William G. Buttlar Glaucio H. Paulino Harry H. Hilton Phillip B. Blankenship Hervé DiBenedetto. All colleagues and friends

Size: px

Start display at page:

Download "William G. Buttlar Glaucio H. Paulino Harry H. Hilton Phillip B. Blankenship Hervé DiBenedetto. All colleagues and friends"

Gwendoline Gallagher
5 years ago
Views:

1 Ph.D. Final Exam Asphalt Pavement Aging and Temperature Dependent Properties using a Functionally Graded Viscoelastic Model Eshan V. Dave June 5th 29 Department of Civil and Environmental Engineering University of Illinois at UrbanaUrbana-Champaign

2 Sincere gratitude to: William G. Buttlar Glaucio H. Paulino Harry H. Hilton Phillip B. Blankenship Hervé DiBenedetto All colleagues and friends 2

3 Acknowledgements NSF-GOALI Program: Project CMS Koch Materials Company / SemMaterials L.P. USDOT Nextrans Research Center FHWA Pooled Fund Study: TPF-5(132) 3

4 Functionally Graded Viscoelastic Asphalt Concrete Model Motivation and Introduction Viscoelastic Characterization of Asphalt Concrete Viscoelastic FGM Finite Elements Correspondence Principle Based Analysis Time Integration Analysis Application Examples: Asphalt Pavement Summary and Conclusions 4

$(stiffening) with time Asphalt Concrete (Asphalt Mixture) Large fraction produced as hot-mix asphalt (HMA) Most common form of pavement surfacing material (96% of pavement surface in$

5 Constituents: Asphalt Binder Aggregates Asphalt Concrete Asphalt Binder: Derived from Crude Oil Many times modified with polymers to enhance properties Undergoes oxidative aging (stiffening) with time Asphalt Concrete (Asphalt Mixture) Large fraction produced as hot-mix asphalt (HMA) Most common form of pavement surfacing material (96% of pavement surface in United States) 5

6 Motivation Cracking in Asphalt Concrete Pavements and Overlays: Big Picture: Reflective cracking Thermal cracking Predict reflective and thermal cracking in asphalt concrete pavements Design pavements and overlays (with/without interlayers) to prevent thermal/reflective cracking 6

$energy measurements Cohesive zone fracture$

7 Motivation: Progress in Recent Years Significant improvements have been made towards accurate simulation of asphalt pavement systems: Viscoelastic characterization and modeling Fracture energy measurements Cohesive zone fracture model Integrated studies 7

8 Pavements are Non-Homogeneous Structures Sources: 1. Oxidative aging 2. Temperature dependence of material properties 3. Other sources (construction, additives etc.) Depth from Surface (mm) Depth from Surface (mm) Complex Modulus, (GPa) Stiffness (GPa) Pavement Age=15years Depth (mm) Temperature (C) Temperature (C) : AM 3: PM 6: PM 9: PM 12: AM 3: AM Aging gradient generated using Global aging model by Mirza and Witczak (1996) Temperature profiles generated using 8 EICM from AASHTO MEPDG (22)

9 Asphalt Concrete is Viscoelastic Asphalt mixtures from US36 (near Cameron, MO) Temperature = -2ºC 9

10 Layered Motivation Simulation Approaches for Non-Homogeneous Structures Graded E 1 E 2 E 3 E(x) Layered approach is the current state of practice AASHTO MEPDG (Aging Gradient) Asphalt Concrete E(t=t, T(t )) Granular Base Subgrade 1

Viscoelastic Lab Characterization: (Chapter 3) (a) Aging Levels (b) Test Temperatures Pavement Analysis and Design Viscoelastic FGM Properties Anticipated aging conditions (based on distress type and

11 Viscoelastic Lab Characterization: (Chapter 3) (a) Aging Levels (b) Test Temperatures Pavement Analysis and Design Viscoelastic FGM Properties Anticipated aging conditions (based on distress type and design life) Pavement structure and field conditions Temperature distribution 1 Temperature Depth : AM 3: PM 6: PM 9: PM 12: AM 3: AM Viscoelastic FGM finite-element method (Chapters 4 and 5) (a) CP-Based Analysis (b) Time-Integration Analysis Pavement Analysis and Design: (a) Study of critical responses (e.g. tensile strains at bottom of AC layer) (b) Prediction of pavement performance (c) Comparison of design alternatives (structure and/or materials) Few examples shown in Chapter 6 11

12 Objectives Develop efficient and accurate simulation scheme for asphalt concrete pavements Viscoelastic characterization of asphalt concrete (Chapter 3) Viscoelastic analysis a) Correspondence Principle (Chapter 4) b) Time Integration Scheme (Chapter 5) Account for: Aging gradients Temperature dependent property gradients Simulate asphalt concrete pavements and overlay systems (Chapter 6) 12

13 Functionally Graded Viscoelastic Asphalt Concrete Model Motivation and Introduction Viscoelastic Characterization of Asphalt Concrete Viscoelastic FGM Finite Elements Correspondence Principle Based Analysis Time Integration Analysis Application Examples: Asphalt Pavement Summary and Conclusions 13

14 Viscoelastic Characterization Asphalt concrete samples Use of indirect tensile test (IDT), AASHTO-T322 Softer/Compliant Mixtures Crushing under loading head 14

15 Flattened IDT Test Increase contact area to prevent crushing under loading head Viscoelastic solution to bi-axial loading Results indicate flat IDT as a viable alternative to IDT α=5º Creep Complaince (1/psi) 1 x 1-5 IDT Regular (AASHTO T322) Flattened (α = 35 o ).8 Flattened (α = 5 o ) R y P α x Reduced Time (sec) 15

16 Viscoelasticity: Commonly used models for asphaltic materials Could be classified as: Prony series forms (Generalized models) Parabolic models Others Prony series form: Generalized Maxwell Model E( t) τ i = h = i=1 η E i i E i Exp [ t / τ ] i E 1 E 2 E 3 E h η 1 η 2 η 3 η h 16

17 Viscoelasticity: Constitutive models Parabolic Models: Huet-Sayegh Model (1965): Parabolic Units Parabolic Unit (time dependent dashpot) σ k ε ( t) = t, < k A < 1 : 2S2P1D Model: Di Benedetto et al. (25, 27) Fewer parameters compared to generalized models Shared parameters between asphalt binders, mastics and mixtures Other Models: Power law, sigmoidal etc. 17

18 Viscoelasticity: Prony Series Models Generalized Maxwell model is selected for the current study: Applicability to asphaltic and other viscoelastic materials Flexibility w.r.t. fitting of experimental data Equivalence between compliance and relaxation forms Transformations are well established Compatibility with previous research (e.g. GOALI study, ABAQUS etc.) Availability of model parameters for variety of asphalt mixtures 18

Functionally Graded Viscoelastic Asphalt Concrete Model Motivation and Introduction Viscoelastic Characterization of Asphalt Concrete Viscoelastic

19 Functionally Graded Viscoelastic Asphalt Concrete Model Motivation and Introduction Viscoelastic Characterization of Asphalt Concrete Viscoelastic FGM Finite Elements Correspondence Principle Based Analysis Time Integration Analysis Application Examples: Asphalt Pavement Summary and Conclusions 19

20 Constitutive Relationship: Viscoelasticity: Basics t = ( ) ' ( x, t ) ' t = t ε ' σ ( x, t) = C ( x, ξ ξ ) dt ' ' t σ : Stresses, C x, ξ : Relaxation Modulus, ε : Strains Model of Choice: Generalized Maxwell Model ' N t C ( x, t) = Eh ( x) Exp h= 1 τ h ηh Relaxation Time, τ = h E h ( x) E 1 E 2 E h η 1 η 2 η h Time-Temperature Superposition t ' ( x t) ( ) ξ = Reduced Time,, a T, x, t dt ' 2

21 Viscoelasticity: Correspondence Principle Correspondence Principle (Elastic-Viscoelastic Analogy): Equivalency between transformed (Laplace, Fourier etc.) viscoelastic and elasticity equations Elastic Transformed Viscoelastic σ d = 2Gε d ~ σ ~~ d = 2 G ε d σ = 3 K ε ~ ~ σ = 3K ~ ε Extensively utilized to solve variety of nonhomogeneous viscoelastic problems: Hilton and Piechocki (1962): Shear center of non-homogeneous viscoelastic beams Mukherjee and Paulino (23): Correspondence principle for viscoelastic FGMs 21

Graded Finite Elements Homogeneous Graded Graded Elements: Account for material non-homogeneity within elements unlike conventional (homogeneous) elements Lee and Erdogan (1995) and Santare and

22 Graded Finite Elements Homogeneous Graded Graded Elements: Account for material non-homogeneity within elements unlike conventional (homogeneous) elements Lee and Erdogan (1995) and Santare and Lambros (2) Direct Gaussian integration (properties sampled at integration points) Kim and Paulino (22) Generalized isoparametric formulation (GIF) Paulino and Kim (27) and Silva et al. (27) further explored GIF graded elements Proposed patch tests GIF elements should be preferred for multiphysics applications Buttlar et al. (26) demonstrated need of graded FE for asphalt pavements (elastic analysis) 22

Generalized Isoparametric Formulation (GIF) Material properties are sampled at the element nodes Iso-parametric mapping provides material properties at integration points Natural extension of the

23 Generalized Isoparametric Formulation (GIF) Material properties are sampled at the element nodes Iso-parametric mapping provides material properties at integration points Natural extension of the conventional isoparametric formulation MaterialProperties (eg. Ε(x, y)) y (, ) = [ 3 2 ] E x y E Exp x y z=e(x,y) y x x (,) Conventional Homogeneous GIF m = i i i= 1 ( ) ( ) E t N E t Ni = Shape function corresponding to node, m = Number of nodes per element i 23

24 General FE Implementation Variational Principle (Potential): π " ( ) ' '' ( t ) ε ( t ) ' '' ' t = t t = t t 1 ε '' ' ' ' '' = C x, ξ ( t t ) ξ ( t ) dt dt dω ' '' '' 2 t t Ω t' = t = u '' t = t u t " '' P( x, t t ) dt dω '' '' t Ω σ t = Where, π is Potential, ε are strains for body of volume Ω, P is the prescribed traction σ Stationarity forms the basis for problem description: δπ '' ( ) '', '' σ u ' '' ( t ) δε ( t ) ' '' ' t = t t = t t ε '' ' ' ' '' = C x, ξ ( t t ) ξ ( t ) dt dt d ' '' Ω '' t t Ω u t' = t = '' t = t δu t '' P( x t t ) dt dω = '' t Ω σ t = on surface and u is the corresponding displacement Ω σ u u 24

25 Non-Homogeneous Viscoelastic FEM Equilibrium: Solution approaches: 1. Correspondence Principle (CP) ' ( t ) u K x t u K x t t dt F x t t ( ( )) ( ) ( ' ( ) ( )) j ' ij, ξ j + ij, ξ ξ =, ' i + t ã(s) is Laplace transform of a(t); s is transformation variable 2. Time-Integration Schemes Recursive Formulation ( ) % t ( ) % ( ) % (, ) = K x sk s u ij j s Fi x s a% ( s) = a( t) Exp[ st] dt ( ) 25

26 Non-Homogeneous Viscoelastic FEM 1. Correspondence Principle (CP) Benefits: Solution does not require evaluation of hereditary integral Direct extension of elastic formulations Limitations: Inverse transformations are computationally expensive Transform/Convolution should exist for material model and boundary conditions 2. Time-Integration Schemes (Recursive formulation) Benefits: Fewer limitations on material model and boundary conditions Limitations: Convergence studies are required to determine time step size Elaborate formulation and implementation Both are explored in this dissertation 26

27 Functionally Graded Viscoelastic Asphalt Concrete Model Motivation and Introduction Viscoelastic Characterization of Asphalt Concrete Viscoelastic FGM Finite Elements Correspondence Principle Based Analysis σ d 3 σ = = 2 K ε ε G d Time Integration Analysis Application Examples: Asphalt Pavement Summary and Conclusions ~ σ ~~ d = 2 ε ~ ~ σ = 3K ~ ε G d 27

28 CP-Based Implementation (Ch. 4) ( ) % t ( ) % ( ) % (, ) = K x sk s u ij j s Fi x s Define problem in time-domain (evaluate load vector Fi x,.. t and stiffness matrix components and K t ) K ( x ) ( ) t Perform Laplace transform to evaluate F x, s and K x, s.. Solve linear system of equations to evaluate nodal displacement, u% s i ij ij ( ) % ( ) % ( ) i ( ) ij Perform inverse Laplace transforms to get the solution, u t i ( ) Collocation is chosen as method of choice Post-process to evaluate field quantities of interest Verification examples: 1. Analytical solution (Creep extension shown here) 2. Comparison with commercial software 28

29 Displacement in y Direction (mm) y E (x) Verification: Analytical Solution x E E ( x, t) = E ( x) Exp t η 7 ( ) = [ ] E x 1 Exp 2x MPa η = u 8 1 MPa.sec = 2 mm ( x) Analytical Solution FE Solution t = 1 sec t= 5 sec t = 2 sec.5 t = 1 sec x (mm) 29

30 1 Verification with ABAQUS: Material Gradation Normalized Relaxati ion Modulus, E(t)/E ( ) = P h( t) P t Time (sec) 3

31 7 Verification: Comparison with ABAQUS Present Approach Commerical Software (ABAQUS) Graded Viscoelastic Normalized Mid-Span Deflection, u(t)/u Present Approach FGM ABAQUS Simulations Layered gradation 6-Layer (ABAQUS) 9-Layer (ABAQUS) Homogeneous Viscoelastic (Averaged Properties) Mesh Structures (1/5 th span shown) 12-Layer (ABAQUS) FGM Average 6-Layer 9-Layer 12-Layer Time (seconds) 31

32 Functionally Graded Viscoelastic Asphalt Concrete Model Motivation and Introduction Viscoelastic Characterization of Asphalt Concrete Viscoelastic FGM Finite Elements Correspondence Principle Based Analysis Time Integration Analysis Application Examples: Asphalt Pavement Summary and Conclusions 32

33 Time Integration Approach (Ch. 5) ( t ') t u j Kij ( x, ξ ) u j ( ) + Kij ( x, ξ ξ ') dt ' = Fi x, t + t ' ( ) Above could be solved sequentially using Newton-Cotes expansion (material history effect needs to be considered) ( ) ( ξ ) ( ξ ξ ) ( ) 2F t K K u i n ij n ij n 1 j 1 ( ) (,) ( ) n 1 j n = ij + ij ξn ξ n 1 u t K x K ( ξ ξ ) ( ξ ξ ) ( ) K K u t m= 1 ij n m 1 ij n m+ 1 j m Alternatively, recursive formulation could be developed that requires only few previous solutions 33

34 Time-Integration Analysis (Ch. 5) Recursive Formulation (Yi and Hilton, 1994): m h= 1 2 K x v x t t v x t u t = F t t e ( ( )) ( ) 1 2 (, ) ( (, )) ( ) ( ) ij h ij n h ij n h 2 j n i n m e ξ ( t ) n ( ( )) Kij x Exp ( vij ( x, tn 1) ) j ( n 1) j ( n 1) h u t u t h h 1 ( τ ij ( x + & = )) t h ( v ( x, t )) u ( t ) + u ( t ) t u ( t ) + v ( x, t ) u t + R t t & ( ) & ( )} ( ) ( ) ij n 1 h j n 1 j n 1 i ij j i n h Where, tn tn ( vij ( x, tn )) = Exp ξ ( t ) / ( τ ij ( x) ) dt ; ( vij ( x, tn )) = ( vij ( x, t )) dt h 1 ' ' 2 1 ' ' h h h t ' 2 / ( ) ( (, )) && ( 1 ) ' ( ) / ( τ ij ( )) ( j ( n 1 )) e ( ( )) ξ ( ) τ ( ) R t = K Exp t x v x t u t i n h ij ij h ij n h j n + Exp ξ t x R t h Verification examples: 1. Analytical solution (Stress relaxation shown here) 2. Comparison with commercial software h n 1 34

35 Stress in y Dir rection (MPa) y Verification: Analytical Solution E (x) x u (, ) ( ) Analytical Solution Step =.1 sec Step =.2 sec Step =.5 sec Step = 1 sec E E x t = E x Exp t η 7 ( ) = ( ) E x 1 Exp 2x MPa η = 8 1 MPa.sec u = 2 mm ( x).1 u time (sec) 35

36 Verification: Comparison with ABAQUS Temperature Dependent Property Gradient ABAQUS Simulations: Using layered gradation 3 y Temperature distribution T ( y) = e TEMPERATURE INPUT Solid Line: FGM (Present Approach) Dashed Line: Layered Approx. (ABAQUS) 6 Layers 9 Layers Height (mm) Height (mm) Temperature (deg. C) Temperature (deg. C) -2 36

37 Normalized Relaxatio on Modulus, E(t)/E Ref. Temperature = -2 C Material Behavior Log Shift Factor, at Temperature (deg. C) Reduced Time 37

38 Normalized Mi id-span Deflection Present Approach FGM 12 Layer ABAQUS Simulations Layered gradation (converges (Overlaps with Analytical present approach) Solution) Dashed Line: ABAQUS Solid Line: Present approach 3 Layer 6 Layer 9 Layer Mesh Structures (1/5 th span shown) FGM 6-Layer 9-Layer 12-Layer Time (sec) 38

Viscoelastic FGM Finite Elements Correspondence Principle Based Analysis

39 Functionally Graded Viscoelastic Asphalt Concrete Model Motivation and Introduction Viscoelastic Characterization of Asphalt Concrete Viscoelastic FGM Finite Elements Correspondence Principle Based Analysis Time Integration Analysis Application Examples: Asphalt Pavement Summary and Conclusions 39

40 Viscoelastic Lab Characterization: (Chapter 3) (a) Aging Levels (b) Test Temperatures Pavement Analysis and Design Viscoelastic FGM Properties Anticipated aging conditions (based on distress type and design life) Pavement structure and field conditions Temperature distribution 1 Temperature Depth : AM 3: PM 6: PM 9: PM 12: AM 3: AM Viscoelastic FGM finite-element method (Chapters 4 and 5) (a) CP-Based Analysis (b) Time-Integration Analysis Pavement Analysis and Design: (a) Study of critical responses (e.g. tensile strains at bottom of AC layer) (b) Prediction of pavement performance (c) Comparison of design alternatives (structure and/or materials) Few examples shown in Chapter 6 4

41 Example--1: Full Depth AC Pavement Example Based on I-155, Lincoln IL Single Tire load simulated (up to 1 sec loading time) Aged material properties (Apeagyei et al., 28) Surface of AC: Long term aged Bottom of AC: Short term aged 5 x 1 Surface Course (38.1 mm) Relaxation Mod. (MPa) 2.5 Base Course (337 mm) 2 Stabilized Subgrade (34-mm, E =138 MPa ) Subgrade (E = 35 MPa ) y 372, Top , Bottom 1 Reduced Time (sec) Height of AC Layer (mm) x 41

42 Example--1: FEM Discretization Example Two mesh refinement levels Coarse mesh: Graded and Homogeneous simulations Fine Mesh: Layered simulations Coarse Mesh Fine Mesh 6 Layers 5 x 1 Relaxation Mod. (MPa) Layers.5 372, Top , Bottom Reduced Time (sec) Height of AC Layer (mm) 7215 DOFs 1296 DOFs 42

43 Example-1: Simulation Results Material Distributions: FGM Layered Aged Unaged Pavement Responses: Tensile strain at bottom of asphalt layer (to investigate cracking and fatigue) Shear strain at wheel edge (longitudinal cracking/rutting) Comparison of FGM and Layered predictions Compressive strain at interface of asphalt layers 43

44 Peak Strain in x-x Direc ction (x1-6 mm/mm) y Example-1: Strain at Bottom of AC FGM Layered Gradation Aged (Homogeneous) Unaged (Homogeneous) x AC Layers Underlying Layers Strain in x-x Dir Time (second) 44

45 Peak Shear Strain (x1-6 mm/mm) y Example-1: Peak Shear Strain FGM Layered Gradation Aged (Homogeneous) Unaged (Homogeneous) x AC Layers Underlying Layers Shear Strain Time (second) 45

46 345 Example-1: FGM vs. Layered FGM Layered Gradation Aged Properties (Homogeneous) Height of the AC Layer (mm) Surface Course Binder Course ~ 2% Jump y AC Layers Underlying Layers Strain in y-y Dir Strain in y-y Direction (x1-6 mm/mm) 46 x

47 Example 2: Graded Interface Pavement: LA34, Monroe LA Two simulation scenario 1. Step interface 2. Graded interface Step Interface Surface Course RCRI 47-mm 24-mm z PCC 12-mm X Subgrade 24-mm Graded Interface 47

48 Relaxation Mod. (MPa) 3 x Material Properties Surface Course (PG7-16, 19-mm Superpave mix) RCRI (Interlayer) Time (sec) Graded Interface Step Interface Relaxation Modulus (MPa) x 1 4 Top Relaxation Modulus (MPa) x 1 4 Top Reduced Time (sec) Bottom Interface Width Reduced Time (sec) Bottom Interface Width 48

49 4 Peak Tensile Stress in Overlay Step Interface, Surface Mix Overlay Interlayer irection (MPa) Step Interface, Average Stress in x-x Di ~ 3% Step Interface, RCRI Graded Interface Time (sec) 49

50 Functionally Graded Viscoelastic Asphalt Concrete Model Motivation and Introduction Viscoelastic Characterization of Asphalt Concrete Viscoelastic FGM Finite Elements Correspondence Principle Based Analysis Time Integration Analysis Application Examples: Asphalt Pavement Summary and Conclusions 5

51 Summary Viscoelastic graded finite elements using GIF are proposed Correspondence principle based formulation is developed and implemented Recursive formulation is utilized for time-integration analysis Verifications are performed by comparison of present approaches with: Analytical solutions Commercial software (ABAQUS) Asphalt pavement systems are simulated: Aged pavement conditions Graded interfaces 51

52 Conclusions Aging and temperature dependent property gradients should be considered in simulation of asphalt pavements Non-homogeneous viscoelastic analyses procedures presented here are suitable and preferred for simulation of asphalt pavement systems Proposed procedures yield greater accuracy and efficiency over conventional approaches Layered gradation approach can yield significant errors Most pronounced errors are at layer interfaces in the stress and strain quantities. 52

53 Conclusions (cont.) Interface between asphalt concrete layers can be realistically simulated using the procedures discussed in the current dissertation When using the layered approach, averaging at layer interfaces may lead to significantly different predictions as compared to the FGM approach The difference is usually exaggerated with time when a significant viscoelastic gradation is present 53

Other Applications and Future Extensions Micromechanical Predictions

Viscoelastic + Stress Dependent Model Other material models: 2S2P1D

Design of Viscoelastic FGMs E( x, t) Analysis of graded viscoelastic

54 Other Applications and Future Extensions Micromechanical Predictions Transition Layers Characteristics Applications and Extensions Graded Viscoelastic + Stress Dependent Model Other material models: 2S2P1D Power law etc. Design of Viscoelastic FGMs E( x, t) Analysis of graded viscoelastic materials: Metals at high temperature Polymers Geotechnical materials PCC/FRC Biomaterials Food industry ABAQUS UMAT Subroutine 54

55 Thank you for your attention!! Questions?? E1 E2 EN τ1 τ2 τn 55

Eshan V. Dave, Secretary of M&FGM2006 (Hawaii) Research Assistant and Ph.D. Candidate. Glaucio H. Paulino, Chairman of M&FGM2006 (Hawaii)

Asphalt Pavement Aging and Temperature Dependent Properties through a Functionally Graded Viscoelastic Model I: Development, Implementation and Verification Eshan V. Dave, Secretary of M&FGM2006 (Hawaii)