Cost Estimation of Fiber Reinforced Polymer (FRP) Repairs on Rail...

Cost Estimation of Fiber Reinforced Polymer (FRP) Repairs on Rail and Highway Bridges

Lokesh Narendran

Problem Report submitted to the

Benjamin M. Statler College of Engineering and Mineral Resources

at West Virginia University

in partial fulfillment of the requirements

for the degree of

Master of Science

In

Industrial Engineering

Robert C. Creese, Ph.D., Chair

Hota V. Gangarao, Ph.D.

Majid Jaridi, Ph.D.

Department of Industrial and Management Systems Engineering

Morgantown, West Virginia

2013

Keywords: Fiber Reinforced Polymer (FRP); FRP Wrapping; Cost Estimation; Highway

Bridges; Railroad Bridges

ABSTRACT

Cost Estimation of Fiber Reinforced Polymer (FRP) Repairs on Rail and Highway Bridges

Lokesh Narendran

Fiber Reinforced Polymer (FRP) wrapping is used in a large number of construction

projects for repair and rehabilitation works. The strong physical properties, ease of repair and

maintainability of FRP wraps make it a preferred alternative over conventional repair methods.

In the United States, the FRP wrapping technique is used for strengthening of bridge elements

and to repair many railway and highway bridges. This study focuses on the cost estimation of

four bridges repaired using FRP wrapping in the Chicago region and also bridges repaired in

Oregon and California. There are many variables associated with the total project costs like the

concrete and FRP area, labor, material and equipment costs, etc. Regression through origin

(RTO) analysis is used to predict the total project costs and identify the relationships between the

variables of rail and highway bridges.

The results show that the total concrete area was the dominant factor of the total costs for

the railway bridges (Total Contract ($) = 107.58 x Concrete Area (ft2) + 195,783). The total

equipment costs were greater than the total material or total labor costs. A relationship between

the total project cost and the total concrete cost (Total Contract ($) = 1.6864 x Total Concrete

Cost ($) + 23,831) and total FRP cost (Total Contract ($) = 3.249 x Total FRP Cost ($) +

6,512.8) was developed. The productivity of FRP repair (10ft2/hr) was found to be higher than

concrete repair (3 ft2/hr).

A cost model was generated for the various cost parameters of highway bridges in

Oregon. The temporary features and roadwork were found to be significant. Finally, a

relationship (FRP Cost ($) = 24.79 FRP Area (ft2) + 23,616) between the FRP cost and the FRP

repair area was obtained. Least squares percentage regression method (FRP Cost ($) = 23.95

FRP Area (ft2) + 4622.97) is used to check the reduction of the percentage error and to compare

the results.

ii

ACKNOWLEDGEMENT

I would like to thank my advisor, Dr. Robert C. Creese for his valuable support and

remarkable patience. I cannot thank him enough for providing help throughout my time here at

West Virginia University.

I would also extend my thanks to my committee members Dr. Majid Jaridi and Dr. Hota

V. Gangarao for their support and valuable comments in completing this problem report.

I am thankful to the Industrial and Management Systems Engineering department for its

continued support, which enabled me to complete my graduate work. I really enjoyed my time at

Safety and Health Extension, WVU for its great people and work environment. I would like to

thank Dr. Mark D. Fullen and my colleagues for providing me with the opportunity to work and

support me throughout my graduate education.

I am very grateful to my mom, dad, and sister for supporting me in all my decisions. I am

also very thankful to my cousins, family, and friends for their loving support and encouragement

which made all this possible.

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TABLE OF CONTENTS

ABSTRACT ................................................................................................................................................... i

ACKNOWLEDGEMENT ............................................................................................................................ ii

LIST OF FIGURES ...................................................................................................................................... v

LIST OF TABLES ..................................................................................................................................... viii

LIST OF ACRONYMS ................................................................................................................................ x

CHAPTER 1 INTRODUCTION .................................................................................................................. 1

1.1 Status of Bridges in the United States ................................................................................................. 1

1.2 Bridge Repair and Rehabilitation ........................................................................................................ 2

1.2.1 Concrete Repair and Rehabilitation ................................................................................................. 2

1.2.2 Steel Reinforcement Repair and Rehabilitation ............................................................................... 4

1.2.3 FRP Repair and Rehabilitation ........................................................................................................ 4

1.3 Objectives ........................................................................................................................................... 6

1.4 Organization of the Report .................................................................................................................. 6

CHAPTER 2 LITERATURE REVIEW ....................................................................................................... 8

2.1 Background ......................................................................................................................................... 8

2.1.1 Fiber Reinforced Polymers (FRP) for Infrastructure ....................................................................... 8

2.1.1.1 Fibers............................................................................................................................................. 8

2.1.1.2 Matrices....................................................................................................................................... 10

2.2 Literature Review .............................................................................................................................. 10

2.2.1 Review on FRP Bridges ................................................................................................................. 11

2.2.2 Review on FRP Wraps ................................................................................................................... 12

2.3 Case Histories ................................................................................................................................... 16

2.4 Previous Projects on Life-Cycle Cost Analysis of FRP Bridges ...................................................... 20

2.5 Cost Estimates of FRP Wrapping from Contractors in the Construction Industry and Various State

Departments of Transportation ............................................................................................................... 21

CHAPTER 3 METHODOLOGY ............................................................................................................... 25

iv

3.1 Methodology ..................................................................................................................................... 25

3.2 Repair Procedure ............................................................................................................................... 27

3.3 Cost Analysis .................................................................................................................................... 28

3.4 Classification of Variables ................................................................................................................ 35

CHAPTER 4 RESULTS AND DISCUSSION ........................................................................................... 38

4.1 Cost Analysis of Railway Bridges .................................................................................................... 38

4.2 Predicting the Unit Cost of the Bridge Repairs ................................................................................. 46

4.3 Calculating the Time Standards or Productivity for Concrete and FRP Repairs .............................. 50

4.4 Cost Analysis of Highway Bridges ................................................................................................... 51

CHAPTER 5 CONCLUSIONS .................................................................................................................. 67

5.1 Chicago Bridge Findings .................................................................................................................. 67

5.2 Oregon and California Bridge Findings ............................................................................................ 68

5.3 Conclusions ....................................................................................................................................... 70

5.4 Recommendations for Future Study ................................................................................................. 71

BIBLIOGRAPHY ................................................................................................................................... 72

APPENDICES ........................................................................................................................................ 75

Appendix A: FRP Costs of All Bidders of Bridge Repairs in the Oregon and California Region

Adjusted for Inflation .............................................................................................................................. 75

Appendix B: Least Squares Percentage Regression for FRP Area and FRP Cost of All Bridges in

Oregon, California and Illinois ............................................................................................................... 82

Appendix C: Scatter Plots of Average and Low Cost of all Bridges in Oregon and California ............. 83

v

LIST OF FIGURES

Figure 1-1: Bridges by Functional Classification (Data from FHWA, 2012)……………………1

Figure 1-2: Epoxy Crack Injection (www.strongtie.com)………………………………………..3

Figure 1-3: Concrete Jacketing (www.corecut-jo.com) ………………………………………….3

Figure 1-4: Column Strengthening Using Steel Plate Bonding (www.marinland.com)……….....4

Figure 1-5: FRP Wraps Being Applied on a Column (www.ncn-uk.co.uk).……………………..5

Figure 2-1: Repaired 56th St. Bridge (AREMA, 2011)………………………………………....17

Figure 2-2: California Avenue Bridge Before Rehabilitation (AREMA, 2011)………...............17

Figure 2-3: California Avenue Bridge After Rehabilitation (AREMA, 2011)………………….18

Figure 2-4: Decatur Bridge Enclosure (AREMA, 2011)………………………………………..18

Figure 2-5: Completed Champaign Bridge (AREMA, 2011……………………………………19

Figure 2-6: Work on Sandy River Bridge in Oregon……………………………………….…...20

Figure 2-7: Preparation on Beaver Creek Bridge in Oregon………………………………...…..20

Figure 3-1: Distribution of Costs for the Repair for Four Bridges in Chicago………………….32

Figure 3-2: Comparison and Distribution of Costs and Area for Concrete and FRP Repairs…..32

Figure 3-3: Seasonal Difference of Costs and Total Work Hours for the Repair of Bridges in

Chicago……………….....………………….…………….........................................33

Figure 4-1: Scatter Plot of Total Repair Cost Against Total Repair Area of the Concrete

Repairs........................................................................................................................38

Figure 4-2: ANOVA of Total Repair Cost Against Total Repair Area of the Concrete Repairs..39

Figure 4-3: Stepwise Regression on Concrete and FRP Repair Area...........................................40

Figure 4-4: Scatter Plot of Total Repair Cost Against Total Area of the FRP Repairs.................41

Figure 4-5: ANOVA of Total Repair Cost Against Total Repair Area of the FRP Repairs..........41

Figure 4-6: ANOVA of Total Project Cost against the Total Concrete Repairs Cost...................41

Figure 4-7: Scatter Plot of Total Project Cost against the Total Concrete Repairs Cost...............42

Figure 4-8: Scatter Plot of Total Project Cost against the Total FRP Repairs Cost......................42

Figure 4-9: ANOVA of Total Project Cost against the Total FRP Repairs Cost..........................42

Figure 4-10: Scatter Plot of Total FRP Cost Against the Total Concrete Cost.............................43

Figure 4-11: ANOVA of Total FRP Repair Cost Against the Total Concrete Repair Cost..........43

Figure 4-12: Scatter Plot of Total Cost to Repair Against the Material Cost of the FRP

Repairs......................................................................................................................44

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Figure 4-13: ANOVA of Total Cost to Repair Against the Material Cost of the FRP Repairs....44

Figure 4-14: Scatter Plot of Total Cost to Repair Against the Equipment Cost of the FRP

Repairs......................................................................................................................45

Figure 4-15: ANOVA of Total Cost to Repair Against the Equipment Cost of the FRP

Repairs......................................................................................................................46

Figure 4-16: Scatter Plot of Total Contract to Repair Against the Total Repair Area..................47

Figure 4-17: ANOVA of Total Contract to Repair Against the Total Repair Area......................47

Figure 4-18: Scatter Plot of Total Concrete Cost to Repair Against the Total Concrete Repair...48

Figure 4-19: ANOVA of Total Concrete Cost to Repair Against the Total Concrete Repair

Area...........................................................................................................................48

Figure 4-20: Scatter Plot of Total FRP Repair Cost Against the Total FRP Repair Area.............49

Figure 4-21: ANOVA of Total FRP Repair Cost Against the Total FRP Repair Area.................49

Figure 4-22: Stepwise Regression Output of Cost Items of Bridges in Oregon............................52

Figure 4-23: Scatter Plot of FRP Area and its Accepted Cost of Bids for the Oregon Bridges....54

Figure 4-24: ANOVA of FRP Area and its Accepted Cost of Bids for the Oregon Bridges........55

Figure 4-25: Scatter Plot of FRP Area and its Accepted Cost of Bids for the Oregon Bridges By

Regression Through Origin Method.........................................................................55

Figure 4-26: Scatter Plot of FRP Area and its Accepted Cost of Bids for the California

Bridges......................................................................................................................56

Figure 4-27: ANOVA of FRP Area and its Accepted Cost of Bids for the California Bridges....56

Figure 4-28: Scatter Plot of FRP Area and its Accepted Cost of Bids for the California Bridges

By Regression Through Origin Method.................................................................. 56

Figure 4-29: Scatter plot of Total FRP Area of the Bridge Against the FRP Cost of the Accepted

Bid of All Bridge Repairs (California, Oregon and Illinois)....................................57

Figure 4-30: ANOVA of Total FRP Area of the Bridge Against the FRP Cost of the

Accepted Bid of All Bridge Repairs (California, Oregon and Illinois).....................57


Bid of All Bridge Repairs (California, Oregon and Illinois) By Regression Through

Origin Method.........................................................................................................58


Bid of All Bridge Repairs (Illinois and Oregon).....................................................60

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Figure 4-33: ANOVA of Total FRP Area of the Bridge Against the FRP Cost of the Accepted

Bid of All Bridge Repairs (Illinois and Oregon)......................................................60


Bid of All Bridge Repairs (Illinois and Oregon) by Regression Through Origin....61


Bid of All Bridge Repairs (California and Oregon).................................................63


Bid of All Bridge Repairs (California and Oregon).................................................63

Figure 4-37: Scatter plot of Total FRP Repair Area of the Bridge Against the FRP Cost of the

Accepted Bid of All Bridge Repairs (California and Oregon) by Regression Through

Origin.........................................................................................................................64

Figure 4-38: Scatter Plot of Total FRP Area of the Bridge Against the FRP Unit Cost of

Accepted Bids in Oregon...........................................................................................66

Figure 4-39: ANOVA of Total FRP Area of the Bridge Against the FRP Unit Cost of Accepted

Bids in Oregon...........................................................................................................66

viii

LIST OF TABLES

Table 2-1: General Properties of Fibers Used in FRP Materials………………………………….8

Table 2-2: Estimated Material and Installation Cost for Glass and Carbon Wrap Systems..........15

Table 2-3: Approximate Unit Costs of Various Cost Items……………………..........................22

Table 2-4: Cost Items of FRP Repairs of 10 Bridges in California……………………...............23

Table 3-1: Producer Price Index (PPI) Values from the Year 1999 to 2012……………….........26

Table 3-2: FRP Area and Cost Data for Four Railway Bridges for the Respective Wrapping

Procedures……………………………………………………………….....................29

Table 3-3: Total FRP Wrapping Cost Data with Sub-Costs……………………………………..29

Table 3-4: Transportation, Overhead & Profit Cost Data with Total Contract Cost.....................29

Table 3-5: Material Costs of Various Concrete and FRP Tasks……………………....................30

Table 3-6: Equipment Costs of Various Concrete and FRP Tasks……………………................30

Table 3-7: Man-Hours Involved of Various Concrete and FRP Tasks..........................................31

Table 3-8: Man-Hours Costs of Various Concrete and FRP Tasks……………………...............31

Table 3-9: Project Costs for the Four Railway Bridges in Chicago……………………..............34

Table 3-10: Categorized List of Variables for Three Main Cost Items…………………….........35

Table 3-11: Other Variables Involved in Predicting the Total Contract of the FRP Repairs........36

Table 3-12: Categorized List of Variables for Three Main Cost Items for Bridges in Oregon.....37

Table 4-1: Predicted Values and Residuals for Total Area of the Concrete Repairs.....................39

Table 4-2: Least Squares Percentage Regression of Total Concrete Area and Total Project

Cost....………………………………………………………………..........................39

Table 4-3: Predicted Values and Residuals for Total Cost of the FRP Repairs Against the FRP

Material Cost………………………………………………………………................44

Table 4-4: Least Squares Percentage Regression of FRP Material Cost and Total Project

Cost.......……………………………………………………………………………....45

Table 4-5: Predicted Values and Residuals for Total Cost of the FRP Repairs against the FRP

Equipment Cost.............................................................................................................46

Table 4-6: Predicted Unit Cost for the Total Repairs…………………………………………....46

Table 4-7: Predicted Unit Cost for the Concrete Repairs……………………………………......47

Table 4-8: Predicted Unit Cost for the FRP Repairs………………………………………….....49

Table 4-9: Estimated Time Required in Man Hours for the Concrete Repairs.............................50

ix

Table 4-10: Estimated Time Required in Man Hours for the FRP Repairs………......................50

Table 4-11: Cost Items of Different Parameters of the Highway Bridges of Oregon…………..51

Table 4-12: FRP Cost Data with Bridge Area Covered by FRP and their Accepted, Average and

Low Bidders’ Unit Cost……………………………………………………………53

Table 4-13: Predicted Values and Residuals of FRP Cost of All Bridges………………………59

Table 4-14: Predicted Values and Residuals of FRP Cost of All Bridges (Oregon and

Illinois).......................................................................................................................62

Table 4-15: Predicted Values and Residuals of FRP Cost of All Bridges (California and

Oregon).......................................................................................................................65

Table 5-1: Relationships Obtained for Rail and Highway Bridges and Their Coefficient of

Determination (R2) and p-values..................................................................................70

x

LIST OF ACRONYMS

AASHTO American Association of State Highway and Transportation Officials

ABS Acrylonitrile Butadiene Styrene

ADT Average Daily Traffic

AREMA American Railway Engineering and Maintenance-of-Way Association

CFRP Carbon Fiber Reinforced Polymer

ERV Explained Relative Variation

FHWA Federal Highway Administration

FRP Fiber Reinforced Polymer

GFRP Glass Fiber Reinforced Polymer

IBRC Innovative Bridge Research and Construction Program

MDOT Michigan Department of Transportation

NBI National Bridge Inventory

NDT Nondestructive Testing

NSM Near Surface Mounted

PAN Polyacrylonitrile

PEEK Polysulfone and Polyether Ether Ketone

PPI Producer Price Index

PR Percentage Regression

PVC Polyvinyl Chloride

RC Reinforced Concrete

SIP Stay-In-Place

RTO Regression Through Origin

TRV Total Relative Variation

URV Unexplained Relative Variation

UMR University of Missouri-Rolla

UK United Kingdom

1

CHAPTER 1 INTRODUCTION

1.1 Status of Bridges in the United States

The United States highway network consists of more than 600,000 bridges that make up a

critical link in the nation’s infrastructure e. The United States rail freight and passenger network

consists of about 70,000 bridges. Many of these structures are close to or have exceeded their

original design life. According to a study conducted by the Federal Highway Administration

(FHWA), 25% of the 607,380 bridges in the United States were structurally deficient or

functionally obsolete as shown in Figure 1-1 [1]. Structurally deficient is defined as when a

highway bridge’s deck, substructure, superstructure or culvert is rated as “poor” (0 to 9 on the

National Bridge Inventory (NBI) rating scale with 0 - 4 as poor, 5 as fair, 6 - 8 as good, and 9 as

excellent condition [2]). Also if the load carrying capacity is significantly lower than the current

design standards or if a waterway below frequently overflows the bridge during floods.

Functionally obsolete highway bridges have lower load carrying capacity, narrower shoulders or

less clearance underneath than bridges built to the current standard [3]. Thus, the designation of

the bridges based on their functional classification has a great impact on the bridge maintenance,

rehabilitation or replacement.

Figure 1-1: Bridges by Functional Classification (Data from FHWA, 2012) [1]

455,883 (75%)

66,749 (11%)

84,748 (14%)

Non Deficient

Structurally Deficient

Functionally Obsolete

2

The US infrastructure rehabilitation cost is estimated at 2.2 trillion dollars [3], the American

Association of State Highway and Transportation Officials (AASHTO) estimated in 2008 that it

would cost roughly $140 billion to repair every deficient bridge in the country, about $48 billion

to repair structurally deficient bridges and $91 billion to improve functionally obsolete bridges

[3]. In the context of this issue, it is necessary to invest in advanced composites and to consider

alternate bridge rehabilitation techniques.

1.2 Bridge Repair and Rehabilitation

There are a wide variety of bridge repair and rehabilitation techniques available. Some of

the techniques are discussed below. They include:

Concrete Repair and Rehabilitation

Steel Reinforcement Repair and Rehabilitation

FRP Repair and Rehabilitation

1.2.1 Concrete Repair and Rehabilitation: The most common method of bridge rehabilitation

has different types of repair techniques. They are:

Repair with Concrete or Mortar: Used to repair the damage caused by impact,

cracking, spalling, delamination, reinforcement corrosion and chemical

contamination.

Polymer Concrete Repair: It is often desirable for patch repairs due to its low

permeability. Polymer concrete patch repairs are often applied by hand.

Crack Injection: Epoxies, polyesters, methacrylates and polyurethanes have all

been used to fill cracks in concrete structures. The injection equipment is inserted

into the ports that are installed at the crack surface and epoxy is injected through

a hand gun until all portions of the crack are filled. Figure 1-2 shows epoxy crack

injection.

3

Figure 1-2: Epoxy Crack Injection (www.strongtie.com)[4]

Coatings and Sealers: There are three primary types of material that are used to

seal concrete and prevent ingress of contaminants: film-forming coatings, pore

liners/blockers and sealers. Most coatings can be applied using brush, roller or

spray.

Concrete Jacketing: Concrete Jacketing involves enlargement of the existing

structural members by placing reinforcing steel rebars around its periphery and

then concreting it as shown in Figure 1-3.

Figure 1-3: Concrete Jacketing (www.corecut-jo.com) [5]

http://www.strongtie.com/products/anchorsystems/adhesives/crackrepair/eti.html

4

1.2.2 Steel Reinforcement Repair and Rehabilitation

Cleaning: When concrete patch repair is implemented, steel reinforcement bars

are cleaned to remove contaminants from the steel surface. Cleaning the

reinforcement bars also promotes adhesion between the steel and the concrete.

Rebar Splicing: New portions of steel rebar are added to the corroded section of

reinforcing steel. This can be done by tying in new sections of steel rebar to

restore the member to its original capacity.

Coating: Fusion bonded coatings, which consists of thermoset polymers in

powder form; undergo an irreversible chemical reaction that causes them to

strongly adhere to the steel.

Steel Plate Bonding: The structural elements are strengthened by bonding steel

plates to their external surfaces by using adhesives as shown in Figure 1-4.

Figure 1-4: Column Strengthening using Steel Plate Bonding (www.marinland.com) [6]

1.2.3 FRP Repair and Rehabilitation

FRP Wrapping: FRP wrapping has emerged as an alternative to traditional

materials for repair of concrete bridges. It can be used to rehabilitate different

structural members of a bridge like columns, girders and beams to improve the

load bearing capacity. The rehabilitation is done by wrapping composite sheets

around the structural members as shown in Figure 1-5. There are many

advantages to using FRP composite systems in structural applications. They are

corrosion resistant, high strength, light weight, easy to install and have a low

5

impact on the existing dimensions of a structure. They provide life-cycle

advantages that make these bridges financially viable even if they do sustain an

initial cost premium. But when considering the entire life-cycle of the

rehabilitation, the initial material cost of the FRP wrap is only a fraction of the

total retrofitting cost; the rest is attributed to the application, labor and

maintenance costs. Also the overall cost of rehabilitation is reduced due to the

ease of installing, storage, handling and transportation benefits of FRP wraps.

Figure 1-5: FRP Wraps Being Applied on a Column (www.ncn-uk.co.uk)[7]

FRP Plates: FRP plates are essentially FRP fabric that has already been

impregnated and cured by the manufacturer. A primer coat is applied to a sound

concrete substrate and then the plates are cut to the desired dimensions and are

placed onto the concrete member with epoxy adhesives.

Near Surface Mounted (NSM) FRP Bars: NSM bars are long and cylindrical like

rebar. A shallow groove is cut into a sound concrete substrate and an embedding

paste is used to half fill the grooves. The bars are then lightly pressed into the

groove so that the paste completely fills the space between FRP and the groove.

6

1.3 Objectives

The objective of this study is to estimate the cost of FRP wrapping and to identify the

variables that affect the total project costs based on the data available from four FRP wrapping

projects for railway bridges in the Chicago area and other highway bridges in Oregon and

California. The data for the railroad bridges have been categorized into many variables. Some of

the variables that are considered here are concrete total area; concrete beam area; injection joint

cost; FRP application task cost; labor, material and equipment cost; total concrete cost; total FRP

cost; overhead and profit.

The main objectives of this study are to:

Obtain and analyze the cost data of previous FRP wrapping projects.

Identify the variables that affect the total cost of FRP wrapping projects.

Predict the total project costs and thereby identify relationships between the variables of

both the railway bridges and highway bridges that affect the total project costs.

Generate regression equations based on the data available and estimate the FRP wrapping

total cost.

Calculate the time standards or the productivity of the concrete and FRP repairs.

Estimate the FRP cost and total cost using least squares percentage regression and

compare with the traditional linear regression.

1.4 Organization of the Report

Chapter 2 presents a literature review of different types of fibers and matrices. It also

gives some background information on the railway bridges and the highway bridges for which

the study is done. A discussion about the technical publications in the areas of FRP wraps by

different researchers is provided in this chapter.

Chapter 3 discusses the methodology. A discussion about the cost analysis of the railway

and highway project is made. The data providing the costs of the railway and highway projects

and the variables considered for estimating the total cost is discussed.

7

Chapter 4 provides the analysis of the data for both the rail and highway bridges. Results

of this report show the variables that have a significant relationship in predicting the project

costs. It provides the productivity of the FRP repair in comparison to the concrete repairs of the

bridges. It also provides the relationships between the FRP area, FRP cost and the Unit cost of

FRP repairs.

Chapter 5 describes the conclusions drawn from the results of this study and

recommendations for further study.

8

CHAPTER 2 LITERATURE REVIEW

2.1 Background

2.1.1 Fiber Reinforced Polymers (FRP) for Infrastructure

Composite materials have been used in civil engineering structures because of their

mechanical properties and their advantages in regards to harsh environmental conditions. A

composite material is defined as a “combination of two or more distinct materials to form a new

material with enhanced properties” [8]. FRP composites are manufactured to the needs of

specific industries like the construction, aerospace, sporting goods and leisure industries. A

variety of forms like reinforcing bars and fabric wraps are used in different applications.

Excellent corrosion and fatigue resistance of FRP composites gives them an economical

advantage in the life-cycle costs of structures, especially bridges which are prone to heavy loads

and environmental hazards [9]. Fiber reinforced polymers (FRP) are made of two constituent

materials: fibers and polymer matrices. The common properties of FRP fibers are presented in

Table 2-1.

Table 2-1: General Properties of Fibers Used in FRP Materials [10]

Specific

Gravity

Tensile

Strength

(ksi)

Tensile

Modulus

(106

)psi

Coefficient of

Thermal Expansion

(10–6

/°C)

Strain to

Failure

(%)

Glass 2.48–2.62 217–700 10.2–13.0 2.9–5.0 4.8–5.0

Carbon PAN 1.76–1.96 220–820 33–70 –0.60 to –0.75 0.38–1.81

Carbon Pitch 2.0–2.15 275–350 55–110 –1.30 to –1.45 0.32–0.50

Aramid 1.39–1.47 435–525 10.1–19.0 –2.0 to –6.0 1.9–4.4

Boron 2.7 450 57 5 0.2

2.1.1.1 Fibers

FRP fiber is generally made from one of three materials: carbon, glass or aramid.

Carbon Fibers (Graphite Fibers): Carbon fiber is defined as a fiber containing at least

90% carbon by weight. Graphite fibers have carbon levels above 95% by weight. Carbon

or graphite fibers have a high tensile strength-to-weight ratio, a high tensile modulus-to

weight ratio, a very low coefficient of linear thermal expansion, high fatigue strength,

9

variety of material properties and excellent chemical resistance, which are considered to

be advantageous. The disadvantages of using carbon fibers are their relatively high cost,

their high brittleness and their high electrical conductivity. The material properties of

carbon fibers greatly depend on what precursors, or raw materials, they were derived

from. The two primary classes of material are polyacrylonitrile (PAN) carbon fibers,

which is stronger, more expensive but also the most common and isotropic pitch carbon

fiber, which is cheaper but not as strong [9].

Glass Fibers: Glass fibers are widely used and are available in a variety of forms suited

for different applications. The most common type is E-glass which is used for its low

susceptibility to moisture and high mechanical properties. Other types of glass fibers that

are used include S-glass, which has approximately 25% greater tensile strength than E-

glass but is more expensive, C-glass, which was developed for application in corrosive

environments, D-glass, which has lower density and dielectric constant than the other

types of glass fibers, and Z-glass, which is used for cement mortars and concretes due to

its resistance towards high alkali attack. Glass fibers are advantageous because they are

very hard, corrosion and chemical resistant, inert, flexible, a good insulator and

inexpensive. The disadvantages of glass fibers are low tensile modulus, high specific

gravity and sensitivity to abrasion during handling, high hardness and low fatigue

resistance [9].

Aramid Fibers: Aramid fibers or Kevlar fibers are made from aromatic polyamides; these

have the lowest specific gravity and highest specific tensile strength among all type of

fibers [10]. Some of the characteristics are no melting point, low flammability and good

fabric integrity at elevated temperatures. The advantages of aramid fibers include very

low thermal conductivity, high damping coefficient and high degree of yielding under

compression. Their disadvantages include low compressive strength, loss of strength and

modulus at high temperatures and are hygroscopic (can absorb moisture up to about 10%

of fiber weight) [9].

Boron Fibers: Boron fibers are usually made of a tungsten-filament core with elemental

boron vapor deposited on it to give strength and stiffness. The advantages of using boron

fibers include very high tensile modulus, in the range of 50x106 to 60x10

6 psi and good

resistance under compressive loads to buckling. The main disadvantage of Boron is its

10

high cost, which is even higher than that of many forms of carbon fibers. For this main

reason, its use is restricted to aerospace applications [9].

2.1.1.2 Matrices

The matrix is considered the secondary material in FRPs and does not contribute any

significant strength. Its major roles are transferring stresses between the fibers and protecting

fibers against the environmental and mechanical conditions. The importance of the matrix in a

composite is its effect on interlaminar and in-plane shear strengths. It also provides support

against buckling of the fibers under compressive loads. Polymer matrices are divided into two

categories:

Thermoplastic Polymers: Individual molecules are in a linear structural form. Weak

secondary bond holds these molecules together. Heat or pressure temporarily breaks the

bonds, which causes movement between the molecules. After cooling the molecules set

into their new position. Thermoplastics have higher impact strength, fracture and micro

cracking resistance compared to thermosetting polymers. Examples of thermoplastic

polymers are acrylonitrile butadiene styrene (ABS), acrylics, fluoropolymers, polyvinyl

chloride (PVC), polycarbonate, polyethylene, polypropylene, polysulfone and polyether

ether ketone (PEEK) [9].

Thermosetting Polymers: They are also known as epoxy resins that are used commonly

for fiber reinforced polymers as a matrix material. The molecules are joined together by

crosslinks, which leads to a more stable three-dimensional form that cannot be reshaped

by heat or pressure. They have better bonding between fibers and the matrix with an

ability to cool at room temperature in the presence of a catalyst. Some of the most

common types of thermosetting polymers are epoxy, polyester and vinyl ester [9].

2.2 Literature Review

There is a lot of research in the area of FRP and its application in various infrastructure

projects, but FRP wrappings undertaken by private companies for various infrastructures projects

are not published in the literature to allow verification of details. This section includes review on

both FRP bridges and FRP wraps to analyze the advantages of FRP over the conventional

rehabilitation methods.

11

2.2.1 Review on FRP Bridges

In a research paper titled “Financial Viability of Fiber-Reinforced Polymer (FRP)

Bridges”, the authors (H. E. Nystrom, S. E. Watkins, A. Nanni, S. Murray, 2003)[11] investigate

current and future costs to determine the cost effectiveness of this technology, by taking into

account the expected improvements in manufacturing, transport, installation and life-cycle

differences. This analysis also examines the future costs for the construction and life cycle costs.

Based on two case studies of short span FRP bridges, the learning curve approach and

comparison with traditional methods, the results show that probable improvements would not be

sufficient to compete on cost with reinforced-concrete bridges. The total direct costs are

estimated to be $3000/m2 ($275/ft

2) for UMR Bridge and $1150/m

2 ($107/ft

2) for St. James

Bridge. The total cost of the UMR Bridge is $76,500 and the total cost for St. James Bridge is

$76,719. The estimated total direct cost for the Future Bridge similar to the other bridge is

approximately $740/m2 ($70/ft

2), which reflects a 35% reduction from the St. James Bridge but it

is still 71% higher than the traditional RC bridge. Unless there is a significant improvement in

the cost of component material, this technology will not be cost competitive for the standard

short-span bridge and the application of FRP technology will be limited to other segments of the

market such as bridge repair and bridge deck construction.

“Construction and cost analysis of an FRP reinforced concrete bridge deck” by the

authors (A. C. Berg, L. C. Bank, M. G. Oliva, and J. S. Russell, 2005) [12] describes the use of

FRP materials as reinforcements and formwork for a concrete highway bridge deck. It provides

the description of the bridge and the FRP reinforcing systems that have been used in many

structures. Three forms of FRP reinforcing were combined to reinforce the concrete deck: FRP

stay-in-place (SIP) forms, deformed FRP reinforcing bars (rebars) and a special prefabricated

pultruded FRP reinforcing grid. The research project, supported by the Innovative Bridge

Research and Construction Program (IBRC), resulted in the construction of a two-span highway

overpass on US Highway 151 in Wisconsin. The total material costs for the FRP reinforced

bridge were $632,718. The material costs for the steel reinforced bridge were $391,649. This

translates to over a 60% materials cost increase over conventional construction (the materials for

the bridge with the steel deck cost 3/5 that of bridge with the FRP deck). The cost of the

individual FRP components was $167,637.60 (deck panels), $64,922.40(grid), and

12

$25,369.10(rebar) for a total FRP material cost of $257,929.10 at $370.17 per m2 ($34.39 per

ft2). The cost of the steel reinforcement was $37,060.10. Based on the analysis of the short-term

material and labor costs it appears that given the savings in construction time and their likely

long-term durability and maintenance benefits, FRP reinforcements for bridge decks may be

cost-effective, notwithstanding their currently high initial costs. The future optimization of the

design of FRP stay-in-place formwork and competitive bidding between FRP manufacturers is

recommended to decrease the cost of the FRP reinforcement system. The use of larger

prefabricated FRP grids in place of the FRP rebars may yield more labor and time savings.

“A Viable Alternative: Fiber-Reinforced Polymer” (by H.S. Ramnath, 2012) [31] talks

about the potential cost savings of fiber-reinforced polymer composites over steel-reinforcement

based on a life cycle cost analysis. The study compares two geometrically identical bridge decks

made from conventional steel-reinforced concrete (SRC) and fiber-reinforced polymer (FRP)

composites. BridgeLCC was the software used to calculate the life cycle cost analysis. The

conditions assumed for the analysis are the length of the study was 70 years, and the base year

was 2011; the inflation rate was 1.80% and the real discount rate was 3.20%. It is assumed that

there are two lanes on and under the bridge and the bridges are of medium length with a deck

area of 4500 ft2 and a length of 100 ft. Finally, the costs of Construction, Operation, Maintenance

and Repair (OM&R), and Disposal costs were given. The total OM&R of the SRC deck is

estimated at $390,005 and the FRP deck is $185,048 in base-year dollars which shows that FRP

bridge decks cost less to maintain than SRC bridge decks. The total cost in base-year dollars for

the FRP bridge deck is $79,957 less, or 14.3% cheaper than the SRC bridge deck. It is to be

noted that the total cost is estimated without considering the inflation. After approximately 20

years, the FRP bridge deck becomes the less expensive option. When inflation is factored in the

FRP is 35% cheaper than SRC.

2.2.2 Review on FRP Wraps

A paper by the “Highways Agency and Network Rail” in the United Kingdom titled

“FRP strengthening of concrete road and rail bridges in the UK” by the authors (N. Loudon and

B. Bell, 2010) [13] discusses the uses of fiber-reinforced composites by the Highways Agency

and Network Rail in the UK to strengthen concrete bridges. In construction, there are still

uncertainties about the use of composites such as glass, aramid and carbon fiber. They are light

13

and easily handled materials and not subject to corrosion, and are therefore a low-maintenance

and durable option for bridge decking and strengthening of structures. There are some potential

disadvantages when using composites such as longer-term durability. Alternatively, the

Highways Agency and Network Rail have successfully undertaken a lot of projects using

composites to strengthen their existing structures. There have been two main applications namely

column strengthening and deck strengthening which are primarily used for impact loading and

bending. The paper highlights case studies and the development of design guidance. The first

project was the strengthening of the M11 Coopersale Bridge in Essex. Aramid was used as a

wrap which was highly effective and resulted in significant savings in budget and installation

times. This led to the use of prefabricated glass fiber shell to surround the columns of most

bridges. The network rail projects such as the Glade Bridge used carbon-fiber-reinforced

polymer (CFRP) plate bonding. Three 100mm wide by 1.2 mm thick CFRP plates on each of the

six beams of the deck increased the capacity from 293KNm to 441KNm, providing 50% strength

gain and 104% increase in load capability. Mill’s Hill Bridge traverse concrete slab was

strengthened with CFRP plates of 80mm wide by 1.2 mm thick. It also summarizes research that

has been carried out with support from the two client organizations and other structural

applications of composites that are being undertaken by these organizations. Finally, the paper

suggests prospective future research activities with FRP system components, design

considerations and testing, and discusses the standards and guidance to manage the use of FRP’s

on their networks.

“Application of FRP laminates for strengthening of a reinforced-concrete T-beam bridge

structure” paper by the authors (O. H.Elsa, S. Alampalli, J. Kunin, 2000) [14] describes

application of fiber-reinforced polymer (FRP) composite laminates to strengthen an aging

reinforced-concrete T-beam bridge in South Troy, Rensselaer County, New York. Leakage at the

end joints of this single-span structure led to substantial moisture and salt infiltration in the

bridge superstructure. Presence of efflorescence was observed and freeze-thaw cracking and

concrete delamination at some locations on the beams were noted. Concerns about integrity of

the steel reinforcing and overall safety of the bridge were raised. These concerns were increased

by the absence of any documents pertaining to the bridge design such as rebar size, steel type,

concrete strength, and design loads. Thus, a decision was made to strengthen the bridge using

14

bonded FRP-laminates. Load tests were conducted before and after installation of the laminates

to evaluate effectiveness of the strengthening system and investigate its effect on structural

behavior. Tests results were analyzed and compared with those obtained using classical analysis.

Using bonded FRP laminates, as a cost-effective bridge rehabilitation technique, total cost of the

rehabilitation is estimated at $300,000, which may be compared to $1.2 million required for

replacement of the structure or, about 25% of the replacement cost.

The paper “Reliability analysis of bridge beams retrofitted with fiber reinforced

polymers” (H. B. Pham, R. A. Mahaidi, 2006) [15] presents a study of reliability of RC beams

retrofitted with FRP. The beam variables and their variability are assessed. Three common

failure modes are considered, flexural failure, intermediate span debond, and end debond. The

prediction models used in this study were developed previously by the authors. Monte Carlo

simulation was carried out to study the variability of the capacity of CFRP-strengthened beams

for each failure mode. A reliability analysis was carried out based on the guidance provided by

Eurocode 2. The analysis provides the bases for recommendation of capacity reduction factors

for different failure modes. It was found that for flexural failure and intermediate span debond a

factor of 0.6 is needed whereas a factor of 0.5 can be applied for end debond. These factors are

relatively low and reflect the uncertainty over FRP failure and debonding.

In a research report titled “Repair of Corrosion-Damaged Columns using FRP Wraps,”

the authors (R. S. Harichandran, M. I. Baiyasi, 2000) [16] performed experiments to assess the

effects of using fiber reinforced polymer (FRP) wraps with fibers oriented in the hoop direction

for rehabilitating corrosion-damaged columns. Issues that were explored are: (1) freeze-thaw

durability of concrete square and cylindrical specimens wrapped with glass and carbon FRP and

subjected to an internal expansive force; (2) effect of wrapping on the rate of corrosion in an

accelerated corrosion test; (3) effect of freeze-thaw and wet-dry cycles on the properties of FRP

panels; (4) impact resistant of FRP panels supported on a concrete substrate; (5) effect of high

temperature on wraps; and (6) field installation of wraps on corrosion-damaged bridge columns.

The results of the freeze-thaw experiment shows that freeze-thaw cycles have no statistically

significant effect on the compressive strength of glass and carbon wrapped specimens. For

cylindrical specimens, glass and carbon wraps increased the strength by a factor of about 2.3 and

2.6, respectively. For square specimens, glass and carbon wraps increased the strength by a

15

factor of 1.4-1.5. Freeze-thaw conditioning generally reduced the longitudinal failure strain of

wrapped specimens. After 190 days of testing the results of the accelerated corrosion experiment

indicate that wrapping reduced the corrosion depth in the reinforcing bars by 46% to 59%. Both

glass and carbon wraps are equally effective in slowing down corrosion. Freeze-thaw and wet-

dry conditioning had no harmful effect on carbon FRP panels other than reduction in the ultimate

strain. Glass FRP panels showed 21% and 20% reductions in ultimate strength and ultimate

strain due to freeze-thaw conditioning, and 18% and 20% reductions in ultimate strength and

ultimate strain due to wet-dry conditioning. At temperatures in excess of 200°C the epoxy in the

FRPs burn and evaporate and the individual plies of wraps unravel. Therefore the wraps become

ineffective at such high temperatures and effective insulation is necessary.

The report also includes the estimated cost for the conventional chip and patch repair

technique that was used in the year 2000 by the Michigan Department of Transportation

(MDOT) which was approximately $500-$725/m2 ($46.50 -$67.37/ft

2) of repaired column

surface. The estimated cost of the glass and carbon wrap systems used in this research study as

provided by the respective suppliers is $425/m2 ($39.50/ft

2) and $360/m

2 ($33.50/ft

2)

respectively. Estimated cost of surface preparation prior to wrap installation was provided by

MDOT is given in the Table 2-2.

Table 2-2: Estimated Material and Installation Cost for Glass and Carbon Wrap Systems

Wrap Type

Material Cost

/m2/layer

(/ft2/layer)

Installation

Cost/m2/layer

(/ft2/layer)

No. of

Layers

Surface

Prep./ m2

(/ft2)

Total

Cost/m2(/ft

2)

Glass $54 ($5) $54 ($5) 3 $101 ($10) $425 ($40)

Carbon $75 ($7) $54 ($5) 2 $101 ($10) $360 ($34)

It is evident from the experimental study conducted that both carbon and glass wrap

systems are sufficiently resistant to freeze-thaw cycles and reduce the corrosion rate by about the

same rate. Therefore, three layers of glass wrap or two layers of carbon wrap may be used to

repair Michigan bridge columns.

A report by the Iowa Department of Transportation titled “Repair of impact damaged pre-

stressed concrete beams with CFRP” by the authors (T. J. Wipf, F. W. Klaiber, J. D. Rhodes, B.

J. Kempers, 2004) [24] is about the testing of CFRP for repair/ strengthening of three damaged

16

bridges in the state of Iowa. The three bridges were load tested before the installation of CFRP.

One bridge was retested after the installation of the CFRP to determine the structural changes

after the repair. The experimental results showed some improvement in the structural behavior of

the bridge. The report also draws comparison between the steel jacket and CFRP repair costs

from a case study of five bridges repaired in Iowa.

The cost to repair a 30 ft. beam by steel jacketing for the Polk 3498 bridge was $24,952,

of which $15,312 is for structural steel. This was approximately $826 per lineal foot for repairs

by steel jacketing. The cost of Polk 3400 bridge repair by CFRP is $34,000. With 80 feet being

wrapped and ignoring the cost of the other five beams, the cost of this repair was $425 per lineal

foot. The CFRP repair on the bridge also includes the cost of flexural strengthening with carbon

fiber plates. The 4in. Sika S1012 plates, cost $44 per lineal foot. Four plates were placed side by

side along the bottom with a length of 75 feet for a total of 300 lineal feet. The total cost of the

plates was $13,000. After subtracting the plates cost from the total FRP cost of $34,000, the unit

price for CFRP wrap was $262.50 per lineal foot, which was less than 1/3 of the cost of the steel

jacket repair.

2.3 Case Histories

The four railway bridges for which the cost estimation was performed were restored with

the implementation of FRP technology. All four structures were located in Chicago, Illinois.

56th Street

This bridge has a constant volume of city traffic. The repair work started in October and

continued through November of 2009. Traffic regulations and mobilization were provided for

speedy rehabilitation of the bridge. The concrete columns, arch beams and slabs were all repaired

and wrapped. The original architecture of the bridge column was to be maintained after the

retrofit, so a thinner GFRP material was applied at these locations so that the column’s

appearance was maintained to minimal or no impact. The 56th St. Bridge in Chicago can be seen

in Figure 2-1 [17].

17

Figure 2-1: Repaired 56th St. Bridge (AREMA, 2011) [17]

California Avenue

The columns and beams of this bridge had been in very poor condition due to constant

usage by trucks. Before the application of GFRP wrapping, approximately 45% of the

column concrete and 30% of the beam /slab concrete was removed and replaced. The original

condition of the bridge can be seen in Figure 2-2 and Figure 2-3 shows the repaired structure

[17].

Figure 2-2: California Avenue Bridge before Rehabilitation (AREMA, 2011) [17]

18

Figure 2-3: California Avenue Bridge after Rehabilitation (AREMA, 2011) [17]

Decatur

This bridge was repaired during extreme cold weather, maintaining a minimum surface

temperature of 40°F throughout installation. Due to low volume of traffic the road was closed

and the entire structure was enclosed and heated for the work, as shown in Figure 2-4.

Figure 2-4: Decatur Bridge Enclosure (AREMA, 2011) [17]

19

Champaign

This structure was enclosed and heated for cold weather conditions during FRP

application. Traffic control and mobilization were provided in this area during construction. In

addition to the columns and slabs, this structure consisted of concrete T-beams and steel encased

beams that were wrapped with GFRP. Construction workers removed and repaired

approximately 40% of the column concrete, 25% of the beam concrete and 50% of the slab

concrete before installing the glass fiber wrap system. Figure 2-5 shows the repaired structure.

Figure 2-5: Completed Champaign Bridge (AREMA, 2011) [17]

The cost estimation of the highway bridges for which the FRP repair and rehabilitation is

performed are located in the states of Oregon and California. The cost data obtained was for 26

bridges located in Oregon and seven bridges in California. Some of the bridges were grouped

into a bundle and the bid for the total contract was obtained for each bundle. A bundle may have

two to five bridges in a contract. The data includes various cost items of all bidders for each

contract. Figures 2-6 and 2-7 show the work on two of the projects involving FRP repairs and

rehabilitation.

20

Figure 2-6: Work on Sandy River Bridge in Oregon [18]

Figure 2-7: Preparation on Beaver Creek Bridge in Oregon [19]

2.4 Previous Projects on Life-Cycle Cost Analysis of FRP Bridges

A life cycle cost estimation model was developed in a thesis submitted by

(Roychoudhury, 2001) [20]. The software model takes inputs like the length of the bridge,

geographical location of the bridge, the ADT (Average Daily Traffic) of the bridge, etc. The

model will then compute all the direct or indirect costs associated with the various stages of the

life of the bridge like maintenance costs, repair costs, and rehabilitation costs.

21

In another cost model for the pultrusion process by (Patrawala, 1999) [21], users input

variables for materials, geometry, weight, area, number of cavities, etc. The model selects

exogeneous, process material adjustment factors, etc. or the user may enter his values for these

parameters. The model calculates the cost and life of different equipments and the material cost.

In the Cost Estimation of FRP Wrapping for Bridge Rehabilitation report by

(Manukonda, 2011) [22], regression analysis was used to estimate the contract values of FRP

wrapping for bridge rehabilitation projects using data from different projects. The variables

studied were: the number of layers, the number of elements, the repair area, the type of material,

the type of application, and the product of layers and area. Two regression equations were built

separately, one each for columns and girders. Another equation was built for all contract values

with all element types. The variables element type, number of layers, area, number of elements

and number of layers × area were obtained as significant variables. Number of layers was the

most significant variable and it is present in all regression equations (Total Cost = −46782 +

41386 x Number of layers). A relationship for the FRP installation costs was given, Cost ($/ft2) =

$27 + 20,980/ Area (ft2). The area covered was for two layers and ranged from 600 to 3000 ft

2.

In a thesis submitted by (Brayack, 2006) [23], a case study project that presents a

recommendation for possible adoption of FRP for bridge repair and retrofit was discussed. It had

some cost estimates by a consultant, the FRP unit cost was very low ($7/ft2) with two layers of

FRP wraps. It can be noted that the ratio obtained between the concrete repair costs and FRP

repair costs was 1.5 – 2.0. Thus the total project cost can be roughly estimated with a factor of

2.5 times the total FRP costs. The FRP repair area was larger with twice the size of the concrete

repair area and the estimated total unit cost adjusted to inflation was $40/ ft2.

2.5 Cost Estimates of FRP Wrapping from Contractors in the Construction Industry and

Various State Departments of Transportation

Sean Wisotzkey, Project Engineer - Buildings Division of Fyfe Company [26] gave an

approximate installed cost for FRP wrapping of the projects done by the company. He provided

an approximate installed cost (includes all labor and material) for glass around $20-$25 per

square foot per layer and carbon around $35-$40 per square foot per layer, also a general rule of

thumb, that glass FRP is about half the price of carbon FRP (just raw materials, this does not

22

always translate to installed costs). The price includes concrete preparation but not restoration

(no demo, patching, etc).

John Huedepohl of HJ3® Composite Technologies [26] gave an approximate unit cost for

FRP wrapping based on the three main cost items.

Table 2-3: Approximate Unit Costs of Various Cost Items

Surface Preparation $8 - $15/sqft

CFRP $10 - $20/sqft

Misc $10 - $20/sqft

Total Unit Costs $28 - $55/sqft

Justin Jar, Bridge Inspection Manager at the Utah Department of Transportation [27]

provided an approximate unit cost for CFRP ($30 - $50/ sqft) and GFRP ($20/ sqft) including

labor and material costs.

FRP wrapping is limited in Utah and the cost involved is very small (about 10% – 30%)

of the total project costs. These costs are for CFRP only. Concrete repair on column, bent cap

can be estimated by their surface areas, depending on minor, moderate or major repair. The

average concrete cost for column 3 ft in diameter, 15 to 20 ft height with cracks, spalls and rebar

exposed repair at $10,000/each or $25/ft2 range.

A report by the structures division of the New York State Department of Transportation

(NYSDOT) estimated the cost to be approximately $14.52 per layer per square feet for E-glass

and $20.33 per layer per square feet for carbon (adjusted to 2011 cost) [29].

Jeff DeFevere, Division of Engineering Services at the California Department of

Transportation [30] provided the cost summaries for FRP wrap work done to its bridges. Table 2-

4 provides the cost details. Information about all other cost items with all bidders are also given

but not included here. The adjusted price is based on latest US government PPI data released on

April 14, 2013 adjusted to the year 2011.

23

Table 2-4: Cost Items of FRP Repairs of 10 Bridges in California [30]

Description Year Unit Quantity

Unit

Cost

Adj.

Unit

Cost*

FRP

Cost

Adj.

FRP

Cost* Total Contact

Composite

Column Casing 2008 Sqft 614 $55.70 $58.19 $34,200 $35,731 $39,726,300

Composite

Column Casing 2010 Sqft 420 $77.65 $80.10 $32,613 $33,643 $995,644

Composite


Composite


Composite

Column Casing 2012 Sqft 3,677 $65.00 $63.51 $239,005 $233,521 $3,352,320

Composite Girder

Strengthening 2012 Sqft 2620 $70.50 $68.88 $184,710 $180,472 $2,559,279

Composite Girder

Strengthening 2012 Sqft 170 $99.00 $96.73 $16,830 $16,444 $735,961

Carbon Fiber

Reinforced

Polymer 2009 lf 10132 $24.00 $25.16 $243,168 $254,958 $7,397,807

Carbon Fiber

Reinforced

Polymer Strips 2008 lf 1303 $12.19 $12.73 $15,880 $16,591 $886,360

Carbon Fiber

Reinforced

Polymer Strips 2012 lf 5500 $15.00 $14.66 $82,500 $80,607 $1,563,592

*Cost adjusted to the year 2011.

The four bridges in West Virginia [33] repaired by using Fiber-Reinforced Polymer

(FRP) wrap are Pond Creek Overpass, East Street Viaduct, Muddy Creek Bridge and Flag Run

Bridge. Five damaged columns on the Pond Creek Overpass were repaired using FRP wraps. The

total cost for the project was $214,940 and the total cost for FRP wrapping was $53,500, with

$10,600 for repair of concrete columns with Fiber Composition Wrap and $42,900 for Fiber.

After the initial repair, the bridge was again damaged by a fire. The total cost of repair was

$42,697.05 and the cost of repair of concrete piers with FRP wrap was $20,000. In 2010, the

periodic inspections of the FRP wraps concluded they are in “good condition” and “have no

visible defects”.

24

The total cost for repairing the East Street Viaduct was $512,000 in which the FRP

installation cost was $160,000. Another estimate for the repair of concrete columns with Fiber

Composites Wrap was $183,408 with additional cost of $5,850 for tack and seal of FRP wrap. In

2002, an inspection concluded that the bridge was in fair condition.

The Muddy Creek Bridge and the Flag Run Bridge cost items could not be obtained. The

inspection of both the bridges rates the overall bridge structures as good.

25

CHAPTER 3 METHODOLOGY

3.1 Methodology

The purpose of this study is to determine the variables that have a significant effect on the

total cost of the FRP wrapping. The data are also analyzed for cost effectiveness and productivity

of the FRP wrapping in the bridge repairs. The steps performed to do the study are:

1. Obtain cost data for FRP wrapped bridges.

2. Literature review to understand the cost estimation processes and cost estimation

models of FRP wrapping projects and the different publications related to this study.

3. Cost data of previous FRP wrapping projects is used to identify the significant

variables.

4. Cost estimation is performed by categorizing the variables based on three main

items:

Concrete Substrate Preparation (surface prep only- grinding,

coatings, etc.)

FRP repair

Miscellaneous (Traffic Control, Mobilization etc.)

5. All costs are adjusted to the inflation rates that were calculated by using the

Producer Price Index (PPI) for the maintenance and repair construction industry. The PPI

values of every year for which the inflation is calculated were obtained from the Bureau

of Labor Statistics (BLS) as shown in Table 3-1[25]. The inflation rate of a particular

year can be calculated by using the formula,

I = ((B - A)/A)*100

Where

I = Inflation rate

B = PPI value in 2011

A = PPI value of the year in which contract was done

26

Table 3-1: Producer Price Index (PPI) Values from the Year 1999 to 2012 [25].

Year PPI

1999 133.3

2000 137.1

2001 137.6

2002 137.0

2003 139.6

2004 151.3

2005 164.4

2006 177.6

2007 184.3

2008 202.1

2009 193.0

2010 207.0

2011 225.0

2012 225.9

6. Regression equations are generated to predict the total project costs and the cost per unit

area of the bridge repairs.

7. Relationships between the variables are identified using the regression analysis and plots

between the variables.

8. The least squares percentage regression is performed and compared to the results with

simple linear regression. The least squares regression based on the percentage error,

which is relative to the observed value is developed. Since the data does not have a

constant variance, this approach is used to provide consistent coefficient estimates. The

formulae used are given as

Slope, b =

(∑

∑

∑

∑

)

∑

∑

(∑

) (3.4)

Intercept, a = (∑

∑

)

∑

(3.5)

27

The coefficient of relative determination is given by

(3.6)

Where Total Relative Variation = Explained Relative Variation + Unexplained Relative

Variation.

∑( )

∑( )

∑

( )

(3.7)

3.2 Repair Procedure

All bridge structures carry the following steps in performing the repairs using FRP wraps.

They are:

Concrete Repairs

FRP Repairs

Non-Destructive Testing

3.2.1 Concrete Repairs:

This step involves preparing the concrete surface before the application of FRP wraps.

The concrete surface is repaired by removing loose concrete, dust and debris from the bridge

column, beam or slab structure. Epoxy cement is applied between the cracks and the reformation

of cross section is performed. The surface is cleaned by sand blasting and localized repair areas

were hand patched using mortar mix. Similarly de-chlorination and re-alkalization is performed.

The report mainly focuses on the cost items of the above mentioned tasks along with traffic

control and permits. Focus is also given to the labor hours and the time standards for the concrete

repairs. Similarly for the highway bridges wearing surfaces, bases are the tasks considered for

the substrate preparation.

3.2.2 FRP Repairs:

After preparing the concrete surface, epoxy primer is applied to all FRP wrap contact

surfaces. The FRP wraps are then applied to the repair areas of any bridge element using hand

layup method to prevent any air bubbles forming on the surface. Painting is done after a required

time to allow the coating and the epoxy to cure together. The focus is given on the labor,

material, and equipment cost along with the FRP application and painting of the FRP repair task.

28

The highway bridges consider the FRP strengthening cost that includes all the cost involved to

do the repair of the bridge sections.

3.2.3 Non-Destructive Testing:

Non-Destructive Testing is performed on the bridge element where the repair work is

completed to evaluate the bonding between the FRP wrap and the surface of the element. The

different types of NDT techniques include infrared thermography, optical microscopy NDT,

microwave sensor techniques, and ultra-sonic testing. There is no data given for the NDT for the

railway brides and the highway bridges.

In the railway project, man hours for concrete repairs, FRP repairs, material, and

equipment and their respective cost items is considered for the estimation. The other costs

involved are transportation and overhead. Regression models are run between the cost items and

the total project costs of the FRP wrapping projects. The highway bridges also use temporary

features, traffic control and right of way cost items along with concrete and FRP repair costs.

3.3 Cost Analysis

According to Sean Wisotzkey, Project Engineer - Buildings Division of Fyfe Company

[26], the cost of the fiber wrap varies greatly depending on the number of wraps and the size of

the job. There are many factors that will affect the price of a project, the major ones being:

Required material (carbon vs. glass)

Performance requirement (how many layers are required)

Application type (wrapping columns vs. applying FRP overhead)

Site conditions (obstructions, night work, confined space, etc)

Wage rates (some projects require union wages which drives the cost of the labor up)

Size of project (larger projects will result in a lower FRP cost per square foot)

From the publications reviewed in Chapter 2, it is observed that the number of layers make a

significant difference in the total FRP cost of the project. The railway bridge projects and the

highway bridge projects had only one layer of FRP for the repairs.

The railway bridges data (Table 3-2 to 3-8) is divided into three categories – concrete

repairs, FRP application and Non-Destructive Testing (NDT). These categories are subdivided

29

into many tasks and provide an opportunity to predict the total FRP cost from many variables.

The type of application used here can have an effect on the total cost. Beams are more labor

intensive than columns, so each application has a different cost per square foot. Based on the

type of application, the variables that are considered here are concrete and FRP total area, beam,

column, and slab area.

Table 3-2: FRP Area and Cost Data for Four Railway Bridges for the Respective Wrapping

Procedures.

Table 3-3: Total FRP and Concrete Wrapping Cost Data with Sub-Costs.

Table 3-4: Transportation, Overhead & Profit Cost Data with Total Contract Cost.

Cost/labor hrs Transportation O/H &Profit Profit% Total Contract

Decatur $ 75 $ 12,000 $ 42,750 12.21% $ 350,000

56th street $ 90 $ 3,000 $ 35,200 13.54% $ 260,000

California $ 90 $ 4,000 $ 95,770 11.82% $ 810,000

Champaign $ 65 $ - $ 86,545 11.39% $ 760,000

Concrete

Repairs Columns Beams Slabs Walls Total Area Labor Material Equipment

Total Concrete

cost

Decatur 715 200 230 1145 40,500$ 26,000$ 128,500$ 195,000$

56th street 390 220 100 200 910 72,000$ 44,000$ 23,000$ 139,000$

California 1650 800 2350 460 5260 101,250$ 93,000$ 274,000$ 468,250$

Champaign 1100 670 3900 5670 129,935$ 81,000$ 223,000$ 433,935$

FRP Areas Columns Beams Slabs Walls Total Area Labor Material Equipment Total FRP cost

Decatur 1860 1850 3500 7210 53,250$ 33,000$ 14,000$ 100,250$

56th street 1200 850 1750 3800 55,800$ 22,000$ 5,000$ 82,800$

California 2450 1610 3760 7820 108,900$ 92,000$ 40,000$ 240,900$

Champaign 800 2400 8800 12000 130,000$ 75,000$ 34,000$ 239,000$

CostsArea

Total Cost Labor Material Equipment Total Cost

Decatur 93,750$ 59,000$ 142,500$ 295,250$

56th street 127,800$ 66,000$ 28,000$ 221,800$

California 211,230$ 185,000$ 314,000$ 710,230$

Champaign 260,455$ 156,000$ 257,000$ 673,455$

30

Table 3-5: Material Costs of Various Concrete and FRP Tasks

Table 3-6: Equipment Costs of Various Concrete and FRP Tasks

Concrete

Tasks

Removal of

Loose

Concrete

Dust and

Debris

Removal

Enclosures

& Heating

for Winter

Application

of Epoxy

Cement

Reformation

of Cross

Section

Inject

Joints

Traffic

Control Permits

Decatur 8,000$ 2,000$ 5,000$ 2,000$ -$ 3,000$ 4,000$ 2,000$

56th street -$ 8,000$ -$ -$ 12,000$ 5,000$ 9,000$ 10,000$

California 20,000$ 9,000$ -$ 4,000$ 12,000$ 13,000$ 15,000$ 20,000$

Champaign 20,000$ 10,000$ -$ 4,000$ 12,000$ 13,000$ 10,000$ 12,000$

FRP Tasks FRP App Resin App Painting

Decatur 29,000$ -$ 4,000$

56th street 16,000$ -$ 6,000$

California 57,000$ 10,000$ 25,000$

Champaign 55,000$ 10,000$ 10,000$

Material Costs of All Tasks

Concrete

Repair

Tasks

Removal of

Loose

Concrete

Sand

Blasting

Dust and

Debris

Removal

Enclosures

& Heating

for Winter

Reformation

of Cross

Section

Inject

Joints Engineering Permits

Decatur 4,000$ 13,500$ 3,000$ 30,000$ 61,000$ 3,000$ 2,000$ 12,000$

56th street 4,000$ 5,000$ 3,000$ -$ 5,000$ 3,000$ 3,000$ -$

California 22,000$ 26,000$ 5,000$ -$ 210,000$ 3,000$ 8,000$ -$

Champaign 20,000$ 25,000$ 5,000$ -$ 165,000$ 3,000$ 5,000$ -$

FRP Repair

Tasks Resin App FRP App Painting Other

Decatur -$ 11,000$ 3,000$ -$

56th street -$ 5,000$ -$ -$

California -$ 32,000$ 3,000$ 5,000$

Champaign -$ 28,000$ 3,000$ 3,000$

Equipment Costs of All Tasks

31

Table 3-7: Man-Hours Involved of Various Concrete and FRP Tasks

Table 3-8: Man-Hours Costs of Various Concrete and FRP Tasks

Concrete Repair

Tasks

Removal of

Loose Concrete

Dust and Debris

Removal

Reformation of

Cross Section Inject Joints

Enclosures &

Heating for

Winter Total Hrs

Decatur 210 110 0 220 120 660

56th street 300 80 200 220 0 800

California 800 150 0 175 0 1125

Champaign 984 189 618 208 0 1999

FRP Repair Tasks FRP App Other (Proj Mgmt) Total Hrs

Decatur 350 360 710

56th street 420 200 620

California 810 400 1210

Champaign 1200 800 2000

Man-hours of All Tasks

Concrete Repair

Tasks

Removal of

Loose

Concrete

Dust and Debris

Removal

Reformation

of Cross

Section Inject Joints Total Hrs

Enclosures

& Heating

for Winter

Decatur 15,750$ 8,250$ -$ 16,500$ 49,500$ 9,000$

56th street 27,000$ 7,200$ 18,000$ 19,800$ 72,000$ 0

California 72,000$ 13,500$ -$ 15,750$ 101,250$ 0

Champaign 63,960$ 12,285$ 40,170$ 13,520$ 129,935$ 0

FRP Repair Tasks FRP App Other (Proj Mgmt)Total Hrs

Decatur 26,250$ 27,000$ 53,250$

56th street 37,800$ 18,000$ 55,800$

California 72,900$ 36,000$ 108,900$

Champaign 78,000$ 52,000$ 130,000$

Man-Hours Cost of All Tasks

32

The three main costs involved are labor, material, and equipment cost as presented in

Figure 3-1. From the initial observation it can be seen that the equipment costs were largest with

39% of the total project costs followed by labor with 36.5% and material with 24.5%. The labor

costs for the four bridges varied from $65 to $90 per hour which can make a difference in the

repair costs.

Figure 3-1: Distribution of Costs for the Repair of Four Bridges in Chicago

Figure 3-2: Comparison and Distribution of Costs and Area for Concrete and FRP

Repairs

Figure 3-2 shows that the concrete repair cost is a major portion in the total repair costs

and the unit cost for FRP repair is lower than the unit cost of the concrete repairs for all the four

36.5%

24.5%

39.0%

Total Labor Cost Total Material Cost Total Equipment Cost

Repair Costs

56% 53% 58% 57%

29% 32% 30% 31%

Decatur 56th street California Champaign

% Concrete Cost % FRP Cost

14% 19%

40% 32%

86% 81%

60% 68%

Decatur 56th street California Champaign

% Concrete Area % FRP Area

33

Chicago bridges. The ratio of the concrete cost to the FRP cost remains similar to all four

bridges, because of different labor costs/ man hours which vary from $65 to $90/hr. for different

concrete and FRP repair areas.

Figure 3-3: Seasonal Difference of Costs and Total Work Hours for the Repair of Bridges in

Chicago

Figure 3-3 shows the cost of doing work during winter is high than in the summer or fall

seasons. The cost of repair work in winter increases total repair cost by 3.7%, and increases

project management cost by 46% from the summer/fall cost. The time required increases by 43%

during winter compared to summer or fall. There was no work done during the spring season for

these four bridges in the Chicago region.

The costs for the railway bridges are divided as concrete repairs, FRP repairs and NDT

costs. Each repair section is categorized into three costs – labor cost, materials cost, and

equipment cost. These costs are further subdivided into many tasks (traffic control, inject joints,

etc.). These tasks provide a scope to perform a detailed analysis with variables that affect the

total cost. There is a limitation with the usage of all variables, as there is minimal or no data for

some tasks. The variables considered for both concrete and FRP repairs are labor cost, material

cost, and equipment cost. Some of the other variables considered here are tasks provided for each

costs; like dust and debris removal, inject joints, traffic control, permits, and FRP application.

Transportation, overhead and profit costs are also considered as variables in predicting the total

Total Cost, $

(1000 Units)

Other (Project

Mgmt), $ (100

Units)

Total Repair, Hrs

(10 Hr)

Summer / Fall 1070 540 375.5

Winter 1110 790 536.9

0

200

400

600

800

1000

1200

34

FRP cost. Table 3-9 provides the concrete repair and FRP repair areas and their price for the four

railway bridges in Chicago. The total unit cost is obtained by dividing the total contract with the

total repair area (Concrete area + FRP area).

TABLE 3-9: Project Costs for the Four Railway Bridges in Chicago

Bridge Spans

(ft) Height

Concrete

Repair

Areas, ft2

Concrete

Repair

Cost, $

Concrete

Unit Cost

$/ft2

FRP

Repair

Areas,

ft2

FRP

Repair

Cost, $

FRP

Unit

Cost

$/ft2

Total

Unit

Cost

$/ft2

Decatur 20/42/20 13'6" 1145 195,000 170.31 7210 100,250 13.90 41.89

56th street 10/23/23

/10 13'6" 910 139,000 152.75 3800 82,800 21.79 55.20

California 10/23/23

/10 13'2" 5260 468,250 89.02 7820 240,900 30.81 61.93

Champaign 13/26/26

/11 15'0" 5670 433,935 76.53 12000 239,000 19.92 43.01

35

3.4 Classification of Variables

From the railway bridges data (Tables 3-2 to 3-8), the cost estimation is performed by

categorizing the variables based on the following three main items as shown in Table 3-10.

Concrete Substrate Preparation (surface prep only- grinding, coatings, etc.)

FRP Repair

Miscellaneous (Traffic Control, Mobilization etc.)

Other Variables considered in the cost predictions as shown in Table 3-11.

Table 3-10: Categorized List of Variables for Three Main Cost Items for Railway Bridges in

Chicago

Concrete Substrate Preparation

Cost

FRP Repair Cost Miscellaneous Costs

Concrete labor cost

Concrete material cost

Concrete equipment cost

Total concrete cost

Dust and Debris removal

task cost (MC + EC +LC)

Inject joints task cost

(MC + EC +LC)

Reformation of cross

section (MC + EC +LC)

Sand blasting (EC)

Removal of loose concrete

(MC + EC +LC)

FRP labor cost

FRP material cost

FRP equipment

cost

Total FRP cost

FRP application

(MC + EC +LC)

Painting (MC +

EC)

Other FRP tasks

(man-hrs)

Traffic control

Permits (MC + EC)

Engineering

Overhead & Profit

Transportation

MC – Material Cost; EC – Equipment Cost; LC – Labor Cost

36

Table 3-11: Other Variables Involved in Predicting the Total Contract of the FRP Repairs.

Repair Areas Total Cost

Concrete Area

Concrete column area

Concrete beam area

Concrete slab area

FRP Area

FRP column area

FRP beam area

FRP slab area

Total labor cost

Total material cost

Total equipment cost

There were many variables considered in predicting the total FRP repair costs of the

railway bridges. This analysis used simple linear regression to predict costs and identify the

relationship between the two variables. A simple linear equation model shows the relationship

between the two variables: the independent and the dependent variables. The relationship

between the response Y and the independent variable x is given in the form

E (Y) = α + βx, (3.8)

where, α is the intercept, a constant that represents fixed set up costs like cost of equipment,

mobilization, traffic control etc., and β is the slope . The total contract value is the response

variable Y and x is the independent variable that is used to predict the total contract cost of the

project.

Microsoft Excel or Minitab can analyze and plot the graphs. An analysis is performed

and the results are shown in Chapter 4.

The highway bridges data can also be categorized based on the three main cost items as

listed in Table 3-12.

37

Table 3-12: Categorized List of Variables for Three Main Cost Items for Bridges in Oregon

Concrete Substrate

Preparation

FRP Repair Miscellaneous

Roadwork

Wearing surfaces

Bases

FRP Strengthening

Cost

FRP Area

Temporary features

Traffic control

Right of way, development

and control

Here more than one independent variable explains the variations in the response variable

Y, i.e. total contract; and a multiple regression model can be used which is of the form

Yij = β0 + β1x1 + β2x2 + ·· ·+βixi + βnxn + εij (3.09)

Where β0 is a constant

β1, β2…βn are regression coefficients and

x1, x2…xn are predictor variables.

List of predictor variables:

X1 – Roadwork

X2 – Wearing surfaces

X3 – Bases

X4 – FRP strengthening cost

X5 – FRP area

X6 – Temporary features

X7 – Traffic control

X8 – Right of way development and control

Therefore the regression equation is of the form

Yij = β0 + β1x1 + β2x2 + β3x3 + β4x4 + β5x5 + β6x6 + β7x7 + β8x8 + εij (3.10)

A regression analysis was performed on these variables using Minitab to predict the cost and to

determine the significance of the variables.

38

CHAPTER 4 RESULTS AND DISCUSSION

The results of this study show the analysis of four Chicago bridges that are repaired using

FRP wraps. The major limitation for the Chicago railway bridges is having only four data points

and large number of variables. So the variables are individually analyzed in predicting the total

project costs.

4.1 Cost Analysis of Railway Bridges

From the initial analysis of data for the four bridges in the Chicago area, the total

concrete repair area has a high correlation with the total project costs as the concrete repair costs

are typically greater than the FRP costs. The concrete repair area ranged between 910 ft2 and

5670 ft2. The analysis shows that 97% of the variation in total contract is explained by variation

in total area of concrete repairs (Figure 4-1). Further, the p-value (= 0.01) obtained in Figure 4-2

is much lower than 0.05 which suggests that the variables are significant. The table also shows

the values of the actual and predicted values of the total repair cost. A deviation of +/- 10% of

the total cost is also found to predict the variation in the total cost. The intercept value of

$195,783 represents fixed set up costs like cost of equipment, mobilization, traffic control etc.

Let TR = Traditional Regression and PR = Percentage Regression. The regression equations

obtained by traditional regression and percentage regression are

Total Contract (TR-$) = 107.58 x Concrete Repair Area (ft2) + 195,783 (4.1)

Total Contract (PR-$) = 110.41 x Concrete Repair Area (ft2) + 181,844.96 (4.2)

Figure 4-1: Scatter Plot of Total Repair Cost Against Total Repair Area of the Concrete Repairs

y = 107.58x + 195783

R² = 0.9723

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

0 1000 2000 3000 4000 5000 6000

Pro

ject

To

tal

Co

ntr

act

, $

Total Concrete Area, ft2

Total Cost

Total cost +10%

Total Cost - 10%

Linear (Total Cost)

Linear (Total cost +10%)

Linear (Total Cost - 10%)

39

S = 57136.8 R-Sq = 97.2% R-Sq(adj) = 95.8%

Analysis of Variance

Source DF SS MS F P

Regression 1 2.29171E+11 2.29171E+11 70.20 0.014

Error 2 6.52923E+09 3.26461E+09

Total 3 2.35700E+11

Figure 4-2: ANOVA of Total Repair Cost Against Total Repair Area of the Concrete Repairs

The regression equation obtained by percentage regression produced a coefficient of

relative determination of 0.9829 as against a coefficient of determination (R2) of 0.9723 by the

traditional approach. The percentage residuals varied between 12% and -9% and didn’t vary

much from the traditional regression.

Table 4-1: Predicted Values and Residuals for Total Area of the Concrete Repairs

Total

Concrete

Area

(Sq.ft)

Actual

Total Cost

Predicted

Total Cost

Total

Cost +

10%

Total

Cost -

10% Residuals

%

Residual

P-

value

1145 $ 350,000 $ 318,957 $350,853 $287,061 31043 9%

0.01 910 $ 260,000 $ 293,677 $323,044 $264,309 -33677 -13%

5260 $ 810,000 $ 761,630 $837,793 $685,467 48370 6%

5670 $ 760,000 $ 805,736 $886,310 $725,163 -45736 -6%

Table 4-2: Least Squares Percentage Regression of Total Concrete Area and Total Project Cost

Total

Concrete

Area

(Sq.ft)

Actual

Total

Cost

Predicted

Total

Cost ERV URV TRV

Coefficient of

Relative

Determination

1145 $350,000 $308,262 0.4575 0.0142 0.4717

0.9829 910 $260,000 $282,316 1.0208 0.0074 1.0281

5260 $810,000 $762,591 0.0722 0.0034 0.0756

5670 $760,000 $807,858 0.1196 0.0040 0.1236

ERV – Explained Relative Variation; URV - Unexplained Relative Variation; TRV – Total

Relative Variation

40

The concrete area variable is significant when run along with FRP area to predict the total

contract cost. The correlation coefficient (r) is 0.82, which says that concrete repair area and FRP

repair area have a moderate to good correlation. Figure 4-3 shows the stepwise regression on

concrete and FRP area. The concrete area was highly significant with a p-value of 0.01.

Alpha-to-Enter: 0.05 Alpha-to-Remove: 0.05

Response is Total Contract on 2 predictors, with N = 4

Step 1

Constant 195783

Total ConcreteArea 108

T-Value 8.38

P-Value 0.014

S 57137

R-Sq 97.23

R-Sq(adj) 95.84

Mallows Cp 1.1

Figure 4-3: Stepwise Regression on Concrete and FRP Repair Area

Similarly the concrete beam area repair is the only type of application that shows some

significant relationship with the total cost of the bridge repair with a p-value of 0.01. It is known

that the beam area of the bridge repair is more difficult to repair than the other repair areas.

There was a large percentage error of more than 10% deviation for two of the bridge data. A

relationship was established with the equation

Total Contract (TR-$) = 894.73 x Concrete Beam Area (ft2) + 122,239 (4.3)

The FRP repair areas ranged from 3800 ft2 to 12000ft

2. A relationship between the total

contract and the total FRP areas is shown in Figure 4-4 with an R2

of 0.5848. The equation

obtained was

Total Contract (TR-$) = 63.71 x FRP Area (ft2) + 53,927 (4.4)

41

Figure 4-4: Scatter Plot of Total Repair Cost Against Total Area of the FRP Repairs

S = 221207 R-Sq = 58.5% R-Sq(adj) = 37.7%


Source DF SS MS F P

Regression 1 1.37835E+11 1.37835E+11 2.82 0.235

Error 2 9.78651E+10 4.89326E+10

Total 3 2.35700E+11

Figure 4-5: ANOVA of Total Repair Cost Against Total Repair Area of the FRP Repairs

Concrete substrate preparation and the FRP repair are the two main components in this

analysis. With the costs involving concrete repairs, the total project costs are approximately two

times the total concrete costs which is given by the relation with a percentage residual of -1% to

1%, (Figure 4-7)

Total Contract (TR-$) = 1.6864 x Total Concrete Repair Cost ($) + 23,831 (4.5)

The concrete repairs included tasks like dust and debris removal, removal of loose concrete,

reformation of cross-sections, sand blasting and injection of joints.

S = 4562.37 R-Sq = 99.9% R-Sq(adj) = 99.9%


Source DF SS MS F P

Regression 1 2.35658E+11 2.35658E+11 11321.46 0.000

Error 2 4.16304E+07 2.08152E+07

Total 3 2.35700E+11

Figure 4-6: ANOVA of Total Project Cost against the Total Concrete Repairs Cost

y = 63.714x + 53927

R² = 0.5848

0

100000

200000

300000

400000

500000

600000

700000

800000

900000

1000000

0 5000 10000 15000

To

tal

Co

ntr

act

, $

FRP Area, ft2

Total Contract, $

Total Cost + 10%

Total Cost -10%

Linear (Total Contract, $)

Linear (Total Cost + 10%

)Linear (Total Cost -10%)

42

Figure 4-7: Scatter Plot of Total Project Cost against the Total Concrete Repairs Cost

The FRP repair areas are larger than the concrete areas for all the four bridges. Similar to

the concrete costs, the total project costs are approximately 3 times the estimate of the FRP

repair costs (Figure 4-8) which is given by

Total Contract (TR-$) = 3.249 x Total FRP Cost ($) + 6,512.8 (4.6)

Figure 4-8: Scatter Plot of Total Project Cost against the Total FRP Repairs Cost

S = 27568.0 R-Sq = 99.4% R-Sq(adj) = 99.0%


Source DF SS MS F P

Regression 1 2.34180E+11 2.34180E+11 308.13 0.003

Error 2 1.51999E+09 7.59997E+08

Total 3 2.35700E+11

Figure 4-9: ANOVA of Total Project Cost against the Total FRP Repairs Cost

y = 1.6864x + 23831

R² = 0.9998

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

$- $200,000 $400,000

To

tal

Co

ntr

act

, $

Total Concrete Repair Cost, $

Total Cost

Total Cost + 10%

Total Cost - 10%

Linear (Total Cost)

Linear (Total Cost +

10%)Linear (Total Cost -

10%)

y = 3.249x + 6512.8

R² = 0.9936

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

$- $100,000 $200,000 $300,000

To

tal

Pro

ject

Co

st, $

Total FRP Repair Cost, $

FRP Repair Cost

FRP Repair Cost +

10%FRP Repair Cost -

10%Linear (FRP Repair

Cost)Linear (FRP Repair

Cost + 10%)Linear (FRP Repair

Cost - 10%)

43

A relationship between the FRP cost and the Concrete cost is obtained with an R² of

0.9913 and p-value of 0.004 as shown in Figure 4-10.The relationship obtained shows that the

total concrete cost is approximately two times the total FRP cost which is similar to the

relationship shown in the literature review in chapter 2.

Total Concrete Repair Cost (TR-$) = 1.9242 x Total FRP Repair Cost ($) - 9874.1 (4.7)

Figure 4-10: Scatter Plot of Total FRP Cost Against the Total Concrete Cost

S = 19021.7 R-Sq = 99.1% R-Sq(adj) = 98.7%


Source DF SS MS F P

Regression 1 8.21417E+10 8.21417E+10 227.02 0.004

Error 2 7.23647E+08 3.61824E+08

Total 3 8.28653E+10

Figure 4-11: ANOVA of Total FRP Repair Cost Against the Total Concrete Repair Cost

Another cost factor is the FRP material cost, which gives a p-value of 0.009 against the

total contract. The FRP repairs included FRP application task, painting and other (management)

tasks. The FRP application took the majority of the FRP repair task and had a high correlation of

R2

= 0.9948. The FRP material costs had better percentage errors that were less than 10 percent

deviation of the predicted total project costs. The relations obtained were

Total Contract (TR-$) = 8.3209 x FRP Material Cost ($) + 83,192 (4.8)

y = 1.9242x - 9874.1

R² = 0.9913

$0

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$0 $100,000 $200,000 $300,000

To

tal

Co

ncr

ete

Rep

air

Co

st, $

Total FRP Repair Cost, $

Total Concrete Cost

Total Concrete Cost +

10%Total Concrete Cost -

10%Linear (Total Concrete

Cost)Linear (Total Concrete

Cost + 10% )

44

Total Contract (PR-$) = 8.46 x FRP Material Cost ($) + 74,017.02 (4.9)

Figure 4-12: Scatter Plot of Total Cost to Repair Against the Material Cost of the FRP Repairs

S = 46797.6 R-Sq = 98.1% R-Sq(adj) = 97.2%


Source DF SS MS F P

Regression 1 2.31320E+11 2.31320E+11 105.62 0.009

Error 2 4.38004E+09 2.19002E+09

Total 3 2.35700E+11

Figure 4-13: ANOVA of Total Cost to Repair Against the Material Cost of the FRP Repairs

The small residuals show a sign of a good fit which varies from -2% to 7%. Table 4-3

and Figure 4-12 shows the predicted cost items and a linear fit of the total repair costs. The least

squares percentage regression equation obtained a coefficient of relative determination of 0.9956

as against an R2 of 0.9814 by the traditional regression.

Table 4-3: Predicted Values and Residuals for Total Cost of the FRP Repairs Against the FRP

Material Cost

Total FRP

Material

Cost

Actual

Total

Cost

Predicted

Total

Cost

Total

Cost +

10%

Total

Cost -

10% Residuals

%

Residual

P-

value

$ 33,000 $ 350,000 $ 357,781 $393,559 $322,003 -7781 -2%

0.009 $ 22,000 $ 260,000 $ 266,251 $292,876 $239,626 -6251 -2%

$ 92,000 $ 810,000 $ 848,711 $933,583 $763,840 -38711 -5%

$ 75,000 $ 760,000 $ 707,257 $777,982 $636,531 52743 7%

y = 8.3209x + 83192

R² = 0.9814

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

$- $40,000 $80,000

Pro

ject

To

tal

Co

ntr

act

, $

Total FRP Material cost, $

Total Cost

Total Cost + 10%

Total Cost - 10%

Linear (Total Cost)

Linear (Total Cost +

10%)Linear (Total Cost -

10%)

45

Table 4-4: Least Squares Percentage Regression of FRP Material cost and Total Project Cost

Total FRP

Material

Cost, $

Actual

Total

Cost, $

Predicted

Total

Cost, $ ERV URV TRV

Coefficient of

Relative

Determination

33000 350000 $353,063 0.3007 0.0001 0.3008

0.9956 22000 260000 $260,047 1.2012 0.0000 1.2012

92000 810000 $851,963 0.1436 0.0027 0.1463

75000 760000 $708,212 0.0461 0.0046 0.0508

ERV – Explained Relative Variation; URV - Unexplained Relative Variation; TRV – Total

Relative Variation

From Figure 4-14 and 4-15, it can be stated from the analysis that 98% of the variation in

total cost of FRP repairs is explained by variation in FRP equipment cost. Further, the p-value (=

0.007) obtained is much lower than 0.05 which suggests that the variables are significant. The

regression equation that can be formed is given by

Total Contract (TR-$) = 16.882 x FRP Equipment Cost ($) + 152,482 (4.10)

Figure 4-14: Scatter Plot of Total Cost to Repair Against the Equipment Cost of the FRP

Repairs

y = 16.882x + 152482

R² = 0.9852

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

$- $10,000 $20,000 $30,000 $40,000 $50,000

Pro

ject

To

tal

Co

ntr

act

, $

Total FRP Equipment cost, $

Total Cost

Total Cost + 10%

Total Cost - 10%

Linear (Total Cost)

Linear (Total Cost + 10%)

Linear (Total Cost - 10%)

46

S = 41722.3 R-Sq = 98.5% R-Sq(adj) = 97.8%


Source DF SS MS F P

Regression 1 2.32219E+11 2.32219E+11 133.40 0.007

Error 2 3.48150E+09 1.74075E+09

Total 3 2.35700E+11

Figure 4-15: ANOVA of Total Cost to Repair Against the Equipment Cost of the FRP Repairs

Table 4.5 shows the values of the actual and predicted values of the total repair cost. A

deviation of +/- 10% of the total cost is also found to predict the variation in the total cost.

Table 4-5: Predicted Values and Residuals for Total Cost of the FRP Repairs against the FRP

Equipment Cost

Total FRP

Equipment

Cost

Actual

Total

Cost

Predicted

Total

Cost

Total

Cost +

10%

Total

Cost -

10% Residuals

%

Residual

P-

value

$ 14,000 $ 350,000 $ 388,837 $427,721 $349,953 -38837 -11%

0.007 $ 5,000 $ 260,000 $ 236,895 $260,584 $213,205 23105 9%

$ 40,000 $ 810,000 $ 827,782 $910,560 $745,003 -17782 -2%

$ 34,000 $ 760,000 $ 726,487 $799,135 $653,838 33513 4%

4.2 Predicting the Unit Cost of the Bridge Repairs

From the given data, a relationship between the total contract and the total area to predict

the unit cost ($/ft2) values, can be established. The scatter plot Figure 4-16 shows the relationship

between the total repair areas of the bridges and the total contract values for the four different

bridges.

Table 4-6: Predicted Unit Cost for the Total Repairs

Total Area (Concrete + FRP

repairs), ft2 Total Contract

Predicted Unit Cost

($/ft2)

Actual Total Unit

Cost $/ft2

8355 $ 350,000 51.23 $41.89

4710 $ 260,000 56.03 $55.20

13080 $ 810,000 48.99 $61.93

17670 $ 760,000 47.96 $43.01

47

Figure 4-16: Scatter Plot of Total Contract to Repair Against the Total Repair Area

S = 145580 R-Sq = 82.0% R-Sq(adj) = 73.0%


Source DF SS MS F P

Regression 1 1.93313E+11 1.93313E+11 9.12 0.094

Error 2 4.23871E+10 2.11936E+10

Total 3 2.35700E+11

Figure 4-17: ANOVA of Total Contract to Repair Against the Total Repair Area

From the regression equation obtained, a relationship to predict the unit cost ($/ft2) of the

bridges can be established. The relationship is given as,

Total Unit Cost (TR-$/ft2) = 45.023 + 51,832/ Total Repair Area (ft

2) (4.11)

Similarly, the unit cost for concrete repairs can also be obtained in a similar manner (Figure 4-

18).

Table 4-7: Predicted Unit Cost for the Concrete Repairs

Concrete Repair

Area, ft2

Total Concrete

Cost

Predicted Unit Cost

($/ft2)

Actual Unit Cost

($/ft2)

1145 $ 225,504 176.13 170.31

910 $ 159,422 203.56 152.75

5260 $ 525,926 93.03 89.02

5670 $ 483,349 91.35 76.53

y = 45.023x + 51832

R² = 0.8202

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

0 5000 10000 15000 20000

To

tal

Co

ntr

act

, $

Total Area (Concrete + FRP repair) ,ft2

Total Contract

Linear (Total Contract)

48

Figure 4-18: Scatter Plot of Total Concrete Cost to Repair Against the Total Concrete Repair

Area

S = 43439.7 R-Sq = 96.2% R-Sq(adj) = 94.4%


Source DF SS MS F P

Regression 1 9.67687E+10 9.67687E+10 51.28 0.019

Error 2 3.77401E+09 1.88700E+09

Total 3 1.00543E+11

Figure 4-19: ANOVA of Total Concrete Cost to Repair Against the Total Concrete Repair Area

Concrete Repair Cost (TR-$) = 69.904 x Concrete Repair Area + 121,625 (4.12)

It can be seen from Figure 4-18 that there is a significant relationship between the

concrete repair area and the total contract values. From the regression equation obtained, the unit

cost for the concrete repairs can be predicted as follows

Concrete Unit Cost (TR-$/ft2) = 69.904 + 121,625/ Concrete Area (ft

2) (4.13)

The scatter plot in Figure 4-20 shows the relationship between the FRP repair area and

the cost required to do the FRP repair work on the bridges. Table 4-8 shows the FRP repair cost

of each bridge, area repaired and their actual and predicted unit cost.

y = 69.904x + 121625

R² = 0.9625

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

0 1000 2000 3000 4000 5000 6000

To

tal

Co

ncr

ete

Co

st (

Wit

h

Ov

erh

ead

), $

Concrete Repair Area, ft2

Total Concrete Cost

Linear (Total Concrete

Cost)

49

Table 4-8: Predicted Unit Cost for the FRP Repairs

FRP Repair

Area, ft2

FRP Repair

Cost

Predicted Unit Cost

($/ft2)

Actual Unit Cost

($/ft2)

7210 $115,932 21.61 $13.90

3800 $94,965 23.03 $21.79

7820 $270,572 21.48 $30.81

12000 $266,216 20.97 $19.92

Figure 4-20: Scatter Plot of Total FRP Repair Cost Against the Total FRP Repair Area

S = 72318.0 R-Sq = 60.9% R-Sq(adj) = 41.4%


Source DF SS MS F P

Regression 1 1.63208E+10 1.63208E+10 3.12 0.219

Error 2 1.04598E+10 5.22990E+09

Total 3 2.67806E+10

Figure 4-21: ANOVA of Total FRP Repair Cost Against the Total FRP Repair Area

FRP Repair Cost (TR-$) = 21.924 x FRP Area + 17,941 (4.14)

The unit cost for the FRP repairs can be predicted from the regression equation obtained

from equation 4.14.

FRP Unit Cost (TR-$/ft2) = 21.924 + 17,941/ FRP Area (ft

2) (4.15)

y = 21.924x + 17941

R² = 0.6094

$0

$50,000

$100,000

$150,000

$200,000

$250,000

$300,000

0 5000 10000 15000

FR

P R

epa

ir C

ost

(W

ith

Ov

erh

ead

), $

FRP Repair Area, ft2

Total FRP Cost

Linear (Total FRP Cost)

50

4.3 Calculating the Time Standards or Productivity for Concrete and FRP Repairs

The information on the labor hours can be used to determine the time required to perform

Concrete and FRP repairs at a varied labor costs ranging from $65 to $90. There was only one

layer used for FRP repairs. The Tables 4-8 and 4-9 show the Concrete and FRP areas in ft2 and

the total hours spent for the repairs.

Table 4-9: Estimated Time Required in Man Hours for the Concrete Repairs

Concrete Total

Area, ft2

Concrete

Repair Hrs

ft2/man

hr

1145 540 2.12

910 800 1.14

5260 1125 4.68

5670 1999 2.84

Table 4-10: Estimated Time Required in Man Hours for the FRP Repairs

FRP Total Area,ft2

FRP Repair

Hrs

ft2/man

hr

7210 350 20.60

3800 420 9.04

7820 810 9.65

12000 1200 10.00

It can be noted from the results that the concrete repair costs are greater than the FRP

repair costs and had a significant relationship with the total repair costs. The average based on

the total hours/ total area would be 2.99 ft2/ hr for the concrete repairs and 10.97 ft

2/ hr for the

FRP repairs. If the outlier (20.60) was removed, the approximate standards for the concrete

repair would be 3 ft2/ hr and the FRP repairs of 10 ft

2/ hr. The FRP areas are much greater than

the concrete areas and the work area covered per man hour is greater than the concrete areas. It

can also be noted that the productivity or the time taken for the FRP repairs (0.10 hr/ft2) is lesser

than the time taken for the concrete repairs (0.33hr/ft2).

51

4.4 Cost Analysis of Highway Bridges

The cost estimation for the highway bridges data is based on the three main cost items, namely concrete substrate preparation,

FRP repair, and miscellaneous cost. The variables considered are FRP area, total FRP cost, permanent traffic control, right of way

development and control, temporary features, road work, drainage and sewers, aggregate base, and wearing surfaces. It can be noted

from Table 4-11, that the areas of the bridges vary greatly. The FRP strengthening costs are a small portion of the total contract costs.

For all the bridges in Oregon and California in this research, only one layer is used for FRP strengthening of the bridge repairs.

Table 4-11: Cost Data of Different Parameters of the Highway Bridges of Oregon

Bundle Date

FRP

Area,

ft2

FRP

Cost, $

Unit

Cost,

$/ft2

Temporary

Features, $

Roadwork,

$ Bases, $

Wearing

Surfaces,

$

Traffic

Control,

$

Right of

Way,

Development

& Control, $

Total

Contract,

$

203 2007 3144 158709 50.48 1998214 588251 211339 475851 140314 156875 15,245,584

208 2008 1955 189263 96.81 2814696 312501 527019 976486 453373 874214 10.193,994

210 2010 840 32609 38.82 12571595 2656258 1055612 2025445 817128 171999 51,025,387

302 2008 360 18370 51.03 2625208 1043976 449833 886152 466776 86089 13,355,576

309 2008 606 52326 86.35 1219980 147519 171225 853145 242660 3919 3,466,763

313 2008 8095 246042 30.39 584904 141840 36973 164369 127773 73469 2,826,025

405 2009 11654 393459 33.76 1440644 66451 10791 13990 34416 14176 3,997,215

409 2010 440 28261 64.23 199478 2174 2717 35870 46565 2163 608,620

426 2010 9920 305435 30.79 279223 15241 60652 40543 99043 2446 1,057,387

428 2010 2000 97826 48.91 888426 100361 22223 25239 191889 87001 2,168,291

352 2011 126 27000 214.29 104880 102225 50000 87011 31585 48700 1,066,420

654 2011 50 6000 120 520174 20140 14030 84000 79078 23913 1,953,567

52

Table 4-11 gives the cost of various parameters that was involved in the repair of the

bridges in Oregon. These costs are given for each bundle as a whole with one or more bridges to

repair in it. The variables used for the analysis is given in the Table 3-12. The result of the

stepwise regression is given in Figure 4-22.

Response is Total contract, $ on 8 predictors, with N = 12

Step 1 2

Constant 327385 494891

Temporary Features, $ 4.08 2.26

T-Value 17.98 3.40

P-Value 0.000 0.008

Roadwork, $ 8.5

T-Value 2.84

P-Value 0.019

S 2575915 1970466

R-Sq 97.00 98.42

R-Sq(adj) 96.70 98.07

Mallows Cp 14.1 5.6

Figure 4-22: Stepwise Regression Output of Cost Items of Bridges in Oregon

The results obtained after the stepwise regression shows the variables Temporary

Features and Roadwork as significant with p- values of 0.008 and 0.019 and an R2 = 0.9842.

The p-values obtained are much lower than 0.05, which shows that the variables are highly

significant. The non-significant variables were Area, FRP Cost, Bases, Traffic Control and Right

of way development. The regression equation can be obtained from the slope and the intercept

values,

Total Contract (TR-$) = 494891 + 2.26 x Temporary Features ($) + 8.5 x Roadwork ($) (4.16)

53

Table 4-12: FRP Cost Data with Bridge Area Covered by FRP and their Accepted, Average and

Low Bidders’ Unit Cost

Location Year

Area,

ft2

Accepted

FRP

Cost, $

Average

FRP

Cost, $

Low

FRP

Cost, $

Accepted

Unit

Cost,

$/ft2

Average

Unit

Cost,

$/ft2

Low Unit

Cost,

$/ft2

OR 2007 3144 158709 154900 140396 50.48 49.27 44.66

OR 2008 1955 189263 199443 172563 96.81 102.02 88.27

OR 2010 840 32609 36109 32609 38.82 42.99 38.82

OR 2007 360 20144 24213 20144 55.95 67.26 55.95

OR 2008 375 24493 27209 23380 65.31 72.56 62.35

OR 2008 231 27833 23714 15586 120.49 102.66 67.47

OR 2010 376 23913 30967 22283 63.60 82.36 59.26

OR 2010 64 4348 7211 3804 67.93 112.66 59.44

OR 2010 320 10870 12529 10870 33.97 39.15 33.97

OR 2010 3200 86957 93897 81522 27.17 29.34 25.48

OR 2010 2600 71739 77200 68478 27.59 29.69 26.34

OR 2010 1900 59783 57715 51087 31.46 30.38 26.89

OR 2010 1900 76087 63130 51087 40.05 33.23 26.89

OR 2009 101 22150 25764 5829 219.31 255.09 57.71

OR 2009 45 7578 11823 2915 168.39 262.74 64.77

OR 2009 9204 123575 128241 79275 13.43 13.93 8.61

OR 2009 2345 249482 234618 198187 106.39 100.05 84.51

OR 2009 105 20402 21252 17487 194.30 202.40 166.54

OR 2008 712 28946 36368 26719 40.65 51.08 37.53

OR 2008 6103 166997 198540 166997 27.36 32.53 27.36

OR 2008 1280 50099 56593 47872 39.14 44.21 37.40

OR 2010 500 30435 30435 30435 60.87 60.87 60.87

OR 2010 500 30435 30435 30435 60.87 60.87 60.87

OR 2010 500 6522 6522 6522 13.04 13.04 13.04

OR 2010 500 30435 30435 30435 60.87 60.87 60.87

OR 2010 5800 173913 173913 173913 29.99 29.99 29.99

OR 2011 126 27000 31481 25000 214.29 249.85 198.41

OR 2010 50 6000 6314 6000 120.00 126.28 120.00

OR 2010 5845 126087 149976 126087 21.57 25.66 21.57

CA 2008 614 38075 59252 31729 62.01 96.50 51.68

CA 2010 420 35449 68452 35449 84.40 162.98 84.40

CA 2011 3375 320625 328821 273375 95.00 97.43 81.00

CA 2012 4163 248157 219561 74318 59.61 52.74 17.85

CA 2012 3,677 238053 228635 139169 64.74 62.18 37.85

CA 2012 2620 183974 237731 183974 70.22 90.74 70.22

CA 2012 170 16763 22181 14392 98.61 130.48 84.66

54

There is also a scope to predict the unit cost of FRP repairs of all bridges. Table 4-12

shows the accepted, average and low unit cost of the bidders for which scatter plots were drawn

to predict the relationships between the area and FRP repair cost. The cost data of all bridges is

checked for both the average and low cost of all bidders to check for a better fit. After analyzing

all the accepted, average and low cost of the bridge repairs (Appendices C1-4), it is established

that the accepted FRP cost gives a better correlation than the others for Oregon, California and

all the bridges combined. The Total FRP area and the accepted Total FRP cost of all bids are

used to predict the FRP unit cost of all bridges. Scatter plots were also developed to look into the

relationships between the total FRP costs, total FRP area and the FRP unit costs.

The regression equation obtained for FRP repair area against the FRP repair cost for all

bridges in Oregon (Figure 4-23) with a R2 value of 0.9501 is given by

FRP Cost (TR-$) = 24.16 FRP Area (ft2) + 13,451 (4.17)

The intercept value of $13,451 represents fixed set up costs like cost of equipment,

mobilization, traffic control etc.

Figure 4-23: Scatter Plot of FRP Area and its Accepted Cost of Bids for the Oregon Bridges

y = 24.16x + 13451

R² = 0.9501

0

50000

100000

150000

200000

250000

300000

0 2000 4000 6000 8000

FR

P R

epa

ir C

ost

, $


Adj FRP cost

Linear (Adj FRP cost)

55

S = 10739.0 R-Sq = 95.0% R-Sq(adj) = 94.8%


Source DF SS MS F P

Regression 1 5.05402E+10 5.05402E+10 438.24 0.000

Error 23 2.65250E+09 1.15326E+08

Total 24 5.31927E+10

Figure 4-24: ANOVA of FRP Area and its Accepted Cost of Bids for the Oregon Bridges

Figure 4-25: Scatter Plot of FRP Area and its Accepted Cost of Bids for the Oregon Bridges By

Regression Through Origin Method

The constant value of 13,451 from equation 4.17 represents the set up costs which is not

very significant. In this case, regression through origin (RTO) approach can be used to develop

the relation between the FRP repair area and the FPR repair cost. The regression equation

obtained through origin for Oregon bridges with a R2 value of 0.8951 is given by

Total FRP Cost (RTO-$) = 27.613 x FRP Repair Area (ft2) (4.18)

Similarly, the regression equation obtained for FRP repair area against the FRP repair

cost for all bridges in California with a R2 value of 0.9907 is given by (Figure 4-26 & 4-27)

FRP Cost (TR-$) = 61.012 x FRP Repair Area (ft2) + 13,451 (4.19)

y = 27.613x

R² = 0.8951

0

50000

100000

150000

200000

250000

300000

0 2000 4000 6000 8000 10000

FR

P C

ost

, $


Adj FRP cost

Linear (Adj FRP cost)

56

The high slope value of 61.02 is due to the large FRP repair area and high FRP cost

associated with the repairs.


S = 11665.6 R-Sq = 99.1% R-Sq(adj) = 98.8%


Source DF SS MS F P

Regression 1 5.81546E+10 5.81546E+10 427.34 0.000

Error 4 5.44344E+08 1.36086E+08

Total 5 5.86989E+10

Figure 4-27: ANOVA of FRP Area and its Accepted Cost of Bids for the California Bridges


By Regression Through Origin Method

y = 61.012x + 8138.6

R² = 0.9907

$-

$50,000.00

$100,000.00

$150,000.00

$200,000.00

$250,000.00

$300,000.00

$350,000.00

0 1000 2000 3000 4000 5000

FR

P R

epa

ir C

ost

, $


Adj. FRP Cost

Linear (Adj. FRP Cost)

y = 63.49x

R² = 0.988

0

50000

100000

150000

200000

250000

300000

0 1000 2000 3000 4000 5000

FR

P R

epa

ir C

ost

, $


Adj. FRP Cost

Linear (Adj. FRP Cost)

57

The regression equation obtained through origin for California bridges with a R2 value of 0.988

is given by

Total FRP Cost (RTO-$) = 63.49 x FRP Repair Area (ft2) (4.20)

Similarly, the regression equation obtained for FRP repair area against the FRP repair

cost for all bridges in California, Oregon and Illinois (Figure 4-29 and 4-30) with a R2 value of

0.7323 is

FRP Cost (TR-$) = 24.79 x FRP Repair Area (ft2) + 23,616 (4.21)

The predicted values of the FRP repair cost and the residuals and percentage residuals are

given in Table 4-12.


Bid of All Bridge Repairs ( - California, - Oregon and - Illinois)

S = 42691.4 R-Sq = 73.2% R-Sq(adj) = 72.4%


Source DF SS MS F P

Regression 1 1.69515E+11 1.69515E+11 93.01 0.000

Error 34 6.19669E+10 1.82256E+09

Total 35 2.31482E+11


Accepted Bid of All Bridge Repairs (California, Oregon and Illinois)

y = 24.79x + 23616

R² = 0.7323

0

50000

100000

150000

200000

250000

300000

350000

0 2000 4000 6000 8000 10000 12000 14000

FR

P

Rep

air

Cost

, $


58

The relationship between the FRP cost and the FRP repair area is compared with the least

squares percentage regression (PR) for a better fit. The coefficient of relative determination is

better than the linear regression approach with the value of 0.9901.

Appendix B shows the complete list of values by this method. The equation obtained by

this method is given as

FRP Cost (PR-$) = 23.95 FRP Area (ft2) + 4622.97 (4.22)

A relationship between the total FRP cost and the total area to predict the unit cost ($/ft2)

values, can be established. The predicted FRP unit cost obtained from equation 4.21 is given by

Unit Cost (TR-$/ft2) = 24.79 + 23,616 / FRP Area (ft

2) (4.23)

The regression equation obtained through an origin with an R2 value of 0.6795 is

FRP Cost (RTO-$) = 28.954 FRP Area (ft2) (4.24)


Bid of All Bridge Repairs ( - California, - Oregon and - Illinois) By Regression Through

Origin Method

y = 28.954x

R² = 0.6795

0

50000

100000

150000

200000

250000

300000

350000

400000

0 2000 4000 6000 8000 10000 12000 14000

FR

P C

ost

, $


59

Table 4-13: Predicted Values and Residuals of FRP Cost of All Bridges (California, Oregon and

Illinois)

Location

FRP

Area,

ft2 FRP Cost, $

Predicted

FRP Cost, $ Residual

%

Residual

Predicted

Unit Cost,

$/ft2

OR

3144 158709 101556 57154 36.01% 32.30

840 32609 44440 -11831 -36.28% 52.90

360 20144 32540 -12397 -61.54% 90.39

375 24493 32912 -8419 -34.37% 87.77

231 27833 29342 -1510 -5.42% 127.02

376 23913 32937 -9024 -37.74% 87.60

64 4348 25203 -20855 -479.66% 393.79

320 10870 31549 -20679 -190.25% 98.59

3200 86957 102944 -15987 -18.38% 32.17

2600 71739 88070 -16330 -22.76% 33.87

1900 59783 70717 -10934 -18.29% 37.22

1900 76087 70717 5370 7.06% 37.22

101 22150 26120 -3970 -17.92% 258.61

45 7578 24732 -17154 -226.37% 549.59

105 20402 26219 -5817 -28.51% 249.70

712 28946 41266 -12320 -42.56% 57.96

6103 166997 174909 -7911 -4.74% 28.66

1280 50099 55347 -5248 -10.48% 43.24

500 30435 36011 -5576 -18.32% 72.02

500 30435 36011 -5576 -18.32% 72.02

500 6522 36011 -29489 -452.17% 72.02

500 30435 36011 -5576 -18.32% 72.02

5800 173913 167398 6517 3.75% 28.86

126 27000 26740 260 0.96% 212.22

50 6000 24856 -18856 -314.26% 497.11

5845 126087 168514 -42425 -33.65% 28.83

CA

614 38075 38837 -762 -2.00% 63.25

420 35449 34028 1421 4.01% 81.02

4163 248157 126817 121342 48.90% 30.46

3677 238053 114769 123285 51.79% 31.21

2620 183974 88566 95409 51.86% 33.80

170 16763 27830 -11067 -66.02% 163.71

IL

7210 115932 202352 -86418 -74.54% 28.07

3800 94965 117818 -22852 -24.06% 31.00

7820 270572 217474 53101 19.63% 27.81

12000 266216 321096 -54877 -20.61% 26.76

60


Bid of All Bridge Repairs ( - Illinois, - Oregon)

S = 25629.8 R-Sq = 88.2% R-Sq(adj) = 87.8%


Source DF SS MS F P

Regression 1 1.37759E+11 1.37759E+11 209.72 0.000

Error 28 1.83928E+10 6.56887E+08

Total 29 1.56152E+11


Bid of All Bridge Repairs (Illinois and Oregon)

Figure 4-32 shows the relationship between the total FRP area and the FRP cost for the

bridges in Oregon and Illinois. The regression equation obtained with a R2 of 0.8822 and p-value

of less than 0.0001 is

Total FRP Cost (TR-$) = 23.033 x FRP Area (ft2) + 16,628 (4.25)

The predicted unit cost can be obtained from the relation (4.25) is

FRP Unit Cost (TR-$/ft2) = 23.033 + 16,628 / FRP Area (ft

2) (4.26)

y = 23.033x + 16628

R² = 0.8822

0

50000

100000

150000

200000

250000

300000

350000

0 2000 4000 6000 8000 10000 12000 14000

FR

P R

epa

i C

ost

, $


61


Bid of All Bridge Repairs ( - Illinois, - Oregon) by Regression Through Origin

The regression equation obtained through origin for bridges in Oregon and Illinois with a R2

value of 0.849 is given by

Total FRP Cost (RTO-$) = 23.395 x FRP Area (ft2) (4.27)

y = 25.769x

R² = 0.849

0

50000

100000

150000

200000

250000

300000

350000

0 2000 4000 6000 8000 10000 12000 14000

FR

P R

epa

ir C

ost

, $


62

Table 4-14: Predicted Values and Residuals of FRP Cost of All Bridges (Oregon and Illinois)

Location

FRP

Area,

ft2

FRP

Cost, $

Predicted

FRP Cost,

$ Residual

%

Residual

Predicted

Unit Cost,

$/ft2

OR

3144 158709 89044 69664 43.89% 28.32

840 32609 35976 -3367 -10.33% 42.83

360 20144 24920 -4776 -23.71% 69.22

375 24493 25265 -773 -3.16% 67.37

231 27833 21949 5884 21.14% 95.02

376 23913 25288 -1376 -5.75% 67.26

64 4348 18102 -13755 -316.35% 282.85

320 10870 23999 -13129 -120.79% 75.00

3200 86957 90334 -3377 -3.88% 28.23

2600 71739 76514 -4775 -6.66% 29.43

1900 59783 60391 -608 -1.02% 31.78

1900 76087 60391 15696 20.63% 31.78

101 22150 18954 3196 14.43% 187.67

45 7578 17664 -10087 -133.11% 392.54

105 20402 19046 1355 6.64% 181.39

712 28946 33027 -4082 -14.10% 46.39

6103 166997 157198 9798 5.87% 25.76

1280 50099 46110 3988 7.96% 36.02

500 30435 28145 2290 7.52% 56.29

500 30435 28145 2290 7.52% 56.29

500 6522 28145 -21623 -331.55% 56.29

500 30435 28145 2290 7.52% 56.29

5800 173913 150219 23693 13.62% 25.90

126 27000 19530 7470 27.67% 155.00

50 6000 17780 -11780 -196.33% 355.59

5845 126087 151256 -25169 -19.96% 25.88

IL

7210 115932 182696 -66765 -57.59% 25.34

3800 94965 104153 -9189 -9.68% 27.41

7820 270572 196746 73826 27.29% 25.16

12000 266216 293024 -26809 -10.07% 24.42

63


Bid of All Bridge Repairs ( - California, - Oregon)

S = 34455.9 R-Sq = 76.8% R-Sq(adj) = 76.0%


Source DF SS MS F P

Regression 1 1.13721E+11 1.13721E+11 95.79 0.000

Error 29 3.44291E+10 1.18721E+09

Total 30 1.48150E+11


Accepted Bid of All Bridge Repairs (California and Oregon)

Figure 4-35 shows the relationship between the total FRP area and the FRP cost for the

bridges in Oregon and California. The regression equation obtained with a R2 of 0.7676 is

Total FRP Repair Cost (TR-$) = 36.096 x FRP Repair Area (ft2) + 12,776 (4.28)

Similarly, from the equation (4.28), a relationship to predict the unit cost ($/ft2) of the

bridges is given as,

Unit Cost (TR-$/ft2) = 36.096 + 12,776 / FRP Repair Area (ft

2) (4.29)

The values of the predicted FRP cost, predicted FRP unit cost and residuals are shown in

Table 4-15.

y = 36.096x + 12776

R² = 0.7676

0

50000

100000

150000

200000

250000

300000

350000

0 1000 2000 3000 4000 5000 6000 7000

FR

P R

epa

ir C

ost

, $


64

Figure 4-37: Scatter plot of Total FRP Repair Area of the Bridge Against the FRP Cost of the

Accepted Bid of All Bridge Repairs ( - California, - Oregon) by Regression Through Origin

The regression equation obtained through origin for the highway bridges in California and

Oregon with a R2 value of 0.6929 is given by

FRP Repair Cost (RTO-$) = 36.409 x FRP Repair Area (ft2) (4.30)

y = 36.409x

R² = 0.6929

-

50,000

100,000

150,000

200,000

250,000

300,000

350,000

400,000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

FR

P R

epa

ir C

ost

, $


65

Table 4-15: Predicted Values and Residuals of FRP Cost of All Bridges (California and Oregon)

Location

FRP

Area,

ft2

Actual

FRP

Cost, $

Predicted

FRP

Cost, $ Residual

%

Residual

Predicted

Unit Cost

($/ft2)

OR

3144 158709 126262 32448 20.44% 40.16

840 32609 43097 -10488 -32.16% 51.31

360 20144 25771 -5627 -27.93% 71.58

375 24493 26312 -1819 -7.43% 70.17

231 27833 21114 6718 24.14% 91.40

376 23913 26348 -2435 -10.18% 70.07

64 4348 15086 -10739 -246.99% 235.72

320 10870 24327 -13457 -123.81% 76.02

3200 86957 128283 -41326 -47.52% 40.09

2600 71739 106626 -34886 -48.63% 41.01

1900 59783 81358 -21575 -36.09% 42.82

1900 76087 81358 -5271 -6.93% 42.82

101 22150 16422 5728 25.86% 162.59

45 7578 14400 -6823 -90.04% 320.01

105 20402 16566 3835 18.80% 157.77

712 28946 38476 -9530 -32.92% 54.04

6103 166997 233070 -66071 -39.56% 38.19

1280 50099 58979 -8880 -17.72% 46.08

500 30435 30824 -389 -1.28% 61.65

500 30435 30824 -389 -1.28% 61.65

500 6522 30824 -24303 -372.64% 61.65

500 30435 30824 -389 -1.28% 61.65

5800 173913 222133 -48218 -27.73% 38.30

126 27000 17324 9675 35.84% 137.49

50 6000 14581 -8581 -143.02% 291.62

CA

614 38075 34939 3136 8.24% 56.90

420 35449 27936 7512 21.19% 66.52

4163 248157 163044 85115 34.30% 39.16

3677 238053 145501 92553 38.88% 39.57

2620 183974 107348 76627 41.65% 40.97

170 16763 18912 -2150 -12.82% 111.25

66

Figure 4-38: Scatter Plot of Total FRP Area of the Bridge Against the FRP Unit Cost of

Accepted Bids in Oregon

A relationship between the area and the FRP unit cost and the area of repair is identified.

From Appendix A, the percentage of FRP cost with respect to the total contract is established. A

scatter plot is plotted between the total FRP repair area and the FRP unit cost, with FRP repair

area greater than 500 ft2 and less than 6,500 ft

2 is only considered for the analysis. The

relationship for the FRP unit cost and the FRP repair area is given by

FRP Unit Cost ($/ft2) = - 0.0049 x FRP Repair Area (ft

2) + 52.664 (4.31)

S = 10.1052 R-Sq = 53.4% R-Sq(adj) = 49.1%


Source DF SS MS F P

Regression 1 1285.15 1285.15 12.59 0.005

Error 11 1123.26 102.11

Total 12 2408.41

Figure 4-39: ANOVA of Total FRP Area of the Bridge Against the FRP Unit Cost of

Accepted Bids in Oregon

Appendix A provides the FRP cost and the FRP unit cost of all the bidders of bridge

repair projects in California and Oregon.

y = -0.0049x + 52.664

R² = 0.5336

0.0

20.0

40.0

60.0

80.0

100.0

120.0

0 2000 4000 6000 8000

FR

P U

nit

Co

st,

$/f

t2


Unit cost, $/ft2

Linear (Unit cost,

$/ft2)

67

CHAPTER 5 CONCLUSIONS

Detailed costs were available on four railroad bridge projects in the Chicago area. These

bridges were repaired in the 2009 – 2010 time frame. Additional data on bridge repairs in

Oregon and California where FRP was a small part of the project were also available. The

problem report started with identifying and analyzing the variables that are significant.

5.1 Chicago Bridge Findings

1. On the Chicago railroad bridges, the concrete repair work was a dominant factor of

the total costs. The analysis also shows that the concrete area of the repairs have a

significant relationship with the total project costs for the data obtained from the

Chicago area. The regression equation with an R2 value of 0.9723 was

Total Contract (TR-$) = 107.58 x Total Concrete Area (ft2) + 195,783 (5.1)

2. The best prediction variable for total project cost was the total concrete area. FRP

area was not a good predictor of Total Contract Cost or the FRP Repair Cost for the

Railroad Bridges in the Chicago region. The equation obtained was

Total Contract (TR-$) = 63.71 x FRP Area (ft2) + 53,927 (5.2)

3. The total equipment cost for the four bridges was greater than either the total material

cost or the total labor cost. The initial analysis shows that the equipment costs were

largest with 39% of the total project costs. The project costs may be reduced by

owning the equipment for future projects.

4. The equipment costs for the concrete repair were approximately seven times the

equipment costs for the FRP repair.

5. With labor costs ranging from $65/hr to $90/hr, the total labor costs were greater than

the material costs for both concrete and FRP repair.

6. The regression equation obtained for the total concrete cost and the total FRP cost

reaffirms the relations obtained from the literature review which gives an

approximate estimate of ratio between the total project costs and the concrete and

FRP costs. The equations obtained were

Total Contract (TR-$) = 1.6864 x Total Concrete Cost ($) + 23,831 (R2=0.9998) (5.3)

Total Contract (TR-$) = 3.249 x Total FRP Cost ($) + 6,512.8 (R2 = 0.9936) (5.4)

68

A relationship between the FRP Cost and the Concrete Cost is obtained with an R² =

0.9913,

Total Concrete Cost (TR-$) = 1.9242 x Total FRP Cost ($) - 9874.1 (5.5)

The relationship obtained shows that the total concrete cost is approximately two

times the total FRP cost which is similar to the ratio from the literature review.

7. The FRP material cost and the FRP equipment cost were found to be significant with

a R2 value of 0.9956 and 0.9852 respectively. The equations are

Total Contract (TR-$) = 8.3209 x FRP Material Cost ($) + 83,192 (5.6)

Total Contract (TR-$) = 16.882 x FRP Equipment Cost ($) + 152,482 (5.7)

8. It can be noted from the results that the concrete repair costs are greater than the FRP

repair costs and had a significant relationship with the total repair costs. The

approximate time standards are calculated for each repair. The average based on the

total hours/ total area would be 2.99 ft2/ hr for the concrete repairs and 10.97 ft

2/ hr

for the FRP repairs. If the outlier (20.60) was removed, the approximate time

standards for the concrete repair would be 3 ft2/ hr and the FRP repairs of 10 ft

2/ hr.

9. The FRP areas are much greater than the concrete areas and the work area covered

per man hour is greater than the concrete areas. It can also be noted that the

productivity or the time taken for the FRP repairs (0.1 hr/ft2) was lesser than the time

taken for the concrete repairs (0.33hr/ft2). This indicates that the FRP repair can be

done faster than the concrete repairs.

5.2 Oregon and California Bridge Findings

1. The FRP costs were only a small portion of the total project costs in most projects.

Only 3 projects had the FRP cost greater than 10% of the total project costs.

2. The second part of the analysis is focused on the cost parameters of highway bridges

of Oregon that can affect the cost of total project costs. Step wise regression was

performed to determine the significant variables and the variables Temporary

Features and Roadwork were found to be significant. The equation obtained with R2

value of 0.9842 was

69

Total Contract (TR-$) = 494891 + 2.26 x Temporary Features ($) + 8.5 x Roadwork ($)

(5.8)

3. A relationship is obtained for FRP cost and the FRP area for the bridges in Oregon

and California separately. The equation obtained for the bridges in Oregon with a R2

value of 0.9501 was

FRP Repair Cost (TR-$) = 24.16 FRP Repair Area (ft2) + 13,451 (5.9)

Similarly the equation obtained for bridges in California with a R2 value of 0.9907

was

FRP Repair Cost (TR-$) = 61.012 x FRP Repair Area (ft2) + 13,451 (5.10)

The value of slope for the equation obtained for California is high because of the

large areas of FRP repair for some of the bridges, which increased the total FRP cost.

4. The analysis focuses on predicting the unit cost of FRP repairs thereby obtaining a

relationship between the FRP cost and the FRP area. The regression equation

obtained for all bridges in California, Oregon, and Illinois region with R2 value of

0.7323 is


5. The regression equation obtained for all bridges in Oregon and Illinois region with R2

value of 0.8822 is


Similarly, the regression equation obtained for the highway bridges in California

and Oregon is


6. The least squares percentage regression performed for all bridges in California,

Oregon, and Illinois, reduced the mean absolute percentage error (MAPE) to 40%

from 48%. It also gave a better fit with a coefficient of relative determination of

0.9901. Appendix B gives the values of all parameters.

70

5.3 Conclusions

Table 5-1: Relationships Obtained for Rail and Highway Bridges and Their Coefficient of

Determination (R2) and p-values

Location Equation R2 p-value

Rail Bridges in

Chicago

Total Contract (TR-$) = 107.58 x Concrete Area (ft2) + 195,783 0.9723 0.01

Concrete Repair Area (x) ranges from 910 ft2 to 5670 ft

2

Total Contract (TR-$) = 1.6864 x Total Concrete Cost ($) +

23,831 0.9998 < 0.001

Total Contract (TR-$) = 3.249 x Total FRP Cost ($) + 6,512.8 0.9936 0.003 Total Concrete Cost (TR-$) = 1.9242 x Total FRP Cost ($) -

9874.1 0.9913 0.004

Total Contract (TR-$) = 8.3209 x FRP Material Cost ($) +

83,192 0.9948 0.009 Total Contract (TR-$) = 16.882 x FRP Equipment Cost ($) +

152,482 0.9913 0.004

Highway

Bridges in

Oregon

Total Contract (TR-$) = 494891 + 2.26 x Temporary

Features ($) + 8.5 x Roadwork ($) 0.9842

Temporary Features 0.008

Roadwork 0.019

FRP Repair Cost (TR-$) = 24.16 FRP Repair Area (ft2) +

13,451 0.9501 < 0.001

FRP Repair Area (x) ranging from 45 ft2

to 6103 ft2

Highway

Bridges in

California

FRP Repair Cost (TR-$) = 61.012 x FRP Repair Area (ft2)

+ 13,451 0.9907 < 0.001


to 4163 ft2

All Bridges in

California,

Oregon, and

Illinois

FRP Repair Cost (TR-$) = 24.79 FRP Repair Area (ft2) +

23,616 0.7323 < 0.001


to 12,000 ft2

All Bridges in

Oregon and

Illinois

FRP Repair Cost (TR-$) = 23.033 x FRP Repair Area (ft2)

+ 16,628 0.8822 < 0.001


to 12,000 ft2

All Bridges in

Oregon and

California

FRP Repair Cost (TR-$) = 36.096 x FRP Repair Area (ft2) +

12,776 0.7676 < 0.001


to 6103 ft2

The total FRP repair cost of the highway bridges in Oregon and California was very low

of the total project costs. The other two cost factors that are highly significant were temporary

features and roadwork. The two methods used in this study to find the relationship of variables

that factor the total project costs are simple linear regression and least squares percentage

71

regression. The least squares percentage regression method with a slope value of 23.95 and a

correlation of 0.9901 had a better relationship with the total FRP cost than the traditional

regression approach with an R2 of 0.7323. The constant (intercept) value represents the set up

costs which is not very significant for the relationships obtained for the highway bridges. In this

case, regression through origin (RTO) approach can also be used to develop the relation between

the FRP repair area and the FPR repair cost. The regression equation obtained through an origin

(RTO) with an R2 value of 0.6795 for all bridges in California, Oregon and Illinois is

FRP Cost (RTO-$) = 28.954 FRP Area (ft2) (5.15)

The equations for FRP cost obtained by the traditional regression (TR) and the

percentage regression (PR) are


FRP Cost (PR-$) = 23.95 FRP Area (ft2) + 4622.97 (5.17)

For the railroad bridges, the total concrete area, total equipment costs and the FRP

material costs of the railroad bridges were dominant factors of the total costs. The relationship

obtained shows that the total concrete cost is approximately two times the total FRP cost which

is similar to the ratio from the literature review. The productivity is higher for FRP repairs than

for the concrete repairs.

5.4 Recommendations for Future Study

This problem report had some limitations in data for the Chicago railroad bridges and

variables for the Oregon and California highway bridges. Some of the recommendations are

1. More variables that affect the total project costs like type of application (beam /

column /slab wrapping) and number of layers can be considered.

2. The study can be verified for more variables with more data for the railway bridges in

Chicago.

3. With more variables and data, interactions between the variables can be considered

for better results.

4. There is a need for doing the least squares percentage regression.

5. Other estimation techniques like Bayesian linear regression and quantile regression

can be used to identify the significant variables.

72

BIBLIOGRAPHY

1. "Bridge" FHWA. 14 Apr. 2013 <http://www.fhwa.dot.gov/bridge/deficient.cfm>.

2. "National Bridge Inventory Rating Scale." MDOT. 18 Aug. 2012

<http://www.michigan.gov/mdot/0,4616,7-151-9618_47418-173571--,00.html>.

3. "Bridge Report." AASHTO. 23 Aug. 2012

<http://www.transportation.org/Pages/default.aspx>.

4. "ETI Injection Epoxy." Strongtie.com. 23 Aug. 2012

<http://www.strongtie.com/products/anchorsystems/adhesives/crackrepair/eti.html>.

5. "Column Jacketing." Diamond Saw Contracting Co. LLC,. 23 Aug. 2012

<http://www.corecut-jo.com/index.php?module=services>.

6. "Steel Plate Bonding." Marinland Concrete Repair. 23 Aug. 2012

<http://www.marinland.com.my/services08.html>.

7. "Case review - FRP for Seismic Strengthening." National Composites Network. 23 Aug.

2012 <http://www.ncn-uk.co.uk/DesktopDefault.aspx?tabindex=126>.

8. E. J. Barbero, “Introduction to Composite Materials Design”, Philadelphia: Taylor and

Francis, 1999.

9. H. V. GangaRao, N. Taly, P. V. Vijay, “Reinforced Concrete Design with FRP

Composites”, CRC Press, 2007.

10. P. K. Mallick, “Fiber-reinforced Composites: Materials, Manufacturing, and Design”,

New York: M. Dekker, 1993.

11. Halvard E. Nystrom; Steve E. Watkins; Antonio Nanni, and Susan Murray, “Financial

Viability of Fiber-Reinforced Polymer FRP Bridges”, 2003.

12. A. C. Berg, L. C. Bank, M. G. Oliva, and J. S. Russell, “Construction and cost analysis of

an FRP reinforced concrete bridge deck”, 2005.

13. N. Loudon and B. Bell, “FRP strengthening of concrete road and rail bridges in the UK”,

2010.

14. O. H.Elsa, S. Alampalli, J. Kunin, “Application of FRP laminates for strengthening of a

reinforced-concrete T-beam bridge structure”, 2000.

15. H. B. Pham, R. A. Mahaidi, “Reliability analysis of bridge beams retrofitted with Fiber

Reinforced Polymers”, 2006.

73

16. R. S. Harichandran, M. I. Baiyasi , “Repair of Corrosion-Damaged Columns using FRP

Wraps”, Department of Civil and Environmental Engineering, Michigan State university,

2000.

17. Aneesh Bethi, Adam Allan, Michael McCullagh, "Fiber Reinforced Polymer (FRP)

Rehabilitation of Concrete Structures" The American Railway Engineering and

Maintenance-of-Way Association (AREMA), 2011.

18. "I-84 Sandy River and Jordan Rd. Bridges." Hamilton Construction. 28 Aug. 2012

<http://www.hamil.com/projects_sandy.php>.

19. MJ Hughes Construction Company. 28 Aug. 2012

<http://www.mjhughes.com/portfolio/highway/or-42-beaver-creek-bridges-bundle-405/>.

20. Pratik Roychoudhury, “A Life Cycle Cost Estimation Model for FRP Bridge Decks”, MS

Thesis, Department of Industrial and Management Systems Engineering, West Virginia

University, R.C. Creese (Advisor), 2001.

21. Taher B. Patrawala, “Decision Support Tool for Costing of the Pultrusion Process”, MS

Thesis, Department of Industrial and Management Systems Engineering, West Virginia

University, R.C. Creese (Advisor), 1999.

22. Manukonda, Srikanth, “Cost Estimation of FRP wrapping for Bridge Rehabilitation using

Regression Analysis”, MS Problem Report, Department of Industrial and Management

Systems Engineering, West Virginia University, R.C. Creese (Advisor), 2011.

23. Brayack, Daniel A. “Technical and Economic Effectiveness for repair with FRP of

Concrete T-Beam Bridges; Case Study for PennDOT-District3”, MS Thesis, College of

Engineering and Mineral Resources, West Virginia University, J.F. Davalos (Advisor),

2006.

24. T. J. Wipf, F. W. Klaiber, J. D. Rhodes, B. J. Kempers, “Repair of impact damaged pre-

stressed concrete beams with CFRP”, Department of Civil, Construction and

Environmental Engineering, Iowa State University, and Iowa Department of

Transportation, 2004.

25. "Producer Price Index-Industry Data." U.S. Bureau of Labor Statistics, 02 Jan. 2013

<http://data.bls.gov/cgi-bin/dsrv?pc>.

26. Sean Wisotzkey, Project Engineer- Buildings Division of Fyfe Co. LLC, 02 Jan. 2013

<http://www.fyfeco.com/corporate-profile/key-employees.aspx>.

74

27. John Huedopohl, HJ3 Composite Technologies

28. Justin Jar, Bridge Inspection Manager – Utah Department of Transportation.

29. Structures Design Advisory, Structures Division – New York State Department of

Transportation.

30. Jeff DeFevere, Division of Engineering Services, Highway Bridge Cost Data, California

Department of Transportation.

31. Harry S. Ramnath, Fazil T. Najafi, “A Viable Alternative: Fiber-Reinforced Polymer”,

2012 ASEE Southeast Section Conference.

32. Bridge Cost Data, Oregon Department of Transportation.

33. Bridge Cost Data, West Virginia Department of Transportation.

34. Joseph G. Eisenhauer, “Regression through Origin”, Canisius College, Buffalo, USA,

2003.

APPENDICES

Appendix A: FRP Costs of All Bidders of Bridge Repairs in the Oregon and California Region Adjusted for Inflation

Location Date

Quantity,

ft2

Unit

Cost,

$/ft2

Adj.

Unit

Cost,

$/ft2

FRP

Cost, $

Adj.

FRP

Cost, $

Total Contact,

$

%FRP

Cost

>

1%

>

2%

>

3%

OL= Q1-

1.5*(range)

OL=Q3+

1.5*(range)

CA 2008 614 55.70 62.01 34200 38075 39726300.00 0.09% 0 0 0 FALSE FALSE

CA 2008 614 62.76 69.87 38532 42898 40996250.00 0.09% 0 0 0 FALSE FALSE

CA 2008 614 51.99 57.88 31920 35537 41696634.48 0.08% 0 0 0 FALSE FALSE

CA 2008 614 46.42 51.68 28500 31729 43120262.80 0.07% 0 0 0 FALSE FALSE

CA 2008 614 148.53 165.36 91200 101534 43565306.80 0.21% 0 0 0 FALSE FALSE

CA 2008 614 55.70 62.01 34200 38075 44483932.26 0.08% 0 0 0 FALSE FALSE

CA 2008 614 185.67 206.71 114000 126917 52709041.00 0.22% 0 0 0 FALSE TRUE

CA 2010 420 77.65 84.40 32613 35449 995644.05 3.28% 1 1 1 FALSE FALSE

CA 2010 420 120.00 130.43 50400 54783 1018018.00 4.95% 1 1 1 FALSE FALSE

CA 2010 420 240.00 260.87 100800 109565 1169733.80 8.62% 1 1 1 FALSE FALSE

CA 2010 420 113.00 122.83 47460 51587 1490471.00 3.18% 1 1 1 FALSE FALSE

CA 2010 420 235.00 255.43 98700 107283 1566090.90 6.30% 1 1 1 FALSE FALSE

CA 2010 420 114.00 123.91 47880 52043 1744910.00 2.74% 1 1 0 FALSE FALSE

CA 2011 3375 95.00 95.00 320625 320625 1482509.00 21.63% 1 1 1 FALSE FALSE

CA 2011 3375 90.00 90.00 303750 303750 1559800.00 19.47% 1 1 1 FALSE FALSE

CA 2011 3375 85.00 85.00 286875 286875 1647904.00 17.41% 1 1 1 FALSE FALSE

CA 2011 3375 93.00 93.00 313875 313875 1693659.00 18.53% 1 1 1 FALSE FALSE

CA 2011 3375 81.00 81.00 273375 273375 1723994.00 15.86% 1 1 1 FALSE FALSE

CA 2011 3375 138.00 138.00 465750 465750 1758758.00 26.48% 1 1 1 FALSE TRUE

CA 2011 3375 100.00 100.00 337500 337500 1970220.80 17.13% 1 1 1 FALSE FALSE

CA 2012 4163 59.85 60.12 249150 248157 148155220.24 0.17% 0 0 0 FALSE FALSE

CA 2012 4163 60.67 60.94 252584 251577 149024961.99 0.17% 0 0 0 FALSE FALSE

CA 2012 4163 58.73 58.99 244475 243501 154011826.80 0.16% 0 0 0 FALSE FALSE

CA 2012 4163 17.92 18.00 74615 74318 155724225.67 0.05% 0 0 0 TRUE FALSE

CA 2012 4163 64.23 64.52 267405 266340 158524905.20 0.17% 0 0 0 FALSE FALSE

CA 2012 4163 56.31 56.56 234404 233470 164022341.35 0.14% 0 0 0 FALSE FALSE

CA 2012 3,677 65.00 65.29 239005 238053 3352320.40 7.13% 1 1 1 FALSE FALSE

CA 2012 3,677 60.00 60.27 220620 219741 3360617.50 6.56% 1 1 1 FALSE FALSE

Appendix A: FRP Costs of All Bidders of Bridge Repairs in the Oregon and California Region Adjusted to Inflation (Cont’d)

76

Location Date

Quantity,

ft2

Unit

Cost,

$/ft2

Adj.

Unit

Cost,

$/ft2

FRP

Cost, $

Adj.

FRP

Cost, $

Total Contact,

$

%FRP

Cost

>

1%

>

2%

>

3%

OL= Q1-

1.5*(range)

OL=Q3+

1.5*(range)

CA 2012 3,677 65.00 65.29 239005 238053 3481435.25 6.87% 1 1 1 FALSE FALSE

CA 2012 3,677 38.00 38.17 139726 139169 3486486.45 4.01% 1 1 1 TRUE FALSE

CA 2012 3,677 65.00 65.29 239005 238053 3561902.00 6.71% 1 1 1 FALSE FALSE

CA 2012 3,677 72.00 72.32 264744 263689 3890532.00 6.80% 1 1 1 FALSE FALSE

CA 2012 3,677 72.00 72.32 264744 263689 3962711.00 6.68% 1 1 1 FALSE FALSE

CA 2012 2620 70.50 70.81 184710 183974 2559279.30 7.22% 1 1 1 FALSE FALSE

CA 2012 2620 75.00 75.33 196500 195717 2639958.40 7.44% 1 1 1 FALSE FALSE

CA 2012 2620 80.00 80.36 209600 208765 2757086.40 7.60% 1 1 1 FALSE FALSE

CA 2012 2620 100.00 100.45 262000 260956 3503301.00 7.48% 1 1 1 FALSE FALSE

CA 2012 2620 130.00 130.58 340600 339243 2411778.40 14.12% 1 1 1 FALSE FALSE

CA 2012 170 99.00 99.44 16830 16763 735961.10 2.29% 1 1 0 FALSE FALSE

CA 2012 170 183.00 183.82 31110 30986 807624.00 3.85% 1 1 1 FALSE FALSE

CA 2012 170 100.00 100.45 17000 16932 899123.00 1.89% 1 0 0 FALSE FALSE

CA 2012 170 100.00 100.45 17000 16932 912670.00 1.86% 1 0 0 FALSE FALSE

CA 2012 170 85.00 85.38 14450 14392 929301.50 1.55% 1 0 0 FALSE FALSE

CA 2012 170 200.00 200.89 34000 33865 964740.00 3.52% 1 1 1 FALSE FALSE

CA 2012 170 150.00 150.67 25500 25398 997151.00 2.56% 1 1 0 FALSE FALSE

OR 2007 3144 41.35 50.48 130000 158709 12487827.25 1.04% 1 0 0 FALSE FALSE

OR 2007 3144 45.23 55.22 142200 173603 13919309.40 1.02% 1 0 0 FALSE FALSE

OR 2007 3144 38.87 47.45 122200 149186 14752653.85 0.83% 0 0 0 FALSE FALSE

OR 2007 3144 36.58 44.66 115000 140396 15478837.00 0.74% 0 0 0 FALSE FALSE

OR 2007 3144 39.76 48.54 125000 152604 15836000.00 0.79% 0 0 0 FALSE FALSE

OR 2008 1955 86.96 96.81 170000 189263 9156471.97 1.86% 1 0 0 FALSE FALSE

OR 2008 1955 87.32 97.22 170720 190064 9499889.32 1.80% 1 0 0 FALSE FALSE

OR 2008 1955 79.28 88.27 155000 172563 9692980.00 1.60% 1 0 0 TRUE FALSE

OR 2008 1955 115.09 128.13 225000 250495 9866755.65 2.28% 1 1 0 FALSE TRUE

OR 2008 1955 89.51 99.66 175000 194829 9976148.50 1.75% 1 0 0 FALSE FALSE

OR 2010 840 35.71 38.82 30000 32609 46943355.67 0.06% 0 0 0 FALSE FALSE

OR 2010 840 35.71 38.82 30000 32609 48460707.69 0.06% 0 0 0 FALSE FALSE

OR 2010 840 41.67 45.29 35000 38043 49766619.83 0.07% 0 0 0 FALSE FALSE

OR 2010 840 40.60 44.13 34100 37065 59960000.00 0.06% 0 0 0 FALSE FALSE


77

Location Date

Quantity,

ft2

Unit

Cost,

$/ft2

Adj.

Unit

Cost,

$/ft2

FRP

Cost, $

Adj.

FRP

Cost, $

Total Contact,

$

%FRP

Cost

>

1%

>

2%

>

3%

OL= Q1-

1.5*(range)

OL=Q3+

1.5*(range)

OR 2010 840 44.05 47.88 37000 40217 71798946.32 0.05% 0 0 0 FALSE FALSE

OR 2007 360 45.83 55.95 16500 20144 11996275.50 0.14% 0 0 0 FALSE FALSE

OR 2007 360 50.00 61.04 18000 21975 12034041.20 0.15% 0 0 0 FALSE FALSE

OR 2007 360 69.44 84.78 25000 30521 12692000.00 0.20% 0 0 0 FALSE FALSE

OR 2008 375 58.67 65.31 22000 24493 3113923.90 0.71% 0 0 0 FALSE FALSE

OR 2008 375 59.20 65.91 22200 24715 3116401.40 0.71% 0 0 0 FALSE FALSE

OR 2008 375 93.33 103.91 35000 38966 3279403.40 1.07% 1 0 0 FALSE TRUE

OR 2008 375 56.00 62.35 21000 23380 3728328.00 0.56% 0 0 0 TRUE FALSE

OR 2008 375 58.67 65.31 22000 24493 4343000.00 0.51% 0 0 0 FALSE FALSE

OR 2008 231 108.23 120.49 25000 27833 3113923.90 0.80% 0 0 0 FALSE FALSE

OR 2008 231 71.43 79.52 16500 18370 3116401.40 0.53% 0 0 0 FALSE FALSE

OR 2008 231 129.87 144.59 30000 33399 3279403.40 0.91% 0 0 0 FALSE FALSE

OR 2008 231 60.61 67.47 14000 15586 3728328.00 0.38% 0 0 0 FALSE FALSE

OR 2008 231 90.91 101.21 21000 23380 4343000.00 0.48% 0 0 0 FALSE FALSE

OR 2010 376 58.51 63.60 22000 23913 559930.00 3.93% 1 1 1 FALSE FALSE

OR 2010 376 79.79 86.73 30000 32609 598160.00 5.02% 1 1 1 FALSE FALSE

OR 2010 376 59.41 64.58 22340 24283 629584.00 3.55% 1 1 1 FALSE FALSE

OR 2010 376 54.52 59.26 20500 22283 644932.00 3.18% 1 1 1 FALSE FALSE

OR 2010 376 93.09 101.18 35000 38043 682106.50 5.13% 1 1 1 FALSE FALSE

OR 2010 376 82.60 89.79 31059 33760 697015.23 4.46% 1 1 1 FALSE FALSE

OR 2010 376 98.40 106.96 37000 40217 697497.00 5.30% 1 1 1 FALSE FALSE

OR 2010 376 58.51 63.60 22000 23913 704544.95 3.12% 1 1 1 FALSE FALSE

OR 2010 376 93.09 101.18 35000 38043 726575.00 4.82% 1 1 1 FALSE FALSE

OR 2010 376 79.79 86.73 30000 32609 781423.00 3.84% 1 1 1 FALSE FALSE

OR 2010 64 62.50 67.93 4000 4348 559930.00 0.71% 0 0 0 FALSE FALSE

OR 2010 64 109.38 118.89 7000 7609 598160.00 1.17% 1 0 0 FALSE FALSE

OR 2010 64 59.38 64.54 3800 4130 629584.00 0.60% 0 0 0 FALSE FALSE

OR 2010 64 62.50 67.93 4000 4348 644932.00 0.62% 0 0 0 FALSE FALSE

OR 2010 64 171.88 186.82 11000 11957 682106.50 1.61% 1 0 0 FALSE FALSE

OR 2010 64 86.52 94.04 5537 6019 697015.23 0.79% 0 0 0 FALSE FALSE

OR 2010 64 203.13 220.79 13000 14130 697497.00 1.86% 1 0 0 FALSE TRUE


78

Location Date

Quantity,

ft2

Unit

Cost,

$/ft2

Adj.

Unit

Cost,

$/ft2

FRP

Cost, $

Adj.

FRP

Cost, $

Total Contact,

$

%FRP

Cost

>

1%

>

2%

>

3%

OL= Q1-

1.5*(range)

OL=Q3+

1.5*(range)

OR 2010 64 54.69 59.44 3500 3804 704544.95 0.50% 0 0 0 FALSE FALSE

OR 2010 64 117.19 127.38 7500 8152 726575.00 1.03% 1 0 0 FALSE FALSE

OR 2010 64 109.38 118.89 7000 7609 781423.00 0.90% 0 0 0 FALSE FALSE

OR 2010 320 31.25 33.97 10000 10870 972795.87 1.03% 1 0 0 FALSE FALSE

OR 2010 320 45.31 49.25 14500 15761 1085190.00 1.34% 1 0 0 FALSE FALSE

OR 2010 320 31.50 34.24 10079 10956 1276774.37 0.79% 0 0 0 FALSE FALSE

OR 2010 3200 25.00 27.17 80000 86957 972795.87 8.22% 1 1 1 FALSE FALSE

OR 2010 3200 23.44 25.48 75000 81522 1085190.00 6.91% 1 1 1 FALSE FALSE

OR 2010 3200 32.55 35.38 104155 113212 1276774.37 8.16% 1 1 1 FALSE FALSE

OR 2010 2600 25.38 27.59 66000 71739 972795.87 6.78% 1 1 1 FALSE FALSE

OR 2010 2600 24.23 26.34 63000 68478 1085190.00 5.81% 1 1 1 FALSE FALSE

OR 2010 2600 32.34 35.15 84071 91382 1276774.37 6.58% 1 1 1 FALSE FALSE

OR 2010 1900 28.95 31.46 55000 59783 972795.87 5.65% 1 1 1 FALSE FALSE

OR 2010 1900 24.74 26.89 47000 51087 1085190.00 4.33% 1 1 1 FALSE FALSE

OR 2010 1900 30.15 32.78 57294 62277 1276774.37 4.49% 1 1 1 FALSE FALSE

OR 2010 1900 36.84 40.05 70000 76087 972795.87 7.20% 1 1 1 FALSE TRUE

OR 2010 1900 24.74 26.89 47000 51087 1085190.00 4.33% 1 1 1 FALSE FALSE

OR 2010 1900 30.13 32.75 57239 62216 1276774.37 4.48% 1 1 1 FALSE FALSE

OR 2009 101 188.12 219.31 19000 22150 576547.00 3.30% 1 1 1 FALSE FALSE

OR 2009 101 441.58 514.80 44600 51995 609981.52 7.31% 1 1 1 FALSE TRUE

OR 2009 101 237.62 277.02 24000 27979 663785.00 3.62% 1 1 1 FALSE FALSE

OR 2009 101 49.50 57.71 5000 5829 753370.00 0.66% 0 0 0 TRUE FALSE

OR 2009 101 217.82 253.94 22000 25648 841493.00 2.61% 1 1 0 FALSE FALSE

OR 2009 101 178.22 207.77 18000 20984 849992.00 2.12% 1 1 0 FALSE FALSE

OR 2009 45 144.44 168.39 6500 7578 576547.00 1.13% 1 0 0 FALSE FALSE

OR 2009 45 541.11 630.83 24350 28387 609981.52 3.99% 1 1 1 FALSE FALSE

OR 2009 45 77.78 90.67 3500 4080 663785.00 0.53% 0 0 0 FALSE FALSE

OR 2009 45 444.44 518.13 20000 23316 753370.00 2.65% 1 1 0 FALSE FALSE

OR 2009 45 88.89 103.63 4000 4663 841493.00 0.48% 0 0 0 FALSE FALSE

OR 2009 45 55.56 64.77 2500 2915 849992.00 0.29% 0 0 0 FALSE FALSE

OR 2009 9204 11.52 13.43 106000 123575 3428722.50 3.09% 1 1 1 FALSE FALSE


79

Location Date

Quantity,

ft2

Unit

Cost,

$/ft2

Adj.

Unit

Cost,

$/ft2

FRP

Cost, $

Adj.

FRP

Cost, $

Total Contact,

$

%FRP

Cost

>

1%

>

2%

>

3%

OL= Q1-

1.5*(range)

OL=Q3+

1.5*(range)

OR 2009 9204 14.12 16.47 130000 151554 3446796.90 3.77% 1 1 1 FALSE FALSE

OR 2009 9204 14.67 17.10 135000 157383 3737000.00 3.61% 1 1 1 FALSE FALSE

OR 2009 9204 10.86 12.67 100000 116580 3762855.18 2.66% 1 1 0 FALSE FALSE

OR 2009 9204 10.86 12.67 100000 116580 3869554.50 2.58% 1 1 0 FALSE FALSE

OR 2009 9204 13.58 15.83 125000 145725 3912486.50 3.19% 1 1 1 FALSE FALSE

OR 2009 9204 12.61 14.70 116019 135255 4029532.50 2.88% 1 1 0 FALSE FALSE

OR 2009 9204 7.39 8.61 68000 79275 4374727.00 1.55% 1 0 0 FALSE FALSE

OR 2009 2345 91.26 106.39 214000 249482 3428722.50 6.24% 1 1 1 FALSE FALSE

OR 2009 2345 77.61 90.48 182000 212176 3446796.90 5.28% 1 1 1 FALSE FALSE

OR 2009 2345 89.55 104.40 210000 244819 3737000.00 5.62% 1 1 1 FALSE FALSE

OR 2009 2345 72.49 84.51 170000 198187 3762855.18 4.52% 1 1 1 FALSE FALSE

OR 2009 2345 72.49 84.51 170000 198187 3869554.50 4.39% 1 1 1 FALSE FALSE

OR 2009 2345 95.95 111.86 225000 262306 3912486.50 5.75% 1 1 1 FALSE FALSE

OR 2009 2345 103.20 120.31 242000 282124 4029532.50 6.01% 1 1 1 FALSE FALSE

OR 2009 2345 84.01 97.94 197000 229663 4374727.00 4.50% 1 1 1 FALSE FALSE

OR 2009 105 166.67 194.30 17500 20402 3428722.50 0.51% 0 0 0 FALSE FALSE

OR 2009 105 152.38 177.65 16000 18653 3446796.90 0.46% 0 0 0 FALSE FALSE

OR 2009 105 161.90 188.75 17000 19819 3737000.00 0.45% 0 0 0 FALSE FALSE

OR 2009 105 142.86 166.54 15000 17487 3762855.18 0.40% 0 0 0 FALSE FALSE

OR 2009 105 142.86 166.54 15000 17487 3869554.50 0.39% 0 0 0 FALSE FALSE

OR 2009 105 142.86 166.54 15000 17487 3912486.50 0.38% 0 0 0 FALSE FALSE

OR 2009 105 174.63 203.58 18336 21376 4029532.50 0.46% 0 0 0 FALSE FALSE

OR 2009 105 304.76 355.29 32000 37306 4374727.00 0.73% 0 0 0 FALSE TRUE

OR 2008 712 36.52 40.65 26000 28946 2538398.05 1.02% 1 0 0 FALSE FALSE

OR 2008 712 35.11 39.09 25000 27833 2592000.00 0.96% 0 0 0 FALSE FALSE

OR 2008 712 37.92 42.22 27000 30059 2864755.20 0.94% 0 0 0 FALSE FALSE

OR 2008 712 77.25 86.00 55000 61232 3283063.85 1.68% 1 0 0 FALSE TRUE

OR 2008 712 33.71 37.53 24000 26719 3310935.05 0.72% 0 0 0 FALSE FALSE

OR 2008 712 54.78 60.98 39000 43419 3807263.50 1.02% 1 0 0 FALSE FALSE

OR 2008 6103 24.58 27.36 150000 166997 2538398.05 5.91% 1 1 1 FALSE FALSE

OR 2008 6103 24.58 27.36 150000 166997 2592000.00 5.79% 1 1 1 FALSE FALSE


80

Location Date

Quantity,

ft2

Unit

Cost,

$/ft2

Adj.

Unit

Cost,

$/ft2

FRP

Cost, $

Adj.

FRP

Cost, $

Total Contact,

$

%FRP

Cost

>

1%

>

2%

>

3%

OL= Q1-

1.5*(range)

OL=Q3+

1.5*(range)

OR 2008 6103 26.22 29.19 160000 178130 2864755.20 5.59% 1 1 1 FALSE FALSE

OR 2008 6103 38.51 42.87 235000 261628 3283063.85 7.16% 1 1 1 FALSE FALSE

OR 2008 6103 24.58 27.36 150000 166997 3310935.05 4.53% 1 1 1 FALSE FALSE

OR 2008 6103 36.87 41.04 225000 250495 3807263.50 5.91% 1 1 1 FALSE FALSE

OR 2008 1280 35.16 39.14 45000 50099 2538398.05 1.77% 1 0 0 FALSE FALSE

OR 2008 1280 33.59 37.40 43000 47872 2592000.00 1.66% 1 0 0 FALSE FALSE

OR 2008 1280 35.16 39.14 45000 50099 2864755.20 1.57% 1 0 0 FALSE FALSE

OR 2008 1280 42.97 47.84 55000 61232 3283063.85 1.68% 1 0 0 FALSE FALSE

OR 2008 1280 39.06 43.49 50000 55666 3310935.05 1.51% 1 0 0 FALSE FALSE

OR 2008 1280 52.34 58.27 67000 74592 3807263.50 1.76% 1 0 0 FALSE TRUE

OR 2010 500 56.00 60.87 28000 30435 1994828.00 1.40% 1 0 0 FALSE FALSE

OR 2010 500 56.00 60.87 28000 30435 1994828.00 1.40% 1 0 0 FALSE FALSE

OR 2010 500 12.00 13.04 6000 6522 1994828.00 0.30% 0 0 0 TRUE FALSE

OR 2010 500 56.00 60.87 28000 30435 1994828.00 1.40% 1 0 0 FALSE FALSE

OR 2010 5800 27.59 29.99 160000 173913 455880.00 35.10% 1 1 1 FALSE FALSE

OR 2011 126 214.29 214.29 27000 27000 1066419.60 2.53% 1 1 0 FALSE FALSE

OR 2011 126 259.51 259.51 32698 32698 1104224.35 2.96% 1 1 0 FALSE FALSE

OR 2011 126 219.84 219.84 27700 27700 1142933.77 2.42% 1 1 0 FALSE FALSE

OR 2011 126 230.16 230.16 29000 29000 1154661.20 2.51% 1 1 0 FALSE FALSE

OR 2011 126 257.94 257.94 32500 32500 1231587.70 2.64% 1 1 0 FALSE FALSE

OR 2011 126 261.90 261.90 33000 33000 1251020.10 2.64% 1 1 0 FALSE FALSE

OR 2011 126 277.78 277.78 35000 35000 1273621.79 2.75% 1 1 0 FALSE FALSE

OR 2011 126 340.55 340.55 42909 42909 1296424.75 3.31% 1 1 1 FALSE TRUE

OR 2011 126 198.41 198.41 25000 25000 1359518.60 1.84% 1 0 0 FALSE FALSE

OR 2011 126 238.10 238.10 30000 30000 1390643.35 2.16% 1 1 0 FALSE FALSE

OR 2011 50 120.00 120.00 6000 6000 1953567.37 0.31% 0 0 0 FALSE FALSE

OR 2011 50 120.00 120.00 6000 6000 1989013.50 0.30% 0 0 0 FALSE FALSE

OR 2011 50 130.00 130.00 6500 6500 2012000.00 0.32% 0 0 0 FALSE FALSE

OR 2011 50 130.00 130.00 6500 6500 2221348.75 0.29% 0 0 0 FALSE FALSE

OR 2011 50 131.39 131.39 6570 6570 2362233.89 0.28% 0 0 0 FALSE FALSE

OR 2010 5,845 19.85 21.57 116000 126087 917771.74 12.64% 1 1 1 FALSE FALSE


81

Location Date

Quantity,

ft2

Unit

Cost,

$/ft2

Adj.

Unit

Cost,

$/ft2

FRP

Cost, $

Adj.

FRP

Cost, $

Total Contact,

$

%FRP

Cost

>

1%

>

2%

>

3%

OL= Q1-

1.5*(range)

OL=Q3+

1.5*(range)

OR 2010 5,845 20.70 22.50 121000 131522 998604.28 12.12% 1 1 1 FALSE FALSE

OR 2010 5,845 20.02 21.76 117000 127174 1038203.25 11.27% 1 1 1 FALSE FALSE

OR 2010 5,845 27.37 29.75 160000 173913 1352799.90 11.83% 1 1 1 FALSE FALSE

OR 2010 5,845 25.66 27.89 150000 163043 1476168.20 10.16% 1 1 1 FALSE FALSE

OR 2010 5,845 28.04 30.47 163870 178119 1647372.51 9.95% 1 1 1 FALSE FALSE

Total data points after removal with outliers 127 96 78

Total data points after removal without outliers 116 90 73

OL – Outer Limit; TRUE – Outlier; 1- satisfies the condition of %FRP > 1, 2, 3 of Total Contract, 0 - Otherwise

82

Appendix B: Least Squares Percentage Regression for FRP Area and FRP Cost of All

Bridges in Oregon, California and Illinois

Location

FRP

Area,

ft2

FRP

Cost, $

Predicted

FRP Cost,

Ŷij($) =

bx+a ERV URV TRV

Actual

Unit

Cost,

$/ft2

Predicted

Unit

Cost,

$/ft2

%

Residual

OR

3144 158709 79933 0.00 0.25 0.25 50.48 25.42 50%

840 32609 24744 3.23 0.06 3.28 38.82 29.46 24%

360 20144 13246 12.10 0.12 12.22 55.95 36.80 34%

375 24493 13606 8.10 0.20 8.30 65.31 36.28 44%

231 27833 10156 6.91 0.40 7.31 120.49 43.97 64%

376 23913 13630 8.49 0.18 8.68 63.60 36.25 43%

64 4348 6156 314.92 0.17 315.10 67.93 96.19 -42%

320 10870 12288 42.70 0.02 42.71 33.97 38.40 -13%

3200 86957 81275 0.00 0.00 0.00 27.17 25.40 7%

2600 71739 66903 0.05 0.00 0.06 27.59 25.73 7%

1900 59783 50135 0.31 0.03 0.33 31.46 26.39 16%

1900 76087 50135 0.19 0.12 0.31 40.05 26.39 34%

101 22150 7042 11.86 0.47 12.32 219.31 69.73 68%

45 7578 5701 104.90 0.06 104.96 168.39 126.69 25%

105 20402 7138 13.94 0.42 14.36 194.30 67.98 65%

712 28946 21678 4.53 0.06 4.60 40.65 30.45 25%

6103 166997 150812 0.16 0.01 0.17 27.36 24.71 10%

1280 50099 35284 0.92 0.09 1.01 39.14 27.57 30%

500 30435 16600 4.80 0.21 5.01 60.87 33.20 45%

500 30435 16600 4.80 0.21 5.01 60.87 33.20 45%

500 6522 16600 104.64 2.39 107.03 13.04 33.20 -155%

500 30435 16600 4.80 0.21 5.01 60.87 33.20 45%

5800 173913 143554 0.12 0.03 0.15 29.99 24.75 17%

126 27000 7641 7.85 0.51 8.37 214.29 60.64 72%

50 6000 5821 166.81 0.00 166.81 120.00 116.41 3%

5845 126087 144632 0.24 0.02 0.26 21.57 24.74 -15%

CA

614 38075 19331 2.82 0.24 3.07 62.01 31.48 49%

420 35449 14684 3.75 0.34 4.09 84.40 34.96 59%

4163 248157 104342 0.01 0.34 0.34 59.61 25.06 58%

3677 238053 92701 0.00 0.37 0.37 64.74 25.21 61%

2620 183974 67382 0.01 0.40 0.41 70.22 25.72 63%

170 16763 8695 19.81 0.23 20.05 98.61 51.15 48%

IL

7210 115932 177329 0.66 0.28 0.94 16.08 24.59 -53%

3800 94965 95647 0.02 0.00 0.02 24.99 25.17 -1%

7820 270572 191941 0.16 0.08 0.25 34.60 24.54 29%

12000 266216 292067 0.61 0.01 0.62 22.18 24.34 -10%

a = 4622.97, b = 23.95 & Coefficient of relative determination = 0.9901

83

Appendix C: Scatter Plots of Average and Low Cost of all Bridges in Oregon and

California

Appendix C-1: Scatter Plot of FRP Area and its Average Cost of All Bids for the Oregon

Bridges

Appendix C-2: Scatter Plot of FRP Area and its Low Cost of All Bids for the Oregon Bridges

y = 30.325x

R² = 0.9183

0

50000

100000

150000

200000

250000

300000

0 2000 4000 6000 8000 10000

FR

P C

ost

, $

FRP Area, ft2

Average FRP cost

Linear (Average FRP

cost)

y = 26.861x

R² = 0.9291

0

50000

100000

150000

200000

250000

300000

0 2000 4000 6000 8000 10000

FR

P C

ost

, $

FRP Area, ft2

Low FRP Cost

Linear (Low FRP

Cost)

84

Appendix C-3: Scatter Plot of FRP Area and its Average Cost of All Bids for the California

Bridges

Appendix C-4: Scatter Plot of FRP Area and its Low Cost of All Bids for the California Bridges

y = 63.881x

R² = 0.8091

0

50000

100000

150000

200000

250000

300000

0 1000 2000 3000 4000 5000

FR

P C

ost

, $

FRP Area, ft2

Average FRP cost

Linear (Average FRP

cost)

Linear (Average FRP

cost)

y = 34.988x

R² = 0.3761

0

20000

40000

60000

80000

100000

120000

140000

160000

180000

200000

0 1000 2000 3000 4000 5000

FR

P C

ost

, $

FRP Area, ft2

Low FRP Cost

Linear (Low FRP

Cost)

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