FRAGILITY CURVES FOR BUILDING STOCKS: DERIVATION FROM...

FRAGILITY CURVES FOR BUILDING STOCKS: DERIVATION FROM MACROSEISMIC AND MECHANICAL-BASED MODELS AND

CALIBRATION THROUGH EMPIRICAL DATA

Serena Cattari

[email protected]

DICCA–Department of Civil,Chemical andEnvironmental Engineering

29th October 2019,LIMA

OUTLINE OF THE PRESENTATION

What do theydepend on?

How are theyobtained?

What do theyrepresent?

How can they beused?

Fromvulnerability torisk assessment

Practical issues & Examples of application

Overview & focus on macroseismicand mechanical-based approaches

Involved uncertainties & influenceon results

Relationship with risk analyses &useful GLOSSARY ….

RISK ANALYSIS - KEYWORDS

HAZARDASSESSMENT VULNERABILITY

& DAMAGE ESTIMATIONEXPOSURE &

CLASSIFICATION

LOSS ESTIMATION

Loss

The risk analysis at territorial scale is intrisically probabilistic (as the PEER-PBA at scale of the single building): it is the result of convolution of various sources of uncertainties and dispersions

RISK ANALYSIS - BASICS

It represents the EXPECTED RATE in a GIVEN TIME (e.g. 1 year, 50 year,…) of possible LOSSES ( economical, associated to the loss of buildings usability, casualties, …) due to the DAMAGE

OCCURRED on the buildings stock or people (EXPOSURE) in a GIVEN AREA (e.g. the municipality, the region, the whole country) as a consequence of possible seismic events (HAZARD)

FRAGILITY

A chain of conditional probabilities….

Notation oftheintegral according toIervolino,2016

RISK ANALYSIS – HAZARD

Hazard function (PSHA - Probabilistic Seismic Hazard Assessment) stands for the probability that a selected scalar measure of seismic intensity at a site exceeds a given value in a given time interval

PGA o Sa 16- 50-849 TR

PHSA provided by the Italian Structural Code

0.000#

0.001#

0.010#

0.100#0.000# 0.500# 1.000# 1.500#

Sa(T1)m#

Sa#(T1)#16%#

Sa#(T1)#84%#

ag#

ag16%#

ag84%#Foragiven site

RISK ANALYSIS –TYPES OF RISK ANALYSISaccording to the notation introduced by FEMA P-58 for performance assessment of buildings

Evaluates the loss over a specifiedperiod of time

(e.g., 1 year, 30 years, or 50 years) considering all earthquakes that

could occur in that time period, and the probability of occurrence

associated with each earthquake.

TIME-BASED INTENSITY-BASED SCENARIO-BASED

The timeperiod depends on the interestsand needs of the decision-maker.Assessments based on a single year are useful for cost-benefit

evaluations, instead over longerperiods of time are useful for other decision-making aims.

UNCONDITIONED

Evaluates the lossassuming a scenario

consisting of a specific magnitude

earthquake occurringat a specific location

relative to the area under examination

CONDITIONED

Useful to support the design of seismic

emergency plan atmunicipality scale

Evaluates the loss assumingthat of a specified

earthquake shakingintensity. In general the

design earthquake shakingconsistent with a Building

Code responseSpectrum is considered.

CONDITIONED

Useful for comparative analysesby considering RARE (e.g. 475 years) and FREQUENT (e.g. 50

uears ) events

IncaseofCONDITIONEDASSESSMENTITISPOSSIBLEALSOADOPTTHEMACROSEISMICINTENSITYas INTENSITYMEASURE

RISK ANALYSIS –SCALES OF RISK ANALYSIS

The whole country

The region

The municipality

RISK ANALYSIS – DAMAGE METRIC

GRADE 1:Negligible to slight damage

GRADE 2:Moderate damage

GRADE 3:Substantial to heavy damage

GRADE 4:Very heavy damage

GRADE 5:Destruction

DAMAGELEVELACCORDINGTOEMS98(Grunthal 1998)

• Usually, the damage is described in DISCRETE terms rather than as a CONTINOUS variable (à thus the integral becomes a sum)

• It is associated to DAMAGE LEVELS (that usually implicitly refer also to PERFORMANCE LEVELS) correlated to Engineering Demand Parameters representative of the Structural Response

• The most common assumption is referring to the 5 grades introduced by the EMS98 scale (the first four are similar to the LSs of Codes)

Risk analyses at large scale can be referred:

q to stock of buildings characterized by homogeneous seismic behaviour – typicalof the assessment on residential buildings spread on the territory

q to buildings portfolio characterized by a group of structures whose assessmentis provided in aggregate terms – typical of the assessment on strategic functionsspread on the territory (e.g. schools, strategic buildings, …)

Thus important steps of a risk analysis are :

q Taxonomy: aimed to define the attributes that influence the vulnerabilityq Classification: group of buildings with the same attributes (similar behavior)

Both can be defined IN GENERAL but then the attributes to be actually consideredin a specific risk analysis depend on the availability of data.

RISK ANALYSIS –EXPOSURE

LIST OF 13 ATTRIBUTES1. Direction2. Material of the lateral load-resisting system3. Lateral load-resisting system 4. Height5. Date of construction or retrofit6. Occupancy7. Building position within a block8. Shape of the building plan9. Structural irregularity10. Exterior walls11. Roof12. Floor13. Foundation system

Reference:GEM Building Taxonomy Version 2.0GEM Technical Report 2013-02Version: 1.0.0Date: November 2013

FRAGILITY CURVES: TAXONOMY & CLASSIFICATIONEXAMPLES

TAXONOMYLIST OF 13 ATTRIBUTES

1. Direction2. Material of the lateral load-resisting system3. Lateral load-resisting system (LLRS) 4. Height5. Date of construction or retrofit6. Occupancy7. Building position within a block8. Shape of the building plan9. Structural irregularity10. Exterior walls11. Roof12. Floor13. Foundation system

MASONRY BUILDINGSYNER-G project (http://www.vce.at/SYNER-G/)

FRAGILITY CURVES: TAXONOMY & CLASSIFICATION

CATEGORY CLASSIFICATION

FRM

Bearing Walls (BW) Out of plane (OP); In plane (IP) [Equivalent Frame (EF), Weak Spandrels Strong Piers (WSSP), Strong Spandrels Weak Piers (SSWP)]

FRM

M

Unreinforced Masonry (URM)

Reinforced Masonry (RM) Confined Masonry (CM) Timber-framed Masonry

(TM)

Blocks: Adobe (A); Fired brick (FB); Soft Stone (SS); Hard Stone (HS) [Regular Cut (RC), Uncut (UC), Rubble (RU)]; Hollow clay tile (HC) [High % of voids (H%), Low % of voids (L%), Concrete Masonry Unit (CMU), Autoclaved Aerated Concrete (AAC)]

Mortar: Lime mortar (LM); Cement mortar (CM); Mud mortar (MM); Hydraulic mortar (HM)

Strengthening: Strengthened masonry (Sm) Timber: Confined and braced masonry

panels (TC); Horizontal timber tie (TT) Concrete and reinforcement: [Average

Strength (20-50 MPa)(ASC), Low Strength (<20 MPa)(LSC)]; [Vertical Reinforcement Bars (RBV), Vertical and Horizontal Reinforcement Bars (RBVH)]

P Regular (R) Irregular (IR)

[Isolated (I), Aggregate (A)]

E Regular geometry (R) Irregular geometry (IR)

CO

Regular openings (RO) Irregular openings (IRO)

[High % voids (H%), Low % voids (L%)]

DM

Details: High quality details (HQD), Low quality details (LQD)

Maintenance: Good Maintenance (HM), Low Maintenance (LM)

Tie rods: Without tie rods (WoT); With tie rods (WT)]

Ring beams: Without ring beams (WoRB); With ring beams (WRB)

FS

Rigid (R) Flexible (F)

Reinforced concrete (RC); Steel (S); Timber (T); Vault (V)

RS

Peaked (P) Flat (F) Gable End Walls (G)

Material: Timber (Ti); Corrugated Metal Sheet (CMS); Reinforced Concrete (RC); Thatch (Th)

Thrusting roof (Tr); Unthrusting roof (UTr)

HL

Low-rise (1-2) (L) Mid-rise (3-5) (M) High-rise (6-7) (H) Tall (8+) (Ta)

Number of stories (indicate the number)

C Pre-Code (PC) Pre-code Aseismic Construction: Low Level

TAXONOMY CLASSIFICATIONby a string of tags

Each vulnerability class, which can be syntheticallynamed by a number or a short acronym, is clearlyidentified by a precise taxonomy:URM2-M: BW-IP\URM-HS-UC-LM\R\R\x\LQD-WT\F-T\P-T\M\PCURM3-H: BW-IP\URM-FB-LM\R\R\x\LQD-WT\R-S\P-RC\H\PC

m*

h*

m*

h*

XY

1"

2"

3"

4"

5"

DATA PROCESSING TO DEFINE THE CLASSES DEFINITION OF PARAMETERS EVALUATION OF CAPACITY CURVES For each class and both directions X and Y

For the random variables

84%

0"

0,01"

0,02"

0,03"

0,04"

0,05"

0,06"

0,07"

40" 45" 50" 55" 60" 65" 70" 75" 80" 85" 90"

16%

50%

X direction Y direction

Mechanical parameters and loadsτk,x shear strengthGx,i shear modulusγi specific weight

ΔS,LS4 ΔF,LS4

drift limit values for the shear and flexural response

κx,i spandrel contribution on the masses

qi - ζx,i load and orientation of floors

Sd

Sa

Du,x

Au,x

4π2/Ty,x2

Sd

Sa

Du,y

Au,y

4π2/Ty,y2

Geometrical features

hi inter-storey heightαx,i ratio of resistant wall

over the gross area A

Modal shape

φx,i i-th component of theassumed modal shape

Corrective factors

Κ1,Κ2,Κ3 , Κ4

for the evaluationof the yieldingacceleration

Κ5 , Κ6 for the evaluationof the period

Failure mode

εx weight assigned to thein-plane SSWPmechanism


MASONRY BUILDINGSYNER-G project (http://www.vce.at/SYNER-G/)

CATEGORY CLASSIFICATION

FRM

Bearing Walls (BW) Out of plane (OP); In plane (IP) [Equivalent Frame (EF), Weak Spandrels Strong Piers (WSSP), Strong Spandrels Weak Piers (SSWP)]

FRM

M

Unreinforced Masonry (URM)

Reinforced Masonry (RM) Confined Masonry (CM) Timber-framed Masonry

(TM)

Blocks: Adobe (A); Fired brick (FB); Soft Stone (SS); Hard Stone (HS) [Regular Cut (RC), Uncut (UC), Rubble (RU)]; Hollow clay tile (HC) [High % of voids (H%), Low % of voids (L%), Concrete Masonry Unit (CMU), Autoclaved Aerated Concrete (AAC)]

Mortar: Lime mortar (LM); Cement mortar (CM); Mud mortar (MM); Hydraulic mortar (HM)

Strengthening: Strengthened masonry (Sm) Timber: Confined and braced masonry

panels (TC); Horizontal timber tie (TT) Concrete and reinforcement: [Average

Strength (20-50 MPa)(ASC), Low Strength (<20 MPa)(LSC)]; [Vertical Reinforcement Bars (RBV), Vertical and Horizontal Reinforcement Bars (RBVH)]

P Regular (R) Irregular (IR)

[Isolated (I), Aggregate (A)]

E Regular geometry (R) Irregular geometry (IR)

CO

Regular openings (RO) Irregular openings (IRO)

[High % voids (H%), Low % voids (L%)]

DM

Details: High quality details (HQD), Low quality details (LQD)

Maintenance: Good Maintenance (HM), Low Maintenance (LM)

Tie rods: Without tie rods (WoT); With tie rods (WT)]

Ring beams: Without ring beams (WoRB); With ring beams (WRB)

FS

Rigid (R) Flexible (F)

Reinforced concrete (RC); Steel (S); Timber (T); Vault (V)

RS

Peaked (P) Flat (F) Gable End Walls (G)

Material: Timber (Ti); Corrugated Metal Sheet (CMS); Reinforced Concrete (RC); Thatch (Th)

Thrusting roof (Tr); Unthrusting roof (UTr)

HL

Low-rise (1-2) (L) Mid-rise (3-5) (M) High-rise (6-7) (H) Tall (8+) (Ta)

Number of stories (indicate the number)

C Pre-Code (PC) Pre-code Aseismic Construction: Low Level

CATEGORY Taxonomy Data at national scale

Data at regional scale

Direction X - Material of the Lateral Load Resisting System − Material type − Material technology − Material properties

X X X

X - -

O

Lateral Load Resisting System − Type of lateral load-resisting system − System ductility

X X

- -

O

Height − Number of stories above the ground − Number of stories below the grown − Height of the ground floor

X X X

X X -

O Date of Construction X X Code Level - Occupancy X X Building Position within a Block X X Shape of the Building Plan X -

Data at national scale (e.g. ITALIAN CENSUS ISTAT) , Material of the lateral load-resisting system: 1) Masonry, 2) R.C. 3) R.C. with “pilotis”, 4) othersData at regional scale, Type of masonry and % of distribution:1a) irregular (25%), 1b) uncut (55%), 1c) soli brick (20%)

FRAGILITY CURVES: TAXONOMY & CLASSIFICATIONAVAILABILITY OF DATA

CATEGORY Taxonomy Data at national scale

Data at regional scale

Structural Irregularity − Plan − Elevation − Type of irregularity (Cladding and Openings)

X X X

-

(X) X

O O

Maintenance - X Exterior walls X - Roof − Shape − Covering Material − Roof system material − Roof connections (Thrusting)

X X X X

- - - -

O O O O

Floor − System material − System type − Connections

X X X

- - -

O O O

Foundation system X -

AVAILABILITY OF DATA

Data at national scale (e.g. ITALIAN CENSUS ISTAT) , NO informationData at regional scale, Type of masonry and % of distribution:1) Timber floor (25%), 2) Vault (35%), 3) Brick – Iron (20%), 4) R.C. (20%)


The case study of GAIOLEIRO buildings in Lisbon between XIX and XX centuries

Rio Tejo

Betão armadoMisto alvenaria – betãoAlvenaria não armadaEdifícios singularesAnexos

Avenidas Novas


REF:Simoes etal.(2019)Fragility functions fortall URMbuildings around early 20° century inLisbon.Part1&2.InternationalJournalofArchitectural Heritage,online.

Tipo I Tipo II Tipo III Tipo IV

MainFacade

BackFacade Plan view Case of study


FRAGILITY CURVES: TAXONOMY & CLASSIFICATIONThe case study of GAIOLEIRO buildings in Lisbon between XIX and XX centuries

Epistemic Uncertainties: geometry, structural details and materials

(…)

• Configuração R/C: habitação ou comércio• Solução paredes de empena: meeiras ou independentes• Paredes de empena: tijolo maciço ou tijolo furado• Paredes interiores: tijolo maciço ou tijolo furado• Paredes divisórias: tijolo furado ou tabique de madeira

LOGIC TREE WITH 32 BRANCHES

Tipo I Tipo II Tipo III Tipo IV


FRAGILITY CURVES: TAXONOMY & CLASSIFICATIONThe case study of GAIOLEIRO buildings in Lisbon between XIX and XX centuries

➟ from 32 to 8 branches



PRELIMINARY NUMERICAL ANALYSES TO OUTLINE THE SIMILARITIES IN THE SEISMIC BEHAVIOUR:

H-S-SH-T-T0.070

H-S-S-S-H0.039

H-I-S-S-H0.078

H-I-SH-T-T0.143

S-S-S-S-H0.078

S-S-SH-T-T0.143

S-I-S-S-H0.159

S-I-SH-T-T0.290

The case study of GAIOLEIRO buildings in Lisbon between XIX and XX centuries

𝑓"#|%# 𝑑𝑚 = 𝑓"# 𝑖𝑚 = 𝑃 𝑑𝑚 ≥ 𝐷𝑀|𝑖𝑚 = 𝑃 𝐼𝑀"# < 𝑖𝑚 = Φ𝑙𝑜𝑔 𝑖𝑚

𝐼𝑀"#𝛽"#

RISK ANALYSIS – FRAGILITY

! "#$|&$ '( "&$ *( '(*()-.

If the damage is described by a CONTINOUS variable

If the damage is described by a DISCRETE variable

FRAGILITY FUNCTIONSThe fragility function of a building class gives the probability that a Damage Levels (DM) is reached given a value im of theIntensity Measure (IM) :

where: IMDM is the median value of the lognormal distribution of the intensity measure imDM for which the DM is attained and βDM

is the dispersion.

IMLS

βLS

βDM

IMDM

𝛽"# = 12𝑙𝑜𝑔 𝐼𝑀89 − 𝑙𝑜𝑔 𝐼𝑀;<

the more the building class is homogenous and the less is b

For IM different possible choicesthe more IM is representative

and the less is b

𝑓"#|%# 𝑑𝑚 = 𝑓"# 𝑖𝑚 = 𝑃 𝑑𝑚 ≥ 𝐷𝑀|𝑖𝑚 = 𝑃 𝐼𝑀"# < 𝑖𝑚 = Φ𝑙𝑜𝑔 𝑖𝑚

𝐼𝑀"#𝛽"#

λ16" λ"

λ84"

λ(IMLS)

IMLS

IMH,84[λ(IMLS)]

IMH,16[λ(IMLS)]

λ"

IM

𝛽"# = 𝛽=>?>@AB + 𝛽@DEB + 𝛽A>F>GDHDIDHB + 𝛽E>J>EKLMB�

PGAwith10%ofexceedance probability

16%quantile 50%quantile 84%quantile

Source:

FRAGILITY FUNCTIONS – involved uncertainties

IMH,16[λ(IMLS)]

Sa1(Sd)

IMH,84[λ(IMLS)]

IMLS

SP

EC

TRA

L A

CC

ELE

RAT

ION

SPECTRAL DISPLACEMENT


!

0

200

400

600

800

1000

1200

1400

1600

1800

0 0,5 1 1,5 2 2,5 3

Sa (c

m/s

2)

T (s)

AQA_NS

AQA_WE

AQG_NS

AQG_WE

AQK_NS

AQK_WE

AQV_NS

AQV_WE

AQU_NS

AQU_WE

0

2

4

6

8

10

12

14

16

18

20

0 0,05 0,1 0,15 0,2 0,25 0,3

Sa[m/s2]

Sd[m]

AQA-WE

AQA-NS

AQK-WE

AQK-NS

AQV-WE

AQV-NS

AQG-WE

AQG-NS

AQU-WE

AQU-NS

0

0,2

0,4

0,6

0,8

1

1,2

1,4

1,6

0 0,05 0,1 0,15 0,2 0,25

Sa[g]

Sd[m]

MEANVALUE(AQA,AQK,AQV,AQG,AQU)

Sa- Tacceleration spectrum format

ADRSacceleration spectrum formatL’Aquila2009event – recordings fromthe10available stations onthearea



Numerical curve

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0.00 0.01 0.02 0.03 0.04

Sa [

m/s

2 ]

Sd [m]

Sd [m]

Sa [m

/s2 ]

Capacity curve

Variability of parameters (mechanical, geometric, …) representative of the behavior of the SINGLE buildings

or the WHOLE CLASS OF BUILDINGS STOCK in accordance with the purposes of a regional loss

assessment

fm - MPa0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

P

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

fm [Mpa]E - MPa

200 300 400 500 600 700 800 900 1000

P

0

0.5

1

1.5

2

2.5

3

3.5

E [Mpa]

Exposure analysis1Single structure at a givensite

Classes of buildings with ahomogeneous seismicbehavior

m*

h*

m*

h*

XY

1"

2"

3"

4"

5"

DATA PROCESSING TO DEFINE THE CLASSES DEFINITION OF PARAMETERS EVALUATION OF CAPACITY CURVES For each class and both directions X and Y


84%

0"

0,01"

0,02"

0,03"

0,04"

0,05"

0,06"

0,07"

40" 45" 50" 55" 60" 65" 70" 75" 80" 85" 90"

16%

50%

X direction Y direction


ΔS,LS4 ΔF,LS4




Sd

Sa

Du,x

Au,x

4π2/Ty,x2

Sd

Sa

Du,y

Au,y

4π2/Ty,y2




Modal shape


Corrective factors

Κ1,Κ2,Κ3 , Κ4



Failure mode


REGI

ONAL

SCA

LESI

NGLE

BUI

LDIN

G

Taxonomy | Inventory



Sd

Simplified Bilinear Curve

Say

SduSdy

?

?

? ?

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0.00 0.01 0.02 0.03 0.04

Sa [

m/s

2 ]

Sd [m] Sd [m]

Sa [m

/s2 ]

Sd / Sdy

0.00

0.20

0.40

0.60

0.80

1.00

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00

Sa/S

ay

Sd/Sdy

Sa /

Say

Normalized Bilinear curve

negligible DL3DL1 DL2 DL4


?

im

FRAGILITY FUNCTIONS – DAMAGE PROBABILITY MATRIX (DPM)

DAMAGE PROBABILITY MATRIX represents a typical results (à the fragilityterm) of a CONDITIONED ASSESSMENT

00,10,20,30,40,50,60,70,80,9

1

0 0,2 0,4 0,6 0,8

Prob

abili

ttà

PGA [g]

IMD3 = 0.3g

βD3 = 0.6

IMD1 = 0.1gIMD5 = 0.9g

0,0

0,1

0,2

0,3

0,4

0,5

0,6

D0 D1 D2 D3 D4 D5

Prob

abilità

im = 0.2g 0,0

0,1

0,2

0,3

0,4

0,5

0,6

D0 D1 D2 D3 D4 D5

Prob

abilità

im = 0.4g

FRAGILITY FUNCTIONS– influence of b

00,10,20,30,40,50,60,70,80,9

1

0 0,2 0,4 0,6 0,8

Prob

abili

ttà

PGA [g]

IMD3 = 0.3g

βD3 = 0.9

IMD1 = 0.1gIMD5 = 0.9g

0,0

0,1

0,2

0,3

0,4

0,5

0,6

D0 D1 D2 D3 D4 D5

Prob

abilità

im = 0.2g 0,0

0,1

0,2

0,3

0,4

0,5

0,6

D0 D1 D2 D3 D4 D5

Prob

abilità

im = 0.4g

00,10,20,30,40,50,60,70,80,9

1

0 0,2 0,4 0,6 0,8

Prob

abili

ttà

PGA [g]

IMD3 = 0.3g

βD3 = 0.6

IMD1 = 0.1gIMD5 = 0.9g

0,0

0,1

0,2

0,3

0,4

0,5

0,6

D0 D1 D2 D3 D4 D5

Prob

abilità

im = 0.2g 0,0

0,1

0,2

0,3

0,4

0,5

0,6

D0 D1 D2 D3 D4 D5

Prob

abilità

im = 0.4g

00,10,20,30,40,50,60,70,80,9

1

0 0,2 0,4 0,6 0,8

Prob

abili

ttà

PGA [g]

IMD3 = 0.3g

βD3 = 0.3

IMD1 = 0.1gIMD5 = 0.9g

0,0

0,1

0,2

0,3

0,4

0,5

0,6

D0 D1 D2 D3 D4 D5

Prob

abilità

im = 0.2g0,0

0,1

0,2

0,3

0,4

0,5

0,6

D0 D1 D2 D3 D4 D5

Prob

abilità

im = 0.4g

FRAGILITY FUNCTIONS– influence of b

00,10,20,30,40,50,60,70,80,9

1

0 0,2 0,4 0,6 0,8

Prob

abili

ttà

PGA [g]

IMD3 = 0.3g

IMD1 = 0.15gIMD4 = 0.43g

βD3 = 0.6

0,0

0,1

0,2

0,3

0,4

0,5

0,6

D0 D1 D2 D3 D4 D5

Prob

abilità

im = 0.2g 0,0

0,1

0,2

0,3

0,4

0,5

0,6

D0 D1 D2 D3 D4 D5

Prob

abilità

im = 0.4g

FRAGILITY FUNCTIONS– influence of the ductility

00,10,20,30,40,50,60,70,80,9

1

0 0,2 0,4 0,6 0,8

Prob

abili

ttà

PGA [g]

IMD3 = 0.3g

IMD1 = 0.07gIMD4 = 0.64g

βD3 = 0.6

0,0

0,1

0,2

0,3

0,4

0,5

0,6

D0 D1 D2 D3 D4 D5

Prob

abilità

im = 0.2g0,0

0,1

0,2

0,3

0,4

0,5

0,6

D0 D1 D2 D3 D4 D5

Prob

abilità

im = 0.4g

q Empirical / Observationalq Expertise-based / Heuristicq Mechanical-basedq Hybrid methods

FRAGILITY CURVES: how are they obtained?

All of them pose various critical issues on:

• the incompleteness/reliability of empirical data (Empirical/Observational/Euristic)• the definition of a robust METRIC of DAMAGE• the representativeness of archetype buildings (Mechanical-based)• the need of calibration & validation• the difficulties on defining proper relationships to relate damage to consequence functions• ……

?REF for the classification of methods: Rossetto T., D’Ayala D., Ioannou I., Meslem A. (2014) Evaluation of existing fragility curves , Chapter 3 In SYNER-G: Typology Definition and Fragility Functions for Physical Elements at Seismic Risk: Elements at Seismic Risk, Geotechnical, Geological and Earthquake Engineering 27 pp. 420


q Empirical / Observational

ü Derived from observed damage after the occurrence of an earthquakeü Empirical data are usually referred to macroseismic intensity, which is not

an instrumental measure but is based on a subjective evaluation but inrecent experiences are also derived directly in terms of PGA thanks tothe use of shake-maps

ü Data are valuable since directly correlated to the actual seismic behavior ofbuildings and can be very useful for validation of the others models

ü Vulnerability is dependent on the local seismic culture and the availablematerials in the area, so the extrapolation of empirical fragility functionsfor traditional masonry buildings to other areas can be questionable.


q Empirical / Observational – Examples for RC structures

REF: Del Gaudio et al. (2017) Empirical fragility curves from damage data on RC buildings after the 2009 L’Aquila earthquake, Bull Earthqyake Eng 15: 1425-1450

Reference stock: L’AQUILA 2009 earthquake; derivation of fragility curves for sub-typologies


q Empirical / Observational – Examples for URM structures

REF: Rosti et al. (2019) Derivazione di curve di fragilità empiriche per edifici residenziali in muratura, ANIDIS Conference, Ascoli Piceno 2019.

Reference stock: L’AQUILA 2009 earthquake; derivation of fragility curves for sub-typologies


q Empirical / Observational – some critical issues

0

1

2

3

4

5

4 5 6 7 8 9 10 11 12

µD

I (MCS)

INTENSITY MEASURE

PROBA

BILITY

Issues related to the actual completeness of data for low intensity level of the seismic inputNOT ALL BUILDINGS ARE SISTEMATICALLY

SURVEYED IN THE AREA FAR TO THE EPICENTER

!!

HOMOGENEITY OF THE BUILDING STOCK

Sometimes different trends varying the intensity can be

associated to differentbuildings features

!!


q Expertise-based / Heuristic – Expert elicitationü Expert elicitation is used to assess vulnerability of building types, if no data is available and structural analysis is not feasible; one or

more experts can offer an opinion on the level of demand at which damage is likely to occur.ü To process expert judgments the Delphi method (Dalkey, 1969) or the Cooke’s method (Cooke, 1991) can be used.

Collapse fragility estimates obtained using expert elicitation process.

(Jaiswal et al 2013)

Experts responding to target questions at the workshop

Lisbon workshop, September 23, 2012 (Jaiswal et al 2013)Organized by U.S. Geological Survey’s Prompt Assessment for Global Earthquakes Response (PAGER) and Global Earthquake Model (GEM) -

Expert solicitation to develop DPM for 20 building classes, after checking the reliability of experts by seed questions


q Mechanical-based

§ Analytical simplified

§ Numerical by nonlinear static analyses

§ Numerical by nonlinear dynamic analyses

archetype buildings are identified and modelled in detail; dispersion of

parameters are related to the whole building stock and not to the

uncertainties of the single building

key features of the building class (structural system, geometry, material

properties) are quantified (median values, dispersion)

Incr

esin

gco

mpu

tatio

nale

ffort

Incr

esin

gam

ount

of d

ata

q BASED ON INSTRUMENTAL INTENSITY MEASURES OF THE SEISMIC INPUT

q THEY ALLOW A HUGE FLEXIBILITY IN SELECTING THE REFERENCE INTENSITY MEASURE TO BE ADOPTED

The macroseismic model starts from the original proposal of Lagomarsino and

Giovinazzi (2006)

REF:Lagomarsino S., Giovinazzi S. (2006) Macroseismic and mechanical models for the vulnerability and damage assessment

of current buildings. Bull Earthquake Eng, 4(4): 415-443

MACROSEISMIC MODEL Then it has further developed by the research group of theUniversity of Genova (UNIGE - S.Lagomarsino,S.Cattari &D.Ottonelli) in recent years through …

a robust calibration on the observed damagecollected after many earthquakes in Italy, available fromthe database Da.D.O. developed by the ItalianDepartment of Civil Protection (DPC) (Dolce et al. 2017).





GRADE 5:Destruction

D.A.D.O. Database DaDO database: more than 300000 buildings surveyed after 9 different earthquakes in Italy since Friuli 1976

REF: Dolce M., Speranza E., Giordano F., Borzi B., Bocchi F., Conte C., Di Meo A.,Faravelli M., Pascale V. (2019)Observed damage database of past Italian earthqyakes:the Da.D.O. Webgis. Bollettino di Geofisica Teorica e Applicata 60 (2) 141-164.

D.A.D.O. Database DaDO database: more than 300000 buildings surveyed after 9 different earthquakes in Italy since Friuli 1976

DAMAGE SECTION

TYPOLOGICAL SECTION with valuable information also on vulnerability

MACROSEISMIC MODEL – Basics of the original proposal of Lagomarsino & Giovinazzi 2006

q Classifiable as Expert-based q It is directly derived from the European Macroseismic Scale (Grunthal 1998 ), which defines six

vulnerability classes (named from A to F) and various building types (seven of them related to masonry buildings).





GRADE 5:Destruction

EMS 98

There isn’t a directcorrespondance between a specific structural typology

& a vulnerability class


q Classifiable as Expert-based q It is directly derived from the European Macroseismic Scale (Grunthal 1998 ), q If a building class is considered, the linguistic definitions of EMS98 may be translated in quantitative terms,

by the fuzzy set theory, and an incomplete Damage states Probability Matrix (DPM) is obtained. The completion is made by using the binomial probability distribution.

EMS 98

μD mean damage ofdistribution

0

0,2

0,4

0,6

0,8

1

0 10 20 30 40 50 60 70 80 90 100

FewManyMost

0

0,2

0,4

0,6

0,8

1

0 10 20 30 40 50 60 70 80 90 100

%DamagedBuilding

FewManyMost

Fuzzy Set Theory

FUZZY SET THEORY BINOMIAL PROBABILITY DISTRIBUTION

translated completed



by the fuzzy set theory, and an incomplete (DPM) is obtained.

q The vulnerability is synthetically expressed by a vulnerability curve (Bernardini et al. 2011), which givesthe mean damage μD as a function of the macroseismic intensity I

!! = 2.5 + 3 !"#ℎ! + 6.25! − 12.7

! 0 ≤ !! ≤ 5 !! = 2.5 + 3 !"#ℎ! + 6.25! − 12.7

! 0 ≤ !! ≤ 5

The curve is defined by two parameters representative of the seismic behavior of a group of homogeneous buildings: the

vulnerability index V and the ductility index Q

LS1

LS2

LS3

LS4

LS5

0

1

2

3

4

5

3 4 5 6 7 8 9 10 11 12

µD

MACROSEISMIC INTENSITY

A - V=0.88 B - V=0.72 C - V=0.56 D - V=0.40 E - V=0.24 F - V=0.08



by the fuzzy set theory, and an incomplete (DPM) is obtained.

q The vulnerability is synthetically expressed by a vulnerability curve (Bernardini et al. 2011), which givesthe mean damage μD as a function of the macroseismic intensity I

!! = 2.5 + 3 !"#ℎ! + 6.25! − 12.7

! 0 ≤ !! ≤ 5 !! = 2.5 + 3 !"#ℎ! + 6.25! − 12.7

! 0 ≤ !! ≤ 5

The curve is defined by two parameters representative of the seismic behavior of a group of homogeneous buildings: the

vulnerability index V and the ductility index Q

Class A B C D E V 0.9 0.74 0.58 0.42 0.26

Q assumed costant and equal to 2.3 for residential buildings

LS1

LS2

LS3

LS4

LS5

0

1

2

3

4

5

3 4 5 6 7 8 9 10 11 12

µD


A - V=0.88 B - V=0.72 C - V=0.56 D - V=0.40 E - V=0.24 F - V=0.08

MACROSEISMIC MODEL – Recent developments made by UNIGE

STATISTICAL REPROCESSING OF DATA AND DEFINITION OF DPM

FIRST STEP: Conversion of damage data of AeDES formsinto a DAMAGE LEVEL compatible with that defined at

global scale according to the EMS98

Different proposals ….

q Rota et al. 2008q Pasquale and Goretti 2001q D.A.D.O proposal by DPCq Proposal by UNIGE within the ReLUIS research

DPM for I=6.5

I N° Nuova Proposta Rota, 2008 Goretti-Di Pasquale

(medio) Angeletti, 1982 Goretti-Di Pasquale

(medio) Goretti, 2001

5

5803

5.5

9820

6

1981

8

6.5

3930

7

3284

7.5

8172

8 966

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

Proposal byUNIGE Rotaetal2008 DiPasqualeeGoretti,2001

REF:LagomarsinoS.,CattariS.,Ottonelli D.(2020)Macroseismic fragility curves forItalian residential URMbuildings calibratedbyobserved damage ,Bulletin ofEarthquake Engineering,tobesubmitted.

MACROSEISMIC MODEL and EMPIRICAL DATA1. Conversion of empirical damage data collected with a DAMAGE SURVEY FORM to a DAMAGE LEVEL

DAMAGE TO EACH ELEMENT• Multiple choice possibility• Combination rule function of the

extension of damage: ∑ei ≤ 1• With i each structural or non-

structural element

ESTIMATE OF THE GLOBAL DAMAGE

LEVEL

?DIFFERENT APPROACH

WEIGHTED AVERAGE among walls, floors and roof – according toDAMAGE , EXTENSION and WEIGHT of thedifferent elements

Rota et al. 2008

PEAKS OF DAMAGE among walls, floors and roof

DAMAGE and EXTENSION of the walls

Dolce et al. 2017

AeDES Damage DL

Nullo 0

D1 < 1/3 1

1/3 < D1 < 2/3 1

D1 > 2/3 1

D2 - D3 < 1/3 2

1/3 < D2 - D3 < 2/3 3

D2 – D3> 2/3 3

D4 – D5 < 1/3 4

1/3 < D4 – D5 < 2/3 4

D4 – D5 > 2/3 5

Full survey Partial survey

Walls 0.6 0.8Floors 0.2 0Roof 0.2 0.2

Criteria from Umbria and MarcheEarthquake, 1997

AeDES Damage di

D0 0D1 1

D2 – D3 3D4 – D5 5

Extension ei

> 2/3 5/61/3 - 2/3 1/2

< 1/3 1/6

Lagomarsino et al. 2020

MACROSEISMIC MODEL and EMPIRICAL DATA2. Application of the different criteria and results in terms of DPM




5

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5.5

9820

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8

6.5

3930

7

3284

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8172

8 966

0"

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1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

I=6.5 I=7.5




5

5803

5.5

9820

6

1981

8

6.5

3930

7

3284

7.

5

8172

8 966

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

WEIGHTED AVERAGE




5

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8 966

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

PEAK OF DAMAGE




5

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8

6.

5

3930

7

3284

7.5

8172

8 966

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"0"

0.5"

1"

0" 1"2" 3"4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"0"

0.5"

1"

0" 1" 2" 3" 4" 5"

WEIGHTED AVERAGE among walls, floors and roof –

according to DAMAGE , EXTENSION and WEIGHT of the

different elements

PEAKS OF DAMAGE among walls, floors

and roof


0

0.5

1

1.5

2

2.5

3

4 5 6 7 8 9 10

μD

I

DannoUniGE

Emilia2012 L'Aquila2009 Pollino1998Marche1997 Irpinia1980 Friuli1976

0

0.5

1

1.5

2

2.5

3

4 5 6 7 8 9 10

μD

I

DannoDado


0

0.5

1

1.5

2

2.5

3

4 5 6 7 8 9 10

μD

I

DannoUniGE


UNIGE Proposal for conversion DADO Proposal for conversion

THE TREND OF INCREASING MEAN DAMAGE WITH INCREASING INTENSITIES IS CONFIRMED , ALSO VARYING

THE APPROACH ADOPTED FOR THE CONVERSION OF AEDES FORM DATA

DATA from Irpinia 1980 and L’Aquila 2009 earthquakesare those more robust for the calibration aims (for number

of data and completeness of area surveyed)

EventoSismico N° EdificiIniziale

N° EdificiconIntensità

N° EdificiinMuratura

Friuli 1976 41852 41852 29641Irpinia1980 38079 33220 26335

Umbria-Marche1997 48525 34873 29512Pollino1998 17442 16689 13887L’Aquila2009 74049 73793 51438Emilia 2012 22554 22489 18194


EVEN THE APPROPRIATENESS OF USING A BINOMIAL DISTRIBUTION IS CONFIRMED

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5

P

DL

Irpinia80Muratura-I=6.5

BINOMIALE

UNIGE

DADO

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5

P

DL

Irpinia80Muratura-I=8

BINOMIALE

UNIGE

DADO


CONVERSELY, DATA RELATED TO URM BUILDINGS HIGHLIGHT AS THE Q FACTOR IS NOT CONSTANT VARYING THE CLASSES

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12

<19-Low

tu3 Q=2.3 Q=3.8

μD

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12

19-45-Low

tu2 Q=2.3 Q=2.6

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12

>1981-Medium

tu5 Q=2.3 Q=1.9

L’AQUILA 2009

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10 12

Low<1919-Q=3.8 Low19-45-Q=2.6

Low19-61-Q=2.7

μD

SUCHARESULTISCONFIRMEDALSOBYTHEIRPINIA1980DATABASE

In the new proposal in the calibration of the model also the Q factor isconsidered as a free variable

INCREASINGTHEAGETHEQ PARAMETERDECREASES0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

<1900 1900-43 44-61 62-81

Q-In

dicedidu+lità

Classidietà

MEDIUMIRPINIAMEDIUMAQUILALOWIRPINIALOWAQUILA


00.10.20.30.40.50.60.70.80.91

0 1 2 3 4 5

P

DL

AquilaMuratura19-45[Num.6688]

00.10.20.30.40.50.60.70.80.91

0 1 2 3 4 5

P

DL

AquilaMuratura<1919[Num.29598]

00.10.20.30.40.50.60.70.80.91

0 1 2 3 4 5

P

DL


00.10.20.30.40.50.60.70.80.91

0 1 2 3 4 5

P

DL


00.10.20.30.40.50.60.70.80.91

0 1 2 3 4 5

P

DL


00.10.20.30.40.50.60.70.80.91

0 1 2 3 4 5

P

DL

AquilaMuratura>2001[Num.780]

μD = 2.06 μD = 2.26 μD = 1.79

μD = 0.32 μD = 0.24 μD = 0.86

DPM FOR L’AQUILA 2009 EARTHQUAKE VARYING THE AGE

EVIDENCES FROM L’AQUILA EARTHQUAKE ON THE CHANGES OF URM BUILDINGS BEHAVIOUR


DEVELOPMENT OF THE MODEL ACCOUNTING FOR THE EVIDENCES FROM REAL DAMAGE DATA

!! = 2.5 + 3 !"#ℎ! + 6.25! − 12.7

! 0 ≤ !! ≤ 5 !" = 2.5 '1 + *+,ℎ./ +6,252− 10.8 − 66 78

Lagomarsino&Giovinazzi 2006 Newproposal withQ=0.9+2.8V

0

1

2

3

4

5

0 1 2 3 4 5 6 7 8 9 10

μD

I

Irpinia1980 Friuli1976 Pollino98 V(2006) V(2011)

V(2006mod) Emilia2012 L'Aquila2009 Marche1997

• V(2006): Lagomarsino e Giovinazzi 2006;• V(2011): Bernardini et al 2011;• V(2006 mod): new proposal

y=2.8066x+0.9135

0

0.5

1

1.5

2

2.5

3

3.5

4

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Q-Indicedidu+

lità

V-Indicedidu+lità

L’Aquila2009

Q =2.8V+0.9


0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

4 6 8 10 12

Dann

omed

io

Intensità

A-L&G2006B-L&G2006C-L&G2006D-L&G2006A-new1B-new1C-new1D-new1

Class A B C DV 0.99 0.80 0.61 0.42

!" = 2.5 1 + )*+ℎ - + 3.450 − 11.72.80 + 0.9

New proposal

Updating of reference values of EMS98 classes in order to obtainresults more consistent with data

from observed damage

MACROSEISMIC MODEL – Recent developments made by UNIGE USE OF DATA AVAILABLE ON SUB-CLASSES TO DEFINE PROPER BEHAVIOUR MODIFIERS IN ORDER

TO DEFINE THE EXPECTED CHANGES IN THE CORRESPONDING VULNERABILITY CURVES

0.0

0.2

0.4

0.6

0.8

1.0

1.2

<1900 1900-43 44-61 62-81

V-In

dicedivulnerab

ilità

Classidietà


AGE

REFERENCE MEAN VALUE

OF THE WHOLE CLASS

MODIFIERS

IF > 0 IT INCREASES THE

VULNERABILITY

IF <= 0IT DECREASES THE

VULNERABILITY


USE OF DATA AVAILABLE ON SUB-CLASSES TO DEFINE PROPER BEHAVIOUR MODIFIERS IN ORDER TO DEFINE THE EXPECTED CHANGES IN THE CORRESPONDING VULNERABILITY CURVES

0.0

0.2

0.4

0.6

0.8

1.0

1.2

<1900 1900-43 44-61 62-81

V-In

dicedivulnerab

ilità

Classidietà


MASONRY TYPOLOGYRC= Regular Cut masonry // UC=Uncut masonryQUALITY OF STRUCTURAL DETAILSHQD=High Quality Detailed (tie rods and ring beams) // LQD=Low Quality Detailed (no tie rods and ring beams)DIAPHRAGMS TYPOLOGYV=Vauls // F=Flexible Floor // R=Semi-rigid Floor // RC=Rigid Floor

TAXONOMY of reference (Lagomarsino and Cattari 2013)

AGE

CALIBRATION AND COMBINATION OF BEHAVIOUR MODIFIERS

Independent processCascade process

RC= Regular Cut masonry // UC=Uncut masonryHQD=High Quality Detailed (tie rods and ring beams) // LQD=Low Quality Detailed (no tie rods and ring beams)

V=Vauls // F=Flexible Floor // R=Semi-rigid Floor // RC=Rigid Floor

TAXONOMY of reference (Lagomarsino and Cattari 2013)

GROUPING THE DATA ON SPECIFIC SUB-CLASSES ACCORDING TO ….


Indipendent Process

V_Global Abruzzo= 0.692 [40781] Buildings] V_Regular Cut Abruzzo = 0.426 [12369] Buildings]V_Uncut Abruzzo = 0.814 [25763] Buildings]

Vulnerability Index

0

1

2

3

4

5

5 6 7 8 9 10 11 12

µ D

Macroseismc Intensity

GlobalRegularUncut

Decreases vulnerabilityΔV<O

Increases vulnerabilityΔV>O

0

1

2

3

4

5

5 6 7 8 9 10 11 12

µ D


GlobalHQDLQD

Decreasesvulnerability ΔV<O


V_Global Abruzzo= 0.692 [40781] Buildings] V_HQD Abruzzo = 0.594 [13749] Buildings]V_LQD Abruzzo = 0.786 [24200] Buildings]

Vulnerability Index

ROLE OF MASONRY TYPE ROLE OF STRUCTURAL DETAILS


0

1

2

3

4

5

5 6 7 8 9 10 11 12

µ D


GlobalFlexibleVaultRigidRigid - RC

Indipendent Process

V_Global Abruzzo= 0.692 [40781] Buildings] V_vault= 0.881 [3864] Buildings]V_rigid = 0.865 [5660] Buildings]V_rigid = 0.631 [9442] Buildings]V_rigid = 0.444 [8300] Buildings]

Vulnerability Index

Decreases vulnerabilityΔV<O


ROLE OF DIAPHRAGMS

SEISMIC BEHAVIOUR MODIFIERS

Type of masonry

LQD: absence of aseismic devices

HQD: presence of aseismic devices

Modifiers in DVm

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

Regular Cut Uncut Regular Cut LQD Regular Cut HQD Uncut LQD Uncut HQD

Macroseismic Modifiers - PRE 1919

Vi decreases –Vulnerability decreases

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

<1919-UC-LQD <1919-UC-HQD <1919-RC-LQD <1919-RC-HQD-V

Macroseismic Modifiers

Cascade process SRSS SUM

Modifiers in DVm

Costruction period < 1919 0.132

Masonry quality - RC -0.180

Masonry quality - UC 0.127

Detail quality - LQD 0.112

Detail quality - HQD -0.064

FROM recent developments made by UNIGE: SRSS RULE MORE APPROPRIATE!!

MACROSEISMIC MODEL – from vulnerability curves to fragility curves

q Firstly, it is necessary to define a reference MEAN DAMAGE VALUE to be associated to each DAMAGE LEVEL

LS1

LS2

LS3

LS4

LS5

0

1

2

3

4

5

3 4 5 6 7 8 9 10 11 12

µD


A - V=0.88 B - V=0.72 C - V=0.56 D - V=0.40 E - V=0.24 F - V=0.08

µD,DL1

µD,DL2

µD,DL5

0

0,1

0,2

0,3

0,4

0 1 2 3 4 5

µD,DL2 = 1.57

µD,DLk = 0.93k − 0.29

Linearregression fromvalues obtained fromthebinomial distribution


q Firstly, it is necessary to define a reference MEAND DAMAGE VALUE to be associated to each DAMAGE LEVELq Then, it is possible computing the fragility curve in terms of Intensity by assessing the I value that produces the

attainment of DLk

𝐼"OP = 11.7 − 3.45𝑉 + 0.9 + 2.8𝑉 𝑎𝑡𝑎𝑛ℎ 0.4𝜇"OP − 1 µD,DLk = 0.93k − 0.29

0

0,2

0,4

0,6

0,8

1

0 2 4 6 8 10 12

Prob

abili

tà

Intensità

Classe A

D1D2D3D4D5

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 2 4 6 8 10 12Pr

obab

ilità

Intensità

Danno D2

Classe A

Classe B

Classe C

Classe D

ForaGIVENvulnerability class varying theDL ForaGIVENDLvarying thevulnerability class

NOTWELLREPRESENTEDBYTHECUMULATIVELOGNORMALFUNCTION…


q Firstly, it is necessary to define a reference MEAND DAMAGE VALUE to be associated to each DAMAGE LEVELq Then, it is possible computing the fragility curve in terms of Intensity by assessing the generic I value that

produces the attainment of DLkq Finally, it is necessary to introduce a proper Intensity – PGA correlation law in order to define the fragility curve in

terms of a instrumental intensity measure

Comparison between some I-PGA Correlation law available in literature and that calibrated by UNIGE on basis of shakemap data from L’Aquila 2009 earthquake

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

4 5 6 7 8 9 10 11 12

PGA

[g]

Intensità Macrosismica

EDIFICI DBMargottini (1992)Murphy and O'Brien (1977)Faccioli e Cauzzi (2006)Faenza e Michelini (2010)L'Aquila 50%L'Aquila 16%L'Aquila 84% CorrelazioneI-PGA c1 c2

Margottini et al. (1992) 0.0430 1.66Murphy and O'Brien (1977) 0.0322 1.78Faccioli e Cauzzi (2006) 0.0464 1.67Faenza e Michelini (2010) 0.0197 2.44

CorrelazioneI-PGA c1 c2daShakeMapL'Aquila(mediana) 0.05 1.66daShakeMapL'Aquila(16%) 0.02 1.82daShakeMapL'Aquila(84%) 0.13 1.48

UNIGEproposal

Literature proposals


q Firstly, it is necessary to define a reference MEAND DAMAGE VALUE to be associated to each DAMAGE LEVELq Then, it is possible computing the fragility curve in terms of Intensity by assessing the generic I value that

produces the attainment of DLkq Finally, it is necessary to introduce a proper Intensity – PGA correlation law in order to define the fragility curve

in terms of a instrumental intensity measure

0

0,2

0,4

0,6

0,8

1

0 0,2 0,4 0,6 0,8

Prob

abilit

à

PGA [g]

Classe A

D1 - log D2 - log D3 - log D4 - log D5 - logD1 D2 D3 D4 D5

The fragility curve in PGA is wellfitted by the lognormal cumulative

function !

!!" !" = ! ! > !!" !" = ! !"!" < !" = Φ!"# !"

!"!"!!"

!"#$% = '(')(+,-./) = '(')1.3.4.)/56(7.86).95):;:<= 7.41%.(.79

MACROSEISMIC MODEL –fragility curves developed by UNIGE

q fragility curve in terms of a instrumental intensity measure

WHAT SOURCES OF UNCERTAINTY ARE CONSIDERED?

0

0,2

0,4

0,6

0,8

1

0 0,2 0,4 0,6 0,8

Prob

abilit

à

PGA [g]

Classe A

D1 - log D2 - log D3 - log D4 - log D5 - logD1 D2 D3 D4 D5

βLS

IMLS

From the fittingUncertainty on the V value - variability at

large scale of vulnerability classes

L’Aquila 16° quantile – Irpinia 84° quantile

!"# = !%% &, (%, ) + !+% )

MACROSEISMIC MODEL –fragility curves developed by UNIGE

HOW WE CAN PASS FROM THE FRAGILITY CURVE OF THE EMS98 VULNERABILITY CLASSES TO OTHER SUB-CLASSES

(à TARGETED TO OUR INVENTORY & OUR AVAILABLE DATA)?

0

0,2

0,4

0,6

0,8

1

<1919 19-45 46-61 62-81 >1981

V

Classi di età

LowMediumHigh

LOWClassi età VEMPIRICI A B C D< 1919 0.952 80 201919 - 1945 0.847 25 751946 - 1961 0.705 50 501962 - 1981 0.550 70 30> 1981 0.420 100

MEDIUMClassi età VEMPIRICI A B C D< 1919 0.914 60 401919 - 1945 0.781 90 101946 - 1961 0.743 70 301962 - 1981 0.648 20 80> 1981 0.496 40 60

Class A B C DV 0.99 0.80 0.61 0.42

BY ASSIGNING PROPER% A - % B - % C - % D

SUB-CLASS

NEW MACROSEISMIC MODEL –VALIDATION

ReLUIS-DPC Project: Italian seismic risk map

For the aim of validation and within the contextof ReLUIS-DPC project addressed to developingItalian seismic risk map the fragility curves have

been implemented in the IRMA Platform

ReferenceefiguradiIRMA

DL1– Simulated bythemacroseismic model

ScenarioofL’Aquila2009earthquake – Validation madebythePlatformIRMADL1– real datafrom

DaDO



ScenarioofL’Aquila2009earthquake- Validation madebythePlatformIRMADL3 – real datafrom

DaDO



DL4– real datafromDaDO


ScenarioofL’Aquila2009earthquake- Validation madebythePlatformIRMA

Barisciano

Sant’EusanioForconese

Shakemap ofL’Aquila2009


COMPARISON IN TERMS OF DPM FOR VARIOUS MUNICIPALITIES WITH DIFFERENT EPICENTRAL DISTANCE

0

0.1

0.2

0.3

0.4

0.5

0 1 2 3 4 5

Probabilità

Danno

L'Aquila

DaDO

IRMA

DANNO0 1 2 3 4 5 TOT.

5276 1686 1639 970 628 490 106891742 1712 2180 2174 1374 254 9436

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5

Probabilità

Danno

Barisciano

DaDOIRMA

0

0.1

0.2

0.3

0.4

0.5

0.6

0 1 2 3 4 5

Probabilità

Danno

Sant'Eusanio

DaDO

IRMA

DANNO0 1 2 3 4 5 TOT. 64 61 71 39 25 40 30042 45 56 54 31 5 234

DANNO0 1 2 3 4 5 TOT. 539 231 204 74 31 18 1097285 245 226 161 62 7 986

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 1 2 3 4 5

Probabilità

Danno

PoggioPicenze

DaDO

DANNO

0 1 2 3 4 5 TOT.

128 63 63 44 14 28 34080 74 76 60 27 3 320

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5

Probabilità

Danno

Sulmona

DaDO

IRMA

DANNO0 1 2 3 4 5 TOT. 778 149 64 12 4 0 10071713 490 116 21 1 0 2341

sulmona

q Classifiable as Analytical method q Structural response described in terms of CAPACITY CURVE (only the GLOBAL IN-PLANE response is considered)

m*

h*

m*

h*

d

m*

h* zi

mi, ψι#

XYSd

Sa

Du,X

Au,X

4π2/Ty,X2#

q Possibility of taking into account the variousparameters that determine the structuralresponse

q Need to define a statistical model for randomvariables

q Definition of the LIMIT STATES on the capacitycurve and the corresponding damping values

Corrective factors

Κ1,Κ2,Κ3 , Κ4




84%

0"

0,01"

0,02"

0,03"

0,04"

0,05"

0,06"

0,07"

40" 45" 50" 55" 60" 65" 70" 75" 80" 85" 90"

16%

50%


ΔS,LS4 ΔF,LS4







Modal shape


Failure mode


REF:Lagomarsino, S., Cattari S. (2014). Fragility functions of masonry buildings (Chapter 5), pp.111-156. In SYNER-G: Typology Definition and Fragility Functions for Physical Elements at Seismic Risk: Elements at Seismic Risk, Geotechnical, Geological and Earthquake Engineering 27 pp. 420

THE MECHANICAL–BASED APPROACH : The DVB-masonry model proposed in Lagomarsino & Cattari 2014

ACCELERATION ULTIMATE DISPLACEMENT CAPACITY

PERIOD

SSW

P

WSS

P

KSTIFFNESS - Corrective factors to account for the flexuralcontribution in piers and the role of spandrels

KSTRENGTH - Corrective factors to account for the irregularity and the role of spandrels


Sd

Sa

Du,X

Au,X

4π2/Ty,X2#


AC

CE

LER

ATIO

N

DISPLACEMENT

WSS

P EF

SS

WP

OV

ER

ALL

BA

SE

SH

EA

R

Presence of r.c. tie beams

Presence of steel tie – rods

Spandrels not coupled to other tensile resistant element


The evaluation of these variables requires:

• the definition of a limited number of mechanical and geometrical parameters

• the assumption of a fundamental modal shape

• the attribution of specific correction factors, aimed to take into account the effects related to the comprehensive set of constructive and morphologicaldetails

e.g. : the presence of tie-rods or r.c. ring beams coupledto the spandrels

PERIOD


ACCELERATION


ULTIMATE DISPLACEMENT CAPACITY

SSW

P

WSS

P

aims to consider the flexuralcontribution in piersK5

K 5 = 1+ 11.2

GE

hb

bp

⎛

⎝⎜⎞

⎠⎟

2⎡

⎣⎢⎢

⎤

⎦⎥⎥

−1

PERIOD


effects on the stiffness related to the spandrelinfluence on the boundary conditions on piersK6

Correction factor EF WSSP SSWPK5 0.4 ÷ 0.8 0.4 ÷ 0.8 0.6 ÷ 0.8K6 0.6 ÷ 1 0.3 ÷ 0.7 1


AC

CE

LER

ATIO

N

DISPLACEMENT

WSS

P EF

SS

WP

KSTIFFNESS

ACCELERATION



AC

CE

LER

ATIO

N

DISPLACEMENT

WSS

P EF

SS

WP

KSTRENGTH

modifies the strength as a function of the main prevailingfailure mode expected at scale of masonry piers.K1

accounts for the influence of thenon homogeneous size of themasonry piers.

K2 K 2 = 1− 0.2Nmxl Axl , j

2

j∑

Axl

2≥ 0.8

K 3 = 1+eyldyl Axl

yk − yCl( )2Axl ,k

k∑

≤1.25

accounts for the influence ofgeometric and shape irregularitiesin the plan configuration.

K3

accounts for the effectiveness of spandrels, whichinfluence the global failure mechanism of the building (EF,WSSP and SSWP).

K4

Correction factor EF WSSP SSWP

K1 0.8 ÷ 1.5 0.8 ÷ 1 1 ÷ 1.5

K2 0.8 ÷ 1 1 1

K3 0.75 ÷ 1 0.75 ÷ 1 0.75 ÷ 1

K4 0.6 ÷ 1 0.5 ÷ 0.8 1

SSW

P

WSS

P

• The same formula also applies to LS3

• Dy,X=Au,X(Ty,X/2p)2 is the yielding displacement

• N: number of stories (i=1,..N is the level counter)

• eX allows considering intermediate failure modes, which occurin Equivalent Frame (EF) behavior



SSW

P

WSS

P

• The same formula also applies to LS3

• Dy,X=Au,X(Ty,X/2p)2 is the yielding displacement

• N: number of stories (i=1,..N is the level counter)

• eX allows considering intermediate failure modes, which occurin Equivalent Frame (EF) behavior

DS (shear) DF (flexural)LS3 0.0025 - 0.004 0.004 - 0.008LS4 0.004 - 0.006 0.008 - 0.012

• Identification of the DL1 and DL2DLS1 =0.7 Dy,XDLS1 =C2 Dy,X

Sd

DEFINITION OF DL

Say

SduSdy

?

? ?


§ c2 is a coefficient that varies as a function of the prevailing global failure mode.It is proposed to assume a value for c2 from 1.2 to 2 (Lagomarsino and Cattari2014), varying from the SSWP to the WSSP failure mode

DL1

DL2

DL3

DL4


DL5 ????

• DLS4 is alternatively assumed equal to DS,LS4 or DF,LS4 as afunction of the prevailing failure mode in masonry piers for theexamined direction (if shear or flexural one)

THE MECHANICAL –BASED APPROACH: definition of fragility curves

q Classifiable as Analytical method q Structural response described in terms of CAPACITY CURVE (only the GLOBAL IN-PLANE response is considered)q Evaluation of IMDL through the comparison between the CAPACITY CURVE and the SEISMIC INPUT

expressed by the response spectrum

IMLS

IMLS Sa(Sd)

(DLS , ALS)

IMLS Sa(Sd) η(x)

LS

Sa(Sd) 1

TLS

overdamped spectrum elastic spectrum

spectrum normalized

AC

CE

LER

AT

ION

DISPLACEMENT

!"!" =!!"

!!1(!!")!(!!")

!(!!") =10

5 + !!"

REF:Discussion on the reliability of nonlinear static procedures in Marino et al. 2019 (Engineering Structures, in press)



expressed by the response spectrum q Evaluation of bDL through the ANALYTICAL EVALUATION of all sources of uncertainties

𝛽𝐿𝑆 = %𝛽𝐻2 + 𝛽𝐷

2 + 𝛽𝑇2 + 𝛽𝐶

2





2 + 𝛽𝑇2 + 𝛽𝐶

2 !"# = %!&2 + !)2 + !*2 + !+2

!! = 0.5 !"# !"!,84 !(!"!") − !"# !"!,16 !(!"!")

λ16" λ"

λ84"

λ(IMLS)

IMLS

IMH,84[λ(IMLS)]

IMH,16[λ(IMLS)]

λ"

IM

IMH,16[λ(IMLS)]

Sa1(Sd)

IMH,84[λ(IMLS)]

IMLS

SPEC

TRAL

AC

CEL

ERAT

ION


Influence on the spectral demand of the epistemic uncertainty on the hazard curve





2 + 𝛽𝑇2 + 𝛽𝐶

2

!! = 0.5 !"# !"!,84 − !"# !"!,16

CAPACITY DEMAND


84%

0"

0,01"

0,02"

0,03"

0,04"

0,05"

0,06"

0,07"

40" 45" 50" 55" 60" 65" 70" 75" 80" 85" 90"

16%

50% 16 e 84% Sa

T

ItrequirestheevaluationoftheintensitymeasuresIMD,16 andIMD,84 that

correspondtoadisplacementdemandequaltoDLS,onthemediancapacitycurveoftheconsideredclassof

buildings,byusingtheconfidencelevelsresponsespectraSa1,16(Sd)andSa1,84(Sd)

respectively

!! = 0.5 !"# !"!,84 − !"# !"!,16

Sa1,16(Sd)

Sa1(Sd)

Sa1,84(Sd)

PGA=1 SP

ECTR

AL A

CC

ELER

ATIO

N


Sa1,16(Sd) Sa1(Sd)

Sa1,84(Sd)

Sa,max=1

SPEC

TRAL

AC

CEL

ERAT

ION


IM=PGA IM=Sa(T1)

Influence of the selection of IM





2 + 𝛽𝑇2 + 𝛽𝐶

2

!! = 0.5 !"# !"!,84 − !"# !"!,16

DLS DLS,84

LS1

LS2 LS3 LS4

p p p

DLS

p

AC

CE

LER

AT

ION

DISPLACEMENT DLS,16





2 + 𝛽𝑇2 + 𝛽𝐶

2

! = !!! !!!!!

xk =(Xk-μk)/σk

CAPACITY DEMAND2N analyses

50% Sa

T

!! = !!!

Through the use of the RESPONSE SURFACE TECNIQUE




FRAGILITY CURVEofDamage States DAMAGE PROBABILITY

&IMLS

IMLS Sa(Sd)

(DLS , ALS)

IMLS Sa(Sd) η(x)

LS

Sa(Sd) 1

TLS

overdamped spectrum elastic spectrum

spectrum normalized

AC

CE

LER

ATIO

N

DISPLACEMENT

VARIATION OF MASONRY QUALITY

VARIATION OF FLOORS

LQD HQD

VARIATION OF NUMBER OF STOREYS

VARIATION OF QUALITY DETAILS

HQD

APPLICATION of ANALYTICAL MODELS FOR MASONRY BUILDINGS

LQD HQD

SEISMIC BEHAVIOUR MODIFIERS

Type of masonry


HQD: presence of aseismic devices

Type of masonry


HQD: presence of aseismic devicesRB - Ring BeamsTR – Tie Rods

Modifiers in DPGA

Modifiers in DPGA

-0.06

-0.01

0.04

0.09

0.14

0.19

Regular Cut Uncut Regular Cut LQD Regular Cut HQD Uncut LQD Uncut HQD

Macroseismic Modifiers - PRE 1919

-0.06

-0.01

0.04

0.09

0.14

0.19

Regular Cut Uncut Regular CutLQD

Regular CutHQD TR

Regular CutHQD TB

Uncut LQD Uncut LQDTR

Uncut LQDRB

Mechanical Modifiers - PRE 1919

PGA increases –Vulnerability decreases

PGA increases –Vulnerability decreases

THE MECHANICAL –BASED APPROACH: fragility curves varying the sub-classes

Vault

Flexible

Rigid

Reinforced concrete

Vault

Flexible

Rigid

Reinforced concrete

Vault

Flexible

Rigid

Reinforced concrete

Low Quality Details

High Quality Details (Tie rods)

Low Quality Details (Ring beams)

Uncut masonry

Masonry – < 1919 –Number of storeys 3

DEFINITION of the CLASSES of REFERENCE

Thesame forthecut masonry……

DIAPHRAGMS GROUPED DETAILS GROUPEDMASONRY TYPOLOGY GROUPED

Combination of the fragility curves to obtain the curve representative of the class: MASONRY – < 1919 – NUMBER OF STOREYS 3

DIAPHRAGMS GROUPED

DETAILS GROUPED

MASONRY TYPOLOGY GROUPED


…..Combination of the fragility curves to obtain the curve representative of the class:

MASONRY – < 1919 – NUMBER OF STOREYS 3

Uncut Masonry 86%Regular cut Masonry 14%

Uncut Masonry Low Quality Details 77%High Quality Details 23%

Regular cut Masonry Low Quality Details 62%High Quality Details 38%

Uncut Masonry

LQD

Vault 26%Flexible 34%

Rigid 36%Reinforcedconcrete

4%

HQD



13%

Regular cut Masonry

LQD



11%

HQD



40%

DIAPHRAGMS GROUPED

DETAILS GROUPED

MASONRY TYPOLOGY GROUPED


• Built in 1930• Interstory heigth: 4.00 m• Gross area:520 m2

• T-shaped plan• 3 story building• Rigid floors• Stone masonry

The school of P. Capuzi in Visso monitored by the Italian Department of Civil Protection

THE P:CAPUZI SCHOOL – preliminary validation of mechanical model

Dataavailable fromReLUIS Project2017/2018.REF:S.Cattarietal.2019DiscussionondatarecordedbytheItalianstructuralseismicmonitoringnetworkonthreemasonrystructureshitbythe2016-2017CentralItalyearthquake,Proc.ofCOMPDYN2019,Crete24-26June2019.

24/8 26/10 30/10

24/8 26/10 30/10

• Significant damage accumulation effects after the subsequent shocks

The school of P. Capuzi in Visso


0

5

10

15

20

0.0 0.5 1.0 1.5 2.0 Sa

[m/s

2 ]

T [s]

24/08/16 26/10/16 30/10/16 NTC

0

5

10

15

20

0.0 0.5 1.0 1.5 2.0

Sa [m

/s2 ]

T [s]

24/08/16 26/10/16 30/10/16 NTC

X directionY direction

NTC = CODE SPECTRUM COMPATIBLE FOR TR=712 years - Soil C

The school of P. Capuzi in Visso


Mechanical modelapplied withthespecific parameters ofVissoSchool(interms ofresistant area,masonry typology,interstorey

height,…)

24/08

26/10

24/08

26/10


Validation through theDVB-masonry modelmadebyS.Cattari,D.Ottonelli &S.Alfano

24 Agosto

Mud X = 2.986

Mud Y = 2.720

DL0 DL1 DL2 DL3 DL40

0.1

0.2

0.3

0.4

0.5

0.6Dir XDir Y

26 Ottobre

Mud X = 3.110

Mud Y = 3.174


0.1

0.2

0.3

0.4

0.5

0.6Dir XDir Y



24 Agosto

Mud X = 2.986

Mud Y = 2.720


0.1

0.2

0.3

0.4

0.5

0.6Dir XDir Y

26 Ottobre

Mud X = 3.110

Mud Y = 3.174


0.1

0.2

0.3

0.4

0.5

0.6Dir XDir Y


DL2/DL3 DL3/DL4inY(withDL5inlocal parts)DL2/DL3inX


ReLUIS-DPC Project: Italian seismic risk map (2018 - ONGOING)

the IRMA Platform - already used for elaborating in 2018 the first set of Italian seismic risk map – is ongoing to be improved in the MARS

project (Coord. Proff.S.Lagomarsino & A.Masi)

ReferenceefiguradiIRMA

REF. National Risk Assessment (2018) Overview of thepotential major disasters in Italy: seismic, volcanic,tsunami, hydro-geological/hydraulic and extremeweather, droughts and forest fire risks, Presidency ofthe Council of Ministers Italian Civil ProtectionDepartment.REF. Dolce et al. (2019) Seismic risk maps for theItalian territory, XVIII ANIDIS Conference, Ascoli Piceno2019


EXAMPLES OF MAPS THAT CAN BE PRODUCED (through the implementation of the macroseismic model developed by UNIGE)

Scenario conditioned to 475 years – soil A

DL3 Mean damage – soil A

Scenario unconditioned to 1 yearTAXANOMY:STRUCTURALTYPOLOGY– AGE– HEIGHTCLASS


Other research groups partecipated to ReLUIS project (from Padua, Naple, Pavia) by defininig fragility curves through different approaches (empirical, hybrid mechanical-based)

REF. Dolce et al. (2019) Seismic risk maps for the Italian territory, XVIII ANIDIS Conference, Ascoli Piceno 2019

The result of maps in terms of damage scenario have been used to assess also the expected LOSSES

It requires theintroduction ofproper correlation laws

EXAMPLESofcorrelation laws between theDAMAGELEVELSand:

CASUALTIES USABILITYSAFEFORUSE/NOTSAFEFORUSE/COLLAPSE

DIRECTECONOMICLOSSRECONSTRUCTIONCOSTS

IRPINIA 1980MESSINA 1908

Loss of life orserious injury requiring hospitalization


Other research groups partecipated to ReLUIS project (from Padua, Naple, Pavia) by defininig fragility curves through different approaches (empirical, hybrid mechanical-based)

REF. Dolce et al. (2019) Seismic risk maps for the Italian territory, XVIII ANIDIS Conference, Ascoli Piceno 2019

USABILITYSAFEFORUSE/NOTSAFEFORUSE/COLLAPSE

DIRECTECONOMICLOSSRECONSTRUCTIONCOSTS

RESULT FROM THE UNCONDITIONED EVALUATION AT 1 YEAR

COSTinBillions

RESONABLE NUMBERS IF COMPARED WITH THE EARTHQUAKE HYSTORY OF LAST 50 YEARS IN ITALY BUT SIGNIFICANT DISPERSION DUE TO DIFFENCES IN VARIOUS MODELS ADOPTED

RESEARCHONGOINGIN2019WITHINMARS– ReLUIS PROJECT!!!!

CASUALTIES

USE OF THE MACROSEISMIC MODEL TO SUPPORT THE DESIGN OF SEISMIC EMERGENCY PLAN

Amatrice, 2016

Accumoli, 2016

Villa Sant’Angelo, L’AQUILA 2009

Amandola, FM, 2016


Inte

nsity

Loss of functionality of the urban system

O

D

LS

NC E

Dwellings are compromised

Normal urban function are damaged

Main urban function are interrupted Strategic urban function are interrupted

Strategic emergency function are interrupted

AT URBAN SCALE AT SCALE OF THE SINGLE BUILDING

The Italian Department of Civil Protection developed in recent years specific procedure to support and improve the emergency managment phase as the I.Opà.CLE method addressed

to define Indices for evaluation of the Operational efficiency of Limit Condition Emergency

REF: Dolce M. et al.(2018) Probabilistic assessment of structural operational efficiency in emergency limit conditions: the I.Opà.CLE method, Bull Earthquake Eng 16:3791-3818



THE SISTEM IS EFFICIENT IF ALL COMPONENTS ARE EFFICIENT: THE STRATEGIC FUNCTIONS, THE EMERGENCY AREAS AND THE CONNECTIONS !!



SPECIFIC FORMS DEVELOPED BY DPC TO PROVIDE RAPID SURVEY AT SCALE OF THE URBAN SYSTEM AND ACQUIRE ESSENTIAL INFORMATION ON STRUCTURES


Use of the macroseismic method to define fragility curves and then damage scenario of the buildings stock on the connections to assess their efficiency

E’ necessario associare i DLi al superamento dello Stato Limite di Operatività (inteso come operatività della strada).

C.A.MURATURA

5 6 7 8 9 10 11 12

µD

I(MCS)

P(DLi)

(PGA)

CURVADIVULNERABILITA’ CURVADIFRAGILITA’

The application in this context requires to define the damage threshold NOT COMPATIBLE with the OPERATIONAL EFFICIENCY of CONNECTION

E’ necessario associare i DLi al superamento dello Stato Limite di Operatività (inteso come operatività della strada).

C.A.MURATURA

5 6 7 8 9 10 11 12

µD

I(MCS)

P(DLi)

(PGA)

CURVADIVULNERABILITA’ CURVADIFRAGILITA’

For URM buildingsthe failure associated

to out-of-planemechanisms

For RC buildings the failure associated to

out-of-plane failure of infills

D2/D3D3/D4


RESEARCH PROJECT FOUNDED BY THE LIGURIA REGION TO APPLY AND DEVELOP THESE METHODS IN THE SANREMO MUNICIPALITY IN COLLABORATION WITH DICCA

AND DISTAV DEPARTMENTS AND DPC

COMUNE DI SANREMO


TRASCURABILE

MODERATO

SIGNIFICATIVI

SIGNIFICATIVI

CONDITIONED SCENARIO AT 101 YEARS CONDITIONED SCENARIO AT 475 YEARS

Exceedance probability oftheDLassumed as reference fortheNOTcompatible damage

NEGLIBIGLE

MODERATE

HIGH

VERYHIGH

THANK YOU FOR YOUR KIND ATTENTION!

?Serena Cattari

[email protected]

DICCA-DepartmentofCivil,ChemicalandEnvironmentalEngineering

FRAGILITY CURVES FOR BUILDING STOCKS: DERIVATION FROM...

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