508 Caption

Figure 1. Flowchart. Hiperpav early-age behavior framework showing improved models in Hiperpav 2. The flowchart depicts a text box on the top with text: Temperature Prediction*, PCC Hydration*, and Environmental Effects*. This text box flows downward into two other sets of text boxes. The left set is the Critical Stress Models with three text boxes: Axial Stress and Axial Restraint*, Curling Stress and Vertical Restraint*, Shrinkage Stress*. The right set is the Mechanical Properties with three text boxes: Coefficient of Thermal Expansion, Relaxation-Creep Model, and Tensile Strength. The top two text boxes from the right set flow toward the top two text boxes from the left set. These sets of text boxes flow downward to one text box containing the text Stress (on the left) and Strength (on the right) connected by a bidirectional arrow. The asterisk represents improved models.

Figure 2. Sketch. Heat transfer mechanisms between pavement and its surroundings. The schematic shows a pavement, Hydrating Concrete on top of a Base Layer on top of a Subbase Layer. There is some sun and cloud cover above, with some wind close to the pavement. Solar radiation is being transmitted from the sun to the hydrating concrete causing solar adsorption. The concrete layer is putting out irradiation. The wind causes convection in the concrete layer. There is conduction happening between the concrete layer and the base layer and between the base layer and the subbase layer.

Figure 3. Graph. Concrete specific heat as influenced by the mixture constituents, temperature, and degree of hydration. Graph depicts Specific Heat on the Y-axis and Degree of Hydration on the X-axis. There are two sets of lines in the graph, the higher set is for limestone and the lower set is for siliceous river gravel. Each set contains three straight solid lines starting from the same point. The highest line is for temperature of 35 degrees Celsius, the middle line is for temperature of 20 degrees Celsius, and the lowest line is for temperature of 5 degrees Celsius. All lines decrease from left to right.

Figure 4. Graph. Comparison of different convection coefficients as influenced by the windspeed. The graph depicts Convection on the Y-axis and Windspeed on the X-axis. There are three lines starting from the same point on the left and increase as they go to the right. The top linear line is from Equation 21 and represents the vertical plate. The middle log line is from Equation 21 with T subscript lowercase C equal to 30 degrees Celsius and T subscript lowercase A equal to 20 degrees Celsius. The lower log line is from equations 22 and 23 with T subscript lowercase C equal to 30 degrees Celsius and T subscript lowercase A equal to 25 degrees Celsius. These two lower lines represent the Hiperpav horizontal plate.

Figure 5. Sketch. Radiant energy exchanges between the sky and an exposed thermally black plate. The sketch depicts a thermally black plate at temperature T subscript lowercase S on top of thermal insulation. This black plate is represented in equation form by sigma time T subscript lowercase S raised to the fourth power. On top is the atmospheric radiation represented by A subscript R. To the side is the total solar radiation represented by lowercase Q subscript lowercase R. The equation for radiation loss rate (R) is R equal to sigma times T subscript lowercase S minus A subscript R.

Figure 6. Graph. Emissivity of moist air at a total pressure of 1 atmosphere and a temperature of 20 degrees Celsius. The graph shows Total Emissivity on the Y-axis and Water-Vapor Density Length Product on the X-axis. There are three lines in the graph. The smooth S-shape line increasing from left to right represents water vapor. Another line that traces this line except for the upward bump along the middle represents mixture of water vapor and carbon dioxide. The small mountain shape line at the bottom that looks like the bump is the second line represents the correction due to the presence of carbon dioxide (P subscript C divided P subscript W equals 0.10).

Figure 7. Graph. Sensitivity of the apparent surrounding temperature to changes in climatic conditions, atmospheric pressure. The graph has the Apparent Surrounding Temperature on the Y-axis and Dry-Bulb Temperature on the X-axis. It has three straight lines, increasing from left to right. The lines are, from top to bottom, for P subscript Z of 1000 millibars, 750 millibars, and 500 millibars, respectively.

Figure 8. Graph. Sensitivity of the apparent surrounding temperature to changes in climatic conditions, relative humidity. The graph has the Apparent Surrounding Temperature on the Y-axis and Dry-Bulb Temperature on the X-axis. It has three straight lines, increasing from left to right. The lines are, from top to bottom, for relative humidity (RH)of 100 percent, 60 percent, and 20 percent, respectively.

Figure 9. Graph. Sensitivity of the apparent surrounding temperature to changes in climatic conditions, ratio of carbon dioxide to water vapor. The graph has the Apparent Surrounding Temperature on the Y-axis and Dry-Bulb Temperature on the X-axis. It has three lines that are virtually on top of each other, except for the lowest line, which starts out lower and curves into the other two lines. The lines are for P subscript C divided by P subscript W that equal 1.0, 0.5, and 0.1, respectively, and increase from left to right.

Figure 10. Sketch. Surface layer zone subjected to drying shrinkage for a slip-formed pavement. The sketch depicts a shaded area that is in the shape of a bench. The thickness of this shaded area is depicted as L subscript SD, and within the shaded area is the symbol alpha subscript SD.

Figure 11. Graph. Influence of water to cementitious materials ratio on total shrinkage predicted by the Jonasson model. The graph shows Total Shrinkage on the Y-axis and Time on the X-axis. There are five lines that start out at zero and stay horizontal until the time reaches approximately 25 hours. The lines then branch out to five log-wavy shaped lines, increasing from left to right. The lines are, from bottom to top, for water-to-cement ratios that equal 0.2, 0.25, 0.3, 0.35, and 0.399, respectively.

Figure 12. Graph. Effect of water-to-cement ratio on total shrinkage predicted by the Baźant-Panula model. The graph shows Total Shrinkage on the Y-axis and Time on the X-axis. There are three wavy lines close to each other and have local peaks at around times of 15 hours, 32 hours, and 55 hours. The lines are for, from bottom to top, water-to-cement ratios that equal 0.4, 0.5, and 0.6, respectively.

Figure 13. Graph. Comparison of the Baźant-Panula and Jonasson-Hedlund shrinkage models. The graph shows Total Shrinkage on the Y-axis and Time on the X-axis. There are three wavy lines. The top line, with significant waves and is much higher than the other two lines, represents the Bazant-Panula's water-to-cement ratio that equals 0.4. The middle line, with small waves, represents the Jonasson's water-to-cement ratio that equals 0.399, TS equal to 1. The bottom line, with small waves, represents the Jonasson's water-to-cement ratio that equal 0.399, TS equal to set time. All three seem to have local peaks at time of 32 hours and 55 hours.

Figure 14. Two Graphs. Time-dependent deformation at time T, for a loading at time T subscript 0. The top graph has Applied Stress on the Y-axis and Time on the X-axis. It has a vertical line (at time T subscript 0) connecting a horizontal line, forming a sideways L. The height of the vertical line represents the Stress at time T subscript 0. The bottom graph has Strain on the Y-axis and Time on the X-axis. It has a vertical line (at time T subscript 0) connected by a log line increasing from left to right and leveling out at time T. The vertical line is the instantaneous elastic strain and the log line is the creep strain. The height of the vertical line is represented by the equation Instantaneous Elastic Strain at time T subscript 0 equal to the quotient of the Stress at time T subscript 0 and the Instantaneous Modulus of Elasticity at time T subscript 0. The height of the log line is represented by the equation Creep Strain from time T subscript 0 to time T equal to the creep coefficient times the Instantaneous Elastic Strain at time T subscript 0. The total height of both is equal to the creep compliance defined as the response at time T after loading at time 0 times the applied stress at time T subscript 0.

Figure 15. Graph. A schematic of the additional creep compliance functions to extend the Triple Power Law for the early-age creep response. The graph shows Creep Compliance on the Y-axis and Time on the X-axis. There are two vertical lines, the left representing time T subscript 1and the right representing T subscript 0. The T subscript 1 line meets two inverse exponential lines, decreasing from left to right. These two lines start at different heights and merge together when they level out. The height between these two lines where they intersect with the T subscript 0 vertical line is represented by the equation psi subscript 1 at time T subscript 0 divided by the initial Modulus of Elasticity. The T subscript 0 line meets three log lines, increasing from left to right. The distance between the top log line and the middle log line is represented by the equation psi subscript 2 at time T, T subscript 0 divided by initial Modulus of Elasticity.

Figure 16. Graph. Decomposition of stress history into stress steps. The graph shows Stress on the Y-axis and Time on the X-axis. The relationship is represented by diagonal line increasing from left to right meeting up with a horizontal line. There are little vertical lines representing the stress increment at time T subscript 0.

Figure 17. Graphs. Discreet subdivision of time for numerical creep analysis. The top graph has Strain on the Y-axis and Time and lowercase R on the X-axis. It shows a vertical line (at time T subscript 0, lowercase R equal to 0 and 1) meeting up with a horizontal line as lowercase R increases by increments of 1. The increment represents the change in T subscript lowercase R. The bottom graph has Stress on the Y-axis and Time and lowercase R on the X-axis. It is similar to the strain graph, except instead of a horizontal line, the vertical line meets up with an inverse exponential line, decreasing from left to right. The incremental height in the inverse exponential line represents the change is sigma subscript lowercase R.

Figure 18. Graph. Superposition of various strains intensities: Loading. The figure has epsilon subscript 1 on the Y-axis and Time and lowercase R on X-axis. It shows a hill-shaped curve (peaking around lowercase R equals 7) with the incremental height representing the change in epsilon subscript lowercase R as lowercase R goes from 3 to 4.

Figure 19. Graph. Superposition of various strains intensities: Unloading. The figure has epsilon subscript 2 on the Y-axis and Time and lowercase R on X-axis. It shows a hill-shaped curve (peaking around lowercase R equals 7) with the incremental height representing the change in epsilon subscript lowercase R as lowercase R goes from 11 to 12.

Figure 20. Graph. Superposition of various strains intensities: Net applied strains. The figure has an equation epsilon subscript T equal to epsilon subscript 1 minus epsilon subscript 2 on the Y-axis and Time and lowercase R on X-axis. It shows a hill-shaped curve (peaking around lowercase R equals 7) that is the difference of epsilon subscript 1 minus epsilon subscript 2.

Figure 21. Graph. Comparison of the results of the relaxation model and model without relaxation. The graph shows Total Stress on the left Y-axis, Total Strain on the right Y-axis, and Concrete Age on the X-axis. The graph has three wavy lines, the bottom most represents the Baźant and Westman model, the one that starts out in the middle but ends up as the highest represents the No Relaxation model, and the one that starts out highest but ends up in the middle represents the Strain model. All three seem to peak at concrete age of 42 hours and seem to dip at concrete age of 28 hours.

Figure 22. Graph. Monthly moisture content variation for lean clay (CL), scenarios 1-4. The graph depicts Moisture Content on the Y-axis and Month on the X-axis. The graph shows four scenarios, represented by four wavy lines. Scenarios 1 and 2 are closer to each other and are lower than scenarios 3 and 4, with scenario 2 having higher and lower peaks than scenario 1. Scenarios 3 and 4 are close to each other with scenario 4 having higher and lower peaks than scenario 3. All scenarios seem to have local peaks in May, July, and November and have low points in March, June, and September.

Figure 23. Graph. Monthly moisture content variation for well-graded silty gravel (GW-GM), scenarios 5-8. The graph depicts Moisture Content on the Y-axis and Month on the X-axis. The graph shows four scenarios, represented by four wavy lines. Scenarios 5 and 6 are close to each other and are lower than scenarios 7 and 8, with scenario 6 having higher and lower peaks than scenario 5. Scenarios 7 and 8 are close to each other with scenario 8 having higher and lower peaks than scenario 7. All scenarios seem to have local peaks in May, July, and November and have low points in March, June, and September.

Figure 24. Graph. Monthly variation for well-graded gravel (GW), scenarios 9-12. The graph depicts Moisture Content on the Y-axis and Month on the X-axis. The graph shows four scenarios, represented by four wavy lines. All scenarios (9, 10, 11, and 12) are very close to each other with scenarios 9 and 10 having lower peaks at times. There are really no peaks, but there are low points in March, June, and September.

Figure 25. Graph. Monthly variation for lean clay (CL) in five U.S. cities. The graph depicts Moisture Content on the Y-axis and Month on the X-axis. The graph shows five wavy lines that are widely spread representing conditions for five cities. The cities are, from highest moisture to lowest, Atlanta (peak in March), Chicago (peak in August), Oklahoma (peak in May), San Antonio (peak in May), and Reno (highest in January). There are periods where the Atlanta line falls below the Chicago line.

Figure 26. Graph. Monthly variation for well-graded silty gravel (GW-GM) in five U.S. cities. The graph depicts Moisture Content on the Y-axis and Month on the X-axis. The graph shows five wavy lines that are closely spaced representing conditions for five cities. The cities are, from highest moisture to lowest, Atlanta (peak in March), Chicago (peak in August), Oklahoma (peak in May), San Antonio (peak in May), and Reno (highest in January). There are periods where the Atlanta line falls below the Chicago line and meets the Oklahoma line.

Figure 27. Graph. Comparison of predicted and measured values from the AASHO road test. The graph depicts Moisture Content on the Y-axis and Month on the X-axis. The graph shows three wavy lines and six dotted lines. The three wavy lines represented the predicted moisture content for embankment (highest), subbase (middle), and base (lowest). The subbase and base wavy lines are close to each other while the embankment line is much higher. All three wavy lines are lowest in January and February and peak in July and September. Each wavy line has two dotted horizontal lines under them representing the measured moisture content. The measured moisture content from March to June is close to the predicted moisture content, while the measured moisture from June to September is much lower than the predicted moisture content.

Figure 28. Graph. Texas LTPP site comparison. The graph depicts Moisture Content on the Y-axis and Month on the X-axis. It shows two wavy lines. The higher one, averaging around 20 percent moisture content, represents the subgrade. The lower one, averaging around 12 percent moisture content, represents the subbase. Both lines have local peaks around May, July, and November, and low points around March, June, and September. There is a horizontal line closely under the subbase wavy line representing the LTPP Value for Subbase moisture content.

Figure 29. Graph. Maine LTPP site comparison. The graph depicts Moisture Content on the Y-axis and Month on the X-axis. It shows two relatively straight solid lines. The higher one, averaging around 15 percent moisture content, represents the subgrade. The lower one, averaging around 8 percent moisture content, represents the subbase. There is a relatively straight dotted line closely under each of the above lines, representing the LTPP Values for Subgrade and Subbase moisture content, respectively.

Figure 30. Graph. Comparison of test results with the correlation proposed in equation 122. The graph shows Modulus of Rupture on the Y-axis and Compressive Strength on the X-axis. It has many data points representing data from Gonnerman and Shuman, Walker and Bloem, Houk, and Grieb and Werner increasing from left to right and is best fitted by a line that has the equation Modulus of Rupture is equal to 2.3 times the Compressive Strength raised to the two-thirds power.

Figure 31. Graph. Modulus of rupture versus compressive strength for Texas data. The graph shows Modulus of Rupture on the Y-axis and Compressive Strength on the X-axis. It has many data points representing data from the Texas DOT quality control/quality assurance project increasing from left to right and is best fitted by Raphael's relationship, which is from the equation the Modulus of Rupture equal to 2.3 times the Compressive Strength raised to the two-thirds power. The ACI relationship, which comes from the equation the Modulus of Rupture equal to 0.7 times the square root of the Compressive Strength falls below the data points.

Figure 32. Graph. Tensile strength and elastic modulus values calculated using the CEB-FIP equation. The graph has Tensile Strength on the left Y-axis and Elastic Modulus on the right Y-axis and Age of PCC on the X-axis. The X-axis is on a log scale. On the Y-axis, 1 megapascal in tensile strength equals 5000 megapascals in elastic modulus. There are two log shape lines increasing from left to right then leveling out, one for tensile strength and one for elastic modulus. The tensile strength line starts out at about 1.7 and levels out at about 6.1. The elastic modulus line starts out at about 16,000 and levels out at about 31,000.

Figure 33. Sketch. Schematic of deflection load transfer (LTE subscript delta) for a doweled JCP. The schematic shows to pieces of slabs jointed by a dowel with the load on top of the left slab. Each slab has a delta divided by 2 symbol underneath representing the same deflection for each.

Figure 34. Flowchart. Schematic of LTE model logic. The flowchart starts out with two text boxes, Dowel Influence and Aggregate Interlock, on the left. These two then flow into a Joint Stiffness textbox. This text box flows to two text boxes, Unloaded Edge Deflection and Unloaded Edge Stress. These two flow to two more text boxes, Loaded Edge Deflection and Stress and Load Transfer Efficiency (LTE). There are two text boxes, Free Edge Stress and Free Edge Deflection that are on top and flowing downward toward the Loaded Edge Deflection and Stress textbox.

Figure 35. Graph. Relationship between the calculated aggregate interlock parameter and measured JTE. The graph shows Dimensionless Aggregate Interlock on the Y-axis and Joint Transfer Efficiency (JTE) on the X-axis. The Y-axis is on a log scale. There are data points that are in the shape of an exponential line starting at 40 percent and seem to go vertical at around 98 percent.

Figure 36. Graph. Relationship between measured crack opening and the calculated aggregate interlock parameter. The graph depicts Dimensionless Aggregate Interlock on the Y-axis and Crack Opening on the X-axis. The Y-axis is on a log scale. There are two sets of data, one for the 229-millimeter data and one for the 178-millimeter data. Each is best fitted by a straight line decreasing from left to right. The line for the 229-millimeter data is higher than the line for the 178-millimeter data.

Figure 37. Sketch. Free edge loading of JCP. The sketch shows a slab on top of a subbase on top of a subgrade. The slab is being loaded at a free edge and is deflecting. That deflection, the free-edge deflection, is represented by delta subscript F.

Figure 38. Sketch. Loaded and unloaded deflections of a JCP. The sketch shows a jointed slab on top of a subbase on top of a subgrade. The left edge is being load and is deflecting a little more than the right edge. The loaded deflection is represented by delta subscript l and the unloaded deflection is represented by delta subscript U.

Figure 39. Graph. Relationship between JTE and LTE subscript delta. The graph depicts Deflection Load Transfer Efficiency (LTE) on the Y-axis and Joint Transfer Efficiency (JTE) on the X-axis. There is a straight line with a slope of 1 increasing from left to right representing the line of equality. The actual line is a curve that is under this line touching the two ends of the straight line forming a thin D shape.

Figure 40. Graph. Relationship between LTE subscript sigma and LTE subscript delta. Deflection Load Transfer Efficiency (LTE) is on the Y-axis and Stress Load Transfer Efficiency (LTE) on the X-axis. There are six log-shaped curves increasing from left to right representing different A-to-L ratios. The curves are for, from highest and most curvy to lowest and flattest, A-to-L ratios of 0.02, 0.05, 0.1, 0.2, 0.5, and 1.0.

Figure 41. Graph. JTE results obtained from the experimental work performed by Colley and Humphrey as a function of loading cycles of a 4086-kilogram load. Percent Effectiveness is on the Y-axis and Loading Cycles from 0 to 1,000,000 are on the X-axis. There are five lines that depict different joint openings at 0.6 millimeters, 0.9 millimeters, 1.1 millimeters, 1.7 millimeters, and 2.2 millimeters. As the size of the openings increases, their effectiveness decreases. All but the 2.2-millimeter joint openings decrease steadily in effectiveness as loading cycles increase, eventually leveling out. The 2.2-millimeter opening also decreases as loading cycles increase, but effectiveness drops to 0 percent at 500,000 loading cycles.

Figure 42. Graph. Influence of joint opening on JTE, 229-millimeter concrete slab, 152-millimeter gravel subbase. Effectiveness is on the Y-axis and Loading Cycles are on the X-axis. There are five curves decreasing from left to right representing different joint openings. The top line is an inverse exponential line that remains straight after the first initial drop and is for joint opening of 0.6 millimeter. The next three lines are inverse exponential lines and are for, from top to bottom, joint openings of 0.9, 1.1, and 1.7 millimeters, respectively. The fifth line, in an S shape, far below the others, is for a joint opening of 2.2 millimeters.

Figure 43. Influence of joint opening on JTE, 178-millimeter concrete slab, 152-millimeter gravel subbase. Effectiveness is on the Y-axis and Loading Cycles are on the X-axis. There are five curves decreasing from left to right representing different joint openings. The top line is a linear line and is for joint opening of 0.4 millimeter. The next three lines are inverse exponential lines that have low slopes and are for, from top to bottom, joint openings of 0.6, 0.9, and 1.1 millimeters, respectively. The fifth line, also an exponential line but with a very steep drop, is for a joint opening of 2.2 millimeters.

Figure 44. Graph. Asymptote dimensionless joint stiffness as a function of joint opening. Aggregate interlock parameter is on the Y-axis and 1 divided by joint opening in millimeters is on the X-axis. The Y-axis is on a log scale. There are two sets of data, the one to the left is for aggregate interlock parameter asymptote (229 millimeter) and the one on the right is for the aggregate interlock parameter asymptote (178 millimeter). Each set of data is best fitted by a straight line increasing from left to right.

Figure 45. Graph. Sensitivity of faulting to joint opening and cumulative traffic loading for nondoweled JPCP (MESAL equals 1,000,000 ESAL). Faulting is on the Y-axis and MESALs is on the X-axis. There are seven log shape lines that are widely spaced from each other increasing from left to right representing joint openings of, from top to bottom, 12.7, 5.1, 2.5, 1.3, 0.5, 0.3, and 0.1 millimeter, respectively.

Figure 46. Graph. Sensitivity of faulting to joint opening and cumulative traffic loading for doweled JPCP (MESAL equals 1,000,000 ESAL). Faulting is on the Y-axis and MESALs is on the X-axis. There are seven log shape lines that are very closely spaced to each other increasing from left to right representing joint openings of, from top to bottom, 12.7, 5.1, 2.5, 1.3, 0.5, 0.3, and 0.1 millimeter, respectively.

Figure 47. Graph. Relationship between joint opening model predictions. Hiperpav Model Joint Opening is on the Y-axis and FHWA Model Joint Opening is on the X-axis. There is a 45-degree line representing the line of equality. The data points left of this line suggest that the Hiperpav model predicts greater joint openings than the FHWA model.

Figure 48. Graph. Relationship between revised joint opening model predictions. Hiperpav Model Joint Opening is on the Y-axis and FHWA Model Joint Opening is on the X-axis. There is a 45-degree line representing the line of equality. The data points falling on the line suggest that the Hiperpav model's predictions of joint openings are virtually the same as the FHWA model's predictions.

Figure 49. Graph. Allowable loads versus stress-to-strength ratio. Allowable Load Applications is on the Y-axis and Stress-Strength Ratio is on the X-axis. There are five lines decreasing from left to right representing five different models. The steep linear line represents the Zero-Maintenance Model. The flat, close to linear line represents the ARE Model. The three inverse exponential lines represent, from bottom to top, the NCHRP Model 126 at 5 percent failure, the ERES-COE Model, and the NCHRP Model 126 at 50 percent failure, respectively.

Figure 50. Graph. Fatigue cracking model with associated data. Percent Slab Cracked is on the Y-axis and Fatigue Damage is on the X-axis. There are scattered data points that are mostly on the right side of the graph and are best fitted by an S-shaped curve increasing from left to right.

Figure 51. Flowchart. Flowchart of stress, damage, and cracking module. Flowchart starts with a "Loop over two times of day" text box that flows to a "Loop over six axle groups" text box that flows to a "Calculate transverse edge stress adjustment" text box that flows to a "Calculate longitudinal corner stress adjustment" text box that flows to a "Loop over 45 load groups" text box that flows to a "Calculate Westergaard transverse edge stress adjustment" text box that flows to a "Calculate Westergaard longitudinal edge stress adjustment" text box that flows to a "Adjust Westergaard stresses" text box that flows to a "Calculate midslab fatigue" text box that flows to a "Accumulate midslab damage" text box that flows to a "Have all load groups been processed?" text box. If the answer is yes, it flows to a "Have all axle groups been processed?" text box. If the answer is no, it flows back to the "Loop over 45 load groups" text box. If the answer to the "Have all axle groups been processed?" text box is yes, it flows to a "Have all times of day been processed?" text box. If the answer is no, it flows back to the "Loop over six axle groups" text box. If the answer to the text box "Have all times of day been processed?" is yes, it flows to a "Compute cracking for season" text box. If the answer is no, then it flows back to the "Loop over two times of day" text box.

Figure 52. Graph. Amount of each individual distress required to reach a PSI of 2.0. The graph is a bar graph describing JCP distresses. The left bar, going past 2000, is the cumulative transverse joint faulting in millimeters per kilometer. The middle bar, reaching 500, is the number of deteriorated (medium and high severity) transverse joints per kilometer. The right bar, almost reaching 1000, is the number of transverse cracks (all severities) per kilometer.

Figure 53. Graph. Shape of IRI versus PSI curve. IRI is on the Y-axis and PSI is on the X-axis. The relationship is represented by a linear line decreasing from left to right that corresponds to the equation IRI (meters per kilometer) equal to 1.0602 times the difference of 5 minus psi.

Figure 54. Graph. Effect of faulting on IRI. IRI (meters per kilometer) is on the Y-axis and Total Faulting per Section (millimeter) is on the X-axis. The relationship is represented by a linear line increasing from left to right that corresponds to the equation IRI (meters per kilometer) equal to 0.0098 times the total faulting per section plus 1.268.

Figure 55. Graph. Comparison of faulting influence between the various IRI models. IRI is on the Y-axis and Faulting is on the X-axis. There are five linear lines increasing from left to right representing five different IRI versus faulting models. The slopes of all the lines tend to be similar. One of the major distinctions is the high initial IRI subscript 0 of the FHWA-RD-97-147 model. The FHWA-RD-00-130 model and the Transtec model are very similar, as are the two 1-37A models.

Figure 56. Graph. Effect of percent cracked slabs on FHWA-RD-00-130, 1-37A Guide, and contractor IRI models. IRI is on the Y-axis and Percent Cracking is on the X-axis. There are four linear lines increasing from left to right representing four different IRI versus cracking models. Increasing percent cracked slabs causes a marked increase in IRI according to the 1-37A model presented in 2000 at the Transportation Research Board (TRB) conference. Its effect on the other three models is not as severe, with the FHWA-RD-00-130 model and the 1-37A model presented in 2001 at TRB being virtually the same.

Figure 57. Graph. Effect of percent spalling on FHWA-RD-00-130, 1-37A Guide, and contractor IRI models. IRI is on the Y-axis and Percent Spalling is on the X-axis. There are four linear lines increasing from left to right representing four different IRI versus spalling models. Increasing the percent spalling causes a slight increase in IRI for all four models. The slopes of the FHWA-RD-00-130 and 1-37A IRI models are approximately the same while the slope of the Transtec model is slightly higher.

Figure 58. Graph. Effect of percent patching on IRI for the 1-37A models. IRI is on the Y-axis and Percent Spalling is on the X-axis. There are two linear lines increasing from left to right representing the 1-37A models. The 1-37A model presented in 2000 is more sensitive to patching than is the one presented in 2001.

Figure 59. Graph. Effect of initial IRI subscript 0 on FHWA-RD-00-130, 1-37A, and contractor IRI models. IRI is on the Y-axis and Initial IRI is on the X-axis. There are four linear lines representing four different IRI versus spalling models. The Transtec model does not account for initial IRI and thus it produced a straight line. The slopes of all the other models are very similar with the two most similar models being the FHWA-RD-00-130 model and the 1-37A model presented in 2001.

Figure 60. Sketch. Schematic representation of analysis of concrete and steel stresses in CRCP-8. The sketch shows a schematic representation of the one dimensional model for analysis of concrete and steel stresses in a CRCP basic analysis unit bounded by two adjacent transverse cracks and longitudinal joints. The schematic also shows a free body diagram depicting different forces at work.

Figure 61. Sketch. Simplified coordinate system for development of bond stress distribution functions. The sketch depicts a slab from midslab to a crack. Bond slippage begins two-thirds of the way from midslab. From midslab to that point is the fully bonded zone. From that point to the crack is the bond development zone.

Figure 62. Graph. Compressive strength as a function of water-to-cement ratio and cement content. Compressive strength is on the Y-axis and water-to-cement ratio is on the X-axis. There are two lines mostly decreasing from left to right representing the Basic Model and the Augmented Model. These two models are very close to each other except at low water-to-cement ratios (less than 0.3); the compressive strength continues to increase according to the basic model. This relationship would be correct for fully compacted concrete, but at lower water-to-cement ratios, it is difficult to achieve full compaction. The augmented model, used in COMET, provides a more reasonable prediction of compressive strength, since it drops slightly at water-to-cement ratios of less 0.3.

Figure 63. Sketch. Schematic of dowel deformation and loading at the joint. The sketch depicts two slabs jointed by a dowel curling upward, causing the dowel bar to curl downward. The dowel is subjected to moments M subscript 0.

Figure 64. Sketch. Schematic of dowel deformation without concrete compliance and with concrete compliance at the joint. Two cases are shown this sketch. In the first case, the gray dowel depicts behavior at the joint assuming that the concrete underneath it does not deform, or that there is no concrete compliance. In the second case, the concrete has deformed underneath the black dowel. The gray dowel bar deforms more than the black dowel bar.

Figure 65. Graph. Effect of varying the dowel diameter (lowercase D subscript D) on the bearing stress. Bearing Stress is on the Y-axis and Dowel Diameter is on the X-axis. As the dowel diameter increases from about 16 millimeters to about 38 millimeters, the Bearing Stress increases linearly from about 4.5 megapascals to about 8.8 megapascals.

Figure 66. Graph. Effect of varying the effective modulus of dowel support (K subscript D) on the bearing stress. Bearing Stress is on the Y-axis and Effective Modulus of Dowel Support (KD) is on the X-axis. As K subscript D increases from about 280,000 megapascals per meter to about 830,000 megapascals per meter, the Bearing Stress increases linearly from about 4.5 megapascals to about 10.5 megapascals.

Figure 67. Graph. Effect of varying the joint opening on the bearing stress. Bearing Stress is on the Y-axis and Joint Opening is on the X-axis. As the joint opening increases from 0 millimeters to 25 millimeters, the Bearing Stress decreases linearly from about 7.8 megapascals to about 5.8 megapascals.

Figure 68. Graph. Effect of varying the concrete modulus (E subscript C) on the bearing stress. Bearing Stress is on the Y-axis and Concrete Modulus is on the X-axis. As the concrete modulus increases from about 21,000 megapascals to about 42,000 megapascals, the Bearing Stress increases linearly from about 7 megapascals to about 8.9 megapascals.

Figure 69. Graph. Effect of varying the concrete CTE (alpha subscript C) on the bearing stress. Bearing Stress is on the Y-axis and Concrete Coefficient of Thermal Expansion is on the X-axis. As the coefficient increases from about 7.2 to about 12.7, the Bearing Stress increases linearly from about 5 megapascals to about 9 megapascals.

Figure 70. Graph. Effect of varying the slab length (L) on the bearing stress. Bearing Stress is on the Y-axis and Slab Length is on the X-axis. As the slab length increases from 3 meters to 4.7 meters, the bearing stress decreases linearly from 100 megapascals to 75 megapascals. From then on, an increase in slab length doesn't seem to affect the bearing stress.

Figure 71. Graph. Effect of varying the slab thickness (lowercase H) on the bearing stress. Bearing Stress is on the Y-axis and slab thickness is on the X-axis. As the slab thickness increases from about 200 millimeters to about 360 millimeters, the Bearing Stress increases very close to linearly from about 62 megapascals to about 115 megapascals.

Figure 72. Graph. Effect of varying the modulus of subgrade reaction (lowercase K) on the bearing stress. Bearing Stress is on the Y-axis and the modulus of subgrade reaction (lowercase K) is on the X-axis. As k increases, the Bearing Stress decreases. The bearing stress is most sensitive to the change in lowercase K if lowercase K is less than 50 megapascals per meter. Changes in lowercase K when lowercase K is more than 50 megapascals per meter does not have significant effect on the bearing stress.

Figure 73. Graph. Effect of varying the linear temperature gradient (T) on the bearing stress. Bearing Stress is on the Y-axis and the linear temperature gradient (T) is on the X-axis. The relationship is represented by a V originating from 0, meaning the bearing stress increases with the increase in the absolute value of the linear temperature gradient.

Figure 74. Sketch. Schematic representation of slabs loaded in shear. The sketch depicts joints in the pavements being loaded in shear and the dowel bars resisting this load. The free edge deflection, lowercase Y subscript 0 (in meters), is restrained by twice the value of lowercase Y subscript 1 (in meters) due to the dowels.

Figure 75. Screen Shot. Hiperpav 2 screen shot showing typical output from the dowel bar module. The screen shot shows the dowel analysis module in Hiperpav 2. The output shows a graph in which the dowel bearing strength and stress is on the Y-axis and time of day is on the X-axis. The graph depicts relationships between bearing strength, curl-curl stress, and flat-curl stress and time of day. The bearing strength increased in a shape of a log line over the total elapsed time while the stresses go through cycles represented by little mound-shaped curves. Both the stresses seem to be greatest at 6 AM.

Figure 76. Graph. Pavement temperature profiles for Illinois JPCP evaluation. Depth is on the Y-axis and Pavement Temperature is on the X-axis. There are three sets of data points representing three different times of day. In the morning, the pavement temperature is slightly higher with increasing depth. During midday and evening times, the pavement temperature is much higher closer to the surface.

Figure 77. Graph. Joint movement for section AA in Illinois JPCP evaluation. Movement is on the Y-axis and Mean Pavement Temperature is on the X-axis. The downward trend is indicative of joints closing under higher temperatures and opening under cooler temperatures. After 36 degrees Celsius, no further movement is observed, possibly because of joint closure after that temperature.

Figure 78. Graph. Longitudinal profiles for section AA, 253-millimeter thickness. Deviation from Grade is on the Y-axis and Distance is on the X-axis. The data points can be best fitted by wavy curves relating to a curling pattern at every 6-meter interval corresponding to the slab length for this section.

Figure 79. Sketch. Ticuman bypass project location. The illustration shows the general location and layout of the road of the Ticuman bypass section, which is located south of Mexico City.

Figure 80. Graph. Mean concrete compressive and flexural strength gain curves for the Ticuman bypass. Strength is on the Y-axis and Time is on the X-axis. The compressive strength increases greatly in the first 3 days and then steadily from there to 28 days, reaching a value of 30 megapascals. The flexural strength increases gradually over a period of 14 days and then seems to stay the same from there to 28 days, reaching a value of 5 megapascals.

Figure 81. Graph. Number of distressed slabs per kilometer for the Ticuman bypass. Number of Distresses per Kilometer is on the Y-axis and Date is on the X-axis. There are four lines increasing from left to right representing four different distresses. It can be observed from the graph that longitudinal cracking is the predominant distress type, reaching 35 per kilometer. Also a considerably large number of slabs have a mix of longitudinal, transverse, and/or corner cracking. These slabs were reported as shattered slabs, reaching 18 per kilometer.

Figure 82. Graph. Faulting distribution for the Ticuman bypass. Frequency is on the left Y-axis, Cumulative is on the right Y-axis, and Faulting is on the X-axis. The frequencies are represented by bars while the cumulative is represented by a line. Faulting of 0 and 1 millimeter have the highest frequency (48 and 53, respectively), followed by faulting of 0.5, 1.5, and 2 millimeters. The cumulative line increases slightly in a linear fashion from negative 3.0 to negative 0.5 millimeters, then it takes the form of a log line increasing from left to right.

Figure 83. Graph. Measured joint opening during August 22 to 24. Number of Joints is on the left Y-axis, Cumulative is on the right Y-axis, and Joint Movement is on the X-axis. The frequencies are represented by bars while the cumulative is represented by a line. Joint movement of negative 0.033 millimeter per degree Celsius has the highest frequency (4 joints) followed by joint movement of negative 0.035 millimeter per degree Celsius (3 joints). There are no joints that experience movement equal to or less than negative 0.041 millimeter per degree Celsius or equal to or more than negative 0.015 millimeter per degree Celsius. The cumulative line seems to take on the form of a slanted S shape with some minor variations in the middle.

Figure 84. Graph. Comparison of PSI ratings on the southbound direction (summer 2001 versus summer 1995). PSI is on the Y-axis and Station is on the X-axis. There are three bars at each station representing readings done in the morning of 2001, afternoon of 2001, and 1995. The morning readings are higher than the afternoon readings are closer to the readings in 1995. Almost all of the readings fall between 2.0 and 3.0 PSI.

Figure 85. Graph. Comparison of PSI ratings on the northbound direction (summer 2001 versus summer 1995). PSI is on the Y-axis and Station is on the X-axis. There are three bars at each station representing readings done in the morning of 2001, afternoon of 2001, and 1995. The afternoon readings are mostly higher than the morning readings while both take turn being close to the 95 readings, depending on the station. Most of the readings fall between 2.0 and 3.0 PSI.

Figure 86. Drawing. Typical cross section for the CRCP instrumented section. The sketch shows the typical cross section at the construction site of part of one of the access ramps on the IH-35/IH-30 interchange. The pavement is 26 feet wide and consists of 8 inches continuously reinforced concrete on top of 4 inches of hot-mix asphalt, type D underlayment on top of 8 inches of lime treated subgrade. For metric conversion, 1 foot equals 0.3048 meters, 1 inch equals 25.4 millimeters.

Figure 87. Photo. Instrumented section delineated by crack inducers. The photo shows the position of the crack inducers on the instrumented area. The crack inducers were spaced at approximately 4.9 meters due to a survey of previous sections that found that the average crack spacing measured was approximately 4.9 meters.

Figure 88. Photo. Strain gages in PCC and on reinforcing steel. The photo shows the strain gages in concrete and on the reinforcing steel at the corner location. Roctest embedment vibrating wire gages type EM-5 were installed on the instrumented area at three different depths at midslab, edge, and corner (150 millimeters from the crack). Type "T" thermocouples were also installed at seven different depths throughout the pavement depth. The thermocouple located at the PCC surface was installed just after the slip form paver passed by the instrumented area. In addition, resistance gages type CEA-06-125UN-120 were epoxied to the steel rebar at different distances from the expected crack along with embedment gages to monitor the steel and concrete strain.

Figure 89. Photo. Shear failure as a result of pushoff test. The photo depicts a plane of failure in the asphalt along the border of the slab against which the load was applied. This plane of failure originated from shear forces that developed in the asphalt due to the strong bond between the concrete and asphalt.

Figure 90. Drawing. Position of strain gages and thermocouples as constructed. The drawing shows the sensor locations with respect to the observed cracks as constructed. The thermal couple is placed in the middle while most of the concrete and steel strain gages are place on the right side with some placed on the left side.

Figure 91. Drawing. Typical cross section for I-29, South Dakota (from opposite direction to traffic). The typical cross section at the construction site on IH-29 is designed to accommodate a 4-lane divided road. Each direction is 12.2 meters wide with a 1.8-meter left shoulder, two 3.65-meter lanes, and a 3-meter right shoulder. The central portion of the pavement was being constructed with CRCP pavement to conform a 3.65-meter-wide right lane with 0.6-meter PCC widened shoulder and a 3.65-meter-wide left lane. The rest of the shoulders were being paved with hot-mix asphalt. A longitudinal joint was being cut between lanes. The CRCP pavement is 279 millimeters thick on top of a 102-millimeter granular subbase.

Figure 92. Photo. Strain gages in PCC and on reinforcing steel. The photo shows the positions of gages in the concrete and on the reinforcing steel. To position the Roctest vibrating wire gages type EM-5, two wood dowels were driven into the subbase (granular subbase) separated approximately 102 millimeters for each set of gages. The gage was then fixed on the dowels at the proper height with plastic zip ties. Wood dowels were also used to install type "T" thermocouples at seven different depths throughout the pavement depth. The thermocouple located at the PCC surface was installed just after the slip form paver passed by the instrumented area.

Figure 93. Drawing. Cracking pattern on instrumented section. The drawing shows cracking patterns observed at 18 hours and at 34 hours. After 18 hours, three cracks were observed; one left, one right, and one in the middle. The left and right cracks are close to the respective crack transducer. The middle crack is close to the sensors. After 34 hours, two more cracks were observed between the left and middle crack.

Figure 94. Drawing. Location of the sensors with respect to the pavement edge and cracks as constructed. The drawing shows the sensor locations with respect to the observed cracks as constructed. According to the drawing, the PCC and steel strain gages were placed very close to the cracks, with the farthest distance being 191 millimeters from a PCC strain gage, and 356 millimeters from a steel strain gage.

Figure 95. Graph. Time growth of Texas compressive strength. Average Compressive Strength is on the Y-axis and Test Age is on the X-axis. The strength increases with time. The strength rate of increase is high in the first day, moderate from then to day 7, and low from day 7 to day 14, reaching an average compressive strength of 29 megapascals.

Figure 96. Graph. Time growth of Texas splitting tensile strength. Average Splitting Tensile Strength is on the Y-axis and Test Age is on the X-axis. The strength increases with time. The strength rate of increase is high in the first day and low from then up to day 14, reaching an average tensile strength of 2.3 megapascals.

Figure 97. Graph. Time growth of Texas modulus of elasticity. Average Modulus of Elasticity is on the Y-axis and Test Age is on the X-axis. Both the ACI- and the ACI 318-predicted values are virtually the same, increasing with time, with the modulus increasing significantly after the first day and then less and less as the test age goes up to day 14. The test data points do not increase with time. The modulus increases from 0.5 to 3 days (the actual values being higher than the ACI values, reaching 30,000 megapascals), and then drops at 7 and 14 days (the actual values being lower than the ACI values, about 20,000 megapascals).

Figure 98. Graph. Time growth of South Dakota compressive strength. Average Compressive Strength is on the Y-axis and Test Age is on the X-axis. The strength increases with time. The strength rate of increase is moderate from day 3 to day 7, and is slightly lower from then to day 28, reaching an average compressive strength of 37 megapascals.

Figure 99. Graph. Time growth of South Dakota splitting tensile strength. Average Splitting Tensile Strength is on the Y-axis and Test Age is on the X-axis. The strength increases with time. The strength rate of increase is high from day 1 to day 3 (measured in the field), and is moderate from day 3 to day 28 (measured in the lab), reaching an average tensile strength of 4 megapascals.

Figure 100. Graph. Time growth of South Dakota modulus of elasticity. Average Modulus of Elasticity is on the Y-axis and Test Age is on the X-axis. Both the ACI- and the ACI 318-predicted values are virtually the same, increasing with time, with the rate of increase is moderate from day 3 to day 7, and is slightly lower from then to day 28. The test data points are higher, reaching 34,000 megapascals but seem to follow the same pattern, although no data points exist for day 3.

Figure 101. Graph. Time growth of Mexico compressive strength. Average Compressive Strength is on the Y-axis and Test Age is on the X-axis. The strength increases with time. The strength rate of increase is moderate from day 1 to day 28, and is slightly lower from day 28 to approximately day 6000, reaching an average compressive strength of 42 megapascals.

Figure 102. Graph. Time growth of Mexico splitting tensile strength. Average Splitting Tensile Strength is on the Y-axis and Test Age is on the X-axis. The graph shows one linear line representing the steady increase in strength with time, with the average tensile strength reaching 3.8 megapascals after approximately 6000 days.

Figure 103. Graph. Time growth of Mexico modulus of elasticity. Average Modulus of Elasticity is on the Y-axis and Test Age is on the X-axis. Both the ACI- and the ACI 318-predicted values are virtually the same, increasing with time, with the rate of increase is moderate from day 1 to day 28, and is slightly lower from day 28 to approximately day 6000. The test data points show a higher rate of increase from day 28, with the average modulus of elasticity reaching 40,000 megapascals. No data points exist for earlier periods.

Figure 104. Graph. Time growth of Illinois compressive strength. Average Compressive Strength is on the Y-axis and Test Age is on the X-axis. The graph shows data points of measured compressive strength and also data points of estimated compressive strength from flexural strength. After 14 days, the data shows a minimal increase in compressive strength, except for the 90-day calculated value, which increases significantly from the 28-day value. According to the graph, the final average compressive strength is about 40 megapascals.

Figure 105. Graph. Time growth of Illinois modulus of elasticity. Modulus of Elasticity is on the Y-axis and Test Age is on the X-axis. Both the ACI-predicted values and the measured values are basically the same, except for the 90-day calculated value as mentioned above. Modulus of elasticity is relatively stable after 14 days, reaching 28,000 megapascals.

Figure 106. Graph. Drying shrinkage of South Dakota concrete. Drying Shrinkage is on the Y-axis and T minus T subscript 0 in days is on the X-axis. The ultimate shrinkage predicted is represented by a log-shape line increasing as time increases. The ultimate shrinkage set is the same as the predicted line, except higher. Higher still are the data points with the highest value being 410 at 13 days. The ultimate shrinkage set line seems to level out at about 360, and the predicted line seems to level out at about 275.

Figure 107. Graph. Drying shrinkage of Texas concrete. Drying Shrinkage is on the Y-axis and T minus T subscript 0 in days is on the X-axis. The ultimate shrinkage predicted is represented by a log-shape line increasing as time increases. The ultimate shrinkage set is the same as the predicted line, except just slightly higher. The data points seem to fall along these two lines with the highest value being 410 at 13 days. The ultimate shrinkage set line seems to level out at about 380, and the predicted line seems to level out at about 350.

Figure 108. Graph. Setting times of concrete for Texas and South Dakota concretes. Penetration Resistance is on the Y-axis and Elapsed Time is on the X-axis. The set time data for Texas is best fit using a power function with R squared equal to 0.99 and the set time data for South Dakota is best fit using a power function with R squared equal to 0.97. The total elapsed time is much longer for the South Dakota data set since the ambient temperature for set time measurements is much lower in South Dakota.

Figure 109. Graph. Concrete and ambient air temperatures for the South Dakota concrete. Temperature is on the Y-axis and Time is on the X-axis. The air temperature stays around 17.5 degrees Celsius. The concrete temperature decreases sharply from 22.5 to 18.5 degrees Celsius in the first 3 hours and then increases slightly to 19.5 degrees Celsius over the next 5 hours then gradually decreases to coincide with the air temperature after 35 hours.

Figure 110. Graph. Concrete and ambient air temperatures for the Texas concrete. Temperature is on the Y-axis and Time is on the X-axis. The air temperature stays around 36 degrees Celsius. The concrete temperature increases sharply from 22.6 to 40.2 degrees Celsius in the first 6 hours then gradually decreases to coincide with the air temperature after 23 hours.

Figure 111. Graph. Measured versus predicted joint opening. Predicted ER is on the Y-axis and Measured ER is on the X-axis. There is a linear line with a slope of 1 representing equality. In general, it can be observed that the Hiperpav 2 joint opening model slightly overpredicts joint movement for most of the sections, since all but one data point fall above this line.

Figure 112. Graph. Typical plot of PCC temperature versus joint LTE, section 37-0201. LTE is on the Y-axis and Temperature is on the X-axis. There is a trend line increasing close to linearly from left to right. For PCC temperatures below the threshold temperature of 27 degrees Celsius, the joint LTE values are scattered and fall below 50 percent. For PCC temperatures above the threshold temperature, the joint LTE values are more closely packed and are all above 80 percent.

Figure 113. Graph. Computed LTE versus PCC temperature for section 49-3011. LTE is on the Y-axis and Temperature is on the X-axis. For PCC temperatures below the threshold temperature of 25 degrees Celsius, the joint LTE values are scattered and fall below 20 percent. For PCC temperatures above the threshold temperature, the joint LTE values are more closely packed and are all above 80 percent. Below freezing (PCC temperature less than 0 degrees Celsius), LTE is slightly higher than at PCC temperatures immediately above freezing.

Figure 114. Graph. Average LTE above freezing and below 25 degrees Celsius, section 49-3011. Average LTE is on the Y-axis and Joint ID and Date of Testing is on the X-axis. For each joint, the computed LTE is grouped into two categories: tests performed before 1996 (B-96); and tests performed in 1996 and thereafter (A-96). The average LTEs are shown in bar graphs. An evident decrease in LTE is noted for the tests performed after 1996 as compared to the tests performed in previous years. The highest LTE is about 76 percent and corresponds to Joint 5, 5.35, B-96. The lowest LTE is about 36 percent and corresponds to Joint 4, 14.15, A-96.

Figure 115. Graph. Variability of LTE for individual joints, section 49-3011. Measured LTE is on the Y-axis and Temperature is on the X-axis. There are two sets of data points, one for joint negative 9.25 and one joint 8.95. These data points are very scattered ranging from 20 percent to 100 percent. The data points for joint negative 9.25 are best fitted by a linear line increasing from left to right with R squared equal to 0.5555. The data points for joint 8.95 are best fitted by a linear line increasing from left to right with R squared equal to 0.1698.

Figure 116. Graph. Effect of joint spacing on LTE, section 49-3011. LTE is on the Y-axis and Spacing is on the X-axis. There are four sets of data points representing four different tests. The data points for approach test before 1996 are best fitted by a linear line decreasing from left to right with an r squared equal to 0.57. The data points for approach test after 1996 are best fitted by a linear line decreasing from left to right with an r squared equal to 0.37. The data points for leave test before 1996 are best fitted by a linear line decreasing from left to right with an r squared equal to 0.19. The data points for leave test after 1996 are best fitted by a linear line decreasing from left to right with an r squared equal to 0.03. The before 1996 values are higher than the after 1996 values for both tests.

Figure 117. Graph. Computed LTE versus PCC temperature for nondoweled section 31-3018. LTE is on the Y-axis and Temperature is on the X-axis. For PCC temperatures below the threshold temperature of 30 degrees Celsius, the joint LTE values are scattered and fall below 20 percent. For PCC temperatures above the threshold temperature, the joint LTE values are more closely packed and are all above 90 percent.

Figure 118. Graph. Computed LTE versus PCC temperature for nondoweled section 06-3042. LTE is on the Y-axis and Temperature is on the X-axis. For PCC temperatures below the threshold temperature of 25 degrees Celsius, the joint LTE values are scattered and fall below 20 percent. For PCC temperatures above the threshold temperature, the joint LTE values are more closely packed and are all above 90 percent.

Figure 119. Graph. Computed LTE versus PCC temperature for nondoweled section 83-3802. LTE is on the Y-axis and Temperature is on the X-axis. For PCC temperatures below the threshold temperature of 22 degrees Celsius, the joint LTE values are scattered and fall below 20 percent. For PCC temperatures above the threshold temperature, the joint LTE values are more closely packed and are all above 90 percent. It is also interesting to note that for temperatures below negative 10 degrees Celsius, the joint LTE values are also closely packed and stay mostly above 80 percent.

Figure 120. Graph. Computed LTE versus PCC temperature for nondoweled section 53-3813. LTE is on the Y-axis and Temperature is on the X-axis. For PCC temperatures below the threshold temperature of 20 degrees Celsius, the joint LTE values are scattered and fall as low as 40 percent. For PCC temperatures above the threshold temperature, the joint LTE values are more closely packed and are all above 85 percent.

Figure 121. Graph. LTE versus PCC temperature for doweled section 04-0215. LTE is on the Y-axis and Temperature is on the X-axis. For PCC temperatures below the threshold temperature of 35 degrees Celsius, the joint LTE values are fairly scattered and fall as low as 40 percent. For PCC temperatures above the threshold temperature, the joint LTE values are more closely packed and are all above 80 percent.

Figure 122. Graph. LTE versus PCC temperature for doweled section 18-3002. LTE is on the Y-axis and Temperature is on the X-axis. The joint LTE values are all above 60 percent and are not that scattered, although for temperatures higher than 25 degrees Celsius, the joint LTE values are above 80 percent.

Figure 123. Graph. LTE versus PCC temperature for doweled section 13-3019. LTE is on the Y-axis and Temperature is on the X-axis. For PCC temperatures below the threshold temperature of 18 degrees Celsius, the joint LTE values are fairly scattered and fall below 60 percent. For PCC temperatures above the threshold temperature, the joint LTE values are more closely packed and are all above 80 percent.

Figure 124. Graph. LTE versus PCC temperature for doweled section 32-0204 . LTE is on the Y-axis and Temperature is on the X-axis. The joint LTE values are all above 80 percent and are closely packed.

Figure 125. Graph. LTE versus PCC temperature for doweled section 89-3015. LTE is on the Y-axis and Temperature is on the X-axis. The joint LTE values are mostly above 80 percent and are closely packed, even for temperatures below freezing. There are a few values that fall below 80 percent for temperatures at and right below 5 degrees Celsius.

Figure 126. Graph. LTE versus PCC temperature for doweled section 39-0204. LTE is on the Y-axis and Temperature is on the X-axis. The joint LTE values are all above 80 percent and are closely packed.

Figure 127. Graph. LTE versus joint opening, for section 49-3011, joint at 5.5 meters from start of section. LTE is on the Y-axis and Joint Opening is on the X-axis. There are two sets of data points, for LTE before 1996 and LTE after 1996. The LTE before 1996 data points are scattered and fall between 40 percent and 100 percent, and are best fitted by a linear line decreasing from right to left. The LTE after 1996 data points are also scattered and fall between 20 percent and 100 percent, and are best fitted by a linear line decreasing from right to left that is of similar slope but is below the before 1996 line.

Figure 128. Graph. Predicted versus computed LTE for section 31-3018, joint 5.5 meters from start of section. LTE is on the Y-axis and Joint Opening is on the X-axis. There are two sets of data points, one for LTE on 1996 and before and one for LTE after 1996. At the same joint opening, tests performed before 1996 show higher LTE values than those performed after 1996. However, a significant variability is noted that makes it slightly difficult to determine a clear difference between testing dates. Also shown in the figure are the 4 lines predicting LTE values for the following loads: 0, 250,000, 500,000, and 12,400,000 ESALs. The predicted LTE at 250,000 ESALs seems to better match the computed LTE from tests at the end of 1996. After 500,000 ESALs the predicted LTE seems to have very little variation with cumulative traffic.

Figure 129. Graph. Predicted versus computed LTE for section 49-3011, joint 5.5 meters from start of section. LTE is on the Y-axis and Joint Opening is on the X-axis. There are two sets of data points, one for LTE on 1996 and before and one for LTE after 1996. At the same joint opening, tests performed before 1996 show higher LTE values than those performed after 1996. However, there is still variability that makes it slightly difficult to determine a clear difference between testing dates. Also shown in the figure are the 4 lines predicting LTE values for the following loads: 0, 280,000, 500,000, and 8,088,000 ESALs. The predicted LTE at 280,000 ESALs seems to better match the computed LTE from tests at the end of 1996. After 500,000 ESALs the predicted LTE seems to have very little variation with cumulative traffic.

Figure 130. Graph. Predicted versus computed LTE for section 06-3042, joint 148.1 meters from start of section. LTE is on the Y-axis and Joint Opening is on the X-axis. There are two sets of data points, one for LTE on 1996 and before and one for LTE after 1996. At the same joint opening, tests performed before 1996 show higher LTE values than those performed after 1996. Also shown in the figure are the 4 lines predicting LTE values for the following loads: 0, 150,000, 500,000, and 29,066,000 ESALs. The predicted LTE at 150,000 ESALs seems to better match the computed LTE from tests at the end of 1996. After 500,000 ESALs the predicted LTE seems to have very little variation with cumulative traffic.

Figure 131. Graph. Predicted versus computed LTE for section 83-3802, joint 149.7 meters from start of section. LTE is on the Y-axis and Joint Opening is on the X-axis. There are two sets of data points, one for LTE on and before 1996 and one for LTE after 1996. At the same joint opening, tests performed before 1996 show lower LTE values than those performed after 1996. Also shown in the figure are the 5 lines predicting LTE values for the following loads: 0, 200,000, 300,000, 500,000, and 1,975,000 ESALs. The predicted LTE at 200,000 ESALs seems to better match the computed LTE from tests after 1996. The predicted LTE at 300,000 ESALs seems to better match the computed LTE from tests on and before 1996. After 500,000 ESALs the predicted LTE seems to have very little variation with cumulative traffic.

Figure 132. Graph. Predicted versus computed LTE for section 53-3813, joint 0.0 meters from start of section. LTE is on the Y-axis and Joint Opening is on the X-axis. There are two sets of data points, one for LTE on 1996 and before and one for LTE after 1996. At the same joint opening, tests performed before 1996 show higher LTE values than those performed after 1996. Also shown in the figure are the 3 lines predicting LTE values for the following loads: 0, 100,000, and 3,790,000 ESALs. The predicted LTE at 100,000 ESALs seems to better match the computed LTE from tests at the end of 1996.

Figure 133. Graph. Sensitivity analysis of LTE model for nondoweled pavements. LTE is on the Y-axis and Parameter is on the X-axis. According to this graph, the most predominant factors affecting LTE are joint opening (difference between 9 percent for 5 millimeters and 98 percent for 0.5 millimeter), cumulative load applications (difference between 45 percent for 270,000 and 93 percent for 0), and slab thickness (difference between 83 percent for 178 millimeters and 97 percent for 330 millimeters). No major effects from PCC stiffness, wheel load, pressure, or k-value were observed on LTE.

Figure 134. Graph. LTE model sensitivity for doweled sections. LTE is on the Y-axis and Parameter is on the X-axis. According to this graph, the most predominant factors affecting LTE are, from most to least are: dowel looseness, load weight, K value, slab thickness, PCC stiffness, joint opening, and cumulative load applications, respectively. No major effects from dowel diameter, dowel diameter, and load pressure were observed on LTE.

Figure 135. Graph. Predicted versus computed LTE for section 37-0201, joint 145.1 meters from start of section. LTE is on the Y-axis and Joint Opening is on the X-axis. There are two sets of data points, one for LTE on 1996 and before and one for LTE after 1996. At the same joint opening, tests performed before 1996 show higher LTE values than those performed after 1996. However, there is still variability that makes it slightly difficult to determine a clear difference between testing dates. Also shown in the figure are four lines predicting LTE values for four different conditions. The line for the condition ESAL's factor equal to 0.048, looseness equal to 0.11 millimeter seems to better match the computed LTE from tests at the end of 1996.

Figure 136. Graph. Predicted versus computed LTE for section 04-0215, joint 144.5 meters from start of section. LTE is on the Y-axis and Joint Opening is on the X-axis. There are two sets of data points, one for LTE on 1996 and before and one for LTE after 1996. The data is so variable that it is difficult to determine the difference between testing dates. Also shown in the figure are four lines predicting LTE values for four different conditions. The line for the condition ESAL's factor equal to 0.074, looseness equal to 0.13 millimeter seems to better match the computed LTE from the tests.

Figure 137. Graph. Predicted versus computed LTE for section 13-3019, joint 21.3 meters from start of section. LTE is on the Y-axis and Joint Opening is on the X-axis. There are two sets of data points, one for LTE on 1996 and before and one for LTE after 1996. The data is so variable that it is difficult to determine the difference between testing dates. Also shown in the figure are five lines predicting LTE values for five different conditions. The line for the condition ESAL's factor equal to 0.09 seems to better match the computed LTE from the tests.

Figure 138. Graph. Predicted versus computed LTE for section 32-0204, joint 8.5 meters from start of section. LTE is on the Y-axis and Joint Opening is on the X-axis. There are two sets of data points, one for LTE on 1996 and before and one for LTE after 1996. At the same joint opening, tests performed before 1996 show higher LTE values than those performed after 1996. However, there is still variability that makes it slightly difficult to determine a clear difference between testing dates. Also shown in the figure are five lines predicting LTE values for five different conditions. The line for the condition ESAL's factor equal to 0.048, looseness equal to 0.000 millimeter seems to better match the computed LTE from tests at the end of 1996.

Figure 139. Graph. Predicted versus computed LTE for section 89-3015, joint 36.3 meters from start of section. LTE is on the Y-axis and Joint Opening is on the X-axis. There are two sets of data points, one for LTE on 1996 and before and one for LTE after 1996. The data is so variable that it is difficult to determine the difference between testing dates. Also shown in the figure are three lines predicting LTE values for three different conditions. The line for the condition ESAL's factor equal to 0.048, looseness equal to 0.000 millimeter seems to better match the computed LTE from the tests.

Figure 140. Graph. Predicted versus computed LTE for section 39-0204, joint 0.0 meters from start of section. LTE is on the Y-axis and Joint Opening is on the X-axis. There are two sets of data points, one for LTE on 1996 and before and one for LTE after 1996. The data is so variable that it is difficult to determine the difference between testing dates. Also shown in the figure are four lines predicting LTE values for four different conditions. The line for the condition ESAL's factor equal to 0.048, looseness equal to 0.000 millimeter seems to better match the computed LTE from the tests.

Figure 141. Graph. Crack spacing history for summer sections, SH-6. Crack Spacing is on the Y-axis and Pavement Age is on the left axis. A typical trend of reduction in crack spacing with age can be observed, however, for most sections, higher average crack spacing were reported for the surveying date at 4700 days than for previous dates. This may be due to omitted cracks during crack spacing measurements since there is no recorded history of rehabilitation.

Figure 142. Graph. Crack spacing history for winter sections, SH-6. Crack Spacing is on the Y-axis and Pavement Age is on the left axis. A typical trend of reduction in crack spacing with age can be observed, however, for most sections, higher average crack spacing were reported for the surveying date at 4700 days than for previous dates. This may be due to omitted cracks during crack spacing measurements since there is no recorded history of rehabilitation.

Figure 143. Graph. Preliminary long-term crack spacing prediction. Predicted Average Crack Spacing is on the Y-axis and Observed Average Crack Spacing is on the X-axis. The 45-degree line represents equality. Most of data points fall slightly above this line, suggesting a slight overprediction of crack spacing. However, a reasonably good R squared of 0.82 was obtained with respect to the 45-degree line, which has an R squared of 0.71.

Figure 144. Graph. Crack spacing prediction at 3 days from construction. Predicted Average Crack Spacing is on the Y-axis and Observed Average Crack Spacing is on the X-axis. The 45-degree line represents equality. Most of the data points fall far from this line, suggesting poor prediction of crack spacing at early ages.

Figure 145. Graph. Measured versus predicted crack widths, SH-6. Predicted Average Crack Width is on the Y-axis and Observed Average Crack Width is on the X-axis. The 45-degree line represents equality. Although a fair trend in crack width prediction is observed, most of data points fall far above this line, suggesting a large overprediction of crack width.

Figure 146. Graph. Conceptual representation of residual drying shrinkage effect (adapted from Otero et al.). Shrinkage is on the Y-axis and Pavement Age is on the X-axis. The relationship is represented by a log curve. According to the graph, the drying shrinkage after crack formation is dependent on the concrete age when the crack occurs.

Figure 147. Graph. Comparison of measured and predicted strength, Illinois site. Flexural Strength is on the Y-axis and Years is on the X-axis. The graph shows flexural strength at 14, 28, and 90 days along with the estimated flexural strength after 16 years from the splitting tensile strength obtained from cores. The graph also shows the early-age and long-term strength predicted with Hiperpav 2. In general, although the 90-day strength is slightly underpredicted, a reasonably good prediction of the measured long-term strength is obtained.

Figure 148. Graph. Comparison of measured and predicted modulus of elasticity, Illinois site. Elastic Modulus is on the Y-axis and Years is on the X-axis. The graph shows the measured modulus of elasticity at 28 days and the one obtained from concrete cores extracted from the field visit in 2001. The graph also shows the early-age and long-term modulus predicted with Hiperpav 2. While the predicted elastic modulus shows an increasing trend, the elastic modulus obtained from field cores in 2001 shows a slight decrease from the 28-day value. A significant difference in predicted versus measured elastic modulus is thus observed after 16 years.

Figure 149. Graph. Comparison of measured versus predicted LTE. LTE is on the Y-axis and Years is on the X-axis. The graph shows the measured and predicted LTE for the sections with a 216-millimeter thickness. The predicted LTE is shown as continuous lines for four times of day: 2 AM, 8 AM, 2 PM, and 8 PM. The fluctuating trend observed is due to seasonal effects. In general, a slight overprediction of LTE is observed for all testing ages.

Figure 150. Graph Early-age analysis for section AA, for placement at 2 PM. Strength or Stress is on the Y-axis and PCC Age is on the X-axis. The strength line increases with time in a log trend. In general, the stress line also increases with time, although in a fluctuating trend. The stress line stays under the strength line.

Figure 151. Graph. Early-age analysis for section IA, for placement at 2 PM. Strength or Stress is on the Y-axis and PCC Age is on the X-axis. The strength line increases with time in a log trend. In general, the stress line also increases with time, although in a fluctuating trend. The stress line stays under the strength line.

Figure 152. Graph. Early-age analysis for section NA for placement at 2 PM. Strength or Stress is on the Y-axis and PCC Age is on the X-axis. The strength line increases with time in a log trend. In general, the stress line also increases with time, although in a fluctuating trend. The stress line at times fluctuates over the strength line, suggesting high stresses.

Figure 153. Graph. Predicted faulting for sections MA and NA (191 millimeters thick). Faulting is on the Y-axis and Years is on the X-axis. The prediction (at 90 percent reliability) is represented by a sort of step function, 0 faulting up to 2 years, 0.25 millimeters from 2 to 12 years, and 0.5 millimeters from 12 to 16 years. No faulting was observed after 16 years as indicated by the data point.

Figure 154. Graph. Comparison of measured and predicted transverse cracking (sections NA and MA). Transverse Cracking is on the Y-axis and Years is on the X-axis. The prediction (at 90 percent reliability) is a horizontal line along the X-axis. Most of section MA data points fall on this line, while the section NA data points are higher than this line showing an increasing trend up to 12 percent.

Figure 155. Graph. Comparison of measured and predicted transverse cracking for sections (IA, JA, KA, LA). Transverse Cracking is on the Y-axis and Years is on the X-axis. The prediction (at 90 percent reliability) is a horizontal line along the X-axis. Most of the section KA data points fall on this line, while the other sections data points are higher than this line, with the highest being sections JA and LA at around 6 to 8 percent.

Figure 156. Graph. Transverse cracking for section AA, thickness equals 241 millimeters. Transverse cracking is on the Y-axis and Years is on the X-axis. The prediction (at 90 percent reliability) is a horizontal line along the X-axis. All of the data points fall on this line.

Figure 157. Graph. Comparison of measured and predicted longitudinal cracking (sections MA and NA). Transverse cracking is on the Y-axis and Years is on the X-axis. The prediction (at 90 percent reliability) is a horizontal line along the X-axis. All of section MA data points fall on this line, and all but 1 data point from section NA fall on this line, and that data point was only slightly above, at 1 percent.

Figure 158. Graph. Comparison of measured and predicted IRI (section NA). IRI is on the Y-axis and Years is on the X-axis. There are three linear lines increasing from left to right representing three prediction lines at different reliability levels. The line at 90 percent reliability is the highest ranging from 1.4 to 1.6 meters per kilometer for IRI, followed by the lines at 50 percent and 10 percent reliability, respectively. Half of the measured IRIs falls along the lines, while half goes up to 1.8 meters per kilometer.

Figure 159. Graph. Comparison of measured versus predicted flexural strength, Ticuman, Mexico. Flexural Strength is on the Y-axis and Years (log scale) is on the X-axis. The graph shows flexural strength at 1, 3, 7, 14, and 28 days along with the estimated flexural strength after 8 years from compressive and indirect tensile strength test results obtained from cores. The graph also shows the early-age and long-term strength predicted with Hiperpav 2. In general, a reasonably good prediction of the strength is achieved.

Figure 160. Graph. Comparison of measured versus predicted modulus of elasticity, Ticuman, Mexico. Modulus Elastic is on the Y-axis and Years (log scale) is on the X-axis. The graph shows modulus at 28 days and 8 years of age. The graph also shows the early-age and long-term strength predicted with Hiperpav 2. A significant underprediction of the elastic modulus at 8 years of age is observed. While the predicted modulus of elasticity shows an increase of 12 percent from 28 days to 8 years, the measured value shows an increase of 55 percent.

Figure 161. Graph. Comparison of measured versus predicted LTE, Ticuman, Mexico. LTE is on the Y-axis and Years is on the X-axis. The graph shows the measured (during the first few months of construction and after 8 years) and predicted LTE. The predicted LTE is shown as continuous lines for four times of day: 2 AM, 8 AM, 2 PM, and 8 PM. The fluctuating trend observed is due to seasonal effects. Compared to the LTE predicted with Hiperpav 2, the LTE predicted is higher than the measured in 1993 and slightly lower than the one measured in 2001.

Figure 162. Graph. Analysis for 229-millimeter slab at different construction times and built-in gradient conditions, Ticuman bypass. Longitudinal Cracking is on the Y-axis and Years is on the X-axis. The graph shows the effect of built-in curling for longitudinal cracking on placement times at 10 AM and 6 PM. It is observed that for the 10 AM placement, the gradient at time of loading with no gradient built-in at set produces higher cracking (up to 4 percent after 8 years) than the condition with built-in curling. In contrast, the placement at 6 PM shows the opposite trend with the condition with built-in curling showing higher longitudinal cracking (at 3 percent after 8 years).

Figure 163. Graph. Comparison of measured versus predicted joint faulting, Ticuman, Mexico. Joint Faulting is on the Y-axis and Years is on the X-axis. There are three lines close to the log, increasing from left to right representing three prediction lines at different reliability levels, with the line at 90 percent reliability being the highest, followed by lines at 50 percent and 10 percent reliability, respectively. The average measured faulting of 1.0 millimeters is lower than the faulting predicted at 50 percent reliability and above the faulting predicted at 10 percent reliability.

Figure 164. Graph. Comparison of measured versus predicted transverse cracking, Ticuman, Mexico. Transverse Cracking is on the Y-axis and Years is on the X-axis. There are three close-to-linear lines increasing from left to right representing three prediction lines at different reliability levels, with the line at 90 percent reliability being the highest (going past 30 percent after 8 years), followed by lines at 50 percent and 10 percent reliability (which stayed under 5 percent after 8 years), respectively. The early measured data points were on and slightly higher than the 90 percent reliability line, while the measured transverse cracking after 8 years is slightly above the 50 percent reliability line at 8 percent.

Figure 165. Graph. Comparison of measured versus predicted longitudinal cracking, Ticuman, Mexico. Longitudinal Cracking is on the Y-axis and Years is on the X-axis. There are three close-to-linear lines representing three prediction lines at different reliability levels, with the line at 90 percent reliability being the highest (going past 30 percent after 8 years), followed by lines at 50 percent (which stayed under 3 percent after 8 years) and 10 percent reliability (which remained horizontal along the X-axis). The early measured data points were slightly higher than the 90 percent reliability line, while the measured longitudinal cracking after 8 years is between the 90 percent and 50 percent reliability line at 15 percent.

Figure 166. Graph. Comparison of measured versus predicted present serviceability index, Ticuman, Mexico. Serviceability is on the Y-axis and Years is on the X-axis. There are three close-to-linear lines decreasing from left to right representing three prediction lines at different reliability levels, with the line at 10 percent reliability being the highest, followed by lines at 50 percent and 90 percent reliability, respectively. The early measured data points were lower than the 90 percent reliability line, while the measured serviceability after 8 years is slightly above the 90 percent reliability line at 2.7 PSI.

Figure 167. Graph. Restraint at the slab/subbase interface. Restraint Stress is on the Y-axis and Displacement is on the X-axis. The graph shows a plot of the measured restraint values, which begins low and then rises, coinciding with the best fitted nonlinear restraint power function with ultimate displacement of 3.8 millimeters, critical restraint stress of 58.6 kilopascals, and power coefficient of 3.5.

Figure 168. Graph. Determination of set time with pulse velocity equipment. PV Time is on the Y-axis and Age is on the X-axis. The relationship is represented by an inverse exponential line with a significant decrease in wave travel between 2.5 and 5.0 hours, which indicates a significant stiffening of the concrete and initial set time occurrence. The estimated set times are indicated in this figure to be within the transition zone between the plastic and hardened state of concrete.

Figure 169. Graph. PCC strains during PCC set time as a function of temperature changes. PCC Strain is on the Y-axis and Temperature is on the X-axis. When the strain gage is initially embedded in the concrete cylinder, relative strain readings do not follow a definitive trend with change in temperature as the concrete is still plastic, it is much lower. As time progresses and the concrete stiffens, the strains tend to follow the temperature changes in the concrete. The transition as observed in the graph occurs between 2.1 and 4.5 hours, corresponding to the set times from laboratory testing.

Figure 170. Graph. Determination of PCC CTE with the use of PCC strains on an unconfined concrete cylinder. PCC Strain is on the Y-axis and Temperature is on the X-axis. The relationship between strain and temperature from the graph (Y equals 6.5703X minus 307.87) results in a CTE of 6.6 times 10 raised to the power of 6 meters per meter per degree Celsius. This is lower than the laboratory testing, which reported a CTE of 7.48 times raised to the power of 6 meters per meter per degree Celsius.

Figure 171. Graph. Steel strains at various distances from the crack location. Steel Measured Strain is on the left Y-axis, PCC Temperature is on the right Y-axis, and Age is on the X-axis. Strains closer to the crack are generally higher than strains away from the crack. Steel strain at the crack seems to increase with time and at lower temperatures. Steel strain 127 millimeters from the crack seems to increase with time but follow the temperature fluctuations. Steel strains 254 millimeters from the crack and further seem to follow the temperature fluctuations but are not affected by time.

Figure 172. Graph. Steel strain along the slab length at different ages. Steel Strain is on the Y-axis and Distance from Crack is on the X-axis. There are three inverse exponential lines representing strain peaks measured at different hours. Strain at 21 hours begins lower but flattens out above the other two. Strain at 44.8 hours begins slightly lower than the strain at 68.5 hours but coincides with it as it flattens out. The distance from the crack to where the strains become horizontal is the bond development length.

Figure 173. Graph. Concrete strains at middepth along slab length. PCC Strains is on the left Y-axis, PCC Temperature is on the right Y-axis, and Age is on the X-axis. The graph shows the strains observed in the concrete at different distances from the crack. The time of crack formation can be identified clearly by the sharp increase in strains (almost vertical) on the gages at 127 millimeters from the crack. All the strains seem to decrease with time in general and follow the temperature fluctuations.

Figure 174. Graph. Drying shrinkage observed in the field on an unrestrained PCC cylinder. Shrinkage Strain is on the Y-axis and Age is on the X-axis. The shrinkage strain seems to decrease with time in general (equaling 0 at 5 hours and ending up equaling negative 50 at 76 hours), although there are fluctuations.

Figure 175. Graph. Strains in concrete and steel at 68.5 hours after construction. Strains are on the Y-axis and Distance from Crack is on the X-axis. The strains in the concrete appear almost constant along the slab at approximately negative 40 microstrains. The strains in the steel also appear within the same order of magnitude along most of the slab, except at the distance farther than 2.2 meters from midslab where they start to increase significantly.

Figure 176. Graph. Displacements in steel and concrete along slab length at 68.5 hours. Displacement is on the Y-axis and Distance from Midslab is on the X-axis. The displacements in steel and concrete are the same, decreasing linearly at a rate of 0.04 millimeters per meter increase in distance from midslab. When the distance from midslab reaches about 2.2 meters, the displacement in steel increases sharply.

Figure 177. Graph. Steel stress along the slab at 68.5 hours. Stress is on the Y-axis and Distance from Crack is on the X-axis. The graph shows predicted steel stress and the stress from measured strains. The predicted steel stress starts out at about 390 megapascals at the crack and decreases close to linearly to about negative 30 megapascals at just above 0.6 meters from the crack, then stays constant. The steel stress from measured strains starts out at about 245 megapascals at the crack and decreases close to linearly to just below 0 megapascals at just above 0.2 meters from the crack, then stays constant.

Figure 178. Graph. Measured versus predicted crack spacing at 3 days of age, Fort Worth, Texas. Cumulative Frequency is on the Y-axis and Crack Spacing is on the X-axis. The measured line increases close to linearly while the predicted line increases in a log form. There is overprediction frequency for crack spacing smaller than 4.5 meters and underprediction for crack spacing larger than 4.5 meters.

Figure 179. Graph. PCC strains during PCC set time as a function of temperature changes. Strains are on the Y-axis and Temperature is on the X-axis. When the strain gage is initially embedded in the concrete cylinder, relative strain readings do not follow a definitive trend with change in temperature, as the concrete is still plastic. As time progresses and the concrete stiffens, the strains tend to follow the temperature changes in the concrete. The transition as observed in the graph occurs between 2.8 hours and 6.5 hours.

Figure 180. Graph. Determination of PCC CTE with the use of PCC strains on an unconfined concrete cylinder. Strains are on the Y-axis and Temperature is on the X-axis. The relationship between strain and temperature from the graph (Y equals 11.61X minus 347.01) results in a CTE of 11.6 times 10 raised to the power of 6 meters per meter per degree Celsius. This is higher than the laboratory testing, which reported a CTE of 10.9 times 10 raised to the power of 6 meters per meter per degree Celsius.

Figure 181. Graph. Steel strains at various distances from the crack location. Steel Measured Strain is on the left Y-axis, Temperature is on the right Y-axis, and Age is on the X-axis. Strains closer to the crack are generally higher than strains away from the crack. Strains closer to the crack also seem to increase slightly with time while the strains away from the crack do not, although there are fluctuations.

Figure 182. Graph. Steel strain along the slab length at different ages. Steel Strain is on the Y-axis and Distance from Crack is on the X-axis. Steel strains decrease with the increase in distance from crack. Steel strains at 20.3 hours are significantly lower than steel strains at 43.2 and 67.2 hours, which are very close to each other. Extrapolating the steel strains to estimate the strain at the crack yields 550 microstrains at 20.3 hours and 1200 to 1500 microstrains for the other two ages.

Figure 183. Graph. Concrete strains at middepth along slab length. PCC Strains are on the left Y-axis, Temperature is on the right Y-axis, and Age is on the X-axis. The graph shows the strains observed in the concrete at different distances from the crack. The time of crack formation can be clearly identified by the sharp increase in strains (almost vertical). All the strains seem to decrease with time in general and follow the temperatures fluctuations.

Figure 184. Graph. Drying shrinkage observed in the field on an unrestrained PCC cylinder. Shrinkage Strain is on the Y-axis and Age is on the X-axis. The shrinkage strain seems to decrease with time in general (equal to 0 at 5 hours and ending up equal to negative 130 at 74 hours), although there are fluctuations.

Figure 185. Graph. Strains in concrete and steel at 67.2 hours after construction. Strains are on the Y-axis and Distance from Midslab is on the X-axis. The strains in the concrete appear almost constant along the slab at approximately negative 40 microstrains. The strains in the steel also appear within the same order of magnitude along most of the slab, except at the distance farther than 1.7 meters from the midslab where they start to increase significantly.

Figure 186. Graph. Comparison of measured and predicted bond development length. Bond Development Length is on the Y-axis and Age is on the X-axis. The bond development length predicted with Hiperpav 2 for this site for the first 3 days of age varies from 0.48 meter to 0.66 meter, which is a good prediction when compared to the measured bond development length, which varies from 0.38 meter to 0.64 meter.

Figure 187. Graph. Steel stress along the slab at 67.2 hours. Stress is on the Y-axis and Distance from Crack is on the X-axis. The graph shows predicted steel stress and the stress from measured strains. The predicted steel stress begins at about 290 megapascals at the crack and decreases close to linearly to right below 0 megapascals at near 0.6 meter from the crack, then stays constant. The steel stress from measured strains begins at about 270 (extrapolated) megapascals at the crack and decreases close to linearly to about negative 20 megapascals at near 0.5 meter from the crack, then stays constant.

Figure 188. Graph. Measured versus predicted crack spacing at 3 days of age, Sioux Falls, South Dakota. Cumulative Frequency is on the Y-axis and Crack Spacing is on the X-axis. The measured line increases close to linearly while the predicted line increases in an S shape. There is underprediction frequency for crack spacing smaller than 4.5 meters and overprediction for crack spacing larger than that.

Figure 189. Graph. Drying shrinkage results for North Carolina site. Strains are on the Y-axis and Time is on the X-axis. The data line and Baźant-Panula strains stay close to each other and decreases with time in general, although there are fluctuations. Both the strains start out at 0 and end up near negative 75 microstrains after 70 hours, with the data strains being positive from 10 to 20 hours.

Figure 190. Graph. Drying shrinkage results for Texas site. Strains are on the Y-axis and Time is on the X-axis. The data line and Baźant-Panula line fluctuates away from each other at times but both slightly decreases with time in general. Both the strains start out at 0 and end up near negative 5 microstrains after 120 hours, with the lowest being negative 30 microstrains at 75 hours, with the data strains being positive from 10 to 20 hours and the Baźant-Panula strains going positive from 90 to 100 hours.

Figure 191. Graph. Drying shrinkage results for Arizona site. Strains are on the Y-axis and Time is on the X-axis. The data line and Baźant-Panula line stay close to each other and decrease with time in general, although there are fluctuations. Both the strains start out at 0 and end up near negative 90 microstrains after 75 hours.

Figure 192. Graph. Drying shrinkage results for Nebraska site. Strains are on the Y-axis and Time is on the X-axis. The data line and Baźant-Panula line fluctuates away from each other at times, but both slightly decrease with time in general. The data strains start out at 0 and end up near negative 25 microstrains after 70 hours, positive from 10 to 20 hours, with the highest being 35 microstrains at 12 hours. The Baźant-Panula strains start out at 0 and end up near negative 12 microstrains after 70 hours, with the lowest being negative 20 microstrains at 52 hours.

Figure 193. Graph. Drying shrinkage results for Minnesota site. Strains are on the Y-axis and Time is on the X-axis. The data line and Baźant-Panula line fluctuates away from each other at times but both slightly decreases with time in general. The data strains start out at 0 and end up at negative 42 microstrains after 120 hours, being positive from 15 to 20 hours and from 35 to 38 hours. The Baźant-Panula strains start out at 0 and end up near negative 30 microstrains after 120 hours, with the lowest being negative 38 microstrains at 80 hours.

Figure 194. Graph. Calibration of drying shrinkage factor for Houston, Texas, sections constructed in summer. Drying Shrinkage is on the Y-axis and Size Factor (effective D) is on the X-axis. Three drying shrinkage curves are plot for 3 days, 28 days, and 1 year of age. The predicted drying shrinkage increases with increase in time and decreases with increase in size factor. At 28 days, the measured drying shrinkage was 171 microstrains, matching up with a size factor of 0.2.

Figure 195. Graph. Calibration of drying shrinkage factor for Houston, Texas, sections constructed in winter. Drying Shrinkage is on the Y-axis and Size Factor (effective D) is on the X-axis. Three drying shrinkage curves are plot for 3 days, 28 days, and 1 year of age. The predicted drying shrinkage increases with increase in time and decreases with increase in size factor. At 28 days, the measured drying shrinkage was 165 microstrains, matching up with a size factor of 0.2.

Figure 196. Graph. Measured concrete and air temperatures for Minnesota, Slab 1. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperatures for concrete (25 millimeters from top, at middepth, and 25 millimeters from bottom) all fluctuate with the air temperature except during the early ages and are generally higher than the air temperature, with the biggest difference of about 15 degrees Celsius occurring from 18 to 24 hours.

Figure 197. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for Minnesota, Slab 1. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures ranging from 12 to 22 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 1 hour.

Figure 198. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for Minnesota, Slab 1. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures ranging from 13 to 22 degrees Celsius, with the biggest difference being about 2 degrees Celsius from 27 to 35 hours.

Figure 199. Graph. Measured versus predicted temperature gradient for Minnesota, Slab 1. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. The predicted temperature gradients are mostly close to the measured temperature gradients ranging from negative 5 degrees Celsius to 5 degrees Celsius, with the biggest difference being about 2 degrees Celsius at 8 hours.

Figure 200. Graph. Measured concrete and air temperatures for Minnesota, Slab 4. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperature in concrete (25 millimeters from top) fluctuates with the air temperature and both increase to about 18 degrees Celsius at 42 hours and stay close to constant from there. The temperatures in concrete (at midslab and 25 millimeters from bottom) increase to about 18 degrees Celsius at 20 hours and stay close to constant from there.

Figure 201. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for Minnesota, Slab 4. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures ranging from 12 to 18 degrees Celsius, with the biggest difference being about 2 degrees Celsius at 40 hours.

Figure 202. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for Minnesota, Slab 4. Temperature is on the Y-axis and Concrete Age is on the X-axis. The predicted temperatures are mostly very close to the measured temperatures ranging from 10 to 18 degrees Celsius, with the biggest difference being about 1 degree Celsius at 48 hours.

Figure 203. Graph. Measured versus predicted temperature gradient for Minnesota, Slab 4. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. The predicted temperature gradients are mostly close to the measured temperature gradients ranging from negative 3 degrees Celsius to 5 degrees Celsius, with the biggest difference being about 2 degrees Celsius at 40 hours.

Figure 204. Graph. Measured concrete and air temperatures for Arizona, Slab 1. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperatures for concrete (25 millimeters from top, at mid-depth, and 25 millimeters from bottom) all fluctuate with the air temperature except at early ages and are generally higher than the air temperature with the biggest difference of about 15 degrees Celsius occurring from 12 to 24 hours.

Figure 205. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for Arizona, Slab 1. Temperature is on the Y-axis and Concrete Age is on the X-axis. The predicted temperatures are mostly very close to the measured temperatures ranging from 6 to 23 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 1 hour.

Figure 206. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for Arizona, Slab 1. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures ranging from 10 to 23 degrees Celsius, with the biggest difference being about 2 degrees Celsius at 25 hours.

Figure 207. Graph. Measured versus predicted temperature gradient for Arizona, Slab 1. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. The predicted temperature gradients are mostly close to the measured temperature gradients ranging from negative 7 degrees Celsius to 3 degrees Celsius, with the biggest difference being about 2.5 degrees Celsius at 46 hours.

Figure 208. Graph. Measured concrete and air temperatures for Arizona, Slab 3. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperatures for concrete (25 millimeters from top, at mid-depth, and 25 millimeters from bottom) all fluctuate with the air temperature except at early ages and are generally higher than the air temperature by about 10 degrees Celsius on average.

Figure 209. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for Arizona, Slab 3. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures ranging from 10 to 22 degrees Celsius, with the biggest difference being about 2 degrees Celsius at 9 hours.

Figure 210. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for Arizona, Slab 3. Temperature is on the Y-axis and Concrete Age is on the X-axis. The predicted temperatures are mostly very close to the measured temperatures ranging from 12 to 20 degrees Celsius, with the biggest difference being about 1 degree Celsius at 24 hours.

Figure 211. Graph. Measured versus predicted temperature gradient for Arizona, Slab 3. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. The predicted temperature gradients are mostly close to the measured temperature gradients ranging from negative 5 degrees Celsius to 5 degrees Celsius, with the biggest difference being about 2 degrees Celsius at 10 hours.

Figure 212. Graph. Measured concrete and air temperatures for Arizona, Slab 6. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperatures for concrete (25 millimeters from top, at middepth, and 25 millimeters from bottom) all fluctuate with the air temperature except at early ages and are generally higher than the air temperature, with the biggest difference of about 15 degrees Celsius.

Figure 213. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for Arizona, Slab 6. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 13 to 23 degrees Celsius, with the biggest difference being about 2 degrees Celsius at 50 hours.

Figure 214. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for Arizona, Slab 6. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are very close to the measured temperatures, ranging from 15 to 22 degrees Celsius, with the biggest difference being about 1 degree Celsius at various ages.

Figure 215. Graph. Measured versus predicted temperature gradient for Arizona, Slab 6. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperature gradients are close to the measured temperature gradients, ranging from negative 4 degrees Celsius to 4 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 26 hours.

Figure 216. Graph. Measured concrete and air temperatures for Lufkin, Texas, Slab 2. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperatures for concrete (25 millimeters from top and 25 millimeters from bottom) fluctuate with the air temperature, except between 12 and 24 hours, and are generally higher than the air temperature, with the biggest difference of about 15 degrees Celsius.

Figure 217. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for Lufkin, Texas, Slab 2. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 20 to 33 degrees Celsius, with the biggest difference being about 2 degrees Celsius at various ages.

Figure 218. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for Lufkin, Texas, Slab 2. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 20 to 35 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 15 hours.

Figure 219. Graph. Measured versus predicted temperature gradient for Lufkin, Texas, Slab 2. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperature gradients are close to the measured temperature gradients, ranging from negative 8 degrees Celsius to 8 degrees Celsius, with the biggest difference being about 3 degrees Celsius at various ages.

Figure 220. Graph. Measured concrete and air temperatures for Lufkin, Texas, Slab 3. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperatures for concrete (25 millimeters from top and 25 millimeters from bottom) fluctuate with the air temperature and are generally higher than the air temperature, with the biggest difference of about 20 degrees Celsius.

Figure 221. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for Lufkin, Texas, Slab 3. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 22 to 47 degrees Celsius, with the biggest difference being about 5 degrees Celsius at 24 hours.

Figure 222. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for Lufkin, Texas, Slab 3. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 20 to 48 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 15 hours.

Figure 223. Graph. Measured versus predicted temperature gradient for Lufkin, Texas, Slab 3. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. The predicted temperature gradients are not that close to the measured temperature gradients, ranging from negative 10 degrees Celsius to 13 degrees Celsius, while the measured temperature ranges from negative 5 to 11 degrees Celsius, with the biggest difference being about 6 degrees Celsius at 18 hours.

Figure 224. Graph. Measured concrete and air temperatures for North Carolina, Slab 2. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperatures for concrete (25 millimeters from top and 25 millimeters from bottom) fluctuate with the air temperature, except at early ages, and are generally higher than the air temperature, with the biggest difference of about 25 degrees Celsius.

Figure 225. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for North Carolina, Slab 2. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 20 to 45 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 12 hours.

Figure 226. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for North Carolina, Slab 2. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 25 to 40 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 12 hours.

Figure 227. Graph. Measured versus predicted temperature gradient for North Carolina, Slab 2. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperature gradients are close to the measured temperature gradients, ranging from negative 10 degrees Celsius to 8 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 25 hours.

Figure 228. Graph. Measured concrete and air temperatures for North Carolina, Slab 3. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperatures for concrete (25 millimeters from top and 25 millimeters from bottom) fluctuate with the air temperature and are generally higher than the air temperature, with the biggest difference of about 15 degrees Celsius.

Figure 229. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for North Carolina, Slab 3. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 20 to 45 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 4 hours.

Figure 230. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for North Carolina, Slab 3. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 25 to 40 degrees Celsius, with the biggest difference being about 3 degrees Celsius at various ages.

Figure 231. Graph. Measured versus predicted temperature gradient for North Carolina, Slab 3. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperature gradients are close to the measured temperature gradients, ranging from negative 10 degrees Celsius to 10 degrees Celsius, with the biggest difference being about 3 degrees Celsius at various ages.

Figure 232. Graph. Measured concrete and air temperatures for Minnesota, Slab 2. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperatures for concrete (25 millimeters from top, at middepth, and 25 millimeters from bottom) all fluctuate with the air temperature, except at early ages, and are generally higher than the air temperature, with the biggest difference of about 20 degrees Celsius.

Figure 233. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for Minnesota, Slab 2. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 12 to 22 degrees Celsius, with the biggest difference being about 2 degrees Celsius at 15 hours.

Figure 234. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for Minnesota, Slab 2. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 14 to 22 degrees Celsius, with the biggest difference being about 2 degrees Celsius at 24 hours.

Figure 235. Graph. Measured versus predicted temperature gradient for Minnesota, Slab 2. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperature gradients are close to the measured temperature gradients, ranging from negative 5 degrees Celsius to 5 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 28 hours.

Figure 236. Graph. Measured concrete and air temperatures for Minnesota, Slab 3. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperature in concrete (25 millimeters from top) fluctuates with the air temperature, and both increase to about 15 degrees Celsius at 42 hours and stay near constant from there. The temperatures in concrete (at midslab and 25 millimeters from bottom) increase to about 15 degrees Celsius at 20 hours and stay near constant from there.

Figure 237. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for Minnesota, Slab 3. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 10 to 18 degrees Celsius, with the biggest difference being about 2 degrees Celsius at 42 hours.

Figure 238. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for Minnesota, Slab 3. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are very close to the measured temperatures, ranging from 9 to 18 degrees Celsius, with the biggest difference being about 1 degree Celsius at 48 hours.

Figure 239. Graph. Measured versus predicted temperature gradient for Minnesota, Slab 3. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperature gradients are close to the measured temperature gradients, ranging from negative 3 degrees Celsius to 5 degrees Celsius, with the biggest difference being about 2 degrees Celsius at 6 hours.

Figure 240. Graph. Measured concrete and air temperatures for Arizona, Slab 4. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperatures for concrete (25 millimeters from top, at middepth, and 25 millimeters from bottom) all fluctuate with the air temperature, except at early ages, and are generally higher than the air temperature, with the biggest difference of about 20 degrees Celsius.

Figure 241. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for Arizona, Slab 4. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 10 to 22 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 27 hours.

Figure 242. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for Arizona, Slab 4. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are very close to the measured temperatures, ranging from 12 to 20 degrees Celsius, with the biggest difference being about 1 degree Celsius at various ages.

Figure 243. Graph. Measured versus predicted temperature gradient for Arizona, Slab 4. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperature gradients are close to the measured temperature gradients, ranging from negative 5 degrees Celsius to 3 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 48 hours.

Figure 244. Graph. Measured concrete and air temperatures for Arizona, Slab 5. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperatures for concrete (25 millimeters from top, at middepth, and 25 millimeters from bottom) all fluctuate with the air temperature, except at early ages, and are generally higher than the air temperature, with the biggest difference of about 17 degrees Celsius.

Figure 245. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for Arizona, Slab 5. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are very close to the measured temperatures, ranging from 12 to 20 degrees Celsius, with the biggest difference being about 1 degree Celsius at various ages.

Figure 246. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for Arizona, Slab 5. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are very close to the measured temperatures, ranging from 12 to 20 degrees Celsius, with the biggest difference being about 1 degree Celsius at various ages.

Figure 247. Graph. Measured versus predicted temperature gradient for Arizona, Slab 5. Temperature Gradient is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperature gradients are close to the measured temperature gradients, ranging from negative 4 degrees Celsius to 4 degrees Celsius, with the biggest difference being about 2 degrees Celsius at 24 hours.

Figure 248. Graph. Measured concrete and air temperatures for Lufkin, Texas, Slab 1. Temperature is on the Y-axis and Concrete Age is on the X-axis. The temperatures for concrete (25 millimeters from top and 25 millimeters from bottom) fluctuate with the air temperature and are generally higher than the air temperature, with the biggest difference of about 20 degrees Celsius.

Figure 249. Graph. Measured versus predicted temperatures 25 millimeters from top of slab for Lufkin, Texas, Slab 1. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 18 to 35 degrees Celsius, with the biggest difference being about 2 degrees Celsius at various ages.

Figure 250. Graph. Measured versus predicted temperatures 25 millimeters from bottom of slab for Lufkin, Texas, Slab 1. Temperature is on the Y-axis and Concrete Age is on the X-axis. Most of the predicted temperatures are close to the measured temperatures, ranging from 18 to 37 degrees Celsius, with the biggest difference being about 3 degrees Celsius at 15 hours.

Figure 251. Graph. Measured versus predicted temperature gradient for Lufkin, Texas, Slab 1. Tem