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Analysis of Flexible Overlay Systems: Application of Fracture Mechanics to Assess Reflective Cracking Potential in Airfield Pavements Fang-Ju Chou and William G. Buttlar FAA COE Annual Review Meeting October 7, 2004 Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign Outline - Progress Since Last Review Meeting Development/Verification of Fracture Mechanics tools for ABAQUS Application of Tools to Study Reflective Cracking Mechanisms in AC Overlays Placed on PCC Pavements - Current/Future Work 2 Problem statement - Review Functions of Asphalt Overlays (OL): To restore smoothness, structure, and minimize moisture infiltration on existing airfield pavements. Problem: The new asphalt overlay often fails before achieving its design life. Cause: Reflective cracking (RC). 3 Problem statement ~ Cont. Current FAA Flexible OL Design Methodology: Rollings (1988’s) Assumptions used: 1. The environmental loading (i.e. temperature) is excluded. 2. A 25% load transfer is assumed to present between slabs. 3. Structural deterioration is assumed to start from underlying slabs. Reflective cracking (RC) will initiate when structural strength of slabs is consumed completely. RC will grow upward at a rate of 1-inch per year. However, joint RC often appears shortly after the construction especially in very cold climatic zones. 4 Ongoing/Upcoming Research • Expand 3D Parametric Study to Investigate: – Additional Pavement Configurations and Loading Conditions – Effect of Joint LTE on Critical Responses and Crack Propagation • Development of Two Possible Methods to Consider Reflective Cracking Potential – Simpler than Crack Propagation Simulation – Less Sensitive to Singularity at Crack/Joint 5 Fracture Analysis: J-integral Estimate Stress Intensity Factors (KI and KII) at Tip of an Inserted Crack (Length will be Varied) Compute Path Integral Around Various Contours 6 Ph.D. Thesis of Fang-Ju Chou: Objectives: 1. Introduce a robust & reliable 4. To investigate how the following parameters affect the method (J-integral & potential for joint RC in rehab. interaction-integral) to obtain airfield pavements. accurate critical OL responses. Bonding condition between slabs 2. Understand the effect of temp. & CTB loading by introducing temp. Load transfer between the gradients in models. underlying concrete slabs 3. Identify critical loading Subgrade support conditions for rehab. airfield Structural condition (modulus pavements subjected to value) of the underlying slabs thermo-mechanical loadings. 7 Limitation of traditional FE modeling at joint FEA applied† on modeling of asphalt overlaid JCP. Limitation: The accuracy of the predicted critical OL responses immediately above the PCC joint was highly dependent on the degree of mesh refinement around the joint. No. of Elements? AC Overlay Concrete Slab CTB Subgrade To seek reliable critical stress predictions, LEFM will be applied in an attempt to arrive at non-arbitrary critical overlay responses around a joint or crack. †Kim and Buttlar (2002); Bozkurt and Buttlar (2002); Sherman (2003) 8 The J-Integral: Path Independence 2 A closed contour = 1 + 2 + 3 + 4 J ui Wn n 1 x ij j ds J1 J 2 J 3 J 4 0 1 1 2 3 4 4 Crack faces On the crack faces (3 and 4 ) n1 = 0 ; Assuming traction free: ijnj = 0 y No contributions to J-integral from segments 3 & 4 J3 = J4 = 0; J2= -J1 ui ui Wn1 x1 ij n j ds Wn1 x1 ij n j ds 2 1 J2 ui Wm1 ij m j ds x1 1 ui Wn1 ij n j ds x1 1 = J1 1 nj nj mj 3 x Elastic homogeneous material reverse the normal of segment 1; new normal mj (points away from tip) Rename mj = nj J-integral is independent of the contour taken around the crack tip 9 Introduction Literature Review Principals of LEFM & Appl. 2D Pav. Model Model Appl. Summary Relation between J and G 1. Rice (1968) showed that the J-integral is equivalent to the energy release rate (G) in elastic materials. (section 3.2.3) For a linear elastic, isotropic material K I2 K II2 K III2 J ' ' (at = ) E E 2 Use J to quantify the propensity of joint RC J Ks J=G For an elastic material G Take Ks as critical stress predictions 2 K I2 K II2 K III G ' ' (at = ) E E 2 For a linear elastic, isotropic material 10 Extraction of Stress Intensity Factors 1. Numerically it is usually not straightforward to extract† K of each mode from a value of the J-integral for the mixed-mode problem. K I2 K II2 K III2 J ' ' (at = ) E E 2 2. 3. The finite element program ABAQUS uses the interaction integral method (Shih and Asaro, 1988) to extract the individual stress intensity factor. The interaction integral method of homogeneous, isotropic, and linear elastic materials is introduced in section 3.3.1. † ABAQUS users manual, 2003, Hibbitt, Karlsson and Sorensen, Inc., Pawtucket, Rhode Island. 11 2D Model Description--Geometry & Material CL Top view • Purpose: analyze a typical pavement section of an airport that serves Boeing 777 aircraft • The selected model geometry and pavement cross sections are based on the structure and geometric info.† of un-doweled sections of runway 34R/16L at DIA in Colorado. 225 in 240 in Traffic Direction Transverse Joint = 0.5in Longitudinal Joint = 0.5in Note: 1-inch = 25.4 mm; 1-psi = 6.89 kPa; 1 pci = 271.5103 N/m3 †Hammons, M. I., 1998b, Validation of threedimensional finite element modeling technique for jointed concrete airport pavements, Transportation Research Record 1629. Cross section AC Overlay Concrete Slabs CTB Subgrade 5 in EAC = 200 ksi; AC = 0.35 0.5 in E = 4,000 ksi 18 in PCC PCC = 0.15 0.2 in 8 in ECTB = 2,000 ksi; CTB = 0.20 k = 200 pci 12 2D Model Description--Loading 57 in 57 in 55in 13.64 in 36 ft (10.97 m) 21.82 in One Boeing-777 200 aircraft: • 2 dual-tridem main gears • Gear width = 36 ft • main gear (6 wheels; 215 psi) • Gross weight = 634,500 lbs (287,800 kg) • Each gear carries 47.5% loading = 301,387.5 lb Boeing 777-200 13 2D Model Description--Loading • Boeing777-200: larger gear width (36 ft = 432 in) • The 2nd gear is about 2 slabs away from 1st gear • Assumption: the distance between gears is large enough such that interactions may be neglected for the study of the OL responses 1 Gear 1 55in 240 in 4 Slab 3 Slab 2 Gear 2 55in 57 in 57 in 432 in 16.32 in 6.82 in 225 in Note: Dimensions not drawn to scale 225 in 14 2D Model Description--Gear Loading Position Modeled range Pos. B Position A AC Overlay Concrete Slab CTB Subgrade Modeled range Subgrade Cut A-A CTB Pos. A Concrete Slab • Position A: edge loading condition; Position B: joint loading condition Corner loading cond. (dash lines) cannot be considered in 2-D models, since the effect of the 3rd dimension cannot be distinguished. Corner AC Overlay • Top view Position B • not practical to investigate every possible gear position four selected positions: have the greatest potential to induce the highest pavement responses under one gear Cut B-B • 2-D pavement crosssection (Cut B-B) 2-D pavement crosssection (Cut A-A) 15 Pos. D Position C AC Overlay Concrete Slab CTB Subgrade Subgrade CTB Rehab. pavements subjected to Pos. A~D modeled as 2D pl condition. Concrete Slab AC Overlay Pos. C Cut C-C Joint discontinuity cannot be correctly modeled using 2D axisymmetric model Modeled range Top view Cut D-D The other two positions: • Position C: selected to study the case where the gear is centered over the joint to maximize bending stresses in the OL • Position D: also has the potential to induce higher bending stresses in an OL Position D 2D Model Description--Gear Loading Position 2-D pavement crosssection (Cut D-D) Modeled range 2-D pavement crosssection (Cut C-C) 16 2D Model Description--Load Adjustment Factor (LAF) One B777-200 wheel P = 50231.25lb 1. 2. 3. 4. 5. Correct excessive wheel load: need to adjust the applied load for pl- models LAF: obtained by reducing the q of the 2-D pl- model until the horiz. stress prediction at the bottom of the asphalt OL matches the 2-D axisymmetric prediction. For this 2-D rehab. pavement model of 5-inch OL under pl- cond., the adjustment factor = 0.697. Reduced contact tire pressure p = 69.7% q will be imposed on 2-D pl- pavement models. Limitations: location, no. of wheel Most simple, effective way 2D axisymmetric model: circular loading CL r = 8.624 in q = 215 psi σX1= -119.1 psi Overlay Concrete Slabs 240 in CTB 2D pl- model: strip loading 17.248 in q =215 psi Overlay σX2=-170.8 psi Concrete Slabs 240 in CTB 17 Results of Selected Loading Positions Before inserting a sharp joint RC into OL, four un-cracked rehab. models subjected to gear loading positions A~D are analyzed. Position A (Cut A-A) Long. Joint Overlay Concrete Slabs 225 in CTB Concrete Slabs 225 in CTB Trans. Joint Overlay Concrete Slabs Long. Joint Overlay CTB Position B (Cut B-B) Position C (Cut C-C) Position D (Cut D-D) Trans. Joint Overlay 240 in Concrete Slabs 240 in CTB 18 Results of Selected Loading Positions (Position A) Tension Comp. PosA: tensile fields are induced at the bottom of OL above PCC joint 19 Results of Selected Loading Positions (Position C) Tension Comp. PosC: tensile fields are also induced at the bottom of OL above PCC joint 20 Results of Selected Loading Positions (Position B) Tension Comp. PosB: compressive fields are present at the bottom of OL above PCC joint 21 Results of Selected Loading Positions (Position D) Tension Comp. PosD: compressive fields are also present at the bottom of OL above PCC joint 22 Inserting Joint RC Crack-tip element Size of crack-tip element influences the accuracy of the numerical solution. (Singular Element) C2 C1 two mesh types are used in the crack-tip region to ensure that a fine enough mesh has been applied around the crack-tip y, v B2 B1 r x, u ℓ 4 ℓ 8 Coarse crack-tip mesh Contour No.8 ℓ 24 Fine crack-tip mesh Contour No.9 0.025” 0.025” Contour No.5 Contour No.2 Crack Faces ( hAC ) 0.025" 5" 0.005 Crack Faces ( hAC ) 0.0075" 5" 0.0015 23 Fracture Model Verification 1. 2. 3. 4. Shih et al. (1976) proposed a disp. correction technique (DCT) to calculate (KI)s using the disp. responses of a singular element Ingraffea and Manu (1980) generalized this approach for mixedmode stress fields at the crack-tip. Showed that the ℓ/a ratio had a pronounce effect on the evaluation of Ks. (note: a = crack length) Using DCT, we can calculate the separate (KI)s & (KII)s in a mixedmode problem based on the displacements of crack flank nodes of singular elements y, v Crack-tip element (Singular Element) Crack faces C2 B2 C1 B1 r x, u ℓ 4 ℓ 2 1 2 K II 1 KI 2 4B 2 C 2 4B1 C1 2 4uB 2 uC 2 4uB1 uC1 u = the sliding disp. at the crack flank nodes = the opening disp. at the crack flank nodes 24 Verification of Reference Sol. (using DCT) v.s. Analytical Sol. 1. 2. To confirm the accuracy of predicting Ks using DCT, a flat plate with an angled crack is modeled under pl- cond. with unit thickness. The closed form solutions for Mode I and Mode II stress intensity factors at either crack-tip are: KI KI (0) cos 2 KII KI (0) cos sin =1000 psi KI(0) = Mode I stress intensity factor ( =0) a = half of the crack width c = half of the plate width Deformation scale factor = 15.0 E = 200 ksi = 0.35 2a 22 v 10" u Right crack tip u v 2c = 10" Deformation scale factor = 27.5 2a = 3.873093344E-02 = tan-1(0.5) Note: drawing not to scale Left crack tip / c 0.0086605" / 5" 1.7321104 25 Verification of Reference Sol. (using DCT) v.s. Analytical Sol. 1. Supplying the disp. responses of the crack flank nodes computed via ABAQUS, the reference Ks using DCT are obtained for both crack tips. 2. Reference Ks compare well with the analytical solutions for both crack tips with the error percentages of 1.58% and 2.8 % for the right and left crack tip. Predicted Stress Intensity Factors (K I and K II) using DCT versus Analytical Solutions Stress Intensity Factors (KI & KII), psi 250 200 204.03 198.48 195.34 150 102.01 99.24 100 97.67 50 0 KI DCT_Prediction_Left KII Analytical Sol. DCT_Prediction_Right 26 Results of Selected Loading Positions 1. 2. Magnitudes of stress predictions immediately above the PCC joint are influenced by the degree of mesh refinement around the joint; not recommended to be taken as critical pavement responses directly In addition to loading positions 1 and 2 (same as positions A and C), 9 gear loading positions are also analyzed for rehabilitated pavements with an initial sharp joint RC Pos1 Pos2 Pos7 of 0.5” or 2.5”. Pos11 (PosC) (PosA) x = 0” x = 34.57” x = 113.46” x = 189.51” Fine & coarse mesh employed AC Overlay 5 in Crack Length = 0.5” or 2.5” 0.5 in Concrete Slab 18 in 0.2 in CTB 4.5 in 13.5 in 225 in 8 in Subgrade 225 in †Pavement geometry not drawn to scale 225 in 27 Determination of Critical Loading Situation (Traffic Loading Only) Eleven traffic loading positions (gear loading positions 1 to 11) Position 7 Two lengths of joint RC Two mesh types (0.5-in and 2.5-in) (fine & coarse at the crack-tip region) 44 Sets of Numerical Results 28 Determination of Critical Loading Situation (Aircraft Loading Only) •Stabilized J-value is obtained when the integral is evaluated a few contours away from the crack tip •J-value of the first contour is least accurate and should never be used in the estimation. •The accuracy of the numerical J-value eventually degrades due to the relatively poor mesh resolution in regions far away from the crack-tip. Loading Position 7 with (a/hAC)=0.1 1.2515E-01 Stable J-value of fine mesh begins J-value (lb/in) 1.2510E-01 1.2505E-01 Stable J-value of coarse mesh begins last available contour or contour far away from the crack-tip 1.2500E-01 1.2495E-01 1.2490E-01 1.2485E-01 1 † 3 5 7 The B777 gear is 113.46" away from the joint 9 11 13 15 17 19 21 23 Contour No. Fine_mesh Coarse_mesh 29 Pos11 KI vs. 11 Loading Positions (Fine Mesh) PosC (Aircraft Loading Only) Mode I SIFs vs. 2 a/hAC ratios 400 0.5 ) 300 Stress Intensity Factor, KI (psi-in 200 -- 11 positions -- Fine & coarse meshes Reduced contact tire pressure = 69.7% 215 psi 100 0 -50 -25 0 25 50 75 100 125 150 175 200 225 -100 Crack-tip mesh -200 Ring8 -300 -400 KI vs. 11 Loading Positions (Coarse Mesh) -500 Pos11 Ring5 PosC -600 400 Distance from joint (inch) 300 Stress Intensity Factor, KI (psi-in 0.5 ) a/hAC =0.5 200 100 0 -50 -25 0 25 50 75 100 125 150 175 200 -100 Crack-tip mesh -200 Ring -300 -400 Ring2 -500 -600 Distance from joint (inch) a/h AC=0.5 a/hAC =0.1 225 a/h AC=0.1 Tensile mode I SIFs are predicted starting from loading position 6, where the center of B777 main gear is at least 93.45” away from the PCC joint. Both mesh types give about the same predictions of mode I SIFs 30 Comparison of Results 1. Castell et al. (2000) applied LEFM for flexible pavement systems and modeled the fatigue crack growth using FRANC2D and FRANC2D/L. 2. A distributed wheel load of 10,000 lb with a 100 psi contact tire pressure was applied above the crack. A compressive KI was found to exist at the crack tip. Differences: conventional FP: softer material below surface; Rehab. pavement: much stiffer slabs below surface. Horiz. Stress distribution would not follow the similar trends. Study of Castell et al. agrees with the present work: The compressive stresses can be predicted at the crack-tip for 2-D pavement models when distributed wheel loads are applied above a crack. 31 Application 1 (Traffic vs. Combined Loadings) Three loading scenarios Aircraft loading position 7 only Aircraft loading position 7 & Temperature loading (TPCC=-23F) Aircraft loading position 7 & Temperature loading (TPCC=-15.3F) 113.46-in Position 7 47.2F Overlay=5”; AC=1.3888910-5 1/F TAC=-1.5F/in 40F TAC=-1.5F/in 54.7F Concrete slabs=18” PCC=5.510-6 1/F 225 in TPCC=-0.85F/in Longitudinal Joint 47.5F TPCC=-1.25F/in 70F 70F 70F 70F CTB=8”; CTB=7.510-6 1/F Subgrade 32 & Appl.K 2D Introduction Literature Review Principals of LEFM Predicted Pav. Model Model Appl. Summary versus Two Crack Lengths I 2500 Num. mode I and mode II SIFs a/hAC = 0.1 and 0.5 Stress Intensity Factor, KI (psi-in 0.5 ) 2260 2000 1811 1669 1351 1500 1000 500 168.3 168.1 0 a/hAC=0.1 Predicted K II versus Two Crack Lengths Aircraft loading only a/hAC=0.5 TPCC= -23 F T PCC = -15.3 F Stress Intensity Factor, KII (psi-in 0.5 ) 100 53.14 50 43.85 13.4 0 -14.2 -50 The predicted mode II SIF is also raised from 14.2 psi-in0.5 to 104 psi-in0.5 or 146.4 psi-in0.5 depending on TPCC. -100 -104 -150 the predicted mode I SIF is raised dramatically from 168.3 psi-in0.5 to 1669 psi-in0.5 or 2260 psi-in0.5 depending on TPCC -146.40 -200 a/hAC=0.1 Aircraft loading only a/hAC=0.5 T PCC = -23 F TPCC = -15.3 F 33 Application 1 (Traffic vs. Combined Loadings) 1. Under the combined loadings, the predicted J-value is much bigger than the one induced by aircraft loading only. 2. The critical loading condition of this 2-D rehabilitated pavement (i.e. 5-inch asphalt overlay on the rigid pavement) is the aircraft loading position 7 plus negative temperature gradients. The bigger the negative temperature differential through the underlying concrete slabs, the higher the predicted mode I SIF. Predicted J-value versus Two Crack Lengths 25 22.50 J-value , (lb/in) 20 14.41 15 12.26 10 8.018 5 0.1251 0.1247 0 a/hAC=0.1 Aircraft loading only a/hAC=0.5 TPCC = -23 F TPCC = -15.3 F 34 Recent Findings Based on the findings of this study, the following conclusions can be drawn: 1. By applying LEFM on modeling of rehab. airfield pavement, reliable critical OL responses (i.e., the J-value, and stress intensity factors at a crack-tip) can be obtained. 2. For the OL system considered in this study, which involved a 5-inch thick asphalt OL placed on a typical jointed concrete airfield pavement system serving the Boeing 777 aircraft, gear loads applied in the vicinity of the PCC joint were found to induce horiz. compressive stress at the RC tip for all load positions considered. The crack lengths studied ranged from 0.5-inch to 2.5inch. 3. Whereas, for un-cracked asphalt OLs, highly localized horiz. tension was found to exist in the asphalt OL just above the PCC joint. 4. Temperature cycling appears to be a major contributor to joint reflective cracking. 35 Research Products 1. 2. 3. 4. UIUC Ph.D Thesis – Fang-Ju Chou: October 1, 2004. FAA COE Report – Fall, 2004. Conference, Journal Papers – In preparation. Models, models, models! 36 Current and Future Work 1. 2. 3. 4. 5. To better simulate the behavior of asphalt OLs, an advanced material model that accounts for the viscoelastic behavior of the asphalt concrete can be implemented in the FEA. However, a thorough understanding of a nonlinear fracture mechanics will be required to properly interpret the modeling results. The use of actual temperature profiles versus the critical OL responses are recommended. This analysis should be conducted in conjunction with the implementation of a viscoelastic constitutive model for the asphalt OL. By inserting appropriate interface elements such as cohesive elements immediately above the PCC joint, a more realistic simulation of crack initiation and propagation can be obtained. Modeling limitations must be addressed. The move to 3D, crack propagation modeling in composite pavements subjected to thermo-mechanical loading pushes the limits of current FEA capabilities. Modeling simplifications and advances in numerical modeling efficiencies are needed. Field Verification 37 Thank you!