BIBLIOGRAPHIC REFERENCE

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2 BIBLIOGRAPHIC REFERENCE Buxton, R.; Dellow, G. D.; Matcham, I. R.; Smith, W. D.; Rhoades, D. A A New Zealand framework for predicting risk due to rainfall-induced landslides, GNS Science Report 2012/ p. R. Buxton, GNS Science, PO Box 30368, Lower Hutt 5040, New Zealand G. D. Dellow, GNS Science, PO Box 30368, Lower Hutt 5040, New Zealand I. R. Matcham, Jumbletree, 101 Tirohanga Road, Tirohanga, Lower Hutt 5010, New Zealand W. D. Smith, GNS Science, PO Box 30368, Lower Hutt 5040, New Zealand D. A. Rhoades, GNS Science, PO Box 30368, Lower Hutt 5040, New Zealand Institute of Geological and Nuclear Sciences Limited, 2013 ISSN ISBN

3 CONTENTS ABSTRACT... II KEYWORDS... II 1.0 INTRODUCTION THE HAZARD MODEL THE RISK MODEL THE FRAGILITY FUNCTIONS OVERVIEW BUILDINGS DAMAGE STATE CASUALTIES HUMAN DISPLACEMENT HUMAN SUSCEPTIBILITY ASSET REPAIR COST CONTENTS REPAIR COST CLEANUP COST DISRUPTION COST FUNCTIONAL DOWNTIME DISCUSSION AND FUTURE WORK ACKNOWLEDGEMENTS REFERENCES EQUATIONS Equation TABLES Table 1 Mapping of derived DR distributions to RiskScape construction types Table 2 Timber 1 storey Table 3 Timber 2 storey Table 4 Brick 1 storey Table 5 Brick 2 storey Table 6 Concrete Table 7 Steel Table 8 The mapping of damage ratio values to currently used RiskScape damage states Table 9 The mapping of casualty rates against building damage state Table 10 Contents repair cost as a function of contents value and building damage state Table 11 Cleanup cost as a function of asset repair cost and building damage state Table 12 Disruption cost as a function of asset repair cost and damage state Table 13 Functional downtime as a function of building damage state GNS Science Report 2012/22 i

4 ABSTRACT An approach for calculating the likely risk to a portfolio of assets due to rainfall-induced landslides is presented. The method allows for the effects of slope, vegetation and geology on the likelihood of landslide hazard for a given rainfall level. The effect of the hazard is then extended to derive the likely direct cost of a rainfall event for a distributed asset portfolio. Only building losses are considered in this report, but with minor modification the general approach could be applied to other asset types. Strengths and shortcomings of the method are discussed, together with proposed extensions to the method to be included as part of an ongoing program of work. Risk, rainfall-induced landslide. KEYWORDS GNS Science Report 2012/22 ii

5 1.0 INTRODUCTION New Zealand is an island nation, located in temperate latitudes with an oceanic climate, sitting astride the tectonic plate boundary between the Pacific and Australian plates. The high tectonic uplift rates coupled with a wet oceanic climate result in thousands of landslides, occurring each year (Hancox et al, 2002; Hancox and Wright, 2005; Joyce et al, 2009). Most of these landslides are triggered by rain. The prevalence of rainfall-induced landslides is driven by the wet, temperate oceanic climate and the extensive areas of steep slopes. Landslides cause millions of dollars ($NZ) of damage every year in New Zealand and have been responsible for at least 420 deaths since EQC Insurance claims for landslide damage to New Zealand s domestic housing stock alone account for more than $16 million per annum in direct costs over the period This figure does not include repair of landslide damage to commercial buildings, transport and utility networks and loss of productivity on agricultural land, nor does it include indirect costs. Whereas a hazard is often defined as a detrimental process that has a chance of occurring, risk can be defined as the consequences of the hazard occurring, and is calculated from a list of assets and their vulnerabilities to the hazard, weighted by the chance of the hazard occurring. The model described herein uses landslide probabilities calculated and spatially distributed by the Dellow et al (2010) rainfall-induced landslide hazard model and combines these with an asset inventory and a set of fragility functions to produce a New Zealand rainfall-induced landslide risk framework for buildings. RiskScape is a multi-hazard risk analysis tool being developed jointly by GNS Science and NIWA, two Crown Research Institutes (CRIs) in New Zealand. This report describes the risk component of the work undertaken to develop and rainfall-induced landslide model for the RiskScape platform. GNS Science Report 2012/22 1

6 2.0 THE HAZARD MODEL A probabilistic rainfall-induced landslide hazard model for New Zealand has been developed where the probability of a landslide affecting a location, in this instance a digital elevation model (DEM) pixel, varies depending on the amount of rain. Determining the probability of a landslide affecting a DEM pixel requires the addition of two probabilities for each pixel over a range of rainfall values. These are the probability that a landslide initiates in a pixel, and the probability that a landslide will move into a pixel from an upslope position. The probabilistic rainfall-induced landslide hazard model estimates the probability of a rainfall-induced landslide affecting any pixel in the DEM in response to a given rainfall level. The probability of a landslide occurring changes as the rainfall input into the model is changed. This in turn allows the impact of changing rainfall patterns to be assessed with respect to their impact on the landslide hazard. The probabilistic rainfall-induced landslide hazard model is able to deliver the probability of a landslide occurring at any location. It can be used to model the impact of landslides using different amounts of rainfall. Provided suitable fragility functions are available, the risk from landslides affecting buildings and network infrastructure can be calculated. This calculation can be done either on a scenario basis or repeated many times to allow aggregated damage curves to be developed for a selected rainfall. This allows assets at the highest risk of landslide damage, at a nominated rainfall frequency, to be identified. GNS Science Report 2012/22 2

7 3.0 THE RISK MODEL The output from the Dellow et al (2010) hazard model is a pixelated map of probabilities that landslides will originate in, or travel through a pixel at a nominated rainfall value. For a portfolio of buildings distributed over the pixelated hazard map, there is an expected amount of damage that can be calculated according to the product of the probability of hazard and the fragility function associated with the portfolio. Obviously not all buildings in a large, spatially distributed portfolio are uniformly constructed and the fragility function discussed here is assumed to be a variable determined from the superstructure construction type which is the part of the building assumed to be most impacted by the landslide. The expected loss E is taken as, N E = p i V µ i= 1 i i Equation 1 where i = 1 N assets in the portfolio, p i is the probability of landslide in the cell occupied by the asset item, V i is the value of the asset and µ i is the mean of the damage ratio distribution for that asset. Damage ratio distributions were determined from a database of EQC payouts associated with landslide damage claims. First, the superstructure construction types were mapped to the equivalent RiskScape types and then the distributions were generated. RiskScape supports the use of discrete damage states rather than a continuous function damage ratio approach which meant that in order derive damage states, an additional mapping between damage ratios and states was needed. Other RiskScape risk measures are generated according to relationships based on the damage states. With the exception of casualties, these are largely or wholly based on the interpretation and judgement of the authors. It is anticipated that some or all of these relationships may change when further data become available to allow calibration to take place. When the risk model is incorporated into the RiskScape framework, the use of a mean damage ratio for each building asset class will mean that all assets of that class are assumed damaged to the same degree. This is statistically the basis of the method, but it is not ideal as a model. For this reason, the building damage ratios were redistributed by a simple optimization scheme that attempted to jointly match the individual asset type damage ratio distributions and match, as closely as possible, the expected damage total for the asset portfolio that is afforded by using the means of the distributions. The expected loss for the building portfolio was calculated by combining the landslide probabilities at each asset s location with the mean asset fragility of that construction type (Table 1 Table 7). The sum over all assets is the estimated expected total loss based upon the mean damage ratios. This expected total loss figure matches the level of losses based on the available EQC data, but it is not what would happen in real life, because, as with all natural processes, there is a level of variation from the central tendency, which must be introduced in some way. If this variety is not introduced then all impacted assets of a similar type would be damaged to the exact same degree. Introducing the variety means that consecutive model runs (with the GNS Science Report 2012/22 3

8 same starting conditions) should result in similar total damage amounts but that the damage of individual assets within the collection may vary. This was achieved by repeatedly reallocating each asset a damage-ratio value randomly sampled from the appropriate fragility distribution (Table 2 - Table 7) and summing the results. The new total is compared to the expected estimate of total damage and the closest match is kept. At present this is something of a brute force solution and it is possible that more efficient Artificial Intelligence (AI) based search techniques could be used in the future. The best match means that a damage state can be attached to each asset based on the rules in Table 8. The other measures of risk are based on the damage state according to their own rules outlined in each section ( ). GNS Science Report 2012/22 4

9 4.0 THE FRAGILITY FUNCTIONS 4.1 OVERVIEW A set of fragility functions are needed in order to establish a level of risk for a given asset inventory distributed over a hazard map. Fragility functions are mathematical relationships that provide an estimate of damage as financial or human losses (or injuries) based upon a given asset attribute. Additionally, in RiskScape, fragility functions are split into subcategories, explained further below. In the landslide-risk model the fragility functions are distributions of damage ratios; some are empirical where there are data, but others are based on subjective judgement (where there are no data). It is anticipated that all the components that make up the risk model will need a period of calibration and that this may extend over a considerable period. Despite the stated limitations, this work is progress in the right direction. 4.2 BUILDINGS This section describes the damage-ratio distributions for each superstructure construction type, Sections describe the method of calculating the losses associated with each sub-category of risk directly related to buildings (e.g. Casualties = the expected casualties associated with a landslide impact on a building). Damage-ratio distributions have been derived for superstructure construction using timber (1 storey, 2 storey and above), brick (1 storey, 2 storey and above), concrete and steel. Table 1 Mapping of derived DR distributions to RiskScape construction types. Construction type mapping Construction type 1:RC Shear Wall 2:RC Moment Resisting Frame 3:Steel Braced Frame 4:Steel Moment Resisting Frame DR Distribution Concrete Concrete Steel Steel 5: Light Timber Timber 6:Tilt-Up Panel 7:Light Industrial 8:Advanced Design 9:Brick Masonry 10:Conc Masonry 11:Unknown Residential 12:Unknown Commercial Steel Steel Concrete Brick Concrete Timber Concrete GNS Science Report 2012/22 5

10 The actual damage ratio distributions for each construction type are listed in Table 2 Table 7. Repeated sampling was used to approximate a mean for each distribution. As the distributions were based on counts from EQC data, the counts associated with each construction type varied considerably with timber (1 storey) being the best represented construction material. Where a damage-ratio range had a zero count in the actual data, a nominal (low) frequency value was inserted so that non-zero values were assigned to all damage-ratio bins for all construction types. Table 2 Timber 1 storey. DR range Freq Mean DR Table 3 Timber 2 storey. DR range Freq Mean DR Table 4 Brick 1 storey. DR range Freq Mean DR GNS Science Report 2012/22 6

11 Table 5 Brick 2 storey. DR range Freq Mean DR 0.09 Table 6 Concrete. DR range Freq Mean DR Table 7 Steel. DR range Freq Mean DR 0.05 GNS Science Report 2012/22 7

12 4.3 DAMAGE STATE The damage state is mapped from the damage ratio according to the rules listed in Table 8. Table 8 The mapping of damage ratio values to currently used RiskScape damage states. Damage state Damage Ratio range 0 <= CASUALTIES New Zealand experiences about 7 fatalities every 3 years due to landslides (Te Ara) with about 2 fatalities in impacted buildings and the rest to people outdoors. The casualty rates were mapped to the building damage states according to the distribution listed in Table 9. The distribution is derived from historical data and expert judgement. Over some simple simulations, the overall casualty figures generated roughly match those expected statistically. Table 9 The mapping of casualty rates against building damage state. DS Dead Critical Serious Moderate The figures for no or light injuries are assumed to be the occupancy rate for the building less the sum of dead, critically injured, seriously injured and moderately injured people. 4.5 HUMAN DISPLACEMENT The human displacement is a state-based measure, assumed, at present, to be equal to the building damage state for a given landslide impact. 4.6 HUMAN SUSCEPTIBILITY The human susceptibility is a state-based measure assumed, at present, to equal the building damage state for a given landslide impact. GNS Science Report 2012/22 8

13 4.7 ASSET REPAIR COST The probable asset repair cost is based on the building values, the mean damage ratio for the superstructure construction type and the probability that the landslide will impact the building. 4.8 CONTENTS REPAIR COST The contents repair is assumed to be a function of the contents value and the damage state of the impacted building. Some data relating to building contents claims was received from EQC. This data proved to be of limited use. The adopted assumption was that contents damage at lower building-damage states is extremely limited and rises rapidly with increasing damage state. Table 10 Contents repair cost as a function of contents value and building damage state. DS * contents value CLEANUP COST The cleanup cost was assumed to be proportional to the asset repair cost (ARC) for a particular damage state. These values were assigned using only judgement. Table 11 Cleanup cost as a function of asset repair cost and building damage state. DS Cleanup cost 0 ARC*1.5 1 ARC*1.2 2 ARC*1 3 ARC* ARC* DISRUPTION COST The disruption cost was assumed to be proportional to the asset repair cost (ARC) for a particular damage state. These values were assigned using only judgement. Table 12 Disruption cost as a function of asset repair cost and damage state. DS Disruption cost 0 ARC*0.2 1 ARC*0.4 2 ARC* ARC*0.9 4 ARC*1.3 GNS Science Report 2012/22 9

14 4.11 FUNCTIONAL DOWNTIME The approach adopted here was to assume that building damage state 4 corresponds to a total rebuild. This was assumed to be 4 months for a normal sized dwelling (but varies considerably). The times for the other damage states were assumed using judgement and this as an upper bound. Table 13 Functional downtime as a function of building damage state. DS Functional downtime(days) GNS Science Report 2012/22 10

15 5.0 DISCUSSION AND FUTURE WORK In the absence of data, parts of this work are based in judgement using simple assumptions. The distributions, rules, relationships and assumptions outlined herein can be changed when suitable calibration data become available. For instance, at present, the mean is used for the measure of central tendency in the fragility distributions whilst, with more and better data with which to calibrate the model, it is expected that the median (50th percentile) value will eventually give more consistent results. The authors are fully aware of the shortcomings, however, documenting the work so far undertaken on the landslide risk approach for RiskScape provides a useful forward path to better constraining landslide risk models in the future. GNS Science Report 2012/22 11

16 6.0 ACKNOWLEDGEMENTS This report was reviewed by Dr. Jim Cousins and Dr. Mauri McSaveney of GNS Science. 7.0 REFERENCES Dellow, G.D.; Buxton, R.; Joyce, K.E.; Matcham, I.R A probabilistic rainfall-induced landslide hazard model for New Zealand. p (paper 124) In: Williams, A.L.; Pinches, G.M.; Chin, C.Y.; McMorran, T.J.; Massey, C.I. (eds) Geologically active: delegate papers 11th Congress of the International Association for Engineering Geology and the Environment, Auckland, Aotearoa, 5-10 September Boca Raton, Fla: CRC Press. Joyce, K.E.; Dellow, G.D.; Glassey, P.J Using remote sensing and spatial analysis to understand landslide distribution and dynamics in New Zealand. p. III-224-III-227 (paper WE2.05.5) IN: IGARSS 2009: 2009 IEEE International Geoscience and Remote Sensing Symposium proceedings: earth observation, origins to applications, July 12-17, 2009, Cape Town, South Africa. Cape Town, South Africa: IEEE Joyce, K.E.; Dellow, G.D.; Glassey, P.J. 2008a Assessing image processing techniques for mapping landslides. paper II-1231 In: Proceedings : IGARSS 2008: geoscience and remote sensing, the next generation, July 6-11, 2008, Boston, Massachusetts, USA. Boston, Mass: IEEE. Joyce, K.E.; Glassey, P.J.; Dellow, G.D. 2008b Methods for mapping landslides in New Zealand using satellite optical remote sensing. paper 69 In: 14 ARSPC: Australasian Remote Sensing & Photogrammetry Conference, incorporating the North Australian Remote Sensing & GIS (NARGIS) Conference, Darwin Convention Centre, 29 September - 3 October Palmerston, NT: Ossi. Hancox, G.T.; Perrin, N.D.; Dellow, G.D Recent studies of historical earthquake-induced landsliding, ground damage, and MM intensity in New Zealand. Bulletin of the New Zealand Society for Earthquake Engineering, 35(2): Hancox, G.T.; Wright, K.C Landslides caused by the February 2004 rainstorms and floods in southern North Island, New Zealand. Lower Hutt: Institute of Geological & Nuclear Sciences Limited. Institute of Geological & Nuclear Sciences science report 2005/ p. GNS Science Report 2012/22 12

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