Appendix A: Annotated Outlineof Model References

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This appendix contains a detailed annotated outline of the primary references reviewed during the information search performed in this study. The literature review is organized in four categories:

1. Currently available early-age behavior models similar to the HIgh PERformance PAVing (HIPERPAV) System.¹
2. Early-age behavior models with potential incorporation into HIPERPAV II.
3. Literature review on jointed plain concrete pavement (JPCP) models.
4. Literature review on continuously reinforced concrete pavement (CRCP) models.

The following sections document the literature reviewed on each of the above categories.

A.1 Currently Available Early-Age Behavior Models Similar to HIPERPAV

In addition to HIPERPAV, four other available software programs that predict the early-age behavior of concrete were identified. These include Durability Models of Concrete (DuCOM^®), HYdration, MOrphology, and STRUCture (HYMOSTRUC^®), Quadrel^®, and 4C-Temp&Stress^®. HYMOSTRUC and Quadrel focus on developing the adiabatic hydration curves for concrete. DuCOM and 4C-Temp&Stress are more robust finite-element programs that calculate the state of stress in early-age concrete structures. These programs are similar in some aspects to HIPERPAV, but also have differences in theory and application. DuCOM, HYMOSTRUC, Quadrel, and 4C-Temp&Stress are summarized below.

A.1.1 DuCOM

Maekawa, K., Chaube, R., and Kishi, T., "Modeling of Concrete Performance," Hydration, Microstructure Formation and Mass Transport, E&FN Spon, New York, NY, 1999.

DuCOM focuses on evaluating the durability of structural concrete. This program assesses the durability of concrete from the green (or fresh) state up to several years of age using a finite-element-based program. DuCOM is a lifespan simulator that can model the microscopic behavior of concrete at early ages and relate this to its long-term performance. This program considers the properties of the concrete material's mix proportions; the casting, curing, and environmental conditions; and the shape and size of the structural concrete. The concrete's mechanistic processes are divided into short and long terms. The short-term processes are related to hydration, microstructure development, moisture transport, temperature rise, shrinkage, and creep. The long-term processes include transport of external agents into the concrete and its long-term creep behavior. Research on DuCOM continues at the Concrete Laboratory of the University of Tokyo, Japan.

A.1.2 HYMOSTRUC

Van Breugel, K. Simulation of Hydration and Formation of Structure in Hardening Cement-Based Materials, Second Edition, Delft University Press, 1997.

HYMOSTRUC is designed to predict the adiabatic (and isothermal) hydration curves of concrete. It combines the fields of cement chemistry, physics, and stereology. The particle size of the cement, the water-to-cement ratio (w/c), the initial curing temperature, and the chemical composition of cement are all considered when formulating the concrete's hydration curves. HYMOSTRUC focuses on the microscopic level. The overall degree of hydration is assumed to be the sum each individual cement particle's degree of hydration. The output from HYMOSTRUC possibly can be used to predict the macroscopic behavior of hardened concrete structures. Connecting the microscopic behavior of the cement to its macroscopic properties, such as strength and stiffness, is one of HYMOSTRUC's future objectives.

A.1.3 Quadrel

Digital Site Systems, Inc. Quadrel, Information Technology Solutions for Construction.

Quadrel is a software program that makes adiabatic heat signature testing and analysis of fresh concrete possible in the laboratory. Fresh concrete samples are placed into a Qdrum calorimeter that simultaneously measures the temperature gain and heat loss. The data are processed using Quadrel, and the adiabatic heat of hydration curve is generated. Using the hydration curve, the concrete's strength can be estimated as a function of maturity. Quadrel can be used to estimate the initial set time of the concrete, evaluate the performance of chemical admixtures and pozzolans, and determine how suitable concrete mixes are in the control of thermal cracking.

A.1.4 4C-Temp&Stress

4C-Temp&Stress. Temperature and Stress Simulation During Hardening, Users Manual, Germann Instruments, Inc., Evanston, IL, 1998.

Using the finite-element method (FEM), 4C-Temp&Stress computes the time-dependent temperatures and the state of stress in concrete structures. The program considers the influence of heat of hydration, thermal boundary conditions, and casting time and temperature on the structure's state of stress. This program also calculates the influence of cooling pipes or heating wires on the concrete's thermal state. Environmental factors like wind and radiation are taken into account. Loading of the structure enters by structural supports, self-weight, point loads, line loads, and momentum. The user can define the materials properties of the system, including those of concrete, soil, or insulation. Likewise, a mix design module for concrete specifies quantities of cement, aggregate, mineral additives, chemical additives, and water. In turn, each of these constituents has its own database with additional properties. Properties of the concrete mix, including slump, air content, thermal conductivity, and density, can be defined. The adiabatic heat development in the fresh concrete can be input, as can the concrete's stiffness and Poisson's ratio. Thermal expansion, creep, and compressive and tensile strength of concrete are all properties that 4C-Temp&Stress takes into account. The concrete structures can have several geometries. For output, the maturity of every point in the structure's cross section is calculated, as are the stresses and strengths.

A.2 Early-Age Behavior Models with Potential Incorporation Into HIPERPAV II

The early-age properties of concrete are influenced significantly by the climatic conditions and temperatures, as well as by the concrete mix components. In this section, a literature review of early-age concrete properties is completed. The properties that are addressed are concrete maturity, drying shrinkage, moisture transport, set time, creep, and various thermal properties.

A.2.1 Concrete Hydration

This section briefly summarizes the primary references that contain candidate models that were identified to characterize the hydration of concrete at early ages.

Byfors, J. "Plain Concrete at Early Ages," Research 3:80, Swedish Cement and Concrete Research Institute, Stockholm, Sweden, 1980.

This document contains many of the models and principles used in HIPERPAV I. This document emphasizes the modeling of the following mechanical properties: compressive strength, tensile strength, ultimate tensile strain, modulus of elasticity, Poisson's ratio, and creep effects. Moisture transport and shrinkage is acknowledged, but limited information is presented. The influences of the following primary factors were studied: cement composition, cement fineness, w/c, curing temperature, moist curing, and effect of some chemical admixtures: accelerator (CaCl₂) and air-entraining agents. This document presents many test results, but limited mechanistic models.

The degree of hydration is used to describe the extent to which reaction between cement and water has developed, and the degree of hydration is linked to compressive strength and creep development. It is concluded that a certain critical degree of hydration is required before any strength gain can be obtained in the cement paste.

Byfors also documents a model that provides an estimate of heat of hydration as a function of time. The model defines the heat development for the four main clinker compounds at ages of 3, 7, 28, 90, and 365 days.

Knudsen, T., "Modeling Hydration of Portland Cement—The Effect of Particle Size Distribution," Conference Proceedings, Characterization and Performance Prediction of Cement and Concrete, Edited by Young, J.F., United Engineering Trustees, Inc., New Hampshire, pp. 125-150, 1983.

This paper presents a mathematical model for the development of the hydration of portland cement with time, called the dispersion model, which is founded on the particle size distribution (PSD) of the cement. The rate and duration of reaction of smaller particles is different from those of larger particles. During hydration, smaller particles might be fully hydrated, and the larger particles might be at a lower degree of hydration. Therefore, at any given time, the degree of hydration has a distribution that is dependent on the PSD. All cement particles are assumed to react independently of each other. It is shown that the particle size has a dominant effect on the shape of the hydration curve.

The model development is based on kinetic theory for solid-state reactions, with the assumption that spherical grains react according to the shrinkage core model. In this model, the growing reaction zone is surrounding the unreacted core. The assumed kinetic function is used with the Rosin-Rammler PSD to obtain a very simple formulation of the degree of hydration in terms of a constant that characterizes the PSD and a rate constant that accounts for the effect of temperature on the form of the hydration curve. The model is compared to data obtained by other researchers, and good agreement with the data is found.

Pinto, R.C.A., "The Effect of Curing Temperatures on the Development of Mechanical Properties of Fresh and Hardened High-Strength Silica Fume Mixtures—A Maturity Approach," Dissertation, Cornell University, Ithaca, NY, 294 pp., 1997.

In this dissertation, Pinto presents expansions on the dispersion model presented by Knudsen, and fits the shape of the strength gain to a hyperbolic model, which has been shown to provide the best fit. Because the different reactions of cement hydration can be controlled through kinetics and/or diffusion processes, Pinto states that "one would not expect a constant value for E_a for all stages of cement hydration." Diffusion-controlled processes are expected to be less temperature sensitive than kinetically-controlled ones. Therefore, a lower activation energy (AE) value is expected as the hydration process progresses. Pinto reports that "as an average, the AE of C₃S hydration, or the apparent AE of portland cement hydration, is twice as high during the early chemically (kinetically) controlled stages than at the late, diffusion-controlled stage." Pinto provides a method to select an appropriate AE value for each of the five stages of hydration. This method is called the variable E-method. Data are further presented to address the selection of the most appropriate value for the AE, and it is shown that if AE values are selected based on strength data, different AE values can be obtained depending on the shape (hyperbolic, exponential, parabolic-hyperbolic) of the strength-age relationship.

Van Breugel, K., Simulation of Hydration and Formation of Structure in Hardening Cement-Based Materials, Second Edition, Delft University Press, Netherlands, 305 pp., 1999.

This book presents a complete review of literature and available techniques to model concrete hydration and structural development in cement-based materials, and the model developed is referred to as HYMOSTRUC. The models are able to allow for the effects of cement composition, PSD, w/c, and the initial mix temperature. For simplicity, the Rosin-Rammler function is recommended to model the cement PSD. A formulation similar to the current model in HIPERAV is recommended to determine the maximum heat of hydration. The degree of hydration is defined in terms of structural formation, and modeled as the ratio of the amount of cement that has reacted, at a certain time relative to the original amount of cement.

The ultimate degree of hydration is determined based on the amount of water available for reaction with the cement particles, and the space available for the hydration products. However, this model is rather complex, and the relative humidity within the pore structure must be modeled. The model also does not account for different cement compositions and fineness of the cement, which will most likely influence this value.

Models are presented to determine the AE of the mix design in terms of the C₃S content of the cement used, the degree of hydration of the mix, and the temperature of the concrete.

Maekawa, K., Chaube, R., and Kishi, T., Modeling of Concrete Performance—Hydration, Microstructure Formation, and Mass Transport, E&FN Spon, New York, NY, 308 pp., 1999.

Models are presented to predict the pore structure development of hydrating concrete, which then is used to determine the mechanical and physical properties of the concrete with respect to long-term durability. To determine the pore structure development, the following components are modeled: heat generation, water consumption, pore water pressure, equilibrium of pore water pressure, and moisture migration. The model described in this book is referred to as DuCOM.

A multicomponent heat of hydration model is presented, where the heat of hydration is determined through summing the heat rates of the different clinker minerals. The heat of hydration rate for each of the mineral compounds is divided into stages in terms of cumulative heat generation. The heat generation rate of the most critical stage (stage 2) was fitted according to values obtained from adiabatic tests. Stage 3 was identified as the diffusion control stage, and a slower heat generation rate was assigned to each compound. Other blending minerals, such as slag or fly ash, are incorporated as additional mineral components. The effect of the development of ettringite on the formation of C₃A and gypsum with C₄AF is accounted for in the proposed multicomponent model.

A temperature model is proposed similar to the one initially developed by Byfors, but numerous modification factors are added. These modification factors account for the reduction of probability of contact between unhydrated compounds and free pore water, the effect of mineral composition of portland cement, the reduction of the pozzolan's reaction due to the shortage of calcium hydroxide, the relative cement fineness expressed as a ratio of the Blaine fineness, and the retardation of the overall rate of cement and slag reaction caused by the presence of fly ash.

A moisture transport model for cementitious materials is presented, which considers the multiphase dynamics of liquid and gas phases. The moisture transport characteristics are dependent on the previously determined microstructure. The model can also consider the effect of wetting and drying cycles for concrete exposed to natural environments with fluctuating moisture levels.

Onken, P. and Rostásy, F.S., "A Practical Planning Tool for the Simulation of Thermal Stresses and for the Prediction on Early Thermal Cracks in Massive Concrete Structures," Proceedings of the RILEM ( French acronym for Réunion Internationale des Laboratoires et Experts des Matériaux, Systèmes de Constructions et Ouvrages) Symposium on Thermal Cracking in Concrete at Early Ages, Edited by Springenschmid, R., E&FN Spon, London, pp. 289-296, 1995.

Models similar to those developed by Byfors are presented, however, the degree of hydration model is modified to only contain two parameters, compared to the three initially proposed by Byfors. It is reported that the shape of the hydration curve is a function of the clinker composition, PSD, the w/c, and the initial mix temperature. No models are presented to define the effect of these variables on the heat of hydration.

Bentz, D.P., Garboczi, E.J., Haecker, C.J., and Jensen, O.M., "Effects of Cement Particle Size Distribution on Performance Properties of Portland Cement-Based Materials," Cement and Concrete Research, 1999.

The effects of cement PSD on a variety of performance properties are demonstrated. Laser diffraction techniques were used to determine the PSD of the two cements analyzed. It is shown that finer grinding results in enhanced hydration, heat release, and strength at all investigated ages. At later ages, the cumulative degree of hydration and heat release of the different cements are nearly equivalent. Even though the finer particles require less time to achieve set due to its increased hydration rate, it actually requires more hydration, as more particle-to-particle bridges need to be built.

Komonen, J. and Penttala, V., "Influence of Admixture Type and Concrete Temperature on Strength and Heat of Hydration of Concrete," 10^th International Symposium on the Chemistry of Cement, Edited by Justnes, H., Trondheim, Norway, 8 pp., 1997.

In this paper, the authors present some valuable results that quantify the effect of different admixtures and initial concrete temperatures on the heat of hydration of concrete. Based on the variables considered, it is concluded that the mixing temperature is the most significant variable. The higher the mixing temperature, the earlier the heat gain took place. Numerous heat of hydration curves are presented for all the variables evaluated. The efficiency of the different plasticizers varied considerably at early ages.

Ma, W., Sample, D., Martin, R., and Brown, P.W., "Calorimetric Study of Cement Blends Containing Fly Ash, Silica Fume, and Slag at Elevated Temperatures," Cement, Concrete, and Aggregates, Vol. 16, No. 2, pp. 93-99, December 1994.

In this paper, the hydration of blended cements containing fly ash, silica fume, and ground-granulated blast-furnace (GGBF) slag over the temperature range of 0 degrees Celsius (°C) to 55 °C was studied by isothermal calorimetery, and the heat evolution during the first 24 hours of hydration was examined. The AE for the different blended cements was determined and the following values were obtained: 39.0, 26.7, 30.4 and 49.3 kilojoule per mole (kJ/mol) for portland cement, fly ash, silica fume, and slag blended cements, respectively.

Andersen, P.J., Andersen, M.,E., and Whiting, D., A Guide to Evaluating Thermal Effects in Concrete Pavements, SHRP-C-321, Strategic Highway Research Program, National Research Council, Washington, DC, 104 pp., 1993.

This paper briefly summarizes all the models required to determine the temperature development in concrete at early ages due to the exothermic reaction and the influence of climatic conditions. The models used are very similar to those developed by Byfors (as mentioned above) and heat transport by thermal conduction, convection, and radiation also is introduced. Based on the analysis performed, final recommendations are made to the extent of thermal cracking based on the slab thickness, concrete placement temperature, air temperatures, and the cement type used in the concrete mixture. In this project it is assumed that the problems could occur when any of the following three conditions are encountered:

• Risk of thermal cracking becomes too large when the temperature differential exceeds 20 °C.
• Risk of temperatures within the concrete slab becoming too high. Permanent strength loss can be experienced when the concrete temperatures are higher than 60 °C.
• Risk of early freezing. According to American Concrete Institute (ACI) 308, freezing must be prevented until the concrete has reached a compressive strength of 3.45 kPa.

The degree of hydration in this study is also defined in terms of two adiabatic parameters, one that defines the curvature of hydration, and the other that defines the time of hydration initiation. Typical values for different cement types are provided. In this study, activation energies for a variety of cement were determined to be as follows: Type I = 48.8 kJ/mol, Type II = 41.3 kJ/mol, Type III = 42.5 kJ/mol, Type I + fly ash = 38.2 kJ/mol, and Type II + fly ash = 36.8 kJ/mol.

Eren, O., Brooks, J.J., and Celik, T., "Setting Times of Fly Ash and Slag-Cement Concretes as Affected by Curing Temperature," Cement, Concrete, and Aggregates, Vol. 17, No. 1, pp. 11-17, June 1995.

The time of setting of different concrete pastes by penetration resistance (American Society for Testing and Materials (ASTM) C 403) is presented. Penetration resistance was determined under isothermal curing temperatures ranging from 6 °C to 80 °C for concrete containing up to 50 percent of fly ash or GGBF slag. At high temperatures, slag concrete has shorter setting times than Type I cement concrete. The setting times of fly ash concrete are longer than those of Type I cement concrete and slag concrete. Empirical relationships are presented for setting time as a function of penetration resistance, temperature, and cement replacement level.

Douglas, E., Elola, A., and Malhotra, V.M., "Characterization of Ground-Granulated Blast-Furnace Slags and Fly Ashes and Their Hydration in Portland Cement Blends," Cement, Concrete, and Aggregates, Vol. 12, No. 2, pp. 38-46, 1990.

In this paper, chemical analysis, PSD, heat evolution rate, total heat evolution, and strength development were studied for three GGBF slags, and two fly ashes of low and high CaO content. At all stages, the heat evolution rates and total heat evolution by the fly ashes were lower than the corresponding values for the GGBF slag.

Rahhal, V.F. and Batic, O.R., "Mineral Admixtures Contribution to the Development of Heat of Hydration and Strength," Cement, Concrete, and Aggregates, Vol. 16, No. 2, pp. 150-158, December 1994.

This paper presents a wide range of test results to quantify the benefits of adding mineral admixtures, such as natural pozzolan, fly ash, and GGBF slag, to control heat development. Blended cements were prepared using ordinary portland cement clinker, gypsum, and mineral admixtures. The percentages of mineral admixtures investigated were 0, 10, 20, 33, 40, 50, 70, and 90, by mass. Tests were performed at 3, 7, 28, 90, and 180 days. Empirical coefficients of the contribution of mineral admixtures to heat of hydration have been obtained, as well as a mathematical expression to estimate the heat of hydration of blended cements based on the mineral admixture selected, the percentage used, and the heat of hydration of the control cement. The following conclusions pertinent to the HIPERPAV II project include:

• The rate of heat evolution of blended cements containing the mineral admixtures accelerates up to 7 days, decelerates towards 28 days, and remains constant toward 180 days.
• Liberated heat at a given age decreases as replacement percentages of the mineral admixtures increase.

Each mineral has an optimum range of replacement percentage that increases mechanical strength and lowers the heat of hydration.

Tazawa, E. and Miyazawa, S., "Influence of Cement Composition on Autogenous Shrinkage of Concrete," Proceedings on the 10^th International Congress on the Chemistry of Cement, Gothenburg, Sweden, Vol. 2, June 1997.

Autogenous shrinkage is defined as the macroscopic volume reduction caused by hydration of cement. Based on the test performed by the authors, it was concluded that autogenous shrinkage was strongly influenced by the type of cement, which is due to the difference in cement composition, and especially the content of C₃A and C₄AF. Compared to normal portland cement, autogenous shrinkage is large for high early-strength cement and is lower for moderate-heat cement. Autogenous shrinkage is very low for low heat cement with high C₂S contents. For the mixtures investigated, autogenous shrinkage increases with a decrease in w/c. This ratio is, therefore, the main variable in the prediction model. An empirical equation is presented to estimate the autogenous shrinkage strain of the concrete based on the time elapsed, the type of cement, and the w/c used. The prediction model is valid for concrete with w/c ranging from 0.2 to 0.56, a coarse aggregate factor of 0.55 to 0.65, and an environmental temperature of 20 °C.

Coole, M.J., "Heat Release Characteristics of Concrete Containing Ground-Granulated Blast-Furnace Slag in Simulated Large Pours," Magazine of Concrete Research, Vol. 140, No. 144, September 1988.

This paper investigates the effect of three different European sources of GGBF slag blended with ordinary portland cement. It is shown that both the peak temperature and the time to reach this temperature are influenced strongly by the slag source. Five levels of slag replacement were investigated, and with a reactive slag at a moderate replacement of cement (20-40 percent), the temperature rise at the center of the pour was higher than when an equivalent cement was used.

A.2.2 Concrete Maturity

Maturity is a technique used to estimate the strength gain of concrete based on the measured temperature history during curing. A maturity function is a mathematical expression that accounts for the combined effects of time and temperature on the concrete's strength development. This function usually is assumed to be a linear function of temperature or to obey the exponential Arrhenius equation.

Carino, N.J., "CRC Handbook on Nondestructive Testing of Concrete, Chapter V—The Maturity Method," Edited by Malhorta, V.M., CRC Press, Florida, 1991.

This reference presents a historical review of all the widely used maturity methods. The equivalent age concept is explained, and the importance of temperature on early-age concrete properties is stressed. The maturity concept was initiated by Saul, where maturity is the sum of change in temperature multiplied by the time interval (Nurse-Saul function). Limitations of this method are that a datum temperature is needed to calculate the temperature change. The equivalent age concept was initiated in 1960 to 1977 by Arrhenius. This age conversion factor is a function of absolute temperature. Maturity is equal to the rate constant multiplied by age (where the rate constant depends on temperature). To relate strength to maturity, hyperbolic and other empirical functions have been developed. The empirical formulas have coefficients that follow the shape of the curve. Equivalent age is the most flexible technique available to represent maturity.

Method of Testing the Strength of Portland Cement Concrete Using the Maturity Method, Iowa Department of Transportation (DOT), Materials. Iowa Method 383. Office of Materials.

The Iowa DOT uses maturity to measure the in-place strength of the concrete. Part 1 describes the destructive testing method to get the relationship between maturity and concrete strength. Part 2 describes instrumentation of the concrete to obtain in-place temperatures. The Nurse-Saul method is used.

Carino, N., Lew, H.S., and Volz, C.K., "Early-Age Temperature Effects on Concrete Strength Prediction by the Maturity Method," ACI Journal, pp. 93-101, March-April 1983.

Early-age temperature is found to influence strength-maturity relationship at later ages. Maturity is calculated using the simplified Nurse-Saul equation. Mathematical models that represent maturity can have either log or hyperbolic functions.

Marzouk, H. and Hussein, A., "Effect of Curing Age on High-Strength Concrete at Low Temperatures," Journal of Materials in Civil Engineering, Vol. 7, No. 3, pp. 161-167, August 1995.

The effect of curing age on the strength of silica fume concrete containing fly ash at cold temperatures is given. This paper describes how properties of the concrete change as a function of temperature, composition, modulus of rupture, and splitting tensile strength. The effect of pozzolans and admixtures are considered. Maturity methods are discussed. This paper states that the maturity method may not be appropriate for concrete placed under freezing temperatures.

Jensen, O. M. and Hansen, P.F., "Influence of Temperature on Autogenous Deformation and Relative Humidity Change in Hardening Cement Paste," Cement and Concrete Research, Vol. 29, pp. 567- 575, 1999.

The autogenous deformation, relative humidity, and temperature changes in hardening cement paste are investigated. Maturity concepts do not apply to these phenomena. Concrete self-desiccates because of the low w/c, shrinking in bulk, which can cause cracking. Self-desiccation shrinkage is a form of chemical shrinkage that can eventually lead to failure of the entire structure.

Kim, J.K., Moon, Y.H., and Eo, S.H., "Compressive Strength Development of Concrete with Different Curing Time and Temperature," Cement and Concrete Research, Vol. 28, No. 12, pp. 1761-1773, 1998.

Previous maturity work focuses on predicting concrete strength under isothermal conditions. In practice, this is not the case. Varying temperatures must be taken into account, and this paper tries to develop a maturity model that does that.

A.2.3 Drying Shrinkage of Concrete

Drying shrinkage happens when the rate of moisture loss from the pavement surface is greater than the rate at which it can be replenished by free moisture in the slab. The desiccated concrete shrinks, and this can lead to warping and cracking of the structure. Most typically, drying shrinkage affects exposed surfaces.

Al-Sugair, F. H. and Almudaiheem, J.A., "Further Modification of the Ross Equation to Predict the Ultimate Drying Shrinkage of Concrete," ACI Materials Journal, Vol. 87, No. 3, May-June 1990.

The Ross equation is used to predict drying shrinkage. A large amount of experimental data (drying shrinkage versus time) are used, and the effect of volume-to-surface-area ratio on drying shrinkage is the focus. Its error is ± 25 percent. Drying shrinkage was predicted from 1 to 28 days in some cases.

Han, M.W. and Lytton, R.L., "Theoretical Prediction of Drying Shrinkage in Concrete," Journal of Materials in Civil Engineering, Vol. 7, No. 4, November 1995.

The water potential is used to estimate the degree of drying shrinkage. Water potential is a type of stress that forces moisture to move and causes hydrated cement particles to shrink and expand. Drying shrinkage is related to water potential by a logarithmic curve.

Kim, J.K. and Lee, C.S., "Prediction of Differential Drying Shrinkage in Concrete," Cement and Concrete Research, Vol. 28, No. 7, pp. 985-99, 1998.

The effect of creep is incorporated into the drying shrinkage prediction. The drying shrinkage profile is obtained; this depends on the distance from the exposed concrete surface and on time.

Persson, B., "Experimental Studies on Shrinkage of High-Performance Concrete," Cement and Concrete Research, Vol. 28, No. 7, pp. 1023-1036, 1998.

Relationships are developed to predict the amount of autogenous shrinkage and drying shrinkage in concrete as a function of w/c, amount of silica fume in the concrete, the ratio of evaporated water to mixing water, and internal relative humidity. The focus of this paper is relating silica fume content (slurry or granular) to total drying, and autogenous shrinkage.

Shah, S.P., Ouyang,C., Marikunte, S., Yang, W., and Becq-Siraudon, E., "A Method to Predict Shrinkage Cracking of Concrete," ACI Materials Journal, pp. 339-346, July-August 1998.

Nonlinear fracture mechanics is used in this reference to predict drying shrinkage of a ring specimen. Cracking of concrete is caused by its creep, free shrinkage, elastic modulus, tensile strength, and fracture toughness properties. Cracking results when there is a difference in the amount of free shrinkage and creep. The effect of creep on shrinkage cracking was determined using the CEB-FIP (French acronym for European Committee for Concrete-International Federation for Prestressing) model. The time dependence of concrete fracture toughness is measured. To use this model, fracture toughness and critical crack tip-opening displacement are needed.

Shimomura, T. and Maekawa, K., "Analysis of the Drying Shrinkage Behavior of Concrete Using a Micromechanical Model Based on the Micropore Structure of Concrete," Magazine of Concrete Research, Vol. 49, No. 181, pp. 303-322, December 1997.

A micromechanical drying shrinkage model is developed by the researchers who developed DuCOM. This model takes into account the concrete's pore structure and microscopic phenomena, described according to simplified mechanical and thermodynamic assumptions. Drying shrinkage is determined using a four-step procedure: 1) analytical pore size distribution, 2) time-dewatering relationship, 3) dewatering-shrinkage relationship, and 4) time-shrinkage relationship. A limitation of this model is that it has been validated on only two specimens. In addition, the theoretical equations require extensive amounts of data and subsequent experimental testing.

A.2.4 Moisture Transport in Concrete

The properties of concrete are highly dependent upon the moisture conditions within. By appropriately monitoring the moisture content of concrete, it is possible to minimize the development of some distresses. Three different pavement distresses associated with moisture loss are plastic-shrinkage cracking, delamination spalling, and drying-shrinkage cracking. Plastic-shrinkage cracking is caused by the loss of water from the surface of a concrete pavement at early ages. If the pavement is cured properly, this cracking can be prevented. Moisture lost from the surface of the concrete pavement can also cause delamination spalling and drying shrinkage. Delamination of the concrete surface results when pavement strength decreases due to insufficient moisture in the concrete at the time of curing. This weakened portion of concrete detaches from the monolithic slab to form a delamination (or flat bottom) spall. Drying shrinkage is caused by moisture lost from the pavement surface during curing. This can lead to increased levels of stress in the pavement and subsequent crack formation.

RILEM Bulletin, "Properties of Set Concrete at Early Ages—State of the Art Report," Materials and Structures, Vol. 14, No. 84, pp. 398-450, 1981.

Most mechanical and physical properties of concrete are affected by moisture. Concrete is a porous material, and volume changes occur due to the presence of water, such as shrinkage and swelling. All porous materials bind water from the atmosphere with a certain relative humidity or from water on contact. Water in concrete is either chemically combined or physically adsorbed. The sorption isotherm relates the material's equilibrium content of water to that of the ambient environment's humidity. To reach an equilibrium state with a higher relative humidity, an adsorption isotherm is used. To decrease the concrete's moisture, a desorption isotherm is used. These isotherms are a function of the concrete's degree of hydration, among other factors. There are no data on sorption isotherms at early ages. The transport of moisture in the concrete is governed by Darcy's law and Fick's first law. Moisture transport depends on the concrete's moisture content. For a fixed relative humidity, transport depends on the concrete's composition, age, and temperature. Age significantly affects the concrete's diffusion prior to 28 days. For mature concrete, w/c and air content are the influential factors.

Xi, Y., Baźant, Z.P. Molina, L., and Jennings, H. M., "Moisture Diffusion in Cementitious Materials," Moisture Capacity and Diffusivity, Journal of Advanced Cement-Based Materials, Vol. 1, pp. 258-266, 1995.

This paper discusses the diffusion of water in concrete. Concrete dries due to three different diffusion mechanisms. They are ordinary drying, Knudsen diffusion, and surface diffusion. An equation for moisture diffusivity is given that is highly dependent on the concrete's w/c. Increasing a concrete's w/c causes diffusivity to increase at low humidity levels.

Maekawa, K., Chaube, R., and Kishi, T., Modeling of Concrete Performance: Hydration, Microstructure Formation and Mass Transport, E&FN Spon, New York, NY, 1999.

Moisture transport in concrete is modeled by the DuCOM researchers. This model should be able to account for the effect of crack formations on water distribution in the concrete structure.

Mjornell, K.N., Moisture Conditions in High-Performance Concrete: Mathematical Modeling and Measurements, Department of Building Materials, Chalmers University of Technology, Sweden, 1997.

A moisture model has been developed for high-strength concrete that accounts for both self-desiccation and moisture transport. The effect of curing on the concrete has been studied at very early ages, as well.

A.2.5 Set Time of Concrete

Concrete set is typically divided into two stages. The first is initial set, when the concrete paste stiffens considerably. The second stage is final set, when the concrete has hardened so that it can sustain load. The setting of concrete referred to here is the final set. This parameter is very important when determining the early-age stress state of the concrete.

Byfors, J., Plain Concrete at Early Ages, Swedish Cement and Concrete Research Institute, 1980.

This paper investigates how different aggregate and admixtures affect the setting time of concrete and its time-dependent stiffness. Aggregates in the concrete that are investigated include quartzite, granite, dolomite, and andesite. Blended cements are investigated, such as ordinary portland cement with silica fume, slag, and fly ash. The linear and nonlinear growth of the concrete modulus as a function of time is recorded at early ages and at later ages.

Uchikawa, H., Hanehara, S., Shirasaka, T., and Sawaki, D., Effect of Admixture on Hydration of Cement, Adsorptive Behavior of Admixture and Fluidity and Setting of Fresh Cement Paste," Cement and Concrete Research, Vol. 22, pp. 1115-1129, 1992.

A rheological discussion on concrete setting times is presented. The yield stress is related to the mortar specimen's set time.

De Siqueira Tango, C.E., "An Extrapolation Method for Compressive Strength Prediction of Hydraulic Cement Products," Cement and Concrete Research, Vol. 28, No. 7, pp. 969-983, 1998.

The determination of concrete set time for pavements is discussed in this report. If drying shrinkage and creep of the concrete are not taken into account, the zero-stress point corresponds to the zero set temperature. However, if these factors are considered, the zero stress point occurs at a higher temperature. Compressive stresses can be alleviated by shrinkage and creep effects. A novel method to determine set temperature is presented. The procedure is to fill a mold with fresh cement mix and determine the set temperature when the mix separates from the sides of the mold.

Struble, L.J. and Lei, W.-G., "Rheological Changes Associated with Setting of Cement Paste," Advances in Cement-Based Materials, Vol. 2, p. 244, 1995.

Set times can be a measure of the cement hydration's AE. The Arrhenius method is used to determine how the rate of chemical reaction depends on temperature. The thermal sensitivity of the reaction is the AE. AE is time dependent, but it is usually assumed to be a single value during all stages of hydration. The hotter the mix, the faster the setting time.

A.2.6 Thermal Properties of Concrete

Because temperature is one of the primary factors that influence the behavior of jointed concrete pavements (JCP) at early ages, the thermal properties of the concrete must be understood. HIPERPAV II incorporates seven thermal properties of concrete. They are coefficient of thermal expansion (CTE), thermal conductivity, specific heat, thermal diffusivity, convection, emissivity, and solar absorptivity. This section defines these parameters and summarizes how these properties change at early ages. Early-age factors that influence concrete's thermal properties are its degree of hydration, the amount and type of aggregate, and the water-to-cementitious materials ratio (w/cm). HIPERPAV II requires an understanding of concrete thermal properties at early ages and in the long term.

A.2.6.1 Coefficient of Thermal Expansion

CTE is defined as the relative length change of a material caused by changing its temperature 1 degree. In concrete, CTE is a function of the paste and the aggregate. The aggregate's CTE depends upon its mineralogical composition, and only slightly on its moisture content. The CTE of paste depends primarily on the moisture content, w/cm, and age of the paste.

Khan, A.A., Cook, W.D., and Mitchell, D., "Thermal Properties and Transient Thermal Analysis of Structural Members During Hydration," ACI Materials Journal, Vol. 95, No. 3, pp. 293-303, May-June 1998.

CTE of concrete is assumed to be equal to the volumetrically weighted average of its ingredient's CTE. Concrete CTE is known to increase with increasing concrete density. CTE is highly dependent on age only during the first few hours after construction. The early-age CTE is significantly higher than the hardened concrete's CTE. After 10 hours of hydration, it decreases, then remains constant.

LaPlante, P. and Boulay, C., "Evolution du Coefficient de Dilation Thermique du Beton en Fonction de sa Maturite Aux Tout Premiers Ages," Materials and Structures, Vol. 27, pp. 596-605, 1994.

CTE of concrete was measured at early ages and plotted as a function of equivalent age at 20 °°C.

A.2.6.2 Thermal Conductivity

Thermal conductivity is the ratio of heat flux to temperature gradient. Thermal conductivity is defined as the amount of heat flowing per unit time between two parallel faces of unit area when the faces are unit distance apart. The plates are maintained at a temperature difference of 1 degree. All the heat entering one face leaves the opposite face.

Khan, A.A., Cook, W.D., and Mitchell, D., "Thermal Properties and Transient Thermal Analysis of Structural Members During Hydration," ACI Materials Journal, Vol. 95, No. 3, pp. 293-303, May-June 1998.

Thermal conductivity varies with concrete density. Heavier aggregates typically have concrete with a higher thermal conductivity. Because thermal conductivity of water and air are different from that of the hydration products, thermal conductivity is expected to change during early hydration. Water has lower conductivity than aggregate. Concrete made with a low w/c and a higher density should have a high thermal conductivity. This is why lightweight concrete with high porosity and, therefore, low conductivity, has good insulating properties.

It is difficult to measure thermal conductivity in early-age concrete. Some researchers report a drop in thermal conductivity from 6 hours to 7 days, while others say there is no change in thermal conductivity after 24 hours. For normal strength concrete (30 megapascals (MPa)), its thermal conductivity during maturation is 33 percent higher than when hardened. For high-strength concrete (100 MPa), there is only a 2-percent difference in the thermal conductivity of maturing and hardened concrete. Thermal conductivity is typically independent of temperature within the normal climactic range. However, above 100 °C, thermal conductivity decreases linearly.

Properties of Set Concrete at Early Ages—State of the Art Report, Materials and Structures, Vol. 14, No. 84, November-December 1981.

This article reports that aggregate type is the most important factor affecting the thermal conductivity of concrete.

Brown, T.D. and Javaid, M.Y., "The Thermal Conductivity of Fresh Concrete," Materials and Structures, Vol. 3, No. 13, pp. 411-416, 1970.

These researchers report a decrease in thermal conductivity of concrete with age for fresh conventional concrete.

A.2.6.3 Specific Heat

Specific heat is defined as heat capacity. Specific heat is determined by measuring the temperature rise in a calorimeter using a predetermined supply of energy. There is limited information about specific heat of concrete in the literature, and some of it is contradictory.

Khan, A.A., Cook, W.D., and Mitchell, D., "Thermal Properties and Transient Thermal Analysis of Structural Members during Hydration," ACI Materials Journal, Vol. 95, No. 3, pp. 293-303, May-June 1998.

Specific heat is a function of time. A 15-percent drop in specific heat a few hours after casting to 5 days later for rapid hardening concrete with a w/c of 0.5 is reported. Moisture content has a significant effect on specific heat. Oven-dry specimens have lower specific heat than do saturated samples. Also, specific heat increases with temperature and decreases with increasing concrete density.

Mindess, S. and Young, J. F., Concrete, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1981.

Specific heat of concrete is not affected by aggregate type. It varies by only 8 percent due to a change in aggregate. Typically, specific heat ranges from 800 to 1200 joules per kilogram (J/kg) °C. It is dependent on porosity (w/c), water content, and temperature. In the reference synthesis, a decrease between 1 and 20 percent in the concrete's specific heat is reported as it hardens. Specific heat is a function of the cement's degree of hydration.

A.2.7 Creep

Knowledge of the nonlinear creep behavior is important when accurately estimating axial stresses. The behavior of young concrete under load is best modeled by including viscoelastic deformations and plastic flow. In HIPERPAV I, the effect of relaxation is accounted for empirically, and a more sophisticated model that combines the effects of creep and viscous response (relaxation) of concrete at early ages is required. This section provides a brief summary of the primary references that contain candidate models.

Umehara, H., Uehara, T., Iisaka, T., and Sugiyama, A., "Effect of Creep in Concrete at Early Ages on the Thermal Stresses," Proceedings of the International RILEM Symposium, Munich, Germany, pp. 79-86, E&FN Spon, October 1994.

This document contains the approach followed to model the creep behavior in HIPERPAV I and II. Models were developed based on tensile and compressive creep tests. The stress level, period of loading, and temperature at the test were the parameters investigated. The effective modulus method is used to characterize the creep, and the viscoelastic nature of concrete loaded at early ages, therefore, cannot be modeled.

Baźant, Z.P., "Numerical Determination of Long-Range Stress History From Strain History in Concrete," Materials and Structures, RILEM Paris, Vol. 5, No. 27, pp. 135-141, May-June 1972.

This paper presents an efficient systematic numerical algorithm for computing the stress history from any prescribed strain history in a linear age-dependent viscoelastic material such as hardening concrete. The method is applicable for any form of the creep function. It is assumed that stress history is a series of sudden (discontinuous) stress increments, then the algebraic equations resulting from the superposition of creep responses due to all the individual stress increments are solved. The disadvantage of this method is that large storage space could be required to store the complete history of stresses for all the elements in the structure. Uncertainty exists about the applicability of the principle of superposition in the case of creep recovery. Baźant and Panula (as referenced below) address this issue more directly and provide an example of the measured creep versus predicted creep where the theory works very well.

Baźant, Z.P., and Panula, L., "Practical Predictions of Time-Dependent Deformations of Concrete," Materials and Structures, Third RILEM, Vol. 11, 1978.

In this document, the Double Power Law is developed to predict concrete creep at constant humidity and temperature from the composition of the concrete mix, strength, age at loading, and load duration. The Double Power Law is perhaps the most well known compliance function, and it has been used by many researchers since its development. With the Double Power Law, creep of concrete at constant moisture and thermal state is described by power curves for load duration (t-t₀), and by inverse power curves to account for the effect of the loading age t₀. The Double Power Law was modified later to the Triple Power Law (discussed next) to improve the accuracy of the long-term creep prediction.

Baźant, Z.P., and Chern, J.C., "Strain Softening with Creep and Exponential Algorithm," Journal of Engineering Mechanics Division, American Society of Civil Engineers (ASCE), Vol. 111, No. 3, 1985.

In this paper, Baźant provides an improved creep model for concrete at constant temperature and water content. It gives the creep rate as a product of power functions of the load duration, the age of loading, and the current age of the concrete. This model was called the Triple Power Law, and the Double Power Law was modified with a binomial function to provide a more accurate description of long-term creep. This model is extensively calibrated with test data obtained from literature.

Emborg, M., Thermal Stress in Concrete Structures at Early Ages, Doctoral Thesis, Luleå University of Technology, Division of Structural Engineering, 285 pp, 1989.

Emborg tested the validity of both the Double and Triple Power Laws at early ages and concluded that neither was calibrated for loading at early ages, and their use was not intended to predict creep for young concrete. Therefore, Emborg adjusted the Triple Power Law to account for loading at ages earlier than about 2 days, and the extended Triple Power Law was developed. Most of the parameters for the Triple Power Laws remained unchanged, and two additional functions were added: one that accounts for the age dependence of the instantaneous deformation, and another to increase the creep when the load has been applied at early ages.

Westman, G., Concrete Creep and Thermal Stresses. Doctoral Thesis, Luleå University of Technology, Division of Structural Engineering, 301 pp, 1999.

Westman modified the shape of the two additional functions first developed by Emborg in 1989 based on early-age creep tests performed. In this thesis, Westman provides the necessary values for each of the parameters in the extended Triple Power Law.

A.3 JPCP Literature Review

The literature review of JPCP models is presented in this section. The models are divided into seven sections. The first section reviews pavement structural models, such as the stresses that develop in the pavement due to temperature, moisture, and traffic loading, for example. The second section reviews available climatic models that can be used in conjunction with the structural models to account for climatic conditions at the time of pavement curing and also over the years as the pavement is subjected to long-term use. Third, the JPCP distress models are presented. These models are primarily empirical in nature. This means that the models are valid only for the pavement sections for which they were developed. In HIPERPAV II, it is preferable that mechanistic models be used that have been calibrated and validated with actual experimental data. Literature review on faulting, transverse cracking, and spalling are presented.

A.3.1 JPCP Structural Models

The JPCP structural models are used to predict the stresses acting on the pavement due to the different forms of loading, such as temperature, moisture, and traffic. Eight references are described below in the annotated bibliography.

Huang, Y.H., Pavement Analysis and Design, Prentice Hall, Englewood Cliffs, NJ, 1993.

Huang discusses KENSLABS, a finite-element program that can be used to predict pavement behavior in detail. The types of foundations that can be accounted for are liquid, solid, and layer. Pavement layers can either be bonded or unbonded and have different or the same material properties. Likewise, the load transfer at multiple slabs can be taken into account, as can the curling/warping loading response. Arbitrary pavement dimensions, loading conditions, and shoulder conditions can all be considered. This program requires a substantial amount of computer storage.

Smith, K.D., Peshkin, D.G., Darter, M.I., and Mueller, A.L., "Performance of Jointed Concrete Pavements, Volume III—Summary of Research Findings," FHWA-RD-89-138, Federal Highway Administration (FHWA), McLean, VA, November 1990.

The ILLI-SLAB program is described in this reference. ILLI-SLAB is a finite-element program that analyzes pavements. It calculates stresses, deflections, and moments directly due to loading or temperature effects. This program is able to analyze pavements of arbitrary dimensions with any number of slab arrangements. Two layers either can be bonded or not bonded, and these layers can have the same or different material properties. The subgrade can either be a liquid or solid subgrade, and the program can account for uniform or nonuniform support due to erosion. Similarly, arbitrary loading (axle) conditions and pavement shoulder conditions can be taken into account with ILLI-SLAB. This program, however, requires large amounts of computer storage.

Lee, Y-H. and Darter, M.I., "Mechanistic Design Models of Loading and Curling in Concrete Pavements," Airport Pavement Innovations: Theory to Practice, Proceedings of the Conference. Edited by Hall, J.W. Jr., ASCE, September 1993.

FEMs are used to analyze the edge stresses on the pavement. The FEM can account for finite slab length, finite slab width, and slab curling. These correction factors can be used to correct Westergaard's solutions based on the infinite slab assumption.

Lee, Y-H. and Lee Y-M., "Corner Stress Analysis of Jointed Concrete Pavements," Transportation Research Record No. 1525, Transportation Research Board (TRB), National Research Council, Washington, DC, 1996.

FEMs again are used to determine the corner stresses on a pavement, similar to the reference above. Design factors considered are widened outer lanes, tied concrete shoulders, and different loading configurations. These correction factors can be used in the fatigue equation for predicting corner cracks.

Ramsamooj, D.V., "Stresses in Jointed Rigid Pavements," Journal of Transportation Engineering, pp. 101-108, March-April 1999.

Fracture mechanics is used to determine design stresses midway between the edge of the rigid pavement and at the corner. The solutions generally agree with Westergaard, finite-element, and American Association of State Highway and Transportation Officials (AASHTO) road test solutions. However, stresses predicted by this equation are 30 percent greater than the Westergaard stresses. Pavement deflections and stresses also are calculated. When wheel load is placed at the middle of the slab, critical stresses are at the bottom. Convex curling in a pavement occurs due to thermal temperature gradients. Traffic loading is critical for this condition.

Liang, R.Y. and Niu, Y-Z., "Temperature and Curling Stress in Concrete Pavements: Analytical Solutions," Journal of Transportation Engineering, Vol. 124, No. 1., pp. 91-101, January-February 1998.

The objective of this paper is to develop a theoretical model to predict the temperature and curling stresses in a concrete pavement. Based on nonlinear temperature gradients through the slab, the authors are able to develop the equivalent temperature bending moment. If a pavement experiences a severe temperature change (10 °C in 1 hour), the nonlinear temperature gradient must be taken into account. However, for more gradual temperature changes, linear temperature gradients are sufficient.

Kuo, C.-M., "Effective Temperature Differential in Concrete Pavements," Journal of Transportation Engineering, Vol. 124, No. 2., pp. 112-116, March-April 1998.

Three-dimensional FEM code is used to evaluate curling stresses in pavements due to temperature gradient, slab self-weight, and support under the concrete slab. The number of allowable traffic loads can be calculated before terminal serviceability is reached.

Grater, S.F. and McCullough, B.F., "Analysis of Jointed Concrete Pavement," Research Report 1244-10, Center for Transportation Research, The University of Texas at Austin, Austin, TX, 1994.

The mechanisms that cause cracking in JCPs are discussed in this report. Climatic factors, such as changing temperatures and moisture conditions 1 year after construction, are used in the analysis. The climatic analysis is extended from several days to 1 year. This program has been revised extensively at the University of Texas at Austin, evolving from JRCP-1 to JRCP-6.

A.3.2 JPCP Climatic Models

The JPCP climatic models are used to predict pavement temperatures and moisture conditions. Climatic conditions are especially influential during early-age curing, but are also critical to the pavement's long-term performance. In the following section, several climatic models are described.

McCullough, B.F. and Rasmussen, R.O., Fast-Track Paving: Concrete Temperature Control and Traffic Opening Criteria for Bonded Concrete Overlays, Publication No. FHWA-RD-98-167, October 1999.

This reference describes the theory behind the software package HIPERPAV I. This program predicts early-age pavement behavior caused by temperature and moisture changes during the first 72 hours after concrete placement. At its core is a finite-element temperature prediction model. The model takes into account heat generated internally due to hydration, solar absorption, convection, irradiation, and age-dependent specific heat and thermal conductivity. The early-age variations in temperature can have a significant influence on the behavior of young concrete. Thermal and moisture stresses must be controlled to minimize early-age damage to the concrete pavements.

Muller, A.L., Peshkin, D.G., Smith, M.I., Darter, M.I., Performance of Jointed Concrete Pavements, Volume VI, Appendix C—Synthesis of Concrete Pavement Design Methods and Analysis Models, FHWA-RD-89-141, FHWA, McLean, VA, July 1990.

A review of climatic models is given in this reference. The models mentioned include Climatic-Material-Structural and Liu-Lytton drainage models.

Lytton, R.L., Pufahl, D.E., Michalak, C.H., Liang, H.S., and Dempsey, B.J., An Integrated Model of the Climate Effects on Pavements, FHWA-RD-90-033, 285 pp., FHWA, McLean, VA, November 1989.

The Integrated Climate Model (ICM) is a one-dimensional coupled heat and moisture flow program that is intended for use with pavements. Based on the location of the selected site, the structure's material properties, and the historical climatic data, the ICM internally generates weather patterns of rainfall, solar radiation, air temperature, cloud cover, windspeed, and snowfall throughout the year. The ICM determines the temperature, frost and heave zone depths, frost heave, layer elastic moduli, and pore water pressure profile at different depths throughout the pavement structure at different stages during the year. The model is the combination of three models developed during previous research efforts. They are the Climatic-Materials-Structures Model, the Infiltration and Drainage Model, and the Frost Heave and Thaw Settlement Model.

Barber, E.S., "Calculation of Maximum Pavement Temperatures from Weather Reports," Bulletin 168, Highway Research Board, Washington, DC, pp. 1-8, 1957.

This reference describes a model that could be used in pavements to determine the initial temperature profile. The model is based on air temperature, wind velocity, and solar radiation inputs, which can all be obtained from weather records. This model provides a solution to the differential equation of conduction of heat in a homogeneous isotropic material. The model has the following limitations:

• Only one pavement layer can be analyzed.
• The effect of rain, snow, and clouds on the pavement surface is not taken into account.
• The model assumes a semi-infinite mass.

A.3.3 JPCP Distresses

Guidelines have been developed in the past that relate design features to pavement distresses. These references are summarized here. Most of the guidelines are based on empirical data, so it is best not to extrapolate these models to sets of inputs outside the realm of those used in their development.

Smith, K.D., Wade, M J., Peshkin, D.G., Khazanovich, L.H. Yu, T., and Darter, M.I., Performance of Concrete Pavements, Volume II: Evaluation of In-Service Concrete Pavements, FHWA-RD-95-110, FHWA, McLean, VA, June 1998.

This report synthesizes the behavior of more than 300 concrete sections. It provides critical levels of distress for the JPCP with regard to joint faulting, transverse cracking, longitudinal cracking, joint spalling, and roughness in terms of Present Serviceability Rating (PSR) and International Roughness Index (IRI). It also synthesizes the behavior of the pavements in terms of the design features. Design features that are investigated are pavement thickness, base type, subgrade type, joint spacing, joint orientation, transverse joint load transfer, joint sealant, drainage, shoulder type, widened lanes, reinforcement, and maximum coarse aggregate size. For example, an increase in pavement thickness translates to a decrease in transverse cracking and joint spalling, while there is no significant change in faulting. The mechanisms behind these trends also are discussed. For the example given, thicker slabs theoretically reduce stresses in the concrete, so the pavement will not be subjected to as severe a load. This translates to a reduction in spalling and transverse cracking. A summary of the influence of design features on pavement distresses is given in table 1.

*AC - asphalt concrete, AGG - aggregate, ATB - asphalt-treated base, JRCP - jointed reinforced concrete pavement, PCC - portland cement concrete

The arrows indicate the conditions that cause the distresses to increase or decrease, and the dash implies that there is no influence. Cells with an "x" indicate that no trend could be concluded or there was not enough data. This reference also examined European and Chilean concrete pavements to learn how pavements in the United States can be improved. In Europe, the four modernity categories expected to increase pavement performance are nonerodible base courses, positive pavement drainage, strengthened structure (dowel bars and CRCP), and the optimization of material use (wider lanes and trapezoidal cross section). Only 25 percent of U.S. pavements incorporate two or more of these features.

Yu, H.T., Smith, K.D., Darter, M.I., Jiang, J., and Khazanovich, L., Performance of Concrete Pavements, Volume III: Improving Concrete Pavement Performance, FHWA-RD-95-111, FHWA, McLean, VA, June 1998.

This reference develops models that predict joint faulting, slab cracking, joint spalling, pavement serviceability, and pavement roughness. Three hundred pavements were used to formulate these empirical models, and most of the pavements are located in the Upper Midwest, have carried 10 million 18-kip equivalent single-axle loads (ESALs) and are 10 to 15 years old. The majority of the JPCP pavements are in the wet-freeze climatic zone and have nonstabilized bases. Trends are given for the distresses as a function of traffic, dowel-bearing stress, drainage, annual precipitation, freezing index, dowel bar size, joint spacing, and stabilized bases. The distresses investigated in this report are faulting for doweled and nondoweled pavements, transverse cracking, transverse joint spalling, and roughness. Guidelines are developed that recommend the preferred pavement design for minimal pavement distress.

Titus-Glover, L., Owusu-Antwi, E B., Hoener, T., and Darter, M.I., Design and Construction of PCC Pavements Volume II: Design Features and Practices that Influence Performance of Pavements, FHWA-RD-98-127, FHWA, McLean, VA, October 1998.

This report uses canonical discriminant analysis to assess how design factors affect the performance of JPCP. The pavement distress analysis is performed for the four climatic regions of wet-freeze, wet-no freeze, dry-freeze and dry-no freeze. The distresses that are analyzed are faulting with and without dowels, transverse cracking, and pavement roughness. A summary table showing the influence of long-term factors and design parameters on pavement transverse cracking is shown in table 2. The pavements are subdivided into slabs that are less than 254 millimeters (mm) thick and those that are more than 254 mm thick. The arrows indicate the conditions that cause transverse cracking to increase or decrease, and "N/A" implies that these factors had no influence. A dash means that no trend could be concluded or that there was not enough data.

*DF - dry freeze, DNF - dry-no freeze, WF - wet freeze, WNF - wet-no freeze

Sensitivity Analyses for Selected Pavement Distresses, SHRP-P-393, Strategic Highway Research Program, National Research Council, Washington, DC, 1994.

This reference provides models for predicting JPCP distresses, namely joint faulting in doweled and nondoweled pavements, transverse cracking, joint spalling, and roughness of doweled and nondoweled JPCP. The models are based on mechanistic and empirical concepts, and a fatigue analysis is used to predict distress formation. A sensitivity analysis is completed for each model, and trends are given showing how the input affects the distress magnitude. Several limitations of these models are apparent. Only a limited number of pavement sections were used to develop these models, so they should not be used to extrapolate to other pavements. Likewise, the data from all four climatic regions are lumped together. The researchers rank input parameters to show the parameters' importance in influencing the performance of PCC pavements. The first parameter is age, followed by traffic loading, slab thickness, modulus of subgrade reaction (k-value), precipitation, percent steel tied with joint spacing, edge support tied with freeze-thaw cycles, and subgrade type.

Smith, K.D., Peshkin, D.G., Darter, M.I., and Mueller, A.L., Performance of Jointed Concrete Pavements, Volume III—Summary of Research Findings, FHWA-RD-89-138, FHWA, McLean, VA, November 1990.

This reference assesses how design features influence the behavior of 95 pavements. Trends show how each design parameter influences pavement distresses. Limitations of these models are the limited database used to develop them and their inability to account for construction-related distresses. The models were developed empirically, and because pavement performance is highly variable, these models should be used only on the pavements for which they were developed.

Titus-Glover, L., Owusu-Antwi, E.B., and Darter, M.I., Design and Construction of PCC Pavements, Volume III: Improved PCC Performance Models, FHWA-RD-98-113, FHWA, McLean, VA, January 1999.

This research report gives a history of JPCP distress model development and lists the prediction equations. The mechanisms behind faulting, spalling, transverse cracking, corner breaks, and roughness are discussed. A mechanistic-empirical basis is used to develop these equations. The empirical data are extracted from the Long-Term Pavement Performance (LTPP) Program database. The regression equations were developed using multiple linear regression, nonlinear regression techniques, and the Statistical Package for Social Sciences. To develop the transverse and corner-cracking models, a linear fracture mechanics approach is used in conjunction with the fatigue damage approach. To develop the spalling model, the spall stress is calculated using a mechanistic model. It is a function of traffic, environment, incompressibles in the joint, and the concrete properties. The IRI model depends on the initial pavement IRI, traffic loading, and pavement aging.

Darter, M.I., Becker, J.M., Snyder, M.B., and Smith, R.E., Portland Cement Concrete Pavement Evaluation System: COPES, National Cooperative Highway Research Program (NCHRP)-277, National Cooperative Highway Research Program, September 1985.

A total of 418 sections were used to develop regression models for predicting JPCP performance. Design factors, material/soil factors, climatic factors, and maintenance-related factors were examined in developing the model. Several recommendations were to use stabilized bases, PCC shoulders, increased subgrade k modulus, increased concrete modulus of rupture, larger dowels, and increased slab thickness.

Perera, R.W., Byrum, C., and Kohn, S.D., Investigation of Development of Pavement Roughness, FHWA-RD-97-147, FHWA, McLean, VA, May 1998.

Roughness models were developed using data taken from the LTPP databases. A model was formulated for each climatic region, and for doweled and nondoweled pavements. Correlation methods were used to find the most influential parameters affecting pavement distresses.

Hansen, W., Jensen, E.A., Mohr, P., Jensen, K., Pane, I., and Mohamed, A., The Effects of Higher Strength and Associated Concrete Properties on Pavement Performance, Volume I—Final Technical Report, The University of Michigan, Department of Civil and Environmental Engineering, July 2000.

This report subdivides pavement variables into six sections: environmental, design, concrete, subbase, traffic loading, and distress factors. It examines how each one influences pavement behavior. The distresses investigated are joint faulting, joint spalling, transverse cracking, and corner breaks. Focus is placed on examining how specific concrete properties influence the distresses. Table 3 shows how flexural strength impacts joint spalling, transverse cracking, and corner breaks, but not joint faulting.

This meets one of the study objectives: to determine the concrete properties that contribute to exceptional long-term pavement performance. The key properties with regard to pavement distress are concrete flexural strength, elastic modulus, CTE, and fracture energy. Fracture properties of the concrete are important with regard to transverse cracking and corner breaks.

A.3.3.1 JPCP Faulting

Faulting often is reported to be caused by the erosion of subbase material from under the approach side of the slab, and its deposition under the leave side. When the slab deflects on the leave side, material is pushed toward the approach slab due to hydraulic action. When the approach slab is loaded by the passing wheel, the material is pushed back to the leave side. The fines accumulate under the leave slab. Over time, there is a difference in the vertical profile of the approach and leave sides of the pavement; this is termed faulting. Erosion of the subbase is due to shear stresses induced by water at the joint. In the following section, several references are summarized that relate to pavement faulting.

Ksaibati, K. and Staigle, R., "Faulting Performance Modeling for Undoweled Plain Concrete Pavements," Transportation Research Record 1482, TRB, pp. 1-6, Washington, DC, 1995.

Faulting of nondoweled JPCP in Wyoming is modeled using an empirical regression model. Wyoming is part of the dry-freeze region of the United States . Factors incorporated into the faulting regression equation are environmental factors, average joint width, edge support, subgrade soil classification, traffic loads, and the presence of positive drainage.

Bendana, L.J. and Yang, W.-S., "Rehabilitation Procedures for Faulted Rigid Pavement," Transportation Research Record 1388, TRB, pp. 200-210, Washington, DC, 1993.

Initially, faulting is found to increase linearly with age. When the fault distance is greater than 1.6 mm, faulting increases nonlinearly. Faulting is caused primarily by traffic loading. Faulting is very difficult to correct after it has occurred. Severe faulting has been found on New York State highways, and remediation efforts are needed. Two rehabilitation methods used were to pump grout under the slab and to grind the pavement surface. If the grout is not installed evenly, or if there is too much grout or too little grout, it is possible that the JCP will blowout or crack due to uneven subbase. Installing load transfer devices is the most effective way to reduce faulting in JPCP.

Bustos, M., de Solminhac, H.E., Darter, M.I., Caroca, A., and Covarrubias, J.P., "Calibration of Performance Models for Jointed Concrete Pavements Using Long-Term Pavement Performance Database," Transportation Research Record 1629, TRB, pp. 108-116, Washington, DC, 1998.

Faulting data found in the LTPP database are analyzed for JPCP pavements. Calibration factors are presented based on the climatic region. It is found that faulting in the dry-no freeze sections is the lowest of all the regions.

Ioannides, A.M., Lee, Y., and Darter, M.I., "Control of Faulting through Joint Load Transfer Design," Transportation Research Record 1286, TRB, pp. 49-56, Washington, DC, 1990.

A mechanistic-empirical faulting model is developed for JPCP with dowels. The major influencing factor is the bearing stress at the dowel-concrete interface, which is determined mechanistically. It is a function of the modulus of dowel support, joint width, wheel load, load transfer efficiency (LTE) (assumed to be 45 percent), dowel stiffness, dowel moment of inertia, critical dowel distribution factors, and relative stiffness of the dowel-concrete system. This model uses both Westergaard and Timoshenko theory. A concern is how close the dowels must be to the joint to provide effective load transfer. In addition, an equation for the faulting of nondoweled pavements is given where the load transfer is provided by aggregate interlock.

Hansen, E.C., Johannesen, R., and Armaghani, J.M., "Field Effects of Water Pumping Beneath Concrete Pavement Slabs," Journal of Transportation Engineering, Vol. 117, No. 6, November-December 1991.

This reference investigates water pressures and velocities due to pumping under slabs. Traffic produces high pressure under the approach slab and suction under the leave slab. Frictional erosion generates loose, fine material. Water flow at the joint is generally in the opposite direction of the traffic. Pumping is more severe under pavements with upward thermal curling.

Van Wijk, A J. and Lovell, C.W., "Prediction of Subbase Erosion Caused By Pavement Pumping," Transportation Research Record 1099, TRB, pp. 45-57, Washington, DC, 1985.

This paper lists erosion tests of subbase material, such as the rotational shear device, the brush test, the jetting test, and the vibrating table. The rotational shear device can be used to investigate the erosion of clay and stabilized materials. Noncohesive materials cannot be tested with it. The jetting test is used for noncohesive materials. The brush test is primarily used for stabilized materials. The most commonly used subbases in the United States are portland cement stabilized, crushed stone, dense graded, asphalt concrete, sand, and asphalt-stabilized subbases. The climatic conditions at the pavement location determine the performance of the pavement layers, especially its temperature and moisture content. Regression equations are given that relate erosion to variables such as pavement age and portland cement content. Materials that resist erosive shear stresses of 50 Pa or greater should not erode for the life of the pavement. Materials that erode for a shear stress between 25 and 50 Pa should have low erosion and those that erode at a shear stress less than 25 Pa should have high erosion.

LTPP Data Analysis: Frequently Asked Questions About Joint Faulting with Answers from LTPP, LTPP Tech Brief, FHWA-RD-97-101, FHWA, McLean, VA, 1997.

The LTPP database was mined to determine the site conditions and pavement design features that affect transverse joint faulting. Dowels are the most effective means of controlling joint faulting. Larger dowels reduce the amount of faulting because of the reduced dowel-concrete bearing stress. Increasing pavement drainage reduces faulting; this is more effective for nondoweled pavements than for doweled pavements. Short joint spacing and widened slabs also reduce faulting.

A.3.3.2 JPCP Transverse Cracking—Midslab

Cracking in JPCP pavements reduces their long-term performance. An annotated bibliography follows of references that discuss pavement design features and their relation to transverse cracking.

Bustos, M., de Solminhac, H.E., Darter, M.I., Caroca, A., and Covarrubias, J.P., "Calibration of Performance Models for Jointed Concrete Pavements Using Long-Term Pavement Performance Database," Transportation Research Record 1629, TRB, pp. 108-116, Washington, DC, 1998.

The LTPP database is used to develop correlation factors between JPCP pavement distress and climatic conditions at the pavement location. To do so, several pavement sections in the database are disregarded, such as those without a subgrade k-value. This decreases the reliability of the transverse cracking model. However, this study finds that transverse cracking depends on climatic conditions. The least severe cracking is found in the dry-no freeze zone, while the most severe is in the wet-no freeze region. These correlations are not obvious, but this may be because cracking is not heavily dependent on environment, as faulting is, for example.

Moody, E.D., "Transverse Cracking Distress in Long-Term Pavement Performance Jointed Concrete Pavement Sections," Transportation Research Record 1629, TRB, pp. 6-12, Washington, DC, 1998.

The mechanisms that cause midslab transverse cracking are divided into three sections. The primary ones are due to pure bending stresses, curling stresses, and subgrade friction. The secondary transverse cracking mechanisms (at the joint) are due to joint saw-cutting timing, loss of load transfer, and locked transverse joints due to dowel bar corrosion or misalignment. These transverse cracks near the joint should not be considered when calibrating the midslab cracking model. The third mechanism causing transverse cracking is related to drying shrinkage. Drying shrinkage cracks do not penetrate the entire pavement thickness. Correlations also are found between traffic loading and transverse cracking. No section with fewer than 600,000 ESALs had transverse cracks. Transverse cracks increased due to increased traffic, increased monthly temperature changes, and the use of cement-treated bases (increased curling and warping stresses). Transverse cracking decreases with thicker pavements and stronger concrete (tensile strength).

Frabizzio, M.A. and Buch, N.J., "Investigation of Design Parameters Affecting Transverse Cracking in Jointed Concrete Pavements (JCPs): A Field Study," paper presented at the TRB 78th Annual Meeting, Washington, DC, 1999.

This paper investigates several design features that influence the formation of transverse cracks in pavements. This is a synthesis of experimental data; no theoretical model is developed. Aggregate interlock across joints is studied using volumetric surface texture (VST) testing. VST measures the roughness of the crack surface. VST shows that the crack propagating through aggregate results in a smoother crack surface (and therefore lower aggregate interlock) than does the crack that propagates around the aggregate (high aggregate interlock). This implies that a poor aggregate-cement bond has improved load transfer at the joint due to aggregate interlock. Four parameters commonly are used to quantify the efficiency of the load transfer across the joint for the doweled and nondoweled pavements. They are the deflection load transfer, the transferred load efficiency, the total load transferred from loaded side to unloaded side, and the aggregate interlock shear stiffness per unit length of crack. Also, it is shown that aggregate type influences the number of transverse cracks in the JPCP. Pavements reinforced with recycled aggregate have more transverse cracks than do those with good quality aggregate. Shoulder type also influences transverse cracking in the pavements, depending on type of aggregate used. Other causes of transverse cracking are plastic and drying shrinkage cracks, fatigue cracking, and induced frictional stresses due to expansion and contraction of the slabs. An increase in temperature causes the slabs to expand and the joint to close if the LTE is between 30 to 50 percent. If it is 90 percent, then increased temperature does not affect the LTE.

A.3.3.3 JPCP Spalling

Spalling of concrete pavements typically has been studied qualitatively. Researchers present possible causes of spalling based on pavement condition surveys. The majority of the models that have been developed to predict spalling are empirical in nature. They often relate rainfall, evaporation rate, and other factors to spalling. An annotated bibliography of spalling references is given below.

Senadheera, S.P. and Zollinger, D.G., "Framework for Incorporation of Spalling in Design of Concrete Pavements," Transportation Research Record 1449, TRB, pp. 114-122, Washington, DC, 1994.

This reference reviews the majority of prior research on spalling, especially on CRCP. The most important factors that affect the rate of spalling are rainfall, coarse aggregate type, and subbase type. Spalling is a two-step process. First, a horizontal delamination crack forms in the pavement. Then fatigue damage accumulates due to traffic and temperature-induced strains, and the concrete spalls. Two forms of spalling have been seen in pavements—a deep spall caused by the popout of an aggregate particle, and a shallow spall due to the horizontal delamination of the concrete. The long-term performance curve for spalling has an 'S' shape and can be modeled using the Weibull probability distribution function.

McCullough, B.F. and Dossey, T., "Considerations for High-Performance Concrete Paving: Recommendations from 20 Years of Field Experience in Texas, " Transportation Research Record 1684, TRB, pp. 17-24, 1999.

This reference deals primarily with CRCP, but also discusses spalling. Factors that significantly influence spalling are surface moisture evaporation at the time of placement and ambient temperatures above 0 °C. To prevent spalling, the amount of water that evaporates from the surface of the pavement must be minimized. High evaporation rates drive delamination cracking deeper into the pavement after construction. The traffic later causes the vertical fracture plane to intersect with the horizontal delamination plane, and the concrete breaks out to form a spall. Wet cotton mats are efficient at reducing surface evaporation, as are plastic sheeting, double membrane curing, and single membrane curing. Constant monitoring of surface evaporation is suggested during concrete construction.

Rollings, R.S., "Joint Spalling in Newly Constructed Concrete Pavement," Journal of Performance of Constructed Facilities, pp. 137-144, August 1998.

A review of spalling work is presented in this paper. Qualitative studies have been performed that list potential causes of spalling. On airport pavements, it appears that poor workmanship is the major cause of spalling. Other possible causes of spalling are listed, such as poor concrete properties, freeze-thaw cycles, poor consolidation and finishing of the concrete, poor repair of the pavement edges, and inadequate curing.

Bustos, M., de Solminhac, H.E., Darter, M.I., Caroca, A., and Covarrubias, J.P., "Calibration of Performance Models for Jointed Concrete Pavements Using Long-Term Pavement Performance Database," Transportation Research Record 1629, TRB, pp. 108-116, Washington, DC, 1998.

In this paper, JPCP distress models were calibrated using LTPP data. Adjustment factors are made to predict JPCP distresses for each region of the United States . Researchers found that a wet climate prevents spalling better than does a dry climate. This agrees with the hypothesis that increased evaporation causes horizontal delamination, a forerunner of spalling.

A.4 CRCP Literature Review

During task B of this project, a literature review of references on CRCP early-age behavior was accomplished. From this effort, a number of references have been compiled and models identified describing the early-age behavior of CRCP.

This section briefly summarizes the primary references identified, including candidate models and useful information on CRCP early-age behavior.

McCullough, B.F, Abou-Ayyash, A., Hudson, W.R. and Randall, J.P., "Design of Continuously Reinforced Concrete Pavements for Highways," Research Project NCHRP 1-15, Center for Highway Research, The University of Texas at Austin, Austin, TX, August 1975.

This document provides some history of CRCP use. To establish optimum CRCP design specifications, it is necessary to understand the major influences controlling the mechanistic behavior of CRCP at early ages. This work is one of the first studies that attempts to correlate the primary factors influencing CRCP behavior to predict theses factors' effects on pavement performance. Based on the findings of that work, a mechanistic design procedure was developed that takes into account the early-age behavior of the pavement. This mechanistic design method proved that the crack spacing and crack width could be properly controlled to fall within certain limits to minimize undesirable conditions. Major factors influencing crack spacing and crack width are explained. A crack spacing between 1.5 and 2.4 m is considered effective in minimizing distress occurrence. Also, it is concluded that crack width should be limited to no more than 0.6 mm to minimize steel corrosion. The limiting criteria for crack spacing and crack width is based on the performance of CRC pavements in several highways nationwide and laboratory tests. Primary factors that were found to influence CRCP performance include:

• Concrete strength: It was found that concrete tensile strength plays an important roll in the development of spalling. For pavements with a concrete tensile strength less than 2756 kPa, a significant increase in spalling is observed.
• Crack spacing distribution and crack width: It was found that the larger the crack spacing, the larger the crack widths, resulting in loss of load transfer. On the other hand, for small crack spacings, load deflections tend to increase, contributing to the development of stresses that can lead to punchouts.
• Coarse aggregate type: The coarse aggregate type, and in particular its angularity, seem to have an important effect on spalling development. Since siliceous river gravel (SRG) tends to be more roundly shaped, it tends to have a lack of bond with the paste. Crushed aggregate tends to have a better bond strength at the aggregate-paste interface, and therefore, fewer spalling problems.

Palmer, R.P., Olsen, M.P.J., and Lytton, R.L., "TTICRCP—A Mechanistic Model for the Prediction of Stresses, Strains, and Displacements in Continuously Reinforced Concrete Pavements," Research Report 371-2F, Texas Transportation Institute, The Texas A&M University System, College Station, TX, 1988.

This study improves on behavior prediction models CRCP-1, CRCP-2, and CRCP-3 by better modeling bond stress distribution and stress-slip prediction. The TTICRCP software program developed under this study has the objective of better characterizing the behavior of CRCP pavements using a more sophisticated, mechanistic-based approach. The model includes the means to better simulate the interaction between the steel reinforcement and the concrete. During its development, numerous derivations were made based on engineering mechanics and energy concepts. The result was a system of linear, second-order ordinary differential equations describing the complex behavior of the CRCP system. The solution to this system of equations is conducted using a combination of matrix and iterative solution schemes. This program was developed as an analysis routine with the crack spacing as an input rather than an output, as opposed to the CRCP-8 program. In addition, it has not been fully validated and is subject to further modification. However, initial review of the model has demonstrated that it can better predict the crack widths due to the improved characterization of the slip zone between the steel and the concrete. Therefore, this program shows promise as a possible improvement to the CRCP-8 modeling system. This report also provides a literature review on bond-stress and stress-slip relationships.

Won, M., Hankins, K., and McCullough, B. F., "Mechanistic Analysis of Continuously Reinforced Concrete Pavements Considering Material Characteristics, Variability, and Fatigue," Research Report 1169-2, Center for Transportation Research, The University of Texas at Austin, Austin, TX, March 1991.

This is one of the main references for the CRCP-8 program. Although it describes the CRCP-5 program, no major improvements to the software have been made after this study. This reference briefly describes the purpose of transverse steel and why the States do not commonly use it. It also describes the factors affecting transverse cracking in CRCP. The primary purpose of this study is to provide enhanced bond stress/slip relationships for the University of Texas at Austin Center for Transportation Research (CTR) software program CRCP series. It describes a stochastic method ( Monte Carlo ) to account for the effect of the variability of materials on CRCP performance variability. The report concludes that variability of steel amount, size, and depth, subbase friction, environmental conditions, slab thickness, CTE, and drying shrinkage are small compared to the variability of tensile strength. Therefore, the report concentrates on the variability of concrete tensile strength as the most significant factors affecting crack spacing. It is assumed that concrete tensile strength has a normal distribution. It is considered that the coefficient of variation (CV) of tensile strength is close to 20 percent, based on the above references. A mechanistic model to predict punchout distress is also presented, taking into account wheel loads and previously predicted crack spacing distribution. The subroutine in CRCP-8 that predicts punchouts is based on a mechanistic-empirical model. During the study, a number of ILLISLAB FEM runs for CRCP of different thicknesses and crack spacings were run. The effect of aggregate interlock and longitudinal steel on load transfer at cracks was ignored during stress calculations. The results of this analysis were used to fit a regression model predicting transverse tensile stress from thickness and crack spacing. Fatigue is then incorporated in this analysis to predict punchout development.

Zollinger, D.G., Buch, N., Xin, D., and Soares, J., "Performance of CRC Pavements Volume 6—CRC Pavement Design, Construction, and Performance," FHWA-RD-97-151, FHWA, McLean, VA, 1997.

This reference presents the FHWA CRCP punchout model. In this work, new predictive models for the behavior and performance of CRCP were developed. Although an explicit punchout prediction model was not included in this reference, several derivations were proposed to improve the prediction of the loss of load transfer across a crack, which is intuitively one of the key factors in punchout prediction. The basic framework of the proposed model includes a more mechanistic-based approach to characterizing the change in stress due to load transfer. The load transfer is comprised of a combination of aggregate interlock, base support, and reinforcement interaction. The study found that accurately characterizing the load transfer due to aggregate interlock could significantly improve the overall distress prediction. The LTE was found to be a function of aggregate interlock, support stiffness, and radius of relative stiffness. This reference also provides guidelines for designing and constructing CRCP. It also extensively describes the factors affecting cracking and describes punchout distress mechanisms. A thickness design procedure for CRCP is presented based on crack spacing, LTE, and fatigue cracking concepts. In this procedure, shear stresses at transverse cracks and curling and warping due to traffic and environmental loads are investigated to predict punchouts. A methodology to take into account design reliability is presented. The authors also present construction methods to improve CRCP crack patterns. Based on experimental test sections, the document concludes that surface crack initiation is more effective than interior crack initiation. From previous recommendations of crack spacing from 1.5 to 2.4 m, it demonstrates results of studies recommending spacings of 0.9 m as a minimum, warning about crack spacings less than 0.9 m. To minimize spalling at cracks, the maximum crack spacing is limited to 1.8 to 2.7 m.

Kim, S.-M., Won, M.C., and McCullough, B.F., "Development of a Finite-Element Program for Continuously Reinforced Concrete Pavements," Research Report 1758-1F, Center for Transportation Research, The University of Texas at Austin, Austin, TX, November 1997.

This report describes the CRCPFEM model, developed under a Texas DOT (TxDOT) effort with the objective of developing a more mechanistic-based model to predict the various responses in CRCP. The CRCPFEM model is a two-dimensional, plane-strain finite-element program developed using a sophisticated set of submodels to predict the behavior of the CRCP due to shrinkage, creep, temperature change, and slab-base restraint. Although the validation of the current version of the software is not extensive, it does show promise as a candidate model for this effort. If selected, further validation of this model can be performed. The ability for this model to account for relaxation creep makes it a worthy candidate for incorporation into the proposed system. This effect, modeled in HIPERPAV, is quite significant for JPCP. The ability to model this important phenomenon is critical to the accuracy of the early-age prediction. Parametric studies were performed in this study to evaluate the effect of factors influencing CRCP responses. Further investigation of an accurate bond slip relationship is recommended.

Suh, Y.C., Hankins K., and McCullough, B.F., "Early-Age Behavior of Continuously Reinforced Concrete Pavement and Calibration of the Failure Prediction Model in the CRCP-7 Program," Research Report 1244-3, Center for Transportation Research, The University of Texas at Austin, Austin, TX, March 1992.

The main purpose of this study was to calibrate the failure (punchout distress) prediction model in the CRCP program. The calibration is based on data from the Texas CRCP database. The report also presents the results of test sections constructed in Houston, TX, to monitor the early-age behavior in CRCP. The effect of different factors such as concrete properties, aggregate type, steel content, concrete curing temperature, and time of day of construction was investigated, among other factors. Condition surveys were performed to monitor cracking patterns and slab movements. This report may provide some ideas for future instrumentation of CRCP sections. The model was validated for only two aggregate types: limestone and siliceous river gravel.

McCullough, B.F., Ma, J.C.M., and Noble, C.S., "Limiting Criteria for the Design of CRCP," Research Report 177-17, Center for Transportation Research, The University of Texas at Austin, Austin, TX, August 1979.

This reference provides limiting criteria for the design of CRCP. Factors considered include crack spacing, crack width, and maximum steel stresses. The limiting criteria are a function of the target pavement distresses (punchouts, spalling, steel corrosion, and steel permanent deformation). This study also recommends fatigue relationships to be used in the design procedure for CRCP. It also provides information on the CTE of various steel types.

McCullough, B.F. and Rasmussen, R.O., "Fast Track Paving: Concrete Temperature Control and Traffic Opening Criteria for Bonded Concrete Overlays: Task G, Volume 1: Final Report," Federal Highway Administration Report, FHWA-RD-98-167, Washington, DC, 1999.

This research demonstrates the importance of early-age behavior on the long-term performance of JPCP and bonded concrete overlays. The authors mention that a number of factors influence early-age behavior, and these can be placed into four different categories: pavement design, materials and mix design, environment, and construction operations. This approach is believed to be applicable to any type of concrete pavement.

"Continuously Reinforced Concrete Pavement," National Cooperative Highway Research Program, Synthesis of Highway Practice No. 16, Highway Research Board, 1973.

This document describes current CRCP construction practices. It provides a table with the primary factors affecting crack spacing and some guidelines for design and construction of CRCP. The authors emphasize the need for good subgrade support and warn about the practice of designing for less thickness than that required for JCP. They also warn about using wire fabric as reinforcement. The guidelines limit the maximum crack width to 0.5 mm and limit the steel percentage to not less than 0.7 percent where high temperature drops and deicing chemicals are used. The document warns about steel strengths greater than 60 ksi that may lead to wide cracks and loss of aggregate interlock, and questions the use of transverse steel.

Tayabji, S.D., Selezneva, O., Jiang, Y.J., "Preliminary Evaluation of LTPP Continuously Reinforced Concrete Pavement Test Sections," FHWA-RD-99-086, FHWA, July 1999.

In this reference, an attempt is made to find initial correlations of factors collected on General Pavement Studies (GPS) sections GPS-5 from the LTPP database to long-term CRCP performance. No definitive correlations were found with the available data. The study concludes that additional data, including early-age information, are required for good correlations of factors influencing pavement performance.

Lee, Ying-Haur, Darter, M. I., "Development of Performance Prediction Models for Illinois Continuously Reinforced Concrete Pavements." Transportation Research Record 1505, TRB, pp. 75-84, Washington, DC, 1995.

In this study, a failure prediction model based on regression techniques was developed. The Illinois Pavement Feedback System database was used for this purpose. The model is limited to a small range of steel content (0.60 to 0.62 percent) and slab thickness (203-229 m). According to this study, crack spacing had no effect on pavement performance.

McCullough, B.F., Hudson, W.R., and Noble, C.S., "Summary and Recommendations for the Implementation of Rigid Pavement Design, Construction, and Rehabilitation Techniques," Research Report 177-22F, Center for Transportation Research, The University of Texas at Austin, Austin, TX, March 1981.

This reference presents a supplementary CRCP design procedure for thickness, subbase, and steel reinforcement for TxDOT. Most of this material is based on the AASHTO Pavement Design Guide.

Won, M., McCullough, B.F., and Hudson, W.R., "Evaluation of Proposed Texas State Department of Highways and Public Transportation (SDHPT) Design Standards for CRCP," Research Report 472-1, Center for Transportation Research, The University of Texas at Austin, Austin, TX, April 1988.

The TxDOT design standards for CRCP are evaluated, taking in consideration the variability in pavement response due to different aggregate types using the software program CRCP.

Won, M., Hankins, K., and McCullough, B.F., "A Twenty-Four Year Performance Review of Concrete Pavement Sections Made with Siliceous and Lightweight Coarse Aggregates," Research Report 472-3, Center for Transportation Research, The University of Texas at Austin, Austin, TX, April 1989.

This study investigates the effect of design variables on long-term pavement performance of experimental test sections constructed in Houston, TX . Variables studied include percent steel, crack spacing, and aggregate type. The findings from that study indicated that lightweight aggregate performed better than sections constructed with standard SRG aggregate. Condition surveys and structural capacity studies were performed to observe the performance of the pavement sections at different ages. Crack spacing for the test sections was preformed, however this crack spacing was reduced with time. Preforming was found to be beneficial, because it reduces spalling and punchouts. Intermediate cracking was reduced.

Weissman, A.J., McCullough, B.F., and Hudson, W.R., "Development of Pavement Performance Models for Continuously Reinforced Concrete Pavements in Texas," Research Report 472-7F, Center for Transportation Research, The University of Texas at Austin, Austin, TX, August 1989.

Performance prediction models for CRCP are developed with the use of the Texas CRCP database. A distress index is used to describe the CRCP deterioration as a function of punchouts and patches. The validity of the model is believed to be to limited, and therefore is not recommended for general practical use.

Aslam, M.F., Carrasquillo, L.R., and McCullough, B.F., "Design Recommendations for Steel Reinforcement of CRCP," Research Report 422-2, Center for Transportation Research, The University of Texas at Austin, Austin, TX, November 1987.

A procedure for comparing the effects of aggregate type on the requirements for steel reinforcement is developed. Lab testing of mixes with limestone and SRG aggregates are tested to determine concrete properties for those aggregate types. The CRCP-4 program is used to develop steel design methods based on the differences in concrete properties for both aggregate types.

Wei, C., McCullough, B.F., Hudson, W.R., and Hankins, K., "Development of Load Transfer Coefficients for Use with the AASHTO Guide for Design of Rigid Pavements Based on Field Measurements," Research Report 1169-3, Center for Transportation Research, The University of Texas at Austin, Austin, TX, February 1992.

This report provides procedures to measure load transfer at joints and cracks for CRCP.

Otero, M.A., McCullough, B.F., and Hankins, K., "Monitoring of Siliceous River Gravel and Limestone Continuously Reinforced Concrete Pavement Test Sections in Houston 2 Years After Placement, and Development of a Crack Width Model for the CRCP-7 Program," Research Report 1244-4, Center for Transportation Research, The University of Texas at Austin, Austin, TX, March 1992.

A model for predicting crack width for CRCP is developed based on experimental sections in Houston, TX . The principal variables having an effect on crack width are identified.

McCullough, B.F., Zollinger, D.G., and Allison, B.T., "Preliminary Research Findings on the Effect of Coarse Aggregate on the Performance of Portland Cement Concrete Paving," Research Report 1244-5, Center for Transportation Research, The University of Texas at Austin, Austin, TX, October 1993.

This report provides concrete properties of mixes made with various coarse aggregates. It summarizes findings of research reports 1244-1 to 1244-4 and describes an experiment to evaluate different curing techniques, saw cutting techniques, and skewed transverse steel on crack width, crack spacing, and concrete strength. In addition, it provides background on the development of different versions of the CRCP program. A description of drying shrinkage and moisture models also are provided.

McCullough, B.F. and Rivero-Vallejo, F., "Drying Shrinkage and Temperature Drop Stresses in Jointed Reinforced Concrete Pavement," Research Report 177-1, Center for Transportation Research, The University of Texas at Austin, Austin, TX, August 1975.

This is a research report for JRCP-1, a tool to predict the behavior of JRCP, which can be used to predict the behavior of CRCP steel in the transverse direction.

Strauss, J.P., McCullough, B.F., and Hudson, W.R., "Continuously Reinforced Concrete Pavement: Structural Performance and Design/Construction Variables," Research Report 177-7, Center for Transportation Research, The University of Texas at Austin, Austin, TX, May 1977.

Probabilistic models are used to predict pavement performance based on several factors. Models for load transfer through steel reinforcement and aggregate interlock are developed. The report describes a 1977 condition survey of CRCP pavements in Texas .

McCullough, B.F. and Ma, J., "CRCP-2, An Improved Computer Program for the Analysis of Continuously Reinforced Concrete Pavements," Research Report 177-9, Center for Transportation Research, The University of Texas at Austin, Austin, TX, August 1977.

This report presents modifications made to the CRCP-1 program to account for wheel load stresses to predict crack spacing, to modify the steel-stress model to cover conditions in which the development length for bond exceeds one-half the crack spacing, and to account for the increase in strength after 28 days for analysis of minimum temperature drop.

McCullough, B.F. and Strauss, J.P., "A Performance Survey of Continuously Reinforced Concrete Pavements in Texas," Research Report 21-1F, Center for Transportation Research, The University of Texas at Austin, Austin, TX, November 1974.

A method for performing condition surveys of CRCP is discussed. A distress index for evaluation of CRCP is developed.

Zollinger, D. and Barenberg, E., "Continuously Reinforced Pavements: Punchouts and Other Distresses and Implications for Design," Project IHR-518, Illinois Cooperative Highway Research Program, University of Illinois at Urbana-Champaign, Urbana-Champaign, IL, March 1990.

This report describes the factors affecting CRC pavement cracking behavior. It also provides an analysis of factors affecting punchout distress. The authors describe previous steel instrumentation efforts and provide mechanistic modeling for prediction of punchout distress, including load transfer mechanisms, shear, spalling on the transverse crack, and transverse bending analysis. Most of this research is also presented in FHWA publication FHWA-RD-97-151.

Wimsatt, A.W., McCullough, B.F., and Burns, N.H., "Methods of Analyzing and Factors Influencing Frictional Effects of Subbases," Research Report 459-2F, Center for Transportation Research, The University of Texas at Austin, Austin, TX, November 1987.

This report provides information on pushoff test procedures and typical friction values.

Chia, W.S., McCullough, B.F., and Burns, N.H., "Field Evaluation of Subbase Friction Characteristics," Research Report 401-5, Center for Transportation Research, The University of Texas at Austin, Austin, TX, September 1986.

This report provides information on pushoff test procedures and typical friction values for various subbase types and bond breakers.

Haque, M., Zaman, M., and Soltani, A., "Cracking Characteristics of Model CRC Pavements," TRB 77th Annual Meeting, Washington, DC, January 11-15, 1998.

The authors investigate the effect of steel reinforcement (rebar spacing) on crack spacing behavior of CRCP using numerical methods and small-scale laboratory experiments. They also evaluate the effect of skewed reinforcement.

Nishizawa, T., Shimeno, S., Komatsubara, A., and Koyanagawa, M., "Study on Thermal Stresses in Continuously Reinforced Concrete Pavement," paper presented at the TRB 77th Annual Meeting, Washington, DC, 1998.

The authors investigate development of thermal stresses in CRCP. Test sections are instrumented in the field, and measured stresses are compared to calculated stresses.

Mains, M.R., "Measurement of the Distribution of Tensile and Bond Stresses Along Reinforcing Bars," ACI Journal, Vol. 48, pp. 225-252, November 1951.

This article investigates bond stresses and bond slip of reinforced concrete. It includes experimentation with strain gauges to measure bond stress and bond slip. Bond stress and bond slip relationships are discussed.

Nilson, A.H., "Internal Measurement of Bond Slip," ACI Journal, Vol. 69, pp. 439-441, July 1972.

Similar to the above article, this reference also investigates bond stresses and bond slip of reinforced concrete.

Haque, M., Zaman, M., and Soltani, A., "Cracking Characteristics of Model CRC Pavements," TRB 77th Annual Meeting, Washington, DC, January 11-15, 1998.

This article investigates the effect of rebar spacing on crack spacing and crack patterns with the use of small-scale laboratory experiments and numerical simulation.

Zollinger, D. and Senadheera, S., "Spalling of Continuously Reinforced Concrete Pavements," Journal of Transportation Engineering, Vol. 120, No. 3, May-June 1994.

This article presents a mechanistic flat-bottom spalling model for CRCP/JCP.

Kerr, A.D., "Assessment of Concrete Pavement Blowups," Journal of Transportation Engineering, Vol. 123, No. 2, pp. 123-131, March-April 1997.

A mechanistic model for analysis of concrete pavement blowups is described. The model can be used for both CRCP and JCP.

Nishizawa, T., Shimeno, S., Komatsubara, A., and Koyanagawa, M., "Study on Thermal Stresses in Continuously Reinforced Concrete Pavement," Transportation Research Record 1629, pp. 99-107, November 1998.

A procedure for estimating the thermal stresses in CRCP is proposed. Measured thermal strains are compared with FEM-predicted strains and divided into axial, curling, and nonlinear components.

Kim, S.-M., Won, M., and McCullough, F., "Three-Dimensional Analysis of Continuously Reinforced Concrete Pavements," TRB 79th Annual Meeting, Washington, DC, January 9-13, 2000.

A three-dimensional analysis of CRCP is performed and compared with results of two-dimensional analysis performed with CRCPFEM. Nonlinear bond slip relationships are studied in this analysis. Primary conclusions include the effect of transverse steel amount and location on crack width; significant stresses at the edge on the farthest transverse steel bar from the crack; significant effect of nonlinear bond-slip relationships on concrete stress; analysis with the two-dimensional model gives a good approximation, compared to the three-dimensional model.

Schindler, A., Henry, P., and McCullough, F., "Validation of CRCP-8 to Predict Long-Term Transverse Crack Spacing Distributions in Continuously Reinforced Concrete Pavements," TRB 79th Annual Meeting, Washington, DC, January 9-13, 2000.

This paper describes validation efforts of the CRCP-8 program to predict crack spacing for experimental sections in Houston, TX .

McCullough, F., Zollinger, D., and Dossey, T., "Evaluation of the Performance of Texas Pavements Made with Different Coarse Aggregates" Research Report 3925-1, Center for Transportation Research, The University of Texas at Austin, Austin, TX, September 1998.

This report presents information on crack spacing and crack width of CRCP for sections monitored in Houston, TX, and Hempstead, TX . It presents the results of an effort to validate CRCP-8 crack spacing and presents information on delamination spalling and the thermal coefficient of concrete. The report describes practices of CRCP design and construction for the State of Texas over a 23-year period.

^1. HIPERPAV alone with no succeeding numeral is used to refer to the overall concrete pavement design and construction guidelines, while HIPERPAV I and HIPERPAV II are used to refer to the two different software generations.