Assessment of usually encountered damage on concrete bridges and its influence on the load carrying capacity capacity and safety of users

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INFLUENCE ON THE LOAD CARRYING

CAPACITY AND SAFETY OF USERS

by

Lizbè Botes

Thesis presented in partial fulfilment of the requirements for the degree

Master of Engineering (Structural Design)

Stellenbosch University

Faculty of Engineering Civil Department Structural Design Division

Promotor: Dr R. Lenner

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DECLARATION

By submitting this thesis electronically, I declare that the entirety of the work contained therein is my own, original work, that I am the sole author thereof (save to the extent explicitly otherwise stated), that reproduction and publication thereof by Stellenbosch University will not infringe any third party rights and that I have not previously in its entirety or in part submitted it for obtaining any qualification.

Date: March 2018

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ABSTRACT

Assessment of Usually Encountered Damage on Concrete Bridges and its Influence on the Load Carrying Capacity and Safety of Users

L. Botes

Thesis: MEng (Research) March 2018

The assessment of existing bridges is becoming increasingly important since it is necessary to ensure that all bridges maintain structural integrity in terms of the ultimate limit state for which they were designed. South Africa uses a Bridge Management System (BMS) to assess and manage existing structures. The assessment is based on visual inspection, and ratings form 0-4 are assigned to the extent of damage (DERU-rating system) which occurs on the bridge. Using the condition analysis, a prioritised list is compiled where ranking all inspected bridges from worst to least degraded. This list is then used to determine what resources should be allocated and which bridges need to be repaired first. A more accurate way of assessing existing bridges is however required to determine which bridge will fail first, if not repaired.

This study developed a method for assessing existing bridges based on their reduction in structural integrity. It was done by relating compiled damage distributions to the DERU-ratings, then using the assigned DERU-ratings in accordance with a reliability-based model, to determine reductions in structural strength.

The critical damages identified were reinforcement corrosion, cracking, and spalling of concrete. These damages were compared and it was assumed that a natural sequence will follow; the reinforcement will start to corrode, induce cracking and lead to concrete spalling. This natural sequence was divided into categories, each representing a state of degradation. Distribution functions were compiled to represent the critical damage and were related to the established categories. To determine the effect of these categories, a representative beam was used and degradation applied. The reduction in structural strength was determined according to a reliability assessment, and these results were compared to the results if the beam was analysed according to the BMS. It was concluded that the reliability assessment gave a better representation of structural degradation since, in this case, most of the degradation was not visible from the outside, and thus could not be correctly assessed by visual inspection.

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OPSOMMING

Assessering van Algemene Skade op Beton Brûe en die Invloed op die Dravermoë en die Veiligheid van Gebruikers

L. Botes

Verhandeling: MIng (Navorsing) Maart 2018

Die strukturele assessering van bestaande brûe is ‘n kritiese aspek van infrastruktuur bestuur, aangesien die integriteit van ‘n struktuur in terme van sy uiterste ontwerps-limiet verseker moet wees oor sy lewensduurte. Die brug bestuur sisteem genaamd “BMS” word in Suid-Afrika gebruik vir die bepaling van bestaande strukture se kondisie, en is meestal gebaseer op visuele inspeksie en ander nie-destruktiewe toetsmetodes. ‘n Objektiewe asseseringsmodel genaamd “DERU” word gebruik om verskeie tipes skade teenwoordig op ‘n brug te dokumenteer. Deur gebruik te maak van kondisie analise kan ‘n geprioritiseerde lys opgestel word vanaf hierdie data, waar alle brûe gerangeer word in terme van skade en herstelwerk benodig. Die instandhoudings outoriteit kan dan objektief besluit of die bestaande brûe herstel of vervang moet word.

Die studie het ‘n metode ontwikkel om bestaande, beskadigde brûe te assesseer in terme van hul strukturele verrigting. Dit was bereik deur die versamelde skade distribusies volgens die DERU-model te vergelyk deur gebruik te maak van ‘n betroubaarheid-gebaseerde model. Die resultate verskaf dan ‘n objektiewe uitslag oor die strukturele integriteit van die struktuur.

Kritiese skade kriteria is geïdentifiseer as die drievoud van bewapening korrosie, kraak van omhullende beton en die dienooreenkomstige aftrek van die buitenste betonlaag. Hierdie skade kondisies is vergelyk en aangeneem as die normale verloop van degradasie op ‘n strukturele bewapende beton element. Hierdie natuurlike gevolg is ingedeel in kategorieë, waar elke afsonderlike kategorie ‘n element van degradasie verteenwoordig het. Distribusie funksies is saamgestel om die kritieke skades te vergelyk met die bestaande kategorieë. Laastens is die effekte vergelyk met die bestaande BMS deur gebruik te maak van ‘n verteenwoordigende strukturele balk met verswakking a.g.v. die kritiese skade kriteria. Die studie het bevind dat die betroubaarheids assesserings model ‘n beter verteenwoordiging van die struktuur se verswakking toon, veral in die spesifieke gevallestudie aangesien die verswakking nie visueel sigbaar was nie.

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ACKNOWLEDGEMENTS

I would like to acknowledge the contributions of the following people and entities who helped me bring this research report into being:

 My supervisor, Dr R. Lenner, who provided me guidance and support and never gave up on me, even when my thesis was at times unreadable.

 The Structural Design Department, Engineering Faculty, University of Stellenbosch for funding my research.

 The South African National Roads Agency Limited for information on the assessment of existing bridges.

 Paul Nordengen for information on South Africa’s Bridge Management System.  Milan Holický for guidance and advice in terms of the reliability analysis  Fran Saunders for editing my thesis. I know this was a challenge.  Antoni Botes for his assistance in translating the abstract.

 All my friends and fellow research colleagues, who provided me with ideas, advice, encouragement and a glass of wine when it was needed.

 My fiancé Marcel, who supported me unconditionally during this time. You were truly my greatest support and I could not have done this without you. I love you.

 To both my parents who provided me with the best education and support in order to achieve my dream. You are my inspiration, motivation and support system. Thank you for everything.

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3 LIST OF FIGURES

Figure 2.1: Structural Assessment Level ... 6

Figure 2.2: A basic BMS [1]. ... 9

Figure 2.3: Bridge classification [12]. ... 11

Figure 2.4: Deterioration models [24]. ... 21

Figure 2.5: PDF and CDF of a Normal Distribution [30]. ... 26

Figure 2.6: PDF and CDF of a Lognormal Distribution [30]. ... 27

Figure 2.7: Load effect E and resistance R as random variables [38]. ... 29

Figure 2.8: Distribution of the safety margin Z [38]. ... 30

Figure 2.9: Main components of a bridge [42]. ... 34

Figure 5.1: Deterioration model of reinforced steel due to corrosion [48]. ... 51

Figure 5.2: Relationship between water-to-cement ratio and diffusion coefficient [69]. ... 56

Figure 5.3: PDF & CDF of the basis distribution of the time to corrosion initiation ... 60

Figure 5.4: PDF & CDF of the basis distribution of icorr(1) ... 67

Figure 5.5: Dominant parameters of a concrete beam [102] ... 74

Figure 6.1: Representative beam ... 82

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LIST OF TABLES

Table 2.1: Bridge Subdivisions ... 12

Table 2.2: Details of the DERU rating system [13] ... 14

Table 2.3: Default values for sub-items with D-rating as U for SACI calculations ... 16

Table 2.4: Proposed inspection item weights for various structures ... 17

Table 2.5: Default values for sub-items with D-rating as U for SPCI calculations ... 18

Table 2.6: Relationship between the failure probability and reliability index [38]. ... 31

Table 2.7: Reliability classification according to EN 1990 [35] ... 31

Table 2.8: General damage found on the main components of a bridge [1] ... 35

Table 2.9: Causes of concrete cracks, before and after hardening [12]. ... 36

Table 4.1: A summary of the identified defects on the critical bridge items in the THM19 [12] ... 47

Table 4.2: Simplified summary of the defects and their ratings ... 48

Table 5.1: Probability distribution properties for concrete cover ... 54

Table 5.2: Probability distribution properties for surface chloride concentration ... 55

Table 5.3: Probability distribution properties for diffusion coefficient ... 56

Table 5.4: Probability distribution properties for threshold chloride concentration ... 58

Table 5.5: Summary of variables chosen ... 59

Table 5.6: Basis distribution function for the time to corrosion initiation. ... 60

Table 5.7: The mean influence on the time to corrosion initiation ... 61

Table 5.8: Summary of the variables' mean influence on the time to corrosion initiation ... 61

Table 5.9: The COV influence on the time to corrosion initiation ... 62

Table 5.10: Summary of the variables' COV influence on the time to corrosion initiation ... 62

Table 5.11: The mean and COV influences on the icorr(1) ... 66

Table 5.12: Mean corrosion rates in µA/cm2 [90] ... 68

Table 5.13: Corrosion rates related to cracking's degree-ratings ... 69

Table 5.14: Corrosion rates related to spalling's degree-ratings ... 71

Table 5.15: Bar diameter loss vs crack width ... 73

Table 5.16: Internal penetration in terms of s/dc and the reinforcement diameter reduction. ... 74

Table 5.17: Reinforcement diameter reduction correlated to the degradation categories. ... 75

Table 6.1: Summary of categories with corrosion rates ... 79

Table 6.2: Variables for corrosion rate for Category A ... 80

Table 6.3: Parameter values of the representative beam ... 82

Table 6.4: Category A corrosion rates for specified time frames ... 84

Table 6.5: Summary of results for example 1, 5-year time-frame intervals ... 85

Table 6.6: Summary of results for example 2, 10-year time-frame intervals ... 85

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Table 6.8: Degree-Ratings for Examples 1-3 ... 87

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LIST OF EQUATIONS

Equation 2.1: The inspection sub-item condition index ... 16

Equation 2.2: The inspection item condition index ... 16

Equation 2.3: The overall condition index for a structure ... 17

Equation 2.4: The inspection sub-item priority index ... 18

Equation 2.5: The inspection item priority index ... 19

Equation 2.6: The structure priority condition index ... 19

Equation 2.7: The distribution function of a random variable ... 24

Equation 2.8: The probability distribution function of a random variable ... 24

Equation 2.9: The mean value of a random variable ... 25

Equation 2.10: The variance of a random variable ... 25

Equation 2.11: The coefficient of variation of a random variable ... 25

Equation 2.12: The skewness value of a random variable ... 25

Equation 2.13: The kurtosis value of a random variable ... 25

Equation 2.14: The probability distribution function of a normal distribution ... 26

Equation 2.15: The cumulative distribution function of a normal distribution ... 26

Equation 2.16: The probability distribution function of a lognormal distribution ... 26

Equation 2.17: The cumulative distribution function of a lognormal distribution ... 27

Equation 2.18: The safety margin of two random variables ... 29

Equation 2.19: The mean value of the safety margin ... 29

Equation 2.20: The standard deviation of the safety margin ... 29

Equation 2.21: The probability of failure of two random variables ... 30

Equation 2.22: The reliability index ... 30

Equation 2.23: The probability of failure in terms of the reliability index ... 30

Equation 2.24: The reliability index as a fraction ... 31

Equation 2.25: The probability of failure limit state for the design working life ... 32

Equation 2.26: The reliability index limit state for the design working life ... 32

Equation 2.27: The time-dependent safety margin of two random variables ... 33

Equation 2.28: The time-dependent probability of failure of two random variables ... 33

Equation 5.1: The penetration of chlorides, Fick’s second law of diffusion ... 51

Equation 5.2: The chloride-ion concentration ... 52

Equation 5.3: The time to corrosion initiation ... 52

Equation 5.4: The time to corrosion initiation with a model uncertainty ... 52

Equation 5.5: The diffusion coefficient probability function ... 56

Equation 5.6: The reduced cross-sectional area of the corroded reinforcement ... 64

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Equation 5.8: The first level of corrosion rate ... 65

Equation 5.9: The second level of corrosion rate ... 65

Equation 5.10: The critical mass of corrosion products ... 72

Equation 5.11: Time to cracking ... 73

Equation 6.1: The bending limit state ... 81

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LIST OF ABBREVIATIONS

AAR Alkali-Aggregate Reaction

BMS Bridge Management System BRIME Bridge Management in Europe CDF Cumulative Distribution Function COV Coefficient of Variation

CSIR Centre for Scientific and Industrial Research DERU Degree Extent Relevancy Urgency

E Load Effect

PDF Probability Density Function R Structural Resistance

SACI Structural Average Condition Index

SANRAL South African National Roads Agency Limited SCCI Structure Combined Condition Index

SFI Structure Functional Index SLS Serviceability Limit State

SPCI Structure Priority Condition Index SSI Stewert Scott International ULS Ultimate Limit State

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4 LIST OF SYMBOLS

(Chapter 2) bc Dmax+ Emax = 4 + 4 = 8

Icij Condition index of inspection sub-item j of inspection item i n Number of relevant inspection sub-items in inspection item i

Ici Condition index of inspection item i wci Condition weight for inspection item i N Number of relevant inspection items

kd Degree coefficient (tentative default value: 1) ke Extent coefficient (tentative default value: 0.25) a Relevancy exponent (tentative default value: 1.5)

Ipij Priority index of inspection sub-item j of inspection item i Ipi Priority index of inspection item i

Wpi Priority index for inspection item I; same as for SACI

X Random variable

x Specific value of the random variable Φx(x) Distribution function or CDF φ(x) PDF μ Mean σ2 _Variance σ Standard deviation α Skewness ε Kurtosis Z Safety Margin E Load effect R Structural Resistance Pf Probability of failure β Reliability Index

Td Design working life

(Chapter 4) dc concrete cover, in mm

Ød bar diameter, in mm

y depth measured from the concrete surface, in mm

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(Chapter 5) x Distance from the surface where C is calculated C Chloride-ion concentration

t Age of the bridge at which the results is needed

D Diffusion coefficient

C(x,t) Concentration at depth x

Cs Surface chloride concentration erf Error function

Ti Time to corrosion initiation

dc Concrete cover

C Chloride concentration

Cth Chloride Threshold Concentration w/c Water-cement-ratio

As Reinforcing cross-sectional area n Total number of reinforcing bars Do Original bar diameter

∆D(t) Reduction in bar diameter

Ti Time in years to corrosion initiation icorr Corrosion rate, measured in µA/cm2

Qcr the critical mass of corrosion products, in g/m2 dc concrete cover, in mm

Ød bar diameter, in mm icorr corrosion rate, in µA/cm2 tcr time to cracking, in years

(Chapter 6) URM Resistance model uncertainty

URM Loading model uncertainty

As Steel Reinforcement area in tension zone fy Steel yield strength, taken as 450MPa

fcu Concrete compressive strength, taken as 30MPa

h Beam height

dc Cover depth

b Beam width

MDL Bending moment due to dead load

MLL Bending moment due to live load, taken as 40% of the dead load.

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1 CHAPTER 1: Introduction

1.1 Background

As civil infrastructures age, the assessment of existing structures including buildings and bridges is becoming increasingly important. Bridges are typically designed for a certain life span of 50-100 years, but to achieve this design life it is necessary to monitor the aging of the bridge and to perform basic maintenance. Bridge management covers all the actions that need to be carried out to ensure that a bridge remains fit for its purpose throughout its design life without the need for excessive maintenance [1].

South Africa uses a Bridge Management System (BMS) which enables road authorities to manage the limited funds available for infrastructure maintenance. According to the South African National Roads Agency Limited (SANRAL) [2] all bridges in South Africa are inspected every five to seven years. This however is only a visual inspection; additional inspections are too expensive to carry out on every bridge. A visual inspection consists of a defects-based rating system (DERU) according to which the defect in each structural element is rated according to degree (D), extent (E), and relevancy (R). An urgency (U) rating, also known as a priority index value, is given to indicate perceived urgency of a proposed remedial activity [3].

Bridge maintenance is carried out according to priority index values and geographic location. Road authorities try to categories bridges which are geographically close to each other in order to submit a whole cluster in a single bid for repair. This saves time and money.

1.2 Problem Statement

The main reason for bridge maintenance is to ensure that every bridge in the country maintains structural integrity in terms of its ultimate limit state for which it has been designed. This means that the bridge’s structural state should be examined to determine what repairs need to be done; a difficult and expensive procedure.

The BMS model is, economically, a relative good system for prioritising structure maintenance, but when it comes to determining structure strength, is it not accurate. The urgency ratings given by the BMS model are only based on visual damage and may not necessarily represent structural inefficiencies. In theory, the most accurate way to prioritise damaged bridges is to test each bridge for structural integrity, and to list the bridges according to their reduction in structural integrity. This will ensure that the bridges which have lost the most structural strength will be prioritised. However, since this is an

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expensive procedure, the BMS, using visual inspection, remains the most effective way of prioritising existing bridges.

If, however a correlation can be found between visual inspection results and reduction in structural strength, the BMS can be updated to incorporate structural integrity using the data already recorded in the database. This will result in a more comprehensive analysis of existing structures without incurring extreme extra costs.

1.3 Research Statement

The research topic for the study is:

Assessment of usually encountered damage on concrete bridges and its influence on the load carrying capacity and safety of users.

The topic is divided into the following sub-topics: damage on bridges, load capacity, the safety of users, and the correlation between these elements. The main research statement is expanded into sub-questions, as listed below:

1) What current assessment methods are used for existing structures? Can they be improved? 2) What are the usually encountered damages on concrete bridges, inspected visually? 3) What influence do the damages have on the structural strength of the bridge? 4) Can visually inspected damages be correlated to strength reduction?

5) How is strength reduction linked to reduction in load carrying capacity and safety of users?

1.4 Objectives of the Study

The main objective of this study is to relate visually inspected damages to reduction in the structural strength of bridges. If this is possible, the BMS can be updated to include this data to determine the carrying capacity and safety of users. An updated BMS will provide more realistic results since bridges will be prioritised according to structural integrity and not only according to appearances.

The primary goal is divided into the following objectives:

 Define a deterioration model which can be used to link damage ratings to the influence of damage on structural strength.

 Determine the usually encountered damages on bridges by research.  Categorise the visually inspected damages and assign ratings to each.

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 Analyse the influence of damage on structural strength, and relate this reduction to the load carrying capacity and safety of users.

1.5 Research Methodology

The study aims to provide a methodology for prioritising the rehabilitation of bridges according to reduction in strength rather than basing it solely on visual inspection and engineering judgement. The first step in this research is to determine what damage on reinforced concrete bridges is considered general and has an influence on their strength. Each type of damage then needs to be examined to determine at what stage it will begin to have an effect on the structural strength. To accomplish this, a deterioration model is chosen to analyse the damage. Since no experiments were carried out during this study, all the information was gathered from the results of previous studies. This fact has to be taken into account when choosing a deterioration method, since the method must be flexible enough to be used in different types of studies. A reliability-based approach was therefore chosen.

The study aims to incorporate its results into the existing data bases developed by the BMS, to avoid incurring extra costs. This means that the influence which the damage has on a structure needs to be linked to the visual inspections done according to the BMS. This is done by correlating the degree of structural influence on a certain identified damage to the visual inspection rating of the same damage. When influences on structural strength are determined in quantifiable terms, for example the reduction of reinforced steel or concrete section loss, they are incorporated into the formulas used to design the bridge. Using a reliability based approach, the difference between a structure’s designed resistance and current resistance can be used to determine the reduction in the load carrying capacity and also the safety of users.

It should be noted that this study is considered as a general approach and the results may be used in preliminary estimates. However, a case-specific approach may be more advisable for individual structures, which can be achieved by this study. The basic framework developed by this research are adaptable and can be tailored to case-specific studies in order to present more realistic values.

1.6 Chapters Overview

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1.6.1 Chapter 1 – Introduction

This chapter serves as introduction to the research study. It outlines the problem statement, as well as the research statement outlining a solution. The research methodology as well as the thesis objectives are defined. The introduction ends with a summary of the contents of each chapter.

1.6.2 Chapter 2 – Literature Study

This chapter gives an overview of the existing BMS in South Africa, comparing it to other BMSs around the world. The main focus of the chapter is on visual inspection and how it contributes to the prioritisation of bridge rehabilitation. The study progresses into different types of deterioration models, concluding that a semi-probabilistic model is the best fit. A probability method and reliability assessment are chosen for this study and discussed in detail. The chapter ends with a discussion of the general damage on bridges and identifies in conclusion which types of damage are covered in this research.

1.6.3 Chapter 3 – Research Design and Methodology

Chapter 3 discusses the underlying quantitative research approach used in the study.

1.6.4 Chapter 4 – Analysis of Critical Bridge Items, Damage and DERU-Ratings

This chapter identifies and discusses critical bridge items and types of damage which have the most influence on structural strength. A table is given which represents the natural degradation on bridge items caused by identified damages.

1.6.5 Chapter 5 – Probability Functions for Damage

Chapter 5 offers results from previous studies to determine the probability distribution functions for identified damages: corrosion of reinforcement steel, concrete cracking and spalling. The probability distribution functions are determined for each of these damages and correlated to the table composed in Chapter 4.

1.6.6 Chapter 6 – Reliability Analysis

This chapter discusses the general design of bridges and a representative beam is chosen to which damage is applied in order to determine the effects of its structural integrity.

1.6.7 Chapter 7 – Conclusion and Recommendations

Chapter 7 ends the study by analysing the information accumulated during the research and provides an overall conclusion. Recommendations are given for further studies which can help to improve research in this field.

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2 CHAPTER 2: Literature Review

2.1 Introduction

This chapter discusses the importance of assessing existing bridges, and the types of assessments available. The assessment used in South Africa is the Bridge Management System. This system together with the DERU-rating system and Condition analyses which serve as the core tools for the assessment of existing bridges, are discussed in detail. The inspection process is described and compared to other countries.

The types of deterioration models required to analyse existing bridges are debated and compared with reference to the semi-probabilistic deterioration model; a reliability-based model, which is used in this research. The chapter progresses to a description of the statistics required to perform reliability based assessments and how this is implemented.

The chapter ends with a discussion of the general damage on bridges and concludes which damages are covered in the study.

2.2 Assessment of Existing Bridges

As structures age they become subject to deterioration and reductions in resistance. It therefore becomes increasingly important to assess existing structures to determine if they still fulfil the purposes they are intended to fulfil, or if they need to be rehabilitated.

Since the assessment of existing bridges can be complicated and tedious, a method to assessment based on structural codes looks like an attractive option because of its simplicity and familiarity to practising engineers. Unfortunately, current structural codes are developed to assess new designs and not existing structures.

Uncertainties and variabilities exist in material properties, loading, geometry and other aspects of any structure and these uncertainties need to be accounted for during the design process [4, 5]. Structural codes typically incorporate these uncertainties by predicting the load and resistance parameters of a new structure and then using partial factors to ensure a certain level of safety. No procedures are generally given for the assessment of actual resistance in a structure. If a structure is assessed on its predicted loads and resistance parameters (including partial factors) rather than the actual resistance, it gives unreliable results which in turn result in over- conservative assessments causing unnecessary and

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costly repairs or replacements [6]. Structural assessment procedures are formulated to take uncertainties into account to produce reliable and acceptable results [5].

Three wide range of assessment procedures with varying degrees of complexity and choices of the appropriate procedures is available, and depends highly on the specified requirements of each assessment. A SAMCO report, Guidelines for the Assessment of Existing Structures, [6], identifies 5 levels of structural assessment as illustrated in Figure 2.1 below.

Figure 2.1: Structural Assessment Level

Three general assessment procedures can be identified: non-formal (qualitative), measurement based (quantitative) and model based (quantitative).

Non-formal assessments are based on judgement and the experience of the assessment/inspection

engineer, which makes it more or less subjective. Most of these assessments take place via the BMS which evaluates structural conditions on the basis of visual inspections.

Measurement based assessments determine the load effects by direct measurement rather than structural

analysis. This method is only able to verify structural sufficiency within the Serviceability Limit State (SLS), since only serviceability measures can be directly determined. This method is a two-component procedure which entails the measurement of load effects and serviceability verification.

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Model based assessments determine the load effects via model-based structural analysis. The Ultimate

Limit State (ULS) as well as the SLS can be modelled using this method. The method is a three-component procedure which entails acquiring the loading and resistance data, calculating the load effects on structural models, and verifying safety and serviceability.

Most assessment applications are processed-based structural models, the only exception being the abovementioned measurement-based serviceability assessment. For this reason, the next section focuses on structural modal based assessment (Level 2 to 5).

According to SAMCO structural assessment procedures can roughly be divided into four categories, namely objectives, data acquisition, structural analysis and reliability verification.

Objectives

The two main objectives in structural assessment are assurance of structural safety and serviceability, and cost minimisation. One of the main reasons for assessment is to ensure that a structure or parts of the structure do not fail under loading, assessment is thus carried out for ULS. However, as the deterioration of a structure increases, serviceability decreases and may lead to a limitation in use. Serviceability assessment thus becomes necessary. Another reason for assessment is to determine the load capacity of structures given the worldwide demand for an increase in maximum live load limits. Cost minimisation is one of the objectives of the BMS model.

Data acquisition

The main difference between design and assessment procedures is that design uncertainties can be reduced significantly by the acquisition of site specific data from real structures. This data includes information like material, structural properties, loading, and deterioration. A wide range of methods can be used to obtain this information with varying degrees of expense and accuracy. The choice of data acquisition depends on the assessment objective and the corresponding structural assessment method. Some of these methods include visual inspection (covered in section 2.4), material testing, performance testing and monitoring live loads and environmental conditions.

Structural analysis

Structural performance is analysed using models that satisfactorily represent loading on the structure, and the behaviour and resistance of its components. The models should represent the actual conditions of existing structures, and are divided into simple, complex and adaptive analysis methods. Simple analysis methods are used in lower assessment levels and often effective in calculating conservative load effects using simple structural models. A typical simple analysis is using a space frame combined with simple load distributions and linear elastic material behaviour. Complex analysis methods are used

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when low-level assessments have failed and refined load effect calculation methods need to be used. Refined methods include finite element analyses and non-linear methods as well as models which include material behaviour such as time-variance. These models may lead to higher strength capacities by uncovering hidden capacity reserves. Adaptive analysis models are used when new information is accumulated during the assessment period, for example long-term modelling. These models are able to automatically update structural variables using measurement data like changes in displacement or strains.

Reliability verification methods

Reliability verification methods, which is an example of a probabilistic deterioration model, enable the actual evaluation of safety and serviceability margins (which can be described as the difference between the actual condition of a structure and the limit state for which it is designed). These methods/models ensure a target reliability level that represents the required level of structural performance. Since this method is regarded as the core of bridge assessment in this research, deterioration models are discussed in more detail in section 2.6.

2.3 Bridge Management System

A bridge management system (BMS) is a mechanism by which tasks are coordinated and implemented in order to determine the state of bridges [1]. These tasks include the gathering of inventory data, regular inspections, assessment of infrastructures, maintenance activities, and fund management. This is a useful and important set of information, however a BMS is more than a collection of facts or just a computer programme. A BMS is a system that includes tools which allow the user to look at all the information to make informed decisions concerning safety and budgetary constraints [1].

According to Wium and Rautenbach [7], a BMS assists bridge managers and managing agencies in four primary fields of activity in the following ways:

 serves as a database with all relevant inventory, condition and maintenance data

 assist in the allocation of funds in an optimum manner by prioritising maintenance and

rehabilitation activities

 assists in determining the need for bridge upgrading, and

 allows predictions of future budget requirements and bridge network conditions.

The main modules of a BMS are represented by Figure 2.2. The inventory module is the basic module and consists of detailed inventory data obtained from the drawings, design reports, and measurements in the field. This data includes information such as the name, location, structural details, design characteristics and maintenance history. The inspection module contains detailed information obtained

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from inspection reports which includes the condition of the bridge as well as proposed remedial work and associated costs. The condition module uses the most recent inspection data as well as historical data to prioritise structures which need repair/rehabilitation. The budget module uses historical information as well as the costs compiled in the inspection module to determine estimated repair costs for individual structures. The database contains all of the historical and extant information about the bridges and therefore forms the central part of the BMS.

An effective BMS requires the ability to receive updated information about stored bridge data such as changes in condition due to deterioration or remedial work, as well as to capture the data of new bridges. Some of the general BMS software used over the world are PONTIS and BRIDGIT in the United States, DANBRO in Denmark and BRIME in the European Community [8]. The BMS most used in South Africa is Struman [9].

Figure 2.2: A basic BMS [1].

2.3.1 Struman BMS

The Centre for Scientific and Industrial Research (CSIR), in partnership with Stewert Scott International (SSI), has developed Struman for SANRAL in the 1990s [1]. This system comprises of customised and regularly updated software, manuals and training programmes for clients. It ensures that qualified engineers who act as bridge inspectors have a consistent approach when rating the condition of bridges [9]. To keep structures at acceptable levels, the CSIR recommends that inspections should take place every 5 years with a maintenance strategy which stretches over a 5-year period, based on a priority list

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of bridges in need of repair. This ensures that defects can be identified timeously and economically repaired [10].

SANRAL states that a bridge inspection must be executed by a civil engineer who is registered as a professional and has a minimum of 5 years full-time experience in bridge design and documentation. It is necessary for all inspectors to attend a 2-day inspection course run by SANRAL in which the BMS is outlined, full inspections are performed, and all participants must provide condition ratings for a bridge [11]. These condition ratings are values that the bridge inspector allocates to a defect, based on his/her judgement about the severity of the defect. These bridge inspector requirements attempt to reduce the differences in various bridge inspectors' judgements about defects, and to ensure continuity between the condition ratings provided by all bridge inspectors.

The two main advantages of this system are that it focuses on actual defects rather than the overall condition of all the bridge elements, and the system is able to prioritise bridges in need of repair in order of importance [10].

SANRAL has implemented the Struman BMS which is currently used in Mpumalanga, KwaZulu-Natal, the Western - and Eastern Cape. International clients of the system include the Taiwan Area National Freeway Bureau, Namibia, Botswana and Swaziland [9, 10].

As previously stated, the Struman system is used by most road agencies in South Africa and is the leading BMS of the country [1]. For this reason, the Struman system serves as reference BMS for South Africa and for the rest of this study.

The key element for any BMS is bridge inspection which helps to collect the necessary information about the condition of each bridge as well as to determine the required actions needed to keep the bridge in an acceptable condition in terms of serviceability and safety. The next section gives a detailed overview of South Africa’s bridge inspection procedures.

2.4 Bridge Inspection in South Africa

All roads in South Africa are classified as ether national, provincial, or a municipal road. The administration, inventory and inspection, of bridges on these roads are managed according to the road agencies allocated to these three types of roads. SANRAL manages the bridges on the national roads, nine provincial departments of transport manage bridges on provincial roads, and municipal transport agencies manage the bridges on municipal roads [11].

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Bridge inspection is the on-site examination of a bridge to identify and rate its defects. This is done to ensure serviceability and safety as well as to determine the possible need for remedial work. The information and photographs collected by inspections are converted to electronic formats and transferred to the BMS, Struman.

2.4.1 Bridge Classification for Inspection

The official document for visual inspection in South Africa is the TMH 19 [12] according to which a structure is classified as a bridge if one or more of the following criteria are satisfied:

 Any single span (as measured horizontally at the soffit along the road or rail centre line between

the faces of its supports) is equal to or greater than 6 m

 The individual clear spans (as measured horizontally at the soffit along the road or rail centre

line between the faces of its supports) exceed 1.5 m and the overall length measured between abutment faces exceeds 20 m

 The opening height, which is the maximum vertical distance measured from the streambed or

structure floor at the inlet or from the top of any base, to the soffit of the superstructure, is equal to or greater than 6 m

 The total cross-sectional opening is equal to or larger than 36 m2

 The structure is a road-over-rail, or rail-over-road structure, even if the span is less than 6 m. The above are illustrated by Figure 2.3.

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The TMH 19 identifies the following as bridge types for inspection purposes:

i. Bridge (General): Consists of separate and clearly identifiable elements such as deck slabs, abutments, deck expansion joints, foundation footings and piers and normally has a concrete deck as roadway.

ii. Bridge (Arch): Includes solid filled arches, open ribbed spandrel arches, and spandrel arches. iii. Bridge (Cable): Includes suspension bridges, cable stayed bridges, and extradosed bridges. iv. Bridge (Cellular): This is a bridge consisting of ‘cellular’ units that can be described as openings

where the overall length is greater than the cell width. Examples include invert slabs, cut-off walls, and apron slabs.

Each bridge type is divided into sub-items for the purpose of inspection. General, arch and cable bridges have 21 sub-items and a cellular bridge has only 14. The 21 sub-items are summarised in Table 2.1 [13].

Table 2.1: Bridge Subdivisions

2.4.2 Types of Inspection

According to G. Hearn [11] there are three types of routine inspections in South African practice:

monitoring, principal and verification.

Monitoring inspections are quick checks done on structures which include the following: an inspection

for new defects, the status of known defects during routine maintenance surveys, and quick surveys conducted after accidents, cyclones, floods or other extreme events. These inspections are done by maintenance personnel and occur at frequent - at least once a year - but irregular intervals. Maintenance personnel report only if there are problems and do not report which bridges have been visited. Monitoring inspections do not produce condition ratings [11].

General Items: Support Items: Span Items:

Approach embankment Pier protection works Longitudinal members (deck)

Guardrail Pier foundations Transverse members (deck)

Waterway Piers & columns Deck slab

Approach embankment protection works Bearings

Abutment foundations Support drainage

Abutments Expansion joints

Wing/retaining walls Surfacing/ballast Superstructure drainge Kerbs/sidewalks Parapet/handrail

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Principal inspections are performed through visual examination by inspectors experienced in the bridge

design, maintenance, or rehabilitation. These inspections consist of thorough bridge examinations and report on all the defects that can influence structural integrity. The reports are done by taking photographs of the assessed defects and completing a prescribed inspection form which describes the defects. Principal inspections should be done every 5 years [7, 11, 12] and the information captured and stored in the BMS [11]. This is however rarely done. According to a study done by P. Nsabimana [14], about 50% of the authorities do not respect the inspection frequencies as required and the main reason for this is lack of personnel and funds.

Verification inspections are part of SANRAL’s quality assurance plan to verify the accuracy of

inspection data. Around 60 bridges are selected each year and their conditions verified by a senior bridge inspector [11].

The TMH 19 [12] conducts further three types of inspections, namely partial, completion and waterway

inspections.

Partial inspections take place when specialised equipment such as the Under-Bridge Inspection Unit is

needed to evaluate certain features.

Completion inspections are carried out after completion of rehabilitation or maintenance on structures.

This ensures that the condition ratings for the new/rehabilitated items are updated, and take place in the form of a principal or partial inspection.

Waterway inspections are conducted on all structures which cross waterways and should be carried out

at least once a year. These inspections are conducted by routine road maintenance.

The main type of inspection is a principal inspection which reports on overall bridge conditions bridges and are included in the BMS.

2.4.3 Principal Inspection Process

Each sub-item of the bridge is visually inspected and rated according to its level of defects. The bridge however is given only one rating which corresponds to the worst defect, identified by the inspector, on the sub-item. The worst defect is usually the one with the highest relevancy rating [12].

A defect is typically divided into three parts: the degree of the defect (D), the extent (E) and the

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rating (U) for defects to be repaired, which is added to the DER rating system to form a DERU rating system [13, 15].

Degree of defect is a visual rating that defines the severity of a defect. This excludes the need to consider

the impact which the defect has on the inspection item and the structure. To rate the defect separately enables the bridge inspector to monitor the deterioration of the defect over time.

Extent of defect expresses how widespread the defect on the inspected element is.

Relevancy of defect defines the importance of the defect in terms of user safety or structural integrity

of the inspected element.

Urgency of defect refers to the necessity to carry out repairs to the defect. This rating takes future risks

concerning the defect into account, and provides a procedure to include a time limit on the repair requirements.

The DERU is a four-point rating system from 0 (no defect) to 4 (critical defect) as summarised in Table 2.2.

Table 2.2: Details of the DERU rating system [13]

After an inspection, the reported data is used to determine the condition index and each bridge is rated in terms of its rehabilitation needs which depend on the condition of each bridge item.

2.4.4 Condition Analysis

A condition analysis is used to prioritise the bridges in the BMS in order of need for repairs/rehabilitation based on the inspection data. According to the TMH19 [12] and THM22 [16] several condition indexes are calculated to produce this priority list. A condition index is the numerical rating of an asset depending on its structural integrity or condition, measured as a percentage [16]. The

Rating Degree (D) Extent (E) Relevancy (R) Urgency (U)

X Not applicable U Unable to inspect

R Record only

0 None Monitor only

1 Minor Local Minimum Routine

2 Fair More than local Moderate < 10 yrs

3 Poor Less than general Major < 5 yrs

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different condition indices which are calculated are: the structural average condition index (SACI); the structural priority condition index (SPCI); the Structural functional index (SFI); and the structural combined condition index (SCCI). These indices are described as follow:

SACI is an indication of the overall condition of the bridge and is used to rank the structure in terms of

average condition as opposed to need for maintenance. Relevancy is not considered when this index is calculated. Therefore, the SACI is not suitable to identify structures that require urgent maintenance. However, this index is the best option when an indication of the whole structure’s condition is needed.

SPCI is used to prioritise bridges in order of need for repairs/rehabilitation. This index only takes into

account the worst rating of the sub-items and ignores items that are in good condition [17]. This method tends to exaggerate the poor condition of a structure, but includes all the ratings (degree, extent, and relevancy) which makes it the best index to rank bridge maintenance priority since it takes the relevancy rating-consequence on the structural integrity of the defect into account. Bridges with the highest SPCI are the structures in greatest need of repair.

SFI is an indication of the strategic importance of the structure and is used for cost analysis. The SFI

takes factors such as the class of the road over/under the bridge, volume of the traffic, the detour length should the structure be closed, heavy vehicle usage and public transport usage into account.

SCCI is a weighted combination of the SPCI and SFI.

The SACI and SPCI are the only indices directly based on bridge damage and their calculation procedures are described below.

Structural Average Condition Index

The SACI is based on an inspection of rating defects, namely degree and extent. According to the TMH 22 [16], the procedure for calculating the SACI is as follows:

Step 1: A condition index is calculated for each relevant inspection sub-item (a sub-item with D-rating of 0 to 4;

Step 2: The condition indices for all the relevant inspection sub-items which make up an inspection item are added together and divided by the number of relevant sub-items to give the condition index for the inspection item

Step 3: The condition index for each inspection item is then multiplied by an inspection item weight, and these weighted inspection item condition indices for all the inspection items are then added together and divided by the sum of the weights to arrive at the SACI.

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For inspection sub-items unable to be inspected (D-rating of U), the following default ratings for degree and extent should be used to calculate the SACI:

Table 2.3: Default values for sub-items with D-rating as U for SACI calculations

Step 1: Determine the inspection sub-item condition index

The condition index of inspection sub-item, for example, j of inspection item, for example, i, Icij is calculated by [16]:

100 100 _(2.1)

With:

D = degree rating for inspection sub-item j of item i

E = extent rating for inspection sub-item j of inspection item i

bc = Dmax+ Emax = 4 + 4 = 8

Icij ranges from 0 for D = 4 and E = 4 (the worst condition) to 100 for D = 0 (no defect, the best condition)

Step 2: Determine the inspection item condition index

The condition index of inspection item, for example, i, Ici is calculated as [16]:

∑ (2.2)

With:

Icij = condition index of inspection sub-item j of inspection item i n = number of relevant inspection sub-items in inspection item i

Ici ranges from 0 (the worst condition) to 100 (the best condition). If the condition index of an inspection item is 100, it means there are no defects on any of the relevant sub-items.

Inspection Item Degree Extent

Foundations 0

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Step 3: Determine the SACI

The overall condition index for the structure, Ic (or SACI), is calculated by [16]:

∑

∑ (2.3)

With:

Ici = condition index of inspection item i

wci = condition weight for inspection item i: see Table 2.4 for proposed inspection item weights for various structures

N = number of relevant inspection items

Inspection items with no relevant inspection sub-items are excluded from the SACI calculation. SACI ranges from 0 (worst condition) to 100 (best condition). If Ic is 100, is means there are no defects on the structure.

Table 2.4: Proposed inspection item weights for various structures

Weight

1 Approach Embankment 2

2 Guardrail 1

3 Waterway 1

4 Approach Embankment Protection Works 2

5 Abutment Foundations 4 6 Abutments 4 7 Wing/Retaining Walls 3 8 Surfacing 1 9 Superstructure Drainage 1 10 Kerbs/Sidewalks 1 11 Parapet 3

12 Pier Protection Works 1

13 Pier Foundations 4

14 Piers, Colmns & Arch Springings 5

15 Bearings 3

16 Support Drainage 1

17 Expansion Joints 1

18 Longitudinal Members & Cable Groups 5

19 Transverse Members 5

20 Deks, Slabs & Arches 5

21 Miscellaneous Items 1

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Structure Priority Condition Index

The priority index is calculated at inspection sub-item level and used to calculate priority indices at inspection item level. These indices are then used to calculate a priority condition index for the structure. The following procedure is given by the TMH 22 [16] for calculating the SPCI:

Each inspection item is marked as “Ignore, “Forced” or “Normal”, where inspection items marked as “Ignore” are excluded from the SPCI calculations.

Step 1: A priority condition index is calculated for each relevant inspection sub-item (an inspection sub item with a D-rating of 0 to 4) of forced and normal inspection items

Step 2: The lowest priority condition index of all the relevant inspection sub-items of forced and normal inspection items are used to determine the lowest category of priority condition indices for normal inspection items that will be used in the calculation of the SPCI, and

For normal inspection items and forced inspection items, separately: the priority indices for

all the relevant inspection sub-items falling in the lowest category, determined for all the relevant inspection items, are added together and divided by the number of relevant sub-items in the lowest category to obtain the priority condition index for the normal inspection item Step 3: The priority index for each normal and forced inspection item is then multiplied by an inspection item weight and these weighted inspection item priority indices for all the normal and forced inspection items are added together and divided by the sum of the weights to arrive at the priority index for the structure.

For inspection sub-items which are unable to be inspected (D-rating of U), the following default ratings for the degree and extent should be used to calculate the SPCI:

Table 2.5: Default values for sub-items with D-rating as U for SPCI calculations

Inspection Item Degree Extent Relevancy

Foundations 0 - -Other items 2 2 2

Step 1: Determine the inspection sub-item priority index

The priority of inspection sub-item, for example, j of inspection item, for example, i, Ipij, is calculated by [16]:

100 100 ∙ ∙

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With:

D = degree rating of inspection sub-item j of item i

E = extent rating for inspection sub-item j of item i

R = relevancy rating for inspection sub-item j of item i

kd = degree coefficient (tentative default value: 1) ke = extent coefficient (tentative default value: 0.25) a = relevancy exponent (tentative default value: 1.5)

Ipij ranges from 0 for D = 4 and E = 4 (the worst condition), to 100 for D = 0 (no defect, the best condition)

Step2: Determine the inspection item priority index The priority of inspection item i, Ipi, is calculated by [16];

∑

(2.5)

With:

Ipij = priority index of inspection sub-item j of inspection item i

n = number of relevant inspection sub-items in the lowest category for inspection item i

Ipi ranges from 0 (the worst condition) to 100, (the best condition. If the priority index of an inspection item is 100, then there are no defects on any of the relevant sub-items making up the inspection item. Step 3: Determine the SPCI

The SPCI is calculated by [16]:

∑ ∙

∑ (2.6)

With:

Ipi = priority index of inspection item i

Wpi = priority index for inspection item I; same as for SACI N = number of relevant inspection items

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SPCI ranges from 0 (the worst condition) to 100 (the best condition). If Ipis 100, is means that there are no defects on the structure.

2.5 BMS and Bridge Inspection Globally

As stated in section 1.1, most BMS have the same main modules, namely inventory, inspection, condition and budget, and although similarities can be found between BMSs, each BMS differs from the next in terms of procedures or requirements.

Bridge inspections intervals can vary between countries from once every year to as much as 10 years, and can even vary from one organisation to another in the same country [11]. One of the reasons for this variation in intervals is the different environments/climates where the bridges are located which influence the deteriorating time of their sub-items. For example, if a bridge is in an environment where it is exposed to extreme temperatures, its deterioration over a period of time will be much higher than a bridge exposed to a climate with relatively constant temperatures for the same period of time. Differences are even noticeable between the deterioration time of two bridges in the same country where the one is situated inland and the other close to the coastline, exposed to high chloride attacks [18]. Another variation is the condition rating systems which differ from one country to the next. For example, the rating scale in South Africa runs from 0 to 4, in France from 1 to 3, and in Denmark from 0 to 5 [11]. In general, defects are rated on a 4 or 5 level scale, with exceptions (such as the USA which uses a 9-level scale) [19]. Each rating level represents a description of the bridge defect and with a limited number of rating levels, the rating system acts as a guideline for bridge inspectors and minimises the influence of subjectivity. Since condition ratings are only based on visual inspections, the information must be analysed by a suitable qualified and experienced engineer.

There are many different ways of arriving at a condition index for a bridge but it is generally based on the nature and extent of defects in a structural member, and the resulting effect on the bridge should the defect be left in its present state allowing it to deteriorate further [1]. Many countries therefore provide supplementary information for each defect to help determine its influence on the structural integrity and safety of the bridge. This information depends on the country and can include the relevancy of the defect, its impact on traffic, and its impact on the durability of the structure. Some countries include indices as part of the supplementary information to serve as maintenance ratings. Examples are the urgency rating in South Africa and the ‘time to repair’ rating in Norway [10]. Other countries use supplementary information to monitor bridge conditions and have an understanding of the rate of deterioration for each defect. There is however a downfall; this method may be expensive because of

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the need to collect and manage the inspection data. Either way, each country has its own method of arriving at a condition index in order to prioritize the maintenance of bridges.

2.6 Deterioration Models

To summarise section 2.2: BMSs have been developed to assist decision makers in maximising the serviceability, functionality and safety of bridges within available budgets. This is done by prioritising bridges with high degradations (according to condition analyses) and allocating available resources to these bridges, ensuring cost-effective rehabilitation and replacement decisions [21]

However, in order to determine and analyse degradation on bridges, it is necessary to develop deterioration models. Deterioration models are used to understand the workings of damage on bridges, to determine the degree of the damage, and to predict time-dependent performance and remaining service life [22].

Ben-Akiva and Gopinaths [23] define a deterioration model as follows:

A deterioration model is a link between a measure of infrastructure condition that assesses the extent and severity of damages, and a vector of explanatory variables that represent the factors affecting infrastructures deterioration such as age, material properties, applied loads, environmental conditions, etc.

BRIME [24] states that deterioration models can be divided into three groups: deterministic, semi-probabilistic and semi-probabilistic; all based on either safety factors or limit states. The deterministic approach is based on safety factors and the semi-probabilistic and probabilistic states on limit state (see Figure 2.4). These deterioration models are briefly discussed in the following sections since this study focuses on the reliability-based approach (section 2.9).

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2.6.1 Deterministic

The deterministic approach is the traditional way of defining safety. It is based on experience and expert opinion and the safety measures are of an empirical nature. This approach is characterised by simplifications and associations with conservative safety measures [6].

The most common deterministic safety measure is the global ‘factor of safety’. This factor of safety represents the ratio of resistance to the load effect, where uncertainties and basic variables are represented by deterministically established values. The resistance values of a bridge are determined from the structure’s condition ratings accumulated during visual inspection proses, and correlating them to the determined allowable stresses [10]. Allowable stresses are values determined to represent resistance, and assumes that the structure will fail when any sub-item of the structure exceeds this value. The accuracy of the factor of safety depends on how well the established allowable stress-value represents real failure in the material and how well the calculated stress represents the actual stress in the assessed structure [6].

Deterministic models are easily understood but present some limitations, such as they do not take into consideration the uncertainties of deterioration and the reliability and consistency of the condition rating, which rely heavily on the subjective judgment of bridge inspectors rather than being explicitly linked to quantitative physical parameters [25].

2.6.2 Semi-Probabilistic

The semi-probabilistic approach is based on limit state. The main concern of the ultimate limit state is to ensure that all the components of a structure and the structure itself do not fail under loading. For structural assessment it may also be important to analyse the serviceability performance as failure can occur due to serviceability loads [5].

The most common semi-probabilistic method is the partial factor method. This has been developed and derived from reliability analysis for specific target reliability, by which the structure is designed for and applied to corresponding design parameters. Partial safety factors eliminate some of the uncertainties that is usually present in the design parameters (during the deterministic approach) which makes this method a better reflection of reality [26]. Since the method has been developed to be incorporated into the designing phase, most design codes already use them. The analysis is simplified by safety factors that supply a wide range of structures and failure modes [27].

According to BRIME [24], a safe structural answer is more important than a realistic one and economic design means ease of construction instead of structural efficiency. For these reasons semi-probabilistic

Assessment of usually encountered damage on concrete bridges and its influence on the load carrying capacity capacity and safety of users

INFLUENCE ON THE LOAD CARRYING

CAPACITY AND SAFETY OF USERS

Lizbè Botes

Master of Engineering (Structural Design)

DECLARATION

ABSTRACT

OPSOMMING

ACKNOWLEDGEMENTS

3

Table of Contents

LIST OF FIGURES

LIST OF TABLES

LIST OF EQUATIONS

LIST OF ABBREVIATIONS

4

LIST OF SYMBOLS

1

CHAPTER 1: Introduction

1.1 Background

1.2 Problem Statement

1.3 Research Statement

1.4 Objectives of the Study

1.5 Research Methodology

1.6 Chapters Overview

2

CHAPTER 2: Literature Review

2.1 Introduction

2.2 Assessment of Existing Bridges

2.3 Bridge Management System

2.4 Bridge Inspection in South Africa

2.5 BMS and Bridge Inspection Globally

2.6 Deterioration Models