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Federal Aviation Administration Airport Pavement Working Group Meeting M echanistic- E mpirical PCN Procedure Gabriel Bazi, PhD, PE. Atlantic City, NJ / April 25, 2012. History of Dynatest ME PCN Procedure. Revised ME PCN Procedure.
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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
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 • PCN Presented today
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)…
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 • …
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
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
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
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
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 Structural Evaluation is Complete
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 If dt > 1 Decrease dt to 1: wp < gross weight PCN < ACN
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
Various Forms of Empirical Models Use B in previous equation to determine wp
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
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
Flexible Pavement Example • 2 Seasons: Season 2 (9 months) Season 1 (3 months) h = 6 in AC: E1= 250 ksi E1= 500 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
Aircraft Mix used in the Analyses B727-200 A330-200 Notes: Coverages assumed to be same for AC fatigue and AB/SG PD failure criteria. Load uniformly distributed throughout the year
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:
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:
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 cracking
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
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
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
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) Consider all failure criteria for PCN Calculation
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)
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
Thank You Thank You
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
Appendix B: Rigid Pavement Example • 2 Seasons: Season 2 (6 months) Season 1 (6 months) h = 14 in PCC: 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 = 141.4 pci 1) Code C SG: h = ∞ 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
Aircraft Mix used in the Analyses A320-100 B737-800 Note: Load uniformly distributed throughout the year
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
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)
PCN • Weighted k-value Subgrade Code C • PCN Calculation: 1) ACN for permissible gross weight calculated using COMFAA • PCN: 54/R/C/W/T