DuraCrete - Final Technical Report

General Guidelines for Durability Design

and Redesign
The European Union – Brite EuRam III

DuraCrete
Final Technical Report

DuraCrete
Probabilistic Performance based Durability Design
of Concrete Structures

Contract BRPR-CT95-0132, Project BE95-1347

Document BE95-1347/R17, May 2000
Although the project consortium does its best to ensure that any information given is accu-
rate, no liability or responsibility of any kind (including liability for negligence) is accepted
in this respect by the project consortium, the authors/editors and those who contributed to
the report.

Acknowledgement
The DuraCrete-project resulted in general guidelines for durability design and redesign of
concrete structures. The work started with defining the design framework, exemplifying the
approach by means of two mini-projects (all in Task 1) and followed by modelling the de-
gradations and the environmental actions (in Task 2). Input parameters for the models come
from compliance tests. Appropriate tests were identified and tests were performed on many
types of concretes (in Task 3). The existing national European standards and codes were
benchmarked in Task 5. The process from statistical quantification and probabilistic calcu-
lations were subject of Tasks 4 and 6 respectively. All results came together and were inte-
grated in Task 7 where the design guide was developed.
The process described above was also applied for concrete pavements. The results however
are presented in a seperate report.

Expertise of twelve companies and institutes, from six European countries, were brought
together to perform the project. The work has been performed by:
Muthena Alisa, TEL Jan P.G. Mijnsbergen, CUR
Carmen Andrade, IETcc Louise Mohr, COWI
Jesus Aragoncillo, Geocisa Lars-Olof Nilsson, Chalmers University
Angel Arteaga, IETcc Jésus Rodriguez, Geocisa
Phil Bamforth, TEL Steen Rostam, COWI
Carola Edvardsen, COWI Peter Schiessl, TU Muenchen, formerly
Svend Engelund, COWI ibac
Christoph Gehlen, Ingenieurburo Prof. Rico van Selst, Intron
Schiessl, formerly ibac Ton Siemes, TNO
Volker Hartmann, Schwenk Mette Sloth, COWI
Michael Havbro Faber, COWI Fedde Tolman, HBG/NPC
Anders Lindvall, Chalmers University Jeannette Visser, TNO
Horst Michael Ludwig, Schwenk Hans de Vries, RWS
Sipke van Manen, RWS Ton Vrouwenvelder, TNO

The DuraCrete-project ‘Probabilistic Performance based Durability Design of Concrete Struc-

tures’ was carried out in the framework of the Brite-EuRam Programme (project BE96-3942),
with a financial contribution of the European Commission.

Information
Steen Rostam, COWI, Parallelvei 15, DK-2800 Lyngby, Denmark
Tel +45 45 972782, e-mail sro@cowi.dk
Jan P.G. Mijnsbergen, CUR, PO Box 420, NL-2800 AK Gouda, The Netherlands
Tel +31 182 540620, e-mail jan.mijnsbergen@cur.nl
The European Union – Brite EuRam III

DuraCrete
Final Technical Report

DuraCrete
Probabilistic Performance based Durability Design
of Concrete Structures

Contract BRPR-CT95-0132, Project BE95-1347

Document BE95-1347/R17 May 2000

CUR, Centre for Civil Engineering Research and Codes, NL

Hollandsche Beton Groep N.V., NL
COWI Consulting Engineers and Planners AS, DK
Taywood Engineering Limited, GB
E. Schwenk Zementwerke KG, DE
Geotecnia y Cimientos S.A., ES
ibac, Institute for Building Research, Technical University of Aachen, DE
Institute Éduardo Torroja of Construction Science of the CSIC of Spain, ES
RWS, Directorate-General for Public Works and Water Management, NL
TNO Building and Construction research, Netherlands Organisation for Applied
Scientific Research, NL
Intron, the Quality Assessment Institute for the Building Industry NL
Chalmers University of Technology, SE
Final Technical Report 1

Preface
In the last decades much effort has been put into the development of models
and methods for predicting deterioration of concrete structures. A number of
methods have matured to a level where these can be used in a formalised ap-
proach to assessment and design of concrete structures with respect to destruc-
tive mechanisms. This report represents a first attempt at providing a code-like
guide for durability design and assessment of concrete structures.

In a period of three years beginning in February 1996 a number of partners

have been involved in the DuraCrete research project with the purpose of de-
veloping the present guide. This report is a summary and synthesis of the work
carried out in a number of task groups.

• Task 1, Design Framework

• Task 2, Modelling of the Degradations
• Task 3, Compliance Tests
• Task 4, Statistical Quantification
• Task 5, Benchmarking of the Conventional Design Methodology
• Task 6, Comparative Probabilistic Design Calculations
• Task 7, Documentation of the new Design Methodology
• Task 8, Exploitation and Management

The following partners have been involved in the project

CUR, Centre for Civil Engineering Research and Codes, NL

HBG, Hollandsche Beton Groep N.V., NL
COWI, Consulting Engineers and Planners AS, DK
TEL, Taywood Engineering Limited, GB
E. Schwenk Zementwerke KG, DE
Geotecnia y Cimientos S.A., ES
ibac, Institute for Building Research,Technical University of Aachen, DE
IET, Institute Éduardo Torroja of Construction Science of the CSIC of Spain,
ES
RWS, Directorate-General for Public Works and Water Management, NL
TNO Building and Construction research, Netherlands Organization for Ap-
plied Scientific Research, NL
Intron, the Quality Assessment Institute for the Building Industry, NL
Chalmers University of Technology, SE.

The methodology described is intended for practising engineers rather than ma-
terials scientists. It presents methods for design of concrete structures subject to
destructive mechanisms. These models are developed on the basis of data from
existing structures and the present knowledge of the complicated mechanisms
determining the deterioration of concrete structures.

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Table of Contents
1 Extended summary 5
1.1 Abstract 5
1.2 Concept for durability design 5
1.3 Modelling of the degradations 8
1.4 Compliance tests 10
1.5 General guidelines for design and redesign 10

2 Reports 12

3 Contacts 14

4 Introduction 16
4.1 Background 17
4.2 Code Format 17
4.3 Purpose 18
4.4 Field of Application 18

5 Definitions and nomenclature 20

5.1 Definitions 20
5.2 Nomenclature 22
5.3 Abbreviations 25
5.4 Units 26

6 Guide for Durability Design 27

6.1 Background 27
6.2 Concept for Durability Design 28
6.3 Basis for Durability Design 29

7 General Framework for Durability Design 36

7.1 Load and Resistance Factor Design 36
7.2 Acceptance criteria 40
7.3 Application of design rules 42

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Final Technical Report 3

8 Chloride Ingress, Initiation of Corrosion 43

8.1 Design Equation 43
8.2 Design Values 43
8.3 Characteristic Values 45
8.4 Partial Factors 48

9 Carbonation, Initiation of Corrosion 50

9.1 Design Equation 50
9.2 Design Values 51
9.3 Characteristic Values 51
9.4 Partial Factors 53

10 Cracking and Spalling 54

10.1 Design Equation 54
10.2 Design Values 55
10.3 Characteristic Values 57
10.4 Partial Factors 60

11 Examples 61
11.1 Chloride ingress 61
11.2 Carbonation 65

12 Quality Assurance 69
12.1 General 69
12.2 Quality Control Concept 70
12.3 Material Variables 71
12.4 Geometrical Variable: Concrete Cover
Thickness 74

13 Assessment and Redesign 78

13.1 Objective of the reassessment 78
13.2 Acceptance criteria for reassessment 79
13.3 General framework for reassessment 79
13.4 Reliability Updating 82

14 Inspection, Maintenance and Repair 85

14.1 Inspection methods 85
14.2 Maintenance and Repair 89

15 Compliance Tests 94
15.1 Introduction 94
15.2 Main Test Programme 97

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4 Final Technical Report

15.3 Test Procedure 98

15.4 The Results 103
15.5 Material Classification 105

16 Benchmarking 109

17 References 112

Table of Appendices
Appendix A: Probabilistic Models
Appendix B: Calibration of partial factors
Appendix C: Decision Analysis
Appendix D: Bayesian updating

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Final Technical Report 5

1 Extended summary

1.1 Abstract
The DuraCrete-project aimed to develop a performance based durability design
methodology, based upon realistic and sufficiently accurate environmental and
material models capable to predict the behaviour of a concrete structure. The
work is based on a design framework in which a/o the probabilistic modelling,
limit states and modelling of deterioration mechanisms are formulated.

Physical models for relevant deterioration processes and compliance tests re-
sulting in necessary input data have been chosen. Compliance tests on several
concrete compositions have been carried out. Results are quantified statisti-
cally, describing basic variables, the type of distribution, the mean, the standard
deviation of variation coefficient and a proper definition of the population,
leading towards the design format.

1.2 Concept for durability design

Design bases for the design of concrete structures have so far been focused on
the load carrying capacity. Effects on the safety and operability from deteriora-
tions are considered only indirectly. In this way durability is assumed by simple
deemed-to-satisfy rules, related to crude environmental classification. Thereby
there is no possibility to relate the quality of structural detailing, the execution,
the quality control, the environmental loading and the future maintenance with
the service life of the structure. This shall be possible with the performance
based durability design format, which is developed within the DuraCrete-
project. In contrast to the presently used design rules the new durability design
format based upon realistic and sufficiently accurate environmental actions,
material parameters and degradation models capable to predict the future be-
haviour of a concrete structure.

It is possible to quantify the performance in relation to the age of the structure.

The outcome is a tailor made design on meso level. After the structure has been
executed updating of the input data for the models, i.e. the incorporation of the
actual material parameters, which are related to execution, maintenance and
repair, may be performed. Thereby a more precise prediction of the ‘real’ dura-
bility of the structure can be determined. The essential elements of the durabil-
ity design are as illustrated in Figure 1.1.

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Definition of the
Required Performance
- Limit State Criterion

Modelling of :
- Deterioration Modelling of :
Mechanisms - Material Resistance
- Environmenttal Parameters
Actions

Statistical
Quantification

Benchmarking Quality Control

Execution Control
Inspection
Maintenance Repair

Durability
Design Format

Documentation of
the New Design
Methodology

Figure 1.1 - Towards durability design in the DuraCrete-project

1.2.1 Performance Criteria

The first step is the definition of the desired/required performance of the struc-
ture. The definition of performance criteria is related to a limit state criterion,
which means that an unwanted event occurs. Examples are collapse, depassiva-
tion, spalling of concrete cover, maintenance or repair costs. This aspect is dealt
with within the first task.

1.2.2 Durability Modelling

The durability design is based on equations modelling the deterioration proc-
esses in the structure and the material resistance against the environmental ac-
tions. The deterioration processes are formulated as models at a so-called meso-
level, essentially meaning that the concrete is considered as a continuum.
Mathematical models of the deterioration processes are formulated in physi-
cal/chemical terms, including time. These models are the basis for the probabil-
istic method of design. In general, the models describe the response of the
structure to the defined exposure conditions. It was the aim of Task 2, to define
mathematical models, which predict the time for events, which lead to loss of
serviceability. The models used for corrosion and penetration of the depassiva-
tion can be regarded as generally accepted. With respect to reliable models for
frost attack, alkali-aggregate reaction, and data regarding material characteris-
tics and environmental factors the basis is less complete.

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Final Technical Report 7

The resistance of the material against deterioration is modelled within Task 3.

The models contain material parameters describing the concrete resistance
against the environmental actions, e.g. a chloride diffusion coefficient describ-
ing the resistance against the ingress of chlorides.

Compliance test methods suitable to verify durability related qualities such as

diffusivity, permeability and capillarity, etc. are evaluated and verified within
Task 3. These test methods shall be applied for the later quality-control-
compliance-tests.

The statistical quantification of the parameters describing the environmental

actions, the deterioration processes and the material behaviour for the defined
limit state criteria is defined within Task 4. The quantification includes the de-
termination of a statistical distribution, corresponding statistical parameters and
possible correlations. The statistical information is used in the calibration of the
design format to the required safety within Task 6. Benchmarking of the con-
ventional design methodology of concrete structures in Europe has been done
within Task 5.

Calculation of the reliability level of all conventional durability designs studied

in task 5 is carried out in Task 6. These levels are used as input for establishing
a set of target reliabilities for the design method defined in task 7. Task 7 pro-
vides the documentation of the design methodology. The documentation will
consist of technical recommendations and guidelines for the design and redes-
ign of concrete structures.

1.2.3 Durability Design Format

As basis for the durability design basis, the principle of the Load and Resis-
tance Factor Design (LRFD) is used in terms of the ‘partial factor’ format. This
system is also used in most other modern semi-probabilistic codes such as e.g.
the Eurocodes.

In brief, the partial factor format takes basis in the formulation of limit state
equations for the representation of the relevant adverse states for the considered
structures. Limit state equations are formulated in terms of random variables
and design parameters (dimensions, nominal qualities) expressing the perform-
ance of the structure corresponding to the considered adverse state.

As a basis for the durability design format the concrete material code of the
Eurocode system with corresponding limit states is taken. In addition time de-
pendent effects are taken into account. A sufficient reliability for the design
working life is ensured by introducing so-called design values for the various
random variables. These design values are in principle evaluated on the basis of
reliability methods. Given the values for these design values, the design pa-
rameters should be chosen in such a way that the limit state function is positive.

In modern building codes two main types of limit states are distinguished: ulti-
mate limit state (ULS) and serviceability limit state (SLS). ULS refers to col-

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8 Final Technical Report

lapse, fracture, and other events where the safety of the structure is of impor-
tance: loss of static equilibrium. SLS refers to comfort for the user, the func-
tionality (fitness for purpose) and aesthetic or cosmetic aspects. Description of
a limit state may require one or more limit state functions. In the case of dura-
bility problems, time enters the limit state function explicitly. In its simplest
form this is presented as a limit state function of the form

R(t) - S(t) > 0

where R(t) is the resistance and S(t) is the load

The resistance R and the load S are both represented as time dependent vari-
ables.

Rostam and Siemes have described approaches to durability based on the ‘in-
tended service period design’ and the ‘lifetime design’, as illustrated in Figure
1.2.

1.3 Modelling of the degradations

The following deterioration processes were considered: carbonation induced
corrosion of the reinforcing steel, chloride induced corrosion of the reinforcing
steel, alkali aggregate reactions and frost attack.

The selected models for carbonation and chloride ingress are similar in form,
both being based on diffusion theory and taking account of ageing. Factors are
used to take account of curing, environment and the difference between values
obtained in a test and in-situ. The corrosion rate model relies on knowledge of
the resistivity of the concrete. This is easy to measure either in the laboratory or
on site for compliance testing. Models for predicting the consequences of cor-
rosion include equations for cracking, bond loss, and loss of structural integrity.
Cracking is predicted using a relationship with bar diameter, cover and concrete
quality. Bond is related to the loss of bar diameter and the confinement pres-
sure. Residual strength and stiffness is determined using conventional analyti-
cal methods, but taking into account the loss of section of both the steel and the
concrete.

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Final Technical Report 9

distribution of R(t)
R(t)

R,S

S(t)
distribution of S(t)

mean service life time

reference failure probability
period
service life distribution

Figure 1.2 - Service life distribution

Validation of the models has been achieved by comparison of predicted per-

formance with results from either structures or large-scale laboratory simula-
tions.

The approach to AAR has necessarily differed from the corrosion model. Al-
though the concept of initiation and propagation may be applied, no reliable
models have been identified and it has been concluded that avoidance is the
best philosophy. This involves the selection of appropriate combinations of ce-
menting materials and aggregates (based on local practices) and/or protection of
the structure from moisture.

Frost attack has been considered in relation to both scaling and to general frost
damage leading to deterioration of physical properties. In the latter case a
model for predicting initiation has been proposed, based on the time to achieve
a critical level of saturation. Input data can be derived from a simple water ab-
sorption test. In relation to propagation of damage, however, reliance must be
placed on the use of empirical relationships between laboratory tests and field
observations, and the development of limiting criteria in relation to the air void
system. With regard to scaling the avoidance philosophy must be adopted.

The study of the effects of cracking has indicated that depassivation of rein-
forcement may occur within a relatively short period (a few years) in relation to
the service life of a structure, whether caused by carbonation or chloride in-
gress. If the cracks are narrow, self-healing and repassivation may occur. In
open cracks, the rate of corrosion is determined by a function which includes
parameters for concrete quality, bar diameter, cover depth and crack frequency.

Investigations into the effect of cement type and concrete composition have
concentrated on those properties, which represent parameters in the predictive
models. For example, in relation to chloride induced corrosion, the benefits of
increased resistance to chloride ingress, greater chloride binding and the in-
creased resistivity (and hence reduced corrosion rates) have been defined for

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10 Final Technical Report

blended cements containing pulverised fuel ash or blastfurnace slag. For car-
bonation, however, the lower CO2 binding capacity of blended cements was
observed.

1.4 Compliance tests

An overview of existing test methods has been prepared. The cement and con-
crete test-programme could be based on this. All key-point input parameters of
the selected deterioration models were covered. Aspects which were the basis
of the evaluation can be summarised as follows: consideration of key-point in-
put parameters of the selected models achieved; reproducibility; short test dura-
tion and the need for relevant parameters to be testable in laboratory as well as
on site.

Tests with regard to carbonation, chloride penetration and corrosion rate have
been performed. In order to have a tool for separating concrete qualities with
regard to their resistance against frost- and frost-thaw attack, two well-defined
test procedures were chosen. The output of these (CF and CDF) is the amount
of scaling, but produced results have not been validated with field experiences
in a quantitative way up to now. Nevertheless, these procedures were found as
relevant. The interaction and the gap between input parameters of the proposed
models, the output (result) of the test method and the related validation are cov-
ered.

1.5 General guidelines for design and redesign

1.5.1 Field of Application

Ideally, the guide should cover all deterioration mechanisms, all types of con-
crete and all types of aggressive environment. Unfortunately, with the time and
resources available this has not been possible. Nevertheless, the methodology
presented in the guide is general in its nature, and all types of deterioration
mechanisms as well as second order structural effects and fatigue can be incor-
porated. Due to the very restricted availability of data in the relevant format to
provide factual input to the probabilistic modelling, the present version of the
durability design guide is restricted to limited models, materials and calcula-
tional methods. In this way it has been documented that the probabilistic per-
formance based durability design methodology, using the well-known LRFD
approach, is viable and operational in practical design. The guidelines cope fol-
lowing degradation processes:

• corrosion of reinforcement due to carbonation;

• chloride induced corrosion;
• effects of corrosion, i.e. cracking and spalling of concrete.
For frost-thaw actions and alkali-silica reactions (ASR) no sufficiently accurate
models for the prediction of the degradation of the structures have been identi-
fied within this project. Therefore, the LRFD approach has not been developed
for these mechanisms. The designer is referred to a DuraCrete Task Report
where preventative procedures are selected to minimise the probability of frost

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Final Technical Report 11

damage and ASR attack. The guidelines are at this stage only developed for
concrete structures with non-prestressing steel. Problems involving combina-
tions of different deterioration mechanisms have also been left to later devel-
opments. The durability design guide is limited to first order cross-sectional
studies. Hence aspects of stability influenced by deterioration have not been
included.

1.5.2 The Design Guide

Following items are being dealt with in the Design Guide, (the final and con-
cluding report of the project), apart from examples and extensive appendices on
probabilistic models, calibration of partial factors, decision analysis and Bayes-
ian updating.

• Guide for durability design

• General framework for durability design

• Chloride ingress, initiation of corrosion

• Carbonation, initiation of corrosion

• Cracking and spalling

• Quality assurance

• Assessment and redesign

• Inspection, maintenance and repair

The Durability Design Guide is written in a code-like format, as stated before.

However, it must be realised that the guide in its present form is not a code and
that it is not a part of an existing system of codes like the Eurocodes and that
the guide has not been submitted to public approval.

A major step forward has been made in bringing together results of many years
of research on durability and elaborating these into a design methodology, ena-
bling designers and owners to incorporate durability in the (re)design and main-
tenance process in a reliable and quantified way.

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12 Final Technical Report

2 Reports
The participants decided that reports R0 – R15 are open and available for third
parties (through the Co-ordinator).
These reports have been given an ISBN number.

R0 Probabilistic Methods for Durability Design

85 pp, January 1999, ISBN 90 376 0424 2

R1 Design Framework
165 pp, March 1997, ISBN 90 376 0390 4

R2a Chloride Induced Corrosion – Mini Project

40 pp, January 1997, ISBN 90 376 0434 x

R2b Probabilistic Design of Concrete Pavements – Mini Project

56 pp, May 2000, ISBN 90 376 0391 2

R3 Models for Environmental Actions on Concrete Structures

273 pp, March 1999, ISBN 90 376 0400 5

R4-5 Modelling of Degradation

174 pp, December 1998, ISBN 90 376 0444 7

R6 Compliance Tests. State-of-the-Art

130 pp, September 1997, ISBN 90 376 0454 4

R7 Compliance Testing for Probabilistic Design Purposes

Evaluaton Report
83 pp, August 1998, ISBN 90 376 0464 1

R8 Compliance Testing for Probabilistic Design Purposes

105 pp, March 1999, ISBN 90 376 0420 x

R9 Statistical Quantification of the Variables in the Limit State Functions

130 pp, January 2000, ISBN 90 376 0374 2

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Final Technical Report 13

R10 Benchmarking of the Conventional Design Methodology

155 pp, November 1999, ISBN 90 376 0241 x

R11 Benchmarking of the Conventional Design Methodology

Summary report
33 pp, November 1999, ISBN 90 376 0251 7

R12-13 Probabilistic Calculations

157 pp, May 2000, ISBN 90 376 0401 3

R14a Durability Design of Concrete Pavements

Compliance Tests, Statistical Quantification and Benchmarking
134 pp, May 2000, ISBN 90 376 0381 5

R14b Durability Design of Concrete Pavements

Design Guide
122 pp, May 2000, ISBN 90 376 0371 8

R15 General Guidelines for Durability Design and Redesign

109 pp, February 2000, ISBN 90 376 0384 x

R16 DuraCrete – Exploitation

44+114 pp, May 2000

R17 DuraCrete – Final Technical Report

139 pp, May 2000

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14 Final Technical Report

3 Contacts
CUR, Centre for Civil Engineering Research and Codes
Ir. Jan P.G. Mijnsbergen
PO Box 420, 2800 AK Gouda, The Netherlands
Tel +31 182 540620, e-mail jan.mijnsbergen@cur.nl

Hollandsche Beton Groep nv

Ir. Fedde Tolman
PO Box 81, 2280 AB Rijswijk, The Netherlands
Tel +31 70 3722482

COWI Consulting Engineers and Planners AS

Dr. Steen Rostam
Parallelvej 15, 2800 Lyngby, Denmark
Tel +45 45 972782, e-mail sro@cowi.dk

Taywood Engineering Limited

Prof.Dr. Phil Bamforth
Taywood House, 345 Ruislip Road, Southall UB1 2QX, Middlesex, United
Kingdom
Tel +44 181 5754578, e-mail phil.bamforth@taywood.co.uk

E. Schwenk Zementwerke KG
Dr.-Ing. Volker Hartmann
PO Box 3850, 89028 Ulm, Germany
Tel +49 731 9341318, e-mail hartmann.volker@schwenk.de

Geotecnia y Cimientos S.A.

Dr. Jesus Rodriguez
Los Llanos de Jerez 10-12, 28080 Madris, Spain,
Tel +34 91 6603073, e-mail jrs-geocisa-madrid@dragados.com

ibac, Institute for Building Research, Technical University of Aachen

Prof.Dr.-Ing. Peter Schiessl
TU Muenchen, IBS, Baumbachstrasse 7, 81245 Muenchen, Germany
Tel +49 89 28927061,
e-mail: schiessl@baustoffe.bauwesen.tu-muenchen.de

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Final Technical Report 15

Institute Éduardo Torroja of Construction Science of the CSIC of Spain

Dr. Carmen Andrade
Apartado 19002, 28080 Madrid, Spain
Tel +34 91 3020440, e-mail andrade@fresno.csic.es

RWS, Directorate-General for Public Works and Water Management

Ing. Hans de Vries
PO Box 20000, 3502 LA Utrecht, The Netherlands
Tel +31 30 2857704, e-mail j.dvries@bwd.rws.minvenw.nl

TNO Building and Construction research, Netherlands Organisation for Ap-

plied Scientific Research
Ir. Ton Siemes
PO Box 49, 2600 AA, Delft, The Netherlands
Tel +31 15 2842281, e-mail A.Siemes@bouw.tno.nl

Intron, the Quality Assessment Institute for the Building Industry

Ir. Rico van Selst
PO Box 5187, 6130 PD Sittard, The Netherlands
Tel +31 46 4204230, e-mail Rse@intronbv.nl

Chalmers University of Technology

Prof.Dr. Lars-Olof Nilsson
Chalmers University of Technology, 41296 Gothenburg, Sweden
Tel +46 31 7722298, e-mail nilsson@bm.chalmers.se

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4 Introduction
Controlling the durability of concrete structures will be a fundamental chal-
lenge for the engineer in the next millennium. Past decades have taught us that
the classical procedures for design, construction and use of concrete structures
have failed to provide reliable long-term performance. Deterioration processes,
in particular corrosion of reinforcement, frost action, alkali aggregate reactions
and sulphate attack have caused serious damage to concrete structures.

To improve this situation a new concept for durability design needed to be es-
tablished. Similar to the current procedures for structural design, durability de-
sign should be performance based taking into account the probabilistic nature
of the environmental aggressivity, the degradation processes and the material
properties involved.

In order to quantify design for durability, the concept of a service life design
has been introduced. In this respect the performance requirements for a service
life design as stated in the CEB-FIP Model Code 1990 [16] have been adopted:

Concrete structures shall be designed, constructed and operated in such a

way that, under the expected environmental influences, they maintain their
safety, serviceability and acceptable appearance during an explicit or im-
plicit period of time without requiring unforeseen high costs for mainte-
nance and repair.

Such a rational design for durability, however, requires both an overall meth-
odology and predictive models for the actual degradation processes of concrete
structures. Similar to the structural design code for loads, safety requirements
and limit states must be defined for the design service life.

The new durability design methodology should be able to predict the efficiency
of the materials in resisting the aggressiveness of typical environments in
Europe. The structural designer will, thereby, be able to document the fulfil-
ment of a specific limit state. For the designer the deterioration models showing
the degradation over time, or showing the service life as a function of appropri-
ate design parameters, are valuable tools. With the aid of this methodology for
durability design, the designer can make decisions on the required dimensions
and material specifications for structures with service life requirements.

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Final Technical Report 17

One consequence of the requirements to design for durability is that structural

engineers and designers need to be educated in the durability aspects of various
materials as well as in the structural layout, the effect of execution on the in situ
qualities, and the interaction between structure and environment. This is a pre-
requisite to enhance cost optimal durability designs incorporated into the over-
all “life cycle” costs, and is thus a prerequisite to be able to satisfy the future
requirements to the performance of concrete structures. An immediate spin-off
will also have to be reflected in the structural engineering curricular.

4.1 Background
The main basis for developing the General Guidelines for Durability Design
and Redesign within Task 7 - in short: A Durability Design Guide - is the work
carried out in the previous tasks of the DuraCrete project:

Task 1 Provides the theoretical framework for Task 7. To a large extent many
of the coming issues have already been described and discussed in the
Task 1 Report "Design Framework" [1] and exemplified by the mini-
project "Chloride induced corrosion" [2].

Task 2 Provides the modelling of the deterioration mechanisms. A simple

form of each of the models is provided for engineering design pur-
poses [3,4].

Task 3 Provides an evaluation of compliance tests available for the key-point

parameters of the models selected in Task 2. Furthermore a number of
test results for different concrete mixes are provided with regard to
carbonation resistance, resistance against chloride penetration, corro-
sion resistance, frost de-icing salt resistance and finally fatigue [5,6,7].

Task 4 Provides the statistical quantification of the uncertain parameters re-

garding the deterioration models. The result of Task 4 are tables iden-
tifying statistical distributions, mean values and coefficients of varia-
tion (standard deviations). Furthermore the environmental parameters
are classified and quantified and the mechanical behaviour of concrete
structures is statistically quantified [8].

Task 5 Provides Task 6 with a range of relevant structural elements designed

using current code recommendations in Europe [9,10].

Task 6 Provides limit state functions, sensitivity measures for the input pa-
rameters and finally target reliabilities corresponding to today's prac-
tice concerning durability [11,12] (Task 5 structural elements).

4.2 Code Format

The Durability Design Guide is written in a code-like format. However, it must
be realised that the guide, in its present form, is not a code and that it is not a

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part of an existing system of codes like the Eurocodes. Further, the guide has
not been submitted to public approval.

In the guide, technical recommendations and general guidelines have been

drawn up for durability design and redesign of reinforced concrete structures.
The guideline for durability design is based on the LRFD approach (Load Re-
sistance Factor Design). The LRFD approach is a so-called level 1 approach
where all variables are represented by deterministic values and where the reli-
ability of the structure with respect to a given event is assured by applying par-
tial safety factors for the load and resistance variables. The safety factors are
developed on the basis of reliability analysis such that a given service life can
be assured with an accepted level of reliability.

The guide is to a large extent based on probabilistic analysis because this meth-
odology offers a consistent basis for updating the reliability of the structure us-
ing information from inspections and measurements.

4.3 Purpose
The purpose of the guide is to ensure that concrete structures designed accord-
ing to the requirements given in the guide and constructed with a sufficient
level of quality control will achieve the required service life with an acceptable
level of reliability.

Like a code, the guide contains a number of requirements which must be ful-
filled in order to obtain an acceptable performance and reliability of concrete
structures exposed to aggressive environments in Europe.

It is expected that the use of this guide will lead to a more homogenous level of
reliability with respect to deterioration, i.e. that structures designed according to
the guidelines given here will all achieve the same acceptable reliability level.

4.4 Field of Application

Ideally, the guide should cover all deterioration mechanisms, all types of con-
crete and all types of aggressive environment present in Europe. Unfortunately,
with the time and resources available this has not been possible.

Nevertheless, the design methodology presented in the guide is general in its

nature, and all types of deterioration mechanisms as well as second order struc-
tural effects and fatigue can be incorporated. Due to the very restricted avail-
ability of data in the relevant format to provide factual input to the probabilistic
models, the present version of the durability design guide is restricted to the
models, the materials and the computational methods listed in the following.
Further, the reader should be aware of the fact that a number of the probabilistic
models used for the calibration of partial factors represent "expert opinion".
Hence, the designs obtained on the basis of the guideline should always be
compared with present "best practise" and the designs should be evaluated by
engineers with experience in durability design.

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The General Guidelines for Durability Design and Redesign covers the follow-
ing mechanisms:

• initiation of corrosion of reinforcement due to carbonation

• initiation of chloride induced corrosion

• consequences of corrosion, i.e. cracking and spalling of concrete

As regards freeze-thaw actions and alkali-silica reactions (ASR) no sufficiently

accurate models for the prediction of the degradation of the structures have
been identified within this project. Therefore, the LRFD approach has not been
developed for these processes. The designer is referred to the Task 2 reports
[13,14] where preventative procedures to minimise the probability of frost
damage and ASR attack are discussed.

The guidelines for durability design are, at this stage, only developed for con-
crete structures with non prestressing steel. Problems involving combinations
of different deterioration processes have also been left to later developments.

A large part of the information available in the appropriate format for a prob-
abilistic treatment was limited to concrete made of Ordinary Portland Cement
(OPC). Hence, the actual data presented in the guide in the present form is to a
large extend limited to treating this type of cement.

The durability design guide is limited to first order cross-sectional studies. This
means that the load-bearing capacity of structures is studied by the design for-
mulae for cross-sections of structures, provided with the time dependent degra-
dation models. Hence aspects of stability influenced by deterioration have not
been included.

Finally, the design formula and the acceptance criteria given in this guideline
are related to individual failure elements. For example, consider the event: ini-
tiation of corrosion. For a large structure the probability of initiation of corro-
sion is larger than for a small structure. This is due to the fact that there is a
higher likelihood of observing a large surface concentration or a small resis-
tance at some point on the large structure. In the same way the strength of a
chain decreases with increasing length because there is a higher likelihood of
having a weak link. This size-effect is not taken into account.

The work being performed, including the design guide on conrete pavements
has been reported in a separate report, where specific results of work on pave-
ments in Tasks 3, 4, 5 and 7 are presented.

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5 Definitions and nomenclature

5.1 Definitions
Assessment: The total set of activities performed in order to verify the reliabil-
ity of an existing structure.

Basic variables: A set of variables entering the limit state equation including
variables accounting for the model uncertainties in the limit state function itself.

Characteristic load: Reference value of a load to be used in a deterministic

analysis.

Characteristic resistance: The nominal capacity that may be used for determi-
nation of design strength or design resistance.

Characteristic value: A nominal value to characterise the magnitude of a sto-

chastic variable. The characteristic value is defined as a fractile of the probabil-
ity distribution of the variable.

Damage: Unfavourable change in the condition of a structure that adversely

affects its performance.

Design equation: A design equation is an equation for deterministic design with

the property that the design equation is negative if and only if the performance
of the structure is unacceptable.

Design life: The period of time for which a structure is expected to be able to
fulfil its requirements with sufficient reliability with or without periodic inspec-
tion and maintenance and without unexpected high costs for maintenance and
repair.

Deterioration: A process that adversely affects the performance over time due
to
- naturally occurring chemical, physical or biological processes
- normal, extreme or accidental actions
- normal or severe environmental conditions
- wear due to use
- improper use or maintenance

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Deterioration model: A mathematical model that describes the performance of

the structure as a function of time taking deterioration into account.

Expected value: First order moment of the probability density function for the
considered variable.

Failure: An event causing an undesirable condition considered as failure.

Inspection: On site non-destructive examination to establish the present condi-

tion of the structure.

Investigation: Collection and analysis of information through inspection, docu-

ment search, load testing and other testing.

Maintenance: Routine intervention to preserve the appropriate performance.

Material properties: Mechanical, physical or chemical properties of materials

used in structures.

Model uncertainty: The inherent uncertainty of the selected calculation models.

Monitoring: Regular or continuous measurement of structural conditions or ac-

tions.

Partial factor: Factor by which the characteristic value of a variable is modi-

fied to give the design value.

Rehabilitation: Work required to restore, and possibly upgrade, the condition of

an existing structure.

Repair: Improve the conditions of a structure by restoring or replacing existing

components that have been damaged.

Reliability: Ability of a component or a system to perform its required function

without failure during a specified time interval. Probability density integrated
over the safe states in the space spanned by the basic variables.

Reliability index: Fractile of the normalised normal probability function corre-

sponding to the reliability.

Resistance: Capability of a structure or part of a structure to resist its environ-

mental and/or structural load effects.

Serviceability: A condition in which a structure is considered to perform its de-

sign function satisfactory.

Serviceability limit state: The limit between the state where the performance of
the structure is acceptable and the state where the structure is no longer service-
able.

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Service life: See design life.

Standard deviation: Square root of the second order central moment of the
probability density function for the considered variable.

Stochastic variable: A variable participating to, or characterising a set of items

where every member has a chance of occurring described by the probability
distribution function.

Ultimate limit state: The limit between the state where the structure is able to
carry the loads acting on it and the state where the structure has collapsed.

Upgrading: Modifications to an existing structure to increase its structural per-

formance.

5.2 Nomenclature
a Geometric quantity

a ca Regression factor for the coefficient of variation of the resistance

of carbonation

a cl Regression factor for the coefficient of variation of the chloride

resistance

a ρ0 Regression factor for the coefficient of variation of the potential

resistivity.

a Action

a1 , a 2 , a 3 Regression factors for the evaluation of the crack width

Acs Regression parameter for the surface chloride concentration

b Regression factor depending on the position of the bar

B Binding capacity of the concrete with respect to carbon dioxide

c Chloride concentration

ccr Critical chloride concentration

cs Surface chloride concentration

C Total cost

CF Cost of failure

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CM Cost of maintenance

CR Cost of repair

d Diameter of reinforcement bar

D 0,cl Chloride diffusion coefficient at the time t 0

D 0,ca Carbonation rate at the time t 0

e Experiment plan

E [ .] The expected value of [ .]

f Resistance variable

fc Compressive strength

f sp Splitting tensile strength

F Load variable

FCl Corrosion rate factor accounting for the presence of chloride.

Fgalv Corrosion rate factor accounting for the galvanic effect.

FO2 Corrosion rate factor accounting for the presence of oxygen.

k c ,ca Factor describing the effect of curing on the resistance of carbona-

tion

k c ,Cl Factor describing the effect of curing on the chloride resistance

k cl ,res Chloride factor for the electrolytical resistivity

k e ,ca Factor describing the effect of the environment on the resistance of

carbonation

k e ,Cl Factor describing the effect of the environment on the chloride re-
sistance

k t ,ca Factor describing the effect of the test method on the resistance of
carbonation

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k RH ,res Factor describing the effect of the relative humidity on the electro-
lytical resistivity.

k t ,Cl Factor describing the effect of the test method on the chloride resis-
tance

K Constant describing the temperature dependence of the conductiv-

ity of concrete

nca Age factor for the resistance of carbonation

nCl Age factor of the chloride resistance

nres Age factor for the electrolytic resistivity

P( .) Probability of the event ( .)

R0,ca Resistance against carbonation at the time t 0

R0,cl Resistance against chloride ingress at the time t 0

s Outcome of the stochastic vector describing the realisations of an

experiment

t Time

t0 The time at which a test for the material parameter was performed

w0 Width of the initial visible crack

wcr Critical crack width

wt Relative period of wetness

w/b Water-binder ratio

x Concrete cover

z Outcome of the vector of basic variables

α Pitting factor

β Reliability index

βt Target reliability index

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εca Error term for the coefficient of variation of the resistance of car-
bonation

εcl Error term for the coefficient of variation of the chloride resistance

εc s
Error term for surface chloride concentration

ερ 0
Error term for the coefficient of variation of the potential resistiv-
ity.

γ Safety factor

Ωa The set of possible actions, e.g. repair strategies

Ωe The admissible set of experiment plans

Ωs The set of possible outcomes of a set of experiments

Ωz The admissible domain of the basic variables

ρ0 Potential electrolytical resistivity

θ Model uncertainty

Superscripts

c Characteristic value

d Design value

5.3 Abbreviations
AAR Alkali Aggregate Reactions

ACT Accelerated Carbonation Test

ASR Alkali-Silica Reactions

CMT Chloride Migration Test

LRFD Load and Resistance Factor Design

OPC Ordinary Portland Cement

GGBS Ground Granulated Blastfurnace Slag Cement

PFA Pulverised Fly Ash

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SF Silica Fume

TEM Two Electrode Method

5.4 Units
All units are given according to the SI-system, see ISO 31/0 and ISO 1000.

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6 Guide for Durability Design

6.1 Background
Traditionally, codes of practice contain requirements for design which are for-
mulated directly in terms of the load carrying capacity of the considered ele-
ment. Durability has often been considered as being of secondary importance.
Hence, requirements to the durability of the design have typically been given
implicitly. In this way the treatment of load carrying capacity and durability has
been separated not only in the codes but also - and this is much worse - in the
profession of structural engineering.

Durability design of concrete structures is in general based on simple deem-to-

satisfy rules, related to a crude environmental classification. Examples of such
deem-to-satisfy rules are the requirements to minimum concrete cover, maxi-
mum water/cement ratio, minimum cement content, air content, and cement
type. Following these rules the designer could assume that the structure would
achieve an acceptable long, but unspecified service life. The deem-to-satisfy
rules are not able to give an explicit relationship between performance and ser-
vice life.

The demand for a new design code, which incorporates durability and service
life aspects, has grown from:

• the increasing interest expressed by owners in setting requirements for the

service life of structures

• the greater awareness that quality and total costs of structures comprise not
only construction costs but also costs for maintenance and repair

• the understanding that durability is an essential part of the quality and per-
formance of structures

• the realisation that the visual appearance and ageing of structures are inte-
grated elements of satisfactory performance.

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6.2 Concept for Durability Design

The aim of the proposed durability design guide is to obtain an acceptable level
of safety with respect to the considered deterioration mechanism.

Like the procedure for load design, the design for durability will be perform-
ance based. Hence, the guide enables the designer to adjust, or adapt, his usual
structural design to cope in a factual way with the aspects of environmental ag-
gressivity and relate this to a specified design service life and the corresponding
overall costs of the structure.

In principle two basically different design strategies for durability can be fol-
lowed:

A. Avoid the degradation threatening the structure due to the type and aggres-
sivity of the environment.

B. Select an optimal material composition and structural detailing to resist, for

a specified period of use, the degradation threatening the structure.

Strategy A can be subdivided into three different types of measures:

A.1: Change the micro environment, e.g. by tanking, membranes, coatings etc.

A.2: Select non-reactive, or inert, materials, e.g. stainless steel reinforcement,

coated reinforcement, non-reactive aggregates, sulphate resistant ce-
ments, low alkali cements etc.

A.3: Inhibit the reactions, e.g. cathodic protection. The avoidance of frost at-
tack by air entrainment is also classified in this category.

It should be noted that most of the measures indicated above do not provide a
total protection. The effect of the measures depends on a number of factors. For
example, the efficiency of a coating depends on the thickness of the coating and
on the permeability of the coating.

Strategy B allows for different types of interventions. For example, corrosion

protection could be achieved by selection of appropriate cover and concrete
mix. In addition, the structure can be made more robust against aggressive en-
vironments of different sorts by appropriate detailing such as minimising the
exposed surface, by rounded corners, or by adequate drainage.

The modelling of the deterioration mechanisms is in principle applicable both

for design strategy A and design strategy B. However, little knowledge is avail-
able for the efficiency of the various protective measures.

The durability design strategy forming the basis of the design in this guide is
formulated for strategy B. Hence, the principle is to resist the relevant deterio-
ration mechanisms by selecting an optimal material composition and/or a suffi-
cient cover thickness. Strategy A aiming to avoid the degradation reaction or to

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resist it by means of more sophisticated measures (i.e. cathodic protection / ca-

thodic prevention), is not considered. In this case the designer is referred to
[15].

The durability design will be based upon

• realistic and sufficiently accurate definitions of environmental actions de-

pending on the considered type of degradation

• material parameters for concrete and reinforcement

• calculation models for degradation processes. In the present version of the

guide the mechanisms which have been modelled have been limited to:

 initiation of carbonation induced corrosion

 initiation of chloride induced corrosion

 cracking and spalling of concrete due to corrosion products.

The outcome of the durability design guide will be a tailor made service life
design with the possibility to update the service life using results of tests and
measurements throughout the lifetime of the considered structure. Inspection
and testing are, therefore, integral parts of the durability design.

Using the guide for durability design does not imply that less effort should be
given to the factors connected with the structural design and construction proc-
ess such as e.g. proper detailing, execution, curing, etc. In fact, the guide can
only be used if sufficient quality assurance is implemented in order to ensure
that the effect of factors connected to the design and construction process is
minimised. A normal level of quality control of the design and construction
process can be said to be achieved if the recommendations given in the CEB-
FIP Model Code 1990 [16] are followed.

Similar to the design concept used in the structural codes, the design for dura-
bility must be developed on the basis of probabilistic analyses taking into ac-
count the environment and the structural performance. In particular environ-
mental factors affecting the degradation processes, material and geometrical
properties etc., may vary substantially.

6.3 Basis for Durability Design

6.3.1 Service life

In designing for durability, the first step is the definition of the desired/required
performance of the structure. The client or the owner of the structure is asked to
define the required target service life and the event which identifies the end of
the service life.

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Figure 6.1 shows in principle the performance of a concrete structure with re-
spect to reinforcement corrosion and related events. In general points 1 and 2
represent events related to the serviceability of the structure, point 3 is related
to both serviceability and ultimate failure and 4 represents collapse of the struc-
ture.

Initiation Propagation

1 2 3 4
Time

Damage
Events
1 Depassivation 3 Spalling
2 Cracking 4 Collapse

Figure 6.1: Events related to the service life.

The following events can be used to identify the service life.

1. Depassivation of reinforcement
The service life is limited to the initiation period, that means the time for
the aggressive substance to reaches the reinforcement and induce depas-
sivation. The initiation phase ends when the chloride concentration at the
reinforcement reaches a critical threshold value or when the carbonation
front reaches the reinforcement. Depassivation does not necessarily repre-
sent an undesirable state. However, this event must have occurred before
corrosion will begin.

2. Cracking of concrete cover

The second event is cracking of the concrete cover due to the expansive
forces generated by the corrosion products. In this case the service life in-
cludes a certain propagation period of corrosion activity during which the
cross section area of the reinforcement is progressively reduced. The crack
width depends on the amount of corrosion, the cover/diameter ratio, the
concrete quality (tensile strength) and the position of the bar. The propaga-
tion time ends when a certain a priori selected or determined allowable
crack width has been reached. Based on available knowledge a value of 0.3
mm has been chosen.

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3. Spalling of concrete cover

Corrosion continuing after cracking has occurred may lead to spalling of
the concrete cover. Depending on the bar spacing, the concrete cover, and
the tensile strength of the concrete, spalling may be either in the form of
local triangular formed parts of concrete along each corroding bar, or the
splitting forces from several corroding bars may interact and spall the
cover over larger areas. The loss of reinforcement cross section and to
some extent also the loss of concrete section will lead to a reduced load
carrying capacity.

Spalling of concrete is usually considered an unacceptable condition. How-

ever, spalling does not necessarily lead to collapse of the structure and can,
therefore, be considered as a serviceability limit state. On the other hand,
spalling of concrete may endanger human life and limb. In such a case
spalling must be considered as an ultimate limit state.

Based on available knowledge spalling is supposed to occur when a crack

width of approximately 1.0 mm has been reached. The propagation time is
assumed to end at this stage.

4. Collapse
Collapse of the concrete structure will occur if the load carrying capacity
of the element is reduced sufficiently due to ongoing corrosion, by further
cross sectional loss of the concrete and steel, or loss of bond.

For this version of the durability design guide, only loss of cross sectional
area of steel and concrete has been taken into account through factual cal-
culations. The loss of concrete section is modelled by the following ap-
proaches:

Column: concrete cover loss from all sides

Beam: concrete cover loss at the compression and/or tension zone
Slab: concrete cover loss at the compression zone

6.3.2 Degradation models

Having identified the failure event the second step of the durability design is to
analyse the environmental actions and to identify the relevant degradation
mechanisms. Mathematical models describing the time dependant degradation
processes and the material resistance are needed. The big step forward to per-
formance related durability design is that these models enable the designer to
evaluate the time-related changes in performance depending on the specific ma-
terial and environmental conditions.

The different models used for this durability design are presented in more detail
in Chapters 8 to 10. A common aspect is that all models consist of design pa-
rameters such as structural dimensions, environmental parameters and material
properties which correspond to the design variables of the structural design pro-
cedure.

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6.3.3 Reliability theory

The new durability design methodology is based on reliability theory tradition-
ally used in structural design. The purpose of a reliability analysis is to deter-
mine the probability of a given event, e.g. the event which marks the end of the
service life.

The considered event is described in terms of a limit state function, g(x, t ) ,

where x denotes the vector of basic variables and t is time. The limit state
function is defined such that it is negative if and only if the considered event
occurs.

The probability of failure within the period of time [0;T ] , Pf ( T ) is

Pf (T ) = 1 − P{ g(x, t ) > 0 for all t ∈[0; T ]} (6.2)

The limit state function can e.g. be written

g ( x , t ) = R( t ) − S ( t ) (6.3)

where R( t ) and S ( t ) denote a time-variant resistance and load variable, re-

spectively. In Figure 6.2 a schematic representation of the problem is shown.

R(t) Distribution of R(t)

R,S
Pf

S(t)
Distribution of
S(t)
Mean service life Time
Failure probability
Pf
Target service life
Sevice life density

Figure 6.2: Failure probability and target service life.

The problem given in eq. (6.2) can be solved by reliability methods described
in e.g. Bryla, Faber and Rackwitz [17]. For problems involving only one or no
time-variant variables the problem can be formulated as a time-invariant prob-
lem. This type of problems can be solved by traditional reliability methods such
as FORM/SORM methods, see e.g. Thoft-Christensen and Baker [18]. or Mad-
sen, Krenk and Lind [19]. In Chapter 7 it is described how the design guide is
developed using these reliability methods.

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6.3.4 Quality control, assessment and repair

The knowledge about the service life of a structural element is uncertain due to
the random variation of the geometry, material characteristics, execution and
environment. This random variation can be assessed and in part controlled by
testing and quality control at several stages during the life of a structure. The
aim of the tests and the quality control is to define and to update the distribution
parameters of these variables.

If a high degree of quality control can be documented and its consequences

quantified, it serves as a basis for documenting service lives. The updating of
the distribution parameters may make it possible to use lower partial factors.

The combined set of problems to be considered can be summarised as follows:

1. The information on the aggressivity of the environment, the characteristics

of the materials in the structure, and the structure-environment interaction, is
uncertain.

2. The amount of uncertainty associated with the estimated lifetime depends on

the type and accuracy of the available information on the above variables.

3. The accuracy of the available information is depends on the considered

stage, i.e.:

• At the design stage, where the specific materials, the quality of execu-
tion, and the structure-environment interaction are all unknown.

• At the construction stage, where the specific materials can be tested and
the quality of execution can be tested.

• At the handing over stage, where the "as-build" conditions of the struc-
ture can be tested in situ.

• During the period of use, where the relevant parameters can be tested
during inspection and maintenance activities, and the time dependency
can be determined. The information obtained during the period of forms
the basis of an assessment of the performance of the structure and can if
necessary be used to determine a repair strategy for the structure.

4. From a durability design point of view this means that design input data with
different levels of accuracy must be used at the different stages:

• At the design stage:

⇒ preliminary assumptions of environmental aggressivity must be

made. Codes and design guides can provide a first set of data.
These assumptions are some of the most important ones to be made
by the designer.

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⇒ a design service life can be fulfilled during this design, but with a
high degree of uncertainty.

⇒ during the durability design stage the most critical parameters can
be identified.

• At the construction stage:

⇒ during the selection and pre-testing of the materials (cement, ag-

gregates, admixtures, concrete mix) an updating of resistance pa-
rameters and loading parameters can be made.

⇒ an updated design service life - and to some extent a revised dura-

bility design - can be determined, giving a result with a reduced
uncertainty.

• At the handing over stage:

⇒ the actual as-build initial parameters and their distributions can be

determined in the form of a "Birth Certificate" of the structure.

⇒ a further - and the most realistic - expected service life prediction

can now be made for the individual structure and its different com-
ponents. This prediction can form the basis for selecting frequency
and intensity of future inspections, tests and possible maintenance
activities.

⇒ in addition, this could also trigger a bonus/fine to the contractor,

depending on the contractual conditions.

• During the period of use:

⇒ the base-line-study (birth certificate) at the handing over provides

the starting point for the tests needed during future inspections in
order to determine most economically the residual service life with
increasing reliability with increasing age of the structure.

Quality control in the sense of this durability design guide is mainly to control
the variation of the material parameters and the geometrical variables at the dif-
ferent stages of design and construction. In Chapter 7 a more detailed descrip-
tion of quality control is given.

For a given existing structure an estimate of the service life distribution can be
determined on the basis of information obtained through inspections and meas-
urements. In Chapter 13 a more detailed description of various inspection and
measurement methods are given. Further, in Chapter 12 it is described how this
information can be used for the evaluation of the service life distribution of the
considered structure.

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Finally, if the assessment of a given structure reveals that the service life of the
structure is insufficient a repair of the structure has to be carried out. In Chapter
13 different repair methods are described and discussed.

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7 General Framework for Durability Design

The guide aims at obtaining a sufficient level of safety with respect to the con-
sidered events. The guide is developed taking into account

• The geometry of the considered structure

• The materials used for construction
• The environment in which the structure is located
• The execution of concrete works
• The planned inspection of the structure

In the following sections it is demonstrated how these factors are taken into ac-
count by the evaluation of the characteristic values of the model parameters and
by the evaluation of the partial factors.

7.1 Load and Resistance Factor Design

The design of concrete structures with respect to durability can be performed
on the basis of the so-called Load and Resistance Factor Design (LRFD)
method. This approach is identical to the conventional approach used in struc-
tural design.

The LRFD method is based upon:

• Design equations
• Characteristic values of load and resistance variables
• Partial factors for the load and resistance variables.

7.1.1 Design equation

A structure can be in a state in which it fulfils all requirements to its perform-
ance or in a state where it is not able to fulfil one or more of the requirements.
The limit state or design equation is a function separating the state where it is
able to fulfil all the requirements and the state where it is not able to fulfil one
or more of the requirements.

A limit state equation (design equation) is an equation with the quality that it is
positive if and only if the considered structure is fully capable to fulfil all of the
performance requirements.

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In general, a design equation can be given by

g (F d , f d , a d , θ d , t ) ≥ 0

where F d , f d and a d are design values of load variables, resistance variables

and geometrical quantities, respectively, θ d is the design value of the variable
accounting for the model uncertainty and t denotes time.

7.1.2 Load and resistance variables

In the following all design variables will be identified as either a geometric
quantity, a load variable, a resistance variable or a variable accounting for the
model uncertainty.

By definition a load variable is a variable where an increase of the numerical

value leads to a reduction of the reliability of the structure, whereas an increase
of the numerical value of a resistance variable leads to an increase of the reli-
ability.

In a design for load carrying capacity the definitions of load and resistance vari-
ables are usually unambiguous. The load variables are actions such as snow,
wind and physical loads. The resistance variables are material parameters such
as the yield strength of steel and the compressive strength of concrete.

These definitions will also be used here, implying that material variables in
general will be resistance variables and variables describing the environment
will be load variables. For example the design will be based on the resistance of
a given material towards chloride ingress and not on the well known diffusion
coefficient.

The definition of the load and resistance variables can be illustrated through the
following simple example:

7.1.2.1 Example
The cover thickness, x , necessary to prevent initiation of corrosion prior to the
time t can be determined from

 c  t
x =2 ⋅ erf -1 1 − cr  ⋅ (7.1)
 cs  R

R0,cl
R= ncl
t 
k e,cl k c ,cl  0 
t 

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1
R0,cl =
D0,cl

D0,cl is the diffusion coefficient. This parameter is not used in the definitions,
since it mistakenly could be understood as a load variable.

Equation (7.1) consists of the load and resistance variables given in Table 7.1:

Load variable Resistance variable

cs : Surface concentration x : Concrete cover

ccr : Critical concentration

R : Resistance

Table 7.1: Load and resistance variables.

The environmental factor k e ,cl , accounting for the effect of the environment on
the resistance, the curing factor k c ,cl , accounting for the effect of curing on the
resistance, and the age factor ncl , describing the development of the resistance
with time, are not defined as either load or resistance factors. These factors are
used to determine the actual, effective chloride resistance.

7.1.3 Characteristic values

The characteristic value of a parameter is defined as a fractile of the probability
distribution function of the given parameter, i.e. the characteristic value is de-
fined as the value for which there is a given probability of the parameter ex-
ceeding this value.

Whenever test samples are available, the characteristic values may be deter-
mined statistically from the test results.

If no test samples are available the characteristic values given in the relevant
sections of this guide shall be used as initial design parameters.

7.1.4 Design values and partial factors

In general the design values are obtained by

• load variable: F d = F c γ F

c
f
• resistance variable: f d
=
γf

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• geometric quantity: a d = a c ± ∆a

1
• variables describing the model uncertainty: θ d = γ D or .
γD

In Appendix B it is demonstrated how the partial factors are evaluated. Using

these expressions a new set of partial factors can be determined, thus updating
the design by incorporating the results of actual tests.

For the evaluation of partial factors it is necessary to introduce the following

types of variables:

• Material variables
• Environment variables
• Execution variables
• Variables depending on both the environment and the materials

The distinction above is introduced in order to identify the variables which are
affected by the level of quality control, verification and inspections. For exam-
ple, it is evident that it is not possible to reduce the variability of a variable de-
scribing the environment by performing quality assurance. Hence, the partial
factor and/or the characteristic value for such a variable should not depend on
the amount and level of quality assurance.

7.1.4.1 Geometric quantities

The characteristic value of a geometric quantity is defined as the mean value.
Further, the geometric quantities are not associated with any partial factor. The
design value is given by

a d = a c = a mean .

An exception to this rule is the cover thickness, which is treated as a resistance

variable. The design value is given by

x d = x c − ∆x .

The margin, ∆x , given in this guide has been evaluated on the basis of a model
where the standard deviation of the cover thickness is assumed to be 10 mm.
By quality assurance the standard deviation of the cover thickness can be re-
duced, see Chapter 7. If such a reduction is achieved a new margin can be de-
termined using the expression given in Appendix B.

7.1.4.2 Material variables

For material variables the characteristic value is defined as a 5 % fractile.

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In Chapter 11 it is demonstrated how the characteristic values of material vari-

ables can be determined on the basis of results of compliance tests as a function
of the number of experiments.

7.1.4.3 Environment variables

The characteristic value of an environment variable is defined as the mean
value.

The variability of the variables describing the environment does not depend on
quality assurance, the chosen inspection plan or any foreseen repair strategy.
Hence, the design value of an environment variable only depends on the char-
acteristic value, i.e. the mean value, and the given partial factor.

7.1.4.4 Execution variables

The characteristic value of an execution variable is defined as the mean value.
The variability depends on the level of quality control. This implies that new
partial factors can be determined using the expression given in Appendix B.

7.1.4.5 Variables depending on environment and materials

In this guide the characteristic values of the variables depending on both the
environment and the materials are defined as mean values.

Characteristic values can alternatively be determined using the information

from structures in a similar environment made with the same type of concrete.

If sufficient information is available to determine the necessary distribution pa-

rameters, new partial factors can be established using the expressions given in
Appendix B.

7.2 Acceptance criteria

The partial factors for the load and resistance variables are introduced to ensure
that structures designed using these partial factors achieve an acceptable reli-
ability with respect to the considered limit states.

The acceptance criteria given here are related to the event that the width of
cracks induced by corrosion exceeds 1.0 mm. This event is chosen because it
requires both that corrosion is initiated and that the corrosion has propagated
for some time. Further, this event may lead to a reduction of the load carrying
capacity due to spalling.

Constraints on the failure probability shall normally be imposed both in terms

of a yearly failure rate, i.e. a maximum failure probability corresponding to a
specific period (e.g. one year) and a maximum failure probability correspond-
ing to the design lifetime of the structure. The first of these constraints is im-
posed to that a reasonable level of risk with respect to loss of human life can be

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maintained and controlled by society. The second requirement is introduced to

ensure that the investment in the structure is secured. In general, the considered
failure event, i.e. spalling of the concrete cover, does not involve any risk to
human life. Therefore, the acceptance criteria given here are related to the ser-
vice life of the structure. The service life is assumed to be 50 years.

If the failure event involves risk of loss of human life more strict requirements
to failure probability should be imposed. By the evaluation of the load carrying
capacity of the structure also the probability of spalling should be taken into
account.

If past practise has led to structures with an acceptable durability, the accept-
able reliability with respect to deterioration should be determined by investigat-
ing past practise. On the other hand, if past practise has not led to an acceptable
durability the acceptable reliability can be determined by investigating a struc-
ture, which a group of experts consider to lead to an acceptable durability. In
other words, the acceptance criteria must be selected such that the designs ob-
tained using the guide represent "best practise", i.e. the acceptance criteria are
determined on the basis of structures designed according to "best practise". This
definition of acceptance criteria naturally introduces the problem of defining
"best practise".

The definition of "best practise" may depend on the nature of the problem con-
sidered. For example, in a given situation it may be optimal to design the struc-
ture such that no repair is foreseen throughout the lifetime of the structure,
whereas in another situation it may be optimal to design a structure where re-
pair is necessary at some time within the service life of the structure. Here "best
practise" is only defined in terms of an acceptable failure probability. These
acceptable failure probabilities are assumed to be the same for all conditions.

The development of the acceptance criteria can be divided into two steps:

1. Identification of different classes of problems where the same "best prac-

tise" apply.
2. Definition of "best practise" for each of these classes.

The acceptable reliability depends on the cost of design and construction, i.e.
the cost of obtaining the given reliability level , and it depends on the cost of
repair, i.e. the cost of maintaining the given reliability level. In cases where the
cost of mitigating the risk is low compared to the cost of repair it is optimal to
design the structure such that a high level of reliability is obtained. If the cost of
mitigating the risk is high compared to the cost of repair it may be optimal to
design the structure with a lower reliability level and to perform inspections
and repairs during the lifetime of the structure in order to maintain an accept-
able reliability level.

Acceptance criteria will be specified for the following three classes of struc-
tures.

1. The cost of mitigating the risk is low compared to the cost of repair

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2. The cost of mitigating the risk is normal compared to the cost of repair
3. The cost of mitigating the risk is high compared to the cost of repair

The acceptance criteria are given in terms of a reliability index, β , defined by

( )
β = − Φ −1 Pf

where Pf is the probability of the considered event occurring within the con-
sidered reference period (service life).

The risk acceptance criteria are selected on the basis of the results of the reli-
ability analyses carried out in Task 6, see the Task 6 Report [12]. In Task 6 a
number of elements designed according to a number of current European Codes
were analysed. More detailed descriptions of the elements and the relevant de-
signs can be found in the Task 5 Report [9,10].

Finally, it is important to note that a specific set of acceptance criteria is devel-

oped on the basis of a specific probabilistic model. Hence, they are only valid
for analyses carried out using the same probabilistic model. The acceptance
criteria given here should only be applied in conjunction with the probabilistic
model given in Appendix B and the design rules given in this guide for durabil-
ity design.

The acceptance criteria for a 50 years service life are given in Table 7.2.

Cost of mitigation of risk rela- Reliability level

tive to the cost of repair
Low 3.72
Normal 2.57
High 1.28
Table 7.2: Acceptance criteria for a 50 years reference period.

7.3 Application of design rules

For structures subject to chloride ingress or carbonation it must, from a formal
point of view, be demonstrated that the sum of the initiation period and the
propagation period must be larger than 50 years. In practice this can be done by
determining the time to initiation of corrosion on the basis of eq. (8.1) or eq.
(9.1). Thereafter, the design can be checked using eq. (10.1). If eq. (10.1) is less
than zero the design is unacceptable.

For structures subject to chloride-initiated corrosion the propagation period will

usually be very short compared to the initiation period. It is, therefore, often
sufficiently accurate to assume that the sum of the initiation period and the
propagation period is equal to the initiation period.

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8 Chloride Ingress, Initiation of Corrosion

Chloride penetration into concrete may cause corrosion of the reinforcement
because chloride dissolves the protective passivating layer on the steel surface.
Corrosion is usually said to be initiated when the chloride concentration around
the reinforcement exceeds a critical threshold value.

Chloride-induced corrosion of the reinforcement bars is not uniform. At local-

ised spots of the reinforcement the attack penetration will be deep. At other lo-
cations no corrosion takes place. This is the so-called pitting corrosion, which
is always considered in the case of chloride-initiated corrosion.

8.1 Design Equation

The design equation, g , stating that corrosion is initiated when the chloride
concentration around the reinforcement exceeds the critical chloride concentra-
tion is given by

  
  
  x d

g = c crd − c d ( x, t ) = c crd − c sd,cl 1 − erf   (8.1)
  t 
2
 
 Rcl (t ) 
d

where

ccrd Design value of the critical chloride concentration

csd,cl Design value of the chloride surface concentration
xd Design value of the cover thickness
Rcld Design value of the chloride resistance
t Time

8.2 Design Values

The design value of the critical chloride concentration can be found as

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1
ccrd = ccrc ⋅ (8.2)
γc cr

where γ ccr is the partial factor of the critical chloride concentration.

The design value of the surface chloride concentration is determined from the
expression

c sd,cl = Acs ,cl ⋅ (w/b ) ⋅ γ cs ,cl (8.3)

where Acs ,cl is a regression parameter describing the relation between the chlo-
ride surface concentration and the water-binder ratio, (w/b), and where γ cs ,cl is
the partial factor for the surface concentration.

The design value of the cover thickness is found from

x d = x c − ∆x (8.4)

where ∆x is the margin for the cover thickness.

Finally, the design value of the time dependent resistance is derived from

Rclc , 0
Rcld (t ) = c
(8.5)
nCl
t 
k ec,cl ⋅ k cc,cl ⋅ 0  ⋅ γ Rcl
t 

where

Rcl , 0 Resistance with respect to chloride ingress determined on the basis of

compliance tests
k c ,cl Curing factor
k e ,cl Environment factor
t0 The age of the concrete when the compliance test is performed
ncl Age factor
γ R cl Partial factor for the resistance with respect to chloride ingress

By the evaluation of the design value of the chloride resistance also the effect
of the temperature should be taken into account.

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8.3 Characteristic Values

8.3.1 Geometry
The characteristic value of the cover thickness is defined as the mean value, i.e.
the value determined through the design process.

8.3.2 Material
For a given type of concrete, outcomes of the effective resistance with respect
to chloride ingress must be generated by the concrete producer using a stan-
dardised test method, i.e. the Rapid Chloride Migration Test (RCM). On the
basis of these test results the characteristic value can be determined according
to the methodology outlined in [6,7].

8.3.3 Environment
All variables depending on the environment also to some extent depend on the
material. Hence, these variables are treated in Chapter 8.3.5.

8.3.4 Execution
In Table 8.1 characteristic values of the curing factor, k c ,cl , are given for dif-
ferent curing of the concrete.

Variable Condition Characteristic value Unit

k c ,cl 1 day curing 2.08 -
k c ,cl 3 days curing 1.50 -
k c ,cl 7 days curing 1 -
k c ,cl 28 days curing 0.79 -

Table 8.1: Characteristic values of the curing factor.

8.3.5 Properties depending on the Material and Environment

For the evaluation of the parameters which depends on both the material and
the environment the following types of environment are introduced

• Submerged
• Tidal zone, marine environment
• Splash zone, marine environment
• Atmospheric zone, marine environment

For structures located close to a roadway subject to de-icing salt the variables
depending on the material and the environment may be assumed to be identical
to the ones valid for the splash zone, marine environment.

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In Table 8.2 characteristic values of the environment factor are given for a
number of different environments and materials.

Variable Condition Characteristic value Unit

k e ,cl OPC, Submerged 1.32 -
k e ,cl OPC, Tidal zone 0.92 -
k e ,cl OPC, Splash zone 0.27 -
k e ,cl OPC, Atmospheric 0.68 -
k e ,cl GGBS, Submerged 3.88 -
k e ,cl GGBS, Tidal Zone 2.70 -
k e ,cl GGBS, Splash zone 0.78 -
k e ,cl GGBS, Atmospheric 1.98 -

Table 8.2: Characteristic values of the environment factor.

Alternatively, the factor k e,cl can be split up into two factors: k e ,0 describing
the environment and k e,c describing the type of cement.

k e ,cl = k e ,0 ⋅ k e ,c (8.6)

In Table 8.3, characteristic values of the factor k e ,0 are given for different envi-
ronments. In Table 8.4, values of the factor k e,c are given for two different ce-
ment types.

Variable Condition Characteristic value Unit

k e ,0 Submerged 1.32 -
k e ,0 Tidal zone 0.92 -
k e ,0 Splash zone 0.27 -
k e ,0 Atmospheric 0.68 -

Table 8.3: Characteristic values of the factor k e ,0 .

Variable Condition Value Unit

k e ,c OPC 1.0 -
k e ,c GGBS 2.9 -

Table 8.4: Values of the factor k e,c .

The characteristic values of the regression parameter, Acs ,cl , used to determine
the chloride surface concentration are given in Table 8.5 for different materials
and environments.

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Variable Condition Characteristic Unit

value
Acs ,cl OPC, Submerged 10.3 [%] relative to binder
Acs ,cl OPC, Tidal and splash 7.76 [%] relative to binder
Acs ,cl OPC, Atmospheric 2.57 [%] relative to binder
Acs ,cl PFA, Submerged 10.8 [%] relative to binder
Acs ,cl PFA, Tidal and splash 7.46 [%] relative to binder
Acs ,cl PFA, Atmospheric 4.42 [%] relative to binder
Acs ,cl GGBS, Submerged 5.06 [%] relative to binder
Acs ,cl GGBS, Tidal and splash 6.77 [%] relative to binder
Acs ,cl GGBS, Atmospheric 3.05 [%] relative to binder
Acs ,cl SF, Submerged 12.5 [%] relative to binder
Acs ,cl SF, Tidal and splash 8.96 [%] relative to binder
Acs ,cl SF, Atmospheric 3.23 [%] relative to binder

Table 8.5: Characteristic values of the regression parameter Acs ,cl .

In Table 8.6 the characteristic values of the age factor are given

Variable Condition Characteristic value Unit

ncl OPC, Submerged 0.30 -
ncl OPC, Tidal and splash 0.37 -
ncl OPC, Atmospheric 0.65 -
ncl PFA, Submerged 0.69 -
ncl PFA, Tidal and splash 0.93 -
ncl PFA, Atmospheric 0.66 -
ncl GGBS, Submerged 0.71 -
ncl GGBS, Tidal and splash 0.60 -
ncl GGBS, Atmospheric 0.85 -
ncl SF, Submerged 0.62 -
ncl SF, Tidal and splash 0.39 -
ncl SF, Atmospheric 0.79 -

Table 8.6: Characteristic values of the age factor for chloride ingress.
The critical chloride concentration not only depends on the environment and
the type of binder but also depends on the w/b-ratio. In Table 8.7 the critical
chloride concentration is shown for a number of different environments for a
number of different w/b-ratios for concrete made of Ordinary Portland Cement.
For the submerged condition initiation of corrosion is not expected.

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Variable Condition Characteristic Unit

value
ccr OPC, w/b=0.5, Submerged 1.6 [%] relative to binder
ccr OPC, w/b=0.4, Submerged 2.1 [%] relative to binder
ccr OPC, w/b=0.3, Submerged 2.3 [%] relative to binder
ccr OPC, w/b=0.5, Splash and 0.50 [%] relative to binder
tidal zones
ccr OPC, w/b=0.4, Splash and 0.80 [%] relative to binder
tidal zones
ccr OPC, w/b=0.3, Splash and 0.90 [%] relative to binder
tidal zone
Table 8.7: Characteristic values of the critical chloride concentration.

8.4 Partial Factors

Different partial factors must be used for structures in a marine environment
and for structures subject to de-icing salt. The partial factors are given below.

8.4.1 Structures in a marine environment

The partial factors relevant for structures in a marine environment are given in
Table 8.8.

Cost of mitigation High Normal Low

of risk relative to
the cost of repair
∆x [mm] 20 14 8
γc cr
1.20 1.06 1.03

γc s , cl
1.70 1.40 1.20

γ R cl 3.25 2.35 1.50

Table 8.8: Partial factors for structures in a marine environment.

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8.4.2 Structures subject to de-icing salt

The partial factors relevant for structures subject to de-icing salt are given in
Table 8.9.

Cost of mitigation High Normal Low

of risk relative to
the cost of repair
∆x [mm] 16.0 12.0 6.0
γc cr
1.08 1.05 1.03

γc s
3.30 2.30 1.60

γR 2.85 2.00 1.25

Table 8.9: Partial factors for structures subject to de-icing salt.

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9 Carbonation, Initiation of Corrosion

Carbonation of concrete leads to a lowering of the pH value of the pore solu-
tion. This implies that the protective passivating layer covering the surface of
the reinforcement cannot be maintained. Corrosion is initiated when the so-
called carbonation front, i.e. the interface between carbonated and non-
carbonated concrete, reaches the reinforcement.

Once the carbonation front reaches the reinforcement a large number of small
corrosion cells are formed leading to a nearly uniform reduction of the cross-
section area of a given reinforcement bar.

9.1 Design Equation

The design equation, g , stating that corrosion is initiated when the carbonation
front reaches the reinforcement is given by

2 ⋅ c sd,ca ⋅ t
g = x d − x cd (t ) = x d − (9.1)
Rcad

where

xd Design value of the cover thickness

x cd Design value of the penetration depth of the carbonation
csd,ca Design value of the surface concentration
t Time
Rcad Design value of the carbonation resistance

The carbonation resistance can be determined on the basis of the so-called ef-
fective diffusion coefficient, Deff , and the binding capacity of the concrete, B ,
as

B 1
Rca = = (9.2)
Deff Dca

where Dca is the carbonation rate.

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9.2 Design Values

The design value of the cover thickness is found from

x d = x c − ∆x (9.3)

where ∆x is the margin for the cover thickness and x c is the characteristic
value of the cover thickness.

The design value of the effective resistance with respect to carbonation is found
from

R0c,ca
Rcad = c
(9.4)
2 nca
t 
k ec,ca ⋅ k cc,ca ⋅  0  ⋅ γ Rca
t 

where

R0c,ca Characteristic value of the carbonation resistance determined on the

basis of compliance tests
k cc,ca Characteristic value of the curing factor
k ec,ca Characteristic value of the environment factor
t0 The age of the concrete when the compliance test is performed
ncac Characteristic value of the age factor
γ Rca Partial factor for the resistance with respect to carbonation

By the evaluation of the design value of the carbonation resistance also the ef-
fect of the temperature should be taken into account.

Finally, the carbon dioxide surface concentration is not associated with a partial
factor, i.e. the design value is equal to the characteristic value.

9.3 Characteristic Values

9.3.1 Geometry
For all geometry variables, including the cover thickness, the characteristic
value is defined as the mean value or the nominal value determined through the
design process.

9.3.2 Material
For a given type of concrete, outcomes of the carbonation resistance must be
generated by the concrete producer using a standardised test method, i.e. the
Accelerated Carbonation Test (ACT) [6,7]. On the basis of these test results the

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characteristic value can be determined according to the methodology outlined

in Chapter 11.

9.3.3 Environment
The only variable, which depends solely on the environment, is the surface con-
centration of carbon dioxide, cs ,ca . The characteristic value of the surface con-
centration is

csc,ca = 5.0 ⋅ 10 −4 kg / m 3 (9.5)

For tunnels and other confined spaces the surface concentration may be higher.

9.3.4 Execution
In Table 9.1 the curing factor for the carbonation resistance is given for differ-
ent curing of the concrete.

Variable Condition Characteristic value Unit

k c ,ca 1 day curing 4.05 -
k c ,ca 3 days curing 2.10 -
k c ,ca 7 days curing 1.0 -
k c ,ca 28 days curing 0.76 -

Table 9.1: Curing factor for carbonation.

9.3.5 Variables depending on the Material and Environment

The environment factor, k e ,ca , depends on both the environment and the mate-
rial. For a number of different combinations of material and environment the
environment factor is given in Table 9.2.

Variable Condition Characteristic value Unit

k e ,ca OPC, Laboratory 65 % RH 1.0 -
k e ,ca OPC, Outdoor sheltered, 81 % RH 0.86 -
k e ,ca OPC, Outdoor unsheltered, 81 % RH 0.48 -
k e ,ca OPC+GGBS, Laboratory, 65 % RH 1.0 -
k e ,ca OPC+GGBS, Outdoor sheltered, 81 0.85 -
% RH
k e ,ca OPC+GGBS, Outdoor unsheltered, 0.50 -
81 % RH
Table 9.2: Characteristic values of the environment factor.
In section 8.3.5 concerning chloride ingress, a distinction between the effect of
environment and material was introduced, i.e.

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k e ,cl = k e ,0 ⋅ k e ,c

A similar distinction may be introduced here. However, as seen in Table 9.2:

Characteristic values of the environment factor. there seems to be little differ-
ence between OPC and GGBS.

In Table 9.3: Characteristic value of the age factor. the characteristic value of
the age factor is given for a number of different materials and environments.

Variable Condition Characteristic value Unit

nca OPC, Laboratory, 65 % RH 0 -
nca OPC, Outdoor sheltered, 81 % RH 0.098 -
nca OPC, Outdoor unsheltered, 81 % RH 0.40 -
nca OPC+GGBS, Laboratory, 65 % RH 0 -
nca OPC+GGBS, Outdoor sheltered, 81 0.132 -
% RH
nca OPC+GGBS, Outdoor unsheltered, 0.43 -
81 % RH
Table 9.3: Characteristic value of the age factor.

9.4 Partial Factors

The partial factors for durability design of structures subject to carbonation are
given in Table 9.4: Partial factors for structures subject to carbonation.

Cost of mitigation High Normal Low

of risk relative to
the cost of repair
∆x [mm] 20 14 8
γR 3.00 2.10 1.30

Table 9.4: Partial factors for structures subject to carbonation.

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10 Cracking and Spalling

Corrosion of the reinforcement leads to the formation of corrosion products
which occupies a larger volume than the original steel. This implies that the
concrete cover will crack and eventually spall. In the following design rules are
given which ensures that the probability of observing a crack with a critical
crack width larger than 1.0 mm is acceptable.

As mentioned in Chapter 6 spalling is assumed to occur when the crack width

exceeds the critical limit of 1.0 mm. However, is should be noted that this limit
does not represent an event where the concrete cover is lost. It represents a
situation where the concrete cover no longer can be considered to contribute to
the load carrying capacity of the structure.

10.1 Design Equation

It is required that the crack width, w , of a given structure must not exceed
some critical limit, wcr , i.e. the limit state can be written

g( x) = wcr − w d (10.1)

The design value of the actual crack width, w d , can be estimated on the basis
of the following expression determined by regression analysis

 w0 p d ≤ p0d
wd = 
 w0 + b ( p − p 0 )
d d d (10.2)
p d > p0d

where

w0 Width of the initial visible crack

bd The design value of a parameter depending on the position of the
bar
pd The design value of the corrosion penetration in microns
p0d The design value of the corrosion penetration necessary
to produce a crack in microns.

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The design value of the corrosion penetration, p0d , needed for initiation of a
crack can be determined on the basis of the following expression

xd
p = a1 + a 2
d
0 + a 3 f cd,sp (10.3)
d

where

a1 , a 2 , a 3 Regression parameters
xd Design value of the cover thickness
d Diameter of reinforcement bar
f cd,sp Design value of the splitting tensile strength in MPa.

The actual attack penetration, p d , can be determined as

 0 t ≤ t id
p = d
d

V wt (t − t i )
d (10.4)
t > t id

where

Vd The design value of the corrosion rate

wt The relative time of wetness
t id The design value of the time to initiation of corrosion.

10.2 Design Values

There are numerous parameters related with the concrete and the environment
which influence the corrosion rate. The most important factor affecting the cor-
rosion rate of depassivated reinforcement is the electrolytic resistivity of the
concrete. This is, in turn, influenced by the mix composition and the moisture
content of the concrete.

Andrade and Arteaga [21] have proposed a parametric equation relating corro-
sion rate and resistivity. The influence of other important factors such as the
nature of depassivating species (carbon dioxide, chlorides), macrogalvanic ef-
fects, formed rust and oxygen availability, are taken into account by introduc-
tion of a member of correction factors. In the proposal of Andrade and Arteaga
the moisture content is related to the corrosion rate (or alternatively to the resis-
tivity) by using average values for each of the exposure classes.

A supplementary approach, modelling the material and environmental influence

of the development of the electrolytic resistivity has been presented by Nilsson
and Gehlen [22], who propose as well a parametric expression for the resistiv-
ity itself. This parametric equation is based in the relative humidity, tempera-
ture and chloride content.

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In the present design guide the global approach of Andrade and Arteaga, sup-
plemented by the approach of Nilsson and Gehlen (parametric expression for
the electrolytic resistivity) has been chosen for demonstrating the practical ap-
plication.

Corrosion will only occur if sufficient oxygen and water is present. If these
conditions are not fulfilled the rate of corrosion can be assumed to be negligi-
ble. Otherwise, the design value of the corrosion rate is given by

m0
Vd = ⋅ α c ⋅ Fclc ⋅ γ V (10.5)
ρc

where

m0 Constant for corrosion rate versus resistivity

Fclc The characteristic value of the chloride corrosion rate factor
αc The characteristic value of the pitting factor
ρc The characteristic value of the resistivity
γV The partial factor for the corrosion rate

The characteristic value of the resistivity, ρ c , is given by

c
nres
 t hydr 
ρ = ρ ⋅
c c
0  ⋅ k cc,res ⋅ k Tc ,res ⋅ k RH
c
,res ⋅ k cl ,res
c
(10.6)
 t0 

where

ρ0c The characteristic value of the potential electrolytical resistivity

t0 The age of the concrete at the time when the compliance test is
performed
t hydr The age of the concrete, maximum value one year
c
nres The age factor for the electrolytical resistivity
c
k c ,res The characteristic value of the curing factor for the resistivity
c
k T ,res The characteristic value of the temperature factor for the resistivity
c
k RH ,res The characteristic value of the humidity factor for the resistivity
c
k cl ,res The characteristic value of the factor accounting for the presence
of chloride

The characteristic value of the temperature factor for the electrolytical resistiv-
ity is given by

1
k Tc ,res = (10.7)
1 + K ( T − 20)
c

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where K c is the characteristic value of a factor describing the temperature de-

pendency of the conductivity and T is the temperature in oC.

The design value of the cover thickness is given by

x d = x c − ∆x (10.8)

where the values of ∆x given in Table 4.6 are used in case of chloride-induced
corrosion and the values given in Table 5.4 are used if corrosion induced by
carbonation is considered.

The design value of the time to initiation of corrosion can be determined on the
basis of the expressions given in Chapter 4 and Chapter 5.

The design value of the parameter, b , depending on the location of the consid-
ered reinforcement bar is determined by

bd = bc ⋅ γ b (10.9)

where b d and b c are the design value and the characteristic value of the pa-
rameter, respectively, and γ b is the partial factor for b .

Finally, the design value of the splitting tensile strength is defined as the char-
acteristic value.

10.3 Characteristic Values

10.3.1 Geometry
The characteristic value is of the cover thickness is defined as the mean value,
i.e. the value determined through the design process.

10.3.2 Material
The potential electrolytical resistivity, ρ0 , acts as a resistance variable. Hence,
the characteristic value is defined as a 5% fractile of the predictive distribution.

For a given type of concrete outcomes of the potential electrolytical resistivity

must be generated by the concrete producer using a standardised test method,
i.e. the Two Electrode Method (TEM). On the basis of these test results the
characteristic value can be determined according to the methodology outlined
in Chapter 7.

The characteristic value of the splitting tensile strength is defined as a 5 % frac-

tile in accordance with the Eurocode 1 [23].

In Table 10.1: Characteristic values of the age factor. the age factor is given.

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Variable Condition Characteristic value Unit

nresR OPC 0.23 -
nresR GGBS 0.54 -
nresR PFA 0.62 -

Table 10.1: Characteristic values of the age factor.

10.3.3 Environment
The temperature and the relative humidity are defined as yearly mean values.
These can be determined using meteorological data relevant for the considered
location.

In Table 10.2, Table 10.3, Table 10.4, Table 10.5 and Table 10.6 the character-
istic values of the corrosion rate chloride factor, Fcl , the equivalent period of
wetness, wt , the temperature factor, K , the pitting factor, α , and the resistiv-
ity chloride factor, k cl ,res , respectively, are given.

Variable Condition Characteristic value Unit

Fcl With chloride 2.63 -
Fcl Without chloride 1.0 -

Table 10.2: Characteristic values of the corrosion rate chloride factor.

Variable Condition Characteristic value Unit
wt Dry 0 -
wt Moderate humidity, sheltered -
Airborne sea water 0.5
wt Cyclic wet-dry, unsheltered 0.75 -
wt Wet, rarely dry, tidal zone 1.0 -

Table 10.3: Characteristic values of the equivalent period of wetting.

Variable Condition Characteristic value Unit
K Temperatures below 20 oC 0.025 o -1
C
K Temperatures above 20 oC 0.073 o -1
C
Table 10.4: Characteristic values of the temperature factor.
Variable Condition Characteristic value Unit
α With chloride 9.28 -
α Without chloride 2.0 -
Table 10.5: Characteristic values of the pitting factor.
Variable Condition Characteristic value Unit
k cl ,res With chloride 0.72 -
k cl ,res Without chloride 1.0 -

Table 10.6: Characteristic values of the resistivity chloride factor.

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10.3.4 Execution
The characteristic value of the execution variable is given in Table 10.7.

Variable Condition Characteristic value Unit

k c ,res - 1.0 -

Table 10.7: Characteristic value of the curing factor.

10.3.5 Properties depending on the Material and Environment

The characteristic value of the humidity factor for the electrolytical resistivity is
given in Table 10.8 for a number of different types of binder and a number of
different environments.

Variable Condition Characteristic value Unit

k RH ,res Unsheltered 1.44 -
k RH ,res BFSC, 50 % RH 14.72 -
k RH ,res BFSC, 65 % RH 7.0 -
k RH ,res BFCS, 80 % RH 3.80 -
k RH ,res BFSC, 95 % RH 1.17 -
k RH ,res OPC, 50 % RH 7.58 -
k RH ,res OPC, 65 % RH 6.45 -
k RH ,res OPC, 80 % RH 3.18 -
k RH ,res OPC, 90 % RH 1.08 -
k RH ,res Submerged, tidal and splash 1.0 -

Table 10.8. Characteristic values of the humidity factor.

10.3.6 Other variables

In Table 10.9 the characteristic values of a number of other variables are given.

Variable Condition Characteristic value Unit

w0 - 0.05 [mm]
wcr - 1.0 [mm]
a1 - 74.4 [µm]
a2 - 7.3 [µm]
a3 - -17.4 [µm/MPa]
b Top 0.0086 [mm/µm]
b Bottom 0.0104 [mm/µm]
m0 - 882 [µm⋅Ωm/year]

Table 10.9: Characteristic values of other variables.

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10.4 Partial Factors

10.4.1 Chloride-induced corrosion, pitting corrosion

In Table 10.10 the partial factors relevant for chloride-induced corrosion are
given. All partial factors are equal to one because the propagation phase con-
tributes little to the service life of the structure.

Cost of mitigation High Normal Low

of risk relative to
the cost of repair
γb 1.0 1.0 1.0

γV 1.0 1.0 1.0

Table 10.10: Partial factors for chloride-induced corrosion.

10.4.2 Carbonation-induced corrosion, general corrosion

In Table 10.11 the partial factors for general corrosion are given.

Cost of mitigation High Normal Low

of risk relative to
the cost of repair
γb 1.55 1.40 1.30

γV 1.50 1.40 1.30

Table 10.11: Partial factors for general corrosion.

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11 Examples
In the following, two examples are given in order to show the calculations of
the design of elements of a structure with regard to durability.

11.1 Chloride ingress

The first example regards the design of a column exposed to chloride being
situated in a tidal zone in an environment with a temperature of 8 °C and a rela-
tive humidity of 80 %. The cost of repair is high compared to the cost of design
and construction. This implies a safety index of β t = 3.72.

The size of the concrete cover together with the resistance and thereby the po-
tential electrolytical resistivity of the concrete are to be determined. Moreover
the characteristic value of the tensile strength of the concrete must be stated but
this parameter is normally specified in the structural design.

In this case, it is chosen to specify the resistance and the potential electrolytical
resistivity of the concrete beforehand in order to determine the size of the con-
crete cover. This is easily done by assessing the cover thickness, then to calcu-
late the time to initiation of corrosion. Using this time in the calculations re-
garding spalling, the actual crack width which has to be compared with the
crack width resulting in spalling is calculated.

First, the time to initiation of corrosion is determined from (rewritten from eq.
(4.1))

1
  
−2
 1− nclc
2 cc 1 R0c,cl
t i =  c
d
⋅ erf −1 1 − cr ⋅ c  ⋅ 
 x − ∆x  γ c AC ⋅ w ⋅ γ c  c
k ec,cl ⋅ k cc,cl ⋅ t 0ncl ⋅ γ Rcl 
  cr s , cl b s , cl  

(11.1)

where

- the characteristic value of the critical chloride concentration: ccrc = 0.9 % rela-
tive to binder

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- the partial factor for the critical chloride concentration: γ ccr = 1.2

- the characteristic value of the regression parameter describing the relation be-
tween the chloride surface concentration and the water-binder ratio: ACs ,cl =
7.76 % relative to binder

- the water-binder ratio: w

b
= 0.3 (specified)

- the partial factor for the surface chloride concentration: γ cs ,cl = 1.7

- the characteristic value of the concrete cover: x c = 67 mm (calibrated)

- the margin for the concrete cover: ∆x = 20 mm

year
- the characteristic value of the resistance: R0c,cl = 0.01585 (correspond-
mm 2
m2
ing to D c0,cl = 2 ⋅ 10 −12 ) (specified)
s

- the characteristic value of the environment factor: k ec,cl = 0.92

- the characteristic value of the curing factor: k cc,cl = 0.79

- the age of the concrete when the compliance test is performed: t 0 = 0.0767
years (corresponding to 28 days)

- the characteristic value of the age factor: nclc = 0.37

- the partial factor for the resistance: γ Rcl = 3.25

The time to initiation of corrosion is found to be

1
 2 −1  0.9 1 
−2
0.01585  1−0.37
t i = 
d
erf 1 − ⋅   
 67 − 20  1.2 7.76 ⋅ 0.3 ⋅ 1.7   0.92 ⋅ 0.79 ⋅ 0.0767 ⋅ 3.25 
0.37

⇔ t id = 45.9 years

Secondly, the critical crack width to induce spalling is determined.

The characteristic value of the temperature factor for the electrolytical resistiv-
ity is given by eq. (10.7)

1
k Tc ,res = (11.2)
1 + K ( T − 20)
c

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where

- the temperature: T = 8 °C

- the characteristic value of the temperature dependency of the conductivity:

K c = 0.025 ° C −1

This gives a value of

1
k Tc ,res = = 1.43
1 + 0.025 ⋅ (8 − 20)

The characteristic value of the resistivity is found from eq. (6.6)

nresR
 thydr 
ρ c = ρ0c ⋅   ⋅ k cc,res ⋅ k Tc ,res ⋅ k RH
c
,res ⋅ k cl ,res
c
(11.3)
 t0 

where

- the characteristic value of the potential electrolytical resistivity: ρ 0c = 475 Ωm

(found from Dclc ,0 / specified)

- the age of the concrete: t hydr = 1 year

c
- the characteristic value of the age factor for the resistivity: nresR = 0.23

- the characteristic value of the curing factor for the resistivity: k cc,res = 1.0

c
- the characteristic value of the humidity factor for the resistivity: k RH ,res = 1.0

- the characteristic value of the factor accounting for the presence of chloride:
k clc ,res = 0.72

The characteristic value of the resistivity can then be calculated to

0.23
ρ c = 475 ⋅ 
1 
 ⋅ 10
. ⋅ 143
. ⋅ 10
. ⋅ 0.72 = 882.8 Ωm
 0.0767 

The corrosion rate is found from eq. (6.5)

m0
Vd = ⋅ α ⋅ Fclc ⋅ γ V (11.4)
ρ c

where

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µm ⋅ Ωm
- the constant for corrosion rate versus resistivity: m0 = 882
year

- the pitting factor: α = 9.28

- the characteristic value of the chloride corrosion rate factor: Fclc = 2.63

- the partial factor for the corrosion rate: γ V = 1.0

The corrosion rate is calculated to

882 µm
Vd = ⋅ 9.28 ⋅ 2.63 ⋅ 10
. = 24.4
882.8 year

The actual attack penetration is determined from eq. (6.4)

(
p d = V d ⋅ wt ⋅ t − t id ) (11.5)

where

- the relative time of wetness: wt = 1.0

- the design service life time: t = 50 years

This gives a value of

p d = 24.4 ⋅ 10 ⋅ (50 − 45.9) = 101.0 µm

The design value of the attack penetration needed for crack initiation is found
by eq. (6.3)

x c − ∆x
p0d = a1 + a 2 + a 3 f cd,sp (11.6)
d

where

- the regression parameter: a1 = 74.4 µm

- the regression parameter: a 2 = 7.3 µm

µm ⋅ mm 2
- the regression parameter: a 3 = -17.4
N

- the diameter of the reinforcement bars: d = 6.0 mm (found by the structural

design)

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N
- the design value of the splitting tensile strength: f cd, sp = 2.61 (found by
mm 2
the structural design)

The design value of the attack penetration needed for crack initiation is calcu-
lated to

69 − 20
p0d = 74.4 + 7.3 ⋅ − 17.4 ⋅ 2.61 = 88.6 µm
6.0

Since p d > p0d , the actual crack width can be estimated from eq. (10.2)

(
w d = w0 + b c ⋅ γ b ⋅ p d − p0d ) (11.7)

where

- the width of the initial visible crack: w0 = 0.05 mm

- the constant parameter depending on the position of the bar: b c = 0.0086

mm
µm

- the partial factor for the constant parameter depending on the position of the
bar: γ b = 1.0

The actual crack width can be determined to

w d = 0.05 + 0.0086 ⋅ 1.0 ⋅ (101.0 − 88.6) = 0.18 mm

It is seen that the actual crack width is less than the critical crack width induc-
ing spalling of 1 mm after 50 years.

Since the cover thickness is always given as a multiple of 5 mm, the cover will
be specified to be 70 mm.

11.2 Carbonation
The second example also concerns a column placed in an environment with a
temperature of 8 °C and a relative humidity of 80 % but situated outdoors and
sheltered. The column is designed with regard to carbonation. The cost of re-
pair is normal compared to the cost of design.

The size of the concrete cover together with the resistance and the potential
electrolytical resistivity of the concrete are to be determined. Moreover the
characteristic value of the tensile strength of the concrete must be specified but
this parameter is normally specified from the structural design.

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In this case, it is chosen to specify the resistance and the potential electrolytical
resistivity of the concrete beforehand in order to determine the size of the con-
crete cover. This is easily done by assessing the cover thickness, then to calcu-
late the time to initiation of corrosion. Using this time in the calculations re-
garding spalling, the actual crack width which has to be compared with the
crack width resulting in spalling is calculated.

First, the time to initiation of corrosion is determined from (rewritten from eq.
(5.1))

ti =
d

 ( 2
)
x c − ∆x ⋅ R0c,ca  1− 2 ncac
 (11.8)
 2 ⋅ c c ⋅ k c ⋅ k c ⋅ t 2 ncac ⋅ γ 
 s , ca e ,ca c ,ca 0 Dca 

where

- the characteristic value of the concrete cover: x c = 29 mm (calibrated)

- the margin for the concrete cover: ∆x = 20 mm

kg
- the characteristic value of the surface concentration: csc,ca = 5.0 ⋅ 10 − 4
m3

- the characteristic value of the resistance with respect to carbonation deter-

kg
year ⋅ 3
mined on the basis of compliance tests: R0c,ca = 2.114⋅10-4 m (corre-
mm 2
m2
sponding to D0,c ca = 15 ⋅ 10 −11 ) (specified)
kg
s⋅ 3
m

- the characteristic value of the environment factor: k ec,ca = 0.86

- the characteristic value of the curing factor: k cc,ca = 0.76

c
- the characteristic value of the age factor: nca = 0.098

- the partial factor for the resistance: γ Rca = 3.0

The time to initiation of corrosion is found to be

1


ti = 
d (29 − 20 ) ⋅ 2.114 ⋅ 10 − 4
2
 1− 2⋅0.098

2 ⋅ 5 . 0 ⋅ 10 −4
⋅ 0 . 86 ⋅ 0 . 76 ⋅ 0 . 0767 2⋅0.098
⋅ 3 . 0 
 

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⇔ t id = 27.7 years

Secondly, the critical crack width to induce spalling is determined.

The characteristic value of the temperature factor for the electrolytical resistiv-
ity is given by eq. (10.2) which gives a value of

1
k Tc ,res = = 1.43
1 + 0.025 ⋅ (8 − 20)

The characteristic value of the resistivity is found from eq. (11.3) where

- the characteristic value of the potential electrolytical resistivity: ρ 0c = 57 Ωm

(selected)

c
- the characteristic value of the humidity factor for the resistivity: k RH ,res = 3.18

- the characteristic value of the factor accounting for the presence of chloride:
k clc ,res = 1.0

The characteristic value of the resistivity can then be calculated to

0.23
ρ = 57 ⋅ 
1 
c
 ⋅ 10
. ⋅ 1.43 ⋅ 318 . = 467.9 Ωm
. ⋅ 10
 0.0767 

The corrosion rate is found from eq. (11.4) where

- the pitting factor: α = 2.0

- the characteristic value of the chloride corrosion rate factor: Fclc = 1.0

- the partial factor for the corrosion rate: γ V = 1.50

The corrosion rate is calculated to

882 µm
Vd = ⋅ 2.0 ⋅ 1.0 ⋅ 1.5 = 5.66
467.9 year

The actual attack penetration is determined from eq. (10.5) where

- the relative time of wetness: wt = 0.5

This gives a value of

p d = 5.66 ⋅ 0.5 ⋅ (50 − 27.7 ) = 63.1 µm

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The design value of the attack penetration needed for crack initiation is found
by eq. (10.6) where

- the diameter of the reinforcement bars: d = 6.0 mm (found by the structural

design)

N
- the design value of the splitting tensile strength: f cd, sp = 2.61 (found by
mm 2
the structural design)

The design value of the attack penetration needed for crack initiation is calcu-
lated to

29.0 − 20
p 0d = 74.4 + 7.3 ⋅ − 17.4 ⋅ 2.61 = 40.0 µm
6.0

Since p d > p0d , the actual crack width can be estimated from eq. (11.7) where

- the partial factor for the constant parameter depending on the position of the
bar: γ b = 1.55

The actual crack width can be determined to

w d = 0.05 + 0.0086 ⋅ 1.55 ⋅ (63.1 − 40.0) = 0.36 mm

It is seen that the actual crack width is less than the critical crack width induc-
ing spalling of 1 mm after 50 years.

Since the cover thickness is always given as a multiple of 5 mm, the cover will
be specified to be 30 mm.

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12 Quality Assurance

12.1 General
This chapter is concerned with the quality assurance in the design and construc-
tion phase and is consequently applied only for new structures.

A proper and sensible quality control concept is in general useful to extent the
service life of a given concrete structure. This is due to the fact that the quality
control is a useful tool to determine the random variation of the considered
variables and to reduce the statistical uncertainty related to the parameters de-
scribing the distribution of the considered variable. Further information can be
found in the Sub-Task Report [35].

Quality control is mainly performed in order to control the variation of the ma-
terial parameters

• Carbonation resistance, R0,ca

• Rapid Chloride Migration Resistance, R0,cl

• Electrolytic Resistivity, ρ0

Th real performance of concrete with regard to the related deterioration mecha-

nism is checked on different QC-levels to get representative values for the de-
sign. The amount and the detailing of the testing will affect the scatter of the
material parameters. As the level of quality control increases the amount of in-
formation about the controlled variables increase and a more accurate model
can be produced, implying that the partial safety factors for the given variables
may be reduced.

Not only the material parameters of the selected deterioration models are af-
fected by quality assurance, but also the geometrical variable

• Concrete Cover, x

For example, the application of already existing directives with regard to con-
crete cover will lead to a considerable reduction of the random variation of the
cover thickness. By a proper quality control of the production process, espe-

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cially in the case of pre-cast reinforced concrete elements, it will be important

not only in which way the chosen production process will influence the varia-
tion, but also to what extent the type of distribution and its parameters are af-
fected.

Finally, the execution and its influence on the material parameters itself may be
controlled.

• Curing factors, k c ,cl , k c ,ca and k c ,res

Unfortunately, it has been hard to report sufficient data concerning this variable
[22,24]. Too many curing methods are in principle applicable. Only a rough
consideration in dependency on the curing period was performed, mainly based
on laboratory data, covering concrete ages up to 2 years [24]. Therefore, these
variables should be updated in the near future mainly to consider the influence
of age and the influence of taken material upon the curing factors. The curing
factors are not treated in more detail in the following sections.

12.2 Quality Control Concept

The economic design of durable structures requires that performance with the
specifications set out in the design process is checked at the various stages of
the concrete production process. This is covered by a quality control concept.
This concept is illustrated in Figure 12.1.

Quality level 3: To be defined by the designer

Quality parameters required in the
structure, e.g. D ca To be guaranteed by the contractor

To be included in QM systems and QC schemes

Requirements for
To be fulfilled by the contractor
execution and curing Performance tests for D ca

Quality level 2:
To be defined by the designer
Quality parameter of the concrete
(potential quality), e.g. D 0,ca To be guaranteed and checked by the
contractor/ready mixer

Interrelation between cement

To be applied in the design
and concrete properties

Quality level 1:
To be defined by the designer
Quality parameter of the cement
To be guaranteed and checked by the cement
producer

Figure 12.1: Quality control concept.

Quality level 1 includes the testing of constituent materials. Cements or binders
are classified in regard to their potential resistance R0. The cement producer
uses an appropriate standard compliance test in order to check the potential ma-

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Final Technical Report 71

terial resistance against deterioration (the quality parameter of the cement-

quality level 1). These tests are carried out on standard mortar specimens.

The influence and interaction of the various concrete compositional parameters

are considered to estimate the potential quality of the concrete mix used. This
task constitutes an important part to the compliance test procedure. The quality
of the concrete supplied is checked against the design requirements using ap-
propriate compliance tests (e.g. R0,ca - quality level 2).

Finally, suitable in-situ tests are applied on the structure to verify the actual
quality of the concrete achieved (e.g. R0,ca - quality level 3).

Testing according to quality levels 1 and 2 is normally conducted under stan-

dardised conditions, which are carefully controlled, measured and documented.
In-situ test results (quality level 3) will inevitably be influenced by the micro-
environment, i.e. the environmental factors k e ,cl or k e ,ca , and the applied exe-
cution, i.e. the curing factors k c ,cl , k c ,ca and k c ,res .

12.3 Material Variables

12.3.1 General Considerations

In the following sections it will be described how the material variables are in-
fluenced by the applied quality control levels 1 to 3.

The compliance tests referred to here are not described in this report. Detailed
descriptions of the compliance tests can be found in [7].

• Carbonation resistance, R0,ca : Accelerated Carbonation Test

• Rapid Chloride Migration Resistance, R0,cl : Rapid Chloride Migration Test

• Electrolytic Resistivity, ρ0 : Two Electrode Method Test

12.3.2 Material Classification

It is recommended to classify the material at the quality levels 1 and 2. To fa-
cilitate the control of the material compliance and to facilitate the evaluation of
characteristic values of the material variables, it is proposed to create a material
classification for each material variable of the deterioration models.

The classifications with regard to the carbonation resistance, the chloride resis-
tance and the potential resistivity are given in Table 12.1, Table 12.2 and Table
12.3, respectively.

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Classification Material Variable:

Rca
5 % fractile

[109 (kgCO2/m3)/(m2/s)]

CAR-1 1

CAR-5 5

CAR-10 10

CAR-50 50

CAR-100 100

Table 12.1: Classification with respect to the carbonation resistance.

Classification Material Variable:

R0
5 % fractile

[1010 s/m2]

CHL-1 1

CHL-5 5

CHL-10 10

CHL-50 50

CHL-100 100

Table 12.2: Classification with respect to the chloride resistance.

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Classification Material Variable:

ρ0
5 % fractile

[Ωm]

COR-10 10

COR-50 50

COR-100 100

COR-500 500

COR-1000 1000

Table 12.3: Classification with respect to the potential resistivity.

For carbonation and chloride ingress it must for a given class be confirmed by
testing at the relevant quality levels that no more than 5 % of the measurements
are below the characteristic values, R0c,ca and R0c,cl . For the potential resistivity,
ρ0 , the tests have to confirm that the probability of outcomes of ρ0 less than
the characteristic value, ρ0c , is 5 %.

The following acceptance criteria must be fulfilled. These acceptance criteria

are developed using the fact that R0,ca , R0,cl and ρ0 are modelled as normally
distributed variables and that the characteristic values are defined as the 5 %
fractile of the predictive distribution according to Eurocode 1 [23].

Having performed n experiments for the evaluation of the characteristic value

of the material parameter, f , the empirical mean value, m , and the empirical
standard deviation, s , can be determined by

1 n 
m = ∑ fi 
n i =1
 (12.1)
1
s2 =
n −1
( f i − m)
2 


where f i is the outcome of the ith observation of f .

If the characteristic value is defined as a 5 % fractile it can be determined from

f c = m − kn s (12.2)

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where k n is a factor which depends on the number of observations. The "true"

value of the standard deviation of f may be known from prior experiments. In
that case a lower value of k n may be used.

The values of k n as a function of n are given in Table 12.4 where σ denotes

the "true" value of the standard deviation of f .

n 1 2 3 4 5 6 8 10 20 30 ∞

Known σ 2.31 2.01 1.89 1.83 1.80 1.77 1.74 1.72 1.68 1.67 1.64

Unknown σ - - 3.37 2.63 2.33 2.18 2.00 1.92 1.76 1.73 1.64

Table 12.4: Values of k n for the 5 % characteristic value

In appendix A, the standard deviations of the carbonation diffusion coefficient,
the chloride diffusion coefficient and the potential resistivity are given for a
number of different types of concrete.

The performance of a given concrete with respect to carbonation, chloride in-

gress and electrolytical resistivity can be determined on the basis of a number
of different test methods. Within the DuraCrete project a number of different
compliance tests have been investigated to determine the relations between the
results obtained using these different test methods. The results of these investi-
gations can be used if other test methods than the ones given here have been
used. See [5,6,7] for a more detailed description.

12.4 Geometrical Variable: Concrete Cover Thickness

The achieved concrete cover of reinforced concrete structures is a result of sev-
eral influences in all phases of the construction process. For overview purposes
the following problematic items of the construction process are identified:

− designing and planning phase (e.g. measures in order to avoid gross errors in
designing concrete covers, to avoid misinterpretations of drawings,...)

− execution phase (e.g. measures in order to install and keep the designed po-
sition of the reinforcement and the form work (dimensional stability),...)

Summarising all influences of the whole planning and execution process, which
lead to considerable variations of the achieved concrete cover, it was concluded
in [24], that the statistical quantities of the concrete cover can simplified be de-
scribed by the following distribution, Table 12.5.

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Variable Unit Distribution Type Mean Value CoV in [%]

xc Mm LN Nominal 30

Table 12.5: Statistical quantities of the parameter concrete cover xc which is

part of the proposed carbonation and chloride penetration model
In order to assess the effect of quality assurance and quality control on the
achievable reduction in coefficient of variation, the historically grown German
directive with regard to concrete cover - Merkblatt Betondeckung - was evalu-
ated in order to correlate taken measures and later on taken modifications of the
already taken measures with afterwards achieved statistical quantities of the
concrete cover.

Several issues [25], [26], [27] of the German directive - Merkblatt Beton-
deckung - were studied. Afterwards, published field observations were studied
to derive the achieved statistical quantities of the stochastic variable concrete
cover in order to judge the improvements in reducing the coefficient of varia-
tion of concrete cover in dependency on the just relevant issue of the - Merk-
blatt Betondeckung. But not every quality control measure can be assigned to a
certain reduction of the standard deviation. Only the introduced catalogue of
measures can be judged as a whole.

Based on the assumption that the stochastic variable concrete cover is Beta dis-
tributed (a = 0 mm, b = half of the structure thickness ≤ 200 mm), it was con-
firmed by various field observations [28], [29] that with each coming into effect
Merkblatt Betondeckung the standard deviation has been decreased, (Table
12.6).

Variable Unit DistributionType Mean StdDev Source

xc,0 mm LN Nominal CoV = 30 % [1]

xc,MB-10/82 mm Beta Nominal No indications [MB, issue 10/82]

xc,MB-03/91 mm Beta Nominal 9.1 [MB, issue 03/91]

xc,MB-01/97 mm Beta Nominal 7.8 [MB, issue 01/97]

Table 12.6: Statistical quantities of the parameter concrete cover xc which is

part of the proposed carbonation and chloride penetration model
For overview purposes distribution plots for a nominal concrete cover of
xc = 35 mm are given below, Figure 12.2.

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76 Final Technical Report

Figure 12.2: Statistical quantities of a nominal concrete cover of xc = 35 mm,

executed under consideration of diverse issues of the German di-
rective - Merkblatt Betondeckung
The Merkblatt Betondeckung 10/82 [25] suggests a catalogue of measures,
which considers the most common faults and most important problems in prac-
tice. The directives of 03/91 [26] and 01/97 [27] always include the previously
suggested measures and supplement the prior directive by adding further as-
pects.

In order to provide the reader with the impression of the introduced and con-
stantly revised catalogue of measures of the directive, the following extracted
items were identified as most decisive. Following the historically grown Merk-
blatt Betondeckung the below reported items, felt to be most important, were
formulated more and more detailed. In particular:

During the phase of the planning a careful documentation is of great impor-

tance in order to provide the construction side with correct and clear instruc-
tions. Therefore, the nominal value should be as well part of the drawings as
other values (i.e. measures of the form work, exact location of built-in units,
type and size of spacer,...). Furthermore, the designer should not only give clear
instructions for the bending procedure but also provide sufficient information in
order to facilitate in-situ quality control.

On the construction side the bending procedure has to be controlled carefully.

Especially an early testing of the already bent bars (each position), concerning
aspects as, for example, the bending dimension, is necessary. During the con-
struction phase a great importance lies in the stiffness of the reinforcement
structure to prevent a bending and a movement of the rebars during construc-
tion and the concrete placing. Especially the extensive installation of bar spac-
ers, which have to be sufficiently load bearing and safe against tilting is of great

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importance. A decisive factor concerning the protection and securing of the po-
sition is the use of working planks, supporting cages and stirrups.

But not only detailed prescriptions in execution, but also considered quality
control measurements, as there are

− the introduction of prescribed acceptance tests in order to control already

bent rebars and

− the introduction of an final examination of the complete structure that the

reinforcement has been installed and kept correctly at the designed position,

− are responsible for the reduction in coefficient of variation (standard devia-

tion).

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13 Assessment and Redesign

Throughout the service life of concrete structures in aggressive environments
inspections and measurements are conducted in order to assess the condition of
the structure and to verify that the reliability of the structure with respect to a
number of different events is acceptable. In the following sections it is shown
how the information gained from such inspections and measurements can be
used to update the reliability of the considered structure.

The procedure aims to give rules and guidance for the assessment and redesign
of existing concrete structures. Further information can be found in [30].

The procedure presented in the following is to a large extent based on the work
performed by ISO/TC98/SC2/WG6 and presented in the Working Draft of the
ISO Standard for "Assessment of existing structures" [31].

13.1 Objective of the reassessment

According to the Working Draft of the ISO Standard for "assessment of exist-
ing structures" [31] in combination with the standard practice with design of
concrete structures, the objective of the assessment of an existing structure shall
be based on the following performance requirements.

1. Safety performance level, which provides appropriate safety for the users of
the structure, i.e. the ultimate limit state.

2. Ultimate performance level, which provides adequate reliability with re-

spect to economical losses.

3. Continued function performance level, which provides continued function

for special structures such as hospitals, communications buildings or key
bridges, in the event of an earthquake, impact or other foreseen hazard.

4. Special performance requirements of the client related to property protec-

tion or serviceability and serviceability requirements for the users.

Usually the requirements to the safety performance level is also sufficient to

ensure the ultimate performance level. Further, requirements to the continued
function performance level is only valid for special structures and is not treated
here. Hence, the objective of an assessment is to prove that a given existing

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structure has an acceptable safety performance level and that it durably fulfils
the performance requirements of the client.

13.2 Acceptance criteria for reassessment

Acceptance criteria for the ultimate limit state can e.g. be found in NKB [32],
in the Working Draft of the ISO Standard for "assessment of existing struc-
tures" [31] and in the Eurocode 1 [23]. Here acceptance criteria is given for the
ultimate limit state and serviceability limit states for different reference periods.
However, as mentioned in Chapter 3.2 the acceptance criteria usually depend
on the probabilistic model on the basis of which the reliability analysis is per-
formed.

The acceptance criteria for the ultimate limit state relevant for a given structure
is here defined as the reliability obtained by a similar structure dimensioned to
the limit according to a valid system of codes as e.g. the EuroCodes. A struc-
ture dimensioned to the limit is a structure where the resistance is equal to the
load. Naturally, the acceptance criteria must be determined using the same
probabilistic model as for the reliability analysis of the considered structure.

To ensure that the safety of the user does not depend on the age of the structure
or the required service life of the structure, the acceptance criteria relevant for
the ultimate limit state should be given in terms of a yearly failure rate and in
term of the failure probability within the reference period (design service life).

If the special performance requirements have no influence on the load carrying

capacity of the structure the acceptance criteria relevant for these requirements
can be determined on the basis of life cycle cost. For further detail see Appen-
dix C and Chapter 3.2.

13.3 General framework for reassessment

In Figure 13.1 the general framework for reassessment as defined in the Work-
ing Draft of the ISO Standard for "assessment of existing structures" [31] is
shown.

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Requests/Needs

Definition of the objectives of the assessment

Scenarios

Preliminary assessment
- Study of documents
- Preliminary inspection
- Preliminary checks
- Decision on immediate actions if necessary Periodical inspection
Maintenance
no
Detailed assessment

yes
Detailed documentary search and review
Detailed inspection and material testing
Determination of actions
Measurement of response
Durability analysis
Target reliability and verification

yes
Further inspection

no
Report

Judgement and decision

yes
Sufficient reliability

no
Intervention

Construction Operation
− Repair − Intensified
- Rehabilitation monitoring
− Upgrading − Change of use
− Demolition

Figure 13.1: General flow of assessment of existing structures.

The first step is to define the objective of the assessment in terms of the re-
quired future performance of the considered structure. Further, the scenarios
leading to an unacceptable state of the structure should be identified.

The preliminary assessment has the aim to remove existing doubts using fairly
simple methods such as:

• visual inspection (qualitative inspection) of the structure in order to judge

its actual condition; special attention is paid to the critical parts of the struc-
ture (critical components, etc.);

• review of existing documentation (drawings, calculations, applied codes,

etc.);

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• compatibility with new codes (comparison between current safety criteria

and design criteria, qualitative conclusions,...);

• evaluation of possible changes during the passed lifetime (new loads,...);

• simplified assessment of actual condition of the structure: this can be done

by a simple assessment of

• the age of the structure;

• the condition of the structure;
• the configuration of the structure and its foundation;
• loading modifications (change of use,...);
• modifications in the structural system (supports, ...);

The inspection of the object in question is extremely important. Amongst other

things the aim is the recognition of typical hazard scenarios, which could en-
danger the structure's residual service life. Further, it is a question of detecting
defects and damage due to excessive loading and deterioration. As soon as
there is some evidence of danger to humans or the environment, protective
measures have to be implemented straightaway.

In studying the available documents, an attempt must be made to gain a deep

insight into the original situation: which aims were followed, which construc-
tion methods and which construction materials were used? What was the eco-
nomic and organisational climate? Was the work affected by pressure to meet
deadlines or due to low price? Such parameters can be called quality indicators.
A study of the static analysis, in addition, provides useful information about
codes, calculation and design methods. At the same time it also shows where
there are reserves of strength which, according to the present state-of-the-art,
could be exploited. The same is also true for the loads. Based on this informa-
tion any doubts about the safety of the structure can be confirmed or dismissed.

All the information gained in the preliminary assessment is summarised in a

report for the owner. If the doubts that led to the commission being undertaken
cannot be overcome in the course of the preliminary assessment, further inves-
tigations must be undertaken in a detailed assessment.

The following tasks are performed in case it is decided to proceed to a more

detailed assessment

• site investigation including quantitative inspections: corrosion, r.c. amount,

deformations, crack dimensions; here, in addition, a specialist firm or
agency or individual experts may have to be called in

• updating of information gained through inspection by using statistical pro-

cedures; structural investigations using updated information are typical of
detailed assessment. It is sensible and cost-effective to build upon the
knowledge gained and on the questions remaining from the preliminary as-
sessment and to compile a list of points requiring further investigation and

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thereby to specify what still needs to be checked. The thoroughly prepared

investigation should be closely supervised by the consulting engineer.

• detailed structural analysis based on conventional or advanced tools, ac-

cording to the problem at hand using limit state analysis, considering non
linear material behaviour, redundancy of the structure, etc.

• reliability analysis to determine the safety of the structure or the probability

of failure of the structure or of its most critical components.

The additional information gained from the investigations can be introduced

into confirmatory calculations with the aim of finally dispelling or confirming
any doubts as to whether the structure is safe – still well aware of the subjective
character of this decision.

All results of the detailed assessment are summarised in a report, which is

handed over to the owner. In particular, the report contains all necessary infor-
mation on the structural safety of the investigated structure and conclusions re-
garding repair and/or future maintenance.

If the reliability is inadequate an intervention is necessary. An acceptable level

of reliability can be obtained by performing a repair or rehabilitation of the
structure or it may prove to be most economic to demolish the structure. Alter-
natively, an acceptable level of reliability may be obtained simply by changing
the use of the structure or by performing an intensified monitoring. Decisions
concerning repair and rehabilitation should be taken on the basis of information
concerning the efficiency of the applied repair methods. For details on various
repair methods, see Chapter 9.

13.4 Reliability Updating

In the assessment of the structural safety of an existing structure several parties
might be involved, each of them contributing with, or requiring, different types
of information. The final decision is gradually reached by pooling all these as-
pects into one.

The aforementioned contributions come from:

• Design: the information relevant to this aspect is generally obtained from

reports, existing drawings etc.

• Field experience: the experience acquired during operation improves the

knowledge on the real behaviour of the structure. Data may be obtained
from monitoring, inspections, etc.

• Requalification analysis: at this stage information obtained from both the

design documentation and the field experience are critically reviewed and
updated and then used to estimate the new conditions of the structure.

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• Economical analysis: the potential consequences in terms of direct or indi-

rect costs are evaluated.

The above listed contributions lead to the collection of information that are of
very diverse nature, e.g. in terms of type of data and category of per-
sons/deciders who provide them. Therefore the evaluation of such information
becomes very important.

Inspection is an investigation intended to update the knowledge about the pre-

sent condition of the structure. Related to inspections typically two types of
interrelated decisions have to be made:

• What inspections shall be performed? For example which are the parame-
ters to be inspected, how many samples and when shall be taken, what are
the techniques to be used.

• What to do with the inspection results? For example type of measures to be

taken (repair, strengthening, etc), development of an inspection plan.

Inspections can be of various types:

• visual
• direct measurement
• non destructive testing
• response measurements
• proof load

A starting point should be that all available data is of value: all information can
lead to a better estimate of the structural capacity and to a reduction of the uncer-
tainties. In principle one should combine all information: visual observations, per-
formance in the past, measurements of various kinds and so on. From a theoretical
point of view, probabilistic methods offer an ideal framework for such a proce-
dure.

Note that the conclusions of an inspection should not only be concerned with the
structure or structural part under consideration. Inspection of one part of a structure
always tells something about other parts which are in similar circumstances. Find-
ing a bad concrete quality in one column may increase the probability of finding a
bad concrete in another one.

In order to use information from tests and measurements, the accuracy of the in-
spection method should be known. This is a weak point in the present state of the
art. There is a great variety of inspection techniques, but only in a limited number
of cases (for instance crack detection in offshore structures) investigations have
been done into the so called probability of detection curves and into the quantifica-
tion of measurement errors. For further details on the accuracy related to different
inspection and measurement methods as well as the probability of detection, the
reader is referred to Chapter 13.

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When assessing a structure all available information about the properties and
behaviour of the structure can lead to a more accurate estimate of the structural
capacity and to a reduction of the uncertainties. In principle, it does not matter
whether the information is quantitative or qualitative. Formal reliability as-
sessment, however, requires a quantitative type of statement as a starting point
for further processing.

Qualitative statements like “the bridge looks fine” should therefore be trans-
lated into quantitative statements like: no cracking of concrete, no sign of cor-
rosion and so on. If one also knows, from other experiments, what the threshold
values are for observing visual cracks and corrosion, these statements can be
used in the formal procedure.

The information for a reliability updating can be given as

• qualitative inspection: this type of information is related to the observation

of parameters such as surface characteristics, visible deformations, cracks,
spalling, corrosion etc. The description of possible damage of the structure
will be in qualitative terms like: no damage, minor damage, moderate dam-
age, severe damage etc. The ranges of each category shall be thereby speci-
fied. However it is possible and sometimes necessary to process the obser-
vation in a more formal way. In this case the updating can be performed by
direct updating as shown in Appendix D.

• quantitative inspection: this type of information results in a set of values of

parameters that characterise the condition of the structural elements. Exam-
ples of such condition parameters are: crack depth and length, corrosion
area and depth, displacements, residual stresses, damping, eccentricities etc.
This is done by Bayesian statistics as demonstrated in Appendix D.

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14 Inspection, Maintenance and Repair

According to the methodology for assessment and redesign given in Chapter 12
the reliability of a given structure can be assessed on the basis of information
obtained through inspections and measurements. Further, if the assessment fails
to prove that the reliability of the structure is unacceptable it may be necessary
to perform a repair. Here various methods for inspection, maintenance and re-
pair are presented.

14.1 Inspection methods

An inspection of a structure which forms the basis for a structural assessment
may include the application of different experimental techniques. These tech-
niques could also be included in the periodic inspection plan, if economic con-
siderations or structural reliability analyses indicate that an early detection of
the deterioration process is important.

Several inspection methods can be applied to an existing structure, e.g. crack

measurement, cover thickness measurement, corrosion rate measurement and
so-called advanced inspection methods.

An optimal plan for inspection can e.g. be determined on the basis of economic
decision analysis as outlined in Appendix C. To perform such an analysis the
following information must be available for all considered inspection methods.

• Purpose of the method. Some inspection methods are general in the sense
that they do not aim at detecting or measuring a given event. The purpose of
such methods is often to obtain some general information about the state of
the structure on the basis of which it can be decided whether or not it is nec-
essary to use more detailed inspection methods. Other more detailed detec-
tion methods are carried out with a specific purpose. To make a decision re-
garding the inspection methods it is naturally important to identify the pur-
pose of a given method, i.e. the event(s) it aims to detect or the variables
which are measured.

• Description of the inspection method. The description of the method sim-

ply gives information about the equipment used for the inspection and a de-
scription of how the inspection is carried out and how the results are regis-
tered.

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• Accuracy and relevance. To choose between a number of different inspec-

tion methods it is important to assess the accuracy of the different methods
and the relevance of the information obtained through the inspection. In or-
der to describe the accuracy it is necessary to distinguish between two dif-
ferent problems. First, the inspection in itself may depend on a number of
factors such as for example the concrete moisture or the chloride content in
half-cell potentials. Secondly, a number of factors may influence the meas-
urement itself such as environmental conditions, the position of the meas-
urement, the measurement procedure, the equipment and the person per-
forming the measurement. The relevance of the information obtained
through a given inspection method can only be assessed on the basis of a
model describing the considered deterioration mechanism. Using such a
model together with the assessment procedure given in Chapter 12 the rele-
vance of a given type of information can e.g. be identified through a sensi-
tivity analysis.

• Cost. For a given structure and a given destructive mechanism it is usually

to apply a number of different inspection methods. To determine the best in-
spection strategy the cost associated with a given method must be identified.
The cost is given in terms of the cost of equipment and the number of man-
hours necessary to perform the inspection, expressed as a cost per length,
area or volume unit of the structure. The relation between the accessibility
and the cost of the measurement itself must also be taken into account.

In the following a number of different inspection and measurement methods are

briefly described. For more detailed information concerning these methods the
reader is referred to the relevant Sub-Task reports [33] and [34].

14.1.1 Crack mapping

As part of a visual inspection process, an inventory of the visible cracks should
be developed not only to know the situation at a specific time but also to allow
a monitoring of the evolution of cracking in the surveyed concrete. This is pos-
sible by mapping the cracks periodically by video, on paper or in photographic
ways and making comparisons between them.

14.1.2 Cover thickness

Measurements of the cover thickness is carried out on new structures to ensure
that the design specifications have been observed. Further, once corrosion has
been initiated, measurements can expose the influence of the cover thickness on
corrosion and potential corroding zones with a lower cover thickness can be
identified.

The most common way to obtain information about the cover thickness and the
location of the reinforcement steel is by means of a so-called covermeter. The
cover-meter is based on the electromagnetic properties of the reinforcing steel,
i.e. its electrical conductivity and its magnetism. There are two different types

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of covermeters: those based on the magnetic reluctance principle and those

based on eddy currents.

14.1.3 Half-cell potential measurement

The main objective of potential measurements on a structure is to locate the
areas in which the reinforcement steel has become depassivated and hence, is
able to corrode if appropriate oxygen and moisture conditions are present.
There are also other applications of potential measurements, like the evaluation
of the efficiency of repair works or as a helpful tool for the design of preventive
methods such as cathodic protection or electrochemical restoration techniques.

Potential measurements can be performed with a single electrode or with one or

several wheel electrodes depending on the type and extension of the structure to
be surveyed. Registered data are related to a reference co-ordinate system that
allows a further 2- or 3-dimensional representation.

Factors that influence the half cell potential measurements are:

− Environmental factors such as oxygen content, concrete moisture and

cover thickness
− The type of electrodes used for the measurement
− The spacing between the individual measurements

14.1.4 Corrosion rate measurement

The measurement of the corrosion current provides information about the
amount of metal that is transformed into oxides as a function of the reinforce-
ment surface area and of time. The amount of oxides generated is directly
linked to the cracking of concrete cover as presented in Chapter 6. Further, it
leads to loss of steel/concrete bond, and a reduction of the cross-sectional area
of the reinforcement which affects the load-bearing capacity of the structure.
Measurements of the corrosion current may also be used to identify corroding
zones or for the evaluation of the efficiency of repair techniques such as corro-
sion inhibitors, patching or re-alkalisation.

Two main aspects must be considered when corrosion rate measurements are
made:

− The morphology of corrosion

− The need of taking into account the differences existing between the auxil-
iary electrode and the surveyed structure. This fact makes it necessary to
confine the current by a guard ring or the application of some mathemati-
cal calculations to avoid errors

Other factors such as temperature and chloride content also influence the corro-
sion rate measurements.

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14.1.5 Concrete resistivity

The resistivity of a given structure provides information about the risk of early
corrosion damage, as it is inversely related to the corrosion rate. That is, a low
concrete resistivity is correlated with a high corrosion rate.

There are several devices made for concrete resistivity measurements. The so-
called four-point method and the one-point method (disk method) are the most
widely used for making superficial measurements of concrete resistivity, while
embedded sensors can be useful for obtaining electrical resistance values.

One of the most important problems arising when measuring the concrete resis-
tivity is the variability due to changes in the environment. Factors like humidity
content or temperature can be decisive when measurements are made.

As referred before, factors like the used technique or the skill of the operator
also influence the uncertainty of the measurement itself.

14.1.6 Infrared scanning

Thermography is a non-destructive method to determine and represent the sur-
face temperature distribution by measuring the infrared ration density emitted
by the surface of a body (structure, building, etc.). The surface temperature can
be used to detect thermal irregularities, due to e.g. moisture content, delamina-
tion or voids close to the surface. Climatic factors or atmospheric conditions
can affect the measurement.

14.1.7 Radar
Basically, radar inspection is an electromagnetic technique based on the differ-
ent dielectric behaviour of materials. When a transmitted impulse of electro-
magnetic energy arrives at an interface between two different materials, part of
the pulse energy is reflected and the rest continues travelling through the new
material. The splitting rate of this energy is determined by the relative dielectric
properties of the media. Reflected energy can be detected by an antenna and
then analysed to detect and characterise the hidden features. Main applications
of GPR (Ground Proving Radar) can be classified as follows:

− Qualitative measurements
− Studies based on the analysis of the signal behaviour
− Quantitative studies

Depth penetration capability, vertical resolution and data interpretation are con-
sidered the most influencing factors on radar survey works.

14.1.8 Ultrasonic measurement

The ultrasonic pulse velocity inspection is a non-destructive method which
measures the direct compression wave velocity and is used in structural appli-
cations to evaluate the condition of materials such as concrete. This method has

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been used to assess the uniformity and relative quality of concrete and to locate
defects (i.e. cracks, voids, etc.) of structural members with two sided access
such as slabs, beams and columns. Measurements are mainly influenced by the
ability of both the operator and the equipment to detect signal arrivals.

14.1.9 Impact-echo
Impact-echo is a non-destructive technique based on the detection and interpre-
tation of the reflection of stress waves generated by a short mechanical impact.
These waves propagate through the structure and are reflected to the surface by
internal flaws or interfaces and by external surfaces of the structure. This tech-
nique allows different objectives such as measurement of the concrete thickness
or mapping of flaws (voids, honeycomb, delamination, cracks, etc.).

In practice, the accuracy of this method depends on the limitations of the

method and on the limitations of the users experience. Due to its difficulty, the
interpretation of the test results is the most important problem arising with this
inspection method.

14.1.10 Measurement of the chloride concentration

For structures subject to chloride ingress the estimation of the time to initiation
may be updated using observations of the chloride concentration at various lo-
cations on the considered structure.

The chloride concentration can be determined using dust samples obtained by

drilling a number of holes in the structure using an ordinary power drill. This
simple test can be performed in situ. Alternatively the chloride concentration
may be determined on the basis of a concrete core usually with a diameter of
100 mm obtained from the considered structure. By grinding this core and
measuring the chloride concentration at various depths a so-called chloride pro-
file is obtained on the basis of which the chloride surface concentration and the
resistance can be estimated.

14.1.11 Measurement of the alcalinity interface

For structures subject to carbonation the location of the alcalinity interface can
be determined by spraying a drilled out test item with phenolphtaleine. In the
regions where the test item has not been carbonated the concrete will be red.
Using this information the rate of carbonation of the considered concrete can be
determined and used for assessment of the service life of the structure.

14.2 Maintenance and Repair

Maintenance and repair refers to the operations performed to keep the structure
in an acceptable condition from both a serviceability and a safety point of view.
It is possible to distinguish between three different groups of strategies:

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− Preventive methods: Preventive methods are methods which aim at pre-

venting deterioration from occurring. The methods included in this cate-
gory are e.g. cathodic protection, chloride removal and re-alkalisation.

− Repair: Repair is an action with the purpose of restoring a damaged struc-

ture to the original condition or upgrading a damaged structure to an ac-
ceptable condition.

− Replacement: The substitution of the existing damaged structure with a

new structure.

The optimal strategy for maintenance and repair can like the optimal strategy
for inspection be determined using the economic decision analysis outlined in
Appendix C. To determine the optimal strategy the following information must
be available.

• Purpose of the repair method: At first, a description of the problem, i.e.

the destructive mechanism, is given together with a description of how the
given repair method solves the problem.

• Description of the repair method: The description includes an explanation

of the developed techniques and of the materials used to achieve the desired
safety and service level of the structure.

• Efficiency and Control: In order to achieve the desired results by mainte-

nance or repair works it is necessary to take into account those factors that
influence them. This include items like environmental factors, the influence
of the process parameters or the side effects of the treatment. The monitor-
ing of the treatment is also considered, not only to control if the desired
goals have been achieved but also to control the essential parameters in or-
der to obtain the best effectiveness of the work.

• Cost: For a given structure and a given destructive mechanism usually a

number of different repair methods can be applied. Each of these methods
will be associated with different costs. The costs must include the cost of all
effects of the repair e.g. in terms of traffic restrictions and effects on the en-
vironment.

In the following a number of different repair methods are briefly described. In

the Sub-Task report [33] more detailed information concerning these methods
is given.

14.2.1 Cathodic protection

Cathodic protection is the only rehabilitation technique that has proven to halt
corrosion in salt contaminated bridge decks regardless of the chloride content
of the concrete. It is based on the use of an electric current to suppress the steel
anodic areas which otherwise would have been present. Two main cathodic

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protection systems can be differentiated: those based on the use of sacrificial

anodes and those that apply an impressed current to the contaminated structure.

A cathodic protection system consists of four different parts: the anode, the
cathode, the electrolyte and the electrical devices.

Cathodic protection needs a continuous monitoring to control the efficiency of

the reinforcement protection, the accuracy of monitoring instrumentation and
the operating levels that must be provided. In this way it is also possible to
minimise the risk of side effects like hydrogen embrittlement or acidification
around the anode.

14.2.2 Re-alkalisation
The objective of electrochemical re-alkalisation is to halt temporarily the corro-
sion processes in reinforcement steel by restoring the passivating properties of
the carbonated concrete. This can be achieved by the application of an electric
current between the reinforcement steel and an external anode located at the
surface of the structure. This anode is embedded in an electrolyte that provides
the alkaline products that will migrate through the concrete. On the other hand,
cathodic reactions at the surface of the reinforcement produce alkaline hydroxyl
ions by oxidation of water and enable the passive layer to re-establish. These
processes are the ones which re-alkalisation is based on.

There are three main aspects that must be considered when re-alkalisation is
selected: the anode, the process parameters and execution and the monitoring of
the system.

14.2.3 Chloride removal

The elimination of chlorides from contaminated concrete can be achieved by
the application of an electric current between the reinforcement steel and an
external anode. When an electric field is applied to an electrolytic medium, the
negative charged ions - such as chloride ions - will migrate from the reinforce-
ment steel to the anode through the concrete pore solution.

Monitoring of the treatment is also of importance when chloride removal is ap-

plied. In this way the efficiency of the treatment can be controlled by compar-
ing chloride content in different phases of the treatment with the original ones.

There are three main effects that must be taken into account when a chloride
removal treatment is considered: the acceleration of alkali-silica reactivity, the
reduction of bond between the concrete and the reinforcement steel and finally,
the hydrogen evolution.

14.2.4 Concrete repair

Concrete repair is a complex process with the aim of restoring the original ex-
ternal conditions of concrete before deterioration advances to a stage where it

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can not be arrested. This kind of work includes a complete integration between
repair materials and existing concrete to obtain a new material capable of en-
during the exposure to the actual environment.

There are several steps that must be developed in every repair work. As impor-
tant as the placement itself, is the work of preparing the existing concrete to
receiving the repair materials. This so-called surface preparation work involves
the following tasks:

• Repair cavity conditioning

• Removal of deteriorated or contaminated
• Cleaning, repair and protection of reinforcement steel
• Bond between repair material and existing material

There are several factors that influence the selection of the repair method:

• The performance requirements of the owner and users. Different aspects like
the expected life of the repair, its tolerance to a repair failure or the interfer-
ence of the repair process with the use of the structure should be taken into
account.

• The service and exposure conditions. The technique and the materials used
must be capable of resisting possible environmental attacks including chlo-
ride ingress or carbonation.

• The load carrying capacity and stress distribution along the structure.

The following techniques may be considered when planning repair works on

deteriorated structures:

Hand-applied mortar. It may be used for repairing defects on exposed, new

concrete surfaces if the damage characteristics do not allow for the use of other
methods as the dry pack method. It can not be used for repairs deeper than the
first layer of reinforcement steel.

Dry pack. This method consists of the application of several layers of a Port-
land cement and sand mixture by tamping with a hardwood dowel and a ham-
mer. It is limited to small areas both in terms of width and relative deepness.
For areas exposed to severe conditions, an epoxy bonded dry pack method can
be used.

Form and cast in place. This is one of the most common methods to repair
mainly vertical damaged surfaces. It consists of casting a repair material with
little expected shrinkage and a viscosity which allows the material to flow into
the to be repaired.

Form and pump. By this technique, repair materials are pumped into the re-
pair cavity and bound by the sound concrete and a form. It is mainly used for
vertical and overhead repair works.

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Preplaced aggregate concrete. This concrete is made by forcing grout into the
voids of a preplaced clean and graded aggregate into the repair cavity. It is
mainly used when conventional techniques of concrete replacing are not possi-
ble or are highly difficult.

Shotcrete. This technique consists of a pneumatically applied Portland cement

mortar/concrete that can be readily placed and successfully used for a variety of
concrete repair applications such as repair of cover damages, concrete replace-
ment and for the strengthening of structural elements.

Overlays. They are mainly used for bridge decks affected by chloride attack,
but also for improving drainage or load carrying capacity conditions of the
structure. The most common ones are made of PCC, latex-PCC and micro-
silica concrete, although also polymer modified concrete can be used for thin
applications.

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15 Compliance Tests

15.1 Introduction
The performance based probabilistic design methodology envisaged within the
DuraCrete project relies on the ability to design a limit state-based service life
of reinforced concrete structures (durability design). In order to enable the de-
signer to carry out such a design it is necessary to model the time dependent
deterioration process of reinforced concrete structures. In doing this many dete-
rioration processes have to be considered. These time dependent deterioration
mechanisms are influenced by various variables. Besides mechanical aspects,
mainly material, environmental, and executional parameters are responsible for
the time dependent performance of a structure. Consequently these parameters
should be controlled carefully to base not only the design itself, but also related
future options (maintenance, repair,...) on a reliable set of data.

Besides executional and environmental influences the performance of a struc-

ture is influenced by a number of material parameters. Consequently it is re-
quired to check these material parameters within the design phase with a de-
fined level of reliability. The economic design of durable concrete structures
requires that the material compliance with the specifications set out in the de-
sign process is checked at the various stages of the concrete production process
(quality control) and, in addition, that the actual performance is monitored dur-
ing various stages in the design life. The identification and the check of mate-
rial quality has been treated in Task 3, 'Compliance Test'.

The deterioration models of Task 2 'Deterioration Modelling' contain material

parameters describing the concrete resistance against the environmental load-
ing. The objective of Task 3 was to identify appropriate test procedures for the
measurement of these parameters. A general overview of available test proce-
dures was conducted in report R6 'Compliance Tests - State of the Art'. Litera-
ture has been reviewed concerning the existing compliance tests related to per-
meability, carbonation, chloride ingress, corrosion rate of steel, risk of alkali
aggregate reaction, freeze thaw resistance and fatigue of concrete. The report
R7 was written to evaluate and recommend test procedures for the deterioration
mechanisms carbonation and subsequent reinforcement corrosion, chloride
penetration and subsequent reinforcement corrosion, frost deterioration and
frost de-icing salt deterioration. The final report R8 summarises all elaborations
dealing with compliance testing at the various test levels, including detailed

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descriptions of the final test procedures, interrelations between test methods

and test results.

Starting from the beginning, the relevant material parameters of the deteriora-
tion models

− Carbonation
− Chloride Penetration
− Reinforcement Corrosion
− Frost Deterioration
− Frost De-Icing Salt Deterioration

are identified in Task 2. With regard to reinforcement corrosion the following

material parameters were under investigation:

− Inverse of the Carbonation Resistance, RCarb,0-1:

(Carbonation Model)

− Rapid Chloride Migration Coefficient, DRCM,0:

(Chloride Penetration Model)

− Electrolytic Resistivity, ρ0:

(Propagation Model)

With regard to concrete attack by frost and frost de-icing salt deterioration the
following material parameters should be checked within the compliance test
procedure:

− Mass of Scaled Material, mn:

(Frost and Frost De-Icing Deterioration)

− Dynamic Modulus of Elasticity, EDyn:

(Frost Deterioration)

The aim of material testing is to design and to verify a required concrete quality
with regard to the expected deterioration mechanism in preliminary tests. The
aim of quality control is to confirm and identify the material at the various qual-
ity levels within the binder and concrete production.

The quality control concept of the material parameters is schematically illus-

trated in Figure 15.1.

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Figure 15.1: Design for durability - quality control concept

Quality level 1 includes the testing of constituent materials. Cements or binders

are classified in regard to their potential resistance R0 (this is analogous to the
strength classification of cements used in structural design). The cement pro-
ducer uses an appropriate standard compliance test in order to check the poten-
tial material resistance against deterioration (Rbinder,0 - quality level 1). These
tests are carried out on standard mortar specimens.

The influence and interaction of the various concrete composition parameters

(e.g. binder content, water/binder ratio,...) are considered to determine the po-
tential quality of the used concrete mix. At this quality level the concrete is
classified with regard to its potential resistance R0 (in analogy to the strength
classification of concretes used in the structural design). This is the most impor-
tant task of the compliance test procedure. The supplied quality of the concrete
is checked and compared to the design requirements using appropriate compli-
ance tests (Rconcrete,0 - quality level 2).

Finally, suitable in-situ tests are applied on the structure to verify the achieved
quality of the concrete achieved (Rconcrete - quality level 3).

Testing according to quality levels 1 and 2 is normally conducted under stan-

dardised conditions which are carefully controlled, measured and documented.
In-situ test results (quality level 3) will inevitably be influenced by environ-
mental and executional parameters.

In R7 the following candidate test methods were proposed for further investiga-
tion.

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− Natural Carbonation (NAC) - Quality Level 2 and 3

− Accelerated Carbonation (ACC) - Quality Level 1 and 2
− CEMBUREAU-Method (CBM) - Quality Level 2
− TORRENT-Method (TOR) - Quality Level 2 and 3

− Rapid Chloride Migration Method (RCM) - Quality Level 1 and 2

− Chloride Profiling Method (CPM) - Quality Level 2 and 3

− Two-Electrode Method (TEM) - Quality Level 2

− WENNER-Probe (WER) - Quality Level 2 and 3
− Multi-Ring-Electrode (MRE) - Quality Level 2 and 3

− Cap. Suction of Water, Intern. Damage and Freeze Thaw Test (CIF)
Quality Level 1 and 2
− Capillary Suction of De-Icing Solutions and Freeze Thaw Test (CDF)
Quality Level 1 and 2

All above listed test methods were found to be useful for compliance testing
(R7), because they are taking into account the following basic requirements:

− The material parameters measured and the mechanisms governing the test
result must be of relevance for the aspects considered.

− The maximum degree of precision with repeatable and reproducable tests

should be achieved. Repeatability is a measure of the within laboratory vari-
ability between successive tests using identical specimens, whilst reproduce-
ability is a measure of between laboratory variability. The reproduceability
can be checked within so-called round-robin tests.

− Measurements proposed for application within the compliance test proce-

dure should be easy to carry out by minor schooled personnel

− Cost should be the minimal feasible within the constraints of technical reli-
ability and precision. Important considerations are the duration of the test
(which must be as short as possible) in order to minimise the disturbtion of
the production process, the commercial availability and the costs of the test
equipment.

15.2 Main Test Programme

For the main test programme which considers the material compliance with re-
gard to the deterioration processes carbonation, chloride penetration and corro-
sion, the taken choice of binders was based on the following knowledge.

With regard to the deterioration process carbonation the binder will fix the po-
tential quantity of calcium hydroxide formed and in addition to that the porosity
of the hydrated binder paste.

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With regard to the deterioration process chloride penetration the binder will fix
the hardened binder paste structure, the quantity of C3A which is responsible
for the chemical chloride binding and the quantity of CSH phases responsible
for the physical binding of chlorides.

Not only considering their common use in europe, but also in order to achieve a
broad range of possible binder related material performances the above men-
tioned dependencies resulted in a final selection of ordinary Portland cements,
sulfate resistant Portland cements and blastfurnace slag cements. The final se-
lection criteria of binders was with regard to ordinary Portland cements the C3A
content and in regard to blast furnace slag cements the blast furnace slag con-
tent.

Nine different mortar and concrete mixes were produced to investigate the ef-
fect of the type of binder. Within the concrete investigations partly some varia-
tions of the w/c-ratio and the binder content were included into the test pro-
gramme. All consideration are summarised in Figure 15.2:

Figure 15.2: Material parameters which were tested in the main test pro-
gramme

15.3 Test Procedure

For overview purposes a short example will be given below in order to demon-
strate the design and quality control concept. This example is related to chloride
penetration:

First of all R8 gives a detailed description how to execute the measurements.

Here, the relevant compliance test is the rapid chloride migration method
(RCM).

The 'Rapid Chloride Migration Method (RCM)' is a procedure used for the de-
termination of a chloride migration coefficient in casted and cored mortar and
concrete specimens.

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The experimental arrangement is shown in Figure 15.3:

Figure 15.3: Test arrangement of the rapid chloride migration method

Needed equipment:

a) Sealing tape
b) Saturated lime water (reagents A, 0.2 mol⋅l-1 KOH-solution)
c) A stainless steel plate (anode)
d) A specimen
e) Chloride containing lime water (reagents B, c(Cl-) = 0.529 - 1.900 mol⋅l-1 in
0.2 mol⋅l-1 KOH-solution)
f) A stainless steel plate (cathode)
g) A plastic support
h) A glass container

− A power supply (capable of supplying a voltage of 60 V (DC) and a current

of 1 A)
− Indicator solution (0.1 mol⋅l-1 AgNO3 solution)
− Splitting equipment

The specimens for testing are cast mortar (Quality Level 1) and cast concrete
cylinders (Quality Level 2) with standard dimensions (Table 15.1), compacted
according the relevant European codes. A standard pre-condition period of
∆tCuring = 28d is recommended. That means after demoulding, the specimens are
stored in chloride-free tap water (T = 20 ± 2°C) until an age of t = 28d. Before
testing, the surface shell of the cylinder is sealed by a special rubber tape. The
top surface of the specimen is in contact with reagents A, which is free of chlo-
rides. The bottom surface of the specimen is in contact with the chloride con-
taining reagents B. Anodic and cathodic steel electrodes will provide the neces-
sary driving force in order to provoke an accelerated migration of the chloride
ions.

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A potential of 30 ± 0.2 V (DC) is applied across the specimen for a period of

time which will be fixed in dependency of the recorded initial current (Table 1).

Table 15.1: Test duration in dependency of the measured initial current

Initial Current Io [mA] Initial Current Io [mA] Test Duration

ds = 50 mm ds = 100 mm [h]
h = 50 mm h = 50 mm
(Mortar) (Concrete)

Io < 1 Io < 5 168

1 ≤ Io < 2 5 ≤ Io < 10 96

2 ≤ Io < 7 10 ≤ Io < 30 48

7 ≤ Io < 15 30 ≤ Io < 60 24

15 ≤ Io < 30 60 ≤ Io < 120 8

30 ≤ Io 120 ≤ Io 4

Directly after the end of the test, the cylinders are removed and split longitudi-
nally into two half-cylinders. The penetration depth of the chlorides is deter-
mined by spraying an indicator solution. This colorimetric method with AgNO3
has a colour change at a chloride concentration of cd = 0.07 mol⋅l-1.
The average penetration depth xd is the output of the test procedure.

The calculation of the chloride migration coefficient will be carried out accord-
ing to the following Equation (15.1):

RTL x d − α x d
D RCM = ⋅ (15.1)
zFU t

with:

RTL −1  2c 
α = 2⋅ ⋅ erf ⋅ 1 − d  (15.2)
zFU  c0 

DRCM.: rapid chloride migration coefficient, m2/s

z: absolute value of ion valence, for chloride ions, z = 1
F: Faraday constant, F = 9.648·104 J·(V·mol)-1
U: absolute value of potential difference, V
R: gas constant, R = 8.314 J·(K·mol)-1
T: solution temperature, K
L: thickness of the specimen, m
xd: penetration depth, m
t: test duration in s

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erf-1: inverse of the error function

cd: chloride concentration for indicator colour change,
cd = 0.07 mol⋅l-1
c0: chloride concentration of reagents B in the upstream cell in mol⋅l-1

−1  2c 
ξ = erf ⋅  1 − d  , values given in Table 15.2:
 c0 

Table 15.2: The values of ξ

c0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 5.0
mol⋅l-1 mol⋅l-1 mol⋅l-1 mol⋅l-1 mol⋅l-1 mol⋅l-1 mol⋅l-1 mol⋅l-1 mol⋅l-1

ξ 0.764 1.044 1.187 1.281 1.351 1.407 1.452 1.491 1.554

The final output is a calculated migration coefficient, DRCM,0 in m2/s.

Test reports should include the following information:

− age of concrete
− date of testing
− concrete mix proportions
− information regarding the curing regime to which the concrete was subjected
− conditions and duration of the pre-conditioning
− concentration of applied salt contamination
− temperature of solution
− exact duration of the migration test
− average depth of penetration
− chloride migration coefficient

The assessment of the presented procedure lead to the statement, that the intro-
duced 'RCM' method is generally applicable to all quality levels, but can ideally
be recommended for the quality levels 1 and 2. Because of the accelerated chlo-
ride transport, the to be measured material compliance can be checked and con-
trolled rapidly. The rate of migration is theoretically related to the diffusion co-
efficient. Among different rapid methods, tabulated in R6, the chloride migra-
tion method revealed to be theoretically the clearest and experimentally the
most simple method. The main advantages are:

− simple apparatus
− short testing period
− simple measurement
− simple calculation
− no strict sealing
− no strict sample size

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In addition to the above listed advantages, for measurements taken at quality

level 1 and 2, a considerable high repeatability was determined. The determined
relationship between the measured mean values DRCM,m (Do,m) and the loga-
rithm of the corresponding coefficient of variation (CoV-repeatability) is given
in the following Figure 15.4. At least variable test durations lead to comparable
precision in the measurement, because the target penetration depth is equal.

A LN-distributed regression parameter a instead of a normal distributed regres-

sion parameter was calculated, to exclude values for the coeffient of variation
CoV smaller than 0.

2
log (CoV), CoV in [%]

0
log (CoV) = a
µa = 0.869
-1
σa = 0.360

-2

-3

-4
0 20 40 60 80 100
-12 2
Do,m in [10 m /s]

Figure 15.4: Regression analysis: Do,m versus log (CoV)

Parameter Estimation of a
Parameter 1: µa = 0.869
Parameter 2: σa = 0.360
Standard deviations for the estimated parameters:
Parameter 1: 0.035
Parameter 2: 0.025
The parameters 1 and 2 are independent

The mean (50 % fractile) and the 90 % fractile of the coefficient of variation
(COV) as a function of the determined mean material compliance can easily be
calculated:

log (CoV) = a = 0.869

CoV = 7.40 %

log (CoV)90% = a = 1.330

CoV90% = 28.52 %

The relationship is in the same way valid for the level 1 as well as for the
level 2.

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15.4 The Results

At quality level 1 the potential binder compliance with regard to chloride pene-
tration was measured. As shown in the following Figure 15.5 the measured
binder compliance (standard mortar composition) is in good correspondence to
the measured concrete compliance which was measured at level 2. In each case
the w/c ratio was fixed to w/c=0.50. Consequently, a correlation was found
which is useful to relate binder and concrete compliance (Figure 15.5).

Binder Compliance versus Concrete Compliance (RCM)

Rapid Chloride Migration Coefficient (RCM) 20

15
in [10 m /s] - Binder

y = 0,6747 x
R2 = 0,7799

10
-12 2

0
0 5 10 15 20
Rapid Chloride Migration Coefficient (RCM)
-12 2
in [10 m /s] - Concrete

Figure 15.5: Binder compliance versus concrete compliance (Rapid Chloride

Migration Method)

The variation of the type of binder and the w/c ratio for the concrete investiga-
tions leads to the following dependencies. There are in fact variations in per-
formance, most important due to the type of binder (Figure 16.6) and second
important due to the variation of the w/c ratio. Some further produced results
indicate that there is also an influence of binder content observable.

Figure 15.6: Binder and concrete compliance (Rapid Chloride Migration

Method, RCM) under variation of cement type

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The relationship to other test methods (in this case the Two-Electrode-Method,
TEM) was statistically analysed in order to have the option to link produced
data from other sources to the DuraCrete elaborations. Figure 15.7 clearly con-
firms already found correlations between chloride migration and electrolytical
resistivity.

50

Rapid Chloride Migration Coefficient 40

DRCM in [10 m /s]

30 DRCM = A ρTEMb
-12 2

A: LN (965; 384)
b = -1.0027
with:
20
DRCM in [10-12m2/s]
ρTEM in [Ωm]

10

0
0 200 400 600 800 1000 1200

Electrolytic Resistivity ρTEM in [Ωm]

Figure 15.7: Concrete compliance (Rapid Chloride Migration Method) versus

concrete compliance (Two-Electrode-Method)

The interrelation of the TEM and another method for determining electrolytical
resistivity (WENNER) is given below.

1000

ρTEM = A ρWER + ε
Electrolytic Resistivity (TEM) in [Ωm]

800
A = 0.680
ε: ND (0; 34)
with:
ρ in [Ωm]
600 ε in [Ωm]

400

200

0
0 200 400 600 800 1000
Electrolytic Resistivity (WER) in [Ωm]

Figure 15.7: Concrete compliance (TEM) versus concrete compliance (WER)

According to the determined interrelations it will be possible in the near future

to check the binder compliance and the concrete compliance in the laboratory

BE95-1347 DuraCrete –Probabilistic Performance based Durability Design of Concrete Structures

Final Technical Report 105

for example by using the rapid chloride migration method (RCM) or the Two-
Electrode-Method (TEM) and to verify the achieved quality within the structure
by applying the non-destructive WENNER device (WER).

Simular procedures are applicable to the other deterioration mechanisms.

In order to facilitate the future design of materials a brief proposal was given
how to classify the material with regard to their measured performance. In prin-
ciple the same procedure as known from the structural design (compressive
strength of binders and concrete) is applied on the material performance with
regard to durability.

15.5 Material Classification

A material classification is made for binders and concrete at quality level 1 and
2 respectively.

The following resistances are classified:

− Carbonation Resistance, RCarb,0: Classification Set CARbonation

(Carbonation Model)
2
1 T
CAR = −1
=  (15.3)
RCarb,0  dc 
with:
CAR: carbonation resistance in [kgCO2/m3/m2/s]
RCarb,0-1: inverse of the carbonation resistance in [m2/s/kgCO2/m3], meas-
ured an a compliance test 'ACC'
T = 419.45 in [(kgCO2/m3/s)0.50]
dc: carbonation depth measured in a compliance test in [m]

− Rapid Chloride Migration Coefficient, DRCM,0: Classification Set CHLorides

(Chloride Penetration Model)
 1 
CHL =   (15.4)
 DRCM,0 
with:
CHL: chloride migration resistance in [s/m2]
DRCM,0: chloride migration coefficient in [m2/s] , measured in a compliance
test 'RCM'

− Electrolytic Resistivity, ρ0: Classification Set CORrosion

(Propagation Model)
COR = ρ o (15.5)
with:
COR: electrolytic resistivity in [Ωm]
ρo: electrolytic resistivity in [Ωm], measured in a compliance test 'TEM'

The following material classification is proposed (e.g. valid for concretes):

BE95-1347 DuraCrete – Probabilistic Performance based Durability Design of Concrete Structures

106 Final Technical Report

Table 15.3: CAR Classification, Carbonation Model

Classification Carbonation Resis- Material Variable:

tance Class D
RCarb,ACC-1 = eff
a
Corresponding Compliance

[1010 kgCO2/m3/m2/s] [10-11 m2/s/kgCO2/m3]

CAR-0.1 CAR = 0.1 100

CAR-0.5 CAR = 0.5 20

CAR-1 CAR = 1.0 10

CAR-5 CAR = 5.0 2

CAR-10 CAR = 10.0 1

Table 15.4: CHL Classification, Chloride Penetration Model:

Classification Chloride Penetration Material Variable:

Resistance Class DRCM,0
Corresponding Compliance

[1010 s/m2] [10-12 m2/s]

CHL-1 CHL = 1 100

CHL-5 CHL = 5 20

CHL-10 CHL = 10 10

CHL-50 CHL = 50 2

CHL-100 CHL = 100 1

Table 15.5: COR Classification, Propagation Model:

BE95-1347 DuraCrete –Probabilistic Performance based Durability Design of Concrete Structures

Final Technical Report 107

Classification Propagation Resis- Material Variable:

tance Class ρo,TEM
Corresponding Compliance

[Ωm] [Ωm]

COR-10 COR = 10 10

COR-50 COR = 50 50

COR-100 COR = 100 100

COR-500 COR = 500 500

COR-1000 COR = 1000 1000

For each class, it has to be confirmed by testing the material at quality level 1
and 2, that only 5.0 % of the measurements exhibit performances which are
lower than the class-corresponding compliance of the tables CAR, CHL or
COR. Similar to the strength quality control, the following alternative accep-
tance criterias are advised. One has to consider that the acceptance criterias are
related to the measured compliance RCarb,0-1, DRCM,0 and ρ0.

Acceptance Criterias:

− Acceptance Criteria A (Example)

m(RCarb,o-1/Do/ρo) n=3 - 1,89 (kσ; Table 6) ⋅ σ(RCarb,o-1/Do/ρo) n=∝ ≥ 5 %-Fractile
with:
m(RCarb,o-1/Do/ρo) n=3: mean value of random sample, n = 3
σ(RCarb,o-1/Do/ρo) n=∝: standard deviation of the population

− Acceptance Criteria B (Example)

m(RCarb,o-1/Do/ρo) n=10 - 1.92 (ks; Table 6) ⋅ s(RCarb,o-1/Do/ρo) n=10 ≥ 5 %-Fractile
with:
m(RCarb,o-1/Do/ρo) n=10 : mean value of random sample, n = 10
s(RCarb,o-1/Do/ρo) n=10 : standard deviation of the random sample, n = 10

The factors kσ und ks are selectable as a function of the amount of testing.

Table 15.6: Acceptance factors kσ and ks

Amount of random sample, n Acceptance factor kσ Acceptance factor ks

BE95-1347 DuraCrete – Probabilistic Performance based Durability Design of Concrete Structures

108 Final Technical Report

1 2.31 -

2 2.01 -

3 1.89 3.37

4 1.83 2.63

5 1.80 2.33

6 1.77 2.18

8 1.74 2.00

10 1.72 1.92

20 1.68 1.76

30 1.67 1.73

∝ 1.64 1.64

This table is adapted from the EC 1, annex D, Table D.1

BE95-1347 DuraCrete –Probabilistic Performance based Durability Design of Concrete Structures

Final Technical Report 109

16 Benchmarking
Task 5 involved the benchmarking of designs using the current deemed-to-
satisfy approach to durability design.

The initial sub-task was concerned with the selection of standard elements and
loading conditions and the establishment of a standardised approach to the
benchmarking exercise.

It was considered important that the elements are selected so that they cover a
range of typical structures and operating conditions. Each element would be
designed based on a design brief giving information on the geometric con-
straints, forces acting on the element, and exposure conditions. It was consid-
ered desirable that a certain degree of freedom be allowed to enable the designs
to be compatible with good practice in the member states considered. Material
data and properties of both concrete and steel will thus be variable. Certain pa-
rameters will, however, be fixed (or prescribed) including the geometrical as-
pects of the whole structure and the elements, loading conditions (unfactored
loads were given), boundary conditions, the procedure for structural analysis,
and the local (meso) environment. In few cases this resulted in designs which
deviated from common practice and these were reported.

Sub-task 5.2 involved reviewing the codes within a representative number of

EU member states in relation to stated exposure classes and durability require-
ments. The review covered the following types of structures:

• Marine and coastal structures tidal, splash, spray, atmospheric

• Bridges piers, beams, decks
• Car Parking structures decks, roofs
• Tunnels bored, sunken
• Buildings offices, domestic
• Pavements roads, runways
Codes from eight member states were considered, reflecting the range of cli-
matic conditions and geographic locations within Europe. These include the
Netherlands, Denmark, the United Kingdom, Spain, Germany, Belgium, France
and Sweden. Additionally, CEN recommendations were examined.

It was found, not surprisingly, that all codes were mainly structurally oriented
employing a prescriptive (deemed-to-satisfy) approach in dealing with durabil-
ity requirements. Exposure conditions are usually defined on the basis of sim-

BE95-1347 DuraCrete – Probabilistic Performance based Durability Design of Concrete Structures

110 Final Technical Report

plified classification systems. It also become apparent that not all codes pre-
sented requirements with regard to service life. In most structural codes, how-
ever, a reference period for the design is specified. In ULS and SLS where de-
gredations can occur (and are taken into account) the target service life is the
same as the reference period. This means that in most codes a service life is ac-
tually defined, albeit implicitly.

Meteorological records in the selected EU member states were investigated

(sub-task 5.3) and a report prepared detailing the climatic conditions which un-
derlay the code provisions. The report was based on information collated from
8 weather stations in each particular state, and the data covered a period of not
less than 30 years (from 1930 to 1960).

In the final stage a number of elements subjected to a range of loading and ex-
posure conditions were designed using the current prescriptive approach of
each of the national codes in the selected member states - 144 designs were per-
formed in total. The elements consisted of three prime types i.e. slab, beam, and
column, each having both medium and high reinforcement ratios in broadly two
environments namely, corrosion due to chloride penetration and corrosion due
to carbonation. The chloride attack was further subdivided into two categories -
marine environment and de-icing salts akin to roads and bridges etc.. This re-
sulted in eighteen different designs. Table 16.1 presents a summary of the spe-
cific elements chosen for the design.

Pavement design has been treated separately. The work is undertaken largely
by HBG/NPC due to their extensive expertise in the field. A review of national
code requirements has been undertaken and two designs were performed cover-
ing the practice in The Netherlands and Germany.

BE95-1347 DuraCrete –Probabilistic Performance based Durability Design of Concrete Structures

Final Technical Report 111

Table 16.1 Details of elements used in benchmarking the national codes

Attack type Environment Structure Element se- Element type

type lection

No.

Chloride Marine Jetty moor- 1 Slab

Attack ing platform 2 slab
3 beam
4 beam
56 column
6 column

De-icing Multi-storey 7 Slab

salts car park 8 wall
9 beam
10 beam
11 column
12 column

Carbonation Urban area Laboratory 13 Slab

and office 14 slab
building 15 beam
16 beam
17 column
18 column

BE95-1347 DuraCrete – Probabilistic Performance based Durability Design of Concrete Structures

112 Final Technical Report

17 References
/1/ BE95-1347/R1 (1997) "Design Guide", Task 1 Report. Prepared by
COWI Consulting Engineers and Planners AS, Denmark, TNO Building
and Construction research, Netherlands Organisation for Applied Scien-
tific Research, The Netherlands and Directorate-General for Public
Works and Water Management (RWS), The Netherlands.

/2/ BE95-1347/R2a (1997) "Mini-Project "Chloride induced Corrosion",

Task 1 Report. Prepared by COWI Consulting Engineers and Planners
AS, Denmark.

/3/ BE95-1347/R3 (1998) "Models for Environmental Actions on Concrete

Structures", Task 2 Report. Prepared by Chalmers University of Tech-
nology, Sweden.

/4/ BE95-1347/R4-5 (1998) "Modelling of Degradation", Task 2 Report.

Prepared by Taywood Engineering Limited (TEL), United Kingdom.

/5/ BE95-1347/R6 (1997) "Compliance Tests - State-of-the-Art", Task 3

Report. Prepared by COWI Consulting Engineers and Planners AS, Den-
mark.

/6/ BE95-1347/R7 (1998) "Compliance Testing for Probabilistic Design

Purpose - Evaluation Report", Task 3 Report. Prepared by Institute of
Building Research, Technical University of Aachen (ibac), Germany, E.
Schwenk Zementwerke KG, Germany and Hollandsche Beton Groep
N.V./Netherlands Pavement Consultants BV, The Netherlands

/7/ BE95-1347/R8 (1999) "Compliance Testing for Probabilistic Design

Purpose", Task 3 Report. Prepared by Institute of Building Research,
Technical University of Aachen (ibac) and E. Schwenk Zementwerke
KG, Germany.

/8/ BE95-1347/R9 (1999) "Statistical quantification of the variables in the

limit state functions: summary", Task 4 Report. Prepared by TNO Build-
ing and Construction research, Netherlands Organisation for Applied Sci-
entific Research, The Netherlands.

BE95-1347 DuraCrete –Probabilistic Performance based Durability Design of Concrete Structures

Final Technical Report 113

/9/ BE95-1347/R10 (1999) "Benchmarking Designs - National Codes", Task

5 Report. Prepared by Taywood Engineering Limited (TEL), United
Kingdom.

/10/ BE95-1347/R11 (1999) "Benchmarking -Summary", Task 5 Report. Pre-

pared by Taywood Engineering Limited (TEL), United Kingdom.

/11/ BE95-1347/R12 (1999) "Procedure Target Reliabilities", Task 6 Report.

Prepared by TNO Building and Construction research, Netherlands Or-
ganisation for Applied Scientific Research, The Netherlands.

/12/ BE95-1347/R13 (1999) "Reliabilities for Probabilistic Design", Task 6

Report. Prepared by TNO Building and Construction research, Nether-
lands Organisation for Applied Scientific Research, The Netherlands.

/13/ BE95-1347/TG2 (1997) "Modelling of alkali-aggregate reaction", Sub-

task 2.4 Report. Prepared by Taywood Engineering Limited (TEL),
United Kingdom.

/14/ BE95-1347/TG2 (1997) "Modelling of frost attack", Sub-task 2.5 Re-

port. Prepared by Intron, the Quality Assessment Institute for the Build-
ing Industry, The Netherlands.

/15/ Rostam, S. and Schießl, P. (1994) "Service Life Design in Practice -

Today and Tomorrow. Proceedings of the International Conference
"Concrete Across Boarders" (Odense, Denmark) (22 - 25 June 1994),
Volume I, pp. 1-11.

/16/ Comité Euro-International du Béton (1991) "CEB-FIP Model Code

1990". Published by Thomas Telford Services LTD (London)

/17/ Bryla, P., Faber, M. and Rackwitz R. (1991) "Second Order Methods
in Time Variant Reliability Problems." Paper submitted for the OMAE-
conference. Volume II, Safety and Reliability, ASME

/18/ Thoft-Christensen, P. and Baker, M.J. (1982) "Structural Reliability

Theory and Its Applications." Published by Springer-Verlag Berlin Hei-
delberg New York

/19/ Madsen, H.O., Krenk, S. and Lind N.C. (1986) "Methods of Structural
Safety." Published by PRENTICE-HALL INC., Englwood Cliffs, N.J.
07632

/20/ BE95-134/TG6 (1999) "Calibration of Partial Factor", Prepared by

COWI Consulting Engineers and Planners AS, Denmark.

/21/ BE95-134/TG4 (1998) "Statistical Quantification of the Propagation Pe-

riod", Sub-task 4.1 Report. Prepared by Institute ´Eduardo Torroja´(IET)
of Construction Science of the CSIC of Spain, Spain.

BE95-1347 DuraCrete – Probabilistic Performance based Durability Design of Concrete Structures

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/22/ BE95-134/TG4 (1998) " Summary of the Statistical Quantification of the

DuraCrete Resistivity Corrosion Rate Model ", Sub-task 4.1 Report. Pre-
pared by Chalmers University of Technology, Sweden and Institute of
Building Research, Technical University of Aachen (ibac).

/23/ European Committee for Standardization (1994) "Eurocode 1 - Basis

of design and actions on structures - Part 1: Basis of design" (ENV
1991-1).

/24/ BE95-134/TG4 (1998) " Statistical Quantification, Onset of Corrosion ",

Sub-task 4.1 Report. Prepared by Institute of Building Research, Techni-
cal University of Aachen (ibac).

/25/ DBV - Deutscher Beton-Verein E.V. (1982) "Merkblatt Betondeckung:

Sicherung der Betondeckung beim Entwerfen, Herstellen und Einbauen
der Bewehrung sowie des Betons". Published by Deutscher Beton-Verein
E.V., Germany

/26/ DBV - Deutscher Beton-Verein E.V. (1991) "Merkblatt Betondeckung:

Sicherung der Betondeckung beim Entwerfen, Herstellen und Einbauen
der Bewehrung sowie des Betons". Published by Deutscher Beton-Verein
E.V., Germany

/27/ DBV - Deutscher Beton-Verein E.V. (1997) "Merkblatt Betondeckung:

Sicherung der Betondeckung beim Entwerfen, Herstellen und Einbauen
der Bewehrung sowie des Betons". Published by Deutscher Beton-Verein
E.V., Germany

/28/ Dillmann, R. (1990) "Toleranzen der Betondeckung". Forschungsbericht

BI5-80 01 89-7 1990. Prepared by Strabag Bau-AG, Germany

/29/ Franke, Pingel, Dobbelmann, Baldauf, Meichsner, et al (1994).

"Wirksamkeit von Maßnahmen zur Sicherstellung der geforderten Min-
destbetondeckung". In: Kurzberichte aus der Bauforschung 36 (1995),
Nr.1, pp. 45-48 (Stuttgart)

/30/ BE95-134/TG4 (1998) " Assessment and redesign ???? ", Sub-task 6.1
Report. Prepared by TNO Building and Construction research, Nether-
lands Organisation for Applied Scientific Research, The Netherlands

/31/ Institute of International harmonization for Building and housing

(iibh) (1998) "Assessment of existing structures" (ISO draft).

/32/ Ditlevsen, O. and Madsen H.O. (1996) "Structural Reliability Methods"

Published by John Wiley & Sons LtD (New York)

/33/ BE95-134/TG7 (1998) "Strategies for inspection and maintenance - In-

spection and Repair methods", Sub-task 7.1 Report. Prepared by Institute

BE95-1347 DuraCrete –Probabilistic Performance based Durability Design of Concrete Structures

Final Technical Report 115

Éduardo Torroja´(IET) of Construction Science of the CSIC of Spain,

Spain.

/34/ BE95-1347/TG7 (1999) "Environmental Actions and Response - Survey,

Inspection and Measurement", Sub- task 7.1 Report. Prepared by
Chalmers University of Technology, Sweden.

/35/ BE95-134/TG7 (1998) "Effect of Quality Assurance", Sub-task 7.1 Re-

port. Prepared by Institute of Building Research, Technical University of
Aachen (ibac).

/36/ BJCSS (Joint Committee on Structural Safety) (1996) Probabilistic

Model Code (draft)

/37/ Lindley, D. V. (1976) "Introduction to Probability and Statistics from a

BayesianViewpoint". Vol 1 + 2. Published by Cambridge University
Press (Cambridge)

/38/ Raiffa, H. and Schlaifer, R. (1991) "Applied statistical theory". Pub-

lished by Harvard University Press (Cambridge)

BE95-1347 DuraCrete – Probabilistic Performance based Durability Design of Concrete Structures

116 Final Technical Report

Appendix A: Probabilistic Models

In the following sections the distributions used for the code calibration are
given for easy reference. For more detailed information the reader is referred to
the individual Task 4 reports.

A.1 Univariate probability density functions

The following types of distributions are used to model the stochastic variables

1. Normal probability density function

1  x − µ 
2

f X ( x) = exp − 0.5  (A.1)

σ 2π   σ  

Mean value: µ
Standard deviation: σ .

Notation: N( µ ; σ )

2. Lognormal probability density function

1  1  ln( x ) / ξ  2 
f X ( x) = exp −    , x>0 (A.2)
xδ 2π  2 δ  

δ 2 
Mean value: ξ exp 
 2
δ 2 
Standard deviation: ξ exp  exp(δ 2 ) − 1
 2

Notation: LN( ξ ; δ )

3. Shifted lognormal probability density function

1  1  ln( x − τ ) / ξ  2 
f X ( x) = exp −    , x >τ (A.3)
( x − τ )δ 2π  2 δ  

δ 2 
Mean value: ξ exp  + τ
 2
δ 2 
Standard deviation: ξ exp  exp(δ 2 ) − 1
 2

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Final Technical Report 117

Notation: sLN( ξ ; δ ; s )

4. Gamma probability density function

1
f X ( x) = λ ( λx ) exp( − λx ) ,
k −1
x>0 (A.4)
(
Γ k )

where Γ( .) denotes the Gamma function.

k
Mean value:
λ
k
Standard deviation:
λ

Notation: Ga( k ; λ )

5. Beta probability density function

r −1 t −1
 x − a  x − a
  1 − 
 b − a  b − a
f X ( x) = , a< x<b (A.5)
B(r ; t )(b − a )

where B(.;.) denotes the Bessel function.

r
Mean value: a + (b − a )
r+t
rt
Standard deviation: ( b − a )
( r + t ) ( r + t + 1)
2

Notation: Beta(r,t,a,b)

A.2 Material Variables

It is the responsibility of the producer of concrete to deliver a concrete with a
given characteristic value of the effective diffusion coefficient with respect to
carbonation, D0,ca , the chloride diffusion coefficient, D0,cl , and the resistivity,
ρ0 .

Within the DuraCrete project, a number of compliance tests have been carried
out. These tests can be used as a basis to estimate the coefficient of variation of
the above mentioned material variables.

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118 Final Technical Report

A.2.1 Carbonation
Using the compliance test Accelerated Carbonation (ACC) a relation between
the mean value of the carbonation rate, µ D0,ca , and the coefficient of variation of
the effective diffusion coefficient, V Deff , has been found

V D0 ,ca = a ca µ Dca0 ,ca ⋅ 10 9 + ε ca

b
(A.6)

where mean value of the carbonation diffusion coefficient is given in the unit
[kgCO2/m3/m2/s]. The constants have been found to be a ca = 9.02 and
bca = −0.33 and the error, ε ca , is normally distributed with zero mean and
standard deviation 0.0175.

For further information see [35] where also the statistical uncertainty related to
the model parameters is given.

A.2.2 Chloride ingress

Using the compliance test Rapid Chloride Migration (RCM) the coefficient of
variation of the chloride diffusion coefficient, V D0,ca , has been found

V D0,ca = exp( a cl + ε cl ) (A.7)

where the coefficient of variation is given in %. The constant has been found to
be a cl = 0.87 and the error, εcl , is normally distributed with zero mean and
standard deviation 0.36. The model shows that the coefficient of variation of
the chloride diffusion coefficient is independent of the mean value of the chlo-
ride diffusion coefficient.

For further information see [35] where also the statistical uncertainty related to
the model parameters is given.

A.2.3 Corrosion rate

Using the compliance test Two Electrode Method (TEM) the coefficient of
variation of the electrolytical resistivity, Vρ0 , has been found

(
Vρ0 = exp a ρ0 + ε ρ0 ) (A.8)

where the coefficient of variation is given in %. The constant has been found to
be a res = 0.83 and the error, εcres , is normally distributed with zero mean and
standard deviation 0.33. The model shows that the coefficient of variation of
the electrolytical resistivity is independent of the mean value of the electrolyti-
cal resistivity.

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Final Technical Report 119

For further information see [35] where also the statistical uncertainty related to
the model parameters is given.

A.3 Geometric variables

All geometric variables are modelled as constants except the cover thickness
whose distribution is given in Table A.1.

Variable Condition Distribution Unit

Cover thickness x LN( x c ;10)1 [mm]

Table A.1: Geometric variables.

1)
Here the mean and standard deviation of the logarithmic normal distribu-
tion are given and not the parameters ξ and δ .

A.4 Environment variables

A.4.1 Carbonation
Variable Condition Distribution Unit
c s ,ca Not valid for tunnels or confined spaces 5.0 ⋅ 10 −4 [kg/m3]

Table A.2: Environment variables for carbonation.

A.4.2 Chloride ingress

Variable Condition Distribution Unit
cs Structures subject to de-icing salt LN(1.28;0.61) [%] relative
to binder
Table A.3: Environment variables for chloride ingress.

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120 Final Technical Report

A.4.2 Corrosion rate

Variable Condition Distribution Unit
Fcl With chloride sLN(0.62;1.35;1.09) -
Fcl Without chloride 1.0 -
FO2 Submerged 0 -
FO2 Other 1.0 -
k cl ,res With chloride N(0.72;0.11) -
k cl ,res Without chloride 1.0 -
o
K Temperatures below 20 C N(0.025;0.005) -
K Temperatures above 20 oC N(0.073;0.015) -
wt Dry 0
wt Moderate humidity, sheltered 0.5
Airborne sea water
wt Cyclic wet-dry, unsheltered 0.75
wt Wet, rarely dry, tidal zone 1.0
α General corrosion 2.0
α Pitting corrosion N(9.28;4.04)
Table A.4: Environment variables in the corrosion rate model.
The temperature and the relative humidity are defined as the yearly average
values. These values are modelled as deterministic parameters for a given loca-
tion.

A.5 Variables depending on both environment and

material

A.5.1 Carbonation
Variable Condition Distribution Unit
k e ,ca OPC, Laboratory 65 % RH 1.0 -
k e ,ca OPC, Outdoor sheltered, 81 % RH LN(0.82;0.30) -
k e ,ca OPC, Outdoor unsheltered, 81 % RH LN(0.82;0.27) -
k e ,ca OPC+GGBS, Laboratory, 65 % RH 1.0 -
k e ,ca OPC+GGBS, Outdoor sheltered, 81 LN(0.42;0.51) -
% RH
k e ,ca OPC+GGBS, Outdoor unsheltered, 81 LN(0.49;0.24) -
% RH
Table A.5: Environment factor for carbonation.

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Final Technical Report 121

Variable Condition Distribution Unit

nca OPC, Laboratory, 65 % RH 0 -
nca OPC, Outdoor sheltered, 81 % Beta(1.95;8.00;0;0.5) -
RH
nca OPC, Outdoor unsheltered, 81 Beta(4.10;0.97;0;0.5) -
% RH
nca OPC+GGBS, Laboratory, 65 0 -
% RH
nca OPC+GGBS, Outdoor unshel- Beta(14.0;40.0;0;0.5) -
tered, 81 % RH
nca OPC+GGBS, Outdoor unshel- Beta(29.0;5.04;0;0.5) -
tered, 81 % RH
Table A.6: Age factor for carbonation.

A.5.2 Chloride ingress

Variable Condition Distribution Unit
k e ,cl OPC, Submerged Ga(35.3;26.6) -
k e ,cl OPC, Tidal zone Ga(35.5;38.5) -
k e ,cl OPC, Splash zone Ga(2.92;11.0) -
k e ,cl OPC, Atmospheric Ga(35.2;52.0) -
k e ,cl GGBS, Submerged Ga(9.00;2.32) -
k e ,cl GGBS, Tidal Zone Ga(4.38;1.62) -
k e ,cl GGBS, Splash zone Ga(0.362;0.465) -
k e ,cl GGBS, Atmospheric Ga(2.34;1.18) -

Table A.7: Environment factor for chloride ingress.

Variable Condition Distribution Unit
ccr OPC, w/b=0.5, Tidal zone N(1.6;0.2) [%] relative to binder
ccr OPC, w/b=0.4, Tidal zone N(2.1;0.2) [%] relative to binder
ccr OPC, w/b=0.3, Tidal zone N(2.3;0.2) [%] relative to binder
ccr OPC, w/b=0.5, Tidal zone N(0.50;0.10) [%] relative to binder
ccr OPC, w/b=0.4, Tidal zone N(0.80;0.10) [%] relative to binder
ccr OPC, w/b=0.3, Tidal zone N(0.90;0.15) [%] relative to binder

Table A.8: Critical chloride concentration for OPC-concrete.

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Variable Condition Distribution Unit

Acs OPC, Submerged N(10.3;0.71) [%] relative to binder
Acs OPC, Tidal and splash N(7.76;1.36) [%] relative to binder
Acs OPC, Atmospheric N(2.57;0.36) [%] relative to binder
Acs PFA, Submerged N(10.8;1.86) [%] relative to binder
Acs PFA, Tidal and splash N(7.46;0.32) [%] relative to binder
Acs PFA, Atmospheric 4.42 [%] relative to binder
Acs GGBS, Submerged N(5.06;0.66) [%] relative to binder
Acs GGBS, Tidal and splash N(6.77;0.28) [%] relative to binder
Acs GGBS, Atmospheric 3.05 [%] relative to binder
Acs SF, Submerged N(12.5;1.54) [%] relative to binder
Acs SF, Tidal and splash N(8.96;1.74) [%] relative to binder
Acs SF, Atmospheric N(3.23;0.24) [%] relative to binder
εc s
OPC, Submerged N(0;0.59) [%] relative to binder
εc s
OPC, Tidal and splash N(0;1.11) [%] relative to binder
εc s
OPC, Atmospheric N(0;0.405) [%] relative to binder
εc s
PFA, Submerged N(0;1.18) [%] relative to binder
εc s
PFA, Tidal and splash N(0;0.75) [%] relative to binder
εc s
PFA, Atmospheric - [%] relative to binder
εc s
GGBS, Submerged N(0;1.08) [%] relative to binder
εc s
GGBS, Tidal and splash N(0;0.33) [%] relative to binder
εc s
GGBS, Atmospheric - [%] relative to binder
εc s
SF, Submerged N(0;1.39) [%] relative to binder
εc s
SF, Tidal and splash N(0;1.57) [%] relative to binder
εc s
SF, Atmospheric N(0;0.25) [%] relative to binder

Table A.9: Variables for surface chloride concentration.

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Variable Condition Distribution Unit

ncl OPC, Submerged Beta(24.9;58.1;0;1) -
ncl OPC, Tidal and splash Beta(17.2;29.3;0;1) -
ncl OPC, Atmospheric Beta(29.5;15.9;0;1) -
ncl PFA, Submerged Beta(58.3;26.2;0;1) -
ncl PFA, Tidal and splash Beta(1234;92.9;0;1) -
ncl PFA, Atmospheric Beta(29.6;15.2;0;1) -
ncl GGBS, Submerged Beta(57.8;23.6;0;1) -
ncl GGBS, Tidal and splash Beta(5.80;3.87;0;1) -
ncl GGBS, Atmospheric Beta(21.3;3.75;0;1) -
ncl SF, Submerged Beta(57.8;35.4;0;1) -
ncl SF, Tidal and splash Beta(18.5;29.0;0;1) -
ncl SF, Atmospheric Beta(26.0;6.90;0;1) -

Table A.10: Age factor for chloride ingress.

A.5.3 Corrosion rate

Variable Condition Distribution Unit
k RH ,res Unsheltered sLN(0.62;0.33;0.79) -
k RH ,res BFSC, 50 % RH sLN(4.71;1.21;4.93) -
k RH ,res BFSC, 65 % RH sLN(1.91;1.08;3.57) -
k RH ,res BFCS, 80 % RH sLN(1.16;0.65;2.36)
k RH ,res BFSC, 95 % RH sLN(0.93;0.13;0.24) -
k RH ,res OPC, 50 % RH sLN(6.70;0.29;0.59) -
k RH ,res OPC, 65 % RH sLN(2.11;1.14;2.41) -
k RH ,res OPC, 80 % RH sLN(1.43;0.72;1.33) -
k RH ,res OPC, 90 % RH LN(1.07;0.14) -
k RH ,res Submerged, tidal and splash 1.0 -

Table A.11: Factor for the relative humidity for the corrosion rate.

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A.5 Execution variables

A.5.1 Carbonation
Variable Condition Distribution Unit
k c ,ca At age 1 day sLN(2.52;0.84;0.46) -
k c ,ca At age 3 days 1.0 -
k c ,ca At age 7 days sLN(0.86;1.03;0.88) -
k c ,ca At age 28 days Beta(1.86;1.10;0.35;1.0) -

Table A.12: Curing factors for carbonation.

A.5.2 Chloride ingress

Variable Condition Distribution Unit
k c ,cl At age 1 day Beta(1.07;1.90;1.0;4.0) -
k c ,cl At age 3 days 1.0 -
k c ,cl At age 7 days Beta(2.15;10.7;1.0;4.0) -
k c ,cl At age 28 days Beta(4.44;2.33;0.40:1.0) -

Table A.13: Curing factor for chloride ingress.

A.5.3 Corrosion rate

Variable Condition Distribution Unit
k c ,res - 1.0 -

Table A.14: Curing factor for resistivity.

A.6 Other variables

Variable Condition Distribution Unit
a1 N(74.4;3.2) [µm]
a2 N(7.3;0.06) [µm]
a3 N(-17.4;5.7) [µm/MPa]
b Bars positioned at top N(0.0086;0.0048) [mm/µm]
b Bars positioned at bottom N(0.0104;0.0013) [mm/µm]
Table A.15: Other variables.
The distributions and distribution parameters of other variables shall be deter-
mined on the basis of JCSS [36].

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Appendix B: Calibration of partial factors

B.1 Introduction
The partial factors are calibrated such that a given design based on these partial
factors obtains the target reliability, βt . This can be achieved by determining
the partial factors such that the values of the design variables used in the deter-
ministic design corresponds to the values of the basic variables in the "most
likely" failure point (The point in the failure region where the joint probability
density function of the basis variables reaches its maximum) when the reliabil-
ity index is equal to the target reliability.

Using this definition, the partial factors can be determined using the target reli-
ability index and the α -vector determined by the reliability analyses.

In the following, the expressions for evaluation of the partial factors for dura-
bility design are given. Partial factors are determined for the following vari-
ables

• Cover thickness
• Critical chloride concentration
• Chloride surface concentration
• Apparent chloride diffusion coefficient
• Effective carbonation diffusion coefficient
• Rate of corrosion

Using the expressions given in the following sections, the partial factors for
these variables can be determined.

The distribution parameters necessary to determine the partial factors are all
given in Appendix A. Further, the definitions of the characteristic values of the
variables are given in Chapter 3.

B.2 Cover thickness

The cover thickness follows a logarithmic Normal distribution. The cover
thickness is treated as a resistance variable. Hence, the partial factor for the
cover thickness can be determined by

∆x = x c − exp(µ ′x + α x β t σ ′x ) (B.1)

where µ x′ is the mean of the logarithm of the cover thickness, σ x′ is the stan-
dard deviation of the logarithm of the cover thickness, α x is the element of the
α -vector related to the cover thickness and x c is the characteristic value of the
cover thickness.

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B.3 Critical chloride concentration

The critical chloride concentration is normally distributed and it acts as a resis-
tance variable. Hence, the partial factor can be determined from

ccrc
γc = (B.2)
cr
µc + α c βt σ c
cr cr cr

where ccrc is the characteristic value of the critical chloride concentration, µccr
and σ ccr denotes the mean and standard deviation of the critical chloride con-
centration, respectively, and α ccr is the element of the α -vector related to the
critical chloride concentration.

B.4 Chloride surface concentration

For a structure in a marine environment the chloride surface concentration is
given by

cs = A( w / b) + ε (B.3)

where w / b is the water-binder ratio and where the regression parameter, A ,

and the error, ε , are both normally distributed. The mean value of the error, ε ,
is zero.

Taking into account that the chloride surface concentration acts as a load, the
partial factor for the surface concentration can be determined by

(µ A + α A βt σ A )( w / b) + α ε σ ε
γc = (B.4)
s
csc

where µ A and σ A denotes the mean and standard deviation of A , respectively,

σ ε is the standard deviation of the error and α A and α ε are the elements of the
α - vector related to A and ε , respectively.

For a structure subject to de-icing salt the chloride surface concentration is

modelled by a logarithmic Normal distribution. The partial factor is given by

γc =
(
exp µc′s + α cs βt σ c′s ) (B.5)
c
s
c s

where µc′s and σ c′s denotes the mean and standard deviation of the logarithm of
the surface concentration, respectively.

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B.5 Chloride diffusion coefficient

The apparent chloride diffusion coefficient is given by

ncl
t 
Da = k t ,cl k e,cl k c ,cl D0  0  (B.6)
t 

where k t ,cl is a constant, k e ,cl follows a Gamma distribution, k c ,cl follows a

Beta distribution, D0 is normally distributed, and ncl follows a Beta distribu-
tion.

The partial factor for the apparent chloride diffusion coefficient can be deter-
mined by

ncld
t 
k t ,cl k ed,cl k cd,cl D0d,cl  0d 

γ Da =  ti  (B.7)
c
Da

where the design values of the variables are given by

((
ked, cl = Fk−e 1,cl Φ α k e ,cl βt )) 

kcd, cl = Fk−c1,cl (Φ(α k c ,cl β ))
t

 (B.8)
D0d, cl = µ D0 ,cl + α D0 ,cl βt σ D0 ,cl 

( (
ncld = Fn−cl1 Φ α ncl βt )) 

where µ D0 and σ D0 denotes the mean and standard deviation of D0 , respec-

tively, Fk−1
e , cl
, Fk−1
c , cl
and Fn−1
cl
are the inverse distributions of k e ,cl , k c ,cl and ncl ,
respectively, and α ke ,cl , α kc ,cl , α D0 and α ncl are the elements of the α -vector
relevant for k e ,cl , k c ,cl , D0 and ncl , respectively. Finally, Φ denotes the stan-
dard Normal distribution function. Note the partial factor depends on the design
value of the time to initiation of corrosion, t id .

B.6 Carbonation diffusion coefficient

The effective carbonation diffusion coefficient is given by

n ca
t 
Deff = kt , ca ke, ca kc , ca D0  0  (B.9)
t 

where k t ,ca and k e ,ca are constants, k c ,ca follows a Beta distribution, D0 is
normally distributed and nca follows a Beta distribution.

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The partial factor for the effective carbonation diffusion coefficient can be de-
termined by
d
n ca
t 
kt , ca ked, ca kcd, ca D0d, ca  0d 
γ Deff =  ti  (B.10)
c
Deff

where the design values are given by

((
ked, ca = Fk−e1,ca Φ α k e ,ca βt )) 

kcd, ca = Fk−c1,ca (Φ(α k c ,ca β ))
t

 (B.11)
D0d, ca = µ D0 ,ca + α D0 ,ca βt σ D0 ,ca 

d
nca ( (
= Fn−ca1 Φ α nca βt )) 

where µ D0 and σ D0 denotes the mean and standard deviation of D0 , respec-

tively, Fk−c 1,ca and Fn−ca1 are the inverse distributions of k c ,ca and nca , respec-
tively, and αk c ,ca , α D0 and αnca are the elements of the α -vector relevant for
k c ,ca , D0 and nca , respectively. Again, note that the partial factor depends on
the design value of the time to initiation of corrosion, t id .

B.7 Corrosion rate

The corrosion rate is given by the following expression

m0
V = Fcl Fgalv FO2 (B.12)
ρ

where m0 is a constant for the corrosion rate versus resistivity, ρ is the resis-
tivity, Fcl is a chloride corrosion rate factor, Fgalv is a galvanic effect factor
and FO2 is a factor accounting for the availability of oxygen.

The resistivity, ρ , is given by

nres
 t hydr 
ρ = ρ0   k t ,res k c ,res k T ,res k RH ,res k cl ,res (B.13)
 t0 

where ρ0 is the potential electrolytical resistivity measured with the standard

test method at the age t 0 =28 days, t hydr is the period of hydration (not exceed-
ing one year), nres is the age factor for the resistivity and k t ,res , k c ,res , k T ,res ,
k RH ,res and k cl ,res are factors accounting for the effect of the test method, the

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curing, the temperature, the relative humidity and the presence of chloride, re-
spectively.

The temperature factor is given by

1
k T ,res = (B.14)
1 + K ( T − 20)

where the temperature, T , is given in degrees Celsius.

The variables m0 , FO2 , t 0 , t hydr , k c ,res and T are modelled as constants. The
distribution type of a number of other variables depends on the exact circum-
stances, e.g. the presence of chloride. Therefore, only a very general expression
for the evaluation of the partial factor is given. The detailed probabilistic model
is given in Appendix A.

The partial factor for the corrosion rate can be determined from

γV =
( (
m0 FF−cl1 Φ α Fcl βt FF−galv
1
))
Φ α Fgalv βt F O2 (( )) (B.15)
ρ dV c

where FF−cl1 and FF−galv

1
are the inverse distribution functions of the factors Fcl
and Fgalv , respectively, α Fcl and α Fgalv are the elements of the α -vector rele-
vant for these factors, V c is the characteristic value of the corrosion rate and
ρ d is the design value of the resistivity given by.
d
nres
 t hydr 
ρ =ρ 
d
 d
o k c ,res k Td,res k RH
d d
,res k cl ,res (B.16)
 t0 

where

ρ0d = µρ + α ρ βt σ ρ 

0 0 0

d
nres ( (
= Fn−res1 Φ α nres βt )) 

d
k RH −1
((
,res = Fk RH , res Φ α k RH , res βt )) 


(B.17)

((
k cld ,res = Fk−cl1,res Φ α kcl ,res βt )) 


where Fρ−01 , Fk−1

RH , res
and Fk−1
cl , res
are the inverse distribution functions of the po-
tential resistivity, the factor accounting for the relative humidity and the factor
accounting for the presence of chloride, respectively, α ρ0 , α nres , α k RH ,res and
αk cl , res
are the relevant elements of the α -vector for these variables, and µρ0

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and σ ρ0 denote the mean and standard deviation of the potential resistivity, re-
spectively. Finally, k Td,res is the design value of the factor accounting for the
effect of the temperature given by

1
k Td,res = (B.18)
1+ F
K
−1
(Φ(α β ))(T − 20)
K t

where FK−1 is the inverse distribution factor of the factor K and where α K is
the element of the α -vector relevant for the variable K .

B.8 Elements of the α-vector

The results of the reliability analyses carried out in Task 6 [12] and in the addi-
tional studies in [20] are used to establish a target reliability and to determine
the relevant α -vectors.

The α-vector necessary to determine and to perform adjustments of the partial

factors are given in Table B., Table B. and Table B. below for chloride ingress
in a marine environment, chloride ingress for structures subject to de-icing salt,
and carbonation, respectively. Notice that this α-vector depends on the reliabil-
ity level. The studies carried out in Task 6 [12,20] also indicates the α-vector
depends on time. Finally, the α-vector depends on the probabilistic model used
for the reliability analyses. This implies that the α-vectors given here should
only be used in conjunction with the target reliabilities also given here, only for
a reference period of 50 years and in conjunction with the probabilistic model
given in Appendix A.

For all elements of the α-vector not given here the value 0.0 can be used.

Cost of repair High Normal Low

relative to design
and construction
α ( x) -0.5573 -0.5844 -0.5796
α ( ccr ) -0.2800 -0.1638 -0.1629
α(D0 ) 0.1568 0.1428 0.1301
α ( k e ,cl ) 0.2647 0.2408 0.2193

α ( k c ,cl ) 0.1706 0.1784 0.1744

α ( ncl ) -0.5932 -0.6136 -0.5804

α ( A) 0.1270 0.1676 0.1997
α (ε ) 0.3440 0.3408 0.4061

Table B.1: Elements of the α-vector for structures in a marine environment.

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Cost of repair High Normal Low

relative to design
and construction
α ( x) -0.4998 -0.4982 -0.4202
α ( ccr ) -0.1177 -0.1418 -0.1696
α ( R0 ) 0.1308 0.1100 0.0741
α ( k e ,cl ) 0.2208 0.1855 0.1248

α ( k c ,cl ) 0.1501 0.1393 0.1003

α ( ncl ) -0.5238 -0.4798 -0.3289

α ( cs ) 0.6096 0.6590 0.8093

Table B.2: Elements of the α-vector for structures subject to de-icing salt.

Cost of repair High Normal Low

relative to design
and construction
α ( x) -0.7032 -0.7279 -0.6747
α ( R0 ) 0.1259 0.1019 0.0797
( )
α k c ,ca 0.1619 0.1569 0.1508

α (k ) e ,ca
0.3842 0.3034 0.2323

α ( nca ) -0.3398 -0.3353 -0.3386

α(β) 0.2244 0.2505 0.3130

α ( ρ0 ) -0.2126 -0.2052 -0.2277

α ( k RH ,res ) -0.2317 -0.2577 -0.3273

α ( nres ) -0.1866 -0.2075 -0.2643

Table B.3: Elements of the α-vector for structures subject to carbonation.

B.9 Adjustment of partial factors

No adjustments of the safety factors have been made.

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Appendix C: Decision Analysis

In practical decision problems such as reassessment, inspection and mainte-
nance planning for structures the number of alternative actions can be ex-
tremely large. Therefore, a framework for the systematic analysis of the actions
and their corresponding consequences is necessary. A framework suitable for
this purpose is decision analysis.

The reassessment decision problem may conveniently be represented by a deci-

sion tree as illustrated in Figure C.1.

e ∈Ω e S ∈Ω s a ∈Ω a Z ∈Ω z

Figure C.1: Decision tree.

Because different methods for collecting information have different costs and
yield information of different accuracy and relevance the owner of a structure
which must be reassessed is typically faced with the problem to choose if and
how to collect additional information about the state of the structure. The in-
formation may concern the state of deterioration, as built, geometry, material
characteristics etc. At the first level of the decision tree shown in Figure C. the
decision related to the planning of measurements and experiments are made, i.e.
the number and type of measurements and experiments is determined. The vari-
ables describing the experiment plan are denoted e and the set of available de-
cisions is denoted Ω e .

At the second level of the decision tree observations of the measurements and
experiments are obtained. It is important to take into account that the informa-
tion gained by the additional measurements and experiments are unknown at
the time where it is decided to collect it. These observations are, therefore,
modelled as stochastic variables, S , with the admissible range Ω s .

Depending on the state of knowledge after (posterior to) having collected the
information, a requalification action such as do nothing, strengthen and/or re-
pair must be chosen. Different requalification actions have different costs and
yield different effects on the state of the structure. At the third node in the deci-
sion tree it is decided which action to take. This decision is made by the owner
of the structure and is denoted a . The set of possible actions is denoted Ω a

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At the fourth level in the decision tree a realisation is observed. Typically this
realisation is related to observations of some critical event, for example failure.
The uncertainties related to the loads (environment) and resistances (material)
are modelled by the stochastic variables Z with the admissible range Ω z . The
limit state function

g(e, s, a , z) = 0 (C.1)

is used to model the critical event. The critical event can also be given in terms
of a union of intersections of a number of events. The critical event describes
the state of the structure. The structure can be in a safe region where all re-
quirements are fulfilled or in some other state where it is not able to fulfil one
or more of the required performance criteria. Each of these states can be associ-
ated with a given cost.

The models for the stochastic variables S and Z must be specified in a prob-
abilistic model which is formulated such that it can be updated on the basis of
the results from the experiments performed according to the experiment plan,
e . This implies that the probabilistic model must be formulated within the
framework of Bayesian statistics which allows the probabilistic model to be
updated in a rational manner on the basis of new information. Before (prior to)
the additional information has been collected the probabilistic description of the
structure is called an a´priori probabilistic model. When the additional informa-
tion has been taken into account in the probabilistic model for the state of the
structure this model is called an a´posteriori probabilistic model. In section 3.3
more formal definitions of the prior and posterior models are given. When the
decision analysis includes both the decision of collecting information and the
decision of requalification actions the analysis is called a pre-posterior decision
analysis.

For a given structure an optimal experiment plan, e , and an optimal requalifi-

cation action, a , can be identified by maximising the expected benefit or utility
or by minimising the expected cost. Corresponding to the decisions by the user,
i.e. e and a , and the realisations by nature of S and Z a cost is obtained. The
optimal decisions e * and a * can be obtained by solving the following optimi-
sation problem involving the costs C(e, S, a , Z ) as a function of the experiment
plan, e , the observations of the experiments, S , the action, a , and the state of
nature, Z

[
C * = min e E S e min a E Z′′ S C(e, S, a , Z ) ] (C.2)

where E S e [ − ] is the expectation with respect to the joint density function for
the variables S in the given experiment plan, e and E Z′′S [ − ] is the expectation
with respect to the posterior joint density function of the variables Z for the
given outcome of the variables S .

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The optimisation problem given in eq. (1) is called the extended form of analy-
sis. In some cases the optimisation problem can be formulated by the so-called
normal form of analysis

[ [
C * = min e min d E Z′ E S e ,Z C( e, S, d( S) , Z ) ]] (C.3)

where d( S) is a decision rule specifying the action, a , to be taken directly on

the basis of the observations of S , E Z′ [ − ] is the expectation with respect to the
prior density function of Z and E S e ,Z [ − ] is the expectation with respect to the
joint density function for S in the chosen experiment plan, e , and for given
outcomes of Z . The normal form can be used when it is possible to formulate a
decision rule. Otherwise the extensive form of analysis has to be used.

From a computational point of view eq. (2) is generally much easier to solve
than eq. (1) since the minimisation with respect to the action, a , is inside the
expectation with respect to S (in eq. (1)).

The cost function is assumed to be written

[
C ( e, S , a , Z ) = C M ( e ) + C R ( e , S , a , Z ) + C F I g ( e, S , a , Z ) ≤ 0 ] (C.4)

where C M is the costs associated with the chosen experiment plan, C R is the
costs of the chosen requailification action and C F is the cost of failure. The
indicator function, I [ −] is equal to one if failure occurs and equal to zero if the
component or system is safe. To evaluate the expected value of the cost, C , it
(
is necessary to evaluate the probability of failure, P g(e, S, a , Z ) ≤ 0 . This can )
be done by the use of modern reliability methods such as FORM/SORM.

The decision problem described here is given in the most general form. In
many cases the problems can be formulated such that the complexity of the
problems and the computational effort involved in the solution of the problems
can be reduced.

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Appendix D: Bayesian updating

D.1 Direct updating

The probability of failure can be updated on the basis of observations of one or
more events, for example :

• Proof loading: where a well defined load action is applied to a structure and
it is observed that the structure does not fail or alternatively, the level of
damage is observed.

• Repair events: where a certain type of repair or maintenance has been per-
formed.

• No-failure events: where the 'simple' observation is made that the struc-
ture/component considered has not failed (it is still functioning as expected).

In order to model the observed events an event function

H = h( Z ) (D.1)

is introduced. The event function h corresponds to the limit state function g.

The actual observations are considered as realisations (samples) of the stochas-
tic variable H.

Some observations can be modelled by an inequality event {H ≤ 0} , i.e. it is

observed that the observed quantity is less than or equal to some limit. The
probability of failure can then be updated using conditional probabilities. The
updated probability of failure is estimated by

P( g( Z) ≤ 0 ∩ h( Z) ≤ 0)
PfU (t ) = P( g( Z) ≤ 0 h( Z) ≤ 0) = (D.2)
P(h( Z) ≤ 0)

where the failure function g( Z ) describing the considered event is defined

such that it is less than zero if and only if the considered event occurs. In eq.
(D.2) it is used that the probability of an event A given an event B (denoted
P( A ∩ B)
P( A B) ) is equal to . Eq. (D.2) can be evaluated by FORM/SORM
P( B)
methods, see Madsen et al. [19].

Other observations can be modelled by equality events {H = 0} , i.e. it is ob-

served that the observed quantity is equal to some limit. In this case the updated
probability of failure can be estimated by

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136 Final Technical Report

∂
P( g(Z) ≤ 0 ∩ h(Z) ≤ x)
∂x x =0
Pf (t ) = P( g(Z) ≤ 0 h(Z) = 0) =
U
(D.3)
∂
P(h(Z) ≤ x)
∂x x =0

The details in the derivation of this formula can be found in Madsen et al. [19].
This formula can also be evaluated by FORM/SORM methods and can easily
be generalised if more than one event is observed. In most software packages
for reliability analysis efficient algorithms are available for solving this prob-
lem.

Finally it should be mentioned that individual random variables may also be

updated by inspections of events involving the outcomes of several random
variables. This should nevertheless be done with care. For instance it is impor-
tant to realise that all the random variables that are present in g(Z) (and all the
variables correlated to Z) are affected by the inspection. For instance, if we
measure a crack length in one point of a bridge structure, this affects the distri-
butions of the load parameters, the stress concentration factors, the residual
stresses, and the parameters of the fatigue model. Moreover, all these parame-
ters become correlated, even if they were independent before inspection.

D.2 Updating of distribution parameters

If observations of one (or more) of the stochastic variables Z are available the
probabilistic model can be updated and thus the probability of failure can be
updated. Consider a stochastic variable Z with density function f Z ( z) . If θ
denotes a vector with parameters defining the distribution for Z the density
function of the stochastic variable Z can be written

f Z ( z,θ ) (D.4)

If Z is normal distributed then θ could contain the mean and the standard de-
viation of Z.

If the parameters θ are uncertain then f Z ( z,θ ) can be considered as a condi-

tional density function : f Z ( z Θ) . θ denotes a realisation of Θ .The prior (ini-
tial) density function for the parameters Θ is denoted f Θ′ (θ ) and is denoted the
prior density function.

It is assumed that N observations (realisations) of the stochastic variable Z are

available making up a sample z$ = ( z$1 , z$2 ,..., z$ N ) of size N. The realisations are
assumed to be independent. The updated density function f Θ′′(θ z$ ) of the uncer-
tain parameters Θ given the realisations is denoted the posterior density func-
tion and is given by, see textbook on Bayesian statistics, e.g. Lindley [37].

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Final Technical Report 137

f N ( z$ θ ) f Θ′ (θ )
f Θ′′(θ z$ ) = (D.5)
∫ f N ( z$ θ ) f Θ′ (θ )dθ

N
where f N ($zθ ) = ∏ f Z ( z$i θ ) is the probability density at the given observa-
i =1
tions assuming that the distribution parameters are θ . The integration in eq.
(D.5) is over all possible values of θ .

The updated density function of the stochastic variable Z given the realisation
z$ is denoted the predictive density function and is defined by,

f Z ( z z$ ) = ∫ f Z ( z θ ) f Θ′′(θ z$ )dθ (D.6)

Given the distribution function for the stochastic variable Z, the prior distribu-
tion is often chosen such that the posterior distribution will be of the same type
as the prior distribution (a so-called conjugated prior). In the literature a num-
ber of prior, posterior and predictive distribution functions can be found, see
e.g. Raiffa & Schlaifer [38]. Analytical solutions concerned with the following
problems can be found

• Normal distribution with unknown mean

• Normal distribution with unknown standard deviation

• Normal distribution with unknown mean and standard deviation

• Gumbel distribution

• Weibull distribution

• Exponential distribution

• Bernoulli distribution

• Poisson distribution

• Multidimensional Normal distribution with unknown means

• Multidimensional Normal distribution with unknown standard deviations

• Multidimensional Normal distribution with unknown means and standard

deviations

The parameters in the prior distribution can be chosen or calculated in such a

way that the prior reflects

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138 Final Technical Report

• known (initial) observations of the stochastic variables Z from which esti-

mates of the parameters in the prior distribution can be calculated.

• subjective knowledge on the distribution of the parameters Θ in the distribu-

tion of Z.

In this way it is possible to choose a prior distribution which reflects a range of

situations from very good prior knowledge on the parameter (small standard
deviation) to almost no knowledge on the parameters (large standard deviation).

BE95-1347 DuraCrete –Probabilistic Performance based Durability Design of Concrete Structures