IMPLEMENTATION OF THE EC 8.3: ASSESSMENT AND INTERVENTIONS IN EARTHQUAKE PRONE AREAS
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Transcript of IMPLEMENTATION OF THE EC 8.3: ASSESSMENT AND INTERVENTIONS IN EARTHQUAKE PRONE AREAS
PERPETUATE PERformance-based aPproach to Earthquake proTection of cUlturAl heriTage in European and mediterranean countries
Performance based assessment of ancient masonry buildings.
Outcome of the European project PERPETUATE
Sergio LagomarsinoUniversity of Genoa, Italy
IMPLEMENTATION OF THE EC 8.3: ASSESSMENT AND INTERVENTIONS IN EARTHQUAKE PRONE AREAS
Athens - April 12, 2013
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.
Earthquake protection of cultural heritage
www.perpetuate.eu
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).
Partners
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
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.
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 principles of PERPETUATE procedure
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.
It is functional to model main seismic behaviour of buildings
Classes Description List of assets
AThis 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
BThis 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
CThis 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
DThis 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
EThis 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
FThis class collects single isolated architectonic assets, which does not delimit an interior space.
F1 columns, F2 trilithes, F3 obelisks, F4 archaeological ruins
GThis 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
AThis 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 A3 Religious houses
A4 Caravansaries
Classification of architectonic assets
Classes Description List of assets
BThis 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
B1 Churches B2 Mosques
B6 Hammam
WIDE HALLS WITHOUT INTERMEDIATE FLOORS (macroelements)
Classification of architectonic assets
SLENDER MASONRY STRUCTURES
Classes Description List of assets
CThis 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
C1 Towers C2 Bell Towers C3 Minarets C4 Lighthouses
Classification of architectonic assets
ARCHED AND VAULTED STRUCTURES
Classes Description List of assets
DThis 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
D4 CloistersD1 Triumphal arches
Classification of architectonic assets
MASSIVE MASONRY CONSTRUCTIONS
Classes Description List of assets
EThis 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
E1 Fortress E2 Defensive city walls
Classification of architectonic assets
DRY BLOCKS STRUCTURES
Classes Description List of assets
F This class collects single isolated architectonic assets, which does not delimit an interior space.
F1 columns, F2 trilithes, F3 obelisks, F4 archaeological ruins
F1 Columns F2 Trilithes F3 Obelisks
Classification of architectonic assets
AGGREGATED BUILDINGS IN HISTORICAL CENTRES
Classes Description List of assets
GThis 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
Classification of architectonic assets
From classification to mechanical models
A B C D E F
CCLM - Continuum Constitutive Laws models
SEM - Structural Element models
DIM – Discrete Interface models
MBM – Macro Block models
ARCHITECTONIC CLASSES
MODELS CLASSES CORRELATION
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.
Safety and conservation requirements
USE and HUMAN LIFE
BUILDING CONSERVATION
IMMEDIATE OCCUPANCY
LIFE SAFETY
NEAR COLLAPSE
SIGNIFICANT BUT RESTORABLE
DAMAGE
DAMAGE LIMITATION
NO DAMAGEOPERATIONAL
PERFORMANCE LEVELS
ARTISTIC ASSETS
LOSS PREVENTION
RESTORABLE DAMAGE
NEAR INTEGRITY
Performance Levels
EC8 part 3
Safety and conservation requirements
USE and HUMAN LIFE
BUILDING CONSERVATION
IMMEDIATE OCCUPANCY
LIFE SAFETY
NEAR COLLAPSE
SIGNIFICANT BUT RESTORABLE
DAMAGE
DAMAGE LIMITATION
NO DAMAGEOPERATIONAL1
2
3
4
DAMAGE LEVEL
PERFORMANCE LEVELS
GLO
BA
L S
CA
LE –
WH
OL
E A
SS
ET
ARTISTIC ASSETS
LOSS PREVENTION
RESTORABLE DAMAGE
NEAR INTEGRITY
1
2
3
ST
RU
CT
UR
AL
ELE
ME
NT
–
LOC
AL
SC
ALE
DAMAGE LEVEL
Performance Levels & correlation with damage
Safety and conservation requirements
Performance and damage Levels & Acceptance Criteria
0
500
1000
1500
2000
2500
0 10 20 30 40
Vtot
[kN]
u [mm]
DLs defined on basis of multicriteriaapproach
DL1 DL2 DL3 DL4
Fragilitycurves
0
0,5
1
0 10 20 30 40
DL1
DL2
DL3
DL4
,
1|
lnd
dds
dds
SPd
sSS
50% of probability ofbeing or exceeding DL3
0
0,5
1
0 10 20 30 40
DL1
DL2
DL3
DL4
d
Probability distribution of DLs
0
0,1
0,2
0,3
0,4
0,5
0 1 2 3 4 5
Damage level
If the acceptance criterion isn’t satisfied , the PL limit threshold may moved back with respect the corresponding DL
Corresponding to Spp=DL3
DL
iP
V
d dDL4dDL3dDL2dDL1
PL3
Safety and conservation requirements
Performance Levels & corresponding Target Seismic Demand Levels
Safety and conservation requirements
Performance Levels & corresponding Target Seismic Demand Levels
EC8.3 - 225 years
IMPORTANCE FACTORS
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) 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);
2) 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).
Seismic hazard
Probabilistic Seismic Hazard Assessment
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)
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) in cultural heritage assets, due to conservation requirements, the impact of investigations should be minimized;
2) 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
Approach used by codes Main drawbacks
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).
ii. 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).
iii. The value of the confidence factor is conventionally proposed by codes only as a function of the reached knowledge level.
i. 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.
ii. In general, as a function of the structure examined, this conventional assumption could not be the best one.
iii. 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) identify the main parameters to be investigated;2) 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
As built information: sensitivity analysis
Notes on steps d) related to the execution of sensititvity analysis
Examples of sensitivity analyses results
0
50
100
150
200
250
300
0 0,5 1 1,5 2 2,5
F* (k
N)
d* (cm)
mean values
drift -
drift +
0
50
100
150
200
250
300
0 0,5 1 1,5 2 2,5
F* (k
N)
d* (cm)
mechanical parameters +
mean values
mechalical parameters -0
50
100
150
200
250
300
0 0,5 1 1,5 2 2,5
F* (k
N)
d* (cm)
mean values
masses -
masses +
SENSITIVITY TO DRIFT
SENSITIVITY TO MECHANICAL PARAMTERS SENSITIVITY TO MASSES
As built information
Sensitivity to epistemic uncertainties
Performance Level
Sensitivity to random variables
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 Y2Coupling effectiveness of piers Shear floor stiffness
A – presence oftension-only rods at
floor level
B – presence of beamelements at floor level
A – rigid floor
B – flexible floor
A – rigid floor
B – flexible floor
YAA
YAB
YBA
YBB
On Y1 : High sensitivity class + KL3
According to information achieved model B has been
adopted
On Y2 : High sensitivity class + KL2
A subjective probability hasbeen assigned to each model in
order to combine the results
wY1_A=0wY1_B=1
wY2_A=0.7wY2_B=0.3
wYAA =0
wYAB = 0
wYBA = 0.7
wYBB = 0.3
As built information: sensitivity analysis
Steps of the proposed procedure:
a) Achievement of a “basic” knowledge level to preliminarly identify the suitable model (or models) to be adopted for the seismic assessment.
b) Identification of all parameters or set of parameters (in case of parameters dependent on each other) affecting the model.
c) For each parameter, identification of the more rational range of variation.
d) 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.
e) 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.
f) Plan of the investigation and testing by using the results obtained from steps d) and e).
g) Execution of investigations and tests;
h) 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.
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 :
i. the actual variability of the parameter which will be applied to (by considering the related fk value);
ii. the “remaining” uncertainties associated to the incomplete knowledge process (since it could be not possible to reach the maximum knowledge level on all parameters ).
As built information: sensitivity analysis
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 ClassKnowledge level Low Medium High
KL1 0.3 0.6 1KL2 0 0.3 0.6KL3 0 0 0
Hence CF is computed as:
)(1
)(1
max
max
bf
afFC
c
c
where fc corresponds to fk associated to the k-th parameter assumed as reference as “main
parameter” that affects the seismic response.
Measure of the sensitivity of the structural performance
at k- th parameter
1,3
,1,31,3,1
PL
kPLPLk a
aa
Measure of the sensitivity of the structural performance
at n- th factors
As built information: sensitivity analysis
Modelling and verification procedures
Verification procedures adopted:
METHODS OF ANALYSIS AND ASSESSMENT PROCEDURES
Pushover analyses and Capacity Spectrum MethodSTANDARD 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
Case Procedure
Architectonic Asset Class
APrevailing in-plane
response
BPrevailing
out-of-plane response
CMonodimens
ional masonry elements
DArched
subject to in-plane
response
EMassive structure
FBlocky
structures subjected to overturning
Asset composed by a single macroelement
- X X - X
Complex assets described by a single capacity curve
Standard Possible -
Complex assets described by N capacity curve
Rare Standard -
A B C D E F
Modelling and verification procedures
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)
5. Computation of the maximum IM value (IMPLi) compatible with the given perfomance level (PLi)
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 KINEMATIC ANALYSIS
MACRO BLOCK MODELS (MBM)
Seismic forces proportional to masses applied in each block
NON LINEAR STATIC ANALYSIS
CONTINUUM CONSTITUTIVE LAWS MODELS (CCLM)
AND STRUCTURAL ELEMENT MODELS (SEM)
Seismic forces proportional to the first mode
CLASS C
F and D CLASSES
Assets composed by a single macroelement
2. Definition of PLs on the pushover curve
NON LINEAR KINEMATIC ANALYSISMBM models
F and D classes
NON LINEAR STATIC ANALYSISCCLM and SEM models
C class
Assets composed by a single macroelement
m*
h*
3. Capacity curve – Equivalent SDOF
NON LINEAR KINEMATIC ANALYSISMBM models
It is assumed as a fundamental shape the block displacements of the kinematism
NON LINEAR STATIC ANALYSISCCLM and SEM models
It is based on the fundamental modal shape
ay=Vy /m*G
m*
h*
d=u/G
*i i
2 2i i i i
m mΓ= =
m m
i
N
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 Probabilistic Seismic Hazard Assessment (PSHA)
In case of more 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
By a set of valuesBy a set of parameters and analytical functions
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
equ el β
1ξ =ξ +α 1-
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
*0ddPLi
TPLi
Sd0 (T,x)
Sd (T, IM ,x)
1
IMPLi
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
The assessment consists in the comparison of TR,Pli with T*R,Pli . It is positive if TR,Pli > T*R,Pli .
IMPLi
lRPLi T RPLi
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
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.
Assets composed by a single macroelement
1. PUSHOVER ANALYSIS
CONTINUUM CONSTITUTIVE LAWS MODELS (CCLM)
B class
NON LINEAR STATIC ANALYSIS
STRUCTURAL ELEMENT MODELS (SEM)
A class
Complex assets described by a single capacity curve
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])
Seismic analysis of 3D complex models -
floor modelled as ortotropic membrane
Rigid nodesSpandrelsPiers
0
0,2
0,4
0,6
0,8
1
0 0,5 1 1,5 2 2,5 3
0
0,2
0,4
0,6
0,8
1
0 0,5 1
DL3
DL4
DL3
DL4
DL5
dE,5
dE [%]dE [%]
V/V
u
V/V
uDL5
dE,4 dE,5dE,4dE,3dE,3
E,3 Vu
E,4 Vu E,3 Vu
-80
-60
-40
-20
0
20
40
60
80
-20 -15 -10 -5 0 5 10 15 20
V [k
N]
U [mm]-100
-80
-60
-40
-20
0
20
40
60
80
100
-8 -6 -4 -2 0 2 4 6 8
V [k
N]
U [mm]
Multilinear laws for single masonry panels
Able to reproduce different hysteretic behaviours
Mechanical models for the assessment
Multicriteria definition of Performance Levels
Multicriteria definition of Performance Levels
Complex assets described by a many capacity curves
Complex assets described by a many capacity curves
TERRITORIAL SCALE
• different scales (single asset or group of buildings in town) • conditions (seismic prevention or reconstruction after an earthquake)
Casbah of Algiers
Bovec Region & Ljubljana City Centre
Earthquake 1976, 1998, 2004
Earthquake 1895
Historical centre of Rhodes
Application of PBA to case studies
SINGLE ASSET SCALENeoclassical School Hassan Bey’s MansionArsenal de Milly
GR
EE
CE
AL
GIE
RS
Great Mosque
Application of PBA to case studies
SINGLE ASSET SCALE
ITA
LY
Santa Maria Paganica Church St.Pardo CathedralArdinghelli Palace
SL
OV
EN
IA
Koljzei Palace
Application of PBA to case studies
www.perpetuate.eu