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Pavement Health Track Remaining Service Life (RSL) Forecasting Models, Technical Information

Pavement Condition Forecasting Models

A summary of performance measures and associated models used to characterize pavement condition is presented in Table 2. Descriptions of each model presented in Table 2 are presented in the following sections.

Table 2. Summary of Performance Measures and Associated Models
Pavement Type Distress Type/Smoothness Unit of Measurements
Jointed plain concrete pavement (JPCP) Transverse "slab" cracking Percent slabs cracked
Jointed plain concrete pavement (JPCP) Mean transverse joint faulting inches
Jointed plain concrete pavement (JPCP) Transverse joint spalling percent joints spalled
Jointed plain concrete pavement (JPCP) Smoothness (IRI) in/mi
New asphalt pavement Alligator cracking Percent lane area
New asphalt pavement Rutting inches
New asphalt pavement Transverse cracking ft/mi
New asphalt pavement Smoothness in/mi
Asphalt concrete (AC) over JPCP Reflection transverse cracking percent lane area with reflection cracking

New JPCP Equations

Transverse "Slab” Cracking Model

Equation 4 - The term CRK is equal to begin complex expression open parenthesis begin fraction begin numerator 100 end numerator over begin denominator 1 addition operator 733085 begin superscript -0.00521 end superscript multiplication operator open parenthesis begin uppercase ESALS multiplication operator LB_TRF_FACTOR end uppercase close parenthesis begin superscript 0.25 addition operator begin uppercase delta symbol end uppercase end superscript end denominator end fraction close parenthesis end complex expression. (4)

Where

CRK = predicted percent slabs cracked
ESALs = cumulative number of 18-kip equivalent single axle load (see section on estimating equivalent single-axle loads, or ESALs)

Equation 5 - The term LB_TRAF_FACTOR is equal to begin complex expression open parenthesis begin fraction begin numerator 1 end numerator over begin denominator 1 addition operator open bracket begin fraction begin numerator uppercase AGE end uppercase end numerator over begin denominator begin uppercase LB_AGE end uppercase addition operator 5.41 end denominator end fraction addition operator 0.0000001 close bracket begin superscript -7.89 end superscript end denominator end fraction end complex expression. (5)

AGE = pavement age in years
LB_AGE = age at which the Portland cement concrete (PCC) slab debonds from the base (see PHT Tool default data tables)
LN(Δ) = γ1 *(EdgeSup) + γ2*EPCC + γ3*JTSP + γ4*PCC_COMP + γ5*PCCTHK + γ6*SUBGCOAR + γ7*CLIMWF+ γ8*CLIMWNF + γ9*CLIMDNF   (6)

A description of the coefficient and input variables used for computing the natural log of Δ is presented in Table 3.

Table 3. JPCP Transverse Cracking Model Coefficients and Input Variables
JPCP Transverse Cracking Model Coefficient Coefficient Value Description of Cracking Model Input Variables Source
γ1 0.1424 EdgeSup (Edge support), 1 if a tied PCC shoulder or widened slab (slab width > 12 ft) is used, otherwise 0 HPMS program (Lane_Width & Shoulder_Type)
γ2 - 3.36E-7 EPCC = 28-day PCC slab elastic modulus in psi PHT Tool default data tables
γ3 - 0.0571 JTSP = JPCP joint spacing or slab length in feet HPMS program (Joint_Spacing)
γ4 0.000188 PCC_COMP = 28-day PCC compressive strength in psi PHT Tool default data tables
γ5 0.0598 PCCTHK = PCC slab thickness in inches HPMS program (Thickness_Rigid)*
γ6 0.2951 SUBGCOAR = 1 if subgrade soil type is coarse grained, otherwise 0 HPMS program (Soil_Type)
γ7 0.1323 CLIMWF = 1 if pavement is located in a wet-freeze climate, otherwise 0 HPMS program (Climate_Zone)
γ8 0.2443 CLIMWNF = 1 if pavement is located in a wet-no-freeze climate, otherwise 0 HPMS program (Climate_Zone)
γ9 0.7636 CLIMDNF = 1 if pavement is located in a dry-no-freeze climate, otherwise 0 HPMS program (Climate_Zone)

*Also available in HPMS Estimates table.

Transverse Joint Faulting Model

PFAULT =
(ESALS0.521)*(1 - 0.6413*DowDia)*( -9.01E-06*ATB
- 9.50E-06*CTB + 0.000013*(1-EdgeSup) + 1.44E-08*FI
+ 3.68E-06*JTSP + 0.000014*WET - 4.91E-06*PCCTHK - 9.36E-06*SubgCoar)    (7)

A description of input variables used for faulting is presented in Table 4.

Transverse Joint Spalling

Equation 8 - The term SPALL is equal to begin complex expression open bracket begin fraction begin numerator begin uppercase AGE end uppercase end numerator over begin denominator begin uppercase AGE end uppercase addition operator 0.01 end denominator end fraction close bracket open bracket begin fraction begin numerator 100 end numerator over begin denominator 1 pus operator 1.005 begin superscript open parenthesis -12 multiplication operator begin uppercase AGE end uppercase addition operator begin uppercase SCF end uppercase close parenthesis end superscript end denominator end fraction close bracket end complex expression. (8)

Where
SPALL = predicted percentage joints spalled (medium- and high-severities)
AGE = pavement age since construction or reconstruction, years
SCF = scaling factor based on site-, design-, and climate-related variables:

SCF = -1400 + 350 * AIR% * (0.5 + PREFORM) + 43.4 f'c ^ 0.4 - 0.2 (FTCYC * AGE) + 43 hPCC - 536 WC_Ratio   (9)

A description of input variables used for computing SCF is presented in Table 5.

Table 4. Description of JPCP Transverse Joint Faulting Model Input Variables
Description of Faulting Model Input Variables Source
PFAULT = predicted mean transverse joint faulting, in —
ESALs = cumulative number of 18-kip equivalent single axle load see Section on estimating ESALs
DowDia = dowel diameter, in HPMS program (Dowel_Bar) & PHT Tool default data tables
ATB = 1 if base type is asphalt treated material, otherwise 0 HPMS program (Base_Type)*
CTB = 1 if base type is cement treated material, otherwise 0, for CTB = 1 HPMS program (Base_Type)*
EdgeSup (Edge support) = 1 if a tied PCC shoulder or widened slab (slab width > 12 ft) is used, otherwise 0 HPMS program (Lane_Width & Shoulder_Type)
FI = freezing index, deg F days PHT Tool default data tables
JTSP = JPCP joint spacing or slab length in feet HPMS program (Joint_Spacing)
WET= 1 if climate is "Wet-Freeze" or "Wet-Nofreeze," otherwise 0 HPMS program (Climate_Zone)
PCCTHK = PCC slab thickness in inches HPMS program (Thickness_Rigid)*
SUBGCOAR = 1 if subgrade soil type is coarse grained, otherwise 0 HPMS program (Soil_Type)

*Also available in HPMS Estimates table.

Table 5. Description of JPCP Transverse Joint Spalling Model Input Variables
Description of Spalling Model Input Variables Source
AIR% =PCC air content, percent PHT Tool default data tables
AGE = time since last construction or reconstruction, years HPMS program (Year_Last_Improvement OR Year_Last_Construction)
PREFORM =1 if preformed sealant is present; 0 if not PHT Tool default data tables
f'c =PCC 28-day compressive strength, psi PHT Tool default data tables
FTCYC = average annual number of air freeze-thaw cycles PHT Tool default data tables
hPCC = PCC slab thickness, in HPMS program (Thickness_Rigid)*
WC_Ratio = PCC water/cement ratio (by weight) PHT Tool default data tables

*Also available in HPMS Estimates table.

Smoothness (IRI)

IRI = IRII + 0. 8203*CRK + 0.4417*SPALL + 0.4929*TFAULT + 25.24*SF    (10)

Where
SF = Site factor = AGE (1+0.5556*FI) (1+P200)*10-6

A description of input variables used for computing IRI is presented in Table 6.

Table 6. Description of JPCP IRI Model Input Variables
Description of IRI Model Input Variables Source
IRI = predicted IRI, in/mi  
IRII = initial IRI, in/mi Assume MEPDG default of 63.4 in/mi OR assume HPMS program IRI corresponding to Year_Last_Improvement OR Year_Last_Construction
CRK = percent slabs with transverse cracks See equation 4
SPALL = percentage of joints with spalling (medium and high severities) See equation 8
TFAULT= Total joint faulting cumulated per mi, in See equation 7
AGE = pavement age since construction or reconstruction, years HPMS program (Year_Last_Improvement OR Year_Last_Construction)
FI = mean annual freezing index, °F-days PHT Tool default data tables
P200 = percent subgrade material passing No. 200 sieve PHT Tool default data tables

* Also available in HPMS Estimates table.

New Flexible Pavement Equations

The first step in computing flexible pavement distress and IRI is to estimate critical strains within the hot mix asphalt (HMA), base, and subgrade layers as described in the following sections.

Input 1: HMA Dynamic Modulus (Witzak Model)

Equation 11 - The term log E asterisk is equal to begin complex expression 1.249937 addition operator 0.02932 rho begin subscript 200 end subscript subtraction operator 0.001767 open parentheses rho begin subscript 200 end subscript close parenthesis begin superscript 2 end superscript subtraction operator 0.002841 rho begin subscript 4 end subscript subtraction operator 0.058097 begin uppercase V end uppercase begin subscript a end subscript subtraction operator 0.802208 open parenthesis begin fraction begin numerator begin uppercase V end uppercase begin subscript beff end subscript end numerator over begin denominator begin uppercase V end uppercase begin subscript beff end subscript addition operator begin uppercase V end uppercase begin subscript a end subscript end denominator end fraction close parenthesis addition operator begin fraction begin numerator 3.871977 subtraction operator 0.0021 rho begin subscript 4 end subscript addition operator 0.003958 rho begin subscript 38 end subscript subtraction operator 0.000017 open parenthesis rho begin subscript 38 end subscript close parenthesis begin superscript 2 end superscript addition operator 0.005470 rho begin subscript 34 end subscript end numerator over begin denominator 1 addition operator e begin superscript open parenthesis 0.603313 subtraction operator 0.313351 log open parenthesis f close parenthesis subtraction operator 0.393532 log open parenthesis eta begin subscript t comma z close parenthesis close parenthesis end denominator end fraction end complex expression (11)

Table 7 describes the input variables used for computing HMA Dynamic Modulus. The input variables and the steps involved in estimating aged HMA binder viscosity and loading frequency of loading are presented below.

Table 7. Description of HMA Dynamic Modulus Equation Input Variables
Description of HMA Dynamic Modulus Equation Input Variables Source
E*= HMA dynamic modulus, psi See equation 11
ηt,z = aged HMA binder viscosity at time t, and depth z, MPoise See equation 18
f = pavement layer loading frequency, Hz See equation 13
Va = as-constructed HMA mix air void content, percent PHT Tool default data tables
Vbeff = effective as-constructed HMA mix bitumen content, percent by volume PHT Tool default data tables
ρ34 = cumulative percent retained on the 3/4 in sieve for the HMA mix PHT Tool default data tables
ρ38= cumulative percent retained on the 3/8 in sieve for the HMA mix PHT Tool default data tables
ρ4 = cumulative percent retained on the No. 4 sieve for the HMA mix PHT Tool default data tables
ρ200 = percent passing the No. 200 sieve for the HMA mix PHT Tool default data tables

A. Input variables for estimating aged HMA binder viscosity (at time t and depth z) (input to HMA dynamic modulus model)

Step 1: Compute unaged HMA binder viscosity (at a reference temperature of 77° F) using the American Society for Testing and Materials (ASTM) viscosity temperature relationship below:

loglogηorig = A + VTSlogTR    (12)

A description of the input variables used for computing unaged HMA binder viscosity is presented in Table 8.

Table 8. Input Variables for the Unaged HMA Binder Viscosity Equation
Description of Unaged HMA Binder Viscosity Equation Input Variables Source
ηorig = unaged HMA binder viscosity (at reference temperature 77 °F), cP See equation 12
TR = temperature, Rankine (reference temperature is 77 °F, convert to Rankine) —
A = regression intercept * PHT Tool default data tables
VTS = regression slope of viscosity temperature susceptibility PHT Tool default data tables

*See Tables 51 and 52 in "Guidelines for Implementing the new MEPDG Pavement Equations." Battelle and ARA. Draft Final report submitted to FHWA Office of Policy. May 2010.

Step 2: Compute HMA binder viscosity at placement as follows:

loglog(ηt=0)=a0 + a1 loglog(ηorig)
a0 = 0.054405 + 0.004082 × code
a1 = 0.972035 + 0.010886 × code    (13)

A description of input variables used for computing HMA binder viscosity at placements presented in Table 9.

Table 9. Input Variables for the HMA Binder Viscosity at Placement Equation
Description of HMA Binder Viscosity at Placement Equation Input Variables Source
ηt=0 = HMA binder viscosity at placement, cP —
ηorig = unaged HMA binder viscosity, cP See equation 10
code = hardening ratio (0, representing average conditions is recommended) Placement Hardening Resistance / Expected Hardening Ratio Values / Code Value
Excellent to Good / HR ≤ 1.030 / -1
Average / 1.030 < HR ≤ 1.075 / 0
Fair / 1.075 < HR ≤ 1.100 / 1
Poor / HR > 1.100 / 2

Step 3: Compute HMA binder viscosity at any given pavement age (at the HMA surface) described as follows:

Equation 14 -The term log log open parenthesis eta begin subscript aged end subscript close parenthesis is equal to begin complex expression begin numerator begin expression log log open parenthesis eta begin subscript t equals zero end subscript close parenthesis end expression addition operator begin uppercase A end uppercase t end numerator over begin denominator 1 addition operator begin uppercase B end uppercase t end denominator end fraction end complex expression. (14)

where
A = -0.004166+1.41213(C)+(C)log(MAAT)+(D)loglogηt=0)
B = 0.197725+0.068384log(C)
C = 10(274.4946-193.831 log(TR)+33.9366 log(TR)2
D = -14.5521+10.47662 log(TR) -1.88161 log(TR)2

A description of input variables used for computing HMA binder viscosity at any given pavement age (at the HMA surface) is presented in Table 10.

Table 10. Input Variables for the HMA Binder Viscosity Equation
(at the HMA surface, for any given age)
Description of HMA Binder Viscosity at Any Age Equation Input Variables Source
ηaged = aged viscosity at HMA surface, cP See equation 14
ηt=0 = HMA binder viscosity at placement, cP See equation 13
MAAT = mean annual air temperature, °F PHT Tool default data tables
TR = pavement surface temperature in Rankine PHT Tool default data tables
t = time in months (pavement age in months) HPMS program (Year_Last_Improvement OR Year_Last_Construction)

Step 4: Adjust aged viscosity at HMA surface (ηaged) for changes in HMA air voids as follows:

loglog(ηaged)´ = Fvloglog(ηaged)    (15)

Equation 16 - The term F begin subscript v end subscript is equal to begin complex expression begin fraction begin numerator 1 addition operator 1.0367 multiplication operator 10 begin superscript -4 end superscript open parenthesis begin uppercase VA end uppercase close parenthesis open parenthesis t close parenthesis end numerator over begin denominator 1 addition operator 6.1798 multiplication operator 10 begin superscript -4 end superscript open parenthesis t close parenthesis end denominator end fraction end complex expression. (16)

Equation 17 - The term VA is equal to the complex expression begin fraction begin numerator begin uppercase VA end uppercase begin subscript orig end subscript addition operator 0.011 open parenthesis t close parenthesis subtraction operator 2 end numerator over begin denominator 1 addition operator 4.24 multiplication operator 10 begin superscript -4 end superscript open parenthesis t close parenthesis open parenthesis begin uppercase MAAT end uppercase close parenthesis addition operator 1.169 multiplication operator 10 begin superscript -3 end superscript open parenthesis begin fraction begin numerator t end numerator over begin denominator eta begin subscript orig comma 77 end subscript end denominator end fraction close parenthesis end denominator end fraction addition operator 2 end complex expression. (17)

A description of input variables used for adjusting aged viscosity at HMA surface (ηaged) for changes in HMA air voids is presented in Table 11.

Table 11. Input Variables for Adjusting Aged Viscosity for Changes in HMA Air Voids (at the HMA surface)
Description of Input Variables for Adjusting Aged Viscosity at HMA Surface (ηaged) for Changes in HMA Air Voids Input Variables Source
VAorig = HMA air voids at placement HMA, percent PHT Tool default data tables
MAAT = mean annual air temperature, °F PHT Tool default data tables
ηorig = unaged HMA binder viscosity (at reference temperature, 77 °F), cP See equation 10
t = time in months (pavement age in months) HPMS program (Year_Last_Improvement OR Year_Last_Construction)

Step 5: Compute HMA viscosity at a given age and depth within the HMA layer as follows:

Equation 18 - The term eta begin subscript t comma z end subscript is equal to the expression begin fraction begin numerator eta begin subscript t end subscript open parenthesis 4 addition operator begin uppercase E end uppercase close parenthesis subtraction operator begin uppercase E end uppercase open parenthesis eta begin subscript t equals zero end subscript close parenthesis open parenthesis 1 subtraction operator 4 z close operator end numerator over begin denominator 4 open parenthesis 1 addition operator begin uppercase E end uppercase z close parenthesis end denominator end fraction end expression. (18)

A description of input variables used for computing HMA viscosity at a given age and depth within the HMA layer is presented in Table 12.

Table 12. Input Variables for Computing HMA Viscosity (at a given age and depth)
Description of Input Variables for Computing HMA Viscosity at a Given Age and Depth Within the HMA Layer Input Variables Source
ηt,z = HMA binder viscosity at time t, and depth z, MPoise See equation 18
(ηaged)' = HMA binder viscosity (aged viscosity at HMA surface adjusted for changes in HMA air voids), MPoise See equation 15
z = depth within HMA layer of interest, in Determined based on critical response location (see Table 13)
E = 23.83e(-0.0308 MAAT) —
MAAT = mean annual air temperature, °F PHT Tool default data tables
Table 13. Locations for Computing Critical Flexible Pavement Responses
New Equation Critical Location (Depth)
Rutting Middle of the HMA layer
Transverse cracking 0.5-in
Alligator cracking Bottom of HMA layer

B. Input variables for estimating frequency of loading (input to HMA dynamic modulus model)

Frequency of loading is determined as follows:

Equation 19 - The term f is equal to the expression begin fraction begin numerator 17.6 multiplication operator begin uppercase V end uppercase begin subscript s end subscript end numerator over begin denominator begin uppercase L end uppercase begin subscript eff end subscript end denominator end fraction end expression. (19)

A description of the variables used for computing frequency of loading is presented in Table 14.

Table 14. Input Variables for Computing Frequency of Loading
Description of Input Variables for Frequency of Loading Source
Vs = travel speed HPMS program (Speed_Limit)
Leff = effective length, ft
= 2(ac + Ζeff) 		—
ac = radius of tire contact area Assume 6-in
Zeff    =   effective depth, in    =    Begin expression d begin subscript i end subscript multiplication operator cube root symbol begin complex expression begin fraction begin numerator begin uppercase E end uppercase begin subscript begin uppercase HMA end uppercase end subscript end numerator over begin denominator begin uppercase M end uppercase begin subscript r end subscript end denominator end fraction end complex expression end expression. —
di = critical location (depth) within HMA layer for which frequency is being calculated See Table 13
EHMA = HMA modulus, psi Assume typical value of 1,000,000 psi
Mr = subgrade resilient modulus, psi PHT Tool default data tables

Input 2: Critical Strains Equation Inputs

A description of input variables required by the equations for computing critical strains is presented in Table 15.

Table 15. Input Variables Required for Computing Critical Strains
Description of Input Variables Required by the Equations for Computing Critical Strains Source
hAC = HMA thickness, in HPMS program (Thickness_Flexible)**
E* = HMA dynamic modulus, psi () See Equation 9
hB = base layer thickness HPMS program (Base_Thickness)**
EB = base layer modulus, psi HPMS program (Base_Type) and PHT Tool default data tables**
ESUBG = subgrade layer modulus HPMS program (Soil_Type) and PHT Tool default data tables**

**Also available in HPMS Estimates table.

Use the inputs assembled to compute critical strain within the pavement structure as needed using the closed-form equations presented in Table 16.

Table 16. Equations for Estimating Critical Strains within HMA Pavement
Model Input Variables/Clusters Model Coefficients
Equation 20
Horizontal Tensile Strain at the Bottom of HMA Layer 		Model Coefficients
Equation 21
Vertical Strain at the Middle of HMA Layer 		Model Coefficients
Equation 22
Vertical Strain at the Middle of Base Layer 		Model Coefficients
Equation 23
Vertical Strain at the Top of Subgrade Layer
Intercept0.007706079-0.010539965-0.013753501-0.005714644
hAC-0.0008750720.0005802930.0017955030.000670647
E*-0.0003713460.0014752170.0005904720.000206993
hB-0.000160482-8.95177E-050.0006960710.000481929
EB-0.000541586-3.38384E-050.0010598053.15126E-05
ESUBG-5.93918E-05-8.15273E-05-3.35863E-050.000518046
hAC* hAC0.000012243.81811E-05-4.18585E-05-9.8384E-06
hAC *E*1.64491E-05-5.76145E-05-0.000026373-5.7542E-06
(E*)*(E*)8.595E-07-5.06666E-05-2.9108E-06-1.0728E-06
hAC *hB8.3575E-067.7843E-06-6.06075E-05-4.32508E-05
hB *E*2.5259E-066.1704E-06-2.25257E-05-1.30924E-05
hB*hB6.1914E-06-7.451E-071.6373E-06-1.4025E-06
hAC *EB4.17036E-052.4867E-06-8.40397E-05-6.8449E-06
EB*E*2.34109E-053.4547E-06-3.06634E-05-1.8974E-06
hB*EB1.5431E-06-2.6824E-06-1.68535E-053.5859E-06
EB*EB2.8965E-06-5.528E-07-1.74637E-051.4018E-06
hAC *ESUBG1.1711E-060.0000054917.128E-07-3.41892E-05
ESUBG*E*-3.461E-074.4916E-065.702E-07-1.04126E-05
hB*ESUBG5.5404E-060.000002114-1.8562E-06-2.26448E-05
EB*ESUBG3.2144E-06-1.213E-075.3833E-06-3.1661E-06
ESUBG*ESUBG3.526E-079.21E-08-2.1207E-06-0.000009591

NOTES: For Equation 18, if the estimated tensile strain is less than 0, set tensile strain to 0.000001.
For Equations 19, 20 and 21, if the vertical compressive strain is greater than 0, set vertical compressive strain to 0.000001, otherwise vertical compressive strain = estimated value * -1.

Compute Distress and IRI for Flexible Pavements

Alligator Cracking

Equation 24 - The term ACRK is equal to begin expression begin fraction begin numerator 89.644 end numerator over begin denominator 0.1331 addition operator 7.6199 summation symbol index equals 1, upper limit n equals k of the term FDAM begin superscript -08361 end superscript end denominator end fraction end expression. (24)

A description of the variables required by the alligator cracking model is presented in Table 17.

Table 17. Input Variables Required by the Alligator Cracking Model
Description of Input Variables Required by the Alligator Cracking Model Source
ACRK = alligator cracking, percent lane area —
k = total number of months in analysis period —
FDAM = fatigue at the bottom of the HMA layer
Is equal to begin expression begin fraction begin numerator begin uppercase MESAL end uppercase end numerator over begin denominator begin uppercase N end uppercase begin subscript f end subscript end denominator end fraction end expression.		 —
MESAL = total 18-kip ESALs for each given month See section on estimating traffic
Nf = allowable number of 18-kip ESALs applications
Is equal to begin complex expression 1.2347 multiplication operator 0.00432 multiplication operator k begin subscript 1 end subscript multiplication operator begin uppercase C end uppercase multiplication operator open parenthesis begin fraction begin numerator 1 end numerator over begin denominator begin uppercase E end uppercase superscript asterisk end superscript end denominator end fraction close parenthesis begin superscript 1.281 multiplication operator beta begin subscript 1 end subscript end superscript multiplication operator open parenthesis begin fraction begin numerator 1 end numerator over begin denominator eta begin subscript t end subscript end denominator end fraction close parenthesis begin superscript 3.9492 multiplication operator beta begin subscript 2 end subscript end superscript.		 —
The term k begin subscript i end subscript is equal to the complex expression begin fraction begin numerator 1 end numerator over begin denominator 0.000398 addition operator begin fraction begin numerator 0.003602 end numerator over begin denominator 1 addition operator e begin superscript open parenthesis 11.02 subtraction operator 3.49 multiplication operator h begin subscript begin uppercase AC end uppercase end subscript end superscript end denominator end fraction end complex expression. —
hAC = HMA thickness, in HPMS program (Thickness_Flexible)**
C = 10M —
The term M is equal to 4.84 open parenthesis begin fraction begin numerator begin uppercase V end uppercase begin subscript b end subscript end numerator over begin denominator begin uppercase V end uppercase begin subscript a end subscript addition operator begin uppercase V end uppercase begin subscript b end subscript end denominator end fraction subtraction operator 0.69 close parenthesis. —
Va = HMA mix as-constructed air voids, percent PHT Tool default data tables
Vb = HMA mix effective as-constructed placed volumetric binder content PHT Tool default data tables
β1 = 1.2 —
β2 = 1.0672 —
E* = HMA dynamic modulus, psi () See Equation 11
εt = tensile strain at the bottom of the HMA layer See Equation 20

**Also available in HPMS Estimates table.

Rutting

TRUT = ACRUT + BASERUT + SUBGRUT    (25)

Where
TRUT = total pavement rutting, in
ACRUT = rutting in the HMA layer, in

Equation 26 - Is equal to 0.000493 multiplication operator begin uppercase MAAT end uppercase begin superscript 1.5606 end superscript multiplication operator summation symbol index equals 1 upper bound equals k open parenthesis eta begin subscript v begin uppercase HMA end uppercase end subscript multiplication operator begin uppercase MESAL end uppercase begin superscript 0.4791 end superscript close parenthesis. (26)

BASERUT = rutting in the base layer, in

= 4.4833*εvBASE*hB*CESAL0.1307   (27)

SUBGRUT = rutting in the subgrade layer, in

Equation 28 - Is equal to open parenthesis 0.0025 begin uppercase PRECIP end uppercase addition operator 0.000080 begin uppercase FI end uppercase close parenthesis open parenthesis begin fraction begin numerator eta begin subscript o end subscript end numerator over begin denominator eta begin subscript r end subscript end denominator end fraction close parenthesis begin superscript 0.9692 end superscript e begin superscript minus sign open parenthesis begin fraction begin numerator rho end numerator over begin denominator begin uppercase CESAL end uppercase end denominator end fraction close parenthesis begin superscript beta end superscript end superscript open parenthesis eta begin subscript v begin uppercase SUBG end uppercase end subscript close parenthesis begin superscript 0.01116 end superscript. (28)

A description of input variables required by the rutting model is presented in Table 18.

Table 18. Input Variables Required by the Rutting Model
Description of Input Variables Required by the Rutting Model Source
MAAT = mean annual air temperature, °F PHT Tool default data tables
k = total number of months in analysis period —
MESAL = total 18-kip ESALs for each given month See section on estimating traffic
εvHMA = vertical strain in the middle of the HMA layer See Equation 21
εvBASE = vertical strain in the middle of the BASE layer See Equation 22 (use representative εvBASE for the entire analysis period)
hB = base layer thickness HPMS program (Base_Thickness)**
CESAL = total 18-kip ESALs for entire analysis period See section on estimating traffic
εvSUBG = vertical strain in the top 12 in. of the subgrade See Equation 22 (use representative εvSUBG for the entire analysis period)
PRECIP = mean annual precipitation or rainfall PHT Tool default data tables
FI = mean annual freezing index, °F days PHT Tool default data tables
β = 0.7*10(-0.61119-0.017638Wc) —
ρ = 10(0.622685 + 0.541524Wc) —
The term open parenthesis begin fraction begin numerator eta begin subscript o end subscript end numerator over begin denominator eta begin subscript r end subscript end denominator end fraction close parenthesis is equal to 10 begin superscript open parenthesis 0.74168 addition operator 0.08109 begin uppercase W end uppercase c subtraction operator 0.000012157 multiplication operator begin uppercase M end uppercase r close parenthesis end superscript. —
Wc = soil moisture content
Is equal to 51.712 multiplication operator begin uppercase CBR end uppercase begin subscript begin uppercase SUBG end uppercase end subscript begin superscript -0.3586 multiplication operator begin uppercase GWT end uppercase begin superscript 0.1192 end superscript end superscript.		 —
GWT = depth to ground water table
The term begin uppercase CBR end uppercase begin subscript begin uppercase SUBG end uppercase end subscript is equal to open parenthesis begin fraction begin numerator begin uppercase M end uppercase begin subscript r end subscript end numerator over begin denominator 2555 end denominator end fraction close parenthesis begin superscript 1.5625 end superscript.		 PHT Tool default data tables (typical range is 5 to 40 ft
Mr = subgrade resilient modulus at optimum moisture content, psi PHT Tool default data tables

**Also available in HPMS Estimates table.

Transverse Cracking

Equation 29 - The term TCRK is equal to open parenthesis begin fraction begin numerator begin uppercase AGE end uppercase end numerator over begin denominator begin uppercase AGE end uppercase addition operator 1 end denominator end fraction multiplication operator begin fraction begin numerator 6000 end numerator over begin denominator 1 addition operator 1.03 begin superscript open parenthesis -5.9033 multiplication operator begin uppercase AGE end uppercase addition operator begin uppercase FACTOR end uppercase close parenthesis end superscript end denominator end fraction. (29)

Where
TCRK = number of transverse cracks per mile
AGE = pavement age in years

FACTOR = 1472.2 + 3.167*HHMA - 879.8*loglogη - 16.98*Va - 3.385*PCT¾ - 0.25*FTCYC    (30)

A description of input variables required to compute FACTOR is presented in Table 19.

Table 19. Input Variables Required to Compute FACTOR
Description of Input Variables Required to Compute Factor Source
hAC = HMA thickness, in HPMS program (Thickness_Flexible)**
ηaged = aged viscosity at HMA surface, cP See Equation 12
Va = HMA mix as-constructed air voids, percent PHT Tool default data tables
PCT3/4 = percent passing 3/4 in sieve for the HMA mix PHT Tool default data tables
FTCYC = mean annual air freeze-thaw cycles PHT Tool default data tables

**Also available in HPMS Estimates table.

Smoothness (IRI)

IRI = INI_IRI + 40.0*MRUT + 0.4*CRACK + 0.008*TRANS_CK + 0.015*SF    (31)

Where
INI_IRI = initial IRI, in/mi (use MEPDG default of 63.4 in/mi)
MRUT = total rutting, in (see Equation 25)
CRACK = alligator cracking, percent lane area (see Equation 18)
TRANS_CK = transverse cracking, ft/mile (see Equation 29)
SF = FROSTH + SWELLP*AGE1.5
FROSTH = LN([PRECIP+1]*FINES*[FI+1])
SWELLP = LN([PRECIP+1]*CLAY*[PI+1])

A description of the variables to compute FROSTH and SWELLP are presented in Table 20.

Table 20. Input Variables Required to Compute FROSTH and SWELLP
Description of Input Variables Required to Compute FROSTH and SWELLP Source
FINES = FSAND + SILT  
AGE = pavement age since construction or reconstruction, years HPMS program
(Year_Last_Improvement OR Year_Last_Construction)
PI = subgrade soil plasticity index  
PRECIP = mean annual precipitation or rainfall PHT Tool default data tables
FI = mean annual freezing index, °F days PHT Tool default data tables
FSAND = amount of fine sand particles in subgrade (percent of particles with sizes between 0.074 and 0.42 mm) PHT Tool default data tables
SILT= amount of silt particles in subgrade (percent of particles with sizes between 0.074 and 0.002 mm) PHT Tool default data tables
CLAY = amount of clay size particles in subgrade (percent of particles less than 0.002 mm) PHT Tool default data tables

*Also available in HPMS Estimates table.

Compute Distress and IRI for Composite (HMA/JPCP) Pavement

Reflection Transverse Cracking

Equation 32 - The term RCRK is equal to begin expression begin fraction begin numerator 100 end numerator over begin denominator 1 addition operator 2.718 begin superscript a open parenthesis c close parenthesis addition operator b open parenthesis begin uppercase AGE end uppercase close parenthesis open parenthesis d close parenthesis end superscript end denominator end fraction end expression. (32)

Where
RCRK = percent of cracks reflected, percent area of reflection cracking assumes a reflected crack width of 1ft.
AGE = pavement age (years after asphalt overlay placement, see HPMS program)
a = 3.5+0.75*Heff
b = -0.688 - 3.373*Heff - 0.9154
c = 1.0
Heff = HHMA - 1 (for JPCP with good joint load transfer efficiency, i.e., faulting < 0.03 in)
Heff = HHMA - 3 (for JPCP with poor joint load transfer efficiency, i.e., faulting ≥ 0.03 in)
HHMA = asphalt layer thickness (see PHT Tool default data tables)

The values of the reflective cracking model parameters d are presented in Table 21.

Table 21. Values of the Reflective Cracking Model Parameter d
Effective Asphalt Overlay Thickness, in Delay Cracking by 2 yrs (Recommended for High Type Pavements) Accelerate Cracking by 2 yrs (Recommended for Other Pavements Types)
< 40.63.0
4 to 60.71.7
> 60.81.4

*The following functional classed are classified as high-type: Interstates and principal arterials (e.g., U.S. highways, expressways, and freeways). Local routes and state highways (e.g., minor arterial, minor and major collectors, and local roadways are mostly classified as other.

Smoothness (IRI)

The IRI prediction model adopted from the MEPDG is as follows:

IRI = INI_IRI + 40.8*MRUT + 0.575*CRACK + 0.0014*TRANS_CK + 0.00825*SF   (33)

All variables are as already defined. Note that TRANS_CK includes all reflection cracking (transverse joints & transverse cracks) from the existing jointed concrete pavement and HMA transverse cracking.

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Updated: 10/18/2012