Landslides (2010) 7:125134DOI 10.1007/s10346-009-0190-3Received: 23 June 2009Accepted: 7 December 2009Published online: 29 January 2010 Springer-Verlag 2010Zhihong Li.Farrokh Nadim.Hongwei Huang.Marco Uzielli.Suzanne LacasseQuantitative vulnerability estimation for scenario-basedlandslide hazardsAbstract Within the engineering profession and natural sciences,vulnerability is widely accepted to be defined as the degree of loss(or damage) to a given element or set of elements within the areaaffected by a threat. The value of vulnerability is expressednondimensionally between 0 and 1. It is a fundamental componentin theevaluationof landsliderisk,and its accurateestimationisessential in making a reasonable prediction of the landslideconsequences. Obviously, vulnerability to landslidesdepends notonly on the characteristics of the element(s) at risk but also on thelandslideintensity. Thispapersummarizespreviousresearchonvulnerability to landslides and proposes a new quantitative modelfor vulnerability of structures andpersons basedonlandslideintensity and resistance of exposed elements. Inaddition, anapproximate function is suggested for estimating the vulnerabilityof persons instructures. Different methods for estimating thevulnerabilityofvariouselementstosloworrapidlandslidesarediscussed. Finally, the application of the new model is illustratedthrough an example.Keywords Landslide.Quantitative vulnerability estimation.Resistance.IntensityIntroductionVulnerability is a fundamental component in the evaluation of risk(Varnes1984; Einstein1988; Leoneetal. 1996). Accordingtotheglossaryofrisk-assessmenttermsoftheInternational SocietyofSoil Mechanics and Geotechnical Engineering, vulnerability refersto the degree of loss to a given element or set of elements within theareaaffectedbythelandslidehazard. Itisexpressedonascaleof 0(noloss) to1 (total loss) (http://www.engmath.dal.ca/tc32/2004Glossary_Draft1.pdf). For property, the loss will be the value ofthe damage relative to the value of the property; for persons, it willbe the probability that a particular life (the element at risk) will belost, given the person(s) is affected by the landslide. Vulnerabilitycould also refer to the propensity to loss (or the probability of loss)and not the degree of loss.A unifiedmethodologyfor classifying and assessing quantita-tively the vulnerability of elements at risk to the types andmagnitudes of specific landslides does not exist (Glade and Crozier2005). The estimationof vulnerability to landslides is usuallyqualitativeandsubjectiveandlargelybasedonhistoricrecords(Dai et al. 2002). It is defined as the level of potential damage ordegree of loss of a given element or a set of elements at risk in someliterature (e.g., Fell 1994; Wong et al. 1997; AGS 2000). It is oftenexpressedas a nondimensional value between0and1. Someresearchers(e.g., Remondoetal. 2008)consideredthatvulnera-bility values could theoreticallybe greater than 1, since repair orreconstruction could cost more than construction of a newstructure. Thispapersummarizespreviousresearchonvulnera-bilitytolandslides andproposes anewquantitativemodel forvulnerability of structures and persons based on landslide intensityand resistance of exposed elements. In addition, an approximatefunction is suggested for estimating the vulnerability of persons instructures.Vulnerability estimation methodsLiterature reviewThe estimation of vulnerability involves analyzing the interactionbetweenagivenlandslideintensityandcorrespondingaffectedelements. Finlay (1996) provided some recommended ranges andvalues on vulnerability of persons in open space, in a vehicle, or ina building derived from historic records of Hong Kong. Leone et al.(1996) introduced the damage matrices (structural, corporal, andfunctional) for landslide hazard to assess the vulnerability ofbuilding, road, person, etc. A new 3D conceptual framework withmagnitude(M), scale(S), andelementsatrisk(E)forassessingvulnerability was proposed by Duzgun and Lacasse (2005).Remondo et al. (2008) estimated vulnerability of transportinfrastructure, land resources, and buildings froma detailedanalysis of past damage during nearly 50 years in the study area.Aninventorywas madefor calculatingthevulnerabilitythroughthe economic loss dividedbythe correspondingnet values ofexposed elements based on landslides records. Zzere et al. (2008)gavethevulnerabilitiesof structuresandroadsunderdifferentintensities of slides based onexperiences or historic data, incombinationwiththeinformationwithstructuretype, structureage, number of floors, etc.Uzielli et al. (2008) proposed a univocal conceptual frameworkfor quantitative estimation of physical vulnerability to landslides,which is defined as a function of landslide intensity andsusceptibilityof vulnerableelements. Vulnerabilitiesof persons,structures, as well as persons in structures were analyzed. Kaynia etal. (2008) explored the applicability of this methodology based onthe first-order second-moment method. This method is mainly tobe used to estimate regional landslide risks because of theintroduction of comprehensive indices such as impact spatialratio, population density, GDP per capita. However, someimportant intensityfactors arenot considered. For this paper,the vulnerability function with intensity and resistance to scenario-based landslide hazards is proposed in the new model.Commonly, in contrast to other natural processes such asflooding and earthquakes, it is very difficult to assess vulnerabilityto landslides due to the complexity and the wide range of landslideprocess(Leroi 1996). Glade(2003) pointedout that thediverseeffects included: (a) vulnerability of different elements at riskOriginal PaperLandslides 7 (2010) 125varies for similar processes; (b) temporal probability of a personbeingpresent during the landslideeventis variable;(c) differentgroups of humans have different coping potentials; (d) earlywarning systems affect the vulnerability of people; and (e) spatialprobability of landslide occurrence varies. In fact, accurateestimationofvulnerabilityismuchmoredifficultthanthis. Forinstance, the locationof personwithinthe damagedstructure(suchasonthegroundfloororotherwise)impactsthevulnera-bility of persons greatly; the sizes of windows affect vulnerability ofbothstructures andpersons. Evenpeoplesleepingindamagedstructures will have a higher vulnerability than other occupants ofthe building (Fell 1994; Fell and Hartford 1997). The factors such asvelocity, blockmass, impact angle, positionof thewall impactpoint, detailed geometry of the wall, and strength of the material allinfluence the vulnerability. It is exasperatingly difficult to handleallof thesefactors.Itisadvisableand convenienttoanalyze thevulnerability in average. For example, the vulnerability of personsin damaged structure is estimated in terms of average value.Vulnerability depends on both the characteristics of the elementat risk and the landslide intensity. It is obvious that different typesof movement should have very quite different impacts on elements.If a person is struck by a rockfall, he or she may only be injured.However, if apersonisburiedbydebris, deathbyasphyxiaisalmost certain (Finlay 1996). Meanwhile, different types oflandslideprocess alsohavequitedifferent intensitylevels. Forlarge rockfalls, it is evident that the intensity level in the exposedareasisalwayshightoveryhigh, whereasforslides, manylargephenomenadisplaylowtomediumintensity, accordingtotheproposed qualitative scale by Amatruda et al. (2004). Someresearchers have tried to take account of the different impacts duetodifferent landslidingprocess. Forinstance, theSwissrecom-mendations publishedin1997 provide orders of magnitude inordertodifferentiatelow, medium, andhighintensityforblockfall, rockfall, slides, andflows. Heinimann(1999) assessedthevulnerability considering different landslide types. For each type,the vulnerability to different magnitude of events was determined.However, Heinimann stated clearly that a major limitation of theapproach is that most of the data have to be assumed.Proposed methodIn this study, vulnerability is analyzed in average. Vulnerability (V)here is defined as a function of the hazard intensity (I) associatedwith exposed elements at risk and the resistance ability (R) of theelements to withstand a threat. This work explores a new model asfollows:V f I; R 2 I2R2IR 0:51:0 2R I 2R20:5 1:0___(1)0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2I/RVulnerability0.00.10.20.30.40.50.60.70.80.91.00.00.10.20.30.40.50.60.70.80.91.00.00.10.2 0.30.40.50.60.7 0.80.91.01.11.21.3 1.41.51.6IntensityVulnerabilityR=0.1R=0.3R=0.5R=0.7R=1.0R=1.5(a) (b)Fig. 1 Theoretical changing trend of V with I/Ra and Ib0.00.51.01.52.02.53.01.00E-08 1.00E-06 1.00E-04 1.00E-02 1.00E+00 1.00E+02 1.00E+04C: Average velocity (mm/s)Idyn-s0.00.30.60.91.21.51.00E-01 1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04C: Average velocity (mm/s)Idyn-p(a) Dynamic intensity factor for structures(b) Dynamic intensity factor for persons in open space Fig. 2 Dynamic intensity modelOriginal PaperLandslides 7 (2010) 126where I is the landslide intensity, andRis the resistance ofthe element at risk. Both intensity and resistance areexpressed in nondimensional terms. Figure 1 shows thetheoretical changing trend of vulnerability with quotient ofintensity and resistance (a) and intensity (b) in terms ofdifferent resistancevalues.From Fig. 1b, it can be seen that the same intensity may result inquite different damage to the exposed elements; some of them maybedestroyedbecauseof thebadresistanceability, but someofthemmaybejust slightlydamaged. For thesameintensity, thevulnerabilityof lower resistance is greater thanthat of higherresistance.The vulnerability of an element with lower resistance ismore sensitive tolowhazardintensity thanthat withhigherresistance. In the model described above, intensity andresistance are defined such that whenthe intensity is equaltohalf of theresistanceof anelement, theexpectedvalueofvulnerabilitywouldbe0.5. Notethatthevalueofintensityandresistancemaybegreaterthan1.0.IntensityFor a landslide, the magnitude can be defined with severalparametersincludingvolume, velocity, depth, run-out, andareaextent (Ojeda-Moncayoet al. 2004; LeeandJones 2004). It isconsidered that for a landslide event, we have one magnitude valuebut infinite intensity values. Intensity can be expressed in terms ofeither impact energy, average velocity, or depthof potentiallyerodible soil zones (Amatruda et al. 2004).In this study, the landslide intensity is defined as a function ofdynamic and geometric intensity factors as follows:I f Idyn; Igem_ _(2)where Idyn is the dynamic intensity factor, and Igem is the geometricintensityfactor. Idynisdefinedbasedonlandslidevelocity. Igemaccounts for thesize-linkedfeatures of elements or landslides.Both factors are expressed in nondimensional terms. For differentlocations, the intensity can be given by:I Idyn IdptFor structures outside landslide areaIdyn IdfmFor structures within landslide area_(3)where Idpt is the debris-depth factor, which is used to evaluate theelements outside rapid landslide area, and Idfm is the deformationfactor, which is mainly used to evaluate the structures within thesliding mass of a slow landslide.Dynamic intensity factorIt is obvious that for stationary (e.g., structures, environment) andnon-stationary elements (e.g., persons, vehicles), the dynamicintensitycriteriashouldbedifferent. AccordingtoCrudenandVarnes (1996), the proposed landslide velocity scale and destructiveTable1 Tentativevulnerabilities at different foundationdepths(fromRagozinand Tikhvinsky 2000)Depth of foundation (including piles),mLandslide debrisdepthVulnerability2 2 13 210 0.00.5Any >10 1.0Table 2 Examples of threshold value of foundation displacement for different structuresDeformation features Foundation soilMedium and low compressive soil High compressive soilMasonry structures Partial inclination of foundation 0.002 0.003Single-storey frame structure Settlement (mm) 120 (only for medium compressive soil) 200Simple shaped high-rise building Average settlement of foundation (mm) 200Common industrial and civil buildingsFrame structure Settlement difference between adjacent piles 0.002l 0.003lOutside columns with masonry wall 0.0007l 0.001lHigh-rise buildingHg24 Integral inclination 0.00424