analysis and verification of stresses and strains and...

ANALYSIS AND VERIFICATION OF STRESSES AND STRAINS AND THEIR

RELATIONSHIP TO FAILURE IN CONCRETE PAVEMENTS UNDER HEAVY VEHICLE SIMULATOR LOADING

By

MAMPE ARACHCHIGE WASANTHA KUMARA

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2005

Copyright 2005

by

Mampe Arachchige Wasantha Kumara

To my parents and to Lakmini, and Sahanya.

iv

ACKNOWLEDGMENTS

I wish to express my deepest gratitude to my supervisory committee chair (Dr.

Mang Tia) for continuously guiding and assisting me throughout my graduate studies at

the University of Florida (UF). Appreciation is also extended to the other members of my

committee (Drs. Byron E. Ruth, Reynaldo Roque, Bjorn Birgisson, and Mark Yang)

whose opinions and guidance have been invaluable in the completion of my study.

I wish to thank the Florida Department of Transportation (FDOT) for sponsoring of

the research that made this dissertation possible. I also give thanks to FDOT Material

Office personnel (particularly Dr. Bouzid Choubane, Dr. Alexander Appea, and Messrs.

Michael Bergin, Tom Byron, Steve Ross, Aaron Philpott, Charles Ishee, Richard

DeLorenzo, Salil Gokhale, Abdenour Nazef, Jerry Moxley and Vidal Francis). I also

extend my thanks to Dr. Chung-lung Wu, and Dr. J. M. Armaghani for their suggestions

and guidance at project meetings. Thanks are also extended for contributions made by

personnel from Dynatest and Florida Rock Industries.

Special gratitude is also expressed to the staff of the Department of Civil and

Coastal Engineering (particularly George Lopp, Doretha Ray, Sonja Lee and Carol

Hipsley) for providing necessary support for my research and academic work during my

study at UF. Thanks are also extended to colleagues in the pavement and infrastructure

materials groups for helping me in different ways. I wish to express my sincere thanks to

my former professor (Dr. Manjriker Gunaratne) at the University of South Florida for his

guidance and help on my studies in the United States (US). I also wish to thank the

v

University of Moratuwa, Sri Lanka for continuous assistance for my higher studies in the

US. Finally, the greatest thanks go to my parents; to my wife, Lakmini Wadanami; and to

my daughter, Sahanya, for their patience and sacrifices throughout my studies.

vi

TABLE OF CONTENTS page

ACKNOWLEDGMENTS ................................................................................................. iv

LIST OF TABLES............................................................................................................. ix

LIST OF FIGURES .............................................................................................................x

ABSTRACT.......................................................................................................................xv

CHAPTER

1 INTRODUCTION ...................................................................................................1

1.1 Background..................................................................................................1 1.2 Problem Statement .......................................................................................2 1.3 Research Hypothesis....................................................................................3 1.4 Objectives ....................................................................................................3

2 LITERATURE REVIEW ........................................................................................4

2.1 Structural Analysis of Concrete Pavements.................................................4 2.1.1 Foundation Models ..........................................................................4

2.1.1.1 Dense-liquid foundation model............................................4 2.1.1.2 Elastic-solid foundation .......................................................5 2.1.1.3 Improved models using a modified Winkler foundation .....6 2.1.1.4 Improved models by using a modified elastic-solid

foundation ............................................................................8 2.1.2 Analytical Solutions for Concrete Pavement Response to Traffic

Loading ............................................................................................9 2.1.3 Numerical Solutions for Concrete Pavement Response to

Traffic Loading ..............................................................................13 2.1.3.1 Discrete element method (DEM).......................................14 2.1.3.2 Finite element method........................................................14 2.1.3.3 Finite difference method (FDM)........................................19

2.2 Review of Concrete Pavement Failures in Slab Replacement...................19 2.3 Accelerated Pavement Testing...................................................................22

vii

3 STRESS ANALYSIS CONVENTIONAL CONCRETE PAVEMENT SLABS..27

3.1 Method of Analysis....................................................................................27 3.2 Results of Analysis ....................................................................................29 3.3 Results of Previous Parametric Studies of Factors Affecting Stresses in

Concrete Pavement ....................................................................................38

4 DESIGN AND CONSTRUCTION OF TEST SECTIONS...................................41

4.1. Description of the Experiment ...................................................................41 4.2 Construction of Concrete Test Track.........................................................42 4.3 Removing of Concrete Slabs .....................................................................44 4.4 Dowel Bar Placement ................................................................................48 4.5 Instrumentation Layout..............................................................................49 4.6 Placement of Strain Gauges .......................................................................53 4.7 Placement of Thermocouples.....................................................................54 4.8 Placement of Concrete ...............................................................................56 4.9 Concrete Finishing and Sawing Joints.......................................................57

5 TESTING OF TEST SLABS.................................................................................61

5.1 Concrete Mix Characteristic ......................................................................61 5.2 Concrete Testing ........................................................................................61 5.3 HVS Loading .............................................................................................61

5.3.1 Slab 1C...........................................................................................66 5.3.3 Slab 2C...........................................................................................67 5.3.4 Slab 2E...........................................................................................67 5.3.5 Slab 2G...........................................................................................68

5.4 Temperature Data.......................................................................................68 5.5 Impact Echo Test .......................................................................................72 5.6 FWD Test...................................................................................................76

6 OBSERVED PERFORMANCE OF THE TEST SLABS.....................................78

6.1 Slab 1C.......................................................................................................78 6.2 Slab 1G.......................................................................................................78 6.3 Slab 2C.......................................................................................................83 6.4 Slab 2E.......................................................................................................87 6.5 Slab 2G.......................................................................................................87

7 ANALYSIS OF DATA..........................................................................................90

7.1 Estimation of Model Parameters................................................................90 7.2 Analysis of Dynamic Strain Data ..............................................................94

7.2.1 Analysis of Measured Dynamic Strains for Detection of Cracks ..94 7.2.2 Comparison of Measured Strains with Computed Strains.............95

7.3 Analysis of Static Strain Data ....................................................................97 7.4 Impact Echo Test Results.........................................................................102

viii

7.5 Analysis of Performance of Concrete Mixes ...........................................102 7.5.1 Computation of Stresses in the Test Slabs...................................102 7.5.2 Relating Stress/Strength Ratio to Observed Performance ...........110 7.5.3 Required Concrete Properties for Performance ...........................118

8 CONCLUSIONS AND RECOMMENDATIONS ..............................................122

8.1 Summary of Findings...............................................................................122 8.2 Conclusions..............................................................................................124 8.3 Recommendations....................................................................................125

APPENDIX

A HVS TESTING AND DATA COLLECTION SCHEDULE ..............................126

B FWD DATA.........................................................................................................137

LIST OF REFERENCES.................................................................................................142

BIOGRAPHICAL SKETCH ...........................................................................................147

ix

LIST OF TABLES

Table page 4-1 Properties of the concrete used on the initial concrete test track...........................43

4-2 Strain gauge locations and identification numbers ................................................52

5-1 Mix designs of concrete used in test slabs .............................................................62

5-2 Fresh concrete properties .......................................................................................63

5-3 Compressive strength, elastic modulus and flexural strength data ........................64

7-1 Stress analysis for slab 1C (Mix 1) ......................................................................111

7-2 Stress analysis for slab 1G (Mix2).......................................................................112

7-3 Stress analysis for slab 2C (Mix3) .......................................................................113

7-4 Stress analysis for slab 2E (Mix 4) ......................................................................114

7-5 Stress analysis for slab 2G (Mix 5)......................................................................115

A-1 Schedule of testing and data collection for test slab 1C ......................................126

A-2 Schedule of testing and data collection for test slab 1G ......................................129

A-3 Schedule of testing and data collection for test slab 2C ......................................132

A-4 Schedule of testing and data collection for test slab 2E.......................................134

A-5 Schedule of testing and data collection for test slab 2G ......................................136

x

LIST OF FIGURES

Figure page 3-1 Loading positions used in the stress analysis.........................................................28

3-2 Distribution of maximum principal stresses due to a 12-kip load at the slab corner for the condition of no load transfer at the joints........................................29

3-3 Distribution of stresses in the xx direction due to a 12-kip load at the slab corner for the condition of no load transfer at the joints........................................30

3-4 Distribution of stresses in the yy direction due to a 12-kip load at the slab corner for the condition of no load transfer at the joints........................................31

3-5 Distribution of maximum principal stresses due to a 12-kip load at the slab corner for the condition of good load transfer at the joints....................................32

3-6 Distribution of stresses in the xx direction due to a 12-kip load at the slab corner for the condition of good load transfer at the joints....................................33

3-7 Distribution of stresses in the yy direction due to a 12-kip load at the slab corner for the condition of good load transfer at the joints....................................34

3-8 Distribution of maximum principal stresses on the adjacent slab due to a 12-kip load at the slab corner for the condition of good load transfer at the joints.......................................................................................................................35

3-9 Distribution of stresses in the xx direction on the adjacent slab due to a 12-kip load at the slab corner for the condition of good load transfer at the joints.......................................................................................................................36

3-10 Distribution of stresses in the yy direction on the adjacent slab due to a 12-kip load at the slab corner for the condition of good load transfer at the joints.......................................................................................................................37

3-11 Distribution of maximum principal stresses due to a 12-kip load at the mid-edge for the condition of no load transfer at the joints ..........................................38

4-1 Layout of concrete slabs on test track....................................................................42

4-2 Placement of concrete on test track .......................................................................43

xi

4-3 Finished concrete test track....................................................................................44

4-4 Making 3-inch deep saw cuts at the joints .............................................................45

4-5 Separation of concrete slab (12 ft ×16 ft) into small pieces (3 ft × 4 ft)................45

4-6 Separated concrete slab using diamond bladed saw ..............................................46

4-7 Removal of separated pieces using the lifter. ........................................................46

4-8 Correcting the damage portion of asphalt base......................................................47

4-9 Removal of concrete pieces adjacent to the surrounding slabs..............................47

4-10 Drilling dowel bar holes.........................................................................................48

4-11 Dowel bars epoxied to an adjacent slab before placement of the test slab ............49

4-12 Strain gauge arrangement in a half bridge circuit ..................................................50

4-13 Connection of the active and dummy strain gauges in the half bridge circuit.......50

4-14 Instrumentation layout for test slab 1C..................................................................51

4-15 Instrumentation layout for test slabs 1G, 2C, 2E and 2G ......................................52

4-16 Strain gauges fixed to the asphalt base using nylon rods.......................................53

4-17 Strain gauges protected by a PVS pipe before placement of concrete ..................54

4-18 Thermocouples fixed to a wooden rod...................................................................55

4-19 Placement of concrete around thermocouples attached to a rod............................55

4-20 Formwork for the free edge of test slab 1C ...........................................................57

4-21 Placing concrete around strain gauges...................................................................58

4-22 Placement of concrete for a test slab......................................................................59

4-23 Placement of concrete around dummy gauges in wooden blocks .........................59

4-24 Leveling of concrete surface..................................................................................60

4-25 Making a 3-inch deep saw cut at the joint .............................................................60

5-1 Comparison of compressive strength of the concrete mixes used .........................65

5-2 Temperature differentials at slab 1C......................................................................69

xii

5-3 Temperature differentials at slab 1G......................................................................70

5-4 Temperature differentials at slab 2C......................................................................70

5-5 Temperature differentials at slab 2E......................................................................71

5-6 Temperature differentials at slab 2G......................................................................71

5-7 Schematic representation of test set-up for wave speed measurement ..................73

5-8 Waveforms from impact echo test for P-wave speed measurement ......................73

5-9 Sketch of steel template for marking impact and receiver locations .....................74

5-10 Receiver and impact locations on test slab for impact echo test............................75

6-1 Shrinkage cracks on test slab 1C ...........................................................................79

6-2 Corner crack on slab 1C.........................................................................................79

6-3 Cracked slab 1C at the end of HVS testing............................................................80

6-4 Crack map of slab 1C.............................................................................................81

6-5 Corner crack at the southern end of slab 1G..........................................................82

6-6 Transverse cracks at the mid-edge of slab 1G .......................................................82

6-7 Crack propagation at the mid-edge of slab 1G with additional loading ................83

6-8 Crack map of slab 1G ............................................................................................84

6-9 Transverse cracks at mid-edge of slab 2C .............................................................85

6-10 Cracks on slab 2C at the end of HVS testing.........................................................85

6-11 Crack map of slab 2C.............................................................................................86

6-12 Transverse crack on lab 2E at the middle of the slab ............................................87

6-13 Crack map of slab 2E.............................................................................................88

6-14 Transverse crack on slab 2G at the mid. ................................................................88

6-15 Crack map of slab 2G ............................................................................................89

7-1 Measured and computed deflection basins caused by a 9-kip FWD load at slab center for slab 1G...................................................................................................91

xiii

7-2 Measured and computed deflection basins caused by a 9-kip FWD load at slab center for slab 2C...................................................................................................92

7-3 Measured and computed deflection basin caused by a 9-kip FWD load at slab joint for slab 1G .....................................................................................................93

7-4 Measured and computed deflection basins caused by a 9-kip FWD load at a free edge for slab 1G..............................................................................................93

7-5 Measured dynamic strains from gauge 3 on slab 2C .............................................95

7-6 Measured dynamic strains from gauge 4 on slab 2E .............................................96

7-7 Maximum measured compressive strain from gauge 4 on slab 2E .......................96

7-8 Measured and computed strains for gauge 1 on slab 1C .......................................98




7-12 Measured and computed strains for gauge 6 on slab 1C .....................................100

7-13 Measured and computed strains for gauge 7 on slab 1C .....................................100

7-14 Measured strains at slab 1G in the first method of applying a static load ...........103

7-15 Measured strains at slab 2G in the second method of applying a static load.......103

7-16 Comparison of maximum measured dynamic and static strains..........................104

7-17 Grid lines for impact echo test and location of corner crack on slab 1G.............105

7-18 P-wave Speed along line 3 at corner of slab 1G ..................................................106

7-19 Measured P-wave speed along line 4 at corner of slab 1G..................................106

7-20 Measured P-wave speed along line 8 at corner of slab 1G..................................107

7-21 Measured P-wave speed along line 10 at corner of slab 1 G ...............................107

7-22 Measured P-wave speed along line 15 at corner of slab 1G................................108

7-23 Measured P-wave speed along line 16 at corner of slab 1G................................108

7-24 Stress/ flexural strength ratio versus HVS passes................................................116

xiv

7-25 easured strains from slab 2C n the first 6 hours...................................................118

7-26 Computed stress/strength ratio versus compressive strength of concrete using ACI equations for relating fc, E and flexural strength .........................................119

7-27 Relationship between compressive strength and elastic modulus .......................120

7-28 Relationship between flexural strength and compressive strength ......................120

7-29 Computed stress/strength ratio as a function of compressive strength using the developed relationship between fc, E and flexural strength...........................121

B-1 FWD test at center of slab 2C..............................................................................137

B-2 Test at center of slab 1G ......................................................................................138

B-3 FWD test at joint 1G-1F ......................................................................................139

B-4 FWD test at free edge-1G ....................................................................................140

B-5 FWD test at a confined edge................................................................................141

xv

Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

ANALYSIS AND VERIFICATION OF STRESSES AND STRAINS AND THEIR RELATIONSHIP TO FAILURE IN CONCRETE PAVEMENTS

UNDER HEAVY VEHICLE SIMULATOR LOADING

By

Mampe Arachchige Wasantha Kumara

May 2005

Chair: Mang Tia Major Department: Civil and Coastal Engineering

Research was performed to evaluate the behavior and performance of concrete

pavement slabs at an early age under heavy vehicle simulator (HVS) loading. A concrete

pavement test track was constructed at the accelerated pavement testing facility of the

Florida Department of Transportation (FDOT). The test sections were instrumented with

strain gauges and thermocouples to collect strain and temperature data. The finite element

model FEACONS IV was used to analyze pavement behavior. Model parameters were

determined by matching the deflection basins caused by the Falling Weight

Deflectometer (FWD) load and the computed deflection basin, using FEACONS IV the

finite element model. The measured maximum strains caused by a moving HVS wheel

load were found to match fairly well with the measured maximum strains caused by a

static wheel load of the same magnitude. The difference between static and dynamic

strains for the same magnitude load was small and fluctuated between positive and

negative values.

xvi

The FEACONS program was used to calculate the maximum stresses in each test

slab due to the HVS loads at various times in this study. The applicable pavement

parameters (effective modulus of subgrade reaction, joint stiffness, and edge stiffness),

concrete elastic modulus, HVS load, and temperature differential in the concrete slab for

each particular condition were used in each analysis. The computed stress-to-strength

ratio can be used to explain the observed performance of the test slabs used in the slab-

replacement study. The properties needed to ensure adequate performance of concrete

pavement at early age were determined.

Impact echo tests were used successfully in this study to detect cracks in a concrete

slab. This was manifested by a sudden drop in the apparent measured speed of P waves

across the location of cracks. Cracks in the concrete slab were also successfully detected

from observed changes in the measured strains from strain gauges that had been installed

in the concrete.

1

CHAPTER 1 INTRODUCTION

1.1 Background

Full-slab replacement is a common method for repairing badly deteriorated

concrete pavement slabs. In Florida, this type of repair work is typically performed at

night, and the repaired slabs are opened to traffic by the next morning. It is essential that

this repair work be finished in a minimal amount of time. High-early-strength concrete is

typically used in this application in order to have sufficient strength within a few hours

after placement.

The Florida Department of Transportation (FDOT) currently specifies that slab-

replacement concrete must have a minimum 6-hour compressive strength of 15.2 MPa

(2200 psi) and a minimum 24 hour compressive strength of 20.7 MPa (3000 psi) (1). The

California Department of Transportation (Caltrans) has conducted research on the use of

fast-setting hydraulic cement concrete (FSHCC) in slab replacement using the HVS.

Fatigue resistance of the FSHCC was found to be similar to the fatigue resistance of the

normal Portland cement concrete (2). Caltrans developed standard special provisions

(SSP) for slab and lane/shoulder replacement. However, there is no SSP for slab

replacement with dowel bars. The current specification for slab replacement with no

dowel requires a minimum modulus of rupture at opening to traffic of 2.3 MPa (333 psi)

and 4.3 MPa (623 psi) at 7 days (3).

A high cement content is usually used to achieve high early strength. However

using a high cement content will increase heat development and drying shrinkage in the

2

concretes and will increase the tendency for shrinkage cracking. Much of the observed

early cracking of replacement slabs in Florida may be attributed to shrinkage cracking.

Question arises as to whether it is possible to reduce the required early strength, so that

cement content can be reduced.

Because of the lack of research in this area, there are uncertainties on the optimum

concrete mixtures to be used in this application. Questions arise as to required curing

time and required early-age properties of concrete for this application. Performance of

the concrete-replacement slabs needs to be evaluated using high-early-strength concrete

under realistic pavement conditions, so that appropriate materials and construction

requirements can be specified for this application. Analysis of stresses and strains in

concrete slab during its early age and development of a relationship between failure and

various concrete properties is essential to determine the optimum concrete mix and curing

time.

1.2 Problem Statement

Questions arise as to whether the specified strength requirement (compressive

strength or flexural strength) of concrete at particular time intervals as provided by the

specification is sufficient to ensure performance. Since the stresses that develop in a

concrete slab are affected by many factors (such as temperature condition, concrete

properties such as elastic modulus and coefficient of thermal expansion, and pavement

conditions such as the subgrade modulus), the effects of these factors on the performance

of concrete replacement slabs need to be specified. If strength requirements are

specified, how do other relevant parameters affect these requirements?

3

1.3 Research Hypothesis

Stress to strength ratio is an important indicator of potential performance of

concrete-replacement slabs. Specifying only water/cement ratio, cement content, and

minimum required strength is not sufficient to ensure good performance of a concrete-

replacement slab.

1.4 Objectives

The main objective of this study was to study the factors affecting performance of

concrete-replacement slabs in Florida using accelerated pavement testing by means of the

HVS.

• Conduct a literature review on analysis methods and experimental work on slab replacement

• Perform stress analysis of concrete-replacement slabs

• Design the experiment to test selected pavement test sections and evaluate the performance of test sections using HVS loading

• Identify a suitable crack-detection method for evaluating concrete pavement

• Verify the models developed for analyzing stresses and strains on concrete pavement subjected to temperature and load effects

• Determine the relationships among the material and pavement parameters and the failure of concrete pavements

4

CHAPTER 2 LITERATURE REVIEW

2.1 Structural Analysis of Concrete Pavements

2.1.1 Foundation Models

As in numerous other engineering applications, the response of the supporting soil

medium under the pavement is an important consideration. To accurately evaluate this

response, we must know the complete stress-strain characteristics of the foundation.

Accurately describing the stress-strain characteristics of any given foundation medium is

usually hindered by the complex soil conditions, which are markedly nonlinear,

irreversible, and time-dependent. Furthermore, these soils are generally anistropic and

inhomogeneous. Idealized models were developed to simulate soil response under

predefined loading and boundary conditions. Certain assumptions about the soil medium

were used for these idealizations. The assumptions are necessary for reducing the

analytical rigor of such a complex boundary value problem. Two of the most frequently

applied assumptions are linear elasticity and homogeneity.

2.1.1.1 Dense-liquid foundation model

In the dense-liquid foundation model (also known as the Winkler foundation

model), the foundation is seen as a bed of evenly spaced, independent, linear springs.

The model assumes that each spring deforms in response to the vertical stress applied

directly to the spring, and does not transmit any shear stress to the adjacent springs. The

relation between an external load, p, applied on any point is given by Equation 2-1

5

P=kw (2-1) Where k is the modulus of subgrade reaction, w= displacement of foundation. No transmission of shear forces means that there are no deflections beyond the

edges of the plate or slab. The liquid idealization of this foundation type was derived for

its behavioral similarity to a medium using Archimedes’ Buoyancy principle. It was

applied to analyze pavement support systems in studies by Westergaard (4, 5, 6).

In the field, the k-value is determined using data obtained from a plate-loading test

performed on the foundation using a 30-inch-diameter plate (7). The load is applied to a

stack of 1-inch-thick plates, until a specified pressure (p) or deflection (∆) is reached.

The k-value is then computed as the ratio of the pressure to the corresponding deflection,

∆=

pk (2-2)

Another method for obtaining a k-value for use in analysis is by back calculation

from measured deflections of the slab surface obtained from nondestructive tests, using

devices such as falling weight deflectometers (FWD).

2.1.1.2 Elastic-solid foundation

The elastic-solid foundation model (sometimes referred to as the Boussinesq

foundation) treats the soil as a linearly elastic, isotropic, homogenous material that

extends semi-infinitely. It is considered a more realistic model of subgrade behavior than

the dense-liquid model, because it takes into account the effect of shear transmission of

stresses to adjacent support elements. Consequently, the distribution of displacements is

continuous; that is, deflection of a point in the subgrade is due to stress acting at that

particular point, and also is influenced by decreasing by stresses at points farther away.

6

Analyzing loaded slab supported on a solid foundation is mathematically more

difficult. Various solutions were available in the literature, such as the Boussinesq

solution, Equation 2-3.

s

s

Epr

w 02 )1(2 µ−

= (2-3)

Where, w = displacement of foundation surface at the center of loaded area, p = contact

pressure, 0r = radious of the loaded area, µs = Poisson’s ratio of foundation, and Es=

elastic modulus of foundation.

Because of its mathematical complexity, the solid-foundation model is less

attractive than the dense-liquid foundation model. Unlike the dense-liquid foundation

model, where the governing equations are differential, the elastic foundation model

requires solving integral or integro-differential equations. The continuous nature of the

displacement function in the elastic-solid model also means that this model cannot

accurately simulate pavement behavior with discontinuities in the structure, especially for

slabs supported on natural soil subgrades. The model is unsuitable for predicting slab

response at edges, corners, cracks, or joints with no physical load transfer.

The elastic-solid foundation model considers the shear force interaction of different

elements in the foundation. Although it improves on Winkler foundation model by

considering shear forces in the foundation, field tests showed inexact solutions for many

foundation materials. Foppl (8) reported that the surface displacements of foundation soil

outside the loaded region decreased faster than the prediction by this model.

2.1.1.3 Improved models using a modified Winkler foundation

Dense-liquid and elastic-solid foundation models represent two extremes of actual

soil behavior. The dense-liquid model assumes complete discontinuity in the subgrade

7

and is better for soils with relatively low shear strengths (natural soils). In contrast, the

elastic-solid model simulates a perfectly continuous medium and is better for soils with

high shear strengths (treated bases). The elastic response of a real soil subgrade lies

somewhere between these two extreme foundation models. In real soils, the

displacement distribution is not continuous; neither is it fully discontinuous. Deflection

under a load can occur beyond the edge of the slab, and goes to zero at some finite

distance. To bridge the gap between the dense-liquid and elastic-solid foundation

models, researchers developed improved foundation models in one of two ways:

• Starting with the Winkler foundation and (to bring it closer to reality) assuming, some interaction among spring elements

• Starting with the elastic-solid foundation, assuming simple expected displacements or stresses

A big problem with these models, is the lack of guidance in selecting the governing

parameters (which have limited or no physical meaning).

Hetenyi foundation: Hetenyi (9,10) suggested achieving interaction of

independent spring elements by embedding an elastic beam in two-dimensional cases and

by embedding a plate in the material of the Winkler foundation in three-dimensional

cases. It is assumed that the beam or plate deforms only in bending . Equation 2-4 shows

the relation between contact pressure p and deflection of foundation surface w for three-

dimensional cases.

wDkwp s2∇+= (2-4)

where ∇2= the Laplace operator and Ds =the flexural rigidity of an imaginary plate in the

Winkler foundation, representing interaction of independent spring elements.

8

Pasternak foundation: Pasternak (11) considered shear interactions in the spring

elements of a Winkler foundation by connecting the ends of the springs with a beam or

plate consisting of incompressible vertical elements that deformed only by transverse

shear. Under this assumption, Equation 2-5 shows the relation between the contact

pressure p and deflection of foundation surface w.

wGkwp b2∇+= (2-5)

where bG =shear modulus of foundation.

“Genelized” foundation by Venckovskii: In this foundation model, in addition to

the Winkler hypothesis, Venckovskii (12) assumed that the applied moment nM is

proportional to the angle of rotation. Equations 2-6 and 2-7 describe this analytically.

kwp = (2-6)

dndwkM n 1= (2-7)

where n is any direction at the point in the plane of the foundation surface, and k and 1k are the corresponding proportionality factors.

2.1.1.4 Improved models by using a modified elastic-solid foundation

Reissner foundation: Assuming that the in-plane stresses throughout the

foundation layer (2-8) are negligibly small.

0=== xyyx τσσ (2-8)

and that the horizontal displacements at the upper and lower surfaces of the foundation

layer are zero, Reissner (13) obtained the relationship in Equation 2-9 for the elastic case

pc

cpwcwc 2

1

2221 4

∇−=∇− (2-9)

where

,1 HE

c s= ,32

HGc = )1(2 µ+

= sE

G (2-10)

9

To apply the Reissner model to the case in which elastic modulus bE varies linearly

with the depth of foundation, Horvath (14) developed a modified Reissner model.

pCpwCwC 232

21 ∇−=∇− (2-11) where 21 ,CC and 3C are constants which are functions of elastic modulus bE and thickness H of the foundation. Beam-column-analogy foundation: From an elastic continuum, Horvath (15)

developed a Pasternak-type, beam-column-analogy foundation model as

wGHwHE

p s 22

∇−= (2-12)

With this model, Horvath (16) analyzed the mat-supported Chemistry Building at

Massachusetts Institute of Technology in Cambridge, Massachusetts. The comparison of

computed and observed settlements showed that this model provided good agreement

with observed behavior.

2.1.2 Analytical Solutions for Concrete Pavement Response to Traffic Loading

A complete theory of structural analysis of rigid pavement was suggested by

Westergarrd (4, 5, 6, 17, 18, 19) using the classical thin-plate based theoretical models.

Westergaard modeled the pavement structure as a homogenous, isotropic, elastic, thin

slab resting on a Winkler (dense-liquid) foundation. He identified the three most critical

loading positions; the interior (also called center), edge, and corner and he developed

equations for computing critical stresses and deflections for those loading positions.

Westergaard’s original equations have been modified several times by different

authors, mainly to bring them into better agreement with measured responses of actual

pavement slabs. Ioannides et al (7) performed an extensive study on Westergaard’s

original equations and the modified formulas.

10

Interior loading: Westergaard defines interior loading as the case when the load is

at a considerable distance from the edge. Equation 2-13 gives the maximum bending

stress at the bottom of the slab for the interior load of radius 0r .

⎥⎦

⎤⎢⎣

⎡+

+= 6159.0ln

2)1(3

2crL

hp

πµσ (2-13)

where p = uniformly distributed pressure, h= slab thickness, E= elastic modulus of concrete, µ = Poisson’s ratio of concrete, k= modulus of subgrade reaction, L is the radius of relative stiffness defined as

( )4

1

2

3

112 ⎥⎦

⎤⎢⎣

⎡−

=k

EhLµ

(2-14)

and, 0rrc = when hr 724.10 ≥ (2-15)

hhrrc 675.06.122

0 −+= when hr 724.10 〈 (2-16)

The modified radius cr was introduced to account for the effect of shear stresses in the

vicinity of the load, which is neglected in the classical thin-plate theory. Equation 2-17

gives the deflection for interior loading (18).

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎟⎠⎞

⎜⎝⎛⎥⎦

⎤⎢⎣

⎡−⎟

⎠⎞

⎜⎝⎛+=

200

2 673.02ln

211

8 Lr

Lr

kLpw

π (2-17)

Corner loading: Westergaard proposed Equations 2-18 and 2-19 for computing

the maximum bending stress and deflection, when the slab is subjected to corner loading.

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

6.0

02

213

Lr

hpσ (2-18)

⎥⎥⎦

⎤

⎢⎢⎣

⎡−=

Lr

kLpw

288.01.1 02 (2-19)

11

Edge loading: Westergaard (4, 5, 6) defined edge loading as the case when the

wheel is at the edge of the slab, but at a considerable distance from any corner. Two

possible scenarios exist for this loading case: (1) a circular load with its center placed a

radius length from the edge, and (2) a semi-circular load with its straight edge in line with

the slab. Equations 2.20 and 2-21 by Ioannides et al. (7) include modifications made to

the original Westergaard equations. For the circular loading, the maximum bending

stress and deflection are computed as

( )( )

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡ ++

−+−+⎟⎟

⎠

⎞⎜⎜⎝

⎛++

=L

rkr

Ehhp

22118.1

21

3484.1

100ln

313 0

20

3

2

µµµµπµσ (2-20)

( )⎥⎦⎤

⎢⎣⎡ +−

+=

Lr

kEh

pw 0

3

4.076.01

2.12 µµ (2-21)

The maximum bending stress and deflection for a semi-circular loading at the edge is

given by

( )( )

( )⎥⎥⎦

⎤

⎢⎢⎣

⎡ ++−+⎟⎟

⎠

⎞⎜⎜⎝

⎛++

=L

rkr

Ehhp

221

3484.3

100ln

313 0

20

3

2

µµµπµσ (2-22)

( )⎥⎦⎤

⎢⎣⎡ +−

+=

Lr

kEh

pw 0

3

17.0323.01

2.12 µµ (2-23)

Westergaard made the following simplifying assumptions in his analysis,

• The foundation acts like a bed of springs (dense liquid foundation model)

• There is a full contact between the slab and foundation

• All forces act normal to the surface where shear and frictional forces are negligible

• The semi-infinite foundation has no rigid bottom

• The slab is of uniform thickness, and the neutral axis is at its mid-depth

12

• The load is distributed uniformly over a circular contact area ( for the edge loading, load is distributed uniformly over a semicircular contact area where the diameter of the semicircle is alone the edge of the slab)

• For corner loading, the circumference of the circular area is tangential to the edge of the slab

• The concrete pavement acts as single semi-infinitely large, homogenous, isotropic elastic slab with no discontinuities.

Despite limitations associated with the simplifying assumptions, Westergaard’s

equations are still widely used today to compute stresses in pavements and to validate

other models developed using different techniques.

Because of simplifications associated with the above assumptions; the Westergaard

theory has some limitations

• Stresses and deflections can be computed only for the interior, edge and corner loading conditions

• Shear and frictional forces on slab surface are ignored

• The Winkler foundation extends only to the edge of the slab

• The theory does not account for unsupported areas resulting from voids or discontinuities

• Multiple wheel loads cannot be considered

• Load transfer between joints or cracks is not considered.

The thin plate based theoretical models for structural analysis of concrete pavement

did not develop much further after Westergaard findings. Pickett and Ray (20) made

Westergaard’s solution easy to use and popular for the design of concrete pavement using

influence chart. Further developments have received less attention because of the

complexities of the mathematics involved.

Hogg and Hall (21) took the subgrade as a semi-infinite elastic-solid and they

developed an analytical model for determining the stresses and deflections of a concrete

13

slab under the action of a single load by using the elastic properties of subgrade. This

model is effectively an infinite thin slab model because the derivation considers a single

interior load far away from any edge or corner of a slab.

Reissner (13, 22, 23) developed a thick- plate theory to analyze two problems: (1)

the problem of torsion of a rectangular plate, and (2) the problems of plain bending and

pure twisting of an infinite plate with a circular hole. The Reissner theory is regarded as

stress-based shear deformable theory as it is based on assumed stress variation through

the plate thickness. Hu (24) further extended Reissner’s theory and developed another set

of basic equations for thick plates that are simpler to solve than the original equations.

Mindlin (25) proposed another formulation to account for shear deformation based on a

proposed displacement field through the plate thickness.

A theoretical solution to the problem of a rectangular thick plate with four free

edges and supported on Pasternak foundation was developed by Shi et al. (26). The

Fundamental equations for the problem were established by applying Reissner thick-plate

theory and solved by applying the method of superposition. Fwa et al. (27) further

extended this solution into analysis of concrete pavement and found differences existed in

both stresses and deflections between thick-plate solutions and Westergaard’s solutions.

2.1.3 Numerical Solutions for Concrete Pavement Response to Traffic Loading

It has been virtually impossible to obtain analytical closed-form solutions for many

pavement structures because of complexities associated with geometry, boundary

conditions, and material properties. With the evolution of high speed computers, the

analysis of such complex problems using numerical technique was possible. The most

commonly used numerical techniques for analyzing concrete pavement structures are: (1)

14

discrete element method (DEM), (2) finite element method (FEM), and finite difference

method (FDM)

2.1.3.1 Discrete element method (DEM)

The first use of DEM for concrete pavement analysis was made by Hudson and

Matlock (28). In this analysis, the subgrade was idealized as a Winkler foundation. The

effects of joints in this model were taken into consideration by reducing the original

bending stiffness of the slab at those locations where a joint existed. The model

developed by Hudson and Matlock (28) was later modified and improved by Vora and

Matlock (29) to include element of different sizes, anisotropic skew slabs, and semi-

infinite elastic solid subgrade. The major disadvantages of DEM formulations are that

elements of varying sizes are not easily incorporated into the analysis, and that special

treatment is needed at the free edge where stresses cannot be determined uniquely.

2.1.3.2 Finite element method

FE techniques have been used to successfully simulate different pavement

problems that could not be modeled using the simpler multi-layer elastic theory. Further,

it provides a modeling alternative that is well suited for applications involving systems

with irregular geometry, unusual boundary conditions, or non-homogenous composition.

Three different approaches were used for FE modeling of pavement system: plane-strain

(2D), axisymmetric, and three-dimensional (3D) formulation. In the FE method, the level

of accuracy obtained depends upon different factors, including the degree of refinement

of the mesh (element dimensions), the order and type of element, and location of

evaluation.

Various finite element models have been developed for analyzing the behavior of

concrete pavement systems. Most of the finite element models use an assemblage of

15

two-dimensional plate bending elements to model behavior of a concrete slab. A plate

with medium thickness is thick enough to carry the load by bending action but is thin

enough such that the transverse shear deformation can be considered negligible. The

subgrade is usually assumed to behave like either a Winkler (dense liquid) or an elastic

solid foundation. The Winkler foundation can be modeled by a series of vertical springs

at the nodes, which means that the deflection at any point of the foundation surface

depends only on the forces at that point and does not depend on the forces or deflections

at any other points. The stiffness of the foundation is represented by the spring constant.

The use of an elastic solid foundation assumes a homogeneous, elastic, and isotropic

foundation with a semi-infinite depth. The deflection at any point depends on the forces

at that point and also on the forces or deflections at other points. The following section

briefly describes the basics and applications of a few finite element computer programs.

KENSLAB(30): The slab is treated in this model is composed of two bonded or

unbonded layers with uniform thickness. The two layers can be either a high modulus

asphalt layer on top of a concrete slab, or a cement-treated base. Rectangular thin-plate

elements with three degrees of freedom per node (a vertical deflection and two rotations)

are used to represent the slab. Load transfer through doweled joint or aggregate interlock

can be considered in this model. Three types of foundation are included in this model,

namely the Winkler foundation, the semi-infinite elastic-solid foundation and layered

elastic-solid foundation. Three contact conditions between slab and foundation can be

considered: full contact, partial contact without initial gaps, and partial contact with

initial gaps. Load transfer effects can be considered in analyzing the pavement slab

system.

16

ILLI SLAB (31): This model can be used to analyze a jointed or continuously-

reinforced concrete pavement with a base or subbase and with or without an overlay,

which can be either fully bonded or un-bonded to the concrete slab. A concrete slab is

modeled as an assemblage of rectangular plate bending elements with three degree of

freedom at each node. When a base or subbase layer and/or an overlay are used, they are

also modeled as assemblages of plate bending elements. If there is no bond between the

layers, the overall stiffness matrix for the multiple layers is obtained by simply adding up

the stiffness matrices of the concrete slab, the base or subbase and the overlay. For the

case of perfect bond between layers, full strain compatibility at the interface is assumed.

Thus, an equivalent layer can be obtained based on a transformed-section concept.

Load transfer across the joints is modeled in various ways depending on the

transfer devices used. Dowel bars are modeled as bar elements with two degrees of

freedom at each node. The two displacement components are a vertical displacement and

a rotation about a horizontal transverse axis. The bar element is capable of transferring

both a vertical shear force and a moment. If the loads are transferred across a joint only

by means of aggregate interlock or keyway, they are modeled by vertical spring elements

with one degree of freedom at each node. Only vertical forces are transferred across the

joint by the spring element. The moment transfer can be neglected for such a joint.

JSLAB (32): The JSLAB program was developed using a similar model as ILLI-

SLAB. The pavement slab, the base or subbase layer, and the overlay are modeled as

rectangular plate bending elements based on the classical theory of thin plates with small

deflections. These layers can be bonded or unbonded. The subgrade is modeled as a

Winkler foundation represented by vertical springs. The effect of temperature gradient in

17

the concrete slab is incorporated. The temperature is assumed to vary linearly along the

slab depth. The subgrade stiffness is set to be zero at the locations where loss of support

occurs.

Dowel bar at the joints are modeled as bar elements with the ability to transfer both

moment and shear forces across the joints. The effects of looseness of dowel bars can

also be considered. Aggregate interlock and keyway are modeled by spring elements

transferring shear forces only.

WESLIQUID and WESLAYER (33): The finite element model used in the

WESLIQUID and WESLAYER programs are also based on the classical theory of a thin

plate with small deflections. The slab is modeled as an assemblage of rectangular plate

bending elements with three degrees of freedom at each node in both programs. The

difference between these two models is that the WESLIQUID model considers the

sublayers as a Winkler foundation, while the WESLAYER model uses an elastic layered

foundation. The Winkler foundation is modeled by a series of vertical springs. For the

elastic foundation, the Boussinesq’s solution is used to compute the deflections at

subgrade surface for the case of a homogeneous elastic foundation and the Burmister’s

equations are used to compute those for the case of a layered elastic foundation.

The two programs are able to take into account the effects of loss of support from

the sublayer to the pavement slab. The loss of support can be due to linear temperature

gradient in the slab or due to voids in the sublayer.

Load is transferred across a joint by both shear forces and moment transfer. Shear

forces are transferred either by dowel bars, key joint or aggregate interlock. The two

models have three options for specifying shear transfer and one for moment transfer. The

18

three methods of determining shear transfer are (1) efficiency of shear transfer, (2) spring

constant and (3) diameter and spacing of dowels. Moment transfer across joints or cracks

is specified by the efficiency of moment transfer which is defined as a fraction of the full

moment.

FEACONS (34, 35, 36): The FEACONS (Finite Element Analysis of CONcrete

Slabs) program was developed by the University of Florida for the analysis of concrete

pavement behavior for the FDOT. FEACONS program was modified several times to

upgrade its capabilities. The latest version, FEACONS IV program can be used for

analysis of plain jointed concrete pavements subjected to load and temperature

differential effects. In the FEACONS program, a concrete slab is modeled as an

assemblage of rectangular plate bending elements with three degree of freedom at each

node. The three independent displacements at each node are (1) lateral deflection, w, (2)

rotation about the x-axis, θx, and (3) rotation about the y-axis, θy. The corresponding

forces at each node are (1) the downward force, fw, (2) the moment in the x direction, fθx,

and (3) the moment in the y direction, fθy. The FEACONS IV program has the option of

modeling a composite slab made up of a concrete layer bonded to another layer of a

different material such as an econocrete. The subgrade is modeled as a liquid or Winkler

foundation which is modeled by a series of vertical springs at the nodes. A spring

stiffness of zero is used when a gap exists between the slab and the springs due to

subgrade voids. Either a linear or nonlinear load-deformation relationship for the springs

can be specified.

Load transfers across the joints between two adjoining slabs are modeled by shear

(or linear) and torsional springs connecting the slabs at the nodes of the elements along

19

the joint. Looseness of the dowel bars is modeled by a specified slip distance, such that

shear and moment stiffnesses become fully effective only when the slip distance is

overcome. Frictional effects at the edges are modeled by shear springs at the nodes along

the edges.

2.1.3.3 Finite difference method (FDM)

FEM has overwhelming advantages over the FDM when applied to the analysis of

pavement structures. However, FDM may be more suitable or convenient to use in some

cases. The FDM is known to utilize a smaller amount of memory than the FEM, it is

likely that the FDM technique may be particularly useful in problems requiring large

computer effort (7)

The FDM in its application to the slabs-on-grade problem replaces the governing

differential equation and the boundary conditions by finite difference equations. These

equations describe the variation of the primary variable (i.e., deflection) over a small but

finite spatial increment. The most important criterion that governs the adequacy of the

finite difference approximation is the level of refinement of the finite difference grid.

2.2 Review of Concrete Pavement Failures in Slab Replacement

Many forms of functional or structural distresses have been reported from the

newly replaced concrete slabs with in short time after construction. A survey on I-10 of

100 replacement slabs ranging in age between 1 to 3 years, showed that 35% of the slabs

had developed cracks and spalls. In these slabs, fatigue damage is clearly ruled out as a

cause of early cracking. Investigators of this study hypothesized that the micro cracks are

developed in the slabs as a results of shortcoming in pavement design, concrete mix or

construction (37).

20

High early strength concrete has been used for slab replacement concrete to allow

earlier use of the paved sections for moving construction equipment and speeding up

construction. High early strength concrete often uses high quantities of cement content.

Increasing the cement content in concrete mixture tends to increase the heat development

in the mixture. For the investigation of effect of cement type, curing method, and joint

type on the performance of high early strength concrete in slab replacement, forty two

(42) test sections were constructed on the out side lane of I-10 . Fourteen different

combinations of above factors were included in the design of test sections with 3 slabs for

each design. Frequent condition surveys of 42 sections on I-10 showed that mid slab

cracking occurred in 39 of the 42 slabs. The cracks developed at different times ranging

from 24 hours to one year (37).

Doweled joints perform better than undoweled joints. A reduction of 20% in

deflection and lower stresses are expected in doweled joints (38). An extensive crack

survey on Florida’s I-10 showed that dowelled pavement sections had 30% less faulting

and fewer corner cracks compared to undoweled sections (38). However, type of joint did

not showed any relations to the rate of transverse and longitudinal cracks.

A survey was conducted on deteriorated sections of I-75 to investigate the impact

of dowel misalignment on rate of cracking(39) Results of this study showed no

correlation between misalignment of dowels and the rate of cracking.

Okamoto et al (40) have identified the expected ranges of variations in concrete

modulus of rupture have a significantly greater effect on early age fatigue life than the

usual variations in other pavement material properties including subgrade support,

subbase thickness, subbase strength and layer thickness. A laboratory study of modulus

21

of rupture coefficient of variation at ages of 1, 3, 7, 14, and 28 days for four different

mixes ranged from 0 to 23.9 and averaged 7.0 percent (41). The study used two type of

cements and two type of aggregates. Guidelines for the concrete strength for early

opening of concrete pavement were determined based on the type of traffic (construction

traffic, commercial and public traffic). A stress ratio of 0.5 was used as the opening

criteria. Stress ratio was computed incorporating the effects of outside subbase support

and strength variabilities.

As a part of the Strategic Highway Research Program (SHRP), fast track full depth

repair test sections were constructed to demonstrate and validate the technologies that allow

early opening of full-depth Portland Cement Concrete (PCC) pavement repairs to traffic and to

document the information needed to apply this technology (42). The experimental factors

included material type, strength at opening, and repair length. A total of 11 different

high-early strength concrete mixes with opening times ranging from 2 to 24 hours were

evaluated at 2 field sites (I-20, Augusta, Georgia and SR-2, Vermilion, Ohio). The

monitoring program consisted of conducting annual visual distress surveys to monitor the

development of cracking, faulting, and spalling.

The results of long-term monitoring showed that full-depth repairs made with high-

early-strength PCC can provide good long-term performance; however, adverse

temperature conditions during installation can cause premature failures. The study also

showed that the fatigue damage due to early opening is negligible, especially for repairs

3.7 m (12 ft) or shorter (observed longitudinal cracking on long span slabs). Based solely

on fatigue considerations, full-depth repairs could be opened to traffic at lower strengths

than those typically recommended; however, opening at strengths much less than

previous recommendations is not advisable because of the risk of random failures caused

22

by single heavy load at early age. Therefore, no changes to the opening criteria

suggested in the SHRP C-206 manual of practice are recommended (PCC modulus of

rupture of 2.0 MPa (300 psi) by third-point testing, Compressive strength of 13.8 MPa (2,000

psi)).

2.3 Accelerated Pavement Testing

Full-scale and accelerated pavement testing (FS/APT) began as early as 1909 with

a test track in Detroit, as identified by Metcalf (43). Results from FS/APT research

activities created significant advances in pavement engineering practice. Historically,

probably the most notable of these in terms of the effect on highway pavement

engineering is the Road Test conducted by the Association of State Highway Officials

(AASHO) in the late 1950s. For airfield pavements, tests at the U.S.Army Corps of

Engineers (USACE) Waterways Experiment Station (WES) since 1940 essentially

defined the state of engineering practice. During the 1970s and 1980s, worldwide

FS/APT activities and results in other countries were significantly more productive than

those in the United States, with important contributions being made by Australia,

Denmark, South Africa, France, Britain, and the Netherlands, among others (44).

Current efforts are marked by the renewed and resurgent interest in FS/APT

programs worldwide since the mid-1980s. In the United States alone, major investments

in FS/APT programs have been committed by FHWA, USACE (both at WES and at the

Cold Regions Research and Engineering Laboratory [CRREL]), and the states of

Minnesota, California, Texas, and Louisiana. In addition, the Federal Aviation Agency

(FAA) is currently commissioning the largest APT machine in the world. The state of

Florida and the National Center for Asphalt Technology (NCAT), in collaboration with

23

the Alabama Department of Transportation, have both initiated major FS/APT efforts,

which are likely to be the first new APT programs of the 21st century (44).

APT is an alternative evaluation approach for full-scale test roads. Here, the

precise weight of applied loads can be controlled. Therefore, the pavement researcher

has accurate information on the load and the number of load repetition throughout the

duration of the test. Pavement condition surveys and pavement response measurement

can be conducted at different time intervals as desired. APT allows the applied loads to

be precisely located on the pavement section and the wheel load can be run directly over

the embedded strain gauges in concrete for dynamic and statistic load measurement.

Accelerated pavement testing of concrete pavements presents unique challenges

and a different technology than APT on flexible pavements. It is recommended that APT

experiments be designed primarily to provide validation data for mechanistic analysis,

rather than for purely empirical comparisons. It is recommended that where possible,

control sections be used to monitor slab behavior under environmental and internal

changes, and that replicate sections be included in experiment designs. It is very useful

to also establish long-term mainline monitoring sections with the same variables as the

APT sections (45). There were very few studies on rigid pavement evaluation using the

HVS. The following section briefly describes the APT tests using HVS conducted on

rigid pavement.

Evaluation of Rapid Setting Concrete using HVS at Palmdale, California (46):

As part of the Caltrans Long Life Pavement Rehabilitation Strategies (CLLPRS), a

concrete blend of fast setting strength hydraulic cement concrete and PCC was evaluated

using HVS. Two full scale test sites with 210 m in length were constructed using this

24

concrete blend on either side of State Route 14 about 5 miles south of Palmadale,

California. The test site in the northbound direction included sections with different

concrete thicknesses on granular base. Joint Deflection Measuring Devises (JDMD) and

Edge Deflection Measuring Devises (EDMD) were installed to measure the surface

deflection of each test section. The JDMD was installed to measure joint deflection and

the EDMD was positioned to record the edge deflection in the middle of the slab. Multi

depth deflectometers were installed to measure the surface and in depth deflections on

few sections. Each test section was instrumented with thermocouples to measure the

temperature at surface, mid-depth and bottom of the concrete. Some sections were

instrumented with strain gauges. Strain gauges were placed along the HVS wheel path at

middle and corner of the test sections. Each location had two embedded gauges; one

placed 40 mm from the bottom and the other placed 40 mm from the surface.

Visual observations, deflections at joint and middle of the slab and load transfer

efficiency were recorded with respect to HVS repetitions for each test sections. The

researchers also observed the crack development of the test sections. Corner cracks were

observed in many sections. The longitudinal cracks appeared on areas out side of the

wheel path, progressed towards the wheel path and ended up as a corner cracks.

Similarly, the transverse cracks appeared on the wheel path, progressed towards the joints

and ended up as corner cracks. The report only summarizes the results and observations

of this study.

Cumulative Fatigue Analysis of Concrete Pavement Using APT results (47):

The goal of this study was to use Accelerated Pavement Testing (APT) of field slabs in

order to examine Miner’s hypothesis along with various fatigue damage models for

25

concrete pavements. Mechanistic-empirical design procedures for concrete pavements

use a cumulative damage analysis process to predict fatigue cracking in slabs. According

to Miner's hypothesis, concrete should fracture when the cumulated fatigue damage

equals unity. In mechanistic-empirical design procedures, this value corresponds to 50

percent chance of fatigue failure (50 percent cracked slabs).

Several test sections constructed using fast-setting hydraulic cement concrete

(FSHCC) in Palmdale, California, consisting of combinations of joint spacings, shoulder

type, dowelled joints, and widened lanes, were constructed and evaluated using the

Heavy Vehicle Simulator (HVS). These instrumented slabs were loaded with dual wheel

and aircraft wheel loads ranging from 40 kN (9,000 lb) to 150 kN (33,750 lb) with no

wander, and were monitored past the concrete fatigue failure. Results indicated the test

slabs cracked at cumulative damage levels significantly different from unity for all

fatigue damage models, and in most cases, by several orders of magnitude. According to

the results of this study, the use of Miner’s hypothesis to characterize the cumulative

fatigue damage in the concrete, did not accurately predict the fatigue failure of the

concrete slabs. As such, the authors suggest alternative methods for incremental failure

prediction should be explored.

Heavy Vehicle Simulator Experiment on A Semi-Rigid Pavement Structure of

a Motorway(48): For the evaluation of a semi rigid pavement design of the A2

motorway in Poland at Poznan two different test sections were built. The two pavement

structures were exposed to accelerated loading by the HVS-Nordic. The pavements at the

test sites were instrumented with strain gauges, soil pressure cells and deflection gauges

in order to assess the pavements response under the load and to compare these response

26

measurements with values calculated from theoretical pavement models (South African

Mechanistic Pavement Design Method (SAMDM))

During the construction of the test pavements as well as during the load application

deflection measurements with the Falling Weight Deflectometer (FWD) were performed

periodically. A method was developed to combine the analysis of the results of the

response measurements and the results of the deflection measurements with the FWD. By

back calculation from the deflection results E-moduli of the pavement layers were

determined which consequently were used for a forward calculation of stresses, strains

and deflections within the pavement. Thus a comparison with the response

measurements was possible. By means of a sensitivity analysis most realistic ranges of

the E-moduli of the pavement layers, especially of the cement treated base layers as the

main bearing element of the pavement, were determined.

27

CHAPTER 3 STRESS ANALYSIS CONVENTIONAL CONCRETE PAVEMENT SLABS

3.1 Method of Analysis

The Finite Element Analysis of CONcrete Slabs version IV (FEACONS IV)

program was used to analyze the anticipated stresses on the test slabs when loaded by the

HVS test wheel. The FEACONS program was developed at the University of Florida for

the FDOT for analysis of concrete pavements subject to load and thermal effects. This

program was chosen for use since both the University of Florida and FDOT have

extensive experience with this program and the reliability of this program has been

demonstrated in previous studies (34, 35, 36, 38, 49, 50, 51). In the FEACONS program,

a concrete slab is modeled as an assemblage of rectangular plate bending elements with

three degrees of freedom at each node. The three independent displacements at each

node are (1) lateral deflection, w, (2) rotation about the x-axis, θx , and (3) rotation about

the y-axis, θy. The corresponding forces at each node are (1) the downward force, fw , (2)

the moment in the x direction, fθx, and (3) the moment in the y direction, fθy.

The FEACONS program was used to analyze the stresses in the test slabs when

subjected to a 12-kip (53-kN) single wheel load with a tire pressure of 120 psi (827 kPa)

and a contact area of 100 square inches (645 cm2), and applied along the edge of the slab,

which represents the most critical loading location. Analysis was done for two different

load positions: load at the corner of the slab, and load at the middle of the edge (Figure 3-

1).

28

Figure 3-1. Loading positions used in the stress analysis

The elastic modulus of the concrete was assumed to be 5,000 ksi (34.45 GPa) and

the modulus of subgrade reaction was assumed to be 0.4 kci (272 MN/m3). The thickness

of the concrete slabs was 9 inches (23 cm). Other pavement parameter inputs needed for

the analysis are the joint shear stiffness (which models the shear load transfer across the

joint), the joint torsional stiffness (which models the moment transfer across the joint)

and the edge stiffness (which models the load transfer across the edge joint). The values

for these parameters are usually determined by back-calculation from the deflection

basins from NDT loads (such as FWD) applied at the joints and edges. In the absence of

data for determination of these parameters, two conditions were used in the analysis. One

condition was for the case of no load transfer. In this case, all the edge and joint

stiffnesses were set to be zero. The other condition was for the case of good load

transfer. In such a case, typical joint and edge stiffness values for good joint and edge

conditions were used in the analysis. A shear stiffness of 500 ksi (3445 kPa), a torsional

stiffness of 1000 ksi (6.89 MPa), and an edge stiffness of 30 ksi (207 kPa) were used for

this condition.

29

3.2 Results of Analysis

Figure 3-2 shows the distribution of the maximum principal stresses at the top of

the test slab caused by a 12 kip (53-kN) wheel load at the slab corner, for the condition of

no load transfer at the joints and edges. Figures 3-3 and 3-4 show the distribution of the

stresses in the x (longitudinal) and y (lateral) direction, respectively, for the same loading

and load transfer condition.

Figure 3-2. Distribution of maximum principal stresses due to a 12-kip load at the slab corner for the condition of no load transfer at the joints

30

Figure 3-3. Distribution of stresses in the xx direction due to a 12-kip load at the slab

corner for the condition of no load transfer at the joints

31

Figure 3-4. Distribution of stresses in the yy direction due to a 12-kip load at the slab

corner for the condition of no load transfer at the joints

Figure 3-5 shows the distribution of the maximum principal stresses in the test slab

caused by a 12-kip wheel load at the slab corner, for the condition of good load transfer at

the joints and edges. Figures 3-6 and 3-7 show distribution of the stresses in the x

(longitudinal) and y (lateral) direction, respectively, for the same loading and load

transfer condition.

Figure 3-8 shows the distribution of the maximum principal stresses on the adjacent

slab caused by a 12-kip (53-kN) load at the slab corner, for the condition of good load

transfer at the joints and edges. Figures 3-9 and 3-10 show the distribution of the stresses

32

in the xx and yy directions, respectively, on the adjacent slab, for the same loading and

load transfer condition.

Figure 3-11 shows the distribution of the maximum principal stresses on the test

slab caused by a 12-kip (53-kN) load at mid edge, for the condition of no load transfer

across the joints and edges.

Figure 3-5. Distribution of maximum principal stresses due to a 12-kip load at the slab

corner for the condition of good load transfer at the joints

33

Figure 3-6. Distribution of stresses in the xx direction due to a 12-kip load at the slab


34

Figure 3-7. Distribution of stresses in the yy direction due to a 12-kip load at the slab


35

Figure 3-8. Distribution of maximum principal stresses on the adjacent slab due to a 12-

kip load at the slab corner for the condition of good load transfer at the joints

36

Distance, direction xx. inch

0 20 40 60 80 100 120 140 160 180

Dis

tanc

e, d

irect

ion

YY, f

t.

0

2

4

6

8

10

12

-200

0

0

0

20

20

2040 4060

80

0

0

0

00

0

Figure 3-9. Distribution of stresses in the xx direction on the adjacent slab due to a 12-


37

Distance, direction xx, inch

0 20 40 60 80 100 120 140 160 180

Dis

tanc

e, d

irect

ion

YY, f

t.

0

2

4

6

8

10

12

0

0

-20

-40-60-20

0

0

Figure 3-10. Distribution of stresses in the yy direction on the adjacent slab due to a 12-


38

Figure 3-11. Distribution of maximum principal stresses due to a 12-kip load at the mid-

edge for the condition of no load transfer at the joints

3.3 Results of Previous Parametric Studies of Factors Affecting Stresses in Concrete Pavement

Variation of temperature and/or moisture in a concrete pavement slab can cause the

slab to curl and lose partial contact with subgrade. During the day, when the top of the

slab is warmer than the bottom, the slab tends to curl up at the center. During the night,

when the top is cooler than the bottom, the slab tends to curl up at the edges and joints.

When loads are applied during these curling conditions, the maximum stresses in the slab

could be substantially higher than those when the slab is fully contact with the subgrade.

Therefore it is necessary to conduct a parametric analysis of structural response of

concrete pavement under critical thermal-loading conditions. Tia et al. conducted a

comprehensive parametric analysis using the FEACONS program (34). The FEACONS

39

program estimations were comparable to those computed by Influence chat and

Westergard equation at the zero temperature differentials (Temperature at top minus

temperature at bottom). The parameters studied include (1) The temperature differential

in the Slab, (2) the concrete slab length, (3) the subgrade modulus (ks), (4) the elastic

modulus of concrete (Ec), (5) the thickness of the concrete slab (Tc), and (6) the joint

load-transfer characteristics.

Effects of Temperature Differential and Slab Length: The maximum stress

increases as the temperature differential increases. When a temperature differential is

present in the slab, the maximum thermal-load induced stress increases with an increase

in the slab length. The study showed that the maximum stresses increases at a higher rate

as the slab length increases from 12 ft to 15 ft and at a slower rate as the slab length

exceeds 15 feet. The effect of the slab length on the maximum stresses decreases as the

temperature differential in the slab decreases.

Effects of Subgrade Modulus and Slab Length: The maximum stresses in the

slab caused by a 20-kip (89 kN) single axle load at the edge center were computed for the

condition of temperature differential of 200F and for the condition of zero temperature

differential. The slab length was varied from 12 feet to 24 feet while the subgrade

modulus was varied from 0.1 kci to 1.4 kci. The results showed that, with a temperature

differential of 200F, the maximum stress increases as the subgrade modulus increases for

a pavement with a slab length of 12 feet. For a pavement with slab length of 15 feet, the

maximum stress remains approximately constant regardless of the change of subgrade

modulus. For a pavement with 20- or 24-foot slabs, the maximum stresses decreases as

40

the subgrade modulus increases. When the temperature differential is not considered, the

maximum stress decreases as the subgrade modulus increases.

The maximum stress increases as the slab length increases from 12 feet to 20 feet

and remains unchanged as the slab length increases from 20 feet to 24 feet.

Effect of Elastic Modulus of Concrete: The maximum stresses in the slab caused

by a 20 kip single axle load at the edge center were computed for the temperature

differential of +20°F and for the condition of zero temperature gradient.

The results showed that, with or without the consideration of temperature

differential in the slab, the maximum computed stress increases linearly as the concrete

modulus increases. However, the rate of increase in the maximum stress is much greater

with the presence of a temperature differential in the slab.

Effects of Concrete Slab Thickness: The maximum stresses in the slab caused by

a 20-kip single axle load were computed for the condition of temperature differential of

+20°F and for the condition of zero thermal gradient. The concrete slab thickness was

varied from 6 inches to 20 inches.

The results showed that, with or without consideration of the temperature

differential, the maximum stress decreases as the concrete slab thickness increases.

41

CHAPTER 4 DESIGN AND CONSTRUCTION OF TEST SECTIONS

4.1. Description of the Experiment

The experiment was designed to test the performance of concrete slabs made with

different concrete mixtures using the HVS. The concrete test track to be used for this

study was constructed at the APT facility at the FDOT State Materials Research Park on

September 25, 2002, by a concrete contractor under the supervision of FDOT personnel.

This concrete test track consists of two 12-foot wide lanes. Each test lane consists of

three 12 ft Χ 16 ft test slabs, placed between six 12 ft Χ 12 ft confinement slabs. Figure

4-1 shows the layout of the concrete slabs on this test track. Slabs were numbered as

shown in the figure for the identification purpose. The thickness of the concrete slabs is

9 inches.

The plan for the testing program was to remove the 12 ft X 16 ft slabs at the time of

test and with the HVS parked over the test slab area, and to place in these locations the

replacement concrete slabs to be evaluated. The HVS was used to apply repetitive

moving loads along the edge of the test slabs, which is the most critical wheel loading

position on the concrete slabs.

Analysis of

analysis and verification of stresses and strains and...

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