB analysis
Site-specific FSL Site-specific Nreq
App
roxi
mat
ed N
req
erformance-Based Liquefaction Evaluation
mparison of Nreq values – chart-based approximate procedure vs. full PB analysis
Site-specific FSL Site-specific Nreq
App
roxi
mat
ed N
req
mple, chart-based adjustment procedure appears to be usefulmple, chart-based adjustment procedure appears to be useful
erformance-Based Liquefaction Evaluation
mparison of Nreq values – chart-based approximate procedure vs. full PB analysis
Site-specific FSL Site-specific Nreq
App
roxi
mat
ed N
req
mple, chart-based adjustment procedure appears to be useful
nefits of performance-based calculations embodied in mapped Nreq value for erence element in reference profile.
mple, chart-based adjustment procedure appears to be useful
nefits of performance-based calculations embodied in mapped Nreq value for erence element in reference profile.
erformance-Based Liquefaction Evaluation
mparison of Nreq values – chart-based approximate procedure vs. full PB analysis
Site-specific FSL Site-specific Nreq
App
roxi
mat
ed N
req
mple, chart-based adjustment procedure is useful – agrees with full PLHA
nefits of performance-based calculations embodied in mapped Nreq value for erence element in reference profile.
er accounts for site-specific conditions through adjustment procedure.
mple, chart-based adjustment procedure is useful – agrees with full PLHA
nefits of performance-based calculations embodied in mapped Nreq value for erence element in reference profile.
er accounts for site-specific conditions through adjustment procedure.
erformance-Based Liquefaction Evaluation475-yr Nreq
2,475-yr Nreq
Can map Nreq values for reference element in reference soil profile
erformance-Based Liquefaction Evaluation
ernative approaches
Map reference CSR value – for given return period
Use CSR-based adjustments
K i F k BYUK i F k BYU
erformance-Based Liquefaction Evaluation
ernative approaches
Map reference CSR value – for given return period
Use CSR-based adjustments
Kevin Franke, BYUKevin Franke, BYU
Site specific N
App
roxi
mat
ed N
req
erformance-Based Liquefaction Evaluation
ernative approaches
Map reference CSR value – for given return period
Use CSR-based adjustments
TR = 475 yrs
erformance-Based Liquefaction Evaluation
ernative approaches
Map reference CSR value – for given return period
Use CSR-based adjustments
TR = 1,033 yrs
erformance-Based Liquefaction Evaluation
ernative approaches
Map reference CSR value – for given return period
Use CSR-based adjustments
TR = 2,475 yrs
erformance-Based Liquefaction Evaluation
ernative approaches
Map magnitude-corrected PGA value
MSFr
gPGACSR d
vo
vo '
65.0
dvo
vo rMSFPGA
'
65.0
dvo
voM rPGA
'65.0
MSFPGAPGAM
Could create program to run USGS PSHA analysis, extract hazard curve and deaggregation data, and compute PGAM at different return periods.Could create program to run USGS PSHA analysis, extract hazard curve and deaggregation data, and compute PGAM at different return periods.Program could be used to create PGAM maps or could be madeProgram could be used to create PGAM maps or could be made
erformance-Based Liquefaction Evaluation
Result:
User goes to map or website, computes PGAM for return period of interest
User computes liquefaction potential (FSL) in same way he/she does now
Issues:
Requires selection of liquefaction potential “model(s)”
In short term (next 5 yrs), Idriss and Boulanger procedure most common
In longer term, NGL relationships will be available
Multiple relationships by different modelers
Epistemic uncertainty characterized
erformance-Based Liquefaction Evaluation
Benefits:
• More complete evaluation of liquefaction potential
Considers all levels of shaking
All PGAs
All magnitudes
• Provides consistent actual liquefaction hazards at sites in different seismo-tectonic environments
Equal hazards across U.S.
Equal retrofit / soil improvement requirements across U.S.
• Would allow realization of full benefits of NGL models