International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP) (12th : 2015)

Identifying the needs and future directions of seismic hazard for probabilistic infrastructure risk analysis Weatherill, Graeme; Pagani, Marco Jul 31, 2015

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12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Identifying the Needs and Future Directions of Seismic Hazard forProbabilistic Infrastructure Risk AnalysisGraeme WeatherillSeismic Hazard Researcher, Global Earthquake Model (GEM), Pavia, ItalyMarco PaganiSeismic Hazard Coordinator, Global Earthquake Model (GEM), Pavia, ItalyABSTRACT: The vulnerability of urban infrastructure to both ground shaking and geotechnical failureduring large earthquakes has been demonstrated by recent earthquakes such as the 2010 - 2011 Canter-bury earthquake sequence (New Zealand, 2010 - 2011) or 2010 Haiti event. Probabilistic seismic riskanalysis to infrastructure systems requires the characterisation of both the transient shaking and perma-nent ground deformation elements of the hazard, and must do so incorporating both the aleatory andepistemic uncertainties and the spatial correlations and dependencies that are inherent in both of these as-pects. Recent developments in characterisation of spatial correlation and cross-correlation in the groundmotion uncertainties form the foundations of a comprehensive Monte Carlo-based methodology for anal-ysis of seismic risk to spatially extended systems. New research directions are needed, however, in orderto ensure that secondary hazard aspects are incorporated in the same way. These include the treatmentof site amplification of the ground shaking, the modelling of permanent ground deformation from slopedisplacement and liquefaction, and permanent displacement due to coseismic slip on and around thefault rupture. Key considerations for integrated probabilistic framework for physically-realistic charac-terisation of the ground shaking and permanent ground displacement are illustrated using the exampleof simulation spatially correlated fault slip on an active fault rupture in a manner that can be integratedwithin a Monte Carlo-based probabilistic seismic hazard methodology.Probabilistic analysis of seismic risk is the mostcommon methodology used by organisations re-sponsible for maintaining infrastructures to makeinformed decisions based on the cost to benefit ra-tios of particular mitigation strategies. But analy-sis of infrastructural risk presents new challenges toboth the hazard and risk modellers to provide mod-els of ground shaking and permanent ground dis-placement that can be applied to spatially extendedand interconnected systems. A single infrastruc-tural system is dependent on many elements over anextended geographical region, and the performanceof the system or systems may depend on the loca-tion of greatest damage. Further compounding thecomplexity is the fact that a single infrastructuralsystem is composed of fragile elements that mayrespond dissimilarly according to different charac-teristics of the hazard. One example might be agas network in which mechanical elements may bemost adversely affected by high frequency accel-eration, storage systems and pumping stations bylow frequency ground motion, whilst undergroundpipes may be most at risk from permanent grounddisplacement due to geotechnical failures.This paper outlines some of the main challengesfacing the seismic hazard modeller in order to pro-vide hazard input into probabilistic seismic riskanalysis for interconnected and spatially extendedinfrastructures. Focus is placed on four critical ele-ments: ground shaking, site amplification, geotech-nical failure due to land-sliding and liquefaction,and finally co-seismic displacement due to ruptureon the fault surface. A summary of current ap-proaches for characterising each of these elements112th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015is presented, along with descriptions of the chal-lenges faced in ensuring that uncertainties are cor-rectly incorporated into the process and that spa-tial correlations within these uncertainties are accu-rately captured within the seismic risk analysis.1. SPATIAL ANALYSIS OF GROUNDSHAKINGThe characterisation of ground shaking hazardin a probabilistic manner is well established, bothfor a single site application using conventionalprobabilistic seismic hazard analysis (PSHA), andacross a spatial extent using the Monte Carlo ap-proach (e.g. Park et al., 2007; Crowley et al., 2008).The use of the Monte Carlo-based approach fa-cilitates the incorporation of spatial correlationsof the ground motion prediction equation (GMPE)residual term (ε) into the probabilistic seismic haz-ard. This permits the generation of ground shak-ing intensities for not just one but many groundmotion intensity measures across multiple sites,whilst preserving the spatial correlation proper-ties observed for each ground motion intensitymeasure across many sites (ρIM1,IM1(hi, j)), thecross-correlation between intensity measure val-ues at the same site (ρIM1,IM2(hi, j = 0)) and thespatial cross-correlation between different inten-sity measure values recorded at separate sites(ρIM1,IM2(hi, j)). Models of spatial correlation andcross-correlation, such as that of Goda and Hong(2008) or Loth and Baker (2013), can be readily ap-plied within a Monte Carlo PSHA approach. Forheterogenous portfolios of building the impact ofincorporating spatial correlation and spatial cross-correlation into the analysis has been illustratedby Weatherill et al. (2015) (Figure 1), who demon-strate for a heterogeneous portfolio of buildings theinclusion of spatial cross-correlation increases thelikelihood of seeing greater losses for lower prob-abilities of exceedance. Conversely, lower lossesfor higher annual probabilities are observed whencompared to the case for which no correlation isconsidered (solid black line), and even for the casein which spatial correlation is modelled but cross-correlation is neglected (dashed dark blue line).For infrastructural systems, the generation ofmultiple fields of ground motion preserving the ob-served correlation and cross-correlation propertiesof ground motion residuals is not merely a meansof increasing or decreasing the probabilistic esti-mates of loss, but a necessity for representing theground motion inputs at multiple points of an in-terconnected network in a manner that can be con-sidered representative of the possible realisation ofground motion. Simpler approaches using eitherthe median ground motion (i.e. without variability)predicted by a GMPE for a given scenario event ora probabilistic seismic hazard map, which is effec-tively aggregating contributions of ground motionfrom multiple different events, cannot fulfil theserequirements, and in doing so will provide an in-correct picture of seismic risk to a network.0 1 2 3 4 5 6 7 8 9 1010−410−310−210−1Aggregated Loss (10 9 Euros)Annual Probability of Being ExceededAggregated Portfolio Firenze (Florence) City District  No Correlation (1)Spatial Only (2)Conditional Hazard (0.2s) (3)Conditional Hazard (1.2s) (4)Full−Block Cross−Correlation (5)LMCR (6)LMCR (Total  σ) (7)0.6 0.8 1 1.2 1.410−410−310−210−1Ratio of Loss CurvesAnnual Probability of Being ExceededFigure 1: Impact of incorporating spatial cross-correlation into a loss analysis of a heterogeneous port-folio of buildings under different correlation strategies(Weatherill et al., 2015)2. PSHA REQUIREMENTS AT THEMETROPOLITAN SCALEMetropolitan areas occupy an anomalous middleground in terms of the requirements and method-ologies applied to PSHA. Local modulations tothe expected strong ground shaking, most notablythose relating to soil conditions, basin structure andnear-fault directivity should be incorporated intothe PSHA process. Many of these aspects are com-monly analysed within seismic microzonation stud-ies. In the ideal case the seismic microzonation in-formation may be sufficient to characterise models212th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015of site amplification that are calibrated to the localsoil conditions.2.1. Site AmplificationIn a detailed seismic microzonation study,period-dependent functions for amplifying accel-eration on a reference bedrock, SrA j (Ti), to thatobserved at the surface SSA j (Ti), may be defineduniquely for each site in the area of interest, whereFj (Ti), defines the amplification at period Ti for sitej such that:Fj (Ti) =SSA j (Ti)SrA j (Ti)(1)These functions can be obtained empirically oranalytically using equivalent linear or nonlin-ear methods for propagating recorded or syn-thesised waveforms through a soil column withgeotechnical properties possibly affected by epis-temic uncertainties. Following the construction ofBazzurro and Cornell (2004b), it is assumed thatboth the spectral acceleration on bedrock is uncer-tain, with a mean, ln(SrA j (Ti)), and standard devia-tion, σlnSrA j(Ti), and that the amplification factor toois distributed such that ln(Fj (Ti))= ln(Fj (Ti))+εlnFj(Ti)σlnFj(Ti). The spectral acceleration on thesurface is given by:ln(SSA j (Ti))= ln(SrA j (Ti))+ ln(Fj (Ti))= ln(SrA j (Ti))+ εlnSrA j(Ti)σlnSrA j(Ti)+ln(Fj (Ti))+ εlnFj(Ti)σlnFj(Ti) (2)where εlnSrA j(Ti) and εlnFj(Ti) are the normalisedresidual terms of the rock ground motion and theamplification factor respectively. This formulationcan be readily incorporated into the PSHA integral,and is well-suited to application within a MonteCarlo framework. The Bazzurro and Cornell(2004b) methodology is widely used in practicefor site-specific PSHA studies, in which the Fj (Ti)is unique to the site in question. Total variabil-ity σlnFj(Ti) is therefore a composite of record-to-record variability and uncertainty in the propertiesof the soil profile. Bazzurro and Cornell (2004a)demonstrate that inclusion of the uncertainty in thesite profile can increase the total uncertainty by afactor of up to 20 %, when compared to inclusionof record-to-record variability alone.In the site specific application the decomposi-tion of σlnFj(Ti) into its mixed effect components(record-to-record variability and uncertainty in thesoil column) may not be necessary. For applica-tion over a spatial scale, however, this distinctioncannot be neglected, nor can the cross-correlationin εlnFj(Ti) between spectral periods nor the spatialcorrelation between sites. There exists the likeli-hood that correlation may be found in the ampli-fication function residuals εlnFj(Ti) by virtue of thesimilarities of the geotechnical properties of the soilprofile. Conversely, however, discontinuities be-tween the geotechnical units or strong lateral vari-ation in the soil properties may erode the correla-tion or introduce local anisotropy into the correla-tion model.2.2. GMPE Modifications and Non-ergodicAleatory VariabilityThe calibration of existing GMPEs to local siteconditions is now standard practice in the analy-sis of seismic hazard for critical and nuclear fa-cilities (Rodriguez-Marek et al., 2014). Two com-mon adaptations are the re-scaling of the GMPEto take into account local variation in kappa (κ),and the use of local records of strong and weak mo-tion to extract the average within-event residual forthe site, thus leaving the site specific within-eventvariability (or single station sigma, σSS). Whilstlargely applied to site-specific PSHA, there is lit-tle reason why these modifications should not beapplied to metropolitan scale analysis. If adopt-ing site-specific amplification functions using theBazzurro and Cornell (2004b) approach, the adop-tion of the single station sigma is a necessary stepto prevent double counting variability that will bereintroduced back into the calculation within theuncertainty in the site amplification factor. In somecases the number of observed records from withinthe region of interest may not be sufficient to de-termine the true single station sigma, but as notedby Rodriguez-Marek et al. (2014) the actual valueof σSS has been shown to be relatively consistent312th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015Figure 2: Amplification factors for a site with unknownproperties and multiple ground motion records (top)and coefficient of cross-correlation between amplifica-tion factors (bottom)across different tectonic regions, and potentially aregional value could be adopted.3. GEOTECHNICAL HAZARDSFor the most widespread application to bothbuilding and infrastructure risk analysis, theHAZUS methodology remains arguably the mostpersistent and practical to implement. This is inpart due to the relatively qualitative categorisationof landsliding and liquefaction susceptibilities andthe practical means by which values of permanentground deformation can be retrieved. These prop-erties also make the geotechnical hazard moduleswithin HAZUS portable to other regions. Indeed,within the European FP7 SYNER-G project, theHAZUS susceptibility definitions, and the corre-sponding probability models, where integrated intothe Monte Carlo assessment methodology adoptedwithin the software (Franchin and Cavalieri, 2014).Nonetheless, the current HAZUS models are rela-tively simplified, and within this approach the un-certainties and correlations within both the spatialdomain and the parameter domain are largely ne-glected within this framework.More comprehensive frameworks for proba-bilistic analysis of liquefaction and/or slope dis-placement can be found in the literature (e.g.Goda et al. (2011) in the case of liquefaction, andRathje and Saygili (2008) in the case of slope dis-placement). These frameworks can be consid-ered conceptually simple extensions of the standardPSHA integral:P(d∗ > D∗) = λ0∫z∫m∫rP [d∗ > D∗|z] fGM (z|m,r)fM (m) fR (r)drdmdz (3)where P(d∗ > D∗) is the probability of exceedinga given level of a geotechnical hazard metric (e.g.permanent ground displacement, or liquefactionprobability index) within a time period of interest,P [d∗ > D∗|z] the probability of exceeding the levelof the geotechnical hazard metric given a groundshaking intensity (z), fGM (z|m,r) the probabilitydensity function of the ground motion (the lognor-mal distribution considered within the GMPE), andfM (m) and fR (r) the probability densities of themagnitude and distance distributions respectively.As with conventional PSHA, these frameworks arereadily adapted, and in many cases better suited,for application within a Monte Carlo framework.It is also important to recognise that in the caseof geotechnical hazards there are levels of groundshaking beneath which the phenomena will not beobserved. Therefore the probability is broken intotwo components, the probability that displacementwill exceed a specified level given that geotechni-cal failure occurs, and the probability of geotechni-cal failure given the earthquake rupture and groundshaking:P [d∗ > D∗|z] = P [d∗ > D∗|failure] ·P [failure|m,r](4)The primary focus therefore is the means by whichP [d∗ > D∗|z] is constrained, and the potential un-certainties and conditional dependencies therein.412th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 20153.1. Slope DisplacementThe fully probabilistic slope displacementhazard methodology is well described inRathje and Saygili (2008), in which the probabilityof exceeding a specific level of displacement givena ground shaking intensity is determined directlyfrom a slope displacement predictive equation.The predictive equation itself is derived from asliding block model subject to many differentground accelerations. This methodology is bothconceptually and computationally efficient fordirect implementation.For application to infrastructure risk, theRathje and Saygili (2008) approach can be readilyapplied over a spatially extended region. Even thevector-based approaches can be readily supportedif taking into account the spatial correlation andcross-correlation of multiple measures of groundmotion in the manner described in section 3 and inDu and Wang (2014). The dependence only on theyield acceleration and the ground motion parame-ters of interest also makes such a model practical toimplement within a variety of environments.Where the probabilistic slop displacement haz-ard analyses are limited, however, is in the inher-ent assumption of the sliding block model, which isa simplified idealisation of the landsliding process.The yield acceleration describes the dynamic sta-bility of the slope, and therefore assumes that twoslopes with the same yield acceleration will yieldthe same Newmark Displacement, regardless of dif-ferences in geometry or material properties. Forother types of landsliding, however, such as debrisflows or rock falls, no such methods exist. Nei-ther, can the sliding block displacement method ad-equately capture differential displacements withinthe slidingmass that would result in patterns of con-centrated displacements at the edge of the mass.In these circumstances probability of exceeding agiven level of displacement, would contain spatialcorrelations that are as yet unaccounted for.3.2. LiquefactionAs with the case of slope displacement a proba-bilistic framework for liquefaction hazard analysishas already been established (e.g. Baker and Faber,2008; Goda et al., 2011). As is also the case, how-ever, the manner by which P [D∗ > d∗|z] is con-strained is an area that is not so well established.Again, a similar problem emerges in that liquefac-tion itself encompasses a range of phenomena (e.g.lateral spread, volumetric settlement, sand blowsetc.), the definition of specific measures from whichpredictive models of displacement can be condi-tioned are not yet consistent. Once again, for pro-viding the information necessarily for loss analyses,the HAZUS approach is simple to implement andhas a solid basis upon the fundamental understand-ing of the liquefaction process. Nonetheless, thesimple characterisation of susceptibility that makesthe process uncomplicated to implement, limits theconsideration of uncertainties that are known to beprevalent in such analyses. A different approachis taken by Baker and Faber (2008), who use geo-statistical simulation of correlated fields of uncer-tain soil properties, conditioned upon those sameproperties measured at known sample sites. Thesesimulations are then used to determine the probabil-ity of exceeding a given proportion of an area thatmay experience liquefaction. This method can ac-count for the considerable uncertainty in soil prop-erties over an extended region, and may even beextended to account for empirical correlations be-tween soil properties using a linear model of core-gionalisation. This effectively mirrors the approachtaken for generating spatially cross-correlated fieldsof ground shaking discussed previously. Whilstthe Baker and Faber (2008) method may offer atheoretical basis for defining liquefaction hazardwith uncertainty and spatial correlation, there arelikely to be practical constraints as to how wellthe full suite of necessary geotechnical propertiescan be defined, and what can be practically imple-mented with available site data. Furthermore, theBaker and Faber (2008) approach defines only theprobability of observing the liquefaction. Consid-erably more research is needed to define models ofthe expected displacement that could be incorpo-rated into a probabilistic approach.4. CO-SEISMIC FAULT DISPLACEMENTHAZARDThe constraint of hazard due to co-seismicfault displacement has become an area of grow-512th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015ing interest, with the conceptualisation in a PSHAframework originating from the SSHAC Level 4Yucca Mountain Nuclear Waste Repository site(Youngs et al., 2003). The probabilistic fault dis-placement hazard analysis (PFDHA) methodologyinitially proposed by Youngs et al. (2003) adopts amodified hazard integral compared to that of equa-tion 3:P(d∗ > D∗) = ∑Nλn(m0)∫mfM (m) ·∫rfR (r|m) ·P(slip|m,r) ·P(d∗ > D∗|m,r,slip)drdm (5)where P(slip|m,r) defines the probability of ob-serving surface slip at a site given an earthquakemagnitude and location, and P(d∗ > D∗|m,r,slip)describes the probability of displacement d∗ ex-ceeding the specified value D∗ given the magni-tude and distance from the fault. Furthermore, theproblem is made more complex by the need to con-sider rupture on the principal fault plane, as wellas ground displacement on smaller distributed rup-tures located away from the principal displacement,even in cases where the principal fault does not rup-ture the surface. Several empirical models describ-ing for both principal and distributed rupture areavailable in the literature, although in some casessuch models are developed using a relatively lim-ited dataset.The PFDHA methodology itself incorporatesaleatory variability in terms of the rupture proper-ties into the hazard curve directly, whilst for someregions, namely active continental transform en-vironments, multiple models are proposed in theliterature that would permit a degree of epistemicuncertainty to be incorporated into the analysis(Petersen et al., 2011). These make the applica-tion of PFDHA to a particular site a robust ap-proach to capture uncertainty in the fault slip pro-cess. For application to infrastructure, however, thepicture is far more complex and the objectives ofthe analysis need to extend beyond those definedin the original PFDHA formulation of Youngs et al.(2003). A critical objective of infrastructural seis-mic risk analysis is that the ground shaking inputmust be compatible with the generating scenario ofthe fault displacement, and vice-versa. Within aMonte Carlo based approach, in order to generatea feasible realisation of the two, the source ruptureused to generate the transient shaking and that usedto determine the co-seismic displacement should bethe same. Furthermore, the location and degree ofdisplacement for distributed rupture around the sur-face, should be consistent with the distribution andmagnitude of displacement modelled on the princi-pal fault. Finally, consideration must be given tothe possibility that connected linear elements maytraverse the same fault rupture at many different lo-cations, and as such the probability of exceeding agiven displacement at one location on the fault can-not be considered as conditionally independent ofthe displacement elsewhere on the fault.The problem of consistency between the generat-ing rupture for the ground shaking and the generat-ing rupture for the co-seismic displacement can belargely addressed by the use of “floating” rupturesacross the fault surface, in the manner that is nowcommon practice in PSHA. For a given fM (m) andfR (r), not only is P(slip|m,r) already modelled butthere exists for each rupture scenario a surface uponwhich the slip distribution can be rendered. Withthe probability of occurrence of the rupture and theprobability of surface slip known, empirical mod-els for P(d∗ > D∗|m,r,slip), such as those found inYoungs et al. (2003) and Petersen et al. (2011) canbe readily applied to complete the evaluation of us-ing either the conventional PSHA approach or itsMonte Carlo alternative. This will incorporate thealeatory uncertainty in the slip given the occurrenceof slip at the surface. At this point, however, spatialcorrelations are neglected. Whilst models of spatialcorrelation using the residual term of the displace-ment predictive model could be derived from geo-statistical methods in the same manner as those forground shaking correlation. Even if such modelswere available, for the greatest consistency with thephysical properties of the fault system it would bedesirable to condition the simulation of the residu-als of distributed displacement upon the distributionof slip upon the principal fault.Instead we opt for an alternative approach inwhich the spatial correlation of slip on the prin-cipal rupture is modelled using the approach de-612th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015scribed in Graves and Pitarka (2010). Here a meanslip value for the fault is sampled from the slip scal-ing relation. An initial slip distribution is assumed,which may be uniform, tapered or may even be de-termined from empirical models such as those ofPetersen et al. (2011). The slip distribution is thentransformed into the wavenumber domain whereis summed with a stochastically generated field ofspatially correlated random wavenumber, with cor-relation length modelled using the von Karman cor-relation function, whose parameters are derived forfault slip distributions by Mai and Beroza (2002).The result is then returned form the wavenumberdomain into the spatial domain and scaled such thatthe total moment is consistent with the moment ofthe earthquake. This process produces a spatiallycorrelated slip model across the whole fault surface(as illustrated in Figure 3) and the surrounding en-vironment.Figure 3: Correlated field of co-seismic displacementfor a rupture on the Tagus Valley fault. Principal rup-ture colour from 0.0 m (green) to 3.0 m (red), and dis-tributed displacement from 0.0 (white) to 0.2 m (pink)To generate the spatial field of distributed slipgiven the principal slip on the fault, the fault meshis broken down into a large number of sub-faults,each with a corresponding slip value. For each sub-fault the surface displacement at the target locationsis calculating using the model of Okada (1985) de-fined for elastic half-space. The final surface dis-placement field is then the sum all of the displace-ment fields from the sub-faults.This approach to the generation of spatially dis-tributed ground motion fields has a direct consis-tency with the rupture physics, in a manner thatmodelling by separate empirical models of correla-tion would not be able to achieve. Given the paucityof models for predicting displacements, particularlyfor distributed slip, a limited and unevenly dis-tributed data set used for deriving empirical mod-els, and a total absence of spatial correlation modelsthe simulation approach described herein may be apractical means by which realistic correlations canbe considered. Unfortunately, the implementationof the distributed slip is computationally costly po-tentially limiting the number of fields the modellermay wish to generate for a given rupture. Nonethe-less, such simulations may also be used to supple-ment existing dataset of distributed slip to provideconstraint of simpler empirical models and correla-tions that may be more efficient to implement.5. CONCLUSIONSThis paper has presented an overview of someof the main elements of seismic hazard analysisthat are of relevance to infrastructure risk analysis,placing this in context with respect to site-specificanalysis. The need to consider both aleatory andepistemic uncertainties in the hazard input is ofparamount importance, but in doing so one shouldnot neglect the role that spatial correlations play inthis situation. For transient ground shaking the spa-tial correlation and spatial cross-correlation can bereadily included into Monte Carlo based probabilis-tic seismic loss analyses, but for geotechnical haz-ards the process is not so well established. The in-corporation of more detailed seismic and geotech-nical microzonation data is fundamental to highquality analysis of seismic risk to infrastructures.Yet whilst this provides the opportunity for moresophistication in the analyses, it is important not toneglect the correlations that are inherent within theuncertainty models of the new parameters. To facil-itate this approach, seismic infrastructure risk anal-ysis should endeavour to adopt practices more com-monly used in site-specific studies, whilst new re-712th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12Vancouver, Canada, July 12-15, 2015search directions are emerging that will require the-oretical and empirical models upon which to basethe simulations of the ground displacement hazard.6. REFERENCESBaker, J. W. and Faber, M. H. (2008). “Liquefaction riskassessment using geostatistics to account for soil spa-tial variability.” Journal of Geotechnical and Geoen-vironmental Engineering, 134(1), 14–23.Bazzurro, P. and Cornell, C. A. (2004a). “Ground-motion amplification in nonlinear soil sites with un-certain properties.” Bulletin of the Seismological So-ciety of America, 94(6), 2090–2109.Bazzurro, P. and Cornell, C. A. 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