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**Federal Aviation Administration Airport Pavement Working Group Meeting**

Mechanistic-Empirical PCN Procedure Gabriel Bazi, PhD, PE Atlantic City, NJ / April 25, 2012

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**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

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**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

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**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)…

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**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 …

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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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

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**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

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**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

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**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

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**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:

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**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:

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**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)

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**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

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**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

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**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

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**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

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**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

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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

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**Discussion & Questions**

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Thank You Thank You

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**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

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**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 = 26k1.284 FAA AC 150/5320-6E page 34 Note: Interface assumed to be bonded

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**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

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**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

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**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

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**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

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