FOREWORD 

This report presents the results of a study to further the development of 

performance-re1 ated speci f i cations For port1 and cement concrete pavement 

1 construction. Laboratory testing was conducted to investigate the 1 relationships between materials variables and primary predictors of pavement 

! distresses. A demonstration performance-related specifications system was 

I developed, allowing users to determine the appropriate percentage of bid price 

1 that a contractor should receive for concrete of a given quality. 

1 Recommendations pertaining to future laboratory studies, field studies, and J I further development of performance-related specification systems are also 

I summarized, 

This work was conducted as part of Nationally Coord'inated Program E8, 

"Construction Control and Management," and is inten~ded for engineers concerned 

with quality assurance, specifications, and construction of concrete 

pavements, 

Sufficient copies of this report are being distributed by Federal Highway 

Adminrstration memorandum to provide a minimum of t,wo copies to each regional 

office, division office, and State highway agency. Direct distribution is 

being made to the division offices. Additional codies for the public may be 

obtained from the National Technical information Sgrvice, U.S. Department of 

Commerce, 5285 Port Royal Road, 

The United States Government does not endorse prod 

Trade or manufacturers' names appear in this repor 

considered essential to the object of the document 

I 

NOTICE ! 

I 

I 

Thi s document i s di ssemi nated under the sponsorshi d of the Department of 

Transportation in the interest of information exchdnge. The United States 

Government assumes no liability for its contents o~ use thereof. This report 

does not constitute a standard, specification, or iegulation. 

cts or manufacturers, 

only because they are 
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I 

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Technical Report Documentation Page 

1. Report No. 

FHWA-RD-89-211 

No restrictions. This document is 

available to the public through the 

National Technical Information Serv&ce, 

Springfield, Virginia 22161 

I 

1 

2. Government Accession No. 

Performance-related specifications, 

pdrtland cement concrete (or PCC), 

rikid pavement, economic life , FCC properties 

3. Recipient's Catalog No. 

4. Title and Subtitle 

DEVELOPMENT OF PERFORMANCE-RELATED SPECIFICATIONS 

FOR PORTLAND CEMENT CONCRETE PAVEMENT CONSTRUCT ION 

7. Author's) 

P.E. Irick, S.B. Seeds, M.G. Myers, and E.D. Moody L 

9. Performing Organization Name and Address 

ARE Inc . 2600 Dellana Lane 

Austkn, Texas 78746 

12. Sponsoring Agency Name and Address .I 

Office of Engineering and Highway Operations R&D 

Federal Highway Administration 

6300 Georgetown Pike 

McLean, Virginia 22101-2296 

IS. Supplementary Notes 

19. Security Classif. (of this report) 

Unclassified 

5. Report Date 

May 1990 

6. erfO rm Organization Code 

, 8. Performing Organization Report No. 

10. Work Unit No. (TRAIS) 

NCP 3E8B-2022 

11. Contract or Grant No. 

DTFH61-87-C-00045 

13. Type of Report and Period Covered 

Final Report 

June 1987-October 1989 

14. Sponsoring Agency Code 

Form DOT F 1700.7 (8-72) Reproduction of completed page authorized 

20. Security Classif. (of this page) 

Unclassified 

PHWA contract manager (COTR): P.A. Kopac (HNR-20) 

. n 

16. Abstract 

The primary product of this study was a demonstration performance-related 

specification (PRS) system for PCC pavement construction. The system is" 

designed to consider three key factors (i.e., PCC strength, slab thickness 

and initial serviceability) in assessing an as-constructed pavement delivered 

by a contractor and calculating an appropriate reward (bonuslincentive) or 

penalty (disincentive). 

Many pavement performance prediction relationships and FCC property 

prediction equations were evaluated to develop the performance-related aspects 

0f the new system. In addition, a rather intensive experimental labophtory 

study of FCC material properties was conducted to develop better multi-factor 

prediction relationships. 

The demonstration PRS was developed using a computerized spreadsheet 

program. It was designed to be parallel to the demonstration PRS system 

developed under NCHRP Project 10-26A for asphalt concrete pavements. As a 

result of the study, recommendations were made for further research in several 

key areas related to PRS systems and field and laboratory studies. 

- * ** 

'17. Key WO& 

219 No. of Paglea 

27 1 

18. Distribution Statement 

22. Price 

TABLE OF CONTENTS \ 

\ 

CHAPTER . PAGE 

I 1 BACKGROUND, OBJECTIVES, AND SCOPE ........................ 1 

I 2 FRAMEWORK FOR DEVELOPMENT OF PERFORMANCE-RELATED 

M&C SPECIFICATIONS ....................................... i I 

4 

3 .................................... 

I 

PRIMARY RELATIONSHIPS 9 

STRESS PREDICTION RELATIONSHIPS ........................ 9\ 

Empirical Models ..................................... Multi-Layered Elastic Analysis Models 113 ................ 11 

Elastic Plate on Dense Liquid Subgrade ............... 15 

Finite Element Idealizations ......................... 18 

DISTRESS PREDICTION RELATIONSHIPS ...................... 23 

PERFORMANCE PREDICTION RELATIONSHIPS ................... 25 

ROLE OF PRIMARY RELATIONSHIPS IN THE DEVELOPMENT 

OF PERFORMANCE-RELATED M&C SPECIFICATIONS ............ 29 

4 SECONDARY RELATIONSHIPS AMONG M&C VARIABLES .............. 31 

SUMMARY OF CURRENT M&C SPECIFICATIONS .................. 31 

SECONDARY RELATIONSHIP VARIABLES ....................... 35 'I\ 

ASSESSMENT OF AVAILABLE SECONDARY RELATIONSHIPS ........ 37 

PCC Strength ......................................... 38 . PCC Bending Stiffness ................................ 40 

PCC Shrinkage ........................................ 41 

PCC Thermal Coefficient ............................... 41 

PCC Durability ....................................... 42 

Summary .............................................. 42 

ASSESSMENT OF EXISTING DATA BASE POTENTIAL ............. 42 

RII Data Base ........................................ 43 

COPES Data Base ...................................... 44 

5 LABORATORY STUDIES FOR DEVELOPMENT OF 

SECONDARY RELATIONSHIPS .................................. 47 

INITIAL EXPERIMENT DESIGN FOR LABORATORY STUDY ......... 47 

IMPLEMENTATION OF LABORATORY STUDY ..................... RATIONALE FOR ANALYSES OF THE LABORATORY STUDY DATA 51! .... 59 

Classification of Data Base Variables ................ 59 I 

. Classification and Scope of Data Analyses ............ 62 

ANALYSES OF THE LABORATORY STUDY DATA ................... 70 

Pairwise Associations Between Study Variables ........ 70 

Analyses of Variance Between Duplicate 

Specimens and Replicate Batcheq .................... 75 

Analysis of Variance and Covariance 

for Mix Properties and PCC Properties .............. 85 . Multiple Regression Analyses for PCC Properties ...... 94 

Sensitivity Analyses for Selected 

Dependent Variables ................................ 121 

SUMMARY RESULTS OF THE LABORATORY STUDY ................ 130. 

iii 
TABLE OF CONTENTS (continued) 

CHAPTER 

6 PROCEDURES AND ALGORITHMS FOR DERIVATIOq OF 

PERFORMANCE-RELATED SPECIFICATIONS ....................... 

PAVEMENT DESIGN FOR THE INITIAL PERFORMANCE PERIOD ..... ACCEPTANCE PLANS FOR SELECT M&C VARIABLES .............. CONSTRUCTION, CONTROL, AND EVALUATION .................. PREDICTION OF DISTRESS AND PERFORMANCE FOR 

DESIGN PAVEMENT AND CONSTRUCTED PAVEMENT ............. PREDICTION OF PERFORMANCE PERIOD COSTS FOR 

DESIGN PAVEMENT AND CONSTRUCTED PAVBMENT ............. COST EVALUATION FOR DESIGN PAVEMENT AWD 

AS-CONSTRUCTED PAVEMENT ............I.................. 

DERIVATION OF PAYMENT PLANS FOR 

PERFORMANCE-RELATED SPECIFICATIONS :.................. 

DEMONSTRATION DEVELOPMENT OF A PERFORMi$E;fCE-RELATED 

M&C SPECIFICATION FOR PCC CONSTRUCTION ................... 

INPUT DATA FOR THE DEMONSTRATION SPECXFICATEON ......... TRAFFIC, SERVICEABILITY, DISTRESS, AND COST HISTORIES .. ECONOMIC PERFORMANCE INDICATORS AND PAiYMENT PLAN ....... SENSITIVITY ANALYSES FOR THE DEMONSTRqTION 

SPECIFICATION ......................................... 

COMMENTS ON THE DEMONSTRATION SPECIFIqATION 

ALGORITHMS AND RESULTS I ............................... 

SUMMARY AND RECOMMENDATIONS FOR FURTHER RESEARCH ......... 

SUMMARY ................................................ Framework for Development of Performance-Related 

Specifications ...................................... Identification of Relationships Available to 

Establish the Connection Between id&^ Factors 

and Various Measures of Pavement performance . . . . . . . Development and Conduct of ~aboratoi~/~ield 

Test Program(s) to Quantify New 

Needed for PRS Development ..... Demonstration Performance-Related ~ 

Specification System ............ .................... FURTHER LABORATORY STUDIES FOR SECON~ARY 

PREDICTION RELATIONSHIPS ......... ................... FIELD STUDIES RELATED TO PERFORMANCE-RELATED 1 SPECIFICATIONS ....................................... FURTHER DEVELOPMENT OF PERFORMANCE-RELATED 

SPECIFICATIONS ........................................ 

1 I 

PAGE 
TABLE OF CONTENTS (continued) 

CHAPTER 

APPENDIX A: SELECTED STRESS PREDICTION RELATIONSHIPS ............... 

MULTILAYERED ELASTIC SOLID ............................. Graphical Solution Technique ......................... Approximation Functions .............................. ELASTIC PLATE ON DENSE LIQUID SUBGRADE ................. 

APPENDIX B: SELECTED DISTRESS/PERFORMANCE PREDICTION 

RELATIONSHIPS FOR RIGID PAVEMENTS ...................... 

APPENDIX C: SUMMARY OF SECONDARY PREDICTION RELATIONSHIPS .......... 

APPENDIX D: RII DATA BASE ANALYSIS ................................. 

CORRELATION MATRIX ..................................... FREQUENCY HISTOGRAMS ................................... SCATTER PLOTS .......................................... MULTIPLE REGRESSION ANALYSES ........................... 

APPENDIX E: COPES DATA BASE ANALYSES ............................... 

PAGE 

CORRELATION MATRIX ..................................... FREQUENCY HISTOGRAMS ................................... SCATTER PLOTS .......................................... REGRESSION ANALYSES .................................... 

APPENDIX F: LABORATORY TESTING RESULTS ............................. 247 
I 

I LIST OF FIGURES I 

h I 

I 

I 4 Finite element idealization of a cylinder J.................,. 19 

I 

5 Finite element configurations used for anaiysis of 

i homogeneous and layered systems ..........,................... 21 1 

1 6 Rationale for selections of a 

? water and cement quantities 49 

I 

I 

1 

7 Two-way plot of FPC7AVE (Y2) versus FR7AVEI(Y1) .............. 

FIGURE 

I 

8 Two -way plot of FT7AVE (Y3) versus FPC7AVE (Y2) .............. 77 

- PAGE 

9 Two-way plot of EC28AVE (Y5) versus FPC7AV 1; (Y2) ............. 78 

'I 

10 Two-way plot of FPC7AVE (Y2) versus VCR (v#) ................. 79 

11 Two-way plot of FPC7AVE (Y2) versus SLMP (41) ................ 80 

1 Framework for development of performance-r lated materials e and construction (M&C) specifications ....+...........,....... 5 

I 

2 Schematic representation of multilayer elah tic pavement 

structure ..................................................... I 12 I 

I 

3 Illustration of plate theory idealization ! ................... 17 

12 Two-way plot of FR7AVE (Y1) versus ACR (V3j .................. 81 

13 Plot of observed versus predicted average !-day PCC 

compressive strength (Y2=FPC7AVE), where o + ly 

mix properties (Xi) were independent variaples ............... 97 

14 Plot of observed versus predicted average 1 ,-day PCC 

flexural strength (Yl=FR7AVE), where only 1 

mix properties (Xi) were independent varialples ............... 98 ! 

I I 15 Plot of observed versus predicted average &day PCC In! 

j 

I tensile strength (Y3=FT7AVE), where only 1 ; mix properties (Xi) were independent variaqles ............... 99 

l1 

16 Plot of observed versus predicted average ++-day PCC 

compressive strength (Y4=FPC28AVE), where ~nly 

mix properties (Xi) were independent variaqies ............... 100 ! I 

'I 

17 Plot of observed versus predicted average 
LIST OF FIGURES (continued) 

FIGURE - PAGE 

Plot of observed versus predicted PCC slump (XI-SUP), 

where only significant design factors (Ui) and design . 

factor functions (Vi) were independent variables ............. 104 

Plot of observed versus predicted PCC unit weight 

(X2=UNWT), where only significant design factors (Ui) and 

design factor functions (Vi) were independent variables ...... 105 

Plot of observed versus predicted PCC yield (X3=Y?.,D), 

where only significant design factors (Ui) and 

design factor functions (Vi) were independent variables ...... 106 

Plot of observed versus predicted PCC air content (X4-AIR), 

where only significant design factors (Ui) and 

design factor functions (Vi) were independent variables ...... 107 

Plot of observed versus predicted average 7-day PCC 

flexural strength (Yl=FR7AVE), where only significant 

design factors (Ui) and design factor functions (Vi) 

were independent variables ................................... 110 

Plot of observed versus predicted average 7-day PCC 

compressive strength (Y2=FPC7AVE), where only significant 

design factors (Ui) and design factor functions (Vi) 

were independent variables ................................... 111 

Plot of observed versus predicted average 7-day PCC 

tensile strength (Y3=FT7AVE), where only significant 

design factors (Ui) and design factor functions (Vi) 

were independent variables ................................... 112 

Plot of observed versus predicted average 28-day PCC 

compressive strength (Y4=FPC7AVE), where only significant 

design factors (Ui) and design factor functions (Vi) 

were independent variables ........................,.......... 113 

Plot of observed versus predicted average PCC elastic 

modulus (Y5=EC28AVE), where only significant 

design factors (Ui) and design factor functions (Vi) 

were independent variables ................................... 

Plot of observed versus predicted average 7-day PCC 

flexural strength (Yl=FR7AVE), where all design 

factors (Ui and Vi) and mix properties (Xi) 

were independent variables ................................... 

Plot of observed versus predicted average '/-day PCC 

compressive strength (Y2=FPC7AVE), where all design 

factors (Ui and Vi) and mix properties (Xi) 

were independent variables ................................... 
LIST OF FIGURES (continued) 

FIGURE 

29 Plot of observed versus predicted average 7-day PCC 

tensile strength (Y3=FT7AVE), where all design 

factors (Ui and Vi) and mix properties (Xi) 

were independent variables ................................... 

30 Plot of observed versus predicted average 28-day PCC 

compressive strength (Y4=FPC28AVE), where all design 

factors (Ui and Vi) and mix properties (Xi) 

were independent variables ................................... I 

31 Plot of observed versus predicted average PCC elastic 

modulus (Y5=EC28AVE), where all design , I 

factors (Ui and Vi) and mix properties (Xi) 1 

were independent variables ................J.................. I 

32 Sensitivity of PCC properties to design facior changes ....... 

33 Derivation of performance-related M&C speci$ications ......... 

34 

35 

pavement and constructed pavement 

Economic life differentials between design 

Economic life indicators ..................................... ............................ 

36 Determination of acceptance plan payment sy$tem based 

on theoretically derived pay function and expected 

payment operating characteristic curve ....................... 

37 Serviceability and traffic histories ......................... 

38 Routine maintenance cost histories ........................... 

39 Vehicle operating cost histories ............................. 

40 Histories for equivalent uniform annual costs (EUAC) ......... 

41 Relationship B: Relation between flexural and 

compressive strengths for concretes made widh different 

aggregates. (73,2) .......................... .................... I 

42 Relationships C and G: Relationships of compressive 

to flexural and tensile strengths of ........... I 

43 Relationship D: Relation between modulus qf rupture 

at 28 days and water/cement ratio. (73.2) .... r .................. 

I 

44 Relationship I: The influence of the 

ratio on strength of concrete. (73.2) 

viii 
LIST OF FIGURES (continued) 

FIGURE . PAGE 

45 Relationship J: Typical compressive strengths for 

air-entrained and non-air-entrained concretes as related 

to curing time . "' - " .......................................... 199 

46 Relationship K: Strength in relation to cement content 

for air-entrained and non-air-entrained concrete 

of constant slump . ....................................... 200 

47 Relationship L: Influence of aggregate size on 

28-day compressive strength of concretes with different 

cement contents . '8'.4' ......................................... 201 

48 Relationship M: Effect of entrained air 

on durability . "'." ........................................... 

49 Relationship Q: Effect of aggregates on the modulus 

of elasticity of concrete . ................................ 

50 Relationship R: Water/cement ratio and aggregate 

content effect on drying shrinkage . ...................... 

51 Pavement condition rating .................................... 

52 Ride condition index ......................................... 

53 Cumulative 18-kip ESAL traffic ............................... 

54 Pavement age ................................................. 

55 Pavement design thickness .................................... 

56 Concrete flexural strength at 7 days ......................... 

57 Concrete compressive strength at 7 days ...................... 215 

58 Concrete core strength ....................................... 215 

59 Concrete slump 

,60 Percent air in mix ...... 

61 Water/cement ratio ........................................... 

62 Concrete flexural strength versus concrete core 

Compressive strength ......................................... 

63 Concrete core strength versus water/cement ratio 218 I 

............. 

64 Concrete slump versus water/cement ratio ..................... 219 
LIST OF FIGURES (continued) 

FIGURE 

65 Concrete slump versus entrained air percentage ............... b ? 

66 Concrete flexural strength versus water/cement ratio ......... 

67 Concrete compressive strength versus entrained 

air percentage ............................................... 

68 Concrete core strength versus entrained air percentage ....... 

69 Concrete flexural strength versus slump ...................... 

70 Concrete flexural strength versus entrained air percentage ... 

71 Concrete flexural strength versus pavement age ............... 

72 Concrete slump versus pavement age ........................... 

73 Entrained air percentage versus age .......................... 

74 Water/cement ratio ........................................... 

75 Mean slump ................................................... 

76 28-day modulus of rupture versus entrained air ............... 

77 28-day modulus of rupture versus water/cement ratio .......... 

78 28-day modulus af rupture versus mean slump .................. 

. 

PAGE 

79 28-day modulus of rupture versus type of cement used ......... 240 

80 28-day modulus of rupture versus amount of water ............. 

81 28-day modulus of rupture versus amount of cement ............ 242 

82 Mean slump versus entrained air .............................. 243 

83 28-day modulus of rupture versus year opened to traffic ...... 244 
I 

1 LIST OF TABLES 

TABLE . PAGE 

1 General classification of variables in primary 

relationships for rigid pavements ....................... ;... 10 

2 Comparison of multilayered elastic analysis 

computer programs'".') ....................................... 14 

3 Distress prediction variables and selected relationships .... 

4 Summary of current M&C specifications in selected States .... 32 

5 Classification and cross references for PCC MGcC variables ... 36 

6 Comparison of available secondary prediction relationships .. 39 

7 Batch input data for the laboratory study ................... 50 

8 Output specimens and measurements for each PCC batch 

of the laboratory study ..................................... 52 

9 Aggregate data used in laboratory study ..................... 54 

10 Experimental design factorial for laboratory study .......... 55 

11 Mix design spreadsheet ...................................... 57 

12 Standard batch testing report form .......................... 58 

13 Classification and definition of data base variables ........ 60 

14 Classification and scope of analyses for the lab 

study data .................................................. 63 

15 Means. standard deviations. and pairwise correlation 

coefficients for variables in data base A ................... 72 

16 Variations in PCC properties between duplicate specimens .... 82 

17 Variations in PCC p-roperties between replicate mixes ........ 84 

18 Analysis of variance and covariance for mix properties (X) .. 87 

19 Analysis of variance and covariance 

for hardened PCC propertfes (V) ............................. 89 

20 Effects of design factors on mix properties 

and hardened PCC properties ................................. 92 

21 Regressions of hardened PCG properties (Y) 

on mix properties (X) ....................................... 95 
LIST OF TABLES (continued) 

TABLE PAGE 

22 Multiple regressions for mix properties (X) on 

significant design factors (U) and factor functions (V) ..... 102 

23 Multiple regressions for hardened properties (Y) on 

significant design factors (U) and factor functions (V) ..... 

24 Multiple regressions for hardened properties (Y) on 

significant design factors (U,V) and mix properties (X) ..... 

25 Simple regressions for selected pairs of 

PCC properties (Y) (N = 60 mixes) ........................... 122 

26 Inputs for sensitivity analysis of selected 

dependent variables ......................................... 124 

27 Sensitivity of mix properties to changes in design factors .. 125 

Sensitivity of PCC properties to changes in design factors .. 

Input data for the demonstration specification .............. 

Traffic, serviceability, distress, and cost histories ....... 

Economic performance indicators and pay factors ............. 

Sensitivity analysis data for performance-related 

payment plan based on economic life ......................... 

Variance and regression analysis for pay factor 

dependence on primary PCC specifications .................... 

Sensitivity of specification pay factor to 

selected changes in PCC and non-PCC factors ................. 

Relationship S: Thermal coefficients for concretes made 

with different types of coarse aggregate. '82.7' ................ 

Description of variables in RII SECTION data file ........... 

Summary statistics for key factors contained in 

"working" RII data base ..................................... 

38 Correlation matrix of factors in "working" RII data base .... 213 

39 Correlations for COPES data base ............................ 

40 Data base A ................................................. 248 

41 Data base B ................................................. 

42 Data base C ................................................. 

xii 
CHAPTER 1 

BACKGROUND, OBJECTIVES, AND SCOPE 

Over the past 10 or 12 years considerable research has been directed 

towards the development of performance-related specifications (PRS) for 

measures of materials and construction (M&C) quality. In 1976, a National 

Cooperative Highway Research Program (NCHRP) synthesis was published on 

statistically oriented end-result specification^.(^^-^)* Fundamental concepts 

for performance-based acceptance plans and associated price-adjustment 

systems were reported in the late 1970's and many further developments were 

reported in the early 1980's as reflected in references 77.1, 78.1, 80.1, 

82.1, 82.2, 82.3, and 84.1. 

A state-of-the-art specification for flexible pavement was published by 

the Federal Highway Administration (FHWA) in 1984.(84.5) At about the same 

time a research program for development of PRS was instituted by the NCHRP, 

beginning with NCHRP Project 10-26. The main objective for that study was 

to identify variables and existing data bases from which appropriate 

relationships between M&C factors and performance indicators might be 

derived as inputs for specifications development. It was concluded that 

existing data bases were probably inadequate for direct derivation of 

essential relationships. (85v4) 

As a consequence of the Project 10-26 study, the NCHRP decided that 

further research on PRS should be within a general framework that provides 

for multistage derivation of the needed relationships. In this framework 

primary relationships would be between performance indicators (e.g., 

distress levels or applications to flfailure") and known performance 

predictors (e.g., surfacing thickness and mechanistic properties). 

Secondary relationships would show the nature and extent of associations 

among the performance predictors and other M&C factors that are amenable to 

M&C control (e.g., asphalt concrete (AC) or portland cement concrete (PCC) 

mix factors). 

Under this new approach, NCHRP Project 10-26A was initiated in 1986 

and is expected to be completed in 1990. Based on the scope of work, the 

research report should cover virtually all aspects of PRS development for AC 

materials and construction, including experimental results from laboratory 

studies and algorithmic demonstrations of particular M&C acceptance plans 

and payment schedules. '88.1) 

Much development of PRS for rigid pavements has been done by the New 

Jersey Department of Transportation (NJDOT). Comprehensive procedures for 

deriving acceptance plans and payment schedules are set forth in reference 

82.4. For the most part, performance-relatedness of these specifications is 

based on the rigid pavement performance equation given in the American 

Association of State Highway and Transportation Officials (AASHTO) Interim 

Guide for Design of Pavement Stru~tures.(~l-~) In turn, this equation is 

* References in this report are identified by a superscript which 

includes the date of the report (first two digits) followed by a 

numerical designation. 
based on a present serviceability index (PSI) prediction equation that was 

reported from the American Association of State Highway Officials (AASHO) 

Road Test, and that contains four performance predictors relating to M&C 

factors, namely, PCC thickness, PCC flexural strength, PCC elastic modulus, 

and modulus of subgrade reaction. (62.1) The NJDOT specifications include 

acceptance and payment plans that are based on as-constructed PCC thickness 

and strength. 

To provide a research program parallel to the NCHRP 10-26A study, the 

FHWA in 1987 requested proposals for development of PRS for PCC pavement 

construction. In response to the FHWA request, the research described in 

this report was initiated in mid-1987 and had the following objectives: 

1. To identify relationships, between measures of material and 

construction quality and pavement performance, that are necessary 

for the development of performance-related rigid pavement 

specifications. 

2. To develop a laboratory/field testing program designed to quantify 

the necessary relationships. 

3. To conduct laboratory/field testing to quantify all necessary 

relationships between one materials and construction specificatian 

variable and rigid pavement performance. 

4. To demonstrate the development of a performance-related 

specification (including incentive/disincentive provisions) for the 

one selected materials and construction specification variable. 

The scope of work used to accomplish the foregoing objectives is 

implied by the following resume of the report contents. 

A general framework for specifications development is given in 

chapter 2. Existing primary relationships for the prediction of rigid 

pavement stress, distress, and performance are assessed in chapter 3, 

wherein specific variables and relationships are proposed for use in the 

demonstration specification development. 

Existing secondary relationships and data bases for rigid pavement M&C 

variables are evaluated in chapter 4, relative to an Moptimum" data base 

that would suffice for the development of demonstration specifications. The 

chapter includes discussion of M&C specifications in current use by a number 

of selected States. 

Chapter 5 gives a description of the laboratory study of needed 

secondary relationships. Initial experiment design, implementation, data 

acquisition, variable classifications, and statistical analysis techniques 

are a11 discussed in detail in this chapter. 

Statistical procedures and computer algorithms for development of 

performance-related M&C specifications are set forth in chapter 6, and 

provlde a basis for the development of demonstration specifications. 

2 
Chapter 7 gives details of the development of a PRS demonstration 

program of performance-related M&C specifications for concrete pavement 

construction. This PRS program was developed around the methodology 

discussed in NCHRP Project 10-26A. This PRS demonstration system uses 

secondary relationships derived from the laboratory study data. Chapter 7 

also includes a sensitivity study and comment section on the PRS 

demonstration system. 

Finally, chapter 8 provides a summary and recommendations for further 

research on. the development of PRS systems for PCC pavements. The 

recommendations include further work on (1) laboratory experiments for the 

development of better so-called secondary prediction relationships, (2) 

field studies for the development/verification of better primary performance 

prediction relationships and (3) analyses to improve the fundamental 

mechanics (i., cost components, acceptance and payment plans, operating 

characteristics, etc.) of future PRS systems. 

Throughout the scope and work of this study, special efforts have been 

made to draw upon and ensure compatibility with relevant results from all 

cited developments of performance-related M&C specifications. 
CHAPTER 2 

FRAMEWORK FOR DEVELOPMENT OF PERFORMANCE-RELATED M&C SPECIFICATIONS 

A general framework for the development of performance-related M&C 

specifications is shown schematically in figure 1. The framework is based 

on concepts that were presented in the Irick paper and is consistent with 

the framework that has been developed in NCHRP Project 10-26A for 

asphaltic- concrete specifications . (87.48 88. 

Shown on the left of figure 1 are four sets of relationships (Rl 

through R4) and two boxes (B and C) that represent variables contained in 

the relationships. Box A represents data bases for all variables that are 

used to derive the relationships, including variables in box B and box C. 

The right side of the figure shows four types of additional inputs (boxes Cr 

through G) to algorithms (R5) that are used to produce the performance 

related M&C specifications represented by box H. 

In this chapter, an overview is given for all 13 framework elements. . , 

More extensive discussion and examples for the elements are given in 

chapters 3, 4 and 6. 

Primary relationships for this study are defined to be those for 

predicting pavement stress (Rl), pavement distress (RZ), and pavement 

performance (R3) from particular combinations of predictors (box B) that 

represent traffic, environmental, roadbed, and structural conditions. It is 

assumed that any relationship among R1 through R3 is an equation (or 

algorithm) that predicts values for an output variable that is a specific 

indicator of stress, distress, or performance. Oqe stress indicator, for 

example, might be a particular strain in the PCC surfacing layer, one 

distress indicator might be inches of wheelpath faulting per mile, and one 

performance indicator might be the number of ESALs at which the pavement's 

present serviceability index has reached PSI=2.0. 

Predictor variables represented by box B are well-defined independent 

variables that appear explicitlv in one or anothen of the primary 

relationships. Examples are surfacing thickness (box B4), roadbed soil -' 

modulus (box B3), annual precipitation (box B2), and annual rate of 

equivalent single axle load (ESAL) accumulation (box Bl). 

A number of specific primary relationships for PCC pavements will be 

identified in chapter 3. In general, each has been derived either from 

mechanistic considerations (M in figure I), from empirical models (E), or 

from some combination of the two methods (ME). A fourth method for deriving 

a particular relationship is through algebraic manipulation (A) of one 6r, 

more relationships that were derived via methods M, E, or ME. 

As indicated in box A, data bases used to derive primary relationships' 

may be either observational, experimental, or some combination thereof. An 

observational data base, for example, might represent observations from a 

set of selected highway construction projects. An experimental data base 

arises from a designed study in which control is planned and exercised over 

the independent variables of the study. Thus, experimental data bases can 

result from sets of specially constructed test sections as in the AASHO Road 

Test, or from the test specimens of a designed laboratory experiment. 
R2. DISTRESS PREDlCTtON RELATIONSHIP 

i METHODS 

Stress Indicators 

AND M&C SPECtFlCATlONS 

Base / Subbase 

1. Observational 

Figure 1. Framework for development of performance-related materials and construction (M&C) specifications. 
Associated with every prediction relationship is at least one 

statistical distribution of prediction errors, i.e., differences between 

predicted values for a given indicator and corresponding observed values of 

the indicator. Characteristics of the error dist~ibution (e.g., shape, mean 

value, standard deviation) are needed for the devqlopment of performancebased M&C specifications, as will be discussed inchapter 6, To the fullest 

extent possible, discussion of specific relations~ips in chapters 3 and 4 

includes what is known about their methods of dertvation and their error 

distributions. 

Certain explicit predictors in boxes B3 and B4 may be materials and/or 

construction factors whose levels are controlled directly during the M&C 

process (e.g., layer thicknesses). In other cases, explicit predictors may 

be controlled indirectly through other M&C factors that are represented by 

box C. All M&C factors that are not explicit predictors for a particular 

set of relationships fall in one or another of three classes of "other" M&C 

factors. 

Class C1 contains factors that are not explic,it predictors but that may 

be used as surrogates for factors that appear in one or another of R1 

through R3. For example, the relationships in use may contain PCC flexural 

strength as an explicit predictor, whereas PCC compressive strength might be 

controlled through M&C specifications. In this csse, compressive strength 

is a surrogate for flexural strength. 

Class C2 contains M&C factors that are not explicit predictors but have 

specifications to provide indirect control for expllicit predictors or their 

surrogates. If, for example, a prediction relationship contains modulus of 

subgrade reaction as an explicit predictor of stress/distress/ performance, 

then class C2 may contain factors, such as density and compaction, whose 

specifications provide at least partial control over soil modulus. Other 

examples of factors in class C2 are those which specify certain PCC mix 

properties (e.g., cement content) that are known 'to affect explicit 

predictors such as PCC flexural strength or modulus of elasticity. 

The remaining M&C factors in box C are called process control factors 

(C3) whose specifications enhance the control of other M&C factors. 

Examples include moisture control during roadbed p&eparation so that 

specified levels of soil density and compaction cap be attained. Other 

examples include -control of subsurface profiles to enable attainment of 

specifications for surfacing profile. Some M&C factors may belong in two 

or more subclasses of box C. Slump of the PCC mix, for example, may be 

controlled to enhance both workability of the PCC and its ultimate strength. 

Secondary relationships (R4) include all equations or algorithms that 

show interrelations among M&C factors that are represented by box C and 

boxes B3 and B4. By definition, secondary relatiotlships do not contain 

indicators for stress/distress/performance, but shbuld account for all M&C 

factors that are explicit predictors in the primary relationships. Chapter 

4 discusses (1) existing secondary relationships that have been identified 

by the research team, and/or (2) available data bases that might be used or 

augmented to produce new secondary relationships aqong M&C factors. Chapter 

5 describes new laboratory studies whose experimental design and 

implementation can lead to secondary relationships that are needed for the 
development of performance-related M&C specifications, but are neither 

available from past research nor attainable from available data bases. 

As for the derivation of primary relationships, existing data bases for 

secondary relationships may be either observational or experimental. In 

chapter 5, however, it is assumed that new data bases for R4 relationships I 

should be developed from planned experiments. 

As shown in figure 1, both primary relationships (R1 through R3) and 

secondary relationships (R4) are inputs to the algorithms (R5) that produce 

performance-related M&C specifications. The specific nature of these 

algorithms will be discussed in chapter 6. The algorithms depend upon 

criteria (box G) that are used to derive performance-related M&C 

specifications. I 

As shown in the figure, certain algorithms in R5 are needed for 

predictions of performance and operational costs associated with pavement 

deterioration and rehabilitation. Other algorithms are needed for the 

derivations of acceptance plans and payment schedules that are associated 

with the M&C specifications. The specifications criteria in box G include, 

for example, acceptance risks and performance-based economic criteria. 

Boxes D through F in figure 1 represent conditions and constraints that 

must be taken into account by the specifications algorithms. Included are 

pavement design criteria (box D) that specify particular stress/distress/ 

performance indicators, limiting values for the indicators, and particular 

primary relationships (Rl through R3) that are to be used as pavement design 

equations. 

It is assumed that the design criteria will also include a design 

period (e.g., 15 years) during which the selected distress/performance 

indicators do not reach their limiting values, and associated predictions of 

expected traffic during the design period, perhaps in terms of ESAL 

accumulation. A third design criterion is design reliability, which is 

basically a factor incorporated in the AASHTO design guide to treat the 

variability of pavement performance from a design standpoint. 

Another class of constraints for the specifications algorithms is 

represented by available M&C resources (box E) and their associated costs 

(box F). As indicated, the M&C resources will generally represent various 

options for materials (e.g., aggregate sources) and construction methods 

(e.g., paving equipment and procedures). 

Unit costs in box F must cover not only options for materials and 

pavement construction, but should also include data for estimating routine 

maintenance costs and user costs for various levels of pavement condition. 

If the optimization criteria relate to perf ormance periods beyond the 

initial period, the cost data must provide inputs for estimation of 

rehabilitation costs. 

The final element of the framework (box H) represents performancerelated M&C specifications that are derived via the algorithms in R5. It is 

assumed that the specifications include target levels (Hl) and/or 

specification limits (H2) for all MGLC factors that relate to the pavement's 

7 
structural design. Specifications for some factors might include target 

levels and lower limits only (e.g., PCC thickness , other specifications 

might have both upper and lower limits but no tar et level (e.g., aggregate i gradation). Other specifications might have onlya lower limit (e.g., PCC 

flexural strength) or an upper limit (e.g., surfat$e profile deviation). I 

In general, it may be assumed that target le~els are based on specific 

relationships among R1 through R4, subject to,criteria, conditions and 

constraints imposed by items in boxes D through GI It can be expected that 

levels will be assumed for some factors and that he algorithms will 

indicate alternative combinations of levels for r t maining M&C factors, at 

least whenever the necessary relationships (R1 th$ough R4) are available. 

Levels for some factors will, of course, be specified through State 

requirements and/or through M&C standards that haqe been set by AASHTO or 

American Society for Testing and Materials (ASTM)h 

Although some specification limits may also $e determined by 

requirements and standards, the algorithms shouldmake appropriate use of 

(1) error distributions for the relationships that determine target levels 

and (2) normal variability in M&C factors. It w+ll be assumed that item 

(2) is an essential aspect of all secondary relatjonships in R4. 

I 

After target levels and/or specification limits are produced by the 

algorithms, acceptance plans (H3) are developed fbr those factors whose 

levels can effect the acceptance or rejection of aterials and/or pavement 

layers. In the simplest case an acceptance plan T ould define the "lots" to 

be sampled, time/space sampling points, measuremeht procedures for the 

samples, and measurement statistics (e . g. , percenk within tolerance limits) 

that will lead either to acceptance or rejection bf a given lot. An 

essential aspect of any acceptance plan is its opyrating characteristic, 

i.e., the probability that lots of given quality (with respect to the M&C 

factor that has been evaluated) will be accepted. It is assumed that the 

unit costs in box F include M&C inspection and quylity control expenditures. 

The fourth facet of PRS includes payment pla*s (H4) that determine the 

extent to which the contractor's bid price will be adjusted as a consequence 

of specific (or multiple) characteristics of the +-built pavement lots. In 

general, payment plans may be expressed as pay fa tors (e.g., ranging from 4 0.5 to 1.2) that correspond to the differences be$ween the expected 

performance of the design pavement and the as -conqktructed pavement. 

I 

The foregoing overview of the framework reprasented by figure 1 implies 

that the algorithms in R5 are necessarily extensi$e and complex. Although 

considerable research effort will be required to Sinalize other framework 

elements, particularly the secondary relationship4 (R4), it appears that 

the algorithm development will be even more demadding. To the fullest 

possible extent, the eventual algorithms will dra4 upon and be consistent 

th counterpart algorithms that have been develo 4 ed in other studies, such 

NCHRP Project 10-26A, and in those representediby references 78.1 and 

.4. 
CHAPTER 3 

PRIMARY RELATIONSHIPS 

This chapter covers and provides specific examples of the three types 

of primary relationships that were shown in figure 1, namely: 

a R1 - Stress prediction relationships for various indicators of 

pavement response to single loading applications. 

R2 - Distress prediction relationships for various indicators of 

pavement distress, including singular distress modes and 

composite indicators of overall distress. 

a R3 - Performance prediction relationships for the time periods 

and/or traffic accumulations for which pavement distress 

remains at acceptable levels. 

Table 1 is a general classification scheme for the variables that are 

contained in the primary relationships. The left-hand column lists the 

indicators whose values are functions of the predictors listed in the 

right-hand column. Thus, the dependent variable for any particular 

relationship is in the first column, the corresponding independent variables 

are among those listed in the second column. 

Stress indicators are dependent variables in R1 relationships but can be 

predictor variables in R2 relationships (see class 226). Moreover, certain 

distress indicators can be dependent variables in some of R2, and auxiliary 

independent variables in other R2 relationships (see class 227). 

Each type of relationship is discussed, respectively, in the sections 

that follow. Withimeach section, specific primary relationships are 

identified and the relevant portions of table 1 are expanded to include more 

specific indicators and predictors. Objectives for each section are to: 

1. Identify all predictors that are related to rigid pavement 

materials and construction, particularly for the PCC surfacing 

component. 

2. Select a small number of relationships that are candidate elements 

of the algorithms that will be used to derive performance-related 

M&C specifications. 

3. Discuss for each selected relationship, the sensitivity of the 

predicted variable to changes in predictor variables. 

4. Estimate the nature and extent of prediction errors that are not 

explained by the predictors. 

STRESS PREDICTION RELATIONSHIPS 

This section describes many of the available analytical (and empirical) 

response models that can be used to predict stresses, strains and/or 

deformations in portland cement concrete (PCC) pavements. This section is 
Table 1. General classification of variables in primary relationships 

for rigid pavements. 1 

I 

Rl. STRESS PREDICTION RELATIONSHIPS 

11. STRESS INDICATORS 12. STR~SS PREDICTORS 

111. Deflections 

112. Strain Components 

113. Stress Components 

Loading Factors 

Moisture/Temperature 

Conditions 

Surfacing Factors 

Base/Subbase Factors 

Roadbed Factors 

R2. DISTRESS PREDICTION RELATIONSHIPS 

21. DISTRESS INDICATORS 22. DIsTRbss PREDICTORS I 

211. Singular Distress Indicators 221. 

2111. Pumping 

2112. Cracking 

2113. ~aulting 

2114. Joint Deterioration 223. 

2115. Other Slab Distresses 

2116. Swells and Depressions 224. 

2117. Skid Resistance Loss Or7C LLJ. 

212. Composite Distress Indicators 

* 2121. Roughness 226. 

2122. Serviceability Loss 

2123. Condition Rating Loss 227. 

Traffic Factors & Age 

Env2ronmental Factors 

Surfacing Factors 

Base/Subbase Factors 

Roadbed Factors 

Stress Indicators 

Auxiliary Distress 

Indicators 

R3. PERFORMANCE PREDICTION RELATIONSHIPS I 

1 

31. PERFORMANCE INDICATORS 32. PER ORPllANCE PREDICTORS 

Number of Equivalent Single Dis ress Predictors in 

Axle Load Applications (ESAL) 1 Clagses 221-227. 

at Acceptable Levels of 

Distress Indicators 
mostly a condensation of reference 86.4 with some enhancements for the 

models that were not covered. 

The models can each basically be classified under one of the following 

four categories: 

Empirical. 

0 Multi-layered elastic solid. 

* Elastic plate on dense liquid. 

* Finite element idealizations. 

The first category refers to models that have been derived through 

mathematical oi statistical analysis of field data. The last three 

categories are all mechanistic models that rely on theory and the 

fundamentals of engineering mechanics in solving for a particular response. 

Emnirical Models 

Results of studies on the original AASHO Road Test data provide 

excellent examples of empirical pavement response models that have been 

derived through statistical analysis of field Following is a 

derived equation that relates dynamic edge strain (STRN, lom6 in/in) to 

design slab thickness (D2, inches), single axle load (Ll, kips) and 

temperature (T, OF) : 

Similar equations were derived for both static and dynamic deflections 

measured at the slab edge and corner. These equations are all very useful 

in evaluating pavement behavior and predicting performance at the Road Test. 

However, they lose their applicability once environmental and loading 

conditions outside those experienced at the Road Test are encountered. This 

explains why the analytical or mechanistic models described next are so much 

more attractive than any empirical models. They are capable of predicting 

pavement behavior and response for a much wider range of conditions. 

Multi-Lavered Elastic Analysis Models 

In this analytical methodology, the pavement is modeled as a series or 

"stack" of individual layers having unique characteristics (see figure 2). 

Each layer is assumed to be infinite in all horizontal directions, and the 

materials that compose the layers are considered to be homogeneous, 

isotropic and linear elastic in response. (Note: There are some models 

that incorporate ad-hoc procedures to treat the nonlinear response of 

materials to stress.) The materials in each layer are characterized by 

their thickness (hi), elastic or Young's modulus (Ei), and Poisson's ratio 

(vi). Some methods also consider the unit weight of the layer materials, 

however, most assume the layers are weightless. 

Loads applied to the pavement surface are assumed to have circular 

contact areas with uniform contact pressures. Most methods can only 
Figure 2. Schematic representation of multilayer elastic 

' pavement structure. 
simulate vertical loading; however, there is at least one that permits 

tangential surface loads. Many of the available methods also permit the 

consideration of multiple surface loads (usually up to 10). Most methods 

also assume that there is full friction (i.e., no slippage) at the 

interfaces between the layers, although there is at least one method that 

does permit variable friction at the layer interfaces. 

As illustrated by the diagrams in figure 2, a variety of normal and 

shear stresses can be computed on the faces of a three-dimensional 

differential element anywhere within the structure. Corresponding strains 

and displacements due to load can also be determined. Some models even 

provide for the computation of maximum principal stresses and strains using 

a Mohrts circle-based procedure. For those that permit the use of multiple 

loadb, the principle of superposition is used to combine the effects at any 

designated point. 

For one-, two- and three-layer structures, hand/graphical solution 

techniques have been developed through an evolutionary process by a 

multitude of researchers. These equations and nomographs have been 

assembled and published under one textbook. (75.1) These methods do, however, 

have some problems (see appendix A). 

By far, the quickest and most accurate way to develop solutions is 

through the use of the computer programs that are currently available. 

These computer programs make use of integral transform procedures and are 

based on the solutions originally developed by Burmister: '45s11 

VESYS . '78.2) 

* CHEVIT. '76+2' 

Table 2 provides a summary comparison of the capabilities of each of these 

multilayered elastic analysis programs. 

Although these computer programs are relatively fast compared to some 

of the other more complex methods, there are occasions (particularly on 

microcomputers) where even faster operational speeds are desirable. This 

and the need to study the statistical significance of many of the 

independent variables has led to the development of regression equations 

that simulate the output of the analytical programs. Appendix A provides 

some examples of these kinds of approximation functions. 

Multilayered elastic solid based modeling procedures have been used for 

the analysis of both rigid (PCC) and flexible pavements. However, they do 

have their weaknesses for both pavement types: 

13 

e For PCC pavements, the procedures are unable to treat the effects 

of discontinuities that may exist in the structure (e, cracks, 

joints, non-uniform support, etc.). Direct computation of 

stresses, strains and displacements is only possible for interior 

load and full support conditions. Edge and corner loads, voids and 

variable load transfer at joints/cracks must all be treated by 

applying an adjustment factor derived by some other analytical 

means, such as finite element idealizations. 

e For flexible pavements, there is a limitation when analyzing 

layered systems consisting of unbound granular layers. Because of 

their lack of cohesion, these materials have little capability to 

withstand the levels of tensile stress that might be generated by 

one of the theoretical elastic layer models. (This problem is less 

profound in rigid pavements since the PCC slab carries most of the 

stress.) The likelihood of prediction of this unrealistic 

condition is greatest when the ratio of elastic moduli between 

adjacent layers exceeds a practical value (generally between 1.5 

and 4.0). To treat this phenomenon, some Itad hoc" procedures have 

been developed that essentially adjust layer moduli to ensure that 

significant tensile stresses are not developedhin the unbound 

layers. 

Elastic Plate on Dense Liauid Suberade 

H.M. Westergaard developed the original plate theory for pavements in 

1925. He presented prediction models for stresses in slabs of uniform 

thickness resulting from loads and the effects of slab curling subjected to 

temperature gradients. (26-1) Modifications to his models based on 

experimental findings have been suggested by various investigators but his 

basic considerations remain unchanged. Westergaard's original work provided 

equations (shown below) for the computation of deflections and stresses for 

interior, edge and corner loading of rigid slabs. No equations were 

presented for strain. (70.1# 85.6) 

Interior Deflection: 

DEFI = 0.125*~/(k*~') (2) 

Edge Deflection: 

DEFE = 0.433*~/(k*~') (3) 

Corner Deflection: 

DEFC = [1.1 - 0.88*(2/L)]*p/(k*L2) (4) 

Interior Stress (v - 0.15): 

SIGI = 0.316*P* [4*loglo (L/b) + 1.0691 /h2 (5) 

Edge stress* (v - 0.15) : 

SIGE = 0. 572*P*[4*logl0(L/b) + 0.359 ]/h2 (6) * This equation has been corrected by We~tergaard.(~~.') 

Corner Stress-: 

SIGC = 3*P[l - (a,/~)~-~]/h~ (7) 
I 1 I 

I 

I I 

I I I I 

I 

Following are definitions for each of the variables in these equations: 

t I 

I P = load magnitude (pounds) . I k = modulus of subgrade reaction (pci). 

i L = radius of relative stiffness (inches). 

I = [ (~*h~)/(12*(1-~~)*k) I 

E = PCC modulus of elasticity (psi). li 

I! h = slab thickness (inches). 1 

, v - Poisson's ratio. I 

k = modulus of subgrade reaction (pci). 

a = load radius (inches). 

a, = distance from center of load to corner o slab; normally 

= (2*a2)0.5. 4 

1 b = a; for a 2 1.742*h (ordinary theory) or 

f 

I I - (1. 6*a2 + hZ)Oa5 - (0.675*h) ; for a < 1.792*h (special theory) . I 

I 

More recent studies by Ioannides based on th$ use of finite element 

analyses have further enhanced these equations. (84 t 9# Appendix A 

summarizes these equations which have also been ificorporated into a computer 

program called WESTER. (84.9) I 

I 

The Westergaard idealization is presented in figure 3. The pavement 

structure is represented as a "medium-thick" elastic plate resting on a 

dense liquid (Winkler) foundation. Assumptions o& this theory include the 

following: l 

o Surface forces act normal to the surface; (i.e., there is no 

shear). I 

I 

The PCC slab is of uniform thickness, stkffness, and elasticity. 

I 

There are no (axial) forces in the plane1 of the slab (such as 

compressive stresses due to thermal expapsion). 

There are no vertical deformations in the slab. 

Perpendicular planes remain perpendicula!~ after bending. 

All materials have linear stress-strain curves. 

e There is no strain in the x-y plane. I 

The interface between the PCC slab and qhe underlying material is 

assumed to be frictionless. 

The slab is uniformly supported. 

1 

i Representing the PCC slab as a medium-thick elastic plate produces i 

1 essentially the same responses as if it were modejled as an elastic layer. I 

!i 

I Thus, the major differences between plate theory and elastic layer theory 

i for rigid pavements is in the representation of the remainder of the 

structure. I 

The Winkler foundation is described by a bed of closely-spaced, 

independent linear springs, each representing thq effects of support 

provided over a unit area. Each spring deforms jn response to the stress 

applied directly to it while neighboring springs remain unaffected. Thus, 

it is assumed that the deflection at any point i~ directly proportional to 

the contact stress at that point on the surface. Support is quantified by a 

spring constant, k, called the modulus of subgrqde reaction, which is the 

ratio of pressure on the unit area divided by the resulting deflection. 

Representing support conditions with a single lajer of material does present 

drawbacks in the analysis of multilayered support$ systems, particularly when 

one or more support layers are especially rigid, as happens when a 

stabilized base or concrete slab is present. Sonje researchers have 

attempted to address these conditions with a verd high k value, but the 

validity of this approach is questionable. I 

I 

I 

In the basic Westergaard idealization, on19 uniform, circular - shaped 

load distributions can be handled. In his 1948 work, however, Westergaard 

did present an equation for an elliptically loadQd area. (48.1' Procedures 

have also been developed by Pickett, et al., andPickett and Ray to handle 

uniform pressure distributions of any shape. ~hdse graphical procedures 

permit analysis with multiple wheel loads as well as single wheel 

loads. (51.1,51.2) \ 

The Westergaard model does provide a means lof analyzing free edges and 

corners. The slab bending stress, vertical defldction and foundation 

reaction pressure can be computed at or near thefree corner or edge of a 

slab that is semi - infinite horizontally. It candot, however, handle more 

than one slab at a time. This prevents the diredt analysis of stress 

reductions that result from various levels of lor/d transfer across 

transverse joints and cracks or support PCC shoulders. 

Empirical adjustments to the free edge be made to account for 

the reduced deflections due to support slabs. 

Equations have also been developed that 

account stresses caused by thermal gradients in &he slab. (38.1) 

Finite Element Idealizations 

I 

The development of the finite element metho$ has produced analysis 

capabilities that far exceed those of plate theoty. There are some tradeoffs, however, in that increased attention is rebuired in data preparation 

and output interpretation. I / 

For analysis by this method, the body to beanalyzed is divided into a 

set of elements connected at their joints or nodal points. The cylinder 

shown in figure 4 is an example. The continuous~variation of stresses and 

strains in the real system is replaced by an assumed linear variation of 

displacements, and hence constant stresses and sfrains within each element. 

This assumption satisfies the requirements of coypatibility of displacements 

between elements. For a given element geometry And constitutive equation, 

the stiffness matrix relating displacements and joads at the corners of each 

of the basic triangular elements is established. The four triangular 

elements forming one rectangular element are generally combined, eliminating 

the common nodal point. Combinations of the element stiffness matrices 

yields the symmetric banded matrix for the entire structural assembly, which I 

is modified using known displacements at bound dxes. Solution of this 

system of linear equations yields all nodal point displacements, from which 

the element strains and stresses are computed. ,The average of the stresses 

in the four triangular elements gives the best estimate of the stresses at 

the centroid of the rectangular element. ! 

I 

The element configuration must be carefully selected to optimize the 

results. (See ,figure 5 for example.) Generally, the accuracy is improved 

by the use of a finer mesh, particularly in areas of rapidly varying 

stresses. However, the greater number of elements increases the 

computational time and therefore the costs. Deblen has suggested that an 

optimum rectangular mesh has finer vertical subdivisions near the surface 

and in both materials near layer interfaces; and finer radial subdivisions 

both near the axis of symmetry and near the edge of the loaded area (see 

figure 5) . (69.1) ! 

For PCC pavements, many types of finite element idealizations exist, 

including plane strain, axisymmetric and prismatic solid elements. All of 

these idealizations introduce certain constraints to the model. Special 

types of elements are used to model discontinuifies (i.e. , cracks and 

joints), special interface conditions, reinforcJng steel and dowel bars. 

Special computational techniques permit cons5de r ation of temperature and 

moisture gradients and voids within the structure . Variable layer 

properties (thickness and deformation propertie$), nonlinear and nonelastic 

material responses can also be modeled. I 

I 

! 

Two- and three-dimensional finite element yodels are available. 

Ideally, it is desirable to use three-dimensionbl models to determine the 

response of the pavement to changes in temperatfire, moisture, etc. 

Unfortunately, the cost difference between two- and three-dimensional models 

can be several orders of magnitude, particularly when very small elements 

(fine meshes) are being used to increase the observed accuracy of 

small-scale responses. However, with the advenc of increasingly advanced 

personal and micro-computers these problems are becoming less critical. 

Finite element programs are available that are capable of modeling the 

following rigid pavement considerations: 

I 

e Various types of joint load transfer systems, including dowel bars, 

aggregate interlock, keyways, or any cbmbination thereof. 

/ 

I 

c The effects of a stabilized base coursp. I 

4 I 

e Placement of asphalt or concrete overlbys with either perfect 

bonding or no bond. 

c The effects of reinforcing steel on the behavior of cracks. 

I 

4 i 

4 o The effects of concrete shoulders withl or without tie bars. 

1 I 

i 

1 Concrete slabs of varying thickness and moduli of elasticity. 

i 

1 I 

1 Subgrades with varying moduli of suppof-t, including voids. 

Required program inputs generally include: ? 

av Geometry of the slab, base and overlay,iload transfer system. I 

a Elastic properties of the slab, base, 04 overlay, load transfer 

system and subgrade. 1 

o Boundary conditions and wheel loadings. 1 

1 

Outputs produced often include: 1 

I o Nodal stresses in the slab, stabilized yase, or overlay. 

i o Vertical surface stresses of the subgrafe. l 

a Dowel bar reactions. I 

l 

o Shear stresses at the joints where aggregate interlock or keyed I 

I joinc systems are assumed. i 

'i Specific dense liquid finite element progrim that are available 4 

4 include : I 

KENWINK (developed at the University of'Kentucky). I 

4 WESLIQID (an enhanced version of KENWIN$ developed by the U. S . Army I Corps of Engineers Waterways ~xperimentd Station) 1 

I 

Z FINITE. (77'6) 

I 

* ILLI-SLAB (developed at the University t$f Illinois and the most 

flexible finite element analysis packag4 available for 

pavements) . (78.3) 1 

I 

Elastic solid and elastic layer finite element programs include: 

o KENELS (developed at the University of 

* WESLAYER (an extension of KENELS develoied by the U.S. Army Corps 

of Engineers Waterways Experiments Stat, X on). (81.7) 

* SOLID SAP (developed at the University Of California at 

Berkeley) . (71.2) I 

i 

Good estimations of stress, strain and deflction can be obtained using 

the finite element technique provided a sufficie tly fine mesh of mostly 

square elements is used with proper element propqrties ! and boundary 

locations. Finite element techniques offer the +st valid approach to 

modeling the response of both flexible and rigid'pavements to all types of 

loadings, climatic conditions and support conditions. 
DISTRESS PREDICTION RELATIONSHIPS 

This section is concerned with relationships (R2 in figure 1) for the 

prediction of specific distress indicators from predictors that include 

traffic factors, environmental factors, roadbed soil factors, and structural 

factors. A high percentage of all existing rigid pavement distress 

prediction relationships are identified in the 1984 FHWA cost allocation 

study and/or in the 1986 AASHTO Guide for Design of Pavement Structures as 

reflected in references 84.3, 86.3, and 86.4. Other sources of R2 

relationships include an FHWA study on COPES and a 1977 FHWA study on 

zero-maintenance design. See references 85.2, 84.2, and 77.3. 

Although additional relationships have been reported elsewhere in the 

pavement research literature, it is assumed that relationships in the 

foregoing references will provide a substantial and adequate basis for 

determining the degree to which various types of rigid pavement distresses 

depend on factors that are associated with the materials and construction of 

rigid pavements. 

A logical structure for the identification of distress relationships 

and predictors is given in table 3 which is an extension of the R2 portion 

of table 1. Distress indicators (class 21) are again listed in two 

categories, one (class 211) for seven types of singular distress and one 

(class 212) for three types of composite distress. Thirteen different 

relationships have been selected from the references shown at bottom left of 

the table, and provide at least one case for each distress type, except for 

roughness (class 2121). This omission is not regarded as serious since 

serviceability loss (class 2122) is almost entirely associated with 

roughness. It is acknowledged that several distress types, most notably 

cracking, could be further classified into still more specific subclasses. 

Appendix B contains details for a number of primary relationships that 

have been selected from the research literature. Some of the appendix B 

relationships are not included in table 3 because each is more or less 

redundant with one or another of the other selected relationships. To the 

fullest possible extent, appendix B details include specific prediction 

equations, the size of the data bases from which the equations were derived, 

and measures of the closeness of fit between the equations and the data base 

observations. Two such measures are the multiple R square and the standard 

deviation of prediction errors, i.e., the standard error of estimate (SEE). 

Distress predictors are listed in the right-hand column of table 3 in 

seven major classes; 221 through 227. The first two classes are for 

traffic, age, and environmental factors that affect pavement distress, 

performance, and therefore pavement design, but do not relate specifically 

to M&C variables. They must, however, be included in the present study so 

that assessments can be made of the relative effects of traffic, 

environment, roadbed soil, and structure on any particular type of distress. 

Primary structural variables are listed in some detail under surfacing 

(class 223), %ase/subbase (class 224), and roadbed (class 225) factors, 

More specificity for these factors, especially those that involve PCC, will 

be given in a later section. 
i 

Table 3. Distress prediction variables and selected relationships. I 

I 

I 

~=========3=============3===x .........................

21. DISTRESS INDICATORS 22. DISTRES~ PREDICTORS ----------------------------------- -_---_-_---C-_--------_-----_---_--- 

Dependent Variables Rel.' Independentvariables ~e1.l 

211. SINGULAR DISTRESS 

2111. Pumping A 

2112. Cracking B,C,G 

2113. Faulting H, I 

2114. Joint Deterior. J 

2115. Other Slab Distress K 

2116. Swells & 

Depressions L 

2117. Skid Resistance 

Loss M 

221. TRAFFI~ FACTORS AND AGE 

2211. ~oa&in~ Characteristics M 

2212. No. of Loadings All but 

i G,J,L 

2213. Age; B,G,L,O,R ------------------------------------ 

222. ENVIRO~MENTAL FACTORS 

2221. ~oiQture/~reciplitation A,L,O,R 

2222: Temperature/ H,J 

Fre;ezing O,R 

212. COMPOSITE DISTRESS 22 3. SURFAC~ING FACTORS 

2231. PCC~ Thickness All but J-M 

2121. Roughness 2232. PCC Strength B,C,G,I,N,O,R 

2122. Serviceability 2233. PCG Stiffness b,c,g,i,N,o 

Loss N,O 2234. PCC! Durability Lo 

2123. Condition Rat- 2235. 0th/er PCC Factors GJR 

ing Loss R 2236. ~eihforcement adt tors G ..................................... 2237. ~opt/~owel 

'~elationshi~ References , and Fa tors F B?H,I,J,N,O,R 

Appendix B Codes 2238. Shqulder Factors H 

2239. 1nJtia1 profile N 

2 24. BASE/S~BBASE FACTORS .................................... 2241. Tyqe Material B?H,L,O 

~ef'. Abbreviated 2242. Thijckness b,c,g?i,o 

No. Citation Rel. -243. Stiffness b,c,g,i,o 

77.3 Zero-Maint., FHWA C 225. ROADB~D SOIL FACTORS 

2251. Typie/Gradation A,B,H 

84.2 Qual. Control, FHWA R 2252. Stdength L,R 

2253. ~tiiffness b,c,g,i,N,o 

84.3 Cost Allot., FHWA L,M _-_--------/------------------------- 

226. STRESS] INDICATORS 

85.3 COPES, NCHRP A,B,H,J,O 2261. Deqlections 

2262. ~trlains 

86.3 AASHTO Guide, Vol. 1 N 2263. Str~esses B,C,G,I,O 

86.4 AASHTO Guide, Vol. 3 INDICATORS 

B,H,O 

81.6 CRCP Distress K J,o 
The last two predictor classes are for stress indicators (class 226) 

and auxiliary distress indicators (class 227) that are used as predictor 

variables in certain distress relationships. 

The final column of table 3 shows which relationships are associated 

with each predictor class. Uppercase letters are used for relationship 

codes in which the predictor appears explicitly in some term of the 

prediction equation. 

Any distress relationship that includes a stress indicator as an 

explicit predictor implicitly includes the predictors that are required to 

predict stress. This situation is represented in the final column of table 

3 by the use of lower case letters for relationships that include stress 

indicators and therefore implicit structural predictors. For example, the 

cracking prediction relationship B includes edge stress (as part of the 

RATIO term) which, in turn, depends upon PCC thickness (class 2231), PCC 

modulus (class 22331, and the stiffness of subsurface layers (classes 2243 

and 2253). Thus, the code letter b appears in table 3 opposite each of the 

relevant implicit predictors associated with cracking relationship B. 

The final class of distress predictors (class 227) includes forms of 

distress other than the distress indicator that is predicted by a given 

relationship. Thus, for example, cracking relationship B, faulting 

relationship H, and serviceability relationship 0, all include pumping 

(class 2271) as an explicit predictor of cracking. 

All but one of the selected relationships are truly distress prediction 

equations in that their distress indicators can cover a range of values. 

The remaining relationship (C) is anomalous in that it does not predict any 

particular amount of cracking, but rather predicts the number of stress 

applications at which fatigue cracking will occur. This special type of 

relationship will be discussed in the section that follows. 

PERFOWNCE PREDICTION RELATIONSHIPS 

For the purposes of this study, pavement performance will be defined as 

the amount of acceptable service that the pavement provides before major 

rehabilitation is required. 

It is assumed that one or more distress indicators, D, are used as 

criteria for the level of service that is provided at any point in time, and 

that for each indicator there is an unacceptable (or terminal) level, D*, 

that represents the need for rehabilitation. For simplicity, it is assumed 

that all distress indicators have zero values at the beginning of any phase 

of the pavement's life cycle. Thus, level of service is represented 

symbolically by: 

Acceptable Service Levels: 0 ( D < D* 

Unacceptable Service Levels: D 2 D* 

where it is understood that D represents one or more distress criteria such 

as cracking, faulting, or serviceability loss. 
Amount of acceptable service will be defined /as the number of load 

applications carried by the pavement during the pkriod of acceptable service 

levels. If the loading characteristics (class 22 1 in table 3) are constant 

for all applications, the symbol N will be used fir 1 the number of 

constant-stress applications that correspond to apy acceptable level of D. 

The symbol N* will be used to denote the number bf constant-stress 

I applications that have accumulated when D reache~~its terminal level, D*. 

If, as in normal highway operations, stress 1 evels (S) vary from 

vehicle to vehicle and from time to time for any iven application, then one 

stress condition can be defined to be a standard stress level, So. The 

standard stress applications is No* (So). 

number of loading applications at stress level S,iwill F be denoted by No 

whenever D is less than D*. When D = D*, the corkesponding number of 

I 

For any non-standard stress level, S,, the n ber of applications at 

which D = D* is Ni* (Si), and the stress equivale ce ratio (SER) between 

standard and non-standard applications is defined as follows: 

For D = D*, SER, = No* a)/ Ni* (Si) 

1 

1 (8) 

If all stress determinants other than axle load (k.g., PCC thickness or 

roadbed soil modulus) are at the same levels for poth So and Si, the 

corresponding SER is a load equivalence ratio (LE ) defined as follows: 

For D = D*, LERi = No* (SAL)/ Hi* (AL,) 

P 

I 

(9) I 

where SAL is a standard axle load and AL, is the 4xle load for stress level 

Si. Conventionally, SAL is taken to be an 18,000!lb (8,172 kg) single axle 

load, but other load factors such as tire pressure, lateral placement, etc., 

must also be specified for the standard loading. i 

I 

Since highway traffic is comprised of many dkfferent axle loadings, 

when D = D* the pavement will have received N, apGlications of axle load ALi, 

for i = 1, 2, ...., but it is not expected that any N, will have reached Ni*. 

It is conventional to assume that any distrkss level D that is reached 

after Ni applications of AL, would also be reached by some number of standard 

axle applications that is a multiple of N,. The multiplier for Ni is called 

the load equivalence factor for AL, and is assume4 to be the load 

equivalence ratio given by equation 9. Thus, by aefinition, 

I 

LEF, = No* / Ni* , (10) 

l 

and is relative to D, D*, SAL, AL,, and other stress determinants. 

For any particular axle loading (AL,) and cofresponding number of 

applications, Ni, the equivalent nurnber of standatd axle load applications 

(ESAL,) is defined by: 

ESAL, = LEF, * Ni = (No*/ Ni*) x N, 

I 

I (11) 

The total number of equivalent applications for ~i applications of AL,, for i 

= 1, 2, ...., will be denoted by W and is given bk either of the following: 
Terms on the right side of equation 13 are often called load cycle 

ratios. It can be seen that W = No* when the summation of these ratios is 

unity. For this reason, the symbol W* will be used to denote the number of 

equivalent standard axle load applications at which D = D*. 

Equation 13 is one form of Miner's hypothesis where terminal distress 

(D*) will be reached when the load cycle ratio summation is unity. Because 

of the duality of equations 12 and 13, the use of Miner's hypothesis for 

aggregating mixed stress applications is algebraically identical to the use 

of load equivalence factors and equivalent load applications for the same 

purpose. It is therefore easy to show that Miner's original analyses of the 

fatigue failure of aluminum specimens would have produced the same results 

had he defined a standard stress level, then calculated equivalent 

applications for all other stress levels used in the studies. 

One obvious flaw in the ESAL summation approach is that the defining 

relationship (equation 11) holds strictly only for relationships in which D 

increases linearly with N. For relationships that are quite non-linear, it 

must be supposed that there can be considerable divergence between W* 

computed from mixed applications and the actual number of standard load 

applications (No*) that would be observed when D = D*. I, 

Other uncertainties associated with the use of ESALs stem from the fact 

that LEFs are generally not the same for different distress indicators (D) 

and have, generally unknown dependencies on the non-load determinants of 

stress levels. If, as is usually the case, LEFs are derived algebraically 

from distress prediction equations, then the LEF values can be highly 

dependent upon the form of the equation, i.e., the mathematical model that 

is used for D, 

In spite of probable shortcomings of LEFs and ESALs , the accumulated 

equivalent axle load applications variable, W, and its terminal level, W*, 

will be used as primary performance indicators for the derivation of 

performance-related specifications, 

If D is any distress indicator in table 3, its relationship with 

distress predictors may be written generally as: 

D = f (2211, W, 2213, 222, 223, 224, 225, 226) (14) 

where the predictor variables in function (f) are denoted by their table 3 

codes, except for W (code 2212). At the terminal value of D = D*, the 

corresponding value of W will be denoted by W*. Thus, for D* and W*, 

equation 14 becomes: 

D* = f (2211, W*, 2213, 222, 223, 224, 225, 226) (15) 
and may be called an implicit performance predict'on equation for W*. If 

equation 15 can be solved explicitly for W*, 

i 

then I 

W7k = f' (D*, 2211, 2213, 222, 223, 224, 225, 1226) (16) 

I 

which is an explicit performance prediction equatfon, relative to distress 

indicator D and its terminal value, D*. I 

I 

A specific example of equation 16 is the AAS~TO Design Guide rigid 

pavement performance equation that may be written ,as : (86.3) i 

W* I: (RHO) [G*(~/~~~~) 1 1 

I (17) 

where RHO and BETA are functions of distress predictors and (l/BETA) is the 

exponent for G*. The variable G is defined by G + (PO-PW)/3, where PO is 

the as -constructed serviceability (PSI) level, and PW is the pavement' s 

serviceability level after W equivalent standard load applications. Thus, G 

is a distress indicator for serviceability loss. when PW reaches a specific 

terminal level PW*, then G* is the corresponding 4erminal level for the 

distress indicator, G. For rigid pavements PO is igenerally in the 

neighborhood of 4.5, and PW* is often selected to /be 2.5. Thus, for these 

values of PO and PW*, G* = 2/3 in equation 17. I 

1 

Nearly all table 3 relationships for distresq indicators have been 

developed in the general form of equation 14 and Srom statistical analyses 

of particular data bases. Any of these distress drediction relationships 

can also be represented in the form of equation 19 or equation 16 and, thus, 

becomes either an implicit or an explicit predict'on equation for the 4 performance indicator W*. Each such performance re diction equation is, of 

course, relative to a particular distress indicatqr, D, and its terminal 

level, D*. The mathematical forms (models) for t distress relationship 

(f) and the performance relationship (f') have bearing on the 

sensitivity of the the distress or performance iddicators (D or W*) to 

changes in the predictor variables. I 

A special class of performance prediction reliationships arises when the 

distress indicator (D) is defined by only the presience or absence of its 

terminal level D*, e.g., the presence or absence oif fatigue cracking in a 

pavement section or laboratory specimen (1 = yes, 0 = no). In these cases 

there are no antecedent distress prediction relatdonships (equation 14), and 

the performance prediction relationships must be 4eveloped directly. The 

general form of these relationships does not incldde a term (D*) -. for the 

distress indicator and may be written: I 

In cases where either equation 16 or equatiob 18 has been derived to 

predict "applications to failuren at constant stress levels for all 

applications, then load equivalence factors (or lo d cycle ratio summations) 

must be used to apply the equations to mixed-traff'c predictions. An 

example is represented by relationship C (appendix B) for predicting the 

number of loading cycles to fatigue failure in con rete beams. These 

prediction equations may be written as: 

E 
log N* = A - B(STRS/STRG) - (19) 

where N* is the number of stress applications to beam failure through 

fatigue, STRS is the constant flexural stress level for each application, 

and STRG is the beam's modulus of rupture. The graph of equation 19 is thus 

an S-N curve for plain PCC beams. 

If it is desired to use equation 19 to predict fatigue failure after N1 

applications at stress level STRS1, N2 applications at STRS2, etc., a 

standard stress level, STRS,, can be defined, and all applications can be 

converted to equivalent number of stress applications. Thus, for STRS, and 

for STRS,, 

log No* = A - B(STRS,/STRG) , (20) 

log Ni* = A - B(STRS,/STRG), for i = 1, 2, ... (21) 

The load equivalence factor for converting Ni applications to an 

equivalent number of No application is: 

Across all stress levels, the accumulated number of equivalent standard 

stress applications is: 

W = Z [ (LEFi) Nil = (B/STRG) X [ (STRSi-STRS,) Nil 

i i 

(23) 

From equation 21, the predicted number of equivalent (standard) 

applications at failure is: 

log W* = A - B(STRS,/STRG) (24) 

Thus, failure is predicted whenever the right side of equation 23 is equal 

to the right side of equation 24. As has been stated, this equality 

condition is algebraically identical to the load cycle ratio condition that: 

2 (Ni/Ni*) = 1 

i (25) 

ROLE OF PRIMARY RELATIONSHIPS IN THE DEVELOPMENT OF PERFORMANCE-RELATED M&C 

SPECIPICATIONS 

The main role of primary relationships in the development and 

application of performance-related specifications is to provide a basis for 

predicting pavement distress and performance for different pavement 

structures within a given environment. For a given environment and design 

levels (target levels) for M&C pavement variables, the primary relationships 

will predict the extent of pavement distress after the pavement has reached 

any particular age and has received a particular number of load 

applications. 

29 
If the as-constructed pavement has levels for' one or more M&C variables 

that differ from the corresponding target levels, the primary relationships 

can predict any differences in distress or performance that arise because 

the as-constructed M&C variables were not at their: specified target levels. 

Thus, the primary relationships can be used as a bl sis for construction 

incentives or penalties that are associated with p E rformance-related M&C 

specifications. I 

Based on an overall assessment, the followin relationships from 

chapter 3 and appendix B were selected for use as initial input for 

algorithms that calculate distress/performance di ferentials associated with 

variations between as-designed pavements and as-constructed pavements. 

a Stress Prediction : ELSYM5 (chapteir i 3) 

i 

a Pumping Prediction : COPES (appendix B, relationship A) I 

Cracking Prediction : COPES (appendix B, relationship B) 

Faulting Prediction : COPES (appendix B, relationship H) 

Joint Deterioration Prediction : COPES (appendix B, relationship J) 

e CRCP Distress Prediction : TXSDH (appendix B, relationship K) 1 

Serviceability Loss Prediction : COPES (appendix B , relationship 0) 

I 

Performance Prediction : AASHTO (appendix B, relationship N) I 

The second role of primary relationships is to provide a basis for 

developing secondary relationships that relate M&6 variables to one another 

and to primary relationship predictors that are allso M&C variables. The 

development of secondary relationships is discussed in chapter 4. 

A third role for primary relationships is to brovide an objective basis 

for estimating the relative changes in distress add performance that are - 

induced by changes in the primary predictors. ~hese so-called sensitivity 

analyses can show, for example, the relative effec,ts of load 

accumulations, environmental factors, roadbed streingth, and structural 

variables. 

Sensitivity analyses are discussed in chapter 5 for both primary and 

secondary relationships in connection with the seclondary relatiohships that 

are developed through laboratory studies. The sedsitivity analyses reflect 

not only the deterministic effects that are provided by prediction 

equations, but also the prediction errors that are, associated with any 

primary or secondary relationship. I 

I 

I 

I 

I 

I 

30 
CHAPTER 4 

SECONDARY RELATIONSHIPS AMONG M&C VARIABLES 

This chapter begins with a review of M&C specifications that are in 

current use by a number of States. Some of these specifications are for 

variables that are predictors in primary relationships, but many are not. 

Variables that are not primary distress and performance predictors, however, 

may be predictors of the primary predictors. Such M&C variables will be 

called secondary predictors of distress and performance. 

By definition, a secondary relationship among M&C variables is one that 

shows how the variables are related to one another and to at least one 

primary predictor. Also, by definition, any M&C variable that is a primary 

or secondary predictor is a performance-related variable. It follows that 

M&C variables that do not appear in established primary or secondary 

relationships are either not performaqce-related, or that the defining 

relationships have not yet been established. 

A classification scheme is presented in this chapter for virtually all 

M&C variables that have been associated with the surfacing layer of concrete 

pavements. A major purpose for the scheme is to show simultaneously which 

variables appear (1) in State M&C specifications, (2) as predictors in 

primary relationships, (3) in established secondary relationships, (4) in 

existing data bases that might produce new secondary relationships, and (5) 

in a data base produced by a laboratory study. 

In the final sections of this chapter, existing secondary relationships 

are discussed, and assessments are made of the potential for deriving new 

secondary relationships from two existing and available data bases. 

SUMMARY OF CURRENT M&C SPECIFICATIONS 

To evaluate and/or develop practical secondary prediction relationships 

between materials and construction (M&C) factors and stress/distress/ 

performance (S/D/P) indicators, it was first necessary to review those M&C 

factors that are currently specified and controlled by State specifications. 

Using revlews of construction specifications from. several States in 

different regions of the country, it can be seen which M&C factors are 

generally controlled by the States. Different types of specifications 

control these variables; upper and lower limits, qualitative, and 

AASHTO/ASTM standard specifications are some examples. Occasionally, 

penalties and incentives may accompany the specifications. The purpose of 

this section is to present and summarize M&C specifications that are 

presently in use and relate them as a subset of the M&C factors to be 

discussed in the next section. 

The State specifications reviewed represent four different Strategic 

Highway Research Program (SHRP) climatic regions. Six States from the SHRP 

Wet/Freeze Zone are included; Illinois, Minnesota, New Jersey, New York, 

Ohio, and Pennsylvania. Two are included from the SHRP Wet/Non-freeze Zone; 

Georgia and Louisiana. Two States represent the SHRP Dry/Freeze Zone; Idaho 

and Colorado. The final two States, California and Texas, represent the 

SHRP Dry/Non-freeze Zone. Table 4 summarizes current M&C specifications for 
Table 4. Summary of current M&C specifica~ions in selected States 

[Caution: table not precise (she text) 1 . 

i sHw WET sHRP DRY sHw DRY 

SHRP WETIFREEZE ZONE (JON-FREEZE FREEZE NON-FREEZE 

r ZONE ZONE ZONE #ST 

I M&C Specification 1 IL IMNI NJINY IOHI PA^ 

Profile LP LPll I LP 

Skid Resistance 1 I 

REINFORCEMENT FACTORS 

Reinforcement Tvw IQA~ A I A IQB~QBIQA I am IIIIII 

Amount of Reinforcement lClQkl I I 1 

JOINT FACTORS 

Load Transfer Devices IIIIII I Joint Geometry I I IQlClCl I 

Flexural Strength L L L 

Compressive Strength L L LPI L LP 

Tensile Strength 

IIIIII I Voids Ratio 

1 Unit Weight I 1 I IULI 0 I I 

MIX FACTORS 

Cement Content 

COARSE AGGREGATE FACTOR 

Aggregate TY pes 

Gradation UL UL UL ULB MAC UL 

I 1lIlII -- - 

Wear IUI IUlUlulUl 

FINE AGGREGATES 

Assregate TY pe 

Gradation UL UL UL UL UL UL 

Sand Equivalent 

Fineness Modulus UL UL UL UL ~ Ill11 

ADDITIVES 

Air Entrainment IIIIII, I Other IQIQDUA / I 1 

CONSTRUCTlON CONSTRAlM 

Ambient Moisture 

Ambient Pour Temperature ULI UL L L UL' 

Curing Temperature L QL QL QL L L 

I 

PCC PVT MILEAGE (1000 miles) 4.2 3.5 0.6 3.8 1.8m 

% OF TOTAL US PCC 6.7 4.0 1 .O 6.3 2.9 5.9' 

A - AASHTO Spedficalion (may involve 0, N. U, L below). 

0 - ASTM Specihfon (may involve 0, N, U, Lbdow). 

C - SpcKificalicm u povided by Enginear an& concbuch~ plans. 

Q - (3ualitaliw Sp6cilicdon (0.9.. prcwenw or absence of M). 

N 3 Ouanlitph Spocificalion for Target Lwd (no tdwano rprdfied). 

U - Uppw Tdwanw kit b Quanlitative SpaihcPliar. 

L - L- Tobrancs Lima for @antitah ~ficelirm. 

P - Speaficabm eccom 'anied by conlractural penality for 

failur* to meet tolr%ce speafiutias. 

I - Spectbabon accomp.@ed by conbacturd incarliw for 

meeking speciticahd tolerance(s). 

I 

Mix Design Requirem f but not a pevement acceptance a-iawi.. - Implied. since maximk watorconk~t end n*imum 

cement content are decified 
these States. Note that the PCC pavement mileage in these States represents 

over 40 percent of all PCC pavements in the United States. Note also that 

table 4 was prepared to take a reading of what State practices have been 

recently in terms of M&C specifications. The table is not exact and may be 

incomplete for some factors. 

The 12-State specification review considered only those specifiable M&C 

factors that relate to functional and structural characteristics for 

surfacing. Each of the M&C factors fit into at least one of four 

categories: (1) explicit predictor of S/D/P (figure 1, box B4), (2) 

surrogates for explicit predictors (figure 1, box Cl), (3) control factors 

for explicit predictors and surrogates (figure 1, box C2), and (4) process 

control factors (figure 1, box C3). As shown in table 4, the structural 

characteristics are broken down into the two subgroups of layer and PCC 

characteristics. 

Several types of specifications were noted during the review of State 

PCC pavement specifications. Many M&C factors were controlled by a 

combination of one or more specification types. The following specification 

classes are currently being used in the States reviewed: 

* AASHTO Specifications. 

ASTM Specifications. 

a Specifications as provided by Engineer and/or on construction plans. 

Qualitative specifications (e.g., presence or absence of dowels). 

* Quantitative specifications for target levels: 

- upper tolerance limit. 

- lower tolerance limit. 

- upper and lower tolerance limit. 

a Contractual penalty for failure to meet tolerance specifications. 

a Contractual incentive for meeting specification tolerance(s). 

Excluding a few special exceptions, all State PCC pavement specifications 

were made using one or more of the above specification types. 

Of the specifications generally reviewed, profile and skid resistance 

are the only functional characteristic factors that are controlled by 

current State specifications. Profile, the relative amount of longitudinal 

roughness, has governing specifications in 6 of the 12 States. Three of 

these were accompanied by contractual penalties for failure to meet 

tolerances. Of the 12, only California places a lower limit specification 

on skid resistance, the resistance of a pavement surface to the sliding or 

skidding of a vehicle. 

At present, there are five major factors controlled by State 

specifications relative to structural layer characteristics. The first and 

most obvious is PCC pavement thickness. All 12 States specify controls over 

thickness. With the exception of Idaho, thickness specifications are made 
I 

using lower quantitative limits and penalties for failure to meet the 

I specified tolerances. In the case of New Jersey,contractual incentives are I 

I also specified for thicknesses exceeding the spectf ied amount. I 

Most States have specifications controlling type. A 

i 

1 majority of the specifications are qualitative an usually accompanied by an 4 AASHTO or ASTM specification. The amount of PCC einforcement is controlled 

by the engineer and/or construction documents in bix States while the 

remainder have no applicable specification. I 

1 

1 

Load transfer devices and joint geometry are /two joint factors that are 

controlled in the reviewed States. Qualitative sbecifications with an 

AASHTO/ASTM companion are used in eight of the Ststes for controlling load 

transfer. Another three States have controls using other specification 

formats. Seven of the 12 States specify joint gebmetry control through the 

engineer and/or construction documents. I 

I 

The most widely controlled M&C factors are P~C characteristics 

(including mix factors). In the 12 State specifi$ations reviewed in this 

study, approximately two thirds of the factors fi into this category. In 

studying table 4, it is noted that current PCC sp k cifications are relatively 

consistent across all of the four climatic region$. The States are 

currently using PCC characteristics as the primary controlling factors for 

rigid pavements. I 

Although not reflected in table 4, aggregate iquality control is also an 

M&C specification that is applied by most States.! Generally, this is 

accomplished through certifying/approving sources 1 of aggregate which meet 

abrasion, soundness, alkali and D-cracking requirkments, etc . I 

Compressive and flexural strength are two fabtors controlled by a 

majority of the States, while none of the 12 stat& in this review have 

specifications regulating tensile strength. NineIStates specify lower 

limits on compressive strength with California allowing the engineer and/or 

construction plans to set limits. Four States haye penalties for 

compressive strengths below tolerance levels with4New Jersey adding 

incentives for superior strengths. Seven set forth lower limits on flexural 

strength. Again, these specifications are consisqent across all four SHRP 

climatic regions. Stiffness characteristics (i.e,, elastic modulus) have no 

controlling specifications in the 12 States revie-ed in this study. 

I 

Durability characteristics are primarily controlled by setting 

quantitative limits on air content. Eight ~tates!place upper and lower 

limits with California setting only an upper limi . Three States control 

unit weight by three different specification typeC; AASHTO, ASTM, and upper 

and lower limits. None control the voids ratio, 1 measurement of bulk 

density . 1 

a 1 Mix factors make up the largest single subsec of M&C factors for FCC 

i characteristics. These factors are routinely cont;rolled in most of the 12 

4 States. Eleven States set lower limits on cement content. Nine specify 1 upper limits on water/cement ratios. All of the ~itates set upper and lower i limits on slump. Cement type is specified with stlandard AASHTO/ASTM 

I 

I specifications along with qualitative type specif $cations. All States use 
this type of control. Yield is specified in three States by three differing 

specification types. 

Coarse and fine aggregates both have a variety of specifications 

controlling their use. Eight States use qualitative controls for both 

coarse and fine aggregate type. All States placed upper and lower limits on 

the gradation of both coarse and fine aggregates. Wearing of the coarse 

aggregate was given an upper limit in ten States. Sand equivalent of the 

fine aggregate was -given a lower limit in five while fineness modulus was 

controlled by upper and lower limits in five States. 

The category of PCC additives is headed by air entrainment additives. 

All 12 States in the study placed controls over the use of air entrainment. 

The types of specifications varied greatly from State to State. Other PCC 

additives (e.g., high-range water reducers, flyash, etc.) were given 

qualitative controls in 7 of the 12 States. 

Three construction constraints were made in the States within the 

study. Ambient moisture has qualitative limits in four of the States. 

Quantitative limits are placed on ambient placement temperature in nine. 

The final characteristic, curing time, is given a lower limit in all of the 

States with four adding qualitative constraints to the limit. 

The State specifications for M&C factors represent much collective 

knowledge and years of experience on the importance of these factors to the 

construction and performance of concrete pavements. For the present study, 

the information shown in table 4 provides a substantive basis in the 

selection of M&C factors for the development of secondary relationships 

among M&C variables. 

SECONDARY RELATIONSHIP VARIABLES 

The purpose of this section is to identify and classify all M&C 

variables that appear in existing secondary relationships and/or that are 

candidates for useful relationships that have not yet been developed. 

In the general research framework of figure 1, any secondary 

relationships among M&C variables must include at least one primary 

relationship predictor (boxes B3 and B4') and should contain one or more 

other M&C factors that are represented by box C. To provide scope 

commensurate with the project resources, secondary relationships in this 

study will be restricted to only those M&C variables that are directly 

related to the surfacing layer of rigid pavements. Relative to figure 1, 

this restriction excludes primary predictors associated with either roadbed 

soil properties (box B3) or base/subbase properties (box B4). At least for 

relationships derived from laboratory studies, other excluded M&C variables 

are those relating to reinforcement, load transfer, joint geometry, and 

shoulder construction. 

Table 5 contains a detailed list of M&C variables that are associated 

with the surfacing layer of concrete pavements. The table includes all 

variables that are candidates for the secondary relationships that will be 

discussed in the remainder of chapter 4 and in chapter 5. As shown in the 

35 
Table 5. Classification and cross reference1 for FCC MLC variables. 1 

M & C VARIABLES ASSOCIATED WITH 

THE SURFACING LAYER OF CONCRETE 

PAVEMENTS 

VARIABLES 

( Surface Profile (As-Constr.) 1 

Surfacing Thickness 

Reinfarcement Variables 

3 Joint Geometry Variables 

Load Transfer Variables 

Shoulders Variables 

Abrasion Resistance 

Permeability 

A. Number of B. Primary C. ~econd/z-uy D. Variables E. Variables F. Variables 

States having Relationships Relationsqips Occurring in Occurring in Selected fa 

Specifications Containing Var, containink RI Data Base COPES Experimental 

fa Variable as a Predictor Variable 1 Data Base Study * 

(see table 4) (see qp. B) (see app $I (see app. D) (see qp. E) (see chapter 5) 

Air C~ntent 

Yield 

Mixin Time 

Time of Set 

Heat of Hvdratim 
first column, the surfacing variables are listed in nine classes that range 

from layer properties through additive properties. 

The remaining columns of table 5 show which variables (column A) have 

State M&C specifications that were shown in table 4, which variables (column 

B) appear either explicitly or implicitly as primary predictors in one or 

another of the primary relationships shown in appendix B, which variables 

(column C) appear in one or another of the secondary relationships given in 

appendix C, which variables (column D) occur in the five-state Resource 

International IRC. (RII) data base that is presented in appendix D, which 

variables (column E) occur in Concrete Pavement Evaluation System (COPES) 

data base presented in appendix E, and which variables (column I?) were 

chosen in chapter 5 for inclusion in the laboratory study. 

Thus, table 5 serves not only as a classification scheme for relevant 

M&G variables, but also provides cross-references for the occurrence of each 

variable in the various elements of the study. 

Comparison of columns A and B shows that, with few exceptions, State 

specifications provide good coverage of predictor variables in primary 

relationships. As will be discussed in the next section, column C shows 

that many secondary relationships exist for relating primary predictors to 

one or two secondary predictors, but none of the available secondary 

relationships provides a comprehensive coverage of all the secondary M&C 

factors that are included in State specifications. The same can be said for 

the sets of variables that appear in the RII and COPES data bases (columns D 

and E), as will be discussed later in this chapter. 

The last column (column F) of table 5 indicates which M&C variables are 

included in the laboratory study that is documented in chapter 5 on the 

development of new and more comprehensive secondary relationships. 

Variables enclosed in parentheses are not included in the proposed initial 

study, but are additional candidates for the larger-scale laboratory and/or 

field studies that are discussed in chapter 8. 

ASSESSMENT OF AVAILABLE SECONDARY RELATIONSHIPS 

As previously discussed, a secondary relationship is one that relates a 

. primary predictor of pavement performance to one or more M&C variables. 

When combined with primary performance prediction relationships, these 

secondary relationships provide the necessary link between recognized 

measures of pavement performance and various M&C factors that have not 

traditionally been used to predict pavement performance. The literature 

review for this project uncovered many useful equations that may be 

classified as secondary relationships. Appendix C provides a list of the 

select relationships that are of interest to this study. 

This section of the report is provided to assess those available 

secondary relationships based on their utility in developing a PRS system. 

Consequently, it is useful at this point to identify the assessment 

criteria: 

Is the dependent variable in the equation a primary predictor that is 

commonly found in the available primary relationships? If not, it is 

37 
not much use in a PRS system. [Concrete flexural strength (modulus 

ofrupture), elastic modulus and slab thiqkness are the most commonly 

used primary predictors, however, there aqe other factors such as 

shrinkage and thermal coefficient that are/ now finding their way into 

newer mechanistic models.] 

e How many other M&C factors are considered :by the relationship in 

estimating the value of the primary prediqtor? It is certainly 

desirable to use an equation that account? for several key M&C 

factors that have an effect on the primary predictor, particularly if 

the factors have interacting effects on tqe predictor. 

I 

Is the relationship accompanied by pertindnt statistical measures 

(i. e. , coefficient of determination, standard error of estimate and 

number of cases used in derivation)? ! 

I 

The primary predictors of PCC pavement perfokmance fall under five 

categories: (1) PCC strength, (2) PCC bending stiffness, (3) PCC shrinkage, 

(4) PCC durability, and (5) slab physical charactpristics, The first four 

of these are all measurable properties of the harbened concrete which are 

not directly controllable during the design/const&uction process and are, 

therefore, amenable to being correlated with cont&ollable M&C factors. Slab 

physical characteristics (i.., load transfer, 

etc.) are also important primary they are directly 

controllable from the design/construction and, therefore, do not 

require secondary relationships. Thus, four categories are 

addressed here. i 

PCC Stren~th 

Based upon the amount of effort that has beeh directed towards 

developing performance prediction relationships that consider concrete 

strength, it is logical to conclude that strength is a very important 

material-related property. Strength has been chakacterized under three 

modes of loading: compression, tension and flexure. Because of concrete's 

great capacity to carry load in compression, compiressive strength is the 

factor that has been given the most attention. ~bis is reflected by the 

fact that of all the strength relationships (A thfough M in table 6 and 

appendix C), the six related to compression (H thtough K) consider the most 

number of independent variables. It is further d#monstrated by the fact 

that six of the seven remaining strength relationkhips include compressive 

strength as an independent variable. unfortunately, compression is not the 

mode through which most concrete pavements develoh cracks. For this reason, 

compressive strength will be regarded as a surrog-e for the primary 

flexural strength predictor. 

In general, concrete pavements develop cracking when externally or 

internally induced tensile stresses exceed the tebsile strength of the 

concrete. It is also generally recognized that cjracking may develop due to 

the cumulative fatigue effects of multiple applications of stress that may 

be well below the tensile strength of the concreth. For this reason, tensile 

stress is the most commonly used concrete pavement behavioral response in 

developing performance prediction relationships. !Unfortunately, because of 

the complexity of test procedures designed to mea$ure concrete tensile 

38 
Table 6. Comparison of available secondary prediction relationships. 

Dependent Independent Variables That 

Variable Are Also Primary Predictors Other Independent variables1 Statistics 

App. C (Primary of Pavement Performance 

Cross - Predictor 

Ref. inPPR) SFSTdSTi SC ECKSKTKD UWSLGRWC CCACAECAMSVA R~ SEE n 

-- 

A SF[]~ -- -[I---- _____-____ -- - 

B SF[] -- -[I---- -------#-- - - 61 

C SF[] -- -[I---- I------ -#- - - 71 

D SF [28] - - - - ---#----#- - - 8 

E SF[] -- -[I---- ------I---- - 

F SF[] -- -[I---- ---------.. -- - 

S KT -- - - ---- -------#-- - - 14 

T KD -- - - ---- -----#---- -- - 

U WC -- [I ---- -#----#--- -- - 

Variable Descriptions : 

SF - PCC Flexural Strength or Modulus of Rupture urJ = PCC Unit Weight 

SC - PCC Compressive Strength SL - PCC Slump 

STd - PCC Tensile Strength (Direct Tension) GR - Gel-Space Ratio 

STi - PCC Tensile Strength (Indirect Tension) WC - ~ater/~ement Ratio 

EC - PCC Elastic Modulus CC - Cement Content 

KS - PCC Shrinkage Coefficient AC - Air Content 

KT - PCC Thennal Coefficient AE - Entrained Air Content 

KD - PCC Durability CA - Coarse Aggregate me 

VA - Volume of Aggregate 

R' = Coefficient of Determination MS - Maximum Size Aggtegate 

SEE = Standard Error of Estimate 

n - Number of Cases (Samples) 

# indicates indipendent variable considered in relationship. 

Numbers in brackets [ ] represent age (days) of specimen when tested. 

For this variable, strength correlations are provided for 1, 3, 7 and 28 days. 
strength, it has not received much attention as a potential primary 

predictor in concrete pavement performance relationships. The 

advent of the indirect or splitting a more 

attractive method to measure concrete tensile sqrength; however, it has had 

very little effect on the most commonly used me sure of concrete strength 

for rigid pavement performance prediction, i . e. 1 flexural strength. 

I 

The flexural strength (or modulus of ruptu e) test has achieved its 

preferred status because of its relative simpli ity and the fact that it 

does simulate the kind of bending stresses that are experienced in concrete 

pavements. One other aspect of the flexural tesit is that besides the 

measurement of ultimate strength, a number of sdudies have been conducted to 

study the effects of cyclic flexural loads on t e fatigue of the concrete. h These studies have resulted in primary predicti n relationships that have 

been used to predict the field performance of cqncrete pavements. 

In terms of the usefulness of the strength equations for use in 

developing secondary prediction relationships, several observations can be 

made : 

e In addition to the fact that compressivestrength is not found in 

many of the available concrete pavement performance prediction 

relationships, there is a problem with all six of the secondary 

prediction relationships studied (H through M) in that none considers 

more than two of the "other" independentvariables. The fact that 

many of the other independent variables have been studied and 

included in one or another of these rela$ionships implies that they 

must have some significance in terms of their effect on concrete 

strength. Unfortunately, there is no ong relationship that accounts 

for all the effects of the independent variables as well as their 

interactions. 

Both tensile and flexural strength relationships (A through G) suffer 

from the same problem discussed above. In fact, these relationships 

consider even fewer of the other indepen ent variables. 

a Another problem with the flexural and te sile strength relationships 

is that six of the seven depend on some 1 nowledge of the compressive 

strength of the concrete. For the needs of this project, it is much 

more preferable to have secondary prediction relationships that are a 

function of M&C factors that are direct1 controllable (i.e., those 

listed under the other independent varia les columns). s 

PCC Bending Stiffness 

The primary measure of concrete bending stikfness is its Young's 

modulus (or modulus of elasticity). Elastic modhlus is a very common 

primary predictor in mechanistically derived pri ary prediction 

relationships. It has appeared directly in at 1 ast one equation but is 

more frequently used as a factor for predicting critical concrete 

tensile stress due to wheel load. 

Four secondary prediction relationships tha 1 relate elastic modulus to 

other M&C factors were discovered in the literature review phase of the 
project. Unfortunately, these relationships suffer from the same kind of 

problems that were discussed for the strength prediction relationships, that 

is, they rely on another primary predictor (concrete compressive strength) 

and/or they do not consider many of the other independent variables that can 

affect a concrete's resistance to bending. 

PCC Shrinkage 

This refers to the drying shrinkage that occurs in portland cement 

concrete once its moisture condition is allowed to vary with the 

environment. Drying shrinkage is affected primarily by the unit water 

content of the concrete. Other factors affecting drying shrinkage include 

cement composition, cement content, quantity and quality of paste, mixture 

proportions, amount of reinforcing steel, maximum size of aggregate, and 

curing conditions. 

Shrinkage is a key factor in continuously reinforced concrete (CRC) 

pavements or concrete pavements that have a long joint spacing. As 

shrinkage occurs and is restrained by friction along the underside of the 

slab, internal stresses build up that can exceed the strength of the 

concrete. When this happens, a crack pattern is established that will 

certainly have an effect on the long-term performance of the pavement. 

Shrinkage is normally controlled by maximizing the amount of aggregate in 

the mix. In jointed pavements, it is further treated by the selection of an 

appropriate joint spacing. In CRC pavements, shrinkage is treated in the 

design process by controlling the strength (and therefore crack spacing) and 

by providing enough steel reinforcement to ensure that the cracks that do 

develop do not become very wide. 

Only one shrinkage relationship was uncovered during the literature 

review phase for this project. This relationship does seem to cover two of 

the key factors that are known to affect shrinkage, (i.e., water/cement 

ratio and volume of aggregate); however, it would be desirable to conduct a 

laboratory study where the effects of the other potential independent 

variables are considered. 

PCC Thermal Coefficient 

Concrete thermal coefficient can have a significant impact on concrete 

pavement performance in that it has an effect on the amount of horizontal 

movement a slab will undergo as it is subjected to changes in temperature. 

When combined with other loading mechanisms, slab contraction (due to low 

temperatures) can result in mid-slab cracking. On the other hand, when a 

slab expands (due to higher temperatures), it can result in severe joint 

distress such as compression failures and blowups, particularly when the 

joint becomes filled with incompressible materials. 

Thermal coefficient is primarily a function of the coarse aggregate 

used in the mix. From that standpoint, a secondary relationship that 

considers only coarse aggregate type may be sufficient for use in a PRS 

system. However, if would be desirable to have a relationship that accounts 

for a wider cross section of coarse aggregate types along with some other 

key characteristics of the coarse aggregate. 

41 
PCC Durabilitv 

Concrete durability refers to the ability of a given concrete to 

withstand the freeze-thaw cycles that occur in nodthern environments. The 

typical type of distress that has been associated:with concrete durability 

is D-cracking. Air content, air entrainment and dir bubble size and 

distribution have been found to be the factors that most affect freeze-thaw 

durability. Other significant factors that can aqfect durability are the Dcracking potential of the coarse aggregate and thd reaction of the coarse 

aggregate to alkali and/or sulfate attack. For t e relationship shown in 

table 6 (labelled T), only the effect of air cont nt i.s reflected. Based on 

this, it would be desirable to have a relationshi, 3 in which other key 

factors are considered. I 

Summarv 

In general, the following observations can be made that essentially 

assess the usefulness of the secondary relationships studied: 

Not one relationship considered all the po ential independent 

variables. Even if a given factor is cons'dered to be insignificant, 

it is desirable to have the experimental r,sults F to support it. 

i 

Many of the equations included terms that konsisted of other primary 

predictors. This causes problems in a PRS: system in that although 

these other primary predictors are signifi ant, they are not directly 

controllable M&C factors. 

None of the equations has the important statistics (i.e., coefficient 

of determination and standard error of est5mate) attached to them, 

In order to consider the variability effecks of the individual 

factors within the system, it is important to have these kinds of 

statistics. 

The assessment of the secondary prediction relationships (in terms of 

their usefulness in developing a PRS system) indicates the strong need for a 

statistically designed laboratory experiment to study the effects of the 

directly controllable M&C factors on selected pri$ary predictors of pavement 

performance. This assessment was used as a basisifor designing the 

small-scale laboratory study discussed in chapter15. It is also used as a 

basis for designing the large-scale laboratory anq field experiments that 

are addressed in chapter 8. 

,i I 1 ASSESSMENT OF EXISTING DATA BASE POTENTIAL 

While attempting to develop secondary relationships among M&C factors 

and performance predictors, the researchers hoped;to draw upon any useful 

information contained in existing data bases. ~ffer an extensive literature . 

review, two data bases seemed sufficiently compreqensive to deserve further 

investigation. These were the Resource Internatidnal Inc (RII) and the 

COPES data bases. Extensive statistical analyses,were performed on each 

data base and secondary relationships were derived using multiple regression 

analysis. The detailed results of these studies aye presented in appendixes 

D and E. In this section, the findings and concl~sions of these analyses 
will be summarized and the potential for developing secondary relationships 

from existing data bases will be evaluated. 

RII Data Base 

The focus of the RII study was the development of primary prediction 

relationships for PCC pavements based on historical data collected in five 

different States. '84*2) This study focused on the development of secondary 

prediction relationships utilizing the same comprehensive RII data base. 

Using standard stepwise multiple regression, two primary and three secondary 

relationships were derived. The primary relationships were developed to 

help gauge the reasonableness of the RII data and to ensure compatibility 

between any derived secondary relationships and generally accepted primary 

relationships. Prior to the regression analyses, an extensive study of the 

individual variables and their interrelations was undertaken. A Pearson 

correlation matrix, frequency histograms and scatter plots were all 

generated for this purpose. The details of these statistical analyses are 

presented in appendix D along with supporting tables and figures. In the 

course of the investigation, several observations were made which question 

the validity of the resulting regression equations. The chief topic of 

discussion here will be the shortcomings of the RII data base for producing 

secondary prediction relationships. 

The early stages of the statistical analyses showed that several key 

variables possessed a substantial number of missing observations. In the 

original RII study, steps were taken to fill some empty cells by developing 

relationships from the existing data. No such effort could be made in this 

study. The difficulties arising from missing observations were greatly 

magnified when two or more variables were studied simultaneously. 

Several unsettling associations among the variables were exposed 

during the investigation. The strong negative correlation between 

water/cernent ratio and concrete slump conflicts with generally accepted 

engineering principles. Obviously, a lower slump value is not consistent 

with a higher water/cement ratio. It was noted, however, that slump was 

strongly correlated with pavement age. The latter variable was included in 

the analyses to help detect changes in common construction techniques and/or 

technology over time. This strong correlation may indicate that such a 

change has occurred and could have been the cause of the inconsistent 

correlation discussed above. For example, the introduction of slip-form 

pavers would push slump values down but not necessarily alter the 

water/cement ratios or flexural strengths. It is vital to identify these 

types of phenomena yet very difficult to do so. For this reason, 

observational data bases are often questionable sources of statisticallybased secondary relationships. Some of the correlations coincided with 

general expectations but the difficulties, such as these mentioned above, 

overshadowed their significance. 

Scatter plots are perhaps the best way to visualize the relationships 

between two variables. Appendix D presents a wide assortment of these 

plots. A majority of the graphs display reasonable associations between the 

variables, but two produced entirely unexpected results. One depicts a 

strong relationship between 7-day flexural strength and concrete slump that 

is inconsistent with expectations. Typically, lower concrete slump predicts 
higher strength; not the lower values predicted by this scatter plot. The 

second questionable relationship presents a that predicts sharply 

higher strengths with increasing air contents. Within the range of the air 

content values in the RII data base, such a dras'tic effect is not expected. 

Again, these inconsistencies could be attributed1 to differences in mix 

design and/or construction practices between the; States . 

Three pavement performance predictors were selected to serve as 

dependent variables for multiple regression analkses. The stepwise approach 

for entering and deleting variables was employeq in the development of these 

secondary relationships. Secondary prediction equations were developed for 

7-day flexural strength, 7-day compressive stredgth and concrete core 

strength. Unfortunately, after a brief review, each of these derived I 

equations displayed questionable attributes. 1 

I 

The equation for 7-day flexural strength +as based on only 53 of the 

733 sections because of the missing value probleh. When the stepwise 

regression was complete, only slump and percent air remained as independent 

variables in the equation. Contrary to expectatiions, however, the 

coefficient on slump was positive indicating thalt an increase in slump 

would, likewise, increase flexural strength. AS mentioned previously, slump 

is strongly correlated with time and this could brovide the source for this 

inconsistency. Only 42 petcent of the variabilijty in 7-day flexural 

strength was accounted for by slump and percent air i. e. , R' = 0.42) . I 

The only independent variable that entere4 the secondary equation for 

predicting 7-day compressive strength was water/cement ratio. A negligible 

8 percent of the variability in compressive sf reigth was accounted for. 

The analysis was performed on 219 sections. I 

I 

I 

perhaps the best of the three derived secobdar~ relationships was for 

concrete core strength. Unfortunately, core strkngth has not generally been 

used as a direct predictor of pavement performance. Only 59 percent of the 

core strength's variability was accounted for by the water/cement ratio, the 

only independent variable to enter the equation.! 

I 

Two primary relationships were developed; bne to predict the pavement 

condition rating, and the other to predict ride buality index. Both of 

these equations contained inconsistencies similak to those mentioned 

previously. The relationship for ride quality had a positive coefficient 

for slump, contrary to general expectations. A term for pavement age 

entered the equation for pavement condition ratihg and possessed a positive 

coefficient. It is not expected that an increasb in the age of a pavement 1 will produce higher ratings of pavement condition. I 

I 

In summary, missing data, non- representativk observations and 

inconsistent correlations are causes for concern1 that lead to the 

conclusions that the RII data base would not serye to develop useful and 

reasonable secondary relationships for PCC pavements. 

COPES Data Base 

The extensive amount of information availab e in the COPES data base 

made it a likely source of statistically-based s condary relationship^.(^^.^) 
One illustrative secondary relationship was developed using multiple 

regression analysis. The equation makes reasonable predictions of 28-day 

modulus pf rupture using three M&C factors as the independent variables. ' 

The details of the relationship are presented in appendix E. Prior to 

developing this equation with regression analysis, extensive effort was 

directed toward studying the variables themselves. Specific variable 

characteristics reviewed were arithmetic means, standard deviations and 

distributions (histograms). The interrelations between the variables were 

studied by producing a Pearson correlation matrix and several scatter plots. 

During this in-depth study of the data, several problematical observations 

were made that question the validity of the derived secondary relationship. 

An item of concern was Minnesota's overwhelming majority of test 

secttons in the data base. Of 1182 observations, 994 were made in 

Minnesota. The balance of the sections were located in California, Georgia, 

Louisiana, and Utah. Initially, it was hoped that the COPES data base would 

supply data collected from six different States evenly dispersed within a 

wide range of geographical locations. Since this was not the case, the 

available data may be nonrepresentative of the M&C variables necessary for 

reasonable and widely accepted secondary relationships. Equations built 

upon this information would be based mostly on Minnesota highway sections. 

While developing the Pearson correlation matrix for key variables in 

the COPES data base, it was observed that'several were subject to high 

missing value counts especially when considered pairwise with other 

variables. The 28-day modulus of rupture was targeted as an explicit 

predictor of performance for which a secondary relationship would be 

derived. Unfortunately, only 199 of the test sections had a modulus value 

present. Therefore, any correlation with modulus could contain, at best, 

only 199 pairs of the variables and in most cases fewer. A list of the 

variables and the number of available cases of each is presented in appendix 

E along with the correlation matrix which shows the pairwise counts. 

Another notable missing value count exists for present serviceability 

index (PSI). It was hoped that this measure of pavement performance could 

be used to derive a primary relationship to measure the reasonableness of 

the available COPES data. The analysis necessary to produce this primary 

relationship was conducted, but the extremely low number of pairwise sets 

did not provide an adequate basis for the analysis. 

A second variable, concrete slump, was chosen to serve as the primary 

predictor for another secondary relationship. It was discovered, however, 

that the distributions of several key variables, including slump, displayed 

modal values which contained the vast majority of the observations. Thus, 

these variables were essentially constant. The correlations between these 

variables and others had little meaning since a reasonable range of values 

was not available and, furthermore, their inclusion in a derived 

relationship could lead to invalid conclusions. As a case in point, the 

histogram of mean concrete slump displayed a mode of 1.5 in (38.1 mm). This 

mode represents 1011 out of 1125 total observations. Engineering reasoning 

would expect more variation in the measured slumps from 1125 sites. In 

appendix E, this problem is discussed further, and other variables with 

modal tendencies are identified. 
Steps were taken to ensure the 

derived secondary relationships with primary 

relationships. Developed in tandem, the relationships 

could provide a plausibility test for the 

pavement performance were the focus of 

transverse cracking. Once again, the analyses produced disappointing 

results. As mentioned above, only 26 observations of PSI were present which 

removed it from any practical use. Next, transyerse cracking displayed 

negligible linear correlation with any of the other variables in the data 

base making further investigation meaningless. , 

Because of the potentially significant efqects of changes in common 

practice and/or technology over time, a variabld relating to the "time 

opened to traffic" was included in the correlatqon matrix to identify such 

occurrences. Pavement thickness, water/cement 4atio and several other 

concrete mix parameters exhibited reasonably st ong correlation with the age 

of the pavement, a variable that is directly re f ated to the date opened to 

traffic. One might conclude that common practiqe has changed over time, but 

further investigation would be required to suppqrt this logic. These types 

of phenomena can have significant effects on th 7 results of statistical 

analyses and must be considered during the formqlation of secondary 

relationships. The difficulty in analyzing thefe is one argument for the 

use of controlled laboratory data in lieu of thgse observational data bases. 

A1 though the original researchers at the 6nivers ity of Illinois had 

successfully developed primary pavement performhnce prediction 

relationships, the effort to derive secondary relationships from the COPES 

data base would have to be characterized as unsuccessful. Missing data, low 

pairwise variable counts, geographic bias, and inability to check the 

reasonableness of the information with primary *elationships from the same 

data base created a formidable barrier. The pri ary result of this 

investigation was the conclusion that a proper1 designed laboratory testing 

program would produce secondary relationships at would be far superior to 

any that could be produced from either the RII pr COPES data bases. 

I 
CHAPTER 5 

LABORATORY STUDIES FOR DEVELOPMENT OF SECONDARY RELATIONSHIPS 

This chapter gives details of the experimental design, implementation 

procedures, and analytical results of the laboratory study for the 

development of secondary relationships among primary predictors of PCC 

distress and key M&C factors that may be controlled during the construction 

process. The initial experimental design and implementation of the study 

are presented in the next tuto sections, respectively. The rationale for the 

analyses of laboratory study data is then presented followed by the actual 

analyses. The chapter is closed by summarizing the results of the 

laboratory study. 

INITIAL EXPERIMENT DESIGN FOR LABORATORY STUDY 

Through a process involving literature reviews and meetings among 

engineers, PCC mix design specialists, and statisticians, seven M&C 

variables were selected as experimental design factors for the initial 

laboratory study. Each factor was controlled at two levels, so that the 

total number of factorial combinations was 2' or 128. The seven factors 

selected are as follows: 

1. Coarse Aggregate Type (CAT): Soft and Hard. 

2. Coarse Aggregate Maximum Size (CAM): Small and Large. 

3. Fine Aggregate Fineness Modulus (FAM): Low and High. 

4. Air Entraining Agent Quantity (AEQ): None and Some. 

5. Coarse Aggregate Quantity (CAQ): Low and High. 

6. Cement Quantity (CEQ): Low and High. 

7. Water Quantity (WAQ): Low and High. 

The first three factors determined the nature of the aggregates used in 

the PCC mixes. Two coarse aggregate types were chosen to cover a wide range 

of hardness. Two coarse aggregate sizes were selected to examine their 

impact, both individually and in interaction with coarse aggregate type. 

Two levels of fine aggregate modulus were chosen to determine the effect on 

air content and slump. 

The fourth factor provided for two levels (amounts) of the air 

entraining agent. At the first level for this factor, no agent was to be 

used. For the second level, a fixed amount of agent was apportioned to 

target a broad range of air contents typical of paving concrete. 

The remaining controlled factors determined the relative quantities of 

coarse aggregates, cement, water and fine aggregates that occur in each FCC 

batch. For the fifth factor, coarse aggregate factor levels of 60 and 75 

percent were targeted for bulk (dry-rodded) quantities per cubic yard. 

These levels were estimated to produce true volume percentages in the 

neighborhood of 33 to 42 percent for the experimental batches. 

47 
Low and high levels for quantities of ceme4t and water (the sixth and 

seventh factors) were to be specified as percenqs of PCC batch volume. The 

four combinations of cement and water quantitie$ were intended to produce 

four different water/cement ratios (WCR) by volyme. As indicated in figure 

6, the four WCR values (shown with rectangles) $ere initially selected to 

provide levels for percent water and percent cenrjent to not only satisfy the 

practical limiting conditions for WCR but also dnclose those WCR values that 

are within the realm of currently utilized mix designs that are based on 

strength criteria and other generally accepted qoncrete mix proportioning 

characteristics such as workability. 4 

I 

I !

Thus, figure 6 implies that the desired low and high levels for water 

quantity might be 13 and 16 percent, and that ldvels for cement quantity 

might be 8 and 12 percent. Final selections ofithese levels were not made 

until the mix criteria were assessed and several test batches were mixed and 

tested. 8 

I 

The fine aggregate quantity was the uncontrblled factor in the 

experiment. Therefore, no indication was given I as to the quantities 

(levels) of fine aggregate used in each batch. !After all the levels for a 

given batch were identified, enough fine aggregqte was added to produce a 

cubic yard. I 

I 

I 

Although there were 128 factorial combinatdons of levels for the 7 

factors, only 64 of the combinations were actually implemented in the study. 

Using principles of experimental design, a one-qalf fraction of the complete 

factorial was used to identify the 64 primary cqmbinations or cells of the 

factorial. This fractional factorial approach niade it possible to collect 

information on as many variables as possible, wf(i1e staying within the 

available funding for specimen preparation and qesting. It did produce 

constraints on the extent of the statistical reqationships that could be 

derived (i.e,, the confounding of higher-order qnteractions between the 

factors) , but these were considered acceptable. 1 

I 

I 

To obtain estimates of "between batch" errqr, eight factorial 

combinations were replicated. The eight repliccfte cells represent a further 

fraction of the complete factorial and provide replicate set of data for 

each of the eight aggregate combinations given the first three factors. 

To summarize, the laboratory study require a total of 72 batches, 64 

of which represent distinctive combinations of 4 he 7 experimental factors 

and 8 of which represent replication of distinc ive combinations. The 72 

batches and associated concrete specimens were qroduced 'i in a completely 

randomized order. 1 

i 

Table 7 is an illustrative table that contajins identification data, 

factorial design specifications, and calculatiods to produce mix weights for 

each mix component. In addition to factorial spiecif ications , the 

calculations require moisture contents and speciific gravities for the two 

aggregates and assumptions on the air volumes tqat will be produced. It is 

noteworthy to mention that the percent volume add weight of the fine 

1 
PERCENT WATER PERCENT a 

1. Cell entries are WCR values computed by 0.31 75 (% Water)/(% Cement) 

where 0.31 75 = 1 /(Specific Gravity of Cement) = 113.15. 

2. La = Combinations for which (WCR) c 0.34 

4. WCR values in rectangles represent one option for levels of percent water and percent cement that cover 

practical ranges of WCR and that contain mix designs that might be used in practice. 

aggregate result from what remains after the coarse aggregate, cement, water 

and air quantities have been taken into account. Thus, table 7 represents a 

form sheet that was completed for each of the 72 batches. In essence, table 

7 provides a completely defined "recipe" for each of the experimental mixes. 

Finally, table 8 lists the characteristics that were assessed for each 

PCC batch, and the various tests and measurements that were performed for 

both the plastic mix and the hardened concrete. Plastic batch measurements 

include slump, air content, unit weight and yield. 

Two 6-in by 6-in by 21-in (152.4-mm by 152.4-mm by 533.4-mm) beams and 

six 6-in by 12-in (152.4-mm by 304.8-mm) cylinders were produced from each 

batch. Each batch required approximately 3 ft3 (0.085 m3) of concrete to 

form all of the necessary specimens. 

As indicated in table 8, two of the beams were used for testing 7-day 

flexural strengths (ASTM C-78). Two cylinders were used for testing 7-day 

compressive strengths (ASTM C-39). Two cylinders were used to obtain both 

28-day compressive strengths and static modulus of elasticity (ASTM C-469). 

The two remaining cylinders were earmarked to produce 7-day splitting 

tensile strengths (ASTM C-496). 

The expected data base for the laboratory study can be inferred from 

tables 7 and 8. It can be seen that the data base contains information for 

72 batches times 8 specimens per batch, or 576 data cells in all. Each line 

represents one batch and contains values for all factorial specifications, 

batch measurements, and strength tests that are associated with the batch. 

IMPLEMENTATION OF LABORATORY STUDY 

The initial experiment design described in the previous section was 

slightly modified when put into practice. This section details these 

differences and outlines the entire laboratory testing process from start to 

finish. '~inal material selections, factorial levels, mixing processes, 

testing procedures, reporting, and quality assurance measures are reviewed. 

Material selections e, concrete mix ingredients) for the laboratory 

study were made with specific goals. in mind. First, it was desirable to 

select materials that would represent a broad spectrum of typical materials 

used in industry. This proved challenging given the limited available 

funds. A second goal, critical from the statistical point of view, was to 

secure a source for each.materia1 that was consistent throughout the 

project. Finally, it was necessary for all selected materials to meet the 

"standards" that are common to concrete mix design in current practice. For 

example, the gradation of the coarse aggregate was required to meet ASTM C33 specifications. In a nutshell, the final material selections were made 

to fix the uncontrolled material characteristics according to currently 

accepted industry standards. 

Most of the project's material selections were related to the aggregates 

to be used in the study. During preliminary design, it was decided that two 

types of*coarse aggregates would be studied; a crushed limestone (soft) and 

a siliceous river gravel (hard). Also, for each of these aggregate types, 

two maximum aggregate sizes, 3/4-in (19.05-mm) and 1/2-in (12.7-mm), would 

be included. Several trips to local aggregate suppliers were made, and 

samples for the four coarse aggregate types were collected. The aggregate 

suppliers possessed fairly detailed data on each of their aggregates, which 

accelerated the selection process. Once candidates were identified, 

additional testing was conducted to verify the accuracy of the supplier's 

data. Once the aggregates were selected, quantities large enough for the 

entire project were set aside to ensure a consistent material throughout the 

experiment. 

Similar searching and testing techniques were used to locate two fine 

aggregate sources with the desired wide range in fineness modulus for the 

factorial experiment. Table 9 presents a summary data table for the six 

aggregates used during the study. 

Other project materials included cement, water, and an air entraining 

agent. A type I cement common to the area was selected for the project and 

enough cement for the entire project was set aside from a single lot to 

ensure consistency. Regular city-supplied tap water was used as the water 

source. No additional testing of the cement or water was performed. 

Finally, a commonly used air entraining agent was selected for the testing 

program. A certification that the air entraining agent met the requirements 

of ASTM C-260 was provided by the manufacturer. 

After all of the materials were selected and acquired, several test 

batches were mixed to refine initial factorial levels for water quantity, 

cement quantity, coarse aggregate quantity, and the amounts of air 

entraining admixture to be added. Two levels for each of these factors were 

identified to supply a broad range for each controlled variable. The test 

batches were extremely beneficial for adjusting all of the mix levels so 

that the "driest mixt' was not unworkable and that the "wettest mix" was not 

unreaii~ticall~ fluid. The two factorial mixes corresponding to these 

theoretical boundary mixes were tested repeatedly until the adjusted mix* 

levels produced acceptable plastic characteristics. This cyclic process 

also included adjustments for air entraining agent and the quantity of 

concrete necessary to prepare a11 of the desired specimens. Table 10 

displays the final levels used for each of the experimental variables within 

their factorial framework. As mentioned in the previous seetion, the fine 

aggregate quantity was not controlled but allowed to fill the remaining 

portion of a fixed volume of concrete for each mix. The paragraphs below 

will discuss, briefly, the rationale used to make initial estimates for the 

controlled mix levels. 

Given the material characteristics, several concrete mix designs were 

studied using the American Concrete Institute (ACI) design procedure. (8z.9) 

The intent of the study was not to simply follow existing design proportions 

and procedures since they are typically biased toward optimizing the 

concrete's strength. The design procedures merely provided a starting point 

for tttypicaltf mix makeup as well as appropriate techniques for classifying 

mix characteristics (e.g., volume of coarse aggregate per unit volume of 

concrete). One requirement for this laboratory study was to stretch beyond 

the limits of typical mix designs and study the effects (i.e., performance 

considerations) of straying from common practice. For example, five- and 

six-sack mixes i., five or six 94-lb (42.68-kg) cement sacks per cubic 

yard) represent typical upper and lower bounds for paving concrete. The 
Table 9. Aggregate data used in la oratory study. "i 

I I 

1 Coarse Aggregate Properties: 1 t 

1 

C 

i 

Coarse Age;reaate Type 

I Siliceous Siliceous Crushed Crushed I 

1 Property River Gravel River Gravel Limestone Limestone I 

I 

1 Maximum Size (in) 1 1/2 1 1/2 3/4 

Specific Gravity 2.615 2.6q1 2.521 2.554 

I 

Absorption(%) 1.29 1.q 3.94 3.42 

Dry Rodded Weight (pcf) 99.9 90.9 90.2 

Gradation 

(% Passing) 2" 100 100 100 100 

1 1/2" 100 100 100 I00 

1" 100 - 100 

3/4" 54.9 89.5 1 60.3 100 

1/2" - 3/8" 18.2 2i.8 1 12.0 44.8 

No. 4 2.5 3.2 3.3 2.8 

No. 8 - 0.2 1 1.4 

No. 16 

- I 

- 

Fine Aggregate Properties: 

Fine Aggregate Type 

Propertv Finish Sand Concrete Sand 

Specific Gravity 2.612 2.615 

Absorption (%) 1.14 1.12 

Dry Rodded Weight (pcf) 97.6 103.9 

Fineness Modulus 2.10 ~ 2.84 I 

Gradat ion 

(% Passing) 1/2" 100 I n/a 

3/8" 100 1 

No. 4 100 I 

No. 8 99.8 I 

No. 16 97.8 

No. 30 74.3 

No. 50 17.1 

No. 100 0.8 

No. 200 0.1 I 

< 

I 

I 

Conversion Factors: 1 in = 25.4 mm 

1 pcf = 16.0 kg/m3 
Table 10. Experimental design factorial for laboratory study. 
selected cement levels for the factorial are slightly beyond these normal 

limits. The ACI mix procedure also shows practic~l limits on water to 

cement ratios and coarse aggregate volume. The logic behind allowing the 

fine aggregate quantity to fill the remaining concrete volume also 

originated with the ACI mix design procedure. This demonstrates the ACI 

method's assumption that concrete strength is not highly correlated to the 

fine aggregate quantity. Using mix design as a backdrop, engineering 

judgement, common practice, and sample test batch's provided for the 

selection of appropriate levels for each of the frctors. 

I 

Batch mixing and specimen creation a large portion of the 

effort expended on the project. It was extremely efficient 

flow of information between the engineers and to 

minimize any errors that would require a batch toibe re-mixed. Several 

measures were taken to achieve these goals. 

Each concrete batch required extensive pre-cilculation prior to mixing. 

One characteristic of mixing concrete is the needlto adjust the amount of 

water to be added to the mix by the current moistqre condition of the coarse 

and fine aggregates. Every morning that a batch &as to be prepared, the 

moisture condition of all aggregates was measured1 Specific gravities and 

absorption levels were measured on a weekly basis to catch any "through the 

pile" variation. The results of these tests were immediately telefaxed to 

the managing engineer for review and preparation Qf that day's mix designs. 

A computerized spreadsheet was prepared to minimiqe the occurrence of 

calculation errors. Hard copies of the mix desig were telefaxed back to 

the laboratory for review by the lab. An exampleimix P design spreadsheet is 

presented in table 11. This technique provided excellent job control, 

minimized errors, and provided a natural quality dontrol chain. The 

laboratory technicians simply read the exact t of each material needed 

directly off the design spreadsheet. Once 's batches were recorded, 

the lab returned the completed standard form shown in table 12. 

All of the designs and reporting forms a single notebook and 

updated as the 7- and 28-day test 

Standard ASTM testing equipment and procedurds were employed for all I 

plastic concrete testing and for cylinder and bea specimen formation, I I 

handling and testing. To add consistency to the atching process, a single 

gasoline powered mixer was used for all of the ba ehes and a single 

technician was in charge of all the mixing and testing. As mentioned 

previously, the mixes were randomly ordered to av id confounding with any 9 I systematic changes in laboratory conditions. ASTT C-192 procedures for , 

mixing order and time were strictly followed. Slwp, air content, and unit I 

weight were all measured in accordance with theirjrespective ASTM I 

specifications. Beam and cylinder specimens werecarefully created and I 

marked for future testing according to ASTM C-1921 A vibrator was used to 

consolidate the freshly molded specimens. Finishing and curing were also 

performed according to specification. 

The hardened concrete beams and cylinders wee tested at 7 and 28 days; 

compressive strength , flexural strength, splittinH tensile strength, and 

static modulus of elasticity were a11 measured. Table 8 summarizes the 

planned hardened concrete testing program and the:respective ASTM 

specifications that were followed for each procedure. All equipment met the 

56 i 
Table 11. Mix design spreadsheet. 

MIX DESIGN FOR FH-231 FACTORIAL CELLS ..................................... 

Batch No. 5 6 

Sequence No. 1 

Description of Batch 

A) Siliceous River Gravel 

B) 1.50nMaximumC.A. Size 

C) FinenessModu1usofF.A. is 2.10 

D) 6.5 ounces per cubic yard of Air Entraining Agent 

E) Coarse Aggregate of 1850 pounds 

F) Cement Quantity is 584 pounds 

G) WaterQuantityis 270pounds 

Background Information Necessary to Complete the Mix Design: 

Bulk Specific Gravity of F.A. = 2.61 using SSD condition 

Bulk Specific Gravity of C.A. = 2.62 using SSD condition 

Fineness Modulus of F.A. - 2,lO 

Dry-rodded Unit Weight of C.A.= 99.90 LB per CF 

Absorption of F.A. - 1.00% - Absorption of C.A. - 1.50% 

Specific Gravity of Cement = 3.15 

Specific Gravity of A.E. Agent= 1.04 

Amount of concrete required = 2.80 CF 

Total Moisture Content of F.A.= 1.50% 

Total Moisture Content of C.A.= 0.12% 

Calculations for Mix Design: 

Amount of Water per Cubic Yard of Concrete = 270 Pounds 

Amount of Cement per Cubic Yard of Concrete = 584 Pounds 

Calculated Water to Cement Ratio by Weight = 0.46 

Amount of AE Agent per Cubit Yard of Concrete = 6.50 oz 

Amount of Coarse Aggregate per Cubic Yard (SSD)= 1850.00 Pounds 

Total Estimated Percent Air Content - 6.0% 

Volumetric Mix Quantities for One Cubic Yard: 

Volume of Water = 4.33 cf 16.03% 

Solid Volume of Cement= 2.97 cf 11.00% 

SSDVo1umeofC.A. = 11.33 cf 41.96% 

Est. Volume of Air = 1.62 cf 6.00% 

Volume of AE Agent = 0.01 cf 0.03% 

SSD Volume of F.A. = 6.75 cf 24.99% 

Mix Totals ----------- > 27.00 cf 100.00% 

Weight Mix Quantities for One Cubic Yard (not adjusted for moisture): 

Weight of Water = 270.00 pounds 7.10% 

Weight of Cement = 584.00 pounds 15.36% 

Weight of C.A. (SSD) = 1850.00 pounds 48.64% 

Weight of Air = nla pounds n/ a 

Weight of AE Agent = 0.44 pounds 0.01% 

Weight of F.A. (SSD) = 1098.75 pounds 28.89% 

Mix Totals ----------- > 3803.18 pounds 100.00X 

Unit Weight of Concrete= 140.86 PCF 

Weights for Small Test Batch (adjusted for moisture): 

Weight of Added Water = 30.08 pounds 

Weight of Cement = 60.56 pounds 

Weight of C.A. (wet) = 189.20 pounds 

Weight of Air = nla pounds 

Weight of AE Agent = 0.05 pounds (or 0.67 ounces) 

Weight of F.A. (wet) = 114.51 pounds 

Mix Totals ----------- > 394.40 pounds 

57 
I 

Table 12. Standard batch testing report form. 

I 

I 

BATCH MEASUREMENTS 

Batch No. 56 

Sequence No. I 

Plastic Mix: (Date 9 1 21 1B8) 

I. Slump = 2" 

2. Unit Weight = /42.5/ PLF 

3. Yield = 26.7 CF 

4. Air Content = 5% 

5. Temperature = 07 "F 

6. Technician = &fHardened Specimens: 1 

Flexural Strength @ 7 days for Beam I = i 670 PSI 

Flexural Strength @ 7 days for Beam 2 = 6 75 ~sr 

Compressive Strength @ 7 days for Cylinder 1 = 37q~ ~sr 

Compressive Strength @ 7 days for Cylinder 2 = 36 JO PSI 

Splitting Tensile Strength @ 7 days for Cyli 415 PSI 

Splitting Tensile Strength @ 7 days for Cyli 

Compressive Strength @ 28 days for 

Compressive Strength @ 28 days for 

Static Modulus @ 28 days for Cylinder 3 = , Static Modulus @ 28 days for Cylinder 4 = ~ 
specifications outlined by ASTM. As testing was completed, the standard 

reporting forms were updated and forwarded to the engineer in charge of 

testing. Any comments or problems encountered by the laboratory during 

testing were noted on the report form. 

As the testing results were accumulated, the data were entered into an 

electronic spreadsheet data base. The spreadsheet was programmed to perform 

simple error checking and quality assurance on the data entered. The 

computerized data bases were very flexible and easy to manipulate and 

enhance. Other advantages to using a spreadsheet were: simple and readily 

available statistical analysis procedures, easy exportation of data to more 

advanced statistical programs, and the ability to create various summary 

reports sorted by various parameters. 

The laboratory testing results for the entire project are summarized in 

appendix F. The complete data base including all duplicate specimens and 

replicate batches (data base C) is presented in this appendix. The data 

base excluding replicate mixes (data base A) is also presented. Each batch 

had a variety of post-calculations performed to allow for a more in-depth 

study and analysis, so appendix F also contains only those batches used for 

replicate analysis (data base B). 

RATIONALE FQR ANALYSES OF THE LABORATORY STUDY DATA 

This section presents rationale for the variables and procedures that 

are used in analyses of the laboratory study data that are contained in 

appendix F, data base C. Purposes and outputs for each procedure are 

discussed, but specific implementation and results of the procedures are 

reserved for a later section. 

Classification of Data Base Variables 

As an aid to the discussion of analytical procedures, it is useful to 

categorize the entire set of data base variables in six classes, class T 

through class Y, as shown in the first column of table 13. I 

Class T: Identification Variables 

Four identification variables are used for the 72 mixes that were 

prepared in the lab study. First is the design sequence number (T1 = DES 

SEQ) for each of the 64 cells of the factorial design given in table 10. 

Since replicate mixes were made for eight of the factorial cells, a second 

identification variable (T2 =REP) is needed to distinguish between the two 

replicates. 

No replicate code letter is used for the 56 unreplicated design 

sequence numbers. The eight replicated design sequence numbers contain mix 

codes A and mix B. Taken together, the design sequence number and the 

replicate mix code provide a unique identification for each of the 72 mixes. 

The third identification variable is the randomized sequence (T3 = MIX 

SEQ) in whichthe mixes were prepared and ranges from 01 through 72. The 

final identification variable is the date (T4 = DATE) upon which each mix 

was prepared. 

59 
I 

Table 13. Classification and definition;of data base variables. I 

Class Subclass or Definition . 

8 I 

variables observed in the Laboratory Study 

CONTROLLED Aggregate CAT = Coarse Aggregate Type 

DESIGN FACTORS Properties 'L,- (0 = C1rushed Stone 1 - Siliceous GkvelL 

(4 (U1, U2, U3) CAM = ~oarike Aggregate Maximum Size 

---.I 

Mix AEQ = Quan ity of Air Entrainment 

Quantities - - Apnxozk) &62 -- 

(U4, U5, U6, U7) CAQ = Coarqe Aggregate Quantity (Ib/cy) 

- - ~42d 89 -------- 

CEQ = ~erndnt Quantity (Ib/cy) 

(426, 4L - - - - - - - - ---4 WAQ = Wate, Quantity (lb/cy) 

(236, $70) I 

DESIGN FACTOR Variables Determined FAQ = Fine Aggregate Quantity 

FUNCTIONS by Class U Factor Values CAQSEQ- WQ) - 

(V) (V1, v2, v3,. . .) 

- - &40#.4&0.55,033L, - - - - - 

ACR = Aggrepate Cement Ratio 

(CAQ -tt FAQ)/CEQ 

CO VARIABLES Uncontrolled TEMP = Mix Temperature (deg. F) 

(w) 

I 

but Measured I j (Wl,. . .) L 

PLASTIC CONCRETE Uncontrolled 

PROPERTIES but Measured 

(X) or Calculated 

from Mix Data 

(XI, X2, x3, X4) I 

HARDENED Flexural Strength 

CONCRETE (y1) 

PROPERTIES , (ASTM C78-84, psi) 

(Y) Compressive 

Strength (Y2, Y4) --- 

(ASTM C39-84, psi) 

Split Tensile Strength 

(Y3) 

(ASTM C496-85, psi) 

Modulus of Elasticity Ec28 = ~lastic/ Modulus at 28 days 

(y5) Ec282J Ec 28 ave., Ec 28 diff. 

(ASTM C469-83, psi) 
Class U: Controlled Design Factors 

The second class of data base variables is comprised of the seven 

two-level factors that were specified by the experimental design (table 10) 

and controlled during mix preparations. Three of these factors are 

aggregate properties: coarse aggregate type (U1 = CAT), coarse aggregate 

maximum size (U2 = CAM), and fine aggregate modulus (U3 = FAM). The 

remaining four factors are for mix quantities by weight of air entrainment 

agent (U4 = AEQ), coarse aggregate (U5 = CAQ), cement (U6 = CEQ), and water 

(U7 = WAQ). During the course of analysis, it was found useful to convert 

the mix quantities to related variables such as percent of mix volume. 

Class V: Design Factor Functions 

The third class of data base variables includes design factor functions 

that are determined by the design factor levels of any particular mix. The 

first of these variables is the quantity of fine aggregate (V1 = FAQ) that 

was added to the coarse aggregate, cement, and water quantities to produce a 

given total mix quantity. The remaining functions are water/cement ratio 

(V2 = WCR), and aggregate/cement ratio (V3 = ACR). The following 

definitions show how each V is related to two or more Us. 

Vl = FAQ = 4320.6 - 1.041 CAQ + 0.032 CAT - 0.828 CEQ 

-2.569 WAQ - 27.862 AEQ (26) 

V2 = WCR = WAQ/CEQ = U6/U5 (27) 

V3 = ACR = (CAQ + FAQ)/CEQ = (U4 + Vl)/U5 (28) 

The foregoing equations show that the Vs are completely defined by the Us 

and may therefore have high correlations with the Us. The design factor 

functions are included as alternative and/or supplemental explanatory 

variables in analyses of the engineering properties of the PCC mixes and 

hardened concrete specimens, 

Class W: Covariables 

A covariable is defined to be an uncontrolled independent variable that 

is measured during the course of mix preparation or specimen testing. It 

may have a significant influence on the dependent variables of the study. 

The only true covariable in the present study is mix temperature at the time 

of mix (W1 = TEMP). 

Class X: Plastic Concrete Properties 
I 

Class Y: Hardened Concrete P 

The main dependent variables in the laboratolry study are the properties 

of the hardened concrete specimens (class Y) that1 were made from each mix. 

Four of these variables are strength properties: flexural strength at 7 days 

(Yl = fr7), compressive strength at 7 days (Y2 = fpc 7) and 28 days (Ylr = 

fpc28), and split tensile strength at 7 days (Y3 C ft7). The fifth property 

is the PCC elastic modulus at 28 days (Y5 = ~s28)I. ASTM procedures for 

measuring these five properties are also 

hardened concrete property is measured for two 

mix. Thus, the data base contains Y values for for the meah 

value of Y, for the two specimens (Y ave), and between 

the two specimens (Y diff). 

Classification and Scope of Data Analvses 1 

I 

As shown in the middle column of table 14, dive types of analyses will 

be performed. Variables that enter into each anal sis type are shown in the 

first column; output tables and figures are sho zn the third column. The 

details and actual results of these analyses the laboratory data are 

presented in the next section entitled, of the Laboratory Study 

Data. It I 

Type 1 Analyses: Two-Variable Relationships 

Initial analytical procedures are to examine all relationships that may 

exist between pairs of variables in appendix F, data base A. These 

procedures enable familiarization with all the eqerimental data and provide 

a means for identifying data that may be anomolous. 

A standard statistical program is used to produce a table of means and 

standard deviations for all individual variables and a table of simple , 

correlation coefficients between pairs of variab1,es. The program identifies 

all correlations that are significant at either tbe 0.01 level or the 0.001 

level. I 

Results are tabulated in a triangular matrix whose diagonal cells 

contain means and standard deviations for all variables, and whose 

off-diagonal cells contain the simple correlation coefficients for all pairs 

of variables. 

Correlations of special interest include those between the covariable 

(W1 = TEMP) and other variables. If, for example,, none of these 

correlations is significant, it is not likely thaf the covariable can be 

used to explain variations in the dependent variable. I 

Another set of useful correlations are those between specimen 

differences (Y diff) and specimen means (Y ave)? If these correlations are 

significant, it is likely that the Y values shoulv be transformed (e.g., to 

log Y) in order to have more homogeneous error vatiation. I 

Next a two-way plot is made for each pair of data base variables in 

classes U through Y, exclusive of Y diff. Each pfot is accompanied by 

simple linear regression statistics that include the intercept and slope of 
Table 14. Classification and scope of analyses for the lab study data. 

I 

I 

I 

a. Means, Standard Deviations & 

Properties 

Y = PCC 

Properties 

Factors 

V = Functions of Ui 

W = Covar. 

X diff & Y diff between 

Replicate Mixes & 

Duplicate Specimens 

Y diff between duplicate 

specifications 

Xi by U only 

Xi U with V 

Yi U only 

Yi U&V 

Xi on U & V 

Yi on U&-V 

Yi on X 

Yi on X, U, & V 

Yi on Yj 

Xi f(U,V) + res 

Y i f(U, V) + res O 

Yi .. f(X, U, V) + res 

Relationships 

Among 

x, y, 

u, v, 

&W 

Correlation Coefficients 

c. Two - Variable Graphs with simple 

regression outputs. 

2. Analysis of 

Variance betweer 

Replicate Mixes & 

Duplicate 

Specimens 

3. Analysis of 

Variance & 

Covariance to 

Estimate Factor 

Effects & 

Residual 

Variances 

4. Regression 

for 

Prediction of 

Mix & PCC 

Properties, and 

for the 

Assessment of 

Prediction 

Reliability 

5. Sensitivity 

Analyses for 

Predictors of 

Mix & PCC 

Properties 

a. Between - Specimen Variance and 

Homogeneity 

b. Between - Replicate Variance and 

Homogeneity 

a. ANQVAs and Significant Effects of 

Design Factors on Mix Properties 

b. ANOVAs and Significant Effects of 

Design Factors on PCC Properties 

a. Regression of Mix Properties on 

Significant Design Factors 

b. Regression of PCC Properties on 

Significant Design Factors 

c. Regression of PCC Properties on 

Mix Properties 

d. Regression of PCC Properties on 

Significant Design Factors & Mix 

Properties 

e. Interrelations Amona PCC Properties 

a. Sensitivity of Mix Properties to Design 

Factors 

b. Sensitivity of PCC Properties to Design 

Factors 

c. Sensitivity of PCC Properties to Mix 

Properties 8 Design $actors 
the least-squares line, standard errors for thes coefficients, R-square, 

and the standard error of estimate (SEE). 

Finally, all relevant two-variable equation@ or graphs among the 

secondary relationships are plotted on the corre ponding two-way graphs of 

the data base variables. This step enables visu lization of similarities 

and differences between the study relationships those that have been 

derived elsewhere. I 

Type 2 Analyses: ANOVA for Duplicate Speci + ens and Replicate Mixes 

The second type of analysis is to and Y values 

between the eight pairs of replicated in Y 

values between the duplicate specimens 

mixes. Both of these variances 

error. Since both replicates 

factors (U) and design factor 

replicates reflect chance variation that is not ttributable to the design 

factors, but instead, represent the net effects 

that are at work when two independent mixes are 

specimens are made and tested for a given mix. replication variance is, 

therefore, the appropriate statistical 

significance of design factor effects on the X 

I Differences in Y values between two duplicate specimens from the same 

mix reflect the net effects of only those extra ous variables that are 

associated with specimen preparation and testing and do T not reflect 

variations between separate mixes. The duplicat variance is, therefore, 

expected to be considerably smaller than the rep icate variance and is not 

that change from mix to mix. 

F 

an appropriate basis for testing the statistical significance of factors 

The two duplicate values for each Y from a Liven mix serve three useful 

purposes. The first is that the mean value of Y (Y ave) for the two 

duplicates provides a more precise value for subjsequent analysis than would 

be provided by a single specimen. Secondly, theiduplicate differences (Y 

diff) can be tested for statistical homogeneity., If certain isolated 

differences are non-homogeneous relative to the emaining differences, 

objective rules can be used to decide that one o 1 the other of the two 

specimens has an extreme Y value and should not be used in subsequent 

analyses. Finally, both the replicate dif ferencbs and the duplicate 

differences can be tested for dependence upon th$ corresponding mean values. 

i 

If replicate differences in X or Y have a sfgnificant relationship with 

the corresponding replicate means, or if specime differences (Y diff) are 

systematically related to their corresponding me ns (Y ave), it may be 

possible to eliminate or reduce the dependency b e transforming the original 

values of X and/or Y, perhaps through the use of, logarithms. The reason for 

such transformations is that subsequent analyseh of variance and regression 

analyses are all based on the assumption of homo eneous chance variation at F all levels of the dependent variable being analy~ed. 

The first step is to construct distribution$ of duplicate differences 

for each Y. Differences in the tail of any distribution can be tested for 
"extreme values" relative to the remainder of the distributions. If, 

however, the correlation table shows significant correlation between Y diff 

and Y ave for any Y, then Y transformations should be made to determine 

whether the correlation can be thereby reduced. If so, the corresponding 

distribution of Y diff should be reconstructed, and extreme values retested. 

The duplicate difference analysis thus identifies (1) transformations 

that may be needed for Y variables, and (2) extreme values (for individual 

Ys) that may be excluded from further analyses. 

The analysis of replication differences begins with a table that is 

produced from data base B and that contains all replicate X and Y values. 

Replicate means and replicate differences are calculated, and replicate 

variances are calculated from the replication differences. As was stated 

earlier, these replication variances will be used in both analyses of 

variance and regression analyses. 

Just as for the duplicate differences, homogeneity tests are made for 

replicate differences to detect needs for transformations and/or for 

exclusion of extreme values. 

Type 3 Analyses: Analysis of Variance and Covariance 

The third type of analysis consists of analyses of variance (ANOVA) and 

covariance (COVAR) to determine which design factors (U) and design factor 

functions (V) have statistically significant effects on the mix properties 

(X) and hardened PCC properties (Y). The ANOVA and COVAR thus serve to 

identify factors and factor functions that are candidate independent 

variables for subsequent regression analyses and to screen out variables 

that should not enter the regression analyses. 

Independent variables for each ANOVA are the 7 design factors (U) and 

the 21 cross products of Ui with Uj, for a total of 28 independent 

variables. Three-factor and higher order interactions cannot be used since 

these interactions were confounded with one, another by the choice of the 

half-factorial for the experimental design (table 10). Each AHOVA covers 

the 64 mixes in data base A and therefore has a total of 63 degrees of 

freedom (df). Since the independent variablles account for 28 df, there 

remain 63 - 28 = 35 df for residual variation that is not explained by the 

design factor effects, 

Each ANOVA shows the total sum of squares (Total SS) for all 63 df; the 

SS for each factor and interaction effect (one df each) and the unpooled 

residual SS (Res SSu). The unpooled residual mean square (Res MSu) is given 

by Res SSu/35, and its square root is the unpooled root-mean-square residual 

(RMSu Res). 

If the SS for any particular independent variable is divided by the 

total SS and multiplied by 100, the result is the percent (SS%) of total SS 

that is explained by the independent variable. The total SS% for all 28 

independent variables is the maximtim percent of the variation in X or Y that 

can be explained by the design factors and corresponds to the multiple 

R-square in regression analyses. 

65 I 
The ANQVA includes a ratio comparison (F rat o) of the SS for each 

independent variable with the Res MSu and shows t e 4 significance level (SL) 

that is associated with the given effect. If (SL is sufficiently small, it 

is inferred that the effect is real and, therefor , is a valid explanatory 

variable for X or Y. A 10 percent significance 1 1 vel, SL = 10 is used 

throughout the analyses to separate significant effects from those which are 

not significant and, therefore, belong to the setof residual effects. If 

the SS for all non-significant factor effects are added to the Res SSu, the 

result is the pooled residual SS (Res Ssp) and has pooled degrees of freedom 

(dfp) equal to 35 plus the number of non-significant effects that were 

pooled. Division of Res Ssp by the dfp thus prodices the pooled residual 

mean square (Res MSp) and corresponding pooled root-mean-square residual 

(Res RMSp). 

All of the foregoing ANOVA results for each X and Y variable are 

displayed in the next section, "Analyses of the Laboratory Study Data." In 

addition, the last two summary lines for each analysis show whether or not 

the Res MS is significant relative to the correspynding replication mean 

square (Rep MS) that was previously derived. 

The Rep MS represents variation that cannot be explained by any of the 

design factor variables and, if Res MSp is not significant relative to Rep 

MS, it is inferred that the ANOVA has identified all explanatory variables. 

Otherwise, it is inferred that the Res MSp may contain factor effects 

(three-factor and higher order interactions) that are significant. In such 

cases, it may be that one of the design factors (Ui) has neither a 

significant main effect nor significant interactions with any other design 

factor (ViVj). If so, the ANOVA can be rerun with the full factorial that 

is represented by the six remaining design factors and significant higher 

order interactions may thereby be identified. 

After ANOVA has been performed for any X or Y, the next step is to 

introduce the design factor functions (V) and covariables (W) in a 

covariance analysis that also contains all Ui and UiUj. 

Although the variables in class V are not true covariables, they are 

treated as such in the COVAR analyses. These analyses show the extent and 

manner in which significant Ui and UiUj effects may be transferred to (or 

subsumed by) significant effects of the V variables. Since by equations 26, 

27 and 28, the Vi have mathematical dependencies on the U variables, it is 

not expected that any COVAR will produce a greater amount of explained 

variation (or less residual variation) than was produced by the 

corresponding ANOVA. Rather, the COVAR analyses should show the ways in 

which V variables can be substituted for U variabTes as alternative inputs 

to subsequent regression analyses. I 

If the linear associations among U and V variables are quite high, the 

variance-covariance matrix for COVAR may be singutar (or nearly so) and it 

will not be possible to perform the covariance an lysis. In such cases, 

only a partial set of the Vi can be used. The us ble Vi can be identified 

by successive runs with different subsets of the i i. 

I 

The computer program for COVAR provides a n ber of options for 

determining the Vi effects. The first option is o 4 calculate the V effects, ~ 
adjust the dependent variables for the V effects, then determine the U 

effects. A second option is to determine the U effects first, then 

calculate the V effects. Through the use of both options, it is possible to 

identify alternatives for input variables to the regression analyses. For 

each X and Y, ANOVA and COVAR results are tabulated and are used to identify 

the most promising sets of independent variables for the regression 

analyses. 

The ANOVA and COVAR programs produce tables of mean values for the Ui 

and Vi effects including interaction effects of the U cross-products. From 

these tables, significant effects of U and V on the Xi and Yi are 

identified. 

Type 4 Analyses: Multiple Regression Analyses 

The fourth analysis type consists of multiple regression analyses for 

the derivation of equations that predict mix properties (X) from various 

combinations of design factors (U and V), and that predict hardened PCC 

properties (Y) from various combinations of design factors and mix 

properties (U, V, and X). The resulting equations are the secondary 

relationships that were set forth in the objectives for the laboratory 

study . 

Prior to each regression analysis it is necessary to decide what 

mathematical model to use for the relationship. Considerations for model 

selection include boundary conditions, transformations of variables, and 

mathematical form. For some models, it may be necessary to use non-linear 

regression analysis. It is assumed, however, that models can be selected 

that are linear in the coefficients (perhaps after transformations) and that 

linear regression analyses will suffice for the laboratory study data. The 

discussion which follows illustrates only the case where the untransformed 

dependent variable is a linear combination of the untransformed independent 

variables as they exist in the data base. 

As shown in table 14, the first set of regressions are for the 

prediction of mix properties (X) from design factor variables (U and V) 

whose effects on X were found to be significant in the variance and 

covariance analyses. Stepwise multiple regression is used with an input 

probability criterion of 10 percent (PIN - 0.10). At each step, an 

additional independent variable (Ui, UiUj, or Vi) is introduced only if it 

will make a contribution to the prior-step regression that is significant at 

the 10 percent level. The procedure ends when there are no remaining 

candidate variables whose inclusions would make a significant contribution 

at the specified (10 percent) level. 

If only the significant Ui and UiUj candidate variables, the 

derived regression equation should inch these variables. men the Vi 

are also included as candidates however expected that some of the Ui 

and Ui Uj that were significant in the ill be supplanted by one or 

more of the Vi, and that the final regr 

subset of the candidate input variables. 

The display of regression results for each X is given in the next 

section and lists the coefficient for each significant predictor of Xi (Ui, 
I 

/i I 

1 UiUj, and Vi) and for the constant term (i.e., th(e X intercept of the I equation's graph). The significance level for eakh candidate input term is 

shown, but no coefficients are given for candidates that were not retained 

in the final equations. 

Following the regression equations, the next set of regression results 

include the total sum of squares for X which has 63 degrees of freedom and 

the regression sum of squares (Reg SS) that is exblained by the equations 

independent variables and that has df equal to the number of variables in 

the equations. The ratio of Reg SS to Total SS 16 the R-square for the 

regression, i. e. , the fraction of total variation in X that is explained by 

the predictor variables. The difference between Total SS and Reg SS is the 

residual sum of squares (Res SS) whose df are 63 minus the df for Reg SS. 

The residual mean square (Res MS) is Res SS divided by its df, and the 

standard error of estimate (SEE) is the square robt of Res MS. 1 

As was done in the analyses of variance and bovariance, an F ratio is 

calculated by dividing the Res MS by the replicath mean square (Rep MS) . If 

this ratio is not significant (say at the 10 perchnt level), it is inferred 

that deviations of the observed X values from corresponding predicted values 

(i . e . , regression residuals) are compatible with % differences between 

replicate mixes. If the F ratio is significant however, it can be said that 

there is a significant lack-of-fit. Lack-of-fit generally arises whenever 

one or more of the following is true (1) the input data contains "extreme 

values" for one or more dependent and/or independknt variables, (2) 

significant predictors have been omitted from the input independent 

variables, and (3) the model for the regression analysis does not have the 

correct mathematical form for the regression relationship. If either case 

(1) or case (2) is true for the regression analysis, the same was true for 

the prior ANOVA and COVAR analyses, and would be evidenced by significant 

ratios of Res MS to Rep MS in those analyses. I 

I 

To assist in the detection of extreme valuest the regression analysis 

includes a display of all 64 residuals, both numerically and graphically. 

Using this display the regression results end with a tabulation of those 

cases whose residuals are greater than 2.8 times SEE. For 64 cases, only 

about one such residual is expected, and if any absolute residual exceeds 3 

times SEE, it is almost certain that extreme values are present in the input 

data. 

Examination of all input data for the extreme residuals may reveal 

previously unnoted errors or may provide no explanations. It must thus be 

decided whether or not to rerun all analyses (ANOVA, COVAR, and regression) 

with corrected data or in the absence of the extrqme data. If lack-of-fit 

cannot be identified with extreme residuals, then an effort should be made 

to find transformations (for the input variables) that will reduce the Res 

MS to a level that is no longer significant relative to the Rep MS. The 

nature of needed transformations can be investigated by regressing residuals 

from the initial equation on U and V. If the resjdual regressidns produce 

significant effects, then the initial forms of the U and V variables were 

not appropriate for explaining the effects of U add V upon X. 

I 

A final step in each regression analysis is do plot observed X values 

versus predicted X values (as shown in the next sdction). These graphs not 
only identify extreme values but may reveal systematic departures from the 

expected linear trend with unit slope. 

All of the foregoing discussion for regressions of Xi on U and V 

variables is equally applicable to the remaining regression analyses. The 

second set of regressions is for each Yi on U and V variables. Results are 

given in the next section. 

The third set of regressions are for Yi versus only the X variables to 

determine the manner and extent to which hardened PCC properties can be 

predicted from only the observed properties of the plastic mix. The results 

of these are also given in the next section. 

The next set of regressions are for the prediction of Yi from the 

complete set of available independent variables (U, V, and X). For each of 

these regessions, the selection of candidate input variables is guided by 

the results of all previous analyses of Yi, including ANOVA, COVAR, and 

regression analyses. The regression results include the major secondary 

relationships that were sought in the laboratory study. 

The last set of regressions are for pairwise associations among 

selected Ys. Of particular interest are regression equations for predicting 

flexural strength (Y1 = fr7) from compressive strength (Y2 = fpc7) and for 

predicting PCC modulus (Y5 = Ec28) from either flexural or compressive 

strength. In these and other YiYj regressions, various transformations of 

the variables (e.g., log Y1 and log Y2) may be introduced to provide for 

boundary conditions and non-linearity that are not given by simple linear 

regressions for the untransformed variables. Results for the YiYj 

regressions are presented in the next section. 

Type 5 Analyses: Sensitivity Analyses 

The term sensitivity refers generally to the amount of change that is 

produced in a dependent variable by specified changes in one or more 

dependent variables. Sensitivity is an important criterion in the 

development of performance-related specifications since greater effects on 

performance will be produced by M&C variables to which performance 

predictors (e.g., PCC strength) are more sensitive than by M&C variables to 

which the predictors are relatively insensitive. It follows that strict 

quality control and acceptance criteria are much more important for M&C 

factors to which the performance predictors are highly sensitive. 

It appears that standard definitions have not been developed for the 

quantification of sensitivity, and that different definitions are used by 

different researchers. For the present report, it will be assumed that the 

sensitivity of a dependent variable to independent variables is relative to 

one or more functional relationships for the prediction of a given dependent 

variable from specific independent variables. Moreover, for the laboratory 

study, the functional relationships of most concern are the regression 

equations that have been developed for the prediction of Xi from U and V, 

for predicting Yi from U and V, and for predicting Yi from U, V, and X. 

Two types of sensitivity will be considered, local and global. Local 

sensitivity refers to the amount of change in Y that is brought about by 
unit changes in the independent variables at a point that is defined by 

values for the independent variables. Local sensitivity is thus defined by 

the partial derivatives of Y with respect to the independent variables, when 

all are evaluated at the point of interest. 

Local sensitivity has its application in the setting of tolerance 

limits for M&G specifications. In this case, the set of target levels for 

the specified variables gives the point at which the partial derivatives are 

evaluated and the evaluated derivatives show the relative degrees of control 

that are needed for the variables. 

Global sensitivity refers to the change in that is brought about over 

the full experimental range of the independent variables. To narrow the 

definition of global sensitivity, it is customary to calculate the 

percentage change in Y that results from percentage changes in a given 

independent variable when all remaining independent variables are at their 

mean values. From these calculations the relative importance of the 

independent variables can be assessed. 

Global sensitivity has its application in the selection of M&C 

variables for quality control and acceptance sampling. Variables associated 

with low sensitivity may be by-passed and control may be exercised on only 

those variables to which the dependent variable is highly sensitive. 

Further discussion and details for sensitivity analyses will be given 

after regression equations have been developed from the laboratory data. 

ANALYSES OF THE LABORATORY STUDY DATA 

This section presents results from the five types of data analyses for 

which rationale was discussed in the previous section. 

Pairwise Associations Between Study Variables 

The classification of variables in table 13 shows 7 design factors (U1 = CAT through U7 = WAQ), 3 design factor functions (V1 = FAQ, V2 = WCR, and 

V3 = ACR), 1 covariable (W1 = TEMP), 4 mix properties (X1 = SLUMP through X4 

= AIR), and 5 properties of the hardened PCC (Y1 = fr7AVE through Y5 = 

Ec28AVE) for a total of 20 independent variables.' 

Four of these variables represent mix that can be expressed 

either by weight in pounds per cubic yard (i.e., U5 = CAQ, U6 = CEQ, U7 = 

WAQ, and V1 = FAQ), or as percents of total volurhe e., U5 = CAP, U6 = 

CEP, U7 = WAP, and V1 = FAP). It is useful to know how both versions of 

these four variables are associated with any of the remaining independent 

variables. Thus, the total number of independent variables is 24 and the 

total number of pairwise associations among these variables is (24 x 23)/2 = 

276. 

Two methods are used to infer the nature and degree of each of the 

pairwise associations. One is to calculate the simple linear correlation 

coefficieht between the two variables in each pa$r; the second is to plot 

the two-way scatter diagram for each pair of variiables. Since values for 

each of the 24 variables were observed (or calcu1,ated) for each of the 64 
mixes in data base A (appendix F), each correlation coefficient is based on 

64 pairs of values and each two-way graph contains 64 data points. The 

correlation coefficient quantifies the direction and degree of linear 

association between the two variables while the two-way graph indicates 

possible non-linearities, the degree of scatter, and which points (if any) 

appear to be extreme values relative to the remaining points. 

Pairwise Correlations 

Means and standard deviations for the 24 primary independent variables 

are shown in the diagonal cells of the first 24 rows of table 15. Cells 

below the diagonal entries contain the pairwise correlation coefficients for 

these variables. Coefficients marked with a single asterisk are 

statistically significant at the 0.01 level; those marked with two asterisks 

are significant at the 0.001 level. Except for the expected high 

correlations between mix quantities by weight and by volume, all 

correlations between pairs of design factors (Ui and Uj) are essentially 

zero because of the orthogonal experimental design. 

Fine aggregate quantity (V1 = FAQ or FAP) is correlated to a 

significant degree with the other mix quantities, especially with coarse 

aggregate quantity (U5 = CAQ or CAP). Water cement ratio (V2 = WCR) has a 

very high correlation with cement quantity (U6 = CEQ or CEP) and a less high 

correlation with water quantity (U7 = WAQ or WAP). The third design factor 

function, aggregate cement ratio (V3 = ACR), has an extremely high 

correlation with cement quantity (U6 = CEQ or CEP). As will be discussed 

later, if two independent variables have pairwise correlation greater than 

about 0.92 in absolute value, then only one should be candidate for any 

regression analysis. Thus, either CEQ/CEP or ACR, but not both, are 

candidate elements of multiple regression equations. 

Table 15 shows that mix temperature (Wl = TEMP) is not correlated 

significantly with any of the remaining independent variables. This fact is 

due to the randomization of mix designs and implies that no temperature 

adjustment need be introduced in any regression analysis. 

The next four lines in table 15 are for mix properties and show that 

the highest correlations are between AEQ and SLMP or UNWT, between CEQ/CEP 

or WCR and UNWT or YLD, and between X3 = YLD and X2 = UNWT. 

Correlations between PCC properties (Y1 through Y5) and the independent 

variables are generally higher for volumetric quantities of coarse aggregate 

and cement (CAP and CEP) than tor weight quantities (CAQ and CEQ). Although 

Y1 through Y5 are highly correlated with V3 = ACR, still higher correlations 

exist for correlations of Y1 through Y5 with U6 = CEQ or CEP. 

Of considerable interest is the fact that all five hardened PCC 

properties (Yl-Y5) have high correlations with one another as shown in table 

15. The bottom lines show the extent of correlation mix sequence numbers 

(TI = MIX SEQ) and Y1 through Y5 differences between specimens with the 

remaining independent variables. It can be seen that the randomized mix 

sequence numbers are uncorrelated with all independent variables except for 
Table 15. Means, standard deviations, and pairwise correlation coefficients for variables in data base A. 

Diagonal Cells Contain Mean/Standard Deviation for Variable 

Below Diagonal Cells Are Pairwise Linear Correlation Foefficients 

All Values are for N = 64 Mixes 

+ 1 -Tailed Significant: -0.91 

" 1-Tailed Significant -0.001 
i 

mix temperature (W1 = TEMP). This fact shows that the randomization was 

effective, and that temperature might have had a systematic influence on the 

dependent variables had the mix order not been randomized. 

Correlations of the differences between specimens (Y1 diff through Y5 

diff) with independent variables are generally of low magnitude. 

Correlations of Yi diff with Yi are not large enough to suggest that the Y 

variables need be transformed to induce greater homogeneity of variance. 

Two-Way Graphs For the Study Variables 

The rows of table 15 represent 30 different variables of which 9 are 

design factors (Ui), 4 are design factor functions (Vi), 1 is a covariable 

(Wl), 4 are mix properties (Xi), 5 are PCC properties (Yi AVE), 1 is mix 

sequence (TI), and 5 are specimen differences (Yi diff). The body of table 

15 contains 480 correlation coefficients for pairwise linear associations of 

the 30 variables. Although a two-way graph (scatter diagram) could be 

plotted for each coefficient, only certain of these graphs have direct 

bearing on the analyses to be presented in later sections. As was explained 

in the preceding section, the correlation coefficients for T1 = MIX SEQ, for 

the five Yi diff, and for W1 suffice to decide that none of these variables 

needs to be considered further in the data analysis. Correlations between 

pairs of design factors (Ui and Uj) are virtually zero, so graphs for these 

pairs are not useful for the analysis. Finally, essentially the same 

association exists between either the by-weight or by-volume versions of the 

a mix variables and any of the remaining variables. Since graphs need be 

plotted for only one of the two versions, the by-weight versions (CAQ, CEQ, 

WAQ, and FAQ) will be used. 

With the foregoing exclusions, the correlations of interest involve 19 

variables and 150 two-way graphs as shown in the following abstract from the 

middle portion of table 15. 
Set YiYj: (5 x 4 / 2 = 10 graphs) 

Set YiUj + YiVj + YiXj: (5 x 14 = 70 graphs) 

Set XiXj: (4 x 3 / 2 = 6 graphs) 

Set XiUj + XiVj : (4 x 10 = 40 graphs) 

Set ViVj: (3 x 2 / 2 = 3 graphs) 

Set ViUj: (3 x 7 = 21 graphs) 

The computer routine for plotting each two-way graph also produces 

regression statistics for the least squares line through the data points. 

These statistics were also examined as part of thp analysis. 

At this stage of analysis, there were three inferences to be drawn from 

each graph, namely: 

1. The degree of association and closeness of fit, as given by Rsquared and the standard error of estimate (SEE). 

I 2. Indications of non-linearity, as'judged @y the presence of 

P 

j systematic (non-random) scatter of data points from the regression 

line. 4 

I 1 

3. Indications of outliers (extreme values) as evidenced by points that 

deviate by (say) more than 2.5 x SEE frod the line. 

In the event of case (2), the term "non-linegr" was printed on the 

graph. For case (3) the outlier points were circled and identified by their 

mix sequence numbers, ~ 1 

1 

I I Inspection of all 150 two-way graphs showed that only four mixes 

i produced outliers for any of the graphs, namely, pix numbers 34, 37, 49, and 

64. All four of these mixes were made from the river gravel aggregate ((Vl 

tl = CAT = 1) and all contained the lower level of water quantity (V7 = WAQ = 

236 lb (107 kg)). I 

'I 

Mix 49 produced outliers for virtually all graphs and has unusually low 

values for all Yi, particularly for Y5 - Ec28AVE at 1.80 million psi 

(127,000 kg/cm2) . In spite of the fact that this mix received no air 

entrainment (U4 = AEQ = O), its air content (W4 = AIR) was 10 percent and 

its yield (X3 = YLD = 30.5) was exceptionally high. 

Mix 64 appears to be extreme only with respect to the tensile strength 

of both cylinders which produced Y3 = ft7AVE = 665 psi (46.8 kg/cm2). All 

other Y AVE values for this mix appear to be consistent with those from the 

remaining mixes. 

Mix 34 produced outliers on most graphs involving flexural strength 

since its Y1 = fr7AVE was low [544 psi (38.2 kg/cm2) ] relative to its other 

Y values [e.g., Y2 = fpc7AVE = 5660 psi (398 kg/c and Y5 = Ec28AVE = 5.45 

million psi (383,000 kg/cm2) 1 . Another aberratio A for mix 34 was its high 

air content (X4 = AIR = 8.2 percent) in view of t ere being no air 

entrainment (U4 = AEQ = 0) for this mix. e 

Finally, mix 37 produced an extreme point on a few two-way graphs, but 

with na particular pattern such as evidenced by m 1 xes 49, 64, and 34. 

I 
The four graphs (figures 7, 8, 9, and 10) in the pages that follow have 

been selected to illustrate the nature of outliers produced by mixes 34, 37, 

49, and 64. Two additional graphs (figures 11 and 12) are also included to 

show that some of the pairwise associations may not be linear. Figure 11, 

for example, shows that the relationship between compressive strength (Y2 = 

fpc7AVE) and slump (XI = SLMP) is probably non-linear since more points lie 

above the regression line than below for low slump, and more points lie 

below than above for high slump values. 

Figure 12 (and other two-way graphs for V3) shows that Y1 increases 

with V3 = ACR when U5 = CEQ is fixed at either 584 lb or 426 lb (265 kg or 

193 kg), but that Y1 decreases as the aggregate/cement ratio moves from 

values around 5 to values around 7. This phenomenon arises because both 

strength and ACR decrease with decreasing cement content when other 

variables are fixed. Since ACR is highly correlated with CEQ (see table 

15), the regression line in figure 12 does not show the true relationship 

between Y1 and V3. For this reason, V3 = ACR was not used in regression 

analyses that also involve U5 = CEQ. 

Figure 12 also serves as a reminder that the points in any two-way 

graph of the study data differ from one another on all remaining variables. 

Thus, any regression line for a two-way graph will ordinarily be an average 

regression for the separate regressions that represent different levels of 

the remaining variables. 

Another use for the two-way graphs is for comparison with corresponding 

pairwise associations that have been developed in previous studies. Most of 

the latter are identified in appendix C, but comparisons with results of 

this study are also made in later sections of this report. 

Analvses of Variance Between Duplicate Specimens and Replicate Batches 

Two levels of chance variation (experimental error) were observed in 

the laboratory study. The first level was quantified by differences in PCC 

properties between the specimens that were made from the same mix. The 

second level of chance variation was between corresponding data for two 

replicate mixes. 

Variance Between Duplicate Specimens 

Specimen differences are-denoted by Y1 diff - fr7diff, etc. for the 72 

mixes in data base C. The frequency distributions for the absolute values 

of Y1 diff through Y5 diff are shown at the top of table 16. Means and 

standard deviations are shown for each of the five distributions. If the 

differences in any distribution all reflect the same set of chance causes, 

it can be expected that none of the 72 differences will deviate more than 

(say) 3 standard deviations from the distribution mean. Table 16 shows, 

however, that one difference in the Y5 d,iff distribution lies nearly 13 

standard deviations from the mean, that one dtfference in both the Y1 diff 

distribution (mix 37) and the Y4 diff distribution (mix 16B) lies more than 

8 standard de?iations from its mean, and that:one difference in the Y2 diff 

distribution (mix 38B) lies more than 7 standard deviations from its mean. 

It was inferred that these four differences ate not homogeneous with their 


64 cases plotted. Regression statistics of EC28AVE on FPC7AVE: 

Correlation ,85173 R Squared .72544 S.E. of Est ,36256 Sig. .OOOO 

Intercept(S.E.) 2.47351( .15053) Slope(S.E,) .(I0052 ( ,00004) 

Figure 9. Two-way plot of EC28AVE (Y5) versus FPC7AVE (Y2). 

XI= SLMP 

64 cases plotted.- Regression statistics of FPC7AVE on SLMP: 

Correlation -.41168 R Squared .I6948 S.E. of Est 1042.18407 Sig. .0007 

Intercept(S.E.) 3952.69302(169.833&5) Slope(S.E.) -191.15562( 53.74151) 

Figure 11. Two-way plot of FPC7AVE (~2;) versus SLMP (XI). I 

80 
V3- ACR 

64 cases plotted. Regression statistics of FR7AVE on ACR: 

Correlation -.73996 R Squared .54754 S.E. of Est 83.83215 Sig. .0000 

Intercept(S.E.) 1040.71030( 59.13814) Slope(S.E.) -79.34650( 9.16031) 

Figure 12. Two-way plot of FR7AVE (Yl) versus ACR (V3). 

81 
Table 16. Variations in PCC properties between duplicate specimens. 

I Des. Seq. No. 1 37 1 16B 
comparison differences and that the Y value of one or the other of the two 

specimens in each case is an outlier relative to the set of chance causes 

that produce specimen differences. 

As shown in the bottom part of table 16, it was decided that the 

outlier specimen was unusually low for Y1 in mix 37, for Y2 in mix 38B, and 

for Y3 in mix 16B. The outlier for Y5 in mix 36 was extremely high [Ec28 = 

7.10 million psi (499,000 kg/cmz) 1 relative to all remaining Ec28 values. 

As shown in the comments column at the bottom of table 16, values for the 

four outliers were each adjusted (arbitrarily) by two standard deviations in 

the direction of the value of its companion specimen. 

The distribution of Y2 diff also includes one difference (mix 28) that 

is more than four standard deviations from the distribution mean, as does 

the Y4 diff distribution (mix 60). As shown at the bottom of table 16, 

however, it was concluded that there is not sufficient evidence for 

adjustment of specimen values associated with these somewhat less extreme 

differences. 

It is noted that the adjustments described in table 16 were 

incorporated in the analysis data base (data base A) but not in the complete 

data base (data base C). Moreover, all two-way graphs described previously 

were plotted from data base A after the specimen values were adjusted for 

outliers. 

Variance Between Replicate Batches 

The experimental design (table 10) identifies eight factorial 

combinations of the Ui for which two independent mixes (replicate A and 

replicate B) would be prepared. Data for the eight pairs of replicate mixes 

are given in appendix F. For each pair, the data for replicate A also 

appears in the analysis data base. Data for replicate B are used strictly 

for comparisons with the A replicates. As can be seen in the mix sequence 

and data columns, all 16 mixes were prepared in a random order relative to 

each other and to the remaining mixes. 

Data from data base B are reproduced in table 17, including adjustments 

that were shown at the bottom of table 16 for Y3 in mix 168 and for Y2 in 

mix 38B. 

For each pair of mixes, table 17 shows differences between the two 

replicate X values, and differences between the two duplicate means for the 

five Y variables. The mean square of the eight mean differences for each 

variable is called Rep MS in the bottom portion of table 17, and its square 

root (Rep RMS) is the standard deviation for variability between replicates. 

Since those mean squares (or standard deviations) represent all chance 

variation in X and Y values that is not attributable to the controlled 

factors (U and V), they are measures of the variation that cannot be 

explained by the controlled factors of the study. 

As will be explained later, the standard deviation of residuals from a 

regression anHlysis for an Xi or Yi will be divided by the corresponding Rep 

RMS for the Xi or Yi. If this ratio is relatively small, the regression 

equation was assumed to be a good fit for the data points. If the ratio is 

83 I 

I 
Table 17. Variations in PCC properties befween replicate mixes. I 

Note: Numbers in parenthews refbd a~ustments given at bottom of Table 16. 

' Coeff. Var. = Rep RIMS / Overall Mean x PWX. 
relatively large, it was inferred that a better-fitting regression model 

should be used. 

The last line of table 17 gives coefficients of variation (GV) that are 

given by dividing the RepRMS values by the respective overall means. It aan 

be. seen that X2 = UNWT and X3 = YLD have extremely small CVs of the order of 

1 percent. This is because both X2 and X3 are governed by the mix 

quantities for aggregates, cement, and water, and are, therefore, closely 

controlled at the same levels for the two replicate mixes. Air~eontent 

,(X4), on the other hand, has a replicate CV of about 10 percent, and the CV 

for slwnp (XI) is nearly 30 percent. 

'Thus, both slump and air content replicate mixes exhibit a relatively 

large degree of chance variation. Replicate variation for compressive 

stzrength (Y2 and Y4) and tensile strength (Y3) are characterized by CVs that 

range from about 7 to 8.5 percent. The replicate CV for PGC mojdulus (Y5) is 

about 4 percent, and for flexural strength about 3 percent. It4~ believed 

that all five CVs for the Ys are relatively small and, therefore, reflect a 

high degree of control for the laboratory study as a whole. 

Analysis of Variance and Covariance for Mix Properties and PCC 

Properties 

* * 

This section presents analyses of variance (ANOVA) and covariee 

analyses (COVAR) for the four mix properties (XI through X4) and~the five 

hardened PCC properties (Y1 through Y5). The ANOVA were made possible by 

the orthogonality of the experimental design (table 10) and serve to 

identify which design factors (U1 through U7) and cross-products thereof (Ui 

,x Uj) have statistically significant effects on any X or Y variable. In a 

sense, ANOVA is a precursor analysis for the regression analyses to follow, 

arid provides a rational basis for inclusion or exclusion of independent 

variables in the regression models. 

Analyses of Variance 

The orthogonality of the experimental design ensures that all main 

effects (e.g., U1 = CAT or U6 = CEQ) and two-factor interactions (e.g., U2 x 

U3 = CAM x FAM) are additive and independent of one another. Because only a 

one-half fraction of the complete factorial was used, each three-factor 

effect (e.g., UlU2U3 = CAT x CAM x FAM) is confounded with a particular 

four-factor effect (e.g., U4U5U6U7 = AEQ x CAQ x CEQ x WAQ). This means 

that any significant three-factor effect is identically equivalent to its 

companion four-factor effect and that the two effects cannot be analytically 

separated. 

The companion three-factor and four-factor interactions can be 

identrfied from the following display of all seven design factors: 

? '. 

U1 = CAT, U2 = CAM, U3 = FAM, U4 = AEQ, U5 = CAQ, U6 = CEQ, U7 = WAQ 

If any three of the factors are selected as a three-factor combination, then 

the remaining factors represent the four-factor combination with which' the 

three-factor combination is confounded. The same rule holds for two- factor 

combiflations, since each is confounded with its five-factor companion. 
Similarly, each single factor is confounded with the remaining six-factor 

combination. 

Past experience with ANOVAs for experimental data show that, like for 

succes~ive~te~ms in a convergent series, the mag~itude of effects generally 

decrease from one-factor effects to two-factor eFfects to three-factor 

effects, etc, and that at some point all higher-order effects are of the 

same size as replication error. 

Each ANOVA for the study data is based on 64 mixes and, therefore, 

represents 64 degrees of freedom (df). One degree of freedom (df) is for 

the mean value of the X or Y being analyzed, seven df are for the one-factor 

main effects, 7x6/2 = 21 are for two-factor combinations and 7x6x5/(3x2) = 

35 df are for the three-factor combinations. 

Table 18 shows ANOVA results for each of the four mix properties (XI 

through X4). The total sum of squares (SS) for each variable is shown in 

the first line of the summary box and is the sum of the 64 X deviations from 

the X mean. The ANOVA procedure begins by calculating how much of the total 

is attributable to each of the 7 main effects (U1 = CAT through U7 = WAQ), 

how much is attributable to each of the 21 two-factor effects (CAT x CAM 

through CEQ x WAQ), and what level of significance is attained by each of 

these effects relative to the remaining (residual) part of the total SS. At 

this point, the residual sum of squares has 35 degrees of freedom (i.e., 63 

- 7 - 21 = 35). Division of the residual SS by 35 gives the unpooled 

residual mean square (Res MSu). F ratios are calculated by dividing the SS 

for each individual effect by Res MSu, and F tables are used to determine 

the level of statistical significance attained by each effect. The 

significance levels are shown in parentheses for all main effects and 

two-factor effects and each represents the probability that the effect SS is 

really a residual effect rather than the effect of the variable to which it 

is attributed. 

For the s3tudy ANOVAs , the 10 percent level (SL = 10) has been used as 

the criterion for separation of significant effects from residual effects. 

Thus, effects having SL < 10 percent are considered to be significant; 

effects with SL > 10 percent are considered to be within the realm of 

residual variation. 

For each X, table 18 shows significance levels for each U effect, and 

if SL < 10, the table shows the percent of total SS that corresponds to the 

SS for the significant effect. For X1 = SLMP, for example, the first 

significant effect is for U3 = FAM. This effect is shown to be significant 

at the 3 percent level (SL = 03) and has SS percent of 2.55. Thus, the 

actual SS for FAM was 0.0255 x 376.07 = 9.59. Although actual SS might 

have been shown in table 18 for each effect, it was assumed that the SS 

percent gave, a more useful indication of the size of the effect than does 

the actual SS. 

For X1 = SLMP, table 18 shows that five main effects (ME) were 

significant at the 10 percent level, and (in the summary box) that these 

five effects explain 62.05 percent of the total variation in XI. Only 4 of 

the 21 two-factor effects (2FI) are significant at the 10 percent level, and 

account for an additional 11.12 percent of the total variation. Thus, for 
Table 18. Analysis of variance and covariance for mix properties (X). 

fl mml 

SS % (SL) SS % (SL) SS % (SL) SS % (SL) 

CAT * FAM CAQ * WAQ 

CAT* FAM* CEQ*WAQ 

FAM *AEQ CAQ * WAQ 

CAT * AEQ CAQ *' WAQ 
slump, the summary box shows that 73.17 percent Olf the total SS is explained 

by nine effects, of which five are main effects.~ I 

I 

The next step is to pool the X1 sum of squares for the 2 nonsignificant ME and the 17 non-significant 2FI wi the unpooled residuals SS 

and form a pooled residual SS that is based on 3 + 2 + 17 = 54 df. For X1, 

(32.0 mm). 

I 

the ResMSp is shown to be 1.58, and its square r pt (ResRMSp) to be 1.26 in 0 I I 

The next step was to compare the pooled re mean square with the 

replicate mean square for X1 that was given in t and that is 

reproduced in table 18. The ratio of these two is called the 

error mean square ratio (EMSR) and for X1 is 1.5?/0.234 = 6.75. From tables 

of the F ratio, it was found that this EMSR (for54 and 8 df) is significant 

at the 0.5 percent level, shown as (00) in tablel8. It was, thus, inferred 

that the pooled residual mean square contains si effects that were 

not accounted for by the main effects and two-fa of the design 

factors. I 

I 

I 

ANOVAs for X2 = UNWT and X3 = YLD in table 118 show that the significant 

main effects and two-factor effects account for 89 percent and 74 

percent of the total variations in X2 and X3, and that the 

EMSR is not significant for either variable. hand, the fact 

that EMSR for X4 = AIR is significant at the 1 pibpcent level implies that 

main effects and two-factor effects (SS% - 81.2) id not provide an adequate 

explanation for X4 variations. 

The ANOVAs for Y1 through Y5 in table 19 sho that main effects and 

two-factor effects account for about 90 percent o the total SS for Y1 = 

fr7AVE, 87 percent of the variation in Y2 = fpc7A I E, 72 percent of the Y3 = 

ft7AVE variation, 85 percent of the variation in Y4 = fpc28AVE, and 75 

percent of the total variation in Y5 = Ec28AVE. owever, the EMSR is 

significant at the 10 percent level for all five ariables, suggesting that 

higher order interactions may be needed as furthe explanatory variables. i 

I . Since additional explanatory variables must home from three-factor 

I and/or four-factor interactions, each ANOVA for 1 through X4 and Y1 through 

Y5 was expanded to show the effects associated with 7 each of the 35 degrees 

of freedom for the unpooled residual sum of squarles. As was explained 

earlier, each of these effects is attributable toi a specific three-factor 

interaction or to its companion four-factor interpction. As shown across 

the bottom of tables 18 and 19, from three (for 13) to'eight (for Y1 and 713) 

three/four-factor interactions were thus identified 1 as being significant at 

the 10 percent level relative to the pooled resipiual mean square. 

i 

To assist in deciding whether each higher orlder effect represented a 

3FI or 4F1, it was noted that one design factor (b2 = CAM) did not produce a 

significant main effect for any of XI through X4,' and was significant for 

only two of Y1 through Y5 (Y1 and Y4). Furthermoxe, of all two factor 

interactions of U2 = CAM with the remaining six esign factors, the 10 

percent significance level was reached only by C $ x CAQ for X2 and X3, by 

CAM x AEQ for Y3 through Y5, and for CAM x CEQ fob Y1. It was, therefore, 

inferred that 3FI and 4FI involving CAM were highlly unlikely, and that ANOVA 
Table 19. Analysis of variance and covariance for hardened PCC properties (V). 

2.0 (10) 3.5 (02) 

CAT FAM AEQ (0.5) FAM * CEQ WAQ (1 .O) CAT CEQ WAQ (1.8) CAT FAM CEQ (1.2) CAT FAM CEQ (1.2) 

CAT* FAM CAQ (0.6) CAT + FAM CEQ (0.7) FAM AEQ WAQ (1.3) CAT* CAQ CEQ (0.9) FAM AEQ CEQ (1 -6) 

CAT * CEQ - WAQ (0.5) FAM * CAQ CEQ (0.7) FAM CAQ * CEQ (1.9) FAM CAQ CEQ (0.9) FAM CEO * WAQ (2.4) 

FAM AEQ CEO (0.5) AEQ * CAQ * CEQ (0.6) AEQ GAQ CEQ (2.0 FAM * CEQ * WAQ (1.1) CAQ CEQ * WAQ (1.4) 

FAM CEO WAQ (0.8) CAT CAQ * CEQ * WAQ FAM CAQ CEQ * WA* 

AEQ CAQ WAQ (1.6) (04 (3.3) FAM CAQ * CEQ + WAQ FAM CAQ CEQ WAQ 

PROBABLE FAM AEQ * CEQ WAQ CAT * CAQ AEQ WAQ CAT AEQ CAQ WAQ (0.9) (1 

(0.5) (0.8) (1 CAT*CAQ*CEQ*WAQ CAT*CAQ*CEQ*WAQ 

CAT FAM * AEQ CAQ FAM CAQ CEO WAQ CAT*FAM*CEQ*WAQ(2.0) (0.9) (1 -4) 

(0.5) (0.6) CAT*FAM*HEQ*CAQ(I .7) 

135,940 / 47 198,970 1 45 
I 

for the remaining six design factors should reveal the distinction between 

possible 3FI and 4FI. I 

With the exclusion of U2 = CAM, the design Gatrix (table 10) represents 

a full factorial for the remaining six design facttors. The corresponding 

ANOVAs produced ME (6df), 2FI (15df), 3FI (ZOdf), 4FI (15df) and residual 

effects (7df) that were used to infer which of tde 3FI and 4FI were 

significant. The resulting inferences are shown at the bottom of tables 18 

and 19, as probable 3FI and probable 4FI. ~ 

The two bottom lines of tables 18 and 19 shdw the maximum SS percent 

that is explained when the probable 3FI and 4FI qre included as explanatory 

variables, and the residual mean squares that wodld remain after inclusion 

of all significant ME, 2F1, 3F1, and 4FI. When ~hese residual mean squares 

were compared with replicate mean squares, however, significant F ratios 

still existed for X1 = SLMP, X4 = AIR, Y1 = fr7AYE, and Y5 = Ec28AVE. 

In summary, the ANOVAs for X1 through X4 and Y1 through Y5 show which 

terms (one- factor through four- factor) are the mdst likely explanatory 

variables for the respective dependent variables. The relative explanatory 

value of each independent variable is indicated dy its SS percent in tables 

18 and 19. Variables whose SS percent exceed 10 Ipercent of the total 

variation are as follows: I 

i * For X1 = SWP: U4 = AEQ (38%) and U7 = WAQ (22%) for 60% total. 1 e For X2 = UNWT: U4 = AEQ (37%) and U6 = CEQ (23%) for 60% total. 1 

e For X3 = YLD: U3 = FAM (lo%), U5 = CEQ(~~&) and U6 = WAQ(30%), for 

54% total. 

I 

3 For X4 = AIR: 04 = AEQ (50%), and U6 = CEO (10%) for 60% total. 

J ! 

I I 

1 For Y1 = fr7AVE: U6 = CEQ (62%). I I 

1 

a For Y2 = fpc7AVE: U6 = CEQ (66%). 

a For Y3 = ft7AVE: U6 = CEQ (51%). I e For Y4 = fpc28AVE: U6 = CEQ (62%). I 

e For Y5 = Ec28AVE: U4 = AEQ (14%), and U6 /= CEQ (36%), for 50% total. 

! 

Thus, the main effects of U4 = AEQ and U6 = ,CEQ are of foremost 

importance in predicting virtually all of the de endent variables. The SS 

percent for two-factor variables are generally l?ss 4 than 5 percent, and SS 

percent for higher-order interactions are generally 1 percent or less. 

Covariance Analysis I 

I 

The design factor functions, V1 = FAQ, V2 = $CR, and V3 = ACR were 

treated as covariables in the COVAR columns of tables 18 and 19. The 

purpose of these analyses was to determine whethdr the Vi had additional 

explanatory value beyond the SS percent producedlby the seven design 
factors. The covariance routines can be run to first show the Vi effects, 

then show the Ui effects after adjustments have been made for the Vi 

effects. Alternatively, the routines can be run to first show the Ui 

effects then show any additional effects that are provided by the Vi. Both 

alternatives were run for each Xi and Yi, but only the results of the second 

alternative are shown in the COVAR columns of tables 18 and 19. It was 

learned that, under the first alternative, the Vi effects are significant 

and relatively large, but that the Vi effects plus the adjusted Ui effects 

give lower total SS percent than those for the Ui main effects only. For 

the second alternative, as shown in tables 18 and 19, the Vi effects are 

seldom significant after the Ui effects were taken into account. 

Furthermore, the second approach often reduces the SS percent that was 

explained by 2FI in the ANOVA. 

As can be seen in the total SS percent row of tables 18 and 19, the 

inclusion of Vi produces a somewhat smaller total SS percent and somewhat 

larger residual mean square for almost every dependent variable. It was 

concluded that since each Vi is completely determined by specific Ui (see 

equations 26, 27 and 28), it is more appropriate to regard the Vi as 

alternative variables for the Ui, rather than to regard the Vi as additional 

explanatory 'variables. 

Finally, each ANOVA produced a table of means that show main effects 

and two-factor effects in units of the dependent variables. The tables of 

means are given in table 20 for all significant effects of the Ui on each Xi 

and Y i . 

The first row of table 20 shows, for example, that the effect of coarse 

aggregate type (U1 = CAT) is significant for only X2 = UNWT of the mix 

variables. For the Y variables, CAT has a significant effect for all but Y5 

= Ec28AVE, and the difference between aggregate types ranges from 28 psi 

(2.0 kg/cm2) -for Y1 = fr7AVE to 520 psi (37 kg/cm2) for Y4 = fpc28AVE. The 

sixth row shows that U5 = CEQ has a significant effect on all Xi and Yi, and 

that the two CAEQ levels produce, for example, a difference of 197 psi (13.9 

kg/cmz) for Y1 = fr7AVE and a difference of 1832 psi (129 kg/cm2) for Y2 = 

fpc7AVE. 

Significant two-factor interactions between two independent variables 

arise when the dependent variable difference for one variable is not the 

same at both levels of the other variable. Examples are the interaction 

between U1 = CAT and U2 = FAM for the two compressive strengths (Y2 and Y4), 

as shown in the first line of two-factor interactions in table 20. For both 

Y2 and Y4, strength differences between the two levels of FAM are over 500 

psi (35 kg/cm2) for the crushed stone aggregate, but are of the order of 

only 100 psi (7.0 kg/cm2) for the gravel aggregate. The calculated 

differences beztween the crushed stone and river gravel aggregates are also 

considerably less at FAN = 2.10 than at PAM = 2.84. 

Table 20 contains only the two-factor interactions that were 

significant (in tables 18 and 19) for at least one Xi or Yi. As noted the 

bottom of table 20, four two-factor effects were not significant for any Xi 

or Yi. 

91 
Table 20. Effects of design factors on mix properties 

and hardened PCC properties. I 

MIX PROPERTIES , ~ HARDENED PCC WOPERTIES 

AND LEVELS XI x2 X3 x4 Y1 Y2 Y3 Y4 Y5 

slW (in) UNWT@d) nD(q.) AIR (%I , 1 fr 7 (PSI) Ip: 7 (PSI) 11 7 (psi) Ip: 28 (psi) Ec 28 

I 

Main Effects and (Significance Levels) 

CAT 

Csm hKegate Type 1 1.84 140.9 27.8 5.8 

a -0.37(NS) 1 1.9 (00) 1 0.1 (NS) 1 0.4 (NS) 

0.75 in. 1.86 139 9 27.7 5 7 

140.0 27 8 5 5 

0.1 (NS) -0 1 (NS) -0 2 (NS) 

0.74 143.0 27 8 3.6 

136.9 27.7 7 6 

2.57 (00) -6 1 (00) -0 1 (NS) 4.0 (00) 

1 1542 Ib. 1 1.45 1 138.8 1 280 1 62 1 

2 48 

157 

131.5 28.1 6 5 

Cemenl 142 4 27.3 4 7 

Wantity DM a (SL) 91 (01) 49(00) -08(00) 1 8(~) , 

553 3826 3 99 4603 4.46 

518 3305 363 4152 4 19 

65 (01) 521 (00) 36 (02) 451 (W) .27 (01) _I7 

0.88 140.9 27 8 

3 17 5.5 

139.0 27 7 5.7 

Wanlily 2 29 (00) -1.9 (00) 1 -0.1 (NS) 0 2 (NS) 

Two factor Interactions Significant at (10) 

FAM - 2.10 

CAT = FAM-210 

Gravel FA_M 9.g - - (NS) 3.1 0 7 (NS) 

140 2 27.9 

141 7 27 6 

(NS) 15 0 3 (NS) 

CAO = 1542 bs. 

CAT = CEO = 4% ks 

Stone - - CEQ_--M&s- - Din 

CAT I CM = 426 ks. 

a - - CEO_= =~&"Es., - an 

WAO = PG lbs. 

W~OZ27? - 

CAT .; WAO=PGlbs 

W4Q227' - 

150n 

1 50 m 

4 9 

5 8 

(NS) (NS) (NS) 0 9 

6 0 

3 6 

(NS) (NS) (NS) 0 4 

(NS) (Ns) (NS) (NS) 

I CAM- I CEO-4261s I 

(NS) (Ns) (NS) (NS) 

150n - CLO =584 lbs- - W 

CAM = WAO = W6 It6 

075m - - WA~-~70&, - M 

CAM = WAO = 236 1bs 

150n - WA0-27j 1% - an 1 I I 

(NS) (Ns) (NS) (NS) 
Table 20. Effects of design factors on mix properties 

and hardened PCC properties (continued). 

MIX PROPERTIES HARDENED PCC PROPERTIES 

AND LEVELS x4 Y 1 Y2 Y3 Y4 Y5 

AIR (%) , fr7 W) kc7 (psi) 17 (pd) iwa(pi) 6c 2s 

CEO-426 b. 

FAM - CEO- 426 lb. 

- so_-arw!?'- -

1.53 

-22 ws) 0 (NS) 

3.21 

1.62 

-1.59 Ws) 0 (Ns) 1 

WAO-236b 

WAO = no lb. 

FAM - WAO-236lb. 

- E"n--no!!', , 

CAO-1542k.a 

CAO - 1542 k.a 

AEO - CEO - 426 lbr 4.18 133.7 28.3 

6.5 02 - - cE%=!?'P, - 2.4s 140.1 n .2 6.0 

-1.73 b .4 -1.1 -3.1 

WAO - 236 lbr 

CEO - 

NOTE: Fa* Twefactor interactions were not significant for any d the nine properties 

and are not included in Table 21. Them are CATxCAM, CATxAEQ, CAMxFAM and CAQxCEQ. 
I Multi~le Regression Analyses for PCC ~ro~ertkes I I 

This section presents results from five set4 of multiple regression 

analyses that produce equations for the predictidn of mix properties (X) and 

I hardened PGC properties (Y) from other study variables. t 

I 

1 The first set is for regressions of Yi on Xi, the second for I 

I regressions of Xi on Ui and Vi, the third for regressions of Yi on Ui and 

I 

i Vi, and the fourth for regressions of Yi on Ui, Vi, and Xi. The final set 

j of regressions is for selected pairs of Yi whose associations were not fully 

developed in previous sections and that have special utility in the 1 development of PCC PRS systems. h 1 I 

i Regressions of PCC Properties (Y) on Mlix Properties (X) ri 

Results for the regression of each Yi on all four mix properties (Xi) 

and cross-products of mix facto.rs (XiXj) are given in table 2'1. The full 

set of N = 64 mixes in data base A was used in each regression. The - stepwise regression procedure was used in connec.t;ion with a 10 percent 

significance level. In this procedure, the indedendent variable that has 

the highest simple correlation with the dependenq variable is entered in 

step 1. The remaining independent variables (ni e in table 21) are thensearched in step 2 for the variable that will at 4 ain the highest level of 

significance in conjunction with the step 1 variable. The procedure ends 

when none of the unentered variables will attain the 10 percent level of 

significance in conjunction with the previously entered variables. 

I 

In table 21, it can be seen that X2 = UNWT and/or X3 = YLD are the only 

two predictors that attain the 10 percent level of significance for any Y. 

In addition to these variables, the step procedude selected two interaction 

effects, UNWT x YLD for the prediction of Y2 and SLMP x UNWT for the 

prediction of Y3. By coincidence, each of the fqve regression equations in 

table 21 for predicting Y1 through Y5 contains three terms, two involving 

the Xi and one for the constant term of the equatjion. I 

The summary lines for each regression show dotal sum of squares, 

regression sum of squares, R-squares (i.e., regrdssion SS divided by total 

SS) ranging from 57 to 74 percent, residual sum qf squares, residual mean 

square, and the residual root-mean-square or starjdard error of estimate 

(SEE). Replicate mean squares are those shown folr each Xi in table 17, and 

the error mean square (EMS) ratio is the quotiend of the residual and 

replicate mean squares. All five EMS are signifilcant at the 5 percent level 

or less. It is therefore inferrGd that all of tMe derived equations show 

lack-of-fit, and that variation in the Y variableis cannot be adequately 

explained by only the X variables. Somewhat better fits might be attained 

through the use of higher-order X interactions, o,r perhaps through 

non-linear regression models, but it did not appeiar that mix variables are 

sufficient by themselves to give good predictions for the hardened PCC 

properties. 

Maximum and minimum residuals are shown follpwing the EMS ratios, and 

mix sequence numbers are shown for residuals that exceed 2.8 times SEE in 

absolute value. The two extreme residuals are shown to be for mixes 49 and 
Table 21. Regressions o (Y) on mix properties (X) . 

I TERM I 

' 518,053163 99,375,898 / 63 

302,044 I2 56,506,068 I2 

58.3% 56.9% 

21 6,008 I61 42,869,831 / 61 

3541 702,784 

59.5 psi 838 psi I 

100818 122,090 I8 

3.5 t (05) 5.76 (01) 

Max Y Res 1 Max Z Rest 

Min Y Res / Min Z Res -1 78 / -2.25 

3 

EMS Ratio = Y Res SEE ( RepSD )2 ttZRes= - SEE 
64, i.e., for two of the four extreme values that were identified 

previously. 

For each of Y1 through Y5, figures 13 through 17 are plots of the 64 

regression residuals (Y observed versus Y predicted) for the five regression 

equations that are shown in table 21. For eachY, the corresponding Y 

observed versus Y predicted figure gives (at bottom) the table 21 regression 

equation for predicting Y, and includes the R-square and SEE that are also 

given in table 21. In each figure, the value of any particular residual is 

either the horizontal or vertical distance of the residual point from the 

line of equality. Residuals exceeding 2.8 SEE are identified by mix number, 

as was done at the bottom of table 21. I 

1 

The results given in table 21 are of considerable importance in the 

construction control of variables that relate tb PCC strength and will be 

discussed further in the next section. I 

I 

I 

Regress ions of Mix Properties (X) on bignificant Design I Factors (U) and Design Factor ?unctions (V) 

The second set of regression analyses were run to determine how and how 

well PCC mix properties (Xi) can be predicted from experimental design 

factors (Uj ) and functions of the design factor (Vj ) . The regression 

results are shown in table 22. Independent var ables used in the 

regressions are shown at the left of the table knd include only those Uj and 

Vj and cross-products thereof that were signifihant for at least one of the 

four Xi in the ANOVAs of table 18. I 

To reduce intercorrelations among independent variables, especially 

those induced by the use of cross-products, each Uj and Vj was first 

transformed by subtraction of its mean value asgiven in the diagonal of 

table 15. For example, table 15 shows that the'mean values (across all 64 

mixes) were 2.47 for U3 = FAM and 0.51 for V2 =WCR. The corresponding 

independent variables for the table 22 regessibns are thus VAMD = (VAM - 

2.47) and WCRD = (WCR - 0.51), where the letter D is used to denote the 

deviation of the original variable from its mean value. 

Without these transformations, the correlation between Ui and Ui x Uj, 

for example, might be around 0.90, whereas the correlation between (Ui - UiAVE) and (Ui - UiAVE)(Uj - UjAVE) might be nearly zero. As a result, the I 

regression coefficients for UiD and UiD x UjD are not confounded because of 

high intercorrelations. 

As shown at the top of table 22, regressions were run both using data 

from all mixes (N = 64) and using data for the 60 mixes that exclude the 4 

mixes noted at the bottom of the table. 

The table 22 results represent 4 x 2 = 8 stepwise regression analyses. 

Except for the constant term in each regression equation, table 22 shows 

regression coefficients for only those independent variables whose effects 

were significant at the 10 percent level (SL = 10). The number of 

independent variables in each regression equation is shown as df for 

regression SS in the regression summary and varies (for N = 60) from 7 

variables for the prediction of X4 = AIR to 10 variables for the prediction 


" a h 

m rl 

z cg LO aJ ,a ma) 

;a k 

0 a) I 5: E 23 

Frc U 


I Table 22. Multiple regressions for mix properties (X) on significant 1 design factors (U) and factor functions (V) . ! 

(57) (41) 

FAMD CEPD -.66 (04) -.60 (08) 

AEQD * CEPD -.14(00) -.14(00) 

AEQD * WAPD .I6 (01) .16 (01) 

. ~ 

Constant Term 1 140.0(00) / 140.1 (00) 

I .369 cy/8 

.75 (NS)~ .62 (NS] 

a 8 I ' - N = 60 omits Mix Numbers 34,37,49, and 64. 

t EMS Ratio = Y Res (NS) - Ratio not significant at the 10% level. )2 ttZRes=- SEE 
of X2 = UNWT. Each equation includes at least three two-factor products and 

one three-factor product of the independent variables. 

R-squares range from about 70 percent for slump to 92 percent for unit 

weight. The standard errors of estimate (SEE) are significantly greater than 

the corresponding replicate standard deviations for slump (Xl) and air (X4), 

but not for unit weight (X2) or yield (X3). It was concluded that the 

predictions equation for X2 and X3 provide good fits to the data, but that 

there are significant lack-of-fits for both the slump and air prediction 

equations. 

Residuals for the N = 60 regression equations are plotted in figures 18 

through 21. As shown at the bottom of table 22 and in figures 19 and 21, 

extreme residuals were identified with mix 15 for unit weight and with mix 

34 for air content. 

Regressions of PCC Properties (Y) on 

Significant Design Factors (U,V) 

The third set of regression results are shown in table 23 and give 

equations for predicting PCC strength (Y1 through Y4) and modulus (Y5) from 

the experimental design factors (U and V). 

Regression terms represent all seven experimental design factors (U) 

and two functions (V) of design factors (FAP and WCR). As was done in the 

table 22 regressions for X, all U and V are included as deviations from 

their respective means. Cross-product terms for two-factors, three-factors, 

and four-factors were included in the regression models in accordance with 

the ANOVA results that were given in table 14. Stepwise regression was used 

to narrow down the final regression equations to those terms that attained 

the 10 percent significance level. 

Regressions for each dependent variable were run with both the full 

data set (N = 64) and the reduced data set (N = 60). Since R-squares are 

generally somewhat larger and SEES are somewhat smaller for the reduced data 

set, the remaining discussion will relate only to those regressions for 

which N = 60. For the N = 60 case, R-squares range from about 83 percent 

for Y3 = ft7AVE to about 97 percent for fpc7AVE. 

Except for flexural strength (Y1 = fr7), all SEE are within chance 

variation of the corresponding replicate standard deviations, and therefore 

give error mean square (EMS) ratio that are not statistically significant. 

As observed earlier, the replicate standard deviation for fr7AVE is quite 

quite low [15.4 psi (1.08 kg/cmz)] and represents a coefficient of variation 

of only about 3 percent. If the standard dev'iation of fr7AVE between 

replicate mixes were around 30 psi (2.1 kg/cd2), the coefficient of 

variation would be 30/535 or about 5.6 percent, and the error mean square 

ratio for fr7 would be around 2.0 and would not be significant. It was 

believed that the assumption of a replicate standard deviation of 30 psi 

(2.1 kg/cmz) for fr7AVE was not unreasonable. , 

With the foregoing assumption, it was concluded that none of the 

regression equations in table 23 show serious; lack-of-fit and that all 

103 
h $4 

rl (d 

d 3 

0 

U 

C 

k (I) 

d) TJ 

s Et 

B cu 

P1 

(I) ha 3 *2 

cn cu 

It k 1-I a, X 3 V 

w 

0 

m 

Regression equation: YIELD (cf/cy) = -0.07CAPD-0.23CEPD-0.03CATD*CAPD-OaO4AEQD*CEPDM.O4AEQD*WAPD 

+Q.O1CATD*FAMD*AEQD 

Figure 20. Plot of observed versus predicted PCC yield (X3=YLD), where only significant 

design factors (Ui) and design factor functions (Vi) were independent variables. 

Table 23. Multiple regressions for hardened properties (Y) on 

significant design factors (U) and factor functions (V) . 

CATD CAMD 

CATD FAMD 

CATD CAPD 

CAMD * CEPD 

FAMD * AEQD 

FAMD CAPD 

FAMD * WAPD 

AEQD CAPD 

CEPD WAPD I 

Constant Term ] 1536.3(001 540.7(001 1 3588.61 3579.4 1383.11 1 4403.91 4410.0l 1 4.3301 4.34q 

R - Square 

Res. SS 1 d 

1 SEE I 

0.163 psi 18 

*I- 

' - N = 60 omits Mix Numbers 34,37,49, and 64. 

(NS) - Ratio not significant at the 10% level. 

Y Res t EMS Ratio = (-) Rep $0 

+t Z Res = - 

SEE 
provide adequate relationships for prediction hardened PCC properties from 

the experimental design factors. 

The number of independent variables in the table 23 regression 

equations range from 7 (for ft7 and Ec28) to 13 for fpc7. These variables 

include individual factors and two-factor products within each equation, and 

two equations (for ft7 and Ec28) contain three-factor cross-products. 

, It was found that all nine factors (7Ui + 2Vi) are involved in the 

regression equations for flexural and compressive strengths, but that CAM, 

WAF and FAP did not enter the equations for tensile strength, nor did FAM 

and WCR enter the equations for PCC modulus. 

Graphs for the residuals between observed and predicted Y values are 

shown in figures 22 through 26, respectively. Each graph includes the 

regression equation from which residuals were calculated, and the R-Square 

and SEE that indicate the closeness of fit. 

Regressions of PCC Properties (Y) on Significant 

Design Factors (U,V) and Mix Properties (X) 

The fourth set of regression analyses produce equations for predicting 

the hardened PCC properties (Y) from not only the experimental design 

factors (U and V), but also from mix properties (X). The analytical results 

for these equations are shown in table 24. The U and V variables of table 

23 are now augmented by the four X variables and certain cross products of 

U, V and X variables that were implied by significant effects in the ANOVAs 

for Y (table 19) and the regressions of Y on X (table 21). 

As for the table 23 analyses, the independent variables were all 

transformed to deviations from their respective means, and regressions were 

run for both data sets (N = 64 and N = 60). The following discussion is for 

the N = 60 regression results. 

In each of the five equations, the total number of terms remains nearly 

equal for the table 23 and table 24 regressions. Each table 24 equation, 

however, contains terms involving X2 = UNWT and X4 = AIR. In addition, the 

prediction equation for Y5 - Ec28AVE contains XI = SLMP as an independent 

variable. 

Comparison of the R-squares, SSE, and EMS ratio lines of tables 23 and 

24 show that all the table 24 regression equations provide somewhat better 

fits to the data than were provided by the table 23 equations. R-squares in 

table 24 range from about 86 percent for Y3 - ft7 to 98 percent for fpc7, 

and are about 2 percent higher than for the table 23 regressions. The SEE 

in table 24 are at least 10 percent less than the corresponding SEE in table 

23. None of the EMS ratios in table 24 are significant, provided that 30 

psi (2.1 kg/cm2) is used as the replicate standard deviation for fr7. 

It was concluded that the regression equations in table 24 are quite 

satisfactory secondary relationships for the prediction of hardened PCC 

properties from the mix design properties (U and V) and the plastic mix 

properties (X). Figures 27 through 31 show residuals for table 24. 

109 
Predicted FR7 ( psi ) 

Regression Equation: FR~ (psi) = ~~~.~-~~.~CATD-~~.~CAMD+~~.OCAPD+~~.~WAPD+~~.~FAPD~~~~

*CEPD-l0.9FAMD*AEQD-6.7FAMD*CAPD-l.OAEQD*CAPD 

Figure 22. Plot of observed versus predicted average 7-day PCC flexural strength (Yl=FR7AVE), 

where only significant design factors (Ui) and design factor functions (Vi) 

were independent variables. 

- ---- 
I Predicted FPC7 ( psi ) 

a 

Regression Equation: FPC7 (psi) = 3580-649.3CATD-193.2CAMD+46.2AEQW201.5CAPD+515.7CEPDC203.4FAPD-1864.lWCRD 

-235.1CATD*CEPD-56.5FAMD*AEQD-38.OFAMD*CAPD-7.9AEQD*CAPD-18.4CAPD*WAPD 

Figure 23. Plot of observed versus predicted average 7-day PCC compressive strength (Y2=FPC7AVE), 

where only significant design factors (Ui) and design factor functions (Vi) were 

independent variables. 
550 - 

500 -- 

a 

450 -- I 

Observed 400 -- 

FT7 

( psi 350 -- 

300 -- 

-- 

- ---- 

250 -- 

zoo ! I I I I t . 

I . I 

250 300 350 400 450 500 550 

Predicted FT7 ( psi ) 

Regression Equation: FT~ (psi) = 381.1-24.9CATD-7.4AEQD-520.7WCRD-78.5CATD*FAMD-16.4CATD*CEPD-7.2FAMD 

*AEQD-0.7FAMD*CAPD*CEPD 

Figure 24. Plot of observed versus predicted average 7-day PCC tensile strength (Y3=FT7AVE), 

where only significant design factors (Ui) and design factor functions (Vi) 

were independent variables. 

t R Square = 0.89 

Standard Error = 205,500 psi 

AD Line of ~~ua1i.t~ ./m 

# 

Predicted EC28 ( mpsi ) 

Regression Equation: EC28 (mpsi) = 4.340-0.207CA~D+O.025AEQDH).169CAPD + 0.280CEPD+0.175FAPD+O.Z79CATD 

*CAMM-0*059CATD*CEPD*WAPD 

Figure 26. Plot of observed versus predicted average PCC elastic modulus (Y5=EC28AVE), 

where only significant design factors (Ui) and design factor functions (Vi) 

were independent variables. 
Table 24. Multiple regressions fo$- hardened properties (Y) on 

significant design factors (U,V) and mix properties (X) . 

CATD=(CAT-0.5) -603.9(00) -662.5(00 -702.7(00) -71 1.8(001 

CAMD=(CAM-1 .I 25) -283.1 (02) -350.1 (00; 

FAM D=(FAM-2.47) 

AEQD=(AE Q-3.25) (53) (59) 

(83) (48; 

CAP D=(CAP-38.59) (95) 17.66(05; 

CEPD=(CEP-9.29) 171.9(03) 226.4(00: 

WAPD=(WAP-14.64) (78) (54: 

FAPD=(FAP-31.55) -25.4(06) 

WCRD=(WCR-0.51) (90: -4761.2(00) -4029.7(0WA 

CATD * FAMD 

CATD CAPD 

CATD CEPD 

CAMD AEQD 

CAMD CEPD 

FAMD * AEQD 

CEPD * WCRD 

mi 

I (8211 Q.Z(OO)~ 1 (901 1 (4211 1 (52)1 12.0(00)( 1 (4311 (4 1 -28,5(00)) -18.5(00)1 1 -21.0(01)1 -16.1 (011 1-i 

Constant Term 1-1 536 O(00) 543 4(00 3543.3(001 3607(00)1 ( 382.8(00) ( 382.6(00)1 14428.5(00j 4425.9(00) ( 4.34(00)1 4.36(0 

Total SS 

E 

Res. SS/df 

.- 0 SEE 

Rep.Std Dev. / df 

EMS Ratio (SL)? , 

31.8 psi /8 

1 * - N = 60 omits Mix Numbers 3437.49, and 64. t EMS Ratio = Y Res (NS) - Ratio not significant at the 10% level. SEE )2 ++ZRes=- ( RepSD SEE 
Predicted FR7 ( psi ) i 

Regression equation: FR7 (psi) = 543.4-45.4CATD-Sl.OCAMDtl8.4WAPD-832.2WCRD+Ol.lUNWTD-24.OCAMD*CEPD 

-10.7FAMD*AEQD-5.3FAMD*CAPD-1.OAEQD&CAPDt30.1AEQD*W'WCRD+l.lCAPD 

*WAPD*AIRD 

Figure 27. Plot of observed versus predicted average 7-day PCC flexural strength (YL=FR7AVE), 

where all design factors (Ui and Vi) and mix properties (Xi) were independent variables. 
Figure 28. Plot of observed versus predicted average 7-day PCC compressive strength (Y2=FPC7AVE), 

where all design factors (Ui and Vi) and mix properties (Xi) were independent variables. 
7 

500 

I 

450 -- 

m= 

Observed 400 -- 

FT7 

( psi 1 350 -- I 

I 

300 -- I I 

- - - -- - pp --- -- -- - - - -- - - -- 

250 -- 

.dm - . ,' 

200 1 

I I I I I I I 

I 1 1 

200 250 300 350 400 450 500 550 

Predicted FT7 ( psi ) 

Regression equation: FT7 (psi) = 382.6-41.6CATD-456.2INCRDt6.9UNWTD-60.1CATD*FAMD-18.7CATD*CEPD 

-1.8CATD*CAPD*WAPD*AIRD 

Figure 29. Plot of observed versus predicted average 7-day PCC tensile strength (Y~=FT~AvE), 

where all design factors (Ui and Vi) and mix properties (Xi) were independent variables. 


Simple Regressions for Selected Pairs of FCC properties 

The final set of regression equations that were derived are for the 

prediction of one PCC property (Yi) from values of another PCC property 

(Yj). Although each two-way (YiYj) graph (previously discussed) was 

accompanied by a simple regression equation, all were based on the complete 

data set of N = 64 mixes. Regression results in this section are given in 

table 25 and are based on the reduced data set (N = 60). 

The first three regressions in table 25 are for the prediction of Y1 = 

fr7 from Y2 = fpc7. Three different models were used, first with Y1 versus 

Y2, then with Yl versus SQRT Y2, and finally with log Y1 versus log Y2. The 

square root transformation was used to provide comparisons with secondary 

relationships A and E in appendix C, both of which express modulus of 

rupture as a constant (7.5 or 9.5) times the square root of compressive 

strength. Table 25 shows that the study data gave the constant 9.2 as a 

multiplier of SQRT fpc7. Table 25 values for R-square, SEE, and extreme 

residuals show that the log transformations for Y1 and Y2 give the best fit 

to the study data, and that the untransformed Y1 and Y2 produce a somewhat 

better fit than the square root transformation. 

The fourth and fifth regressions for Y1 show how well fr7 can be 

predicted from Y3 = ft7 and from Y4 = fpc28. The results show that fpc28 is 

a much better predictor of fr7 than is ft7. It can also be seen that fpc7 

is a somewhat better predictor of fr7 than is fpc28. 

The final Y1 equation in table 25 is for the prediction of Yl* = fr28 

from Y1 = fr7. Since the laboratory study did not include 28-day tests of 

flexural strength, the Yl* versus Y1 relationship has been assumed to be the 

same as for converting fpc7 to fpc28. 

The next equation is for predicting Y4 = fpc28 from Y2 = fpc7. This 

relationship is very close (R square = 0.942), and shows that 28-day 

compressive strength at 28 days is about 122 percent of the corresponding 7- 

day compressive strength. 

The next pair of equations are for predicting tensile strength from 

either flexural strength (Y3 versus Y1) or compressive strength (Y3 versus 

Y2). It is apparent that compressive strength is considerably better than 

flexural strength for predicting tensile strength. 

The final set of regressions are for the prediction of Y5 = Ec28 from 

Y1 = fr7, from Y2 = fpc7, from Y3 = ft7, from Y4 = fpc28, and finally from 

the combination of fpc28 and X2 = UNWT. In the last case, log 

transformations were used for all three variables. The results show that 

fr7 is the best single predictor of Ec28, but that much better predictions 

for Ec28 are given by the combination of fpc28 and UNWT. 

&Sensitivity Analvses for Selected Dependent Variables 

Forty-six regression equations have been derived from the laboratory 

data and appear in tables 21 through 23. Three of these equations have been 

selected from table 22 for analysis of the sensitivity of mix properties (X) 

to the design factors (U, V), and three equations have been selected from 
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table 24 for analysis of the sensitivity of PCC properties (Y) to design 

factors (U, V) and mix properties (X). The six selected equations are 

reproduced in the right-hand columns of table 26. All six equations are 

based on N = 60 mixes. 

The three selected mix properties are X1 = SLMP, X2 = UNWT, and X4 = 

AIR. Slump is an important indicator of concrete workability and air 

content is a valid predictor of PCC durability. Both are included as PCC 

specifications variables by 9 of the 12 States represented in table 4. 

Regression equations in table 24 show that unit weight is an important 

predictor of PCC strength; it may be the simplest and best strength 

indicator that can be evaluated from the plastic PCC mix, but only 3 of 12 

States include unit weight in their current specifications. 

The three selected PCC properties in table 26 are Y1 = fr7, Y2 = fpc7, 

and Y5 = Ec28. Flexural strength (fr) is a primary predictor of PCC 

performance, not only in the AASHTO rigid pavement design equation, but also 

in all mechanistic models that contain the PCC stress/strength ratio. The 

PCC modulus (Ec) is also a primary element of stress and performance 

predictions. Compressive strength (fpc) is not only highly correlated with 

flexural strength and PCC modulus, but is relatively easy to evaluate from 

samples taken during construction. Table 4 shows that compressive strength 

is a specifications variable in 10 of 12 States, and that flexural strength 

specifications are used in the other 2 States. 

For the foregoing reasons, it is believed that the six dependent 

variables that have been selected for sensitivity analysis in table 26 are 

of foremost importance in the development of M&C acceptance plans and 

performance-related specifications for rigid pavements. 

All independent variables for each regression equation in table 26 are 

expressed as deviations from their respective means, as shown in the second 

column of the table. Thus, the mean value for each deviation variable is 

zero. Minimum and maximum values for the deviation variables are shown in 

the third and fourth columns. Since predictions for any dependent variable 

are calculated by summing the products of regression coefficients times the 

independent variable deviations, the max/min values provide general 

indications of the amount of change that the independent variables (and 

their cross-products) can produce in the dependent variable predictions. 

More specific sensitivity analyses are shown in table 27 for the SLMP, 

UNWT, and AIR prediction equations, and in table 28 for the fr7, fpc7, and 

Ec28 prediction equations. The remainder of this section describes the 

methods used to produce the tables and the sensitivity results that are 

contained in the tables. 

~aih of the seven experimental design factors (U1 = CAT through U7 = 

WAP) was run at two levels in the laboratory study. For example, levels for 

U1 = CAT were gravel and stone, levels for U2 = CAM were 0.75 in (19.05 mrn) 

and 1.50 in (38.1 mm), levels for U6 = CEP were 7.7 percent and 10.9 

percent, and levels for U7 = WAP were 13.6 percent and 15.6 percent., The 

four combinations of CEP and WAP levels produce four different levels for U2 

= WCR, namely, 0.40, 0.46, 0.55, and 0.63. Based on the ANOVA means for PCC 

strength (fr7, fpc7, and fpc28 in table 20), one level of each U factor was 

123 
Table 26. Inputs for sensitivity analysis of selepted dependent variables. 

REGRESSION VARIABLES TABLE N EQUATIONS TABLE P EQUATIONS 

CODE DEFINITIONS MINIMUM MAXIMUM 

I VALUE VALUE SLMP 

I 

CATD = (CAT - 0.5) 

CAMD = (CAM - 1 .I 251 I 2 I : I 

U3 FAMD = ~FAM - 2.47) ' -.37 +.37 

U4 AEQD = (AEQ - 3.25) -3.25 +3.25 

US CAPD = (CAP - 38.6) -3.8 +3.8 

U6 CEPD = (CEP - 9.3) ' -1.6 I, +I .6 

U7 WAPD = (WAP - 14.6) -1 .O +1 .O 

V2 WCRD = (WCR - 0.51) -.l1 +.I2 

XI SLMPD = (SLM P - 2.03) -2.0 +6.7 

X2 UNWTD = (UNWT - 140) -1 2.0 +8.8 

X4 AlRD = (AIR - 5.6) -3.9 +6.6 

U1U3 ICATD*FAMD I UlU5 CATD-CAPD 11 . I . I 

U2 U6 CAMD*CEPD -0.6 +0.6 

U3 U4 FAMDdEQD -1.2 +1.2 

U3 U5 FAMDGAPD -1.4 +1.4 

U1 U3 U4 CATD*FAMD*AEQD -.60 +.60 

U4 U5 U7 AEQDGAPD-WAPD -1 2.4 +12.4 

I MEAN VALUE = EQUATION CONSTANT 

R - Square 

Standard Error of Estimate 1.5 in. 1.5 pd 1 .O% 34 psi 172 psi .I8 mpsi I 

Error Mean Square Ratio 

Significance Level of EMS Ratio 
Table 27. Sensitivity of mix properties to changes in design factors. 

_I___ I_ 

EXPERIMENT DESIGN FACTOR X1. SUP (in) X2. UNWT (pcf) X4. AIR (%) 

LEVELS AND CHANGES SEE - 1.5 in SEE - 1.5 pcf SEE = 1.0 % 

Value Change Value Change Value Change -- A ---- - 

ALL U,V AT LOW-STR LEVELS 6.6 in 130 pcf 10.5% .......................... -------------- -------------- -------------- 

U1. CAT Gravel to Stone 5.8 -.8 129 -1 10.5 0 

U2. CAM 1.50" to 0.75" 6.6 0 130 0 10.0 -.5 

U3. FAM 2.10 to 2.84 7.3 +.7 132 +2* 10.5 0 

U4. AEQ 6.5 az to 0 oz 0.6 -6.0** 140 +lo*** 4.1 -6.4*** 

U5. CAP 34.8% to 42.4% 5.8 -.8 133 +3** 9.0 -1.5* 

U6. CEP 7.7% to 10.9% 4.3 -2.3* 137 +7*** 7.3 -3.2*** 

(& WCR .63 to .46) 

U7. WAP 15.6% to 13.6% 2.6 -4.0** 133 +3** 8.9 -1.6* 

(& WCR .63 to .55) 

V2. WCR .63 to .40 0.5 -6.1** 140 +lo*** 5.9 -4.6*** 

(& CEP & WAP changes) IDC-p-PPeD- IIDIl 

ALL U,V AT MID-STR LEVELS 2.1 in -4.5 140 pcf +I0 5.4% -5.1% .......................... -------------* ---..-*---_---- ----*--------- 

I U1. CAT mid to Gravel 2.1 0 141 +1 5.4 0 I CAT mid to Stone 2.1 0 139 -1 5.4 0 

I U2. CAM 1.125" to 1.50" 2.1 0 140 0 5.4 0 

CAM 1.125" to 0.75" 2.1 0 140 0 5.4 0 

U3. FAM 2.47 to 2.10 2.1 0 139 -1 5.4 0 

FAM 2.47 to 2.84 2.1 0 141 +1 5.4 0 

U4. AEQ 3.25 oz to 6.5 oz 3.5 +1.4 137 -3** 7.5 2.1** 

AEQ 3.25 oz to 0 oz 0.7 -1.4 143 +3** 3.3 -2.1** I U5. CAP 38.6% to 34.8% 1.7 -.4 139 -1 5.9 +.5 

CAP 38.6% to 42.4% 2.4 +.3 141 +1 4.9 0.5 

U6. CEP 9.3% to 7.7% 2.9 +.8 138 -2* 6.3 +.9 

(& WCR .51 to .60) 

CEP 9.3% to 10.9% 1.3 -.8 142 +2* 4.5 -.9 

(& WCR .51 to .42) 

U7. WAP 14.6% to 15.6% 3.0 +.9 139 -1 5.6 +,2 

(& WCR .51 to .53) 

WAP 14.6% to 13.6% 0.9 -1.2 141 +I 4.9 -.S 

(& WCR .51 to .46) 

V2. WCR .51 to .63 3.9 +1.8* 138 -2* 6.6 +1.2* 

(& CEP & WAP changes) 

WCR .51 to .40 0.3 -1.8* 142 +2* 4.3 -1.1* 

(& CEP & WAP changes) =E=P==--=+~=I====IE~E=~= PE==----E a- PII-L.III.-PI=- 

ALLU,VATHI-STRLEVELS 0.2in -1.9 146pcf +6 3.1% -2.3% ......................... -------------- -------------- -------------- U1. CAT ~tone to Gravel 0 -.2 148 +2 3.0 -.1 

U2. CAM .75" to 1.5" 0.2 0 146 0 2.6 -.5 

U3. FAM 2.84 to 2.10 0.9 +.7 144 -2* 3.0 -.l 

U4. AEQ 0 oz to 6.5 oz 0.5 +.3 143 -3** 4.9 +1.8* 

U5. CAP 42.4% to 34.8% 0 - .2 138 -8*** 3.6 +.5 

U6. CEP 10.9% to 7.7% 0.9 +.7 143 -3** 3.2 +.l 

(& WCR .40 to .55) 

U7. WAP 13.6% to 15.6% 2.0 +1.8* 145 -1 2.9 -.2 

(& WCR .40 to .46) 

V2. WCR .40 to .63 2.8 +2.6* 143 -3** 3.1 0 

(& CEP & WAP changes) PeE--i.sEp.cppe=P==-11==1-1==== - -- -=a= ------- - --___ -_C 

* Change exceeds 1 SEE, ** Change excee SEE, *** Change exceeds 3 SEE 
Table 28. Sensitivity of PCC properties to changes in design factors. 

IFP, I --IICIIPE=-1= --PIIII-lliLP 

EXPERIMENT DESIGN FACTOR Y1. fr7 ~2.~ fpc7 Y5. Ec28 

LEVELS AND CHANGES SEE - 34 psi SEE 4 172 psi SEE - .18 mpsi 

Value Change Value ' Change Value Change I 

---n__- .-o--r--------ryr -- 

ALL U,V AT LOW-STR LEVELS 354 1790 2.89 .......................... -------------- -------------- -------------- 

U1. CAT Gravel to Stone 346 -8 1504 -286* 3.17 +.28* 

U2. CAM 1.50" to 0.75" 363 +9 1923 +I33 2.85 -.04 , 

U3. FAN 2.10 to 2.84 380 +26 2167 +377** 3.10 +.21* 

U4.AEQ6.50ztoO oz 395 +41* 2267 +477** 3.97 +LOB*** 

U5. CAP 34.8% to 42.4% 364 +10 1818 +28 3.25 +.36** 

U6.CEP7.7%to10.9% 522 +168*** 3303 +1513***3.96 +1.07*** 

(& WCR .63 to ,46) 

U7. WAP 15.6% to 13.6% 405 +51* 2808 +1018***3.58 +.69*** 

(& WCR .63 to .55) 

V2. WCR .63 to .40 560 +206*** 3957 +2166*** 4.47 *1,58*** 

(& CEP & WAP changes) - =-=-== ---__I_= a 

ALLU,VATMID-STRLEVELS 543 +I89 3607 +I817 4.36 +1.47 .......................... -------------- -------------- -------------- 

U1. CAT mid to Gravel 521 -23 3276 -331* 4.34 -.02 

CAT mid to Stone 566 +23 3938 +331* 4.37 +.01 

U2. CAM 1.125" to 1.50" 524 -19 3528 -79 4.36 0 

CAM 1.125" to 0.75" 562 +19 3686 +79 4.36 0 

U3. FAM 2.47 to 2.10 534 0 3607 0 4.21 -.15 

FAM 2.47 to 2.84 543 0 3607 0 4.47 +.ll 

U4.AEQ3.250zto6.50~ 543 0 3607 0 4.05 -.31* 

AEQ 3.25 oz to 0 oz 543 0 3607 0 4.62 +.26* 

U5. CAP 38.6% to 34.8% 543 0 3607 0 4.28 -.09 

CAP 38.6% to 42.4% 543 0 3607 0 4.40 +.04 

U6. CEP 9.3% to 7.7% 448 -95** 2748 -859*** 4.09 -.27* 

(& WCR .51 to .6O) 

CEP 9.3% to 10.9% 638 +95** 4444 +837*** 4.67 +.31* 

(& WCR .51 to ,42) 

U7. WAP 14.6% to 15.6% 535 -8 3397 -21O* 4.15 - .21* 

(& WCR .51 to .53) 

WAP 14.6% to 13.6% 578 +35* 3913 +306* 4.55 +.19* 

(& WCR .51 to .46) 

V2. WCR .51 to "63 442 -101** 2630 -977*** 3.93 -.43** 

(& CEP & WAP changes) 

WCR .51 to .40 637 +94** 4522 +915*** 4.73 +.37** 

(& CEP & WAP changes) =s=,--=~=sE====iire===re:ti13iiE= =-=====dm-= -=. 

ALL U,V AT HI-STR LEVELS 772 +229 5830 +2223 5.28 +.92 ......................... -------------- -------------- ---.--..-------- 

U1. CAT Stone to Gravel 774 +2 4921 -909*** 5.28 0 

U2. CAM .75" to 1.5" 709 -63* 5679 -151 5.24 -.04 

U3. FAM 2.84 to 2.10 754 -18 5600 -230* 5.00 - .28* , 

U4. AEQ 0 oz to 6.5 oz 675 -97** 5129 -701*** 5.09 -.19* 

U5. CAP 42.4% to 34.8% 642 -130*** 4753 -1257*** 4.30 -.98*** 

U6. CEP 10.9% to 7.7% 566 -206*** 3949 -1881*** 4.63 -.65*** 

(& WCR .40 to .55) 

U7, WAP 13.6% to 15.6% 704 -68** 5224 -606*** 4.97 - .31* 

' (& WCR .40 to .46) 

V2. VCR .40 to .63 492 -280*** 3201 -2629*** 4.46 -.82*** 

(& CEP & WAP changes -=-------e31======= 

* Change exceeds 1 SEE, ** Change exceeds 

=-====53--SI 

2 

-=PiES.- 

SEE, *** Change 

- 

exceeds 3 SEE 
designated as its "low-strength" level and one as its "high-strength" level, 

depending upon which level generally produced lower or higher PCC strength. 

Because Ec28 is highly correlated with strength, the low and high strength 

levels for each U also produce low and high Ec28 levels. The water/cement 

ratio, V2 - VCR, is completely determined by CEP and WAP, and has its 

low-strength-level (0.63) when U6 = CEP is at its low-strength level of 7.7 

percent, and U7 = WAP is at its low-strength level of 15.6 percent. The 

high-strength level for WCR (0.40) occurs when CEP and WAP are at their 

high-strength levels of 10.9 percent and 13.6 percent, respectively. It 

should be noted that the high-strength level for any U is not necessarily 

its higher numerical value. For example, the low-strength level for AEQ is 

6.5 az (192 mL) and the high-strength level is 0 oz (0 mL). 

As shown in the top lines of tables 27 and 28, substitution of the low 

strength levels for all U and V in the regression equations produces 6.6 in 

(167.64 mrn) for slump, 130 pcf (2080 kg/m3) for unit weight, 10.5 percent 

for air, 354 psi (24.9 kg/cm2) for fr7, 1790 psi (126 kg/cm2) for fpc7, and 

2.89 mpsi (203,000 kg/cm2) for Ec28. 

As shown near the bottom of tables 27 and 28, substitutions of the 

high-strength levels for all U, V produces 0.2 in (5.08 rnm) for slump, 146 

pcf (2336 kg/m3) for unit weight, 3.1 percent for air, 772 psi (54.3 kg/cm2) 

for fr7, 5830 psi (410 kg/cm2) for fpc7, and 5.28 mpsi (371,000 kg/m3) for 

Ec28. Comparisons of the foregoing calculations with the observed data in 

data base A (appendix F) shows close agreement between the calculated and 

observed highs and lows for the dependent variables. 

Tables 27 and 28 also show calculated values for the dependent 

variables when all U, V are at mid-strength levels. It is noted, however, 

that U1 = CAT has only the qualitative levels of gravel (low-strength) and 

stone (high-strength), whose coded values are 1 for gravel and 0 for stone. 

Thus, the coded mid-value for CAT is 0.5, but has no physical 

interpretation. 

The purposes of the sensitivity analyses are to show how each dependent 

variable changes as: 

1. Each U, V changes from its low-strength level to its high-strength 

level when all remaining U, V are at low-strength levels. 

2. Each U, V changes from its mid-strength level to its low-strength 

level, and from its mid-strength level to its high-strength level when 

all remaining U, V are at mid-strength levels. 

3. Each U, V changes from its high-strength level to its low-strength 

level when all remaining U, V are at high-strength levels. 

In general terms, it can been said that all-low levels produce "weak" 

PCC, all-mid levels produce "medium" strength PCC, and all-high levels 

produce "strong" PCC. Thus, purpose (1) is to see by how much weak PCC can 

be improved by a gross change in only one factor. At the other extreme, 

purpose (3) is to see by how much strong PCC can be denigrated by a gross 

change in only one factor. Purpose (2) is to see by how much mediumstrength PCC will be changed through partial changes in each factor. 
All of the foregoing changes for U, V are $horn at the left in both 

tables 27 and 28. It must be noted that any chqnge in CEP when WAP is fixed 

will produce a change in WCR, and that any change in WAP for fixed CEP will 

also produce a change in WCR. It is also true ehat a change in WCR must 

generally be accompanied by changes in both CEP and WCR. The left-hand 

columns of tables 27 and 28 show how WCR changeA when CEP or WAP is changed, 

and how CEP and WAP must change when WCR is chaqged. 

Standard errors of estimate (SEE) for the regression equations were 

given at the bottom of table 26 and are repeated in the top rows of tables 

27 and 28. For each dependent variable, the corresponding column in table 

27 or 28 shows the amount of dependent variable change that is associated 

with the row-by-row changes in U, V. Dependentvariable changes are marked 

with *, **, or *** if the dependent variable changes by 1, 2, or 3 times its 

SEE, respectively. Unmarked changes are less than one SEE and have no 

statistical significance. 

At low-strength levels, table 27 shows thaq the largest changes in X1 = 

SLMP, X2 = UNWT, and X4 = AIR are produced by changing U4 = AEQ, U6 = CEP, 

and V2 = WCR from low to high levels. Much lesier changes are produced when 

all U, V are at high levels. No great changes $n XI, X2, or X4 are produced 

by U, V changes from mid levels to low levels or high levels. I 

None of XI, X2, or X4 is changed appreciabiy by CAT, CAM, or FAM 

changes at any level. An increase or decrease qn coarse aggregate quantity 

(CAP) has a sizeable effect only upon unit weight, as,rnight be expected. 

Major changes occur in Xl, X2, and X4 as CEP, W4P, and WCR change from low 

to high levels when all other U, V are at low levels. Corresponding changes 

do not occur, however, when all U, V are at midlevels or high levels. I 

Table 28 shows that the greatest effect of changing CAT from stone to 

gravel occurs in fpc7 when all remaining U, V are at high levels. Changes 

in coarse aggregate maximum size (CAM) have almolst no effect on any of Yl, 

Y2, or Y5. The only pronounced effect of an indrease in FAM is on fpc7 when 

all remaining U,V are at low levels. 

Reduction of AEQ from 6.5 oz (192.2 mL) to 0 oz (0 mL) produces 

sizeable increases in fpc7 and Ec28 when other q, V are at lowlevels. The 

reverse is true when AEQ is increased from 0 oz (0 mL) to 6.5 oz (192.2 mL) 

at high levels for the remaining U, V. 

The effect of CAP reduction is quite large for all of Y1, Y2, and Y5 

when other U, V are at high levels, but CAP changes - have small effects when 

the other factors are at mid or low levels. 

By far, the greatest sensitivities are those of Yl, Y2, and Y5 to 

changes in CEP, WAP, and WCR. These results are consistent with past 

research and underscore the fact that PCC strengths (and modulus) are 

largely determined by the PCC cement quantity in conjuntion with water 

quantities that lead to relatively low water/cewent ratios. 

A graphical representation of table 28 is given in figure 32. In 

general, it can be seen that the FCC properties are least affected by 

aggregate type and gradation (CAT, CAM, and FAM). Of greater importance are 
-I,--=-=-- -I=---- ri 

DEPENDENT VARIABLE (Y) CHANGES IN Y IFOR INDIVIDUAL U/V CHANGES 

& DESIGN FACTORS (U/V) U/V ufl up u/V 

(U/V Levels in Tab. 28) L to H MtoL MtoH H to L 

Y1 = fr7 psi 

All UJV at L, M, or H 

U1. Y1 change with CAT 

U2. Y1 change with CAM 

U3. Y1 change with FAM 

U4. Y1 change with AEQ 

U5. Y1 change with CAP 

U6. Y1 change with CEP I1 If I1 I1 

U7. Yl change with WAP 

V2. Yl change with WCR 11 It 11 It 

=---*-=----=3P -==-------------- 

Y2 = fpc7 psi 2000 3000 4000 5000 6000 

All U/V at L, M, or H 1790 3607 5830 ...................... 1--L-1---------1-----~---l---------l-------H-l--- 

<<<<<<<<<I 

I 

U1. Y2 change with CAT <<<I <<< I >>> 

U2. Y2 change with CAM I> <I> << I 

U3. Y2 change with FAM I >>>> I << I 

U4. Y2 change with AEQ I >>>>> 1 <<<<<<< I 

U5. Y2 change with CAP I I <<<<<<<<<<<<<I 

U6. Y2 change with CEP I>>>>>>>>>>>>>> .................... It I1 tl It <<<<<<<<<I>>>>>>>> 

U7. Y2 change with WAP I >>>> << I >>> <<<<<< I 

V2. Y2 change with WCR ....................... 11 I1 11 H ........................... I* It It 11 .................... 7-aas 

m-aaraY5 - Ec28 mpsi 3.0 3.5 4.0 4.5 5.0 

All U/V at L, M, or H 2.89 4.36 5.28 

---------------------- ~L-~---------~------~--I------M--I---------I----- H 

U1. Y5 change with CAT I>>>>>> I 

<<< I >> 

I 

U2. Y5 change with CAM I> <<<<<< I 

U3. Y5 change with FAM I>>>> <<< I >> <<<<<< I 

U4. Y5 change with AEQ ..................... <<<<<<I>>>>> <<<< I 

U5. Y5 change with CAP I>>>>>>> <<I> <<<<<<<<<<<<<I 

U6. Y5 change with CEP ...................... <<<<<<<<<<<<<I 11 It I1 I1 <<<<<I>>>> 

U7. Y5 change with WAP I>>>>>>>>>>>>>> <<<< 1 >>>> <<<<<< I 

V2. Y5 change with WCR ................................ It I1 It tt <<<<<<<<<<<<<<<<I 11 I1 11 tf <<<<<<<<<<I>>>>>> =-ss=nc=-=r=et ,_-- ---- -------------- ,,----------=---

--- 

< is a decrease of 10 psi in fr7, 100 psi in fpc7, and 0.05 in Ec28 

> is an increase of 10 psi in fr7, 100 psi in fpc7, and 0.05 in Ec28 

1 psi - 0.07036 kg/cmz 

Figure 32. Sensitivity of PCC properties to design factor changes. 
the amounts of air entrainment agent (AEQ) and coarse aggregate (CAP) in the 

PCC mix. Finally, the greatest changes in Y1, Y2, and Y5 are produced by 

changes in cement quantity (CEP), water quantity (WAP), and the concomitant 

changes in water/cement ratio (VCR). 

SUMMARY RESULTS OF THE LABORATORY STUDY 

As evidenced by the experimental design (table 10) and the resulting 

data bases (appendix F), the laboratory study has produced a wide range of 

PCC mix factor combinations and measured propertkes of both the plastic 

mixes and the hardened PCC specimens. The study inputs and outputs provided 

an adequate basis for the many analyses that were performed. 

Much has been learned about the intercorrelgtions (table 15) among the 

experimental variables and about their batch-to-batch and specimen-tospecimen variability (tables 16 and 17) under controlled laboratory 

conditions. 

Extensive analyses of variance (tables 18, a9 and 20) have shown that 

every experimental design factor (U, V) has a statistically significant 

effect upon one or more of the measured PCC properties (X, Y), and that many 

of the factors have interactive effects that may involve two-, three-, or 

even four-factors. 

More than 20 different types of regression equations were derived 

(tables 21, 22, 23, 24, 25) and represent secondkry relationships among PCC 

properties and their M&C determinants. ~quations derived for prediction of 

flexural, compressive, and tensile strength, and for prediction of PCC 

elastic modulus have R-squares greater than 0.90 and standard errors 

equivalent to the variation between replicate mikes. 

The regression equations compare favorably with counterpart 

relationships that have been derived in previous studies and include new 

relationships that have not heretofore been published. The equations should 

be quite useful for the development of M&C acceptance plans, specifications 

for rigid pavement construction, and perhaps eve$ for better PCC mix design 

procedures. I 

~ 

More than 10 of the derived equations are fbr the pairwise association 

between two different PCC properties (table 25). These relationships 

provide a rational basis for choosing between al$ernative field tests on the 

basis of time and cost. An example might be theiuse of 7-day compressive 

strength as a surrogate for the PCC modulus at 28 days. 

Rather complete sensitivity analyses were dqveloped from the equations 

that predict slump, unit weight, air content, flexural strength, compressive 

strength, and PCC modulus. The analyses showed that strength and modulus 

are relatively insensitive to changes in aggregaqe type and gradation, and 

moderately sensitive to changes in quantities ofair entrainment and coarse 

aggregates. The analyses verified previous knowledge that strength and 

modulus are highly sensitive to changes in cement content, water content, 

and to the concomitant changes in water/cement ratio. I 
It is concluded that the laboratory study was quite effective in 

producing data and analytical results that are needed for the development of 

a wide range of performance-related specifications for PCC materials ~nd 

construction. 
I 

I 

i 

I CHAPTER 6 I 

PROCEDURES AND ALGORITHMS FOR DEeIVATION 

I OF PERFORMANCE-RELATED SPECIFICATIONS 

1 This chapter describes procedures and algorithms that can be used to 

1 derive PRS for the construction of PCC pavements. Thus, the contents of 

this chapter represent a detailed expansion of box H in figure 1 of chapter 

2. For convenience of presentation, the procedures are grouped in'seven 

modules as indicated in the center column of figu,re 33. 

Procedures for each module, including inputs and outputs, will be 

discussed in the seven sections that follow. There are generally a number 

of alternative procedures that might be used within each module. For the 

most part, the alternatives relate either to (1) a methodology that has been 

developed in NCHRP Project 10-26A for asphaltic concrete pavements, or (2) a 

methodology that has been developed by the New Jersey DOT for rigid pavement 

construction, or (3) methods that have been conceptualized as part of this 

study (see references 88.1, 80.1, 82.2, 82.3, and 82.4). 

Details shown in figure 33 for the first five modules represent a 

mixture of the three methodologies. Details shown for modules 6 and 7 

I represent only the NCHRP 10-26A methods based on economic life and that will 

I be used for the demonstration procedures described in chapter 7. 

PAVEMENT DESIGN FOR THE INITIAL PERFORMANCE PERIOD 

The derivation of PRS begins with a specific pavement design that is 

assumed to have been developed by the State highway agency (SHA) for the 

initial performance period. It will also be assumed that the revised AASHTO " 

design guide for rigid pavements is used to determine design levels for all 

variables that have direct bearing on the pavement structure and its 

expected life.86-4 In particular, it is assumed that the pavement design has 

been derived through use of the AASHTO design equation for rigid pavements, 

as represented by relationship N in appendix B. 

As shown at the left in figure 33, design inputs include design 

criteria, environmental assumptions, and roadbed assumptions. Design 

criteria include design years for the initial performance period, 

rehabilitation criteria that indicate the pavement's condition at the end of ; 

the initial performance period, expected ESALs during the.-performance 

period, and reliability criteria that govern the probability that the 

constructed pavement will indeed survive the design period years. 

For the AASHTO design equation, the rehabilitation criterion is simply 

a terminal level for PSI, e.g., PSI = 2.5. The design equation provides 

many alternative pavement structures that will meet this criterion along 

with other criteria and assumptions in boxes A, B, and C. From these 

4 alternatives, the SHA presumably selects an optimum structure relative to 

L 

11 the economics of local materials and construction options. 1 

Outputs from the design procedures are design levels for both PCC and . 

non-PCC variables, as shown at the right in figure 33. The non-PCC 

variables in box D include design period ESALs, base layer variables, and 
t 

Inputs 

A. D&IGNCRITERIA- - - - t * Design Years 

* Rehab Criteria (pt ) 

Design Lane ESAL (Year 1) 

['. - Annual 

Reliability Criteria 

ESAL Growth Rate 

(R%, So ) 

(%) 1 b 

*_ 

PIe.apitation Temperafure - 

Freeze - Thaw 

C. REDBBASSSUMPEONS,, - - 

Soil Type (Fine, Coarse) - 

* Subgr* Modulus (MR ) C 

Outputs lIzIzzl Procedures and u Algorithms 

1. PAVEMENT DESIGN FOR INITIAL D. DESIGN LEVELS FOR NON-PCC 

PERFORMANCE PERIOD (By SHA) ---I--- - VARIAEES - - - - 

F Design Period ESAL (Ann. & Cum.) 

* Using WSHTO Pavement Design * Base Layer Specifications 

Guide for Rigid Pavements - - Type (GranJStab) - Thickness (D2) 

- Modulus (E BS ) - Drainage (Cg) 

Surfwing Layer Specifications 

Design Equation NB -Type (JPCPIJRCP) C -Joints (Spacing, Dowels, J Factor) 

- Edge Support (ACtTied PCC) 

Optimum Structure for Local 

B Materials and Conditions 

VARI&ES- - - - - 

* Profile (Po) Thickness (D) 

2. DEVELOPMENT OF ACCEPTANCE PLANS 

Aggregates * ~emeni " FOR SELECT M&C VARIABLES -- PLANS FOR SELECT M&C VARIABLES 

Additives -C----- 

NJDOT Methodology * Primary Performance Determinants 

G. AEEPzrJCE-CRITERIA&HA)- - * Lot Sizes * Sampling Plans - Profile - Thickness - Strength 

* Variability Assumptions Test Variables and Procedures Secondary Variables: Unit Weight - Consumer 81 Producer Risks ; , * Aceaptan- Levels and 

I. RELATIONSHIPS AMONG PCC 1 3. CONSTRUCTION. CONTROL. 

VEIABES (Ec 5.52 App-6) - - 

fr, fpc, Ec vs Mix Variables 

* Base 

Surfacing (NonPCC Variables) 

CwiDES(ONLEM- 4 . PCC Va,.iabla I 

C. ROADBED ASSUMPTIONS 

D. DESIGN LEVELS=- 

MAINTENANCE b USER COST 

LSSUMPTI0L - I - - 

Option a: Wintenance Costs 

- 

Optiqn 

- ($lsy) 

b: 

based 

Maintenance 

y-Diitress -- 

Costs 

Levels C 

(Slsy) based on PSI Levels 

Options a & b: User Operating Costs 

J. AS CONSTRUCTED (CON) LEVELS FOR 

PCC PERFORMANCE DETERMINANTS -_I--_.--- 

= Profile (po est. from samples) 

Thickness (D est. from samples) 

Strength 

f'c estimated from samples 

fr estimated from f'c 

Modulus (Ec est. from f'c) 

4. PREDICTION OF DESIGN PERIOD K. DISTRESS & PSI HISTORIES FOR 

c ------ DISTRESS AND PSI (DES L CON) DESIGN PVT. & ASCONSTRUCTED PVT. -----_.- 

Option a: Prediction of Pumping, Cracking Option a: Cracking, Faulting, Joint Faulting, Joint Deterioration, PSI from Deterioration, and PSI Histories COPES Equations (app B) -i----- - - - - - - - 

Option b: Prediction of PSI from * Option b: PSI History (Only) AASHTO Equation NA 

5. PREDICTION OF DESIGN PERIOD M. COST HISTORIES FOR DESIGN PVT. 

MAINTENANCE AND USER COSTS -- AND AS-CONSTRUCTED PAVEMENT 

3 Annual and Cumulative 

Maintenance Costs * Maintenance ($BY) (DES & CON) 

(DES and CON) - Annual and Cumulative 

User ($/SY) (DES & CON) 

Annual and Cumulative - Annual and Cumulative 

User Costs * Total ($/SY) 

(DES and CON) -Annual & Cumulative (DES & CON) 

* Bid Price for PCC (my) Present Worth of Annual Costs Minimum EUAC 

Discount Rate (i%) * Years at Min. EUAC 

Q. PAyMEESCHEDULfi - - 

Differences in economic Payment = Bid Price plus * Pay factor equation /table 

performance of DES & CON present worth of cost difference OC for payment plan 

* Sensitivity analysis 

Figure 3,3. Derivation of performance-related M&C specifications. 
surfacing layer variables that are not directly related to the PCC itself, 

e.g., variables relating to reinforcement, joints, and shoulders. 

As indicated in box E, the AASHTO design eduation contains only four 

PCC variables: initial profile (or PSI), PCC thi,ckness, PCC modulus of 

rupture, and PCC elastic modulus. The design process therefore results in 

design levels for all four of these variables. It follows that performancerelated specifications for construction of the rigid pavement surfacing 

layer must take all four into account. 

Sensitivity analyses of the original AASHTO design equation have been 

made by the NJDOT and show that changes in the PCC modulus (Ec) from 3 

million to 5 million psi (211,000 to 352,000 kg/cm2) have negligible effects 

on the predicted pavement 1if e . (82.3) Thus, only initial PSI (Po) , PCC 

thickness (D), and PCC flexural strength (fr) need be considered in the PRS 

sys tem. 

Depending upon the choice of cost evaluation alternatives for module 6, 

it may be necessary for module 1 to include pavepent designs for not only 

the initial performance period, but also for subbequent rehabilitation 

periods. Both the NCHRP 10-26A and NJDOT methodplogies require only initial 

pavement designs, while the new procedure conceptualized in this study is 

based on a specified analysis period that extends into at least one 

rehabilitation period. I 

i, ACCEPTANCE PLANS FOR SELECT M&C VARIABLES 

The second module in figure 33 contains procedures for the development 

of acceptance plans for select M&C variables whose levels are to be 

controlled during pavement construction. For a given M&C variable (e.g., 

PCC thickness), the acceptance plan is a set of definitions and rules for: I 

I 

The construction lot that is to be sampled. 

A sampling plan that specifies how and how many samples (e.g., cores) 

are to be selected from each lot. I 

Test procedures and output values that quantify the sample 

characteristics. 

Acceptance criteria that determine whether the lot quality is 

acceptable in view of the test outputs. 

I 

An operating characteristic (OC) that gives the probability that a 

specific lot quality will result in accep~tance via the sampling plan 

and acceptance criteria. I 

As indicated in box G of figure 33, accepta$ce plans and associated 

operating characteristics are governed by assump$ions about the inherent 

variability of lots with respect to sample charadteristics and by consumer 

and producer risks. The consumer (SHA) risk for a given acceptance plan is 

the probability that a truly unacceptable lot will nevertheless be accepted. 

The producer (contractor) risk, on the other hand, is the probability that a 

truly acceptable lot will nevertheless be rejectqd. The risks arise, of 
course, because only a relatively small portion of any lot has actually been 

sampled and tested, and, because of inherent variation throughout the lot, 

the selected samples will sometimes give good results from a bad lot or bad 

results from a good lot. 

Acceptance plans for rigid pavement M&C variables have been wdrked 

out in great detail by the NJDOT.(82.3) It is assumed for purposes of this 

study that these plans are quite adequate for the development of the new 

PRS. Salient aspects of the NJDOT acceptance plans are listed below and are 

recommended for both the demonstration and further development of PCC 

specifications: 

Lot size should be I-day's production of the finished PCC pavement 

layer. 

* M&C variables to be evaluated through samples from each lot should 

include slump, air content, 28-day compressive strength, PCC 

thickness, and as-constructed PCC profile. 

* Samples for evaluation of slump and air content should be taken 

randomly from the trucks that provide PCC mix for the lot (day's 

production). Provisions should be specified for retempering and 

resampling rejected material. 

a Material for evaluation of compressive strength should be taken from 

the same trucks that are sampled for slump and air content and should 

produce two standard cylinders per sample for 28-day tests. 

a Cores for evaluation of PCC thickness should be taken via ;a 

stratified random sampling plan over the area covered by the day6s 

production. 

a One hundred percent sampling in wheel paths may be used for initial 

profile evaluation. 

a Lot acceptability should be judged in terms of sample statistics from 

which the lot percent defective can be estimated. Consumer risk may 

be in the neighborhood of 20 percent (of being accepted when bad) for 

lots that are 50 percent defective while producer risks may be in the 

neighborhood of 10 percent (of being rejected when good) for lots 

that are 10 percent d.efectiue. 

It may be assumed'that slump is included as a construction control for 

workability of the concrete and that air content is included as a 

construction control for PCC durability. In the light of the laboratory 

study results that are reported in chapter 5, it may be that unit weight 

should also be included as a construction control for PCC strength as shown 

in box H of figure 33. 

Available resources preclude development of specific acceptance plans 

within the present study, but follow-on studies should produce acceptance 

plans in detail for all M&C variables that are evaluated in the performancerelated construction specifications. 

I 
I 

CONSTRUCTION, CONTROL, AND EVALUATION I ~ I I 

The third module in the derivation of PRS bontains the procedures for 

pavement construction, sampling, sample evaluation, and lot acceptance or 

rejection via the acceptance plans that were developed in the second module 

for both the primary and secondary M&C variables. 

It is assumed that M&C quality control is the contractorts 

responsibility, and that SHA responsibility is for acceptance or rejection 

of construction lots in terms of observed variables that are set forth in 

the PRS. If the NJDOT sampling and evaluation plans are used, two 

performance determinants in the AASHTO design equations are estimated 

directly, namely, initial profile and PCC thickness. The two remaining 

determinants (PCC modulus of rupture and PCC elastic modulus) are to be 

estimated from the 28-day compressive strengths of the sample cylinders. 

Thus, secondary relationships among PCC variables, as given in chapter 5 and 

appendix C, must be used to 'convert observed compressive strength (fpc28) to 

estimates for flexural strength (fr28) and elastic modulus (Ec28). It is 

important to note that these estimates are made for each and every 

construction lot, and that all four estimates have uncertainties relative to 

the corresponding "true" values for the entire lot, partly because of 

sampling variability and partly because of uncertainties in the secondary 

relationships that have been used for the conversions. 

It is recommended that serious consideration be given to the use of 

7-day compressive strength for the sample cylinders, especially since it was 

shown in chapter 5 that there is little difference in the statistical 

uncertainty between estimation of fr28 and Ec28 from fpc28 or fpc7. 

The NJDOT procedure uses a square root relationship similar to appendix 

C, relationships A or E to convert compressive strength to flexural 

strength. Results of this study, however, provide alternative equations for 

this conversion (see table 25). 

PREDICTION OF DISTRESS AND PERFORMANCE FOR DESIGN PAVEMENT AND CONSTRUCTED 

PAVEMENT 

The fourth module in PRS development contains equations and algorithms 

for predicting distress and performance for both the pavement as-designed 

(DES) and as-constructed (CON). Inputs for the as-constructed pavement are 

assumed to be the same as for the as-designed pavement for all variables in 

boxes B, C, and D, but contain the as-constructed estimates for PCC 

variables (box J) instead of the as-designed levels in box E. 

As shown in module 4 of figure 33, one option is to use the COPES 

prediction equations in appendix B for pumping, cracking, faulting, joint 

deterioration and serviceability loss. (85.2) Use of these equations produces 

annual and cumulative distress histories for both the as-designed and 

as-constructed pavements throughout the initial performance period. 

A second option is to predict only the PSI history for the initial 

performance period using the AASHTO design equation (appendix B, 

relationship N). If both options are employed, the output distress and 

performance histories indicated in box K are annual and cumulative vectors 
for ESAL, pumping, cracking, faulting, joint deterioration, PSI (COPES), and 

PSI (AASHTO). 

The foregoing procedures are analogous to those used in NCHRP Project 

10-26A wherein annual and cumulative vectors are produced for ESAL, AC 

cracking, AC rut depth, and AC roughness. On the other hand, the NJDOT 

procedures involve only the time at which the terminal serviceability level 

(PSI = 2.5) is reached and do not require distress or PSI predictions during 

the initial performance period years. 

PREDICTION OF PERFORMANCE PERIOD COSTS FOR DESIGN PAVEMENT AND CONSTRUCTED 

PAVEMENT 

The fifth procedural module is directed at the transformation of annual 

and cumulative distress quantities into corresponding unit costs for both 

the as-designed pavement (DES) and the as-constructed pavement (CON). As 

shown in box L, input assumptions can be made for dollars per square yard 

costs ($/SY), for annual maintenance when distress variables and PSI are at 

given levels, or more simply, for annual maintenance costs ($/SY) when PSI 

is at given levels. If user operating costs are also to be considered, then 

assumptions must be made for user costs (in $/SY) at given PSI levels. 

From the input asswnptions, the algorithms in module 5 produce cost 

histories, both annual and cumulative, that show mailntenance costs, user 

costs and total costs for both the as-designed pavement (DES) and the asconstructed pavement (CON). As noted in box L of figure 33, one option is 

to predict both annual maintenance and user costs from the PSI levels that 

are predicted on a year-by-year basis. 

It should be noted that the: 

1) NCHRP 10-26A methodology employs both maintenance and user opeeating 

costs. 

2) Life cycle cost methodology conceptualized in this study employs only 

maintenance costs, but could consider user costs, if necessary. 

3) NJDOT methodology does not depend at all upon maintenance or user 

costs. 

COST EVALUATION FOR DESIGN PAVEMENT AND AS-CONSTRUCTED PAVEMENT 

The sixth module contains algorithms for conversion of the cost 

histories produced in module 5 into summary indicators of the economic 

performances of the design pavement and the constructed pavement. 

The NCHRP 10-26A methodology employs indicators that are based on 

economic life, as illustrated in figure 34. Economic life is defined as the 

year (YMAC) within the initial performance period at which the equivalent 

uniform annual cost (EUAC) has a minimum value (MAC). Thus, in figure 34, 

MAC and YMAC are coordinates of the minimum point on the EUAC curve, To 

calculate EUAC, the cumulative present worth of construction, maintenance, 

and user operating costs is calculated for each year of the performance 
I 

Years ~ 

~ 

I 

EUAC = Cumulative Present Worth of ~ota/ Costs Through Year Y 

times i W(k-1) where i = discount rpte and k = (l+i)' I 

~ 

~ 

I 

~ 

~ I 

~ Ii 

I 

Figure 34. Economic life $ndicators. 

I 

j 
period, using the cost histories that were produced in module 5. For each 

year, Y: 

EUAC = (Cumul. Present Worth of Total Costs) [i(l+i)']/[ (l+ilY-l] 

where i is an assumed discount rate. In general, the EUAC values will first 

decrease, then increase after passing through the minimum point at which 

EUAC = MAC at year YMAC. 

If the foregoing calculations are made for both the design pavement and 

the constructed pavement, the outputs (box 0 of figure 33) are arrays of 

annual EUAC for both pavements. As shown in figure 35, coordinates for the 

minimum EUAC in the respective arrays are designated by (DES MAC, DES YMAC) 

for the design pavement and by (CON MAC, CON YMAC) for the constructed 

pavement. 

The NJDOT methodology for cost evaluation uses the AASHTO design 

equation to compute the expected life (L) for both the design pavement 

(LDES) and the constructed pavement (LCON), using inputs from boxes D, E, 

and J in figure 33. Furthermore, it is assumed that the present unit cost 

of the first overlay is C1, the present unit cost of each subsequent overlay 

is C,, and that every overlay has the same expected life, LOL. Maintenance 

and user operating costs are not considered, so the present worth of all 

costs (PWC) for the design pavement is given by: 

DES PWC = C, + R~~~~[C, + C~R~O~/(~ - ] 

where : 

Co = unit cost of initial construction. 

C, = unit cost of first overlay. 

C2 = unit cost of each subsequent overlay. 

LDES = expected life (years) of design pavement. 

LOL = expected life of each overlay (assumed to be constant). 

R = (l+inflationrate)/(l+interestrate). 

Corresponding present worth costs for the constructed pavement are given by 

equation 30 with LDES replaced by LCON, the expected life of the constructed 

pavement. 

The new methodology conceptualized in this study evaluates the present 

worth of life-cycle costs over a specified analysis period for both the 

design pavement and the Lonstructed pavement. Cost elements cover initial 

construction, overlay construction, maintenance and salvage value. The 

methodology also assumes that different overlay designs will be required if 

there are differences in the initial performance period for the design and 

constructed pavements. 

Whatever methodology may be used, the outputs of module 6 (box Q of 

figure 33) are economic indicators of pavement performance and are assumed 

to be essential to a true PRS system. 
Years 

Design Pavement: 

DES MAC = Minimum EUAC for design pavement 

DES YMAC = Year at minimum EUAC for design pavement 

Constructed Pavement: 

CON MAC = Minimum EUAC for constructed pavement 

CON YMAC = Year at minimum EUAC for constructed pavement 

Figure 35. Economic life differentials between design pavement 

and constructed pavement. 
DERIVATION OF PAYMENT PLANS FOR PERFORMANCE-RELATED SPECIFICATIONS 

The last module in figure 33 is for the derivation of payment plans 

associated with performance-related specifications. Payment plans for all 

three methodologies that have been discussed assume that the contractor's 

bid price should be paid for every construction lot whose true life 

expectancy and associated costs are precisely those of the design pavement. 

All three methods also assume that pay adjustments to the bid price should 

be based on differences between the ecbnomic indicators of pavement 

performance for the design pavement and the constructed pavement. More 

specifically, the criterion for any payment plan (box P of figure 33) is the 

degree to which the economic performance of the constructed pavement is 

greater than or less than that of the design pavement. 

It should be remembered that the acceptance plans (module 2) and 

construction evaluations (module 3) are based on construction lots and that 

the payinent plan refers to payments that are calculated for each lot. It 

can thus be expected that overall payment is calculated from the credits and 

debits associated with individual lot payments. 

For the NCHRP 10-26A methodology, the lot payment plan is the bid price 

minus the present worth of the difference between CON MAC and DES MAC (see 

figure 35) over the years given by CON YMAC, i.e., the economic life of the 

constructed pavement. Thus, the payment formula is: 

Payment = Bid Price - (CON MAC - DES MAC) * 

[(I + i)'ONYMAC - l]/[i(l + i)'ON YMAc 1 (31) 

If the bid price is factored out from the right side of equation 31, the 

bid price multiplier is defined to be the pay factor: 

Pay Factor = 1 - [(CON MAC - DES MAC)/Bid Price] * 

[(I + i)'ON - I]/[i(l + i)'ON 1 (32) 

For example, if i - 6 percent, bid price is $30/sy, DESMAC is $6/sy, CONMAC 

is $7/sy, and CONYMAC = 15 years, then, the pay factor is equal to 1 - 

[$1/$30][2.40-1]/[0.06(2.40)] = 1 - 0.32 = 0.68 or 68 percent of the bid 

price. If CON MAC is less than DES MAC, the pay factor will be greater than 

1. 

In connection with the chapter 7 demonstration of the economic life 

methodology, a sensitivity analysis was performed to show how the pay factor 

in equation 32 changes with changes in PCC variables, cost variables, and 

associated changes in the explicit variables within equation 32. 

In the NJDOT methodology, the payment for each lot is given by: 

Payment = Bid Price + (RLDES - R~~~~) [C1 + c21tLoL/(1 -RLoL) ] 

where C1, C2, and LOL are overlay costs and life (as in equation 30). The 

NJDOT pay factor multiplier for bid price is, therefore: 

Pay Factor = 1 + [ (RLDES-RLCUN)/~id Price] [c1+c2RLoL/ (1 -RLoL) ] 
Thus, both the life of the constructed pavement and of the design pavement 

enter into the pay factor equation. If the forver should be zero, for 

example, the pay factor will be about 0.60 for LDES = 20 years, Bid Price = 

$30/sy, R = 0.96, C1 = $8/SY, C, = $7/SY, and LlQL = 10 years. 

I 

Since the methodology conceptualized in th$s study has not been fully 

developed, no counterparts to equations 32 and 34 are given in this report. 

The NJDOT approach makes it possible to wr5te the pay factor equation in 

terms of the "load ratio", LCON/LDES, i.e., the ratio of the constructed 

life to the design life. Thus, the pay factor can be graphed as a function 

of the load ratio as shown in figure 36. For ratios between (say) 0.50 and 

1.50, the curve for equation 34 can be approximated by a straight line whose 

equation, for example, might be F = 0.75 + 0.25*(load ratio). For ratios 

below 0.5, a pay factor of (say) 0.60 can be askumed; for ratios above 1;50, 

the pay factor might stay constant at 1.12. These substitutions for the pay 

factor curve provide both minimum and maximum play factors, and permit simple 

pay factor calculations between the limiting load ratios. Similar 

approaches can be developed for both the NCHRP 10-26A methodology and the 

conceptual approach identified in this study , bbt such developments are left 

for further research. I 

A final important consideration for any sp4cification payment plan is 

its so-called operating characteristic (OC), e., the contractor's expected 

payment, relative to the acceptance sampling plians that were discussed 

earlier in this chapter. For each construction, lot (e.g., 1 day's pavement 

production), only a few samples (e.g., five) have been selected and 

evaluated to estimate the PCC properties of the entire lot. All outputs 

from module 4 (distress predictions), module 5 (cost predictions), and 

module 6 (economic indicators of performance) are based on sample 

characteristics that vary by chance about the true characteristics of the 

entire lot. These same sampling variations affect the pay factors that are 

calculated for individual lots, and thus lead to pay factors that are 

sometimes smaller and sometimes larger than woulld be produced from 100 

percent sampling of each lot. The contractor's expected payment, shown in 

figure 36 as the OC curve, is derived from probabilities that relate to 

differences between pay factors derived from sample data and pay factors 

that would result from full knowledge of the quality characteristics of the 

entire lot. As has been done by NJDOT, it is ukeful to derive sampling and 

acceptance plans whose expected payment OCs give close approximations to the 

pay factor equations that are part of the PRS. Again, development of 

expected payment OCs for either the NCHRP 10-26A approach (or the new 

methodology conceptualized in this study) will require further research, as 

is discussed in chapter 8. 

Additional research will also be required to develop PRS that take into 

account the uncertainties of equations that are used to predict both 

physical and economic performance. In both the present study and in the 

NCHRP 10-26A report, prediction equation errorshave been disregarded, but 

eventually, the OCs for acceptance and payment plans must take these 

uncertainties into account. 
PAY 

FACTOR 

(F) 

- MiMlYUM 

Figure 36. Determination of acceptance plan payment system 

based on theoretically derived pay function 

and expected payment operating characteristic curve. (82 *3) 

# 

143 
CHAPTER 7 

DElfONSTRATION DEVELOPMENT OF A PERFORMANCE-RELATED 

M&C SPECIFICATION FOR PCC CONSTRUCTION 

This chapter presents a demonstration of the procedures and algorithms 

that were discussed in chapter 6. The primary methodology is based on 

i 

1 economic life, as has been the basis for AC construction specifications in 4 NCHRP Project 10-26A. The demonstration procedures are computerized through t 

I the use of a spreadsheet program (Lotus 1-2-3). 

Z 

The first section explains and illustrates all input data for the 

procedure. The second section presents procedures and outputs for the 

year-by-year histories of illustrative traffic, gerviceability, distress, 

and costs for a specified design pavement and fok a corresponding 

as-constructed pavement. In the third section, bhe historical data are used 

to develop indicators of economic performance (ebg., economic life) for both 

pavements and to produce an illustrative payment plan for the as-constructed 

pavement. I 

I 

I 

Sensitivity analyses for the payment plan afe given in the fourth 

section and show how payment factors depend upon determinants of the plan, 

both for physical determinants (e.g., PCC strengph) and for economic 

determinants (e.g., maintenance costs). I 

~ 

The final section 

by the research team with respect to the demonst 

results. It is acknowledged that the represents only the 

formative stages of the complete M&C 

specification for the 

INPUT DATA FOR THE DEMONSTRATION SPECIFICATION 1 

I 

Inputs for the demonstration specification $re listed in table 29 in 

six categories (A through F). Input requirements are dictated by the use of 

the AASHTO design equation for rigid pavements (appendix B, relationship N), 

by the COPES equations for prediction of various types of distress (appendix 

B, relationships A, B, H, J, and O), and by the 'cost evaluation procedures 

and equations that were presented in chapter 6. ~ 

Category A in table, 29 is for the primary l?CC specifications factors 

that have been selected for the demonstration. ~hese factors are (1) 

initial serviceability level, Po; (2) PCC slab thickness, D,; (3) 28-day 

compressive strength, Ff; (4) 28-day flexural sprength, Sfc; and (5) PCC 

elastic modulus, E,. As was shown in box J of fbgure 33, it is assumed that 

only Po, D,, and Ff , are evaluated through constduction sampling and 

acceptance plans. Since the AASHTO design equaqion requires inputs for Sf, 

and E,, the demonstration assumes that these proberties can be estimated 

adequately from equations that were developed iq chapter 5 and presented in 

table 25. The equation used for estimating flebural strength from 

compressive strength is: I 
Table 29. Input data for the demonstration specification. " ' 

A. Primary PCC Specifications Factors Design Pvt. Constructed Pvt. 

1. Initial PSI (Po) 

(DES) f (CON) 

- 4.3 4.0 --- 

2. Slab Thickness (D,) 9.0 in 8.5 in 

3. 28-day Compressive Strength (FtC) 4000 psi 3500 psi 

4. 28-day Flexural Strength (Stc) 

(estimated from Ftc by equation 35) 614 psi 557 psi 

5. PCC Elastic Modulus (E,) 

(estimated from Ft, by equation 36) 4.17 mpsi 3.96 mpsi 

B. Non-PCC M&C Factors DES & CON 

1. Load Transfer Coefficient (J) 3.2 

2. Drainage Coefficient (Cd) 1.0 

3. Subbase Thickness 6.0 in 

4. Joint Spacing 20 ft 

5. Subbase Type (0 = Gran, 1 = Stab) 1 (Stab) 

6. Shoulder Type (0 = AC, 1 = PCC Tied) 0 (AC) 

7. Dowel Bar Diameter 1.25 in 

8. Reinf. Steel Quantity 0.12 in2/f twidth 

9. Type of Joint Filler (0 = None, 1 = Unitube) 1 (~nitube) 

10. Modulus of Subgrade Reaction (k) 60 pci 

C. Traffic Factors 

1. Initial 4-lane ESAL (W,) 500,000 

2. Direction Distribution Factor 50% 

3. Lane Distribution Factor 90% 

4. Annual Growth Rate (r) 5% 

D. Environmental Factors 

1. Freeze Index 625 

2. Avg. Monthly Temperature 18OC 

3. Max. Annual Temp. Range 3 3°C 

4. Avg Annual Precipitation 25 in 

E. Other Distress Factors (for COPES equations) 

1. D-Crack Potential (0 = No, 1 = Yes) 0 

2. Reactive Aggregates (0 = No, 1 = Yes) 0 

3. Incompressible Potential (0 = No, 1 = Yes) 0 

4. Joint Damage Potential (0 = Low, 1 = Med/High) 0 

F. Economic and Cost Factors 

1. Interest Rate (i) 6% 

2. Cost of PCC Construction (Bid Price) $ 30. OO/sy 

3. Annual Maintenance Costs when PSI = 2.5 

(m in equation 37) $ 0.28/sy 

4. Percent of Vehicle Operating Costs 

(q in equation 38) 10% 
S', = 1.22 (131.2 + 0.093 F',) 

and the equation for estimating elastic modulus from compressive strength 

is: 

B 

t Thus, the demonstration data input begins with entries for Po, D,, and 

6 

! F', for both the design pavement (DES) and the as-constructed pavement 

I (CON). The spreadsheet program then uses equatigns 35 and 36 to produce 

estimates for both S', and E,. All remaining entries in table 29 are for i 1 

11 factors whose levels are assumed to be the same for both the design pavement 

and the as-contructed pavement. 

Category B is for M&C factors that are independent of the PCC 

properties in category A. The first two factors, load transfer (J) and 

drainage coefficient (Cd) and the tenth factor, modulus of subgrade reaction 

(k), are values required by the AASHTO design equation. The remaining 

factors are required by one or another of the COPES equations for predicting 

rigid pavement distress. 

Category C contains traffic factors that identify the cumulative number 

of 18-kip ESALs (W,) that will be applied to the pavement design lane during 

its life. Entries are made for the number of ESALs in all traffic lanes 

(W), for the percent of Wo in the design lane direction and for the percent 

of directional traffic that is in the design lane. W1, the product of these 

three values, is computed by the spreadsheet program and the result is 

displayed. The final traffic factor required is the annual rate of ESAL 

growth (r) that is used to project future traffik. 

Category D contains environmental moisture and temperature factors that 

are inputs to certain of the COPES distress equations. Category E contains 

additional factors that are also required by one or another of these 

equations. I 

Finally, category F of table 29 contains all factors that are needed 

for spreadsheet calculation of annual costs and 'their present worth. The 

first entry is the annual interest rate (i). The second is for the unit 

cost of PCC construction, and is assumed to be tpe bid price (BP) in dollars 

per square yard. I 

The third cost factor required is the annual routine maintenance cost 

($/sy) when the serviceability level is PSI = 245. For the demonstration, 

the routine maintenance cost for year Y, RMC,, i$ approximated based on its 

predicted PSI during year Y, PSI,. 

RMC, ($/sy) = m * (5 - ~~1,)'/6.25 (37) 

I 

The equation shows that RMC equals m, when PSI = 2.5. 

It is assumed that vehicle operation costs for any particular year (Y) 

depend both on the pavement's serviceability level (Py) and the number of 

ESAL (w,) that it receives during the year. Forthe demonstration, it is 
assumed that vehicle operating costs for year Y (VOC,) are given by the 

equation: 

VOC, = q (0.00203 w,) (1.397 - 0.088 P,) 

where q is the percentage of the total predicted VOC that is to be 

considered in determining the contractor's penalty or reward. This 

percentage was included to adjust the potentially large effect VOC can have 

on contractor payment. The VOC equation was derived from the results of a 

1982 FHWA study of vehicle operating costs and required several simplifying 

assumptions as traffic distribution, vehicle loading, operating speed, etc. 

There are obviously many alternatives for equations 37 and 38, but 

further research is needed to determine which alternatives are optimal for 

any particular PRS system. 

TRAFFIC, SERVICEABILITY, DISTRESS, AND COST HISTORIES 

After all inputs are entered in table 29, the spreadsheet,program 

calculates and displays year-by-year histories for the design pavement 

traffic, serviceability, distress, and costs as shown in part A of tab1 

then produces corresponding histories in part B for the as-constructed 

pavement. Although the example shows only the first 6 years, all histo 

cover a span of 30 years. 

ries 

Two traffic histories are shown in category A, the annual design lane 

ESAL and the cumulative design lane ESAL. For any year, Y, the annual ESAL 

(w,) is given by: 

w, (ESAL) = W1 (1 + r)y-l 

where W1 is the first year ESAL and r is the annual ESAL growth rate. Both W1 

and r are indicated in the traffic category of table 29. 

The number (Wy) of cumulative ESAL through year Y is given by: 

where the right side represents the sum of the geometric series that arises 

from substitution for wy from equation 39. 

The second set of histories in table 30 is for yearly levels of 

serviceability (Py) that are given for PSI by the AASHTO design equation, 

and for PSR (present serviceability rating) levels that is given by the 

COPES equation (appendix B, relationship 0). 

After substitutions are made for Cd = 1, J = 3.2, and k = 60 pci (1.66 

kg/cm3) (see table 29), the AASHTO equation may be written in the form: 
I 

~ 

Table 30. Traffic, serviceability, distress, qnd cost histories (part A). I I 

4 

A. DESIGN PAVEMENT (DES) YEARS, O 1 ----- 21 3 4 5 6 f I 

I 

I 

Traffic Histories 

1. Design Lane ESAL, millions 

i 

I wy/lOOO from equation 39 -- 0.225 0.296 0.248 0.260 

1 2. Cumulative ESAL, millions 

3 Wy/lOOO from equation 40 -- 0.225 0.441 0.709 0.970 

j 

i Serviceability Histories 

3. AASHTO PSI (P, in table 29) 

(P, from equation 41) 4.3 4.2 

4. COPES PSR (4.5 initial) 

(PSR from relationship 0, 

appendix B) 4.5 4.4 

Distress Histories (from COPES Equations) 

5. Pumping (0 - 3) 

(relationship A, appendix B) -- 0 

6. Faulting (in/fault) 

(relationship H, appendix B) -- 0.74 

7. Joint Deterioration (j ts/mi) 

(relationship J, appendix B) -- 0.05 

8. Slab Cracking (ft/mile) 

(relationship B, appendix B) -- 4 

Cost Histories 

9. PCC Construction ($/sy) 

(Bid Price) 30.00 0.00 0.00 0.00 0.00 0.00 0.00 

10. Routine Maintenance ($/sy) 

(RMC, from equation 37) - - 0.03 0.03 0.03 0.04 0.04 0.05 

11. Vehicle Operating Cost ($/sy) 

(VOC, from equation 38) - 47.03 49,742 51.94 55.05 57.85 61.31 

12. Total Annual Cost ($/sy) 

(TAC, from equation 43) 30.00 47.06 49.45 51.97 55.09 57.89 61.36 

13. Present Worth of TAC ($/sy) 

(PWC, from equation 44) 30.00 44.39 44.bl 43.63 43.63 43.26 43.25 

14. Cum. Present Worth ($/sy) I 1 

(CPW, from equation 47) 30.00 74.39 118~.4 162.0 205.7 248.9 292.2 

15. CPW Factor I 

(F, from equation 52) -- 1.060 0.546 0.374 0.289 0.237 0.203 

16. Equiv. Unif. Ann. Cost ($/sy) I 

(EUAC, = Fy * CPW,) -- 78.86 64.68 60.62 59.35 59.09 59.42 

17. EUAC Min. Diff. Factor I 

(G, from equation 55) -- 0.943 1.832 2.674 3.460 4.219 4.926 

I 
Table 30. Traffic, serviceability, distress, and cost histories (part B). 

B. CONSTRUCTED PVT. (CON) YEARS 0 1 2 3 - 4 *~-.." 5 6 

Traffic Histories 

1. Design Lane ESAL, millions 

wy/lOOO from equation 39 -- 0.225 0.236 0.248 0.260 0.273 0.287 

2, Cumulative ESAL, millions 

Wy/lOOO from equation 40 

Serviceability Histories 1 

3. AASHTO PSI (P, in Table 29) 

(P, from equation 41) 4.0 3.9 3.8 3.7 3.6 3.5 3.3 

4. COPES PSR (4.5 initial) 

(PSR from relationship 0, 

appendix B) 4.5 4.4 4.3 4.1 4.0 3.9 3.7 

Distress Histories (from COPES Equations) 

5. Pumping (0 - 3) 

(relationship A, appendix B) -- 0 0 0 0 8 0 

6. Faulting (in/fault) 

(relationship H, appendix B) -- 0.74 1.04 1.28 1.48 1.67 1.84 

7. Joint Deterioration (jts/mi) 

(relationship J, appendix B) -- 0.05 0.27 0.69 1.34 2.24 3.41 

8. Slab Cracking (f t/mile) 

(relationship B, appendix B) -- 4 8 13 18 24 30 

Cost Histories 

9. PCC Construction ($/sy) 

(Bid Price) 30.00 0.00 0.00 0.00 0.00 0.00 0.00 

10. Routine Maintenance ($/sy) 

(RMC, from equation 37) - - 0.06 0.07 0.08 0.09 0.11 0.12 

11. Vehicle Operating Cost ($/sy) 

(VOC, from equation 38) -- 48.24 51.12 54.16 57.38 60.79 64.40 

12. Total Annual Cost ($/sy) 

(TAC, from equation 43) 30.00 48.29 51.18 54.24 57.48 60.90 64.52 

13. Present Worth of TAG ($/sy) 

(PWC, from equation 44) 30.00 45.56 45.55 45.54 45.53 45.51 45.49 

14. Cum. Present Worth ($/sy) 

.* (CPW, from equation 47) 30.00 75.56 121.1 166.6 212.2 257.7 303.2 

15. CPW Factor 

(F, from equation 52) -- 1.060 0.546 0.374 0.289 0.237 0.203 

16. Equiv. Unif. Ann. Cost ($/sy) 

(EUAC,, = Fy * CPW,) -- 80.09 66.06 62.35 61.23 61.17 61.65 

17. EUAC Min. Diff. Factor 

(G, from equation 55) -- 0.943 1.832 2.674 3.460 4.219 4.926 

149 
where : 

f, = 1 + 16240000/(Dc + 1)8.46 

fz = 7.35 log(Dc + 1) - 0.06 

f, = log [Stc (D,'.~~ - 1.132) 1 / [690.02 (D~~.~~ - 51.266 E~-~'~~) 1 

To show the more specific nature of equation 41, the design pavement in 

part A of table 29 has Po = 4.3, Dc = 9.0 in (228.6 mm), Stc = 614 psi (43.2 

kg/cm2), and E, = 4.17 mpsi (293,000 kg/cmZ). Substituting these values in 

equation 41 gives: 

log(4.3 - P,) + 0.0171 Py = 1.0563 log Wy - 6.9982 

Since equation 42 cannot be solved explicitly for P,, the spreadsheet 

program includes a procedure for approximating Py when W, is given. 

The PSI history produced by equation 42 with Wy inputs from equation 40 

is tabulated in part A of table 30 and is shown graphically in figure 37. 

The figure also shows the PSI history for the as-constructed pavement, as 

tabulated in part B in table 30. The figure shows that the design pavement 

reached PSI = 2.5 after about 20 years and 8 million ESAL, whereas the 

as-constructed pavement life (at PSI = 2.5) was only about half that of the 4 

design pavement. 

The spreadsheet program includes PSR values that are given by the COPES 

' equation, mainly to show that rather large differences exist between the 

AASHTO and COPES equations. For example, table 30 shows that the COPES 

equation gives PSR = 3.7 at about 6 years and 1.5 million ESAL for both the 

design pavement and the as-constructed pavement, whereas the corresponding 

AASHTO values are 3.9 and 3.3, respectively. After 12 years, the difference 

would be even more significant. In terms of the NJDOT methodplogy, the 

AASHTO equation would give a load ratio of about 0.5 (4 million ESAL/ 

8 million ESAL), whereas the COPES equation would give a load ratio of 1.0 

for the example pavements. These observations imply that a PRS system may 

give different results not only for two different methodologies but also for 

different primaryperformance equations within a given methodology. 

The next four histories in table 30 are for rigid pavement pumping, 

faulting, joint deterioration, and slab cracking as given by prediction 

equations that were developed in the COPES As was noted in box 

L of figu"re 33, annual maintenance costs might be based on levels that have 

been reached in a given year for one or more of these four distress types 

(option a), or they might simply be based on the serviceability level that 

has been reached (option b). Although option b has been selected for the 

demonstration specification, inclusion of distress histories makes it 

possible to incorporate option a as a future alternative. (Note: The COPES 

faulting equation obtained from reference 85.2 does have an apparent error 

that would need to be corrected before this option could be exercised.) 

Comparison of serviceability and distress histories for the design 

pavement (table 30, part A) and the as-constructed pavement (table 30, 

part B) shows that the COPES equations give identical annual serviceability 

and distress levels for both pavements. It follows that, unlike the AASHTO 

serviceability relationship, both pavements would have the same annual 

maintenance costs for any cost formula based on the COPES serviceability 

and/or distress formulas. 

None of the COPES equations includes initial serviceability as a 

construction variable, but all include PCC thickness and flexural strength 

as determinants of serviceability and distress. Until further study is 

made, it is presumed that the AASHTO equation has greater sensitivity to 

changes in D, and St, than do the COPES equations. 

The final set of histories in table 30 contains year-by-year values for 

eight different cost factors. The first cost factor (history 9) is the unit 

cost of PCC construction that occurs only in year zero, i.e., before traffic 

has started. This cost is assumed to be the bid price for PCC pavement 

construction and has been entered as $30.00/sy for both the design pavement i 

! and the as-constructed pavement. 4 

Routine maintenance costs for each year are given in history 10 and are 

calculated from equation 37. History 11 is for annual vehicle operating 

costs as calculated from equation 38, and the total annual cost (history 12) 

is given by: 

TACO = Bid Price for year zero 

TAC, = RMC, + VOC, for Y = 1, 2,. . . 

Plots of RMC, and VOC, over time are shown ifi figures 38 and 39, 

respectively. Each figure contains the cost histories for both the design 

pavement and the as-constructed pavement, as given in table 30, part A and 

part B, respectively. For the demonstration PRSsystem, it can be seen that 

the relative cost differences between the two paqements are considerably 

larger for RMC than for VOC. Although not showni a corresponding graph for 

total annual costs (TAC,) would look much the sanie as figure 39, simply 

because the VOC in figure 39 are about two orders of magnitude greater than 

the RMC in figure 38. 

As an adjunct to the sensitivity studies in this chapter, it is useful 

to display equation 43 in terms of all variables and input factors that 

'determine TAC,. Substitution from equations 37, 38, and 39 gives the 

following result: 

TAC, = 0.16 m Q~~ + 0.00203 4 W1 (1 + r) (0.957 + 0.088 Q,) (44) 

where Qy = 5 - P,, m = RMCy when Py = 2.5, q = fraction of VOCy used, W1 = 

initial year ESAL in the design lane, and r = traffic growth rate. 

For the input values given in table 29, equqtion 44 becomes: 
Year 

Figure 38. Routine maintenance cost histories. 

and will produce the TAC, cost histories shown in table 30. 

The next line of table 30 (history 13) is for the present worth of each 

total annual cost and is defined by: 

PWC,($/sy) =TAC,/(l+ i)y forY-0, 1, 2, ... (46) 

For Y = 0, the total cost and its present value is simply the bid price 

(BP). For Y > 0, the total annual cost is given by either equation 43 or 

equation 44. If table 30 costs were depicted through year 30, it would be 

seen that PWC, stays between approximately $42 and $44 (avg = $42.85) for, 

the design pavement and between approximately $45 and $50 (avg = $47.29) for 

the qs-constructed pavement. Analytic study of equations 41, 44, and 46, 

would be required to determine whether and how the relative constancy for 

CPW, (or PWC,) is dependent upon the input variables and levels. 

Histbry 14 is for the cumulative 

summation of equation 46, i.e., 

a Y 

If PWCk is relatively constapt and has 

approximated by: 

present worth at 

mean value MPWC, 

each year and is the 

(47 

then equation 47 is 

CPW, = BP + Y MPWC (48) 

Thus, for the two pavements in table 30, equation 48 gives the approximation 

formulas : 

CPW, - 39.00 + 42.85 Y (49) 

for the design pavement, and 

for the constructed pavement. 

In application, it will be found that equations 49 and 50 give CPW, 

approximations that are essentially within 1 percent of the values given by 

equation 48 over years 1 through 30. 

The last two histories in table 30 are for the conversion of CPW, to an 

equivalent uniform annual cost (EUAC,) for years 1, 2, ... The conversion 

formula was given in chapter 6, and is repeated below: 

EUAC, = Fy (i) * CPWy (51) 

where 
I 

The successive values of Fy are given in histpry 15 of table 30 and are 

common to both the design pavement and the as-cons~tructed pavement. It can 

be shown that Fy(i) is a hyperbola whose vertical asymptote is Y = 0 and 

whose horizontal asymptote is i (or 0.06 for the demonstration 

specification). Annual values for EUAC, are given in the final line 

(history 16) of table 30, and are plotted for both the design and 

constructed pavements in figure 40. Though not shown, very nearly the same 

graphs would be produced from the approximation equations 49 and 50. 

At least for the demonstration specification, equation 48 gives a 

satisfactory approximation for CPW,, as was shown above. If the 

approximation formula is used, then equation 51 becomes: 

EUAC, - Fy(i) * (BP + Y MPWC) 

Analytical study of equations 52 and 53 shows that EUAC must first decrease, 

pass a minimum, then increase as years increase beyond Y = 1, provided that 

MPWC > 0, i.e., that not all TAC are zero. 

ECONOMIC PERFORMANCE INDICATORS AND PAYMENT PLAN 

This section illustrates the economic indicators of pavement 

performance and the associated payment plans that were addressed in chapter 

6. Numerical results for the demonstration specifications are shown in 

table 31. Part A of the table gives results for the economic life 

methodology. For comparison purposes, part B of the table gives data that 

pertain to the load ratio methodology that is favored by the NJDOT. 

Essential data for the economic life methodology are the coordinates 

(in figure 40) for the minimum point on the EUAC history of both the design 

pavement and the as-constructed pavement. The value of EUAC at the minimum 

point is denoted by MAC; the corresponding year is denoted by YMAC and is 

the pavement's economic life. 

For both the design pavement and the as-constructed pavement, the 

spreadsheet program scans the EUAC histories to locate the minimum EUAC 

(MAC) and corresponding year (YMAC) for each pavement. More formally, YMAC 

is defined to be the smallest value of Y for which: 

EUAC, < EUAC(y+ll 

Table 31 shows that both DES YMAC and CON YMAC occur at Y = 5 years for the 

demonstration specification. Thus, both pavements have an economic life of 

5 years. The corresponding minimum EUAC values are DES MAC = $59.09/sy and 

CON MAC = $61.17/sy. 

As was discussed in chapter 6, the payment adjustment to the bid price 

for each construction lot is the present worth oE the difference 

between the annual cost minimums (DES MAC - CON MAC), i.e., the present 

worth of -$2.08/sy for the demonstration specification. 

Table 31. Economic performance indicatbrs and pay factors. 

Design Constructed 

Pavement Pavement Difference 

(DES) (CON) (DES-CON) 

1 A. Economic Life Methodology I 

~ 

1 

i 

I 

1. Years at Min. EUAC 

(YMAC from equation 54) 

2. Minimum EUAC ($/sy) 

(MAC from equation 51) 

3. Pres. Worth Factor 

[Gy(YMAC) from equation 551 

4. Bid Price Adjustment 

[G,(YMAC)*MAC Diff.] 

5. Bid Price ($/sy) $30.00 

I 

6. Payment ($/sy) 

(BP + Adjustment) $21.22 

7. Pay Factor 

(Payment/Bid Price) 0.707 

DES CON 

B. Load Ratio Methodology 

1. Terminal PSI Level (Pt) 2.5 2.5 

2. Year for Pt (Yt) 21 11.5 

3. ~kulative ESAL (W,) at Pt 

(W, in millions of ESAL) 8.04 3.39 . 

4. Load Ratio (CON Wt / DES Wt) 0.422 

5. Bid Price ($/sy) $30.00 

6. Payment ($/sy, from equation 59) $26.34 

7. Pay Factor = Payment / BP 0.878 
The present worth factor for the MAC difference is the reciprocal of 

the present worth factor given by equation 52 for total annual costs, and is 

computed for the economic life of the as-constructed pavement. Thus, the 

present worth factor is given by: 

and is shown in table 31 to be 4.219 for CON YMAC = 5 years. As was shown 

in chapter 6, the unit payment for each construction lot is given by: 

Payment - Bid Price - G,(CON YMAC)(CON MAC - DES MAC) (56) 

where the second term is the payment adjustment to the bid price and can be 

either positive or negative. Table 31 shows that the demonstration 

adjustment is -$2.08 * 4.219 or -$8.78/sy which is minus 29.2 percent of the 

bid price. Thus, the demonstration payment is $30.00 - $8.78 or $21.22/sy. 

By definition, the specification pay factor is given by: 

Pay factor = Payment ($/sy) / Bid Price ($/sy) (57) 

The pay factor for the demonstration is, therefore, $21.22/ $30.00 or 0.707. 

If equation 53 is used to approximate EIJAC, it can be shown that the 

minimum value for EUAC (MAC) occurs at the year YMAC that satisfies the 

equation: 

[(jwc - 1 ) / In j ] - YMAC = BP / MPWC 

where j = 1 + i and in j is the natural logarithm of j. 

(For the demonstration data, BP - $30.00/sy and MPWC from equations 49 

and 50 is $42.85/sy for CON and-$47.29 for DES. Thus, the right side of 

equation 58 is 0.70 for DES and 0.63 for CON. It will be found that, to the 

nearest year, the corresponding YMAC is 5 years for both the DES and CON 

pavements as was shown in table 30. Equation 58 also shows that YMAC is 

about 10 years when MPWC is $8.00/sy, and is about 20 years when MPWC is 

around $2.00/sy. Thus, the YMAC year depends strongly upon the average 

present worth of annual costs. 

If the YMAC relationship in equation 58 is substituted into equation 

53, the minimum value of EUAG is given by: 

MAC = (MPWC) * i * j yMc / ln j (59) 

Equation 59 can then be written for both DES and MAC, and the results 

substituted into equation 56 to have the approximation formulas for the pay 

adjustment and pay factor. The new equations 58 and 59 not only provide 

good approximations for the specification pay factor, but also show that the 

major determinants of the pay factor are the mean present value of annual 

costs for DES and CON. 

Part B of table 31 gives data that are required and results that might 

be obtained if the NJDOT load ratio methodology was used. As was discussed 

in chapter 6, these methods require the definition of a terminal 
serviceability level for the pavement's first performance period. The' 

selected value is shown to be PSI = 2.5 in table 31. 

From the AASHTO PSI histories and the cumulative ESAL history, the 

number of ESAL at PSI = 2.5 (W,) is determined for the design pavement (DES 

W,) and the as-constructed pavement (CON Wt). Fdr the demonstration, table 

31 shows that DES W, = 8.04 million ESAL at 21 years and (by interpolation) 

that CON W, = 3.39 million ESAL at about 11.5 years. The load ratio is 

defined by: 

Load Ratio = (CON W,) / (DES W,) (60) 

and is 3.39 / 8.04 = 0.422 for the demonstration data. Equation 33 in 

chapter 6 provides the basis for calculating coqtractor payment. For the 

demonstration, it is assumed that C, = $8/sy, C2 = $7/sy, and LOL = 10 years. 

Thus, equation 33 becomes: I 

Payment = Bid Price + $16.77 (R~~~ Yt - Yt ) 

where R = (1 + inflation rate)/(l + interest rate), and DES Y, and CON Yt are 

the respective years at which the terminal PSI is reached by the two 

pavements. If R is assumed to be 1.00/1.06 = 0.943, then for the 

demonstration example, 

Payment = $30.00 + $16.77 (0.292 - 0.509) 

= $30.00 - 3.64 

= $26.36/sy 

and the specification pay factor is $26.36 / $30.00 = 0.879. 

It is interesting to note that the load rat;io pay factor would have 

been about 0.60, even if there was immediate failure (CON Yt = 0) for the 

constructed pavement. 

SENSITIVITY ANALYSES FOR THE DEMONSTRATION SPECIFICATION I 

This section describes sensitivity analyses, that were run to illustrate 

how the demonstration specification pay factor changes when changes are made 

for selected input factors in table 29. Analyses were first made for pay 

factor sensitivity to only changes in the primary PCC specifications 

factors, and secondly for pay factor sensitivity to changes in economic 

factors in conjunction with PCC factor changes. Input data for the 

illustrative analyses are shown in table 32. 

i4 

8 The first two columns of table 32 identify the design pavement (DES) 

4 and the as-constructed pavement (CON) for each of 47 runs of the spreadsheet 8 demonstration PRS system. The next four columns give physical inputs for 1 initial four- lane ESAL (W,) , initial serviceabil,.~ty (Po) , PCC thickness (D,) , D and PC6 compressive strength (F',). For all cases in the study (DES and 

P I$ CON), the initial design lane ESAL (W,) is specified to be 45 percent of W,. 

1 The next four columns give economic inputs 'for discount or interest 

g rate (i), bid price (BP in $/sy), the maintenance cost parameter (rn in $/sy) ia; 
Table 32. Sensitivity anal nee-related payment plan 

WS 31 400 4.3 9.0 4.0 0.28 1o.00 24 8.01 48.70 6 0 0 30 100. CON A 400 4.6 9.5 4.5 

CON : >30 ? 47.41 6 6.35 21.2 36.35 121.2 Z 400 4.0 8.5 3.5 14 3.36 50.1 6 5 -6.15 -20.5 23.85 79.5 

DES 3.1 !WI 4.3 1 9.0 4.0 028 10.00 , 11 8.04 58.81 5 0 0 30 100 CON A >30 ? 57.28 5 6.83 228 36.83 1P.8 

4 12 3. 60.91 5 -0.33 31.1 20.67 68.9 

8 3.2. $00 4.3 0.0 4.; - 21 1 8. 61.53 5 0 030100 

CON A 4.6 9.5 4.5 1, ? 57.87 5 6.07 20.2 36.07 120.2 

CON Z 4.0 8.5 3.5 8 ' -8.24 47.5 21.76 72.5 

+--+++Q- >3o a8.04 7 59.10757 5 6-45 o21.5 o 36.45 3o 121.5 10- 

CON Z 0.34 ' 12 3.39 61.19 5 -8.80 -29.3 21 26 70.7 I 

hvated to k28 - 1 22 fr7 - 1.241 31.2 + 0.063 fpc28] 

" Vehi Opw. Cosb (Smile) - 14.32 x (Tot ESAk) x (1.40 - 0.088 x PSI) 
in equation 37, and the vehicle operating cost parameter (q in percent) in 

equation 38. I 

In the right half of table 32, four performance indicator outputs and 

four payment plan outputs are shown. These correspond to the demonstration 

outputs that were listed in table 31. The four performance indicators are 

the year at which PSI = 2.5, the corresponding cumulative ESAL, the year 

(YMAC) at which EUAC is minimum, and the corresponding minimum value (MAC) 

of EUAC . 

Payment plan outputs in the last four columns of table 32 are the bid 

price adjustments, both in $/sy and as a percent of bid price, and the 

resultant payment, both in $/sy and as a percent of bid price. The last 

column contains 100 times the pay factor for the as-constructed pavement 

lot. Values in the last column, after division by 100, have been used as 

the dependent variable in the illustrative sensitivity analyses. More 

extensive analyses would involve one or more of the remaining output 

variables, and would perhaps include load ratios that are determined by the 

ESAL for which PSI = 2.5. 

The physical input columns show that all elbven designs have the same 

PCC specifications, namely, Po = 4.3, D, - 9.0 in (22.9 cm), and F', = 4000 

psi (281 kg/cm2). Moreover, nine of the designs have Wo = 500,000 ESAL (Wl = 

225,000 ESAL), whereas DES 2.1 and DES 2.2 have Wo = 400,000 ESAL and W, = 

600,000 ESAL, respectively. The remaining pairs of designs differ from DES 

1 only with respect to either the interest rate (DES 3.1 and DES 3.2), the 

bid price (DES 4.1 and DES 4.2), the maintenance cost parameter (DES 5.1 and 

DES 5.2), or the vehicle operating cost factor (DFS 6.1 and DES 6.2). I 

1 

For DES 1, the associated as-constructed pave'ments (CON A through CON Z) 

differ from DES 1 only with respect to the three primary specification 

factors (Po, D, , and F' ,) . Taken together, DES 1 and CON A through CON Z 

represent a 3 by 3 by 3 factorial. study of Po vallbes at 4.6, 4.3, and 4.0, D, 

values at 9.5 in (24.1 cm), 9.0 in (22.9 cm), and 8.5 in (21.6 cm), and F', 

values at 4,500 psi (316 kg/cm2), 4,000 psi (281 Kg/cm2), and 3,500 psi 

(246 kg/cm2). It can be seen that DES 1 is at th4 middle level for all 

three factors, that CON A is at the high levels, bnd that CON Z is at the 

low levels. Levels and increments of the three PCC factors have been 

selected so that DES 1 represents an average AASH~ Road Test rigid pavement 

section. The CON A pavement is assumed to be as huch superior to DES 1 as 

might be expected in construction practice. The $ON Z pavement is assumed 

to be the minimum level of construction that woulb be tolerated by the 

specification acceptance plans. The final column of table 32 shows that, 

relative to DES 1, pay factors calculated by the bpreadsheet program range 

from 1.214 for CON A to 0.708 for CON Z. i 

I 

For each remaining desiga in table 32, CON A and CON Z have the same 

PCC factor levels as for DES 1, and the same level for non-PCC factors as 

the design with which they are compared. For example, DES 6.1 and DES 6.2 

and the corresponding CON A and CON Z differ fromlDES 1 only with respect to 

the vehicle operating cost parameter (q = 5 perceQt for DES 6.1 and q = 15 

percent for DES 6.2). I 
In summary, DES 1 with CON A through CON Z provide sensitivity data for 

a complete factorial of PCC factors. The remaining five pairs of design 

pavements, together with CON A and CON 2, provide sensitivity data for five 

different non-PCC factors when all remaining non-PCC factors are at the DES 

1 level. . _ I.* 

Analysis of variance (ANOVA) and regression analysis were performed for 

the 26 pay factors in the top part of table 32 for CON A through CON Z 

relative to DES 1. Results of the analyses are given in table 33. The 

dependent variable for the analyses is the decimal value of the pay factor 

and not the percentage values that are given in table 32. The three 

independent variables are Po, D,, and F',, where ea~h is7expressed as a 

deviation from its central (DES 1) value divided by its half-range. Thus, 

for example, Po becomes Pod = (Po - 4.3)/0.3. The deviation variables thus 

have values of -1, 0, and +I for their linear form. Corresponding quadratic 

forms are, for example (3pOdZ - 2), and have values of 1, -2, and 1 at the . 

three values of Po. 

As shown in the ANOVA portion of table 33, the 27 observations give two 

degrees of freedom for each main effect, one for the linear term and one for 

the quadratic term. Each two-factor interaction has 4 degrees of freedom 

and can be separated into linear x linear, linear x quadratic, quadratic x 

linear, and quadratic x quadratic. Finally, the three-factor interactions : 

provide 8 degrees of freedom and are considered to represent unexplained 

variation (experimental error). 

The middle ANOVA column shows that 95.5 percent of the total variation 

is explained by the linear component of P,, and that 2.32 percent and 1.62 

percent, respectively, of the total variation is explained by the linear 

components of D, and Ft,. Thus, the three linear components account for 

99.44 percent of the total variation among the 27 pay factors. The ANOVA 

shows that the quadratic effect of D,, the quadratic effectof F',, and two 

interaction effects are also highly significant at less than the 1 percent 

level, i.e., SL = (00). The regression coefficients for the seven 

significant terms are shown in the last column of table 33, including the 

constant term for the equation which is the mean value of the pay factor 

(0.9851). The R-square for the regression analysis is 0.999, and the 

root-mean-square residual is RMS = 0.0053. Thus, the pay factor regression . equation gives an exceptionally close fit to the pay factor data, and 

predicts all observed values to within 0.01. 

If the significant quadratic and interaction terms are ignored, the 

resulting approximation equation in terms of the original factors is: 

Pay Factor (PI?) = -2.5254 + 0.6435 Po + 0.0602 D, 

+ 0.0503 F', (in ksi) (62) 

whose R-square is 0.994 and whose RMS residual is 0.013. Thus, the 

approximation equation predicts all observed pay factors to within about 

0.02. ' 
Table 33. Variance and regression analyqis for pay factor 

dependence on primary PCC specifications. I 

........................... ------------------- -------------------=------ ------ ------------- ------------ 

PCC SPECIFICATIONS AND ANOVA REGRESSION 

REGRESSION VARIABLES df Percent of Signif. EQUATION FOR 

Total SS Level PAY FACTOR ----_---------A_---------- 

------------I------------- ......................... .......................... ------------- -------------- 

Initial PSI = Po 2 95.50% (001 --- ........................... -------------------------- -------------- 

Lin: Pod = (Fo- 4.3)/0.3 1 95.50% (00) 0.1931 

Quad: (3 Pod - 2) 1 0.00% (NS) --- ....................... ........................... 8-4=========== 

PCC Thick. (in) - D, 2 2.40% (00) --- ........................... -------------------------- -------------- 

Lin: Dd = (D, - 9.0)/0.5 1 2.32% (00) 0.0301 

Quad: (3 ~d~ - 2) 1 0.07% (00) -0.0031 ==--------i--- -----------=----------------------- ......................... .......................... ------------- ------,--,-

PCC Compr. Str. (ksi) = I?', 2 1.67% (00) - - - --------------------------- -------------------------- -------------- 

Lin: Fd= (F'c - 4.0)/0.5 1 1.62% (00) 0.0252 

Quad: (3 F: - 2) 1 0.04% (00) - 0.0024 ........................... .......................... ---------------------I_--- 

.......................... ---------I_-- ----------_.-- 

Po * D, Interactions 4 0.01% (NS) - - - ........................... .......................... -------------- Po *Ft , Interactions 4 0.03% (NS ) --- ........................... .......................... -----------*-- 

D, * F', Interactions 4 0.36% (00) - - - ........................... -------------------------- -------------- 

Dd 2k Fd I 0.33% (00) -0.0138 

Dd * (3 Fd2 - 2) 1 0.03% (05) 0.0024 

Other 2 0.00% (NS) --- ........................... ........................... .......................... ......................... -------------- -------------_ 

Po * D, * F', 8 0.02% 

Interactions (Error Term) MS = 0.218 ........................... ........................... -----------_-------------- .......................... 

Mean Pay Factor = 0.9851 

R-square = 0.999 

RMS residual = 0.0053 

Approximation Regression Equation Without Quadratic and Interaction Terms: 

Pay Factor (PI?) = - 2.5254 + 0.6435 Po + 0.0602 D, + 0.0503 F*, 

R-Square = 0.994 RMS Residual = 0.013 
The practical importance of the foregoing regression analysis is that 

it provides a way to derive pay factor equations for the economic life 

methodology. Although the pay factor is given in principle by equations 55, 

56, and 57, these equations involve CON YMAC, the year at which EUAC is a 

minimum for the as-constructed pavements. Although CON YMAC is indeed a 

function of P,, D, and F', , it is virtually impossible to derive an6 explicit 

relationship among CON YMAC and its determinants. 

On the other hand, it would be quite feasible to extend the PRS 

spreadsheet program to include the derivation of a pay factor regression 

equation that covered specified ranges for Po, D,, and F',. If desired, the 

procedures could be further e~tende~to include other construction 

variables. 

It is noted that the NJDOT load ratio methodology involves a pay factor 

equation (equation 34) whose determinants are the years to terminal 

serviceability for the design pavement and the as-constructed pavement. 

Thus, in conjunction with the AASHTO equation 41, the pay factor equation 62 

is "almost explicit" with respect to Po, D,, and F', 

Sensitivities of the specification pay factor to selected changes in 

PCC and non-PCC factors are shown in table 34. In part A, PF sensitivites 

to Po, D,, and F', are calculated from the approximation pay factor equation 

62. For this linear equation with no-cross products, the PF change per unit 

of any determinant is simply the determinant's coefficient. For example, 

the change in PF per inch of PCC thickness is the coefficient for D,. Thus, 

the equation predicts that PF will change by about 0.06 per inch (0.0236 per 

cm) of thickness change. 

The first three lines of table 34 give base levels for each PCC factor, 

10 percent changes in the base levels, and PF changes that result from the 

factor changes. It can be seen that a 10 percent change in Po produces 

almost five times as much PF change as does a 10 percent change in D,, and 

over ten times the change produced by a 10 percent change in F',. 

The PF change for 10 percent change in D, is over twice as much as for 

a 10 percent change in F',. Thus, it appears that the relative impact of Po, 

D,, and F', changes on PF are in the approximate ratio of 10-2-1. These 

relative sensitivities are of course related to the relative effects of the 

three factors on the PSI histories (table 30 and figure 37), and the 

subsequent effects on maintenance and vehicle operating costs. 

The last two lines in table 34 show how much each factor must be 

changed to produce a 0.01 change in the pay factor. The required percent 

changes from base levels are 0.4 percent for Po, 1.9 percent for D,, and 5 

percent for Ft,. Pay factor sensitivity to changes in non-PCC factors is 

also illustrated in table 34. The results shown are derived from the data 

given in the bottom part of table 32. 

The five non-PCC factors are initial 4-lane ESAL rate (W,), interest 

rate (i), bid price (BP), annual maintenance cost (m) at PSI - 2.5, and the 

percent (q) of vehicle operating costs to be considered. For each factor, 

base levels are those for DES 1 in table 32, as shown in the top line of 

table 34. The next line shows a 10 percent increase for each base level, 

165 
Table 34. Sensitivity of specification pay factor to selected changes 

in PCC and non-PCC factors. 

A. Illustrative Pay Factor Sensitivities to Changes in Primary PCC Factors 

PRIMARY PCC SPECIFICATIONS FACTORS 

__------------------------------------------------- -_--------------_------------------------------------ 

Initial PSI PCC Thickness PCC Compressive 

(Po> (D,) Strength (F',) 

__----_-----------------------------------_-----_ ___-----__--_--_--------------------------------------------------------- 

Base Level for 

PCC Factor 4.3 9.0 in. 4.0 ksi ___-__------_-------*--------------------__ ----_---------_--------------------------------------------------------- 

10% Change in 

Base Level 0.43 0.9 in. 400 psi ......................................................................... 

Corresponding Pay 

Factor Change 0.276 0.054 '0.020 

__--_____---_--_--_--------------------_-__-___________ --__--_-_-_---_--_----------------------------------_-------------------- 

Factor Change Needed 

to Produce 0.01 PF 

Change 0.02 0.17 in 200 psi 

__--------------_-_------------------------------------------------------ 

Corresponding Percent 

of Base ~evel 0.4% of 4.3 1.9% of 9.0 in 5% of 4 ksi 

_____-__----_--_--_-_---------------------------------------~--------- _____-__-_d_--_-__-__--_--_-------------------------------------------- 

B. Selected Pay Factor Sensitivities to Changes in Non-PCC Factors 

SELECTED NON-PCC FACTORS ..................................................... _--_-------------------------------------------------- 

Initial Interest 

ESAL (W,) Rate (i) I Price Cost (m) Bid I Maint. for VOC 

____--------_--_-------~---------_-----___~----__---__-__ __-___-___-_--_--------------------------------------------------------- 

Base Level for 

Non-PCC Factor 500,000 ESAL 6% $30.00/sy $0.28/sy 10% 

___----_---_--_-__-----------------------------------------------_~--- _----_--___---__------------------------------------------------_----- 

10% Increase in 

Base Level 50,000ESAL 0.6% $3.00/sy $0.028/sy 1% 

__-----_--__------------------------------------------------------------- 

Corresponding 

Change in Pay 

Factor for CON A +0.012 -0.004 +0.022 +0.0002 +O .009 

___-__--_-------_-------------------------------------------------------- 

Corresponding 

Change in Pay 

Factor for CON Z -0.010 +0.005 -0.003 -0.0005 -0.013 

_____--___-__--_--_----_----------------------------_------------------- ______-_______-_-_----------------------------------------------------- 

Estimated 

Factor For +40,800 -1.5% +1.37/sy +$1.20/sy +1.1% 

Change to CON A ESAL 

Produce _____________*_____------------------------------------------- 

+O.OlPF For -51,300 +1.1% - $9.09/sy -$0.60/sy -0.8% 

Change CON Z ESAL 
and the following two lines show corresponding PF changes for the CON A and 

CON Z as-constructed pavements. In table 32, it was shown that the CON A 

pavement has Po = 4.6, D, = 9.5 in (24.1 cm) , F', = 4500 psi (316 kg/cm2), 

and that the CON Z pavement has P, = 4.0, D, = 8.5 in (21.6 cm), and F', = 

3500 psi (246 kg/cm2) . Thus, table 34 shows PF sensitivities to non-PCC 

factor changes for the two extremes of change for CON Z. For the interest 

rate (i), the CON A change is negative, but is positive for the remaining 

factors. In magnitude, the only pay factor change that equals the 

corresponding changes for PCC factors is the bid price effect (t0.02) on 

as-constructed pavements. 

For the 10 percent change in base levels of the non-PCC factors, the 

third and fourth lines of table 34 show corresponding pay factor changes 

that range in magnitude from 0.00 to 0.02, approximately. For all five 

factors, the pay factor change for CON A is opposite in sign to the PF for 

CON A. Next lower in magnitude are the effects of changes in initial ESAL 

(W,) and the percent (q) of VOC used. These changes produce PF changes of 

around 0.01 in magnitude. A 10 percent interest rate (i) change produces 

about 0.005 change in the pay factor, and virtually no PF change is induced 

by 10 percent change in the annual maintenance cost parameter (m). Since 

initial ESAL and bid price cannot be controlled in practical applications, 

it appears that only the VOC factor needs further attention in further 

development of PRS systems. 

COMMENTS ON THE DEMONSTRATION SPECIFICATION ALGORITHMS AND RESULTS 

The following comments relate to the procedures and results that were 

presented in the first four sections of this chapter. For the most part the 

comments are extensions of statements that were made in the course of the 

chapter presentation, and are generally listed in the order of their 

occurrence within the chapter. 

1. It is quite clear that further development is needed for the 

algorithms that have been used for routine maintenance costs (equation 37) 

and for vehicle operating costs (equation 38). The present formulations 

appear to give imbalance between the two types of costs, and may give unduly 

low weight to RMC and unduly high weight to VOC. A better rationale needs 

to be determined for annual costs. 

2. The annual cost rationale might be related to estimated costs for 

various distress levels and types (option a in figure 33). However, the 

only available distress prediction equations appear to be those produced in 

the COPES It has not been fully determined to what extent the 

predicted distress levels are sensitive to the PCC factor changes. Thus, 

costs based on the COPES equations might produce the same economic lives for 

both the design and constructed pavement, and therefore pay factors of 1.00 

for all types of construction. 

3. If serviceability levels are used to produce cost histories, 

economic life and load ratios will depend strongly upon the serviceability 

prediction equation that is used. It was demonstrated, for example, that 

pay factors based on COPES serviceability predictions would give the same 

pay factors for all constructed pavements in table 32. 
4. The demonstration specification gave what appears to be an unusually 

small number of years (WC) at which minimum EUAC was reached (see table 

32). For most cases the minimum occurs when seyviceability is quite high 

after only 4 to 6 years of performance, It is t~hus questionable as to 

whether YMAC years are indeed turning points in rigid pavement life. 

5. Since the AASHTO PSI equation is much mofe sensitive to initial 

profile in terms of P, than to any other M&C factor, it may be advisable to 

derive one payment plan for P, and another for the remaining PCC 

specification factors. Perhaps the overall pay Eactor could be the product 

of the individual pay factors. 

6. In the economic life methodology, the difference between minimum EUAC 

for the CON and DES pavements is multiplied by the Gy factor (equation 55) 

whose variables are the interest rate and the CON economic life. Strong 

consideration should be given to the use of DES economic life in the G, 

factor. Thus, G, would be a constant multiplier for all EUAC differences 

throughout the construction project. Otherwise,, it appears that Gy is 

relatively low for poorly constructed lots and relatively high for superior 

lots. 

7. More study needs to be made of the conditions for which the 

cumulative present worth of total annual costs (equation 47) is relatively 

constant over all years, as was the case for the demonstration 

specification. If this constancy prevails for all practical cases, then a 

much simpler algorithm (equation 53) can be used to calculate EUAC. Such 

simplification would greatly enhance further study of the mathematical 

properties (e.g., VOC derivatives with respect to years) of the EUAC 

function. 

8. No effort was made in the present study to determine practical 

limits for the pay factor (equation 57). Further study should produce a 

rationale for such limits, as has been done for the NJDOT load ratio 

methodology. 

9. Further attention should be paid to the question of incorporating 

inflation rate into the discount factor, as has been done in the NJDOT 

methodology (see equation 30). 

10. It would be quite useful to extend the demonstration specification 

algorithms to include (1) factorial pay factor data as in the top portion of 

table 32, and (2) regression analysis as shown in table 33. It seems likely 

that the resulting regression equation would be quite adequate for all 

applications of the pay factor function, including the development of its 

associated operating characteristic. Although these procedures are 

unnecessary to the load ratio methodology, they represent the only practical 

way to derive a pay factor function for the economic life methodology. 

11. The importance of sensitivity analyses for the specification 

payment plan cannot be overestimated. Only when these analyses have been 

fully developed for a given plan can both the contractor and SHA be well 

informed on how the pay factor changes with changes in any input variable. 

12. Sensitivity analyses have not been fully developed for the 

demonstration PRS system. For example, no effort was made to determine pay 

168 
factor sensitivity to changes in the subgrade modulus (k) or to simultaneous 

changes in PCC and non-PCC factors. Further development should not only 

extend to additional variables but should produce factorial pay factor data 

for all factors within the same matrix. It will thus be possible to learn of 

curvilinear and interacting'effects of the incut factors. 

13. Although a formidable task, differential calculus should be applied 

to the whole set of equations that are used to determine the specification 

pay factor. If this taskcan be accomplished, sensitivities can be 

calculated from pay factor derivatives with respect to all input factors. 

The results can be used'.to make improvements in the specification rationale. 

14. At present, there are three competing methodologies for rigid 

pavement PRS development: (1) economic life methods as used in NCHRP Project 

10-26A, (2) pavement life or load ratio as used in the NJDOT approach, and 

(3) life-cycle cost methods as conceptualized in this study. Further 

research is needed to determine major pros and cons for the three methods. 

Many of the needed comparisons can be done through sensitivity analyses. 

15. The valj-dity of any PRS methodology depends greatly upon the 

validity of the primary performance equations that are used to estimate 

pavement condition and life. Validation of existing equations and 

derivation of new equations must perhaps await the results of SHRP and other 

field studies of pavement performance. 
I 

I 

I I 

I 

i CHAPTER 8 I 

i SUMMARY AND RECOMMENDATIONS FOR FURTGER RESEARCH 

i 

I I 

S Y 

i 

Much emphasis has been placed recently on the development of 

performance-related specifications (PRS) for both rigid and flexible 

pavements; so much so that the Federal Highway Administration has made it 

one of its High-Priority National Program Areas. This emphasis has come 

about. as a result of a recognized need to better kontrol the materials and 

construction (M&C) factors that have the most effect on performance while 

simultaneously relaxing (or de-emphasizing) the c~ntrols over those M&C 

factors that have little effect on performance. In other words, procedures 

are needed to design and construct better and more cost-effective pavements 

by inducing highway engineers and contractors tofocus more attention on 

such factors as slab thickness, PCC strength and initial smoothness and less 

attention (perhaps) to such factors as subbase t+$.ckness and strength. 

These PRS procedures (or systems) have been ?nd are being programmed to 

reward contractors for constructing better pavements than specified and 

penalize them for building poorer pavements. The basis for the rewards and 

penalties are selected pavement performance prediction models that consider 

measured values for various M&C factors (as proviged by the contractor) in 

estimating future performance. Thus, if the conpractor builds a pavement 

that does not provide the expected (predicted degign) performance because of 

failure to meet one or more M&C specifications, a penalty would be assessed 

by receiving only a fraction of the bid amount. Conversely, if a pavement 

is built that exceeds the expected performance, the contractor would receive 

an amount higher than the original bid. The amount of the penalty 

(disincentive) or reward (bonus/incentive) depends upon how far the 

contractor was below or above the various M&C specifications. In M&C 

specifications that are highly performance-related, a contractor would be 

penalized heavily for falling a half-inch (1.27 cm) below the specification 

for a significant factor like slab thickness but only minimally for falling 

an inch (2.54 cm) or so below the specification for a less significant 

factor like subbase thickness. Obviously, the idpal PRS system would 

account for the levels of all the M&C factors delivered by the contractor 

(on a day-to-day or lot-to-lot basis) in assessing the penalty or reward. 

In keeping with the objectives of the contract, this study has 

furthered the development of a PRS system for PCC pavements (such as that 

described above) in several key areas: 

Framework for Development of Performance-Relaced Specifications 

Under NCHRP Project 10-26, "Data Bases for Performance-Related 

Specifications," completed in 1985, it was basically concluded that existing 

data bases were not adequate for direct derivatio~ of the necessary 

relationships for PRS. (85.4) As a result, a key member of the NGHRP Panel, 

derived an approach that overcame the biggest proqlem with using existing 

data bases and performance prediction relationshias for PRS development. (88.4) 

His approach became was the basis for PRS develop4ent under NCHRP Project 

10-26A for asphalt concrete pavements as well as qhis study for PCC 
pavements. (87.4y 88.1) Chapter 2 of this report provides a refinement and 

summary of that framework as it applies to PCC pavements. 

Identification of Relationships Available to Establish the Connection 

Between M&C Factors and Various Measures. of Pavement Performance 

Since there are no existing pavement performance prediction relationships that expressly consider the multitude of M&C factors, a two-stage 

mechanism was established which allowed the existing performance prediction 

relationships to account for the effects of more M&C factors. The first 

stage consisted of the actual pavement performance prediction relationships 

(referred to as primary prediction relationships or PPRs) which did include 

some M&C factors such as slab thickness, concrete strength and initial 

serviceability (riding quality). To allow other M&C factors to have an 

influence on these PPRs, a second stage of relationships (referred to as 

secondary prediction relationships or SPRs) was identified. Using these 

SPRs, the effect of additional M&C variables could be considered by 

predicting what are now independent variables in the PPRs. ~lthough these 

SPRs could be used to estimate the value of more than one independent 

variable in the PPRs, the focus in this study was on those that could be 

used to predict various properties of the hardened concrete, particularly, 

strength and elastic modulus. 

Chapters 3 and 4 document the work that was accomplished in this study 

by identifying the available primary and secondary prediction relationships 

and in evaluating existing data bases that could be used to develop these 

relationships. Appendixes A through E are also part of this documentation. 

Development and Conduct of Laboratorv/Field Test Programls) to Quantifv 

New Relationships Needed for PRS Development 

Because of its extensive use as the measure of concrete strength in 

most of the available rigid pavement performance prediction relationships, 

PCC flexural strength was selected in this study as the one key determinant 

of rigid pavement distress/performance to use in demonstrating the two-stage 

approach to PRS development. Although flexural strength is considered an 

M&C variable, it (unlike slab thickness) is not directly controllable. 

Since it is dependent on so many other M&C factors (i.e., water content in 

mix, cement content, aggregate type, air content, etc.), it was the ideal 

choice for the demonstration PRS system. 

Based upon a thorough review of existing secondary prediction 

relationships, it was determined that there were none available which had 

more than two M&C factors as .independent variables. This included those 

relationships for PCC flexural strength. In addition, none of the 

relationships provided any of the basic measures of statistical accuracy 

(i.e., coefficient of determination, standard error of estimate, etc.) 

needed to treat their variability or lack-of-fit. Consequently, a 

laboratory study was planned and executed in order to provide a basis for 

developing new prediction relationships. A fractional factorial of seven 

factors (each at two levels) was used in the experiment design. The seven 

factors included: (1) coarse aggregate type, (2) coarse aggregate maximum 

size, (3) fine aggregate modulus, (4) air entraining agent quantity, (5) 

coarse aggregate quantity, (6) cement quantity, and (7) water quantity. 

171 
Tests on the plastic concrete (just after mixing~) included slump and air 

content. Tests on the hardened FCC specimens copsisted of compressive 

strength (7- and 28-day), flexural strength (7-d~y), elastic modulus 

(28-day) and splitting (indirect) tensile streng~th. In addition, 

measurements were made to determine the average unit weight and yield of 

each batch. Using standard analysis of variance and statistical regression 

procedures, a series of relationships was derived, most of which were 

directly applicable to the new demonstration PRS system. 

The results of the laboratory studies and experiments are presented in 

chapter 5 of this report. Because of the comprehensive nature of the lab 

study, many of the relationships derived have wider application (for 

engineering purposes) than for PRS development. 

With respect to field studies, none were conducted. It was initially 

envisioned that some field measurements and performance data could be 

collected to either verify or calibrate existing PPRs. As the study 

progressed, however, it was decided that the data necessary to improve any 

existing PPRs would be expensive to obtain and not very cost-effective. 

Thus, the primary efforts were directed towards the laboratory experiment 

while field studies were deferred to future research. 

Demonstration Performance-Related S~ecification System 

The last major objective of the study was the development of a 

demonstration PRS for PCC pavements that was to be as parallel as possible 

to the PRS for asphalt concrete pavements developed under NCHRP Project 

10- 26A. '88-1) The specific procedures and algorithms needed for PRS 

development were covered in chapter 6 of this report while the development, 

application, and sensitivity of a computerized demonstration PRS for PCC 

pavements was presented in chapter 7. It is important to note that although 

the demonstration PRS is very comparable to the NCHRP 10-26A system, it did 

have some shortcomings (from both a conceptual and application standpoint) 

that led to the identification of two other appoaches for assessing 

contractor penalties and rewards. One of these was the method developed at 

New Jersey DOT; the other is a method conceptualized based on the life-cycle 

cost analysis model presented in the 1986 AASHTO Guide.(84.6a86.3) 

I 

The demonstration PRS for PCC pavements wasdeveloped in the form of a 

Lotus 1-2-3 spreadsheet. It allows users to determine the fraction of a 

contractor's bid price that should be received for the pavement that is 

actually built (on a lot-by-lot basis). If the contractor builds a pavement 

that is projected to perform better than the design (specified) pavement, 

the fraction will be greater than 1 and a bonus will be received. If the 

contractor builds a pavement that will perform worse than the design 

pavement, the fraction will be less than 1 and a penalty will be assessed. 

The demonstration PRS considers the three primary M&C factors in the AASHTO 

rigid pavement performance prediction equation; slab thickness, initial 

serviceability and, of course, PCC flexural strqtgth. Thus, it is possible 

for the contractor to not meet the specificationfor one factor (while 

exceeding the other two) and still be rewarded. ' 

I 

The rest of this chapter is devoted to proyiding recommendations for 

further research in the development and enhancedent of performance-related 
specifications. All of these recommendations apply to PRS systems for PCC 

pavements, however, some also apply to asphalt concrete pavements. 

FURTHER LABORATORY STUDIES FOR SECONDARY PREDICTION RELATIONSHIPS I 

This study identified initial pavement profile (serviceability), slab 

thickness and PCC flexural strength as the principal determinants of rigid 

pavement distress and performance. This assessment was based on an 

examination of the existing primary prediction relationships (PPRs), 

particularly the AASHO Road Test rigid pavement performance equation which 

has serviceability as its performance criteria. To permit consideration of 

the effects of other M&C variables on rtgid pavement distress and 

performance, several new secondary prediction relationships (SPRs) were 

derived to relate other PCC mix factors to flexural strength. The 

derivation of the new SPRs was based on a small but statistically 

sophisticated laboratory study. The results of the laboratory experiments 

and statistical analyses turned out to be quite good, however, they by no 

means constitute a comprehensive study. Rigid pavements can exhibit 

excessive distress and poor performance as a result of (1) low freeze-thaw 

durability, (2) high concrete shrinkage, (3) high concrete thermal 

coefficient, (4) high permeability, and (5) rapid loss of skid resistance. 

There are laboratory tests for each of these and some of them are even found 

in some of the available primary prediction relationships, both empirical 

and mechanistic. Thus, it is recommended that effort in a future laboratory 

study be directed towards measuring these concrete properties (as a function 

of the various M&C factors related to the PCC mix) as well as all the tests 

that were conducted in this study (both on the plastic and hardened mix). 

Besides the limitation on the amount of PCC testing carried out under 

this project, only two levels for each of the seven experimental variables 

was considered in the factorial design. Other factors such as cement type, 

fine aggregate type and air-entraining agent type were held at only one 

level. Also, to better treat curvilinearity that may exist between the 

dependent variable and some of the independent variables, some of the 

experimental factors ought to be run at three levels in a future lab study. 

Candidates for three level variables to consider this potential nonlinearity 

include water content, cement content and air-entraining agent content. 

Coarse aggregate type, fine aggregate type and cement type are examples of 

factors that could be run at three ormore levels because of the number of 

different types of each there are. Following are recommendations on the 

extent of a future laboratory test program: 

Coarse aggregate type (CAT) - Five levels: Choose the most commonly 

used types from a list that includes limestone, sandstone, quartzite, 

granite, syenite, and dolomite. Only a siliceous river gravel and a 

crushed limestone were considered in this study. 

Coarse aggregate maximum size (CAM) - Two levels: Experimental 

results indicated that this was significant in some cases, but not 

enough to justify more than two levels. 

* Fine aggregate modulus (FAM) - Two levels: The grain size of the 

fine aggregate appeared to be more significant in some cases than the 

173 
maximum size of the coarse aggregate (CAM), but again not enough to 

warrant more than two levels. 

e Air-entraining agent quantity (AEQ) - Three levels: Of the two 

levels this was run at in this study, one was zero (none). It is a 

significant factor and it is not likely that factors such as air 

content and concrete strength are linearly proportional to the line 

that connects the "none" endpoint to the "some" endpoint, Thus, a 

midlevel between the two would be very useful. 

e Coarse aggregate quantity (CAQ) - Two levels: Although this was a 

significant factor in the analysis, from an engineering standpoint it 

is not worth examining at more than two levels unless the funds are 

available. 

e Cement quantity (CEQ) - Three levels: This has a large effect on PCC 

mix properties (particularly strength) ind is definitely worth 

studying at more than two levels. 

Water quantity (WAQ) - Three levels: Like cement quantity (CEQ), 

this had a large effect on the various PCC mix properties and should 

be studied at more than two levels. 

Fine aggregate type (FAT) - Two levels: A commonly used quartzitic 

sand was used for this experiment. Since its size did have some 

effect on various properties of the mix, it may be worth studying the 

effects of one other commonly used fine aggregate (perhaps a 

manufactured sand). 

Consolidation (CSL) - Two levels: All samples tested for this study 

were prepared according to ASTM specifications. Since proper 

consolidation is not always achieved in the field, it may be 

desirable to examine the effects of poor consolidation in a future 

laboratory study. Two levels of rodding should be sufficient to 

provide a high and a low entrapped air content. 

Mineral Admixture (Fly Ash) - Three levels: One beneficial admixture 

not considered in this laboratory study is fly ash. In addition to 

its cost effectiveness, pozzolans such as fly ash can improve 

concrete physical characteristics such as workability, strength, and 

durability. Consequently, fly ash admixtures are being used more and 

more frequently by SHAs. The suggested levels of fly ash are zero 

(none), and an optimum substitution of cement with either an ASTM 

Type F or Type C fly ash. This is probably not a high-priority 

factor compared to those identified above. 

e Cement type (CET) - Two levels: The most commonly used cement (Type 

I) was used to prepare the PCC test specimens for this experiment, 

This probably would be sufficient for use in a performance-related 

specification system, however the common use of Type I1 and Type I11 

cements with varying chemical and physical properties may make it 

worthwhile to consider two types of cemQnt. This is probably a lowpriority factor. 
* High-range water reducer (HRWR) - Three levels: Although potentially 

significant, this study did not examine the effects of high-range 

water reducers (also known as superplasticizers) on the various PCC 

mix properties. Because of its significance, it may be desirable to 

examine the effects of an ASTM C494 Type G high-range water reducer 

in a future laboratory study. The three levels indicated would 

include zero (none), and two dosage levels (concentrations) as 

recommended by the manufacturer of the selected high-range water 

reducer. This is probably a low-priority factor. 

A full factorial of all these combinations would produce an experiment 

of (5*26*35 or) 77,760 cells. Eliminating the last three factors, taking 

advantage of fractional factorial experiment design techniques, and the fact 

that some tests would not need to be run in all the cells would probably 

still produce an experiment that would be too costly to conduct. Thus, it 

would likely be necessary to do some further prioritizing and "cutting backM 

of factors and/or levels to achieve the most cost-effective results in the 

recommended future laboratory study. 

FIELD STUDIES RELATED TO PERFORMANCE-RELATED SPECIFICATIONS 

The principal objective of any future field studies would be to verify 

existing relationships and/or derive new relationships for relating the 

principal determinants of rigid pavement distress and performance to rigid 

pavement response under a single load and to rigid pavement distress after 

repeated (known) loadings. These relationships would further the 

development of PRS since they would likely provide a better means of 

treating various M&C factors in the analysis process. 

The experiment design for such a field study would use the secondary 

prediction relationships to identify the most appropriate M&C factors and 

levels that determine PCC strength, durability, thickness and initial 

pavement profile (serviceability) of the experimental pavement test 

sections. For example, 32 test sections could be constructed as a one-half 

replicate of a 26 experiment design. The six experimental factors, each at 

two levels would be as follows: 

* Initial pavement profile. 

Slab thickness. 

* Coarse aggregate type. I 

Cement content. 

I 

Water content, 

I Air content. 

The last four of these factors all have a measurable effect on the flexural 

strength of the concrete. 

From a- construction standpoint, all other pertinent factors for the 32 

experimental sections (ie, soil support, subbase type, thickness and , 
strength, reinforcement, j oint spacing, load transfer, etc . ) would be held 

constant. The test sections would be evaluated for response (i. e. , deflection and strain) under a load of varying magnitude and then for 

fatigue cracking, faulting, serviceability (roughness) and other types of 

distress after repeated uniform loadings. The Aesults would demonstrate the 

role and relative importance of each experiment41 factor in the prediction 

of pavement response and performance. They wou4d thus provide improved 

primary prediction relationships for the development of better PRS systems. 

It is important to note that several of these factors will be 

implemented in SHRP SPS-2, but not to the detail that is recommended above 

for the pavement field studies. 

FURTHER DEVELOPMENT OF PERFORMANCE-RELATED SPECIFICATIONS 

One of the major accomplishments of this study was the development of a 

demonstration PRS system for PCC pavements. It was based in large part on 

the conceptual system outlined in NCHRP Project 10-26A for asphalt concrete 

Where the NCHRP 10-26A work fell short in some of the key 

areas related to PRS development for rigid pavements, methods and techniques 

were adopted from PRS developed by NJDOT.(84.6) The new PRS does produce 

results, but as observed in chapter 7, there are some problems that need to 

be overcome before it can be reasonably applied for rigid pavements. Below 

is a list of the key areas where further work is needed to overcome these 

problems. They are not in order of importance, but in the order they are 

addressed in chapter 6. 

1. Development of specific acceptance plans. As indicated in chapter 

6, this refers to the set of rules and definitions that govern acceptance 

and rejection of the contractor's work for a given lot. The acceptance 

developed by NJDOT are quite good and make an excellent starting point in 

developing plans for wider application. 

2. Treatment of material and construction variability. One factor that 

was not treated in the demonstration PRS system was the effect of 

variability in the material properties and construction characteristics 

delivered by the contractor. At present, if twa contractors deliver 

pavements that have the same predicted (design) performance, but vastly 

different variabilities in M&C factors, both would receive the same penalty 

(or reward). Obviously, the one with the least variability ought to receive 

better consideration in terms of payment. One approach is in the 

development of specific acceptance/rejection plans as described above. 

However, an alternate or additional approach would be to consider the 

effects of measured variability on reliability, i.e., the probable 

distribution of performance. Using this latter approach, a contractor who 

exercises good quality control (and achieves low variability) would receive 

more favorable consideration. 

3. Development of optimum M&C variables to be evaluated during 

construction. Three MGrC variables are used in the demonstration PRS system 

to evaluate construction: initial profile, slab thickness, and 28-day 

compressive strength. The 28-day compressive strength is used to estimate 

the 28-day flexural strength and elastic modulus used as primary 

determinants of distress, but it would be better to use 7-day compressive I 

176 
strength, since this is a more common measurement. Unfortunately, only the 

7-day flexural strength was measured in the lab study. 

4. Selection of optimum distress variables, The current demonstration 

PRS system only considers serviceability history in the analysis process, 

however, it does calculate and display pavement distress values using the 

COPES equations. At some point, it may be better to consider more types of 

distress than just serviceability. Since the COPES equations are based on 

the analysis of an observational data base, they should be studied more 

carefully before incorporating them into the system. 

5. More rational selection of cost evaluation procedures. Chapter 6 

provides a description of the conceptual cost evaluation procedure 

recommended under NCHRP Project 10-26A for PRS development. As observed, 

however, this is one key area where, in application, the NCHRP 10-26A 

methodology develops problems. In order to identify the economic life using 

"real" numbers for both the design and constructed pavement, it was 

necessary to consider vehicle op~rating costs. (Future maintenance costs 

were not enough to produce the tlupturn" in the EUAC curve). Once vehicle 

operating costs were introduced, however, they so overwhelmed the initial 

construction cost that the associated economic life (at minimum EUAC) was 

only one year. Thus, in order to produce reasonable results, only a 

fraction of the vehicle operating cost could be considered. Conceptually, 

it also did not seem correct to penalize (or reward) the contractor based 

upon the difference in costs incurred over economlc life of the 

as-constructed pavement. (It ought to be the economic life of the design 

pavement). These kinds of problems need to be thoroughly examined and 

corrected to produce more reasonable and defensible results in future PRS 

sys terns . 

6. Critical comparison of methodologies. In addition to the review of 

the NCHRP 10-26A methodology, chapter 6 also identifies and describes 

certain features of two alternative approaches to developing a PRS system 

for PCC pavements. One was the fully operational method developed and 

currently used by NJDOT. Like the demonstration PRS presented in chapter 7, 

it is based on the AASHO Road Test rigid pavement performance equation and 

considers initial serviceability (profile), slab thickness, and PCC strength 

as its primary distress determinants. Future costs are calculated based on 

a fixed (10-year cyclic) overlay policy which begins once the initial 

pavement (design and )as-constructed) is projected to reach terminal 

serviceability. Although they could easily be adapted, the NJDOT PRS does 

not currently consider future costs associated with maintenance or user 

operation in assessing contractor penalty/reward. The method has been 

thoroughly tested, however, and is complete in the sense that it has its own 

set of acceptance and payment plans. 

The other alternative method for PRS system development is one that has 

been conceptualized as part of this study and which is based on the rigid 

pavement design and life-cycle cost analysis procedure presented in the 

latest AASHTO Guide for Design of Pavement structure^.('^.^) It would also 

consider initial serviceability, slab thickness and PCC strength as its 

primary distress determinants. The life-cycle (future) costs that would be 

considered in assessing contractor penalty/reward currently include 

maintenance and rehabilitaion costs incurred over a specified analysis 
period. Rehabilitation costs would be calculated based upon the projected 

needs of both the design or as-constructed pavement to last the analysis 

period. (Thus, if the contractor builds a pavement that does provide the 

life associated with the design pavement, part of his penalty would be 

determined based upon the earlier timing and need for a thicker overlay). 

Like the NJDOT PRS, this one could be easily adapted to consider the 

difference in user costs associated with the difference between the design 

and as-constructed pavement. 

Based upon the practical difficulties associated with the current NCHRP 

10-26A approach (at least for rigid pavements), it is strongly recommended 

that additional effort be directed in the future towards examining these 

three PRS methods (as a minimum) to derive the one that is best-suited for 

concrete pavements. An essential tool for the comparisons is extensive 

sensitivity analyses for the dependence of pay factors on all pay factor 

determinants. 

7. Development of operating characteristic curves for payment plans 

that consider prediction equation uncertainties. Chapter 6 describes how 

the operating characteristic curves were developed for use in the NJDOT PRS. 

Although, this represents the state of the art as far as its application to 

pavements, it lacks the consideration of the effects of prediction equation 

uncertainties (as well as other uncertainties) in assessing contractor 

penalty/reward. Consideration of uncertainty (reliability/risk) would 

ultimately make both the client and the contractor feel better about the 

output of the PRS, therefore, it should not be overlooked in future research 

efforts. 
APPENDIX A 

SELECTED STRESS PREDICTION RELATIONSHIPS 

This appendix provides some additional select relationships and models 

that may be used to predict the response (i., stress, strain, and 

deformation) of PCC pavements subject to various kinds of loading. It is 

subdivided according to two of the four major types of PCC pavement response 

prediction models identified in chapter 3: 

Multilayered Elastic Solid. 

* Elastic Plate on Dense Liquid Subgrade. 

Selected examples of the other two types of prediction models are not 

provided here for two reasons: (1) additional empirical models were 

overlooked because of their limited application in a PRS system and 

(2) finite element models are well covered in chapter 3. 

MULTILAYERED ELASTIC SOLID 

Chapter 3 addresses many of the computer programs available for the 

prediction of pavement response using elastic layer theory concepts. In 

addition to these programs, there are two other methods for estimating 

response, graphical solution techniques and approximation functions. 

Graphical Solution Technique 

Several researchers have been involved with the evolution of graphical 

techniques to solve for elastic layer responses. These methods are 

applicable to one-, two- and three-layer pavements and increase in 

complexity with the inclusion of each additional layer. Yoder and Witczak 

provide an excellent summary of the available graphical methods which 

identifies many of the primary problems associated with : 

Superposition is required to treat the effects of more than one load. 

There is error associated with reading coefficients from graphs. 

There is error associated with linear interpolation for radii or 

depth factors not included in tables and graphs. 

Time and labor requirements are excessive. 

These problems make the use of graphical techniques impractical; however, 

they do provide an indication of the complexity of the elastic layer 

solution process. 

Approximation Functions 

Computer programs are by far the best ns for estimating pavement 

response due to load. However, there are s specific areas where even 

more rapid solutions may be required. In t 

the independent variables can be fixed (suc 

layers, Poisson's ratios, and range of laye 

derived approximation functions may be deve d to replace the standard 
computer programs. Examples of these specific cases include nondestructive 

testing based back-calculation techniques, systems-oriented pavement 

structural design programs and even performance-related specification 

i SYS terns. 

The following are regression equations developed as part of a recent 

study for the Trucking Research Institute. (89.1) These equations are for ei 

three-layer rigid pavement structure in which the load configuration is a 

simulated dual-tired single axle. All are based on interior loading 

conditions, i.e., away from the slab edge or corner. I 

Maximum Surface Deflection: 

LDEFL = - 1.870 + 0.0114*~~1*~~1*(~~3)~ + 0.998*LLOAD 

- O.l17*LEl*LE3 - 0.513*LDl*LE3 

= 0.994, SEE = 0.0298, n = 3" 729 

I 1 Maximum Principal Slab Stress: 

1 

LSTRS = - 2.200 + 0.00476*(~~1)~*~~3 + 0.914xLLOAD 

+ 0.427*LE1 - O.O593*LD2*LRAT 

I 

- 0.231*LDl*LE1 - 0.0270*(~~3)~ I 

I 

RZ = 0.998, SEE = 0.0129, n = 36 = 729 

Maximum Roadbed Soil Vertical Strain: I 

LSTRN = - 0.510 + 0.00598*(~~1)~*~~1*(~~3)~ 

+ 0. ~o~~~-~LLoAD*(LD~)~K(LE~)~ - Oe787*LD1*LE3 I 

I 

- O.699*LE1 + O.902*LLOAD I 

RZ = 0.994, SEE = 0.282, n = 36 = 793 

Definitions of the variables used in these equations are as follows: 

LDEFL = log of maximum surface deflection (inches). 

LSTRS = log of maximum principal slab stress (psi). 

LSTRN - log of maximum roadbed soil vertical strain. 

LD1 = log of slab thickness (inches). 

LD2 = log of baselsubbase thickness (inches). 

LEI = log of slab elastic modulus (psi). 

LE3 = log of roadbed soil elastic modulus (psi). 

LRAT = log of the ratio between the subbase elastic modulus to that 

of the roadbed soil. 

LLOAD = log of wheel load magnitude (lb). 

Note; All logs are in base 10. 

EUSTIC RUTE ON DENSE LIQUID SUBGRADE 

4 

4 The following are equations developed by I~annides for the prediction 

of slab stress and surface deflection for interior, edge and corner loading 

I conditions. (8"Qp 85.6) These equations were derived based on an in-depth I 
study of the equations developed by other researchers and an analysis of the 

ILLI-SLAB finite element program. (78.3) 

Maximum Deflection, Interior (Circular) Load: 

DEFIC = [p/(8*k*lZ) 1 * 

(1 + (0.5*x)*[ln(0.5*a/l) + EUL - 5/4]*(a/~)~) 

Maximum Bending Stress, Ordinary Theory, Interior (Circular) Load: 

BSIOT = {[3*~*(1+~)]/(2*lr*h~)) * 

[ln(2*R/a) + 0.5 - EUL] + BSI20T 

Maximum Bending Stress, Special Theory, Interior (Circular) Load: 

BSIST = { [3*~*(l+v) 1 /(2*7r*h2) } * 

[ln(2*R/b) + 0.5 - EUL] + BSI2ST 

BSI2ST = ( [3*P*(l+v) 1 /(64*hZ) ) * (b/R)' 

1 

Maximum Bending Stress, Interior (square) Load: 

BSISQ = {[3*~*(1+~)/(2*x*h~)) * 

[ln(2*R/c1) + 0.5 - EUL] + BSI2SQ 

BSI2SQ = { [3*~*(1+v) ]/(64*h2) ) * (~'/l)~ 

Maximum Deflection, Edge (Circular) Load: 

DEFEIC = P*[(Z + 1.2*~)~.~]*[1 - (0.76 + 0.4*v)*(a/P) ]/(~*h~*k)0.~ 

Maximum Deflection, Edge (Semicircular) Load: 

DEFEIS = P7k[ (2 + 1. 2*v)*-']*[I - (0.323 + 0. 17*v)*(a2/~) ]/(~*h~*k)O.~ 

Maximum Bending Stress, Edge (Circular) Load: 

BSEIC = {3*(l+v)7~P/[x*(3+v)*h2 ] 1 * 

{ln[~*h~/(100*k*a~)] + 1.84 - 4*~/3 + [(I-v)/2] + 

1.187k(1 + 2*u)*(a/R) ) 

Maximum Bending Stress, Edge (Semicircular) Load: 

BSEIS = {3*(l+v)*~/[lr*(3+~)7kh~]) * 

{ln(~*h~/(100*k~~a,~) ] + 3.84 - 4*v/3 + 

0.5*(1 + 2*v)7k(az/k!) ) 

Maximum Deflection, Corner (Square) Load: 

DEFCS = (~/k*R')7t(l.205 - 0.697kc/l) 

181 
Maximum Bending Stress, Corner (Square) Load: 

The variables used in these equations are as follows: 

P = Total applied load (lb). 

E = Slab elastic modulus (psi). 

v = Slab Poisson's ratio. 

h = Slab thickness (in). 

k = Modulus of subgrade reaction (pci). 

a - Radius of circular load (in). 

b = a, if a < 1.724*h, = (1.6*a2 + h2)*e5 - 0.675*h, if a > 1.724*h. 

a2 = Radius of semicircular load (in). 

b, = a,, if a2 5 1.724*h, = (l.6*aZ2 + h2)OS5 - 0.675*h, if a2 > 1.724*h. 

c = Side length of square load (in). {ercn/4)-11/20.5)*C* 

EUL = Euler's constant (0.57721566490). 

r = 3.141592654. 

R = Radius of relative stiffness (in). = {~*h~/[12*(l-~~)*k])~.~~. 
APPENDIX B 

SELECTED DISTRESS/PERFORMANCE PREDICTION REUTIONSHIPS 

FOR RIGID PAVEMENTS 

This appendix gives details for distress/performance prediction 

relationships that were discussed in chapter 3. The 18 entries, coded'~ 

through R, represent selections from the research literature and are 

intended to give representative coverage of air reported relationships for 

the various types of rigid pavement distress. 

A. Prediction of Pumping. [From COPES Report] (85-2) 

For JPCP: 

PUMP = (ESAL'.~~~) [-I. 224 + 0.0605 SUMPREC'." 

+ 0.00027 FI'.~" + THICK^-^^^ 

- 0.255 SOILCRS] 

R~ - 0.68, SEE = 0.42, n = 289 pavement sections " 

For JRCP : 

PUMP = (ESAL'.~~') [ - 22.82 + 13.224 SUMPREC'.'~~~ 

+ 6.834 (FI + 1)0.00805 + 26102/~~1~~~.' 

- 0.129 DRAIN - 0.118 SOILCRS] 

R~ - 0.57, SEE = 0.52, n = 481 pavement sections 

PUMP = 0 (none), 1 (low), 2 (medium), 3 (high severity). 

ESAL - Accumulated 18-kip equivalent single axle loads. 

SUMPREC = Average annual precipitation (cm). 

FI - Freezing index. 

THICK = Slab thickness (in). 

DRAIN = 0 (no subdrain), 1 (subdrain pipes). 

SOILCRS = 0 (fine grained soil), 1 (coarse roadbed soil). 
B . Prediction of Cracking [From COPES Report] (85-2) 

For JPCP : 

CRACKS = (ESAL''~') 13092 (1 - SOILCRS) RATIO^'.'] 

+ (ESAL~.~') [I. 233 (TRANGE) RATIO'-^^] 

+ (ESAL~.~~) [O .23 (~1'0~~) MTIO'*~~] 

R' = 0.69, SEE = 176 feet per mile, n = 303 pavement sections 

For JRCP : 

CRACKS = (ESAL',~~~) [7130 JTSP/(ASTEEL*THICK) 5.0] 

+ (ESALO-~') [2.281 PUMP^.'] 

+ (ESAL'.'~) [I. 81/(BASETYP + 1) 1 

+ AGE'.^) [0.0036 (FI + 

R2 = 0.41, SEE = 280 ft per mi, n = 314 pavement sections 

CRACKS = Total crack length (ft per mi): 

for JPCP - all cracks; 

for JRCP - medium and high-severity temperature and shrinkage 

cracks. 

ESAL = Accumulated 18-kip equivalent single axle loads. 

FI = Freezing index. 

THICK = Slab thickness (in). 

PUMP = 0 (none), 1 (low), 2 (medium), 3 (high severity). 

SOILCRS = 0 (fine grained soil), 1 (coarse roadbed soil). 

AGE = Years since construction. 

TRANGE = (Maximum July temperature) - (minimum January temperature). 

RATIO = (Westergaard 9-kip wheel load edge stress)/(PCC modulus of 

rupture) . JTSP = Transverse joint spacing (ft). 

ASTEEL = Area of reinforcing steel (inches per foot of width). 

BASETYP = 0 (granular base), 1 (stabilized base). 

C. Prediction of Load Cycles to Concrete Fatigue Failure (flexural beam 

break) . [From FHWA Zero-Maintenance Report] (77-3) 

log N = 16.61 - 17.61*(o/f) 

R2 = 0.50 (est), SEE (log) = 0.40 (est), n = 140 plain PCC beams 

N = Number of stress applications to beam failure. 

a = Repeated flexural stress (psi). 

f = Concrete modulus of rupture (psi). 
D. Prediction of Load Cycles to Fatigue Failure (exact failure criteria - unknown) [From PCA thickness design manual] (84*4) 

~2 = ?? 

SEE = ?? 

n = ?? 

0.4 lo2 lo3 I o4 I o5 I o6 I o7 

LOAD REPETITIONS 

STRESS RATIO = Wheel load flexural stress divided by 28-day 

modulus of rupture. 

LOAD REPETITIONS = Allowable number of load repetitions corresponding 

to stress level. 

E. Prediction of Load Cycles to Pavement Fatigue Failure (Class 3&4 

Cracking) . [From initial FHWA rehabilitation design study] (77.4) 

R' = 0.83, SEE (log) = ??, n = ?? AASHO Road Test Sections 

N - Number of stress applications to onset of class 3&4 cracking. 

f = Concrete modulus of rupture (psi). 

a = Maximum wheel load slab stress (psi). 
F. Prediction of Load Cycleas to Pavement Fatigue Failure (cracking index 

of 50). [From Center for Transportation Research Report] (81.2). 

log N = 4.66 + 3.00*log(f/a) I 

R' = ??, SEE (log) = ??, n = (all) AASHO &ad Test Sections " 

N = Number of stress applications to AASHO crhcking index of 50 feet 

per 1000 square feet. I 

f = Modulus of rupture (psi). 

0 = Maximum slab stress (psi). I 

I I 

4 

i I 

G. Prediction of CRCP Shrinkage Cracking. [From AASHTO Guide] (86.4) 

1 

1 To predict subsequent spacing between crack^:^ i I 

I 

CRACKSPACE = 1.32 [ (1 + TSTRG/~O~O)~.'~] * [(b - THERMRAT/~)~.~~] * [ (1 + BDIAM)~.'~] * [ ( 1 + TSTPS/~OOO)-~.~~] * [(I + PCTST)-~.~~] * [(I + 1009 SHRN)-~.~~] 

I 

R2 = ??, SEE = ??, n = ?? I 

I 

I 

To predict subsequent crack width: I 

.> + I * 

CRACKWIDTH = 0.00932 [ (1 + TSTRG/IOOO)~.~~] * [ (1+BDIAM)2.201 * [ (1 + TSTRS/~O~O)-~.~~] * [ (~+~cTsT)-~-~~] I 

R~ = ??, SEE = ??, n = ?? 

I 

CRACKSPACE = Mean distance (ft) between crack$. 

CRACKWIDTH = Mean crack width (in). ~ 

TSTRG = Concrete indirect tensile strength (psi). 

THERMRAT = Ratio of steel thermal coefficie+t to concrete thermal 

coefficient . I 

TSTRS = Tensile stress (psi) due to wheel load. 

PCTST = Percent steel. I 

SHRN = Concrete shrinkage at 28 days. 
H. Prediction of Faulting. [From COPES ~e~ort] '85-2) 

For JPCP : 

FAULT 7 (ESALO* 144) [ - 0.298 + 0. THICK^^^'^) 

- 0.0285 BASETYP + 0.00406 (FI + 1)0*3598 - 0.0462 EDGSUP 

+ 0.2384 (PUMP + l)O.O1Og - 0.0340 (DOW)~.~~~' J 

R~ - 0.79, SEE = 0.02 inches, n - 259 pavement sections 

For JRCP: 

FAULT = (ESAL~.~~~') [-3.8536 - 1.536 SOILCRS 

+ 197.1 (THICK * + 0.00024 FI 

+ 0.0986 JTSP + 0.2412 PUMP^^^] 

R' = 0.69, SEE = 0.06 inches, n - 384 pavement sections 

FAULT = Mean transverse joint faulting (in). 

PUMP = 0 (none), 1 (low), 2 (medium), 3 (high severity). 

ESAL - Accumulated 18-kip equivalent single axle loads. 

FI = Freezing index. 

THICK = Slab thickness (in). 

SOILCRS - 0 (fine grained soil), 1 (coarse roadbed soil). 

AGE = Years since construction. 

JTSP - Transverse joint spacing (ft). 

BASETYP = 0 (granular base), 1 (stabilized base). 

DOW = Dowel bar diameter (in). 

EDGSUP = 0 (for AC shoulder), 1 (for tied PCC shoulder). 

I. Prediction of Faulting. [From AASHTO Guide, Volume 3](8604) 

ln' (FAULT + 1) = [In (ESAL + 1) J [ -0.09013 + 0.00014 BSTRESS] 

RZ = ??, SEE = ??, n = ?? 

FAULT - Mean transverse joint faulting (in). 

ESAL = Accumulated 18-kip equivalent single axle loads. 

BSTRESS = Maximum bearing stress of dowel bar (depends on PCC 

thickness and modulus, dowel diameter and modulus, and 

roadbed modulus). 
J. Prediction of Joint Deterioration. [From COP~S Rep~rt](~~.~) 

For JPCP : 

DETJT = AGE'.^'^) (0.9754 DCRACK) + AGE'.^^') (0.01247 UNITUBE) 

+ AGE^,'^^) (0.00135 INCOMP) 

R' = 0.59, SSE = 16 joints per mile, n = 252 pavement sections 

For JRCP : 

DETJT = AGE'.^^^) (2.437 DCRACK + 2.744 REACTAG) 

+ AGE^.^^') (0.052 + 0.0000254 FI + 0.0111 TJSD 

- 0.00338 KI*JTSP - 0.000645 K2*JTSP) 

R' = 0.61, SEE = 15 joints per mile, n = 319 pavement sections 

DETJT = Number of medium and high-severity deteriorated joints/mile. 

ESAL = Accumulated 18-kip equivalent single axle loads. 

PUMP = 0 (none), 1 (low), 2 (medium), 3 (high severity). 

AGE = Years since construction. 

JTSP = Transverse joint spacing (ft). 

DCRACK = 1 (D cracks), 0 (none). 

UNITUBE = 1 (Unitube joints), 0 (none). 

INCOMP = 1 (visible incompressibles in joint), 0 (none). 

REACTAG = 1 (reactive aggregates), 0 (none). 

TJSD = 1 (medium or high-severity joint real damage), O (none or low). 

Kl = 1 (if JTSP at least 27 ft), 0 (if nat). 

K2 = 1 (if JTSP at least 39 ft), 0 (if not). 

K. Prediction of CRCP Slab Distress. [From study for Texas SDHPT](~~.~) 

N = - 0.381 - 0.0356 X1 + 0.000131 ~2~ + 0.0461 X3 (X2-XI) 

+ 0.0000494 X2 X4 + X5 

R' = 0.67, SEE = 2.44, n = 147 

N = Number of defects (punchouts + patches) per mile at future time 

chosen for prediction. 

Xl = Pavement age at time of condition survey (months). 

X2 = Pavement age at future time for distress prediction (months). 

X3 = Number of defects at time of condition survey. 

X4 = Texas SDHPT District Temperature Constant. 

X5 = -5.840 + 0.0988 X2 (for pit run gravel subbase aggregate), 

0 (for other subbase aggregates). 
L. Prediction of Swells and Depressions. [From FHWA Cost-Allocation 

Report] (84.3) 

For JPCP : 

(D + S)/10 = AGE [0.0016 IMOIST - 0.00045 CBR - 0.0155 BASETYP 

+ 0.00706 F2 + 0.00171 F3 + 0.023753 

R' = 0.78, SEE = 0.56, n = 65 pavement sections 

For JRCP: 

(D + S)/10 = AGE (0.00035 SUMPREC - 0.0074 BASETYP - 0.017851 

R' = 0.68, SEE = 0.78, n = 50 pavement sections 

D + S = Number of depressions and swells per mile (medium and highseverity). 

AGE = Years since construction. 

BASETYP = 0 (granular base), 1 (stabilized base). 

IMOIST = Thornthwaite Moisture Index. 

F2 = 1 (pavement in cut), 0 (not in cut). 

F3 = I (pavement in fill), 0 (not in fill). 

SUMPREC = Average annual precipitation (cm). 

M. Prediction of Skid Number Loss. [From FHWA Cost-Allocation 

Report] (84-3) 

In (70 - SN) = - 2.372 + 0.258 In TRUCKS + 0.137 In ESAL 

- 0.033 In AXLES 

R~ = 0.70, SEE = ??, n = 33 pavement sections 

SN = Skid number at 40 mi/h (skid trailer). 

TRUCKS = Total number of truck passes (excepting pickups and panels). 

AXLES = Total number of axle passes in traffic lane. 
1 

N. Prediction of Serviceability Loss. [From AASH~O ~uide] (86.3) 

BETA = 1 + 0.0563/[ (THICK + 

RHO = [ (THICK + 1)7035 ] - 0.06 

ADJ = ( NUN / DEN )(4022 - a*32 

NUM = MODROP * DRACO * [ S THICK'.^^) - 1.1321 

DEN = 215.63 * JFACT * THICK'.^^) - 18.42 RAT'.^^)] 

RAT = (KVAL/EMOD) 

PSIL 

PO 

PW 

THICK 

MODRUP 

DRACO 

JFACT 

EMOD 

KVAL 

= Serviceability loss from PSI = PO to PSI -.PW. = As-constructed present serviceability index (PSI). 

= PSI when accumulated 18-kip single a4le load applications 

(ESAL) equals W. = PCC slab thickness (in). I 

= PCC modulus of rupture (psi). ~ = Drainage coefficient (ranges from 0.70 = poor I % 

to 1.25 = excellent). I 

= Load transfer coefficient (ranges frqm 2.3 = excellent 

to 4.4 = poor). I 

I 

= PCC modulus of elasticity (psi). ~ = Roadbed modulus of subgrade reactionl(pci). 

Note: The standard error of estimate (SEE) of this relationship has not 

been evaluated from an observational data base but is likely to be at least 

0.34 PSI units. 
0. Prediction of Serviceability Loss. [From COPES Report] 

For JPCP : 

PSRL = (4.5 - PSRE) 

= 1.486 (ESAL~.'~~') - 0.4963 [(ESAL~~~~~)/(RATIO~.~)] 

+ 0.01082 (ESALO-~~~) [ (SUMPREC~~')/(AVGMT~.~~) ] * (AGEO-~~~) 

R' = 0.69, SEE = 0.25, n = 316 pavement sections 

For JRCP : 

PSRL = (4.5 - PSRE) 

= (ESAL'.~~~) [do. 00188 + 14.417 RATIO^.^^) + 0.0399 PUMP 

+ 0.002153 JTSP + 0.1146 DCRACK + 0.05903 REACTAG 

+ 0.00004156 FI + 0.00163 SUMPREC - 0.070535 BASETYP] 

R' = 0.78, SEE = 0.30, n - 377 pavement sections 

PSRE = Panel present serviceabiliXy rating (PSR) when pavement has 

received ESAL equivalent standard load applications. 

PSRL = Initial serviceability (adsumed to be 4.5) minus PSRE. 

ESAL = Accumulated 18-kip equivalent single axle loads. 

FI = Freezing index. 

AVGMT = Average monthly temperature (OF). 

PUMP = 0 (none), 1 (low), 2 (medium), 3 (high severity). 

SUMPREC = Average annual precipitation (cm). 

AGE -- Years since construction. 

RATIO - (Westergaard 9-kip wheel load edge stress)/(PCC modulus of 

rupture) . JTSP. = Transverse joint spacing (ft). 

BASETYP - 0 (granular base), 1 (stabilized base). 

JTSP = Transverse joint spacing (ft). 

DCRACK = 1 (D cracks), 0 (none). 

REACTAG = 1 (reactive aggregates), 0 (none). 

P. Prediction of Load Applications to Pavement Failure (terminal serviceability of 2.5). [From NCHRP Report 971 (70.') 

log N = 5.352 - 4 (o/f) 

R' = ??, SEE (log) = ??, n = 29 (?) Road Test Sections 

N = number of stress applicati01ls to te serviceability of 2.5. 

f = concrete modulus of rupture (psi). 

a - maxim wheel load slab stress (psi). 
Q. Prediction of Load Cycles to Pavement ~ailurk (AASHO Serviceability 

of 2.0) . [From follow-up FHWA rehabilitatioh design study] (83.7) 

log N = 4.35 + 4.29*log(f/a) 

R~ = 0.92, SEE (log) = 0.23, n = 99 AASHO Road Test Sections 

N - number of wheel load stress applications to terminal serviceability of 2.5. 

f = concrete modulus of rupture (psi). 

a = maximum wheel load slab stress (psi). 

R. Prediction of Pavement Condition Rating. [From Resource International 

Inc Study for FHWA] (84.2) 

Non PCC Terms PCC Terms 

PCR = -96.7 + 96.7/10g (C+3) 

+ 0.0474 (C+3)/log(C+3) 

+ 0.560 D 7k log(C+3) 

+ 2.27 [log(B+3) ]/[log(C+3) 1 , 

+ 43.9 F/D 

- 18.2 F / root C 

- 0.0174 C*G 

+ 0.479/G>kG 

- 6.65/log F 

- 6.70 log F 

+ 0.0497 A*G 

- 0.220 D*G 

+ 1.90 [log(C+3)] / log F 

R~ = 0.634, SSE = ??, n = 734 pavement sections (max) 

Variables Meanvalue Std. Dev. 

PCR = Pavement Condition Rating (100 max.) 

A = Annual rainfall (in) 

B = Frost penetration (in) 

C = Freeze Index 

D = Subgrade CBR (percent) 

E - Joint spacing (ft) 

F = Cumulative ESAL (millions) 

G = Age (years) 

H = Design thickness (in) 

I = Actual thickness (in) 

J = Min PCC pour temperature (deg F) 

K = Air entrained (percent) 

L = Core compressive strength (psi) 

72 (est.) 

45.3 

12.0 

148 

8.1 

44.0 

4.4 

11.3 

9.1 

9 3 

58.6 

5.6 

5450 

- 

4 (est.) 

9.8 

9.6 

178 

1.8 

22.1 

3.6 

3.8 

0.5 

0.7 

10.3 

1.0 

1076 
APPENDIX C 

SUMMARY OF SECONDARY PREDICTION RELATIONSHIPS 

The following secondary relationships (coded A through U) among M&C 

variables have been selected from the research and engineering literature. 

Some relationships are expressed in algebraic form, others are presented 

in graphical or tabular form. 

A. Modulus of Rupture. [ACI 318-831 (84.8) 

SF = PCC modulus of rupture (psi). 

SC = PCC compressive strength (psi). 

B. PCC Flexural Strength. [Jones and Kaplan via Neville] (73.2) 

See figure 41 - Relation between flexural and compressive strengths 

for concretes made with different aggregates. 

R2 = ??, SEE = ??, n = ?? 

C . PCC Flexural Strength. [Walker and Bloem via Mindess] (81.4) 

See figure 42 - Relation between flexural strength and compressive 

strength for concretes made with different maximum 

size coarse aggregate. 

R' = ??, SEE = ??, n = ?? 

D. PCC Modulus of Rupture. [Wright via Ne 

See figure 43 - Relation between mod 

water/cement ratio. 

R~ = 17, SEE = ??, n = ?? 

900 I I I I I I 

Max. size aggregate I 

- -- -- - - 

E. PCC Modulus of Rupture. [European Concrete Committee via ~eville] (73+2) 

R~ = ??, SEE = ??, n = ?? 

SF = PCC modulus of rupture (psi). 

SC = PCC compressive strength (psi). 

F. PCC Modulus of Rupture. [Univ. of Illinois via Neville] (73-2) 

R2 = ??, SEE = ??, n = ?? 

SF = PCC modulus of rupture (psi). 

SC = PCC compressive strength (psi). 

G. PCC Splitting (Indirect) Tensile Strength, [Walker and Bloem via 

Mindess] (81-4) 

See figure 42 - Relation between splitting tensile strength and 

compressive strength for concretes made with 

different maximum size coarse aggregate. 

R2 = ??, SEE = ??, n - ?? 

GR = (0.68*A)/(0.32*A + WC) 

R2 = ??, SEE = ??, n = ?? 

SC = FCC compressive strength (psi). 

GR = Gel/space ratio. 

A = Degree of cement hydration, i.e., fr ion of cement that is 

hydrated. 

WC = Water/cement ratio. 
I. PCC Compressive Strength. [Singh via Neville] (73.2) 

See figure 44 - Influence of water/cement raltio and aggregate/cement 

ratio on 7-day compressive sltrength. 

R' = ??, SEE = ??, n = ?? 

J. PCC Compressive Strength. [Portland Cement Association via Flinn and 

Troj an] (81.5) 

See figure 45 - Compressive strengths for air-entrained and non-airentrained concretes as related to curing time. 

K. PCC Compressive Strength. [Bureau of Reclamation via Mindess] (81-4) 

See figure 46 - 28-day compressive strength in relation to cement 

content for air-entrained ana non-air-entrained 

concrete of constant slump. 

R2 = ??, SEE = ??, n = ?? 

L. PCC Compressive Strength. [American Concrete Institute via Mindess] (*lB4) 

See figure 47 - Influence of aggregate size on 28-day compressive 

strength of concretes with different cement 

contents. 

R' = ??, SEE = ??, n = ?? 

M. PCC Compressive Strength. [Bureau of Reclamation via ~indess](~l.~) 

See figure 48 - Effect of entrained air content on compressive 

strength . 

R~ = ??, SEE = ??, n = ?? 
(Y 

f 60 % 

f 8000 I 

950 

c 7000 

gi 

Si 

9 40 

6000 .- 

J1 ul 

5000 

830 4000 

b 3000 

2002 0-3 0 4 0.5 06 0.7 

water / cement Ratio 

Figure 44. Relationship I: The influence of the 

aggregate/cement ratio on strength of concrete. '73*2) 

Non-air-entrained concrete 

L Specimens: 6 in. X 12 in. $ 7000 - cylinders U Cement: Type I or normal m 

0.35 0.45 0.55 0.65 

Water-cement ratio Water-cement ratio 

Figure 45. Relationship J: Typical compressive strengths 

for air-entrained and non-air-entrained concretes 

as related to curing 

(: in.) (j in.) (1fin.I t3in.) (6 in.) 

Maximum size of aggregate (mm) 

Figure 47. Relationship L: Influence of aggregate size 

on 28-day compressive strength of concretes with 

different cement contents. (81.4) 

N. PCC Modulus of Elasticity. [ACI Code 318-831 (84.8) 

EC = uw1s5 *33*(~~) Oe5 

R2 = ??, SEE = ??, n = ?? 

EC = PCC modulus of elasticity (psi). 

UW - PCC unit weight (pcf). 

SC = PCC compressive strength (psi). 

0. PCC Modulus of Elasticity. [Jensen via Lin] (63.1' 

R2 = ??, SEE = ??, n = ?? 

EC - PCC modulus of elasticity 

SC - PCC compressive strength (psi). 

P. PCC Modulus of Elasticity. [Hognestad via Lin] (63*1) 

EC = 1800000 + 460*SC i 

RZ = ?.?, SEE = ??, n = ?? 

EC = PCC modulus of elasticity (psi). 

SC = PCC compressive strength (psi). 

Q. PCC Modulus of Elasticity. [Ishai via ~indess] (81-4) 

See figure 49 - Effect of aggregates on the modulus of elasticity 

of- concrete. 

R. PCC Shrinkage. [Nawy 1 (85.3 

See figure 50 - Water/cement ratio and aggregate content effect on 

concrete drying shrinkage. 

R~ = ??, SEE = ??, n = ?? 
Figure 

Air 

Aggregate fractions (by volume) 

I 

I 

I 

49. Relationship Q: Effect of aggregates 

modulus of elasticity of concrete. 

on the 

S . PCC Thermal Coefficient . [Seeds, McCullough and Carmichael] (82.7) 

See table 35 - Thermal coefficients for concretes made with 

different types of coarse aggregate. 

Et2 = ??, SEE -. ??, n = 14 

T. PCC Durability. [Bureau of Reclamation via Mindess] (81m4) 

See figure 48 - Effect of entrained air on concrete freeze-thaw 

durability. 

R' = ??, SEE = ??, n = ?? 

U. Water/Cement Ratio. [Federal Highway Administration] (84.2) 

R~ = 0.73, SEE = 0.06, n = 558 

WC = Water/cement ratio. 

SL = Concrete slump (inches). 

AE - Entrained air content (percent). 

SC = PCC compressive strength (PSI). 
Table 35. Relationship S: Thermal coefficients for concretes 

made with different types of coarse aggregate. (82-') 

fficients fnr cnqcretes 

VY V 

'1 

Mean Value af 

Coarse PCC Thermal 

Aggregate Coeff icient Number of 

Type (lom6 in/in/' F) Specimens 

Syenite 4.7 2 

Dolomite 4.0 2 

Limes tone 4.4 2 

Sands tone 5.7 4 

Gravel - A 5.8 2 

Gravel - B 7,2 2 

1 in = 25.4 mm 

"C = 5("F-32)/9 
APPENDIX D 1 

RII DATA BASE ANALYSTS 

The Resource International Inc (RII) data $ase was generated as part of 

a previous study for the Federal Highway Adminidtration. (84.2) The purpose of 

this study was to examine the interrelationship? between quality indicators 

and the performance of portland cement concrete(PCC) pavements. 

Historical, construction and condition data relative to selected quality 

variables were collected for 104 concrete pavemcfnt projects in five 

different States (Florida, Louisiana, Maryland, New York, and Ohio). A 

number of statistical analyses were then perforded to establish prediction 

relationships between PCC pavement performance and the available quality 

indicator data. 

Since the focus of the study was on development of primary prediction 

relationships, the thrust of it was to evaluate the potential for using the 

RII data base in developing secondary predictio+ relationships. Basically, 

it was believed that all potential avenues of pjimary prediction 

relationship development had been explored by the original researchers. 

The data that was used in the analysis was extracted from the RII 

SECTION file. The SECTION file contains data for 733 sections within the 

104 projects. Data for up to 66 variables is provided for each section. 

The names and descriptions of the 66 variables are presented in table 36. 

With the primary objective of analyzing the data to develop secondary 

prediction relationships, a statistical approach consisting of four basic 

steps was derived. These four steps are: 

o Correlation matrix. 

o Frequency histograms. 

e Scatter plots. 

Multiple regression analyses. 

Eachiof these steps is discussed below. 

CORRELATION MATRIX 

After examining the pertinent factors and the extent to which they 

exist to the data base, only a small subset were chosen for inclusion in 

what was termed a "working data base". Table 37 identifies these pertinent 

factors as well as their corresponding summary statistics. Observations 

worth noting in this table include: 

* The distress-performance and traffic/time factors were included more 

as a means for testing the reasonableness of the strength and M&C 

factor data than for developing primary prediction relationships. 

As observed in the original RII SECTION data base, flexural and 

compressive strengths each have four data "slots" allocated. These 

slots were included in order to account for the age at which the 
Table 36. Description of variables in RII SECTION data file. 

No. Variable 

STATE 

co 

RTYP 

ROUTE 

PROJ 

BEGST 

ENDST 

PRTYP 

NSPP 

PCRCL 

CLIM 

BSTYP 

SGTYP 

JTYP 

JTSP 

TRAF 

AGE 

RCI 

STR 

SURF 

JOIN 

SUPP 

CRAK 

LFT 

SQP 

NP 

MINT 

MAXT 

SLUMP 

PAIR 

AIR 

WT 

WC 

YIELD 

FS3 

FS 7 

FS15 

FS 

CS3 

CS7 

CS15 

CS 

COREST 

CAGE 

DTHICK 

SMINT 

Description 

State Code 

County Code 

Route Type 

Route No. 

Project No. 

Begin Station 

End Station 

Project Type (l=CRC, 2JCP) 

No. of sections/proj ect 

PCR Class (ignore) 

Climate (W=wet, WF-wet freeze) 

Base Type (GRANULAR or STABILIZED) 

Subgrade Type (G=good, F-fair , P-poor) 

Joint Type (DOW-dowel bars, PLAI-plain) 

Joint Spacing (applicable to JCP only) 

Cumulative (millions of 18-kip ESALs) 

Age of pavement, years 

Pavement design thickness, inches 

Pavement condition rating 

Ride comfort index 

Structural deduct value 

Surface deduct value 

Joint deduct value 

Support deduct value 

Cracking deduct value 

Lineal ft of transverse cracking/200 ft, 

Square yards of patching/200 ft. 

Number of punchouts/200 ft. 

Minimum pour temperature, OF 

Maximum pour temperature, OF 

Concrete slump, inches 

Percent entrained air 

Air content, percent 

Unit weight, ib/ft3 

Water-cement ratio 

Cubic feet of concrete per sack of cement 

Flexural strength, psi (0-3 days) 

Flexural strength, psi (4-7 days) 

Flexural strength, psi (8-15 days) 

Flexural strength, psi ( > 15 days) 

Compressive strength, psi (0-3 days) 

Compressive strength, psi 04-7 days) 

Compressive strength, psi (8-15 days) 

Compressive strength, psi ( > 15 days) 

Core compressive strength, psi 

Core age at testing, months 

Design thick-core thick, inches 

Std. Deviation of MINT (No. 29) 
I 

I 

Table 36. Description of variables in RII SECTION data file (continued) . I 

No. Variable Description 1~ 

l1 

I 

49. SWT Std. Deviation of MAXT (No. 30) 

50. S SLUMP Std. Deviation of SLUMP (No. 31) 

51. SPAIR Std. Deviation qf PAIR (No. 32) 

52. SAIR Std. Deviation qf AIR (No. 33) 

53. SWT Std. Deviation qf WT (No. 34) 

54. SWC Std. Deviation f WC (No. 35) 

55, SY IELD 4 Std. Deviation gf YIELD (No. 36) 

56. SFS3 Std. Deviation of FS3 (No. 37) 

57. SFS7 Std. Deviation hf FS7 (No. 38) 

58. SFSl5 Std. Deviation of FS15 (No. 39) 

59. SFS Std. Deviation of FS (No. 40) 

60. SCS3 Std. Deviation of CS3 (No. 41) 

61. SCS7 Std. Deviation of CS7 (No. 42) 

62. SCSl5 Std. Deviation of CS15 (No. 43) 

63. SCS Std. Deviation of CS (No. 44) 

64. SCORES Std. Deviation of COREST (No. 45) 

65. SCAGE Std. Deviation of CAGE (No. 46) 

66. SDTHIK Std. Deviation of DTHICK (No. 47) 
Table 37. Summary statistics for key factors contained 

in "working" RII data base, 

SELECTED VARIABLES RI1 NO. OF MEAN STD. ,5th 95th CODE CASES VALUE DEV. %tile Yotile 

Distress-Performance Factors 

PCR (Pavement Condion Rating) 734 " 74.24 7.55 62 87 

RCI (Riding Comfort Index) 727 7.33 0.80 6.1 8.0 

Traffiflime Factors 

TRAF (Cumulative ESAL) N16 733 4.40 3.60 1 .o 12.0 

AGE (Years) N17 733 11.25 3.85 5.1 17.1 

Surfacing Factors 

PDT (Pavement Design Thickness) 

FS7 (7-Day Flexural Strength) 

cS7 (7-Day Compressive Strength) 

COREST (Core Strength) N46 

PCC M&C Factors 

733 

1 79 

336 

458 

SLUMP 

PAIR (% Air Entrained) 

WC (Water Content Ratio) 

9.13 

627 

3369 

5455 

N32 

N33 

N36 

0.52 

123 

620 

1142 

531 

495 

262 

8.0 

422 

2400 

3462 

2.05 

5.45 

0.43 

10.0 

812 

4400 

7065 

0.64 

0.98 

0.17 

1 .O 

4.0 

0.0 

3.0 

7.0 

1 .o 
I 

3 

i specimens were tested. Only the 7-day strengths were considered in 

this study, since in both cases, they weje the ones that contained 

1 the largest numbers of cases. 

Y 

c Like the distress -performance factors, pdi.vernent design thickness was 

included more as a means of testing the 4ata than for developing 

1 primary or secondary prediction relationships. I 

I 

[Note: The microcomputer version of the ~t$tistical Package for the 

Social Sciences program, SPSS/PC+ (V2.0), was uEjed to conduct all 

statistical analyses of the working data base.] I 

Using the SPSS package, a correlation matrtx was generated to examine 

the magnitude of the correlations between the vfrious factors. This matrix 

is shown in table 38. The top number in each c 11 of the matrix represents 

the actual Pearson correlation coefficient whil the bottom number (shown in 

parentheses) represents the number of pairwise eases that went into the 

determination of the corresponding correlation doefficient. 

I 

I 

FREQUENCY HISTOGRAMS I 

Frequency histograms provide information $out the distribution of 

values for each variable within their observedirange. Figures 51 through 61 

provide frequency histograms for each of the s lected variables contained in 

the working data base. Note that several of t e histograms (i.e., traff, 

age, WC and PDT), are far from being normally ! ,istributed. This should cast 

some doubt on the interpretation of the valuesof standard deviation 

provided. Furthermore, it should also be recognized when conducting further 

statistical analyses that assume normally distributed variables. 

I 

In examining the magnitudes of the correlahion coefficients , it is 

helpful to recognize that an absolute value of kreater than 0.7 generally 

indicates a strong degree of linear correlationr Furthermore, absolute 

values in the range of 0.4 to 0.7 are consider& to be reasonably well 

correlated such that a meaningful relationship bould be derived. 

Correlation coefficients that approach 0 indicate no linear correlation 

between the two variables. With this as a backbround, one can begin to 

understand the strong degree of correlation bet r een the 7-day flexural 

strength (FS7) and the long-term concrete core ptrength (COREST) and also 

the strong negative correlation between water/cbrnent ratio (WC) and concrete 

4' %! SCATTER PLOTS I 4; 

$ Several "scatter" plots were prepared to $isually examine the # 

'1 relationships between many of the key variables. Figures 62 through 65 

core strength (COREST). On the other hand, there 

concern because of the strong negative correlation 

should be some reason for 

between water/cement 

ratio (WC) and concrete slump and also the strolng positive relationship 

between concrete slump and pavement age. Both of these correlations between 

the variables are examined in further detail id the following sections. 
Table 38. Correlation matrix of factors in wworkingw RII data base. w-su * w mT 
4.25 5.25 6.25 7.25 8.25 9,OO 

I RCI 

I 

~1 

Figure 51. Pavement condition rating. Figure 52. Ride condition index. 

~ ~ 

I AGE (years) I 

Figure 53. Cumulative 

traffic. 

18-kip ESAL Figure 54. Pavement age. 



+----+----+----+----+----+----+----+----+----+----+----+----+----* 

,2375 .3325 .4275 .5225 .6175 .7125 .8075 

,285 .38 -475 .57 .665 .76 

Water/Cement Ratio 

203 cases plotted. 

Figure 63. Concrete core strength versus water/cement ratio. 
+----+----+----+----+----+----+----+----+----+----+----+----+----+--- -++ 

6.4+ + 

I 

I 

I 

I 

I 

I 

I 

5.6+ 

I 

+ 

I 

I 

I 

1 

I 

I 

I 

4.8+ 

I 

+ 

I 

I 

I 

I 

I 

I 

I 

4+ 

I 

+ 

I 

I 1 

I 

I 1 

I 

I 

I 

3.2+ 2 11 1 

I 

+ 

I 1 1 211 

I 2 44435 

I 

I 1315332354 1 

1 

I 4 1 322254 11 I 

2.4+ 1 1 5212621 1 

I 

+ 

I 1 141 143 1 21 

I 1 11314 1 2 

I 

1 11 1 

I 

I 221 1411 2 32 24 1 

1.6+ 11 31 111 1 2 21 

I 

+ 

I 1 51 2 15152 

I 11313 

I 

3 7 

I 11 111 235 

I 

I 22 31 12 

I 

.8+ 1 

I 

+ 

I . 

I 

I 

I 

I 

I 

I 

o+ 

I 

+ 

+----+----+----+----+----+----+----+----+----+----+----+----+----++ 

.2375 .3325 ,4275 .5225 .6175 .7125 .8075 

,285 .38 .475 .57 .665 .76 

Water/Cement Ratio 

cases plotted. 

Fcgure 64. Concrete slutnp versus water/cement ratio. 

illustrate some of the better linear correlations between the surfacing and 

PCC M&C factors. In contrast, figures 66 and 67 provide examples of the 

factors that are poorly correlated. Figure 68 provides a plot between two 

factors that have a poor linear correlation but that may be better related 

in some non-linear fashion. The next two plots depict rather strong but 

unsettling relationships between 7-day flexural strength and concrete slump 

(figure 69) and 7-day flexural strength and percent entrained air (figure 

70). From an engineering standpoint, it is illogical to believe that highslump concrete produces high strength. Similarly, it is also not reasonable 

to believe that high air entrainment results in high strength (although it 

is generally acknowledged that high air entrainment does produce more 

workable concrete that is also more durable from a freeze-thaw standpoint). 

The reasons for this are perhaps explained by the plots in figures 71, 72 

and 73. Each plot indicates that the characteristics of the concrete are 

highly dependent on the year the pavement was constructed. Thus, the 

relationships here may be more reflective of changes in design/construction 

practice rather than the true relationships between strength and mix 

factors. For example, over the years more and more contractors have gone to 

the use of high-production slip-form pavers that require low-slmp concrete. 

It is also likely that better quality control procedures have permitted 

contractors to lower their target concrete strength and still satisfy 

minimum specifications. Unfortunately, these kinds of problems make it 

difficult to develop practical secondary prediction relationships that could 

be used in developing a performance-related specification system. 

MULTIPLE REGRESSION ANALYSES 

The final step in the process of analyzing the RII SECTION data base 

was the development of prediction relationships between the key variables 

using standard stepwise linear regression analysis techniques. Initially, 

it was hoped that the resulting relationships could be used in the final 

specifications system. However, because of the confounded nature of the 

data, the results now show the danger associated with using observational 

data bases to develop prediction equations. 

Five separate prediction relationships were derived: two primary and 

three secondary. The two primary relationships had (respectively) pavement 

condition rating (PCR) and ride condition index (RCI) as the dependent 

variables with pavement age (AGE), cumulative traffic (TRAF), 7-day concrete 

flexural strength (FS7), concrete slump (SLUMP), water/cement ratio (WC), 

and entrained air percentage (PAIR) as potential independent variables. The 

three secondary relationships had (respectively) 7-day concrete flexural 

strength (FS7), 7-day concrete compressive strength (CS7) and concrete core 

strength (COREST) as dependent variables with water/cement ratio (WC), 

concrete slump (SLUMP), and entrained air percentage (PAIR) as potential 

independent variables. The results are presented below. 

Primary Relationships: 

PCR = 137.0 + 10.2(AGE) - 15,2(TRAF) - 146.7(WC) 

R' = 0.82, n - 53, S.E.E. = 3.93 


Entrained Air (percent) 

345 cases plotted. 

Figure $8. Concrete core strength versus enerained air percentage. 1 

I 

Entrained Air (percent) 

151 cases plotted. 

Figure 70. Concrete flexural strength versusentrained air percentage. 
Pavement Age (years) 

179 cases plotted. 

Figure 71. Concrete flexural strength versus payement age. 

rn 

227 


2. RCI - 11.0 - 1.46(TRAF) - 0.509(PAIR) + 0.734(SLUMP) 

R' = 0.71, n = 53, S.E.E. = 0.40 

Secondary Relationships: 

3. FS7 = 437 + 167(SLUMP) - 38.7(PAIR) 

R~ = 0.42, n = 53, S.E;E. = 64.0 

4. CS7 = 3890 - 965(WC) 

R' = 0.08, n - 219, S.E.E. = 552 

5. COREST = 7370 - 4448(WC) 

R' = 0.59, n = 199, S.E.E. = 657 

Initial examination of the relationships shows that although the 

available independent variables did have a reasonable to good correlation 

with the dependent variable, not all entered the equation. The reason for 

this is that much of the variability observed in the dependent variables is 

explained by almost any one of the independent variables., This phenomenon 

is detectable by stepwise regression analysis methods so that redundant 

terms can be ignored. 

Following are some other observations and comments that can be made 

about the relationships. Some of these (indicated below) arc the logical 

consequences of some of the data inconsistencies discussed previously: 

1. For the PCR equation, the limits of PCR are from 0 (very bad) to 100 

(very good) : 

a. 82 percent of the variability observed in PCR was predictable 

using three independent variables AGE, TRAF, and WC. However, of 

the 733 sections, there were only 53 in which all 4 factors were 

available to derive the relationship. 

b. The coefficient on the AGE term is a +lo. This means that for 

every year the pavement ages, its predicred PCR increases by 10. 

Obviously, this is offset by the traffic term; however, for low 

levels of traffic, the equation would predict that the pavement 

gets better with time. 1 

c. The range of water/cement ratio (WC) observed in the data was 

from 0.3 to 0.7. With this kind of range, the effect of the WC 

term is relatively large but not unreasonable. I 

2. In the RCI equation, the range of RCI is from 0 (poor) to 10 (good): I 

1 

1 

a. 71 percent of the observed variation in RCI is explained by three 

independent variables; in this case TRAF, PAIR, and SLUMP. But 

again, only 53 of the available 733 sections could be used to 

derive the relationship. 

b. The coefficient in the PAIR term is very significant, but 

opposite to practical expectations. Increasing the entrained air 

230 
in concrete should improve its durability and, therefore, its 

performance. L 

c. The coefficient on the SLUMP term is also very significant and 

contrary to practical expectations. To improve projected future 

ride condition, one would not recommend high slump concrete. 

3. 7-day flexural strengths (FS~) in the SECTION data base are on the 

order of 400 to 900 psi (28 to 63 kg/cm2): 

a. 42 percent of the observed variation in FS7 is explained by SLUMP 

and PAIR. Again, the equation is based on only 53 sections. 

b. The equation is not practical, however, since the positive 

coefficient on, SLUMP indicates that in~reasing~concrete slump 

increases its strength. 

4. The,observed range of 7-day compressive strength-( S7) is between 

about 2,000 and 5,000 psi (140 and 350 kg/cm2) : 

4 

a. Apparently none of the available independent variables could 

predict the variation observed in CS7. Using 219 of the 

available 773 sections, WC explained only 8 percent. 

b. Although the equation does not explain very much of the variation 

in the data, it does, interestingly, seem to produce reasonable 

results. 

5. The observed range of COREST, the long-term compressive strength of 

the concrete (as determined from pavement cores), is between 3,000 

and 8,000 psi (210 and 560 kg/cm2): 

a. 59 percent of the variation of COREST could be explained by just 

one variable, WC. Furthermore, this equation is based on a more 

reasonable number (percentage-wise) of the total number of 

sections. 

b. The equation does seem to provide reasonable results; 

unfortunately, core strength has not typically been used as 

factor for predicting pavement performance. 
API?ENDIX1 E 

COPES DATA BASE ANALYSES 

The Concrete Pavement Evaluation System (COPES) was developed under 

NCHRP Proj ect 1-19. (85.2' COPES provides a framework and procedure for 

collecting field data on the characteristics and performance of inservice 

portland cement concrete (PCC) pavements. As part of the research study, 

data were collected in six States using standard COPES data collection 

procedures. These data were subsequently analyzed by the researchers to 

develop PCC pavement distress prediction relationships and also to evaluate 

various design, construction, maintenance and rehabilitation aspects of PCC 

pavements. Because of the extent of the data available in COPES, it seemed 

a likely candidate for the development of additional relationships 

(primarily secondary) that might be useful in this project for the 

development of a performance-related specifications system for PCC 

pavements. 

The COPES data available for this research effort represented only five 

of the original six States. Included were California, Georgia, Louisiana, 

Minnesota, and Utah. Illinois data could not be considered, since it had 

not been reconfigured in time for these analyses. There are 1182 

observations (pavement sections) in the five-State data base that was 

analyzed. Of these, 994 observations make up Minnesota's recently updated 

portion. 

Upon extracting the desired information from the COPES data base, the 

data was placed in ASCII format for use with SPSS/PC+ (V2.0), a 

microcomputer-based statistical analysis program. A list of the key 

variables is presented in table 39. The data base analyses consisted of 

four basic steps: 

a Correlation matrix. 

Frequency histograms. 

a Scatter plots. 

Multiple regression analyses. 

Each of these is discussed below. 

CORRELATION MATRIX 

Pearson correlation coefficients were generated for all pairwise 

combinations of the variables in the COPES database. A partial correlation 

matrix is presented in table 39. The top number in each cell is the actual 

Pearson correlation coefficient while the lower number (shown in 

parentheses) represents the number of pairwise observations included in the 

determination of the coefficients. Several noteworthy observations can be 

made based upon inspection of the table. 

Three M&C variables are well correlated with 28-day modulus of rupture, 

an explicit performance predictor. These factors and their corresponding 

232 

correlation coefficients are: cement type (D105) at -0.723, percent air 

content (D107A) at 0.574, and water to cement ratio (WTOC) at -0.499. In 

each case, the sign of the coefficient is in line with practical engineering 

expectations. The ~orrel~ation coefficients, however, are based on a 

relatively small number of observations due primarily to missing modulus 

values. 

In the prockss of producing primary and secondary relationships from 

purely statistical data, it is critical to identify all variables that. 

contribute significantly to'the relationship. Failure to include a 

significant variable can cause a derived relationship to make inaccurate 

predictions. In this study, the correlation analysis include4 every 

available M&C variable. In some cases, however, missing value^ effectively 

removed a variable from the data base. It is also possible that a relevant 

variable was never included in.the data base to begin with. Another source 

of problems can be "spurious" correlations which are those that appear 

statistically significant but are actually irrekevant. For example, 

pavement p'erformance might appear highly correlbted with slump. when in 

actuality changes in construction practice over time are the cause. Time 

(i.., age) is an important variable to observe when looking for these types 

of phenomena. In the effort of trying to locatk these types of problems, 

pavement age was included in the correlation anhlyses. In fact, pavement 

thickness was found to have a somewl~at high corkelation with age which 

indicates a possible change in construction over time (i. e. , pavement thickness has historically increased with time). Identifying 

significant variables and spurious correlations are both vital to the 

development of plausible relationships. This is a difficult task and an 

argument against the use of, observational data bases in the development of 

primary and secondary relationships. I 

The correlation analysis was extended to include pavement performance 

variables (i.e., PSI and transverse cracking). The purpose was to study how 

well primary relationships based on the COPES dkta base parallel generally 

accepted primary relationships. By selecting a primary predictor that 

appears in both the primary and secondary relatlionship, the ttreasonablenessm 

of the data can be measured. Unfortunately, no observations are available 

to correlate present serviceability index (PSI) with pavement thickness, a 

known predictor of pavement performance. Only 26 observations of PSI are 

present in the current version of the COPES dat~a base. One correlation of 

note relative to primary relationships is betweien 28-day modulus of rupture 

and PSI. The Pearson correlation coefficient fpr this pair of variables is 

a relatively small (0.'333). PSI does, however, show very strong negative 

correlation with age while showing no correlati~on with the effect of 

cumulative ESALs. Once again, low pairwise obs~ervation counts make these 

numbers suspect. The second performance variab~le, transverse cracking 

(S37RH), was added and, inexplicably, displayed no correlation with any of 

the other variables in the study. The effort f!o show that primary 

relationships based OQ, COPES data are congruou~' with generally accepted 

primary relationships was unsuccessful. \I 

I 
FREQUENCY HXSTOGRAMS 

Frequency histograms are very helpful in analyzing the distribution of 

observations for a given variable. Two representative examples from the 

COPES data base are presented in figures 74 and 75. The first shows a 

histogram for water/cement ratio which fits a normal distribution 

fairly well. In contrast, the second figure shows a frequency distribution 

for concrete slump in which a mode of 1.5 in (38.1 mm) is represented by 

1011 of the 1125 non-zero observatiolis in the data base. These two frequeny 

histograms represent extremes but demonstrate the large variation in the 

distributions. 

The frequency plots allowed for rapid identification of modal values 

for the variables. Notable examples include: cement content, 53 percent 

are six-sack mixes; cement type, 97 percent are Type I cement; pavement 

thickness, 42 percenttare 9 in (229 mm); slump, 90 percent are 1.5 in (38.1 

mm); air-content, 82 percent are 5.5 percent. Potentially relevant 

variables with unfortunately large numbers of missing values are concrete 

additives with only 113 available observations, present serviceability index 

(RlR) with 26, and flexural strength (D102A) with 199 observations. No 

attempts were made to replace the missing values. 

SCATTER PLOTS 

'Scatter plots were generated to further study the relationships between 

variables, with emphasis on secondary relationships. The 28-day modulus of 

rupture, an explicit performance predictor,iwas chosen as the dependent 

variable,for these analyses. Several M&C actors were selected for use as 

1 independent variables. Figure 76 presents one 7 of the most notable plots in 

which strength as a function of entrained,air exhibits a reasonably good 

linear relationship. This coincides wity the correlation analysis performed 

earlier. However, since 82 percent of the air content measurements are near 

5.5 percerit, the figure may be misleadirig. i 1 

, I 1 

Several additional scatter plots df interest are presented in figures 

77 through 81{ In figure 77, water/cekent ratio appears to have a sharp 

;effect +on 28-day modulus of rupture. /The majority of the plots, however, 

display littie if any relationship bekween the variables. This is 

consistent with the results of the correlation analyses. 

1, 

A similar set of plots was created with slump as the independent 

var'iable. The large percentage of slump observations at the 1.5 in (38.1 

mm) level .resulted in mostly meaningless plots. Figure 82 is an example. 

Motlulus of rupture was plotted against the year opened to,traffic to 

study the correlation between these two variables. As discussed earlier, it 

is important to be aware of any correlation with time. This often hints at 

changes in common practice or technology. wSpuriousu correlations can also 

be a problem. As seen in figure 83, though, no relationship exists for the 

data. 

235 I 

I 

/ 
0.33 0.35 0.37 0.39 0.41 0.43 0.45 0.47 0.49 0.51 0.53 0.55 0.57 0.59 0.61 0.63 0.64 

WATER / CEMENT RATK) (%) 






Entrained Air (percent): 

I 

1119 cases plotted. I 

Figure 82. Mean slump versus entrained air. \ 

1 i' 

I 

I I 

REGRESSION ANALYSES 1 

I 

Multiple linear tegression analyses were used to .develop one primary 

and one secondary relationship from the COPES data. Given the results of 

the previous statistical analyses, key variables were chosen for inclusion 

in the regression study. Stepwise selection of the independent variables 

was employed using SPSSPC+ default probabilities for variable entry and 

removal based on the partial F-test. The probability of F-to-enter was 

(0.05) and the probability of F-to-remove was (0.10). This approach allowed 

the effect of individual variables to be studied when added to or taken from 

the regression equati n. Unfortunately, the high missing value count and I modal tendencies of sjeveral P key variables cast doubt on any practical use of 

the derived equation . B 

/ 

A secondary r/elationship was developed to predict 28-day modulus of 

rupture using three M&C factors as independent variables. The regression 

equation is as follows: 

D102A = 1068.1 - 103.7 (D105) - 0.045 (DlOlA) - 456.6 (WTOC) 

where : 

D102A - strength, 28-day modulus of rupture 

Dl05 - type of cement (Type I = 1, Type II 

DlOlA = amount of coarse aggregate (lb/cy). 

WTOC = water/cement ratio (by weight). 

DlOlB = amount of fine aggregate (lb/cy). 

DlOlC = amount of cement (lb/cy). 

DlOlD 7 amount of water (lb/cy). 

D104A = mean slump (in). 

D107A = entrained air (percent). 

After five regression steps, only three variables remained in the 

equation; cement type (D105), amount of coarse aggregate (DlOlA) and 

water/cement ratio (WTOC). The other available independent variables were 

excluded from the equation by the stepwise approach. The standard error for 

the prediction of 28-day modulus of rupture is 42.9 psi (3.02 kg/cm2) and 

the coefficient of determination (R2) is 0.54. The latter figure may 

indicate that a nonlinear regression model might be more appropriate though 

careful study of the scatter plots does no,t support this notion. The 

analysis included 118 observations (degrees of freedom). 

All three coefficients in tho secondary equation for predicting 

modulus of r'upture are negative and each will reduce the 1068.1 constant. 

The effect of each variable toward predicting 28-day modulus appears 

reasonable when near average values are used for the Independent variables. 

To reiterate, however, the low nmber of degrees of freedom compared to the 

overall data base and the noncanclusive R2 value make broad use of this 

equation unadvisable. 

Stepwise regression analysis was also performed to derive a primary 

performance equation for present serviceability index (RlR). As discussed 

previously, <he purpose of this analysis is to study the "reasonableness" of 

the variables that are common to both primary and secondary relationships. 
The independent variables available for considetation were pavement age 

(AGE), cumulative 18 kip ESALs (TCUMR), PCC pavqment thickness (D41), and 

modulus of rupture (D102A). As shown below, thestepwise regression process 

resulted,in an equation with only one variable qerm for pavement age (AGE) 

~mitting'modulus (D102A), the variable common tq the derived secondary 

relationship. I 

= 5.28 - 0.126 (AGE) 

where : 1 

I 

i 

R1R = present serviceability index (PSI) of pavement from roughness 

and distress measurements (ranges from 0 to 5). 

AGE = number of years pavement has been in service. 

TCUMR = one-way cumulative 18-kip single-axle loads in the right 

lane over the life of the pavement. 

D102A = 28-day modulus of rupture (psi). 

D41 = PCC pavement thickness (in). 

This equation is obviously useless since it omits many important 

factors known to have significant effect on pavement performance. It was 

hoped that traffic volume, pavement thickness, and PCC flexural strength 

would enter the equation; unfortunately, there was not enough data. 

Pavement thickness was omitted,beca.use no test section contained both 

thickness and PSI data. Only 25 observations were included in the 

regression analysis producing an R' of 0.61 and standard error of 0.40. 

A second regression analysis was performed to derive a primary relationship 

for severe transverse crackingl, another measure of pavement performance. 

Using the same set of available variables and identical criteria for entry 

and removal of independent variables, none were added during the stepwise 

regression. This is consistent with correlation matrix which presents the 

low Pearson correlation coefficients for transverse cracking (S37RH). 
I I 

\ i \ 

\, \ 

I 

I 

I 

/ APPENDIX F 

LABORATORY TESTING RESULTS 

This appendix contains the results of all laboratory testing carried out 

in this study. The results are contained within three data bases described 

below. 

m Data Base A - Results for all 64 cells, not including 8 replicate 

batches. 

e Data Base B - Results for 8 cells having one original and one 

replicate batch. 

e Data Base C - Results for all 64 cells, including replicate batches. 
Desi~n Rep Ulx Date 

Sequence Seqirence 

A 

or 

0 

------------------------------ 1 14 lOl05 

2 17 10107 

3 A 30 10118 

4 58 11117 

5 33 10120 

6 18 10107 

7 43 10131 

8 24 10111 

9 40 10128 

10 10 09130 

11 67 11121 

12 65 11119 

13 12 10105 

1 69 11/21 

15 53 11115 

16 A 5 09/27 

17 4 09126 

18 54 11116 

19 31 10119 

20 19 10108 

21 A 57 11117 

22 42 10131 

23 21 10110 

2 4 36 10124 

25 28 10llk 

26 A 48 11/03 

27 39 10128 

28 64 11119 

29 50 11115 

30 11 09/30 

31 41 10131 

32 41 11102 

3 3 70 11122 

36 45 11102 

35 29 10114 

36 51 11115 

3 7 2 09/21 

38 W 71 12106 

39 22 10110 

40 56 t3.117 

41 A 49 1114 

02 46 11102 

43 3 09/23 

11 7 09/27 

45 20 10108 

46 32 10120 

47 26 10112 

48 60 11/18 

49 23 10111 

SO 13 10105 

51 6 09127 

52 A 35 10124 

53 27 10113 

54 9 09130 

55 63 11119 

56 1 09121 

57 8 09/28 

58 15 10106 

59 61 11118 

60 66 11119 61 36 10125 

62 34 10120 

63 A 72 12/06 

64 47 11102 

CAT 

O=CLS 

1=SRC 

. - - - - - - 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

0 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

.1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

1 

Clln FAn AEQ CAQ 

(In) (02) fib) 

0.75 2.10 0.0 1542 

OK or or or 

1.50 2.84 6.5 1850 

0.75 2.10 0.0 1542 

0.75 2.10 0.0 1542 

0.75 2.10 0.0 1850 

0,75 2.10 0.0 1850 

0.75 2.10 6.5 1542 

0.75 2.10 6.5 1542 

0.75 2.10 6.5 1850 

0.75 2.10 6.5 1850 

0.75 2.84 0.0 1542 

0.75 2.84 0.0 1542 

0.75 2.84 0.0 1850 

0.75 2.84 0.0 1850 

0.75 2.84 6.5 1542 

0.75 2.84 6.5 1542 

0.75 2.84 6.5 1850 

0.75 2.84 6.5 1850 

1.50 2.10 0.0 1542 

1.50 2.10 0.0 1542 

1.50 2-10 0.0 1850 

1.50 2.10 0.0 1850 

1.50 2.10 6.5 1542 

1.50 2.10 6.5 1542 

1.50 2.10 6.5 1850 

1.50 2.10 6.5 1850 

1.50 2.84 0.0 1342 

1.50 2.84 0.0 1542 

1.50 2.84 0.0 1850 

1.50 2.84 0.0 1850 

1.50 2.84 6.5 1542 

1.50 2.84 6.5 1542 

1.50 2.84 6.5 1850 

1.50 2.84 6.5 1850 

0.75 2.10 0.0 1542 

0.75 2.10 0.0 1850 

0.75 2.10 0.0 1850 

0.75 2.10 0.0 1850 

0.75 2.10 6.5 1542 

0.25 2.10 6.5 1542 

0.75 2.10 6.5 1850 

0.75 2.10 6.5 1850 

0.75 2.84 0.0 1542 

0.75 2.84 0.0 1542 

0.75 2.84 0.0 1850 

0.75 2.84 0.0 1850 

0.75 2.84 6.5 1542 

0.75 2.84 6.5 1542 

0.75 2.84 6.5 1850 

0.75 2.14 6.5 1850 

1.50 2.10 0.0 1542 

1.50 2.10 0.0 1542 

1.50 2.10 0.0 1850 

1.50 2.10 0.0 1850 

1.50 2.10 6.5 1542 

1.50 2.10 6.5 1542 

1.50 2.10 6.5 1850 

1.50 2.10 6.5 1850 

1.50 2.84 0.0 1542 

1.50 2.14 0.0 1542 

1.50 2.84 0.0 1150 

1.50 2.84 0.0 1050 1.50 2.64 6.5 1542 

1.50 2.84 6.5 1542 

1.50 2.84 6.5 1850 

1.50 2.84 6.5 1850 

FAQ WCR ACR SLHP 

flb) (lbl (lbl (In) SSD lb) lb) 

UNUT 

(pcf 

..------- 

137.5 

141.4 

140.1 

143.7 

128.4 

138.3 

132.4 

134.9 

142.2 

143.9 

144.5 

144.8 

138.7 

137.8 

128.1 

144.3 

137.8 

142.5 

141.0 

142.0 

133.7 

132.1 

134.3 

138.7 

141.3 

143.0 

144.0 

146.3 

132.2 

142.2 

136.2 

139.9 

141.5 

144.9 

142.8 

144.3 

135.8 

137.6 

133.0 

143.8 

140.1 

145.4 

145.4 

148.8 

131.1 

143.1 

137.6 

141.4 

131.3 

144.0 

143.0 

146.4 

131.2 

141.2 

139.1 

142.5 

143.4 

146.4 

145.4 

148.0 

132.3 

137.1 

135.4 

145.5 

YLD 

(CY) 

-------- 28.9 

27.9 

28.0 

27.7 

29.2 

27.7 

28.6 

27.9 

27.5 

27.8 

27.4 

27.1 

27.4 

27.3 

29.0 

26.4 

28.3 

27.9 

27.9 

27.5 

28.2 

28.2 

27.6 

27.3 

28.0 

27.4 

26.9 

27.1 

28.1 

26.7 

27.6 

26.7 

27.9 

27.9 

28.1 

27.6 

28.2 

27.6 

28.4 

26.8 

28.7 

27.4 

27.2 

27.1 

28.9 

27.0 

27.9 

26.8 

30.3 

27.6 

27.6 

27.6 

28.8 

27.3 

27.5 

26.7 

27.6 

27.6 

27.6 

26.9 

29.0 

27.8 

27.8 

26.5 

AIR 

(X) 

---------- 3.1 

4.4 

3.4 

3.6 

10.5 

5.5 

10.0 

7.3 

3.5 

3.0 

3.1 

1.9 

6.1 

6.8 

12.0 

4.0 

5.0 

4.7 

4.1 

2.5 

6.6 

10.0 

7.2 

5.5 

3.8 

2.8 

1.5 

2.5 

9.0 

5.8 

7.0 

5.3 

3.0 

8.2 

4.0 

2.9 

11.6 

7.6 

9.4 

5.1 

3.4 

3.1 

2.3 

2.5 

11.0 

6.0 

8.2 

5.2 

10.0 

3.0 

4.2 

3.2 

11.0 

5=2 

7.2 

5.0 

3.6 

3.0 

3.6 

2.8 

11.0 

7.5 

8.5 

4.4 
Design Rep 

Seq . A 

or 

B 

Mix 

Seq . I,::;;,::;;:::;~:;;;;F ;;:;;:;::;f;;:;y:;:;;F ,;:::,::;;:;:E::;;F :;::y3:;;:~"~i:~"f~~~~~1FI~f~)~~~)E~~Eft:F p"ENTAGEs By "OL" I I I OV CEP YAP FAP AzW CWL I DAY FLEX. STRENGTH. 7-DAY Caw. SIM(GT11. 17-DAY TENSILE STRENGTHI 28-DAY CWR. STRENGTH 128-DAY ).0. OF ELASTICITY I (2) I%) (1) (I) (I) I 

Desien Rep Mln 

seq. Seq A 

or 

E 

3 A 30 

3 E 55 

fr71 frtZfr7AVEfrfDIF fpc7lfpc72fpc7AVEfpcDfF Ec283 Ec284 Ec28AnEc28DfF 

(psl)(pl)(pri) (psi) (psl)(pri) (psi) [psi) (WSI)(WSI)o(PSf) (m'sI) 

- I W CEP YAP PAP AIRP CUI(UL 

7-DAY FLW. StaENGTH. 7-DAY CWR. STRERGTFI. 28-DAY )(OD. OF EtASTICIrY (g) (g) (X) fX) I I 
CEQ WAQ FAQ WCR ACR SLHP UNWT YLD AIR TEMP 

(lb) (lb) (lb) (lbl (lbl (in) (pcf) (CY! (XI (OF) 

426 236 SSD lb) lbf 

0 r 0 r 

584 270 ------------------------------------------------------------------------------------------ 426 236 1772 0.55 7.78 0.00 137.5 28.9 3.1 79.0 

584 270 1552 0.46 . 5.30 0.00 141.4 27.9 4.4 80.0 

Design Rep Mix Date CAT CAM 

Sequence Sequence (in) A O=CLS 0 75 

or l=SRG o r 

B 1 50 .................................................. 

1 14 10105 0 0.75 

2 17 10107 0 0.75 

3 A 30 10118 0 0.75 

3 B 55 11116 0 0.75 

4 58 11/17 0 0.75 

5 33 10120 0 0.75 

6 18 10107 0 0.75 

7 43 10131 0 0.75 

8 24 10111 0 0.75 

9 40 10128 0 0.75 

10 10 09/30 0 0.75 

11 67 11121 0 0.75 

12 65 11119 0 0.75 

13 12 10105 0 0.75 

14 69 11121 0 0.75 

15 53 11115 0 0.75 

16 A 5 09127 0 0.75 

16 B 59 11117 0 0.75 

AEQ CAQ 

(OL) (lb) 

0.0 1542 

0 r or 

6 5 1850 ----------------- 

0.0 1542 

0.0 1542 

0.0 1850 

0.0 1850 

0.0 1850 

6.5 1542 

6.5 1542 

6.5 1850 

6.5 1850 

0.0 1542 

0.0 1542 

0.0 1850 

0.0 1850 

6.5 1542 

6.5 1542 

6.5 1850 

6.5 1850 

6.5 1850 

0.0 15h2 

0.0 1542 

0.0 1850 

0.0 1850 

6.5 1542 

6.5 1542 

6.5 1542 

6.5 1850 

6.5 1850 

0.0 1542 

0.0 1542 

0.0 1542 

0.0 1850 

0.0 1850 

6.5 1542 

6.5 1542 

6.5 1850 

6.5 1850 

0.0 1542 

0,O 1850 

0.0 1850 

0.0 1850 

6.5 1542 

6.5 1542 

6.5 1542 

6.5 1850 

65 lE50 

0.0 1542 

0.0 1542 

0.0 1542 

0.0 1850 

0.0 1850 

6.5 1542 

6.5 1542 

6.5 1850 

6,5 1850 

0.0 1542 

0.0 1542 

0.0 1850 

0.0 1850 

0.0 1850 

6.5 1512 6.5 1542 

6.5 1850 

6.5 1850 

0.0 1542 

0.0 1542 

0.0 1850 

0.0 1850 

6.5 1542 

6.5 1542 

6.5 1850 

6.5 1850 

6.5 1850 
7-DAY FLEX. STRENGTH. 7-DAY COneR. STRENGTH. 2-DAY TENSILE STRENGTH 28-DAY CONPR. STRENGTB 28-DAY W. OF ELASTICITY I I I I 

Desl~n Rep Mix 

Seq. Seq. 

A 

or 

B -----..---------- 

1 14 

2 17 

3 A 30 

3 B 55 

4 58 

5 33 

6 18 

7 4 3 

8 24 

9 40 

10 10 

11 67 

12 65 

13 12 

14 69 

15 5 3 

16 A 5 

16 B 59 

17 4 

18 54 

19 31 

20 19 

21 A 57 

21 B 25 

22 42 

23 21 

24 36 

25 28 

26 A 48 

26 B 16 

27 3 9 

28 64 

29 50 

30 11 

3 1 4 1 

32 4 4 

3 3 70 

34 45 

35 29 

36 51 

37 2 

38 A 71 

38 B 37 

39 22 

40 56 

41 A 49 

41 B 52 

42 46 

43 3 

4 4 7 

45 20 

46 32 

4 7 26 

48 60 

4 9 23 

50 13 

51 6 

52 A 35 

52 B 62 

5 3 27 

- 54 9 

55 63 

56 1 

57 8 

58 15 

59 61 

60 66 

61 38 

62 34 

63 A 72 

63 B 68 

64 47 

L PERCENIAGEC BY VOLUME 

CAP CEP WAP FW AIRP CWL 

(2) (XI (X1 (X) (XI tX) 
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I 

I 

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I 

I , 

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45.1 D. M. Burmister, "The General Theory of Stresses and ~is~lacements in 

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I 

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I 

69.1 G. L. Dehlen, "The Effects of on- in ear Response on the Behavior of 

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I 

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I 

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255 
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I 

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82.10 J. P. Zaniewski, B. C. Butler, G. C. Cunningham, G. E. Elkins, M. S. 

Paggi and R. B. Machemehl, "Vehicle Operating Costs, Fuel Consumption, 

and Pavement Type and Condition Factors," Report No. FHWA-PL-82-001, 

Federal Highway Administration, Washington, D.C., 1982. 

83.1 Georgia Department of Transportation, Specifications for Portland 

Cement Concrete Pavement, 1983. 

83.2 Idaho Department of Transportation, Specifications for Portland Cement 

Concrete Pavement, 1983. 

83.3 Illinois Department of Transportation, Standard Specifications for 

Road and Bridge Construction, 1983. 

83.4 Minnesota Department of Transportation, Standard Specifications for 

Construction, 1983. 

83.5 Commonwealth of Pennsylvania, Department of Transportation 

Specifications, 1983. 

K. Majidzadeh, G. J. Ilves, and H. Skylut, "Mechanistic Design of 

Rigid Pavements," Final Report, Vol. 1 (unpublished), Contract No. 

DTFHll-9568, Federal Highway Administration, Washington D.C., 1983. 
i '" \ " 

- 83.7 K. Majidzadeh and G. J. Ilves, ttEvaluatiqn of Rigid Pavement Overlay 

1 Design Procedures," Report No. FHWA/RD-831/090, Federal Highway 

j 

1 Administration: Washington, D. C . , ~ecembdr I 1983. I i I 

84.1 R. M. Weed, "Adjusted Pay Schedules: New Concepts and Provisions," 

i Transportation Research Record No. 986, 1984. 

84.2 K. Majidzadeh and G. J. Ilves, "Correlation of Quality Control 

I Criteria and Performance of PGC- Pavements," Report No. FHWA/RD-83/014, 

Federal Highway Administration, Washington, D.C., March 1984. 

84.3 J. B. Rauhut, L. Lytton and M. I. Darter, "Pavement Damage Functions 

for Cost Allocations, Volume 1 - Damage Equations and Load Equivalency 

Factors," Report No. FHWA/RD-84/018, FeQeral Highway Administration, 

Washington, D.C., June 1984. 

1 ' 

1 

4 84.4 R. G. Packard, "Thickness Design for Concrete Highway and Street 

\ Pavements," Portland Cement Association, Skokie, Illinois, 1984. 

84.5 "State-of-the-Art in Asphalt Pavement Specifications," Report No. 

FHWA/RD-84/075, Federal Highway Administration, Washington, D.C., 

1984. \ 

eed, Memorandum entitled, "Combined Thickness/Strength/Smooth84*6 R* ness 7 Specifications for Concrete Pa~ement,~ New Jersey Department of 

Transportation, June, 1984. 

84.7 California Department of Transportation, Specifications for Portland 

Cement Concrete Pavement, 1984. 

84.8 "Building Code Requirements for Reinforced Concrete (ACI 318-83)," 

American Concrete Institute, 1984. 

84.9 A. M. Ioannides, "Analysis of Slabs-on-Grade for a Variety of Loading ! and Support Conditions," Ph.D. Dissertation, University of Illinois, 

I I Urbana, 1984. 

85.1 R. G. Packard and S. D. Tayabji (Portland Cement Association), "New 

PCA Thickness Procedure for Concrete Highway and Street Pavements," 

Proceedings, Third International Conference on Concrete Pavement 

Design and Rehabilitation, pp. 225-236, April 1985. 

85.2 M. I. Darter, J. M. Beuker, M. B. Snyder and R. E. Smith (University 

of Illinois), "Portland Cement Concrete Pavement Evaluation System 

(COPES)," NCHRP Project 1-19, Report NO.' 277, September 1985. 

85.3 State of New York, Department of Transportation Office of Engineering, 

Standard Specifications, 1985. 

85.4 "Data Bases for Performance-Related Specifications for Highway 

Construction", ARE Inc - Engineering Consultants, NCHRP Project 

10-26, January 1985. 
I 

85.5 E. G. Nawy , Reinforced Concrete, Prentice Hall .'.. Inc. , ~nglewood 

Cliffs, New Jersey, 1985. 

I 

85.6 A. M. Ioannides, M. R. Thompson and E. J. Barenberg, "Westergaard 

Solutions Reconsidered," TRR 1043, Transportation Research Board, 

Washington, D.C., 1985. 

'85.7 MVMA Motor Vehicle Facts,& Figures, 1985. 

86.1 R. M. Weed, "Contractor Earns Bonus for High Quality Concrete," 

Concrete International, November 1986. 

86.2 M. L. Powell, "Quality - Contractors Cannot Afford Less," 

Transportation Research Record News, December 1986. 

86.3 "AASHTO Guide for Design of Pavement Structures," Volume 1, American 

Association of State Highway and Transportation Officials, Washington, 

D.C., 1986. 

86.4 "AASHTO Guide for Design of Pavement Structures," Volume 3, American 

Association of State Highway and ~rans~brtation Officials, Washington, 

D.C., 1986. 

i 

86.5 Colorado State Department of Highways, Specifications for Portland 

Cement Concrete Pavement, 1986. 

87.1 J. E. Smiley, S. B. Seeds, R. F. Carmichael and B. F. McCullough, 

ilComputerized Pavement Design Users Manual - City of Austin," 

Transportation and Public Services Department, June 1987. 

87.2 W. J. Green, R. L. Carrasquillo and B. F. McCullough, "Coarse 

Aggregate for PCC Pilot Study Evaluation," Center for Transportation 

Research Center, University of Texas at Austin, Research Report No. 

422-1, August 1987. 

87.3 State of Ohio, Department of Transportation, Construction and Material 

Specifications. 1987. 

87.4 P. E. Irick, "A Conceptual Framework for the Development of 

Performance-Related Materials and Construction Specifications1',, 

Transportation Research Record 1126, ~ranbportation Research Board, 

Washington, DIG., 1987. / 

88.1 "Performance -Related Specifications for Hot -Mix ~s~haltic Concrete, " 

Pennsylvania Transportation Institute, NCHRP Project 10-26A, Final 

Report in preparation, (as of June 1990). 

89.1 P. E. Irick and ARE Xnc-Engineering Consultants, tl~haracteristics of 

Load Equivalence Relationships Associated with Pavement Distress and 

Performance," Final Report, Trucking Research Institute, American ' 

Trucking Association, Washington, D.C., September 1989; 

*U.S.GOVERNMENT PRINTING OFFICE:1990-717-000:27134