reliability based approach for structural design and assessment performance criteria and indicators...

64 Int. J. Lifecycle Performance Engineering, Vol. 1, No. 1, 2012

Copyright © 2012 Inderscience Enterprises Ltd.

Reliability based approach for structural design and assessment: performance criteria and indicators in current European codes and guidelines

Stefania Arangio Sapienza University of Rome, Via Eudossiana 18, 00184 – Rome, Italy E-mail: [email protected]

Abstract: This paper deals with the reliability based approach for design and assessment of civil engineering systems: in particular the performance criteria and indicators given in current structural codes are discussed. The paper is organized in three parts. In the first part the general aspects related to the structural design are discussed, while in the second part the performance indicators for the reliability assessment of existing structures are presented. In this regard, the contents of current European standards for structural design and assessment are briefly presented. In the third part the concept of robustness is discussed and the main definitions and methods for reliability verification taking into account the structural robustness are given. At the end, the concept of dependability is introduced. This is a quite new concept in the field of Civil Engineering and could be useful to describe the overall quality of a structural system.

Keywords: safety and reliability; structural assessment; performance indicator; codes and guidelines; Eurocodes; system engineering; dependability.

Reference to this paper should be made as follows: Arangio, S. (2012) ‘Reliability based approach for structural design and assessment: performance criteria and indicators in current European codes and guidelines’, Int. J. Lifecycle Performance Engineering, Vol. 1, No. 1, pp.64–91.

Biographical notes: Stefania Arangio is an Associate Researcher at Sapienza University of Rome where she also obtained her PhD in Structural Engineering in 2008. She has been developing her research in Italy and in the USA. Her work is focused on safety and reliability of complex structural systems with specific attention to bridges integrity monitoring, structural identification, and analysis of the structural behavior in accidental situations. In order to handle with complexity and uncertainty, the investigation is oriented toward probabilistic methods and heuristic techniques.

Part I Structural design

1 Structural system design

In recent years more and more demanding structures, like tall building, bridges or offshore structures, are designed, built and operated to satisfy the increasing needs of the society. These constructions require high performance levels and should be designed

Reliability based approach for structural design and assessment 65

taking into account their durability during the entire life cycle and their behaviour in accidental situations. A modern framework for structural design should consider that a structure is a real physical object; it is composed by many elements and components that interact with each other and with the design environment and these interactions can lead to strong non-linearities and can be source of different uncertainties.

All these requirements are often in contrast with the simplified formulations that are still widely applied. It is possible to handle these aspects evolving from the simplistic idealisation of the structure as a ‘device for channeling loads’ to the idea of the structural system, intended as a “set of interrelated components working together toward a common purpose” (NASA, 2007), and acting according system engineering, which is a robust approach to the creation, design, realisation and operation of an engineered system.

Figure 1 System engineering approach for design

Functional Analysis/Resources Allocation- Decomposition to lower-level function- Allocate performance- Define functional interfaces- Define functional architecture

Requirementloop

Design loop

PROCESSINPUT

Historic AnalysesEvolutive / Innovative Design

Risk Management PROCESSOUTPUT

Synthesis- Transform architecture- Define alternative product concepts- Define physical interfaces- Define alternative productand process solutions

Requirements Analysis- Analyze missions and enviroments- Identify functional requirements- Define performance and designconstraint requirement

SystemModeling

AndAnalysis

Source: Adapted from Bentley (1993)

According to the system approach, the design of a generic system is carried out according to the three main phases shown in Figure 1 (Bentley, 1993):

1 requirements analysis, where the design environment is considered, the functional requirements are identified and design performance and constraints are fixed

2 functional analysis and resources allocation, where the task is broken down into lower-level details

3 synthesis of the solution.

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System design is an iterative (and non-linear) procedure, so if the first solution is not satisfactory the design process is iterated; it is possible to note a requirement loop between phase 1 and 2, and a design loop between phase 2 and 3. Iterations may be required for several loops. These phases are carried out by means of an integration of ‘soft’ heuristic tools (left bottom side of Figure 1) and ‘hard’ computational techniques (right top side of Figure 1).

A key concept of the system approach that can be applied to the structural systems is the decomposition: for a global understanding of the structural behavior, information on both the entire structure and the single elements are needed (Figure 2). The structural design should be carried out at different levels of detail and the results of the various levels should be properly integrated in order to gain an overall understanding.

The whole structural design process can be framed within this system view leading to the so called performance-based design (PBD) (Smith, 2001, Petrini et al., 2010).

Figure 2 Decomposition of a steel structural system

Struttura

Sottostruttura

Componenti

Structural system

Substructure

Components

Elements

1.1 Structural system quality

Another key concept related to the system approach is the assurance of the system quality. In recent years, in order to meet international standards and customer demands,


some general standards on system quality, which can be applied also to structural systems, have been developed. An important and well known family of standards is the ISO 9000 series, which represent an international consensus on good quality management practises. According to the ISO 9000, as synthetically shown in Figure 3, the quality management can be represented as a cycle, set up with the aim of assuring consistency in the quality of system products and services, combined with continual improvement in customer satisfaction. A quality management system is a fundamental tool for achieving the required performance and for checking their accomplishment during time.

Figure 3 Quality management according to ISO 9000

MANAGEMENT RESPONSIBILITY

CUSTOMER

REQUIREMENTS

CUSTOMER

SATISFACTIONPRODUCT &

SERVICE REALIZATION

MEASUREMENT ANALYSIS

IMPROVEMENTRESOURCE ,

MANAGEMENTManagement

system

CONTINUAL

IMPROVEMENT

INPUTS OUTPUTS

Source: Adapted from quality-factors.com (2010)

1.2 Quality management and Eurocodes

The European structural codes (Eurocodes) assume that an appropriate quality policy is implemented by parties during all stages of the life-cycle. For example, the measures highlighted in EN 1990 comprise:

• accurate definitions of the reliability requirements

• organisational measures

• control at the stage of design, execution and maintenance.

Quality management is an essential consideration in every stage of the life cycle of any construction. The various stages and the associated specific quality assurance activities are identified schematically in the quality loop diagram in Figure 4 (Gulvanessian et al., 2009).

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Figure 4 Quality loop for structural systems

75

50

25

15

1390

Maintenance

Demolition and recycling

Specifications for design

0

Design

New building

Operation and maintenance

Maintenance

Rehabilitation

years

Source: Adapted from Gulvanessian et al. (2009)

2 Criteria for reliability based design

The aim of structural design is to realise structures that meet the expected performance, which can be often represented by a target reliability level (Schneider, 1997). As shown in Figure 5, there are different approaches for reliability verification:

a deterministic

b probabilistic

c semi-probabilistic.

The most common deterministic safety measure is the global factor of safety, defined as the ratio of the resistance over the load effect. The concept of the allowable stresses is a traditional deterministic method, where failure of the structure is assumed to occur when any stressed part of it reaches the permissible stress. Deterministic verification methods based on a single global safety factor do not properly account for the uncertainties associated with strength and load evaluation.

The semi-probabilistic approach is based on the limit state principle and makes use of partial safety factors for checking the structural safety. These partial factors have been calibrated so that a structure that satisfies the safety check using a set of design parameters will also satisfy the target reliability level. The semi-probabilistic verification


method is still a simplified method but it can much better account for the uncertainties of some design parameters.

Probabilistic verification procedures are also based on the principle of limit states, by checking that predefined target structural reliability levels are not exceeded. This approach takes into account explicitly the uncertainties.

Figure 5 Reliability verification approaches

Reliability verification approaches

Analytical and numeric

Simulation

Partial safety factors

Allowable stress

Probabilistic

Semi-probabilistic

DeterministicSafety factors

Limit States

3 European codes and guidelines for reliability based design

Most of the modern codes for constructions have recognised the need of using advanced reliability based design methods that allow taking into account various sources of uncertainty. To verify whether or not a structural design is acceptable, the uncertainties are modelled by using statistical tools and the failure probability is estimated with respect to all relevant limit states.

The three main documents that have been drawn on reliability based design, which are briefly presented in the following sections, are the standard ISO 2394 (1998), the probabilistic model code developed by the Joint Committee on Structural Safety (JCSS, 2001) and the structural Eurocodes.

3.1 The international standard ISO

The ISO 2394 – General principles on reliability of structures – is an important international standard that specifies general principles for the verification of the reliability of structures subjected to different types of actions. Reliability is considered in relation to the performance of the structure throughout its design working life. This international standard is applicable in all the stages of the construction process as well as during the use of the structure, including maintenance and repair. The principles are also

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applicable to the structural appraisal of existing constructions or assessing changes of use.

3.2 The JCSS probabilistic model code

The probabilistic model code developed by the Joint Committee on Structural Safety (JCSS, 2001) represents an important step in the direction of the necessary standardisation of the reliability based method. In 1971, the Liaison Committee, which coordinates the activities of six international associations of Civil Engineering (FIB, CIB, ECCS, IABSE, IASS, and RILEM), created a Joint Committee on Structural Safety (JCSS) with the aim of improving the general knowledge in structural safety. In 1992, the JCSS set as a long term goal the development of a probabilistic model code for new and for existing structures. The JCSS code gives guidance on the modelling of the random variables in structural engineering and it is intended as the operational part of codes like the ISO 2394 (1998), the Eurocodes and other national codes that allow for probabilistic design but do not give any detailed guidance.

The code consists out of three main parts that deal with general requirements, modelling of loads and modelling of structural properties. The code gives no information, however, on mechanical models like buckling, shear capacity, foundation failure and so on. Little or no information is given on other modelling aspects, like for example the wind pressure coefficients.

3.3 Structural Eurocodes

The idea of common modern structural specifications for the countries of the European economic area was born in 1975, when the Commission of the European Community decided on an action programme in the field of construction based on Article 95 of the Treaty of Rome. The objective of the programme was the elimination of technical obstacles to trade and the harmonisation of technical specifications.

Figure 6 Links between the Eurocodes

EN 1990

EN 1998EN 1997

EN 1991

EN 1992 EN 1993 EN 1994

EN 1995 EN 1996 EN 1999

Basis of Structural Design

Action on structures

Design and detailing

Geotechnical and Seismic Design

The Eurocodes are used for the design of new structures but they also cover engineering principles that could be used to form the basis of assessment of existing structures. The


ten structural Eurocodes are linked as shown in Figure 6. The first one, EN 1990 – Basis of Structural Design is the head code, which gives the basis of structural design adopted by the whole suite and needs to be used alongside of the remaining standards. The second one (EN 1991 – Actions on structures) gives actions. Then, there are six standards for design and detailing, grouped by material (EN 1992 – Concrete, EN 1993 – Steel, etc.), and two standards for Geotechnical (EN 1997) and Seismic (EN 1998) design. The Eurocodes are being implemented by each member country trough national standards which comprise the full text of the Eurocode and may be followed by a national Annex.

3.4 The Italian approach

In Italy a new structural code is in force from July 2009 (Norme Tecniche delle Costruzioni (NTC) – passed with D.M. 14/01/2008). This code has been written in accordance with the principles of the Eurocodes. Many parts have been quoted from the Eurocodes, others have been modified, according to the Italian needs. The NTC represents an important step in the Italian approach: for the first time the national code is based on a modern probabilistic approach (that actually in most of the cases can be brought to a semi-probabilistic approach with the use of the partial factors). It deals with both design of new structures and assessment of existing ones.

Part II Existing structures

4 Structural assessment process

The assessment of existing structures aims at producing evidence that they will function safely over a specified residual service life. It is mainly based on estimating the material properties and strength capacity of the members taking into account the present state of the structure, and evaluating its ability to withstand anticipated hazards and future loads.

Nowadays, this problem is particularly important in the case of infrastructures. In fact, the rate and extent of the deterioration of existing bridges have lately significantly increased. Indeed, the current low funding in the infrastructure sector of many European countries has forced highway agencies to postpone necessary investments in new road and bridges and consequently stretch the service life of their existing old stock. The prioritisation of the distribution of funds among maintenance, repair and rehabilitation activities is a major problem that bridge authorities everywhere are facing (Frangopol and Das, 1999; Casas, 2006).

The structural assessment is assuming a key role in the management of existing structures and different approaches exist. The most commonly used method is the so called condition rating method, where, on the basis of visual inspections, a grade is assigned to the structure. The grade can be either numerical ranging for example between one for very poor condition to ten for excellent condition, or descriptive by classifying infrastructures as poor, acceptable, good, etc. The main drawback of this approach is that often it lacks of objectivity because it is based on the sensibility of the engineer, so the same structure, assessed by two different engineers, can be rated with different grades.

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In the past three decades, a new measure for the assessment of existing structures has been developed within the probabilistic framework based on the reliability index (Melchers, 1999).

According with the decomposition approach previously discussed, the most efficient processes are based on the verification of the reliability at different levels. Looking at the example in Figure 7 (Bontempi et al., 2009), the verification can be carried out at a global level (called 4th level in the figure), at the level of the single structural element (3rd level), on the section of the element (2nd level), and at the material level (1st level). For each level appropriate methods and tools are available.

Figure 7 Reliability verification levels in the limit states approach

Source: Adapted from Bontempi et al. (2009)

It is also important to note that the choice of the assessment method and level of accuracy is strictly related to the specific phase of the life-cycle and to the complexity and importance of the structure (Bontempi, 2006). The use of advanced methods is not justified for all structures; the restriction in terms of time and cost is important (Arangio et al., 2010): for each structural system a specific assessment process, which would be congruent with the available resources and the complexity of the system, should be developed. In Bontempi et al. (2008) for example, the structures are classified for monitoring purposes in the following categories: ordinary, selected, special, strategic, active and smart structures. The information needed for an efficient monitoring, shown in Figure 8 by means of different size circles, increases with the complexity of the structure.


Figure 8 Relationship between classification of structures and characteristics of the monitoring process

Source: From Bontempi et al. (2008)

Another hierarchical model, based on six levels of assessment, is proposed in various guidelines (e.g., SAMARIS, 2006; Rücker et al., 2006 for bridges). The various levels are summarised in Figure 9 and Table 1. They are numbered from 0 to 5 with level 0 (informal qualitative assessment) being the simplest and level 5 (full probabilistic assessment) the most sophisticated. Figure 9 Structural assessment levels

Structural Assessment

Level 0

Experience based subjective

assessment of deterioration

effects and other damage after

visual inspection

Level 1

Direct assessment of serviceability values from

measured load effects

Level 2

Assessment of safety and

serviceability using simple model based

methods

Data from documents

Level 3

Assessment of safety and

serviceability using refined model based

methods

Data from test, monitoring, etc

Level 4

Adaptation of target reliability

methods ad assessment of

safety and serviceability with modified

structure-specific values

Level 5

Probabilistic assessment of

safety and serviceability

values

Data from test, monitoring, etc.

Measurement based Assessment

QualitativeAssessment

QuantitativeAssessment

Model based Assessment

Source: Adapted from Rücker et al. (2006)

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Table 1 Structural assessment levels

Assessment level

Strength and load models Calculation models Assessment methodology

1 Strength and load models as in design code

Simple linear elastic calculation

2

Material properties based on design documentation and standards

3

LFRD-based analysis, load combinations and partial factors as in the design code

4

Material properties can be updated on the basis of in situ testing and observations using Bayesian approach

LRFD-based analysis, modified partial factor are allowed

5

Strength model including probability distribution for all variables

Refined, load redistribution is allowed, provided that the ductility requirements are fulfilled

Probabilistic analysis

Source: Adapted from Rücker et al. (2006)

It is important to note that there are some substantial differences between the design of new structures and the assessment of existing ones. Consider for example the following aspects:

• the structural codes for design consider generic situations and the inputs of the design process are established according to standard rules. On the other hand, the assessment of existing structures is carried out case by case, evaluating the real actions

• in the assessment of existing structures the real constraints are uncertain

• the required performance are easier to be accomplished in the design phase than in the assessment

• some structures could have adequate performance even if they have exceeded their nominal life.

The probabilistic framework for assessment of existing structures can thus be seen as an extension of the probabilistic framework for the design of new structures, providing a rational and consistent basis for the inclusion of new information and uncertainties. An example is schematically illustrated in the JCSS document (Figure 10). The assessment of existing structures by using methods of modern reliability theory is seen as a successive process of model building, consequence evaluation and model updating by introduction of new information or by modification of the structure. The analysis to be performed involves various steps:

• formulation of a priori uncertainty models

• formulation of limit state functions

• establishing posterior probabilistic models

• setting acceptable levels for the probability of failure.


The issue of setting acceptable levels for probabilities of failure, that is setting target reliability levels, assumes a key role. In the following sections some strategies suggested by different guidelines and codes for the selection of the target reliability indices are presented.

Figure 10 Probabilistic approach for structural assessment

UncertaintyModeling

Limit state equation Consequence

Modify design

Introduce new information

Change use of structure

Actions

Probabilistic modeling

Source: Adapted from JCSS (2001)

5 European codes and guidelines for structural reliability assessment

Guidelines for evaluating the safety of existing structures are available in some countries. For example, in Canada, Germany, Slovenia, the Netherlands, Switzerland, and in some states of the USA they have been prepared with a careful attention to details. In the UK, a considerable amount of guidance on the design, management and assessment of bridge structures is provided in the Design Manual for Roads and Bridges (DMRB) (HMSO, 2001). A good example of evaluation code is the recently developed Danish BMS DANPRO+ (Bjerrum et al., 2006). In Italy, the recently issued structural code (NTC, 2008) includes an entire chapter on the assessment of existing constructions. Even if some countries in Europe are using specific guidelines or standards for structural safety assessment, many European countries still do not have specific methods.

While for the design of new structures there are common European specifications (the Eurocodes), there are no common standards for the assessment of existing structures. As already said, some indications are given in the Eurocodes but they are not enough. In the light of the development of common European standards, there is a need to harmonise the various existing specifications. For example, a report by the European Convention for Construction Steelwork (ECCS) and the Joint Research Center has been prepared to

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provide technical insight on the way existing steel structures could be assessed and the remaining life could be estimated (Kühn et al., 2004). These recommendations follow the principles of the Eurocodes.

It is important to note that, even if all the mentioned specifications provide a philosophical basis and a theoretical framework for the assessment of structures, most of them propose procedures based on deterministic approaches. There have been a number of applications of reliability based assessment in some countries (Frangopol and Strauss, 2008) but the probabilistic approaches are not yet commonly used in practise, mainly due to the lack of information and standardisation. A remarkable exception is presented for example in the work by Biondini et al. (2004a). Some important documents that have been drawn up in this sense are the standards ISO 2394 and 13822, and the JCSS Probabilistic Code. Also various research projects [e.g., Rücker et al. (2006) and BRIME (2003)] have proposed guidelines on monitoring and reliability-based assessment.

5.1 The international standard ISO

The already mentioned ISO 2394 – General Principles on Reliability of Structures, and the ISO 13822 – Assessment of Existing Structures – deal with reliability assessment of existing structures. The general principles for the verification of the reliability are introduce in clause 10 of ISO 2394, where it is explained how the basic variables, such as loads, material properties and model uncertainties, shall be taken. This approach allows drawing conclusions with respect to the bearing capacity of single tested members, to the capacity of other non-tested members and other load conditions as well as to the behaviour of the entire system. The International Standard ISO 13822 provides general requirements and procedures for the assessment of existing structures (buildings, bridges, industrial structures, etc.) based on the principles of structural reliability and consequences of failure. It is intended to serve as a basis for preparing national standards or codes of practise in accordance with current engineering practise and the economic conditions.

5.2 The JCSS probabilistic model code

An important step in the direction of the necessary standardisation of the reliability based method is the probabilistic model code developed by the Joint Committee on Structural Safety (JCSS, 2001). The JCSS document includes general guidelines on reassessment, methodologies for reliability updating, acceptability and safety criteria, with examples and case studies. This document was created because the classical code approaches were often not suited to address questions such as the evaluation of the risk of structures, and the choice of the adequate type of inspection. Thus, the document was created with the following basic goals:

a to standardise methods and terminology

b to be operational for the consulting engineers

c to be generally applicable for various materials and various structural types

d to build the basis of future codes and standards.


5.3 Structural Eurocodes

As specified above, the structural Eurocodes deal with the design of new structures but they also cover engineering principles that could be used to form the basis of structural assessment. For example, according to UNI EN (1990), a concrete structure shall be designed in such a way that deterioration of concrete and/or steel should not impair the durability and performance of the structure. In other words, an adequate maintenance strategy is part of the design concept of the structural Eurocodes. However, clause 1.1(4) does recognise that additional or amended rules and provisions might be necessary where appropriate.

5.4 The Italian approach

Italy represents a particular case in the field of structural assessment because of the huge number of historic and valuable existing structures. There are numerous typologies of structures, built in various historic epochs and by using different methods. For these reasons it was very difficult to define standards able to deal with the issue of structural assessment in a general way. Another important aspect is that, in Italy, the indications given in the structural codes are compulsory, so the existing guidelines cannot be used and, even if the Eurocodes are standards for all the member states, they need a specific document, approved as a law, for their effective application in Italy.

In the last Italian structural code (NTC, 2008) an entire chapter is devoted to the existing structures. The indications regarding the assessment are mainly oriented toward a performance based approach: few rules and general indications are given and the engineer is free to choice the method to guarantee the required performance. In this code it is noticeable the introduction of two new concepts related to the performance approach: the so called knowledge levels and confident factors. Both are used to modify the capacity parameters. Three different levels of knowledge (Livelli di conoscenza, LC) are defined:

• level of knowledge 1 (LC1): limited knowledge

• level of knowledge 2 (LC2): adequate knowledge

• level of knowledge 3 (LC3): accurate knowledge.

For each level of knowledge a confident factor, which is used together with the other partial factors, is assigned (Table 2). The aspects that are considered in order to classify the level of knowledge are:

• the geometrical characteristics of the structure

• the mechanical properties of the materials, obtained from both project documents and specific tests

• the geotechnical characterisation.

More details are available in the code and in specific publications (see for example Franchin et al., 2010).

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Table 2 Level of knowledge and confident factor

Level of knowledge Confident factor

LC1 – limited knowledge 1.35 LC2 – adequate knowledge 1.20 LC3 – accurate knowledge 1

Source: Adapted by NTC (2008)

6 Acceptability and target criteria for the reliability index

For the assessment of existing structures, target reliability levels different than those used in the design must be considered (Vrouwenvelder and Scholten, 2010). The differences are based on the following considerations (ISO 13822).

• economic consideration: the cost between accepting and upgrading an existing structure can be very large, whereas the cost of increasing the safety of a structural design is generally very small; consequently conservative criteria are used in design but should not be used in assessment

• social considerations, as the consequences of disruption of ongoing activities

• sustainability considerations: reduction of waste and recycling, which are considerations of lower importance in the design of new structures.

Table 3 Target reliability indices for the reference period of 50 years and 1 year and ‘moderate’ relative costs of safety measures

Codes Consequences

EN 1990 Low Normal High ISO 9324 Small Some Moderate Great JCSS Minor Moderate Large

EN 1990 – 50 years - 3.3 3.8 4.2 ISO 9324 – life time 1.3 2.3 3.1 3.8 JCSS – 50 years - 2.5 3.2 3.5

EN 1990 – 1 year - 4.2 4.7 5.2 ISO 9324 – 1 year 2.9 3.5 4.1 4.7 JCSS – 1 year - 3.7 4.2 4.4

Target values are given in several codes and guidelines (e.g., Moses, 2001; CAN/CSA-S6-00, 2000; COWI, 2007; JCSS, 2001; UNI EN, 1990, 2002). For the definition of the reliability indices various factors are considered as for example consequences of failure (e.g., low, normal, high for EN 1990), reference period, relative cost of safety measures (e.g., small, moderate, great for ISO 9324), importance of structure (bridges, public structures, residential buildings, etc.) and so on. In Table 3, some target reliability levels proposed by international codes for design and assessment are shown. They vary with the consequences of failure and the reference periods (in the table 50 years for design and


1 year for assessment). The proposed values consider ‘moderate’ relative costs of safety measure

The target limits are obtained from different procedures. For example, the Canadian Standards Association (CSA, 2000) has adopted the following life-safety criterion for bridge assessment. To take into account that some failures are much less likely to result in death or injury than others, they define the conventional probability of failure:

conventionalA KP

W n⋅

=⋅

where Pconventional is defined as the target annual probability of failure based on life-safety consequences, K is a constant based on calibration to existing experience which is known to provide satisfactory life safety, A is the activity factor which reflects the risk to human life associated with activities for which the structure is used, W is the warning factor corresponding to the probability that, given a failure, a person at risk will be killed or seriously injured, and n is the importance factor based on the number of people n at risk if failure occurs.

The CAN/CSA-S6-00 (2000) proposes also to adjust the target reliability indices for bridges according to the consequences of failure of one element. For example, if the failure of one element does not lead to collapse because of redundancy then the risk to life is reduced; if an element fails gradually, then the failure is likely to be noticed before collapse takes place. Table 4 provides some examples of adjustments for single elements and for the entire system. Table 4 Reliability index adjustment for bridge assessment

Source: Adapted from CAN/CSA-S6-00 (2000)

( )3.5 E S I PCβ = − Δ + Δ + Δ + Δ

Adjustment for element behaviour ΔE

Sudden loss of capacity with little or no warning 0.0 Sudden failure with little or no warning but retention of post-failure capacity 0.25 Gradual failure with probable warning 0.5 Adjustment for system behaviour ΔS Element failure leads to total collapse 0.0 Element failure probably does not lead to total collapse 0.25 Element failure leads to local failure only 0.5 Adjustment for inspection level ΔI Component not inspectable – 0.25 Component regularly inspectable 0.0 Critical component inspected by evaluator 0.25 Adjustment for traffic category ΔPC All traffic category except PC 0.0 Traffic category PC 0.6

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Part III Structural system robustness and dependability

7 Structural robustness

The traditional approach for structural design and assessment aims at the verification of the safety of the structure under assigned loads and boundary conditions, but it does not take into account some advanced aspects: for example the fact that also a small initial failure could result in a disproportionate structural damage as shown by several cases of building collapses in the past (see for example Crowder et al., 2008). Such behaviour is commonly interpreted as a lack of structural robustness (Starossek, 2009; Giuliani, 2009).

To clarify the role assumed by structural robustness, it is necessary first to clarify its meaning. The term robustness appears often in the structural engineering literature and it has been widely discussed in international scientific conferences (see for example the special sessions on structural robustness organised at the IABMAS Conferences (2008, 2010) by Bontempi and Starossek, and the Conferences ‘Handling the Exceptions’ in Rome (HE, 2008; 2010). Even so, it is used differently by the various authors and there is no general agreement today about its precise meaning. A set of definitions has been selected in a recent work by Starossek and Haberland (2010). Two qualitative definitions are the following:

• ability of a structure to withstand actions due to fires, explosions, impacts or consequences of human error, without suffering damages disproportionate to the triggering causes (EN 1991-1-7: 2006)

• insensitivity of the structure to local failures (Starossek et al., 2007).

The main difference in these definitions, which reflects also a certain dispute in recent literature (Starossek and Wolff, 2005; Faber, 2006), consists in the identification of the cause a structure should withstand in order to be considered robust. According to the first definition, a structure is robust if a disproportionate collapse is not triggered in consequence of an accidental action, while the second definition of robustness refers directly to the ability of a system to tolerate structural damages, apart from the actions that could have determined them.

In the latter case, the robustness is intended as a property inherent to the structural system and can represent a direct measure of the susceptibility of a structure to disproportionate collapses. According to the first definition instead, the robustness of a structure would depends on the accidental action considered.

Summing up the different definitions, it is possible to say that robustness refers to the ability of a structure not to respond disproportionately to either abnormal events or initial local failure. It is important to point out that it is not to be expected that the structure will resist all the possible occurrences without any damage: not only is practically impossible the foreseeing of any possible critical event, but hardening a structure to resist perfectly integer to hazards that have such a low probability of occurrence, would be not economically feasible. More detail can be found in Starossek (2009), Giuliani (2009), Bontempi et al. (2007) and Brando et al. (2010).

The robustness of a structure strongly influences its reliability but it very difficult to measure the contribution. In most of the existing codes and guidelines the subject of structural robustness in treated in a general way and only indirect design criteria are provided. The task of the quantitative evaluation of robustness, and consequently the


modification of the reliability indices have been treated by several authors. Four main approaches exist: risk based (Faber, 2006), topology based (Agarwal et al., 2003), energy based (Starossek and Haberland, 2008) damage based (Biondini and Frangopol, 2008; Yan and Chang, 2006; Bontempi et al., 2007). A summary of the main quantitative definitions proposed in the past few years is given in Giuliani and Bontempi (2009).

7.1 Robustness and the Eurocodes

The topic of robustness is essentially covered by two Eurocodes, EN 1990 – Basis of Structural Design, which provides the high level principles for achieving robustness and EN 1991: Part 1-7 – Accidental Actions (EN 1991-1-7), which provides strategies, and methods to obtain robustness and the actions to consider.

The leading principle is that, in case of accidental actions, local damage is acceptable, provided that it will not endanger the structure, and that the overall load-bearing capacity is maintained during an appropriate length of time to allow necessary emergency measures to be taken (Gulvanessain and Vrouwenvelder, 2006).

Figure 11 The arrow indicates the point where the rock impacted the pile, (a) impacted point (b) rock (c) maximum height of the debris flow during the event (d) height of debris at the end of the landslide (see online version for colours)

Messina – Catania Highway

Racinazzo Torrent

Source: From Ortolani and Spizuoco (2009)

An example of lack of structural robustness in an accidental situation is shown in Figure 11. The highway bridge in the picture is located at the entrance of the city of Messina (Sicily Island, Italy) where in October 2009 a large landslide occurred; the debris flow impacted the bridge and a big rock (visible in Figure 12) strongly damaged one of the piers. The traffic was interrupted for entire days causing trouble to the circulation of the entire city. In Figure 11, the arrow indicates the point where the rock

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impacted and the marked surface represents the volume of the debris flow. In Figure 12 the zone is viewed from the other side. In such a case, it would have been necessary to quantify the structural robustness and evaluate the residual life of the structure before reopening the bridge to the normal traffic. In fact this structure was designed to carry mainly vertical loads and the sudden impact with the heavy rock changed its structural behavior. A robust design approach of bridges located in hazardous areas should properly take into account accidental situations in order to avoid disruption of the service or even the collapse of the structure. Other examples of structural behaviour under accidental scenarios are given for example in Crosti (2009) and Gentili et al. (2010).

Figure 12 The arrow indicates the damaged pier (see online version for colours)

Damaged pier

Messina – Catania Highway

Notes: On the right it is possible to see the big rock that impacted on the bridge. Source: From Ortolani and Spizuoco (2009)

7.2 Redundancy in Eurocodes and NCHRP

According to the Eurocodes, redundancy is the availability of alternative load-carrying components and alternative paths for a load to be transferred from a point of application to a point of resistance. This implies the absence of critical components whose failure would cause the collapse of the structure (Frangopol and Curley, 1987).

There is a strong connection between redundancy and robustness (Starossek and Haberland, 2010). Redundancy is a key factor for robustness: a redundant structure has alternative load carrying components; if one or more components fail, the remaining structure is able to redistribute the force originally carried by the failed components into alternative load paths. However, the terms robustness and redundancy denote different properties of the structure and they should be clearly distinguished (Biondini et al., 2008; Starossek, 2009). Using them as synonyms obscures the fact that redundancy is not the only means to achieve robustness. Both concepts should be considered in a reliability based assessment of structures.

It is important to note that the definitions given above are generally used in Europe; the term redundancy is used in a different way in the literature of the USA: the concept of redundancy is mainly related to the ability of a structure to withstand the failure of a single structural member without collapsing. For example, NCHRP 406 defines bridge redundancy as “the capability of a bridge to continue to carry loads after the damage or the failure of one of its member (the first member to fail)” (Ghosn and Moses, 1998). In a sense, their definition of redundancy is equivalent to the definition of the robustness


given in the Eurocodes. Thus, the methods proposed in USA (as for example in the NCHRP Report 406, 1998) for the assessment of the reliability taking into account the redundancy, in the European point of view, could be applied for reliability assessment taking into account the robustness. Actually, this is the same concept called in different ways (Arangio and Ghosn, 2010).

NCHRP Report 406 (Ghosn and Moses, 1998) developed a process for quantifying redundancy (i.e., robustness according to the European view) in bridge super structures. Subsequently, this approach was extended to substructures (Liu et al., 2001). A bridge is considered safe if:

• it provides a reasonable safety against first member failure

• it provides an adequate level of safety before it reaches its ultimate limit states

• it does not deform excessively under expected loads

• it is able to carry some traffic loads after damage or loss of members.

Accordingly four limit states are defined as:

• member failure, which is a check of individual member safety using elastic analysis

• ultimate limit state, which is defined as the ultimate capacity of the bridge system or the formation of a collapse mechanism

• functionality limit states, which is defined as the capacity of the structure to resist a main member live load displacements of specified magnitude

• damaged condition limit state, which is defined as the ultimate capacity after removal of one main load carrying component.

The four limit states should be checked to ensure the satisfactory safe performance of the bridge system under extreme and regular conditions. ‘Adequate’ safety margins can be determined using reliability based techniques. A reliability index can be defined for each limit state, thus there will be βmember for the member failure, βu for the ultimate limit state, βfunct for the functionality limit state, and the system reliability index βdamaged for damaged conditions.

To study the redundancy of a system, it is useful to examine the differences between the reliability indices of the system expressed as βu, βfunct, and βdamaged and the reliability index of the most critical member as βmember. The relative reliability indices are defined as:

u u member

f func member

d damage member

β β ββ β ββ β β

Δ = −

Δ = −

Δ = −

These relative reliability indices give measures of the relative safety provided by the bridge system compared with the nominal safety of first member failure. On the basis of analyses of typical bridge configurations, a direct redundancy evaluation procedure has been proposed in the NCHRP reports. It is based on satisfying minimum values of the relative reliability indices. According to these analyses, a bridge will provide adequate levels of redundancy if all three following conditions are satisfied:

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u

f

d

0.850.25

2.70

βββ

Δ ≥

Δ ≥Δ ≥ −

8 Structural systems dependability

For the purpose of the evaluation of the overall quality of structural systems a new concept has been recently proposed: the structural dependability. It can be introduced looking at the scheme in Figure 13, where the various aspects discussed in the previous paragraphs are ordered and related to this concept. It has been said that a modern approach to structural design requires evolving from the simplistic idea of structure to the idea of structural system, and acting according to the system engineering approach. In this way it is possible to take into account the interaction between the different structural parts and between the whole structure and the design environment. The grade of non-linearity and uncertainty in these interactions determines the grade of complexity of the structural system. In case of complex structural systems, it is important to evaluate how the system works as a whole, and how the elements behave singularly. In this contest, dependability is a global concept that describes the aspects assumed as relevant to describe the quality of a system and their influencing factors (Bentley, 1993). It has been originally developed in the computer science field but it can be reinterpreted in the civil engineering field (Arangio et al., 2010). The dependability reflects the user’s degree of trust in the system, i.e., the user’s confidence that the system will operate as expected and will not ‘fail’ in normal use: the system shall give the expected performance during the whole lifetime.

Figure 13 Roadmap for the analysis and design of complex structural systems

STRUCTURAL SYSTEM

Interaction among different structural

parts Interactions are characterized by

strong nonlinearityand uncertainty

QUALITY of the

whole structural

system:

DEPENDABILITY

ATTRIBUTES

THREATS

MEANS

COMPLEXITYDECOMPOSITION STRATEGY

PERFORMANCE BASED DESIGN

SYSTEMAPPROACH

Interaction between the whole structure

and the design environment


The assessment of dependability requires the definition of three elements (Figure 14):

• the attributes, i.e., the properties that quantify the dependability

• the threats, i.e., the elements that affect the dependability

• the means, i.e., the tools that can be used to obtain a dependable system.

In structural engineering, relevant attributes are reliability, safety, security, maintainability, availability, and integrity. Not all the attributes are required for all the systems and they can vary over the life-cycle. They are essential to guarantee:

• the ‘safety’ of the system under the relevant hazard scenarios, that in current practise is evaluated by checking a set of ultimate limit states (ULS)

• the survivability of the system under accidental scenarios, considering also the security issues; in recent guidelines, this property is evaluated by checking a set of ‘integrity’ limit states (ILS)

• the functionality of the system under operative conditions (availability), that in current practice is evaluated by checking a set of serviceability limit states (SLS)

• the durability of the system.

These attributes can be divided in high level or active performance (reliability, availability, and maintainability) and low level or passive performance (safety, security, and integrity) (Petrini et al., 2010).

The threats to system dependability can be subdivided into faults, errors and failures. According to the definitions given in Avižienis et al. (2004), an active or dormant fault is a defect or an anomaly in the system behaviour that represents a potential cause of error; an error is the cause for the system being in an incorrect state; failure is a permanent interruption of the system ability to perform a required function under specified operating conditions. Error may or may not cause failure or activate a fault. In case of civil engineering constructions, possible faults are incorrect design, construction defects, improper use and maintenance, and damages due to accidental actions or deterioration.

The problem of conceiving and building a dependable structural system can be considered at least by four different points of view:

1 how to design a dependable system, that is a fault-tolerant system

2 how to detect faults, i.e., anomalies in the system behaviour (fault detection)

3 how to localise and quantify the effects of faults and errors (fault diagnosis)

4 how to manage faults and errors and avoid failures (fault management).

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Figure 14 Dependability: attributes, threats and means

ATTRIBUTES

THREATS

MEANS

MAINTAINABILITY

RELIABILITY

AVAILABILITY

INTEGRITY

FAULT

ERROR

FAILURE

FAULT TOLERANT DESIGN

FAULT DETECTION

FAULT DIAGNOSIS

FAULT MANAGING

DEPENDABILITY

SAFETY

SECURITY

Source: Arangio et al. (2010)

The task of fault management includes the so called fault forecasting, that is the set of methods and techniques for performing evaluations of the system behaviour with respect to fault occurrence or activation. These evaluations have two aspects:

a qualitative, aimed at identifying the possible failure modes or hazardous scenarios

b quantitative, aimed at evaluating in terms of probabilities some of the attributes of dependability.

A system is taken as dependable if it satisfies all requirements with regards to various dependability performance and indices, so the various attributes, such as reliability, safety or availability, which are quantitative terms, form a basis for evaluating the dependability of a system. The evaluation of the dependability is a complex task because this is a term used for a general description of the quality of a system and it cannot be easily expressed by a single measure. The approaches for dependability evaluation can be qualitative or quantitative and usually are related to the phase of the life cycle that it is considered (design or assessment). In the early design phase a qualitative evaluation is more appropriate than a detailed one, as some of the subsystems and components are not completely conceived or defined. Qualitative evaluations can be performed, for example, by means of failure mode analyses approaches, as the failure mode effects and criticality analysis (FMECA) or the failure tree analysis (FTA), or by using reliability block


diagrams. Note that these models assume independence among modeled components. On the other hand, in the assessment phase, numerous aspects should be taken into account and all of them are affected by uncertainty and interdependencies, so quantitative evaluations, based on probabilistic methods, are more suitable. It is important to evaluate whether the failure of a component may affect other components, or whether a reconfiguration is involved upon a component failure. These stochastic dependencies can be captured for example by Markov chains models, which can incorporate interactions among components and failure dependence. Others methods are based on Petri Nets and stochastic simulation. At the moment, most of the applications are on electrical systems (e.g., Nahman, 2002) but the principles can be applied in the civil engineering field. When numerous different factors have to be taken into account and dependability cannot be described by using analytical functions, the use of linguistic attributes by means of the fuzzy logic reasoning can be helpful (Ivezić et al., 2008; Biondini et al., 2004b).

9 Conclusions

In this work a state of the art about the European reliability based approach for the design and assessment of civil engineering systems is presented. The first part deals with the issues related to the design phase, while the second part considers the reliability based assessment of existing structures. In the last part the concept of structural robustness is discussed showing the difference between the European point of view and the US one. Looking at the recent literature and structural standards, it is possible to notice that there is an increasing interest in the reliability based approach. However it has been shown that most of the regulations are still based on over simplified approaches that are not able to take into account the intrinsic complexity of the modern structural systems and the concept of robustness. The existing measures are mostly local indices whereas the reliability of a structural system should be evaluated in global way, taking into account the possible non-linearities and the various sources of uncertainties. For the purpose of the evaluation of the overall quality of structural system a new concept has been recently proposed and it is discussed in the last part of the paper: the dependability. It is a global concept that describes the aspects assumed as relevant and their influencing factors. It has been originally developed in the computer science field but it can be applied to civil engineering systems.

Acknowledgements

The present paper is a result of a work conducted within a collaboration with the Task Group 2 of the SEI-ASCE Technical Council on Life-Cycle Performance, Safety and Reliability and Risk of Structural Systems. Prof. Franco Bontempi and his team www.francobontempi.org from Sapienza University of Rome, and Prof. Michel Ghosn from CUNY of New York are gratefully acknowledged for their suggestions. Prof. Casas of the UPC, Prof. Malerba of the Polytechnic of Milan and Dr. Starnes of the TRB are also acknowledged. The opinions and conclusions presented in this paper are those of the author and do not necessarily reflect the views of the sponsoring organisations.

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