challenges in sampling extreme events: a case study of …€¦ · the evaluation of liquefaction...

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IntroductionChallenges In Evaluating Liquefaction

References & Acknowledgment

Challenges in Sampling Extreme Events: A CaseStudy of Probabilistic Earthquake-Induced

Liquefaction Hazard Evaluation

Thomas Oommen

Assistant ProfessorDepartment of Geological Engineering

Michigan Technological University

November 30, 2011

Oommen, Michigan Tech European Science Foundation Conference

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What is liquefaction?

It is the process of changing a saturated cohesionless soil from a solid to liquid state due toincreased pore pressure

Low pore-water pressure

Large contact forces

Earthquake⇒

Large pore-water pressure

Low contact forces

Liquefaction induced ground failures: flow slides, lateral spreading, ground settlements, andsand boils


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Significance of Liquefaction Characterization

In tectonically active regions of the world, liquefaction presents a major threat to communities

1989 Loma Preita (M = 6.9)Marina District San Francisco

2010 Haiti (M = 7.0)Port-Au-Prince

2011 New Zealand (M = 6.3)Christchurch

2011 Japan (M = 9.0)

(Photo courtesy: USGS)


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Evaluation of Liquefaction Potential

The evaluation of liquefaction potential first began to evolve after thetwo devastating earthquakes that occurred in 1964; the GreatAlaskan Earthquake (M=8) and the Niigata Earthquake (M=7.5) bothof which produced significant liquefaction damage


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Current Evaluation Methods

DeterministicSeed et al. 1971

Youd et al 2001

SPT

Youd et al. 2001

P b bili ti

Logistic Regression

Liao et al. 1988

ProbabilisticBayesian Updating

Cetin et al. 2004

Clean Sand

CPT

DeterministicSeed et al. 1983

Youd et al. 2001

Logistic Regression

uefaction

ProbabilisticToprak et al. 1999

Bayesian Updating

Moss et al. 2006Sh W

Liq Shear Wave

VelocityDeterministic

Fine Grained Lab TestFine Grained Lab Test

In situ tests

Standard Penetration Test (SPT)

Cone Penetration Test (CPT)

Shear wave velocity (Vs)

Empirical Liquefaction Models (ELMs)

Deterministic: ”yes/no”

Probabilistic: 0 to 1


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Class Imbalance and Sampling BiasSpatial Issues

Geo-hazard Database Issues

Large number of events/instances from one class whilethe other is represented by only a few instances andthis imbalance in the dataset is referred as classimbalance

CPT database for liquefaction, the class ratio ofinstances of liquefaction: non-liquefaction is76:24

The difference in the class ratio of the sample to itspopulation is referred as sampling bias

For natural hazard applications, it is common forthe hazard event to be sampled much morefrequently than the non-hazard event

Example-1

Population = 50:50Sample = 50:50

No class imbalance

No sampling bias

Example-2

Population = 80:20Sample = 50:50

No class imbalance

Has sampling bias


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Maximum Likelihood Logistic Regression (MLLR)

Specific research question

Analyze the issues of sampling bias and class imbalance on theperformance of MLLR models

Logistic regression is a variation of linear regression

Widely used for empirical modeling of geo-hazards

ISI Web of Knowledge: 11,725 papers in which logisticregression appeared in either the title or keyword


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Controlled Experiments

Data

Generated two datasets with knowndistribution parameters

Dataset - 1: Case-A (50:50)

Dataset - 2: Case-B (80:20)

φ(x, α, β) =exp(α + β · x)

1 + exp(α + β · x)

ln[φ

(1 − φ)] = α + β · x

Samples

Generated samples from these datasetswith class ratio of (50:50, 60:40, 70:30,80:20, 90:10, 95:5, 98:2, & 99:1)

Theoretical properties of the simulated datasets

Case-A Case-B


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Case-A: Analysis (50:50)


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Case-B: Analysis (80:20)


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Solution: Re-sampling

Over-sampling (repeating minority class)

Under-sampling (removing majority class)


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Conclusion: Sampling Bias and Class Imbalance

The predicted probability using a MLLR model is closest to the actual probability whenthe sample has the same distribution as the original dataset/population

When the sampling bias is reduced using basic re-sampling techniques, bothover-sampling and under-sampling will reduce the difference in the actual and predictedprobabilities


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MotivationHow much does liquefaction extent?

Does the absence of surfaceexpression of liquefaction guaranteethat the site did not liquefy?

ObjectiveHow accurate is Liquefaction PotentialIndex (LPI) at predicting locations ofliquefaction

What buffer distance is appropriate forseparating liquefied and nonliquefiedmaterials


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17 January 1995, Hyogo-ken Nanbu Earthquake (M = 6.9)

Amount of damage caused by the eventfar exceeded what would be expectedfor a typical event of this magnitude

Widespread liquefaction (Elgamal et al.1996)

City of Kobe has built a geotechnicaldatabase system ”Kobe Jibankun”

Over 7000 boreholes with SPTmeasurements

http://gdc.cee.tufts.edu/databases


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Liquefaction Potential Index


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LPI classification at each borehole overlaid on the surficial geology units

Very high LPI category is primarily on the reclaimed land

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LegendLithology

Upper TerraceMiddle TerraceLower TerraceAlluvial LowlandAlluvial FanReclaimed LandLandslide

Obs. Lique.Sandboil

LPINon-liqueifiableLowModerateHighVeryhigh


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Spatial distribution of TPL and FPL for the LPI class very high (using 200m buffer)

200m - 91.9% TPL

100m - 83.0% TPL

0m - 18.8% TPL

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LegendLithology


Obs. Lique.Sandboil

Very HighTPL

l FPL


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Spatial distribution of TPL and FPL for the LPI class high (using 200m buffer)

200m - 74.7% TPL

100m - 57.6% TPL

0m - 5.0% TPL

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LegendLithology


Obs. Lique.Sandboil

HighTPL

l FPL


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Spatial distribution of TPN and FPN for the LPI class low (using 200m buffer)

200m - 41.7% TPN

100m - 57.6% TPN

0m - 95.0% TPN

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´0 0.75 1.5 Miles

LegendLithology


Obs. Lique.Sandboil

LowTPN

l FPN


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Spatial distribution of TPN and FPN for the LPI class non-liquefiable (using 200m buffer)

200m - 40.5% TPN

100m - 56.1% TPN

0m - 94.8% TPN

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LegendLithology


Obs. Lique.Sandboil

Non-liqufiableTPN

l FPN


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Conclusion: Spatial Issues

Majority of the liquefaction occurred in a reclaimed land

When a buffer distance in not used the ability of the LPI to identify locations of observedliquefaction is poor

A buffer zone of 100m balances the ratio of TPL and TPN

When a buffer zone of 200 m is used, the TPL for the very high LPI category jumps to92% but TPN decrease to 40.5%


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References

T Oommen, L G Baise, and R M Vogel., Sampling bias and class imbalance in maximum likelihood logistic regression,Mathematical Geosciences, Vol. 43(1), p.99-120, 2011.

T Oommen, E Thompson, H Tanaka, L G Baise, Y Tanaka, and R E Kayen., Spatial extent of liquefaction hazard using datafrom the 1995 Hyogo-Ken Nambu earthquake in Kobe, Japan, 5th International Conference on Earthquake GeotechnicalEngineering, Santiago, Chile, p.580-589, 2011.


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