Atlantic City, NJ / April 25,

2012

Federal Aviation AdministrationAirport Pavement Working Group Meeting

Mechanistic-Empirical PCN Procedure

Gabriel Bazi, PhD, PE

DCI History of Dynatest ME PCN Procedure

ELPCN ≈1987 – 1998 DOS Version

WinPCN 1998 – 2003 Windows Version

ELMOD PCN 2003 – Present ELMOD sub-module

2

DCI 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 response

Permissible gross weight

» PCN3

Presented today

DCI 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)…

4

DCI 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

…

5

DCI 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

6

DCI Layer Moduli

New Design

WES modulus procedure for unbound layer moduli [UFC

TM 5-822-13/AFJMAN 32-1018]

Currently used in FAARFIELD

Lab/Assumed

Existing structures (Rehabilitation)

HWD testing and backcalculation

LWD for unbound layers

7

DCI

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

Horizontal tensile strain at the bottom of the AC layer

Vertical compressive stress or strain on top of the base layer

Vertical compressive stress or strain on top of the subgrade

AC

AB

SG

DCI

9

Rigid Pavement Design

Calculate critical stresses under load

Fatigue cracking: Horizontal tensile stress at bottom of

PCC

Horizontal tensile stress at the bottom of the PCC layer

PCC

Support

DCI 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

10

td

PeriodDesign Life Remaining

Structural Evaluation

is Complete

DCI Permissible Gross Weight (wp)

11

Total damage (dt) calculated for all

aircrafts combined

Each aircraft from mix is evaluated separately (or just evaluate aircraft

with largest ACN):

If dt < 1 Increase dt to 1:wp > gross weight PCN > ACN

If dt > 1 Decrease dt to 1:wp < gross weight PCN < ACN

DCI 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

12

Btp dww

1) Assuming one model is used per criterion2) Refer to Appendix A for alternative calculation procedure

B

w

Life Remaining

PeriodDesign

Permissible Weight Multiplier

Btd

DCI Various Forms of Empirical Models

13

ClogBconstantσor εlog

Cconstantσor ε

σor ε

constantC

σor εlogB

1constantClog

B

B

1

Use B in previous equation to determine wp

DCI 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 2max. weights

Select the largest PCN from the mix as the PCN for the

structure

14

DCI 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

15

DCI Flexible Pavement Example

2 Seasons:

16

E1 = 500 ksi

E3 = 6 ksiCBR = 4Code D

AC:

SG:

Season 1 (3 months)

E2 = 37.5 ksi AB:

h = 6 in

h = ∞

h = 36 in

Season 2 (9 months)

E3 = 24 ksiCBR = 16Code A

E2 = 50 ksi

E1 = 250 ksi

= 0.35 for all layers

DCI

17

Aircraft Mix used in the Analyses

Aircraft MTOW(lb)

% Grosson OneMainGear

GearType

WheelSpacing

(in)

AxleSpacing

(in)

TirePressu

re (psi)

Annual Coverage

s n

Adv. B727-200C Basic

185,200 47.5 Dual 34 -- 148 1,000

A330-200 std 509,047 47.5 Dual

Tandem 55 78 206 1,000

A330-200B727-200

Notes: Coverages assumed to be same for AC fatigue and AB/SG PD failure criteria. Load uniformly distributed throughout the year

DCI AC Fatigue Cracking Failure Model

AC Fatigue Cracking Failure Model (USACE/FAA)

log(C) = 2.68 – 5log() – 2.665log(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: 18

0.2B5B

1

DCI 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: 19

Cp E

EN )(0174.0

0

307.0,1

0.307B

DCI 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 = 0.826 PCN analysis is controlled by the AC

layer fatigue cracking20

Layer

CriterionTotal

Damage dt

Remaining Life

(Years) 1)

BPermissible

Weight Multiplier (dtB)

1 AC Fatigue Cracking 2.604 7.7 – 0.2 0.826

2AB Permanent Deformation

1.683 11.9–

0.3070.852

3SG Permanent Deformation

0.103 > 40–

0.3071.237 2)

Lowest Permissible Weight Multiplier (dtB) 0.826

DCI 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

21

AircraftGross

Weight w(lb)

Permissible Weight

Multiplier (dtB)

Permissible Gross

Weight (wp)

ACN = PCN 1)

Adv. B727-200C Basic 185,200 0.826 152,975 36.0

A330-200 std 509,047 0.826 420,473 45.4

Select largest ACN as PCN for the structure 45.4

ksi 19.512

42963

DCI 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

22

Aircraft ACN

A330-200 std 57/F/A

DCI 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

23

Subgrade Code ACN PCN ACN-PCN Ratio

A 57.0/F/A 45.4/F/A/X/T 1.26

1.3B 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

DCI If Only SG Criterion was Considered!!

Permissible Weight Multiplier (dtB) = 1.237 > 1.0

PCN >ACN

Knowing that the pavement is failing (RL = 7.7 years)

24

CONSIDER ALL FAILURE CRITERIA FOR PCN

CALCULATION

DCI 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)25

DCI 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

26

DCI

27

Discussion & Questions

DCI

28

Thank You

DCI Appendix A: Permissible Gross Weight (wp)

1. 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)

2. Calculate the allowable stress or strain using the empirical model

for the equivalent number of load repetitions calculated in step 1

3. 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 weight29

DCI Appendix B: Rigid Pavement Example

2 Seasons:

30

E1 = 4,000 ksi, = 0.15

E3 = 7.5 ksi, = 0.35k = 82.4 pci 1)

Code D

PCC:

SG:

Season 1 (6 months)

h = 14 in

h = ∞

Season 2 (6 months)

E3 = 15 ksi, = 0.35

k = 141.4 pci 1)

Code C

E1 = 4,000 ksi, = 0.15

1) Equation used to convert E (psi) to k (pci):ESG = 26k1.284 FAA AC 150/5320-6E page 34

Note: Interface assumed to be bonded

DCI

31

Aircraft Mix used in the Analyses

Aircraft MTOW(lb)

% Grosson OneMainGear

GearLoad

(lb)

GearType

WheelSpacin

g(in)

TirePressur

e (psi)

Annual Coverage

s n

B737-800 174,700 46.78 81,725 Dual 34 205 1,200

A320-100 150,796 47 70,874 Dual 36.5 200 1,500

A320-100

B737-800

Note: Load uniformly distributed throughout the year

DCI 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 model32

5000408.0 0575.0 E

NPCC

0.0575B

DCI 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)

33

Layer

CriterionTotal

Damage dt

Remaining Life

(Years) 1)

BPermissible

Weight Multiplier (dtB)

1 PCC Fatigue Cracking 1.0 20.0–

0.0571.0

DCI PCN

Weighted k-value

Subgrade Code C

PCN Calculation:

1) ACN for permissible gross weight calculated using COMFAA

PCN: 54/R/C/W/T

34

AircraftGross

Weight w(lb)

Permissible Weight

Multiplier (dtB)

Permissible Gross

Weight (wp)

ACN = PCN 1)

B737-800 174,700 1.0 174,700 54.1

A320-100 150,796 1.0 150,796 44.3

Select largest ACN as PCN for the structure 54.1

pci 111.912

141.4682.46