Improved Liquefaction Hazard Evaluation through PLHA. Steven L. Kramer University of Washington

Improved Liquefaction Hazard Evaluation through PLHA Steven L. Kramer University of Washington

il Liquefaction hree primary questions to answer: Is the soil susceptible to liquefaction? If so, is the anticipated loading strong enough to initiate liquefaction? If so, what will be the effects of liquefaction? Yes Yes Susceptibility Initiation Effects No No hazard No No hazard Lateral spreading Flow sliding Settlement

Using mapped parameters, engineers can obtain benefits of fully probabilistic approach using conventional calculations uefaction Potential urrent procedures produce inconsistent liquefaction potential Inferred damage levels are inconsistent Inferred loss levels are inconsistent Inferred risk is inconsistent robabilistic performance-based approach can solve this problem Full-blown probabilistic analyses (PLHA) are time-consuming Approximate procedures are available

aluation of Liquefaction Potential Simplified Method SPT CPT V s FS CRR CSR Resistance Loading Capacity Demand Youd et al. Cetin-Seed

aluation of Liquefaction Potential Simplified Method SPT CPT V s FS CRR CSR Resistance Loading Capacity Demand Peak acceleration Magnitude PGA vo 1 = 0.65 r g d MSF vo Intensity Measure (IM): PGA Measure of amplitude of motion M Measure of duration (number of loading cycles)

onventional Evaluation of Liquefaction Potential 1. Determine 475-yr (or 2,475-yr) PGA One PGA 2. Determine corresponding M w from deaggregation 3. Compute CSR PGA vo 1 = 0.65 r g d MSF vo One M w One CSR 4. Based on (N 1 ) 60, compute CRR Probabilistic representation of 5. Compute FS L = CRR / CSR ground motion hazard is combined with deterministic representation of liquefaction resistance Conventional criterion: FS min = 1.1 1.3

tball Defense 11 players Different sizes Different speeds Different consequences

tball Defense Free safety Small Really fast Makes tackles all over field

tball Defense Middle linebacker Big Fast Makes tackles in middle of field

tball Defense Defensive tackle Huge Slow Little range, but hits really hard

ent Liquefaction Procedures Smaller, more frequent quefaction proach to lay calling Bigger, more rare Only block one player

proved Liquefaction Procedure Probabilistic Liquefaction Hazard Analysis (PLHA) Coupled probabilistic liquefaction potential procedure with PSHA

proved 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 FS* L Sum over all peak accelerations Sum over all magnitudes

proved Liquefaction Procedure Probabilistic Liquefaction Hazard Analysis (PLHA) Coupled probabilistic liquefaction potential procedure with PSHA Application of PEER PBEE framework Short T R Weak motions High FS L log FS Long T R Strong motions Low FS L

Illustration of procedure Idealized soil profile Liquefiable in weak motions Liquefiable in strong motions Element at 6 m depth: (N 1 ) 60 = 18

Seismic environments Mean annual rate of exceedance, amax (yr -1 ) 0.01 0.001 USGS National Hazard Mapping Program But we also need M w to evaluate liquefaction potential 0.0001 0.0 0.2 0.4 0.6 0.8 1.0

Selection of magnitude Multiple magnitudes contribute to PGA at a given return period

Selection of magnitude Multiple magnitudes contribute to PGA at a given return period Contributions are different at different return periods 108 yrs 975 yrs USGS Seattle Deaggregation 224 yrs 2475 yrs 475 yrs 4975 yrs

Selection of magnitude Multiple magnitudes contribute to PGA at a given return period Contributions are different at different return periods k down hazard curve into ponents associated with different nitudes sum is equal to Total

ssume idealized site is located in 10 different U.S. cities Location Lat. (N) Long. (W) 475-yr a max 2,475-yr a max Butte, MT 46.003 112.533 0.120 0.225 Charleston, SC 32.776 79.931 0.189 0.734 Eureka, CA 40.802 0.01 124.162 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 Annual rate of exceedance, 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 0.001 118.492 0.432 0.710 Seattle, WA 47.530 122.300 0.332 0.620 Butte Charleston Eureka Memphis Portland Salt Lake City San Francisco San Jose Santa Monica Seattle 0.0001 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

eterministic analysis using mean magnitudes Higher PGA 475 leads to: Lower FS L Higher N

erformance-based analysis Hazard curves for FS L, N req for element at 6 m depth

erformance-based analysis Hazard curves for FS L, N req for element at 6 m depth 0021

erformance-based analysis Hazard curves for FS L, N req for element at 6 m depth

erformance-based analysis Hazard curves for FS L, N req for element at 6 m depth compute deterministic N req es associated with ventional criterion for adequate efaction resistance (FS L > 1.2 g PGA 475 and mean magnitude then use liquefaction hazard ves for N req to compute return iod for liquefaction (N < N req ) el of agreement will provide ght into consistency of efaction hazards as evaluated g conventional approach

erformance-based analysis compute deterministic N req es associated with ventional criterion for adequate efaction resistance (FS L > 1.2 g PGA 475 and mean magnitude then use liquefaction hazard ves for N req to compute return iod for liquefaction (N < N req ) el of agreement will provide ght into consistency of efaction hazards as evaluated g conventional approach nsistent application of conventional procedures for evaluation of liquefaction

ssume idealized site is located in 10 different U.S. cities Deterministic analysis using mean magnitudes Similar FS L Similar N req

compute deterministic N req es associated with ventional criterion for adequate efaction resistance (FS L > 1.2 g PGA 475 and mean magnitude then use liquefaction hazard ves for N req to compute return iod for liquefaction (N < N req ) el of agreement will provide ght into consistency of efaction hazards as evaluated g conventional approach nsistent application of conventional procedures for evaluation of liquefaction

Relative factors of safety det N req N PB CRR N Location req CRR N Butte, MT 6.6 7.3 0.95 Charleston, SC 15.9 12.1 1.32 Eureka, CA 34.9 34.8 1.01 Memphis, TN 19.4 15.7 1.31 Portland, OR 17.9 18.8 0.94 Salt Lk. City, UT 22.5 21.1 1.11 San Fran., CA 31.8 31.5 1.02 San Jose, CA 28.3 29.6 0.91 Santa Mon., CA 27.3 27.5 0.99 Seattle, WA 23.5 24.2 0.95 det req PB req

Relative factors of safety < 1.0 = unconservative > 1.0 = conservative det N req N PB CRR N Location req CRR N Butte, MT 6.6 7.3 0.95 Charleston, SC 15.9 12.1 1.32 Eureka, CA 34.9 34.8 1.01 Memphis, TN 19.4 15.7 1.31 Portland, OR 17.9 18.8 0.94 Salt Lk. City, UT 22.5 21.1 1.11 San Fran., CA 31.8 31.5 1.02 San Jose, CA 28.3 29.6 0.91 Santa Mon., CA 27.3 27.5 0.99 Seattle, WA 23.5 24.2 0.95 nsistent application of conventional procedures for evaluation of liquefaction det req PB req 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, r d 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 0.22g M w =6.4 0.10g M w =6.0 0.26g M w =8.4 0.33g M w =6.6 0.07g M w =5.9 0.30g M w =6.8 0.12g M w =6.4 0.27g M w =8.4 0.25g 0.08g M w =5.9

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 N req for a specified return period lations performed on cross state (247 pts) ch point, PB calcs dered 100 PGA levels 0 magnitudes f 247 deterministic 94,000 probabilistic

Contours of N req for FS L = 1.2 in 6-m-deep element based on conventional analysis with 475-yr PGA and mean M w N req ~ 22 for Seattle

Contours of N req for FS L = 1.2 in 6-m-deep element based on conventional analysis with 475-yr PGA and mean M w N req ~ 22 for Seattle From N req hazard curve, corresponding return period is 400 yrs To obtain uniform hazard across state, use hazard curves to determine 400- yr N req values everywhere

Contours of N req based on performance-based analysis with 400-yr return period N req ~ 22 for Seattle

Contours of N req based on performance-based analysis with 400-yr return period N req ~ 22 for Seattle N req values east of Seattle are very nearly the same as deterministic values

Contours of N req based on performance-based analysis with 400-yr return period N req ~ 22 for Seattle N req values east of Seattle are very nearly the same as deterministic values N req values west of Seattle are lower

Contours of difference in N req 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 N req 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,

The image part with relationship ID rid6 was not found in the file. rformance-based Liquefaction Evaluation ite-specific correction Cetin equation CRR N exp (1 0.004FC) 29.53ln M 3.70 ln( ' ) 0.05FC 16.85 1 1,60 w vo a L 13.32 / p ( P ) Letting we can write N 13.32lnCSR 29.53ln M 3.70ln( ' / ) 16.85 1 1,60, cs w vo a L Substituting for CSR and using P L = 0.6 (equivalent to standard curve) a max vo N1,60, 13.32ln 0.65 29.53ln 3.70ln( ' / ) 16.85 ' cs rd M w vo pa g vo p ( P ) 0.253

ite-specific correction Defining these terms for a reference site condition, 13.32 ln amax vo N1,60,, 0.65 ' cs ref d ref w vo a ref g vo ref r 29.53ln M 3.70 ln( ' / p ) 16.85 0.253 Then the site-specific required penetration resistance can be defined as N 1,60,cs,req = N 1,60,cs,ref + N Site- and profile-specific blowcount adjustment So N = N 1,60,cs,req - N 1,60,cs,ref a max vo 13.32ln 0.65 r 29.53ln 3.70 ln( ' / ) 16.85 0.253 ' d M w vo pa g Initial stress-related terms vo ' 13.32 ln max 0.65 vo - r Response-related 29.53ln M 3.70 term ln( ' a g vo ref d ref w vo / p a ) ref 16.85 0.253 vo / ' r ' / vo d vo p a

Then N vo / ' vo 13.32 ln ( vo / ' vo ) ref ' vo 3.70 ln ( ' vo ) ref rd 13.32 ln ( rd ) ref N N r d = N + N rd Function of: density groundwater level depth Function of: depth shear wave velocity peak acceleration earthquake magnitude

Correction of stress-related terms

Correction of r d -related terms

parison of N req values chart-based approximate procedure vs. full PB analysis Site-specific FS L

parison of N req values chart-based approximate procedure vs. full PB analysis Approximated N req Site-specific FS L Site-specific N req

parison of N req values chart-based approximate procedure vs. full PB analysis Approximated N req ple, chart-based adjustment procedure appears to be useful Site-specific FS L Site-specific N req

parison of N req values chart-based approximate procedure vs. full PB analysis Approximated N req ple, chart-based adjustment procedure appears to be useful efits of performance-based calculations embodied in mapped N req value for rence element Site-specific in reference FS profile. L Site-specific N req

parison of N req values chart-based approximate procedure vs. full PB analysis Approximated N req ple, chart-based adjustment procedure is useful agrees with full PLHA efits of performance-based calculations embodied in mapped N req value for rence element Site-specific in reference FS profile. L Site-specific N req r accounts for site-specific conditions through adjustment procedure.

475-yr N req Can map N req values for reference element in reference soil profile 2,475-yr N req

rnative approaches Map reference CSR value for given return period Use CSR-based adjustments

rnative approaches Map reference CSR value for given return period Use CSR-based adjustments Kevin Franke, BYU Approximated N req

rnative approaches Map reference CSR value for given return period Use CSR-based adjustments T R = 475 yrs

rnative approaches Map reference CSR value for given return period Use CSR-based adjustments T R = 1,033 yrs

rnative approaches Map reference CSR value for given return period Use CSR-based adjustments T R = 2,475 yrs

rnative approaches Map magnitude-corrected PGA value CSR 0.65 PGA g ' vo vo rd MSF 0.65 PGA MSF ' vo vo r d 0.65PGA M ' vo vo r d PGA M PGA MSF Could create program to run USGS PSHA analysis, extract hazard curve and deaggregation data, and compute PGA M at different return periods.

Result: User goes to map or website, computes PGA M for return period of interest User computes liquefaction potential (FS L ) 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