15th WORLD CONFERENCE ON EARTHQUAKE ENGINEERINGSpecial Session

SEISMIC RETROFIT OF MASONRY STRUCTURESSeptember 24, 2012 - Lisbon, Portugal

Sergio LAGOMARSINOUniversity of Genoa, Italy

sergio.lagomarsino@unige.it

Vulnerability assessment by macroseismic and mechanical-based models

Seismic analysis of masonry buildings

• Evaluation methods (at National scale)• Numerical simulation methods

Observational methods: DPM (Damage Probability Matrix), based on observed vulnerability. Implicitly contained in the macroseismic scaleSeismic input: IntensityDamage representation: 5 observed damage grades: D1 - D5

Class A I = VII

0510152025303540

0 1 2 3 4 5Damage Grade

Prob

abili

ty

Mechanical methods: Capacity Spectrum Method: vulnerability represented by a capacity curve; demand-capacity - performance evaluationSeismic input: Acceleration Displacement Response SpectraDamage representation: 4 Damage Limit States (performance levels)

Non-linear equivalent s.d.o.f. structure Capacity Curve

Sa

Sd

Au

Ay

Dy Du

LS1

LS2

LS3

LS4

Acceleration-Displacement Response Spectrum

Performance Point

0,670,470,201,3E-020,00183,2E-0950,280,380,389,2E-020,0237,8E-074

4,6E-020,120,2870,250,1177,6E-053

3,9E-032,0E-020,1080,340,2960,0382

1,6E-041,6E-032,0E-020,230,370,09212,7E-065,4E-051,5E-030,060,180,900

XIXVIIIVIIVIV

0,670,470,201,3E-020,00183,2E-0950,280,380,389,2E-020,0237,8E-074

4,6E-020,120,2870,250,117-3

3,9E-032,0E-020,1080,340,2960,0382

1,6E-041,6E-032,0E-020,230,370,09212,7E-065,4E-051,5E-030,060,180,900

XIXVIIIVIIVIV

Risk assessment of strategic masonry buildings at National scale

Macroseismic Method – vulnerability curves from EMS-98(Giovinazzi and Lagomarsino, 2006)

0

1

2

3

4

5

5 6 7 8 9 10 11 12I

m D

Bmin V=0.66Bmax V=0.82

mDmax= 2.88mDmin= 1.72

0

0.1

0.2

0.3

0.4

D0 D1 D2 D3 D4 D5

I=8 min

0

0.1

0.2

0.3

0.4

0.5

D0 D1 D2 D3 D4 D5

I=8 max

DI 6.25V -12.82.5 1 tanh

2.1 m

mean damage grade

PRIORITY LIST

Vulnerability index

Performance modifiers

DBV-masonry (Displacement Based Vulnerability model) (Cattari and Lagomarsino, 2008)

T fundamental period

Bilinear capacity curve defined by:

4T2

DDS1 DDS2 DDS3 DDS4

Entities directly defined on mechanical basis (the others are computed starting from these ones)

Ay

Sd

Sa

1,dir u,dir 1 2 3diry,dir * *

dir dir dir dir

A τ ξ ζ ζ ζFA =m Γ m Γ

* *dir dir

dir * *dir 4 5 dir(shear)

m mT =2π 2πk ζ ζ k

Du = DDS4 ultimate displacement capacity

Ay acceleration capacity

Geometrical features

h inter-storey height

bdir ratio between the resistant wall area at level i in the direction dir and the resistant wall area at top floor level in the same direction

adir ratio between the resistant wall area at top floor level in the direction dir and the total floor area A

Mechanical parameters and loads

tk shear strength

G shear modulus

g material density

du drift value

q floor load

Corrective factors

z1, z2, z3 which affect the evaluation of the yielding acceleration

z4, z5 which affect the evaluation of the period

DS4 udir

N hD = δΓ

dirDS4 u y,dir

ΓD = δ h + D 1-N

uniform soft - storey

OUT-OF-PLANE MECHANISMS(1st failure mode)

IN-PLANE MECHANISMS(2nd failure mode)

SEISMIC ANALYSIS OF MASONRY BUILDINGS

They can be prevented by proper interventions (tie-rods, connections)

H in

ters

tory

,i DISCRETIZION OF THE WALL BY FINITE ELEMENTSLofti and Shing 1991, Gambarotta and Lagomarsino 1997, Lourenço et al. 1997, Lourenço and Rots 1997, Luciano and Sacco 1997, Zhuge et al. 1998, Pietruszczak and Ushaksaraei 2003, Massart 2003, Schlegel 2004, Calderini and Lagomarsino 2008

SIMPLIFIED MODELS

STRONG SPANDREL –WEAK PIER

WEAK SPANDREL –STRONG PIER

(as proposed in FEMA 356 – FEMA 306 – POR Method) (Tomaževič and Weiss 1990, D’Asdia and Viskovic 1995, Brencich and Lagomarsino 1998, Magenes and Della Fontana 1998, Galasco et al. 2004)

EQUIVALENT FRAME MODEL

MODELLING STRATEGIES

Base

shea

r

Node

Pier

Spandrel

Assumed as rigid or linear elastic

Drift ratio

H in

ters

tory

,i

SIMPLIFIED MODELS EQUIVALENT FRAME MODEL

MODELLING STRATEGIES

STRONG SPANDREL –WEAK PIER

WEAK SPANDREL –STRONG PIER

(as proposed in FEMA 356 – FEMA 306 – POR Method) (Tomaževič and Weiss 1990, D’Asdia and Viskovic 1995, Brencich and Lagomarsino 1998, Magenes and Della Fontana 1998, Galasco et al. 2004)

TREMURI PROGRAMA.Galasco, S.Lagomarsino, A.Penna,

S.Cattari for research: ask to

tremuri@gmail.com Commercial version: www.stadata.com

TREMURI: 3D EQUIVALENT FRAME MODELLING

3-D equivalent frame is made of masonry walls, elastic floors, r.c. elements out-of-plane stiffness and strength of masonry walls are neglected floors are plane elements with only in-plane stiffness

Mixed masonry-r.c. buildings

CYCLIC PUSHOVER and NONLINEAR DYNAMIC ANALISYS

-3000000

-2000000

-1000000

0

1000000

2000000

3000000

-0,08 -0,06 -0,04 -0,02 0 0,02 0,04 0,06

V ba

se [N

]

U medio roof [m]

-3000000

-2000000

-1000000

0

1000000

2000000

3000000

-0,08 -0,06 -0,04 -0,02 0 0,02 0,04 0,06

V ba

se [N

]

U medio roof [m] with r.c. ring beams

without r.c. ring beams

PERFORMANCE-BASED APPROACH TO EARTHQUAKE PROTECTION OF CULTURAL HERITAGE IN EUROPEAN AND MEDITERRANEAN COUNTRIES

European Research Project funded by FP7

15th WORLD CONFERENCE ON EARTHQUAKE ENGINEERINGSpecial Session SS25.4

Earthquake Protection of Cultural HeritageResults from NIKER and PERPETUATE European FP7 Projects

Tuesday 25, 17:15-19:15 - Room P3a 

Conveners: Claudio Modena and Sergio Lagomarsino

www.perpetuate.eu

www.perpetuate.eu