1. Federal Aviation Administration Airport Pavement Working Group Meeting
Mechanistic-Empirical PCN Procedure Gabriel Bazi, PhD, PE
Atlantic City, NJ / April 25, 2012

2. History of Dynatest ME PCN Procedure
ELPCN
 ≈1987 – 1998
 DOS Version
WinPCN
 1998 – 2003
 Windows Version
ELMOD PCN
 2003 – Present
 ELMOD sub-module
Same PCN procedure for all versions

3. Revised ME PCN Procedure
Existing and revised procedures are similar except for the last step in PCN calculation
Existing Procedure
Permissible response
ESWL
PCN
Revised procedure
Permissible gross weight
Presented today

4. ME PCN Procedure Advantages
ME PCN procedure has same advantages as ME analysis
Flexible and rigid pavements
Rehabilitation or new design
Layer moduli (stiffnesses)
No need for layer equivalency factors/equivalent pavement…
Considers the failure modes of all layers:
Fatigue cracking for AC and PCC layers
Permanent deformation for unbound layers (base, subbase, subgrade)…

5. ME PCN Procedure Advantages
Considers various seasons
AC moduli change due to temperature
Unbound layer moduli change due to moisture (& freezing and thawing)
Different aircrafts (weights, repetitions….)
Aircraft lateral wander
Normal distribution
P/C …

6. ME PCN Procedure 100% compatible with ME design
If Remaining life (RL) = Design Life (DL)  PCN = ACN
If RL < DL  PCN < ACN
If RL > DL  PCN > ACN

7. Layer Moduli New Design
WES modulus procedure for unbound layer moduli [UFC TM /AFJMAN ]
Currently used in FAARFIELD
Lab/Assumed
Existing structures (Rehabilitation)
HWD testing and backcalculation
LWD for unbound layers

8. Flexible Pavement Structural Evaluation
Calculate critical stresses and strains under load
Fatigue cracking: Horizontal tensile strain at bottom of AC
Permanent deformation in unbound layers: Vertical compressive stress or strain on top of layer
Vertical compressive stress or strain on top of the base layer AC
Horizontal tensile strain at the bottom of the AC layer
Vertical compressive stress or strain on top of the subgrade AB SG

9. Rigid Pavement Design Calculate critical stresses under load
Fatigue cracking: Horizontal tensile stress at bottom of PCC
PCC
Horizontal tensile stress at the bottom of the PCC layer
Support

10. ME Structural Evaluation
For each failure criterion, calculate the total damage (dt) using empirical models
If dt  1.0  Structure is adequate
If dt > 1.0  Structure is not adequate
Remaining life
Limit remaining life to 40 years
So far calculation is done similar to FAARFIELD
Structural Evaluation is Complete

11. Permissible Gross Weight (wp)
Each aircraft from mix is evaluated separately (or just evaluate aircraft with largest ACN):
Total damage (dt) calculated for all aircrafts combined
If dt < 1  Increase dt to 1:
wp > gross weight  PCN > ACN
Typically ACN with largest aircraft will produce largest PCN (not always)
If dt > 1  Decrease dt to 1:
wp < gross weight  PCN < ACN

12. Permissible Gross Weight (wp) 1) 2)
The permissible gross weight is the weight that would cause a total damage of 1.0 with the traffic mix converted to each aircraft.
where w: gross weight of aircraft,
wp: permissible gross weight, and
dt: total damage
B: parameter from empirical model
Permissible Weight Multiplier
1) Assuming one model is used per criterion
2) Refer to Appendix A for alternative calculation procedure

13. Various Forms of Empirical Models
Use B in previous equation to determine wp
Check
First equation is similar to FAA AC fatigue model
Second equation is similar to FAA SG PD model

14. PCN Calculation
Using the permissible gross weight, calculate the ACN for each aircraft and assign it as its PCN
COMFAA
Power curve fit using ACNs for min. and max. weights
Polynomial curve fit using ACNs for min., max., ½ min. and 2max. weights
Select the largest PCN from the mix as the PCN for the structure

15. Subgrade Category for ACN/PCN
If subgrade category (CBR or k-value) changes
along a feature (e.g. FWD test points along a runway, or various CBR tests on a taxiway…)
determine average conditions for PCN calculation
over various seasons
determine weighted average conditions for PCN calculation

16. Flexible Pavement Example
2 Seasons:
Season 1 (3 months)
Season 2 (9 months)
AC:
h = 6 in
E1 = 500 ksi
E1 = 250 ksi
AB:
h = 36 in
E2 = 37.5 ksi
E2 = 50 ksi
E3 = 6 ksi
CBR = 4
Code D
E3 = 24 ksi
CBR = 16
Code A
SG:
h = ∞
 = 0.35 for all layers

17. Aircraft Mix used in the Analyses
MTOW
(lb)
% Gross
on One
Main
Gear
Type
Wheel
Spacing
(in)
Axle
Tire
Pressure
(psi)
Annual Coverages n
Adv. B C Basic
185,200
47.5
Dual 34 --
148
1,000
A std
509,047
Dual Tandem 55 78
206 B A
Notes:  Coverages assumed to be same for AC fatigue and AB/SG PD failure criteria.
 Load uniformly distributed throughout the year

18. AC Fatigue Cracking Failure Model
AC Fatigue Cracking Failure Model (USACE/FAA)
log(C) = 2.68 – 5log() – 2.665log(E)
where: C = number of coverages to failure
E = AC modulus (psi)
 = horizontal strain at the bottom of the surface asphalt layer
For this model:

19. AB/SG Permanent Deformation Model
Unbound Material Permanent Deformation (Kirk)
where: 1,p = vertical stress on top of unbound layer, ksi
N = number of coverages in millions
E = modulus of material, ksi
E0 = 23.2 ksi
C = 1.16 for E<E0
C = 1 for E E0
For this model:

20. Flexible Pavement Example
Analysis period = 20 years
1) Analysis performed using ELMOD (w/ LET)
2) Calculated using a maximum remaining life of 40 years
Lowest dtB =  PCN analysis is controlled by the AC layer fatigue cracking
Layer
Criterion
Total Damage dt
Remaining Life (Years) 1) B
Permissible Weight Multiplier (dtB) 1
AC Fatigue Cracking
2.604
7.7
– 0.2
0.826 2
AB Permanent Deformation
1.683
11.9
– 0.307
0.852 3
SG Permanent Deformation
0.103
> 40 )
Lowest Permissible Weight Multiplier (dtB)

21. PCN Weighted subgrade modulus CBR = 13  Subgrade code A
PCN Calculation:
1) ACN for permissible gross weight calculated using COMFAA
PCN: 45/F/A/X/T
Aircraft
Gross Weight w
(lb)
Permissible Weight Multiplier (dtB)
Permissible Gross Weight (wp)
ACN = PCN 1)
Adv. B C Basic
185,200
0.826
152,975
36.0
A std
509,047
420,473
45.4
Select largest ACN as PCN for the structure

22. ACN-PCN Comparison Largest ACN: PCN: 45/F/A/X/T
Remaining life (7.7 years) < Design life (20 years)  PCN < ACN
Analysis controlled by AC fatigue cracking
About 3-inch of AC are needed to restore the structural capacity
Aircraft
ACN
A std
57/F/A

23. Subgrade Category Selection
ACN-PCN Ratios calculated for various subgrade categories
ACN-PCN ratios are almost the same for all subgrade categories
Subgrade code selection is not critical (at this level)
Subgrade properties are important in ME analysis
Subgrade Code
ACN
PCN
ACN-PCN Ratio A
57.0/F/A
45.4/F/A/X/T
1.26
1.3 B
61.9/F/B
48.3/F/B/X/T
1.28 C
71.6/F/C
54.8/F/C/X/T
1.31 D
96.8/F/D
73.1/F/D/X/T
1.32

24. If Only SG Criterion was Considered!!
Permissible Weight Multiplier (dtB) = > 1.0
PCN >ACN
Knowing that the pavement is failing (RL = 7.7 years)
If large ACN aircrafts are allowed, then the damage would be accelerated
Refer to Appendix B for rigid pavement example
Procedure is similar to USACE PCASE procedure as shown in M.Y. Shahin “Pavement Management for Airports, Roads and Parking Lots” book – second edition on pages
Consider all failure criteria for PCN Calculation

25. Notes For PCN calculation, limit calculated remaining life to 40 years
PCN values are associated with the traffic used in the evaluation
An increase in traffic during the evaluation period will reduce the PCN
PCN is highly dependent on aircraft mix
Existing structures: PCN to be calculated for existing conditions and after rehabilitation, if needed
When PCN is evaluated for several points on a feature, report 84th percentile (Average – standard deviation)
In this case it is the 16th %ile

26. Notes
Possibly complement the PCN number with the additional number of allowable coverages of aircraft having ACN = PCN
Instead of having unlimited operations when
ACN/PCN ≤ 1.0

27. Discussion & Questions

28. Thank You
Thank You

29. Appendix A: Permissible Gross Weight (wp)
For every aircraft, calculate the equivalent number of load repetitions that would cause the same total damage (dt) as the aircraft mix = Allowable number of load reps. (N)  Total damage (dt)
Calculate the allowable stress or strain using the empirical model for the equivalent number of load repetitions calculated in step 1
Calculate the permissible gross weight (wp) as the MTOW multiplied by the ratio of allowable stress or strain (from step 2) and the actual stress or strain of that aircraft (use of response ratio is valid if contact area is constant)
Note: If various seasons are available, the use of any season would provide same permissible gross weight

30. Appendix B: Rigid Pavement Example
2 Seasons:
Season 1 (6 months)
Season 2 (6 months)
PCC:
h = 14 in
E1 = 4,000 ksi,  = 0.15
E1 = 4,000 ksi,  = 0.15
E3 = 7.5 ksi,  = 0.35
k = 82.4 pci 1)
Code D
E3 = 15 ksi,  = 0.35
k = pci 1)
Code C
SG:
h = ∞
Master2FAA.mde
1) Equation used to convert E (psi) to k (pci):
ESG = 26k1.284 FAA AC 150/5320-6E page 34
Note: Interface assumed to be bonded

31. Aircraft Mix used in the Analyses
MTOW
(lb)
% Gross
on One
Main
Gear
Load (lb)
Type
Wheel
Spacing
(in)
Tire
Pressure
(psi)
Annual Coverages n B
174,700
46.78
81,725
Dual 34
205
1,200 A
150,796 47
70,874
36.5
200
1,500
R = in (B )
R = in (A ) A B
Note: Load uniformly distributed throughout the year

32. PCC Fatigue Cracking Failure Model
PCC Fatigue Cracking Failure Model (PCA)
where: PCC = Tensile stress at bottom of PCC (ksi)
N = No. of coverages to failure in millions
E = Modulus of PCC (ksi)
For this model
Used E = 57000*f’c^0.5 and Mr = 9.5*f’c^0.5

33. Rigid Pavement Example
Analysis period = 20 years
1) Responses calculated using MnLayer at center of slab
dtB = 1  PCN = ACN
Remaining life = Analysis period (20 years)
Layer
Criterion
Total Damage dt
Remaining Life (Years) 1) B
Permissible Weight Multiplier (dtB) 1
PCC Fatigue Cracking
1.0
20.0
– 0.057

34. PCN Weighted k-value  Subgrade Code C PCN Calculation:
1) ACN for permissible gross weight calculated using COMFAA
PCN: 54/R/C/W/T
Aircraft
Gross Weight w
(lb)
Permissible Weight Multiplier (dtB)
Permissible Gross Weight (wp)
ACN = PCN 1) B
174,700
1.0
54.1 A
150,796
44.3
Select largest ACN as PCN for the structure