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Evaluating desktop methods for assessing liquefaction-induced damage to infrastructure for the insurance… Kongar, Indranil; Rossetto, Rossetto; Giovinazzi, Sonia Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20151Evaluating Desktop Methods for Assessing Liquefaction-InducedDamage to Infrastructure for the Insurance SectorIndranil KongarResearch Engineer, Earthquake and People Interaction Centre, University College London, UKTiziana RossettoProfessor, Earthquake and People Interaction Centre, University College London, UKSonia GiovinazziSenior Research Fellow, Dept. Civil Engineering, University of Canterbury, Christchurch, NZABSTRACT: The current method used by insurance catastrophe models to account for liquefactionsimply applies a factor to shaking-induced losses based on liquefaction susceptibility. There is a needfor more sophisticated methods but they must be compatible with the data and resource constraints thatinsurers have to work with. This study compares five models: liquefaction potential index (LPI)calculated from shear-wave velocity; two implementations of the HAZUS software methodology; andtwo models based on USGS remote sensing data. Data from the September 2010 and February 2011Canterbury (New Zealand) earthquakes is used to compare observed liquefaction occurrences topredictions from these models using binary classification performance measures. The analysis showsthat the best performing model is LPI although the correlation with observations is only moderate andstatistical techniques for binary classification models indicate that the model is biased towards positivepredictions of liquefaction occurrence.1. INTRODUCTIONThe recent earthquakes in Haiti (2010),Canterbury, New Zealand (2010-11) andTohoku, Japan (2011) highlighted thesignificance of liquefaction as a cascading effectof seismic events. The insurance sector wascaught out by these events, with catastrophemodels underestimating the extent and severityof liquefaction that occurred. A contributingfactor was that the method used by some modelsto account for liquefaction is based onliquefaction susceptibility, which only considerssurficial characteristics. Furthermore, lossesarising from liquefaction are predicted by addingan amplifier to losses predicted by groundshaking (Drayton and Vernon, 2013).Consequently, significant liquefaction-inducedlosses will only be predicted if significant lossesare already predicted from ground shaking,whereas it is known that liquefaction can betriggered at relatively low ground shakingintensities (Quigley et al., 2013). Therefore thereis scope for the insurance sector to find moresophisticated methods to predict liquefaction.This is particularly important for assessingpotential damage to critical infrastructuresystems, which are more likely to be affected byliquefaction (Bird and Bommer, 2004) and canhave significant impacts on indirect economiclosses caused by business interruption.There are three options that loss estimatorscan attempt in dealing with ground failurehazards (Bird and Bommer, 2004). They canignore it; use a simplified method; or conduct adetailed geotechnical assessment. The firstoption will likely lead to underestimation oflosses in earthquakes where liquefaction is amajor hazard. The last option, detailedassessment, is appropriate for single-site riskanalysis but is impractical for insurance loss12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20152estimation purposes because of three constraints:limited accessed to detailed geotechnical data;lack of expertise in method application; and thegeographic scale of the exercise which maymake detailed assessment expensive and time-consuming.The overall aim of this research is toproduce a methodology for assessingliquefaction hazard, which abides by theseconstraints and this paper focuses on one aspectsof that research: the evaluation of existingmethods for desktop liquefaction prediction.2. LIQUEFACTION ASSESSMENT MODELSThere are two steps in the prediction ofliquefaction occurrence (Bird et al., 2006). Firstit is necessary to determine whether soils aresusceptible to liquefaction, based solely onground conditions with no earthquake-specificinformation. This is often done qualitatively andsometimes, as currently the case with catastrophemodels (Drayton and Vernon, 2013), this is alsothe full extent of liquefaction hazard that isconsidered. The next step is to determineliquefaction triggering, which extends theliquefaction susceptibility to determineearthquake-specific likelihood of liquefaction,based on earthquake parameters.2.1. Liquefaction Potential IndexThe most common approach used to predictliquefaction triggering is the factor of safetyagainst liquefaction, FS. This can be defined asthe ratio of the cyclic resistance ratio, CRR, andthe cyclic stress ratio, CSR, for a layer of soil atdepth, z. CSR can be expressed by:ܴܵܥ = 0.65ቀ௔೘ ೌೣ௚ቁቀఙೡఙೡᇲቁݎௗ (1)where amax is the peak horizontal groundacceleration; g is the acceleration of gravity; ߪ௩is the total overburden stress at given depth; ߪ௩ᇱ isthe effective overburden stress at depth, z; and rdis a shear stress reduction coefficient dependenton depth. CRR is usually calculated fromgeotechnical parameters from cone penetrationtest or standard penetration tests. Andrus andStokoe (2000) proposed an alternative methodfor calculating ܴܴܥ based on shear-wavevelocity, Vs, in which:ܴܴܥ = ൞0.022ቀ௏ೄభଵ଴଴ቁଶ+2.8൬ଵ௏ೄభ∗ ି௏ೄభ−ଵ௏ೄభ∗ ൰ൢܯ ܵܨ (2)where ௌܸଵ is the stress-corrected shear wavevelocity; ௌܸଵ∗ is the limiting upper value of ௌܸଵfor cyclic liquefaction occurrence, and MSF is amagnitude scaling factor. The equations for ௌܸଵand MSF are not repeated here.Liquefaction is predicted to occur when FS≤ 1 and predicted not to occur when FS > 1.However Juang et al. (2005) found that the ܴܴܥmodel is conservative, resulting in lower factorsof safety and over-prediction of liquefactionoccurrence. To correct for this, Juang et al.(2005) propose a multiplication factor of 1.4 toobtain an unbiased estimate of the factor ofsafety, ܵܨ∗ = 1.4 × ܨ .ܵܵܨ∗ is an indicator of potential liquefactionat a specific depth, i.e. for a single soil layer,however Iwasaki et al. (1984) noted that damageto structures due to liquefaction was affected byliquefaction severity. They proposed anextension to this approach – the liquefactionpotential index, LPI, to predict the likelihood ofsurface-level manifestation of liquefaction basedon integrating a function of the factors of safetyacross the top 20m of soil. LPI is calculatedfrom:ܲܮ ܫ= ∫ 10)∗ܨ − 0.5ݖ݀(ݖଶ଴଴(3)where ܨ∗ = 1 –ܵܨ∗ for a particular soil layerand the inclusion of the depth function ensuresgreater weighting is given to factors of safetycloser to the surface. The original guidancecriteria from Iwasaki et al. (1984) proposes thatthe potential for liquefaction was very low forLPI = 0; low for 0 < LPI ≤ 5; high for 5 < LPI ≤ 15; and very high for LPI > 15. With respect toits usefulness to the insurance sector, there arelimitations to this methodology. In order todetermine the overburden stresses, it is necessary12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20153to know or estimate the water table depth and thesoil unit weights both above and below the watertable. Furthermore, while the use of Vs tocalculate CRR negates the requirement forground investigation, Vs data is not necessarilyreadily available at many locations.2.2. HAZUSHAZUS®MH MR4 (NIBS, 2003) is a lossestimation software package for the UnitedStates and includes a module for predicting theprobability of liquefaction. The first step is todetermine zones of liquefaction susceptibilityfrom an existing map or from surficial geology.Both of these approaches may pose problems forinsurers since surface geology maps are notwidely and freely available to non-academicorganizations and even where existing maps areavailable, the zone characteristics may nottranslate directly. For a given liquefactionsusceptibility zone, the probability ofliquefaction occurrence is given by:ܲ[݅ܮ ݍ] =௉[௅௜௤|௉ீ஺ୀ௔]௄ಾ ௄ೢ௠ܲ ௟ (4)where P[Liq|PGA=a] is the conditionalprobability of liquefaction occurrence for a givensusceptibility zone at a specified level of peakhorizontal ground motion, a; KM is the momentmagnitude correction factor; Kw is the groundwater correction factor; and Pml is the proportionof map unit susceptible to liquefaction, whichaccounts for the real variation in susceptibilityacross similar geologic units. The equations forcalculating these factors are not repeated here. Inaddition to the problems in determiningliquefaction susceptibility zones, the HAZUSmethod also requires the water table depth to beknown or estimated.2.3. Zhu et al. (2014)Zhu et al. (2014) have developed empiricalfunctions to predict liquefaction probabilityspecifically for use in rapid response and lossestimation. They deliberately use predictorvariables that are quickly and easily accessibleand do not require specialist knowledge to apply.For a given set of predictor variables, theprobability of liquefaction is then given by thelogit link function:ܲ[݅ܮ ݍ] =ଵଵା௘ష೉(5)Two linear models for X are proposed in theirpaper: a regional model for use in coastalsedimentary basins and a global model that isapplicable more generally. The functions are notrepeated here, but in the global model X isdependent on PGAM,SM, which is the product ofthe peak horizontal ground acceleration fromShakeMap estimates (USGS, 2014a) and amagnitude weighting factor; Vs30, the averageshear wave velocity to 30m depth from theUSGS Global Map Server (USGS, 2013); andCTI, which is the compound topographic index,used as a proxy for saturation, and which can beobtained globally from the USGS Earth Explorerweb service (USGS, 2014b). The regional modeluses the same parameters and additionally ND,which is the distance to the coast, normalized bythe size of the sedimentary basin, which isdetermined from surface roughness. This methodis advantageous over LPI and HAZUS as it doesnot require knowledge of water table depth orsoil weight.3. MODEL TEST APPLICATION3.1. Observed dataThe models are tested by comparing site specificpredictions to liquefaction observations from theܯ௪ 7.1 and ܯ௪ 6.2 earthquakes that struckChristchurch, New Zealand on September 4th2010 and February 22nd 2011 respectively. Thisstudy considers binary observations ofliquefaction occurrence based on groundinvestigation data provided by Tonkin & Taylor(geotechnical consultants to the New ZealandEarthquake Commission) and maps from theCanterbury Geotechnical Database (CGD,2013a). It is important to note that theseobservations account for surface manifestationsof liquefaction only and so may under-representthe true extent of liquefaction, although it issufficient for this study given that LPI is12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20154developed to predict surface liquefaction and theHAZUS prediction model only considers surfacecharacteristics in its assessment.3.2. Prediction model inputsFor the LPI model, Vs profiles for 13 sites acrossthe city (Wood et al., 2011) are used andordinary kriging is applied between points tocreate Vs surfaces at 1m intervals to a depth of20m. A water table depth of 2m is assumedacross Christchurch, reflecting the averagesdescribed by Giovinazzi et al. (2011) and soilunit weights of 17kPa above the water table and19.5kPa below the water table are assumed.Whilst Andrus and Stokoe (2000) advise that themaximum Vs1 can range from 200-215m/sdepending on fines content, subsequent work byZhou and Chen (2007) indicates that themaximum Vs1 could range between 200-230m/s.In the absence of specific fines content data, amedian value of 215m/s is assumed to be themaximum.Because of the regional scale of thisanalysis, site-specific soil profile is not taken intoaccount in determining whether layers areliquefiable. Borehole data at sites close to the Vsprofile sites are available from the CanterburyGeotechnical Database (CGD, 2013b). Theseindicate that in the eastern part of Christchurch,soil typically consists predominantly of cleansand to 20m depth, with some layers of siltysand. In the western parts of Christchurchhowever there is an increasing mix of sand, siltand gravel in soil profiles, particularly at depthsdown to 10m. Therefore it is possible,particularly in western suburbs, that calculatedVs1 values may indicate liquefiable soil layerswhen the soil type is not appropriate, whichwould consequently lead to overestimation ofliquefaction potential. The PGA ‘shakefield’ forthe LPI model is taken from the CanterburyGeotechnical Database (CGD, 2013c).For application of the HAZUS method,liquefaction susceptibility zones are determinedfrom the liquefaction susceptibility map forCanterbury (ECan, 2014), from which it ispossible to identify four susceptibility categories:None, Low, Moderate and High. Since theseneed to be translated into the six susceptibilitycategories defined by HAZUS, twoimplementations of the HAZUS method are usedin this study. In both implementations, the‘None’ and ‘Moderate’ categories translatedirectly. In the first implementation, the ‘Low’and ‘High’ categories also translate directly, butin the second, ‘Low’ on the map translates to‘Very low’ in HAZUS, and ‘High’ from the maptranslates to ‘Very high’ in HAZUS.Both the global and regional modelsproposed by Zhu et al. (2014) are tested. ThePGA ‘shakefield’ from the CanterburyGeotechnical Database (CGD, 2013c) is used asan equivalent to the USGS ShakeMap, whilstCTI, Vs30 and the DEM to calculate ND, havebeen acquired from the relevant USGS webresources. In total five models are tested, basedon three general methodologies, as described inTable 1.Table 1: Liquefaction prediction methods beingtestedModel DescriptionLPI1 LPI with VS profilesHAZ1 HAZUS with direct translationfrom liquefaction susceptibility mapHAZ2 HAZUS with modified translationfrom liquefaction susceptibility mapZHU1 Global model by Zhu et al. (2014)ZHU2 Regional model by Zhu et al.(2014)3.3. Test areaTo ensure equivalence in the test, all methods areapplied to the same test area, which is the regionin which input data for all models is obtainable,whether directly or by geostatistical estimation.The test area is divided into a 100m x 100m grid,generating 25,100 grid blocks. Each block isattributed a classification based on observedliquefaction and a series of values representingthe input parameters needed for the range ofliquefaction prediction methods. From these, LPIand four liquefaction probabilities are calculated12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20155for each block, creating five sets of site-specificassessment indices.3.4. Site-specific predictionWhen using semi-probabilistic predictionframeworks, one can interpret the calculatedprobability as a regional parameter that describesthe spatial extent of liquefaction rather thandiscrete site specific predictions, and indeed Zhuet al. (2014) specifically suggest that this is howtheir model should be interpreted. So forexample, one would expect 30% of all sites witha liquefaction probability of 0.3 to exhibitliquefaction and 50% of all sites with aprobability of 0.5 etc. However, when usingliquefaction predictions to estimate structuraldamage over a wide area, it is useful to know notjust how much liquefaction is predicted to occurbut also where. This is particularly important forinfrastructure systems since the complexity ofthese networks means that damage to twoidentical components can have significantlydifferent impacts on overall systemicperformance depending on service areas andsystem redundancy.One approach to generate site-specificpredictions from probabilities is to group sitestogether based on their probability, and thenrandomly assign liquefaction occurrence to siteswithin the group to correspond to the probability.This method is good for ensuring that the spatialextent of the site specific predictions reflect theprobabilities, but since the locations are selectedrandomly it has limited value for comparison ofpredictions to real observations.Another method is to set a threshold valuefor liquefaction occurrence, so that only siteswith a probability above the threshold arepredicted to exhibit liquefaction. Thedisadvantage of this approach is that the resultingpredictions may not reflect the originalprobabilities if the number of sites above andbelow the threshold are not proportionallydistributed. However since there is no randomelement to the determination of liquefactionoccurrence, the predictions are more definitiveand hence more useful for the model testing inthis study. No guidance is given for thresholds inHAZUS, whilst Zhu et al. (2014) propose athreshold of 0.3 to preserve spatial extent,although they also consider thresholds of 0.1 and0.2. Thresholds can also be used to assignliquefaction occurrence based on LPI and Toprakand Holzer (2003) found that surfacemanifestation of liquefaction is unlikely for LPI< 5. Goda et al. (2011) note that this thresholdfor LPI is only appropriate if the bias-correctionfactor of Juang et al. (2005) is adopted in the LPIcalculations.4. MODEL TEST RESULTSComparison of binary classification predictionswith observations is performed by summarizingdata into 2 x 2 contingency tables for eachmodel, identifying the quantity of true positives(TP), true negatives (TN), false positives (FP,Type I error) and false negatives (FN, Type IIerror) amongst the predictions. The true positiverate (TPR or sensitivity) is the ratio of TP toobserved positives. The true negative rate (TNRor specificity) is the ratio of TN to observednegatives. The false positive rate (FPR or fall-out) is the ratio of FP to TN. An initial set ofresults using 5 as a threshold for LPI1, 0.3 as athreshold for the ZHU models and 0.5 as athreshold value for the HAZ models is shown inTable 2.Table 2: Initial diagnostic scores for all liquefactionmodelsMethod TPR TNR FPRLPI1 0.811 0.731 0.269HAZ1 0.002 1.000 0.000HAZ2 0.035 1.000 0.000ZHU1 0.240 0.953 0.047ZHU2 0.401 0.909 0.091An ideal model would have a high TPR andTNR (> 0.5) and low FPR (< 0.5). The LPI1model is the only model that meets these criteria.The small discrepancy between the TPR andTNR rates indicates some bias towards positivepredictions, i.e. some ‘over-prediction’ of12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20156liquefaction. This could be explained by the non-inclusion of site-specific soil profiles in LPIcalculations. The high TNR and low TPR of theother models indicate a strong bias towardsnegative predictions of liquefaction. In the caseof the two HAZ models this bias is extreme andin fact suggests that they nearly always predictnon-liquefaction. However it is possible for thesemodels that the extreme scores are due thethreshold chosen.For a single model, the receiver operatingcharacteristic (ROC) curve is a plot of TPR onthe y-axis against FPR on the x-axis for a rangeof threshold values. The ROC curves for eachmodel are shown in Figure 1 where the ‘chanceline’ (TPR = FPR) is equivalent to randomguessing.Figure 1: ROC curves for all liquefaction predictionmodelsA good model has a ROC above and to theleft of the diagonal, with perfect classificationoccurring at (0,1). Since better models havepoints towards the top left of the plot, the areaunder the ROC curve, AUC, is a generalizedmeasure of model quality that assumes nospecific threshold. ROC curves for the fivemodels and corresponding AUC values aregenerated using the ROCR package in R (Sing etal., 2005) and the results are shown in Table 3.Since the diagonal is equivalent to randomguessing, AUC = 0.5 suggests a model has novalue, while AUC = 1 is a perfect model. It canbe seen that the two HAZ models have AUCsclosest to the ‘no value’ criterion, suggesting thatthe issue with these models may not just thethreshold, but rather that they fundamentallyunder-predict liquefaction when used asimplemented in this study. The only reason theyare to the left of the chance line is that becausethey are making negative predictions at nearlyevery site, they are guaranteed to generate a lowFPR value. The two ZHU models are animprovement on the HAZ models but there islittle difference between them. As expectedbased on the data from Table 2, the LPI model isthe best performing over the chance line.The performance of the models can befurther optimized by testing alternativethresholds. For a single ROC point, Youden’s J-statistic is the height between the point and thechance line. When measured for every point onthe ROC curve, the point which maximizes the J-statistic is representative of the optimalthreshold. The optimum thresholds andcorresponding J-statistics for each model areshown in Table 3. For the ZHU and HAZmodels, the optimization is subject to a minimumthreshold probability of 0.1.Table 3: Statistics related to ROC curves for allliquefaction modelsMethod AUC Threshold J-statisticLPI1 0.845 7 0.573HAZ1 0.691 0.1 0.261HAZ2 0.623 0.1 0.314ZHU1 0.753 0.1 0.355ZHU2 0.760 0.1 0.371The model with the largest J-statistic, i.e. themodel that offers the greatest improvement overrandom guessing, is LPI1 with a threshold of 7.For LPI, Toprak and Holzer (2003) and Maureret al. (2014) suggest triggering thresholds of 412th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20157and 5 respectively. The optimum threshold of 7for model LPI1 indicates that the methodology ispredicting slightly high values for LPI, even withthe bias correction. The likely cause of this isthat site-specific soil profiles have not been takeninto account and so layers that are not liquefiableare being mis-classified and contributing tohigher LPI values. For the ZHU models andHAZ models, the optimum threshold is aprobability of 0.1 based on the minimumconstraint. This further indicates that thesemodels may strongly underestimate liquefactionoccurrence.Based on all the scores used – TPR, TNR,FPR, AUC and Youden’s J-statistic – the LPI1model performs favorably over other desktopmethods. As well as comparing to other desktopmodels however, it is also useful to measure thequality of the LPI1 model in its own right. TheMatthews correlation coefficient, MCC, isrelated to the chi-squared statistic for a 2 x 2contingency table and its interpretation is similarto Pearson’s correlation coefficient. As such itcan be treated as a measure of the goodness-of-fitof a binary classification model. The MCC valuefor the LPI1 model is 0.480 so it shows only amoderate correlation with the observations.5. CONCLUSIONSThis study compares a range of simplifieddesktop liquefaction assessment methods thatmay be suitable for insurance sector where dataavailability and resources are key constraints. Itfinds that the model based on LPI calculatedfrom Vs profiles performs favorably over othermethods based on statistical measures of binaryclassification, although it is better at correctlypredicting the occurrence of liquefaction thannon-occurrence and so may over-predict overall.A possible explanation for the over-prediction isthat soil profiles have not been taken intoaccount and so layers may be misclassified asbeing liquefiable. An important considerationwith soil profiles though is that loss estimatorsmay not have access to this data and where it isavailable it is not necessarily feasible to includein a regional scale model. The use of typical soilprofiles (e.g. Goda et al., 2011) is a usefulcompromise to reduce but not necessarilyeliminate the over-prediction problem. There issome correlation between the observed data andmodel predictions with this LPI methodology.Although it is not strong, it may be consideredacceptable by loss estimators when consideringthe simplifications that are necessary to meet theconstraints imposed by regional scale catastrophemodeling.The HAZUS methodology for estimatingliquefaction probabilities performs poorlyirrespective of triggering threshold. This issignificant since HAZUS methodologies areoften used as a default model outside of the USwhen no more locally (or regionally) specificmodel is available. The two models proposed byZhu et al. (2014) perform better than HAZUS,but not as well as LPI, and show a negativeprediction bias. It is important to note that theirmodels have been developed for prediction ofliquefaction extent, not site-specific predictionsso this result is not surprising. Given that datainput requirements for the Zhu models are morestraightforward than for the LPI model, they maystill have potential for site-specific prediction ofliquefaction within insurance sector if the biascan be accounted for.There are four pieces of work that would beuseful for building on and improving on thisstudy. The first is to repeat the analysis for otherevents to see if the models produce similar scoreswhen applied elsewhere. The second is to test towhat extent the use of these methods would haveimproved loss estimates for real case studiessuch as Christchurch. The third is to useobserved data to develop new liquefactionprediction models or adapt existing ones. Finally,the study can be extended to test the accuracy ofmodels that predict measurements of thepermanent ground deformation.6. ACKNOWLEDGMENTSThis research has been funded by the WillisResearch Network and the UK Engineering andPhysical Sciences Research Council through theUrban Sustainability and Resilience program at12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20158University College London. The authorsacknowledge the support of Sjoerd vanBallegooy at Tonkin & Taylor for provision ofChristchurch ground investigation GIS data.7. REFERENCESAndrus, R. D. and Stokoe, K. H. (2000).“Liquefaction resistance of soils from shear-wave velocity.” J. Geotech. Geoenviron.,126(11), 1015-1025.Bird, J. F. and Bommer, J. J. (2004). “Earthquakelosses due to ground failure.” Eng. Geol., 75,147-179.Bird, J. F., Bommer, J. J., Crowley, H. and Pinho, R.(2006). “Modelling liquefaction-inducedbuilding damage in earthquake lossestimation.” Soil Dyn. Earthq. Eng., 26, 15-30.CGD. (2013a). 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Geoenviron., 133, 959-972.Zhu, J., Daley, D., Baise, L. G., Thompson, E. M.,Wald, D. J., Knudsen, K. L. (2014). “Ageospatial liquefaction model for rapidresponse and loss estimation.” Earthq. Spectra,in press.

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