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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations

Report
This report is an archived publication and may contain dated technical, contact, and link information
Publication Number: FHWA-HRT-06-121
Date: November 2006

Long-Term Pavement Performance (LTPP) Data Analysis Support: National Pooled Fund Study Tpf-5(013)

Appendix B. Performance Prediction Models

This appendix provides details on the prediction models for each of the performance measures evaluated in the study. In addition, the use of each model is illustrated through examples. Following is a list of the performance measures:

IRI = Pavement roughness (m/km (ft/mi))—flexible and rigid.
RUT = Rut depth (mm (inch))—flexible.
FWPC = Fatigue and wheelpath cracking (deduct value)—flexible.
fwpc = Fatigue and wheelpath cracking (percentage of wheelpath area)—flexible.
TC = Transverse cracking (deduct value)—flexible.
TC = Transverse cracking (percentage of total section area)—rigid.
LC = Longitudinal cracking (percentage of total section area)—rigid.
FLT = Transverse joint faulting (mm (inch))—rigid.

Following is a list of the explanatory variables input into the equations:

ACTHICK = Thickness of AC layer (mm (inch)).
ADJ_AGE = Pavement age after distress initiation (years).
AGE = Pavement age (years).
BASE = Base type (DGAB, ATB, PATB, LCB, NONBIT, NONE).
CI = Cooling index (degree-Celsius days).
DEPTH = Thickness of PCC layer (mm (inch)).
FC = Functional classification of roadway.
FI = Freezing index (degree-Celsius days).
FTC = Annual number of freeze-thaw cycles (each).
LESN = Logarithm of annual ESAL divided by structural number.
LEDT = Logarithm of annual ESAL divided by PCC layer thickness.
MIRI = Initial IRI (m/km (ft/mi)).
MIRI_AGE = Pavement age when MIRI was recorded (years).
Pavement Structure = AC nonoverlay with unbound base, AC nonoverlay with bound base, AC overlay (either bound or unbound base), JPCC.
PRECIP = Annual precipitation (mm (inch)).
SG = Subgrade classification (FINE, COARSE, ROCK/STONE, OTHER).

ABSOLUTE IRI PREDICTION MODEL FOR FLEXIBLE PAVEMENTS

Equation 12 shows the IRI regression equation (R-squared = 0.78, total observations = 4,544) and equation 13 defines the delta equation.

 View Alternate Text(12)

Where:

 View Alternate Text(13)

Table 37 shows the coefficients for a flexible IRI model.

Table 37. Coefficients for flexible IRI model.
a Values for FINE SUBGRADE
BASENonoverlay,Unbound BaseNonoverlay,Bound BaseOverlay, Bound or Unbound Base
ATBNA-0.714-0.759
DGAB-0.713NA-0.753
LCBNA-0.658-0.702
NONBITNA-0.674-0.718
NONE-0.658NA-0.698
PATBNA-0.734-0.779
a Values for COARSE SUBGRADE
ATBNA-0.77-0.815
DGAB-0.769NA-0.810
LCBNA-0.714-0.759
NONBITNA-0.730-0.774
NONE-0.714NA-0.755
PATBNA-0.790-0.835
a Values for ROCK/STONE SUBGRADE
ATBNA-0.671-0.716
DGAB-0.670NA-0.711
LCBNA-0.615-0.660
NONBITNA-0.631-0.676
NONE-0.615NA-0.656
PATBNA-0.691-0.736

Example of Absolute IRI Prediction Model for Flexible Pavements

As discussed in the main body of the report, the flexible IRI prediction model incorporates a delta factor that shifts the model to correspond with the measured initial IRI value (MIRI). The first step in predicting IRI for flexible pavements is to calculate that delta factor. With this factor determined, the IRI can be estimated from the regression equation. A pseudopavement section was fabricated with the explanatory conditions in table 38 for use as an example.

Table 38. Example pavement section information.
InputValue
Pavement Structure Nonoverlay, Unbound Base
BASE DGAB
SG FINE
ESAL 126,000
SN 5.0
ACTHICK 6.5
FTC 80
FI 688
CI 205
PRECIP 1,140
MIRI_AGE 1
MIRI 1
Age 2

Substituting the inputs from table 38 into the delta equation and extracting the alpha value from table 37 based on pavement structure, base type, and subgrade type appears in equation 14.

 View Alternate Text(14)

Therefore, the result is equation 15.

 View Alternate Text(15)

Using this delta and the regression equation, the result is equation 16.

 View Alternate Text(16)

Therefore, the results appear in equations 17 and 18.

 View Alternate Text(17)
 View Alternate Text(18)

ABSOLUTE IRI PREDICTION MODEL FOR RIGID PAVEMENTS

Equation 19 shows the IRI regression equation (R-squared=0.78, total observations=2,652) for rigid pavements.

 View Alternate Text(19)

Table 39 lists the coefficients for a rigid IRI model.

Table 39. Coefficients for rigid IRI model.
a Values for FINE SUBGRADE
 ATB BaseDGAB BaseLCB BaseNONBIT BasePATB Base
FC 1-0.478-0.499-0.497-0.413-0.539
FC 2-0.488-0.510-0.507-0.423-0.550
FC 6-0.529-0.551-0.548-0.464-0.591
FC 7-0.492-0.514-0.511-0.427-0.554
FC 9-0.402-0.424-0.421-0.337-0.464
FC 11-0.455-0.476-0.473-0.389-0.516
FC 12-0.469-0.491-0.488-0.404-0.531
FC 14-0.526-0.547-0.544-0.460-0.587
FC 17-0.408-0.430-0.427-0.343-0.470
a Values for COARSE SUBGRADE
FC 1-0.475-0.497-0.494-0.410-0.537
FC 2-0.486-0.507-0.505-0.420-0.547
FC 6-0.527-0.548-0.545-0.461-0.588
FC 7-0.489-0.511-0.508-0.424-0.551
FC 9-0.400-0.421-0.419-0.334-0.461
FC 11-0.452-0.473-0.471-0.387-0.513
FC 12-0.467-0.488-0.485-0.401-0.528
FC 14-0.523-0.544-0.542-0.458-0.584
FC 17-0.406-0.427-0.424-0.340-0.467
a Values for ROCK/STONE SUBGRADE
FC 1-0.540-0.562-0.559-0.475-0.602
FC 2-0.551-0.573-0.570-0.486-0.612
FC 6-0.592-0.614-0.611-0.527-0.653
FC 7-0.555-0.576-0.574-0.490-0.616
FC 9-0.465-0.487-0.484-0.400-0.526
FC 11-0.517-0.539-0.536-0.452-0.579
FC 12-0.532-0.553-0.551-0.467-0.593
FC 14-0.588-0.610-0.607-0.523-0.650
FC 17-0.471-0.493-0.490-0.406-0.532
a Values for OTHER SUBGRADE
FC 1-0.482-0.504-0.501-0.417-0.544
FC 2-0.493-0.514-0.512-0.428-0.554
FC 6-0.534-0.555-0.553-0.468-0.595
FC 7-0.497-0.518-0.515-0.431-0.558
FC 9-0.407-0.428-0.426-0.341-0.468
FC 11-0.459-0.481-0.478-0.394-0.520
FC 12-0.474-0.495-0.492-0.408-0.535
FC 14-0.530-0.551-0.549-0.465-0.591
FC 17-0.413-0.434-0.431-0.347-0.474

Example of Absolute IRI Predictions Model for Rigid Pavements

The rigid IRI model does not incorporate a delta factor; therefore, the regression equation can be used directly. The pavement structure shown in table 40 illustrates the use of the regression model.

Table 40. Example pavement section information.
InputValue
Pavement Structure JPCC
BASE DGAB
SG FINE
ESAL 410,000
FC 2
D 9.5
FTC 80
FI 688
CI 205
PRECIP 1,140
MIRI_AGE 1
MIRI 1
AGE 2

Substituting the inputs from table 40 into the regression equation and extracting the alpha value from the table 39 based on pavement structure, base type, and subgrade type leads to equation 20.

 View Alternate Text(20)

Equations 21 and 22 show the results.

 View Alternate Text(21)
 View Alternate Text(22)

FWPC PREDICTION MODEL FOR FLEXIBLE PAVEMENTS (DEDUCT VALUE)

Equation 23 shows the logistic FWPC prediction model for flexible pavements (total observations = 1977).

 View Alternate Text(23)

Table 41 lists the coefficients for the flexible FWPA logistic model.

Table 41. Coefficients for flexible FWPC (deduct value) logistic model.
 a1 Values
Nonoverlay, Unbound Base -1.06
Nonoverlay, Bound Base -0.635
Overlay, Bound or Unbound Base 0.101

Where crack initiation age is determined as the AGE at which P, cutoff probability, equals 0.7 (percent correct = 72.6). If the crack initiation age is determined to be less than zero from the logistic model, a value of zero is used.

Equation 24 shows the regression equation (R-squared = 0.63, total observations = 1,486).

 View Alternate Text(24)

Table 42 lists the coefficients for the flexible FWPC regression model.

Table 42. Coefficients for flexible FWPC (deduct value) regression model.
a2 Values for FINE SUBGRADE
BASENonoverlay,Nonoverlay,Overlay, Bound
ATBNA3.132.88
DGAB3.25NA2.94
LCBNA2.792.54
NONBITNA2.762.51
NONE2.91NA2.60
PATBNA3.062.81
a2Values for COARSE SUBGRADE
ATBNA2.882.63
DGAB3.00NA2.68
LCBNA2.542.29
NONBITNA2.512.25
NONE2.65NA2.34
PATBNA2.812.56
a2 Values for ROCK/STONE SUBGRADE
ATBNA3.172.91
DGAB3.28NA2.97
LCBNA2.822.57
NONBITNA2.792.54
NONE2.94NA2.63
PATBNA3.092.84

Where ADJ_AGE equals pavement age minus crack initiation age. If the pavement age is less than or equal to the crack initiation age, the predicted FWPC equals zero.

FWPC PREDICTION MODEL FOR FLEXIBLE PAVEMENTS (PERCENTAGE WHEELPATH AREA)

Equation 25 gives the logistic model (total observations = 1977).

 View Alternate Text(25)

Table 43 lists the coefficients for the flexible FWPC logistic model.

Table 43. Coefficients for flexible FWPC (percentage of wheelpath) logistic model.
 a1 Values
Nonoverlay, Unbound Base -1.06
Nonoverlay, Bound Base -0.635
Overlay, Bound or Unbound Base 0.101

Where the crack initiation age is determined as the AGE at which P, cutoff probability, equals 0.7 (percent correct = 72.6). If the crack initiation age is determined to be less than zero from the logistic model, a value of zero is used.

Equation 26 shows the regression equation (R-squared = 0.63, total observations = 1486).

 View Alternate Text(26)

Table 44 lists the coefficients for the flexible FWPC regression model.

Table 44. Coefficients for flexible FWPC (percentage of wheelpath) regression model.
a2 Values for FINE SUBGRADE
BASENonoverlay, Unbound BaseNonoverlay, Bound BaseOverlay, Bound, or Unbound Base
ATBNA2.431.97
DGAB2.51NA2.14
LCBNA2.802.33
NONBITNA1.971.51
NONE2.15NA1.78
PATBNA2.451.98
a2Values for COARSE SUBGRADE
ATBNA2.061.59
DGAB2.14NA1.77
LCBNA2.431.96
NONBITNA1.601.13
NONE1.77NA1.40
PATBNA2.081.61
a2Values for ROCK/STONE SUBGRADE
ATBNA2.111.64
DGAB2.19NA1.81
LCBNA2.472.01
NONBITNA1.651.18
NONE1.82NA1.45
PATBNA2.121.66

Where ADJ_AGE = pavement Age—crack initiation age. If the pavement age is less than or equal to the crack initiation age, the predicted FWPC equals zero.

Example for FWPC Prediction Model for Flexible Pavements

The prediction model for FWPC involves a two-step process. In the first step, the logistic equation in equation 25 is used to estimate the age of crack initiation. This is done solving for the AGE variable so that P is equivalent to the cutoff value (0.7 for this model). This AGE is denoted as the crack initiation age. In some cases, the resulting crack initiation age may be less than zero. A value of zero is used in place of the estimated negative crack initiation age.

If the FWPC estimate is for a pavement age less than or equal to the crack initiation age, the predicted FWPC value is equal to zero. If the FWPC estimate is for a pavement age greater than the crack initiation age, the ADJ_AGE is calculated as the pavement age of interest less the crack initiation age. Table 45 lists information for an example pavement section.

Table 45. Example pavement section information.
InputValue
Pavement Structure Nonoverlay, Unbound Base
BASE DGAB
SG FINE
ESAL 126,000
SN 5.0
ACTHICK 6.5
FTC 80
FI 688
CI 205
PRECIP 1,140
MIRI_AGE 1
MIRI 1
AGE 12

Equation 27 substitutes information from table 45 as well as a P value of 0.7 into the logistic equation and extracting the a1 value from the appropriate table.

 View Alternate Text(27)

Equation 28 is solving for AGE through an iterative process.

 View Alternate Text(28)

FWPC prediction of interest occurs at a pavement age of 12. Therefore, ADJ_AGE = 12-9.13 = 2.87. Equation 29 substitutes this age and the information from table 45 into the regression equation.

 View Alternate Text(29)

Therefore, the results are shown in equations 30 and 31.

 View Alternate Text(30)
 View Alternate Text(31)

TC PREDICTION MODEL FOR FLEXIBLE PAVEMENTS

Equation 32 shows the logistic model (observations = 1,920).

 View Alternate Text(32)

Table 46 lists the coefficients for the flexible TC logistic model.

Table 46. Coefficients for flexible TC logistic model.
 a1 Values
Nonoverlay, Unbound Base -3.75
Nonoverlay, Bound Base -3.29
Overlay, Bound or Unbound Base -1.97

Where the crack initiation age is determined as the AGE at which P, cutoff probability, equals 0.7 (percent correct = 78.4). If the crack initiation age is determined to be less than zero from the logistic model, a value of zero is used.

Equation 33 is the regression equation (R-squared = 0.71, total observations = 1,077).

 View Alternate Text(33)

Table 47 lists the coefficients for the flexible TC regression model.

Table 47. Coefficients for flexible TC regression model.
a2 Values for FINE SUBGRADE
BASENonoverlay, Unbound BaseNonoverlay, Bound BaseOverlay, Bound or Unbound Base
ATBNA1.481.10
DGAB1.03NA0.996
LCBNA1.581.20
NONBITNA1.551.17
NONE1.41NA1.37
PATBNA1.821.44
a2 Values for COARSE SUBGRADE
ATBNA1.170.792
DGAB0.72NA0.687
LCBNA1.270.891
NONBITNA1.240.859
NONE1.10NA1.06
PATBNA1.511.13
a2 Values for ROCK/STONE SUBGRADE
ATBNA0.9760.599
DGAB0.527NA0.494
LCBNA1.080.698
NONBITNA1.040.666
NONE0.905NA0.871
PATBNA1.320.939

Where ADJ_AGE equals pavement age less the crack initiation age. If the pavement age is less than or equal to the crack initiation age, the predicted TC equals zero.

Example for TC Prediction Model for Flexible Pavements

The prediction model for TC involves a two-step process. In the first step, the logistic model in equation 32 is used to estimate the age of crack initiation. This is done by solving for the AGE variable so that P is equivalent to the cutoff value (0.7 for this model). This AGE is denoted as the crack initiation age. In some cases, the resulting crack initiation age may be less than zero. A value of zero is used in place of the estimated negative crack initiation age.

If the TC estimate is for a pavement age less than or equal to the crack initiation age, the predicted TC value is equal to zero. If the TC estimate is for a pavement age greater than the crack initiation age, the ADJ_AGE is calculated as the pavement age of interest less the crack initiation age. Table 48 lists information for an example pavement section.

Table 48. Example pavement section information.
InputValue
Pavement Structure Nonoverlay, Unbound Base
BASE DGAB
SG FINE
ESAL 126,000
SN 5.0
ACTHICK 6.5
FTC 80
FI 688
CI 205
PRECIP 1,140
MIRI_AGE 1
MIRI 1
AGE 12

Equation 34 substitutes information from table 48 as well as a P value of 0.7 into the logistic equation and extracts the alpha 1 value from the appropriate table.

 View Alternate Text(34)

Solving for AGE through an iterative process results in equation 35.

 View Alternate Text(35)

TC prediction of interest occurs at a pavement age of 12. Therefore, ADJ_AGE = 12-7.54 = 4.46. Equation 36 substitutes this age and the information in table 48 into the regression equation.

 View Alternate Text(36)

Therefore, the results are shown in equations 37 and 38.

 View Alternate Text(37)
 View Alternate Text(38)

LC PREDICTION MODEL FOR RIGID PAVEMENTS

Equation 39 shows the logistic model (total observations = 400).

 View Alternate Text(39)

Where the crack initiation age is determined as the AGE at which P, cutoff probability, equals 0.55 (percent correct = 63.5). If the crack initiation age is determined to be less than zero from the logistic model, a value of zero is used.

Equation 40 is the regression equation (R-squared = 0.38, total observations = 240).

 View Alternate Text(40)
Table 49. Coefficients for rigid LC regression model.
BASEa1
ATB -1.36
DGAB -1.89
LCB -1.03
NONBIT -0.84
PATB -2.14

Where ADJ_AGE equals pavement age less the crack initiation age. If the pavement age is less than or equal to the crack initiation age, the predicted LC equals zero. If the predicted LC is less than zero for pavement age is greater than crack initiation age, the predicted LC was set to zero.

Example for LC Prediction Model for Rigid Pavements

The prediction model for LC involves a two-step process. In the first step, logistic equation 39 is used to estimate the age of crack initiation. This is done solving for the AGE variable so that P is equivalent to the cutoff value (0.55 for this model). This AGE is denoted as the crack initiation age. In some cases, the resulting crack initiation age may be less than zero. A value of zero is used in place of the estimated negative crack initiation age.

If the LC estimate is for a pavement age less than or equal to the crack initiation age, the predicted TC value is equal to zero. If the LC estimate is for a pavement age greater than the crack initiation age, the ADJ_AGE is calculated as the pavement age of interest less the crack initiation age.

Table 50 gives the information for an example pavement section.

Table 50. Example pavement section information.
InputValue
Pavement Structure JPCC
BASE DGAB
SG FINE
ESAL 410,000
FC 2
D 9.5
FTC 80
FI 688
CI 205
PRECIP 1,140
MIRI_AGE 1
MIRI 1
AGE 14

Equation 41 substitutes information from the table 50 as well as a P value of 0.55 into the logistic equation and extracts the alpha 1 value from the appropriate table.

 View Alternate Text(41)

Equation 42 is solving for AGE through an iterative process.

 View Alternate Text(42)

LC prediction of interest occurs at a pavement age of 14. Therefore, ADJ_AGE = 14-11.86 = 2.14. Substituting this age and the information in table 50 into the regression equation results in equation 43.

 View Alternate Text(43)

Therefore, the results are shown in equations 44 and 45.

 View Alternate Text(44)
 View Alternate Text(45)

TC PREDICTION MODEL FOR RIGID PAVEMENTS

Equation 46 shows the logistic model (total observations = 414).

 View Alternate Text(46)

Where The crack initiation age is determined as the AGE at which P, cutoff probability, equals 0.6 (percent correct = 63.5). If the crack initiation age is determined to be less than zero from the logistic model, a value of zero is used.

Equation 47 shows the regression equation (R-squared = 0.54, total observations = 228).

 View Alternate Text(47)

Table 51 lists the coefficients for the rigid TC regression model.

Table 51. Coefficients for rigid TC regression model.
BASEa2
ATB -3.05
DGAB -2.28
LCB -1.76
NONBIT -2.65
PATB -2.55

Where ADJ_AGE equals pavement age less the crack initiation age. If the pavement age is less than or equal to the crack initiation age, the predicted TC equals zero

Example for TC Prediction Model for Rigid Pavements

The prediction model for TC involves a two-step process. In the first step, the logistic model in equation 46 is used to estimate the age of crack initiation. This is done by solving for the AGE variable so that P is equivalent to the cutoff value (0.6 for this model). This AGE is denoted as the crack initiation age. In some cases, the resulting crack initiation age may be less than zero. A value of zero is used in place of the estimated negative crack initiation age.

If the TC estimate is for a pavement age less than or equal to the crack initiation age, the predicted TC value is equal to zero. If the TC estimate is for a pavement age greater than the crack initiation age, the ADJ_AGE is calculated as the pavement age of interest less the crack initiation age.

Table 52 lists information for an example pavement section.

Table 52. Example pavement section information.
InputValue
Pavement Structure JPCC
BASE DGAB
SG FINE
ESAL 410,000
FC 2
D 9.5
FTC 80
FI 688
CI 205
PRECIP 1,140
MIRI_AGE 1
MIRI 1
AGE 18

Equation 48 substitutes information from table 52 as well as a P value of 0.6 into the logistic equation and extracts the alpha 1 value from the appropriate table.

 View Alternate Text(48)

Equation 49 is solving for AGE through an iterative process.

 View Alternate Text(49)

The TC prediction of interest occurs at a pavement age of 18. Therefore, ADJ_AGE = 18-11.86 = 6.14. Equation 50 substitutes this age and the information in table 52 into the regression equation shown in equation 50.

 View Alternate Text(50)

Therefore, the results are as shown in equations 51 and 52.

 View Alternate Text(51)
 View Alternate Text(52)

RUT DEPTH PREDICTION MODEL FOR FLEXIBLE PAVEMENTS

Equation 53 shows the regression equation (R-squared = 0.45, total observations = 1,966).

 View Alternate Text(53)

Table 53 lists the coefficients for the flexible RUT model.

Table 53. Coefficients for flexible RUT model.
a Values for FINE SUBGRADE
BASENonoverlay, Unbound BaseNonoverlay, Bound BaseOverlay, Bound or Unbound Base
ATBNA0.1360.124
DGAB0.367NA0.31
LCBNA0.6240.612
NONBITNA0.4360.425
NONE-0.539NA-0.597
PATBNA-0.309-0.321
a Values for COARSE SUBGRADE
ATBNA0.09580.084
DGAB0.327NA0.269
LCBNA0.5830.572
NONBITNA0.3960.384
NONE-0.580NA-0.637
PATBNA-0.350-0.361
a Values for ROCK/STONE SUBGRADE
ATBNA-0.0199-0.0317
DGAB0.211NA0.154
LCBNA0.4680.456
NONBITNA0.2800.269
NONE-0.695NA-0.753
PATBNA-0.465-0.477
ß and ? values
BASEß?
ATB0.331-.000228
DGAB0.225-.000266
LCB0.0236-.00507
NONBIT0.108.00120
NONE1.13.000283
PATB0.769.000150

Example for Rut Depth Prediction Model for Flexible Pavements

The prediction model for rut depth on flexible pavement uses one regression equation.
Table 54 lists information for the example pavement structure to illustrate the model.

Table 54. Example pavement section information.
InputValue
Pavement Structure Nonoverlay, Unbound Base
BASE DGAB
SG FINE
ESAL 126,000
SN 5.0
ACTHICK 6.5
FTC 80
FI 688
CI 205
PRECIP 1,140
MIRI_AGE 1
MIRI 1
AGE 2

Equation 54 substitutes the information from table 54 into the delta equation and extracts the alpha value from table 53 based on pavement structure, base type, and subgrade type.

 View Alternate Text(54)

Therefore, the results are shown in equations 55 and 56.

 View Alternate Text(55)
 View Alternate Text(56)

TRANSVERSE JOINT FAULTING PREDICTION MODEL FOR RIGID PAVEMENTS

Equation 57 shows the regression equation (R-squared = 0.47, total observations = 1,384).

 View Alternate Text(57)

Table 55 lists the coefficients for the rigid FLT model.

Table 55. Coefficients for rigid FLT model.
a Values
BASEFine SubgradeCoarse SubgradeOther SubgradeRock/Stone Subgrade
ATB0.7550.8101.200.515
DGAB0.7320.7861.180.492
LCB0.6650.7201.11 0.425
NONBIT0.8340.8891.280.595
PATB0.6930.7481.140.453

Example for Fault Prediction Model for Rigid Pavements

The prediction model for faulting on rigid pavement uses one regression equation. Table 56 lists information for an example pavement structure to illustrate the use of the model.

Table 56. Example pavement section information.
InputValue
Pavement Structure JPCC
BASE DGAB
SG FINE
ESAL 410,000
FC 2
D 9.5
FTC 80
FI 688
CI 205
PRECIP 1140
AGE 15

Equation 58 substitutes the information from table 56 into the delta equation and extracts the alpha value from table 55 based on base type and subgrade type.

 View Alternate Text(58)

Therefore, equations 59 and 60 show the results.

 View Alternate Text(59)
 View Alternate Text(60)

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