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ABSTRACT

This dissertation is a report of the investigation carried out on the Probabilistic analysis of reinforced concrete columns subjected to corrosion. Corrosion of reinforcement bars is one of the most significant causes of deterioration of reinforced concrete columns. The deterioration leads to a loss of serviceability, functionality and ultimately affects the structural safety. The probabilistic analysis was carried out using MATLAB. The reliability index, β, was computed for various points on the interaction curve using First Order Reliability Method (FORM). The variations of the safety index with respect to the basic variables (Load ratio, yield strength and concrete grade) were examined to analyzed the behavior of columns subjected to corrosion, given the values of the design parameters. Graphs were developed for each mode of the columns. The results indicated that the safety index of the reinforced concrete column decreases as the load ratio of the column is increasing while an increase in yield strength and concrete grade leads to corresponding increase in the safety indices. For reinforced concrete columns and other aggressive environment prone to corrosion attack, a minimum of 0.5 load ratio, 500 N/mm2 yield strength and 30 N/mm2 of concrete grade at corrosion rate of 0.4mm/year with good anti-corrosion properties (epoxy resins) be used in the construction of columns as load carrying components is therefore recommended.

 

 

TABLE OF CONTENTS

Title…………………………………………………………………………………………ii
Declaration …………………………………………………………………………………iii
Certification………………………………………………………………………………..iv
Abstract………………………………………………………………………………………v
Dedication………………………………………………………………………………….vi
Acknowledgement…………………………………………………………………………vii
Table of contents………………………………………………………………………….viii
List of Figures………………………………………………………………………………………………………..xi
List of Tables……………………………………………………………………………………………………….xiii
CHAPTER ONE. INTRODUCTION…………………………………………………………………….1
1.1 Introduction………………………………………………………………………………………………….1
1.2 Problem Statement………………………………………………………………………………………..6
1.3 Aim and Objectives……………………………………………………………………………………….7
1.4 Scope of the Research……………………………………………………………………………………7
CHAPTER TWO. LITERATURE REVIEW…………………………………………………………8
2.1 Review work on Structural Reliability……………………………………………………………8
2.1.1 Theoretical Framework on Structural Reliability…………………………………13
2.2 Concept of Structural Reliability Analysis………………………………………15
2.3 Reliability Based Designed…………………………………………………………………………..16
2.4 First Order Reliability Method…………………………………………………………………… 17
2.4.1 First Order Reliability Method (FORM)………………………………………….18
2.4.2 Probabilistic Methods of Safety Checking………………………………………….21
2.4.3 Computation of Reliability Index…………………………………………………22
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2.5 Interaction between Resistance and Applied Load………………………………24
2.6 Evaluation of the Performance function using Genetic Algorithm base FORM..…………………………………………………………………………….29
2.6.1 Structural Reliability Using Genetic Algorithm…………………………………….30
2.6.2 Development of Flow chart for Genetic Algorithm (GA) Base FORM……………32
2.7 Background of Probabilistic Calculation…………………………………………33
2.9 Corrosion of Reinforcing Steel in Concrete………………………………………35
CHAPTER THREE. ANALYTICAL TECHNIQUE……………………………………………43
3.1 BS 8100: Design Criteria of Reinforced Concrete columns……………………..43
3.2 The Structural Model of the Corroded Columns……………………………….44
3.3Limit State Function…………………………………………………………………45
3.4 Statistical Model of the Basic Design Variables of the Columns……………….46
3.5 Computional Analysis Procedure…………………………………………………47
3.6 Development of the MATLAB……………………………………………………47
3.6.1 Main Directory……………………………………………………………………48
3.6.2 Form Directory……………………………………………………………………48
3.6.3 Distribution model set up Directory………………………………………………48
3.6.4 Distribution transformation Directory…………………………………………….48
3.6.5 Coefficient of Variation Directory………………………………………………..48
3.6.6 Probability of Failure Directory…………………………………………………..49
3.7 Hasofer-Lind Reliability Index (1974)……………………………………………49
3.8 Set up of Reliability analysis by Genetic Algorithm………………………………51
3.9 Matlab Program……………………………………………………………………55
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CHAPTER FOUR. RESULTS AND DISCUSSION………………………………………………59
4.1 Presentation of Results……………………………………………………………59
4.1.1 Variation of corrosion rates on the safety index with respect to load ratio on Reinforced Concrete columns……………………………………………………59
4.1.2 Variation of corrosion rates on the safety index with respect to Yield strenght on Reinforced Concrete columns…………………………………………………63
4.1.3 Variation of corrosion rates on the safety index with respect to Concrete grade on Reinforced Concrete columns…………………………………………………66
4.2 Discussion of Results………………………………………………………………70
CHAPTER FIVE. CONCLUSION AND RECOMMENDATIONS………………………..72
5.1 Conclusion…………………………………………………………………………72
5.2 Recommendations…………………………………………………………………73
References…………………………………………………………………………………75
Appendix A (Program Listing)………………………………………………………….83
Appendix B (Results Generated)………………………………………………………..86

 

Project Topics

 

CHAPTER ONE

1.0 INTRODUCTION
1.1 Introduction
Corrosion of reinforcement is recognized as the predominant factor that limits the service life of reinforced concrete (RC) structures exposed to aggressive environments. This corrosion deterioration can lead to damage resulting in capacity loss or even failure. For structures exposed to coastal marine environments or deicing or anti-icing applications, this deterioration is often accelerated. The deterioration is often attributable to the corrosion of steel, which can significantly reduce the strength of both steel and reinforced concrete structures. Robert et al (1997) Corrosion rates are highly variable and dependent on the local environment, quality of the material strengths, geometry and applied loads vary during the life of a structure. There is therefore a high degree of uncertainty associated with the assessment of deteriorating structures.
The corrosion deterioration in RC structures has raised significant attention from researchers and analytical studies and experimental tests have been performed worldwide. Durability and serviceability of corroded RC structures have been investigated to determine the relationship between the corrosion process and the service life of these structures and these relationships have been used to develop service life models. In addition the Predominantly, with the extensive use of de-icing salt in cold weather regions, bridge decks and bridge piers are vulnerable to corrosion of steel reinforcement (ACI 1999).
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The concept of the application of reliability theory to the assessment of bridges and other structures has been accepted and adopted in North America. In the UK, the Highways Agency has recently commissioned a number of projects to develop a whole-life performance assessment method based on reliability theory.
The main corrosion-induced damage mechanisms in RC are:
(i) the decrease in the reinforcement cross-sectional area,
(ii) the possible loss of steel ductility,
(iii) the cracking and spalling of the concrete cover, and
(iv) the loss of bond along the steel/concrete interface.
There has been an increasing effort in recent years to quantify the damage progress in RC due to the advance of steel reinforcement corrosion. Particularly, quantifying concrete cracking propagation with respect to reinforcement corrosion propagation is of great relevance in the serviceability assessment of deteriorated RC structures with corroded reinforcement, and it must be included in estimations of residual service life (Andrade and Alonso, 1996; Liu and Weyers, 1998).
There have been limited studies on the effect of reinforcement corrosion on the serviceability and structural performance of RC columns (Lee et al, 2000; Rodriguez et al, 1996; Saito et al, 2007). A major observation from these studies is that the load carrying capacity of corroded columns is lower than that of non-corroded columns. This reduction in resistance capacity is attributed to: (a) the increase in load eccentricity due to uneven
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corrosion of the longitudinal reinforcement; (b) buckling of the longitudinal reinforcing bars when column ties are corroded; and,
(c) the actual deterioration of the concrete section due to cracking, spalling and/or delamination of the concrete cover.
However, none of the above studies were conducted on RC columns that were subjected to sustained axial loads and reinforcement corrosion simultaneously.
The high alkaline environment of good quality concrete forms a passive film on the surface of the embedded steel that normally prevents the steel from further corroding. However, under the influence of chloride and carbonation, the passive film is disrupted or destroyed and the steel corrodes. The corrosion products occupy a larger volume and these induce stresses in the cover concrete resulting in cracking, delamination and spalling. In addition to loss of cover concrete, a RC member may undergo structural damage due to loss of bond between steel and concrete and loss of rebar cross-sectional area as shown in Figure 1.1
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Figure 1.1: Possible damage of RC beam-col umn subjected to combined exter nal loads and corrosion; (a) flexural and corrosion cracks; (b) initial spalling; (c) one stirrup failure; (d) spalling on all sides; (e) two stirrups failure; (f) l oss of confinement and possible buckling.
To plan repair strategy for damaged structures, the strength of the existing structures needs to be estimated. The past research addressed on the flexural behavior of corrosion damaged concrete members (Mangat,1999; Rodriguez,1997; Almusallam, 1996) They indicated that load carrying capacity and ductility decreased as the reinforcing steel bars were corroded. Relatively limited literature exists on the axial behavior of corrosion damaged reinforced concrete columns. Uornoto studied the effects of corrosion damage on the load bearing
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capacity of reinforced concrete columns. He reported that the bearing capacities of corroded columns was not simply caused by reductions in strength or effective areas of the reinforcing bars but also by cracks formed during the corrosion process. Tapan [2008] proposed a bridge pier column strength evaluation method that can be adapted into a currently used bridge condition evaluation method. The proposed evaluation method provided a good estimate of the condition and load-carrying capacity of bridge piers that currently cannot be obtained by normal visual surveys. The research studies have shown the influence of corrosion on bond characteristics between steel and concrete. They demonstrated that loss of bond increased with sectional loss.
One of the main reasons responsible for the deterioration is member corrosion and reinforcement corrosion in steel and reinforced concrete structures, respectively. Latter case structural repairing could be a harder task since the reinforcement is not easily accessible. Also in reinforced concrete (RC) structures the corrosion effect cannot be seen as simply as a reinforcement area reduction. In fact, corrosion mechanism leads to the development of several side effects (rust expansion, concrete cracking, bond strength decreasing, among others) responsible for the bridge deterioration acceleration. For this reason it is fundamental to correctly assess the reliability of an existing corroded RC structure in order to adequate a safety service level. On the other hand, the structure reliability or the safety level decreasing due to damage occurrence is related to the robustness concept which has seen growing interest in the last decades as a result of the occurrence of tragic consequences (Eagar and Musso 2001, Pearson et al. 2003, NTSB 2008) due to extreme events such as terrorist attacks. However the concept can also be
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very useful when applied to deterioration scenarios allowing for instance for a reinforcement concrete column to evaluate the safety susceptibility to corrosion.
Therefore this paper intends to be a contribution to the robustness assessment of reinforced concrete structures subjected to corrosion.
The design of any structure should be able to safely meet the requirements of functionality, aesthetics and economy (Clarke, and Converman,1987). When an engineering structure is loaded in some way it will respond in a manner which depends on the type and magnitude of the load, and the strength as well as stiffness of the structure. Whether the response is considered satisfactory depends on the requirements which must be satisfied.
1.2 Problem statement and Justification of Study
The aim of structural design is to ensure that the designed structure withstands the load to which it is subjected. Safety level assessment is therefore carried out to determine the safety inherent in the structure. It gives an estimate of the safety or failure conditions of the structure taking into account the various uncertainties associated with the design and constructions of the structure, thus reducing structural accidents and minimizing losses during the associated design life of the structure.
It is in this bid that the formulation for reliability-based performance of reinforced concrete columns is evaluated in this work in order to obtain the safety level inherent in the concrete structure as design using the relevant codes aforementioned, also the prediction for durability of reinforced concrete columns exposed to marine environment as reviewed from literature will be evaluated as necessary.
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1.3 Aim and Objective
1.3.1 Aim
The aim of this research is to carry out a Probability analysis of reinforced concrete columns subjected to corrosion.
1.3.2 Objective
The research objectives are to:
i. Identify the modes of failure of reinforced concrete columns;
ii. Develop limit state function for each failure;
iii.Develop reliability-based analysis program for the column using MATLAB; and.
iv.Perform reliability-based durability analysis on the column to investigate the effect of uncertainty and corrosion.
1.4 Scope of the Study
The research work covers the probabilistic analysis of reinforced concrete columns subjected to corrosion. The column are designed based on BS8110(1997). The data on the statistical properties of the basic design variables would be obtained from previous research.

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