Copyright 2013, Wujun Zhou

EFFECT OF PAVEMENT SUPPORT CONDITION ON CRCP BEHAVIOR AND

PERFORMANCE

by

Wujun Zhou, B.S.; M.S.E.

A Dissertation

In

Civil Engineering

Submitted to the Graduate Faculty of Texas Tech University in

Partial Fulfillment of the Requirements for

the Degree of

DOCTOR OF PHILOSOPHY

Approved

Moon C. Won Chair of Committee

Priyantha W. Jayawickrama

Sanjaya P. Senadheera

Dar-Hao Chen

Dominick Casadonte

Interim Dean of the Graduate School

August, 2013

Copyright 2013, Wujun Zhou

Texas Tech University, Wujun Zhou, August 2013

ii

ACKNOWLEDGMENTS First, I would like to thank my supervisor Dr. Moon C. Won for his valuable

support, guidance, and advice during my doctoral research. This dissertation could not

have been come to realization without his help. It’s the greatest fortune in my life to

have him as my supervisor.

Also I would like to thank Drs. Priyantha W. Jayawickrama, Sanjaya P.

Senadheera and Dar-Hao Chen for accepting to serve in my committee and providing

me with great comments, guidance, and suggestions for my dissertation work.

My special thanks are extended to all former and current researchers at Texas

Tech University – Drs. Pangil Choi, Seongwoo Ryu and Renjuan Sun. I cannot

express in words how much I appreciate their help, advice, and encouragement.

Finally, I wish to express my deepest and extreme appreciation to my family

members for their unconditional love, support, and patience. This dissertation is

dedicated to my family.


iii

TABLE OF CONTENTS ACKNOWLEDGMENTS .................................................................................... ii

ABSTRACT .......................................................................................................... vi

LIST OF TABLES .............................................................................................. vii

LIST OF FIGURES ........................................................................................... viii

I. INTRODUCTION ............................................................................................. 1

1.1 Background and Research Need .................................................................... 1

1.2 Objective and Scope ...................................................................................... 3

II. SUPPORT CONDITION OF CONCRETE PAVEMENT .......................... 5

2.1 Amarillo IH 40 (May 2010) .......................................................................... 5

2.2 Amarillo IH-40 (May 2012) ........................................................................ 11

2.3 Atlanta US 59 (September 2012) ................................................................ 13

2.4 Wichita Falls US 81 (September 2012) ....................................................... 15

2.5 Summary ...................................................................................................... 19

III. REVIEW OF CURRENT PRACTICE ...................................................... 20

3.1 Definition of Pavement Support in Pavement Design ................................. 20

3.1.1 Pavement Support Model ..................................................................... 20

3.1.2 Development of k-value for Pavement Design ..................................... 24

3. 2 Erosion ........................................................................................................ 44

3.2.1 Erosion Mechanism .............................................................................. 44

3.2.2 Erosion Models ..................................................................................... 47

3.2.3 Erosion in Pavement Design ................................................................. 54

3.3 Current Practice ........................................................................................... 58

3.3.1 AASHTO 1993 Approach .................................................................... 58


iv

3.3.2 MEPDG Approach................................................................................ 71

3.3.3 TxCRCP-ME ........................................................................................ 72

3.3.4 Comparison ........................................................................................... 75

IV. SITE CHARACTERIZATION AND PAVEMENT SUPPORT

CONDITION ....................................................................................................... 77

4.1 Test Site Characterization ............................................................................ 77

4.2 Pavement Support Condition Evaluation .................................................... 79

4.2.1 DCP ...................................................................................................... 79

4.2.2 FWD ..................................................................................................... 81

4.2.3 PBT ....................................................................................................... 83

4.3 Pavement Support Results ........................................................................... 86

4.4 Summary ...................................................................................................... 89

V. PAVEMENT BEHAVIOR INVESTIGATION .......................................... 91

5.1 Overview of gage installation locations ...................................................... 91

5.2 Material Properties ...................................................................................... 92

5.3 Various Gauges and Instrumentation .......................................................... 93

5.3.1 Total Strain Measurement in Pavement ................................................ 93

5.3.2 Relative Humidity Measurements in Pavement ................................... 96

5.3.3 Stress-Independent Strain Calculation in Pavement ............................. 98

5.3.4 Warping and Curling Measurements at Pavement Edge .................... 101

5.3.5 Base Friction Evaluation..................................................................... 103

5.4 Summary .................................................................................................... 106

VI. DATA ANALYSIS ...................................................................................... 107

6.1 Pavement Support Condition ..................................................................... 107


v

6.1.1 k-values on Natural and Cement Treated Subgrade ........................... 107

6.1.2 Deflections and k-values on Base Layers ........................................... 109

6.1.3 Deflections and k-values on Concrete Layers .................................... 111

6.1.4 FWD Deflection Basin Determination using Linear Elastic Program 113

6.2 CRCP Behavior and Performance ............................................................. 116

6.2.1 Effect of Base Type on CRCP Transverse Curling ............................ 116

6.2.2 Effects of Base Type and Transverse Crack on CRCP Longitudinal

Curling ......................................................................................................... 130

6.3 Summary .................................................................................................... 132

VII. IMPLEMENTATION .............................................................................. 134

7.1 Design Input .............................................................................................. 134

7.2 Job Control Testing ................................................................................... 136

VIII. FINDINGS AND CONCLUSIONS ........................................................ 141

8.1 Findings and Conclusions .......................................................................... 141

8.2 Recommendations for Future Research ..................................................... 144

REFERENCE .................................................................................................... 146


vi

ABSTRACT

Based on visual survey, dynamic cone penetrometer testing, and falling weight

deflectometer testing on several continuous reinforced concrete pavement (CRCP)

sections with or without distresses and high or low deflection, different support

condition is the main cause of difference between CRCP behaviors and performances.

Currently, the support provided by the base layer under Portland cement

concrete (PCC) pavement is most commonly characterized by elastic medium such as

a spring constant. Analysis of PCC pavement behavior with a spring constant for

pavement performance prediction has severe limitations, with the primary limitation

being that base stiffness has little effect on the stresses and resulting performance in

PCC pavement.

Field performance evaluations indicate a strong correlation between base

support and PCC pavement performance. The uniformity of the base support also

plays an important role in determining PCC pavement behavior and performance. This

area hasn’t been investigated as thoroughly as warranted.

The prevailing distress mechanism in the Mechanistic Empirical Pavement

Design Guide (MEPDG) developed under NCHRP 1-37(A) involves warping and

curling stresses, which are alleviated with softer base materials. There is a discrepancy

between the need for a strong base support for wheel load applications and weak base

support for warping and curling stresses. In general, field performance evaluations

show better performance in PCC pavement with a strong base support. Efforts should

be made to determine the optimum base support.

It is expected that this research effort will provide useful information for

pavement engineers and researchers to understand the effect of pavement support on

CRCP behavior and performance and foundation to improve the durability of CRCP.


vii

LIST OF TABLES 3.1 Subgrade k values and concrete elastic moduli backcalculated from

slab deflections at Arlington Road Test (Teller and Sutherland 1943) ........................................................................... 31

3.2 Backcalculation results for concrete pavements and concrete overlays at Willard Airport (NCHRP 1-30 1994). ........................ 42

3.3 Typical Ranges of Loss of Support (LS) Factors for various Types of Material (McCullough and Elkins 1979) .................................. 54

3.4 Recommendations for erosion potential of base/subbase material (MEPDG 2002 Appendix LL) ...................................................... 57

3.5 Input variables and values for composite k-value computation (Ha et al 2011) ...................................................................................... 74

5.1 PBT k-value on top of base at each test section. ............................................. 92

5.2 Concrete mixture design and concrete properties. .......................................... 93

6.1 Summary of AREA Backcalculation Method Parameters ............................ 113

6.2 Summary of Field Testing Data .................................................................... 121


viii

LIST OF FIGURES 2.1 CRCP sections with different performance ...................................................... 6

2.2 FWD test locations at punchout section ............................................................ 6

2.3 FWD data at punchout section (a) outside lane side, (b) shoulder side .................................................................................................. 8

2.4 FWD data at small crack spacing section with good performance ................... 9

2.5 DCP locations at full depth repair section. ..................................................... 10

2.6 DCP test results ............................................................................................... 10

2.7 DCP initial penetrations reading ..................................................................... 11

2.8 Visual surveys for pavement support condition evaluation ............................ 12

2.9 DCP testing and locations in FDR section ...................................................... 12

2.10 Result of DCP test at all locations ................................................................ 13

2.11 FWD deflections along US 59 test section .................................................. 14

2.12 DCP results ................................................................................................... 14

2.13 Drill hole through existing CRCP for DCP test ............................................ 15

2.14 FWD deflections along US 81 test section ................................................... 16

2.15 DCP test results ............................................................................................. 17

2.16 FWD and DCP locations ............................................................................... 18

3.1 Dense liquid and elastic solid extremes of elastic soil response (Darter et al. 1995) ........................................................................ 22

3.2 Flexible beam acted upon at mid-length by load Q (Engesser 1893) ............. 26

3.3 Influence of width of beam on depth of bulbs of pressure (Terzaghi 1955) ............................................................................................. 27

3.4 Schematic illustration and calculation of k from deflected volume (Darter et al. 1995) ........................................................................ 29

3.5 Effect of load size and deflection magnitude on k (Teller and Sutherland 1943). .......................................................................... 30

3.6 Results of PCA plate tests on granular and cement-treated bases (Childs 1967) ................................................................................. 34

3.7 Base k curves from 1973 PCA airport pavement design manual (Packard 1973). ............................................................................. 35

3.8 k values for fine-grained AASHTO soil classes and degree of saturation (Darter and Barenberg 1977). ....................................... 37


ix

3.9 k values for coarse-grained AASHTO soil classes and degree of saturation (Darter and Barenberg 1977). ....................................... 38

3.10 Relationship of backcalculated k value to static k value (Foxworthy 1985). ........................................................................ 40

3.11 Movement of water under the slab (Van Wijk 1985) ................................... 44

3.12 Effect of void size and velocity of slab deflection on the average water velocity (Phu and Ray 1979) ............................................... 45

3.13 Effect of void size and velocity of slab deflection on the shear stress (Phu and Ray 1979) ............................................................. 46

3.14 Shear stress induced erosion (Jung et al. 2009) ............................................ 47

3.15 Correction of Effective Modulus of Subgrade Reaction for Potential Loss of Support (McCullough and Elkins 1979) ............................................................................................. 55

3.16 Typical Ranges of Loss of Support (LS) Factors for various Types of Material (American Association of State Highway and Transportation Officials 1986) ............................................... 56

3.17 Plate bearing test simulation on top of elastic layer (American Association of State Highway and Transportation Officials 1986) .............................................................................. 59

3.18 Mesh and geometry for finite element model ............................................... 60

3.19 Soil deflection contours................................................................................. 61

3.20 Nodes deflection in Soil FEM model ............................................................ 61

3.21 Elastic Modulus E vs. k-value ....................................................................... 62

3.22 Plate Diameter vs. k-value............................................................................. 63

3.23 Diana Results vs. AASHTO 1986 ................................................................. 64

3.24 Nomograph for composite k-value determination (American Association of State Highway and Transportation Officials 1986) .............................................................................. 65

3.25 Modification of k-value to consider rigid foundation effect within 10 ft (American Association of State Highway and Transportation Officials 1986) ...................................................... 66

3.26 Relative damage nomograph based on slab thickness and composite k-value (American Association of State Highway and Transportation Officials 1986) ............................... 67

3.27 Simulated plate load for composite k-value (American Association of State Highway and Transportation Officials 1986) .................. 68


x

3.28 Comparison of AASHTO k-value equation and back-calculated k-values for unprotected subgrades (Darter et al. 1995). ................. 70

3.29 Structural model for rigid pavement structural response computations (ARA Inc. ERES Consultants Division 2004). ............................................................................................ 71

3.30 Plate bearing test simulation and composite k-value computation (Ha et al. 2011). ............................................................................. 74

3.31 Example of different k-value evaluation methods ........................................ 75

4.1 Test site of FM 1938. ...................................................................................... 77

4.2 Test section layout........................................................................................... 78

4.3 Field testing. .................................................................................................... 79

4.4 DCP testing. .................................................................................................... 80

4.5 DCP testing. .................................................................................................... 80

4.6 DCP test after placement of stabilized base. ................................................... 81

4.7 FWD testing. ................................................................................................... 82

4.8 FWD data on top of each layer. ...................................................................... 83

4.9 Plate bearing test setup at field........................................................................ 84

4.10 Typical plate bearing test data....................................................................... 85

4.11 Variations in k-value and deflection (1st Section). ....................................... 86

4.12 Variations in k-value and deflection (2nd Section). ...................................... 87

4.13 Variations in k-value and deflection (3rd Section). ...................................... 88

4.14 Variations in k-value and deflection (4th Section). ....................................... 89

5.1 Various gages installation. .............................................................................. 92

5.2 VWSGs at top, middle, and bottom of CRCP in both longitudinal and transverse direction................................................................. 94

5.3 Typical measured concrete strain data by VWSGs at longitudinal direction......................................................................................... 95

5.4 Typical measured concrete strain data by VWSGs at transverse direction......................................................................................... 96

5.5 RH sensor installed at different depth of CRCP. ............................................ 97

5.6 RH sensor SHT75 (figure courtesy: sensirion.com). ...................................... 97

5.7 Typical measured RH data at field. ................................................................. 98

5.8 NC design detail. ............................................................................................. 99


xi

5.9 Non-stress cylinders (NC). .............................................................................. 99

5.10 Typical stress-independent strain measured by NC system. ....................... 100

5.11 In-situ CoTE. ............................................................................................... 101

5.12 Concrete displacement gage installation. .................................................... 102

5.13 Typical vertical movement measured by concrete displacement gage. ............................................................................................ 102

5.14 Concrete prisms for friction evaluation....................................................... 103

5.15 Concrete prisms cast at field. ...................................................................... 104

5.16 Concrete prisms strain. ................................................................................ 105

5.17 Transverse cracking pattern. ....................................................................... 105

6.1 (a) k-value on CTS versus elastic modulus of CTS and natural soil, (b) k-value on natural soil versus elastic modulus of at upper and lower layers of natural soil and (c) FWD deflection on CTS versus k-values. ............................................. 109

6.2 FWD deflections on CTS and base. .............................................................. 110

6.3 FWD deflections on base and CRCP. ........................................................... 112

6.4 FWD deflection basin simulations on base and CRCP. ................................ 114

6.5 Simulated FWD deflection basins on base layer........................................... 115

6.6 Simulated FWD deflection basins on PCC slab. ........................................... 116

6.7 (a) Pavement edge vertical displacement at test section #2, (b) Pavement edge vertical displacement at test section #3-1, (c) Pavement edge vertical displacement at test section #3-2, (d) Pavement edge vertical displacement at test section #4-1, and (e) Pavement edge vertical displacement at test section #4-2................................................. 119

6.8 (a) Total strain of concrete at top-middle-bottom at #4-1, and (b) Pavement edge vertical movement at #4-1. ................................ 120

6.9 k-values versus CRCP edge vertical daily movement................................... 122

6.10 Gage Locations of each Section. ................................................................. 123

6.11 k-values versus concrete strain daily variation............................................ 124

6.12 Pavement edge vertical movement versus variation of temperature difference between top and bottom (Delta T). ............................ 125

6.13 (a) Correlation between edge vertical movement versus Delta T at test section #2, (b) Correlation between edge vertical movement versus Delta T at test section #3-2, and (c)


xii

Correlation between edge vertical movement versus Delta T at test section #4-1.......................................................... 127

6.14 Pavement edge vertical movement ratio. .................................................... 128

6.15 k-values versus pavement edge vertical daily movement and concrete strain difference between top and bottom..................... 129

6.16 Concrete strain variations at pavement bottom in longitudinal direction....................................................................................... 131

7. 1 (a) AREA k-value versus AREA on base, (b) AREA k-value versus maximum deflection D0 on base. ................................................ 138

7. 2 AREA k-value versus combined parameter ................................................. 139

7. 3 AREA k-value versus combined parameter for two base types ................... 140


1

CHAPTER 1

INTRODUCTION

1.1 Background and Research Need

Currently, the support provided by the base layer under Portland cement

concrete (PCC) pavement is most commonly characterized by elastic medium such as

a spring constant. Analysis of PCC pavement behavior with a spring constant for

pavement structural design and performance prediction has severe limitations, with the

primary limitation being that base stiffness has little effect on the wheel load stresses

in concrete and required slab thickness of PCC pavement.

Field performance evaluations indicate a strong correlation between base

support and PCC pavement performance. The uniformity of the base support also

plays an important role in determining PCC pavement behavior and performance. This

area has not been investigated as thoroughly as warranted.

Field evaluations of the behavior and distress mechanisms of continuously

reinforced concrete pavement (CRCP) indicate that base stiffness has substantial

effects on CRCP performance. More specifically, strong correlations exist between

base stiffness and concrete stresses near the longitudinal steel when wheel loading is

applied. The higher the stiffness of the base support, the lower the pavement

deflections and concrete stresses near the longitudinal steel, resulting in better

performance. The prevailing CRCP distress mechanisms in any mechanistic-based

pavement design procedures, including the Mechanistic Empirical Pavement Design

Guide (MEPDG) developed under NCHRP 1-37(A), involve warping and curling

(environmental) stresses, in addition to the stresses due to wheel loading applications.

The stiffness of base support has conflicting effects on environmental and wheel load

stresses. In general, higher stiffness of a base support is desirable if wheel loading

stresses are to be controlled. On the other hand, higher stiffness of a base support will

result in larger environmental stresses. In jointed plain concrete pavement (JPCP),


2

environmental stresses constitute a large portion of the total stresses in concrete slab,

and efforts were made to “optimize” base stiffness. The reason for the significance of

environmental stresses in JPCP is that any cracking is considered as a distress and

environmental stresses in JPCP could indeed induce mid-slab transverse cracking,

when combined with wheel load stresses. On the other hand, the importance of

environmental stresses in CRCP is much reduced, primarily because numerous

transverse cracks develop due to environmental stresses. Transverse cracks in CRCP

are not considered as distresses, and reduce environmental stresses substantially. At

the same time, critical concrete stresses in CRCP that are responsible for distresses are

near the longitudinal steel due to the interactions between longitudinal steel and

surrounding concrete when subjected to wheel load applications. The concrete stresses

near the longitudinal steel when subjected to wheel loading applications depend, to a

large extent, on slab deflections, which are controlled by a slab thickness and the

stiffness of a base support. Accordingly, in general, the larger the stiffness of a base

support, the better the performance of CRCP. However, most of the mechanistic-based

CRCP design methodologies use the same concept of environmental stresses that was

developed and adopted for JPCP design. This apparent mis-application of base

stiffness effect on CRCP behavior and performance analysis could result in

undesirable CRCP designs. It is partly because, in addition to the beneficial effects of

base stiffness the on concrete stress near longitudinal steel, there is a strong correlation

between base stiffness and erodibility of base materials. In general, as the base

stiffness increases, it becomes more resistant to erosion. Any effort to “optimize” base

stiffness in consideration of minimizing the sum of environmental and wheel loading

stresses could result in a less erosion-resistant base layer. Field evaluations of CRCP

performance indicate the primary cause of a structural distress in CRCP – punchout –

is deterioration and erosion of base materials. Research is needed to evaluate the effect

of base stiffness on CRCP behavior and performance, so that proper credit is given to

base stiffness and optimum pavement designs could be developed.


3

The conflicting effect of a slab support condition on concrete stresses from

environmental and wheel loadings has resulted in less emphasis on providing sound

slab support under the concrete slab during pavement design and construction,

especially in the United States. Accordingly, much of the research effort in rigid

pavement design has been on the mechanistic analysis of concrete slabs themselves,

with very little on a base support condition. To improve the design procedures and

performance of CRCP, more research effort should be made on the base support issues.

In addition, the selection of proper input values for the slab support condition during

pavement design is still a difficult task, partly because there are no good field

evaluation methods available for support condition under the concrete slab. The most

widely used method in mechanistic-based concrete pavement design is to estimate

subgrade stiffness in terms of modulus of subgrade reaction and combine with

modulus of base layer to estimate a slab support condition. This method has

disadvantages, one of which is the difficulty in quantifying the slab support condition

during pavement construction. Research is needed to develop a simple method that can

be used to estimate slab support condition during pavement construction as a job

control test.

1.2 Objective and Scope

The purpose of this study was to establish the effect of pavement support

condition on CRCP behavior and performance, and to develop test procedures to

quantify a slab support condition for pavement design input as well as a job control

testing. The objectives included comparing k-values obtained from various methods,

identifying the best way to describe support condition accurately for the CRCP

analysis, and identifying the relationship between support conditions and CRCP

behaviors and performance.

In order to achieve the objectives, the following tasks have been framed:


4

1. Pavement support condition study: field tests such as plate bearing test (PBT),

dynamic cone penetrometer (DCP) and falling weight deflectometer (FWD)

were conducted to evaluate the pavement support condition.

2. Installed various gages to evaluate PCC pavement structural responses.

3. Additional laboratory and field tests were performed as needed.

4. Analyzed pavement support condition data with PCC pavement structural

responses.


5

CHAPTER 2

SUPPORT CONDITION OF CONCRETE PAVEMENT

To evaluate the effect of slab support condition on CRCP performance, field

evaluations were conducted at 4 CRCP projects. The evaluation methods included

visual survey, dynamic cone penetrometer (DCP) testing, and deflection testing with

Falling Weight Deflectometer (FWD). This chapter presents brief descriptions of the

field evaluations.

2.1 Amarillo IH 40 (May 2010)

A CRCP section from 2.0 miles east and to 2.0 miles west of City of Groom

was constructed in 1979. The pavement structure consisted of 9-in CRCP on 4-in

asphalt stabilized base. Subgrade was treated with lime. Field evaluations were

conducted in May 2010, and at that time, the pavement was 31 years old. Even though

the overall performance was satisfactory, there were distresses in the form of

punchouts and longitudinal joint separations. TxDOT was conducting full-depth repair

(FDR) operations on the distresses, which provided a good opportunity for field

testing and evaluations. The evaluations consisted of visual survey, dynamic cone

penetrometer (DCP) testing, and deflection testing with Falling Weight Deflectometer

(FWD). To evaluate the structural differences in pavement condition between

distressed area and good performing area, in addition to the distressed areas, areas

with no distresses were also selected for structural evaluations and comparison. The

areas were in the westbound of IH 40 in the vicinity of mile marker 114. Figure 2.1

illustrates the two areas selected, one with distress and the other without, for field

evaluations. The distressed area is confined within 2 closely spaced transverse cracks,

with prior repairs with asphalt. It is also observed that distressed concretes are near the

longitudinal joints only. The joint at the bottom left is a longitudinal warping joint,


6

while the one on the top is a longitudinal construction joint. Figure 2.2 illustrates the

locations of FWD drops.

Figure 2.1 CRCP sections with different performance

Figure 2.2 FWD test locations at punchout section

As can be seen, FWD data were collected at inside and outside of the

longitudinal warping joint, which is between outside lane and shoulder. Deflections

near the longitudinal construction joint were not evaluated due to the traffic control

issues. Figures 2.3 (a) and (b) show the deflection testing results at inside and outside

of the longitudinal warping joint, respectively. Deflections at different loading levels

were normalized at 9000 lbs loading. The observations from Figures 2.3 (a) and (b)

can be summarized as follows:


7

1) In general, deflections are quite large. Based on the deflection data

obtained from TxDOT rigid pavement database project, deflections of

about 3.5 mils are expected for 9-in CRCP. Even at a longitudinal warping

joint, the deflections observed in this location are much higher than

normally observed.

2) The deflections at outside of the warping joint are lower than those at

inside of the warping joint.

3) The variability in deflections is larger at the inside of the warping joint than

at the outside.

These observations indicate different slab support conditions under the slab at

both sides of the longitudinal joint. According to the plan set, the same materials were

used for base and subgrade stabilization at both sides of the warping joint. It appears

that repeated wheel loading applications deteriorated the condition of the base in the

inside of the warping joint.

(a)

0

5

10

15

20

25

30

35

0 12 24 36 48 60 72 84

Def

lect

ion[

mils

]

Geophone Location[in.]

Loaction 1

Loaction 2

Loaction 3

Loaction 4


8

(b)

Figure 2.3 FWD data at punchout section (a) outside lane side, (b) shoulder side

As shown in Figure 2.4, FWD data from the same short crack spacing CRCP

section with good performance was collected. The data were compared with the data

from a punchout section with similar crack spacing. Both S1 and S2 are short crack

spacing without distress. 1,2,3,4 represent 4 points close to two transverse cracks.

0

3

6

9

12

15

0 12 24 36 48 60 72 84

Def

lect

ion[

mils

]

Geophone Location[in.]

Location 5

Location 6

Location 7

Location 8


9

Figure 2.4 FWD data at small crack spacing section with good performance

Based on the FWD data above, deflections at punchout section are much

higher than the good performance sections. CRCP has the same nine-inch thickness

and reinforcement. This section was built in 1979 and has experienced the same traffic

loading and climate condition after several decades of service; however, the concrete

segments perform totally differently even though they have the same crack spacing.

The only reason for the difference between deflections is the different support

conditions. Different support conditions cause the difference between CRCP

performances.

DCP testing was conducted at the repair section as shown in Figure 2.5. Wet

soil was found near the top of the base at the near shoulder location 2. The DCP

results were very close to each other as shown in Figure 2.6 and the only difference is

the initial penetration reading as shown in Figure 2.7. The initial reading depends on

the loose state of the base surface and the self-weight of DCP setup. The location near

shoulder-2 shows large initial readings, indicating a weak base surface.

0

3

6

9

12

15

0 12 24 36 48 60 72 84

Def

lect

ion

[mils

]

Geophone Location [in.]

S1_1 S1_2

S1_3 S1_4

S2_1 S2_2

S2_3 S2_4


10

Figure 2.5 DCP locations at full depth repair section.

Figure 2.6 DCP test results


11

Figure 2.7 DCP initial penetrations reading

2.2 Amarillo IH-40 (May 2012)

Full-depth repairs (FDR) were conducted on a CRCP section on IH 40 near

City of Groom in the Amarillo District. Existing pavement was 9-in, built in 1979.

CRCP on 4-in asphalt stabilized base. After the old concrete slab with distresses was

removed, visual survey and DCP were conducted to evaluate the existing pavement

support condition. Existing base, which was 4-in asphalt stabilized base, broke easily

into small particles like small aggregates as shown in Figure 2.8. There is little asphalt

binder remaining in the base materials in some very bad FDR sections. It appears that

moisture damage occurred to the asphalt stabilized layer.


12

Figure 2.8 Visual surveys for pavement support condition evaluation

Figure 2.9 shows DCP testing on top of existing base and the test points at

FDR section. Figure 2.10 illustrates the DCP test results. From visual observations, the

condition of asphalt stabilized base at Locations #1, #4, #5, and #6 was normal, with

little degradation. On the other hand, asphalt stabilized base at Locations #2 and #3

experienced degradations, as shown in Figure 2.8. However, DCP testing results show

not so good correlations between observed condition of asphalt stabilized base and

DCP readings, except for Location #3. It indicates, as discussed earlier, the inability of

DCP to accurately detect the condition at the very top of the layer under evaluation.

However, it should not be interpreted as a weakness of DCP testing as a tool for

stiffness evaluations. DCP presents a good and practical tool for the estimation of

“overall” layer stiffness.

Figure 2.9 DCP testing and locations in FDR section


13

Figure 2.10 Result of DCP test at all locations

2.3 Atlanta US 59 (September 2012)

This section is 12 in. CRCP with concrete shoulder and was built in 2001.

FWD deflection data was collected 3.5 ft. away from the joint between the outside

lane and concrete shoulder for every 50 ft from the starting point, which is 500 ft from

a transverse construction joint. The normalized FWD deflection data are shown in

Figure 2.11. FWD deflections are quite uniform throughout this test section except the

location 1000 ft. from the start point, which shows twice the deflection of the average.

This point and the two other points 50 ft. before and after were chosen for DCP tests.

The DCP results are shown in Figure 2.12. The correlations between FWD deflections

and DCP readings are quite poor, which indicates, as discussed earlier, the inability of

DCP to accurately assess the stiffness of the very top of the layer under evaluation.


14

Figure 2.11 FWD deflections along US 59 test section

Figure 2.12 DCP results


15

The poor correlations between FWD deflections and DCP readings could be

explained by the existence of deteriorated materials or even voids under the concrete

slab. If the material just below concrete slab is severely deteriorated, that material will

come out during the drilling process of concrete slab, as shown in Figure 2.13. If a

void exists under the concrete slab, DCP will not detect the void. In either case, the

information on the very top of the base stiffness is not captured during DCP testing.

As discussed earlier, DCP testing is a good tool for the evaluation of overall support

condition of the layers below concrete slab, but not for the evaluation of the slab

support condition at the very top of the base layer.

Figure 2.13 Drill hole through existing CRCP for DCP test

2.4 Wichita Falls US 81 (September 2012)

This section on US81 near the City of Bowie in the Wichita Falls District, 8-in

CRCP on 4-in asphalt stabilized base, was built in 1972. FWD deflection data was

collected on the outside lane, which is 3.25 ft. away from the asphalt shoulder, every

50 ft. from the start point. Normalized FWD deflection data were shown in Figure

2.14. Except the FDR section, three locations with higher deflection and three

locations with lower deflections were chosen for DCP tests. DCP test results are

shown in Figure 2.15. No obvious correlation can be found between DCP test results


16

and FWD deflection on top of CRCP. As mentioned earlier, the possible reason is that

FWD deflections are more related with the layer directly underneath the pavement

slab. The FWD deflection will be large with voids or severely deteriorated asphalt

base materials underneath, which will not be detected by DCP. The relative locations

between test points and transverse cracks are shown in Figure 2.16.

Figure 2.14 FWD deflections along US 81 test section


17

Figure 2.15 DCP test results


18

Figure 2.16 FWD and DCP locations

There is a poor correlation between the location of the FWD relative to

transverse cracks and deflections. It is generally accepted that transverse cracks in

CRCP are weak points, and substantial efforts have been made to correlate transverse

crack spacing and distresses. However, numerous field evaluations revealed that

almost no correlations exist between transverse crack spacing and distresses. In

general, with adequate amount of longitudinal steel, transverse cracks are kept quite


19

tight in CRCP, thus the loss of slab stiffness due to transverse cracks is minimal. On

the other hand, a quite strong correlation was observed between base support condition

and distresses in CRCP.

2.5 Summary

In this chapter, support conditions at 4 CRCP projects and their relations with

distresses were evaluated by visual survey, DCP and FWD. It was identified that

pavement support condition has a significant effect on CRCP performance and

behavior. Poor support conditions will cause high deflections, and finally distresses

such as punchout.

FWD evaluations conducted at distressed and non-distressed areas in the same

project indicate larger deflections in the distressed areas than in the non-distressed

areas, even though both areas had the same slab thickness and reinforcement. Those

areas also were built in the same year and experienced the same traffic loading and

climate condition. After several decades of service, the concrete segments performed

totally differently even though they have same crack spacing. The only reason for the

difference in performance and deflections was the difference in support conditions.

Voids or deteriorated materials directly underneath pavement slabs, caused by

erosion or recompaction of base material, play important roles in distresses formation.

This conclusion was supported by the visual survey at the FDR test section on IH 40

Amarillo.

Even though DCP testing is a good tool for the evaluation of overall support

condition of the layers below concrete slab, it does not have a capability to evaluate

the slab support condition at the very top of the base layer. For the proper evaluations

of slab support condition, deflection testing using FWD is a better tool than DCP

testing.


20

CHAPTER 3

REVIEW OF CURRENT PRACTICE

3.1 Definition of Pavement Support in Pavement Design

3.1.1 Pavement Support Model

As a complex engineering system, the interaction between natural supporting

layers, constructed layers and geometry of the applied loads is the main focus of

pavement design and structural behavior analysis (Ioannides 1991a). The first two

components are related to pavement structure itself and the importance is self-evident.

Conventional characterizations for natural supporting layers are dense liquid (Winkler

1867) and elastic solid (Boussinesq and Caquot 1969).

3.1.1.1 Dense Liquid

“Dense liquid” foundation is a conceptual model proposed by Winkler in 1867

with assumption – deflection under an applied vertical force in direct proportion to the

force, without shear transmission to adjacent areas not under the loaded area. The

relationship between deflection and force is evaluated by one single constant

parameter – k-value (Winkler 1867). Physical interpretation of the “dense liquid”

model is that the foundation acts like a bed of springs with spring constant k-values

(McCullough and Boedecker 1968). According to the assumption, the key features of

dense liquid models are summarized as below (Darter et al. 1995):

• The deflection under the plate equals plate pressure divided by k-value.

• Deflection equals zero beyond the edge of the plate.

• Deflection is the same for rigid and flexible plates.

• For a given pressure and deflection, k-value is independent of plate size.

After the first application of the dense liquid model to floating ice sheets by

Hertz in 1884, the dense liquid model was applied to slab support by a number of


21

researches. The dense liquid model is better for characterizing natural subgrade soils

and granular bases, which have relative low shear strength (Darter et al. 1995).

3.1.1.2 Elastic Solid

Compared to the dense liquid model, the elastic model is at the other end of the

spectrum. Two parameters, including modulus of elasticity and Poisson’s ratio, are

used to characterize material properties. The surface of this foundation will have a

continuous and infinite deflection basin when a load is applied. The key features of

elastic solid model are summarized below (Darter et al. 1995):

• Deflection depends on subgrade elastic modulus, plate size, and distance.

• The deflection basin is continuous and infinite.

• Rigid and flexible load plates produce different deflections.

According to the key features, the elastic solid model is considered to be better

for characterizing treated bases which have relatively high shear strength (Darter et al.

1995).

3.1.1.3 Real Soil

Under applied loading, the response and behavior of real soils lie somewhere

in between dense liquid and elastic solid (Darter et al. 1995; Ioannides 1991b). The

basic behaviors of real soil are summarized below (Darter et al. 1995):

• Plate punches down somewhat, producing discontinuous deflection basin.

• Some surface deflection occurs beyond edge of the load plate.

• Deflection equals zero at some finite distance.

• For a given pressure and deflection, k varies with plate size.

Figure 3-1 shows the response of dense liquid, elastic solid, and real soil under

applied loads.


22

Figure 3.1 Dense liquid and elastic solid extremes of elastic soil response (Darter et al. 1995)

3.1.1.4 Two-Parameter Elastic Models

Since real soil behavior is somewhere between two idealization models – dense

liquid and elastic solid, several researchers proposed two-parameter models for real

soil characterization (Ioannides 2006). Two basic approaches of two-parameter elastic

models simulation are based on the dense liquid model and the elastic solid model: (a)

adopt the elastic solid model and introduce simplified assumptions (Kerr 1985;

Reissner 1958; Reissner 1967); and (b) adopt the dense liquid model and introduce

interaction between adjacent foundation springs (Kerr 1965; Pasternak 1954).

Pasternak (1954) derived a relation between subgrade reaction q and deflection

w with the consideration of shear interactions between adjacent spring elements.

𝑞 = 𝑘𝑤 − 𝐺∇2𝑤

where k is vertical spring stiffness, G is the coefficient introduced to describe the shear

interactions between adjacent springs (Pasternak model equal to dense liquid model

when G = 0), and ∇2 is the Laplace operator.The predicted deflection profile under

applied loads is much closer to the deflection observed in a real soil condition. By

changing G-values, the vanish rate of predicted deflection profile can be controlled.

The Pasternak model still has the advantage of being relatively simple for analysis.

The most important thing is how to decide a proper G-value for different soil types

under different conditions. Kerr (1985) discussed the determination of foundation

model parameters.


23

Kerr (1964; 1965) proposed a three-parameter model which is similar to the

Pasternak (1954) model. The three-parameter model includes a spring bed on top of a

Pasternak foundation. One more parameter, spring stiffness kU, is introduced for the

upper spring layer.

3.1.1.5 Soil Model Used in Concrete Pavement Analysis and Design

There are two main reasons that the dense liquid model is used in concrete

pavement analysis and design. Firstly, it is simpler to calculate concrete slab

deflection and critical stress on top of the dense liquid model compared to the elastic

solid model. Secondly, it is more accurate to predict slab deflection and stress at the

edge and corners by using the dense liquid model, when slabs rest on natural soil

subgrades or granular bases (Darter et al. 1995). At the same time, loading at the edges

or corners of the concrete slab is considered most critical for stress and deflection

(Huang 2004), so the dense liquid model is widely used in pavement analysis and

design.

In the modern era, the simplicity of calculation has become less significant

than it was before due to the advancement of the speed in personal computers.

Although two-parameter elastic models have more theoretical appeal and can simulate

more realistic subgrade response than the dense liquid model, the Mechanistic

Empirical Pavement Design Guide (MEPDG) does not include this model. The

MEPDG research team lists the reasons as below (ARA Inc. ERES Consultants

Division 2004):

• Two-parameter elastic model is not well known by practitioners and may cause

confusion.

• Lack of established and field-verified guidelines for the selection of model

parameters for different soil types.

• Lack of extensive field testing data for slab on two-parameter elastic model

calibration, even though ILLISLAB can be used for pavement analysis under

environmental and traffic loading.


24

• Most of the available performance prediction models are based on the dense

liquid model; they need recalibration if two-parameter elastic model was used.

The research team also believes the dense liquid model is the best model for

simulating subgrade at the time MEPDG was developed (ARA Inc. ERES Consultants

Division 2004). The dense liquid model is well tested with field testing results and

several major researches have established field-verified guidelines for the dense liquid

model k-value determination. The differences in rigid pavement responses from the

use of dense liquid and two-parameter elastic models have not been fully studied, even

though the differences may not be substantial. Considering the wide spread use of and

the extent of existing database with dense liquid model, it is advisable to further

improve procedures to estimate k-value using dense liquid model for rigid pavement

design and behavior analysis.

3.1.2 Development of k-value for Pavement Design

In 1925, Westergaard published the first paper on the analysis of concrete

pavement on a dense liquid foundation (Westergaard 1926). In this paper, equations

for concrete slab deflection calculation under interior, edge, and corner loading were

presented. Modulus of subgrade reaction k-value was introduced and the relation with

another introduced term “radius of relative stiffness 𝑙” was described as below:

𝑙 = �𝐸ℎ3

12(1 − 𝑢2)𝑘4

where E = modulus of elasticity of the concrete

h = concrete slab thickness

u = concrete Poisson’s ratio of lateral expansion to longitudinal

shortening

k = modulus of subgrade reaction


25

The three equations proposed by Westergaard for calculating deflection under

the edge, corner and interior loading have the quantity kl2 in common. With known

loading level and measured deflections, quantity kl2 can be calculated; modulus of

subgrade reaction k-value can be obtained with a known modulus of concrete E,

concrete Poisson’s ratio u and slab thickness h (Westergaard 1926). Westergaard

suggested the modulus of subgrade reaction k-value could be back-calculated by

comparing deflected surface profile obtained by full-sized slab field tests and by

theory (Westergaard 1925). Westergaard’s back-calculated method for modulus of

subgrade reaction k-value is useful for evaluating existing pavements, and it was

considered valuable for engineers to get some general idea for k-value range in other

new pavement design.

However, Westergaard did not address the way to determine a k-value for use

in new pavement design and construction. No relationship was mentioned between k-

value obtained from plate load tests and k-value back-calculated from Westergaard

deflection equations (Westergaard 1926). Westergaard did realize there will be some

differences between actual slab behavior and the theory due to the nature of

assumptions. Some of the major concerns were identified as: slab curling and warping

effect, non-uniform support, friction between slab and foundation, and dynamic

loading effect. Westergaard suggested increased modulus of subgrade reaction k-

values for slab dynamic loading response evaluation.

3.1.2.1 k-value and load size

Westergaard (1926) pointed out that load tests on soil depend on the load size,

which means k-value obtained from load tests varies with different load area. Several

field test results support Westergaard’s statement (Goldbeck 1925; Goldbeck and

Bussard 1925).

In the area of beam on elastic foundation analysis, Hayashi (1921) stated that

the coefficient of subgrade reaction k-value should be obtained by a loading test

without mentioning that the results also depend on the size of the load. Hetényi (1946)


26

did not contain any statement about the factors which affect the coefficient of

subgrade reaction k-value in his book about beams on elastic foundations. Terzaghi

(1955) discussed the widespread erroneous perception among engineers that k-value

depends only on properties of natural subgrade. Engesser (1893) pointed out that

coefficient of subgrade reaction k-value decreases with beam width B increasing as

shown in Figure 3.2. Equation was given as below to calculate k-value due to load size

effect.

𝑘 = 𝑎 +𝑏𝐵

where a, b = empirical constants

B= beam width

Figure 3.2 Flexible beam acted upon at mid-length by load Q (Engesser 1893)

Terzaghi (1955) used the concept of the bulb of pressure to better illustrate the

influence of the beam width B on the coefficient of subgrade reaction k-value. Figure

3.3 shows bulbs of pressure for beam width B1 and nB1.


27

Figure 3.3 Influence of width of beam on depth of bulbs of pressure (Terzaghi 1955)

Two types of subgrade characteristics were discussed (Terzaghi 1955).

1. For subgrade deformation characteristics less sensitive of depth, like stiff clay:

With the assumption that settlement y increases in simple proportion to the

depth of the pressure bulb, the coefficient of subgrade reaction can be

calculated based on the equation below:

𝑘𝑠 = 𝑘𝑠11𝐵

where Ks1 is the coefficient of subgrade reaction for a beam with 1 ft width.

2. For subgrade deformation characteristics that change with depth, like clean

sand: Terzaghi (1932) found the modulus of elasticity of sand increases with

increasing depth. That means with the same pressure bulb, settlement

decreases with increasing depth. Based on experimental investigations, the

coefficient of subgrade reaction for a beam with width B is (Terzaghi and Peck

1948):

𝑘𝑠 = 𝑘𝑠1 �𝐵 + 1

2𝐵�2

where Ks1 is the coefficient of subgrade reaction for a beam with 1 ft width.

Since the publications of papers by Westergaard in the 1920s, several

pavement field tests were conducted to better understand pavement support condition

in pavement design and analysis from early 1930s. The Bureau of Public Roads


28

conducted field tests at the Arlington Experiment Farm in Virginia in the early 1930s

(Teller and Sutherland 1935a; Teller and Sutherland 1935b; Teller and Sutherland

1935c; Teller and Sutherland 1936; Teller and Sutherland 1943). One of the major

objectives was to verify Westergaard’s equation with field testing results.

Measurement of modulus of subgrade reaction k-value was needed for Westergaard’s

equation verification.

Due to the limitations of rigid plates bearing tests of soils conducted many

years before the Arlington road test (soil condition may have changed with time and

large deformations produced), three alternative methods were proposed for k-value

evaluation. (1) relatively small size rigid circular plates, (2) relatively large dimension

flexible rectangular or circular plates, and (3) full-size pavement slabs. Arlington

researchers believed it was more practical to test with small rigid plates than with

large flexible plates, because small rigid plates need lighter loads and it is easier to

measure deflection. Methods with small rigid circular plates and full-size pavement

slabs were chosen for k-value evaluation in the Arlington test. Teller and Sutherland

(1943) explained modulus of subgrade reaction k-value also could be obtained by

dividing the load by the volume of displaced soil within the plate area as shown in

Figure 3.4.


29

Figure 3.4 Schematic illustration and calculation of k from deflected volume (Darter et al. 1995)

In order to avoid error caused by the small plate size, researchers realized it

was necessary to determine the plate size effect on k-value. Different circular plates

with 2, 4, 6, 8, 12, 16, 20, 26, 36, 54, and 84 inches diameter were used to test for

plate size effect evaluation. The deflection was controlled from 0.01 to 0.05 inch,

which was considered to be the same range as concrete pavement deflections under

truck loading. k-value was calculated by dividing plate pressure by corresponding

elastic deflection. As shown in Figure 3.5, k-values obtained from plate bearing tests

(PBT) show the effect from different plate sizes and deflection magnitudes.


30

Figure 3.5 Effect of load size and deflection magnitude on k (Teller and Sutherland 1943).

Based on the plate bearing tests results, Teller and Sutherland (1943) made the

conclusion that the plate size for k-values determination should be large enough (48 to

60 inches) and deflection should be less than 0.2 to 0.3 inch. As shown in Figure 3.5,

PBT k-value with 30-inch plate diameter is around half of the k-value of the 12-inch

plate diameter. Subgrade soil at Arlington test field was uniform brown silt loam

(AASHTO classification A-4) as documented. This agrees with Terzaghi (1932)

findings for subgrade deformation characteristics changing with depth as shown below.

𝑘2.5𝑓𝑡 = 𝑘1.0𝑓𝑡 �2.5 + 12 × 2.5

�2

= 0.49𝑘1.0𝑓𝑡

According to Westergaard’s deflection equation under interior, edge and

corner loading, k-values were back-calculated based on the measured data from

deflection tests on concrete slabs (Westergaard 1926). As shown in Table 3.1, the


31

back-calculated concrete modulus of elasticity values are in the same range as

concrete modulus obtained from laboratory tests. And back-calulated k-values,

obtained from deflections on top of concrete slab, agree well with PBT k-values

determined by 30-inch diameter plate size with 0.05 in deflection.

Table 3.1 Subgrade k values and concrete elastic moduli back-calculated from slab deflections at Arlington Road Test (Teller and Sutherland 1943)

It is important to keep in mind that the concrete slabs were cast directly on the

subgrade.


32

Static and dynamic load tests were conducted by the Corps of Engineers at

Wright Field, Ohio in 1941 (Sale and Hutchinson 1959; U.S. Army Corps of

Engineers 1942; U.S. Army Corps of Engineers 1943). With the objective of

developing a standard procedure for modulus of subgrade reaction k-values

determination, plate size effect was studied. A series of plate bearing tests with plate

diameters from 12 to 27 inches were conducted on top of subgrade, and the measured

PBT k-values were compared with k-values obtained from volumetric subgrade

deflection under a full-size slab test (Sale and Hutchinson 1959). PBT k-values

obtained with 30-inch diameter plate were in good agreement with volumetric

subgrade deflection. Phillippe (1947) indicated PBT k-value with 30-inch diameter

plate at 0.05 in deflection has a reasonable correlation with k-value back-calculated

from static plate loading test on top of full-size concrete slabs. A circular plate with

30-inch diameter in the plate bearing test became a standard for modulus of subgrade

reaction evaluation from that time.

3.1.2.2 Effect of base layers on k-value.

At the same Arlington test field location with the same uniform brown silt

loam (AASHTO classification A-4), the subgrade was improved by mixing sand to

several inches with proper compaction (Teller and Sutherland 1943). PBT with 36-

inch plate diameter was conducted on top of improved subgrade and the k-values were

compared with k-values back-calculated from the concrete slab deflection. PBT k-

value increased from 280 psi/in to 400psi/in due to subgrade improvement; however,

the back-calculated k-value from concrete slab deflection was 285 psi/in, which is

close to the PBT k-value on top of subgrade before improvement. PBT k-value with

larger plate diameter (54 inches) was 315 psi/in, lower than PBT k-value with 36-inch

diameter. Teller and Sutherland (1943) concluded the influence of improved subgrade

tended to disappear with a relatively large loading area. It might depend on the relative

value between loading size and the depth of improved subgrade according to bulbs of

pressure (Terzaghi 1955).


33

Comparing the results from the plate bearing tests on subgrade and on base

layers, Hittle and Goetz (1946) reported that base type and base thickness are two of

the factors influencing load-carrying capacity of base-subgrade combinations. Campen

and Smith (1947) also found load carrying values increase with increasing base

material thickness, based on PBT tests at several airports in Nebraska and Iowa.

McLeod (1948) reported similar results based on PBT tests on natural subgrade,

granular base, and bituminous surface at several Canadian airports. Those and other

researches made similar findings that base material properties and thickness are two

important factors for subgrade k-value improvement (Darter et al. 1995).

According to the information from Ahlvin (1991)’s report, airfield pavements

were constructed on natural subgrades in the 1940s. In the early 1950s, base layer was

introduced only for pumping prevention without considering its structural advantage,

which is consistent with previous field test findings. In the late 1950s, the Corps of

Engineers included plate bearing tests on top of base in its design, and developed

curves to predict k-value on base with known k-value on subgrade and base thickness.

The Corps of Engineers did not compare PBT k-value on base with back-calculated k-

values from deflection tests on full-size concrete slab (Ahlvin 1991).

A series of experiments, including full-size concrete slabs and PBT tests on top

of different pavement structure layers, were conducted in the laboratory by Portland

Cement Association (PCA) in the 1960s (Childs 1967; Childs and Kapernick 1963;

Nussbaum and Larsen 1965). Untreated granular bases and cement-treated bases can

increase PBT k-value significantly as shown in Figure 3.6.


34

Figure 3.6 Results of PCA plate tests on granular and cement-treated bases (Childs 1967)

The improvement of PBT k-value on a different base is a function of base

properties and base thickness. Curves for determining k-values on top of base were

developed based on PCA laboratory test results and used in the PCA concrete airport

pavement design manual 1973. The curves are shown in Figure 3.7.


35

Figure 3.7 Base k curves from 1973 PCA airport pavement design manual (Packard 1973).

Based on the results from deflection of the full-size concrete slab, Childs (1967)

pointed out that k-value improved by base layer does decrease maximum deflection at

the edge and interior, and has less effect on pavement thickness design. However,

back-calculated k-values from full-size slab deflection were not reported in PCA

studies.

k-values were back-calculated by using full size slab deflection data and elastic

modulus of concrete slabs reported by Childs (1967). The results show back-

calculated k-values from concrete slab deflection are close to PBT k-value on subgrade

and much less than PBT k-values on base. However, base layer may reduce stress in

concrete slabs because it can decrease maximum deflection significantly (Darter et al.

1995).


36

In general, a stiff layer between natural subgrade and pavement slab can

increase the PBT k-values; however it has less effect on back-calculated k-values from

concrete slab deflection.

3.1.2.3 Effect of subgrade condition on k-value.

In k-value studies in the Arlington road tests, lower summer moisture content

corresponded to an increase in PBT k-values (Teller and Sutherland 1943). Trends of

decreasing k-value with increasing subgrade moisture content were found in the

AASHO Road Test between 1958 and 1960. No correlation between k-value and

subgrade dry density were quantified; however, a good trend of increasing k-value

with decreasing percent saturation were observed. Degree of saturation S was defined

as below and incorporated in MEPDG (ARA Inc. ERES Consultants Division 2004).

𝑆 =𝑤

�𝐺𝑠 ∙ 𝑟𝑤𝑟𝑑𝑟𝑦− 1�

= 𝐺𝑠𝑤𝑒

where S = degree of saturation

Gs = specific gravity

w = moisture content

𝑟𝑤 = unit weight of water

𝑟𝑑𝑟𝑦 = dry unite weight

e = void ratio

Relationships between subgrade k-values and degree of saturation were

developed for different soil types with AASHTO classification based on field and

laboratory tests, and incorporated in the concrete pavement design in 1977 Zero

Maintenance study (Darter 1977; Darter and Barenberg 1977; Thompson and Robnett

1976). Those relationships are shown in Figures 3.8 and 3.9.


37

Figure 3.8 k values for fine-grained AASHTO soil classes and degree of saturation (Darter and Barenberg 1977).


38

Figure 3.9 k values for coarse-grained AASHTO soil classes and degree of saturation (Darter and Barenberg 1977).

For all soil types, modulus of subgrade reaction k-value decreases with

increasing degree of saturation of soil.

Due to different vertical stress levels between laboratory tests for resilient

modulus MR and in situ subgrade soil under pavement slab and base, laboratory

measured resilient modulus MR should be different compared to in situ subgrade soil

modulus (Darter et al. 1995). The AASHTO 1986 Guide simply considered resilient

modulus MR equal to in situ subgrade soil modulus. State of stress was taken into

consideration for modulus changes prediction in MEPDG (ARA Inc. ERES

Consultants Division 2004).


39

3.1.2.4 Dynamic k-value and Static k-value

Three types of solutions were developed for back-calculating modulus of

subgrade reaction k-value for concrete pavement. (1) Iowa Road Rater method, (2)

solutions based on AREA concept, and (3) other solutions for radius of relative

stiffness back-calculation (Darter et al. 1995).

The Iowa Road Rater method was developed by the Iowa Department of

Transportation in the 1980s for correlating springtime static PBT k-values with Road

Rater deflection basin parameters (Potter and Dirks 1989). The relationship was

developed by comparing several years’ springtime Road Rater deflection data with

static k-values from PBT testing. It only represents the springtime conditions and

cannot be widely used.

In order to provide more information than the maximum deflection and

minimize the effect of possible sensor malfunction, the parameter “AREA” of the

deflection basin was first proposed by Hoffman and Thompson (1981) for flexible

pavement evaluation. The deflection basin “AREA” is a function of sensor deflection

with the units of length and was defined as:

AREA = 6 + 12 �d12d0� + 12 �

d24d0� + 6 �

d36d0�

where, di = deflection in mils at 9,000 lbs at distance i inches from the loading plate

AREA thus determined is a non-dimensional parameter, which is determined

by the shape of the deflection bowl. Accordingly, AREA and maximum deflection d0

are two independent parameters. With known AREA and maximum deflection d0, a

model with two parameters can be characterized.

Hoffman and Thompson (1981) compared the deflections on flexible pavement

caused by static loading from the Benkelman Beam test, vibratory loading from Road

Rater, and impulse loading from Falling Weight Deflectometer (FWD), and found that


40

deflections caused by static loading were 2 to 10 times larger than deflections caused

by dynamic loading.

Finite element program ILLI-SLAB was used to develop the relationships

between deflection profile on concrete pavement and two pavement structure

parameters (k-value and concrete modulus) (ERES Consultants Inc. 1982). With the

known relationship, k-value and concrete modulus can be back-calculated from FWD

deflection data on concrete slab. Foxworthy (1985) back-calculated k-value and

concrete modulus from FWD data at several U.S. Air Force bases and compared them

with the results from PBT and laboratory concrete modulus test. Back-calculated

dynamic k-values exceeded PBT static k-values by an average ratio of 2.7 (ranging

from 1.6 to 4.4) as shown in Figure 3.10.

Figure 3.10 Relationship of backcalculated k value to static k value (Foxworthy 1985).

Ioannides (1990) stated that there is a unique relationship between AREA and

the radius of relative stiffness 𝑙. Hall (1991) calculated the deflections of a PCC slab

on a dense liquid foundation given by Losberg (1960) at the radial distance of 0, 12,

24, and 36 inches with radius of relative stiffness 𝑙 values from 15 to 80 by using a

numerical computing application. AREA values were calculated by using the


41

computed deflections and the relationship with radius of relative stiffness 𝑙 was

obtained by using SAS statistical analysis software. A simple equation for 𝑙 versus

AREA was presented for approximation.

Radius of relative stiffness 𝑙 = �𝑙𝑛 �36 − 𝐴𝑅𝐸𝐴

1812.279 �−2.559

�

4.387

Once the radius of relative stiffness is determined, dynamic k-value is

estimated as follows (Ioannides et al. 1989):

𝑘 = �d0D0� �

P 𝑙2�

where, P is load magnitude [lbs]; d0 denotes non-dimensional sensor deflections

corresponding to the measured deflection D0:

d0 = D0DP 𝑙2

= D0𝑘 𝑙2

P

where, D is the slab flexural stiffness, given by

D = Eh3

12(1 − u2)

where, E is concrete modulus of elasticity [psi]; h is PCC slab thickness [in.]; u is

concrete Poisson’s ratio.

The above equations for k indicate that back-calculated k-values depend on the

radius of relative stiffness, maximum deflection value corresponding to applied

loading, and a non-dimensional parameter that is related to Westergaard’s deflection

in the interior condition. The non-dimensional parameter d0 is a function of the radius

of relative stiffness, and the value is almost constant, between 0.121 and 0.124, for

practical ranges of the radius of relative stiffness. Since the maximum deflection for a

given pavement structure is proportional to the applied loading, from a practical

standpoint, two variables – maximum deflection and the radius of relative stiffness –


42

determine the back-calculated k-values. The larger the maximum deflection or the

radius of relative stiffness, the smaller the k-value.

Barenberg and Ratterree (1979) found the mean static k-value on the silty clay

subgrade is 73 psi/in at the University of Illinois’ Willard Airport in Savoy, Illinois.

FWD testing was conducted on several pavements with different thicknesses in 1992,

as shown in Table 3.2. Back-calculated dynamic k-values were compared with the

static k-value obtained by Barenberg and Ratterree (1979).

Table 3.2 Back-calculation results for concrete pavements and concrete overlays at Willard Airport (Darter et al. 1995).


43

For thinner pavements, with thicknesses between 8 and 9 in, the mean back-

calculated k-value is 148 psi/in. Dividing by two yields an estimated static k-value

equal to the PBT static k-value (Darter et al. 1995).

Equations for back-calculation of subgrade k-value and concrete modulus

proposed by Hall (1991) were incorporated in the AASHTO Guide 1993 (American

Association of State Highway and Transportation Officials 1993). Back-calculated k-

value was suggested to be divided by two to get a subgrade PBT static k-value for

pavement design. Two reasons were proposed for using a factor of two to convert

back-calculated dynamic k-value to PBT static k-value for pavement design (Darter et

al. 1995).

1. This produced reasonable values in many cases based on field data.

2. It is difficult to suggest a more advance method for conversion because of the

complexities of modeling material dynamic behavior.

3.1.2.5 Limitation of AREA back-calculated method

The AREA method is a two-layer solution with the ability to back-calculate

subgrade k-value and modulus of elasticity of a concrete slab based on deflection of an

infinite slab. Research indicates that the base layer effect on back-calculated k-value is

insignificant. The use of base layer usually increases the apparent back-calculated

modulus of elasticity of concrete pavement (Ioannides and Khazanovich 1994).

Analysis of LTPP deflection data also obtained the same conclusion as previous

researches (Darter et al. 1995).

The limitation of AREA back-calculated method is caused by the plate theory

assumptions that pure bending of a concrete slab and the base layer. The study of a

model slab and base as elastic layers on dense liquid foundation with k-value was

suggested for future work (Darter et al. 1995).


44

3. 2 Erosion

3.2.1 Erosion Mechanism

According to studies by state highway departments and Portland Cement

Association in the 1930s and 1940s and further experience, the basic factors that

caused pumping to occur were determined as below (American Concrete Pavement

Association (ACPA) 2007):

• Heavy and fast moving loads.

• Joint with no dowel or poor load transfer efficiency.

• Presence of water.

• Erodible subbase or base material.

Van Wijk (1985) proposed the pumping modeling by simulating a flat stiff

plate rotating around an axis as shown in Figure 3.11. It can represent the movement

of a slab near the joint when traffic loading moves onto the slab.

Figure 3.11 Movement of water under the slab (Van Wijk 1985)


45

According to theoretical equations, laboratory and in-situ observations, Phu

and Ray (1979) developed the guideline for evaluating water velocities and shear

stresses due to traffic loading. The effects of deflection velocity and void thickness on

water velocity and shear stress are shown in Figures 3.12 and 3.13. Water velocity and

shear stress increase with increasing deflection velocity. The maximum water velocity

and corresponding shear stress were assumed to occur in the “transition zone” with a

void thickness of about 0.04 in. Shear stress and water velocity decrease dramatically

when void thickness is larger than 0.04 in.

Figure 3.12 Effect of void size and velocity of slab deflection on the average water velocity (Phu and Ray 1979)


46

Figure 3.13 Effect of void size and velocity of slab deflection on the shear stress (Phu and Ray 1979)

As shown in Figure 3.14, Jung et al. (2009) presented the schematic view of

stress distribution generated by moving traffic loading and stated that the unbound

material will separate once the shear stress caused by traffic loading exceeds the

material shear strength.


47

Figure 3.14 Shear stress induced erosion (Jung et al. 2009)

Van Wijk and Lovell (1986) conducted a series of laboratory tests and

presented the way to minimize erosion from material properties aspect. The content of

Portland cement and asphalt is an important factor in erodibility of cement stabilized

material and asphalt stabilized material, respectively. The compaction effort and base

material gradation have a large effect on base erodibility. Environmental factors such

as wetting and drying, freezing and thawing play an important role as well in erosion

development.

3.2.2 Erosion Models

Predicting erosion is a challenge since erosion is controlled by a number of

factors as follows:

1. The presence of water;

2. The erodibility of a subbase material;

3. The rate of water ejection;


48

4. The amount of slab deflection;

5. The number of load applications.

Several empirical models were presented in the literature for erosion prediction

by considering some of the factors listed above (Van Wijk 1985).

3.2.2.1 RAUHUT, 1982

Rauhut developed an empirical model based on nonlinear regression analysis

of a concrete pavement evaluation system database. The parameter level of pumping

damage 𝑔 was used for erosion evaluation and correlated with traffic, drainage,

precipitation, load transfer, subbase type, foundation soil type, Thornthwaite moisture

index, freezing index, foundation soil California bearing ratio (CBR), and slab

thickness. Different equations were developed for jointed plain concrete pavement

(JPCP) and jointed reinforced concrete pavement (JRCP).

𝑔 = �𝐸𝑆𝐴𝐿𝜌

�𝛽

JPCP

𝑙𝑛𝜌 = 1.39 × 𝐷𝑅𝐴𝐼𝑁 + 4.13

𝛽 = 0.772 × (𝐷 − 2.3)1.61

𝑃𝑃𝑇𝑁+ 0.0157 × 𝐽𝐿𝑇𝑆 × 𝐷 + 0.104 × 𝑆𝑇𝐴𝐵 + 0.17

× 𝐷𝑅𝐴𝐼𝑁 + 0.137 × 𝑆𝑂𝐼𝐿𝑇𝑌𝑃 − 0.247

JRCP

𝑙𝑛𝜌 = 1.028 × 𝑆𝑇𝐴𝐵 + 0.0004966 × 𝐷3.47 − 0.01248 × 𝐹𝑅𝐼𝑁𝐷𝐸𝑋 + 1.667

× 𝐶𝐵𝑅 + 5.476

𝛽 = −0.01363 × 𝐷𝑀𝑂𝐼𝑆𝑇 + 0.02527 × 𝐷 − 0.423

where: g = amount of distress as a fraction of a pumping level of 3 (severe)

DRAIN = 0; no underdrains, 1; underdrains

PPTN = average annual precipitation (cm)


49

JLTS = 0; undoweled, 1; doweled

STAB = 0; unstabilized subbase, 1; stabilized subbase

SOILTYP =0; granular foundation soil, 1; coarse foundation soil

DMOIST = Thornthwaite moisture index

FRINDEX = freezing index

CBR = California bearing ratio of foundation soil

D = slab thickness (in)

3.2.2.2 MARKOWL, 1984

This empirical model is based on the AASHO Road Test results; the erosion

evaluation parameter is pumping index 𝑃𝑖which indicated the potential for erosion.

Pumping index was defined as the pumped material volume per unit length of the

pavement (cubic inches per inch). The pumping index was related with slab thickness,

traffic, drainage, and subbase permeability.

𝑃𝑖 = 𝑚 × �𝐸𝑆𝐴𝐿 × 𝑓𝑑

𝑙𝑜𝑔𝑚 = 1.07 − 0.34𝐷

where: 𝑃𝑖 = pumping index

𝐷 = slab thickness (in.)

𝐸𝑆𝐴𝐿 = equivalent 80 kN (18,000 lb) single axle loads

𝑓𝑑 = drainage adjustment factor

= 0.2 for good drainage (k = 10,000 ft/day)

= 0.6 for fair drainage (k = 100 ft/day)

= 1.0 for poor drainage (k = 0.1 ft/day)

k = subbase permeability


50

According to the pumping index equation, the potential for erosion increases

with decreasing drainage ability and cumulative ESAL. It decreases significantly with

increased slab thickness.

3.2.2.3 LARRALDE, 1984

This empirical model is based on the AASHO Road Test data, and normalized

pumping index (𝑁𝑃𝐼) was proposed for erosion evaluation. 𝑁𝑃𝐼 is only related to the

amount of deformation energy and traffic, and eliminates slab size and reinforcement

effects. The relation between deformation energy and slab thickness was developed by

using finite element modeling.

𝑁𝑃𝐼 = 𝑒𝑥𝑝 �−2.884 + 1.652 × 𝑙𝑜𝑔 �∑𝐸𝑆𝐴𝐿 × 𝐷𝐸

10,000��

where: 𝑁𝑃𝐼 = normalized pumping index of volume of pumped material (in3)

𝐸𝑆𝐴𝐿 = equivalent 80 kN (18,000 lb) single axle loads

𝐷𝐸 = deformation energy per one application of ESAL = log (DE) =

3.5754-0.3323D

D = slab thickness (in.)

3.2.2.4 VAN WIJK, 1985

This is a modified Larralde 1984 model since the Larralde model fits the

AASHO Road Test data better than others. More factors were taken into consideration

such as subbase type, drainage, load transfer, climates, and subgrade type. The volume

of erosion material 𝑃 was defined as below:

𝑃 = 36.67 × 𝐹 × 𝑁𝑃𝐼

where: 𝑃 = volume of pumped material (ft3/mile)

𝑁𝑃𝐼 = normalized pumping index of volume of pumped material (in3) (same as in Larralde 1984 model)


51

𝐹 = fJPCP if nonreinforced PCC, fJRCP if reinforced PCC fJPCP = fsbl · fd · flt · fprec · fsg

fsbl = subbase adjustment factor

1; unstabilized,

0.65+0.18 log(ΣESAL); stabilized

fd = drainage adjustment factor

1; poor drainage,

0.91+0.12 log(ΣESAL)-0.03D; fair drainage,

0.68+0.15 log(ΣESAL)-0.04D; good drainage,

0.01; excellent drainage

flt = load transfer adequacy adjustment factor

1; with dowel,

1.17-0.68 log(ΣESAL)-0.078D; without dowel

fprec = rainfall adjustment factor

0.89+0.26 log(ΣESAL)-0.07D; dry climates

0.96+0.06 log(ΣESAL)+0.02D; wet climates

fsg = subgrade adjustment factor

1; granular subgrades,

0.57+0.21 log(ΣESAL); coarse subgrade

fJRCP = fsb2 · fe

fsb2 = subbase adjustment factor

1; unstabilized,

0.91-0.02 log(ΣESAL); stabilized

fe = adjustment for climate

0.011+0.003 log(ΣESAL)-0.001D; dry, warm climates,

1.44-0.03 log(ΣESAL)-0.06D; wet, warm climates,

1.04-0.32 log(ΣESAL)-0.08D; dry, cold climates,

0.54-0.85 log(ΣESAL)-0.19D; wet, cold climates


52

3.2.2.5 JEONG and ZOLLINGER, 2003

The empirical models mentioned above are limited in nature and can only

generate reasonable results within the range of database data. A mechanistic-empirical

erosion model was developed by accommodating the water-induced shear stress (Jung

et al. 2009). According to this erosion mechanism, shear stress level depends on traffic

loading speed and void thickness (Phu and Ray 1979). Traffic loading and speed, load

transfer, and climate were included in this mechanistic-empirical model as key factors.

Erosion depth 𝑣 was the parameter for erosion evaluation.

𝑣 = 𝑣0𝑒−� 𝜌𝑁𝑖

�𝑎

where: 𝑣0 = ultimate erosion depth (L)

𝑁 = number of axle loads per load group

𝜌 = calibration coefficient based on local performance

𝑎 = 𝑎′𝛼𝑓

𝑎′ = environmental calibration coefficient

𝛼𝑓 = inverse of the rate of void development

= �𝜕𝑣𝑖𝜕𝑡�−1

= �𝐿𝑜𝑔−1(𝑎𝑚𝜏+𝑏𝑚)

𝛾𝑏�−1

= � 𝛽𝛾𝑏�−1

𝜏 = shear stress = ηB𝛿𝑣𝑜𝑖𝑑

�1 − 𝐿𝑇𝐸100

�

η = dynamic viscosity of water (FL-2t)

= �2056.82 + 10.65𝑇 − 248.93√𝑇 − 265.02𝑒−𝑇�10−6

𝑇 = water temperature (C)

B = 𝑉𝑧𝑖𝑠𝑖𝑛𝜃 + 6𝑉𝑧𝑖 �𝑠𝑖𝑛𝜃2

+ 𝑐𝑜𝑠2𝜃𝑠𝑖𝑛𝜃

� (𝐿/𝑡)

𝛿𝑣𝑜𝑖𝑑 = void space below slab for water movement

𝜃 = slab angle = 𝑡𝑎𝑛−1 �𝑍0𝑆�

𝑍0 = edge gap (L) = (1+𝑣)𝐻

Δ𝜀𝑡𝑜𝑡𝑙2

𝑉𝑧𝑖 = 𝛿𝑖𝑛𝑡𝑆𝑉𝑖�


53

𝛿𝑖𝑛𝑡 = 𝑃𝑖8𝑘𝑙

�1 + �0.3665𝑙𝑜𝑔 �𝑎𝐿𝑙� − 0.2174 �𝑎𝐿

𝑙�2��

𝑎𝐿 = loaded radius (L)

𝑃𝑖 = axle load (F)

𝑆 = slab liftoff distance (L) = √2𝑙(𝛾 − 1)

𝛾 = �𝑍0𝑤0

𝑤0 = 𝜌𝐻𝑘

Accurate model calibration was suggested by the authors since it is a

mechanistic-empirical erosion model.

It should be recognized that voids of any depths greater than a certain small

value will have similar detrimental effects on rigid pavement behavior and

performance. It is not only the depths of voids, but the size as well that have

substantial effects on rigid pavement performance. For example, the effects of voids

limited to a substantially small area on rigid pavement performance might be quite

limited. On the other hand, voids in a large area, even though the void depth is not

substantial, could cause distresses and performance issues. Accordingly, it is not just

the amount of pumped material, but the combination of void depth and area that are

critical to rigid pavement performance. Predicting both void depth and area is a real

challenge. The models discussed so far only predict pumping material volumes or

erosion depth. Considering the complex nature of erosion and the difficulty to predict

erosion depth and area, it would be more practical to specify the quality of base

materials to resist erosion and not to include the erosion aspect in the pavement design

process. One of the justifications for this approach is that simply increasing slab

thickness to counter the erosion effect is not the most cost-effective design approach.

However, it would be insightful to review how the current rigid pavement design

procedures take erosion effect into rigid pavement designs.


54

3.2.3 Erosion in Rigid Pavement Design

3.2.3.1 AASHTO 1993

In the AASSHTO 1993 Guide, loss of support (LS) is utilized in rigid

pavement design to account for the potential loss of support by adjusting the

composite k-value. Suggested loss of support values were given to different material

types as shown in Table 3.3. The AASHTO 1993 Guide suggests that agency’s

experience in this area should be the key element in LS determination.

Table 3.3 Typical Ranges of Loss of Support (LS) Factors for Various Types of Material (McCullough and Elkins 1979)

Type of Material Loss of Support (LS) Cement Treated Granular Base (E=1,000,000 to 2,000,000 psi) 0.0 to 0.1

Cement Aggregate Mixtures (E=500,000 to 1,000,000 psi) 0.0 to 0.1

Asphalt Treated Base (E=350,000 to 2,000,000 psi) 0.0 to 0.1

Bituminous Stabilized Mixtures (E=40,000 to 300,000 psi) 0.0 to 0.1

Lime Stabilized (E=20,000 to 70,000 psi) 1.0 to 3.0

Unbound Granular Materials (E=15,000 to 45,000 psi) 1.0 to 3.0

Fine Grained or Natural Subgrade Materials (E=3000 to 40,000 psi) 2.0 to 3.0

As discussed above, modulus of subgrade reaction is adjusted in accordance

with the nomograph as shown in Figure 3.15. Figure 3.15 shows a significant effect of

LS on modulus of subgrade reaction. For example, for the composite k-value of 540

psi/in, LS of 1.0 reduces the value to 170 psi/in, which is less than one-third of the

original composite k-value. On the other hand, the range of suggested LS values for

both cement and asphalt stabilized bases varies between 0 and 1. When cement or

asphalt stabilized bases are used, users are forced to select a number between 0 and 1,

which will have substantial effects on k-value to be used in the design. For other base

types, the situation is worse, with LS values varying from 1 to 3. In the previous


55

numerical example, k value is reduced from 170 psi/in to less than 10 psi/in, when LS

value is increased from 1 to 3.

Figure 3.15 Correction of Effective Modulus of Subgrade Reaction for Potential Loss of Support (McCullough and Elkins 1979)

This nomograh was developed using the SLAB-49 discrete element program.

Slab and void conditions selected for the modeling and analysis are shown in Figure

3.16. Void areas and shape near transverse crack were defined corresponding to

different LS factors based on experience and engineering judgment. Stresses and

deflections were analyzed when traffic loads were applied directly on top of a

transverse crack with a void underneath. Original k-value with a given void size was


56

converted to a lower corrected full support k-value by matching the same slab

response in terms of concrete stresses.

Figure 3.16 Typical Ranges of Loss of Support (LS) Factors for various Types of Material (American Association of State Highway and Transportation Officials 1986)


57

3.2.3.2 MEPDG

In the MEPDG, erodibility index EROD was introduced to evaluate erosion

potential of base and subbase material. Materials descriptions corresponding to five

erodibility indexes are shown in Table 3.4. This erodibility classification was

obtaioned by modifying the original Permanent International Association of Road

Congresses (PIARC).

Table 3.4 Recommendations for erosion potential of base/subbase material (ARA Inc. ERES Consultants Division 2004)

EROD Material Description

1 Lean concrete with 8 percent cement; asphalt concrete with 6 percent asphalt cement, or a permeable drainage layer.

2 Cement treated granular material with 5 percent cement manufactured in plant; asphalt treated granular material with 4 percent asphalt cement.

3 Cement-treated granular material with 3.5 percent cement manufactured in plant; asphalt treated granular material with 3 percent asphalt cement.

4 Granular material treated in place with 2.5 percent cement, treated soils. 5 Untreated granular material.

Voids due to erosion were characterized by width of eroded base/subbase,

measured inward from the slab edge. Monthly rate of base erosion from the slab edge

can be estimated by known precipitation, erodibility index and subgrade gradation as

follows.

𝑅𝐸𝑖 = (−0.37 + 0.0171𝑃200 + 0.0779𝐸𝑅𝑂𝐷 + 0.0117𝑃𝑅𝐸𝐶𝐼𝑃)/12

where: REi = monthly rate of base erosion from the slab edge, in/month

P200 = percent subgrade passing the no.200 sieve

EROD = erodibility index

PRECIP = mean annual precipitation, inch.

No model, procedure, and field data were available for establishing a relation

between so many factors and erosion. The erosion width prediction model as shown in

the equation above is an empirical model and based on expert opinion. It was

incorporated into the punchout model by affecting total bending stress at the critical

point (ARA Inc. ERES Consultants Division 2004).


58

3.3 Current Practice

3.3.1 AASHTO 1993 Approach

3.3.1.1 k-value versus MR

The AASHTO 1993 Guide has only one volume, and uses the same Volume 2

as the AASHTO 1986 Guide.

The relationship between modulus of subgrade reaction k-value and roadbed

soil resilient modulus 𝑀𝑅 was developed by using an elastic layer computer program.

𝑘 − 𝑣𝑎𝑙𝑢𝑒 = 𝑀𝑅

19.4

A plate bearing test was simulated on top of elastic half-space with 30-inch

diameter circular load and 10 psi pressure. The elastic layer’s modulus E ranged from

1,000 psi to 50,000 psi, with the same Poisson’s ratio 0.45. k-value was calculated by

plate load P divided by deflection volume V within the load plate as shown an

equation below, instead of pressure divided by deflection, since rigid plate loading

cannot be simulated in an elastic layer program.

𝑘 =𝑃𝑉

where: P = plate loading (LBs)

V = defected volume within the radius of the load plate

Figure 3.17 shows the plate bearing testing simulation and the way to calculate

k-value by using deflection volume.


59

Figure 3.17 Plate bearing test simulation on top of elastic layer (American Association of State Highway and Transportation Officials 1986)

To independently derive the relationship between k-value and soil resilient

modulus, finite element analysis was performed with an axis-symmetric 2D analysis

by using DIANA software, which is a well-proven and tested software package on

various landmark projects. Geometry, boundary conditions and initial stresses have a

rotational symmetry around a central axis. Displacements in the circumferential

direction are considered to be zero. For the sake of simplicity, soil is assumed to be

linearly elastic half space and isotropic. The linear elastic model requires two elastic

parameters E and ν. The radius and height are 5D (D = plate diameter) (Azizi 2000;

Desai and Christian 1977). Eight-node quadrilateral isoparametric plate bending

elements with quadratic interpolation were used to define the finite element mesh

shown in Figure 3.18. The sizes of element were reduced for refinement near the

loaded area.


60

Figure 3.18 Mesh and geometry for finite element model

For all the nodes along the bottom boundary of the mesh, displacement in the

horizontal and vertical direction are assumed to be zero. Horizontal displacement on

both vertical side boundaries have been assumed to be zero, too. To better understand

the load size effect, circular load with different radii (9in, 12in, 18in, 24in, 36in and

48in.) were used for analysis, with a Poisson’s ratio ν = 0.45 and E ranging from 1000

to 50,000 psi. k-value was computed following Appendix HH of the 1986 AASHTO

(American Association of State Highway and Transportation Officials 1986).

Soil deflection shape under circular loading and the nodes deflection are shown

in Figures 3.19 and 3.20.


61

Figure 3.19 Soil deflection contours

Figure 3.20 Nodes deflection in Soil FEM model

According to elastic theory and FEM results, k-value is independent of the load

magnitude. For the same elastic modulus E, k-values calculated based on different


62

plate diameters are different. The relationship between elastic modulus E and k-value

for different plate diameters are shown in Figures 3.21 and 3.22.

Figure 3.21 Elastic Modulus E vs. k-value


63

Figure 3.22 Plate Diameter vs. k-value

Compared with the relationship between k and resilient modulus derived in the

1986 AASHTO Guide, DIANA FEM results, with a plate diameter of 30 inches,

generate a little higher k-value than the AASHTO 1986 equation as shown in Figure

3.23. The reason for the higher value is the limitation of deflected volume V

calculation method, which yields a smaller deflected volume V than the actual value.


64

Figure 3.23 Diana Results vs. AASHTO 1986

With the limitation of deflected volume calculation method, the results would

be somewhat different than the actual k and E relationship. Nevertheless, the results do

serve to demonstrate that k-value is not a unique value for certain soils, and it varies

with the plate diameter.

3.3.1.2 Composite k-value

Composite k-value was defined as a function of subgrade resilient modulus and

the thickness and elastic modulus of the base layer. It can be determined by the

nomograph presented in the AASHTO 1993 Guide, which is the same as in the

AASHTO 1986 Guide as shown in Figure 3.24. k-value that will be used in pavement

design is determined in accordance with the procedure below:

1. Use known seasonal roadbed soil resilient modulus, subbase thickness and

subbase elastic modulus, to determine seasonal composite k-values according

to Figure 3.24.


65

2. As shown in Figure 3.25, modify seasonal composite k-values to take the effect

of rigid foundation into consideration.

Figure 3.24 Nomograph for composite k-value determination (American Association of State Highway and Transportation Officials 1986)


66

Figure 3.25 Modification of k-value to consider rigid foundation effect within 10 ft (American Association of State Highway and Transportation Officials 1986)

1. Estimate the slab thickness and use Figure 3.26 to determine the relative

damage.

2. Average the relative damage and use Figure 3.26 to find the corresponding

effective k-value.

3. Adjust effective k-value to account for potential loss of support (as discussed

in section 3.2.3).


67

Figure 3.26 Relative damage nomograph based on slab thickness and composite k-value (American Association of State Highway and Transportation Officials 1986)

The nomographs Figure 3.24 and 3.25 were developed by simulating a plate

bearing test on top of subbase with elastic layer program ELSYM5, as shown in

Figure 3.27. The circular plate bearing pressure was 10 psi with a 30-inch diameter.


68

For each combination of subgrade MR, subbase ESB, subbase thickness and depth to

rigid foundation, k-value was calculated as pressure divided by maximum deflection at

the center of the circular plate load.

Figure 3.27 Simulated plate load for composite k-value (American Association of State Highway and Transportation Officials 1986)

Five hundred different combinations were analyzed for developing Figure 3.24

and 3.25. Based on results from the elastic layer program, equations for the

relationship between k-values and layers properties were developed using statistical

regression analysis.

Equation for a semi-infinite roadbed soil thickness:

log 𝑘 = −2.807 + 0.1253 × (𝑙𝑜𝑔𝐷𝑆𝐵)2 + 1.062 × 𝑙𝑜𝑔𝑀𝑅 + 0.1282 × 𝑙𝑜𝑔𝐷𝑆𝐵× 𝑙𝑜𝑔𝐸𝑆𝐵 − 0.4114 × 𝑙𝑜𝑔𝐷𝑆𝐵 − 0.0581 × 𝑙𝑜𝑔𝐸𝑆𝐵 − 0.1317 × 𝑙𝑜𝑔𝐷𝑆𝐵× 𝑙𝑜𝑔𝑀𝑅


69

where: 𝑘 = composite modulus of subgrade reaction (assuming a semi-infinite roadbed soil)

𝐷𝑆𝐵 = subbase thickness (in.)

𝐸𝑆𝐵 = subbase elastic modulus (psi)

𝑀𝑅 = roadbed soil elastic (resilient) modulus (psi)

Equation for the effect of rigid foundation near surface:

(log 𝑘)𝑟𝑓 = 5.303 + 0.0710 × 𝑙𝑜𝑔𝐷𝑆𝐺 × 𝑙𝑜𝑔𝑀𝑅 + 1.366 × 𝑙𝑜𝑔𝑘∞ − 0.9187

× 𝑙𝑜𝑔𝐷𝑆𝐺 − 0.6837 × 𝑙𝑜𝑔𝑀𝑅

where: (log 𝑘)𝑟𝑓 = composite k-value considering the effect of rigid foundation near surface.

𝑘 = composite modulus of subgrade reaction (with semi-infinite roadbed soil)

𝐷𝑆𝐺 = depth to rigid foundation (in.)

𝑀𝑅 = roadbed soil elastic (resilient) modulus (psi)

The chart for estimating relative damage to rigid pavements based on slab

thickness and composite k-value, as shown in Figure 3.26, was developed based on the

concept of the same amount of damage. It is derived from the rigid pavement

performance equation (American Association of State Highway and Transportation

Officials 1986), so they have the same limitations.

In the NCHRP 1-30 study, another elastic layer program BISAR was used to

evaluate whether the nomographs in the AASHTO 1993 Guide yield a reasonable k-

value (Darter et al. 1995). In the elastic layer program simulation, concrete slab was

defined as an infinite elastic layer. As in the FWD field data collection, static load

with a magnitude of 9000 lbs and radius of 5.9 in. was modeled on top of concrete

layer. Dynamic k-value was back-calculated using the method described in Part 3 of

AASHTO 1993 Guide, which is the AREA back-calculation method. As shown in

Figure 3.28, the relation between subgrade elastic modulus and back-calculated k-

value was compared with equation k = MR/19.4 in the AASHTO 1993 guide.


70

Figure 3.28 Comparison of AASHTO k-value equation and back-calculated k-values for unprotected subgrades (Darter et al. 1995).

Several subgrade and base combinations were analyzed, and k-values obtained

from AASHTO 1993 Guide nomographs and back-calculated FWD data from BISAR

were compared. According to the comparison, the following conclusions were made

(Darter et al. 1995):

• AASHTO 1993 Guide equation (k = MR/19.4) yields unreasonable high values.

• Nomograph for composite k-value on top of base produces unreasonable high

k-values as well.

• Base layers of typical thickness do not have a significant effect on back-

calculated k-value. It can increase back-calculated apparent slab modulus and

decrease slab bending stresses.


71

It is interesting to note that the relations between k-value and modulus of

subgrade reaction in both the AASHTO 1993 Guide and the analysis conducted by

Darter et al were derived from layer elastic analysis, with the latter utilizing AREA

method, instead of using a maximum deflection value in the former, for k-value

derivations. As discussed by Darter et al, the k-value from the AASHTO 1993 Guide

is unreasonably high, implying that the inclusion of the AREA method is more

reasonable than the use of a maximum deflection in estimating k-value with elastic

layer analysis.

3.3.2 MEPDG Approach

The MEPDG transforms pavement real structure to an equivalent structure

with effective k-value for structural response computations. All layers under the base

course were converted to an effective k-value as shown in Figure 3.29.

Figure 3.29 Structural model for rigid pavement structural response computations (ARA Inc. ERES Consultants Division 2004).

Effective k-values used in MEPDG can be obtained by the following procedure

(ARA Inc. ERES Consultants Division 2004):

1. Assign layer parameters (E and Poisson’s ratio). 2. Using the elastic layer program JULEA, simulate a 9,000-lb Falling Weight

Deflectometer (FWD) load with the plate radius 5.9 in and compute PCC


72

surface deflections at 0, 8, 12, 18, 24, 36, and 60 in. from the center of the load plate.

3. Adjust the subgrade resilient modulus to account for the lowered deviator stress level beneath a PCC slab and base.

4. Using the elastic layer program JULEA, again simulate a 9,000-lb FWD load with the plate radius equal to 5.9 in, and with the recalculated subgrade resilient modulus and subbase moduli.

5. Calculate PCC surface deflections at 0, 8, 12, 18, 24, 36, and 60 in from the center of the load plate.

6. Use the Best Fit method to compute the dynamic modulus of subgrade reaction using the PCC surface deflections.

The effective k-value used in MEPDG is dynamic k-value, which is different

than the k-value used in previous pavement design procedures. Since the effective k-

value was calculated from the JULEA FWD deflection data, it reflected the presence

of bedrock layer.

3.3.3 TxCRCP-ME

Since AASHTO 1993 Guide for rigid pavement was developed based on the

AASHTO JCP (jointed plain concrete pavement) test data, it is not appropriate to use

AASHTO 1993 for CRCP design. TxDOT initiated a research project and developed a

mechanistic empirical (ME) CRCP design program – TxCRDP-ME – for the design of

CRCP (Ha et al. 2011).

The composite k-value on top of base layer was used for pavement structural

analysis in TxCRCP-ME. Composite k-value was defined as a function of subgrade k-

value, base elastic modulus and thickness. The authors mentioned two reasons for this

approach (Ha et al. 2011):

1. Stabilized base layer properties including elastic modulus and Poisson’s ratio

can be measured more easily than those of unbound soil properties.


73

2. Subgrade k-value can be determined from previously well-developed methods

such as FWD back-calculation method, DCP correlation method, or plate

bearing test.

Composite k-value can be obtained by the following equation:

𝑘∞ = −395.7 + 92.3𝑇𝑏 + 0.223𝐸𝑏 + 1.829𝑘𝑠𝑔

where: 𝑘∞ = composite k-value on top of base layer (psi/in)

𝑇𝑏 = base thickness (in)

𝐸𝑏 = base elastic modulus (ksi)

𝑘𝑠𝑔= k-value on top of subgrade (psi/in)

As shown in Figure 3.30, this regression equation was developed by simulating

a plate bearing testing on top of base layer, using a general purpose finite element

analysis computer program, ABAQUS 6.7. Instead of using deflected volume and

maximum deflection at the center of the load plate, composite k-value was obtained by

dividing the plate load pressure by the average vertical deflection of plate center and

edge. So the composite k-value used in TxCRCP-ME is static k-value.


74

Figure 3.30 Plate bearing test simulation and composite k-value computation (Ha et al. 2011).

Independent input variables include thickness and modulus of base layer, and

subgrade k-value. Their ranges are shown in Table 3.5. A total of 180 combinations

were analyzed for composite k-value on top of base. The SPSS computer program was

used to perform regression analysis and generated the composite k-value equation with

R2-value of 85.1%.

Table 3.5 Input variables and values for composite k-value computation (Ha et al. 2011)

Variables Values Thickness of base [in] 2,3,4,5,6

Elastic modulus of base [ksi] 50, 100, 300, 500, 1000, 2000 Subgrade k-value [psi/in] 50, 100, 150, 200, 250, 300


75

3.3.4 Comparison

In general, previous researches include two ways to estimate composite k-value

for pavement design. One is by simulating plate bearing test on top of base and

calculating static k-value by known deflection and corresponding load pressure. The

other way is by simulating FWD on top of pavement and using the deflection basin to

back-calculate dynamic k-value by using the AREA method. Based on these two

different analysis methods, two relationships between unprotected subgrade elastic

modulus and k-value were presented in previous researches as shown in Figure 3.28.

An example based on BISAR elastic layer analysis, which compares different

ways to determine k-value for pavement design, is shown in Figure 3.31.

Figure 3.31 Example of different k-value evaluation methods

A typical combination of base layer and Winkler foundation in TxCRCP-ME

was chosen for analysis and comparison. A 4-inch base layer (E = 500 ksi) on


76

subgrade with a k value of 200 psi/in. was converted to base layer on top of elastic

subgrade layer. The elastic modulus of subgrade was converted from modulus of

subgrade reaction k value of 200 psi/in. In Case #1, the relation between subgrade

modulus MR and k-value obtained from field data, which will be presented in Section

6.1.1, was used. The equation in the AASHTO 1993 guide was used for Case #2. In

Case #3, subgrade elastic modulus was obtained according to Figure 3.28 (Darter et al.

1995).

The first load was modeled on top of the base with 100 psi pressure and 30-

inch diameter, which is the same as in TxCRCP-ME. Static composite k-values were

obtained from known load pressure and the average deflection at the center and edge

of plate. By comparing the composite k-values in the three cases, the relationship

between subgrade k-value and subgrade modulus obtained is more reasonable than in

the AASHTO 1993 guide and NCHRP report 1-30.

In the second load case, load with 9000 lbs and radius of 5.9 in. was modeled

on top of 9 in. PCC slab with an elastic modulus of 4 million psi. Deflection profiles

were recorded, and dynamic k-values were back-calculated based on the AREA

method. Dynamic k-values were much smaller than composite k-values on top of base.

In Case #1, dynamic k-value is 66 psi/in which is lower than ksg value of 200 psi/in.

Simulating FWD dynamic loading by static load in elastic layer program is

questionable. Further analysis will be done section 6.1.4 with real FWD deflection

data on base and PCC presented.


77

CHAPTER 4

SITE CHARACTERIZATION AND PAVEMENT SUPPORT CONDITION

In Chapter 3, it was discussed that various methods for the evaluation of slab

support condition were developed and adopted for different pavement design methods.

At the same time, it was also illustrated that, at this point, there is no consensus among

researchers regarding the technically correct method to evaluate slab support condition

for pavement design purposes. Detailed, in-depth field testing program was conducted

with various base types in order to further investigate the nature of slab support under

rigid pavement slab.

4.1 Test Site Characterization

The test section is located in FM 1938 in the Fort Worth District. The section

is 2.02 mile long, and consists of 9 in. CRCP on various bases as shown in Figure 4.1.

The construction began in May 2011.

Figure 4.1 Test site of FM 1938.


78

Figure 4.2 shows the test section layout. Throughout the project, the top 8 in.

of subgrade was treated with 4 percent Portland cement. The test section was divided

into four subsections and a different base structure was used in each subsection. The

four different base structures were: (1) 2 in. type B asphalt concrete pavement (ACP),

(2) 1 in. type D ACP over 6 in. cement stabilized base (CSB), (3) geotextile over 6 in.

CSB, and (4) 4 in. type B ACP.

Figure 4.2 Test section layout.

At each subsection, 10 test locations were selected for support condition

evaluations, except for in the second subsection, where only five sections were

selected due to the vertical slope of the section. There were two or three phases for

slab support preparations as shown in Figure 4.3. The first phase was to stabilize the

subgrade with cement. The next phase was the placement of asphalt concrete or

cement stabilized base. In the case of cement stabilized base, further placement of

asphalt concrete or non-woven fabric was made on top of cement stabilized base. In

this study, DCP, PBT and FWD testing were conducted at the same locations on top of

different layers as shown in Figure 4.3. DCP testing was conducted at natural subgrade

and cement treated subgrade. PBT testing was conducted on natural and cement

treated subgrade and base. FWD testing was conducted in all layers. All testing was

conducted at the same selected locations.


79

Figure 4.3 Field testing.

4.2 Pavement Support Condition Evaluation

4.2.1 DCP

Dynamic Cone Penetrometer (DCP) testing is widely used in pavement and

subgrade soil evaluation due to its simplicity and economy. The cone penetration

caused by one blow of a 17.6 lb sliding hammer from a height of 22.6 inches is

recorded. The cone has an angle of 30 degrees with a diameter of 0.79 inches. The

DCP test was conducted in accordance with ASTM D 6951-03 as shown in Figure 4.4.


80

Figure 4.4 DCP testing.

Figure 4.5 presents an example of typical measured DCP data. Two different

layers were detected with different penetration resistance (PR) value. Upper layer and

lower layer have PR value of 2.92 and 7.79, respectively. The thickness of each layer

can be obtained from Figure 4.5.

Figure 4.5 DCP testing.


81

Over the years, a substantial amount of research work has been conducted to

develop empirical correlations between DCP penetration resistance and resilient

modulus. In this study, correlations developed by the Army Corps of Engineers were

followed. The following conversion equations were used for California Bearing Ratio

(CBR) and elastic modulus (E) (Texas Department of Transportation (TxDOT) 2011)

from DCP data.

CBR = 292/PR1.12 E = 2550 × CBR0.64

where PR = penetration rate (mm per blow)

In order to develop more accurate comparisons of the support conditions from

DCP and PBT, the DCP test locations were chosen close to each plate bearing test

location. When a bound layer is above the non-bound layers, a 7/8-inch hole was

drilled through the bound layers before the DCP test, as shown in Figure 4.6.

Figure 4.6 DCP test after placement of stabilized base.

4.2.2 FWD

TxDOT’s Dynatest 8000 FWD unit, with a 5.9-inch radius loading plate, was

used for deflection data collection in this study. Seven geophones were spaced at 0, 12,

24, 36, 48, 60, and 72 inches from the center of the loading plate, as shown in Figure

4.7. In each testing, four loading drops corresponding to approximately 6,000, 9,000,


82

12,000, and 16,000 lb of loading were made after two seating drops. FWD testing was

conducted on top of subgrade, base and CRCP. Normalized FWD deflections on top of

subgrade and base were used for support condition evaluation directly.

Figure 4.7 FWD testing.

Figure 4.8 shows an example of normalized FWD deflection basin on top of

each pavement structure layer at the same test location. It shows the effect of base on

the reduction in maximum deflection is significant.


83

Figure 4.8 FWD data on top of each layer.

As presented in the section 3.1.2, AREA method A4 (Hall 1991; Hall et al.

1997) was used to analyze FWD deflection data on top of CRCP for the evaluation of

pavement support condition. Back-calculated dynamic k-values need to be reduced by

a factor of approximately two for use in pavement design as static elastic k-value (Hall

1991).

4.2.3 PBT

Plate bearing test (PBT) evaluates the stiffness of subgrade soil in either

compacted condition or the natural state. In this testing, a steel bearing plate was

pressed into the surface by a hydraulic jack. The surface deflection and load level were

measured by linear variable differential transformers (LVDTs) and load cell,

respectively, and recorded automatically. PBT was conducted in accordance with

ASTM D 1196-93 (ASTM 2004), as shown in Figure 4.9. Figure 4.10 presents PBT


84

results with high, medium and low PBT k-values. Stiffer support condition with a

larger k-value needs higher load pressure to achieve the same deflection.

The modulus of subgrade reaction (k-value) can be determined by the equation

below:

𝑘 = 𝑝/𝑆 where, p = contact pressure, S = settlement of the loading area.

Figure 4.9 Plate bearing test setup at field.


85

Figure 4.10 Typical plate bearing test data.

According to ASTM D 1196-93, the diameters of bearing plates should range

from 6 to 30 in. In this study, a 12 in. diameter bearing plate was used because the

PBT with the 30-in. bearing plate would require a truck with quite heavy loading,

which was not available. The k-value obtained from the PBT with the 12-in. plate was

converted to the k-value with the 30-in. plate by dividing by two (Teller and

Sutherland 1943).

Load was applied at a moderately rapid rate in uniform increments. A

sufficient number of load-settlement points (more than six) should be made to develop

accurate load-settlement curves by controlling the magnitude of each load increment.

Load intensity and corresponding settlement were plotted for modulus of subgrade

reaction calculation at the point with 0.05 in. deflection (Texas Department of

Transportation (TxDOT) 2012).


86

4.3 Pavement Support Results At each section, 10 test locations were selected for support condition

evaluations, except for the second section where only five locations were selected due

to the vertical slope of the section. The comparisons of static k-values obtained from

PBT and normalized FWD deflection on the top of CRCP are shown in Figures 4.11-

4.14. In Figure 4.11, at locations P5, P6, and P10, k-values on top of 2-inch asphalt

stabilized base are smaller than those on cement treated subgrade, which is counter-

intuitive. It is postulated that k-values from PBT are sensitive to localized density of

asphalt, and the densities in these three locations were low. It is also shown that, in

general, there is no good correlation between k-values and deflections on CRCP.

Figure 4.11 Variations in k-value and deflection (1st Section).

Figure 4.12 shows the comparisons between k-values from PBT and AREA

method, as well as deflections on CRCP in the second section. Except for location P3,

k-values from the AREA method are much smaller than those from PBT, which

indicates that PBT is not an appropriate method to evaluate k-values on top of


87

stabilized base. It also shows a decent correlation between k-values from the AREA

method and deflections on CRCP, while a poor correlation was obtained between k-

values from PBT and deflections on CRCP.

Figure 4.12 Variations in k-value and deflection (2nd Section).

Figure 4.13 illustrates k-values and deflections on CRCP in the third section. It

is shown that: (1) no good correlation exists between k-values on top of natural soil

and on top of cement treated subgrade, (2) 4-percent cement treatment of natural

subgrade increased k-value substantially, (3) k-values from the AREA method are

much smaller than those on top of cement-treated subgrade, and (4) a poor correlation

exists between deflections on CRCP and k-values from either method. It should be

noted that nonwoven geotextile was used in this section, and the correlation between

deflections on CRCP and k-values from the AREA method is not as good.


88

Figure 4.13 Variations in k-value and deflection (3rd Section).

Figure 4.14 illustrates k-values and deflections on CRCP in the fourth section.

It is noted that, except for location P8, k-values from the AREA method are larger than

those from PBT on cement-treated subgrade. It is believed that the use of nonwoven

geotextile in the third section resulted in larger deflections on CRCP and lower k-

values from the AREA method.


89

Figure 4.14 Variations in k-value and deflection (4th Section).

4.4 Summary

This chapter focused on the pavement support condition evaluation methods

and the relations between the results obtained from those methods. The findings from

the testing results can be summarized as follows:

1. The Falling Weight Deflectometer and Dynamic Cone Penetrometer data can

be used to evaluate the stiffness of stabilized subbases before concrete paving

commences. FWD and DCP were recommended to be considered for use in

evaluating such subbases in construction projects.

2. No good correlations were observed between k-values from the PBT on cement

treated subgrade and on asphalt stabilized base, which implies that k-values


90

from the PBT are sensitive to the stiffness of the material immediately below

the loading plate.

3. In general, k-values on stabilized base from the AREA method are smaller than

those obtained by the PBT, which indicates that the PBT is valid only on

natural subgrade.

4. When nonwoven fabric is used as base material, the AREA method should not

be used to estimate k-values.

5. No good correlations were observed between deflections on CRCP and k-

values from PBT on natural subgrade or cement treated subgrade. It appears

that the deflections on CRCP are more influenced by the thickness and

stiffness of the base layer. Decent correlations were observed between

deflections on top of base and on top of CRCP.


91

CHAPTER 5

PAVEMENT BEHAVIOR INVESTIGATION

In the previous chapters, it was discussed that base support condition has

substantial effects on pavement responses and performance. In Chapter 4, slab support

conditions for various base courses were evaluated using several non-destructive

methods. In this Chapter, general CRCP behavior in response to environmental

loading for various base support conditions is presented.

5.1 Overview of gage installation locations

Various gages were installed in concrete slabs in the test section described in

the previous chapter and the data downloaded on a periodic basis. Various gages,

including vibrating wire strain gages (VWSGs), relative humidity (RH) sensors,

thermo-couple wires, concrete displacement gages, and steel strain gages (SSGs), were

installed in the slabs to measure in-situ drying and plastic shrinkage, in-situ coefficient

of thermal expansion of concrete (CoTE), concrete strains and displacements in

various directions, and other pertinent parameters of the in-situ concrete and steel.

Figure 5.1 shows an example of how the various gages described above were

installed. Gages installation locations were chosen based on PBT k-values on top of

base as shown in Table 5.1. In order to compare the effect of different support

conditions on CRCP behavior and performance, locations with relatively high and low

k-value were chosen as following: P4 in 2nd section with PBT k-value of 1335 psi/in.,

P8 and P10 in 3rd section with PBT k-value of 2113 and 1448 psi/in., P3 and P4 in 4th

section with PBT k-value of 432 and 1703 psi/in.


92

Figure 5.1 Various gages installation.

Table 5.1 PBT k-value on top of base at each test section.

k-value [psi/in] (PBT on Base) Test Section P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 1st Section 860 1135 1406 1506 1281 1165 1453 1441 1597 1120 - 2nd Section 1564 1569 1076 1335 1675 - - - - - - 3rd Section 2556 2603 2728 2259 3417 1508 2965 2113 2319 1448 1636 4th Section 495 390 432 1703 1202 1241 798 1902 1425 1275 -

5.2 Material Properties

Concrete was placed on August 8, 2011, for the second section and on March

15, 2011, for the fourth section. Testing on concrete materials was conducted for the

evaluation of concrete properties including setting of concrete, concrete workability,

compressive strength, and flexural strength. The concrete mixture design and concrete

properties are summarized in Table 5.2. The water to cement ratios for the 2nd section

and 4th section were 0.36 and 0.37, respectively. Water reducing admixture was added

in both section concrete.


93

Table 5.2 Concrete mixture design and concrete properties.

Unit 2nd Section 4th Section

Cement lb/yd3 300 362

Fly ash lb/yd3 156 155

Water gl/yd3 19.8 23.0

Coarse Aggregate lb/yd3 2106 1965

Fine Aggregate lb/yd3 1197 1194

Air entraining agent oz/yd3 2.50 1.00

Water reducing admixture oz/yd3 27 31

Air content % 4.5 5.0 Slump in 2.0 0.8 Initial setting min 303 402 Final setting min 357 539 28-day compressive strength psi 5280 4629 28-day flexural strength psi 587 625

5.3 Various Gauges and Instrumentation

5.3.1 Total Strain Measurement in Pavement

In-situ concrete strains were measured by the vibrating wire strain gages

(VWSGs) (Geokon Model 4200). Concrete strain was measured and recorded right

after concrete placement. Figure 5.2 shows VWSGs installed at top, middle, and

bottom of CRCP in both the longitudinal and transverse directions. The overall

concrete behavior in CRCP due to environmental loading can be monitored by the set

of VWSGs. Thermistor was included in each VWSG; concrete temperature at gage

location can be measured and recorded at the same time.


94

Figure 5.2 VWSGs at top, middle, and bottom of CRCP in both longitudinal and transverse direction.

Figures 5.3 and 5.4 present an example of concrete strain data obtained from

VWSGs at the longitudinal and transverse directions, respectively. The data shows the

concrete strain variation at top, middle, and bottom during the first 10-days after

concrete was placed. Figure 5.3 shows that longitudinal concrete strains at different

depths vary the same way as concrete temperature varies at the beginning of concrete

placement. Concrete moves in an axial direction without curling behavior. Transverse

crack in CRCP usually occurs when concrete temperature decreases to a certain level.

Figure 5.3 shows that a transverse crack occurred in the morning of March 24, 2011.

At the time a crack occurs, the top concrete strain goes to compression, and bottom

concrete goes to tension. After transverse cracks occur, concrete strain variation

increases significantly at each depth. A curling effect can also be found after cracking.


95

Figure 5.3 Typical measured concrete strain data by VWSGs at longitudinal direction.

In the transverse direction, concrete strains at different depths vary the same

way they vary at the beginning after concrete placement, as shown in Figure 5.4. One

possible reason for this is that VWSGs were installed in the center of the lane, where

concrete volume changes in the transverse direction were restrained.


96

Figure 5.4 Typical measured concrete strain data by VWSGs at transverse direction.

5.3.2 Relative Humidity Measurements in Pavement

Even though relative humidity (RH) in the concrete has little effect on the

behavior of CRCP slab as affected by base stiffness, the information on RH and

resulting drying shrinkage could provide valuable information on the overall behavior

of CRCP. RH sensors were installed at various depths of the slab as shown in Figure

5.5 to evaluate the effect of moisture variation along pavement depth on CRCP

behavior and response. The SHT75 developed by CMOSens® (Figure 5.6) was

selected for field testing. As shown in Figure 5.5, SHT75 was capped by a white

plastic tube and black semi-permeable fabric at the tip to prevent any inaccuracies

caused by direct contact with water. The assembled RH sensor is small and can

monitor localized RH variations.


97

Figure 5.5 RH sensor installed at different depth of CRCP.

Figure 5.6 RH sensor SHT75 (figure courtesy: sensirion.com).

Figure 5.7 presents the typical measured RH variation at different depths three

weeks after concrete placement, which measured from the gages installation plan as

shown in Figure 5.5. RH in concrete varies with the same trend as ambient RH

variation. Comparing to ambient RH variation, RH variations in concrete are much

less and more stable. RH variation and absolute RH value decrease with increasing


98

distance from pavement surface. One exception is at 8.5 in. depth, the possible reason

being that it is close to the base and there is moisture exchange between pavement and

base.

Figure 5.7 Typical measured RH data at field.

5.3.3 Stress-Independent Strain Calculation in Pavement

To measure the concrete strains due to temperature and moisture variation, a

special designed device called non-stress cylinder (NC) was used in the field. The NC

system for measuring thermal strain and drying shrinkage was validated in a study by

Choi et al (2010).

Concrete in NC is separated from outside stress by two components – a white

polyvinyl chloride (PVC) pipe and two yellow plastic caps at the end of PVC pipe, as

shown in Figure 5.8. To prevent any stress caused by restrain inside NC, a piece of

Styrofoam® was attached on the inner side of the yellow plastic caps and a layer of


99

fabric was used to separate concrete inside the NC with PVC pipe. The NC

dimensions are 3.0 in. (diameter) × 9.5 in (length).

Figure 5.8 NC design detail.

The installation of non-stress cylinders (NC) is shown in Figure 5.9. NC

includes “porous non-stress cylinder (PNC)” and “impervious non-stress cylinder

(INC).

Figure 5.9 Non-stress cylinders (NC).

As shown in Figure 5.9, PNC has enough number of holes to allow moisture

exchange with outside concrete. Concrete in INC experience the same temperature

variation as the outside concrete at the same depth. VWSG was embedded in the

center of the concrete specimen in the longitudinal direction to measure the concrete

strain variation in both PNC and INC. Concrete strain variations in PNC are caused by


100

moisture and temperature variations, which can be considered as stress-independent

strain. Concrete strain variations in INC are only affected by temperature variations

since moisture exchange is prevented. The concrete strain difference between PNC

and INC is due to moisture variation.

Figure 5.10 shows a typical data of strain due to environmental loading

measured by the NC system. Concrete drying shrinkage can be obtained from the

concrete strain difference between INC and PNC. It shows that the drying shrinkage is

quite small. The NCs were installed at the mid-depth of the PCC slab, which could

explain low drying shrinkage in concrete.

In-situ coefficient of thermal expansion (CoTE) of concrete was measured by

using concrete strain and temperature data from INC. As shown in Figure 5.11, a

CoTE value of 4.84 microstrain/°F was obtained.

Figure 5.10 Typical stress-independent strain measured by NC system.


101

Figure 5.11 In-situ CoTE.

5.3.4 Warping and Curling Measurements at Pavement Edge

Concrete displacement gages were installed as shown in Figure 5.12. After

concrete placement, the gages were vertically installed on the edge of pavement and

protected by a metal box. Vertical movement at the pavement slab edge was

monitored and recorded continuously after the gage was installed. Vertical movements

represent pavement curling effects. The typical vertical movement at pavement edge

right after gage installation is shown in Figure 5.13. Compared to concrete

temperature, pavement edge vertical movement was better related to the variation of

temperature difference between top and bottom of the slab. With the similar variation

of temperature difference, the pavement edge curls up due to more drying shrinkage

near the pavement surface at early age.


102

Figure 5.12 Concrete displacement gage installation.

Figure 5.13 Typical vertical movement measured by concrete displacement gage.


103

5.3.5 Base Friction Evaluation

Base friction effect on CRCP behavior is not directly related to slab support

condition; however, base friction characteristics will provide valuable information on

overall behavior of CRCP due to environmental loading. As discussed in the previous

chapter, two distinctive base surface types were used in this testing project: Type D

hot mix and non-woven geotextile. The frictional characteristics of those two base

types were evaluated using the concrete prisms as shown in Figure 5.14. VWSGs were

embedded at the bottom of concrete prisms to capture the difference of concrete strain

variation caused by base friction. RH sensors were also installed inside and outside

concrete prisms to monitor RH variations.

Figure 5.14 Concrete prisms for friction evaluation.

Prisms with 4"x4"x7" and 4"x4"x14" with vibrating wire strain gages and RH

sensors embedded were cast on two different subbase types as shown in Figure 5.15.


104

Figure 5.15 Concrete prisms cast at field.

Figure 5.16 shows the concrete strain variations in the concrete prisms on

nonwoven geotextile are much larger than those on Type D hot mix surface. This

difference indicates that the friction on Type D hot mix surface is larger than on

nonwoven geotextile. With less friction, restraints from subbase will be smaller and

concrete prisms can move more freely. Figure 5.17 shows transverse crack spacing

distributions in the second and third sections. Nonwoven geotextile was used in the

third section. Figure 5.17 shows that the portion of crack spacing larger than 10 ft is

greater in the third section than in the second section. Higher restraint caused by

asphalt stabilized base produced a higher stress level in concrete, resulting in more

transverse cracks or cracks with shorter crack spacing.


105

Figure 5.16 Concrete prisms strain.

Figure 5.17 Transverse cracking pattern.


106

5.4 Summary

A set of various gages, including vibrating wire strain gages (VWSGs), relative

humidity (RH) sensors, and concrete displacement gages, were installed in the slabs at

selected test locations. Concrete pavement behavior due to environmental loading

(temperature and moisture variations) was evaluated with various gages. Base

frictional characteristics of two base materials—asphalt and nonwoven geotextile—

were evaluated with concrete prisms. The findings from this chapter can be

summarized as follows:

1. Before transverse cracks occur, concrete at top, middle, and bottom moves the

same way in the longitudinal direction. Once a crack occurs, concrete strain

variation increases significantly. A curling effect can be found in pavement

behavior after a crack developed.

2. Concrete RH value near the pavement surface is the lowest, with large daily

variations several days after concrete placement. RH value increases and the

level of RH variation decreases with increasing depth from the pavement

surface. One exception is RH at 8.5 in., depth which is close to base. RH value

is slight lower than middle depth and 6.0 in. depth. The possible reason is there

is a moisture exchange between pavement concrete and base.

3. Drying shrinkage at the mid-depth of the slab was quite small, which is

consistence with RH data.

4. Pavement edge vertical movement was related to the variation of temperature

difference between top and bottom of the slab. Pavement edge curls up due to

more drying shrinkage near the pavement surface at early age, which is

consistent with RH data.

5. Base friction of the nonwoven geotextile was smaller than that of the asphalt

layer. Smaller friction in the nonwoven geotextile section resulted in larger

transverse crack spacing.


107

CHAPTER 6

DATA ANALYSIS

6.1 Pavement Support Condition

6.1.1 k-values on Natural and Cement Treated Subgrade

The relationship between elastic modulus of natural and cement-treated

subgrade and k-value on CTS layer is illustrated in Figure 6.1 (a). Elastic modulus

values were obtained from DCP testing results, and k-values from PBT on CTS layer.

Data points from two locations were removed, since the thickness of the CTS layer

was less than 6 in in those locations. Data shows a good correlation between the

modulus of CTS and k-value. On the other hand, a rather poor correlation was

observed between the modulus of natural subgrade and k-value on top of CTS layer.

This implies that the stiffness of the material near the surface has more influence on

the k-value. It also illustrates wide variations in CTS modulus values – from 20 ksi to

80 ksi, which implies that the distribution of cement in subgrade soil and/or the

compaction effort was not uniform. The average increase of modulus by cement

treatment was about 30 ksi. During the DCP testing in natural subgrade, it was

observed that there were two distinctive layers with different PR values. Figure 6.1 (b)

shows the correlation between elastic modulus at upper and lower layers of the natural

subgrade and k-values obtained on natural subgrade by PBT. It is interesting to note

that there is no consistent trend in the stiffness of the upper and lower layers of

subgrade. At half of the locations, the upper layer was stiffer than the lower layer, and

at the remaining locations, it was the other way around. However, k-values are better

correlated with the stiffness of the upper layer.

Figure 6.1 (c) shows correlations between k-values and FWD deflections on

CTS layer. The correlations are quite poor for the third and fourth sections, while a

decent correlation was observed in the first section. General poor correlations might

indicate that k-value from PBT is primarily effected by soil stiffness near the surface


108

as shown in Figure 6.1 (b), while larger depth of soil influences FWD deflections. This

could be due to the use of a smaller size loading plate in PBT.

(a)

(b)


109

(c)

Figure 6.1 (a) k-value on CTS versus elastic modulus of CTS and natural soil, (b) k-value on natural soil versus elastic modulus of at upper and lower layers of natural soil and (c) FWD deflection on CTS versus k-values.

6.1.2 Deflections and k-values on Base Layers

Deflections were measured on top of various base layers using FWD. Figure

6.2 shows the correlation between deflections on cement treated subgrade and on 2 in.

and 4 in. asphalt base layers and 6 in. cement stabilized base. In general, 4 in. asphalt

layer results in lower deflections than in 2 in. asphalt layer. Note that each data point

represents two deflections at the same location – one on CTS and the other on asphalt

layer. It is observed that the variations in deflections on CTS are larger in Section #4

than in Section #1; however, those in deflections on asphalt layers are much smaller in

Section #4 than in Section #1. This implies that the 4 in. asphalt layer provides more

uniform support than the 2 in. asphalt layer, even when the support condition of CTS

layer under the 4 in. asphalt layer was not as uniform as that under the 2 in. asphalt


110

layer. It is well known that the uniformity of the support is a key to good performance

of PCC pavement, and a 4 in. asphalt layer would provide better PCC pavement

performance than a 2 in. asphalt layer in this project. It is also interesting to note that

the 2 in. ACP layer did not reduce the deflections, while the 4 in. ACP reduced

deflections substantially. As a matter of fact, the 2 in. asphalt layer actually increased

the deflections in some locations. On average, there was no reduction in deflections by

the use of 2 in. ACP. It could be that the compaction effort of 2 in. ACP was not as

effective as that for 4 in. ACP. Figure 6.2 also shows that 6 in. CSB had the greatest

reduction in deflections.

Figure 6.2 FWD deflections on CTS and base.


111

6.1.3 Deflections and k-values on Concrete Layers

Figure 6.3 illustrates the correlation between deflections on base and on 9 in.

CRCP. It indicates the distinctive effects of various base types on deflections on

CRCP, even though the slab thickness is the same. In general, deflections on CRCP

are smallest at the second section, where 1 in. ACP + 6 in. CSB was used, and largest

in the third section, where 1 in. ACP in the base on top of 6 in. CSB was replaced with

non-woven fabric. As noted in Figure 6.2, deflections on the base in the third section

were the lowest, with an average of 7 mils. It is also observed that the variability of the

deflections is largest in the third section. It is believed that the use of non-woven

geotextile is responsible for the increased deflections with a large variability. Since

large deflections in CRCP are not desirable for the pavement performance for any

pavement types, the value of geotextile as a replacement of 1 in. ACP for base in

CRCP is questionable. It is especially true for CRCP, since large deflections increase

the concrete stress due to the interactions between longitudinal steel and surrounding

concrete, resulting in horizontal cracking and distresses. Deflections in the fourth

section, where 4 in. ACP was used, are low and quite uniform, while those in the first

section, where 2 in. ACP was used, are larger than in the second and fourth sections.

The average reduction in deflections is about 40 percent.


112

Figure 6.3 FWD deflections on base and CRCP.

Table 6.1 summarizes the back-calculation results. The first section was not

included, because during the FWD testing, geophone sensor #2 malfunctioned and

AREA values were not reliable. The values in Table 6.1 are the averages of all the

values in a specific section. The static k-values vary from 300 psi/in to 1,000 psi/in.

The lowest k-value was obtained in the third section, where geotextile was used on top

of 6 in. CSB. Even though the AREA value in the third section is smaller than that in

the fourth section, which would result in a larger k-value than that for the fourth

section if maximum deflections were the same and concrete modulus was also similar,

which is a reasonable assumption, the k-value was smallest due to the largest average

deflection. It is not known whether the k-value obtained from the AREA method is

valid when geotextile is used in the base layer. Radius of relative stiffness was the

smallest in the second section, where 1 in. ACP on 6 in. CSB was used, which is

reasonable considering the differences in stiffness between concrete and base layers

would be the lowest. As a result, along with the smallest average deflection, the back-


113

calculated k-value is the largest. Based on the information obtained in this study, it

appears that the use of the same k-value (300 psi/in) for both base types typically used

in Texas may not be reasonable.

Table 6.1 Summary of AREA Backcalculation Method Parameters

Test section AREA Radius of relative stiffness l, in Deflection D0, mils Static k-value,

psi/in 2nd Section 24.6 20.3 1.382 1009 3rd Section 26.9 24.9 3.165 305 4th Section 27.2 25.1 1.706 516

6.1.4 FWD Deflection Basin Determination using Linear Elastic Program

The new Windows version of MODULUS 6.0 was developed with the same

basic features of the DOS MODULUS 5.1 system (Liu and Scullion 2001). The

system of using the MODULUS program to process FWD data has been used for

evaluating layer moduli values for flexible pavement design since the early 1990s.

BISAR 3.0 is a Windows-based computer program developed by Shell

Research(Shell International Oil Products B.V. The Hague 1998). Stresses, strains and

displacements can be evaluated by using BISAR 3.0 in an elastic multi-layer system.

Pavement structural layers’ moduli were obtained by analyzing FWD

deflection data on top of ACP base layer using MODULUS 6.0. With the back-

calculated structural layers’ moduli, FWD loading was simulated on top of ACP layer

and CRCP concrete pavement by using the elastic layer program BISAR 3.0. FWD

deflection basins from actual field data and the elastic layer program simulation were

compared. The procedures are presented in Figure 6.4. Testing data in section #4 was

used for analysis.


114

Figure 6.4 FWD deflection basin simulations on base and CRCP.

Since bedrock depth information in section #4 is not available, pavement

structure was simplified in step #1. Infinite stiffer cement treated subgrade (CTS) layer

was used instead of 8-in. CTS + Subgrade + Bedrock. Ten FWD deflection basins in

section #4 were processed by MODULUS 6.0 in step #2; the average base layer

modulus was around 500 ksi and average CTS modulus value was 44.1 ksi, which is

similar to the modulus value obtained from DCP testing. In step #3, FWD with a 5.9-

in diameter loading was simulated on top of base layer by using BISAR 3.0.

Deflection basins on top of base layers are shown in Figure 6.5, and compared with

actual FWD deflection basins. Simulated FWD deflection basin is within the range of

actual FWD deflection data. There was a good agreement between deflection data

from the simulated static FWD loading and real dynamic loading, which means

simplification in step #1 is reasonable. Reasonable deflection data can be obtained by

simulating FWD testing on top of ACP layer using the elastic layer program.


115

Figure 6.5 Simulated FWD deflection basins on base layer.

In step #3, FWD loading also was simulated on top of infinite PCC slab. Three

different PCC modulus values were used to analyze the effect of PCC modulus.

Simulated FWD deflection basins on top of PCC slab are shown in Figure 6.6.

Simulated FWD deflections are much larger than actual deflection values. Back-

calculated dynamic k-value is 531 psi/in., 499 psi/in., and 473 psi/in. corresponding to

PCC modulus values 4 M psi, 5 M psi, and 6 M psi, respectively. k-value decreases

with increasing PCC modulus, which is as expected. However, the back-calculated

dynamic k-value is around the same as back-calculated static k-value of 522 psi/in.

from the actual FWD data.

The possible reasons are infinite slab size and simulating static loading on PCC.

It is unreasonable to simulate FWD on top of PCC slab by using the elastic linear

program.


116

Figure 6.6 Simulated FWD deflection basins on PCC slab.

6.2 CRCP Behavior and Performance

6.2.1 Effect of Base Type on CRCP Transverse Curling

As shown in Figures 6.7 (a), (b), (c), (d), and (e), pavement edge vertical

movement at each test location was presented with temperature difference between the

pavement top and bottom (Delta T). Overall, pavement curls up after concrete

placement because more drying shrinkage occurs near the pavement surface. One year

after concrete placement, the total amount of the pavement curls up was largest at

section #4 with 4-in ACP base. However, edge vertical daily variation is smallest at

section #4 with the same Delta T variation.


117

(a)

(b)


118

(c)


119

(d)

(e)

Figure 6.7 (a) Pavement edge vertical displacement at test section #2, (b) Pavement edge vertical displacement at test section #3-1, (c) Pavement edge vertical displacement at test section #3-2, (d) Pavement edge vertical displacement at test section #4-1, and (e) Pavement edge vertical displacement at test section #4-2.

Figure 5.10 shows that the in-situ drying shrinkage becomes stable from 14

days after concrete placement. It can be considered that the effect of drying shrinkage

for a specific period does not change. Hence, the data between 29th August and 2nd

September was selected to analyze the curling behavior in accordance with three

different base types.

Figures 6.8 (a) and (b) show a typical concrete strain variation in the transverse

direction at the top-middle-bottom and pavement edge vertical movement at each

section during the selected period.


120

(a)

(b)

Figure 6.8 (a) Total strain of concrete at top-middle-bottom at #4-1, and (b) Pavement edge vertical movement at #4-1.


121

Support condition of each gage installation location can be obtained from

Figures 4.11 to 4.14 and Table 5.1. This information was summarized as k-values

obtained by PBT on base and AREA back-calculation method. CRCP edge vertical

daily movement and concrete strain daily variation at the top-middle-bottom in the

transverse direction at the same period in different test sections were obtained and

summarized with k-values as shown in Table 6.2.

Table 6.2 Summary of Field Testing Data

Transverse VWSG

Locations

Concrete strain variation (VWSGs) [με] Edge vertical

movement (crackmeter) [mils]

k-value [psi/in]

Top Middle Bottom PBT on base

AREA method

#2 79.7 114.0 65.9 24.4 1335 1212 #3-1 97.5 72.7 62.1 15.9 2113 349 #3-2 83.9 76.6 62.3 13.9 1448 246 #4-1 113.2 94.2 90.5 19.0 432 501 #4-2 106.1 96.0 83.4 17.8 1703 535

Compared with the k-value obtained from PBT testing on base, CRCP edge

vertical movement has a much better correlation with the k-value back-calculated from

deflection data on top of CRCP by AREA method as shown in Figures 6.9. Under the

same enviromental conditions, CRCP edge vertical daily movement increases with

higher AREA k-value, which means a stiffer support condition and is as expected.


122

Figure 6.9 k-values versus CRCP edge vertical daily movement.

Even though PBT was considered to be the most direct pavement support

condition evaluation testing and it can accurately evaluate support property on top of

subgrade, PBT is not suitable for the evaluation of support condition on top of

stabilized base layer. AREA k-value back-calculated from FWD deflection data is

more reasonable for evaluating pavement support condition.

Figure 6.10 represents the gage locations of each section including transverse

crack spacing. Cracks in the first section are a little different from most of the

transverse cracks. VWSGs are close to the crack in the #3-2 and the #4-1; VWSGs are

located in the middle of two transverse cracks in the #3-1 and the #4-2.


123

a. Gage Location of Section #2 b. Gage Location of Section #3-1

c. Gage Location of Section #3-2 d. Gage Location of Section #4-1

e. Gage Location of Section #4-2

Figure 6.10 Gage Locations of each Section.


124

The transverse concrete strain variations were compared with AREA k-values

to identify their correlation as shown in Figures 6.11. Since back-calculated k-values

by AREA method have better correlation with the CRCP behavior, they were chosen

to represent the overall pavement support condition and used to evaluate the effect of

base support on concrete strain daily variations.

Concrete at the CRCP surface moves more freely than at the middle, and the

bottom concrete moves the least. Concrete strain variations in the second section are

different, and the possible reason for this difference is that the crack pattern is

different than normal CRCP crack pattern in the second and third sections. However,

the pavement edge vertical daily movement still has good correlation with AREA k-

values even with different crack patterns as shown in Figure 6.9. This means that

cracks in CRCP are tight and CRCP behaves axially in transverse curling no matter

what the crack pattern is.

Figure 6.11 k-values versus concrete strain daily variation.

Figures 6.11 shows the comparison between transverse VWSGs strain and k-

value from AREA method. The result shows that there is a good correlation between

transverse concrete strain daily variation and AREA k-value under the same crack


125

pattern. The concrete strain daily variations are increasing as AREA k-value is

increased.

The relative location between VWSG location and transverse crack does have

some effect on the concrete movement. The concrete movement is larger when it

comes closer to the transverse crack even with the similar support condition.

Pavement edge vertical movement has better correlation with variation of

temperature difference between pavement top and bottom as shown in Figure 6.12.

Pavement edge vertical displacement becomes largest when Delta T reaches its lowest

value, which means pavement curls down. Correlations at test sections with different

base types are shown in Figures 6.13 (a), (b), and (c). At test sections with different

base types, the same good correlations were obtained with increasing pavement age

and in different environmental conditions – summer and winter. Overall, with the

same Delta T variation, pavement vertical movement is less in winter than in summer.

Figure 6.12 Pavement edge vertical movement versus variation of temperature difference between top and bottom (Delta T).


126

(a)

(b)


127

(c)

Figure 6.13 (a) Correlation between edge vertical movement versus Delta T at test section #2, (b) Correlation between edge vertical movement versus Delta T at test section #3-2, and (c) Correlation between edge vertical movement versus Delta T at test section #4-1.

The ratio of pavement edge vertical movement and variation of Delta T at each

test location were obtained every 30 days after concrete placement. The results are

shown in Figure 6.14. No matter when concrete was placed, pavement curling effect in

winter is not as obvious as in summer. ACP becomes stiffer due to lower temperature

in winter; however, pavement curling effects becomes less significant. The possible

reason is that pavement curling was related to the overall support condition rather than

the material properties directly underneath it.


128

Figure 6.14 Pavement edge vertical movement ratio.

Concrete strain difference between pavement top and bottom was used for

CRCP bending evaluation in the transverse direction. The daily variation of

temperature difference between pavement slab top and bottom is slightly different at

the second, third, and fourth test sections, so the edge vertical movement and concrete

strain difference between top and bottom per degree Fahrenheit were used for

pavement slab behavior evaluation. The results versus k-values are shown in Figure

6.15.


129

Figure 6.15 k-values versus pavement edge vertical daily movement and concrete strain difference between top and bottom.

Figure 6.15 shows transverse curling effects are more obvious with increasing

pavement support stiffness. Concrete strain difference between top and bottom

becomes less with stiffer support conditions. The possible reason for the results is that

VWSGs for concrete strain were located at the middle of driving lane; since a stiffer

base cannot accommodate pavement slab bending near the center area of slab, the

strain difference between slab top and bottom are smaller.

It is interesting to note that the bending in transverse direction near the slab

center is larger with less stiff slab support; however, unit pavement edge vertical

movement is smaller at those areas with less stiff slab support. The reason is that the

slab can settle more when bending under environmental loading at locations with less

stiff slab support.

A smaller concrete strain difference between top and bottom was found at the

location with stiffer support, which means the pavement center bends less. Stress level


130

will be higher under environmental loading at the pavement center part due to higher

restraint. Also, the pavement edge vertical movement is larger which means near the

wheel path part away is curling more. It may cause higher stress with the combination

of traffic loading.

The overall trend is that, with stiffer support, the strain difference between top

and bottom decreases, while pavement edge vertical movement increases. However, it

was the opposite at the third section with geotextile over 6-in. CSB. The possible

reason might be the non-uniform support condition of the geotextile provided. Overall,

4-in. type B ACP at the fourth section provided a better support condition for

pavement.

6.2.2 Effects of Base Type and Transverse Crack on CRCP Longitudinal Curling

Transverse crack location has a significant effect on concrete strain in the

longitudinal direction. Figures 6.10 shows the crack location compared to gage

location.

Concrete strain shrinkage at the bottom of pavement in the longitudinal

direction is controlled by the amount of concrete shrinkage due to temperature drop

and pavement curling down due to the variation of temperature difference between top

and bottom (Delta T_Top-Bottom). As shown in Figure 6.16, the variation of

pavement bottom temperature and Delta T were presented with concrete strain at the

bottom in the longitudinal direction. Without considering the concrete curling effect,

concrete strains in all test sections were supposed to reach the lowest value at the time

of black line when temperature becomes lowest. Concrete strain should reach its

lowest value when Delta T becomes largest at the red line, without considering

concrete axial shrinkage due to temperature drop. The time that concrete strain reaches

its lowest value can be used to evaluate the curling effect at this location. Curling


131

effect in the longitudinal direction becomes more significant when the time of

minimum concrete strain is closer to the red line with the largest Delta T.

The curling effect at a specific pavement location depends on the stiffness of

support and crack location. As shown in Figure 6.16, the curling effect is most obvious

in section #2 because concrete strain reaches its lowest value at the closest time to the

red line. Similar moderate support stiffness was found in sections #4-1 and #4-2 with

similar AREA k-values. The curling effect is more significant in #4-1 because it is

close to the transverse crack, which is as expected. In section #3, crack location does

not have a significant effect on curling effect because of relatively softer support

condition. The whole slab between transverse cracks can curl up and down. This was

also found in concrete strain variation in the transverse direction.

Figure 6.16 Concrete strain variations at pavement bottom in longitudinal direction.


132

The curling effect is less significant in section #3-2 than in section #4-1, even

though the gage location is closer to the crack in section #3-2, as shown in Figure 6.10.

From the crack location stand point, curling should be more significant in section #3-2.

Compared to one ft distance to crack difference, the support condition is more

dominant in the curling effect.

6.3 Summary

Testing data obtained from the plate bearing test, dynamic cone penetrometer

testing, and falling weight deflectometer testing on top of various pavement structural

layers were analyzed in detail. CRCP behavior was monitored by various gages and

was compared with pavement support condition. The following findings were obtained.

1. k-values obtained from plate bearing testing depend on the stiffness of upper

portion of a layer. This could be due to the use of relatively small loading

plate size. k-values from PBT have poor correlation with k-values from FWD

deflection data.

2. Good correlations were obtained between slab support condition derived from

AREA method and CRCP slab behavior. On the other hand, poor correlations

were obtained when the CRCP slab behavior was evaluated in terms of slab

support condition evaluated with PBT.

3. Curling of concrete slab in the transverse direction is substantially influenced

by the support condition. Stiffer support condition could increase the potential

for longitudinal cracking; however, the use of tied concrete shoulder or

widened lanes will minimize the longitudinal crack potential.

4. CRCP edge vertical daily movements have better correlation with k-values

back-calculated from FWD deflection data than with k-values from PBT.


133

5. Reasonable results can be obtained by simulating FWD testing on top of ACP

base layer using an elastic layer program. FWD testing simulation on top of

CRCP yields an unreasonably larger deflection basin than actual field data.

6. CRCP edge vertical daily movements have good correlation with temperature

difference between top and bottom (Delta T). A seasonal effect on edge

vertical daily movements was observed. Pavement transverse curling becomes

significant in summer when the modulus of ACP layer is low. It was also

discovered that PBT is not a proper method to evaluate support condition for

analyzing CRCP structural behavior.

7. Both pavement support condition and transverse crack location have a

significant effect on concrete strain in longitudinal directions. Support

condition is more dominant in the curling effect. A significant curling effect

was found with stiff support condition.


134

CHAPTER 7

IMPLEMENTATION

7.1 Design Input

The performance of Portland cement concrete (PCC) pavement depends, to a

great extent, on the quality of base support – durability, uniformity, and stiffness. The

Texas Department of Transportation (TxDOT) recognized the importance of support

condition, and has required since the mid-1980s the use of non-erodible base under

concrete slab – either 4 in. hot mix asphalt layer or a minimum 1 in. asphalt concrete

over 6 in. cement stabilized layer. Evaluation of field performance of PCC pavement

in Texas revealed that these two types of base provided good PCC pavement

performance.

TxDOT currently uses the AASHTO 93 Design Guide for the rigid pavement

designs. The required slab thickness from this pavement design procedure is not

sensitive to the base support condition in terms of modulus of subgrade reaction (k-

value). Moderate variations in k-value result in minute changes in required slab

thickness. It is primarily due to the way the original design equations were expanded

to account for conditions other than those that existed at the AASHO Road Test. In

that effort, the Spangler equation was used to estimate concrete stresses due to wheel

loading applications. According to both the Westergaard and Spangler equations,

wheel load stresses in the concrete slab are slightly sensitive to k-values in the

practical range. Based on the insensitivity of wheel load stress and the resulting

required slab thickness to k-value, 300 psi/in has been used as a default value in

pavement design for the modulus of subgrade reaction (k-value) for the support

provided by these bases. The use of 300 psi/in for k-value in rigid pavement design

was partly due to the insensitivity of the required slab thickness to the modulus of

subgrade reaction in the current TxDOT rigid pavement design procedure.


135

In order to optimize the rigid pavement designs, TxDOT developed a

mechanistic-empirical design procedure for continuously reinforced concrete

pavement (CRCP), called TxCRCP-ME, and plans to implement the design procedure.

TxCRCP-ME is based on 3-dimensional finite element analysis of the pavement

system, and it was discovered that the stresses in concrete slab due to environmental

(temperature and moisture variations) and wheel loading applications are much more

sensitive to k-value than in the Westergaard or Spangler equations. In this design

procedure, the slab support has rather substantial effects on required slab thickness.

The primary reason for the discrepancy between the Westergaard or Spangler

equations and the results from 3-dimensional analysis is the location of the critical

stresses in concrete slab. In both Westergaard and Spangler equation, the critical

stresses are at the bottom of the concrete slab, except for the corner loading condition,

which does not exist in CRCP with tied-concrete shoulders. On the other hand, typical

distresses in CRCP are due to the interactions between longitudinal steel and

surrounding concrete slab when subjected to wheel loading applications. In other

words, the accuracy of Westergaard and Spangler equations has been verified in a

number of studies, those equations are not applicable to CRCP analysis and design. To

increase the reliability of the new pavement design procedure, accurate evaluations of

k-value are important. According to field tests on various types base, the current

practice of using one default value of 300 psi/in needs to be revised. Based on this

study, it is recommended that TxDOT consider the use of different k-values for

different base types for pavement design.

Mechanistic empirical pavement design program (MEPDG) uses an equivalent

structure with modulus E for base course and effective k-value for all layers

underneath base course for pavement support characterization. However, effective k-

value was not obtained by field testing; rather, effective k-value was obtained through

backcalculation as described in Section 3.2.2. Estimation of k-value with PBT is quite

time consuming. In addition, as discussed earlier, field testing revealed that the setup

of the PBP testing with 18-in diameter of loading plate does not accurately simulate


136

the support condition typically experienced by the subgrade under actual traffic

loading. The estimation of modulus of base layer in the field is a real challenge. It is

because the modulus of base layer varies significantly depending on (1) the localized

cement content and compaction effort, in the case of cement stabilized base, and (2)

compaction effort or temperature of asphalt material during compaction as discussed

earlier. In addition, the modulus of base layer in the field is a function of the stiffness

of subgrade as well.

7.2 Job Control Testing

Currently, rigid pavement designs require k-value for slab support. On the

other hand, during the construction, specifications require density control for subgrade

soil using nuclear density gages, and practically no job control testing for stabilized

base layers. There is a disconnect between pavement design and construction. If the k-

value has limited effects on required slab thickness, as the current rigid pavement

designs imply, this disconnect between design and construction may not have

substantial effects. However, it has been demonstrated that the slab support is one of

the most important variables for CRCP performance. Theoretical study using 3-

dimensional analysis clearly indicates the importance of the slab support. This gap

between what is required for rigid pavement designs and construction needs to be

narrowed or filled with proper construction quality control testing schemes. At this

point, the level of job control testing for concrete slab during rigid pavement

construction is quite extensive. Strength, air content, slump, and slab thickness are just

few examples of required job control testing. The penalty for not meeting the

specification requirements for these properties is quite severe. On the other hand, job

control testing requirements for slab support are quite minimal, even though the effect

of slab support on rigid pavement performance is quite significant. To improve rigid

pavement performance, it is strongly recommended that proper job control testing

procedures are developed and implemented for slab support, which will also be able to

verify that the design assumptions for k-value are met during construction.


137

AREA concept was originated from asphalt concrete pavement. Since then,

efforts have been made to utilize the AREA concept for the evaluations of slab support

condition in rigid pavements, with a reasonable success. Technical correctness and

adequacy of the application of the AREA method to the estimation of slab support

condition have been demonstrated. To fully utilize the AREA method and obtain

reasonable results, both FWD deflection basin shape and maximum deflection D0 at

loading location are needed for the overall support condition evaluations. Compared

with other potential job control schemes, FWD deflection data can be obtained easily

and in a timely manner in the field during construction. TxDOT has 15 Dynatest FWD

units and large districts that utilize rigid pavements substantially, such as Dallas,

Houston, Fort Worth and El Paso Districts have access to FWD units for job control

testing.

In an effort to demonstrate the feasibility of using FWD as a job control testing,

a data set of ten test points with FWD on top of base course and AREA backcalculated

k-values in the 4th test section discussed in Section 4.3 on CRCP was analyzed. AREA

values were calculated using different numbers of geophone deflection data. AREA X

represents AREA value calculated by using X numbers of deflections data. As shown

in Figure 7.1, poor correlations were found between AREA k-values and AREA X or

normalized maximum deflection D0. The reason could be that support condition is

depended on both AREA X and maximum deflection D0.

As discussed in Section 3.1.2.4, the value of non-dimensional parameter d0 is

almost constant, between 0.121 and 0.124, for all practical ranges of the radius of

relative stiffness. k-value is only sensitive to D0l2. According to the unique

relationship between AREA and radius of relative stiffness l, a parameter combining

AREA and D0 was developed to evaluate the relationship between FWD results on top

of base course and CRCP. AREA values calculated using different numbers of

geophone data were analyzed as shown in Figure 7.2.


138

(a)

(b) Figure 7. 1 (a) AREA k-value versus AREA on base, (b) AREA k-value versus maximum deflection D0 on base.


139

Figure 7. 2 AREA k-value versus combined parameter

As shown in Figure 7.2, backcalculated AREA k-value has better correlation

with the combined parameter when AREA 7 was selected. It is as expected because

stresses can be spread on large area on base due to the rigidity of concrete slab. The

calculation of AREA 7 value uses larger area deflections data on base.

The same analysis method was used for the 2nd test section with 1 inch ACP +

6 inches CSB. The results are shown in Figure 7.3. Relative good correlations were

found in both two typical base types used in Texas for CRCP. It provides a method to

estimate pavement support condition by running FWD on base course during new

construction. However, this combined parameter needs to be refined by more field

data and further theoretical analysis. Figure 7.3 illustrates a rather large difference in

k-values between the two typical base courses used by TxDOT. This finding is

supported by the differences in field performance of CRCP with the two base courses.

The use of 300 psi/in for both base course types may not be reasonable.


140

Figure 7. 3 AREA k-value versus combined parameter for two base types

The implementation of a job control testing for k-value will provide a valuable

tool for improving overall construction quality of base layer, thereby filling a gap

between rigid pavement design and construction and improving rigid pavement

performance.


141

CHAPTER 8

FINDINGS AND CONCLUSIONS

This study investigated the effects of slab support on the behavior and

performance of continuously reinforced concrete pavement (CRCP), with the primary

objective identifying a most appropriate method to evaluate slab support condition for

CRCP design. Currently, there are conflicting ideas and opinions regarding the

desirable slab support condition for rigid pavements. Even though the behavior of

joined plain concrete pavement (JCP or CPCD) is quite different than that of CRCP,

the same effect of slab support condition on the behavior and performance of both

pavement types has been assumed and utilized in most of the rigid pavement design

programs. This study reviewed historical developments on slab support in rigid

pavement, conducted field evaluations on the performance of CRCP in terms of slab

support, and performed field testing to evaluate the effect of slab support condition on

CRCP behavior in a project with 4 different base types.

8.1 Findings and Conclusions

In order to optimize rigid pavement design, TxDOT developed new design

procedures for continuously reinforced concrete pavement (CRCP) based on

mechanistic-empirical principles and plans to implement the procedures. In this design

procedure, the modulus of subgrade reaction has rather substantial effects on required

slab thickness. To increase the reliability of the new pavement design procedure,

accurate evaluations of k-value are important. A test section was constructed where

various base types were used, and a number of field tests were conducted to estimate

the range of k-values of the support systems that are currently used or expected to be

utilized. The field testing conducted included plate bearing testing, dynamic cone

penetrometer testing, and falling weight deflectometer testing on top of various layers.


142

Based on the information obtained in the investigation, the following findings

and conclusions were obtained:

General Time-Dependent CRCP Behavior

• Concrete at the top, middle, and bottom of a slab moves the same way in the

longitudinal direction. Stress was relieved once transverse cracking occurred;

concrete strain variation in the longitudinal direction increases significantly at

the same time. A curling effect can be found in the longitudinal direction after

cracks occur.

• Relative humidity (RH) near the pavement surface is the lowest with large

daily variations. RH value increases and the level of RH variation decreases

with increasing depth from the pavement surface. One exception is RH at 8.5

in. depth, which is close to the base because of the moisture exchange between

pavement concrete and base.

• Drying shrinkage at the slab mid-depth was quite small, which is consistent

with RH data.

• CRCP edge vertical daily movement has a good correlation with the variation

of temperature difference between top and bottom of the slab. Pavement edge

curls up due to more drying shrinkage near the pavement surface.

Pavement Support Condition

• It appears that k-values of subgrade from plate bearing testing are significantly

influenced by the stiffness of the upper layer of the soil. This could be due to

the use of a smaller size loading plate. A poor correlation was obtained

between FWD deflections and k-values from PBT.

• Compared with other base types, non-woven geotextile in the base layer

increased deflections from FWD on CRCP rather substantially. CRCP

performance partly depends on the slab deflections – the smaller the

deflections, the better the performance, primarily due to the decrease in


143

concrete stresses resulting from interactions between longitudinal steel and

surrounding concrete.

• The thickness of asphalt base layer has substantial effects on CRCP deflections.

ACP with 4 in. thickness reduced deflections by about 40 percent, compared

with ACP with 2 in. thickness.

• Treatment of subgrade with 4 percent cement increased the modulus values by

about 30 ksi. Also, there were better correlations between stiffness of CTS and

k-value on CTS from PBT than stiffness of natural subgrade and k-value.

• AREA method was used to back-calculate k-values for various base types.

Largest k-value was obtained on CRCP with 1 in. AC and 6 in. CSB, followed

by 4 in. AC. The smallest k-value was obtained on CRCP with non-woven

fabric on 6 in. CSB. The difference in k-values between the two different base

types typically used in Texas (4-in ACP and 1-in ACP+6-in CSB) is rather

large.

• Reasonable deflection basins can be obtained by simulating FWD testing on

top of ACP base layer using an elastic layer program. FWD testing simulation

on top of CRCP yielded an unreasonably larger deflection basin than actual

field data.

Effect of Support Condition on Concrete Behavior in CRCP

• CRCP edge vertical daily movements have better correlation with k-values

back-calculated from FWD deflection data than k-values from PBT. The

curling effect becomes more significant with increasing k-value from FWD

deflection.

• Good correlations were obtained between slab support condition derived from

AREA method and CRCP slab behavior. On the other hand, poor correlations

were obtained when the CRCP slab behavior was evaluated in terms of slab

support condition evaluated with PBT.


144

• A seasonal effect on edge vertical daily movements was observed. Pavement

transverse curling becomes significant in summer when the modulus of ACP

layer is low. It also proved PBT is not a proper method to evaluate support

condition for analyzing CRCP structural behavior.

• The bending in transverse direction near the slab center is large with flexible

support. However, unit pavement edge vertical movement is smaller at those

flexible support locations. Flexible support conditions can accommodate more

slab deformation.

• Both pavement support condition and transverse crack location have a

significant effect on concrete strain in longitudinal directions. Support

condition is more dominant in the curling effect. A significant curling effect

was found with stiff support conditions.

Most Appropriate Testing Method for Slab Support in Pavement Design

• It appears that FWD testing on top of stabilized base and data reduction using

AREA method provide the best design input for CRCP design.

• Considering the substantial effects of slab support on CRCP performance and

the near absence of quality control testing of base layer during the construction,

FWD testing during the construction as a job control testing will provide a

right direction for improving CRCP performance.

• The current TxDOT requirement of the use of 300 psi/in for k-value for both 4-

in ACP or 1-in ACP+6-in CSB needs to be re-evaluated.

8.2 Recommendations for Further Research

Even though this study investigated and identified the most appropriate test

procedures for the determination of slab support condition for CRCP design, the field

data was obtained from only one project. Considering a number of variables involved


145

in slab support condition, additional field testing and data analysis need to be

conducted to enhance the reliability of the proposed method.


146

REFERENCE

Ahlvin, R. G. (1991). "Origin of Developments for Structural Design of Pavements." U.S. Army Corps of Engineers, Waterways Experiment Station, Vicksburg, Mississippi.

American Association of State Highway and Transportation Officials (1986). Guide for Design of Pavement Structures: 1986, Washington, D.C.

American Association of State Highway and Transportation Officials (1993). AASHTO Guide for Design of Pavement Structures:1993, Washington, D.C.

American Concrete Pavement Association (ACPA) (2007). "Subgrades and Subbases for Concrete Pavements." American Concrete Pavement Association Engineering Bulletin, EB204P.

ARA Inc. ERES Consultants Division (2004). "Guide for Mechanistic-Empirical Design of New and Rehabilitated Pavement Structures." NCHRP Project 1-37A, Transportation Research Board of the National Academies, Washington, D.C.

ASTM (2004). "Nonrepetitive Static Plate Load Tests of Soils and Flexible Pavement Components, for Use in Evaluation and Design of Airport and Highway Pavements to Evaluate Modulus of Subgrade Reaction." D 1196-93, ASTM International, West Conshohocken, PA.

Azizi, F. (2000). Applied analyses in Geotechnics, E & FN Spon, London. Barenberg, E. J., and Ratterree, B. L. "Fully Bonded Concrete Overlay for an Airport

Runway." Proc., ASCE International Air Transportation Conference. Boussinesq, J., and Caquot, M. A. (1969). Application des potentiels à l'étude de

l'équilibre et du mouvement des solides élastiques, Albert Blanchart. Campen, W. H., and Smith, J. R. (1947). "Use of Load Tests in the Design of Flexible

Pavements." Symposium on Load Tests of Bearing Capacity of Soils, American Society of Testing and Materials, Special Technical Publication(79).

Childs, L. D. (1967). "Cement-treated Subbases for Concrete Pavements." Highway Research Record(189).

Childs, L. D., and Kapernick, J. W. "Tests of Concrete Pavements on Crushed Stone Subbases." Proc., Proceedings, American Society of Civil Engineers.

Choi, S., and Won, M. C. (2010). "Thermal Strain and Drying Shrinkage of Concrete Structures in the Field." ACI Materials Journal, 107(5), 498-507.

Darter, M. I. (1977). "Design of a Zero-maintenance Plain Jointed Concrete Pavement, Volume One-Development of Design Procedures." University of Illinois at Urbana-Champaign.

Darter, M. I., and Barenberg, E. J. (1977). "Design of a Zero-maintenance Plain Jointed Concrete Pavement, Volume Two-Design Manual."University of Illinois at Urbana-Champaign.


147

Darter, M. I., Hall, K. T., and Kuo, C.-M. (1995). "Support Under Portland Cement Concrete Pavements." Transportation Research Board, National Research Council, Washington,DC. .

Desai, C. S., and Christian, J. T. (1977). Numerical Methods in Geotechnical Engineering, McGraw Hill, New York.

Engesser, F. (1893). The Theory of Site Foundations. Zur Theorie des Baugrundes. ERES Consultants Inc. (1982). "Nondestructive Structural Evaluation of Airfield

Pavements." prepared for U.S. Army Corps of Engineers Waterways Experiment Station, prepared for U.S. Army Corps of Engineers Waterways Experiment Station, Vicksburg, Mississippi.

Foxworthy, P. T. (1985). "Concepts for the Development of a Nondestructive Testing and Evaluation System for Rigid Airfield Pavements." Ph.D Ph.D thesis, University of Illinois at Urbana-Champaign.

Goldbeck, A. T. (1925). "Researches on the Structural Design of Highways by the United States Bureau of Public Roads." Transactions of the American Society of Civil Engineers,, 88.

Goldbeck, A. T., and Bussard, M. J. (1925). "The Supporting Value of Soil as Influenced by the Bearing Area." Public Roads,, 5(11).

Ha, S., Yeon, J., Choi, B., Jung, Y., Zollinger, D. G., Wimsatt, A., and Won, M. C. (2011). "Develop Mechanistic–Empirical Design for CRCP." Texas Tech University, Lubbock, Texas.

Hall, K. T. (1991). "Performance, Evaluation, and Rehabilitation of asphalt-overlaid concrete pavements." University of Illinois, Urbana, IL.

Hall, K. T., Darter, M. I., Hoerner, T. E., and Khazanovich, L. (1997). "LTPP Data Analysis. Phase I: Validation of Guidelines for k-value Selection and Concrete Pavement Performance Prediction." FHWA, U.S. Department of Transportation.

Hayashi, K. (1921). Theorie des Trägers auf elastischer Unterlage (Theory of Beams on Elastic Foundation), J. Springer, Berlin.

Hetényi, M. (1946). Beams on Elastic Foundation, University of Michigan Press Ann Arbor.

Hittle, J. E., and Goetz, W. H. "Factors Influencing the Load-Carrying Capacity of Base-Subgrade Combinations." Proc., Proceedings, Highway Research Board.

Hoffman, M. S., and Thompson, M. R. (1981). "Mechanistic Interpretation of Nondestructive Testing Deflections." Civil Engineering Studies. Transportation Engineering Series No. 32. Illinois Cooperative Highway and Transportation Research Program Series No. 190.University of Illinois, Urbana, IL.

Huang, Y. H. (2004). Pavement Analysis and Design, Pearson Education, Inc., New Jersey.

Ioannides, A. M. (1990). "Dimensional Analysis in NDT Rigid Pavement Evaluation." Journal of Transportation Engineering. ASCE,, 116(1), 23-36.


148

Ioannides, A. M. (1991a). "Theoretical Implications of the AASHTO 1986 Nondestructive Testing Method 2 for Pavement Evaluation." Transportation Research Record 1307, 211-220.

Ioannides, A. M. "Subgrade Characterization for Portland Cement Concrete Pavements." Proc., Proceedings, International Conference on Geotechnical Engineering for Coastal Development—Theory and Practice, Port and Harbour Institute, Ministry of Transport, Yokohama 3-6, 809-814.

Ioannides, A. M. (2006). "Concrete Pavement Analysis: the First Eighty Years." International Journal of Pavement Engineering,, 7(4), 233-249.

Ioannides, A. M., Barenberg, E. J., and Lary, J. A. "Interpretation of Falling Weight Deflectometer Results Using Principles of Dimensional Analysis." Proc., Proceedings, Fourth International Conference on Concrete Pavement Design and Rehabilitation, 231-247.

Ioannides, A. M., and Khazanovich, L. "Backcalculation Procedures for Three-Layered Concrete Pavements." Proc., 4th International Conference, Bearing Capacity of Roads and Airfields.

Jung, Y. S., Zollinger, D. G., Won, M. C., and Wimsatt, A. J. (2009). "Subbase and Subgrade Performance Investigation for Concrete Pavement."

Kerr, A. D. (1965). "A Study of a New Foundation Model." Acta Mechanica, 1(2). Kerr, A. D. (1985). "On the Determination of Foundation Model Parameters." Journal

of Geotechnical Engineering, 111(11), 1334-1340. Liu, W., and Scullion, T. (2001). "Modulus 6.0 for Windows: User's manual." Texas

Transportation Institute, Texas A&M University System, College Station, Texas.

Losberg, A. (1960). "Structurally Reinforced Concrete Pavements." Doktorsavhandlingar Vid Chalmers Tekniska Hogskola, Goteborg, Sweden.

McCullough, B. F., and Boedecker, K. J. (1968). "Use of Linear-Elastic Layered Theory for the Design of CRCP Overlays." Highway Research Record(291).

McCullough, B. F., and Elkins, G. E. (1979). "CRC Pavement Design Manual." Austin Research Engineers, Inc. Prepared for the Associated Reinforced Bar Producers− CRSI. Austin, Texas.

McLeod, N. W. "A Canadian Investigation of Load Testing Applied to Pavement Design." Proc., Symposium on Load Tests of Bearing Capacity of Soils, American Society for Testing and Materials, Special Technical Publications.

Nussbaum, P. J., and Larsen, T. J. (1965). "Load-deflection Characteristics of Soil-cement Pavements." Highway Research Record(86).

Packard, R. G. (1973). "Design of Concrete Airport Pavement." Portland Cement Association, Skokie, IL.

Pasternak, P. L. (1954). "Fundamentals of a New Method of Analysis of Structures on Elastic Foundation by Means of Two Subgrade Coefficients." Gosudarstvennoe Izdatel'stvo Literatury po Stroitel'stvu i Arkhitekture, Moscow (in Russian).


149

Phillippe, R. R. "Field Bearing Tests Applied to Pavement Design." Proc., Symposium on Load Tests of Bearing Capacity of Soils, American Society for Testing and Materials, Special Technical Publication.

Phu, N. C., and Ray, M. (1979). "The Erodibility of Concrete Pavement Subbase and Improved Subgrade Materials." Bulletin de Liaison des Laboratoires des Ponts et Chaussees, France, Special(8), 32-45.

Potter, C. J., and Dirks, K. L. (1989). "Pavement Evaluation Using the Road RaterTM Deflection Dish." Highway Division, Iowa Department of Transportation.

Reissner, E. (1958). "A Note on Deflections of Plates on a Viscoelastic Foundation." Journal of Applied Mechanics, 25(1).

Reissner, E. (1967). "Note on the Formulation of the Problem of the Plate on an Elastic Foundation." Acta Mechanica, 4(1), 88-91.

Sale, J. P., and Hutchinson, R. L. (1959). "Development of Rigid Pavement Design Criteria for Military Airfields." Journal of the Air Transport Division, 85(AT3).

Shell International Oil Products B.V. The Hague (1998). "BISAR 3.0 User Manual." Bitumen Business Group, 3-5.

Teller, L. W., and Sutherland, E. C. (1935a). "The Structural Design of Concrete Pavements, Part 1, A Description of the Investigation." Public Roads, 16(8).

Teller, L. W., and Sutherland, E. C. (1935b). "The Structural Design of Concrete Pavements, Part 2, Observed Effects of Variations in Temperature and Moisture on the Size, Shape, and Stress Resistance of Concrete Pavement Slabs." Public Roads, 16(9).

Teller, L. W., and Sutherland, E. C. (1935c). "The Structural Design of Concrete Pavements, Part 3, A Study of Concrete Pavement Cross Sections." Public Roads, 16(10).

Teller, L. W., and Sutherland, E. C. (1936). "The Structural Design of Concrete Pavements, Part 4, A Study of the Structural Action of Several Types of Transverse and Longitudinal Joint Designs." Public Roads, 17(7 and 8).

Teller, L. W., and Sutherland, E. C. (1943). "The Structural Design of Concrete Pavements, Part 5, An Experimental Study of the Westergaard Analysis of Stress Conditions in Concrete Pavement Slabs of Uniform Thickness." Public Roads, 23(8).

Terzaghi, K. V. "Bearing Capacity of Shallow Foundations." Proc., Proceeding First Congress of International Association for Bridge and Structural Engineering.

Terzaghi, K. V. (1955). "Evalution of Conefficients of Subgrade Reaction." Geotechnique, 5(4), 297-326.

Terzaghi, K. V., and Peck, R. B. (1948). Soil Mechanics in Engineering Practice, Wiley, New York.

Texas Department of Transportation (TxDOT) (2011). "Pavement Design Guide Manual, Chapter 4 Section 4 Non-Destructive Evaluation of Pavement Structural Properties."

Texas Department of Transportation (TxDOT) (2012). "Determining Modulus of Subgrade Reaction (k-value)." Tex-125-E.


150

Thompson, M. R., and Robnett, Q. L. (1976). "Resilient Properties of Subgrade Soils." Civil Engineering Studies, Transportation Engineering Series, University of Illinois and Illinois Department of Transportation.

U.S. Army Corps of Engineers (1942). "Wright Field Slab Tests." Ohio River Division, Cincinnati Testing Laboratories, Cincinnati, Ohio.

U.S. Army Corps of Engineers (1943). "Reports on Special Field Bearing Tests on Natural Subgrade and Prepared Subbase Using Different Size Bearing Plates." Ohio River Division, Cincinnati Testing Laboratories, Cincinnati, Ohio.

Van Wijk, A. J. (1985). Rigid Pavement Pumping:(1) Subbase Erosion and (2) Economic Modeling, Joint Highway Research Project File 5-10, School of Civil Engineering, Purdue University, West Lafayette, Indiana.

Van Wijk, A. J., and Lovell, C. W. (1986). "Prediction of Subbase Erosion Caused by Pavement Pumping." Transportation Research Record(1099), 45-57.

Westergaard, H. M. "Theory of Stresses in Road Slabs." Proc., Proceedings, Fourth Annual Meeting of the Highway Research Board.

Westergaard, H. M. (1926). "Stresses in Concrete Pavements Computed by Theoretical Analysis." Public Roads, 7(2).

Winkler, E. (1867). "Die Lehre von der Elastizitat and Festigkeit (the theory of elasticity and stiffness)." H. Dominicus Prague, Czechoslovakia.

Documents

Copyright 2013, Wujun Zhou