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 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 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

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

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

Application of PEER PBEE framework

Mean annual rate of non-exceedance of FSL

Sum over all peak accelerations

Sum over all magnitudes

Short TRWeak motionsHigh FSL

Long TRStrong motionsLow FSL

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

0.0001

Seismic environments

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

• Contributions are different at different return periods

108 yrs 975 yrs

475 yrs

224 yrs 2475 yrs

4975 yrs

USGS Seattle DeaggregationUSGS Seattle Deaggregation

• Contributions are different at different return periods

ak down hazard curve into mponents associated with different gnitudes – sum is equal to Total ve

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

0.0001

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

0.0001

Assume idealized site is located in 10 different U.S. cities

Deterministic analysis – using mean magnitudes

Higher PGA475 leads to:Higher PGA475 leads to: Lower FSL

Higher Nreq

Lower FSL

Higher Nreq

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 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

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

0.0001

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

0.0001

Equal PGA475

erformance-Based Liquefaction Evaluationerformance-Based Liquefaction Evaluation

Deterministic analysis – using mean magnitudes

Similar FSLSimilar FSL Similar NreqSimilar Nreq

N reqdet N PB

req NCRRNCRR

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

N reqdet N PB

req NCRRNCRR

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 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

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

0.27gMw=8.4

0.26gMw=8.4

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

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

Nreq ~ 22 for Seattle

From Nreq hazard curve, corresponding return period is 400 yrs.

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

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

Contours of Nreq based on performance-based analysis with 400-yr return period

Nreq ~ 22 for SeattleNreq ~ 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 difference in Nreq for conventional and performance-based analyses

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

Contours of relative factor of safety inherent in use of conventional analyses

Risk-consistent design using conventional analyses should use

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?

ite-specific correction

32.13)(85.1605.0)/'ln(70.3ln53.29)004.01(

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

vocs pMr

Substituting for CSR and using PL = 0.6 (equivalent to standard curve)

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

vorefcs pMr

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

vo pMrg

253.085.16)/'ln(70.3ln53.29'

65.0ln32.13 max

refavowrefd

vo pMrg

a- Response-related termResponse-related term

Initial stress-related termsInitial stress-related terms

Site- and profile-specific blowcount adjustment

drrefd

refvovo

vovo NNrr

)(ln32.13

)'('ln70.3

)'/('/ln32.13N

= N + Nrd

Function of:densitygroundwater leveldepth

Function of:depthshear wave velocitypeak accelerationearthquake magnitude

drrefd

refvovo

vovo NNrr

)(ln32.13

)'('ln70.3

)'/('/ln32.13N

= N + Nrd

Function of:densitygroundwater leveldepth

Function of:depthshear wave velocitypeak accelerationearthquake magnitude

Correction of stress-related terms

Correction of rd-related terms

mparison of Nreq values – chart-based approximate procedure vs. full PB analysis

Site-specific FSL

Site-specific FSL Site-specific Nreq

mple, chart-based adjustment procedure appears to be usefulmple, chart-based adjustment procedure appears to be useful

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

mple, chart-based adjustment procedure is useful – agrees with full PLHA

er accounts for site-specific conditions through adjustment procedure.

mple, chart-based adjustment procedure is useful – agrees with full PLHA

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

ernative approaches

Map reference CSR value – for given return period

Use CSR-based adjustments

K i F k BYUK i F k BYU

ernative approaches

Kevin Franke, BYUKevin Franke, BYU

Site specific N

ernative approaches

TR = 475 yrs

ernative approaches

TR = 1,033 yrs

ernative approaches

TR = 2,475 yrs

ernative approaches

Map magnitude-corrected PGA value

gPGACSR d

vo rMSFPGA

voM rPGA

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

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

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

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