Transcript Lagomarsino_ATENE_12_04_2013.ppt

IMPLEMENTATION OF THE EC 8.3: ASSESSMENT AND
INTERVENTIONS IN EARTHQUAKE PRONE AREAS
Athens - April 12, 2013
Performance based assessment
of ancient masonry buildings.
Outcome of the European project
PERPETUATE
Sergio Lagomarsino
University of Genoa, Italy
[email protected]
PERPETUATE
PERformance-based aPproach to Earthquake proTection of
cUlturAl heriTage in European and mediterranean countries
Earthquake protection of cultural heritage
PERformance-based aPproach to Earthquake proTection of
cUlturAl heriTage in European and mediterranean countries
Main objectives of the project:
Development of European Guidelines for the evaluation and
mitigation of seismic risk to cultural heritage assets.
Both architectonic assets (historic buildings; macroelements) and
artistic assets (frescos, stucco-works, statues, pinnacles,
battlements, banisters, balconies …) will be considered. Only
masonry structures will be considered.
www.perpetuate.eu
Partners
The Consortium consists of:
- 6 Universities (Genoa, Thessaloniki, Athens, Ljubljana, Bath, Algiers)
- 2 Public/Research Institutions (ENEA, Italy; BRGM, France)
- 3 SMEs from Slovenia (ZRMK) and Italy (CENACOLO, PHASE).
Basic principles of PERPETUATE procedure





The protection of cultural heritage needs an improvement in methods
of analysis and assessment procedures, rather than the
development of new intervention techniques.
A reliable assessment procedure is the main tool to respect the principle
of “minimum intervention” under the constraint of structural safety.
The displacement-based approach for vulnerability assessment of
cultural heritage assets and design of interventions is adopted as
standard method of analysis.
Nonlinear models are necessary. Nonlinear static (pushover) analyses
are considered as the main tool for the application of the assessment
procedure. Nonlinear dynamic analyses are considered as an
alternative tool, only for certain types of assets.
If, after a reliable seismic assessment, it comes out the monument is
not safe, then its retrofitting is unavoidable, first of all in order to
preserve its life along the time and also for the safety of occupants.
Basic principles of PERPETUATE procedure
The outcome of the assessment is the maximum Intensity Measure (e.g. PGA)
compatible with the fulfilment of each performance level that has to be considered.
AIM OF PERFORMANCE-BASED ASSESSMENT OF ARCHITECTONIC ASSET
Force
NON LINEAR ANALYSES & DEFINITION OF PLs ON THE
CAPACITY CURVE
BUILDING PERFORMANCE LEVELS
(CONSERVATION AND USE)
2B- 2U
Computa on of the maximum
IM compa ble with the i-th
given PL
(and from the hazard curve the
corrisponding return period TR,PLI )
IMPLi
T R,PLi ! l RPLi
3B
V"[kN]"
2A
2A
TR,PLI
> TARGET RETURN PERIOD?
YES
PERFORMANCE LEVELS OF ARTISTIC ASSETS
Displacement
d"[m]"
OK!
NO
REHABILITATION
DECISIONS
Basic principles of PERPETUATE procedure
The format of the assessment proposed by PERPETUATE guidelines is
deterministic, except for the occurrence of the earthquake, as well as in
all codes and recommendations worldwide adopted at present.
However, it is well know many uncertainties, aleatory and epistemic, affect
the assessment of an existing masonry building, with reference to:
a) the characteristics of seismic input (duration, frequency content, etc.)
b) the reliability of mechanical models
c) the material parameters
d) the incomplete knowledge of the construction
PERPETUATE takes into account probabilistic aspects in some steps of the
procedure:

acceptance criteria for the definition of PLs

sensitivity analysis for drawing the protocol of in-situ investigations and
defining the Confidence Factors
Basic steps of PERPETUATE procedure
Classification of architectonic assets
PERPETUATE considers a classification of architectonic assets which is
useful for addressing the choice of proper mechanical models to be
adopted for the assessment.
DAMAGE MODES AT
MACROELEMENT SCALE
CLASSIFICATION OF
ARCHITECTONIC ASSETS
IDENTIFICATION OF THE BEST
MODELLING APPROACH
MACROELEMENT: FACADE
Architectonic asset class
Assets subjected to prevailing in-plane
damage
Assets subjected to prevailing out-ofplane damage
A
CLASS B – BUILDINGS WITH
WIDE WALLS WITHOUT
INTERMEDIATE FLOORS
B
Assets characterized by
monodimensional masonry elements
Arched structures subject to in-plane
damage
Massive structures in which local failure
of masonry prevails
Blocky structures subjected to
overturning
Built systems subjected to complex
damage
C
D
E
F
G
Rare
DAMAGE CLASS B
CCLM
Possible
Continuum finite element model with non-linear
cons titutive law
D iscrete interface model
Structural element model (piers and spandrels )
Discrete Macro-block model
B1 Ch u r ch e s
n2 8
t 2E39
E4
E1
n2 1
E 1t204
E5
E7
t2 1
n2 6
n2 5
n2 4
E2
n2 2
n2 9
E6
E8
t2 2
n2 7
E3
n2 3
Models
SEM
DIM
MBM
Global
Local
Global
Local
Standard
Classification of architectonic assets
It is functional to model main seismic behaviour of buildings
Classes
Description
List of assets
A
This class collects architectonic assets with two main bearing structural elements: vertical walls
and horizontal floors. If they are properly connected, mutual cooperation between the structural
elements allows the building to behave as a box.
A1 palaces, A2 castles, A3
religious houses, A4 caravansaries,
A5 madrasas
B
This class collects architectonic assets which are characterized by wide spaces without
intermediate floors and few inner walls. Independent damage mechanisms occurs in the
different parts of the building, and it is often possible to recognize specific structural
macroelements (façade, triumphal arch, apse, dome, transept,…).
B1 churches, B2 mosques, B3
temples, B4 baptisteries, B5
mausoleum, B6 hammam B7
theatres
C
This class collects architectonic assets in which the vertical dimension prevails on the other
ones. Since usually, these buildings are characterized by significant slenderness, their seismic
response may be assumed as a global flexural behavior.
C1 towers, C2 bell towers, C3
minarets, C4 lighthouses, C5
chimneys
D
This class collects architectonic assets in which the main structural element is an arch or a vault.
Both single arches or much more complex constructions based on this basic structural element
are included.
D1 triumphal arches, D2
aqueducts, D3 bridges, D4 cloisters
E
This class collects massive constructions in which the wide thickness of walls, if compared to
other dimensions, doesn’t allow the idealization as plane structural element. Local failure
occurs as, for example, the detachment of external leaf.
E1 fortresses, E2 defensive city
walls
This class collects single isolated architectonic assets, which does not delimit an interior space.
F1 columns, F2 trilithes, F3
obelisks, F4 archaeological ruins
F
G
This class refers to historical centers, made of ordinary buildings’ aggregates, which assume the
relevance of cultural heritage asset as whole in the urban context. The seismic response must
consider the interaction among adjacent buildings.
Classification of architectonic assets
BOX-TYPE STRUCTURES (vertical walls and horizontal floors)
Classes
Description
List of assets
A
This class collects architectonic assets with two main bearing structural elements: vertical
walls and horizontal floors. If they are properly connected, mutual cooperation between the
structural elements allows the building to behave as a box.
A1 palaces, A2 castles, A3
religious houses, A4 caravansaries,
A5 madrasas
A1 Palaces
A2 Castles
A4 Caravansaries
A3 Religious houses
Classification of architectonic assets
WIDE HALLS WITHOUT INTERMEDIATE FLOORS (macroelements)
Classes
Description
List of assets
B
This class collects architectonic assets which are characterized by wide spaces without
intermediate floors and few inner walls. Independent damage mechanisms occurs in the
different parts of the building, and it is often possible to recognize specific structural
macroelements (façade, triumphal arch, apse, dome, transept,…).
B1 churches, B2 mosques, B3
temples, B4 baptisteries, B5
mausoleum, B6 hammam B7
theatres
B6 Hammam
B1 Churches
B2 Mosques
Classification of architectonic assets
SLENDER MASONRY STRUCTURES
Classes
Description
C
This class collects architectonic assets in which the vertical dimension prevails on the other
ones. Since usually, these buildings are characterized by significant slenderness, their seismic
response may be assumed as a global flexural behavior.
C1 Towers
C2 Bell Towers
List of assets
C3 Minarets
C1 towers, C2 bell towers, C3
minarets, C4 lighthouses, C5
chimneys
C4 Lighthouses
Classification of architectonic assets
ARCHED AND VAULTED STRUCTURES
Classes
Description
List of assets
D
This class collects architectonic assets in which the main structural element is an arch or a
vault. Both single arches or much more complex constructions based on this basic structural
element are included.
D1 triumphal arches, D2
aqueducts, D3 bridges, D4 cloisters
D1 Triumphal arches
D4 Cloisters
Classification of architectonic assets
MASSIVE MASONRY CONSTRUCTIONS
Classes
Description
E
This class collects massive constructions in which the wide thickness of walls, if compared to
other dimensions, doesn’t allow the idealization as plane structural element. Local failure
occurs as, for example, the detachment of external leaf.
E1 Fortress
List of assets
E1 fortresses, E2 defensive city
walls
E2 Defensive city walls
Classification of architectonic assets
DRY BLOCKS STRUCTURES
Classes
Description
F
This class collects single isolated architectonic assets, which does not delimit an interior
space.
F1 Columns
F2 Trilithes
List of assets
F1 columns, F2 trilithes, F3
obelisks, F4 archaeological ruins
F3 Obelisks
Classification of architectonic assets
AGGREGATED BUILDINGS IN HISTORICAL CENTRES
Classes
Description
G
This class refers to historical centers, made of ordinary buildings’ aggregates, which assume
the relevance of cultural heritage asset as whole in the urban context. The seismic response must
consider the interaction among adjacent buildings.
Navelli, L’Aquila, Italy
Skofja Loka, Slovenia
List of assets
From classification to mechanical models
ARCHITECTONIC CLASSES
B
C
D
A
MODELS CLASSES
Architectonic asset
assetclass
class
Architectonic
A
A
B
B
C
C
MBM – Macro Block
models
F
CORRELATION
CCLM - Continuum
SEM - Structural Element
Constitutive Laws models models
DIM – Discrete Interface
models
E
D
D
E
E
FF
G
G
CCLM
CCLM
Assets subjected
subjected to
to prevailing
prevailing in-plane
in-plane
Assets
damage
damage
Assets subjected
subjected to
to prevailing
prevailing out-ofout-ofAssets
plane damage
damage
plane
Assets characterized
characterized by
by
Assets
monodimensionalmasonry
masonryelements
elements
monodimensional
Arched structures
structures subject
subjectto
to in-plane
in-plane
Arched
damage
damage
Massivestructures
structuresin
in which
which local
localfailure
failure
Massive
of masonry
masonry prevails
prevails
of
Blocky structures
structures subjected
subjected to
to
Blocky
overturning
overturning
Builtsystems
systems subjected
subjected to
to complex
complex
Built
damage
damage
RARE
POSSIBLE
Models
Models
SEM
DIM
SEM
DIM
MBM
MBM
Global
Global
Local
Local
Global
Global
Local
Local
STANDARD
Classification and modelling
Some types of assets (can be studied by a global 3D model, while in other cases it is
necessary to develop more than one model, even of different types. Moreover, the
assessment requires taking into accont the possible activation of local mechanisms.
ASSETS MADE BY ONE MACROELEMENT
ASSESSMENT OF THE BUILDING
AS A WHOLE
MACROELEMENT
APPROACH
ARCHITECTONIC CLASSES
FROM A TO F
ASSESSMENT OF
LOCAL MECHANISMS
DESCRIBED BY A SINGLE CAPACITY CURVE
ag
PL 2
PL 3
PL 4
d
V
DESCRIBED BY A SINGLE CAPACITY CURVE
ASSETS
RESPONDING AS
A BOX
PL2
+
PL3
PL4
PL1
3D Model
MACROELEMENT
APPROACH
COMPLEX ASSETS MADE BY MANY
MACROELEMENTS
GLOBAL
APPROACH
d0
d
DESCRIBEB BY N CAPACITY CURVES
ag
ASSETS
RESPONDING AS A
SET OF
MACROELEMENTS
PL 2
PL 3
PL 4
ag
d0
d
d0
d
PL 2
PL 3
PL 4
Safety and conservation requirements
Performance Levels
PERFORMANCE LEVELS
USE and
HUMAN LIFE
BUILDING
CONSERVATION
ARTISTIC
ASSETS
EC8 part 3
NEAR
COLLAPSE
SIGNIFICANT BUT
RESTORABLE
DAMAGE
LOSS
PREVENTION
IMMEDIATE
OCCUPANCY
DAMAGE
LIMITATION
RESTORABLE
DAMAGE
OPERATIONAL
NO DAMAGE
NEAR
INTEGRITY
LIFE SAFETY
Safety and conservation requirements
Performance Levels & correlation with damage
PERFORMANCE LEVELS
USE and
HUMAN LIFE
BUILDING
CONSERVATION
DAMAGE
LEVEL
ARTISTIC
ASSETS
NEAR
COLLAPSE
4
SIGNIFICANT BUT
RESTORABLE
DAMAGE
LOSS
PREVENTION
3
IMMEDIATE
OCCUPANCY
DAMAGE
LIMITATION
RESTORABLE
DAMAGE
2
OPERATIONAL
NO DAMAGE
NEAR
INTEGRITY
1
3
LIFE SAFETY
2
1
STRUCTURAL ELEMENT – LOCAL SCALE
GLOBAL SCALE – WHOLE ASSET
DAMAGE
LEVEL
Safety and conservation requirements
V
2500
DL1 DL2 DL3 DL4
Vtot [kN]
2000
PL3
Fragility curves
1
0,5
Corresponding to Spp=DL3
1
1500
Probability distribution of DLs
0,4
50% of probability of
being or exceeding DL3
DL1
0,3
0,5
1000
DL2
DL1
0,5
DL2
500
DL3
PDLi
DLs defined on basis of multicriteria
approach
 1
 S
P  ds | Sd    
ln  d

  ds  Sd ,ds

 
 
Performance and damage Levels & Acceptance Criteria
0,2
DL3
DL4
0,1
DL4
0
0
0
0
dDL1
10
dDL2
dDL330dDL4
20
d40
0
u [mm]
0
0
10
10
20
20
30
30
d40
0
1
2
3
Damage level
40
If the acceptance criterion isn’t satisfied , the PL limit threshold may moved back with respect the corresponding DL
Acceptance criteria
Performance
level (PL)
B - Building Conservation Targets
U - Use and Human Life Targets
Correlation with damage
levels (DL)
Limit value
Correlation with damage
levels (DL)
Limit value
2
-
-
0,4 PDL3+ PDL4+ PDL5
1%
3
PDL5
3%
0,3 PDL5
3%
4
PDL5
15%
-
-
4
5
Safety and conservation requirements
Performance Levels & corresponding Target Seismic Demand Levels
PERFORMANCE LEVELS
USE and
HUMAN LIFE
4
3
2
1
BUILDING
CONSERVATION
ARTISTIC
ASSETS
NEAR
COLLAPSE
SIGNIFICANT BUT
RESTORABLE
DAMAGE
LOSS
PREVENTION
3
IMMEDIATE
OCCUPANCY
DAMAGE
LIMITATION
RESTORABLE
DAMAGE
2
OPERATIONAL
NO DAMAGE
NEAR
INTEGRITY
1
LIFE SAFETY
SEISMIC
DEMAND
DAMAGE
LEVEL
STRUCTURAL ELEMENT – LOCAL SCALE
GLOBAL SCALE – WHOLE ASSET
DAMAGE
LEVEL
4
TR=2475
3
TR=475
2
TR=72
1
TR=50
Safety and conservation requirements
Performance Levels & corresponding Target Seismic Demand Levels
IMPORTANCE FACTORS
SEISMIC
DEMAND
1. USE AND HUMAN LIFE USE (gu)
FUNCTION OF: BUILDING USE; CROWDING LEVEL.
gu < 1 WETHER THE BUILDING IS RARELY USED. IF gu < 1, THE
ASSESSMENT OF PERFORMANCE LEVEL “IO” IS NOT REQUIRED.
4
TR=2475
3
TR=475
2
TR=72
1
TR=50
2. ARCHITECTONIC ASSETS ARCHITECTONIC RELEVANCE (gb)
FUNCTION OF: CULTURAL VALUE OF THE BUILDING ITSELF.
gb > 1 WETHER THE BUILDING HAS A PARTICULAR CULTURAL
RELEVANCE. gb > 1, THE ASSESSMENT OF PERFORMANCE LEVEL “RU” IS
REQUIRED
3. ARTISTIC ASSETS ARTISTIC RELEVANCE (ga)
FUNCTION OF: CULTURAL VALUE OF THE ARTISTIC ASSETS
PRESENT IN THE BUILDING.
ga > 1 WETHER THE ASSETS HAVE A PARTICULAR CULTURAL RELEVANCE.
ga > 1, THE ASSESSMENT OF PERFORMANCE LEVEL “LP” IS REQUIRED
EC8.3 - 225 years
Seismic hazard
A proper definition of the seismic demand is addressed by the information and
choices that have been assumed in the first step (Classification).

Intensity Measure (IM): it depends on the Class of the architectonic asset.

Seismic Input can be described by:
1)
2)
in case of nonlinear static analyses, an
Acceleration-Displacement Response Spectrum
(ADRS), completely defined for the specific site of
the building under investigation as a function the
Intensity Measure (IM);
in case of non linear dynamic analyses, a proper
set of time-histories, selected from real recorded
accelerograms, obtained through numerical models
of the seismic source and the propagation to the
site or artificially generated, in order to be
compatible with a target response spectrum (this
last option is questionable).
Vs,30=826 m/s
1.0
0.0
-1.0
1.0
0
2
4
6
8
10
0
2
4
6
8
10
0.0
-1.0
Seismic hazard
Probabilistic Seismic Hazard Assessment
1
0
1
2
3
4
Vector-valued
PSHA
0.1
lV R 0.01
R
0.001
0.0001
ag [m/s2]
PGA [g]
e.g. PGA & PGD
Seismic hazard
For architectonic assets that require the adoption of an IM representative of the ADRS
in the long periods range (e.g. Class F), or more than one IM (Vector-Valued PSHA),
the shape of the response spectrum must change, in order to be compatible with the
information provided by GMPEs for short a long periods
Seismic hazard
Floor spectra (for the assessment of local mechanisms in the higher levels)
4,50E+03%
?
Input accelerogram
for the bell cell
z
Example of Floor spectra proposed in PERPETUATE
4,00E+03%
3,50E+03%
Base%input%
3,00E+03%
T=0.3%th%
Sa
2,50E+03%
T=0.3%an%
T=0.6%th%
2,00E+03%
T=0.6%an%
T=0.1%th%
1,50E+03%
T=0.1%an%
1,00E+03%
5,00E+02%
0,00E+00%
Ground accelerogram
0,00%
5,00%
10,00%
15,00%
20,00%
25,00%
30,00%
Sd
35,00%
40,00%
45,00%
50,00%
As built information
In this sub-step, geometrical, technological and mechanical features of the
asset are analysed in depth, with the aim of defining the structural model of
the building and related artistic assets.
Although it is necessary to investigate in detail the construction, in case of
ancient masonry buildings it is necessary to consider that:
1)
2)
in cultural heritage assets, due to conservation requirements, the impact
of investigations should be minimized;
in seismic assessment of an existing building epistemic uncertainties
due to the incomplete knowledge and reliability of models add up to
aleatory uncertainties, in particular related to material parameters.
The approach adopted in PERPETUATE is based on the use of Confidence
Factors.
As built information
Main drawbacks
Approach used by codes
i.
i.
Usually the reaching of a certain knowledge
level implies an almost homogeneous
degree of accuracy to be reached on all the
different knowledge aspects (material,
geometry, constructive details).
The confidence factor is conventionally
applied only to the parameter which is
assumed to mainly affect the structural
response. This parameter (or set of
parameters) is proposed by codes a priori:
usually, in fact, it coincides with strength
mechanical parameters (only some codes –
such as the ASCE/SEI 41-06 – proposes to
apply it to the drift values, only in case of
deformed controlled modes).
i.
i.
i.
i.
The value of the confidence factor is
conventionally proposed by codes only as a
function of the reached knowledge level.
Since in general different parameters may
differently (more or less significantly) affect the
structural
behaviour,
it
seems
more
reasonable to allows a calibration of the
improvement of knowledge required as a
function of the degree of sensitivity of the
response. In some cases, a lower level of
knowledge has been accepted because no
remarkable building details have been
analysed
notwithstanding
these
abovementioned information could not be so
relevant in terms of seismic safety.
In general, as a function of the structure
examined, this conventional assumption could
not be the best one.
The actual variability of from time to time
examined parameters which may affect the
response of the building is not considered.
As built information
The idea is that investigation program should be based on a preliminary
sensitivity analysis aimed to:
1)
2)
identify the main parameters to be investigated;
define proper Confidence Factors (CFs), to be used for the assessment
in order to take into account uncertainties.
The identification of main parameters influencing the structural response of
the asset allows to finalize the investigation to few important points (thus
reducing costs and time) and to reduce the number of destructive tests.
The calibration of CFs on the basis of sensitivity analyses instead of a-priori
assumptions (as usually done for standard buildings) provides more
reliable models and results.
As built information: sensitivity analysis
SENSITIVITY ANALYSES
EPISTEMIC UNCERTAINTIES
LOGIC TREE APPROACH
INFILLED OPENINGS
TYPE 1
q MATERIAL PROPERTIES
q PAR. FOR MULTILINEAR
CONSTITUTIVE LAWS
q IN-PLANE STIFFNESS OF FLOORS
[Mpa]
TYPE 2
MASONRY MATERIAL PROPERTIES
STATISTIC UNCERTAINTIES
RANDOM VARIABLES
[Mpa]
Model B – with
openings
MODEL A
Model A – without
openings
MODEL B
As built information: sensitivity analysis
Notes on steps d) related to the execution of sensititvity analysis
Examples of sensitivity analyses results
300
250
F* (kN)
200
150
mean values
100
drift -
50
drift +
SENSITIVITY TO DRIFT
0
0
0,5
1
1,5
2
2,5
d* (cm)
300
300
250
250
200
F* (kN)
F* (kN)
200
150
mean values
SENSITIVITY
TO MECHANICAL
mechalical parameters PARAMTERS
50
0
0
0,5
1
1,5
d* (cm)
2
mean values
100
mechanical parameters +
100
150
2,5
masses -
50
masses +
SENSITIVITY TO MASSES
0
0
0,5
1
1,5
d* (cm)
2
2,5
As built information
SENSITIVITY ANALYSES
EPISTEMIC UNCERTAINTIES
LOGIC TREE APPROACH
INFILLED OPENINGS
Sensitivity to random
[Mpa]
variables
TYPE 2
Sensitivity to epistemic
q MATERIAL PROPERTIES
uncertainties
q PAR. FOR MULTILINEAR
CONSTITUTIVE LAWS
q IN-PLANE STIFFNESS OF FLOORS
TYPE 1
MASONRY MATERIAL PROPERTIES
STATISTIC UNCERTAINTIES
RANDOM VARIABLES
Model B – with
openings
MODEL A
Performance Level
[Mpa]
Model A – without
openings
MODEL B
As built information
In sensitivity analyses both statistical uncertainties, treated by proper random
variables, and epistemic uncertainties, treated by a logic tree approach, are
considered.
Y1
Coupling effectiveness of piers
wY1_A=0
wY1_B=1
A – presence of
tension-only rods at
floor level
Y2
Shear floor stiffness
wY2_A=0.7
wY2_B=0.3
A – rigid floor
YAA
wYAA =0
On Y1 :
High sensitivity class + KL3
B – flexible floor
YAB
wYAB = 0
According to information
achieved model B has been
adopted
A – rigid floor
YBA
wYBA = 0.7
On Y2 :
High sensitivity class + KL2
wYBB = 0.3
A subjective probability has
been assigned to each model in
order to combine the results
B – presence of beam
elements at floor level
B – flexible floor
YBB
As built information: sensitivity analysis
Steps of the proposed procedure:
a)
a)
a)
a)
a)
Achievement of a “basic” knowledge level to preliminarly identify the suitable model (or
models) to be adopted for the seismic assessment.
Identification of all parameters or set of parameters (in case of parameters dependent on
each other) affecting the model.
For each parameter, identification of the more rational range of variation.
Execution of the sensitivity analysis onto selected parameters in order to evaluate how
much each one really affects the seismic behaviour of the examined building. Non linear
static analysis is assumed as the standard one.
Attribution of a “sensitivity class” (low, medium or high), on the basis of the post processing
of results provided from the sensitivity analysis, for each parameter.
a)
Plan of the investigation and testing by using the results obtained from steps d) and e).
a)
Execution of investigations and tests;
a)
Definition of the confidence factor, possible updating of the mean value of parameters (on
the basis of tests/investigations results) and final definition of parameters to be used in
models for the seismic assessment.
As built information: sensitivity analysis
Notes on steps h) related to the definition of confidence factor
According to the common approaches based on the use of confidence factor , it
seems reasonable to apply CF to the “main parameter” which affect the structural
seismic response.
In the case of PERPETUATE procedure, it is possible choosing the “main
parameter” among those associated to a high sensitivity class and not
conventionally a priori.
Regarding the value to be adopted for CF it has to take into account :
the actual variability of the parameter which will be applied to (by considering the
related fk value);
i.
the “remaining” uncertainties associated to the incomplete knowledge process
(since it could be not possible to reach the maximum knowledge level on all
parameters ).
i.
As built information: sensitivity analysis
Notes on steps h) related to the definition of confidence factor
It is necessary to increase the knowledge level for parameters that have a higher
sensitivity class.
Sensitivity Class
Knowledge level
KL1
KL2
KL3
Low
0.3
0
0
Medium
0.6
0.3
0
High
1
0.6
0
Hence CF is computed as:
1   max f c
FC  
1   max f c
(a)
(b)
where fc corresponds to fk associated to the k-th parameter assumed as reference as “main
parameter” that affects the seismic response.
As built information: sensitivity analysis
Measure of the sensitivity of
the structural performance
at n- th factors
Measure of the sensitivity of
the structural performance
at k- th parameter
1,k 
Variable
Type
Set of
variables
1
Xk
2
3
Yi
Y1
Y2
aPL3,1  aPL3,1,k
aY1 =
aPL3,1
Variable
fk
x1a
x1b
x2a
x2b
x2c
x2d
x3
0.25
0.25
0.25
0.25
0.20
0.20
0.20
-
+ aPL3,YB
)
Sensitivity
class
Knowledge
Level
b Xk
0.1313
H
KL2
0.6
a X ,k
0.07221
M
KL2
0.3
a Yi
0.0037
0.125
0.147
L
H
H
KL1
KL3
KL2
0
-
a
Inf
Sup
-
(a
PL3,YA
+/-
Inf
aPL3,YA - aPL3,YB
Modelling and verification procedures
Verification procedures adopted:
PUSHOVER ANALYSES AND CAPACITY SPECTRUM METHOD
(STANDARD METHOD)
NON-LINEAR DYNAMIC ANALYSIS (IDA)
(MORE ACCURATE – HIGH COMPUTATIONAL EFFORT)
Non linear sta c analyses
3
2
a (m/s2)
Control node
1
0
-1
0
10
20
30
-2
-3
t (s)
20000000%
Incremental equilibrium analyses
15000000%
Te
10000000%
Sa
Vtot(N)'
5000000%
Tmax
!0,03%
!0,02%
!0,01%
0%
0%
!5000000%
Txs
!10000000%
PL4
dPL4
Displacemenet
demand
*
0
d
!15000000%
d'(m)'
Sd
0,01%
0,02%
0,03%
WE-x
Modelling and verification procedures
METHODS OF ANALYSIS AND ASSESSMENT PROCEDURES
Pushover analyses and Capacity Spectrum Method
STANDARD METHOD
Nonlinear dynamic analysis (IDA)
MORE ACCURATE METHOD – APPLICABLE WITH A REASONABLE
COMPUTATIONAL EFFORT ONLY FOR SOME CLASSES
Linear elastic analysis and assessment based on
behaviour factor (q)
ONLY IN CASE OF VERY COMPLEX ASSETS
Modelling and verification procedures
ASSESSMENT PROCEDURES AND ARCHITECTONIC ASSET CLASSES
Homogeneous and coherent criteria are adopted for the development of the
assessment procedures which have to be applied to the different classes of
assets defined in D4 (from A to F)
In particular three main cases may be identified:
1)
Asset composed by a single macroelement;
2)
Complex assets described by a single capacity curve;
3)
Complex assets described by a N capacity curves
Case 1)
Case 2)
Case 3)
Modelling and verification procedures
ASSESSMENT PROCEDURES AND ARCHITECTONIC ASSET CLASSES
Architectonic Asset Class
Case Procedure
A
B
C
D
E
F
Prevailing
in-plane
response
Prevailing
out-of-plane
response
Monodimens
ional
masonry
elements
Arched
subject to
in-plane
response
Massive
structure
Blocky
structures
subjected to
overturning
X
X
-
X
Asset composed by a
single macroelement
A
-
Complex assets described
by a single capacity curve
Standard
Possible
-
Complex assets described
by N capacity curve
Rare
Standard
-
B
C
D
E
F
Assets composed by a single macroelement
SUMMARY OF THE PROCEDURE:
1.
Pushover analysis
2.
Definition of PLs on the pushover curve
3.
Capacity curve – Equivalent SDOF
4.
Seismic demand and hazard curve (Intensity Measure - IM)
Computation of the maximum IM value (IMPLi) compatible with the given
perfomance level (PLi)
5.
6.
Comparison of IMPLi with the corresponding target value IM*PLi
7.
Use of seismic assessment outcome for the rehabilitation decisions
Assets composed by a single macroelement
1.
PUSHOVER ANALYSIS
NON LINEAR STATIC ANALYSIS
NON LINEAR KINEMATIC ANALYSIS
CONTINUUM CONSTITUTIVE LAWS MODELSMACRO BLOCK MODELS (MBM)
(CCLM)
AND STRUCTURAL ELEMENT MODELS
F and D CLASSES
(SEM)
CLASS C
Seismic forces proportional to the first mode
Seismic forces proportional to masses
applied in each block
Assets composed by a single macroelement
2. Definition of PLs on the pushover curve
NON LINEAR STATIC ANALYSIS
CCLM and SEM models
NON LINEAR KINEMATIC ANALYSIS
MBM models
C class
F and D classes
Assets composed by a single macroelement
3. Capacity curve – Equivalent SDOF
NON LINEAR STATIC ANALYSIS
CCLM and SEM models
NON LINEAR KINEMATIC ANALYSIS
MBM models
It is based on the fundamental modal shape
It is assumed as a fundamental shape the
block displacements of the kinematism
m
 mi i
Γ=
=
2
2
m

m



i
i
i
i
m
*
SDOF equivalent system
d=u/G
N
i
m*
m*
Sa /a*(
h*
h*
)
ay=Vy /m*G
Te
*
Assets composed by a single macroelement
4. Seismic demand and hazard curve (Intensity Measure - IM)
Seismic demand is an Acceleration Displacement Response Spectra (ADRS).
It may be defined (for a given soil condition):
o
by a set of parameters (PGA, TC, TB, F0, …..) and analytical functions;
o
by a set of values (T, Sa)



An Intensity Measure (IM) has to be defined as representative for the
By a setSeismic
of parameters
Probabilistic
Hazard and
Assessment (PSHA)By a set of values
analytical
In case
of more functions
IM Vector-valued PSHA
In general, the Peak Ground Acceleration (PGA) is assumed as IM
The IM varies with the return period (TR) (that is with the annual probability of
occurrence
Assets composed by a single macroelement
5. Maximum IM value (IMPLi) compatible with the given perfomance level (PLi)


PERPETUATE procedure needs, for each PLi, the evaluation of IMPLi: to this
end, it is sufficient to define the damping coefficient (xPLi) and period (TPLi)
Use of Capacity Spectrum Method (overdamped spectra)
Through cyclic pushover
Through analitycal laws
proposed in literature
 1 
ξequ =ξel +α  1- β 
 μ 
Law calibrated on experimental campaigns on full scale masonry
building (S2 Project)
Assets composed by a single macroelement
5. Maximum IM value (IMPLi) compatible with the given perfomance level (PLi)
Sa
Sd (T, IM, x ) = IM × Sd0 (T, x )
IM PLi
dPLi
=
Sd0 (TPLi , x PLi )
Sd (T, IM ,x)
IMPLi
Sd0 (T,x)
1
TPLi
dPLi
d
*
0
Sd
Assets composed by a single macroelement
6. Comparison of IMPLi with the corresponding target value IM*PLi

By using the hazard curve the return period TR,PLi corresponding to IMPLi may
be evaluated
IMPLi
lRPLi

T RPLi
The assessment consists in the comparison of TR,Pli with T*R,Pli .
It is positive if TR,Pli > T*R,Pli .
Assets composed by a single macroelement
7. Use of seismic assessment outcome for the rehabilitation decisions

Evaluation of the nominal life VN
Hazard levels are usually defined for probabilities of exceedance in 50 years
TR,PLi
VN = 50 *
TR,PLi
If VN > 50 years
the seismic performance of the architectonic asset is adequate!
If VN < 50 years
rehabilitation decisions have to be taken!
It is an useful parameter to define the priority list of interventions in case of
assessment of a group of buildings.
This approach is correct from a conceptual point of view only if a time dependent
hazard is available.
Complex assets described by a single
capacity curve
1.
PUSHOVER ANALYSIS
NON LINEAR STATIC ANALYSIS
TRUCTURAL ELEMENT MODELS
SEM)
class
CONTINUUM CONSTITUTIVE LAWS
MODELS (CCLM)
B class
Mechanical models for the assessment
Within the context of equivalent frame approach, multilinear constitutive laws for
masonry panels on phenomenological base have been formulated and implemented
in TREMURI Program
(Lagomarsino et al. 2007, ask to: [email protected])
DL3
1
0,8
E,3 Vu
0,6
E,4 Vu
V/Vu
Seismic analysis of
3D complex models floor modelled as
ortotropic membrane
V/Vu
Multilinear laws for single masonry panels
DL4
0,8
0,6
DL5
0,4
DL3
1
E,3 Vu
DL4
DL5
d E,3
d E,4
d E,5
0,5
1
0,4
0,2
dE,4
dE,3
0
0
0,2
dE,5
0,5
0
1
dE [%]
0
1,5
2
2,5
3
dE [%]
Able to reproduce different hysteretic behaviours
100
80
80
60
60
40
40
V [kN]
20
20
-6
-4
-2
0
-20
2
4
6
8
V [kN]
0
-8
0
-20
-40
Rigid nodes
Spandrels
Piers
-60
-15
-10
-5
0
-20
-40
-80
-60
-100
-80
U [mm]
U [mm]
5
10
15
20
Multicriteria definition of Performance Levels
ELEMENT SCALE : dDLi,E
Control node
Node
Checks at level of each single element:
V/Vu
Pier
Spandrel
æ
æ
ö
æ
öö
xj
xj
minç max ç
= 1÷; max ç
= 1÷ ÷
÷
ç X DL , j
÷÷
S
ç P ç X DL , j
i +1
i +2
è
ø
è
øø
è
Equi val ent frame ideal isation of Wal l 8
1
DL3
0,8
0,6
DL4
0,4
DL5
0,2
0
0
0,1
0,2
0,3
0,4
0,5
Vwall 8
MACROELEMENT SCALE : dDLi,M
V
2500
350
DL1
300
DL2
DL4
Vtot[kN]
200
bM ,4Vmax
150
global
2000
bM ,3Vmax
250
100
1500
DL3
DL1
1000
50
DL4
500
0
0
5
10
15
20
25
30
35
dwall 40
8
u_wall8 [mm]
0
0
interstory_1
interstory_2
interstory_3
0,009
Interstorydrift
0,008
0,007
0,006
0,005
0,004
dis,2
0,003
dis,1
0,002
0,001
10
20
d
40
30
u [mm]
Damage levels at scale
of elements
Cumulative rate of piers
Interstory drift wall 8
0,01
State variables and XDLi for
DL1 and DL2
0,7
Checks based on cumulative rate of damage
levels reached in elements
DL2 DL3
Wall 8
Vmax
400
V _wall8[kN]
State variables and XDLi for
DL3 and DL4
450
0,6
Drift [%]
DL2
DL3
DL4
DL5
bcum,P
0
0
5
10
15
20
25
30
35
U_wall 8
40
dwall
8
d
GLOBAL SCALE : dDLi,G
2500
V
2500
DL3
V
bG,3Vtot,max
2000
DL3 =min (dDL3,G,dDL3,M,dDL3,E)
2000
bG,4Vtot,max
1500
DL4
1500
global
V [kN]
Vtot[kN]
The worst condition among those evaluated at different scales is
assumed as reference to define the DL : min (dDL3,E , dDL3,M, dDL3,G )
Vglobal
tot,max
1000
Wall 1
Wall 7
Wall 8
Wall 3
1000
500
DL3M1
500
0
0
0
10
20
u [mm]
30
40
d
0
5
10
15
20
DL3M3
dDL3,G
25
30
d
DL3,M
u [mm]
DL3M8
35
40
dDL3,E
d
Multicriteria definition of Performance Levels
ELEMENT SCALE : dDLi,E
C on tr ol n ode
Node
Checks at level of each single element:
V/Vu
Pi er
Spandrel
æ
æ
xj
minç max ç
ç
P
ç
è X D L i +1 ,
è
Equi val ent fr ame i deal i sati on of W
al l 8
j
ö
æ
xj
= 1÷; max ç
÷
ç
S
ø
è X D Li +2 ,
j
öö
= 1÷ ÷
÷÷
øø
1
DL3
0 ,8
0 ,6
DL4
0 ,4
DL5
0 ,2
0
0
0,1
0,2
0,3
0,4
0,5
Vwall 8
State variables and XDLi for
DL3 and DL4
450
V
2500
350
DL1
300
DL2
DL4
200
bM ,4Vmax
150
global
2000
bM ,3Vmax
250
Vtot[kN]
V_wall8[kN]
0,7
Checks based on cumulative rate of damage
levels reached in elements
DL2 DL3
Wall 8
Vmax
400
0,6
Drif t [%]
MACROELEMENT SCALE : dDLi,M
100
1500
DL3
DL1
1000
50
DL4
500
0
0
5
10
15
20
25
30
35
dwall
u_wall8 [mm]
40
8
0
0
interstory_1
interstory_2
interstory_3
Interstorydrift
0,008
0,007
0,006
0,005
0,004
dis,2
0,003
dis,1
0,002
10
0,001
20
d
40
30
u [mm]
Damage levels at scale
of elements
Cumulative rate of piers
Interstory drift wall 8
State variables and XDLi for
DL1 and DL2
0,01
0,009
DL2
DL3
DL4
DL5
bcum,P
0
0
5
10
15
20
25
30
35
U_wall 8
40
dwall
8
d
GLOBAL SCALE : dDLi,G
2500
2500
V
V
DL3
bG,3Vtot,max
DL3 =min (dDL3,G,dDL3,M,dDL3,E)
2000
bG,4Vtot,max
1500
DL4
1500
global
V[kN]
Vtot[kN]
The worst condition among those evaluated at different scales is
assumed as reference to define the DL : min (dDL3,E , dDL3,M, dDL3,G )
V
global
tot,max
2000
1000
Wall 1
Wall 7
Wall 8
Wall 3
1000
500
DL3M1
500
0
0
0
10
20
30
40
0
d
5
10
15
20
dDL3,G
25
30
d
DL3,M
DL3M8
35
40
dDL3,E
d
u [mm]
u [mm]
C on tr ol
DL3M3
ELEMENT SCALE : dDLi,E
n ode
Node
Checks at level of each single element:
V/Vu
Pi er
S
pandr el
Equi val ent fr ame i deal i sati on of W
al l
æ
æ
xj
minç max ç
ç X DL
P
ç
i +1 ,
è
è
8
j
ö
æ
= 1÷; max ç
÷
ç X
S
ø
è
x
j
D Li +2 , j
öö
= 1÷ ÷
÷÷
øø
1
DL3
0 ,8
0 ,6
DL4
0 ,4
DL5
0 ,2
0
0
0,1
0,2
0,3
0,4
0,5
Vwall 8
V
2500
3 50
DL1
3 00
DL2
DL4
Vtot [kN]
2 00
bM ,4Vmax
1 50
global
2000
bM ,3Vmax
2 50
1 00
1500
DL3
DL1
1000
50
DL4
500
0
0
5
10
15
20
25
30
35
dwall
u_wall8 [mm]
40
8
0
0
interstory_1
interstory_2
interstory_3
0,009
Interstory drift
0,008
0,007
0,006
0,005
0,004
dis,2
0,003
dis,1
0,002
0,001
10
20
d
40
30
u [mm]
Damage levels at scale
of elements
Cumulative rate of piers
Interstory drift wall 8
0 ,0 1
State variables and XDLi for
DL1 and DL2
0,7
Checks based on cumulative rate of damage
levels reached in elements
DL2 DL3
Wall 8
Vmax
4 00
V_wall8[kN]
State variables and XDLi for
DL3 and DL4
4 50
0,6
Drif t [%]
MACROELEMENT SCALE : dDLi,M
DL2
DL3
DL4
DL5
bcum,P
0
0
5
10
15
20
25
30
35
U_wall 8
40
dwall
8
d
GLOBAL SCALE : dDLi,G
2500
2500
V
V
DL3
bG,4Vtot,max
1500
DL3 =min (dDL3,G,dDL3,M,dDL3,E )
2000
DL4
1500
global
V[kN]
Vtot [kN]
The worst condition among those evaluated at different scales
is
assumed as reference to define
the DL : min (dDL3,E , dDL3,M, d DL3,G )
V
global
tot,max
bG,3Vtot,max
2000
1000
Wall 1
Wall 7
Wall 8
Wall 3
1000
500
DL3M1
500
0
0
0
10
20
u [mm]
30
40
d
0
5
10
15
20
DL3M3
dDL3,G
25
30
d
DL3,M
u [mm]
DL3M8
35
dDL3,E
40
d
Complex assets described by a many
capacity curves
Modelling of single macroelement
ODAL SOLUTION
3D CCLM as help to define the loading
distribution among the macroelement
JAN 8 2013
15:34:47
XY
(AVG)
SYS=0
MX =.038728
MN =-139499
MX =128557
MX
MN
+
-139499
-12000
-25000
25000
12000
500000
ile: torre_3
!
Complex assets described by a many
capacity curves
Case a) IM associated to PPLi (IM ) ³ 0.5 greater than min (IM PLi+1,n)
PLi
PLi+1
1
0.5
IM PLi,g
IM
Case b) IM associated to PPLi (IM ) ³ 0.5 lower than min (IM PLi+1,n)
PLi
PLi+1
1
0.5
IM PLi,g
IM
Application of PBA to case studies
•
•
different scales (single asset or group of buildings in town)
conditions (seismic prevention or reconstruction after an earthquake)
Historical centre of Rhodes
TERRITORIAL SCALE
Casbah of Algiers
Bovec Region & Ljubljana City Centre
Earthquake 1976, 1998, 2004
Earthquake 1895
Application of PBA to case studies
SINGLE ASSET SCALE
Neoclassical School
GREECE
Arsenal de Milly
GIERS
Great Mosque
Hassan Bey’s Mansion
Application of PBA to case studies
SINGLE ASSET SCALE
ITALY
Ardinghelli Palace
Santa Maria Paganica Church
OVENIA
Koljzei Palace
St.Pardo Cathedral
www.perpetuate.eu