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Publication Number: FHWA-HRT-05-150
Date: February 2006

Review of The Long-Term Pavement Performance (LTPP) Backcalculation Results

Section 508 Compliant Captions

Figure 1. Equation. Composite subgrade modulus at an offset.
E subscript 0, R equals the multiplication of: 0.84, A squared, and sigma subscript 0. This product is divided by the product of D subscript R and R, where E subscript 0, R equals surface or composite modulus of the subgrade beneath the sensor, A equals the radius of the FWD loading plate, sigma subscript 0 equals the peak pressure of FWD impact load under loading plate, D subscript R equals the peak FWD deflection reading at offset distance R, and R equals distance of deflection reading D subscript R from center of loading plate.
Figure 2. Equation. Hogg subgrade modulus.
E subscript 0 equals the product of the following: I times the sum of 1 plus mu subscript 0, this sum times the sum of 3 minus 4 times mu subscript 0, the result of this expression is divided by 2 times the sum of 1 minus mu subscript 0. This product times S subscript 0 divided by S, times P divided by the product of delta subscript 0 times l, where E subscript 0 equals the subgrade modulus, mu subscript 0 equals Poisson’s ratio for subgrade, S subscript 0 is the theoretical point load stiffness, S is the pavement stiffness, P equals the applied load and delta subscript 0 equals the deflection at center of load plate.
Figure 3. Equation. Offset distance where deflection is half of center deflection.
The equation is R subscript 50 equals R times the following expression: 1 over alpha raised to one over beta, this result minus B. The result of this expression is divided by the following expression: 1 over alpha times the sum of delta subscript 0 divided by delta subscript R minus 1. This product is raised by 1 over beta and the result is subtracted by B, where delta subscript R equals deflection at center of load plate, R subscript 50 equals the offset distance where delta subscript R divided by delta subscript 0 equals 0.5, and alpha and beta are curve fitting coefficients.
Figure 4. Equation. Characteristic length of deflection basin.
The equation L equals Y subscript 0 times R subscript 50 over 2 plus the following expression: the square of Y subscript 0 times R subscript 50 minus 4 times mar subscript 50 and the result raised to 1 over 2. If A over l is less than 0.2, then L equals the sum of Y subscript 0 minus 0.2 times M, this sum times R subscript 50, where L equals characteristic length, Y subscript 0 and M equal characteristic length coefficients.
Figure 5. Equation. Theoretical point load stiffness/pavement stiffness ratio.
S subscript 0 over S equals 1 minus M bar times A over L minus 0.2. If A over L is less than 0.2 then S subscript 0 over S equals 1, where M bar equals stiffness ratio coefficient.
Figure 6. Equation. Composite modulus under FWD load plate.
E subscript 0 equals 1.5 times A times sigma subscript 0 divided by D subscript 0,.where E subscript 0 equals the composite modulus of the entire pavement system under the load plate, A equals the radius of the FWD load plate, sigma subscript 0 equals the peak pressure of FWD impact load under the load plate and D subscript 0 equals the peak center FWD deflection reading.
Figure 7. Equation. 36-inch AREA equation for rigid pavements.
A subscript 36 equals 6 times the sum of 1 plus 2 times D subscript 12 over D subscript 0 plus 2 times D subscript 24 over D subscript 0 plus D subscript 36 over D subscript 0 where A subscript 36 equals area under the first 36 inches (914 millimeters) of the deflection basin, and D subscript 12, D subscript 24, D subscript 36 are deflection measured one, two and three feet, respectively, from the center of the plate.
Figure 8. Equation. 12-inch AREA equation for flexible pavements.
A subscript 12 equals to 2 times the sum of 2 plus 3 times D subscript 8 over D subscript 0 plus D subscript 12 over D subscript 0, where A subscript 12 equals area under the first 12 inches (305 millimeters) of the deflection basin, and D subscript 8, D subscript 12 are deflection measured eight and twelve inches from the center of the plate.
Figure 9. Equation. Area factor for rigid pavements.
AF subscript PCC equals the following expression: K subscript 2 minus 1 divided by the sum of K subscript 2 minus AREA subscript 36 over K subscript 1. The result of this expression is raised to 1.79, where AF subscript PCC equals the improvement in AREA from 11.04 to 1.79 power, K subscript 1 equals11.04or the AREA when the stiffness of the concrete layer is the same as the lower layers and K subscript 2 equals 3.262, the maximum possible improvement in AREA.
Figure 10. Equation. Area factor for flexible pavements.
AF subscript AC equals the following expression: K subscript 2 minus 1 divided by the sum of K subscript 2 minus AREA subscript 12 over K subscript 1. The result of this expression is raised to 1.35, where AF subscript AC equals AREA factor or improvement in AREA to the 1.35 power, K subscript 1 equals 6.85 or the AREA when the stiffness of the asphalt layer is the same as the lower layers and K subscript 2 equals 1.752, the maximum possible improvement in AREA.
Figure 11. Equation. Stiffness or modulus of the upper PCC layer.
E subscript PCC equals E subscript 0 times AF subscript PCC times K subscript 3 raised to 1 over AF subscript PCC. This product is divided by K subscript 3 raised to 2.38, where E subscript PCC equals stiffness or modulus of the upper PCC bound layers and K subscript 3 equals thickness ratio of upper layer thickness/load plate diameter.
Figure 12. Equation. Stiffness or modulus of the upper AC layer.
E subscript AC equals E subscript 0 times AF subscript AC times K subscript 3 raised to 1 over AF subscript AC. This product is divided by K subscript 3 raised to 2, where E subscript AC equals stiffness or modulus of the upper AC bound layers.
Figure 13. Equation. Modulus of the unbound base layer using the Dorman and Metcalf relationship.
E subscript Base equals 0.2 times H subscript 2 raised to 0.45 times E subscript Sub where E subscript Base equals Dorman and Metcalf base modulus in megapascals, H subscript 2 equals thickness of the intermediate base layer in millimeters and E subscript Sub equals the subgrade modulus in megapascals.
Figure 14. Graph. Back- versus forwardcalculated subgrade moduli for 15 trial LTPP flexible sections.
The graph depicts the power relationship between the subgrade backcalculated modulus versus the forwardcalculated modulus ranging from 10 to 10,000 megapascals on both axes for 15 AC test sections. This relationship shows that the backcalculated modulus equals 1.4493 times the forwardcalculated modulus raised to 1.0355, with an R-square, the coefficient of determination, of 0.3905.
Figure 15. Graph. Back- versus forwardcalculated subgrade moduli for three trial LTPP rigid sections.
The graph depicts the linear relationship between the subgrade backcalculated modulus versus the forwardcalculated modulus ranging from 100 to 400 megapascals on the vertical axis and 100 to 300 megapascals on the horizontal axis for 3 PCC test sections. This relationship shows that the backcalculated modulus equals 1.7436 times the forwardcalculated modulus minus 82.095, with an R-square of 0.8401.
Figure 16. Graph. Back- versus forwardcalculated asphalt layer moduli for 15 trial LTPP flexible sections.
The graph depicts the power relationship between the asphalt layer backcalculated modulus versus the forwardcalculated modulus ranging from 1,000 to 100,000 megapascals on both axes for 15 AC test sections. This relationship shows that the backcalculated modulus equals 1.2382 times the forwardcalculated modulus raised to 0.9617, with an R-square of 0.6694.
Figure 17. Graph. Back- versus forwardcalculated concrete layer moduli for three trial LTPP rigid sections.
The graph depicts the power relationship between the PCC backcalculated modulus using dense liquid and elastic solid methods versus the forwardcalculated modulus ranging from 10,000 to 100,000 megapascals on the vertical axis and 10,000 to 1 million megapascals on the horizontal axis for 3 PCC test sections. These relationships show that the dense liquid backcalculated modulus equals 1304.8 times the forwardcalculated modulus raised to 0.346, with R-square of 0.6139; and the elastic solid backcalculated modulus equals 390.26 times the forwardcalculated modulus raised to 0.4313, with an R-square of 0.6955.
Figure 18. Graph. Back- versus forward-based base layer moduli for 15 flexible LTPP sections.
This graph depicts the power relationship between the backcalculated versus pseudo-backcalculated modulus of the intermediate layer ranging from 1 to 100,000 megapascals on both axes for 15 AC test sections. This relationship shows that the backcalculated modulus equals 2.0137 times the forwardcalculated modulus raised to 0.7852, with an R-square of 0.1503.
Figure 19. Graph. Back- versus forwardcalculated asphalt layer moduli for one trial LTPP flexible section with two upper (bound) layers.
This graph depicts the power relationship between the second backcalculated versus the forwardcalculated modulus of the surface layer ranging from 1,000 to 100,000 megapascals on both axes for 15 AC test sections. This relationship shows that the backcalculated modulus equals 60 million times the forwardcalculated modulus raised to -1.0511, with an R-square of 0.0932.
Figure 20. Graph. Back- versus forwardcalculated subgrade moduli for five trial LTPP flexible sections with two subgrade (lower unbound) layers.
This graph depicts the power relationship between the second backcalculated versus the forwardcalculated modulus of subgrade ranging from 10 to 100,000 megapascals on both axes for 5 trial AC test sections. This relationship shows that the backcalculated modulus equals 203.83 times the forwardcalculated modulus raised to 0.173, with an R-square of 0.0054.
Figure 21. Graph. Back- versus forwardcalculated base course moduli for four trial LTPP flexible sections with two intermediate layers.
This graph depicts the power relationship between the second backcalculated versus the forwardcalculated modulus of the intermediate layer ranging from 10 to 100,000 megapascals on both axes for 4 trial AC test sections. This relationship shows that the backcalculated modulus equals 2 times 10 raised to 15 times the forwardcalculated modulus raised to -5.1193, with an R-square of 0.294.
Figure 22. Equation. Interquartile range.
IQR equals Q subscript 3 minus Q subscript 1 where Q subscript 3 equals the twenty-fifth quartile and Q subscript 1 equals the seventy-fifth quartile of the logs of the moduli.
Figure 23. Charts. Screening results of the elastic moduli of the subgrade for all flexible sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model (the level E records only).
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 428,026 records (97 percent) and the backcalculated assumed values are 13,938 (3 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 367,897 records (86 percent) with both values reasonable, 259 (0 percent) with only backcalculated values reasonable, 59,870 (14 percent) with only forwardcalculated values reasonable, and 417 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 145,518 records (39 percent) acceptable, 91,965 (25 percent) marginal, 88,007 (24 percent) questionable, and 42,407 (12 percent) unacceptable.
Figure 24. Charts. Screening results of elastic moduli of the subgrade for all the flexible sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model (contains both level E and nonlevel E records).
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 557,528 records (96 percent) and the backcalculated assumed values are 22,494 (4 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 459,107 records (83 percent) with both values reasonable, 946 (0 percent) with only backcalculated values reasonable, 96,242 (17 percent) with only forwardcalculated values reasonable, and 1,233 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 175,162 records (38 percent) acceptable, 115,197 (25 percent) marginal, 110,941 (24 percent) questionable, and 57,807 (12 percent) unacceptable.
Figure 25. Charts. Screening results of elastic moduli of the asphalt concrete layer for the flexible sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model.
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 205,458 records (99 percent) and the backcalculated assumed values are 1,352 (1 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 179,440 records (88 percent) with both values reasonable, 8,558 (4 percent) with only backcalculated values reasonable, 12,981 (6 percent) with only forwardcalculated values reasonable, and 4,479 (2 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 127,164 records (71 percent) acceptable, 25,543 (14 percent) marginal, 14,930 (8 percent) questionable, and 11,803 (7 percent) unacceptable.
Figure 26. Charts. Screening results of elastic moduli of the subgrade for the flexible sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model.
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 557,528 records (96 percent) and the backcalculated assumed values are 22,494 (4 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 459,107 records (83 percent) with both values reasonable, 946 (0 percent) with only backcalculated values reasonable, 96,242 (17 percent) with only forwardcalculated values reasonable, and 1,233 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 175,162 records (38 percent) acceptable, 115,197 (25 percent) marginal, 110,941 (24 percent) questionable, and 57,807 (13 percent) unacceptable.
Figure 27. Charts. Screening results of elastic moduli of the base layer for the flexible sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model.
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 181,056 records (97 percent) and the backcalculated assumed values are 6,255 (3 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 119,747 records (66 percent) with both values reasonable, 6,011 (3 percent) with only backcalculated values reasonable, 47,109 (26 percent) with only forwardcalculated values reasonable, and 8,189 (5 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 38,373 records (32 percent) acceptable, 29,659 (25 percent) marginal, 29,678 (25 percent) questionable, and 22,037 (18 percent) unacceptable.
Figure 28. Charts. Screening results of elastic moduli of the asphalt concrete layer for the flexible sections in the MON_DEFL_FLX_ NMODEL_POINT table based on the nonlinear elastic model.
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 37,551 records (100 percent) and the backcalculated assumed values are 86 (0 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 32,256 records (86 percent) with both values reasonable, 1,252 (3 percent) with only backcalculated values reasonable, 3,254 (9 percent) with only forwardcalculated values reasonable, and 789 (2 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 18,429 records (57 percent) acceptable, 5,955 (18 percent) marginal, 4,085 (13 percent) questionable, and 3,787 (12 percent) unacceptable.
Figure 29. Charts. Screening results of elastic moduli of the base layer for the flexible sections in the MON_DEFL_FLX_ NMODEL_POINT table based on the nonlinear elastic model
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 19,639 records (99 percent) and the backcalculated assumed values are 232 (1 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 13,265 records (67 percent) with both values reasonable, 526 (3 percent) with only backcalculated values reasonable, 5,540 (28 percent) with only forwardcalculated values reasonable, and 308 (2 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 4,970 records (37 percent) acceptable, 3,128 (24 percent) marginal, 3,025 (23 percent) questionable, and 2,142 (16 percent) unacceptable.
Figure 30. Charts. Screening results of elastic moduli of the subgrade for the flexible sections in the MON_DEFL_FLX_ NMODEL_POINT table based on the nonlinear elastic model.
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 70,742 records (97 percent) and the backcalculated assumed values are 2,427 (3 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 61,399 records (87 percent) with both values reasonable, 7 (0 percent) with only backcalculated values reasonable, 9,293 (13 percent) with only forwardcalculated values reasonable, and 43 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 23,329 records (38 percent) acceptable, 15,543 (25 percent) marginal, 14,097 (23 percent) questionable, and 8,430 (14 percent) unacceptable.
Figure 31. Equation. PCC slab modulus—100 percent unbonded case.
E subscript 1 equals H subscript 1 cubed divided by the sum of H subscript 1 cubed plus beta times H subscript 2 cubed. This quotient times E subscript PCC, APP, where E subscript PCC, APP equals the apparent modulus of the PCC layer with no base course effect, E subscript 1 equals modulus of the upper plate (PCC layer), H subscript 1 equals thickness of the upper plate (PCC slab), H subscript 2 equals thickness of the lower plate (base layer), and beta equals the modular ratio.
Figure 32. Equation. PCC slab modulus—100 percent bonded case.
E subscript 1 equals the division of H subscript 1 cubed by the following expression: the sum of H subscript 1 cubed plus beta times H subscript 2 cubed plus 12 times the square of X minus H subscript 1 divided by 2, end of square, plus 12 times beta times H subscript 2 times the square of H subscript 1 minus X plus H subscript 2 divided by 2, end of square, end of expression. This quotient times E subscript lowercase E.
Figure 33. Equation. Layer thickness relationship—both cases.
The equation X equals the division of the following expression: H subscript 1 squared over 2 plus beta times H subscript 2 times the sum of H subscript 1 plus H subscript 2 over 2, end of expression, divided by the sum of H subscript 1 plus beta times H subscript 2.
Figure 34. Equation. Modular ratio b—both cases.
The equation beta equals E subscript 2 divided by E subscript 1, where E subscript 2 equals modulus of the lower plate (base layer).
Figure 35. Charts. Screening results of elastic moduli of the interior concrete slab for the rigid sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model for backcalculation and a bonded condition between the slab and base for forwardcalculation.
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 11,555 records (100 percent) and the backcalculated assumed values are 45 (0 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 9,955 records (86 percent) with both values reasonable, 442 (4 percent) with only backcalculated values reasonable, 848 (7 percent) with only forwardcalculated values reasonable, and 310 (3 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 6,155 records (61 percent) acceptable, 2,044 (21 percent) marginal, 1,379 (14 percent) questionable, and 377 (4 percent) unacceptable.
Figure 36. Charts. Screening results of elastic moduli of the interior concrete slab for the rigid sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model for backcalculation and an unbonded condition between the slab and base for forwardcalculation.
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 11,555 records (100 percent) and the backcalculated assumed values are 45 (0 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 10,072 records (87 percent) with both values reasonable, 325 (3 percent) with only backcalculated values reasonable, 617 (5 percent) with only forwardcalculated values reasonable, and 541 (5 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 8,339 records (83 percent) acceptable, 1,536 (15 percent) marginal, 176 (2 percent) questionable, and 21 (0 percent) unacceptable.
Figure 37. Charts. Screening results of elastic moduli of the base layer for the rigid sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model for backcalculation and a bonded condition between the concrete slab and base layer for forwardcalculation.
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 6,762 records (46 percent) and the backcalculated assumed values are 7,933 (54 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 2,171 records (32 percent) with both values reasonable, 861 (13 percent) with only backcalculated values reasonable, 2,547 (38 percent) with only forwardcalculated values reasonable, and 1,183 (17 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 747 records (35 percent) acceptable, 398 (18 percent) marginal, 461 (21 percent) questionable, and 565 (26 percent) unacceptable.
Figure 38. Charts. Screening results of elastic moduli of the base layer for the rigid sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model for backcalculation and an unbonded condition between the concrete slab and base layer for forwardcalculation.
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 6,762 records (46 percent) and the backcalculated assumed values are 7,933 (54 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 2,133 records (32 percent) with both values reasonable, 899 (13 percent) with only backcalculated values reasonable, 2,587 (38 percent) with only forwardcalculated values reasonable, and 1,143 (17 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 661 records (31 percent) acceptable, 392 (18 percent) marginal, 525 (25 percent) questionable, and 555 (26 percent) unacceptable.
Figure 39. Charts. Screening results of elastic moduli of the subgrade for the rigid sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model.
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 10,220 records (88 percent) and the backcalculated assumed values are 1,380 (12 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 8,970 records (88 percent) with both values reasonable, 0 (0 percent) with only backcalculated values reasonable, 1,249 (12 percent) with only forwardcalculated values reasonable, and 1 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 4,440 records (50 percent) acceptable, 1,184 (13 percent) marginal, 1,172 (13 percent) questionable, and 2,174 (24 percent) unacceptable.
Figure 40. Charts. Screening results of elastic moduli of the PCC slab for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the elastic solid model for backcalculation and assuming bonded condition between the slab and the base for back- and forwardcalculation.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 33,777 records (98 percent) with both values reasonable, 855 (2 percent) with only backcalculated values reasonable, 14 (0 percent) with only forwardcalculated values reasonable, and 106 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 32,761 records (97 percent) acceptable, 936 (3 percent) marginal, 80 (0 percent) questionable, and 0 (0 percent) unacceptable.
Figure 41. Charts. Screening results of elastic moduli of the PCC slab for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the elastic solid model for backcalculation and assuming unbonded condition between the slab and the base for back- and forwardcalculation.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 32,511 records (96 percent) with both values reasonable, 975 (3 percent) with only backcalculated values reasonable, 137 (0 percent) with only forwardcalculated values reasonable, and 433 (1 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 32,278 records (99 percent) acceptable, 210 (1 percent) marginal, 23 (0 percent) questionable, and 0 (0 percent) unacceptable.
Figure 42. Charts. Screening results of elastic moduli of the base layer for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the elastic solid model for backcalculation and assuming bonded condition between the slab and the base for back- and forwardcalculation.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 30,955 records (92 percent) with both values reasonable, 129 (0 percent) with only backcalculated values reasonable, 1,991 (6 percent) with only forwardcalculated values reasonable, and 777 (2 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 29,544 records (96 percent) acceptable, 737 (2 percent) marginal, 100 (0 percent) questionable, and 574 (2 percent) unacceptable.
Figure 43. Charts. Screening results of elastic moduli of the base layer for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the elastic solid model for backcalculation and assuming unbonded condition between the slab and the base for back- and forwardcalculation.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 31,199 records (94 percent) with both values reasonable, 202 (1 percent) with only backcalculated values reasonable, 1,019 (3 percent) with only forwardcalculated values reasonable, and 736 (2 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 29,677 records (95 percent) acceptable, 356 (1 percent) marginal, 332 (1 percent) questionable, and 834 (3 percent) unacceptable.
Figure 44. Charts. Screening results of elastic moduli of the subgrade for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the elastic solid model for backcalculation.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 35,878 records (100 percent) with both values reasonable, 0 (0 percent) with only backcalculated values reasonable, 6 (0 percent) with only forwardcalculated values reasonable, and 0 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 35,529 records (99 percent) acceptable, 346 (1 percent) marginal, 3 (1 percent) questionable, and 0 (0 percent) unacceptable.
Figure 45. Charts. Screening results of elastic moduli of the PCC slab for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the dense liquid model for backcalculation and assuming bonded condition between the slab and the base for back- and forwardcalculation.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 34,727 records (96 percent) with both values reasonable, 573 (2 percent) with only backcalculated values reasonable, 389 (1 percent) with only forwardcalculated values reasonable, and 188 (1 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 32,094 records (92 percent) acceptable, 2,632 (8 percent) marginal, 1 (0 percent) questionable, and 0 (0 percent) unacceptable.
Figure 46. Charts. Screening results of elastic moduli of the PCC slab for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the dense liquid model for backcalculation and assuming unbonded condition between the slab and the base for back- and forwardcalculation.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 31,256 records (96 percent) with both values reasonable, 168 (1 percent) with only backcalculated values reasonable, 965 (3 percent) with only forwardcalculated values reasonable, and 101 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 27,790 records (89 percent) acceptable, 3,465 (11 percent) marginal, 1 (0 percent) questionable, and 0 (0 percent) unacceptable.
Figure 47. Charts. Screening results of elastic moduli of the base layer for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the dense liquid model for backcalculation and assuming bonded condition between the slab and the base for back- and forwardcalculation.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 32,712 records (94 percent) with both values reasonable, 767 (2 percent) with only backcalculated values reasonable, 1,135 (3 percent) with only forwardcalculated values reasonable, and 348 (1 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 29,221 records (90 percent) acceptable, 2,358 (7 percent) marginal, 464 (1 percent) questionable, and 669 (2 percent) unacceptable.
Figure 48. Charts. Screening results of elastic moduli of the base layer for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the dense liquid model for backcalculation and assuming unbonded condition between the slab and the base for back- and forwardcalculation.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 29,813 records (94 percent) with both values reasonable, 719 (2 percent) with only backcalculated values reasonable, 817 (3 percent) with only forwardcalculated values reasonable, and 227 (1 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 25,245 records (85 percent) acceptable, 3,244 (11 percent) marginal, 1,041 (3 percent) questionable, and 283 (1 percent) unacceptable.
Figure 49. Equation. Subgrade K-value.
The equation is K-value equals 0.296 times E subscript subgrade. The R-square equals 0.87, where K-value equals subgrade modulus of reaction in kilopascals per millimeter and E subscript subgrade equals subgrade modulus of elasticity in megapascals.
Figure 50. Charts. Screening results of the subgrade k-values for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the dense liquid model for backcalculation.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 35,876 records (97 percent) with both values reasonable, 0 (0 percent) with only backcalculated values reasonable, 1,111 (3 percent) with only forwardcalculated values reasonable, and 0 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 32,830 records (92 percent) acceptable, 3,010 (8 percent) marginal, 36 (0 percent) questionable, and 0 (0 percent) unacceptable.
Figure 51. Charts. Screening results of elastic moduli of the point base layer for the flexible sections in the MON_DEFL_FLX_BAKCALC_POINT table based on the linear elastic model.
This graphic consists of three pie charts. The left one represents all the data, where the backcalculated values not assumed are 181,056 records (97 percent) and the backcalculated assumed values are 6,255 (3 percent). The middle pie chart represents a breakdown of backcalculated values not assumed from the left pie chart showing 119,747 records (66 percent) with both values reasonable, 6,011 (3 percent) with only backcalculated values reasonable, 47,109 (26 percent) with only forwardcalculated values reasonable, and 8,189 (5 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable from the middle pie chart showing 38,373 records (32 percent) acceptable, 29,659 (25 percent) marginal, 29,678 (25 percent) questionable, and 22,037 (18 percent) unacceptable.
Figure 52. Charts. Screening results of elastic moduli of the section base layer for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT table based on the linear elastic model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 2,505 records (74 percent) with both values reasonable, 171 (5 percent) with only backcalculated values reasonable, 616 (18 percent) with only forwardcalculated values reasonable, and 118 (3 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 840 records (34 percent) acceptable, 601 (24 percent) marginal, 636 (25 percent) questionable, and 428 (17 percent) unacceptable.
Figure 53. Charts. Screening results of the subgrade point K-value table for the rigid sections in the MON_DEFL_RGD_BAKCALC_POINT table using the dense liquid model for backcalculation.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 35,876 records (97 percent) with both values reasonable, 101 (0 percent) with only backcalculated values reasonable, 1,111 (3 percent) with only forwardcalculated values reasonable, and 0 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 32,830 records (92 percent) acceptable, 3,010 (8 percent) marginal, 36 (0 percent) questionable, and 0 (0 percent) unacceptable.
Figure 54. Charts. Screening results of the subgrade section K-value table for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT table using the dense liquid model for backcalculation.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 1,110 records (98 percent) with both values reasonable, 0 (0 percent) with only backcalculated values reasonable, 18 (2 percent) with only forwardcalculated values reasonable, and 0 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 1,061 records (96 percent) acceptable, 48 (4 percent) marginal, 1 (0 percent) questionable, and 0 (0 percent) unacceptable.
Figure 55. Charts. Screening results of section average elastic moduli of the asphalt concrete layer for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT table based on the linear elastic model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 4,925 records (86 percent) with both values reasonable, 220 (4 percent) with only backcalculated values reasonable, 400 (7 percent) with only forwardcalculated values reasonable, and 155 (3 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 3,564 records (72 percent) acceptable, 644 (13 percent) marginal, 376 (8 percent) questionable, and 341 (7 percent) unacceptable.
Figure 56. Charts. Screening results of section average elastic moduli of the base layer for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT table based on the linear elastic model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 2,505 records (74 percent) with both values reasonable, 171 (5 percent) with only backcalculated values reasonable, 616 (18 percent) with only forwardcalculated values reasonable, and 118 (3 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 840 records (34 percent) acceptable, 601 (24 percent) marginal, 636 (25 percent) questionable, and 428 (17 percent) unacceptable.
Figure 57. Charts. Screening results of section average elastic moduli of the subgrade for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT table based on the linear elastic model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 9,913 records (82 percent) with both values reasonable, 8 (0 percent) with only backcalculated values reasonable, 2,253 (18 percent) with only forwardcalculated values reasonable, and 12 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 3,651 records (37 percent) acceptable, 2,693 (27 percent) marginal, 2,420 (24 percent) questionable, and 1,149 (12 percent) unacceptable.
Figure 58. Charts. Screening results of section average elastic moduli of the asphalt concrete layer for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT table based on the nonlinear elastic model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 690 records (87 percent) with both values reasonable, 40 (5 percent) with only backcalculated values reasonable, 59 (7 percent) with only forwardcalculated values reasonable, and 11 (1 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 438 records (63 percent) acceptable, 144 (21 percent) marginal, 59 (9 percent) questionable, and 49 (7 percent) unacceptable.
Figure 59. Charts. Screening results of the section average elastic moduli of the base layer for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT table based on the nonlinear elastic model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 377 records (78 percent) with both values reasonable, 18 (4 percent) with only backcalculated values reasonable, 74 (16 percent) with only forwardcalculated values reasonable, and 8 (2 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 149 records (40 percent) acceptable, 106 (28 percent) marginal, 65 (17 percent) questionable, and 57 (15 percent) unacceptable.
Figure 60. Charts. Screening results of the section average elastic moduli of the subgrade for the flexible sections in the MON_DEFL_FLX_BAKCALC_SECT table based on the nonlinear elastic model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 1,258 records (85 percent) with both values reasonable, 0 (0 percent) with only backcalculated values reasonable, 219 (15 percent) with only forwardcalculated values reasonable, and 0 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 444 records (35 percent) acceptable, 352 (28 percent) marginal, 299 (24 percent) questionable, and 163 (13 percent) unacceptable.
Figure 61. Charts. Screening results of the section average elastic moduli of the PCC slab for the rigid sections in the MON_DEFL_FLX_BAKCALC_SECT table based on the linear elastic model using MODCOMP.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 1,250 records (93 percent) with both values reasonable, 4 (0 percent) with only backcalculated values reasonable, 86 (6 percent) with only forwardcalculated values reasonable, and 13 (1 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 1,148 records (92 percent) acceptable, 95 (8 percent) marginal, 5 (0 percent) questionable, and 2 (0 percent) unacceptable.
Figure 62. Charts. Screening results of the section average elastic moduli of the base layer for the rigid sections in the MON_DEFL_FLX_BAKCALC_SECT table based on the linear elastic model using MODCOMP.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 875 records (51 percent) with both values reasonable, 153 (9 percent) with only backcalculated values reasonable, 551 (32 percent) with only forwardcalculated values reasonable, and 129 (8 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 388 records (44 percent) acceptable, 149 (17 percent) marginal, 165 (19 percent) questionable, and 173 (20 percent) unacceptable.
Figure 63. Charts. Screening results of the section average elastic moduli of the subgrade for the rigid sections in the MON_DEFL_FLX_BAKCALC_SECT table based on the linear elastic model using MODCOMP.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 1,235 records (91 percent) with both values reasonable, 0 (0 percent) with only backcalculated values reasonable, 118 (9 percent) with only forwardcalculated values reasonable, and 0 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 655 records (53 percent) acceptable, 158 (13 percent) marginal, 194 (16 percent) questionable, and 228 (18 percent) unacceptable.
Figure 64. Charts. Screening results of the section average elastic moduli of the PCC slab for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT table based on the slab-on-elastic-solid model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 1,150 records (99 percent) with both values reasonable, 11 (1 percent) with only backcalculated values reasonable, 0 (0 percent) with only forwardcalculated values reasonable, and 0 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 1,133 records (99 percent) acceptable, 17 (1 percent) marginal, 0 (0 percent) questionable, and 0 (0 percent) unacceptable.
Figure 65. Charts. Screening results of the section average elastic moduli of the PCC slab for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT table based on the slab-on-dense-liquid model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 1,117 records (99 percent) with both values reasonable, 8 (1 percent) with only backcalculated values reasonable, 0 (0 percent) with only forwardcalculated values reasonable, and 0 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 1,077 records (97 percent) acceptable, 39 (3 percent) marginal, 1 (0 percent) questionable, and 0 (0 percent) unacceptable.
Figure 66. Charts. Screening results of the section average elastic moduli of the base layer for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT table based on the slab-on-elastic-solid model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 1,021 records (92 percent) with both values reasonable, 3 (0 percent) with only backcalculated values reasonable, 61 (6 percent) with only forwardcalculated values reasonable, and 21 (2 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 993 records (98 percent) acceptable, 14 (1 percent) marginal, 14 (1 percent) questionable, and 0 (0 percent) unacceptable.
Figure 67. Charts. Screening results of the section average elastic moduli of the base layer for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT table based on the slab-on-dense-liquid model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 1,033 records (96 percent) with both values reasonable, 19 (2 percent) with only backcalculated values reasonable, 18 (2 percent) with only forwardcalculated values reasonable, and 4 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 966 records (94 percent) acceptable, 36 (3 percent) marginal, 31 (3 percent) questionable, and 0 (0 percent) unacceptable.
Figure 68. Charts. Screening results of the section average elastic moduli of the subgrade for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT table based on the slab-on-elastic-solid model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 1,165 records (100 percent) with both values reasonable, 0 (0 percent) with only backcalculated values reasonable, 0 (0 percent) with only forwardcalculated values reasonable, and 0 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 1,158 records (99 percent) acceptable, 7 (1 percent) marginal, 0 (0 percent) questionable, and 0 (0 percent) unacceptable.
Figure 69. Charts. Screening results of the section average K-values of the subgrade for the rigid sections in the MON_DEFL_RGD_BAKCALC_SECT table based on the slab-on-dense-liquid model.
This graphic consists of two pie charts. The left one represents all the data, where the breakdown is 1,110 records (98 percent) with both values reasonable, 0 (0 percent) with only backcalculated values reasonable, 18 (2 percent) with only forwardcalculated values reasonable, and 0 (0 percent) with both values unreasonable. The right pie chart represents a breakdown of both values reasonable showing 1,061 records (96 percent) acceptable, 48 (4 percent) marginal, 1 (0 percent) questionable, and 0 (0 percent) unacceptable.

 

FHWA-HRT-05-150

Table of Contents

 


The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT).
The Federal Highway Administration (FHWA) is a part of the U.S. Department of Transportation and is headquartered in Washington, D.C., with field offices across the United States. is a major agency of the U.S. Department of Transportation (DOT). Provide leadership and technology for the delivery of long life pavements that meet our customers needs and are safe, cost effective, and can be effectively maintained. Federal Highway Administration's (FHWA) R&T Web site portal, which provides access to or information about the Agency’s R&T program, projects, partnerships, publications, and results.
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United States Department of Transportation - Federal Highway Administration