User Manual for the Earthquake Loss Estimation Tool: SELENA

Transcription

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User Manual for the Earthquake Loss Estimation
Tool: SELENA
Sergio Molina
NORSAR and Universidad de Alicante
Dominik H. Lang, Conrad D. Lindholm and Fredrik Lingvall
NORSAR
DR
October 1, 2010
1 Introduction
1.1
Scope and methodology of SELENA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Copyright
2.1
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Contents
Disclaimer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Technical Description of SELENA
1
3
5
6
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
Site-dependent Seismic Demand — Amplification of Ground Motion . . . . . . . . . . . .
8
3.3
3.3.1
IBC-2006 (International Code Council, 2006) . . . . . . . . . . . . . . . . . . . . .
10
3.3.2
Eurocode 8 (European Committee for Standardization CEN, 2002) . . . . . . . . .
14
3.3.3
Indian Standard IS 1893 (Part 1) : 2002 (Bureau of Indian Standards, 2002) . . .
14
Structural Performance Under Seismic Action . . . . . . . . . . . . . . . . . . . . . . . . .
17
3.4.1
The Capacity Spectrum Method (CSM) as Proposed in ATC-40 . . . . . . . . . .
17
3.4.2
The Modified Capacity Spectrum Method (MADRS) . . . . . . . . . . . . . . . . .
23
3.4.3
Improved Displacement Coefficient Method (I-DCM) . . . . . . . . . . . . . . . . .
27
3.5
Fragility Curves and Damage State Probability . . . . . . . . . . . . . . . . . . . . . . . .
28
3.6
Economic Losses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
3.7
Humanloss — Casualties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
3.7.1
The Basic Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
3.7.2
The HAZUS Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
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3.4
4 Installation
4.1
34
System Requirements and Resent Code Changes . . . . . . . . . . . . . . . . . . . . . . .
34
4.1.1
Installing the GNU Scientific Library . . . . . . . . . . . . . . . . . . . . . . . . . .
34
4.2
The Directory Structure of SELENA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
4.3
The SELENA m-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
4.3.1
The SELENA mex-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
4.3.2
The SELENA oct-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
38
5 Running SELENA
5.1
Preparation of Input Files
38
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
5.1.1
Input Files for Deterministic Analysis . . . . . . . . . . . . . . . . . . . . . . . . .
39
5.1.2
Input Files for Probabilistic Analysis . . . . . . . . . . . . . . . . . . . . . . . . . .
40
5.1.3
Input Files for Analysis with Real-time Data . . . . . . . . . . . . . . . . . . . . .
41
5.1.4
Common Input Files for all Analysis Types . . . . . . . . . . . . . . . . . . . . . .
41
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5.1.5
Input Files for the Calculation of Economic Losses . . . . . . . . . . . . . . . . . .
44
5.1.6
Input Files for the Calculation of Human Losses — Casualties . . . . . . . . . . .
44
5.1.7
Mandatory Input Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
Mean Damage Ratio Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
5.2.1
Median Values and Confidence Levels . . . . . . . . . . . . . . . . . . . . . . . . .
51
The SELENA Program Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
5.3.1
The Stand-alone SELENA Application . . . . . . . . . . . . . . . . . . . . . . . . .
51
5.3.2
The Matlab and Octave Command-line Interface . . . . . . . . . . . . . . . . . . .
51
5.3.3
The Matlab Graphical User Interface . . . . . . . . . . . . . . . . . . . . . . . . . .
53
5.4
Dealing with Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
53
5.5
Output Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
5.5.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
5.5.2
Format of the Output Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
56
5.5.3
Mean Damage Ratio Output Files . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
5.2
5.3
6 Examples
62
6.1
The Bucharest Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
6.2
Determistic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
6.3
Probabilistic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
6.4
Realtime Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
63
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7 Plotting results in Geographic Information Systems (GIS)
63
8 Known Issues
63
9 Summary
64
Bibliography
64
A Tables
68
B Compiling the C-code
74
B.1 Tools and Libraries for Windows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
75
B.2 Building the Stand-alone Application on Linux/Unix . . . . . . . . . . . . . . . . . . . . .
75
B.3 Building the Stand-alone Application on Windows . . . . . . . . . . . . . . . . . . . . . .
75
B.4 Building the Stand-alone GUI Application on Linux/Unix . . . . . . . . . . . . . . . . . .
75
B.5 Building the Stand-alone GUI Application on Windows . . . . . . . . . . . . . . . . . . .
76
B.6 Building the Linux/Unix mex-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
B.6.1 Building the Windows mex-files . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
B.7 Building the oct-Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
77
1
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INTRODUCTION
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Introduction
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HE earthquake loss estimation tool SELENA, which is described herein, provides local, state and
regional 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 future
earthquakes 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 response
strategies.
Some of the first earthquake loss estimation studies were performed in the early 1970’s following the
1971 San Fernando earthquake. These studies put a heavy emphasis on loss of life, injuries, and the
ability 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 as
well as gross economic losses.
Earlier the National Institute of Building Sciences (NIBS) has developed the tool HAZUS-MH [2–4]
for the federal emergency management agency (FEMA) in order to provide a powerful technique for
developing earthquake loss estimates. This to be used in:
• anticipating the possible nature of an earthquake disaster and the scope of the emergency response
needed to cope with an earthquake disaster,
• developing plans for recovery and reconstruction following a disaster, and
• mitigating the possible consequences of earthquakes.
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The methodology generates an estimate of the damage consequences for a city or a region based on
a ‘scenario earthquake’, i.e., an earthquake with a specified magnitude and location. The resulting loss
estimate 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 damaged
buildings and lifeline system components; direct costs associated with loss of function (e.g., loss of
business 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 as
hospitals, and components of transportation and utility lifeline systems and simplified analyses of
loss-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 building
value 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 through
a geographical information system (GIS) which is called HAZUS-MH [2]; the ESRI GIS system is used
by 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 earthquake, 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 different
classes of buildings, facilities, and lifeline system components and loss-of-function estimates are
made.
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 economy
are 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 and
type of debris are estimated. If an inundation map is provided, exposure to flooding can also be
estimated.
The earthquake-related hazards considered by the methodology in evaluating casualties, and resulting
losses are collectively referred to as potential earth science hazards (PESH). Most damage and loss caused
by 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 ground
displacements and have an adverse effect upon structures, roads, pipelines, and other lifeline structures
which are also considered.
Soil type can have a significant effect on the intensity of ground motion at a particular site. The
software contains several options for determining the effect of soil type on ground motions for a given
magnitude and location.
Tsunamis and seiches are also earthquake-caused phenomena that can result in inundation or waterfront damage. In the methodology, potential sites of these hazards may be identified, but they are
evaluated only if special supplemental studies are performed.
The type of buildings and facilities considered in HAZUS-MH are as follows:
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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 36
model building types and 28 occupancy classes and degrees of damage are computed for groups of
buildings.
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 buildingby-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 roadway
or track, terminal, and port warehouses. The damage and losses are computed for each component
of 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 installations
which need supplementary specific studies to be evaluated.
All results from HAZUS-MH are provided as “best estimates”, and no uncertainty in the results is
provided for.
The downside of these fascinating developments implemented in HAZUS-MH is that it has been so
intimately connected to the U.S. environments that it is practically impossible to apply it to the rest of
the world.
We have in the present study developed and adapted the core of the HAZUS methodology to greater
flexibility 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 parameters
has been incorporated, and an example of seismic damage scenarios for the city of Oslo have been
conducted 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 tailored so intimately to U.S. situations and to a specific GIS software makes it difficult to apply in other
environments 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 software
tool in order to compute the seismic risk in urban areas using the capacity spectrum method named
SELENA (SEimic Loss EstimatioN using a logic tree Approach). The user will supply built area or number
of buildings in the different model building types, earthquake sources, empirical ground-motion prediction
relationships, soil maps and corresponding ground-motion amplification factors, capacity curves and
fragility curves corresponding to each of the model building types and finally cost models for building
repair or replacement. This tool will compute the probability of damage in each one of the four damage
states (slight, moderate, extensive, and complete) for the given building types. This probability is
subsequently used with the built area or the number of buildings to express the results in terms of
damaged area (square meters) or number of damaged buildings. Finally, using a simplified economic
model, the damage is converted to economic losses in the respective input currency and human casualties
in terms of different injury types are computed [6].
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The algorithm is transparent in writing and loading the input files and getting the final results. The
main 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 properly
included, and the final results are provided with corresponding confidence levels. Until now the method
has 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 ground
motion input in terms of response spectra (see, for example, the spectral acceleration versus spectral
displacement illustrated in Figure 1) with the building’s specific capacity curve (see the example shown
in Figure 2. The philosophy is that any building is structurally damaged by its permanent displacement (and not by the acceleration by itself). For each building and building type the inter-story drift
(relative drift of the stories within a multistory structure) is a function of the applied lateral force that
can be analytically determined and transformed into building capacity curves (capacity to withstand
accelerations without permanent displacements). Building capacity curves naturally vary from building
type to building type, and also from region to region reflecting local building regulations as well as local
construction practice. Under the HAZUS-umbrella FEMA developed capacity curves for 36 U.S. building
types for four earthquake code regimes (reflecting the variation in building regulations as a function of
time across the U.S.). These 144 capacity curves are developed analytically, but adjusted so that empirical knowledge is incorporated in the curves whenever possible. The building capacity curve is defined
through three control points: Design, Yield and Ultimate capacity (Figure 2). Up to the yield point,
the building capacity curve is assumed to behave elastically linear. From the yield point to the ultimate
point, the capacity curve changes from an elastic to a fully plastic state (curved form), and the curve
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 vulnerability curves (also
called fragility curves) are developed as log-normal probability distributions of damage from the capacity
curves (see the illustration in Figure 3). The structural damage states are (as in most other proposed
schemes and neglecting the state no damage) divided into four damage states: slight, moderate, extensive,
and complete. A detailed description of these damage states are found many places. For example, the
description for light frame wood buildings are:
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Spectral acceleration Sa [g]
1
0.75
0.5
0.25
0
0
0.05
0.1
0.15
0.2
0.25
0.3
Spectral displacement Sd [m]
0.35
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Figure 1: The methodology is based on presenting the ground-motion response spectral ordinates (at
given damping levels) of spectral acceleration versus spectral displacement.
(dd , ad) − design capacity
(dy , ay) − yield capacity
(du , au) − ultimate capacity
au
ay
ad
dd dy
median +1σ
median
median −1σ
demand curve
du
Spectral displacement Sd [cm]
Figure 2: The principle of the building specific capacity curve intersected by the load curve representing
the seismic demand.
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de
ex
ten
s
iv
e
mo
0.8
rat
e
slig
ht
Damage probability P (ds | Sd)
1
0.6
te
le
mp
0.4
co
0.2
0
0
10
20
30 40 50 60 70 80
90
100
Figure 3: Example fragility curves showing the probabilities P (ds |Sd ) of being in or exceeding the different
damage states, ds , for building type C1M as given in HAZUS99.
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slight: Small plaster cracks at corners of door and window openings and wall-ceiling intersections; small
cracks in masonry chimneys and masonry veneers. Small cracks are assumed to be visible with a
maximum 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 diagonal
cracks across shear-wall panels exhibited by small cracks in stucco and gypsum wall panels; large
cracks in brick chimneys; toppling of tall masonry chimneys.
extensive: Large diagonal cracks across shear-wall panels or large cracks at plywood joints; permanent
lateral movement of floors and roof; toppling of most brick chimneys; cracks in foundations; splitting
of wood sill plates and/or slippage of structure over foundations.
complete: Structure may have large permanent lateral displacement or be in imminent danger of collapse
due to cripple wall failure or failure of the lateral load resisting system; some structures may slip
and fall off the foundation; large foundation cracks. Three percent of the total area of buildings
with Complete Damage is expected to be collapsed, on average.
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HE SELENA program is an open source software and the source code for the program is freely
redistributable under the terms of the GNU General Public License (GPL) as published by the Free
Software Foundation (http://www.gnu.org). See also the file COPYING which is distributed with the
SELENA program.
The SELENA program can be downloaded at: http://selena.sourceforge.net At this website you
can also find information how to contact the authors and report bugs etc.
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Disclaimer
3 TECHNICAL DESCRIPTION OF SELENA
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The SELENA program is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY. More specifically:
THE PROGRAM IS PROVIDED “AS-IS” WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OR CONDITIONS
OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL ANY
OF THE AUTHORS OF THE SELENA PROGRAM AND/OR NORSAR, NORWAY, UNIVERSIDAD DE
ALICANTE, SPAIN, BE LIABLE FOR ANY SPECIAL, INCIDENTAL, INDIRECT, OR CONSEQUENTIAL 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 BEEN
ADVISED 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.
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Technical Description of SELENA
N this section the main features of SELENA is discussed.
3.1
Basic Procedure
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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 human losses
related to these physical damages. All results are provided with ranges of uncertainty facilitating the
easy computation of, e.g., median value and 16%- respectively 84%-fractiles of damage.
It has to be noted that SELENA requires quite extensive basis information within a number of input
files. 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 the
matrices.
Since a resolution of the damage outputs on the level of individual buildings would require huge computation efforts, SELENA as 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 or smaller city districts. The decision on the extent of each geographical unit has to be
made considering different aspects such as having equal soil conditions, constant surface topography or a
homogeneous level of building quality within the demarcated area. The main basis information consists in
the building inventory database (which is also somewhat difficult to generate). This type of information
sometimes is provided by local agencies or governmental institutions. In any case, a thorough investigation of the local building stock by walk-downs and on-site inspections should be conducted in order to
allow a representative classification of the prevalent building typologies. The building inventory database
should contain a maximum of details about building materials, building techniques, built area, floors of
the building, height, foundations, seismic regulations used in the construction, use of the building, number of 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
an individual building if a site-specific study is going to be done. The classification of the building type
can be either done according to the HAZUS methodology (see http://www.fema.gov/hazus documents
or previous HAZUS reports) or following a user-defined classification scheme being more specific for the
available building stock.
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3.2
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Provision of Seismic Demand
A key point in any seismic risk assessment is the provision of seismic ground motion (level and spectral
characteristics of earthquake shaking). In order to carry out a seismic risk and loss assessment with
SELENA, 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 geographical
unit (probabilistic analysis),
• definition of deterministic earthquake scenarios (e.g., historical or user-defined events) and appropriate ground-motion prediction equations in order to compute the spectral ordinates in each
geographical unit (deterministic analysis),
• provision of recorded ground-motion amplitudes at the locations of seismic (strong-motion) stations
(analysis with real-time data).
Following the provisions of the international building code 2006 (IBC-2006) [8], 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. Most other earthquake
codes (e.g., Eurocode 8 [9]) define the shape of the design spectrum such that only a 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 accelerations values Sa0.3 and Sa1.0 are
not regarded.
3.2.1
Probabilistic Analysis
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The probabilistic analysis procedure denotes the use of spectral ordinates which are taken from probabilistic shake maps. In addition to the acceleration values (PGA, Sa0.3 , Sa1.0 ) for each minimum geographical
unit, the geographical coordinates of the centroid have to be provided. Probabilistic shake maps are generally developed 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 scenario 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 scenario
earthquake, this process is done separately for each geographical unit. A considerable number of wellestablished ground-motion prediction relations is already incorporated in the SELENA code (Appendix A,
Table 19) but any user-provided relation can be easily implemented. It should be considered that all
provided prediction relations refer to rock site conditions and thus compute ground-motion amplitudes
without soil amplification since this is covered in a separate (subsequent) calculation step. Even though
the respective soil terms are provided in the code they are not considered during the analysis.
Depending on the type of design spectrum chosen for the analysis, predicted ground-motion amplitudes
are either used to define the shape of the elastic design spectrum (e.g., IBC-2006) or only to scale the
amplitudes of the spectrum (e.g., Eurocode 8) which later represents the seismic demand for the capacity
spectrum method (CSM) procedure. As Table 1 illustrates, all predefined ground-motion prediction
equations can be used to derive mean values of ground-motion amplitudes as well as their ±1σ (standard
deviation) values in order to account for aleatoric uncertainty.
Since each ground-motion prediction equation is dependent on a particular distance, SELENA automatically computes four different types of distances: epicentral distance Repi , hypocentral distance
Rhypo , “Joyner-Boore” distance Rjb (shortest distance to the vertical surface projection of the fault
rupture plane), and the shortest distance to the subsurface fault rupture plane Rrup (see Figure 4).
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Figure 4: Schematic illustration of the different distance types.
Thereby, the expected value of the surface fault rupture length, L, is based on the relationship by
Wells and Coppersmith [10]:
log10 (L) = −3.55 + 0.74M
log10 (L) = −2.86 + 0.63M
for strike-slip faults
for reverse faults
(1)
(2)
log10 (L) = −3.22 + 0.69M
for all other fault types
(3)
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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 for
which ground-motion data is available will certainly not comply with the center points of the defined
geographical units (i.e., centroids). Consequently, the provided spectral ordinates at these locations have
to be assigned to the centroids in a somehow reliable way. The procedure applied here is schematically
illustrated in Figure 5. Basically it is checked which of the available points (here the nodes of an equallyspaced grid pattern) are within a 5 km-radius around each centroid. If at least 5 points meet this criterion
the mean value and corresponding 16%- resp. 84%-fractiles of the spectral ordinates of all stations are
computed and assigned to the respective centroid. If less than 5 points are within this 5 km-radius, a
new circle of 10 km diameter is drawn. Given that the location of a centroid is more or less identical
with the location of one recording station, its spectral ordinates are directly assigned to the centroid
without further processing. It should be regarded, that the provided spectral ordinates already cover soil
amplification effects as they are realistic ground-motion data recorded at the ground surface. Therefore
any additional consideration of soil amplification has to be avoided. [In practice, this means that the
SELENA soil input files (i.e., soilcenteri.txt) do not contain soil class indecies other than those for
rock, i.e., 2 for IBC-2006, 1 for Eurocode 8].
3.3
Site-dependent Seismic Demand — Amplification of Ground Motion
In case that sedimentary soil materials are present at a site, the seismic ground motion at the ground
surface is modified both in amplitude and frequency content. Respective amplification factors and/or
corner periods which basically describe shape of the design spectra for the different soil classes are given
in the corresponding code provisions. Currently, the procedures of IBC-2006, Eurocode 8 (Type 1 and
8
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Author(s) (year)
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]
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]
Gülkan and Kalkan [35]
Lussou et al. [36]
Dahle et al. [37]
Bommer et al. [38]
Marmureanu et al. [39]
Sharma et al. [40]
Target ground-motion parameter
mean value (mv)
mv+1σ
mv - 1σ
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
DR
Table 1: Selection of the empirical ground-motion prediction methods which are implemented in the
current SELENA-version (see the m-file att sub.m or the C-file att sub.c distributed with SELENA).
Figure 5: Spectral ordinates at the sites of randomly-distributed recording stations are assigned to the
centers of the geographical units (centroids).
9
2
Spectral acceleration Sa [m/s ]
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response spectrum
Sa0.3
damping ξ = 5 %
Sa1.0
PGA
0 TA
TAV
TVD
Period T [s]
DR
Figure 6: Standard shape of the response spectrum.
Type 2), and Indian standard IS 1893 [41] are incorporated while more will follow in upcoming SELENAversions.
3.3.1
IBC-2006 (International Code Council, 2006)
The methodology characterizes ground shaking using a standardized response spectrum shape as given
in IBC-2006 [8], which consists of four parts: PGA, a region of constant spectral acceleration at periods
from 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 (Sa1.0 ). The region
of 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 ) =
Sa(T ) =
Sa0.3
Sa1.0 /T
for T < T < TAV
for TAV < T < Tvd
(5)
(6)
Sa(T ) =
Sa1.0 Tvd /T 2
for Tvd < T < 10 s
(7)
The period Tav is based on the intersection of the region of constant spectral acceleration and constant
spectral velocity and its value varies depending on the values of spectral acceleration that define these
two intersecting regions:
Tav = Sa1.0 /Sa0.3
(8)
10
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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/T 2 and is anchored
to the spectral acceleration value at the period Tav , where constant spectral velocity transitions to constant
spectral displacement.
The period Tvd is based on the reciprocal of the corner frequency fc , which is proportional to stress
drop and seismic moment. This frequency is estimated from the Joyner and Boore [42] relationship as a
function of moment magnitude:
1
Tvd =
= 10(M −5)/2
(10)
fc
where fc is the corner frequency and M is the moment magnitude. When the moment magnitude is not
known (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 PGA
is given, the following expressions have to be regarded:
Sa0.3
Sa1.0
= Saas
= Sasl
= 2.5apga
= apga
(11)
(12)
Amplification of ground shaking to account for local site conditions is based on the site classes (see
Table 2) and soil amplification factors as given by the IBC-2006 provisions. These code provisions do not
site class description
Hard rock, eastern U.S. sites only
Rock
Very dense soil and soft rock
Stiff soil
Soft soil, profile with > 3 m of soft clay defined as soil
with plasticity index PI> 20, moisture content w > 40%
Soils requiring site-specific evaluations
DR
Site
class
A
B
C
D
E
F
shear-wave velocity
vs,30 [m/s]
> 1500
760–1500
360–760
180–360
< 180
–
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 class
B) PGA by the same factor as that specified in Table 3 for short period (0.3 s) spectral acceleration, as
Site Class B
Spectral Acceleration
Short-Period, Sas [g]
≤ 0.25
(0.25, 0.50]
(0.50, 0.75]
(0.75, 1.0]
> 1.0
1-Second Period,Sal [g]
≤ 0.1
(0.1, 0.2]
(0.2, 0.3]
(0.3, 0.4]
> 0.4
Site Class
A
B
C
D
E
Short-Period Amplification Factor, FA
0.8
1.0
1.2
1.6
2.5
0.8
1.0
1.2
1.4
1.7
0.8
1.0
1.1
1.2
1.2
0.8
1.0
1.0
1.1
0.9
0.8
1.0
1.0
1.0
0.9
1-Second Period Amplification Factor, FV
0.8
1.0
1.7
2.4
3.5
0.8
1.0
1.6
2.0
3.2
0.8
1.0
1.5
1.8
2.8
0.8
1.0
1.4
1.6
2.4
0.8
1.0
1.3
1.5
2.4
Table 3: Site amplification factors as given in IBC-2006 [8].
expressed in the following expression:
apga
= apga FAi
i
11
(13)
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where apga
is the PGA for site class i (in units of [g]); apga is that for site class B (in units of [g]) and FAi
i
is the short period amplification factor for site class i, for spectral acceleration Sas . The construction of
demand spectra including soil effects is done using the following equation for short periods:
and for long periods:
Sasi = Sas Fai
(14)
Sali = Sal Fvi
(15)
while the period TAVi , which defines the transition period from constant spectral acceleration to constant
spectral velocity is a function of the site class. It can be determined by the following equation:
TAVi =
where:
Sasi Fvi
Sas Fai
(16)
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
DR
Tavi : transition period between constant spectral acceleration and constant spectral velocity for site
class i (in [s]).
Note that the period Tvd , which defines the transition period from constant spectral velocity to constant
spectral 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 spectrum as a function of the spectral displacement (rather than the period). This could be achieved due to
the relation between the different spectral parameters:
Sa
= Sv = Sdω
ω
(17)
where ω is the angular (natural) frequency of the oscillator (i.e., ω = 2πf , where f is the frequency in
[Hz]).
The final result of this process is the computation of a 5% damped response spectrum at the center
of each geographical unit (where values of ground motion were computed) or at the specific site under
study. In the following, this will be done exemplary for selected site classes according to the IBC 2006
provisions, i.e., NEHRP site classes A–E.
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): aPGA
= 0.20 g
b
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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 can
not 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
Sas = 0.50 g resp. Sal = 0.20 g
Fa
Fv
Site Class
B
C
D
1.0 1.2 1.4
1.0 1.6 2.0
3. Calculation of short-period and long-period spectral accelerations as well as transition period Tavi
Parameter
DR
apga
= apga Fai
i
Sasi = Sas Fai
Sali = Sal Fvi
Site Class
B
C
D
0.20 g 0.24 g
0.28 g
0.50 g 0.60 g
0.70 g
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 s
3.16 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 ξ = 5%):
Site Class: B
C
D
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
Period T [s]
2
2.5
13
1
1
Site Class: B
C
D
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
60
3.3.2
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Eurocode 8 (European Committee for Standardization CEN, 2002)
For the description of seismic action, two different types of design spectra are provided within Eurocode
8 [9]. This mainly in order to account for the differing level of seismic hazard in Europe and the different
earthquakes susceptible to occur. In case that earthquakes with a surface-wave magnitude Ms > 5.5 are
expected it is suggested to use Spectrum Type 1, else (Ms ≤ 5.54) Type 2. The question which spectrum
type to choose for a specific region should be based upon “(...) the magnitude of earthquakes that are
actually expected to occur rather than conservative upper limits defined for the purpose of probabilistic
hazard assessment”.
For the sake of completeness both spectrum types are incorporated in the current version of SELENA
even though scenario earthquakes with magnitudes smaller than 5.5 are not expected to cause considerable
structural damages to the general building stock.
Both types of the horizontal design spectrum are defined by the following expressions:
h
i
Sa(T ) = ag S 1 + TTB (η2.5 − 1) for T < TB
Sa(T ) =
Sa(T ) =
Sa(T ) =
where:
ag Sη2.5
ag Sη2.5 1 + TTC
ag Sη2.5 1 + TTC T2D
(18)
for TB < T < TC
(19)
for TC < T < TD
(20)
for TD < T < 4 s
(21)
ag : design ground acceleration (here: PGA) on soil type A ground,
TB , TC : corner periods of the constant spectral acceleration branch (plateau),
DR
TD : corner period defining the beginning of the constant displacement range,
S: soil factor (see Table 4),
η: damping correction factor (η = 1 for 5% viscous damping).
The shape of the design spectrum is thus determined by the corner periods, soil factor, and the level
of input ground motion. Both, corner periods TB , TC and TD as well as soil factor S are dependent
on ‘ground type’ which is mainly distinguished by the average shear-wave velocity of the uppermost 30
m vs,30 into 5 different soil classes (Table 4). Both, soil factor and corner periods for the different soil
classes are given in Table 5 and Table 6 for Type 1 and Type 2 design spectra, respectively. Figure 7
illustrates 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 IS
1893 (Part 1) : 2002 [41] can be compared with the procedure of Eurocode 8. The amplitude level of
the spectrum solely is dependent on the value for peak ground acceleration (PGA). The shape of the
horizontal design spectrum is thus defined by the following expressions:
h
i
Sa(T ) = ag S 1 + TTB (η2.5 − 1) for 0 ≤ T < TB
(22)
Sa(T ) =
Sa(T ) =
ag Sη2.5
ag Sη2.5 1 +
TC
T
where:
14
for TB < T < TC
(23)
for TC < T < 4.0s
(24)
(25)
Ground type
A
B
C
D
E
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Shear wave velocity
vs,30 [m/s]
Description of stratigraphic profile
Rock or rock-like geological formation,
incl. at most 5 m of weaker material at the surface
Deposits of very dense sands, gravel, or very stiff clay
(at least several tens of m in thickness) characterized by
a gradual increase of mechanical properties with depth
Deep deposits of dense or medium-dense sand, gravel or
stiff clay with thickness from several tens
to many hundreds of m
Deposits of loose-to-medium cohesionless soil
(with or without some soft cohesive layers), or of predominantly
soft-to-firm cohesive soil
Soil profile consisting of a surface alluvium layer with vs,30
values of type C or D and thickness H varying between
5-20 m underlain by stiffer material with vs,30 > 800 m/s.
DR
Table 4: Ground types.
Ground type
A
B
C
D
E
Soil factor S
1.00
1.20
1.15
1.35
1.40
TB [s]
0.15
0.15
0.20
0.20
0.15
TC [s]
0.40
0.50
0.60
0.80
0.50
TD [s]
2.00
2.00
2.00
2.00
2.00
Table 5: Values of the parameters describing Eurocode 8 Type 1 spectra.
Ground type
A
B
C
D
E
Soil factor S
1.00
1.35
1.50
1.80
1.60
TB [s]
0.05
0.05
0.10
0.10
0.05
TC [s]
0.25
0.25
0.25
0.30
0.25
TD [s]
1.20
1.20
1.20
1.20
1.20
Table 6: Values of the parameters describing Eurocode 8 Type 2 spectra.
15
> 800
360-800
180-360
< 180
n.a
Ground type: A
B
C
D
E
Type 1
5
4
3
2
1
0
0
0.5
Normalized spectral acceleration
6
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1
1.5
2
2.5
Period T [s]
3
3.5
4
6
Ground type: A
B
C
D
E
Type 1
5
4
3
2
1
0
0
0.5
1
1.5
2
2.5
Period T [s]
3
3.5
4
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,
η: damping correction factor (η = 1 for 5% viscous damping).
DR
The periods TB and TC are the only parameters which depend on the soil conditions. An explicit soil
amplification 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
I
II
III
Description of stratigraphic profile
Rock or Hard Soil:
well graded gravel and sand gravel mixtures with or without
clay binder, and clayey sands poorly graded or sand clay
mixtures (GB, CW, SB, SW, and SC) having N > 30)
Medium Soils:
a) all soils with 10 < N < 30
b) poorly graded sands or gravelly sands with little
or no fines (SP) with N > 15
Soft Soils:
all soils other than SP with N < 10
Shear wave velocity
vs,30 [m/s]
TB [s]
TC [s]
> 400
0.10
0.40
200-400
0.10
0.55
< 200
0.10
0.67
Table 7: Soil types, deduced ranges of shear wave velocities as well as corner periods of the horizontal
design spectra. N is the standard penetration value and values of shear wave velocities, vs,30 , are not
provided by the Indian standard IS 1893 (Part 1) [41]; ranges of vs,30 are derived by comparing the
standard 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 allow
a classification of the soil conditions. A comparison with different soil classification schemes (e.g., IBC2006; Turkish seismic code TMPS [44]) providing both SPT-values N and ranges of shear wave velocities
vs,30 enabled a coarse allocation of vs,30 ranges to the three soil classes. Normalized elastic (R = 1.0)
design spectra for soil types I–III are reproduced in Figure 8.
16
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4
IS 1893 (Part 1) : 2002
3
Soil type: I
II
III
2
1
0
0
0.5
1
1.5
2
2.5
Period T [s]
3
3.5
4
Figure 8: Elastic design spectra for Soil Types I-III [IS 1893 (Part 1) : 2002] [41].
DR
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 easily
implemented by the user itself.
3.4
Structural Performance Under Seismic Action
In order to determine the seismic performance of a building, the spectral displacement along its capacity
curve 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 the
so-called performance point on the capacity spectrum. In the following the CSM as proposed by ATC40 [45] and FEMA 273 [46] , a recent modification of this procedure, the MADRS method, and the
displacement coefficient method (DCM) of FEMA-356 [47] with the improvements proposed in FEMA440 [48] [referred henceforth as improved displacement coefficient method (I-DCM)] will be described to
determine the performance point and thus to establish the basis in order to estimate the structural
damage state under an estimated seismic demand. All three procedures are implemented in SELENA,
such that the user can choose which one to use.
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 demand
spectrum and the building capacity curve. The demand spectrum is based on the PESH input spectrum
reduced for effective damping (when effective damping exceeds the 5% damping level of the PESH input
spectrum).
The elastic response spectra provided as a PESH input applies only to buildings that remain elastic
17
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during the entire ground shaking time history and have elastic damping values equal to 5%. This is
generally 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 divided
to obtain the damped demand spectra. The methodology reduces demand spectra for effective damping
greater than 5% based on statistically-based formulas of Newmark and Hall [49]. These relationships
estimate elastic response spectra at different damping ratios B (expressed as a percentage) and represent
all 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 RA
and 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)
DR
and where Be is the elastic damping and Bh is the hysteretic damping, which is a function of the yield
and ultimate capacity points (see Figure 2 in ATC-40 [45]) as follows:
Ayi
Dyi
Bh = 63.7κ
(29)
−
Au
Du
where κ is a degradation factor that defines the effective amount of hysteretic damping as a function of
earthquake duration and energy-absorption capacity of the structure during cyclic earthquake load (see
HAZUS 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),
5–7% for steel buildings (S),
7% for concrete (C) and pre-cast concrete buildings (P),
7–10% for reinforced masonry buildings (RM),
10% for un-reinforced masonry (URM) and masonry buildings (M),
10–15% for wood buildings (W).
The methodology recognizes the importance of the duration of ground shaking on building response by
reducing the effective damping (i.e., κ-factors) as a function of shaking duration. Dependent on the
magnitude of the scenario earthquake, the effective damping is based on the assumption of different
ground shaking durations:
magnitude M ≤ 5.5: short duration
18
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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 (acceleration
domain), 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:
where:
Sa(T ) =
Sa(T ) =
Saasi (0.4 + T /TA )/Ra (Beff )
Saasi /Ra (Beff )
Sa(T ) =
Sa(T ) =
(Saali /T )/Rv (Beff )
(Saali Tvd /T 2 )/Ra (Beff )
for 0 < T < Ta
for Ta < T < Tavb
(30)
(31)
for TAVb < T < Tvd
for T > Tvd
(32)
(33)
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 damping
at this period which is defined by the equation:
Tavb = Tavi
DR
where:
RA (Btavb )
RB (Btavb )
(34)
Tavi : transition period between 5%-damped constant spectral acceleration and 5%-damped constant
spectral 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 magnitude, as previously said.
Example 3.2 Performance point calculation between inelastic demand spectra for site classes B, C and
D and a given capacity curve by the Capacity spectrum method (CSM) described in ATC-40 Chapter
2.4.1 [45]
Steps:
1. Determination of the structure’s yield capacity and ultimate capacity:
19
1
capacity curve
0.8
0.6
(Du, Au)
0.4
0.2
(Dy, Ay)
0
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0
10
20
30
40
50
e.g.,: capacity curves as given in HAZUS, here: C1M
for moderate-code design
60
• yield capacity point: Ay = 0.104 g, Dy = 0.58
in. = 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 Table 5.18 in HAZUS99 [50]: degradation factor, κ, depending on earthquake duration and energyabsorption capacity of the structure during cyclic earthquake load

moderate duration

moderate-code design
⇒ κ = 0.4

building type C1M
Dy
Ay
−
= 4%
Bh = 63.7κ
Au
Du
DR
Be = 7.0%
Beff = Bh + Be = 11.1%
3. Calculation of reduction factors Ra and Rv , short-period and long-period spectral accelerations as
well as transition period Tavi
Parameter
2.12
Ra (Beff ) = 3.21−0.68
log(Beff ) [Eq. (26)]
1.65
Rv (Beff ) = 2.31−0.41
log(Beff ) [Eq. (27)]
Sasbi = Sasi /Ra [Eq. (31)]
Salbi = (Sali /T )/RV [Eq. (32)]
a
Savb = Savi R
Rv [Eq. (34)]
Site Class
C
D
1.35
1.35
0.37 g 0.44 g 0.52 g
0.16 g 0.26 g 0.32 g
0.43 g 0.57 g 0.62 g
B
4. Generation of reduced (inelastic) demand spectrum (damping ξ = 11.1%):
20
Site Class: B
0.8
0.6
0.4
0.2
0
10
20
30
40
50
Site Class: D
Site Class: C
0.8
demand spectra:
Be = 5 %
Beff = 11.1 %
0.6
0.4
0.2
0
0
1
0.8
0.6
0.4
0.2
0
10
0
60
10
20
30
40
50
60
demand spectra:
Be = 5 %
Beff = 11.1 %
20
30
40
50
60
DR
0
1
demand spectra:
Be = 5 %
Beff = 11.1 %
1
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1. Calculation of the spectral accelerations and spectral displacements at the site in question taking
into 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 building’s
performance 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 be
realized.
4. Reduction of the elastic response spectrum by reduction factors RA and RV to account for the
increased 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 (demand curve). The resulting building displacement is estimated from the intersection of the building
capacity 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 of
the fragility curve and the damage probability curve (see Figure 10).
21
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PESH spectrum (elastic)
reduced spectrum (inelastic)
capacity curve
performance point
(dp , ap)
DR
Figure 9: Estimation of building displacement from a given PESH input.
no damage
Damage probability P (ds | Sd)
1
slight
0.8
0.6
moderate
0.4
damage state: slight
moderate
extensive
extensive
complete
complete
0.2
0
dp − expected spectral
displacement
dp
Figure 10: The expected displacement (obtained from the performance point) is overlaid with the fragility
curves in order to compute the damage probability in each one of the different damage states.
22
3.4.2
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The Modified Capacity Spectrum Method (MADRS)
The conventional capacity spectrum method (ATC-40 [45]) uses the secant period as the effective linear
period in determining the maximum displacement (performance point). This assumption results in the
maximum displacement occurring at the intersection of the capacity curve for the structure with the
demand curve for the effective damping in ADRS format. However it has been shown in several studies
that this method can not be used with a non-IBC response spectrum and that it does not provide an
accurate performance point in some cases. Later, some improvements of the method have been published
in FEMA 440 [48]. This revised methodology has some advantages. First, it provides the engineer with
a visualization tool by facilitating a direct graphical comparison of capacity and demand. Second, there
are very effective solution strategies for equivalent linearization that rely on a modified ADRS demand
curve (MADRS) that intersects the capacity curve at the maximum displacement. As it is also explicitly
stressed in FEMA 440 “the user must recognize that the results are an estimate of median response and
imply no factor of safety for structures that may exhibit poor performance and/or large uncertainty in
behavior”. Furthermore it should be noted that the results of the MADRS method as described in the
following may not be reliable for extremely high ductility values, e.g., greater than 10 to 12.
DR
The MADRS method basically relies on the determination of effective damping, βeff , and effective
period, Teff , with which a maximum spectral displacement can be derived. This in turn matches with the
intersection point of the radial effective period (radiating line from the origin in the Sa-Sd-domain) and the
ADRS 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 period
Tsec . Figure taken from FEMA 440 [48].
is generally shorter than the secant period Tsec defined by the point on the capacity curve corresponding
to the maximum displacement dmax . The effective acceleration aeff is not meaningful since the actual
maximum acceleration amax must lie on the capacity curve and coincide with the maximum displacement
dmax . Multiplying the ordinates of the ADRS demand corresponding to the effective damping βeff by the
modification factor:
amax
(35)
M=
aeff
results in the modified ADRS demand curve (MADRS) that may now intersects the capacity curve at
the performance point. Since the acceleration values are directly related to the corresponding periods,
the modification factor can be calculated as:
2 2 2
T0
Teff
Teff
=
(36)
M=
Tsec
T0
Tsec
23
where
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T0
Tsec
2
=
s
1 − α(µ − 1)
µ
(37)
and where the post-elastic stiffness, α, and the ductility demand, µ, are:
α=
and
api −ay
dpi −dy
ay
dy
(38)
dpi
,
dy
(39)
µ=
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 βeff . These
factors are a function of the effective damping and are termed damping coefficients B(βeff ). They are
used to adjust spectral acceleration ordinates as follows:
(Sa)β =
where
B(βeff ) =
with βeff given in [%].
(Sa)5%
B(βeff )
4
5.6 − log(βeff )
(40)
(41)
DR
Since the effective period Teff and the effective damping βeff 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 building’s inelastic behavior. Within
FEMA 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 the
following description is based on the stiffness degrading hysteretic model. The effective viscous damping
eff can be calculated by the following equations dependent on ductility demand. Values of the coefficients
A to F can be found in Table 8.
βeff = A(µ − 1)2 + B(µ − 1)3 + β0
for µ < 4.0
(42)
βeff =
for 4.0 ≤ µ ≤ 4.0
(43)
for µ > 6.5
(44)
C + D(µ − 1) + β0
h
i
Teff
E FF(µ−1)−1
(µ−1)2 T0
βeff =
The effective period values, Teff , are to be computed using the following equations. Values of the
α [%]
0
2
5
10
20
A
5.1
5.3
5.6
5.3
4.6
B
-1.1
-1.2
-1.3
-1.2
-1.0
C
12
11
10
9.2
9.6
D
1.4
1.6
1.8
1.9
1.3
E
20
20
20
21
23
F
0.62
0.51
0.38
0.37
0.34
Table 8: Coefficients in order to calculate effective damping values βeff .
24
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coefficients G to L can be found in Table 9.
Teff =
Teff =
Teff =
[G(µ − 1)2 + H(µ − 1)3 + 1]T0
[I + J(µ − 1) + 1]T0
n hq
i
o
µ−1
K
1+L(µ−2) − 1 + 1 T0
α [%]
0
2
5
10
20
G
0.17
0.18
0.18
0.17
0.13
H
-0.032
-0.034
-0.037
-0.034
-0.027
I
0.10
0.22
0.15
0.26
0.11
J
0.19
0.16
0.16
0.12
0.11
for µ < 4.0
for 4.0 ≤ µ ≤ 4.0
(45)
(46)
for µ > 6.5
(47)
K
0.85
0.88
0.92
0.97
1.00
L
0.00
0.02
0.05
0.10
0.20
Table 9: Coefficients in order to calculate effective damping values Teff .
DR
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 damping
βeff . One of these procedures consists in the automated derivation of a ‘locus’ of possible performance
points. This by generating a number of modified ADRS (MADRS) demand spectra for different values
of ductility demand µ. As Figure 12 illustrates, the performance point is defined by the intersection of
the capacity spectrum and the line being described by all respective performance points on the different
MADRS curves. In the following, the single steps of the method are subsequently described taking up
the 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 response
spectrum (MADRS). Figure taken from FEMA 440 [48].
Example 3.3 Performance point calculation following the MADRS method (Chapter 2.4.2 in [48])
Steps:
25
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1. Selection of a spectral representation of the ground motion of interest with an initial damping βi
(i.e., normally 5%) and conversion into an ADRS ⇒ elastic design spectrum for NEHRP site class
C (see Example 3.2).
2. Generation or selection of a capacity curve ⇒ capacity curve described by yield (ay , dy ) and ultimate capacity points (au , du ); in case of a generated capacity curve, the development of a bilinear
representation has to be conducted (ATC-40 [45]) ⇒ here: capacity curve as given in HAZUS for
model 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, βeff , and modification factor, M for
pinteger increments of ductility
µ (µ = 2, 3, 4, . . .) ⇒ initial (elastic) period T0 (µ = 1): T0 = 2π dy /ay 0.7542 s ⇒ post-elastic
stiffness parameter: α =
api −ay
dpi −dy
ay
dy
= 0.1828 [Eq. (38)]
Parameter
dpi = µdy [m] [Eq. (39)]
βeff [%] [Eqs. (42)-(44)]
Teff [sec] [Eqs. (45)-(47)]
Tsec [sec] [Eq. (37)]
B(βeff ) [Eq. (41)]
”2
“
[Eq. (36)]
M = TTeff
sec
2
0.0294
8.686
0.836
0.981
1.163
3
0.0441
15.606
0.997
1.118
1.402
Ductility µ
4
5
0.0588
0.0735
18.740
20.143
1.109
1.194
1.212
1.282
1.499
1.540
6
0.0882
21.546
1.278
1.335
1.581
7
0.1029
22.654
1.332
1.378
1.613
0.727
0.795
0.838
0.916
0.935
0.867
DR
4. Adjustment of the initial ADRS to the effective damping βeff ⇒ reduction of spectral acceleration
(Sa)5%
ordinates (Sa)5% by damping coefficients B for all considered ductility values µ: (Sa)β = B(β
eff )
[Eq. (40)]
5. Multiplication of the ADRS for βeff by the modification factor M reduction of spectral acceleration
ordinates (Sa)β by damping coefficients M for all considered ductility values µ.
6. Generation of possible performance point by the intersection of radial secant period Tsec with
the MADRS for all considered ductility values µ ⇒ Determination of performance point by the
intersection of the locus line with the capacity spectrum:
26
0.8
locus of possible
performance points
T0 (µ=1)
Tsec (µ=2)
Tsec (µ=3)
...
Tsec (µ=7)
0.6
0.4
ap
0.2
0
ADRS: µ=1
MADRS: µ=2
...
µ=7
30
dp
0
10
20
Improved Displacement Coefficient Method (I-DCM)
DR
3.4.3
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The displacement coefficient method modifies the displacement demand of the equivalent linear single
degree of freedom (SDOF) system by multiplying it by a series of coefficients in order to generate an
estimate of the maximum displacement demand of the nonlinear oscillator. The process begins with the
generation of the capacity curve of the nonlinear oscillator. The effective period of the system is then
computed as (Figure 13):
s
Te = 2π
Dy
Ay
(48)
When plotted on an elastic response spectrum representing the seismic ground motion, as peak spectral
acceleration, Sa , vs. period, T, the spectral acceleration demand of the equivalent linear SDOF system,
Sael , can be computed (Figure 13). The peak elastic spectral displacement demand, Sdel is then directly
related to the Sael by:
T2
(49)
Sdel = e2 Sael
4π
The target displacement, δt , is then computed as:
δt = C1 C2 Sdel
(50)
where:
C1 = Modification factor to relate the expected maximum displacement demand of a nonlinear oscillator
with elastic-perfectly-plastic (EPP) hysteretic properties to the peak displacement demand of the
linear oscillator,
27
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Sa
(Dy , A y)
Capacity Curve
Te = 2π
Dy
Ay
Sd
2
el Te
2
δ t = C 1C 2Sa
4π
el
Sa
Demand Curve
Te
Period, T
Figure 13: Schematic illustraion of process I-DCM which is used to compute the target displacement
demand of a nonlinear oscillator for a given capacity curve and response (demand) spectrum
.
DR
C2 = Modification factor to represent the effect of pinched hysteretic shape and stiffness degradation
on the maximum displacement response.
The coefficeints C1 and C2 can be computed using the approximation relationships given in FEMA440 [48]:
C1 =
C2 =
R−1
aTe2
(51)
1 R−1 2
800 ( Te )
(52)
1+
1+
where
R = Ratio of elastic strength demand to the calculated strength capacity; R=Sael /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 spectral
shapes.
3.5
Fragility Curves and Damage State Probability
The conditional probability of being in, or exceeding a particular damage state, ds , given by the spectral
displacement Sd (or other seismic demand parameter) is defined by the following equation:
Sd
1
ln
(53)
P (ds|Sd ) = Φ
βds
S̄d,ds
where
S̄d,ds : median value of spectral displacement at which the building reaches the threshold of damage
state ds,
28
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Spectral shape
IBC
Eurocode I and II
Indian Code
Soil type
A
B
C
D
E
A
B
C
D
E
I
II
III
a
130
130
90
60
60
130
90
60
60
60
90
60
60
Table 10: Assumed values for the parameter a for different site classes and spectral shapes.
βds : is the standard deviation of the natural logarithm of spectral displacement for damage state ds,
Φ(·): is the standard normal cumulative distribution function.
In HAZUS99, for instance, both mean displacement threshold of damage state and its corresponding
standard deviation βds are table values (see Table 5.9) which depend on the model building type and its
seismic design level. However, it should be regarded that the parameters defining the fragility functions
for a certain building type are closely connected to its respective capacity curve.
DR
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 built
area [m2 ] normalized by the total built area in each geographical unit or by the total built area in the
studied region, i.e., summed all geographical units). Nonetheless, results can also be given as absolute
numbers of damaged buildings.
3.6
Economic Losses
The SELENA software can also estimate the total amount of economic losses (in any input currency) in
any geographical unit caused by the structural damage.
The economic losses for building repair (and in case of complete damage for replacement) are computed
in the following way:
Nds
Nbt X
Not X
X
Ai,j Pj,k Ci,j,k
(54)
Leco = Cr
i=1 j=1 k=1
where Not is the number of occupation types, Nbt is the number of building types, Nds is the number of
damage states, and where
Cr : regional cost multiplier (currently is set to 1.0, but can have different values for each geographical
unit 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 ])
29
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0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
none
slight
moderate extensive complete
Damage state ds
Figure 14: Discrete damage probabilities derived from the cumulative damage probabilities for an expected displacement as illustrated in Figure ??.
DR
Pj,k : damage probability of a structural damage k (slight, moderate, extensive or complete) for the
model 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 damage
are computed. Those being caused by non-structural damage (acceleration sensitive damage) are not
considered. The absolute values for building repair costs in the different damage states will be determined
by the user. HAZUS expresses the cost of damage for damage states slight, moderate and extensive as a
percentage 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 reliable
or 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 the
analysis type dependent on damaged building area. In case of an analysis dependent of the number of
damaged buildings, no economic losses are computed.
30
3.7
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Humanloss — Casualties
The methodology applied in order to calculate the number of human casualties follows basically the
HAZUS approach but is somewhat simplified using the formulas given by Coburn and Spence [52]:
K = K s + K ′ + K2
where
(55)
K s : 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 = Kis + Ki′ + 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 given
in Table 11. However, the loss model applied in the current version of SELENA is only considering
the direct human losses caused by structural damage not due to non-structural damage or follow-on
hazards. By using SELENA, the number of human losses (casualties) can be computed using two different
Injury Level
DR
Severity 1
Description
Injuries requiring basic medical aid that
could be administered by paraprofessionals.
These types of injuries would require bandages or
observation.*
Severity 2
Severity 3
Severity 4
Injuries requiring a greater degree of
medical care and use of medical
technology such as x-rays or surgery, but not expected
to progress to a life threatening status.
Injuries that pose an immediate life
threatening condition if not treated
adequately and expeditiously.
Examples
- sprains
- severe cuts requiring stitches
- minor burns (first or second degree on a
small part of the body)
- bumps on the head without loss of consciousness
- bump on the head that causes loss of consciousness
- fractured bones
- dehydration or exposure
-
punctured organs
other internal injuries
spinal column injuries
crush syndrome
instantaneously killed or
mortally injured.
Table 11: Injury Classification Scale according to HAZUS. *Injuries of lesser severity which can be self
treated are not covered by HAZUS.
methodologies:
1. Basic methodology → in case that no detailed information on population distribution is available
or 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 the
day (i.e., school occupancy only during daytime), the number of casualties will be computed for three
different times of the day:
1. nighttime scenario (called 02:00 am): i.e., earthquake striking during nighttime.
31
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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 (nighttime), 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 building
damage, and injury severity can be calculated by:
Kis = {Injuries (severity i)} =
Nds
Nbt X
X
csr
Ci,j
Pj,k Njpop
(57)
j=1 k=1
where:
csr
Ci,j
: casualty rate of severity i for damage state j 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 = 3
extensive, k = 4 complete or complete with collapse) for the jth model building type.
Njpop : number of people in the jth model building type.
DR
The total number of people in all buildings of the j:th model building type (MBT), for one geographical
unit (i.e., census tract) at a specific time period (time of the day), is computed in a simplified way:
Njpop = N tp C po Cjombt
(58)
where N tp is the total number of people living in the respective geographical unit provided by input file
population.txt, C po is the percentage of people staying indoors or outdoors dependent on the time
of the day provided by input file poptime.txt (compare to Table 12), and Cjombt is the percentage of
occupancy class for the jth model building type (MBT) provided by input file ocupmbtp.txt.
Occupancy type
INDOOR
OUTDOOR
P
Sum
night (2:00 am)
98%
2%
100%
day (10:00 am)
90%
10%
100%
commuting (5:00 pm)
36%
64%
100%
Table 12: Population percentages indoors and outdoors dependent on the time of the day. Note that
these values are strongly dependent on the country and its cultural peculiarities and consequently may
vary 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
Occupancy
residential
commercial
educational
industrial
hotels
residential
commercial
educational
DR
industrial
hotels
Distribution of people in census tract
2:00 pm
5:00 pm
Indoors
(0.999) 0.99 (NRES)
(0.70) 0.75 (DRES)
(0.70) 0.50 (NRES)
(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)
–
(0.90) 0.80 (AGE 16) +
0.80 (COLLEGE)
(0.80) 0.50 (COLLEGE)
(0.999) 0.10 (INDW)
(0.90) 0.80 (INDW)
(0.90) 0.50 (INDW)
0.999 (HOTEL)
0.19 (HOTEL)
0.299 (HOTEL)
Outdoors
(0.001) 0.99 (NRES)
(0.30) 0.75 (DRES)
(0.30) 0.50 (NRES)
(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)]
–
(0.10)0.80 (AGE 16) +
(0.20) 0.50 (COLLEGE)
0.20 (COLLEGE)
(0.001) 0.10 (INDW)
(0.10) 0.80 (INDW)
(0.10) 0.50 (INDW)
0.001 (HOTEL)
0.01 (HOTEL)
0.001 (HOTEL)
2:00 am
Table 13: Default relationships for estimating population distribution (taken from HAZUS) where POP
is the census tract population taken from HAZUS, DRES is daytime residential population inferred from
census, NRES is nighttime residential population inferred from census data, COMM is the number of people
commuting inferred from census data COMW is the number of people employed in the commercial sector
INDW is the number of people employed in the industrial sector GRADE is the number of students in grade
school (usually under 17 years old) COLLEGE is the number of students on college and university campuses
in the census tract (over 17 years old), HOTEL is the number of people staying in hotels in the census
tract, PRFIL is a factor representing the proportion of commuters using automobiles, inferred from profile
of the community (0.60 for dense urban areas, 0.80 for less dense urban or suburban areas and 0.85 for
rural). 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, the
default is that 99% of the nighttime residential population (NRES) will be in residential occupancy while
99.9% of those will be indoors. If more detailed information is available on these issues, these factors can
be changed in the m-file humanlosshz.m. The methodology takes into account a wider range of causal
relationships in the casualty modeling. It is an extension of the model proposed by Stojanovski and
Dong [53].
By using an event tree as shown in Figure 15 and multiplying the population in each of the occupancy
types and model building types by the damage probabilities and casualty rates, the total number of
casualties for each severity level can be estimated. Figure 15 is illustrating an event tree for indoor
casualties (but also outdoor casualties are contemplated within this methodology). The outdoor casualty
model tries to quantify the number of casualties outside of buildings due to falling materials with respect
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Figure 15: Indoor casualty event tree model (taken from HAZUS). Bridge casualties are currently not
implemented in SELENA.
to areas where people congregate such as sidewalks. To accomplish this, the number of people on sidewalks
or similar exterior areas is estimated from Table 13. The table is designed to prevent double counting of
casualties from outdoor falling hazards with building occupancy casualties.
4
N this section the details for intalling SELENA is treated, both for Windows stystems and POSIX
(Linux/Unix) systems.
DR
I
Installation
4.1
System Requirements and Resent Code Changes
There has been a change in the system requirements from version 4.x to version 5.x (and above) of
SELENA. Starting with version 5.0.0 of SELENA, the Matlab m-code has been translated into C-code
which allows SELENA to run without using Matlab; it is, however, still possible to use SELENA from
Matlab. Furthermore, the m-code has been changed in such way that it now can run without any special
Matlab Toolboxes (which was required before) and it now also now runs using the free (open source)
Matlab clone Octave (http://www.gnu.org/software/octave/).
In order to avoid Matlab toolbox dependencies, SELENA now uses the open source GNU Scientific
Library (GSL) which is available for most systems, such as, Linux/Unix, MacOS, and Windows. Another
change is that SELENA previously used some input files in Matlab’s binary mat-format. This has now
been changed and SELENA now only uses input files in a plain (ascii) text format.
4.1.1
Installing the GNU Scientific Library
The GNU Scientific Library can be found here: http://www.gnu.org/software/gsl/
The GSL for Windows must be installed in a directory where Matlab/Octave or the stand-alone binary selena.exe can find it. The easiest way is just to copy the libgsl.dll and libgslcblas.dll files to
C:\WINDOWS\System32\ These files can be found at: http://gnuwin32.sourceforge.net/packages/gsl.htm
or in the dll/bin folder (see also Section B.1).
For Linux, the GSL is probably included in the package system for your Linux distribution so that
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you can use your package installer (yast, emerge etc.) to install it. For example, on a Gentoo Linux
distribution just type,
# emerge gsl
If GSL is not included in your Linux distribution’s package manager system then you can install it from
source which is described at the GSL webpage.
4.2
The Directory Structure of SELENA
Unpacking the compressed (zip) file onto your computer automatically creates the main folder SELENA
under which a number of sub-folders can be found:
examples
gnumex
include
dll
src
userman
m_files
mexopts
DR
The dll folder contain Windows specific files (for GSL) which is needed for building the Windows
binaries (both stand-alone application and the mex/oct-files). The examples folder contain some example
input files which can be used to test SELENA, the m files folder contain the m-files and the mex/octfiles Matlab/Octave (e.g., the mex/oct files must be copied from the src after compilation). The src
contain the C-source files (and Makefiles) for both the stand-alone application and the mex/oct-files, and
the include folder contain the header files for C-code. The mexopts folder contain two bat-files which
is used when building the mex-files using the MinGW compiler, and finally, the userman folder contain
various files for the user manual.
The main folder also contain the four text:
COPYING
Make.inc
README.txt
README_INSTALL_MinGW_Windows.txt
README_SVN.txt
build_mexfiles.m
build_mexfiles_mingw.m
build_mexfiles_win.m
build_oct_files.m
where the two m-files, build mexfiles mingw.m and build mexfiles win.m, are for building the
mex-files using Windows, build oct files.m is for building the oct-files (on all systems) and Make.inc
is a file for setting compiler options for Linux/Unix. Furthermore the README.txt is a quick guide on
how to install and run SELENA (and the README SVN.txt contains some information for developers on
setting svn keywords). Also for license information see the COPYING file. For more build and compilation
instructions, see Appendix B.
4.3
The SELENA m-files
The SELENA comprises 34 different m-files files (*.m) which are consecutively accessed during the program sequence. Their respective functions and tasks are briefly described below:
selena gui.m core file that starts the graphical user interface (calling for startwin.m).
selena.m core file (the command line interface of SELENA).
startwin.m initialization of the window environment in order to choose between a probabilistic, a deterministic or an analysis based on real-time data.
dettool.m Function (called by startwin.m) to initialize the window environment for a deterministic
analysis.
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probtool.m Function (called by startwin.m) to initialize the window environment for a probabilistic
analysis.
realtool.m Function (called by startwin.m) to initialize the window environment for an analysis with
real-time data (grid pattern shaking scenario).
computetool.m Function (called by dettool.m) which starts the main processes of a seismic risk computation for a deterministic earthquake.
computetoolp.m Function (called by probtool.m) which starts the main processes of a seismic risk
computation based on a probabilistic shake map.
computetoolr.m Function (called by realtool.m) which starts the main processes of a seismic risk
computation based on real-time data.
gmotion.m Function which gets the ground motion at the center of each geographical unit from a deterministic earthquake (numerous attenuation relationships are provided, while new attenuation
relations can be easily implemented) and computes ground-motion amplification using the factors
as e.g., given in IBC-2006 [8] (called by computetool.m)
att sub.m Function with attenuation relationships from different authors which provides the groundmotion values (units of [g]) for PGA, Sa at 0.3s and Sa at 1.0s (called by gmotion.m).
dtorry.m Function used to compute the closest distance from a point (latitude, longitude) to a segment
(lat1, lon1)-(lat2, lon2) (called by gmotion.m).
gmotionp.m Function which amplifies the ground motion at the center of each geographical unit from
probabilistic shaking maps using the factors as e.g., given in IBC-2006.
DR
gridtogeounit.m Function selecting the concerning nodes of the grid pattern, making a statistical evaluation of their ground-motion ordinates (mean value, standard deviation), and assigning them to
the centers of the geographical units (called by computetoolr.m).
damagep.m Function which computes the probability of damage for the building stock using the capacity
spectrum method (called by computetool.m, computetoolp.m, and computetoolr.m)
spectralshape.m Computation of spectral ground-motion ordinates following different code provisions,
e.g., IBC-2006 (called by damagep.m)
csm.m Performance point calculation based on the “traditional” capacity spectrum method (CSM) following ATC-40 [45] (Procedure A) (called by damagep.m).
madrs.m Performance point calculation by using the modified capacity spectrum method (MADRS)
following FEMA 440/ATC-55 (called by damagep.m).
curveintersect.m Function which finds the intersection points of two curves in the X-Y plane (called
by csm.m and madrs.m).
local parseinputs.m Script used by curveintersect.m.
mminvinterp.m 1-D inverse interpolation (called by curveintersect.m)
squaredam.m fFnction which computes the absolute square meters of damaged built area for each
model building type in each geographical unit (called by computetool.m, computetoolp.m, and
computetoolr.m)
numdam.m Function which computes the absolute number of damaged buildings for each model building
type in each geographical unit (called by computetool.m, computetoolp.m, and computetoolr.m)
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losssqm.m function which computes the total economic losses due to structural damage (called by
computetool.m, computetoolp.m, and computetoolr.m).
tree.m Function used to fit the damage estimation results coming from each branch of the logic tree to
a normal distribution function; computes median (mean) value and 16% and 84% fractiles (called
by computetool.m, computetoolp.m, and computetoolr.m).
treeloss.m Function used to fit the economic loss results coming from each branch of the logic tree to
a normal distribution function; computes median (mean) value and 16% and 84% fractiles (called
by computetool.m, computetoolp.m, computetoolr.m).
meanest.m Function to compute (estimate) the mean and the variance from a set of data when the variance is unknown. The confidence intervals are therefore obtained using the Student t-distribution
for a chosen alpha (0.16 and 0.84) (16% and 84% fractiles)1 This function is used by tree.m,
treemdr.m and treeloss.m.
wfigmngr1.m Function to manage SELENA windows.
wfighelp1.m Function to manage SELENA help in main window.
wfigobj1.m Function to manage objects in windows.
humanloss.m Function to compute the number of human casualties according to the basic methodology
(called by computetool.m , computetoolp.m , and computetoolr.m).
humanlosshz.m Function to compute the number of human casualties according to the HAZUS-methodology
(called by computetool.m , computetoolp.m , and computetoolr.m).
distance.m Function which computes the distance between points on a sphere.
DR
deg2km.m Function that converts distance from degrees to kilometers.
km2deg.m Function that converts distance from kilometers to degrees.
4.3.1
The SELENA mex-files
The mex-files currently implemented in SELENA are:
att_sub.mex*
csm.mex*
curveintersect.mex*
damagep.mex*
gmotion.mex*
gmotionp.mex*
gsl_interpolate.mex*
humanloss.mex*
humanlosshz.mex*
imp_dcm.mex*
interp1.mex*
losssqm.mex*
madrs.mex*
meanest.mex*
normcdf.mex*
numdam.mex*
spectralshape.mex*
squaredam.mex*
tinv.mex*
tree.mex*
treeloss.mex*
treemdr.mex*
These files have the same functionality as the corresponding m-files but runs much faster. The file
extension of the mex-files depends of which architecture you are using; Windows 32-bit has the extension
∗.mexw32, Linux x86 ∗.mexlx, Linux x86 64 ∗.mexa64, Intel MacOS X ∗.mexmaci etc. The biniary
packages for SELENA comes with pre-compiled mex-files for Windows 32-bit and Linux 32 and 64 bit.
These files can be found in the m files folder and to use them one just need to set the Matlab path
using the menu in the Matlab GUI or with (add your path),
>> addpath(’/home/<the user>/selena/m_files’)
1 For
different alpha please change the value in the function callback.
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which also can be added to your startup.m file to permanently add the path.
There are also m-files available in the same folder which can be useful for evaluating and testing the
code (easy to add plots, print intermediate results etc.) If Matlab finds a mex-files with the name as an
m-file then the mex-file will take precedece so to use the m-files one need to remove the mex-files from
the m files folder. Note, however, that the gsl interpolate.mex∗ file is mandatory to use since it calls
the interpolation routines in the GNU Scientific Library (which is used by SELENA).
4.3.2
The SELENA oct-files
The oct-files currently implemented in SELENA are:
att_sub.oct
csm.oct
curveintersect.oct
damagep.oct
gmotion.oct
gsl_interpolate.oct
humanloss.oct
humanlosshz.oct
imp_dcm.oct
madrs.oct
spectralshape.oct
squaredam.oct
tree.oct
treemdr.oct
Note that there are no binary oct-file distributed with SELENA since they often need to be build for
the particular version of Octave that is used. See Appendix B for build instructions.
5
Running SELENA
T
DR
O run SELENA, a certain number of files containing the input data have to be prepared. These
input files have to be available in the “input” folder. Note that a selection of necessary input files
already exist in the examples folder and preferably can be modified for any new analysis run. The input
files needs to be prepared in ASCII-format and provided as plain text files (*.txt). In addition, a number
of input files are required which either contain fixed parameter values (variables) or which include the
spectral acceleration and displacement values of the single capacity curves. Input files containing the
fixed parameter values (e.g., ec8t1.txt) will normally not be modified by the user and should be kept
as they are. In the following, the format of the different input files will be explained separately in more
detail. Their order conforms to SELENA’s sequence of prompting the different inputs.
Note that the results of any new analysis with SELENA will be written into a sub-folder called output.
The user has to be careful when running SELENA a second time, since the sub-folder output is automatically recreated and so all files of previous runs will be overwritten.
The contents of the input folder can, for example, look like this:
attenuation.txt
builtarea.txt
capacity1.txt
capcurves/
collapserate.txt
cpfile.txt
earthquake.txt
ecfiles.txt
elosscd1.txt
elossed1.txt
elossmd1.txt
elosssd1.txt
fragility1.txt
header.txt
headermdr.txt
headerocc.txt
indcasratec.txt
indcasratecc.txt
indcasratee.txt
indcasratem.txt
indcasrates.txt
injury1.txt
injury2.txt
injury3.txt
injury4.txt
newconstruction.txt
ocupmbt_files/
ocupmbtp.txt
outcasratec.txt
outcasratee.txt
outcasratem.txt
poptime.txt
population.txt
soilcenter1.txt
soilcenter2.txt
soilcenter3.txt
soilfiles.txt
ubcampfact.txt
vulnerfiles.txt
where the sub-folder capcurves contain the capacity curve files, such as,
capc_C1M-pre.txt
capc_C2M-pre.txt
capc_C3M-pre.txt
and the sub-folder ocupmbt files contain, for example,
ocupmbt1.txt
ocupmbt2.txt
ocupmbt3.txt
The input files are described in Section 5.1.
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Preparation of Input Files
Input Files for Deterministic Analysis
For a deterministic analysis 5 different input files are required.
cpfile.txt: see Section 5.1.4: Common input files for all analysis types.
earthquake.txt: Input file containing the information about the earthquake to be used in the seismic
risk study. This file includes different earthquakes with corresponding weights to be run by the logic tree
methodology.
Format:
%Earthquake scenarios information
%1st column is the weight for the logic tree scheme:weight
%2nd column is latitude in degrees:lat
%3rd column is longitude in degrees:lon
%4th column is focal depth in km:depth
%5th column is Ms magnitude:Ms
%6th column is Mw magnitude:Mw
%7th column is fault orientation in degrees from North:strike
%8th column is dip angle in degrees:dip
%9th column is fault mechanism:strike-slip/normal(1);reverse(2);all(3)
%10th column is the numerical code for the spectral shape, e.g. 1 for IBC-2006
0.33 59.90 10.90 20.00 5.50 5.50 0.00 90.00 2 1
0.34 59.90 10.90 20.00 6.00 6.00 0.00 90.00 2 1
0.33 59.90 10.90 20.00 6.50 6.50 0.00 90.00 2 1
DR
where weight is the weight for the logic tree scheme, lat is the latitude in degrees, lon is th longitude
in degrees, depth is the focal depth in [km], Ms is the surface wave magnitude Ms , Mw is the moment
magnitude Mw , strike is the fault orientation in degrees from North, dip is the dip angle in degrees,
fault is the fault mechanism: 1 - strike-slip/normal; 2 - reverse; 3 all, sshape is the numerical code for
the spectral shape as given in spectralshape.m and spectralshape.c (see Table 14)
soilfiles.txt: see Section 5.1.4: Common input files for all analysis types
attenuation.txt: Input file containing the labels of the different empirical ground-motion prediction
equations (short: att. rel.) to be used in the study and its corresponding weights for the logic tree
methodology.
Format:
%Ground motion information.
%1st column is weight: weight
%2nd column is the label of PGA att.rel.: PGA
%3rd column is the label of Sa at 0.3 s att.rel.: Sa03
%4th column is the label of Sa at 1.0 s att.rel.: Sa10
0.6 22 322 1022
0.2 23 323 1023
0.2 24 324 102
where: weight is the weight for the logic tree scheme, PGA is the label of the applied att.rel. in order
to determine PGA (see Table 19), Sa03 is the label of the applied att.rel. in order to determine Sa at 0.3
s (see Table 19), Sa10 is the label of the applied att.rel. in order to determine Sa at 1.0 s (see Table 19),
In the sample file above, the ground-motion prediction equations by Ambraseys et al. [21] are used in
order to derive:
• the mean values of PGA (no=22 in the att sub function), Sa at 0.3 s (no=322), and Sa at 1.0 s
(no=1022) weighted 0.6,
• the mean values plus standard deviation σ of PGA (23), Sa at 0.3 s (323), and Sa at 1.0 s (1023)
weighted 0.2, and
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• the mean values minus standard deviation σ of PGA (24), Sa at 0.3 s (324), and Sa at 1.0 s (1024)
weighted 0.2.
Note: For each attenuation relationship periods at 0 s (PGA), 0.3 s and 1.0 s should be given with the
same weights since each computation will need the ground-motion values at these three periods.
vulnerfiles.txt: see Section 5.1.4: Common input files for all analysis types.
ecfiles.txt: see Section 5.1.4: Common input files for all analysis types.
5.1.2
Input Files for Probabilistic Analysis
For a probabilistic analysis 4 different input files are required.
shakefiles.txt: Input file referring to the sub-files of the probabilistic ground-motion information
shakecenter(i).txt (2nd column), indicating their corresponding weight for the logic tree methodology
(1st column) and referring to the numerical code for the spectral shape (3rd column) as given in Table 14
and implemented in the files spectralshape.m and spectralshape.c.
Index
1
2
3
4
Site classification scheme
United States: IBC-2006 [8]
Eurocode 8: Type 1 (CEN, 2002)
Eurocode 8: Type 2 (CEN, 2002)
India: IS 1893 (Part 1) : 2002 [41]
Site classes
A-E (Table 15)
A–E (Table 16)
A–E (Table 16)
I–III (Table 17)
DR
Table 14: Indexing of the incorporated site classification schemes.
Format:
0.60
0.20
0.20
shakecenter1.txt 1
shakecenter2.txt 1
shakecenter3.txt 1
Each shakecenter(i).txt file contains the spectral ground-motion values PGA, spectral acceleration
Sa at 0.3 seconds, and spectral acceleration Sa at 1.0 seconds for each geographical unit (center coordinates) while i indicates the number of the different regarded probabilistic shakecenter. All values are for
rock and in % of g. Note that the coordinates of the centroids have to be externally assigned in a GIS
program.
Format of the sub-file shakecenter(i).txt:
%GEOUNIT
0100100001
0100100002
0100100003
0100100004
01001...
Lat
59.914
59.916
59.919
59.916
Lon Soil PGA Sa_03 Sa_10
10.719 2 0.2548 0.3160 0.0866
10.711 2 0.2548 0.3160 0.0866
10.707 2 0.2548 0.3160 0.0866
10.698 2 0.2548 0.3160 0.0866
in which:
GEOUNIT is the label for the identification of the geographical unit, Lat is the label for the geographical
coordinates (degree of latitude), Lon is the label for the geographical coordinates (degree of longitude),
Soil is the label for the for the soil type in each geographical unit.
soilfiles.txt: see Section 5.1.4: Common input files for all analysis types.
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5.1.3
Input Files for Analysis with Real-time Data
For an analysis with real-time data 4 different input files are required.
realtimefile.txt: Input file referring to the names of the sub-files realtimegrid.txt (1st column), the moment magnitude, Mw , of the respective earthquake (2nd column) and referring to the
numerical code for the spectral shape (3rd column) as given in Table 14 and described in the file(s)
spectralshape.m/spectralshape.c (here: 1 for IBC-2006).
Format:
realtimegrid.txt
6.0
1
The sub-file realtimegrid.txt contains the information of Peak Ground Acceleration (PGA), spectral
acceleration Sa at 0.3 s, and spectral acceleration Sa at 1.0 s at the equally-spaced points of a grid pattern.
These have to be provided by the user for example by real-time shake maps.
Format of the sub-file realtimegrid.txt:
PGA Sa03 Sa10
0.0819 0.1617 0.0394
0.0832 0.1642 0.0399
0.0846 0.1669 0.0405
0.0861 0.1697 0.0411
DR
%Lat Lon
59.80 10.60
59.80 10.61
59.80 10.62
59.80 10.63
...
Note: Given that soil effects are already included in the available real-time shake maps then the soil
types in input files soilcenter(i).txt have to be set as rock (2) so that the ground-motion ordinates
are not amplified a second time. In case that the available real-time shake maps are confined to rock
then the soil types in input files soilcenter(i).txt have to be set as normal.
soilfiles.txt: see Section 5.1.4: Common input files for all analysis types.
5.1.4
Common Input Files for all Analysis Types
cpfile.txt: Input file which decides on the type of analysis method to be used in order to calculate the
performance point and whether the damage results are dependent on number of damaged buildings or
damaged building area.
Format:
%
%
%
2
1st column is the type of analysis method used (1-CSM; 2-MADRS; 3-I-DCM)
2nd column is the type of damage results (1-square meters; 2-nr of buildings)
3rd column is the human losses method (1-basic method; 2-HAZUS method)
1
2
soilfiles.txt: Input file referring to the names of the sub-files soilcenter(i).txt and indicating
their corresponding weight for the logic tree methodology.
Format:
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soilcenter1.txt
soilcenter2.txt
soilcenter3.txt
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with i indicating the number of the different regarded soil columns.
Each soilcenter(i).txt file contains the information about the geographical coordinates of the
center of each geographical unit in which the studied region had been divided as well as a column with
the soil type associated to that specific geographical unit.
The soil column will be labeled with a code following the soil classification scheme applied by the user.
Currently, four different classification schemes are available which have to be appointed in the respective
input file earthquake.txt, shakefiles.txt, or realtimefile.txt by an index (Table 14).
Code
1
2
3
4
5
NEHRP site class
A
B
C
D
E
Site class description
hard rock
Rock
very dense soil and soft rock
stiff soil
soft soil
Shear-wave velocity vs,30 [m/s]
> 1500
760-1500
360-760
180-360
< 180
Table 15: Site classification according to the NEHRP provisions [43] used by the International Building
Code IBC-2006 [8].
Code
Ground type
1
2
3
A
B
C
4
D
5
E
DR
rock or rock-like formation
very dense sands, gravel or very stiff clay
deep deposits of dense or medium-dense sand,
gravel of stiff clay
deposits of loose-to-medium cohesionless soil,
or of soft-to-firm cohesive soil
soil profile of a surface alluvium layer of C or D and
H = 5-20 m underlain by A
Shear-wave velocity
vs,30 [m/s]
> 800
360-800
180-360
< 180
n.a.
Table 16: Site classification according to Eurocode 8 (CEN, 2002).
Code
1
2
3
Ground type
I
II
III
rock or hard soil
medium soils
soft soils
Shear-wave velocity vs,30 [m/s]
> 400
200-400
< 200
Table 17: Site classification according to the Indian standard IS 1893 (Part 1) : 2002 [41].
The center coordinates must be defined independently of SELENA. [If unknown: when the shapefiles
of all the geographical units have been created in ArcView, the center of each geographical unit is easily
obtained using the internal scripts of ArcView.]
Format of the sub-file soilcenter(i).txt:
%GEOUNIT
Lat
Lon Soil
0100100001 59.91401 10.71870 2
0100100002 59.91562 10.71144 2
01001...
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where GEOUNIT is the label for the identification of the geographical unit, Lat is the label for the
geographical coordinates (degree of latitude), Lon is the label for the geographical coordinates (degree of
longitude), Soil is the label for the for the soil type in each geographical unit.
In the sample file the GEOUNIT column has a string format of 10 characters since it was created to fit
the HAZUS input files, however the SELENA code accepts any integer numerical format. Coordinates
must be provided in geographical coordinates for the representation in ArcView and can be used later to
prepare maps in other coordinate systems.
The respective soil amplification factors (and corner control periods) in order to construct the response
spectra for the different soil types are provided by input files ubcampfact.txt (for NEHRP site classes
as given in IBC-2006, Table 15) and ec8t1.txt (for site classes of Eurocode 8 Type 1, Table 16),
ec8t2.txt (for site classes of Eurocode 8 Type 2, Table 15) and IS1893.txt (for site classes of Indian
code, Table 17).
vulnerfiles.txt: Input file referring to the sub-files capacity(i).txt and fragility(i).txt, as
well as indicating their corresponding weight for the logic tree methodology.
Format:
0.33
0.34
0.33
capacity1.txt
capacity2.txt
capacity3.txt
fragility1.txt
fragility2.txt
fragility3.txt
with i indicating the number of different sets of capacity curves capacity(i).txt respectively fragility
curves fragility(i).txt for the logic tree computation scheme.
DR
In turn, each of the capacity(i).txt files refers to one particular set of building capacity curves
which have to be provided as text (ASCII) files. Very often there may be three or more sets (and
thus capacity(i).txt files) representing the variability of the capacity curve (e.g., median, 84%- and
16%-fractile).
Format of the sub-files capacity(i).txt:
capc_C1M-pre.txt
capc_C2M-pre.txt
capc_C3M-pre.txt
7 0.0052 0.40
7 0.0046 0.40
10 0.0046 0.40
0.20 0.00 %C1M
0.20 0.00 %C2M
0.20 0.00 %C3M
where
1st column: filename of the respective capacity curve,
2nd column: elastic damping in percentage, for each one of the model building types mbt according
to the recommendations of Newmark and Hall [49] for materials at or just below their yield point
(explained in the technical description of this report),
3rd column: spectral displacement corresponding to the elastic limit (in [m]),
4th column: kappa value for short duration earthquake (Table 5.18 in HAZUS [2]),
5th column: kappa value for moderate duration earthquake (Table 5.18 in HAZUS [2]),
6th column: kappa value for long duration earthquake (Table 5.18 in HAZUS [2]),
7th column: comment on the denomination of the respective (model) building type.
The files containing the spectral displacement and spectral acceleration values of the actual capacity
curve (e.g., capc C1M-pre.txt) in general are provided as plain ASCII text files in the following format:
0 0
0.0005 0.0049
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0.0015 0.0147
0.002 0.0196
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where the first column is the spectral displacement (in [m]) and the secone column is the spectral
2
acceleration (in [m/s ])
Each fragility(i).txt file contains the information of the fragility curve which has to be used in
combination with its corresponding capacity curve.
Format of the sub-file fragility(i).txt:
%mbt smedian sbeta mmedian mbeta
1 0.0305 0.73 0.0488 0.77 0.1219
2 0.0244 0.86 0.0465 0.83 0.1204
3 0.0183 0.90 0.0366 0.86 0.0914
emedian ebeta cmedian cbeta Pre-Code
0.83 0.3048 0.98 %C1M
0.80 0.3048 0.98 %C2M
0.90 0.2134 0.96 %C3M
where mbt is the index of model building type, xmedian is the median value of spectral displacement
in unites of [m] at which the building reaches the threshold of the damage state, x, which can be one of:
s(slight), m (moderate), e (extensive), and c (complete), and where xbeta is the standard deviation of
the natural logarithm of spectral displacement of damage state, x, which also can be one of: s (slight),
m (moderate), e (extensive), and c (complete).
5.1.5
Input Files for the Calculation of Economic Losses
In order to calculate the economic losses the user has to provide the monetary values per [m2 ] dependent
on model building type, occupancy, and structural damage state.
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ecfiles.txt: Input file referring to the sub-files elosssd(i).txt (slight damage), elossmd(i).txt
(moderate damage), elossed(i).txt (extensive damage), and elosscd(i).txt (complete damage) as
well as indicating their corresponding weight for the logic tree methodology.
Format:
0.50
0.50
elosssd1.txt elossmd1.txt elossed1.txt elosscd1.txt
elosssd2.txt elossmd2.txt elossed2.txt elosscd2.txt
with i indicating the number of different loss models reflecting the monetary loss in a predefined currency per square meters. Consequently, the sub-files elosssd(i).txt, elossmd(i).txt, elossed(i).txt
and elosscd(i).txt contain the economic information in order to compute economic (monetary) losses
due to slight, moderate, extensive and complete structural damage to a specific model building type
dependent on occupancy type. The quantities are given in the user-desired predefined currency.
Format of the sub-file elossxd(i).txt:
%oct W1
W2
S1 S2 S3 S4 S5 C1 C2 C3 PC1 PC2 RM1 RM2 URM MH LABEL
1 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 3.0 0.0 %RES1
2 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 0.0 %RES3
3 ...
where x can be one of: s (slight), m (moderate), e (extensive), and c (complete).
5.1.6
Input Files for the Calculation of Human Losses — Casualties
population.txt: Input file containing the population distribution in the studied area (compare also
with Table 13 for more detailed information). In case that the ‘Basic methodology’ is used to calculate
human losses only the numbers of total census tract population (2nd column) are necessary to provide.
Format:
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%GEOUNIT POP DRES NRES COMW INDW COMM GRADE COLLEGE HOTEL PRFIL VISIT
0102500001 4125 1701 3929 716 153 278 275 400 50 0.80 0.0
0102500002 7874 3004 7368 694 47 377 350 600 80 0.80 0.0
0102500003 6777 2510 6415 918 57 252 300 500
20 0.80 0.0
0102500004 6534 1879 6333 631 102 337 280 450 20 0.80 0.0
where POP is the total census tract population, DRES is the daytime residential population inferred from
census data, NRES is the nighttime residential population inferred from census data, COMW is the number
of people employed in the commercial sector, INDW is the number of people employed in the industrial
sector, COMM is the number of people commuting inferred from census data, GRADE is the number of
students in grade school (usually under 17 years old), COLLEGE is the number of students on college and
university campuses in the census tract (over 17 years old), HOTEL is the number of people staying in
hotels in the census tract. Furthermore, PRFIL is the factor representing the proportion of commuters
using automobiles inferred from profile of the community (0.60 for dense urban areas, 0.80 for less dense
urban or suburban areas and 0.85 for rural) where the default value is 0.80, and where, 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).
poptime.txt: Input file reflecting the population percentages (in decimal numbers) staying indoors
or outdoors dependent on the time of the day. This file is only needed if the human losses are going to
be computed using the ‘Basic methodology’.
Format:
%HOUR INDOOR OUTDOOR Label
1 0.99 0.01 %night 02:00 am
2 0.10
0.90 %day 10:00 am
3 0.15
0.85 %commuting 17:00 pm
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ocupmbtp.txt: Input file indicating the share of each model building type (MBT) and its occupancy
at the entire building stock. This file is only needed if the human losses are going to be computed using
the ‘Basic methodology’.
Format:
%mbt RES COM EDU Label
1 0.0042 0.0006 0.0 %C1M
2 0.1342 0.0081 0.0 %C2M
3 0.8042 0.0487 0.0 %C3M
4 0.0 0.0 0.0 %NONE
injury(i).txt: Input files containing the casualty rates of severity i in percentages (i = 1, 2, 3, 4)
for the different damage states (i = 1 slight, i = 2 moderate, i = 3 extensive, i = 4 complete or complete
with collapse). These files are only needed if the human losses are going to be computed using the ‘Basic
methodology’.
Format:
% Slight Moderate Extensive Complete CompleteCollapse Label
1 0.05 0.20 1.00 10 50 %W1
2 0.05 0.20 1.00 10 50 %W2
3 0.05 0.20 1.00 10 50 %S1L
...
collapserate.txt: Input files containing the percentage of collapsing buildings when they reach the
complete damage state according to each model building type. This file is only needed is human losses
are going to be computed using the ‘HAZUS methodology’.
Format:
%No COLLAPSE_RATE LABEL
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1 10.00 %C1M
2 10.00 %C2M
3 13.00 %C3M
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indcasrates.txt: Indoor casualty rate for slight damage. This file is only needed if the human losses
are going to be computed using the ‘HAZUS methodology’.
Format:
%No SEVERITY1 SEVERITY2 SEVERITY3 SEVERITY4 LABEL
1 0.05 0.00 0.00 0.00 %C1M
2 0.05 0.00 0.00 0.00 %C2M
3 0.05 0.00 0.00 0.00 %C3M
indcasratem.txt: Indoor casualty rate for moderate damage. This file is only needed if the human
losses are going to be computed using the ‘HAZUS methodology’.
Format:
1 0.25 0.030 0.00 0.00 %C1M
2 0.25 0.030 0.00 0.00 %C2M
3 0.20 0.025 0.00 0.00 %C3M
indcasratee.txt: Indoor casualty rate for extensive damage. This file is only needed if the human
Format:
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1 1.00 0.10 0.001 0.001 %C1M
2 1.00 0.10 0.001 0.001 %C2M
3 1.00 0.10 0.001 0.001 %C3M
indcasratec.txt: Indoor casualty rate for complete damage without collapse. This file is only needed
if the human losses are going to be computed using the ‘HAZUS methodology’.
Format:
1 5.00 1.00 0.01 0.01 %C1M
2 5.00 1.00 0.01 0.01 %C2M
3 5.00 1.00 0.01 0.01 %C3M
indcasratecc.txt: Indoor casualty rate for complete damage with collapse. This file is only needed
if the human losses are going to be computed using the ‘HAZUS methodology’.
Format:
1 40.00 20.00 5.00 10.00 %C1M
2 40.00 20.00 5.00 10.00 %C2M
3 40.00 20.00 5.00 10.00 %C3M
outcasratem.txt: Outdoor casualty rate for moderate damage. This file is only needed if the human
Format:
1 0.05 0.005 0.00 0.00 %C1M
2 0.05 0.005 0.00 0.00 %C2M
3 0.05 0.005 0.00 0.00 %C3M
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outcasratee.txt: Outdoor casualty rate for extensive damage. This file is only needed if the human
Format:
1 0.20 0.02 0.0002 0.0002 %C1M
2 0.20 0.02 0.0002 0.0002 %C2M
3 0.40 0.04 0.0004 0.0004 %C3M
outcasratec.txt: Outdoor casualty rate for complete damage. This file is only needed if the human
Format:
1 2.20 0.70 0.20 0.20 %C1M
2 2.20 0.70 0.20 0.20 %C2M
3 3.00 1.20 0.30 0.40 %C3M
occmbtp1.txt: Represents the distribution of population in each census tract and model building
type for RESIDENTIAL occupancy (percentage). The percentages of each line summed up have to be
1.0 (100%). This file is only needed if the human losses are going to be computed using the ‘HAZUS
methodology’.
Format:
%MBT C1M C2M C3M NONE RESIDENTIAL
0102500001 0.20 0.30 0.50 0
0102500002 0.00 0.00 1.00 0
0102500003 0.00 0.00 1.00 0
0102500004 0.00 0.40 0.60 0
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occmbtp2.txt: Represents the distribution of population in each census tract and model building type
for COMMERCIAL occupancy (percentage). The percentages of each line summed up have to be 1.0 (100%).
This file is only needed if the human losses are going to be computed using the ‘HAZUS methodology’.
Format:
%MBT C1M C2M C3M NONE COMMERCIAL
0102500001 0.25 0.25 0.50 0
0102500002 0.00 0.00 1.00 0
0102500003 0.00 0.00 1.00 0
0102500004 0.00 0.50 0.50 0
type for EDUCATIONAL occupancy (percentage). The percentages of each line summed up have to be
methodology’.
Format:
%MBT C1M C2M C3M NONE EDUCATIONAL
0102500001 0.00 0.00 0.00 0.00
0102500002 0.00 0.00 0.00 0.00
0102500003 0.00 0.00 0.00 0.00
0102500004 0.00 0.00 0.00 0.00
type for INDUSTRIAL occupancy (percentage). The percentages of each line summed up have to be
methodology’.
Format:
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%MBT C1M C2M C3M NONE INDUSTRIAL
0102500001 0.00 0.00 0.00 0.00
0102500002 0.00 0.00 0.00 0.00
0102500003 0.00 0.00 0.00 0.00
0102500004 0.00 0.00 0.00 0.00
occmbtp5.txt: Represents the distribution of population in each census tract and model building type
for HOTEL occupancy (percentage). The percentages of each line summed up have to be 1.0 (100%).
This file is only needed if the human losses are going to be computed using the ‘HAZUS methodology’.
Format:
%MBT C1M C2M C3M NONE HOTEL
0102500001 0.00 0.00 0.00 0.00
0102500002 0.00 0.00 0.00 0.00
0102500003 0.00 0.00 0.00 0.00
0102500004 0.00 0.00 0.00 0.00
5.1.7
Mandatory Input Files
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In addition to the input files described above in Section 5.1 there are a number of additional input files
which are required in order to run SELENA which need to be located in the same folder as the other
input files. These files are described in this section.
header.txt: a file providing the necessary header data in order to create the damage output files
(which then, for example, can be plotted with ArcView). The first four columns in the header.txt file
(GEOUNIT, lon, lat, and soil) remain always the same. All other columns standing for the damage
extent of each model building type can be modified or extended subject to the number of considered
model building types. Note that the number of additional columns has to be always a multiple of 5 (here:
15 model building types × 5 damage states = 75 additional columns in the header). If, e.g., a new model
building type called NB is to be considered, then five columns have to be added in the header: NBN, NBS,
NBM, NBE, NBC (for the damage states: Nnone, Sslight, Mmedian, Eextensive and Ccomplete). Finally, the
last label NUMB stands for a column with an order number.
Format:
%GEOUNIT Lat
Lon
Soil W1N
W1S
W1M
W1E
W1C ...
where GEOUNIT is the label for the identification of the geographical unit, Lat is the label for the geographical coordinates (degree of latitude), Lon is the label for the geographical coordinates (degree of
longitude), Soil is the label for the for the soil type in each geographical unit, and Numb is the order
number.
The herein predefined model building types are those given in HAZUS. More details on these types
including ranges of typical building heights and number of stories are given in Appendix A, Table 19.
headerocc.txt: file providing the necessary header for the input files ocupmbt(i).txt allocating the
built area (in square meters) according to their occupancy in each geographical unit for the different
model building types i.
Format:
%GEOUNIT RES1 RES3 RES4 RES5 COM1 COM2 ...
The herein predefined occupancy classes are those given in HAZUS. A more detailed description of
these classes is given in Appendix A, Table 20.
headermdr.txt: file providing the necessary header for the output files mdr(i).txt and mdrtot(i).txt
for allocating the mean damage ratio computations i.
Format:
%GEOUNIT MDRT W1
W2
S1L
S1M
S2L ...
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builtarea.txt: input file containing the total built area of each model building type (in square
meters) for each geographical unit. This type of input file can be easily obtained through the databases
provided by the local agencies using MS Access, Matlab, or Octave. This file is only needed if risk
scenarios are going to be computed in terms of damaged built area with economic losses.
Format:
%GEOUNIT W1
W2
S1L S1M S2L ...
0100100001 8964 0.0 0.0 0.0 0.0 ...
0100100002 5549 0.0 0.0 0.0 0.0 ...
...
where GEOUNIT is the census tract identifier (has to be always in the same order), W1... is the built
area information for each of the model building types (if more building types are included then more
columns have to be added) NONE is the built area which can not be assigned to any of the model building
typesbecause of the lack of information.
Note: The NONE ‘building type area’ is excluded from the computations (since it covers the area of
all unknown model building types). This means that if a large percentage of the building mass is of
unknown building type, then all cumulative end-results will be wrong due to the fact that a large part
of the building mass is excluded from the computations. Anyway, if the input file builtarea.txt is
modified e.g. by adding or removing model building types, the column NONE always has to remain. If
there are no ‘unknown’ buildings, then a 0 has to be inserted in column NONE.
DR
numbuild.txt: input file containing the total number of buildings of each model building type for
each geographical unit. This type of input file can be easily obtained through the databases provided by
the local agencies using MS Access, Matlab, or Octave. This file is only needed if risk scenarios are going
to be computed in terms of damaged number of buildings without economic losses.
Format:
%GEOUNIT
W1
0100100001 10
33
0
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01001...
W2
S1L S1M S2L ...
0 0 0 0 0
...
where GEOUNIT is the census tract identifier (has to be always in the same order), W1... is the
number of buildings for each one of the model building types (if more building types are included then
more columns have to be added) NONE is the number of buildings which can not be assigned to any of
the model building types because of the lack of information.
Note: Input files builtarea.txt and numbuild.txt are not needed at the same time if only one of the
damage results is desired.
ocupmbtj.txt: input files containing the built area (in square meters) according to their occupancy
in each geographical unit for the different model building types i. They are needed for the computation
of economic losses.
Format:
%GEOUNIT RES1 RES3 RES4 RES5 COM1 ...
0100100001 130.000 690.000 0.000 0.000 0.000 ...
0.000 0.000 0.000 20.000 0.000 0.000 0.000 ...
0.000 0.000 7454.000 0.000 350.000 320.000
...
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Mean Damage Ratio Computation
According to FEMA (2003) [2] a useful parameter in order to be able to compare the risk estimation for
the different geounits within a city or between different cities or countries is named the mean damage
ratio (MDR); the MDR is defined the cost ratio corresponding to each damage state expressed as a ratio
of the cost of new construction.
The MDR computation needs to read a definition of the damage ratio (DR). This information is given
in the input file named newconstruction.txt which has the following format:
%NO C3L C3M C3H RM2L RM2M S1M S5L URML PDC CC LABEL
1 770.00 733.92 693.00 770.00 733.92 694.89 660.00 611.60 990.00 805.20 %RES
2 895.27 853.30 805.75 895.27 853.30 807.95 709.50 657.47 1064.25 865.59 %COM
3 699.59 666.80 629.63 699.59 666.80 631.36 524.95 486.45 787.44 640.44 %IND
4 1375.04 1310.58 1237.53 1375.03 1310.58 1240.92 1031.79 956.12 1547.70 1258.80 %REL
5 987.80 941.50 889.02 987.80 941.50 891.45 741.22 686.85 1111.84 904.29 %GOV
6 987.80 941.50 889.02 987.80 941.50 891.45 741.22 686.85 1111.84 904.29 %EDU
7 1023.00 975.05 920.70 1023.00 975.05 923.22 767.64 711.33 1151.46 936.51 %HOTEL
Several MDRs can be defined, and here, the following definitions are used:
MDR for each model building type and for each geounit : This factor can be computed using
the following formula
MDRki =
k
k
k
k
k
k
DRkS NSi
+ DRkM NM
i + DRE NEi + DRC NCi
k
NT i
(59)
DR
where DRk j is the damage ratio of the model building type, k, corresponding the damage state,
j, where j=S for slight, M for moderate, E for extensive and C for complete. Nji k is the damaged
built area corresponding to the damage state j (S,M,E,C) for the model building type, k at the
ith geounit. NTi k is the total built area corresponding to the kth model building type at the ith
geounit.
MDR for each geounit and all model building types :
Pmbt
k
k
k
k
k
k
(DRkS NSi
+ DRkM NM
i + DRE NEi + DRC NCi )
MDRi = k=1
NT i
(60)
where DRkj : is the damage ratio of the model building type k corresponding the damage state j
where j =S for slight, M for moderate, E for extensive and C for complete. Nji k : is the damaged built
area corresponding to the damage state j (S,M,E,C) for the model building type k at the geounit
i. NTi :is the total built area at the geounit i. for all the model building types i = 1, . . . , mbt.
MDR for each model building type and all geounits :
Pgeounit
k
k
k
k
k
k
(DRkS NSi
+ DRkM NM
i + DRE NEi + DRC NCi )
MDRk = i=1
k
NT
(61)
where DRk j : is the damage ratio of the model building type k corresponding the damage state j
where j=S for slight, M for moderate, E for extensive and C for complete. Nji k : is the damaged
built area corresponding to the damage state j (S,M,E,C) for the model building type k at the
geounit i. Nk T :is the total built area for the model building type k and added to all the geounits
i = 1, . . . , geounits.
MDR for all model building type and all geounits :
Pgeounit Pmbt
k
k
k
k
k
k
k
k
k=1 (DRS NSi + DRM NM i + DRE NEi + DRC NCi )
MDR = i=1
NT
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where DRkj : is the damage ratio of the model building type k corresponding the damage state j
where j =S for slight, M for moderate, E for extensive and C for complete. Nji k : is the damaged
built area corresponding to the damage state j (S,M,E,C) for the model building type k at the
geounit i. NT :is the total built area for all the model building types and for all the geounits.
5.2.1
Median Values and Confidence Levels
Similarly to the other SELENA results, data from the mdri.txt files will be used to obtain the expected value and confidence values (based on a normal distribution assumption) given in the output files
mdrmedian.txt, mdr16prctile.txt, mdr84prctile.txt, respectively, Also, expected value and confidence values, based on data in the mdrtoti.txt files is given in the output files mdrtotmedian.txt,
mdrtot16prctile.txt, and mdrtot84prctile.txt, respectively.
5.3
The SELENA Program Sequence
In Figure 16 a flowchart of the SELENA is shown. As noted above, SELENA can be used as a stand-alone
application, from Matlab, or from Octave. The stand-alone and Octave versions currently only has a
comand line interface, wheras, the Matlab version both have a simple graphical user interface (GUI) and
a command line interface; the Matlab SELENA GUI is only used for selecting input files. The different
interfaces are discribed in Sections 5.3.1, 5.3.2, and 5.3.3, below.
Also, the MDR computation will be performed only if SELENA can find the newcontruction.txt
file in the input file folder.
5.3.1
The Stand-alone SELENA Application
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To use the stand-alone version you first need to at it the the path (or use the full path to the binary)
then start a start a shell (csh, bash, Windows cmd etc. and type
$ selena -p (or selena --probabilistic)
for probabilistic analysis,
$ selena -d (or selena --deterministic)
for deterministic analysis, or
$ selena -r (or selena --realtime)
for “real-time” (based on aquired real data) analysis. The stand-alone biniary expects that it can find
the input files for respective analysis method as described in Section 5.1.
5.3.2
The Matlab and Octave Command-line Interface
The command-line interface for Matlab/Octave is similar to the stand-alone version. Type
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Figure 16: Flowchart of SELENA.
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$ selena(’p’); [or selena(’probabilistic)’;]
for probabilistic analysis,
$ selena(’d’); [or selena(’deterministic’);]
for deterministic analysis, or
$ selena(’r’) [or selena(’realtime);]
for real-time analysis. Also here it is expected that the input files, described in Section 5.1, can be found.
5.3.3
The Matlab Graphical User Interface
After having started Matlab, the user has to switch with the Matlab environment to the folder where the
input files are located. After prompting
>> selena_gui
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the main menu window, shown in Figure 17, will appear where the user can choose whether to carry out
a probabilistic analysis, a deterministic analysis or an analysis based on “real-time” (aquired real) data
by clicking the corresponding button.
By choosing one of the three possibilities, either the logic tree scheme window for the probabilistic
analysis (Figure 18), the deterministic analysis (Figure 19) or the analysis with real-time data (Figure 20)
is opened. By clicking onto the single buttons, the user will be requested to specify the single input files
as defined in Section 5.1). After defining the five respectively six different input files the user needs to
click onto the Run Analysis button in order to launch the analysis process.
The computation time basically depends on the size of the studied region (number of geographical
units GEOUNIT), the details of the building information [the number of model building types (MBT) and
the number of building occupancy types (OCT)], and the number of branches used in the logic tree
methodology.
5.4
Dealing with Uncertainties
Currently, SELENA computes median values as well as 16% and 84% fractiles of the risk results. This to
be done by means of a logic tree methodology in which the different branches of the tree can be weighted
so that at the end of the computation, the risk results are multiplied by their corresponding weights and
then are fitted to a normal distribution in order to get the median values as well as the fractiles. The
single branches of the logic tree (Figure 21) currently represent uncertainties in:
• earthquake source, attenuation relationship, soil type, vulnerability curves and economic values of
damaged built area in case of a deterministic analysis, or
• ground shaking probabilistic maps, soil type, vulnerability curves and economic values of damaged
built area in case of a probabilistic analysis.
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Figure 17: Main menu of the SELENA Matlab graphical user interface.
Figure 18: Logic tree scheme windows and requested input files for the probabilistic analysis.
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Figure 19: Logic tree scheme windows and requested input files for the deterministic analysis.
Figure 20: Logic tree scheme windows and requested input files for the real-time data analysis.
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!
"#
!
"
$%
%&!
!
Figure 21: Logic tree structure. Each branch will be weighted in order to compute the expected values
and confidence levels.
Output Files
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5.5
5.5.1
Overview
All output files being generated during the analysis will be written in the sub-folder output. Table 18
lists and describes these output files.
5.5.2
Format of the Output Files
gmotionsceni.txt: Output files for each logic tree branch i which contain the respective ground-motion
ordinates in the geographical units (GEOUNITS) without (rock) and with (soil) soil amplification as well
as the soil amplification factors (AF) according to the applied earthquake code.
Format:
Column:
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th 11th 12th 13th
%GEOUNIT Lat Lon Soil PGA
(rock) Sa_0.3
(rock) Sa_1.0
(rock) AF
PGA AF
Sa_0.3 AF
Sa_1.0 PGA
(soil) Sa_0.3
(soil) Sa_1.0
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Output file
gmotionsceni.txt
douti.txt
sqmctdouti.txt
nobctdouti.txt
16prctilect.txt**
medianct.txt**
84prctilect.txt**
eclossesi.txt
Description
files containing ground-motion ordinates
with/without soil amplification,
and amplification factors
damage probability for each branch of
the logic tree (number of the file i)
damage results corresp. to the branch
of the logic tree (number of the file i)
16% fractiles of damage
mean value (median) of damage
84% fractiles of damage
results corresponding to the branch of
containing the economic losses
16% fractiles of economic loss
mean value of economic loss
84% fractiles of economic loss
results corresponding to the branch of
containing the human casualties
16% fractiles of injured persons
mean value of injured persons
mean value of injured persons
weight of the damage results (excluding
the branches of economic losses)
final weight of the economic results (including
all possible branches)
DR
loss16prctile.txt
lossmedian.txt
loss84prctile.txt
totalinjuri.txt
hlbyinjuri.txt
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hlbyinjur16pr.txt
hlbyinjurmean.txt
hlbyinjur84pr.txt
totalinjur16.txt
totalinjurmean.txt
totalinjur84.txt
ltreewgth.txt
endwgth.txt
User-requested output type*
damaged area damaged buildings
Sas and Sal [g],
Sasi and SAli [g],
FA and FV
probabilities
[m2 ]
–
–
numbers
[m2 ]
numbers
economic loss in user-defined
currency (e.g. US-$, e, NOK)
economic loss in user-defined
currency (e.g. US-$, e, NOK)
injured persons (cumulative)
injured persons (disaggregated
by injury type)
number of injured persons
(disaggregated by injury type)
cumulative number of injured
persons (from slight to dead)
weights
weights
Table 18: Description of output files and units of results dependent on user-requested output type.
*output type is decided in the input file cpfile.txt. **some columns may carry the term ‘-1’ which
indicates that no inventory data for this respective building type was available in order to compute
damage; the term ‘0’ would mean that no building or square meters of this building type will undergo
this particular damage state.
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(soil)
102500003 59.921 10.660 5 0.2050 0.4298 0.1194 2.5 1.7 3.2 0.5125 0.7307 0.3821
102500004 ... ...
Units: All ground-motion ordinates (PGA, spectral accelerations) are provided in [g]-units.
douti.txt: Output files for each logic tree branch i carrying the damage probabilities of each model
building type for the five different damage grades (no, slight, moderate, extensive, complete). The file is
structured according to background file header.txt.
Format:
Column:
1st 2nd 3rd 4th 5th 6th 7th 8th 9th ... last
%GEOUNIT Lat Lon Soil C1MN C1MS C1MM C1ME C1MC ... NUMB
102500001 59.933 10.682 2 0.1446 0.2020 0.4657 0.1282 0.0595 ... 1
102500002 ... ...
where GEOUNIT is the label for the identification of the geographical unit, Lat is the label for the geographical coordinates (degree of latitude), Lon is the label for the geographical coordinates (degree of
longitude), Soil is the soil type according to the chosen soil classification scheme, C1MN is the damage
probability of model building type C1M for state ‘no damage’, C1MS is the damage probability of model
building type C1M for state ‘slight damage’, C1MM is the damage probability of model building type C1M
for state ‘moderate damage’, C1ME is the damage probability of model building type C1M for state ‘extensive damage’, C1MC is the damage probability of model building type C1M for state ‘complete damage’,
and NUMB is the order number. Units: Damage probabilities are given in decimal numbers with four
decimal places (e.g., 0.1446).
DR
Note: the summed up damage probabilities for one model building type must yield to 1.
sqmctdouti.txt respectively nobctdouti.txt: Output files for each logic tree branch i containing the
damage results (either damaged building area or number of damaged buildings) of each model building
type for the five different damage grades (no, slight, moderate, extensive, complete). The file is structured
according to background file header.txt.
Format (e.g., sqmctdouti.txt):
Column:
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th last
102500001 59.933 10.682 2 40.63 56.76 130.86 36.02 16.72 ... 1
102500002 ... ...
Units: damage results are either given in square meters (sqmctdouti.txt) or number of buildings
(nobctdouti.txt).
medianct.txt , 16prctilect.txt, and 84prctilect.txt: Output files with total damage results
after statistical analysis of the logic tree branches (mean value, mean value standard deviation). Dependent on the type of output results chosen, the output files either contain damaged building area or
number of damaged buildings of each model building type for the five different damage grades (no, slight,
moderate, extensive, complete). The file is structured according to background file header.txt.
Format (here in dependence on square meters):
Column:
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th last
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102500001 59.933 10.682 2 92 63 100 17 9 ... 1
102500002 ... ...
Units: damage results are either given in square meters (m2 ) or number of buildings.
eclossesi.txt: Output files for each logic tree branch i containing the total economic loss (in a
user-defined currency) in each geographical unit.
Format:
Column:
1st 2nd
%GEOUNIT EURO
102500001 179118.4
102500002 469430.2
102500003 ...
Units: economic losses are given in the user-defined currency [here: Euro (e)].
lossmedian.txt, loss16prctile.txt, and loss84prctile.txt: Output files with total economic
losses after statistical analysis of the logic tree branches (mean value, mean value standard deviation) in
each geographical unit.
Format:
DR
Column:
1st 2nd 3rd
%GEOUNIT EURO Order
102500001 517265.729 1
102500002 245537.129 2
102500003 ... ...
Units: economic losses are given in the user-defined currency [here: Euro (e)].
totalinjuri.txt: Output files for each logic tree branch i with cumulative numbers of human losses
(from slightly injured to dead) for the three different daytime scenarios in each geographical unit.
Format:
Column:
1st 2nd 3rd 4th
%GEOUNIT INJUR_2:00 INJUR_10:00 INJUR_17:00
102500001 5.0 0.5 0.8
102500002 9.6 1.0 1.5
102500003 8.3 ... ...
Units: human losses are given in numbers of casualties (injured or dead persons).
hlbyinjuri.txt: Output files for each logic tree branch i with distinct numbers of human losses
(from slightly injured to dead) for the three different daytime scenarios in each geographical unit.
Format:
Column:
%GEOUNIT INJUR
LOW_
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2:00 INJUR
LOW_
10:00 INJURLOW_
17:00 INJUR
MED_
2:00 INJUR
MED_
10:00 INJUR
MED_
17:00 INJUR
HEAV_
2:00 INJUR
HEAV_
10:00 INJUR
HEAV_
7:00 INJURV
DEATH_
2:00 INJURV
DEATH_
10:00 INJURV
DEATH_
17:00
102500001 3.0 0.3 0.5 1.2 0.1 0.2 0.4 0.0 0.1 0.4 0.0 0.1
102500002 ... ...
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hlbyinjurmean.txt, hlbyinjur16pr.txt, and hlbyinjur84pr.txt: Output files with numbers of
human losses (from slightly injured to dead) for the three different daytime scenarios after statistical
analysis of the logic tree branches (mean value, mean value standard deviation) in each geographical
unit.
Format:
Column:
%GEOUNIT INJUR
LOW_
2:00 INJUR
LOW_
10:00 INJURLOW_
17:00 INJUR
MED_
2:00 INJUR
MED_
10:00 INJUR
MED_
17:00 INJUR
HEAV_
2:00 INJUR
HEAV_
10:00 INJUR
HEAV_
7:00 INJURV
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DEATH_
2:00 INJURV
DEATH_
1 0:00 INJURV
DEATH_
17:00
102500001 15.6 1.6 2.4 1.6 2.4 8.1 2.4 8.1 0.8 8.1 0.8 1.2
102500002 ... ...
totalinjurmean.txt, totalinjur16.txt, and totalinjur84.txt: Output files with cumulative
numbers of human losses (from slightly injured to dead) for the three different daytime scenarios after
statistical analysis of the logic tree branches (mean value, mean value standard deviation) in each
geographical unit.
Format:
Column:
1st 2nd 3rd 4th
%GEOUNIT INJUR_2:00 INJUR_10:00 INJUR_17:00
102500001 30.8 3.1 4.6
102500002 58.7 5.9 8.9
102500003 50.5 5.1 ...
Mean Damage Ratio Output Files
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5.5.3
For the damage ratio (MDR) computation there will be a file mdri.txt for each branch, i, of the logic
tree (see Section 5.2). These files will contain the results of MDR for each model building type and for
each geounit and the second column of the output file will contain the MDR for each geounit and all
model building types.
Format:
%GEOUNIT MDR C3L C3M C3H RM2L RM2M S1M S5L URML PDC CC
101 0.19218600 0.28462806 0.52991545 -1 0.05215911 0.27170182 -1 -1 -1 -1 0.05066373
102 0.29652423 0.38219628 0.52629182 0.63284273 0.05155185 0.25478273 -1 -1 0.13397214 ...
104 0.39414670 0.39333182 0.53828636 -1 0.05332634 0.30766455 -1 -1 -1 0.04183736 ...
105 0.10640911 0.37688768 0.52042182 -1 0.05079273 0.22691088 -1 -1 0.13015636 -1 0.04914456
106 0.33274322 0.38893441 0.53353182 -1 0.05260550 0.28760177 -1 0.35689455 -1 0.04127933 ...
107 0.35963197 0.39865541 0.54384000 -1 0.05418364 0.33119364 0.45359613 -1 0.14599178 ...
108 0.37836659 0.39362086 0.53862544 0.64316636 0.05343548 0.30881818 -1 -1 0.14218388 -1 ...
When -1s are found in these output files it means that no built area of the corresponding model
building type exists so the MDR can not be computed.
There will be a mdrtoti.txt file for each branch, i, of the logic tree. This file will contain the MDR
results for all model building types and all geounits and for each geounit; the second column of the output
file will contain the MDR for all model building type and all geounits.
Format:
%GEOUNIT MDR C3L C3M C3H RM2L RM2M S1M S5L URML PDC CC
1 0.32518213 0.38878658 0.53521644 0.63821245 0.05231050 0.29422597 ...
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Examples
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ELENA comes with one set of example input files (for Bucharest) which are located the examples
folder.
6.1
The Bucharest Example
DR
The Bucharest example is for an earthquake at long 26.76 lat 45.77 (see Figure 22). There are 6 geographical units and ?? building types.
Figure 22: Map (from http://www.openstreetmap.org) of location of the geounits (red markers) and
the earthquake (red asterisk) for the Bucharest example.
The earthquake.txt file specifies the 10 parameters for each earthquake scenarios (magnitude, location, etc.):
0.12
0.16
0.12
0.09
0.12
0.09
0.09
0.12
0.09
45.77
45.77
45.77
45.77
45.77
45.77
45.77
45.77
45.77
26.76
26.76
26.76
26.76
26.76
26.76
26.76
26.76
26.76
60.00
90.00
180.00
60.00
90.00
180.00
60.00
90.00
180.00
7.40
7.40
7.40
7.30
7.30
7.30
7.20
7.20
7.20
7.40
7.40
7.40
7.30
7.30
7.30
7.20
7.20
7.20
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
45.00
90.00
90.00
90.00
90.00
90.00
90.00
90.00
90.00
90.00
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
For this example there are 9 earthquake scenarios (for various depths) and the probabilies (“weights”)
for each scenario is given in the first column. The depths . . .
6.2
Determistic Data
Nothing here yet. . .
62
6.3
Probabilistic Data
6.4
Realtime Data
7
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Plotting results in Geographic Information Systems (GIS)
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INCE most of the SELENA results are provided in ‘geo-referenced’ output files, the illustration in a
Geographic Information System is recommended. This of course can be also done with those input or
inventory files whose data is connected to the geographical units (geounit) or the geographical coordinates
of its respective center (centroid).
DR
In the following it is briefly described how the GIS package ArcView [1] can be applied to plot the
damage and loss results derived by SELENA. SELENA’s output files have been prepared such that they
can be easily imported into a spreadsheet (MS Excel, OpenOffice, etc.) in terms of a delimited format
with tab and comma or space as delimiters. The user can then use the spreadsheet program to sum
all columns with moderate damage (for example) and get a column with moderate damage for all the
building types or sum all columns with moderate, extensive and complete damage obtaining a column
with at least moderate damage for all the building types. In the sum the user has to be carefully with
the dummy value of ‘1’ in some cells, so we suggest to change this dummy value to 0 before summing
up. Finally, the files to be plotted in ArcView must be exported to *.dbf (Dbase 4) formatted files and
they must contain at least the following columns:
% GEOUNIT LONGI
LATI other-columns-to-be-plotted NUMB
The user can run ArcView, create a new project, add a new view, include a theme in the view (e.g.,
with the Oslo census tracts) and add a table (the *.dbf file which is going to be plotted). The user must
then click into the view window, in THEME+TABLE in order to open the main table e.g., of the Oslo census
tracts. Now, it is possible in the table window to see two different tables (Attributes of. . . , which is
the main table, and output.dbf which is the output file going to be plotted). Both tables should have a
common column (maybe with different headers but with the same data structure, e.g., GEOUNIT or NUMB.
Then, the user has to click first in the common column of output.dbf (make a click in the header of
the column) and then in the common column of Attributes of . . . (also in the header of the column). In
that way it is possible to go to ‘Join both tables’ using (CTRL+J), and the theme which is currently in
the view window will contain all the information of the output results. The user can then make a click in
THEME+EDIT LEGEND and choose a Legend Type: Graduated Color and as Classification Field the column
which is going to be plotted. Then, the user can make a click in START EDITING and SAVE the EDITS AS
a new theme file which will be added to the view. Then the process can be repeated for other columns
keeping always the original theme without changes. The same methodology of plotting can be used to
plot results from ground motion.
8
Known Issues
• The MADRS C-function produces a slightly different result compared to the corresponding m-code
for very large amplitudes. This is due to numerical issues when there is an infinite gradient in the
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Sa-Sd curve for such input files. Note that the m-file version is not necessarily more accurate than
the C-version.
• On Windows platforms the MEX-files can not be aborted by pressing CTRL-C since Windows lacks
real asynchronous signals, see: http://www.mathworks.com/support/solutions/data/1-188VX.html
Therefore, when CTRL-C is pressed, using Windows, the operation is interrupted after the MEX-file
has finished.
• All input (*.txt) files must end with a carrage return (CR), otherwise the stand-alone (command
line and GUI) versions of SELENA will crash.
9
Summary
T
DR
HE herein described software tool SELENA can be used to provide damage results, economic and
human losses for the general building stock and population of a city or country on the level of
minimum geographical units (geounit or census tracts). The level of resolution of the damage and loss
predictions basically depends on the size of the geographical units which can be defined by the user. The
code has been developed such that the user can introduce most of the needed inputs using a simple text
editor independ of which computer platform that is used. The Matlab/Octave-code, the C-code, and the
ASCII input files are fully transparent allowing the user to apply own modifications and adjustments.
Furthermore, it was an aim to include as many comments as possible into the code such that the user
can go through the lines and easily change them when necessary. It should be noticed that the presented
tool for seismic risk and loss assessment, SELENA, is an ongoing development and thus will undergo
a number of changes and extensions. Consequently, the authors depend on the users’ feedback and
suggestions which are very much appreciated.
Acknowledgments
T
HIS work has been developed thanks to the agreement between NORSAR and the University of
Alicante under the umbrella of the International Centre for Geohazards (ICG) [54]. The funding
through the SAFER [55] project and through ICG has facilitated major developments of SELENA from
its first version in 2004.
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DR
[47] Prestandard and commentary for the seismic rehabilitation of buildings. Technical report, Federal
Emergency Management Agency (FEMA), Washington DC, 2000. FEMA 356.
[48] Improvement of nonlinear static seismic analysis procedures. Technical report, Applied Technology
Council (ATC, California, USA, 2005. FEMA-440.
[49] N.M. Newmark and W.J. Hall. Earthquake spectra and design. Technical report, Earthquake
Engineering Research Institute (EERI), Oakland, CA: EERI, 1982.
[50] Earthquake Loss Estimation Methodology: User’s Manual. Federal Emergency Management Agency,
Washington DC, USA.
[51] Earthquake damage evaluation data for california. Technical report, Applied Technology Council
(ATC), Redwood City, California, 1985. Report ATC-13.
[52] A. Coburn and R. Spence. Earthquake Protection. J. Wiley and Sons Ltd, 2002.
[53] P. Stojanovski and W. Dong. Simulation model for earthquake casualty estimation. In Proc. Fifth
U.S. National Conference on Earthquake Engineering, Paper No. 00592, Chicago, Illinois, July 10–
14, 1994.
[54] http://www.geohazards.no/.
[55] http://www.saferproject.net/.
67
A
A TABLES
Tables
AF
T
Selena
Index
mean value (mv) mv+σ
Author(s) (year)
DR
Boore et al. [11], Boore et al. [12],
Boore et al. [13]
Toro et al. [15]
Campbell and Bozorgnia [16], Campbell [17]
Campbell and Bozorgnia [18]
Abrahamson and Silva [19]
Sabetta and Pugliese [20]
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 McGuireciteCrouse1996
Gülkan and Kalkan [35]
Lussou et al. [36]
Dahle et al. [37]
Bommer et al. [38]
Marmureanu et al.; *
for hypocentral distance, Eq. (17) in [39]
Marmureanu et al.; *
for epicentral distance, Eq. (3) in [39]
mv−σ
01
04
07
10
13
16
19
22
25
28
31
34
37
40
43
46
02
05
08
11
14
17
20
23
26
29
32
35
38
41
44
47
03
06
09
12
15
18
21
24
27
30
33
36
39
42
45
48
49
52
55
58
61
64
67
50
53
56
59
62
65
68
51
54
57
60
63
66
69
77
78
79
80
81
82
Table 19: Empirical ground-motion prediction equations which are implemented in the current SELENAversion. *Note: prediction equations for spectral accelerations, Sa, are not provided.
68
A TABLES
AF
T
Selena
No.
Label
Description
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
W1
W2
S1L
S1M
S1H
S2L
S2M
S2H
S3
S4L
S4M
S4H
S5L
S5M
S5H
C1L
C1M
C1H
C2L
C2M
C2H
C3L
Wood, Light Frame (≤ 5,000 sq.ft. / 465 m2 )
Wood, Commercial and Industrial (> 5,000 sq.ft. / 465 m2 )
Steel Moment Frame
23
24
25
26
C3M
C3H
PC1
PC2L
27
28
29
PC2M
PC2H
RM1L
30
31
RM1M
RM2L
32
33
34
35
36
RM2M
RM2H
URML
URMM
MH
Steel Braced Frame
Steel Light Frame
Steel Frame with Cast-in-Place Concrete Shear Walls
Steel Frame with Unreinforced Masonry Infill Walls
Concrete Moment Frame
Concrete Shear Walls
DR
Concrete Frame with Unreinforced
Masonry Infill Walls
Pre-cast Concrete Tilt-Up Walls
Pre-cast Concrete Frames
with Concrete Shear Walls
Reinforced Masonry Bearing Walls
with Wood or Metal Deck Diaphragms
Reinforced Masonry Bearing Walls
with Pre-cast Concrete Diaphragms
Unreinforced Masonry Bearing Walls
Mobile Homes
Table 20: Model building types as defined by HAZUS.
69
Height
range
typical
name
stories stories ft.
–
all
1
14
–
all
2
24
Low-Rise
1–3
2
24
Mid-Rise
4-7
5
60
High-Rise
8+
13
156
Low-Rise
1-3
2
24
Mid-Rise
4–7
5
60
High-Rise
8+
13
156
–
all
1
15
Low-Rise
1-3
2
24
Mid-Rise
4-7
5
60
High-Rise
8+
13
156
Low-Rise
1-3
2
24
Mid-Rise
4-7
5
60
High-Rise
8+
13
156
Low-Rise
1-3
2
20
Mid-Rise
4–7
5
50
High-Rise
8+
12
120
Low-Rise
1-3
2
20
Mid-Rise
4–7
5
60
High-Rise
8+
12
120
Low-Rise
Mid-Rise
High-Rise
–
1-3
4–7
8+
all
2
5
12
1
20
50
120
15
Low-Rise
Mid-Rise
High-Rise
1-3
4–7
8+
2
5
12
20
50
120
Low-Rise
Mid-Rise
1-3
4+
2
5
20
50
Low-Rise
Mid-Rise
High-Rise
Low-Rise
Mid-Rise
–
1-3
4–7
8+
1–2
3+
all
2
5
12
1
3
1
20
50
120
15
39
12
A TABLES
AF
T
Selena
DR
No. Label
Occupancy class
Residential:
1
RES1
single family dwelling
2
RES2
mobile home
3
RES3
multi family dwelling
4
RES4
temporary lodging
5
RES5
institutional dormitory
6
RES6
nursing home
Commercial:
7
COM1
retail trade
8
COM2
wholesale trade
9
COM3
personal and repair service
10
COM4
professional/technical services
11
COM5
banks/financial institutions
12
COM6
hospital
13
COM7
medical office/clinics
14
COM8
entertainment and recreation
15
COM9
theatres
16
COM10 parking
Industrial:
17
IND1
heavy
18
IND2
light
19
IND4
food/drug/chemicals
20
IND3
metals/mineral processing
21
IND5
high technology
22
IND6
construction
Agriculture:
23
AGR
agriculture
Religion/Non-Profit:
24
REL
church
Government:
25
GOV1
general services
26
GOV2
emergency response
Education:
27
EDU1
schools/libraries
28
EDU2
universities/colleges
Description
detached house
mobile home
apartment/condominium
hotel/motel
group housing (military, college), jails
store
warehouse
service station/shop
offices
office
restaurants/bars
theatres
garage
factory
factory
factory
factory
factory
office
office
police/fire station
does not include group housing
Table 21: Occupancy types as defined in HAZUS.
70
mbt
dy (ord.) [m]
[m]
0.0061
0.0041
0.0038
0.0112
0.0295
0.0041
0.0155
0.0493
0.0041
0.0025
0.0069
0.0221
0.0030
0.0086
0.0277
0.0025
0.0074
0.0127
0.0030
0.0066
0.0188
0.0030
0.0066
0.0188
0.0046
0.0030
0.0066
0.0188
0.0041
0.0089
0.0041
0.0089
0.0249
0.0061
0.0069
0.0046
ay (ord.)
[m/s2 ]
1.9620
0.9810
0.6082
0.3826
0.2354
0.9810
0.8142
0.6180
0.9810
0.7848
0.6573
0.5003
0.9810
0.8142
0.6180
0.6082
0.5101
0.2354
0.9810
0.8142
0.6180
0.9810
0.8142
0.6180
1.4715
0.9810
0.8142
0.6180
1.3047
1.0889
1.3047
1.0889
0.8339
1.9620
1.0889
1.4715
du (ord.)
[m]
0.1097
0.0597
0.0699
0.1354
0.2662
0.0478
0.1232
0.2951
0.0478
0.0330
0.0625
0.1494
0.0305
0.0577
0.1384
0.0447
0.0879
0.1148
0.0457
0.0660
0.1400
0.0343
0.0495
0.1049
0.0549
0.0366
0.0528
0.1120
0.0488
0.0704
0.0488
0.0704
0.1494
0.0610
0.0460
0.0549
au (ord.)
[m/s2 ]
5.8860
2.4525
1.8345
1.1478
0.7161
1.9620
1.6383
1.2459
1.9620
1.7658
1.4715
1.1183
1.9620
1.6383
1.2459
1.8345
1.5304
0.7161
2.4525
2.0405
1.5598
2.2073
1.8443
1.4028
2.9430
1.9620
1.6383
1.2459
2.6193
2.1778
2.6193
2.1778
1.6579
3.9240
2.1778
2.9430
de (ord.)
[m]
0.0043
0.0028
0.0027
0.0078
0.0206
0.0028
0.0108
0.0345
0.0028
0.0018
0.0048
0.0155
0.0021
0.0060
0.0194
0.0018
0.0052
0.0089
0.0021
0.0046
0.0132
0.0021
0.0046
0.0132
0.0032
0.0021
0.0046
0.0132
0.0028
0.0062
0.0028
0.0062
0.0174
0.0043
0.0048
0.0032
DR
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
A TABLES
AF
T
Selena
k
(ord/sh)
0.5
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.6
k
(ord/md)
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.3
k
ord(lg)
0.1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0.1
be
fraction
pre-code
15
10
5
5
5
5
5
5
7
7
7
7
10
10
10
7
7
7
7
7
7
10
10
10
7
7
7
7
10
10
7
7
7
10
10
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
W1
W2
S1L
S1M
S1H
S2L
S2M
S2H
S3
S4L
S4M
S4H
S5L
S5M
S5H
C1L
C1M
C1H
C2L
C2M
C2H
C3L
C3M
C3H
PC1
PC2L
PC2M
PC2H
RM1L
RM1M
RM2L
RM2M
RM2H
URML
URMM
MH
Table 22: Parameters of capacity curves as provided by HAZUS for Pre-code seismic design.
71
mbt
dy (ord.) [m]
[m]
0.0061
0.0041
0.0038
0.0112
0.0295
0.0041
0.0155
0.0493
0.0041
0.0025
0.0069
0.0221
0.0030
0.0086
0.0277
0.0025
0.0074
0.0127
0.0030
0.0066
0.0185
0.0030
0.0066
0.0185
0.0046
0.0030
0.0066
0.0185
0.0041
0.0089
0.0041
0.0089
0.0249
0.0061
0.0069
0.0046
ay (ord.)
[m/s2 ]
1.9620
0.9810
0.5886
0.3924
0.1962
0.9810
0.7848
0.5886
0.9810
0.7848
0.6867
0.4905
0.9810
0.7848
0.5886
0.5886
0.4905
0.1962
0.9810
0.7848
0.5886
0.9810
0.7848
0.5886
1.4715
0.9810
0.7848
0.5886
1.2753
1.0791
1.2753
1.0791
0.8829
1.9620
1.0791
1.4715
du (ord.)
[m]
0.1097
0.0597
0.0582
0.1128
0.2217
0.0399
0.1026
0.2459
0.0399
0.0274
0.0521
0.1245
0.0305
0.0577
0.1384
0.0373
0.0732
0.0958
0.0381
0.0549
0.1166
0.0343
0.0495
0.1049
0.0457
0.0305
0.0439
0.0932
0.0406
0.0587
0.0406
0.0587
0.1245
0.0610
0.0460
0.0549
au (ord.)
[m/s2 ]
5.8860
2.4525
1.8639
1.1772
0.6867
1.9620
1.6677
1.2753
1.9620
1.7658
1.4715
1.0791
1.9620
1.6677
1.2753
1.8639
1.5696
0.6867
2.4525
2.0601
1.5696
2.2563
1.8639
1.3734
2.9430
1.9620
1.6677
1.2753
2.6487
2.1582
2.6487
2.1582
1.6677
3.9240
2.1582
2.9430
de (ord.)
[m]
0.0043
0.0028
0.0027
0.0078
0.0206
0.0028
0.0108
0.0345
0.0028
0.0018
0.0048
0.0155
0.0021
0.0060
0.0194
0.0018
0.0052
0.0089
0.0021
0.0046
0.0130
0.0021
0.0046
0.0130
0.0032
0.0021
0.0046
0.0130
0.0028
0.0062
0.0028
0.0062
0.0174
0.0043
0.0048
0.0032
DR
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
A TABLES
AF
T
Selena
k
(ord/sh)
0.7
0.6
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.6
0.5
0.5
0.6
k
(ord/md)
0.4
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.4
k
ord(lg)
0.2
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.2
be
fraction
low-code
15
10
5
5
5
5
5
5
7
7
7
7
10
10
10
7
7
7
7
7
7
10
10
10
7
7
7
7
10
10
7
7
7
10
10
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
W1
W2
S1L
S1M
S1H
S2L
S2M
S2H
S3
S4L
S4M
S4H
S5L
S5M
S5H
C1L
C1M
C1H
C2L
C2M
C2H
C3L
C3M
C3H
PC1
PC2L
PC2M
PC2H
RM1L
RM1M
RM2L
RM2M
RM2H
URML
URMM
MH
Table 23: Parameters of capacity curves as provided by HAZUS for Low-code seismic design.
72
mbt
dy (ord.) [m]
[m]
0.0091
0.0079
0.0079
0.0226
0.0592
0.0079
0.0307
0.0983
0.0079
0.0048
0.0140
0.0442
ay (ord.)
[m/s2 ]
2.9430
1.9620
1.1772
0.7848
0.4905
1.9620
1.6677
1.2753
1.9620
1.5696
1.2753
0.9810
du (ord.)
[m]
0.1643
0.1194
0.1397
0.2705
0.5324
0.0955
0.2464
0.5903
0.0955
0.0658
0.1247
0.2987
au (ord.)
[m/s2 ]
8.8290
4.9050
3.7278
2.2563
1.4715
3.9240
3.2373
2.4525
3.9240
3.5316
2.9430
2.2563
de (ord.)
[m]
0.0064
0.0055
0.0055
0.0158
0.0414
0.0055
0.0215
0.0688
0.0055
0.0034
0.0098
0.0309
k
(ord/sh)
0.9
0.8
0.8
0.8
0.8
0.6
0.6
0.6
0.6
0.6
0.6
0.6
k
(ord/md)
0.6
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
k
ord(lg)
0.3
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.0051
0.0147
0.0254
0.0061
0.0132
0.0373
1.1772
0.9810
0.4905
1.9620
1.6677
1.2753
0.0894
0.1755
0.2299
0.0914
0.1318
0.2799
3.7278
3.0411
1.4715
4.9050
4.1202
3.1392
0.0036
0.0103
0.0178
0.0043
0.0092
0.0261
0.8
0.8
0.8
0.8
0.8
0.8
0.4
0.4
0.4
0.4
0.4
0.4
0.0091
0.0061
0.0132
0.0373
0.0081
0.0175
0.0081
0.0175
0.0498
2.9430
1.9620
1.6677
1.2753
2.6487
2.1582
2.6487
2.1582
1.6677
0.1097
0.0732
0.1054
0.2240
0.0975
0.1407
0.0975
0.1407
0.2987
5.8860
3.9240
3.2373
2.4525
5.1993
4.3164
5.1993
4.3164
3.3354
0.0064
0.0043
0.0092
0.0261
0.0057
0.0123
0.0057
0.0123
0.0348
0.6
0.6
0.6
0.6
0.8
0.8
0.8
0.8
0.8
0.0046
1.4715
0.0549
2.9430
0.0032
0.6
DR
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
A TABLES
AF
T
Selena
be
fraction
mod-code
15
10
5
5
5
5
5
5
7
7
7
7
0
0
0
0
0
0
0
0
0
0
0
0
0.2
0.2
0.2
0.2
0.2
0.2
7
7
7
7
7
7
0
0
0
0
0
0
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.4
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
7
7
7
7
10
10
7
7
7
0
0
0
0
0
0
0
0
0
0.4
0.2
5
0
W1
W2
S1L
S1M
S1H
S2L
S2M
S2H
S3
S4L
S4M
S4H
S5L
S5M
S5H
C1L
C1M
C1H
C2L
C2M
C2H
C3L
C3M
C3H
PC1
PC2L
PC2M
PC2H
RM1L
RM1M
RM2L
RM2M
RM2H
URML
URMM
MH
Table 24: Parameters of capacity curves as provided by HAZUS for Moderate-code seismic design.
73
mbt
dy (ord.) [m]
[m]
0.0122
0.0160
0.0155
0.0450
0.1184
0.0160
0.0617
0.1969
0.0160
0.0097
0.0277
0.0886
ay (ord.)
[m/s2 ]
3.9240
3.9240
2.4525
1.5696
0.9810
3.9240
3.2373
2.4525
3.9240
3.1392
2.6487
1.9620
du (ord.)
[m]
0.2924
0.3183
0.3726
0.7214
1.4194
0.2545
0.6574
1.5740
0.2545
0.1755
0.3327
0.7968
au (ord.)
[m/s2 ]
11.7720
9.8100
7.3575
4.6107
2.8449
7.8480
6.5727
5.0031
7.8480
7.0632
5.8860
4.5126
de (ord.)
[m]
0.0085
0.0112
0.0108
0.0315
0.0829
0.0112
0.0432
0.1378
0.0112
0.0068
0.0194
0.0621
k
(ord/sh)
1
0.9
0.9
0.9
0.9
0.7
0.7
0.7
0.7
0.7
0.7
0.7
k
(ord/md)
0.8
0.6
0.6
0.6
0.6
0.5
0.5
0.5
0.5
0.5
0.5
0.5
k
ord(lg)
0.5
0.4
0.4
0.4
0.4
0.3
0.3
0.3
0.3
0.3
0.3
0.3
0.0099
0.0292
0.0511
0.0122
0.0264
0.0747
2.4525
2.0601
0.9810
3.9240
3.2373
2.4525
0.2385
0.4684
0.6129
0.2436
0.3515
0.7465
7.3575
6.0822
2.8449
9.8100
8.1423
6.2784
0.0069
0.0204
0.0357
0.0085
0.0185
0.0523
0.9
0.9
0.9
0.9
0.9
0.9
0.6
0.6
0.6
0.6
0.6
0.6
0.0183
0.0122
0.0264
0.0747
0.0163
0.0351
0.0163
0.0351
0.0996
5.8860
3.9240
3.2373
2.4525
5.1993
4.3164
5.1993
4.3164
3.3354
0.2924
0.1948
0.2812
0.5974
0.2598
0.3749
0.2598
0.3749
0.7963
11.7720
7.8480
6.5727
5.0031
10.4967
8.7309
10.4967
8.7309
6.6708
0.0128
0.0085
0.0185
0.0523
0.0114
0.0245
0.0114
0.0245
0.0697
0.7
0.7
0.7
0.7
0.9
0.9
0.9
0.9
0.9
0.0046
1.4715
0.0549
2.9430
0.0032
0.6
DR
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
B COMPILING THE C-CODE
AF
T
Selena
be
fraction
high-code
15
10
5
5
5
5
5
5
7
7
7
7
0
0
0
0
0
0
0
0
0
0
0
0
0.4
0.4
0.4
0.4
0.4
0.4
7
7
7
7
7
7
0
0
0
0
0
0
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.6
0.3
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0.4
7
7
7
7
10
10
7
7
7
0
0
0
0
0
0
0
0
0
0.4
0.2
5
0
W1
W2
S1L
S1M
S1H
S2L
S2M
S2H
S3
S4L
S4M
S4H
S5L
S5M
S5H
C1L
C1M
C1H
C2L
C2M
C2H
C3L
C3M
C3H
PC1
PC2L
PC2M
PC2H
RM1L
RM1M
RM2L
RM2M
RM2H
URML
URMM
MH
Table 25: Parameters of capacity curves as provided by HAZUS for Moderate-code seismic design.
B
Compiling the C-code
T
HIS section describes how to build SELENA from the C/C++ source code and which tools that are
needed for the different platforms. First download the source code for SELELA. The source code can
be found in the download section on the SELENA/RISe web page at: http://selena.sourceforge.net
If you want to compile the development code from the SVN repository you first need to install a
subversion (svn) client. On windows one can, for example, use TortoiseSVN which integrates into the
Windows file browser, or a command line client from here http://www.sliksvn.com/en/download. On
Linux there exist several GUI based front ends to svn like, for example, KDESvn, RapidSVN or eSvn.
One can also use the command line client. To download the development code one need to do a svn
checkout. First create a folder for the SELENA code, say selena sourceforge and go to that folder.
Then, using the command line client, type
$ svn checkout https://selena.svn.sourceforge.net/svnroot/selena/selana/trunk
at the shell command line. This will download all the C# source code, user manual files etc. If you are
using a GUI client then choose the checkout menu/button in the particular GUI client that you are using.
74
AF
T
Selena
For example, if you are using TortoiseSVN on Windows then right-click on the selena sourceforge folder
that you just created, select the SVN Checkout menu item, and add the path
https://selena.svn.sourceforge.net/svnroot/selena/selena/trunk
in the URL or Repository line. Then click on the OK -button and the files should start downloading.
The C/C++ source code can be found in the trunk/src folder.
B.1
Tools and Libraries for Windows
1. Install the GNU Scientific Library (GSL): Binary packages for GSL can be found here:
http://gnuwin32.sourceforge.net/packages/gsl.htm but you can also find these files in the
dll folder.
2. Copy the libgsl.dll and libgslcblas.dll files to C:\WINDOWS\System32\
3. Install a compiler and mex-tools:
The mex-files, oct-files, and the stand-alone binaries should build with most standard C-compilers
such MSVC or MinGW. Here we only describe building with MinGW [but there is an untested
build mexfiles win.m script which should (may) work with MSVC].
4. Install the MinGW compiler that comes with Qt, from: http://qt.nokia.com/products (recommended), or get directly from: http://www.mingw.org. Set the path to the build tools (mingw32-make.exe,
mingw32-gcc.exe etc.) by right-clicking on ”My Computer” and edit (append) Advanced− >Enviroment
Variables− >Path variable. For example, add C:\Qt\2010.04\mingw\bin. Avoid ”Program
Files” or any folder with a space (blank) in the folder name.
DR
5. Install the GNUmex tools from: http://gnumex.sourceforge.net and run the setup script (follow
the instructions on the GNUmex website).
B.2
Building the Stand-alone Application on Linux/Unix
Here we assume that the gcc tools are installed on the system. To build the SELENA application just
cd to the src folder and type make which will build the binary selena. It is recommended that you put
the selena binary in a directory which is in your PATH varaiable, such as, /usr/local/bin/, otherwise,
you have to use the full path to the binary to run it.
B.3
Building the Stand-alone Application on Windows
Given that you have installed the MinGW tools (described in Section B.1) you can build the Windows
stand-alone binary by cd to the src folder and type mingw32-make -f Makefile mingw32 clean all
(in a cmd window) which will create the file selena.exe
B.4
Building the Stand-alone GUI Application on Linux/Unix
The SELENA GUI is using the QT toolkit which must be installed to build the selena gui application.
1. First you need to install the QT toolkit from http://qt.nokia.com/products for your platform
or use your particular Linux distribution’s package manager (emerge, yast etc.).
2. Run qmake (in the src/gui folder).
75
3. Run make
AF
T
Selena
The executable is named selena gui. You can clean everything with make clean (make distclean
which removes the Makefile and binaries as well).
B.5
Building the Stand-alone GUI Application on Windows
Building the stand-alone SELENA GUI is similar in Windows and Linux (UNIX).
1. First you need to install the QT toolkit from http://qt.nokia.com/products for your platform.
On Windows you also need to add the path to the QT tools (qmake etc) and the MinGW compiler
that comes with QT to the Windows PATH (right-click on My Computer − > Advanced − > env.
variables. Typically you append something like:
;C:\Qt\2010.04\mingw\bin;C:\Qt\2010.04\qt\bin
to the PATH variable.
2. Run qmake (in the src/gui folder).
3. Run mingw32-make
You can also run the bat-file make gui.bat to build the gui.
The executable is named selena gui.exe. You can clean everything with mingw32-make clean
(mingw32-make distclean which removes the Makefile and binaries as well).
Building the Linux/Unix mex-files
DR
B.6
1. Open the Make.inc file and check that the paths to Matlab fits your installation.
2. Go ro the src folder:
#cd src
3. Build the mex-files:
# make -f Makefile_matlab clean all install
The mex-files will be installed in the m files folder. Note you can edit the Make.inc file to fine-tune
the build for your particular hardware (set CFLAGS etc.).
Alternatively you can also use the build mexfiles.m script to build and install the mex-files (just
run the script in Matlab in the main SELENA folder).
B.6.1
Building the Windows mex-files
1. First look (open in a text editor) at the mexopt.bat file which the setup script generates. SELENA
has two mexopt-files in the mexopt folder which may need to be edited to fit the your installation.
That is, you need to set the paths to Matlab, GNUmex tools, and GSL in the two files:
mexopts/mexopts_mingw.bat.inc
mexopts/mexopts_gsl_mingw.bat.inc
76
AF
T
Selena
Copy (or rename) these files to mexopts mingw.bat and mexopts gsl mingw.bat, respectively.
Then edit the paths in these files to fit your installation (eg., set compiler and Matlab paths).
2. Start Matlab
3. Run the build script:
>> build_mexfiles_mingw
This should build the following files:
att_sub.mexw32
csm.mexw32
curveintersect.mexw32
damagep.mexw32
gmotion.mexw32
gmotionp.mexw32
gsl_interpolate.mexw32
humanloss.mexw32
humanlosshz.mexw32
imp_dcm.mexw32
losssqm.mexw32
madrs.mexw32
meanest.mexw32
normcdf.mexw32
numdam.mexw32
spectralshape.mexw32
squaredam.mexw32
tinv.mexw32
tree.mexw32
treeloss.mexw32
treemdr.mexw32
and install them in the m files folder.
B.7
Building the oct-Files
1. Start Octave
2. Run the build script
DR
octave:1> build_oct_files
This should build the following files:
att_sub.oct
csm.oct
curveintersect.oct
damagep.oct
gmotion.oct
gsl_interpolate.oct
humanloss.oct
humanlosshz.oct
imp_dcm.oct
madrs.oct
spectralshape.oct
squaredam.oct
and install them in the m files folder.
Alternatively (on Linux), one can build the oct-files with:
# make -f Makefile_octave clean all install
77
tree.oct
treemdr.oct

User Manual for the Earthquake Loss Estimation Tool: SELENA

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