# NUMERICAL AND ANALYTICAL MODELING OF CONCRETE  CONFINED WITH FRP WRAPS.

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NUMERICAL AND ANALYTICAL MODELING OF CONCRETE  CONFINED WITH FRP WRAPS.

Abstract

This thesis is intended at studying and comparing empirical models that have been proposed for the modeling of the stress-strain response of a FRP confined concrete subjected to axial load. An attempt has been made to model the experimental set up for the compression test of a concrete cylinder confined with FRP sheet in AbaqusCAE. The results so obtained have been compared and analyzed against the experimental test results & the results obtained from a chosen mathematical model (Modified Lam & Teng). An attempt was made to create a new material model in Opensees that follows the chosen mathematical model. However, this was not achieved due to the reasons that will be explained in the later sections.

Reinforced concrete confined with steel is typically designed by considering the Manders model (Mander et al., 1988), which assumes a constant confining pressure. This is true with the case of steel as it is a ductile material and one assumes the steel to be yielded. However with the case of FRP jackets, this is not true. FRP is a linear elastic and brittle material and does not yield, which makes the Manders model inaccurate for its analysis. Many models have been proposed which take into account the increasing confining pressure due to the FRP wrap. A comparative study of the constitutive models proposed for FRP confined reinforced concrete has been done in this study.

Finally after a series of numerical interpretations of different specimens and their comparison with the experimental data, the utility and accuracy of the new modified Lam & Teng’s model was validated. The validation process included comparison and analytical data obtained via finite element simulation in Abaqus, empirical model results and the experimental data.

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Contents

List of Figures                                                                                                                                                                                  v

Chapter 1 Introduction                                                                                                                                                                  1

1.1 Introduction                                                                                                                                                                               1

1.2 Scope of the study                                                                                                                                                                   2

Chapter 2 Literature Review                                                                                                                                                       4

2.1 Introduction                                                                                                                                                                               4

2.2 Mechanism for Concrete Confinement by Transverse Reinforcement                                                                 4

2.3 Modeling of Concrete in Compression                                                                                                                            6

2.3.2 Kent and Park model                                                                                                                                                          7

2.4 Stress-Strain Response of FRP-Confined Concrete                                                                                                    9

2.4.1 First Zone                                                                                                                                                                               9

2.4.2 Transition Point                                                                                                                                                                  10

2.4.3 Second Zone                                                                                                                                                                        10

2.4.4 Failure Mode                                                                                                                                                                       10

2.4.5 Post Failure                                                                                                                                                                          12

2.5 Proposed models                                                                                                                                                                   15

2.5.1 Samaan and Mirmiran Model (1998)                                                                                                                         16

2.5.1 Mander’s Model (1984)                                                                                                                                                  18

2.5.3 Lam & Teng Model (2003)                                                                                                                                            24

2.5.4 Modified Lam & Teng (Liu et al., 2013)                                                                                                                  26

2.5.5 Drucker-Prager Plasticity Model                                                                                                                                  30

2.6 Conclusions                                                                                                                                                                             34

Chapter 3 Experimental Database & Preliminary results                                                                                               35

3.1 Introduction                                                                                                                                                                             35

3.2 Preliminary study                                                                                                                                                                  39

3.3 Test Database                                                                                                                                                                         39

3.4 Abaqus modeling                                                                                                                                                                  40

3.5 Opensees Modeling                                                                                                                                                              41

3.6 Results and Discussion                                                                                                                                                        41

Chapter 4 AbaqusCAE Finite Element Modelling                                                                                                           45

4.1 Introduction                                                                                                                                                                             45

4.2 Concrete                                                                                                                                                                                   45

4.2.1.  Elastic Properties                                                                                                                                                             46

4.2.2.  Plastic Properties                                                                                                                                                             47

4.3 Fiber Reinforced Polymeric Jacket                                                                                                                                 48

4.4 Abaqus model:                                                                                                                                                                       49

4.4.1.  Assembly                                                                                                                                                                           49

4.4.2.  Boundary Conditions & Analysis Step                                                                                                                    49

4.4.3.  Interaction                                                                                                                                                                          49

4.4.4.  Meshing                                                                                                                                                                              49

4.5 Conclusions                                                                                                                                                                             50

Chapter 5 Comparison Study and Analysis of Results                                                                                                    52

5.1 Introduction                                                                                                                                                                             52

5.2 Performance of the Drucker-Prager Model                                                                                                                  54

5.3 Performance of the Modified Lam & Teng model                                                                                                    57

5.4 Regression Analysis                                                                                                                                                             61

5.3 Field Retrofitting cases                                                                                                                                                       66

Chapter 6 Conclusions                                                                                                                                                                68

6.1 Summary                                                                                                                                                                                  68

6.2 Conclusions                                                                                                                                                                             69

References                                                                                                                                                                                       71

Appendix A : Numerical and Analytical modeling results (Tabular)                                                                         76

Appendix B : Numerical and Analytical modeling results (Graphical)                                                                     79

Appendix C : Graphical comparison with Confinement ratios                                                                                  106

Appendix D-1 : Bridge Retrofitted Data                                                                                                                            107

Appendix D-2 : CalTrans retrofitting guidelines                                                                                                            109

# Chapter 1 Introduction

## 1.1 Introduction

Today, many reinforced concrete structures are in a bad condition. According to the ASCE report card 2013 for America’s infrastructure, one in nine of the bridges in the United States is structurally deficient. (2013 Report card for America’s Infrastructure,ASCE) The report also mentions that the average age of the bridges in the country is 42 years. Most of them need some rehabilitation and repair work to either restore them to their full capacity or to increase their design capacity in order to meet their growing demand.

Causes of deterioration can range from corrosive environmental conditions, damage due to natural cause such as earthquakes & tornadoes or by human factors such as traffic accidents, use of substandard quality of construction material, faulty construction practices or increase in the load demand for the structure.

Indication of a deteriorated reinforced concrete column is the spalling action of the concrete cover leading to exposure of the steel reinforcement in the column which leads to corrosion of the steel, eventually leading to reduced performance of that structure element. With respect to deteriorated reinforced concrete columns, one could conclude that the causes stated above result in deterioration because of lack of lateral confinement. The longitudinal reinforcement in the reinforced concrete columns provide very little lateral confinement effect, which is not adequate for most loading conditions.

As a structural designer one always tries to design the reinforced concrete structures in a manner so that they exhibit ductile behavior. Lateral confinement in a reinforced concrete column provides the column with the required ductility. Under seismic loading, this additional confinement could ensure adequate strength for the column and increase its deformation capacity which improves its performance in an event like an earthquake. (Park et al., 1982; Mander et al., 1988; Shams & Saadeghvaziri, 1997)

Many confinement techniques have been developed over the years; designing the columns with steel hoops (stirrups) or by providing steel jacketing techniques. The steel jacketing technique has been proved quite useful in the field of retrofitting the columns. However, corrosion of the steel can be of concern. It also increases the self-weight of the structure to a great extent which is always a tradeoff. In situations where the concrete cover is very loose and weak one cannot use the steel jacketing techniques as it might damage the column even more due to the bolting of the jackets.

During recent decades, many researchers have been trying to replace the conventional steel jacketing technique by usage of fiber reinforced polymer (FRP) wraps. FRP wraps used as confinement can increase the ultimate compressive strength and the ultimate strain of the concrete. (Samaan et al.,1998; Toutanji, 1999). A lot of research has been carried out on developing a retrofitting technique with these FRP wraps. The main advantages these FRP wraps possess over the steel jackets are very high strength to weight ratio & high resistivity to corrosion.

## 1.2 Scope of the study

The objective is achieved and restricted within the following scope of study:

• Literature review to identify and choose the most relevant models for modeling of concrete confined with fiber reinforced polymers in compression.
• Modelling and finite element analysis of the confined concrete compression test in AbaqusCAE.
• Developing the stress-strain curve from several proposed empirical model (Modified Lam

& Teng).

• Survey of experimental data on confined concrete with FRP in order to generate an experimental database.
• Comparison of the analytical results in order to define the strengths and limitations of the empirical model chosen to study.
• Validation of the model chosen and a study on its relevance for use in typical bridge columns retrofitted with FRP jackets.

Proposing & validating changes to the empirical model for more accurate results.

NUMERICAL AND ANALYTICAL MODELING OF CONCRETE  CONFINED WITH FRP WRAPS.