Selena Manual

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DRAFTUser Manual for the Earthquake Loss EstimationTool: SELENA v6.0

Sergio Molina

NORSAR and Universidad de Alicante

Dominik H. Lang, Conrad D. Lindholm, Fredrik Lingvall, and Emrah Erduran

NORSAR

June 28, 2012


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DRAFTContents1 Introduction 11.1 Scope and methodology of SELENA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Copyright 5

2.1 Disclaimer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3 Technical Description of SELENA 6

3.1 Basic Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

3.2 Provision of Seismic Demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2.1 Probabilistic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2.2 Deterministic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3.2.3 Analysis with Real-time Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3.3 Amplification of Ground Motion for Design Spectra . . . . . . . . . . . . . . . . . . . . . 10

3.3.1 IBC-2006 (International Code Council, 2006) . . . . . . . . . . . . . . . . . . . . . 10

3.3.2 Eurocode 8 (European Committee for Standardization CEN, 2002) . . . . . . . . . 15

3.3.3 Indian Standard IS 1893 (Part 1) : 2002 (Bureau of Indian Standards, 2002) . . . 15

3.4 Structural Performance Under Seismic Action . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.4.1 The Capacity Spectrum Method (CSM) as Proposed in ATC-40 . . . . . . . . . . 19

3.4.2 The Modified Capacity Spectrum Method (MADRS) . . . . . . . . . . . . . . . . . 24

3.4.3 Improved Displacement Coefficient Method (I-DCM) . . . . . . . . . . . . . . . . . 28

3.5 Fragility Curves and Damage State Probability . . . . . . . . . . . . . . . . . . . . . . . . 29

3.6 Economic Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

3.7 Humanloss Casualties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.7.1 The Basic Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.7.2 The HAZUS Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.8 Direct Social Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.9 Debris Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4 Installation 37

4.1 System Requirements and Resent Code Changes . . . . . . . . . . . . . . . . . . . . . . . 37

4.1.1 Installing the GNU Scientific Library . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.2 The Directory Structure of SELENA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.3 The SELENA m-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.3.1 The SELENA mex-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

4.3.2 The SELENA oct-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5 Running SELENA 41

5.1 Preparation of Input Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.1.1 Input Files for Deterministic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . 42

5.1.2 Input Files for Probabilistic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 43

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DRAFT5.1.3 Input Files for Analysis with Real-time Data . . . . . . . . . . . . . . . . . . . . . 445.1.4 Common Input Files for all Analysis Types . . . . . . . . . . . . . . . . . . . . . . 455.1.5 Input Files for the Calculation of Economic Losses . . . . . . . . . . . . . . . . . . 485.1.6 Input Files for the Calculation of Human Losses Casualties . . . . . . . . . . . 485.1.7 Input Files for the Calculation of Debris . . . . . . . . . . . . . . . . . . . . . . . . 525.1.8 Mandatory Input Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

5.2 Mean Damage Ratio Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

5.2.1 Median Values and Confidence Levels . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.3 The SELENA Program Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.3.1 The Stand-alone SELENA Application . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.3.2 The Matlab and Octave Command-line Interface . . . . . . . . . . . . . . . . . . . 57

5.3.3 The Matlab Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.4 Dealing with Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5.5 Output Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.5.2 Format of the Output Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.5.3 Mean Damage Ratio Output Files . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.5.4 Debris Computation Output Files . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.5.5 Direct Social Losses Computation Output Files . . . . . . . . . . . . . . . . . . . . 66

6 Plotting results in Geographic Information Systems (GIS) 66

7 Known Issues 67

8 Summary 67

Bibliography 68

A Tables 72

B Compiling the C-code 78

B.1 Tools and Libraries for Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

B.2 Building the Stand-alone Application on Linux/Unix . . . . . . . . . . . . . . . . . . . . . 79

B.3 Building the Stand-alone Application on Windows . . . . . . . . . . . . . . . . . . . . . . 79

B.4 Building the Stand-alone GUI Application on Linux/Unix . . . . . . . . . . . . . . . . . . 79

B.5 Building the Stand-alone GUI Application on Windows . . . . . . . . . . . . . . . . . . . 80

B.6 Building the Linux/Unix mex-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

B.6.1 Building the Windows mex-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

B.7 Building the oct-Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81


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Selena 1 INTRODUCTION

1 Introduction

THE earthquake loss estimation tool SELENA, which is described herein, provides local, state andregional officials with a state-of-the-art decision support tool for estimating possible losses from

future earthquakes. This forecasting capability enables users to anticipate the consequences of futureearthquakes and to develop plans and strategies for reducing risk. GIS-based software (e.g., ArcView [1])can be utilized at multiple levels of resolution to graphically show loss results and to prepare responsestrategies.

Some of the first earthquake loss estimation studies were performed in the early 1970s following the1971 San Fernando earthquake. These studies put a heavy emphasis on loss of life, injuries, and theability to provide emergency health care. More recent studies have focused on the disruption of roads,telecommunications and other lifeline systems. The present loss estimation tool computes analytically,based on ground shaking estimates, the degree of damage on specific construction groups and detailed aswell as gross economic losses.

Earlier the National Institute of Building Sciences (NIBS) has developed the tool HAZUS-MH [24]for the federal emergency management agency (FEMA) in order to provide a powerful technique fordeveloping earthquake loss estimates. This to be used in:

anticipating the possible nature of an earthquake disaster and the scope of the emergency responseneeded to cope with an earthquake disaster,

developing plans for recovery and reconstruction following a disaster, and

mitigating the possible consequences of earthquakes.

The methodology generates an estimate of the damage consequences for a city or a region based ona scenario earthquake, i.e., an earthquake with a specified magnitude and location. The resulting lossestimate will generally describe the scale and the extent of damage and disruption that may result from

such an earthquake. Using such computations the following information can principally be obtained by:

Quantitative estimates of losses in terms of direct costs for repair and replacement of damagedbuildings and lifeline system components; direct costs associated with loss of function (e.g., loss ofbusiness revenue, relocation costs); casualties; people displaced from residence; quantity of debris;and regional economic impacts.

Functionality losses in terms of loss-of-function and restoration times for critical facilities such ashospitals, and components of transportation and utility lifeline systems and simplified analyses ofloss-of-system-function for electrical distribution and potable water systems.

Extent of induced hazards in terms of fire ignitions and fire spread, exposed population and buildingvalue due to potential flooding and locations of hazardous materials.

All the system, methods, and data have been coded into a user-friendly software that operates througha geographical information system (GIS) which is called HAZUS-MH [2]; the ESRI GIS system is usedby HAZUS-MH.

In a simplified form, the steps followed by the HAZUS methodology are:

1. Select the area to be studied. This may be a city, a county or a group of municipalities.

2. Specify the magnitude and location of the scenario earthquake. In developing the scenario earth-quake, considerations should be given to the potential fault locations.

3. Provide additional information describing local soil and geological conditions, if available.

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4. Using formulas embedded in HAZUS, probability distributions are computed for damage to differentclasses of buildings, facilities, and lifeline system components and loss-of-function estimates aremade.

5. The damage and functionality information is used to compute estimates of direct economic loss,casualties, and shelter needs. In addition, the indirect economic impacts on the regional economyare estimated for the years following the earthquake.

6. An estimate of the number of ignitions and the extent of fire spread is computed. The amount andtype of debris are estimated. If an inundation map is provided, exposure to flooding can also beestimated.

The earthquake-related hazards considered by the methodology in evaluating casualties, and resultinglosses are collectively referred to as potential earth science hazards (PESH). Most damage and loss causedby an earthquake is directly or indirectly the result of ground shaking, but there are also other features

of an earthquake (such as fault rupture, liquefaction, land sliding etc.) that can cause permanent grounddisplacements and have an adverse effect upon structures, roads, pipelines, and other lifeline structureswhich are also considered.

Soil type can have a significant effect on the intensity of ground motion at a particular site. Thesoftware contains several options for determining the effect of soil type on ground motions for a givenmagnitude and location.

Tsunamis and seiches are also earthquake-caused phenomena that can result in inundation or wa-terfront damage. In the methodology, potential sites of these hazards may be identified, but they areevaluated only if special supplemental studies are performed.

The type of buildings and facilities considered in HAZUS-MH are as follows:

General Building Stock: The commercial, industrial and residential buildings in the studied region

are not considered individually when calculating losses. Instead, they are grouped together into 36model building types and 28 occupancy classes and degrees of damage are computed for groups ofbuildings.

Essential Facilities: These include medical care facilities, emergency response facilities and schools.Specific information is compiled for each building so the loss-of-function is evaluated in a building-by-building basis.

Transportation lifeline systems: These include highways, railways, light rail, bus systems, ports,ferry system and airports and they are broken in components such as bridges, stretches of roadwayor track, terminal, and port warehouses. The damage and losses are computed for each componentof each lifeline.

Utility lifeline systems: These include potable water, electric power, waste water, communications,

and liquid fuels (oil and gas) and are treated in a manner similar to transportation lifelines.

High-potential loss facilities: These include dams, nuclear power plants, or military installationswhich need supplementary specific studies to be evaluated.

All results from HAZUS-MH are provided as best estimates, and no uncertainty in the results isprovided for.

The downside of these fascinating developments implemented in HAZUS-MH is that it has been sointimately connected to the U.S. environments that it is practically impossible to apply it to the rest ofthe world.

We have in the present study developed and adapted the core of the HAZUS methodology to greaterflexibility compared to non-free tools, such as, ArcGIS [5].

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A more important extension is that a logic tree scheme with weighted input of uncertain parametershas been incorporated, and an example of seismic damage scenarios for the city of Oslo have beenconducted and published.

1.1 Scope and methodology of SELENA

While the HAZUS approach is attractive from a scientific/technical perspective, the fact that it is tai-lored so intimately to U.S. situations and to a specific GIS software makes it difficult to apply in otherenvironments and geographical regions.

Aware of the importance of a proper seismic risk estimation, the international centre for geohazards(ICG), through NORSAR (Norway) and the University of Alicante (Spain), has developed a free softwaretool in order to compute the seismic risk in urban areas using the capacity spectrum method namedSELENA (SEimic Loss EstimatioN using a logic tree Approach). The user will supply built area or numberof buildings in different model building types, earthquake sources, empirical ground-motion predictionrelationships, soil maps and corresponding ground-motion amplification factors, capacity curves andfragility curves corresponding to each of the model building types and finally cost models for buildingrepair or replacement. This tool will compute the probability of damage in each one of the four damagestates (slight, moderate, extensive, and complete) for the given building types. This probability issubsequently used with the built area or the number of buildings to express the results in terms ofdamaged area (square meters) or number of damaged buildings. Finally, using a simplified economicmodel, the damage is converted to economic losses in the respective input currency and human casualtiesin terms of different injury types are computed [6]. Optionally, the amount of debris resulting from theshaking damage to buildings and the total number of uninhabitable buildings and displaced householdscan also be computed.

The algorithm is transparent in writing and loading the input files and getting the final results. Themain innovation of this tool is the implementation of the computation under a logic tree scheme, allowing

the consideration of epistemic uncertainties related with the different input parameters to be properlyincluded, and the final results are provided with corresponding confidence levels. Until now the methodhas been successfully applied to the city of Oslo and Naples [6, 7].

The basic approach is often called the capacity-spectrum method, because it combines the groundmotion input in terms of response spectra (see, for example, the spectral acceleration versus spectraldisplacement illustrated in Figure 1) with the buildings specific capacity curve (see the example shown inFigure 2. The philosophy is that any building is structurally damaged by its permanent displacement (andnot by the acceleration by itself). For each building and building type the inter-story drift (relative drift ofthe stories within a multistory structure) is a function of the applied lateral force that can be analyticallydetermined and transformed into building capacity curves. Building capacity curves naturally vary frombuilding type to building type, and also from region to region reflecting local building regulations aswell as local construction practice. Under the HAZUS-umbrella, FEMA developed capacity curves for 36U.S. building types for four earthquake code regimes (reflecting the variation in building regulations as afunction of time across the U.S.). These 144 capacity curves are developed analytically, but adjusted sothat empirical knowledge is incorporated in the curves whenever possible. The building capacity curveis defined through three control points: Design, Yield and Ultimate capacity (Figure 2). Up to the yieldpoint, the building capacity curve is assumed to behave linearly elastic. From the yield point to theultimate point, the capacity curve changes from an elastic to a fully plastic state (curved form), and thecurve is assumed to remain fully plastic past the ultimate point (linear form). A bi-linear representation(two linear parts) is sometimes used to simplify the model shown in Figure 2. The fragility functions aredeveloped as log-normal probability distributions of damage from the capacity curves (see the illustrationin Figure 3). The structural damage states are (as in most other proposed schemes and neglecting thestate no damage) divided into four damage states: slight, moderate, extensive, and complete. A detaileddescription of these damage states are found many places. For example, the description for light frame

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0

0.25

0.5

0.75

1

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

SpectralaccelerationSa

[g]

Spectral displacement Sd [m]

Figure 1: The methodology is based on presenting the ground-motion response spectral ordinates (atgiven damping levels) of spectral acceleration versus spectral displacement.


[g]

Spectral displacement Sd [cm]

dd dy du

ad

ay

au

demand curve

(dd , ad) design capacity

(dy, ay) yield capacity

(du , au) ultimate capacity

median

median +1

median 1

Figure 2: The principle of the building specific capacity curve intersected by the load curve representingthe seismic demand.

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Selena 2 COPYRIGHT

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60 70 80 90 100

D

amageprobabilityP(ds|Sd

)


sli

gh

t

moderate

extensive

comp

lete

Figure 3: Example fragility curves showing the probabilities P(ds|Sd) of being in or exceeding the differentdamage states, ds, for building type C1M as given in HAZUS99.

wood buildings are:

slight: Small plaster cracks at corners of door and window openings and wall-ceiling intersections; smallcracks in masonry chimneys and masonry veneers. Small cracks are assumed to be visible with amaximum width of less than 1/8 inch (cracks wider than 1/8 inch are referred to as large cracks).

moderate: Large plaster or gypsum-board cracks at corners of door and window openings; small diagonalcracks across shear-wall panels exhibited by small cracks in stucco and gypsum wall panels; largecracks in brick chimneys; toppling of tall masonry chimneys.

extensive: Large diagonal cracks across shear-wall panels or large cracks at plywood joints; permanentlateral movement of floors and roof; toppling of most brick chimneys; cracks in foundations; splittingof wood sill plates and/or slippage of structure over foundations.

complete: Structure may have large permanent lateral displacement or be in imminent danger of collapsedue to cripple wall failure or failure of the lateral load resisting system; some structures may slipand fall off the foundation; large foundation cracks. Three percent of the total area of buildingswith Complete Damage is expected to be collapsed, on average.

2 Copyright

THE SELENA program is an open source software and the source code for the program is freelyredistributable under the terms of the GNU General Public License (GPL) as published by the FreeSoftware Foundation (http://www.gnu.org). See also the file COPYING which is distributed with theSELENA program.

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Selena 3 TECHNICAL DESCRIPTION OF SELENA

The SELENA program can be downloaded at: http://selena.sourceforge.netAt this website youcan also find information how to contact the authors and report bugs etc.

2.1 Disclaimer

The SELENA program is distributed in the hope that it will be useful but WITHOUT ANY WAR-RANTY. More specifically:

THE PROGRAM IS PROVIDED AS-IS WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSOR IMPLIED, INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OR CONDITIONSOF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL ANYOF THE AUTHORS OF THE SELENA PROGRAM AND/OR NORSAR, NORWAY, UNIVERSIDAD DEALICANTE, SPAIN, BE LIABLE FOR ANY SPECIAL, INCIDENTAL, INDIRECT, OR CONSEQUEN-TIAL DAMAGES OF ANY KIND, OR DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE,DATA, OR PROFITS, WHETHER OR NOT THE AUTHORS OF THE SELENA PROGRAM HAVE BEENADVISED OF THE POSSIBILITY OF SUCH DAMAGES, AND/OR ON ANY THEORY OF LIABILITY

ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.

3 Technical Description of SELENA

IN this section the main features of SELENA is discussed.

3.1 Basic Procedure

The HAZUS methodology covers a wide range of different damages and losses to buildings, lifelines,people etc.; however, in the present version of SELENA we have only implemented the first part of

the methodology, the estimation of damage to the general building stock, the economic and humanlosses related to these physical damages, and optionally the estimation of amount of debris, number ofuninhabitable buildings and number of displaced households. All results are provided with ranges ofuncertainty facilitating the easy computation of, e.g., median value and 16%- respectively 84%-fractilesof damage.

It has to be noted that SELENA requires quite extensive basis information within a number of inputfiles. These can be easily generated as tables in, for example, a spreadsheet program (e.g., MS-Excel,OpenOffice, MS-Access etc.) and exported as ASCII-table files with all required information given in thematrices.

It should be noted that, HAZUS-MH methodology has been developed for a population of buildingsand cannot be used to estimate the damage or losses associated to individual buildings unless a detailedfinite element analysis that considers the pecularities of the building is conducted. Further, the capacity

curves and fragility functions used for different building typologies represents a mean curve for all thebuildings in that building typology. As such, the results of SELENA are meaningful as long as they areused to estimate the damage and associated losses for a population of buildings. As a result, SELENAas most other risk estimation software tools considers the minimum geographical unit (GEOUNIT),i.e., the census tract, as the smallest area unit. In practice, this unit is related to building blocks orsmaller city districts. The decision on the extent of each geographical unit has to be made consideringdifferent aspects such as having equal soil conditions, constant surface topography or a homogeneouslevel of building quality within the demarcated area. The main basis information consists in the buildinginventory database (which is also somewhat difficult to generate). This type of information sometimesis provided by local agencies or governmental institutions. In any case, a thorough investigation ofthe local building stock by walk-downs and on-site inspections should be conducted in order to allow arepresentative classification of the prevalent building typologies. The building inventory database should

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contain a maximum of details about building materials, building techniques, built area, floors of thebuilding, height, foundations, seismic regulations used in the construction, use of the building, numberof occupants, year of construction, etc. The building information is classified according to building type,built square meters in each one of the geographical units which form the region under study or as anindividual building if a site-specific study is going to be done. The classification of the building typecan be either done according to the HAZUS methodology (see http://www.fema.gov/hazus documentsor previous HAZUS reports) or following a user-defined classification scheme being more specific for theavailable building stock.

3.2 Provision of Seismic Demand

A key point in any seismic risk assessment is the provision of seismic ground motion (level and spectralcharacteristics of earthquake shaking). In order to carry out a seismic risk and loss assessment withSELENA, the user can provide the seismic ground-motion amplitudes on three different ways:

provision of spectral ordinates (taken out from probabilistic shaking maps) for each geographicalunit (probabilistic analysis),

definition of deterministic earthquake scenarios (e.g., historical or user-defined events) and ap-propriate ground-motion prediction equations in order to compute the spectral ordinates in eachgeographical unit (deterministic analysis),

provision of recorded ground-motion amplitudes at the locations of seismic (strong-motion) stations(analysis with real-time data).

In the previous versions, spectral accelerations at the three periods T = 0.01 [s] peak ground acceleration(PGA), T = 0.30 [s] (Sa0.3) and T = 1.00 [s] (Sa1.0) have to be provided in order to describe the elastic

design spectrum following the provisions of the international building code 2006 (IBC-2006) [8]. Mostother earthquake codes (e.g., Eurocode 8 [9]) define the shape of the design spectrum such that onlya design acceleration value, generally the PGA, is required to scale the amplitudes of the spectrum.Consequently, in case that Eurocode 8 design spectra are chosen for the analysis, spectral accelerationsvalues Sa0.3 and Sa1.0 are not regarded.

Starting from v6.0, site-specific elastic response spectrum can also be used to define the ground motion.If this option is selected, the spectral accelerations at nine periods T = 0.01 [s] peak ground acceleration(PGA), T = 0.10 [s] (Sa0.1), T = 0.20 [s] (Sa0.2), T = 0.30 [s] (Sa0.3), T = 0.50 [s] (Sa0.5), T = 0.75 [s](Sa0.75), T = 1.00 [s] (Sa1.0), T = 1.50 [s] (Sa1.5), and T = 2.00 [s] (Sa2.0) have to be provided.

3.2.1 Probabilistic Analysis

The probabilistic analysis procedure denotes the use of spectral ordinates which are taken from proba-bilistic shake maps. In addition to the acceleration values (PGA, SaT) for each geographical unit, thegeographical coordinates of the centroid have to be provided. Probabilistic shake maps are generallydeveloped for rock conditions such that soil amplification is not included in the spectral ordinates.

3.2.2 Deterministic Analysis

For the deterministic analysis the ground-motion parameters (PGA, Sa0.3, Sa1.0) produced by the sce-nario earthquake are calculated by selectable ground-motion prediction relations (attenuation relations).Since all geographical units are located in different distances to the assumed epicenter of the scenarioearthquake, this process is done separately for each geographical unit. A considerable number of well-established ground-motion prediction relations is already incorporated in the SELENA code (Appendix A,

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Figure 4: Schematic illustration of the different distance types.

Table 19) but any user-provided relation can be easily implemented. It should be noted that, when usingthe elastic design spectra, all provided prediction relations refer to rock site conditions and thus computeground-motion amplitudes without soil amplification since this is covered in a separate (subsequent) cal-culation step. On the other hand, when the site-specific response spectra are used, the soil conditions areconsidered in the ground motion prediction equations and no further amplification is necessary.

Depending on the type of design spectrum chosen for the analysis, predicted ground-motion amplitudesare either used to define the shape of the elastic design spectrum (e.g., IBC-2006) or only to scale theamplitudes of the spectrum (e.g., Eurocode 8) which later represents the seismic demand for the capacityspectrum method (CSM) procedure. As Table 1 illustrates, all predefined ground-motion predictionequations can be used to derive mean values of ground-motion amplitudes as well as their 1 (standarddeviation) values in order to account for aleatoric uncertainty.

Since each ground-motion prediction equation is dependent on a particular distance, SELENA au-tomatically computes four different types of distances: epicentral distance Repi , hypocentral distanceRhypo, Joyner-Boore distance Rjb (shortest distance to the vertical surface projection of the faultrupture plane), and the shortest distance to the subsurface fault rupture plane Rrup (see Figure 4).

Thereby, the expected value of the surface fault rupture length, L, is based on the relationship byWells and Coppersmith [10]:

log10(L) = 3.55 + 0.74M for strike-slip faults (1)

log10(L) = 2.86 + 0.63M for reverse faults (2)

log10(L) = 3.22 + 0.69M for all other fault types (3)

where L is the rupture length in [km] and M is the moment magnitude of the earthquake.

3.2.3 Analysis with Real-time Data

In case of an analysis with real-time data, a major problem consists in the fact that the locations forwhich ground-motion data is available will certainly not comply with the center points of the definedgeographical units (i.e., centroids). Consequently, the provided spectral ordinates at these locations haveto be assigned to the centroids in a somehow reliable way. The procedure applied here is schematicallyillustrated in Figure 5. Basically it is checked which of the available points (here the nodes of anequally-spaced grid pattern) are within a 5 km-radius around each centroid. If at least 5 points meetthis criterion the mean value and corresponding 16%- resp. 84%-fractiles of the spectral ordinates of allstations are computed and assigned to the respective centroid. If less than 5 points are within this 5

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Author(s) (year)Target ground-motion parameter

mean value (mv) mv+1 mv - 1

Boore et al. [11], Boore et al. [12], Boore et al. [13] * * *Ambraseys et al. [14] * * *Toro et al. [15] * * *Campbell and Bozorgnia [16]), Campbell [17] * * *Campbell and Bozorgnia [18] * * *Abrahamson and Silva [19] * * *Sabetta and Pugliese [20] * * *Ambraseys et al. [21] * * *Akkar and Bommer [22] * * *Sadigh et al. [23] * * *zbey et al. (2003) * * *Spudich et al. [24] * * *Bommer et al. [25] * * *Atkinson and Boore [26] * * *Zonno and Montaldo [27] * * *

Schwarz et al. [28], Ende and Schwarz [29] * * *Ambraseys and Douglas [30], Douglas [31],Ambraseys and Douglas [32] * * *Chapman [33] * * *Crouse and McGuire [34] * * *Gulkan and Kalkan [35] * * *Lussou et al. [36] * * *Dahle et al. [37] * * *Bommer et al. [38] * * *Marmureanu et al. [39] * * *Sharma et al. [40] * * *

Table 1: Selection of the empirical ground-motion prediction methods which are implemented in thecurrent SELENA-version (see the m-file att sub.m or the C-file att sub.c distributed with SELENA).

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Figure 5: Spectral ordinates at the sites of randomly-distributed recording stations are assigned to thecenters of the geographical units (centroids).

km-radius, a new circle of 10 km diameter is drawn. If the location of a centroid is more or less identicalwith the location of one recording station, its spectral ordinates are directly assigned to the centroidwithout further processing. It should be regarded, that the provided spectral ordinates already cover soilamplification effects as they are realistic ground-motion data recorded at the ground surface. Thereforeany additional consideration of soil amplification has to be avoided. [In practice, this means that theSELENA soil input files (i.e., soilcenteri.txt) do not contain soil class indecies other than those forrock, i.e., 2 for IBC-2006, 1 for Eurocode 8].

3.3 Amplification of Ground Motion for Design Spectra

In case that sedimentary soil materials are present at a site, the seismic ground motion at the groundsurface is modified both in amplitude and frequency content. Respective amplification factors and/orcorner periods which basically describe shape of the design spectra for the different soil classes are givenin the corresponding code provisions. Currently, the procedures of IBC-2006, Eurocode 8 (Type 1 andType 2), and Indian standard IS 1893 [41] are incorporated while more will follow in upcoming SELENA-versions.

3.3.1 IBC-2006 (International Code Council, 2006)

The methodology characterizes ground shaking using a standardized response spectrum shape as givenin IBC-2006 [8], which consists of four parts: PGA, a region of constant spectral acceleration at periodsfrom zero seconds to Tav, a region of constant spectral velocity between periods from Tav to Tvd, and a

region of constant spectral displacement for periods of Tvd and beyond (see Figure 6).

The region of constant spectral acceleration is defined by the constant Sa at 0.3 s (Sa 1.0). The regionof constant spectral velocity has Sa proportional to 1/T and is anchored to the constant Sa at 1.0 s(Sa1.0). In general, the elastic design spectrum Sa(T) is defined by the following equations:

Sa(T) = Sa0.3(0.4 + T /TA) for T < TA (4)

Sa(T) = Sa0.3 for T < T < TAV (5)

Sa(T) = Sa1.0/T for TAV < T < Tvd (6)

Sa(T) = Sa1.0Tvd/T2 for Tvd < T < 10 s (7)

The period Tav is based on the intersection of the region of constant spectral acceleration and constantspectral velocity and its value varies depending on the values of spectral acceleration that define these

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0

Spectral

accelerationSa

[m/s2]

Period T [s]

TA TAV TVD

PGA

Sa0.3

Sa1.0

damping = 5 %

Figure 6: Standard shape of the response spectrum.

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two intersecting regions:Tav = Sa1.0/Sa0.3 (8)

The period Ta representing the left corner period of the spectral plateau can be determined as follows:

Ta = 0.2TAV = 0.2(Sa1.0/Sa0.3) (9)

The constant spectral displacement region has spectral acceleration proportional to 1/T2 and is anchoredto the spectral acceleration value at the period Tav, where constant spectral velocity transitions to constantspectral displacement.

The period Tvd is based on the reciprocal of the corner frequency fc, which is proportional to stressdrop and seismic moment. This frequency is estimated from the Joyner and Boore [42] relationship as afunction of moment magnitude:

Tvd =1

fc= 10(M5)/2 (10)

where fc is the corner frequency and M is the moment magnitude. When the moment magnitude is notknown (probabilistic earthquake scenario), the period Tvd is assumed to be 10 seconds (M = 7.0).

In order to be able to describe the elastic design spectra (for rock: site class B) in case that the PGAis given, the following expressions have to be regarded:

Sa0.3 = Saas = 2.5apga (11)

Sa1.0 = Sasl = apga (12)

Amplification of ground shaking to account for local site conditions is based on the site classes (seeTable 2) and soil amplification factors as given by the IBC-2006 provisions. These code provisions do not

Sitesite class description

shear-wave velocityclass vs,30 [m/s]

A Hard rock, eastern U.S. sites only > 1500

B Rock 7601500C Very dense soil and soft rock 360760D Stiff soil 180360E Soft soil, profile with > 3 m of soft clay defined as soil

with plasticity index PI> 20, moisture content w > 40% < 180F Soils requiring site-specific evaluations

Table 2: NEHRP site classification [43] as applied by IBC-2006 [8].

provide specific soil amplification factors for PGA or PGV. The methodology amplifies rock (site classB) PGA by the same factor as that specified in Table 3 for short period (0.3 s) spectral acceleration, asexpressed in the following expression:

apgai = apgaFAi (13)

where apgai is the PGA for site class i (in units of [g]); apga is that for site class B (in units of [g]) and FAi

is the short period amplification factor for site class i, for spectral acceleration Sas. The construction ofdemand spectra including soil effects is done using the following equation for short periods:

Sasi = SasFai (14)

and for long periods:Sali = SalFvi (15)

while the period TAVi, which defines the transition period from constant spectral acceleration to constantspectral velocity is a function of the site class. It can be determined by the following equation:

TAVi =SasiSas

FviFai

(16)

where:

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Site Class B Site ClassSpectral Acceleration A B C D E

Short-Period, Sas [g] Short-Period Amplification Factor, FA 0.25 0.8 1.0 1.2 1.6 2.5

(0.25, 0.50] 0.8 1.0 1.2 1.4 1.7(0.50, 0.75] 0.8 1.0 1.1 1.2 1.2(0.75, 1.0] 0.8 1.0 1.0 1.1 0.9

> 1.0 0.8 1.0 1.0 1.0 0.91-Second Period,Sal [g] 1-Second Period Amplification Factor, FV

0.1 0.8 1.0 1.7 2.4 3.5(0.1, 0.2] 0.8 1.0 1.6 2.0 3.2(0.2, 0.3] 0.8 1.0 1.5 1.8 2.8(0.3, 0.4] 0.8 1.0 1.4 1.6 2.4

> 0.4 0.8 1.0 1.3 1.5 2.4

Table 3: Site amplification factors as given in IBC-2006 [8].

Sasi: short-period spectral acceleration for site class i (in units of [g])

Sas: short-period spectral acceleration for site class B (in units of [g])

FAi: short-period amplification factor for site class i and for spectral acceleration Sas

Sali: 1-second (long) period spectral acceleration for site class i (in units of [g])

Sal: 1-second (long) period spectral acceleration for site class B (in units of [g])

Fvi: short-period amplification factor for site class i and for spectral acceleration Sal

Tavi: transition period between constant spectral acceleration and constant spectral velocity for siteclass i (in [s]).

Note that the period Tvd, which defines the transition period from constant spectral velocity to constantspectral displacement, is not a function of site class [see Eq (10)].

For the evaluation of structural damage it is more convenient to plot the acceleration response spec-trum as a function of the spectral displacement (rather than the period). This could be achieved due tothe relation between the different spectral parameters:

Sa

= Sv = Sd (17)

where is the angular (natural) frequency of the oscillator (i.e., = 2f, where f is the frequency in[Hz]).

The final result of this process is the computation of a 5% damped response spectrum at the centerof each geographical unit (where values of ground motion were computed) or at the specific site understudy. In the following, this will be done exemplary for selected site classes according to the IBC 2006provisions, i.e., NEHRP site classes AE.

Example 3.1 Generation of elastic demand spectra for NEHRP site classes B, C and D

Given parameters:

PGA for rock site conditions (site class B): aPGAb = 0.20 g

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Sa (0.3 s) for rock site conditions (site class B): Sa0.3b = 0.50 g

Sa (1.0 s) for rock site conditions (site class B): Sa1.0b = 0.20 g

Steps:

1. Calculation of spectral parameters for soil demand spectra: In case that Sa0.3B and Sa1.0B cannot be derived by spectral attenuation equations, both can be provided by: Sa0.3 = Sas = 0.50 g[Eq. (11)] and Sa1.0 = Sal = 0.20 g [Eq. (12)].

2. Determination of site amplification factors for site classes (according to Table 3).

Site amplification factors for Site ClassSas = 0.50 g resp. Sal = 0.20 g B C D

Fa 1.0 1.2 1.4Fv 1.0 1.6 2.0

3. Calculation of short-period and long-period spectral accelerations as well as transition period Tavi

ParameterSite Class

B C D

apgai = apgaFai 0.20 g 0.24 g 0.28 g

Sasi = SasFai 0.50 g 0.60 g 0.70 gSali = SalFvi 0.20 g 0.32 g 0.40 g

0.40 s 0.53 s 0.57s

0.08 s 0.106 s 0.114 s3.16 s (for M 6.0), 5.62 s (for M 6.5), 10.0 s (for M 7.0)

4. Generation of elastic demand spectrum (damping = 5%):

0

0.2

0.4

0.6

0.8

1

0 0.5 1 1.5 2 2.5


[g]

Period T [s]

Site Class: BCD

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60


[g]


Site Class: BCD

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3.3.2 Eurocode 8 (European Committee for Standardization CEN, 2002)

For the description of seismic action, two different types of design spectra are provided within Eurocode8 [9]. This mainly in order to account for the differing level of seismic hazard in Europe and the differentearthquakes susceptible to occur. In case that earthquakes with a surface-wave magnitude Ms > 5.5 areexpected it is suggested to use Spectrum Type 1, else (Ms 5.54) Type 2. The question which spectrumtype to choose for a specific region should be based upon (...) the magnitude of earthquakes that areactually expected to occur rather than conservative upper limits defined for the purpose of probabilistichazard assessment.

For the sake of completeness both spectrum types are incorporated in the current version of SELENAeven though scenario earthquakes with magnitudes smaller than 5.5 are not expected to cause considerablestructural damages to the general building stock.

Both types of the horizontal design spectrum are defined by the following expressions:

Sa(T) = agS

1 + TTB (2.5 1)

for T < TB (18)

Sa(T) = agS2.5 for TB < T < TC (19)

Sa(T) = agS2.5

1 + TCT

for TC < T < TD (20)

Sa(T) = agS2.5

1 + TCTDT2

for TD < T < 4 s (21)

where:

ag: design ground acceleration (here: PGA) on soil type A ground,

TB, TC: corner periods of the constant spectral acceleration branch (plateau),

TD: corner period defining the beginning of the constant displacement range,

S: soil factor (see Table 4),

: damping correction factor ( = 1 for 5% viscous damping).

The shape of the design spectrum is thus determined by the corner periods, soil factor, and the levelof input ground motion. Both, corner periods TB , TC and TD as well as soil factor S are dependenton ground type which is mainly distinguished by the average shear-wave velocity of the uppermost 30m vs,30 into 5 different soil classes (Table 4). Both, soil factor and corner periods for the different soilclasses are given in Table 5 and Table 6 for Type 1 and Type 2 design spectra, respectively. Figure 7illustrates the corresponding sets of normalized elastic design spectra.

3.3.3 Indian Standard IS 1893 (Part 1) : 2002 (Bureau of Indian Standards, 2002)

The construction of the horizontal design spectra following the provisions of the Indian standard IS1893 (Part 1) : 2002 [41] can be compared with the procedure of Eurocode 8. The amplitude level ofthe spectrum solely is dependent on the value for peak ground acceleration (PGA). The shape of thehorizontal design spectrum is thus defined by the following expressions:

Sa(T) = agS

1 + TTB (2.5 1)

for 0 T < TB (22)

Sa(T) = agS2.5 for TB < T < TC (23)

Sa(T) = agS2.5

1 + TCT

for TC < T < 4.0s (24)

(25)

where:

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Ground type Description of stratigraphic profileShear wave velocity

vs,30 [m/s]

ARock or rock-like geological formation,

> 800incl. at most 5 m of weaker material at the surface

BDeposits of very dense sands, gravel, or very stiff clay

360-800(at least several tens of m in thickness) characterized bya gradual increase of mechanical properties with depth

CDeep deposits of dense or medium-dense sand, gravel or

180-360stiff clay with thickness from several tensto many hundreds of m

DDeposits of loose-to-medium cohesionless soil

< 180(with or without some soft cohesive layers), or of predominantlysoft-to-firm cohesive soil

ESoil profile consisting of a surface alluvium layer with vs,30

n.avalues of type C or D and thickness H varying between5-20 m underlain by stiffer material with vs,30 > 800 m/s.

Table 4: Ground types.

Ground type Soil factor S TB [s] TC [s] TD [s]A 1.00 0.15 0.40 2.00B 1.20 0.15 0.50 2.00C 1.15 0.20 0.60 2.00D 1.35 0.20 0.80 2.00E 1.40 0.15 0.50 2.00

Table 5: Values of the parameters describing Eurocode 8 Type 1 spectra.

Ground type Soil factor S TB [s] TC [s] TD [s]

A 1.00 0.05 0.25 1.20B 1.35 0.05 0.25 1.20C 1.50 0.10 0.25 1.20D 1.80 0.10 0.30 1.20E 1.60 0.05 0.25 1.20

Table 6: Values of the parameters describing Eurocode 8 Type 2 spectra.

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0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3 3.5 4

Normalizedspectralacceleration

Period T [s]

Type 1Ground type: A

BCDE

0

1

2

3

4

5

6

0 0.5 1 1.5 2 2.5 3 3.5 4

Normalizedspectralacceleration

Period T [s]

Type 1Ground type: A

BCDE

Figure 7: Elastic design spectra of Type 1 and Type 2 for ground types AE (prEN 1998-1:200x).

ag: design ground acceleration (here: PGA),

TB, TC: corner periods of the constant spectral acceleration branch (plateau),

TD: corner period defining the beginning of the constant displacement range,

: damping correction factor ( = 1 for 5% viscous damping).

The periods TB and TC are the only parameters which depend on the soil conditions. An explicit soilamplification factor is not defined. Table 7 describes the three different soil types and assigns their

control periods. Unfortunately, no characteristic values of shear wave velocities vs,30 are assigned to the

Spoil type Description of stratigraphic profileShear wave velocity

TB [s] TC [s]vs,30 [m/s]

I

Rock or Hard Soil:

> 400 0.10 0.40well graded gravel and sand gravel mixtures with or withoutclay binder, and clayey sands poorly graded or sand claymixtures (GB, CW, SB, SW, and SC) having N > 30)

II

Medium Soils:

200-400 0.10 0.55a) all soils with 10 < N < 30b) poorly graded sands or gravelly sands with littleor no fines (SP) with N > 15

IIISoft Soils:

< 200 0.10 0.67all soils other than SP with N < 10

Table 7: Soil types, deduced ranges of shear wave velocities as well as corner periods of the horizontaldesign spectra. N is the standard penetration value and values of shear wave velocities, vs,30, are notprovided by the Indian standard IS 1893 (Part 1) [41]; ranges of vs,30 are derived by comparing thestandard penetration values with soil classification schemes of other earthquake codes (e.g., IBC-2006;Turkish code TMPS [44]) providing both values of N and vs,30.

soil classes thus standard penetration test (SPT) values N are the only tangible parameters which allowa classification of the soil conditions. A comparison with different soil classification schemes (e.g., IBC-2006; Turkish seismic code TMPS [44]) providing both SPT-values N and ranges of shear wave velocitiesvs,30 enabled a coarse allocation of vs,30 ranges to the three soil classes. Normalized elastic (R = 1.0)design spectra for soil types IIII are reproduced in Figure 8.

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0

1

2

3

4

0 0.5 1 1.5 2 2.5 3 3.5 4

Norm

alizedspectralacceleration

Period T [s]

IS 1893 (Part 1) : 2002Soil type: I

IIIII

Figure 8: Elastic design spectra for Soil Types I-III [IS 1893 (Part 1) : 2002] [ 41].

Note: Since most earthquake codes adopt a comparable procedure in order to generate the design

spectra as the one described in Eurocode 8, any new set of site-specific design spectra can be easilyimplemented by the user itself.

When site-specific response spectrum is used, the soil conditions are considered in the ground motionprediction equation by using the specified Vs30 values for each geographical unit. Hence, no further soilamplification is required.

3.4 Structural Performance Under Seismic Action

In order to determine the seismic performance of a building, the spectral displacement along its capacitycurve must be determined that is consistent with the seismic demand and at the same time being reduced

for nonlinear effects. Currently a number of different methodologies are available in order to identify theso-called performance point on the capacity spectrum. In the following the CSM as proposed by ATC-40 [45] and FEMA 273 [46] , a recent modification of this procedure, the MADRS method, and thedisplacement coefficient method (DCM) of FEMA-356 [47] with the improvements proposed in FEMA-440 [48] [referred henceforth as improved displacement coefficient method(I-DCM)] will be described todetermine the performance point and thus to establish the basis in order to estimate the structuraldamage state under an estimated seismic demand. All three procedures are implemented in SELENA,such that the user can choose which one to use.

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3.4.1 The Capacity Spectrum Method (CSM) as Proposed in ATC-40

The building response (e.g., peak displacement) is determined by the intersection of the seismic demandspectrum and the building capacity curve. The demand spectrum is based on the PESH input spectrumreduced for effective damping (when effective damping exceeds the 5% damping level of the PESH inputspectrum).

The elastic response spectra provided as a PESH input applies only to buildings that remain elasticduring the entire ground shaking time history and have elastic damping values equal to 5%. This isgenerally not true on both accounts. Therefore, elastic response spectra are modified in case of:

a) buildings with elastic damping not equal to 5%, and

b) buildings pushed beyond their elastic limits and thus dissipating hysteretic energy.

Modifications are represented by reduction factors through which the spectral ordinates are dividedto obtain the damped demand spectra. The methodology reduces demand spectra for effective dampinggreater than 5% based on statistically-based formulas of Newmark and Hall [ 49]. These relationshipsestimate elastic response spectra at different damping ratios B (expressed as a percentage) and representall site classes (soil types) distinguishing between domains of constant acceleration and constant velocity.Ratios of these formulas are used to develop an acceleration-domain (short-period) reduction factor RAand a velocity-domain (1-second spectral acceleration) reduction factor RV, in order to modify the 5%-damped elastic response spectra. These reduction factors are based on effective damping Beff:

Ra(Beff) =2.12

3.21 0.68 log(Beff)(26)

Rv(Beff) =1.65

2.31 0.41 log(Beff)(27)

where Beff is the effective damping given by the expression:

Beff = Be + Bh (28)

and where Be is the elastic damping and Bh is the hysteretic damping, which is a function of the yieldand ultimate capacity points (see Figure 2 in ATC-40 [45]) as follows:

Bh = 63.7

AyiAu

DyiDu

(29)

where is a degradation factor that defines the effective amount of hysteretic damping as a function ofearthquake duration and energy-absorption capacity of the structure during cyclic earthquake load (seeHAZUS documents, Table 5.18 in [2]), and Ayi and Dyi are obtained through an iterative process as a

part of the capacity curve bilinearization.Following the recommendations of Newmark and Hall [49], Be is the elastic (pre-yield) damping of

the model building type, which is:

5% for mobile homes (MH),

57% for steel buildings (S),

7% for concrete (C) and pre-cast concrete buildings (P),

710% for reinforced masonry buildings (RM),

10% for un-reinforced masonry (URM) and masonry buildings (M),

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1015% for wood buildings (W).

The methodology recognizes the importance of the duration of ground shaking on building response byreducing the effective damping (i.e., -factors) as a function of shaking duration. Dependent on themagnitude of the scenario earthquake, the effective damping is based on the assumption of differentground shaking durations:

magnitude M 5.5: short duration

magnitude 5.5 < M < 7.5: moderate duration

magnitude M 7.5: long duration

The new demand spectral acceleration Sa(T) in units of gravity [g] is defined at short periods (accelerationdomain), long periods (velocity domain), and very long periods (displacement domain) using the 5%

damped response spectrum and dividing by the before mentioned factors following the expressions:

Sa(T) = Saasi(0.4 + T /TA)/Ra(Beff) for 0 < T < Ta (30)

Sa(T) = Saasi/Ra(Beff) for Ta < T < Tavb (31)

Sa(T) = (Saali/T)/Rv(Beff) for TAVb < T < Tvd (32)

Sa(T) = (SaaliTvd/T2)/Ra(Beff) for T > Tvd (33)

where:

SASi: 5% damped, short-period spectral acceleration for site class i (in [g])

Ssli: 5% damped, 1-second (long) period spectral acceleration for site class i (in [g])

Btvd: value of effective damping at the transition period Tvd

Tavb: transition period between acceleration and velocity domains as a function of the effective dampingat this period which is defined by the equation:

Tavb = TaviRA(Btavb)

RB(Btavb)(34)

where:

Tavi: transition period between 5%-damped constant spectral acceleration and 5%-damped constantspectral velocity for site class i

Btavb: value of effective damping at the transition period Tavb.

The transition period Tvd is independent of effective damping and only depends on the moment magni-tude, as previously said.

Example 3.2 Performance point calculation between inelastic demand spectra for site classes B, C andD and a given capacity curve by the Capacity spectrum method (CSM) described in ATC-40 Chapter2.4.1 [45]

Steps:

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1. Determination of the structures yield capacity and ultimate capacity:

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60


[g]


(Dy, Ay)

(Du, Au)

capacity curve

e.g.,: capacity curves as given in HAZUS, here: C1Mfor moderate-code design

yield capacity point: Ay = 0.104 g, Dy = 0.58in. = 1.47 cm.

ultimate capacity point: Au = 0.312 g, Du =6.91 in. = 17.55 cm

2. Determination of effective damping Beff by calculating hysteretic damping Bh according to Ta-ble 5.18 in HAZUS99 [50]: degradation factor, , depending on earthquake duration and energy-absorption capacity of the structure during cyclic earthquake load

moderate durationmoderate-code designbuilding type C1M

= 0.4

Bh = 63.7

AyAu

DyDu

= 4%

Be = 7.0%Beff = Bh + Be = 11.1%

3. Calculation of reduction factors Ra and Rv, short-period and long-period spectral accelerations aswell as transition period Tavi

ParameterSite Class

B C D

Ra(Beff) =2.12

3.210.68 log(Beff)[Eq. (26)] 1.35

Rv(Beff) =1.65

2.310.41 log(Beff)[Eq. (27)] 1.35

Sasbi = Sasi/Ra [Eq. (31)] 0.37 g 0.44 g 0.52 g

Salbi = (Sali/T)/RV [Eq. (32)] 0.16 g 0.26 g 0.32 gSavb = SaviRaRv

[Eq. (34)] 0.43 g 0.57 g 0.62 g

4. Generation of reduced (inelastic) demand spectrum (damping = 11.1%):

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0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60


[g]


Site Class: Bdemand spectra:

Be = 5 %Beff= 11.1 %

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60SpectralaccelerationSa

[g]


Site Class: Cdemand spectra:

Be = 5 %Beff = 11.1 %

0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50 60


[g]


Site Class: Ddemand spectra:

Be = 5 %Beff= 11.1 %

1. Calculation of the spectral accelerations and spectral displacements at the site in question takinginto account soil response, so that the elastic response spectrum can be generated.

2. Creation or selection of a capacity curve for the respective building type reflecting the buildingsperformance under an increasing, laterally applied (earthquake) load.

3. Determination of effective damping Beff by specifying elastic damping Be and by computing the

hysteretic damping Bh. Based on this the calculation of both reduction factors RA and RV can berealized.

4. Reduction of the elastic response spectrum by reduction factors RA and RV to account for theincreased damping that occurs at higher levels of ground motion and consequently building response(non-linear behavior).

5. Superposition of the building capacity curve with the modified (inelastic) response spectrum (de-mand curve). The resulting building displacement is estimated from the intersection of the buildingcapacity curve and the response spectrum (performance point; see also Figure 9).

6. The estimated building displacement is later used to define the damage degree at the intercept ofthe fragility curve and the damage probability curve (see Figure 10).

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Sp

ectralaccelerationSa

[g]


performance point

(dp , ap)

PESH spectrum (elastic)reduced spectrum (inelastic)

capacity curve

Figure 9: Estimation of building displacement from a given PESH input.

0

0.2

0.4

0.6

0.8

1

Dam

ageprobabilityP(ds|Sd

)


no damage

slight

moderate

extensive

complete

dp

dp expected spectraldisplacement

damage state: slightmoderateextensivecomplete

Figure 10: The expected displacement (obtained from the performance point) is overlaid with the fragilitycurves in order to compute the damage probability in each one of the different damage states.

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3.4.2 The Modified Capacity Spectrum Method (MADRS)

The conventional capacity spectrum method (ATC-40 [45]) uses the secant period as the effective linearperiod in determining the maximum displacement (performance point). This assumption results in themaximum displacement occurring at the intersection of the capacity curve for the structure with thedemand curve for the effective damping in ADRS format. However it has been shown in several studiesthat this method can not be used with a non-IBC response spectrum and that it does not provide anaccurate performance point in some cases. Later, some improvements of the method have been publishedin FEMA 440 [48]. This revised methodology has some advantages. First, it provides the engineer witha visualization tool by facilitating a direct graphical comparison of capacity and demand. Second, thereare very effective solution strategies for equivalent linearization that rely on a modified ADRS demandcurve (MADRS) that intersects the capacity curve at the maximum displacement. As it is also explicitlystressed in FEMA 440 the user must recognize that the results are an estimate of median response andimply no factor of safety for structures that may exhibit poor performance and/or large uncertainty inbehavior. Furthermore it should be noted that the results of the MADRS method as described in thefollowing may not be reliable for extremely high ductility values, e.g., greater than 10 to 12.

The MADRS method basically relies on the determination of effective damping, eff, and effectiveperiod, Teff, with which a maximum spectral displacement can be derived. This in turn matches with theintersection point of the radial effective period (radiating line from the origin in the Sa-Sd-domain) and theADRS demand for the effective damping (Figure 11). The effective period of the improved procedure Teff

Figure 11: Modified acceleration-displacement response spectrum (MADRS) for use with secant periodTsec. Figure taken from FEMA 440 [48].

is generally shorter than the secant period Tsec defined by the point on the capacity curve correspondingto the maximum displacement dmax. The effective acceleration aeff is not meaningful since the actualmaximum acceleration amax must lie on the capacity curve and coincide with the maximum displacementdmax. Multiplying the ordinates of the ADRS demand corresponding to the effective damping eff by themodification factor:

M =amaxaeff

(35)

results in the modified ADRS demand curve (MADRS) that may now intersects the capacity curve atthe performance point. Since the acceleration values are directly related to the corresponding periods,the modification factor can be calculated as:

M =

TeffTsec

2=

TeffT0

2T0

Tsec

2(36)

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where

T0

Tsec2

=1 ( 1)

(37)

and where the post-elastic stiffness, , and the ductility demand, , are:

=

apiaydpidy

aydy

(38)

and

=dpidy

, (39)

respectively.

Equivalent linearization procedures applied in practice normally require the use of spectral reduction

factors to adjust an initial response spectrum to the appropriate level of effective damping eff. Thesefactors are a function of the effective damping and are termed damping coefficients B(eff). They areused to adjust spectral acceleration ordinates as follows:

(Sa) =(Sa)5%B(eff)

(40)

where

B(eff) =4

5.6 log(eff)(41)

with eff given in [%].

Since the effective period Teff and the effective damping eff are both functions of ductility demand,the calculation of a maximum displacement using equivalent linearization is not direct and requires an

iterative procedure (Figure 11).

Both, effective damping and period are strongly dependent on the buildings inelastic behavior. WithinFEMA 440 [48] three different inelastic hysteretic systems have been studied including bilinear hysteretic,stiffness degrading and strength degrading behavior. The procedure incorporated in SELENA and thefollowing description is based on the stiffness degrading hysteretic model. The effective viscous dampingeff can be calculated by the following equations dependent on ductility demand. Values of the coefficientsA to F can be found in Table 8.

eff = A( 1)2 + B( 1)3 + 0 for < 4.0 (42)

eff = C+ D( 1) + 0 for 4.0 4.0 (43)

eff = EF(1)1F(1)2

TeffT0

for > 6.5 (44)

The effective period values, Teff, are to be computed using the following equations. Values of the

[%] A B C D E F

0 5.1 -1.1 12 1.4 20 0.622 5.3 -1.2 11 1.6 20 0.515 5.6 -1.3 10 1.8 20 0.38

10 5.3 -1.2 9.2 1.9 21 0.3720 4.6 -1.0 9.6 1.3 23 0.34

Table 8: Coefficients in order to calculate effective damping values eff.

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coefficients G to L can be found in Table 9.

Teff = [G( 1)2 + H( 1)3 + 1]T0 for < 4.0 (45)

Teff = [I+ J( 1) + 1]T0 for 4.0 4.0 (46)

Teff =

K

11+L(2) 1

+ 1

T0 for > 6.5 (47)

[%] G H I J K L

0 0.17 -0.032 0.10 0.19 0.85 0.002 0.18 -0.034 0.22 0.16 0.88 0.025 0.18 -0.037 0.15 0.16 0.92 0.05

10 0.17 -0.034 0.26 0.12 0.97 0.1020 0.13 -0.027 0.11 0.11 1.00 0.20

Table 9: Coefficients in order to calculate effective damping values Teff.

In order to find the performance point (di, ai), FEMA 440 [48] provides three alternative procedures,which all are based on reducing the initial ADRS demand spectrum by the effective viscous dampingeff. One of these procedures consists in the automated derivation of a locus of possible performancepoints. This by generating a number of modified ADRS (MADRS) demand spectra for different valuesof ductility demand . As Figure 12 illustrates, the performance point is defined by the intersection ofthe capacity spectrum and the line being described by all respective performance points on the differentMADRS curves. In the following, the single steps of the method are subsequently described taking upthe previous example with the given capacity curve and NEHRP site class C.

Figure 12: Finding the performance point (red star) using the modified acceleration-displacement responsespectrum (MADRS). Figure taken from FEMA 440 [48].

Example 3.3 Performance point calculation following the MADRS method (Chapter 2.4.2 in [48])

Steps:

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1. Selection of a spectral representation of the ground motion of interest with an initial damping i(i.e., normally 5%) and conversion into an ADRS elastic design spectrum for NEHRP site classC (see Example 3.2).

2. Generation or selection of a capacity curve capacity curve described by yield (ay, dy) and ulti-mate capacity points (au, du); in case of a generated capacity curve, the development of a bilinearrepresentation has to be conducted (ATC-40 [45]) here: capacity curve as given in HAZUS formodel building type C1M and moderate-code seismic design level (ses HAZUS [2], Table 5.7 b):ay = 0.1044 g, dy = 0.58 in. = 1.47 cm, au = 0.312 g, and du = 6.91 in. = 17.55 cm.

3. Calculation of effective damping, eff, and modification factor, M for integer increments of ductility ( = 2, 3, 4, . . .) initial (elastic) period T0 ( = 1): T0 = 2

dy/ay0.7542 s post-elastic

stiffness parameter: =

apiay

dpidyaydy

= 0.1828 [Eq. (38)]

ParameterDuctility

2 3 4 5 6 7dpi = dy [m] [Eq. (39)] 0.0294 0.0441 0.0588 0.0735 0.0882 0.1029eff [%] [Eqs. (42)-(44)] 8.686 15.606 18.740 20.143 21.546 22.654Teff [sec] [Eqs. (45)-(47)] 0.836 0.997 1.109 1.194 1.278 1.332Tsec [sec] [Eq. (37)] 0.981 1.118 1.212 1.282 1.335 1.378B(eff) [Eq. (41)] 1.163 1.402 1.499 1.540 1.581 1.613

M =TeffTsec

2[Eq. (36)] 0.727 0.795 0.838 0.867 0.916 0.935

4. Adjustment of the initial ADRS to the effective damping eff reduction of spectral acceleration

ordinates (Sa)5% by damping coefficients B for all considered ductility values : (Sa) =(Sa)5%B(eff)

[Eq. (40)]

5. Multiplication of the ADRS for eff by the modification factor M reduction of spectral accelerationordinates (Sa) by damping coefficients M for all considered ductility values .

6. Generation of possible performance point by the intersection of radial secant period Tsec withthe MADRS for all considered ductility values Determination of performance point by theintersection of the locus line with the capacity spectrum:

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0

0.2

0.4

0.6

0.8

0 10 20 30


[g]


ap

dp

T0(=1)Tsec(=2)

Tsec(=3)...

Tsec(=7)

ADRS: =1

MADRS: =2...=7

performance points

locus of possible

3.4.3 Improved Displacement Coefficient Method (I-DCM)

The displacement coefficient method modifies the displacement demand of the equivalent linear singledegree of freedom (SDOF) system by multiplying it by a series of coefficients in order to generate anestimate of the maximum displacement demand of the nonlinear oscillator. The process begins with thegeneration of the capacity curve of the nonlinear oscillator. The effective period of the system is thencomputed as (Figure 13):

Te = 2

DyAy

(48)

When plotted on an elastic response spectrum representing the seismic ground motion, as peak spectralacceleration, Sa, vs. period, T, the spectral acceleration demand of the equivalent linear SDOF system,Sela , can be computed (Figure 13). The peak elastic spectral displacement demand, S

eld is then directly

related to the Sela by:

Seld =T2e42

Sela (49)

The target displacement, t, is then computed as:

t = C1C2Seld (50)

where:

C1 = Modification factor to relate the expected maximum displacement demand of a nonlinear oscillatorwith elastic-perfectly-plastic (EPP) hysteretic properties to the peak displacement demand of thelinear oscillator,

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Dy

Sa

(D , A )yy

T = 2e

Demand Curve

Te Period, T

Sael

= C C St 1 2 ael

42

Te2

Capacity CurveAy

Sd

Figure 13: Schematic illustraion of process I-DCM which is used to compute the target displacementdemand of a nonlinear oscillator for a given capacity curve and response (demand) spectrum

.

C2 = Modification factor to represent the effect of pinched hysteretic shape and stiffness degradationon the maximum displacement response.

The coefficeints C1and C2 can be computed using the approximation relationships given in FEMA-440 [48]:

C1 = 1 +R1aT2e

(51)

C2 = 1 +1800(

R1Te

)2 (52)

where

R = Ratio of elastic strength demand to the calculated strength capacity; R=Sela /Ay,

a = Equation constant; a is equal to 130, 90, and 60 for NEHRP site classes B, C, and D, respectively.Table 10 summarizes the assumed values for the parameter a for different site classes and spectralshapes.

3.5 Fragility Curves and Damage State Probability

The conditional probability of being in, or exceeding a particular damage state, ds, given by the spectraldisplacement Sd (or other seismic demand parameter) is defined by the following equation:

P(ds|Sd) =

1

dsln

Sd

Sd,ds

(53)

where

Sd,ds: median value of spectral displacement at which the building reaches the threshold of damagestate ds,

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Spectral shape Soil type a

IBC A 130B 130C 90D 60E 60

Eurocode I and II A 130B 90C 60D 60E 60

Indian Code I 90II 60III 60

Table 10: Assumed values for the parameter a for different site classes and spectral shapes.

ds: is the standard deviation of the natural logarithm of spectral displacement for damage state ds,

(): is the standard normal cumulative distribution function.

In HAZUS99, for instance, both mean displacement threshold of damage state and its correspondingstandard deviation ds are table values (see Table 5.9) which depend on the model building type and itsseismic design level. However, it should be regarded that the parameters defining the fragility functionsfor a certain building type are closely connected to its respective capacity curve.

Cumulative probabilities are defined to obtain discrete probabilities of being in each of the five different

damage states (Figure 14).The final damage results are given as absolute square meters of the respective damaged building type,

so that users are able to present and further process these results using a spreadsheet program (MS Excel,OpenOffice, etc.) or any other software applications in any desired format (e.g., as percentage of builtarea [m2] normalized by the total built area in each geographical unit or by the total built area in thestudied region, i.e., summed all geographical units). Nonetheless, results can also be given as absolutenumbers of damaged buildings.

3.6 Economic Losses

The SELENA software can also estimate the total amount of economic losses (in any input currency) inany geographical unit caused by the structural damage.

The economic losses for building repair (and in case of complete damage for replacement) are computedin the following way:

Leco = Cr

Noti=1

Nbtj=1

Ndsk=1

Ai,jPj,kCi,j,k (54)

where Not is the number of occupation types, Nbt is the number of building types, Nds is the number ofdamage states, and where

Cr: regional cost multiplier (currently is set to 1.0, but can have different values for each geographicalunit in order to take into account the geographic cost variations),

Ai,j: built area of the model building type j in the occupancy type i (in [m2])

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0

0.1

0.2

0.3

0.4

0.5

DiscretedamageprobabilityP

Damage state ds

none slightmoderateextensivecomplete

P(ds)i = 1.0

Figure 14: Discrete damage probabilities derived from the cumulative damage probabilities for an ex-pected displacement as illustrated in Figure ??.

Pj,k

: damage probability of a structural damage k (slight, moderate, extensive or complete) for themodel building type j,

Ci,j,k: cost of repair or replacement (by [m2]) in the input currency of structural damage k for occupancy

type i and model building type j (provided by input files eloss .txt).

In the current version of SELENA only the direct economic losses caused by structural damageare computed. Those being caused by non-structural damage (acceleration sensitive damage) are notconsidered. The absolute values for building repair costs in the different damage states will be determinedby the user. HAZUS expresses the cost of damage for damage states slight, moderate and extensive as apercentage of the complete damage state:

slight damage: 2% of complete damage,

moderate damage: 10% of complete damage,

extensive damage: 50% of complete damage.

These relationships are consistent with those damage ratios given in ATC-13 [51]. However, more reliableor suitable values can be defined by the user.

It should be regarded that economic losses will only be calculated by SELENA if the user chooses theanalysis type dependent on damaged building area. In case of an analysis dependent of the number ofdamaged buildings, no economic losses are computed.

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3.7 Humanloss Casualties

The methodology applied in order to calculate the number of human casualties follows basically theHAZUS approach but is somewhat simplified using the formulas given by Coburn and Spence [ 52]:

K = Ks + K + K2 (55)

where

Ks: number of casualties due to structural damage

K: number of casualties due to non-structural damage

K2: number of casualties due to follow-on hazards, such as landslides, fires, etc.

The above equation can also be modified such that the level of injury (severity) is considered:

Ki = Ksi + K

i + K2i (56)

where i is representing the level of severity, ranging from light injuries (i = 1), moderate injuries (i = 2),heavy injuries (i = 3), to death (i = 4). A more detailed description of the severity levels is givenin Table 11. However, the loss model applied in the current version of SELENA is only consideringthe direct human losses caused by structural damage not due to non-structural damage or follow-onhazards. By using SELENA, the number of human losses (casualties) can be computed using two different

Injury Level Description Examples

Severity 1

Injuries requiring basic medical aid that - sprainscould be administered by paraprofessionals. - severe cuts requiring stitchesThese types of injuries would require bandages or - minor burns (first or second degree on aobservation.* small part of the body)

- bumps on the head without loss of consciousness

Severity 2

Injuries requiring a greater degree of - bump on the head that causes loss of consciousnessmedical care and use of medical - fractured bonestechnology such as x-rays or surgery, but not expected - dehydration or exposureto progress to a life threatening status.

Severity 3

Injuries that pose an immediate life - punctured organsthreatening condition if not treated - other internal injuriesadequately and expeditiously. - spinal column injuries

- crush syndrome

Severity 4instantaneously killed ormortally injured.

Table 11: Injury Classification Scale according to HAZUS. *Injuries of lesser severity which can be selftreated are not covered by HAZUS.

methodologies:

1. Basic methodology in case that no detailed information on population distribution is availableor can not be inferred from available data,

2. HAZUS methodology in case that detailed information on population distribution is available.

In order to also cover extreme cases of occupancy which are strongly dependent on the time of theday (i.e., school occupancy only during daytime), the number of casualties will be computed for threedifferent times of the day:

1. nighttime scenario (called 02:00 am): i.e., earthquake striking during nighttime.

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2. daytime scenario (called 10:00 am): i.e., earthquake striking during day time.

3. commuting time scenario (called 05:00 pm): i.e., earthquake striking during the commuting time(rush hour).

These scenarios are expected to generate the highest casualty numbers for the population at home (night-time), the population at work/education (daytime), and the population during rush hour, respectively.

3.7.1 The Basic Methodology

The number of casualties due to direct structural damage for any given structural type, level of buildingdamage, and injury severity can be calculated by:

Ksi = {Injuries (severity i)} =Nbt

j=1

Nds

k=1

Ccsri,j Pj,kNpopj (57)

where:

Ccsri,j : casualty rate of severity i for damage statej as provided by input files injury1.txt to injury4.txt(these statistical values have to be provided by local authorities),

Pj,k: structural damage probability for the kth damage type (k = 1 slight, k = 2 moderate, k = 3extensive, k = 4 complete or complete with collapse) for the jth model building type.

Npopj : number of people in the jth model building type.

The total number of people in all buildings of the j:th model building type (MBT), for one geographicalunit (i.e., census tract) at a specific time period (time of the day), is computed in a simplified way:

Npopj = NtpCpoCombtj (58)

where Ntp is the total number of people living in the respective geographical unit provided by input filepopulation.txt, Cpo is the percentage of people staying indoors or outdoors dependent on the timeof the day provided by input file poptime.txt (compare to Table 12), and Combtj is the percentage ofoccupancy class for the jth model building type (MBT) provided by input file ocupmbtp.txt.

Occupancy type night (2:00 am) day (10:00 am) commuting (5:00 pm)

INDOOR 98% 90% 36%OUTDOOR 2% 10% 64%

Sum

100% 100% 100%

Table 12: Population percentages indoors and outdoors dependent on the time of the day. Note thatthese values are strongly dependent on the country and its cultural peculiarities and consequently mayvary considerably.

3.7.2 The HAZUS Methodology

The total population of each census tract is classified into five different groups:

1. residential population,

2. commercial population,

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3. education population,

4. industrial population,

5. hotel population.

The default population distribution is calculated for the three times of the day for each census tract.Table 13 provides the relationships used to determine the default distribution. Each element of the table

Distribution of people in census tractOccupancy 2:00 am 2:00 pm 5:00 pm

Indoors

residential (0.999) 0.99 (NRES) (0.70) 0.75 (DRES) (0.70) 0.50 (NRES)commercial (0.999) 0.02 (COMW) (0.99) 0.98 (COMW) + 0.98 [0.50(COMW) +

(0.80) 0.20 (DRES) + 0.10 (NRES) + 0.70 (HOTEL)]0.80 (HOTEL) + 0.80 (VISIT)

educational (0.90) 0.80 (AGE 16) + 0.80 (COLLEGE)(0.80) 0.50 (COLLEGE)industrial (0.999) 0.10 (INDW) (0.90) 0.80 (INDW) (0.90) 0.50 (INDW)

hotels 0.999 (HOTEL) 0.19 (HOTEL) 0.299 (HOTEL)

Outdoors

residential (0.001) 0.99 (NRES) (0.30) 0.75 (DRES) (0.30) 0.50 (NRES)commercial (0.001) 0.02 (COMW) (0.01) 0.98 (COMW) + 0.02 [0.50 (COMW) +

(0.20) 0.20 (DRES) + 0.10 (NRES) + 0.70 (HOTEL)] +0.20 (VISIT) + 0.50(1-PRFIL)

0.50 (1-PRFIL) 0.05 (POP) [0.05 (POP) + 1.0 (COMM)]educational (0.10)0.80 (AGE 16) + (0.20) 0.50 (COLLEGE)

0.20 (COLLEGE)industrial (0.001) 0.10 (INDW) (0.10) 0.80 (INDW) (0.10) 0.50 (INDW)

hotels 0.001 (HOTEL) 0.01 (HOTEL) 0.001 (HOTEL)

Table 13: Default relationships for estimating population distribution (taken from HAZUS) where POPis the census tract population taken from HAZUS, DRES is daytime residential population inferred fromcensus, NRES is nighttime residential population inferred from census data, COMM is the number of peoplecommuting inferred from census data COMW is the number of people employed in the commercial sectorINDW is the number of people employed in the industrial sector GRADE is the number of students in gradeschool (usually under 17 years old) COLLEGE is the number of students on college and university campusesin the census tract (over 17 years old), HOTEL is the number of people staying in hotels in the censustract, PRFIL is a factor representing the proportion of commuters using automobiles, inferred from profileof the community (0.60 for dense urban areas, 0.80 for less dense urban or suburban areas and 0.85 forrural). Default value is 0.80. VISIT is the number of regional residents who do not live in the study area,visiting the census tract for shopping and entertainment. Default is set to zero.

contains two multipliers of which the second one indicates the fraction of a population component (e.g.

NRES) present in an occupancy type at a particular scenario time. The first multiplier (given in brackets)divides this population component into indoor and outdoor occupancy. For example: At 02:00 am, thedefault is that 99% of the nighttime residential population (NRES) will be in residential occupancy while99.9% of those will be indoors. If more detailed information is available on these issues, these factors canbe changed in the m-file humanlosshz.m. The methodology takes into account a wider range of causalrelationships in the casualty modeling. It is an extension of the model proposed by Stojanovski andDong [53].

By using an event tree as shown in Figure 15 and multiplying the population in each of the occupancytypes and model building types by the damage probabilities and casualty rates, the total number ofcasualties for each severity level can be esti

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