Hazards Maps - Fragility and Shake Maps. How to develop them. Case Study Honduras.

1. Hazard Maps
Risk Projects
Fragility Maps & Shake Maps
Presented by: David Gutierrez Rivera
Supervised by:
Dipl.-Ing. Lars Abrahamczyk
Dr.-Ing. Jochen Schwarz

2. Hazard Maps: Contents
1) Introduction
2) Motivation
3) Fundamentals
a. Fragility
b. Performance: Capacity & Demand
c. Probability
d. Simulations
4) Fragility Maps
a. Fragility Curves
b. Building Stock
5) Shake Maps
a. Ground Motion Prediction Equation (GMPE)
b. Sensors Data

3. Hazard Maps: Introduction
Hazard Maps
A Hazard Map highlights areas that are affected or
vulnerable of a particular hazard.
They help use describe qualitatively and quantitatively a
specific area in order to assess its vulnerability to a
particular hazard.

4. Introduction: Seismic Hazard Map
Ref. http://www.seismo.ethz.ch/static/GSHAP/

5. Introduction: Fire Hazard Map
Ref. http://www.battle-creek.net/docs/fire/fire_hazard_map_final.jpg

6. Introduction: Tsunami Vulnerability Map
Ref. “Tsunami fragility curves and tsunami vulnerability” - http://bymur.bo.ingv.it/frames/wg4.html

7. Introduction: Building Stock Vulnerability Map
Ref. “Determination of Fragility Curves” - http://www.merci.ethz.ch

8. Fragility Maps: Motivation
Applications of Fragility Maps & Fragility Curves are:
Probabilistic Risk Assessment
Construction Code Development
Urban Planning
Loss Estimation
Retrofitting
Shake Maps

9. Fragility Maps: Loss Estimation
A group of buildings of different types subjected to a hazard
may experience damage states of different types.
With Fragility Curves at
your disposal for each of
this building types and
damages states, and also
knowing the expense for
repairing this damages
on the buildings, we can
estimate the expected
annual or monthly loss.
€ 3,000
€ 1,000
€ 500
€ 1,500
€ 2,500

10. Fundamentals: Fragility
Fragility
It is a measure of part of the Vulnerability of a structure to
loads induced by a hazard.
Risk = Fun ( Hazard, Vulnerability, Cost )

11. Fundamentals: Fragility
Mathematically, a fragility relationship can be defined as:
Where:
Pf is the failure probability for a specific damage state
Sd is the structural demand, and
Sc is the structural capacity.

12. Fundamentals: Fragility
Fragility
Fragility of a Structure is affected by:
 Type of Hazard (EQ, Wind, Flood,...)
 Strength of Hazard
 Structural Type
 Construction Materials
 Soil-Structure Interaction

13. Fundamentals: Capacity
Capacity
Is a measure of the maximum load, or any other parameter, a structure
can sustain for it to achieve a predefined damage state. This will
depend on the structural system, materials and other structural
attributes that affect the resistance of a structure.
Ref. Application of the Applied Element Method to the Seismic Vulnerability Evaluation of Existing Buildings –
http://www.extremeloading.com/upload/Karbassi%20et%20Nollet_CSCE2008_without%20logo.pdf

14. Capacity: Pushover Analysis
Pushover Analysis
Using this method we can obtain the Capacity of a Structure. The
procedure consists on applying either a small lateral displacement or
force to the structure, iteratively increasing this amount, re-analizing the
structure at each step, until the predefined damage state is obtained.
Ref. Seismic Risk Assessment and Loss Estimation –
http://web.mit.edu/istgroup/ist/documents/earthquake/Part1.pdf

15. Fundamentals: Demand
Demand
It‘s a measure of the loads, or any other parameter, that a structure
would be subjected to by a given hazard. It will depend on characteristics
of the hazard and site conditions, which affect the overall effect on the
structure. Seismic Demand is represented by using Response Spectra.
Ref. Eurocode 8 - Design of structures for earthquake resistance

16. Demand: Seismic Response Spectra
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
Period T, [sec]
Sa
Seismic Response Spectra
Is a plot of the peak or steady-state response (displacement, velocity or
acceleration) of a series of buildings of varying Natural Frequency or
Period, forced into motion by the
same base Ground Motion.
Using the available Ground
Motion Data from a region a
general Seismic Response
Spectra can be develop for
use in this region.
Ground Motion Data

17. Demand: Seismic Response Spectra
Seismic Response Spectra

18. Fundamentals: Performance
Performance
Hammurabi, King of Babylon once said:
“Article 229: The builder has built a house
for a man and his work is not strong and
if the house he has built falls in and
kills a householder, that builder shall be …
slain”.
This is a performance statement.
He addressed structural safety
entirely in terms of user requirements,
did not state how to construct the building,
and did not refer to building structure or building materials.

19. Performance: Performance-Based Design
Performance-Based Design
The Performance approach consists of working in terms of Ends
rather than Means. It is concerned with what a building is
required to do, and not with how it is to be constructed.
- Capacity
Performance-Based Design Ingredients:
- Demand
-> Determination of the Performance Point
-> Check Structural Behavior under Defined Seismic Action
with your Defined Limit States.

20. Performance: Performance Point
Performance Point
Capacity Curve
Base Shear – Roof Displacement
Capacity Curve
Sa – Sd
Response Spectrum
Sa – Period
Response Spectrum
Ref. “Performance-based design ” – NHRE 3rd Course Lecture: Risk Projects

21. Performance: Comparison
Ref. “Seismic Risk Assessment and Loss Estimation”– http://web.mit.edu/istgroup/ist/documents/earthquake/Part1.pdf

22. Fragility Maps: Fragility Curves
Fragility Curves
By assuming material properties and certain other structural
attributes that affect the overall Capacity of a structure, and with
additional assumptions about the ground motion and site
conditions—both factors that affect the seismic Demand, we can
deterministically calculate the performance of a structure.
Naturally, values of these parameters are not exact — they
invariably have a measure of both randomness and uncertainty
associated with them.
When we take into account this probabilistic characteristics we
generate what we know as Fragility Curves.

23. Fragility Curves: Shape
Ref. “Determination of Fragility Curves” - http://www.merci.ethz.ch

24. Fragility Curves: Normal (Gaussian) Distribution
Normal (Gaussian) Distribution
μd σd
μc
σc
Ref. “Fragility Curve Development for Assessing the Seismic Vulnerability of Highway Bridges” –
http://mceer.buffalo.edu/publications/resaccom/99-sp01/ch10mand.pdf

25. Fragility Curves: Normal (Gaussian) Distribution
Probability Density Function
Ref. http://en.wikipedia.org/wiki/Normal_distribution

26. Fragility Curves: Normal (Gaussian) Distribution
Cumulative Distribution Function
Ref. http://en.wikipedia.org/wiki/Normal_distribution

27. Normal Distribution: Parameter Estimation
Maximum Likelihood Method
Capacity Demand
C(x) D(x)
C1 D1
C2 D2
C3 D3
.
.
.
.
.
.
Cn Dn
For the Normal Distribution:
μ

28. Normal Distribution: Parameter Estimation
c d A     2 2
c c d    

29. Normal Distribution: Parameter Estimation
c d A    
2 2
c c d    
For Civil Engineering
Structures:
 0.5  0.6 c 
Ref. “Fragility Curve Development for Assessing the Seismic Vulnerability of Highway Bridges” –
http://mceer.buffalo.edu/publications/resaccom/99-sp01/ch10mand.pdf

30. Normal Distribution: Cumulative Distribution Function
 Newton-Cotes Integration
 Trapezoidal Rule
 Simpson Rule
 Gaussian Quadratures
 Gauss-Legendre
 Gauss-Hermite
Numerical Integration Methods

31. Building Stock: Building Categories
Building Categories
A Classification of the Building Stock needs to be made in
order to develop their respective fragility curves.
Classification can be made according to:
• Structural Type
• Building Purpose
• Building Quality

32. Building Stock: Structural Type

33. Building Stock: Building Purpose
IBC Building Occupancy Classifications
Assembly (Group A) - places used for people gathering for entertainment, worship,
and eating or drinking. Examples: churches, restaurants (with 50 or more possible
occupants), theaters, and stadiums.
Business (Group B) - places where services are provided (not to be confused with
mercantile, below). Examples: banks, insurance agencies, government buildings
(including police and fire stations), and doctor's offices.
Educational (Group E) - schools and day care centers up to the 12th grade.
Factory (Group F) - places where goods are manufactured or repaired.
High-Hazard (Group H) - places involving production or storage of very flammable
or toxic materials. Includes places handling explosives and/or highly toxic materials.
Institutional (Group I) - places where people are physically unable to leave without
assistance. Examples: hospitals, nursing homes, and prisons. In some jurisdictions,
Group I may be used to designate Industrial.
Mercantile (Group M) - places where goods are displayed and sold. Examples:
grocery stores, department stores, and gas stations.
Residential (Group R) - places providing accommodations for overnight stay
(excluding Institutional). Examples: houses, apartment buildings, hotels, and motels.
Storage (Group S) - places where items are stored (unless considered High-
Hazard). Examples: warehouses and parking garages.
Utility and Miscellaneous (Group U) - others. Examples: water towers, barns,
towers.

34. Fragility Curves: Construction

35. Fragility Curves: Construction
Ref. “Determination of Fragility Curves” - http://www.merci.ethz.ch

36. Fragility Curves: Construction
Numerical Simulation
 Determine Site-Specific
Seismic Ground Motion
 Construct Numerical Model
accounting for
Soil-Structure Interaction
 Definition of failure criteria
 Uncertainty quantification,
Modeling and Propagation
μ

37. Fragility Curves: Construction
Monte Carlo Simulation
μ
σ
E, I
μ
σ
Load
μ
σ

38. Fragility Curves: Construction
Monte Carlo Simulation
μ
σ
Fragility Curve

39. Retrofitting Effects on
Fragility of Structures
Ref. “Deterministic and Probabilistic Evaluation of Retrofit Alternatives for a Five-Story Flat-Slab RC Building” -
https://www.ideals.illinois.edu/bitstream/handle/2142/8784/Deterministic%20and%20Probabilistic%20Evaluation%20of%20Retrofit%20Alt
ernatives%20for%20a%20Five-Story%20Flat-Slab%20RC%20Building.pdf?sequence=2

40. Shake Maps: Introduction
Shake Maps
Is a representation of ground shaking produced by an earthquake.
ShakeMap focuses on the ground-shaking produced by the earthquake, rather than
the parameters describing the earthquake source.
Depending on distance from the earthquake, depth, rock and soil conditions at
sites, and variations in the propagation of seismic waves from the earthquake due
to complexities in the structure of the Earth's crust, it produces a range of ground
shaking levels at sites throughout the region.
PAGER –
Prompt Assessment of Global Earthquakes
for Response
The PAGER system provides fatality
and economic loss impact estimates
following significant earthquakes
worldwide.
Ref. http://earthquake.usgs.gov/earthquakes/pager/

41. Shake Maps: Motivation
Application of Shake Maps are:
Seismological Research - Calibration of GMPE
Earthquake Scenarios Preparedness
Emergency Response
Loss Estimation

42. Shake Maps: Emergency Response
Fire Department

43. Shake Maps: Emergency Response
Search & Rescue

44. Shake Maps: Emergency Response
Red Cross

45. Shake Map: ShakeCast
http://earthquake.usgs.gov/earthquakes/shakemap/

46. Shake Map: openSHA
Intensity-Measure
Relationship
http://www.opensha.org/

47. Shake Map: openSHA
Region & Site Parameters

48. Shake Map: openSHA
Site Data Providers

49. Shake Map: openSHA
Earthquake Rupture

50. Shake Map: openSHA
Exceedance Level/Prob.

51. Shake Map: openSHA
Map Attributes

52. Shake Map: openSHA Generated Maps
Honduras

53. Shake Map: openSHA Generated Maps
California

54. Shake Map: openSHA Generated Maps
Japan

55. Shake Map: Construction

56. Shake Map: GMPE

57. Shake Map: GMPE

58. Shake Map: GMPE

59. Shake Map: GMPE

60. Shake Map: GMPE

61. Shake Map: Sensors Data
Interpolation and Extrapolation
Sensors Data is prioritize over GMPE
when calculating site Ground-Shaking (PGA),
IF there is enough data available.
Interpolation and Extrapolation Schemes
must be implemented to calculate interior
and exterior PGA values, respectively.
Methods (Uni-Dimensional)
-Linear
-Polynomial
-Spline , others ...
Methods (Multi-Dimensional, Spatial)
-Bilinear
-Natural & Nearest Neighbor
-Kriging , others ... Ref. ShakeMap Manual

62. Shake Map: Interpolation and Extrapolation
MATLAB Commands
• Yi = interp1( X, Y, Xi ) ; Zi = interp2( X , Y, Z, Xi, Yi )
•Zi = griddata( X , Y, Z, Xi, Yi )
•interFun = TriScatteredInterp( X , Y , method )
 Zi = interpFun( Xi , Yi )

63. Case Study: Honduras
1. Building Stock
2. Fragility Curves
3. PGA Map – GSHAP
4. Fragility Map Construction
5. Brick Fragility Map
6. Masonry Fragility Map
7. Timber Fragility Map
8. Concrete Fragility Map
9. Adobe Fragility Map
10. Overall Fragility Map
11. ShakeMaps for EQ1 South Coast
12. ShakeMaps for EQ2 North Coast
Software Tools Used:
- MapInfo
- Matlab
- Excel
- openSHA

64. Honduras: Building Stock

65. Honduras: Fragility Curves
Brick Building
Type
FILE: AhmadEtAl2010-MABrick-HighPercentageVoids-2storeys-PGA
Unreinforced Masonry bearing wall structure –
Fired Brick with high percentages of voids – 2 storeys
The considered building stock represents the Euro-
Mediterranean buildings in general and Italian and
Slovenian in particular.
Uncertainties in lateral stiffness, strength, and
damage limit states are expressed by using controlled
Monte Carlo simulations.
Masonry Building
Type
FILE: KostovEtAl2004-Type1-1-4storeys-Before1919
Masonry buildings with deformable floors (wooden,
steel floor) - 1-4 storeys - Constructed Before 1919
RC frame and wall, masonry buildings of different
periods in Sofia-Bulgaria
Deterministic event (1858 earthquake)
The uncertainty is related to material strength, load
combination, computational model, construction
quality and behaviour factor.
MEAN_SLIGHT STD_SLIGHT MEAN_HEAVY STD_HEAVY MEAN_COLLAPSE STD_COLLAPSE
0.184 0.115 0.304 0.194 0.318 0.196
MEAN_SLIGHT STD_SLIGHT MEAN_HEAVY STD_HEAVY MEAN_COLLAPSE STD_COLLAPSE
0.14 0.13 0.23 0.22 0.33 0.31

66. Honduras: Fragility Curves
Concrete Building
Type
FILE: LielAndLynch2009-RC-MR
RC buildings - mid rise
Italy
L'Aquila Earthquake, 6th April 2009.
Ground-shaking intensity is estimated for each site
based on Italy Shakemap
The collapse fragility curve is not shown because
there are not sufficient data to estimate it correctly
* Therefore I changed the Damages States accordingly to:
Heavy -> Collapse
Moderate -> Heavy
MEAN_SLIGHT STD_SLIGHT MEAN_HEAVY STD_HEAVY MEAN_COLLAPSE STD_COLLAPSE
0.34 0.06 0.38 0.05 0.45 0.07

67. Honduras: Fragility Curves
Timber Building
Type
Assumed.
Couldn’t find suitable Fragility Curve for Timber,
therefore assumed values which are in between an
Adobe and a Masonry Building.
Adobe Building
Type
Ref. “SEISMIC RISK ASSESSMENT OF ADOBE DWELLINGS” -
www.roseschool.it/files/get/id/4480
MEAN_SLIGHT STD_SLIGHT MEAN_HEAVY STD_HEAVY MEAN_COLLAPSE STD_COLLAPSE
0.189 0.25 0.314 0.33 0.353 0.38
MEAN_SLIGHT STD_SLIGHT MEAN_HEAVY STD_HEAVY MEAN_COLLAPSE STD_COLLAPSE
0.025 0.55 0.125 0.54 0.22 0.59

68. Honduras: PGA Map - GSHAP

69. Honduras: Fragility Map Construction
PGA = 2.75 m/s2 = 0.275 g

70. Honduras: Fragility Map Construction
Masonry Building
Type
Prob = 0.30
PGA = 2.75 m/s2 = 0.275 g

71. Honduras: Fragility Map Construction
Masonry Buildings Fragility Map
Prob = 0.30 = 0.25 to 0.35

72. Honduras: Fragility Map Construction
PGA = 2.00 m/s2 = 0.20 g

73. Honduras: Fragility Map Construction
Adobe Building
Type
Prob = 0.45
PGA = 2.00 m/s2 = 0.20 g

74. Honduras: Fragility Map Construction
Collapse Damage State
Prob = 0.45 = 0.35 to 0.50
Adobe Buildings Fragility Map

75. Honduras: Data Handling
MATLAB
InterpFun = TriScatteredInterp( X, Y , FRAG)

76. Honduras: Data Handling
MATLAB
InterpFun = TriScatteredInterp( X, Y , FRAG)
inFRAG = InterpFun( inX, inY)

77. Honduras: Brick Buildings Fragility Map
Collapse Damage State

78. Honduras: Masonry Buildings Fragility Map
Collapse Damage State

79. Honduras: Timber Buildings Fragility Map
Collapse Damage State

80. Honduras: Concrete Buildings Fragility Map
Collapse Damage State

81. Honduras: Adobe Buildings Fragility Map
Collapse Damage State

82. Honduras: Overall Fragility Map
Collapse Damage State

83. Honduras: Overall Fragility Map
Collapse Damage State
Overall FRAG. = (#ofBuildingType_i X Frag_BuildingType_i) / (#ofBuildingType_i)

84. Shake Map: Construction
PGA ?
PGA = GMPE( Mw, Depth, Dist, … )
“Dahle”
PGA = 0.81 m/s2 Choluteca

85. Shake Map: Construction
Overall Fragility Map
PGA = 0.81 m/s2
Overall FRAG. = (#ofBuildingType_i X Frag_BuildingType_i) /
(#ofBuildingType_i)
PROB. = 0.015162
Choluteca
Choluteca

86. Shake Map: Construction
Prob = 0.015162

87. Shake Map: Honduras South Coast
Buildings Collapsed
EQ: Mw = 6.5, Depth 30 km Long. = -87.5° , Lat. = 13.25°

88. Shake Map: Honduras South Coast
Probability of Exceedance
EQ: Mw = 6.5, Depth 30 km Long. = -87.5° , Lat. = 13.25°

89. Shake Map: using openSHA
Probability of Exceedance
EQ: Mw = 6.5, Depth 30 km Long. = -87.5° , Lat. = 13.25°

90. Shake Map: using openSHA
Intensity MMI
EQ: Mw = 6.5, Depth 30 km Long. = -87.5° , Lat. = 13.25°

91. Shake Map: Honduras North Coast
Buildings Collapsed
EQ: Mw = 7.5, Depth 25 km Long. = -88.0° , Lat. = 16.0°

92. Shake Map: Honduras North Coast
Probability of Exceedance
EQ: Mw = 7.5, Depth 25 km Long. = -88.0° , Lat. = 16.0°

93. Shake Map: using openSHA
Probability of Exceedance
EQ: Mw = 7.5, Depth 25 km Long. = -88.0° , Lat. = 16.0°

94. Shake Map: using openSHA
Intensity MMI
EQ: Mw = 7.5, Depth 25 km Long. = -88.0° , Lat. = 16.0°

95. Thank You ☺