deliverable d22

PERPETUATE PERformance-based aPproach to Earthquake proTection of cUlturAl

heriTage in European and mediterranean countries FP7 - Theme ENV.2009.3.2.1.1 - ENVIRONMENT

Grant agreement n: 244229

DELIVERABLE D22 Definition of confidence factors for the safety

verification

Delivery date: 30 December, 2011

Date of approval: .........., 2012

PERPETUATE Proposal n 244229 Deliverable D22- Date 30 december 2011

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AUTHORS: Cattari S., Degli Abbati S., Lagomarsino S. (UNIGE)

Lead Beneficiary: UNIGE

Reviewer in charge: DAyala D.

WP: 4 Task: 4.5 Nature: R Dissemination Level: PU

SUMMARY The seismic safety assessment of an existing building is affected by more uncertainties than the one related to the design of a new building: in fact, uncertainties related to the incomplete knowledge of the asset (epistemic uncertainties) add up to the statistical ones. Approaches usually proposed in the codes treat epistemic uncertainties by introducing confidence factors to be applied to some of the parameters which may affect the seismic response. Confidence factors (CF) are defined on the basis of the knowledge level which constitutes a measure of the degree of accuracy reached depending on the amount and quality of the information collected (on materials, geometry, constructive details,); moreover, the parameters, which the CF has to be applied to, are selected at priori without taking into account the actual sensitivity of the structural response. Despite some unavoidable approximations, this approach has the main advantage to allow a reasonable effort more compatible with engineering practice aims than others much more detailed (as the full probabilistic one). Thus, it seems reasonable to adopt also in the PERPETUATE procedure this approach as the standard one. Starting from the review of some international and national codes (2), the main aims of Deliverable 22 are: firstly, to discuss the use of traditional approaches proposed in the literature in the context of cultural heritage asset (2.6); then, to propose an innovative procedure (3) aimed to improve its effectiveness for application in this context (and more in general in that of existing buildings). In particular, the application of the traditional approaches proposed in codes to cultural heritage assets could significantly increase the minimum number of investigations/testing to be performed in order to reach a certain knowledge level: this could be unadmissible due to the need of guaranteeing the primary conservation objective. To this aim, a proper criterion to optimize the traditional approach reveals to be essential. To this aim, the most innovative aspects of the procedure proposed in PERPETUATE project are: (i) the use of sensitivity analysis to identify parameters which significantly affect the structural response; (ii) the development of a procedure to optimize investigations and testing; (iii) the calibration of the confidence factor on the basis of the actual influence of parameters instead of an a priori assumption.


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INDEX 1 Introduction ........................................................................................................................... 4 2 Review of approaches based on the use of knowledge factors proposed in the literature and codes ...................................................................................................................................... 4

2.1 Introduction ....................................................................................................................... 4 2.2 Eurocode 8 Part 3 and Italian Technical Code ............................................................... 4

2.2.1 Additional recommendations related to investigation to be performed on geometry, materials and details ............................................................................................................... 8

2.3 ASCE/SEI 41-06 ............................................................................................................. 15 2.3.1 Additional recommendations related to investigation to be performed on geometry, materials and details ............................................................................................................. 20

2.4 Guidelines for the seismic-risk assessment and mitigation in case of the cultural heritage (D.P.C.M 9/10/2011) ................................................................................................................. 26 2.5 Comparison among procedures proposed in examined codes ........................................ 27 2.6 Critical issues related to cultural heritage ........................................................................ 29

3 Procedure proposed in PERPETUATE project .................................................................. 30 3.1 The use of sensitivity analysis for planning investigations and defining confidence factors 30 3.2 Overview of the proposed procedure .............................................................................. 30

3.2.1 Achievement of a basic knowledge level (step a) and definition of parameters (steps b and c) 31 3.2.2 Sensitivity analysis (step d) ...................................................................................... 31 3.2.3 Evaluation of the sensitivity class for each parameter (step e) ................................. 35 3.2.4 Plan of investigations and testing (steps f and g) ..................................................... 36 3.2.5 Evaluation of confidence factors (step h) ................................................................. 38

3.3 Example of application of the procedure ......................................................................... 40 4 Conclusions......................................................................................................................... 51 5 References ........................................................................................................................... 52


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1 Introduction The seismic safety assessment of an existing building is affected by more uncertainties than the one related to the design of a new building: in fact, uncertainties related to the incomplete knowledge of the asset (epistemic uncertainties) add up to the statistical ones. Approaches usually proposed in the codes treat epistemic uncertainties by introducing confidence factors to be applied to some of the parameters which may affect the seismic response. Confidence factors are defined on the basis of the knowledge level which constitutes a measure of the degree of accuracy reached depending on the amount and quality of the information collected (on materials, geometry, constructive details,). Despite some unavoidable approximations, this approach has the main advantage to allow a reasonable effort more compatible with engineering practice aims than others much more detailed (as the full probabilistic one). Thus, it seems reasonable to adopt also in the PERPETUATE procedure this approach as the standard one. Starting from the review of some international and national codes (2), the main aims of Deliverable 22 are firstly, to discuss the use of traditional approaches proposed in the literature in the context of cultural heritage asset (2.6); then, to propose an innovative procedure (3) aimed to improve its effectiveness for application in this context (and more in general in that of existing buildings).

2 Review of approaches based on the use of knowledge factors proposed in the literature and codes

2.1 Introduction As abovementioned, all the approaches usually proposed in literature and codes, based on the use of knowledge factors, define different knowledge levels (usually three) which are characterized by an increasing knowledge of the building features, essentially related to three main aspects: geometry, constructive details and materials. Depending on the amount and quality of the information collected on these three aspects, it is possible to reach a specific knowledge level and assume a corresponding value of the confidence factor to be applied to some mechanical parameters which are conventionally assumed as significantly affecting the seismic response. These parameters are usually related to the strength, but in few cases they are related to masonry piers displacement capacities.

In this paragraph, the following documents will be analyzed:

o Eurocode 8 Part 3 (2005) and Italian Technical Code (2008); o ASCE/SEI 41-06 (2007)

Guidelines for the seismic-risk assessment and mitigation in case of the cultural heritage (Valutazione e riduzione del rischio sismico del patrimonio culturale con riferimento alle Norme Tecniche per le Costruzioni D.M. 14/01/2008, D.P.C.M 9/10/2011 In Italian)

For each code, the following aspects will be discussed:

o definition of Knowledge Levels and of the amount and accuracy of the information to be reached, in order to obtain the corresponding knowledge level;

o adopted procedure for the Confidence Factors determination, depending on the obtained Knowledge Level;

o values to be assumed as reference for the Confidence Factors; o use of the Confidence Factors in the seismic analysis and possible repercussions in terms

of choice and limitations of the analysis methods.

2.2 Eurocode 8 Part 3 and Italian Technical Code


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Eurocode 8 defines three different Knowledge Levels (KL1, KL2 and KL3), characterized by an increasing knowledge of the building features (limited, normal or full); the aspects determining the appropriate knowledge level are geometry, details and materials. It is possible to reach a specific Knowledge Level and use a corresponding Confidence Factor, depending on the level of details and on the amount of collected information related to each aspect. The following table summarizes the qualitative information, related to knowledge, needed depending on the considered knowledge level. Eurocode 8 gives extra indications (such as the number of experimental tests to be performed) which will be briefly illustrated in 2.2.1.

Table 1 Requested information for geometry, details and materials and corresponding knowledge levels

GEOMETRY DETAILS MATERIALS

KL1: LIMITED KNOWLEDGE

The overall structural geometry and member sizes are known either from survey or from original outline construction drawings used for both the original construction and any subsequent modifications. In the latter case, a sufficient sample of dimensions of both overall geometry and member sizes should be checked on site; if there are significant discrepancies from the outline construction drawings, a fuller dimensional survey should be performed.

The structural details are not known from detailed construction drawings and may be assumed based on simulated design in accordance with usual practice at the time of construction; in this case, limited inspections in the most critical elements should be performed to check that the assumptions correspond to the actual situation. Otherwise, more extensive in-situ inspection is required.

No direct information on the mechanical properties of the construction materials is available, either from original design specifications or from original test reports. Default values should be assumed in accordance with standards at the time of construction, accompanied by limited in-situ testing in the most critical elements.

KL2: NORMAL KNOWLEDGE

The structural details are known either from extended in-situ inspection or from incomplete detailed construction drawings. In the latter case, limited in-situ inspections in the most critical elements should be performed to check that the available information corresponds to the actual situation.

Information on the mechanical properties of the construction materials is available either from extended in-situ testing or from original design specifications. In this latter case, limited in-situ testing should be performed.

KL3: FULL KNOWLEDGE

The structural details are known either from comprehensive in-situ inspection or from a complete set of detailed construction drawings. In the latter case, limited in-situ inspections in the most critical elements should be performed to check that the available information corresponds to the actual situation.

Information on the mechanical properties of the construction materials is available either from comprehensive in-situ testing or from original test reports. In this latter case, limited in-situ testing should be performed.

Once obtained a specific knowledge level (depending on the amount and details of the information about geometry, details and materials), it is possible to use a corresponding Confidence Factor.


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The relationship between knowledge levels, applicable methods of analysis and confidence factors will be illustrated in the following table.

Table 2 - Knowledge levels and corresponding methods of analysis (LF: Lateral Force procedure, MRS: Modal Response Spectrum analysis) and Confidence Factors FC (Table 3.1, Eurocode8)

Eurocode recommends values for the Confidence Factors, by deferring to the different countries National Annex to establish more accurate values. Table 3 shows the recommended values of the Confidence Factors proposed by Eurocode 8.

Table 3 Confidence Factors values recommended by Eurocode 8 Part 3 KNOWLEDGE LEVEL RECOMMENDED CONFIDENCE FACTORS

KL1 CFKL1 =1.35 KL2 CFKL2=1.20 KL3 CFKL3=1.00

Eurocode 8 suggests to apply the confidence factors to the parameters related to strength, which mainly affect the structural response, although all masonry panels failure modes considered (rocking or shear modes) are classified as ductile. Eurocode 8 establishes further specification in the use of the confidence factors for single structural elements verifications, but these recommendations are actually to be applied to structural typologies different from masonry, such as concrete or steel. The achieved level of knowledge determines the possible method of analysis, too. In particular, with a limited knowledge (KL1), the information collected should be sufficient to perform local verifications of element capacity and to set up a linear structural analysis model; structural evaluation based on a state of limited knowledge should be performed through linear analysis methods, either static or dynamic. On the other hand, with a normal or full knowledge level (KL2, KL3), the information collected should be sufficient to perform local verifications of


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element capacity and to set up a linear or nonlinear structural model. Structural evaluation based on these states of knowledge may be performed through either linear or nonlinear analysis methods, either static or dynamic.

As abovementioned, despite the general common prescriptions established by Eurocode 8, every countrys National Annex specifies some aspects, such as the reference values for the confidence factors and the limitation of the analysis methods.

In particular, the Italian Technical Code (N.T.C. 2008 and Istruzioni per lapplicazione delle Nuove Norme Tecniche per le costruzioni N.T.C.- n617/09) aligns with Eurocodes general prescriptions, but specifying some aspects, mainly related to masonry buildings. However, differently from Eurocode 8 (that in case of KL1 suggests the use of linear analyses methods), the Italian Technical Code allows the use of nonlinear static analysis aside from the knowledge level reached; in fact, due to the strong non linearity of masonry building response, nonlinear methods are considered more reliable than the linear ones. In general, the Italian Technical Code proposes to apply the confidence factor to the strength parameters. However, when these parameters (according to the hyphoteses adopted for the analysis) do not affect directly the seismic assessment, the confidence factor has to be applied to the structural capacity computed. Tthis is the case of the analysis of assets subjected to a prevailing out-of-plane behavior through discrete macro-block models (by adopting the kinematic analysis). Actually, in this case the limited compressive strength of masonry may be taken into account in indirect way by withdrawing the hinges position; when this effect is neglected in the analysis, the Italian Technical Code suggests to apply the confidence factor directly to the seismic activation multiplier. Despite the abovementioned differences, the values of the confidence factors proposed by Italian Technical Code are the same of the reference values recommended by Eurocode 8, as shown in Table 4.


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Table 4 - Knowledge levels related to available information and corresponding confidence factors for masonry buildings (Table C8A.1.1, Italian Technical Code, 2008)

2.2.1 Additional recommendations related to investigation to be performed on geometry, materials and details

In the following, a more accurate analysis of the procedures required by Eurocode 8 in order to collect information about the three different aspects of knowledge (geometry, details and materials) will be pointed out. In this paragraph, the analysis will be structured as follows :

a) definition of the examined knowledge aspect (geometry, details or materials), according to Eurocode 8;

b) description of the extra specific recommendations included in Annex C for the assessment and design of masonry buildings in seismic regions;

c) description of the procedure (related to the considered aspect and named in Table 2) proposed to collect the information, by specifying its aim.

Whereas Italian Technical Codes prescriptions will be quite different from Eurocodes ones, the differences will be underlined.

Geometry

Geometry is defined by Eurocode 8 as the whole geometrical properties of the structural system and such non-structural elements which can affect structural response.

In particular, for masonry building, the knowledge aspect of geometry is related to different aspects contained into Annex C, such as:

- type of masonry unit (e.g., clay, concrete, hollow, solid, etc.);


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- physical condition of masonry elements and presence of any degradation; - properties of constituent materials of masonry elements and quality of connections; - presence and attachment of veneers, presence of nonstructural components, distance

between partition walls; - information on adjacent buildings potentially interacting with the building under

consideration.

The proposed procedure to collect information about Geometry is survey, classified by Eurocode 8 as visual or full, depending on the aim and the details of the information collected. The following table illustrates the procedure to collect information about geometry, its classification according to Eurocode 8, the needed pre-requirement and finally the aim of each type of procedure.

Table 5 Analysis of the aspect Geometry PROCEDURE TO

COLLECT INFORMATION ABOUT

GEOMETRY CLASSIFICATION PRE-REQUIREMENT AIM

SURVEY

VISUAL SURVEY Outline construction drawings are available

Check correspondence between the actual

geometry and outline construction drawings, by performing sample

geometry measurements on selected elements

FULL SURVEY Outline construction

drawings are not available

Produce structural drawings (which include the structures geometry

and the identification and dimensions of

structural components)

In particular, Full survey is necessary where there are possible structural changes which may have occurred during or after the buildings construction.

Details

In general, for Eurocode 8, this aspect include all the buildings structural details (such as the amount and detailing of reinforcement in reinforced concrete, the connections between steel members, the connection of floor diaphragms to lateral resisting structure, the bond and mortar jointing of masonry and the nature of any reinforcing elements in masonry).

In particular, Annex C specifies that for masonry buildings, details include:

- the classification of the walls as un-reinforced, confined, or reinforced; - the amount of horizontal and vertical reinforcement for reinforced masonry walls; - the identification of the number of leaves; - the evaluation of the type and condition of mortar and mortar joints; - the examination of mortars resistance, erosion and hardness; - the identification of cracks, internal voids and weak components; - the identification of the type and condition of connections between orthogonal walls and

between walls and floors or roofs ;


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- the examination of walls vertically deviations and separation of exterior leaves or other elements as parapets and chimneys.

The following table shows the different reliable types of procedure which may be adopted in the inspections of details and minimum requirements recommended by Eurocode 8.

Table 6 Analysis of the aspect Details PROCEDURE TO

COLLECT INFORMATION ABOUT

DETAILS CLASSIFICATION PRE-REQUIREMENT AIM

SIMULATED DESIGN _

Regulatory documents and state of the practice used at the time of construction are available

Define the amount and layout of reinforcement (both longitudinal and transverse)

INSPECTIONS

(with a recommendation on the minimum

percentage of elements to be checked)

LIMITED IN-SITU INSPECTION

Detailed construction drawings are available

Check correspondence between actual details with either the detail construction drawings or the results of simulated design

EXTENDED IN-SITU INSPECTION

Detailed construction drawings are not available

Collect information about details when detailed construction drawings are not available

COMPREHENSIVE IN-SITU INSPECTION

Collect information about details when detailed construction drawings are not available and to pursue a higher knowledge level

The classification of the levels of inspection depends on the percentage of structural elements that have to be checked for details. Table 7 shows the minimum required inspections number, for each type of primary element (beam, column, wall).

Table 7 Recommended minimum requirements for different levels of inspection LEVEL OF INSPECTION PERCENTAGE OF ELEMENTS TO BE CHECKED

LIMITED 20 EXTENDED 50

COMPREHENSIVE 80

Materials

This aspect is related to the mechanical properties of the constituent materials.

Information about materials can be collected into two different ways (named procedures in the following table): by using some original documents or information (such as standards at the building time construction, or original design specification, or original test reports) or by performing some tests, which are classified by Eurocode as destructive or non destructive. Eurocode specifies that the use of non destructive tests should not be in isolation, but in conjunction with destructive ones, too. Table 8 summarizes the different types of procedures suggested by Eurocode 8 to collect information about material and their aims.


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Table 8 Analysis of the aspect Materials PROCEDURE TO COLLECT

INFORMATION ABOUT MATERIALS

CLASSIFICATION AIM

ORIGINAL DOCUMENTS OR INFORMATION

STANDARDS AT THE TIME CONSTRUCTION

Collect some preliminary information

ORIGINAL DESIGN SPECIFICATIONS

ORIGINAL TEST REPORTS

TESTING

(with a recommendation on the minimum samples per floor)


Complete information on material properties belonged to either from

standards at the time of construction, or from original design specifications or from

original test reports


Obtain some information when neither original design

specification nor test reports are available


Obtain some information when neither original design

specification nor the test reports are available and to pursue a

higher knowledge level

The classification of the levels of testing depends on the number of material samples per floor that have to taken for testing. Table 9 shows the minimum required inspections number, for each type of primary element (beam, column, wall).

Table 9 Recommended minimum requirements for different levels of testing LEVEL OF TESTING MATERIAL SAMPLES PER FLOOR

LIMITED 1 EXTENDED 2

COMPREHENSIVE 3

It is important to point out that Eurocode establishes that to determine the properties of existing materials to be used in calculation, it has to evaluate the mean values obtained from in-situ tests and from the additional sources of information, once adequately applied the confidence factor corresponding to the reached knowledge level.

For masonry building, Eurocode 8s Annex C gives extra information. In particular, it distinguishes between non destructive testing and supplementary testing and illustrates the aim of each category, by suggesting the types of tests may be used and their output, as in Figure 10.


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Table 10 Testing typologies suggested by Eurocode for masonry buildings TYPOLOGY AIM TEST TYPES TEST OUTPUT

NON DESTRUCTIVE TESTING

Quantify and confirm the uniformity of construction quality and the presence

and degree of deterioration

Ultrasonic or mechanical pulse velocity

Detect variations in the density and modulus of

masonry materials Verify the presence of

cracks and discontinuities

Impact echo test Confirm whether

reinforced walls are grouted

Radiography and cover meters (where appropriate)

Confirm location of reinforcing steel

SUPPLEMENTARY TESTING

Enhance the level of confidence in masonry material properties or to

assess masonry condition

Schmidt rebound hammer test

Evaluate surface hardness of exterior

masonry walls Hydraulic flat jack test

(also in conjunction with flat jacks applying a

measured vertical load to the masonry units

under test)

Measure the in-situ shear strength of

masonry

Hydraulic flat jack test

Measure the in-situ vertical compressive

stress resisted by masonry

Provide other information such as

gravity load distribution, flexural stresses in walls and stresses in masonry

veneer walls compressed by

surrounding concrete frame

Diagonal compression test

Estimate shear strength and shear modulus of

masonry

Large-scale destructive tests (on particular

regions or elements)

Increase the confidence level on overall structural properties or to provide particular information such as out-of-plane strength, behavior of

connections and openings, in-plane

strength and deformation capacity

As abovementioned, about the aspects of details and materials, Eurocode 8 recommends a minimum requirements for different levels of inspection (Table 7) and testing (Table 9); the amount of inspection and testing to be used in each country may be found in its National Annex.

Regarding this, for example, the Italian Technical Code (2008) proposes further prescriptions, illustrated in Table 11.


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Italian Technical Code (2008) distinguishes between destructive and non destructive tests, by suggesting some test types which can be performed in order to collect more information about details and materials and to obtain a specific knowledge level.

Table 11 Italian Technical Codes specifications related to the aspects Material and Details

LEVEL OF INSPECTION AND

TESTING TYPE SUGGESTED INSPECTION AND TESTING TYPE

RECOMMENDED REQUIREMENTS


NON DESTRUCTIVE Visual check of masonry facade No prescriptions on the minimum

number to be performed DESTRUCTIVE --


NON DESTRUCTIVE Sonic test

Rebound hammer test Penetrometric test Minimum one test for each masonry

type DESTRUCTIVE Double flat jack test Test for mortar characterization


NON DESTRUCTIVE Some non destructive tests can be combined with the destructive ones

Amount and type shall be

appropriate to define masonry

mechanical characteristics

DESTRUCTIVE Diagonal compression test Combined Shear/Compression test

Depending on the level of inspection and testing, the evaluation of the mechanical parameters to be used in the analyses changes, as illustrated in the following. The Italian Technical Code (2008) suggests for historical masonry some reference values (minimum and maximum) for mechanical parameters, which are different for each type of masonry (Table 12). These values might be corrected with appropriate coefficients if some building rules are observed (e.g. related to the presence of good quality mortar, good interlocking,), which increase or reduce the values of strength and stiffness (Table 13).


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Table 12 - Reference values of the mechanical parameters proposed by N.T.C. 2008 (Table C8A.2.1/ Circolare 617/09)

Table 13 - Corrective coefficient proposed by N.T.C. 2008 for each masonry type (Table C8A.2.2/ Circolare 617/09)

Depending on the level of inspection and testing, the mechanical parameters are evaluated like in Table 14 (where reference range is the range proposed by Italian Code illustrated in Table 12).


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Table 14 Evaluation of the mechanical parameters, according to Italian Technical Code (2008) LEVEL OF

INSPECTION LEVEL OF TESTING MECHANICAL PROPERTIES STRENGHT YOUNG MODULUS

LIMITED IN-SITU INSPECTION LIMITED IN-SITU

Minimum value of reference range

Mean value of the reference range


EXTENDED IN-SITU Mean value of reference range

Mean value of experimental results or mean value of reference range

COMPREHENSIVE IN-SITU

a) if three or more experimental values of strength are available

Mean value of experimental results


b) if two experimental values are available

If experimental mean value is contained into reference range, the mechanical parameter of strength is the mean value of it; if it is higher than the maximum, the mechanical parameter of strength will be the maximum as well; (as in the case of a lower value it becomes the minimum as well).


c) if one experimental value are available

If experimental result is contained into reference range or higher, the mean value of the range will be considered.; if it is lower than the minimum, the experimental result is to be considered.

Experimental results or mean value of reference range

2.3 ASCE/SEI 41-06 ASCE/SEI 41-06 distinguishes different data collection requirements which are defined as data on the as-built condition of the structure, components, site and adjacent buildings; their extent is related to three different levels of knowledge: minimum, usual or comprehensive. The factors determining the appropriate knowledge level are related to testing, drawings, condition assessment and material properties. The following table summarizes the minimum information to collect in order to reach a corresponding knowledge level, according to ASCE/SEI 41-06.


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Table 15 Analysis of each data collection requirement LEVEL OF KNOWLEDGE MINIMUM DATA COLLECTION REQUIREMENTS (related to geometry, material properties and details)

MINIMUM

Information shall be obtained from design drawings with sufficient information to analyze component demands and calculate component capacities. For minimum data collection, the design drawings shall show, as a minimum, the configuration of the vertical- and lateral-force-resisting system and typical connections with sufficient detail to carry out linear analysis procedures. Where design drawings are available, information shall be verified by a visual condition assessment; in the absence of sufficient information from design drawings, incomplete or nonexistent information shall be supplemented by a comprehensive condition assessment, including destructive and non-destructive investigation; In the absence of material test records and quality assurance reports, use of default material properties shall be permitted; Information needed on adjacent buildings shall be gained through field surveys and research of as-built information made available by the owner of the subject building; Site and foundation information shall be collected.

USUAL

Information shall be obtained from design drawings with sufficient information to analyze component demands and calculate component capacities. For usual data collection, the design drawings shall show, as a minimum, the configuration of the vertical- and lateral-force-resisting system and typical connections with sufficient detail to carry out the selected analysis procedure. Where design drawings are available, information shall be verified by a visual condition assessment; In the absence of sufficient information from design drawings, incomplete or nonexistent information shall be supplemented by a comprehensive condition assessment, including destructive and non-destructive investigation; In the absence of material test records and quality assurance reports, material properties shall be determined by usual materials testing; Information needed on adjacent buildings shall be gained through field surveys and research of as-built information made available by the owner of the subject building; Site and foundation information shall be collected.

COMPREHENSIVE

Information shall be obtained from construction documents including design drawings, specifications, material test records and quality assurance reports covering original construction and subsequent modifications to the structure. Where construction documents are available, information shall be verified by a visual condition assessment; If construction documents are incomplete, missing information shall be supplemented by a comprehensive condition assessment, including destructive and non-destructive investigation; In the absence of material test records and quality assurance reports, material properties shall be determined by comprehensive materials. The coefficient of variation in material test results shall be less than 20%; where materials testing results have a coefficient of variation greater than 20%, additional materials testing can be performed until the coefficient of variation is less than 20% or a knowledge factor consistent with a lesser data collection requirement can be used. Information needed on adjacent buildings shall be gained through field surveys and research of as-built information made available by the owner of the subject building; Site and foundation information shall be collected.

The relationship between knowledge levels, applicable methods of analysis and confidence factors is illustrated in the following table.


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Table 16 Data collection requirements (Table 2.I, ASCE)

As from the previous table, despite Eurocode 8, the achieved knowledge level is not arbitrarily chosen by the designer/customer, but the code guides the choice depending on safety level assumed as reference, too. For this reason, the required level of knowledge shall be determined considering the selected Rehabilitation Objective, which can be basic, limited or enhanced. Obviously, higher data requirements are needed in order to ensure safety levels higher than the basic one.

The rehabilitation objectives are a basis for building and interventions design and they will determine the cost and feasibility of any rehabilitation project, as well as the benefit to obtain in terms of improved safety, reduction in property damage and interruption of use in the event of future earthquakes. They result from a combination of a target building performance and an earthquake hazard level, defined by the code as illustrated in the following.

The target building performance is a parameter which can be qualitatively described in terms of the safety afforded building occupants during and after the event, the cost and the feasibility of restoring the building to its pre-earthquake condition and the time the building is removed from service. These parameters are directly related to the extent of damage that would be sustained by the building and they are classified by ASCE/SEI 41-06 into the following categories:

a. OPERATIONAL PERFORMANCE LEVEL (1-A) b. IMMEDIATE OCCUPANCY PERFORMANCE LEVEL (1-B) c. LIFE SAFETY PERFORMANCE LEVEL (3-C) d. COLLAPSE PREVENTION PERFORMANCE LEVEL (5-E)

The earthquake hazard level corresponds to mean return periods (the average number of years between events of similar severity). The relationship between earthquake probability exceedance and mean return period are illustrated in Table 17,.


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Table 17 Relationship between earthquake having probability of exceedance and mean return period EARTHQUAKE HAVING PROBABILITY OF

EXCEEDANCE MEAN RETURN PERIOD (YEARS)

50% / 50 years 72 20% / 50 years 225 10% / 50 years 474 2% / 50 years 2,475

Table 18 shows the different combination of Target building performance level and Earthquake hazard level.

Table 18 Different combination to define a Rehabilitation Objective (Table C1-1, ASCE/SEI 41-06)

As abovementioned, ASCE/SEI 41-06 defines three different Rehabilitation Objectives (basic, enhanced or limited), according to the selected target building performance- earthquake hazard level combination. The definition of each rehabilitation objectives is summarized in the following table. In order to consider the uncertainty in the collection of as-built data, the knowledge factor K shall be deduced from Table 16, according to the selected rehabilitation objectives, analysis procedure and data collection process.


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Table 19 Rehabilitation objectives REHABILITATION OBJECTIVES DEFINITION

BASIC SAFETY OBJECTIVE (BSO)

It is a rehabilitation that achieves the dual rehabilitation goals of Life Safety Building Performance Level (3-C) for the BSE-l Earthquake Hazard Level and Collapse Prevention Building Performance Level (5-E) for the BSE-2 earthquake hazard level. Buildings meeting the BSO are expected to experience little damage from relatively frequent, moderate earthquakes and significantly more damage and potential economic loss from the most severe and infrequent earthquakes that could affect them.

ENHANCED REHABILITATION OBJECTIVE

It is a rehabilitation that provides building performance exceeding that of the BSO. It shall be achieved using one or both of the following two methods: 1) By designing for target Building Performance Levels that exceed those of the BSO at the BSE-I hazard level, the BSE-2 hazard level, or both; 2) By designing for the target Building Performance Levels of the BSO using an Earthquake Hazard Level that exceeds either the BSE-I or BSE-2 hazard levels, or both.

LIMITED REHABILITATION OBJECTIVE

REDUCED REHABILITATION

OBJECTIVE

It is a rehabilitation that addresses the entire building structural and nonstructural systems, but uses a lower seismic hazard or lower target Building Performance Level than the BSO.

PARTIAL REHABILITATION

OBJECTIVE

It is a rehabilitation that addresses a portion of the building without rehabilitating the complete lateral force-resisting system.

In order to determine the component capacities, the knowledge factors shall be applied to the strength or to the deformation capacity, depending on the type of component. In fact, ASCE/SEI 41-06 classifies components as deformed or force controlled. Knowledge factors will be applied to drift limit value, in the case of deformation-controlled mode (rocking behavior, which is classified as ductile), or to mechanical parameters of strength, in the case of force-controlled mode (shear behavior, which is classified as brittle), as in Table 20.

Table 20 Calculation of component action capacity in Linear and Non Linear Procedures

The achieved knowledge level determines the possible method of analysis, too. In particular, where linear procedures are used, data collection is related to the minimum level of knowledge shall be permitted, while where nonlinear procedures are used, data coIlection is related to either the usual or comprehensive levels of knowledge can be performed. The Code permits to perform a preliminary analysis before the data collection process, by using an assumed value of confidence factor (K). If this assumed value is not supported by subsequent data


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collection, the analysis shall be revised to include a revised K related to the data collected in accordance with the requirements of Table 16. If the analysis performed by using an assumed value of K results into no structures required rehabilitation, the value of K shall be substantiated by data collection (in accordance with the requirements of Table 16, again) before the analysis will be finalized.

2.3.1 Additional recommendations related to investigation to be performed on geometry, materials and details

The following tables analyze in detail each parameter of Table 16 which compete to define a knowledge level and its corresponding knowledge factor. As previously illustrated in 2.2.1 for Eurocode 8, the analysis will consider every aspect of knowledge (geometry, materials and condition assessment) by illustrating the description of the different procedures proposed to collect the required information, according to ASCE.

Geometry

The procedure proposed by ASCE/SEI 41-06 to collect information about geometry is represented by the use of drawings. The Code classifies drawings into two different categories, without giving any extra information:

1. Design drawings or equivalent; 2. Construction documents or equivalent.

Material Properties

According to ASCE, mechanical properties can be evaluated by using two different procedures: the former by using some original construction documents or information (such as available drawings or standards or historical information for a particular type of masonry construction), the latter by performing some tests. Table 21 summarizes the different types of procedure suggested by ASCE/SEI 41-06 to collect information about material properties and their pre-requirement.

Table 21 Analysis of the aspect Materials PROCEDURE TO COLLECT

INFORMATION ABOUT MATERIALS

CLASSIFICATION PRE-REQUIREMENT

ORIGINAL DOCUMENTS OR INFORMATION

AVAILABLE DRAWINGS, SPECIFICATIONS AND OTHER

DOCUMENTS FOR THE EXISTING CONSTRUCTION

If original documents or information are available and provide adequate information

AVAILABLE HISTORICAL INFORMATION FOR A

PARTICULAR TYPE OF MASONRY CONSTRUCTION,

PREVAILING CODES, AND ASSESSMENT OF EXISTING

CONDITIONS MATERIAL TEST RECORDS OR

MATERIAL TEST REPORTS TESTING

(with a recommendation on the minimum samples)

USUAL TESTING If documents do not provide adequate information COMPREHENSIVE TESTING

The Code establishes that materials testing is not required if material properties are available from original construction documents that include material test records or material test reports; otherwise, minimum number of tests shall be performed, like described in the following.


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The classification of the levels of testing depends on the number of material samples and on the condition of existing masonry, which can be classified in good, fair or poor as defined in the following table, depending on nature and extent of damage or deterioration.

Table 22 Definition of existing masonry condition CONDITION OF EXSISTING

MASONRY NATURE AND EXTENT OF DAMAGE

GOOD CONDITION Masonry characterized by mortar and units intact with no visible cracking.

FAIR CONDITION Masonry characterized by mortar and units intact but with minor cracking.

POOR CONDITION Masonry characterized by degraded mortar, degraded masonry units, or significant cracking.

Table 23 shows the minimum required inspections number for each type of primary element (beam, column, wall). It is important to stress that if the coefficient of variation in test measurements exceeds 25%, the number of tests performed shall be doubled.

ASCE/SEI 41-06 underlines that the number and location of material tests should be selected to provide sufficient information to adequately define the existing condition of materials in the building. Test locations should be identified in those masonry components that are determined to be critical to the primary path of lateral-force resistance. It is important to point out that samples for tests shall be taken as representative of the material conditions throughout the entire building, taking into account variations in workmanship at different story levels, variations in weathering of the exterior surfaces and variations in the condition of the interior surfaces due to deterioration caused by leaks and condensation of water and/or the deleterious effects of other substances contained within the building. An increased sample size shall be permitted to improve the confidence level.


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Table 23 Minimum requirements for different levels of testing LEVEL OF TESTING PRE-REQUIREMENTS

MINIMUM MATERIAL SAMPLES

CONDITION OF EXISTING MASONRY

USUAL TESTING

When specified design strength of the masonry is known

At least one test on samples of each different strength used in the construction of the building (minimum: three tests performed for the entire building)

Good/Fair condition

Additional tests shall be performed to determine the extent of the reduced material property

Poor condition

When specified design strength of the masonry is not known

At least one test on each type of component, with a minimum of six tests performed on the entire building

Every condition When specified design of the reinforcing steel is known

Use of nominal or specified material properties shall be permitted without additional testing

When the specified design of the reinforcing steel is not known

At least two tests coupons of reinforcing steel shall be removed from a building for testing

COMPREHENSIVE TESTING

Always (both in case of available or not original construction)

Two tests for each wall or line of wall elements providing a common resistance to lateral forces (a minimum of eight tests for each building)

Good/Fair condition When original construction records are available

Three tests for each masonry type and for each three floors of construction or 3,000 sf of wall surface

When original construction records are not available

Six tests

When some regions properties differ and to quantify variations

Additional tests or non-destructive condition assessment tests

Poor condition


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Table 24 Factors to translate lower-bound masonry properties to expected masonry properties

The values which can be taken as lower-bound material properties, according to ASHE/SEI 41-06 are nominal material properties or properties specified in construction documents. The Code gives some default lower-bound masonry properties, depending to masonry condition (good, fair or poor), which can be used to determine component strengths with the linear analysis procedures. The following table illustrates the default lower-bound masonry properties proposed by the Code.

Table 25 Default lower-bound masonry properties (Table 7.1- ASCE)

If some tests are available, expected material properties shall be based on mean values from test data (unless specified otherwise) while lower-bounded material properties shall be based on mean values from test minus one standard deviation (unless specified otherwise). Condition Assessment (details)

A condition assessment includes the following aspects:

o The physical condition of primary and secondary components and the presence of any degradation;

o The presence and configuration of components and their connections, and the continuity of load paths between components, elements, and systems;

o Other conditions, including the presence and attachment of veneer, neighbouring party walls and buildings, presence of non-structural components prior remodelling, and limitations for rehabilitation that may influence building performance.

The following table shows the description of the procedure proposed to collect information about details, their classification, their aim and the information to be collected (output), according to ASCE.


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Table 26 Analyses of the aspect Condition Assessment PROCEDURE TO

COLLECT INFORMATION ABOUT DETAILS

CLASSIFICATION AIM OUTPUT

VISUAL CONDITION ASSESSMENT _

Collect some preliminary information

Size and location of all masonry shear and bearing; orientation and placement of the walls; overall dimensions of masonry components ( including wall heights, lengths, and thicknesses); locations and sizes of window and door; distribution of gravity loads; type and condition of the mortar and mortar joints; cracks, bulging or undulations in walls shall be observed, as well as separation of exterior wythes, out-of-plumb walls, and leaning parapets or chimneys.

COMPREHENSIVE ASSESSMENT

NON-DESTRUCTIVE

TESTS Quantify and confirm the uniformity of construction quality and the presence

and degree of deterioration

Experimental data and mechanical parameters

SUPPLEMENTAL TESTS

The Code gives some detailed extra indications, especially about the output related to the visual condition assessment, by specifying the required information to be collected for different types of construction (such as reinforced masonry construction, multi-wythe masonry construction, grouted construction, and so on) and the minimum number of connections to verify if construction drawings are available or not. Furthermore, it suggests some destructive and non-destructive tests which can be performed in order to quantify and confirm the uniformity of construction quality and the presence and degree of deterioration and ensure a comprehensive assessment. Table 27 illustrates the different test types suggested by the Code in order to reach a comprehensive assessment, by specifying their aim. Where ASCE underlines further important indication, they will be illustrated in the Further indication section.


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Table 27 Testing typologies suggested by ASCE in order to reach a comprehensive assessment TYPOLOGY TEST TYPES AIM FURTHER INDICATION

NON DESTRUCTIVE TESTS

ULTRASONIC OR MECHANICAL PULSE

VELOCITY

Detect variations in the density and modulus of masonry materials and the presence of cracks and discontinuities

Their location and number shall be determined providing sufficient information to adequately define the existing condition of materials in the building; test locations are to identified in those masonry components critical to the primary path of lateral-force resistance

IMPACT ECO-TEST

Determine voids location and to confirm whether reinforced walls are grouted

_

RADIOGRAPHY Identify reinforcing steels location

_

SUPPLEMENTAL TESTS

SURFACE HARDNESS Evaluate surface hardness _

VERTICAL COMPRESSINE STRESS

Measure gravity load distribution, flexural stresses in masonry veneer walls that are compressed by a surrounding concrete frame

Not less than three tests should be performed for each section of the building where in-situ vertical stress is to be evaluate. The number and location of the tests should be determined based on the building configuration

DIAGONAL COMPRESSION TEST

Estimate shear strength and shear modulus

_

LARGE-SCALE LOAD TESTS

Obtain performance data on archaic building materials and construction materials; to quantify effects of complex edge and boundary conditions around openings; to verify and calibrate analytical models

_


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2.4 Guidelines for the seismic-risk assessment and mitigation in case of the cultural heritage (D.P.C.M 9/10/2011)

The Guidelines underline the importance of knowledge for the cultural heritage and the necessity to collect detailed information in order to ensure the prevention of historical buildings. They define,in fact, different levels of knowledge (characterized by an increasing detail) and the corresponding confidence factor. The aspects of knowledge are very similar to those proposed in the codes illustrated in the previous paragraphs (essentially geometry, materials and details), but Guidelines particularly underline the importance of some aspects (such as the historical analysis), considered as crucial in order to ensure an adequate preservation of the building and minimize any external intervention. Once the construction features have been identified, the designer assigns a confidence factor FC, ranging from 1 to 1.35 in order to graduate structural analysis models reliability and to evaluate the seismic safety index. The calculation of the confidence factor is determined by defining different partial confidence factors, FCk (k=1,4) - where the FCk factor is related to the k-th analyzed aspect (geometry, material, constructive details, etc.) - so that it is possible to combine different levels of detail reached in the different aspects. The values of the partial confidence factors will be illustrated in Table 28, while the equation to calculate the coefficient factor will be identifies as follows:

=

+=4

1kCkC F1F (1)

Table 28 Definition of details levels related to knowledge and corresponding partial confidence factors

Geometric Survey

The Geometric survey has been completed FC1 = 0.05

The Geometric survey has been completed along with the graphic rendering of cracking and deformations

FC1 = 0

Material and Construction Survey

Limited survey of materials and constructive elements FC2 = 0.12

Extensive survey of materials and constructive elements FC2 = 0.06

Exhaustive survey of materials and constructive elements FC2 = 0

Mechanical Properties of the Materials

Mechanical parameters deduced from available data FC3 = 0.12

Limited research of mechanical parameters of materials FC3 = 0.06

Extensive research of mechanical parameters of materials FC3 = 0

Terrain and Foundations

Limited survey of terrain and foundations, in absence of Geological data or availability of information about the foundation

FC4 = 0.06

Geological data and information regarding the foundation structures is available; limited research on terrain and foundation

FC4 = 0.03

Extensive or exhaustive research on the terrain and foundation FC4 = 0

Once the confidence factor has been calculated, it will be applied differently depending on the model chosen to evaluate seismic safety:

- if the model considers material and structural elements deformability and resistance, the confidence factor is to be applied to material properties, by reducing the parameters related to strength;

- if the model considers the balance limits of the different discrete macro-block (in case, for example, of models adopted for the analysis of assets subjected to prevailing out of plane behavior-where material resistance is not considered), the confidence factor is to be applied directly to the structural capacity, by reducing the acceleration corresponding to the different limit states.


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It is important to point out that, if some surveys have been performed in order to determine masonrys mechanical properties, it is possible to assign a value of the partial confidence factor lower than 0.12, only if masonry compressive strength is considered in the model. In both cases, confidence factors definition has to be referred to the material/typology which mainly penalizes the considered mechanism of damage/collapse.

2.5 Comparison among procedures proposed in examined codes All the examined codes propose a graduation of different knowledge levels (usually three) depending on the amount and quality of the information collected. The information required for the structural assessment are usually related to these main aspects: geometry; constructive details; materials. The reaching of a certain level of knowledge leads to the assumption of the corresponding confidence factor value and in some cases to some limitations on the use of some analysis method. Usually, the knowledge level to be reached is arbitrarily chosen by the designer/customer; while only in the case of ASCE/SEI 41-06, the Code orients the choice also depending on the safety level (the rehabilitation objective) assumed as a reference. In this latter case, a data requirement with increasing degree of accuracy is required for safety levels more ambitious than the basic one.

Usually, the reaching of a certain knowledge level (which the confidence factor value is associated to) implies an almost homogeneous degree of accuracy to be reached on all different knowledge aspects. It means that a high level of knowledge presumes a comprehensive investigations either on geometry and on constructive details and materials. Only the Guidelines for the seismic-risk assessment and mitigation in case of the cultural heritage (D.P.C.M 9/10/2011) admits the possibility of combining different levels of accuracy reached on these various aspects (since

=

+=4

1kCkC F1F , where the FCk factor is related to the k-th examined aspect, that is geometry,

constructive details, materials and soil characterization).

Each code recommends for each knowledge aspect - specific criteria to reach a certain level of accuracy. In particular, in case of materials, these criteria usually combine both visual investigations and experimental campaigns (through both non destructive and destructive tests). Usually, a minimum number of investigations and testing to be performed is suggested in addition to a list of advisable tests to be adopted. In some cases, such as in the Italian Technical Code (2008), the use of specific tests are also proposed to achieve a specific level of knowledge. In the case of ASCE/SEI 41-06, a distinction in the criteria related to material properties is proposed also as a function of the condition of masonry (if good, fair or poor). Moreover, this document recommends to increase (double) the minimum number proposed in case of poor reliability of results achieved from experimental tests; where the poor reliability is quantify in case of the coefficient of variation in test measurements exceeding 25%.

Once defined the level of knowledge, all these documents propose to apply the corresponding confidence factor to the parameter which is implicitly assumed to mainly affect the structural response (usually the strength parameters). Some distinctions is introduced in these various documents as a function of the failure mode occurred in masonry panels (if classified as ductile or brittle, that is deformed or force controlled) and of the actual capability of the model to take into account the dependence on these mechanical parameters. In the case of Eurocode 8 and the Italian Technical Code, all the considered failure modes of masonry panels (rocking or shear) are classified as ductile (by introducing a proper limit value in terms of drift). Despite this, the confidence factor is applied only to the mechanical parameters related to strength. In case of the Italian Technical Code and Guidelines for the seismic-risk


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assessment and mitigation in case of the cultural heritage, if mechanical parameters of strength do not affect directly the models adopted for the seismic analysis, the confidence factor has to be applied to the structural capacity computed. In particular, this is the case of models adopted for the analysis of assets subjected to prevailing out-of-plane behavior (such as discrete macro-block models). In the case of ASCE/SEI 41-06, failure modes of masonry are classified as ductile in case of prevailing rocking behavior and brittle in case of prevailing shear behavior. In case of deformed controlled mode (rocking), confidence factor is applied to drift limit value, whereas in case of force controlled mode (shear) it is applied to mechanical parameters of strength.

Regarding the limitation on analysis methods allowed as a function of the knowledge level achieved, in general in case of a low/poor knowledge level only the use of linear analysis methods is admitted. Despite this, in case of the Italian Technical Code and the Italian Guidelines, in case of masonry buildings, all methods are always allowed; indeed non linear static analysis is considered as the standard method to be assumed as reference.

The value of the confidence factor varies in all these documents from 1.35 to 1 as a function of increasing knowledge levels. Table 29 shows a comparing synthesis of the prescriptions contained in the different documents.

Table 29 Synthesis of the prescriptions contained in the different codes DOCUMENT FC ASSINGNING METHODOLOGY

FC APPLYING METHODOLOGY

DESIGNERS CHOICE FOR FC

Eurocode 8

FC is related to a specific obtained knowledge level

The reaching of a specific knowledge level implies a homogeneous detail obtained in all the aspects related to knowledge

For masonry, FC is applied to parameters related to strength

Free Italian Technical Code (N.T.C. 2008 and Circolare

617/09)

As in Eurocode 8, if mechanical parameters of strength do not affect directly the models adopted for the seismic analysis, FC has to be applied to the structural capacity computed. (e.g. in the case of models adopted for the analysis of assets subjected to prevailing out-of-plane behavior, such as discrete macro-block models).

ASCE

FC is applied to drift limit value, in the case of deformed controlled mode (rocking); otherwise, in the case of force controlled mode (shear) it is applied to mechanical parameters of strength

Forced by the safety level the designer wants to obtain (rehabilitation objective)

Guidelines for the seismic-risk assessment and

mitigation in case of the cultural heritage (D.P.C.M

9/10/2011)

FC is calculated by combining different partial confidence factors, making possible to assign differently accurate judgments to each aspect related to knowledge

Like Italian Technical Code Free


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2.6 Critical issues related to cultural heritage From the review of the international and national abovementioned codes, the usual application of the approach based on the use of confidence factor shows the following main drawbacks:

- 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). 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. For example, in some cases, a lower level of knowledge has been accepted because no remarkable building details have been analyzed (by penalizing a higher level of knowledge on other aspects), notwithstanding these abovementioned information could not be so relevant in terms of seismic safety.

- 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). In general, as a function of the structure examined, this conventional assumption could not be the best one.

- the value of the confidence factor is conventionally proposed by codes only as a function of the reached knowledge level. The actual variability from time to time examined parameters which may affect the response of the building is not considered.

These drawbacks seem to have soundness in most of the general cases of all existing buildings (both ordinary and monumental). The soundess of the traditional format of approaches based on the use of CF proposed in codes with particular reference to the case of Eurocode 8 is discussed also in Franchin et al. (2010).

In addition, in case of cultural heritage assets, it seems important pointing out that the primary conservation objective implies also the need to minimize the invasiveness of destructive investigations and testing. Moreover, since cultural heritage assets may have been subjected to many transformations, they may be characterized by a great variability of details or masonry typologies: it is evident that following a rigorous logic like that proposed in codes - this variability could significantly increase the minimum number of investigations/testing to be performed in order to reach a certain knowledge level until not achievable (due to the invasiveness) values. To this aim, a proper criterion to optimize the plan of investigation reveals to be essential.

In the following paragraph, an innovative procedure aimed to overcome all the abovementioned drawbacks will be proposed.


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3 Procedure proposed in PERPETUATE project

3.1 The use of sensitivity analysis for planning investigations and defining confidence factors With respect to the approaches based on the use of confidence factors actually proposed in the codes, the most innovative aspects of the procedure proposed in PERPETUATE project are:

i. the use of sensitivity analysis to identify parameters which significantly affect the structural response;

ii. development of a procedure to optimize investigations and testing; iii. the calibration of the confidence factor on the basis of the actual influence of parameters

instead of an a priori assumption.

In the following, a general overview of the proposed procedure is illustrated in 3.2 clarifying from a conceptual point of view all steps at the base and, then, an application of it to a simple two storeys masonry building will be discussed in 3.3.

3.2 Overview of the proposed procedure The procedure may be summarized through the following steps:

a. Achievement of a basic knowledge level. This minimum knowledge level is addressed to preliminarily identify the most suitable model (or models, as classified in Deliverable 4 and 7) to be adopted for the seismic assessment.

b. Identification of parameters, or groups of correlated parameters, which affect the structural response. Parameters are related to geometry, mechanical parameters and constructive details (e.g. presence and effectiveness of tie rods).

c. For each parameter xk(k=1..N, where N is the total number of groups of parameters related to geometrical data or mechanical parameters), identification of a rational range of variation (that is xk,inf and xk,sup ). Once specified the range of variation it is possible to define:

sup,inf,

inf,sup,

sup,inf,

2

kk

kkk

kkk

xx

xxf

xxx

+

=

+=

(2)

where kx is the mean value and fk will be used to calibrate the confidence factor on the basis of the actual variation expected for each parameter. Some parameters are not defined by a range of variation but lead to the adoption of different models; for example, in case of uncertainties related to the effectiveness of tie-rods, in order to evaluate how the seismic response of the examined structure may change, it would be necessary to consider two models: with or without the actual modelling of these structural elements. These parameters are enumerated in the following as Yi (i= 1..M, with M total number of parameters leading to the adoption of different models). For each Yi factor, two possible models can be adopted, quoted as A and B.Thus, in general, it could be possible to have M2 models (since a combination of all possible configurations has to be considered). In the following, models will be enumerated through a j counter (j= 1..M2).

d. Execution of the sensitivity analysis with selected parameters, in order to evaluate how much each one really affects the seismic behaviour of the examined building.

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 investigations and testing by using the results obtained from steps d) and e).


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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.

3.2.1 Achievement of a basic knowledge level (step a) and definition of parameters (steps b and c)

As abovementioned, the achievement of a basic knowledge level is addressed to firstly identify the most suitable model (or models, as classified in Deliverable 4 and 7) to be adopted for the seismic assessment.

To this aim, this preliminary process has to be extended to all the aspects of knowledge, introduced in 2, such as geometry, constructive details, materials and historical analysis. Despite this analogous and in some way foregone - classification of the aspects related to knowledge, it is worth noting a fundamental difference from the approaches commonly adopted in codes reviewed in 2. In fact, whereas in these documents these aspects follow a separate knowledge path (leading then to an univocal definition of the confidence factor), in the proposed procedure they concur to an integrate approach, particularly related to the definition of the set of parameters to be included in the sensitivity analyses. According to this, once defined the list of parameters (which may come from any of the examined knowledge aspects), the knowledge level to be reached is planned as a function of the sensitivity class associated to each parameter (as discussed in detail in 3.2.2 and 3.2.3) rather than of the specific knowledge aspect (that is geometry, details, ..) which it is associated to.

This preliminary phase will be essentially based on available data (e.g. from construction drawings, archive records, literature review, etc.) and easily achievable by in situ survey (no tests are in fact strictly necessary).

Historical analysis should be particularly relevant to identify the subsequent integrations and modifications suffered from the building; for example, in the identification of possible discontinuities in connections among adjacent portions or in materials. The evidence of these discontinuities could provide useful information not only to define the suitable model to be adopted for the seismic assessment but also to properly identify all the necessary set of parameters (e.g. in case of discontinuities in materials).

To understand the seismic behaviour, the interpretation of the actual damage pattern (if present) and the one suffered from the building in the past seems to be particularly useful.

Regarding mechanical properties of materials, to define ranges of variation which are rational it is important to proceed to a review of the data available in the literature and codes or available from experimental campaigns on analogous masonry types. In fact, the more this preliminary assignment reveals to be rational, the more the reliability of the sensitivity analyses will be improved.

3.2.2 Sensitivity analysis (step d)

Regarding step d) and, in particular, the criteria to be adopted for the execution of the sensitivity analyses, it should be stated as follows. First of all, it is important to stress that the use of non linear static analyses is assumed as the standard one; in fact, as discussed in other deliverables (e.g. D7), it may be assumed as the standard method to be used for the seismic assessment in case of masonry buildings (due to both


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its reasonable computational effort and the need to take into account the non linear response which strongly affect the behaviour of masonry buildings). It is worth noting that, in order to proceed to the seismic safety verification, non linear static analyses are usually performed, for each of the main directions (X and Y), by considering the effect of different load patterns (e.g. uniform as proportional to mass, pseudo-triangular as proportional to the mass and height product and modal, proportional to the first modal shape, in each node respectively), that of the direction (either positive or negative) and also the one of accidental eccentricity (usually proposed by codes as 5% of the maximum length in the direction orthogonal to that examined). By combining all these possible conditions, a total of 24 analyses could be performed (once fixed a certain set of parameters which model is founded on). As a consequence, in order to limit the number of the sensitivity analyses to be performed, it seems necessary to define a basic combination of these parameters (main direction, load pattern and accidental eccentricity) to be adopted as reference. To this aim, it seems reasonable to assume the combination (among the possible 24 ones) that leads to the most cautionary result. For each model defined (as consequent to the definition of parameters discussed at steps b and c) this preliminary set of analyses will be performed by adopting as reference the mean values for all parameters ( kx ). In order to compare the results of these preliminary analyses (to define the basic combination to be adopted as a reference) with those resulting from the next sensitivity analyses (to proceed to step e)), it is necessary to establish an indicator of the structural performance. To this aim, it seems reasonable referring to the non linear static procedures (commonly adopted as tool reference for the seismic safety verification). It is worth noting that, the focus of these procedures is the identification of the performance point, computed from the intersection between the capacity curve (obtained by properly converting the pushover curve representative of the non-linear response of the original multi degree of freedom into that of an equivalent SDOF system) and the elastic spectrum properly reduced. Usually, a bi-linear behaviour is adopted to establish the equivalent SDOF system, basically defined by three variables: i) the initial stiffness (or the initial period T); ii) the yield force; iii) the ultimate displacement capacity. In particular, the peak ground acceleration (aPL3) is assumed as a reference, compatible with the condition for which the target displacement (performance point) is equal to the displacement capacity (dPL3) related to the life safety performance level (PL3 associated to the damage level 3 evaluated at global scale, as discussed in detail in Deliverable 17 Correlation between limit states and damage levels).

Fragility curve

Sd

Sa

SppSd1 Sd4Sd3Sd2

Spettro anelastico ridottoPL1 PL2 PL3 PL4

Capacity curve

Reduced spectrumPerformance point

Figure 1- Illustration of the PBA procedure

This indicator (aPL3) permits to summarize and combine the effects related to changes in strength, stiffness and ductility on the overall capacity curve. According to this criteria, it is possible to establish the reference structural performance indicator jPLa ,3 computed for each j-th model - by referring, for all parameters, to the mean value ( kx ); in case of a single model, the subscript j is omitted in the following. In order to define the


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basic combination related to the choice on the load pattern, direction and accidental eccentricity), that associated to the minimum value of aPL3 obtained could be assumed as reference.

Once defined the criterion to establish the basic combination and a proper structural performance indicator (such as aPL3) to be adopted as reference, it is possible to proceed with the sensitivity analyses. In particular, for each model examined (as a function of the Yi factors identified), 2N+ 1 analyses are needed; by considering also the number of models, a total of M2(2N + 1) analyses should be performed. In fact, for each j-th model, it could be necessary performing the following analyses :

- a first one by adopting as reference for all the parameters the mean value: this analysis is addressed to define the reference value of jPLa ,3 ;

- a set of 2N analyses by adopting for the selected k-th parameter the minimum value (xk,inf) or the maximum one (xk,sup), with all others fixed at the mean value, in order to evaluate the actual sensitivity for each parameter.

If it is possible to establish a priori the worst combination (e.g. associated to the minimum or maximum value), the total number of analyses could be reduced.

Once the sensitivity analyses have been performed, it is possible to summarize the results, for each j-th model, in the following table:

Table 30 Results of sensitivity analyses (to be filled in for each j-th model) Set of

parameters Parameter

xk kf kPLa inf,,3 kPLa sup,,3 Ref (if inf or

sup) kPLa ,3

[g] 3

,33,

PL

kPLPLkX

a

aa =

1 x1a 1inf,,3PLa 1,,3 suoPLa Inf 1,3PLa 1,X x1b

2

x2a

.. .. .. .. ..

x2b x2c x2d

3 x3 .. .. .. .. .. ... .. .. .. .. .. ..

N xN NPLa inf,,3 NsuoPLa ,,3 Sup NPLa ,3 NX ,

Where: - aPL3,inf,k : is the value associated for the selected k-th parameter - to the analysis related to

the application of the minimum value xk,inf; - aPL3,sup,k : is the value associated for the selected k-th parameter - to the analysis related

to the application of the maximum value xk,sup; - ref: denotes the analysis which leads to the worst evaluation (that is associated to the

minimum value of aPL3 between aPL3,inf,k and aPL3,sup,k). In general, it could be related to the application of the minimum value xk,inf(ref= inf) or the maximum one xk,sup (ref=sup);

- aPL3,k : is the aPL3 associated to the minimum value between aPL3,inf,k and aPL3,sup,k; - X,k : measures the sensitivity of the structural performance at k- th parameter; the subscript

X indicates that the sensitivity is associated to a parameter with a range of variation. In particular it is computed as:

3

,33,

PL

kPLPLkX

a

aa =

(3)


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The X,k variables will be useful to attribute the sensitivity class to each set of parameter (step e).

- In case of set of parameters (such as the cases 1 and 2 in Table 22), the corresponding parameters have been denoted adding to the subscript a consequential letter in order to distinguish each one within the same set.

It is worth noting that for simplicity the subscript j (aimed to denote the j-th examined model) has been omitted in Table 30. In more general terms, the previous entities should be indicated as: aPL3,inf,k,j; aPL3,sup,k,j;ref,j;aPL3,k,j; X,k,j; jPLa ,3

.

In case of presence of factors that lead to the adoption of more models, it is necessary to take into account also the sensitivity to models. To this aim, the Yi variable is introduced to measure the sensitivity of the structural performance at the i- th Yifactor. As abovementioned, to each Yi factor (i=1..M), corresponds the possible adoption of two models (A and B); thus, in general, the combination of possible configurations leads to a total of M2 models (numbered by the counter j=1..M2). In addition to the counter j, each model should be identified by a sequence of letters aimed to indicate respectively: the first one always equal to Y - the need to consider more models (due to the uncertainties related on Yi factors); the following ones, consequentially for each i-th Yfactor the configuration examined between A and B. Thus, as an example, YABA indicates (in case of M=3) the model in which the A, B and A configuration has been adopted for Y1 , Y2 and Y3 factors, respectively. In case of M=1, the Yi variable may be computed as follows:

( )3, 3,

13, 3,

PL YA PL YBY

PL YA PL YB

a a

a a

=

+ (4)

Where: 3,PL YAa and 3,PL YBa correspond to the results obtained in case of YA and YB models, respectively - by assuming the mean value for all the Xk parameters.

In case of M=2, it is necessary computing:

( )

( )

3, 3, 3, 3,1

3, 3, 3, 3,

3, 3, 3, 3,2

3, 3, 3, 3,

PL YAA PL YAB PL YBA PL BBY

PL YAA PL YAB PL YBA PL YBB

PL YAA PL YBA PL YAB PL BBY

PL YAA PL YAB PL YBA PL YBB

a a a a

a a a a

a a a a

a a a a

+ =

+ + +

+ =

+ + +

(5)

In case of M > 2, the above expressions may be easily generalized.

Thus, in general table 30 may be extended as follows (in case of M=2):


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Table 31 Results of sensitivity analyses in terms of X,k,j and Yi variables (in case of M=2)

Parameter Type

Set of parameter Parameter kf

Ref (if inf or sup)

X,k,j or Yi YAA YAB YBA YBB

1,,kX

2,,kX 3,,kX 4,,kX

Xk (k=1..N)

1 x1a .. .. ..

..

..

..

x1b ..

2

x2a

.. .. .. .. ..

x2b x2c x2d

3 x3 .. .. .. .. Yi

(i=1..M) Y1 - - Y1

Y2 - - Y2

3.2.3 Evaluation of the sensitivity class for each parameter (step e)

Once the sensitivity analyses have been completed and the results post processed, it is possible to proceed to step e), that is the attribution - for each k-th parameter and i-th factor - of a sensitivity class (low, medium or high). To this aim, reference is made to the list of X,k,j or Yi variables.

First of all, in order to proceed to the attribution of sensitivity class for each k-th parameter (step e), an univocal reference value of x,k has to be defined (from those resulting from the different models analyzed, that is from x,k,j values). In a cautionary way, it seems reasonable assuming the maximum value obtained for each k-th parameter, than is: x,k= max (x,k,j).

Thus, in order to attribute the sensitivity classes, it is necessary to define some conventional ranges to be adopted as reference for establishing the high, medium and low sensitivity. To this aim:

- firstly, a reference max value is calculated as max (x,k), by referring only to the sensitivity of parameters characterized by a range of variation;

- then, some conventional ranges are defined as a function of max , for example: o High sensitivity (H) : for max, 3/2)( >YikX or o Medium sensitivity (M): for [ ]maxmax, 3/2;3/1)( YikX or o Low sensitivity (L): for max, 3/1)(


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Table 32 Attribution of sensitivity classes

Parameter Type

Set of parameter Parameter kf

Ref (if inf or

sup) X,k or Yi

Sensitivity Class

Xk (k=1..N)

1 x1a .. ..

Reference to corresponding

X,k = max(X,k,j)

..

x1b ..

2

x2a ..

.. ..

x2b .. x2c .. x2d ..

3 x3 .. .. .. Yi

(i=1..M) Y1 - - Reference to

corresponding

deliverable d22

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