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    EverFE Workshop

    Sacramento, CAMarch 11, 2004

    Bill Davids, PhD, PEUniversity of Maine

    [email protected]

    JPCP Is a Complex Structure

    A 7-12 layer of concrete on a base, sub-base, soil

    Subjected to a variety of axle loads and fatigue effects

    Experiences seasonal and daily temperature changes

    Sawn transverse joints every 12 15 (+/-)

    Transverse joints often doweled for better load transfer

    Adjacent slabs may be tied at longitudinal joints

    Can experience substantial early-age shrinkage

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    JPCP Is a Complex Structure

    I-90 in Washington State

    Dowel Retrofit

    Contraction Joint

    Failure Modes in JPCP

    Panel Cracking

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    Failure Modes in JPCP

    Corner Break

    Failure Modes in JPCP

    TransverseJoint Faulting

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    Failure Modes in JPCP

    Shrinkage Cracking

    Mechanistic-Empirical Designof JPCP

    1. Estimate design

    parameters(thickness, joint

    spacing, etc.)

    2. Predict responseunder axle loads,

    temperature

    changes, etc.

    3. Assess effect ofstresses on

    fatigue life and

    durability

    NotOK

    4. Plans andSpecs, Bid,

    Construct

    OKConstructionProblems?

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    Neg. gradient

    Pos. gradient

    2. Linear thermal gradients through the slab thickness

    Predicting Response of JPCPUsually a Westergaard-type analysis

    ~slab~

    wheel

    1. Three critical wheel load positions are assumed

    Edge Interior Corner

    3. Slabs are founded directly on a dense liquid

    4. Assumes an infinitely large slab, no joint load transfer

    Essential for understanding pavement behavior Critical for developing rational design methods Important in forensic analysis of pavement failures

    2. Predictions of pavement structural response are:

    1. Limitations of Westergaard-type analysis are severe

    3. Clear need exists for better JPCP analysis tools

    Predicting Response of JPCP

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    What is EverFE? Software for the 3D Finite Element (FE) analysis of JPCP

    Incorporates specialized strategies for modeling importantresponse characteristics

    Utilizes problem-specific solvers for efficiency

    Integrated modeling software and graphical user interface

    Intuitive model construction and result visualization

    Allows the generation of models with varying complexity

    Anatomy of an EverFE ModelBasic model characteristics: Up to nine slab/shoulder units Up to three base/subgrade layers Dense liquid supports model Dowels, ties, aggregate interlock

    Loading: Multiple axle types Thermal gradients

    Extensive post-processing: Slab stresses and displacements Dowel results

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    Workshop Objectives

    1. Familiarize you with EverFEs capabilities

    Overview basic finite-element concepts Cover details of EverFE unique capabilities

    2. Give you hands-on experience with the software

    Generate and run models Increasing level of model complexity

    3. Explain what EverFE can and cant do

    Workshop Topics Introduction

    Overview of Finite-Element Concepts

    Generation and Solution of a Simple Model

    Slab-Base Interaction

    Analysis of Thermal Gradients and Slab Shrinkage

    Modeling Dowel Joint Load Transfer

    Modeling Aggregate Interlock Joint Load Transfer

    Example of a More Complex Simulation

    Obtaining EverFE and Program Architecture

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    Finite-Element Concepts

    Mathematical definition: functional method forsolving partial differential equations

    Our definition: well-established numericaltechnique for determining stresses, strains and

    displacements in engineering structures

    Finite-Element Concepts

    Why is FEA so popular?

    Applies to wide classes of problems

    Excellent for irregular geometries

    Easily treats different boundary conditions

    Easily generalized for computer implementation

    Easily handles spatially varying material properties

    Well-suited to nonlinear and dynamic problems

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    Finite-Element Concepts

    Optimization in Mechanical Design

    Analysis of a Welded Connection Analysis and Design of a Floor Slab

    Structural Analysis of a Frame

    Finite-Element ConceptsFE Procedure in a Nutshell:

    Divide a structure into discrete inter-connected finiteelements that meet at nodes

    Make each finite element responsible for defining anapproximate solution over its domain

    Take the original governing differential equation and

    re-cast it using the properties of the finite elements(the mathematically difficult part)

    Solve the resulting system of equations for unknowndisplacements, recover stresses, etc.

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    Finite-Element ConceptsSimple problem from structures/strength of materials

    x

    f(x)

    Elastic rod of length L, elastic modulus E, area A, fixed ends

    Governing differential equation: )(2

    2

    xfdx

    udEA =

    Finite-Element ConceptsFinite-element discretization and solution

    element nodes

    stress

    exact solution

    FE solution

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    Finite-Element ConceptsHow does each element represent the solution?

    1D linear element

    nodal displ.

    interpolated displ.

    1D quadratic element

    constant stress linearly varying

    stress

    Finite-Element ConceptsBasic Element Types in Structures and Solid Mechanics

    2D Elements

    Beam/Truss Element

    Plate/Shell Elements

    t

    3D Elements

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    Finite-Element ConceptsHistory of FE Modeling of Concrete Pavements

    Earliest models treated slabs as plates on elastic solids

    ILLISLAB, JSLAB, etc. released in late 1970s, early 1980sModeling of multiple slabs with 2D plate elements

    Methods for handling joint load transfer

    Researchers began using existing general-purpose 3D codesDetailed models of doweled joints

    Treatment of slab-base interaction

    EverFE was first released in 1998Development started in 1995, has continued until present

    Finite-Element Concepts

    Important Issues to Bear in Mind:

    FEA is an approximate method

    Model must closely mimic physical reality

    Accurate material properties

    Appropriate boundary conditions

    Reasonable representation of loads

    The proper elements need to be used in discretization

    Sufficient mesh refinement is essential

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    Finite-Element ConceptsWhat is the peak tensile stress in a large slab with:

    40 kN wheel load applied at the edge, r= 228 mmSlab properties: t= 254 mm, E= 27,600 MPa, v= 0.20Subgrade k= 0.027 MPa/mm

    40 kN

    ~ Very large slab ~

    Finite-Element Concepts

    1948 Westergaard Solution: max = 1.43 MPa

    Finite-Element Solution:

    Build model with quadratic solid elements

    Represent load with a 405mm x 405mmsquare contact area (equivalent area to circle)

    Critical questions:

    How large a slab to model? How many elements to use in the model?

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    Finite-Element ConceptsFinite-Element Solution:

    Start with a large slab (5000mm x 5000mm)

    Study the effect of mesh refinement on solution

    2 x 2 elements

    5000mm

    5000mm

    24 x 24 elements

    increase #of elements

    Examine the effect of model size on solution

    Finite-Element Concepts

    0 10 20 300.6

    0.8

    1

    1.2

    1.4

    1.6

    Westergaard

    Number of Elements Along Edge(Only even number of elements used)

    Max

    imum

    Stress(MPa)

    Effect of Mesh Refinement on Results

    2 elements throughthickness

    1 element through

    thickness

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    Discretization

    12 u 12

    24 u 24

    Stress (MPa)

    1.48

    1.43

    2 Elements through thickness

    What if we change our discretization slightly?

    Load is centered in element: Element captures linearvariation in stress

    Element cant see peakstress!

    13 u 13

    25u

    25

    1.23

    1.33

    Finite-Element Concepts

    Finite-Element ConceptsEffect of Model Size on Results

    1000 3000 5000 7000 90000.5

    0.7

    0.9

    1.1

    1.3

    1.5

    Max

    imum

    Stress(MPa)

    Slab Size (mm)

    12x12x2 elements for all runs

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    Workshop Topics Introduction

    Overview of Finite-Element Concepts

    Generation and Solution of a Simple Model

    Slab-Base Interaction

    Analysis of Thermal Gradients and Slab Shrinkage

    Modeling Dowel Joint Load Transfer

    Modeling Aggregate Interlock Joint Load Transfer

    Example of a More Complex Simulation

    Obtaining EverFE and Program Architecture

    Generating an EverFE Model

    16-noded interface element

    20-noded brick element

    8-noded dense liquid element

    xy

    z

    beam elementsfor dowels and

    transverse ties

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    Generating an EverFE ModelExample Analysis

    Single slab, 5000mm long x 3600mm wide x 250mm thick Founded on 125mm thick bonded CTB with E= 7000 MPa Single 120 kN, dual wheel axle located at edge

    Plan

    Elevation

    120 kNaxle

    5000mm

    3600mm

    slab

    bonded CTB

    Workshop Topics Introduction

    Overview of Finite-Element Concepts

    Generation and Solution of a Simple Model

    Slab-Base Interaction

    Analysis of Thermal Gradients and Slab Shrinkage

    Modeling Dowel Joint Load Transfer

    Modeling Aggregate Interlock Joint Load Transfer

    Example of a More Complex Simulation

    Obtaining EverFE and Program Architecture

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    Slab-Base InteractionThe base layer is rarely bonded to the slab

    Slip (relative horizontal movement) between slab and base Vertical separation of slab and base may occur

    z=1.01mm, max = 2.53 MPa

    Unbonded Base

    Consider the model we just solved

    Bonded Base (as solved)

    z=0.91mm, max = 1.42 MPa

    Slab-Base InteractionEverFEs treatment of slip and vertical separation

    Slab-base interface may be fully bonded or tensionless

    Slab and base layer are meshed separately

    1mm or 0.1 inslab

    base

    corresponding pairs of nodespermanently tied if base is bonded (linear)

    released under tension if base is unbonded (nonlinear)

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    Slab-Base InteractionWhat are typical values for kand 0?

    Data reported by Rasmussen and Rozycki (2001):

    Base Type

    Rough HMA

    Smooth HMARough Asphalt Stabilized

    Smooth Asphalt StabilizedCement Stabilized

    Granular

    kSB(MPa/mm)

    0.270

    0.0680.200

    0.0654.100

    0.027

    0

    (mm)

    0.250

    0.5100.510

    0.6400.025

    0.510

    Slab-Base InteractionQuick parametric study

    Re-run our single-slab model with an unbonded base Let 0 = 1mm, vary kSB use say 0, 0.5, 1, 2, 5, 10, 50 Study the effect of varying kSB on peak tensile stress

    kSB0.0

    0.5

    1.02.0

    5.010.0

    50.0

    2.532.25

    2.142.01

    1.831.71

    1.51

    Notes

    Shear transfer has a large effect on stress Slab and base maintained full contact Model remained linear

    Approaches bonded solution for large kSB

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    Workshop Topics Introduction

    Overview of Finite-Element Concepts

    Generation and Solution of a Simple Model

    Slab-Base Interaction

    Analysis of Thermal Gradients and Slab Shrinkage

    Modeling Dowel Joint Load Transfer

    Modeling Aggregate Interlock Joint Load Transfer

    Example of a More Complex Simulation

    Obtaining EverFE and Program Architecture

    Analysis of Thermal Gradients

    Corners of slab

    curl upward

    slab

    thickness

    - T

    + T

    Nighttime curling: top of slab cools relative to thebottom after a warm day

    Weight of slab

    pulls downward

    Tension on topof slab

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    Analysis of Thermal Gradients

    Center of slab

    lifts upward

    slabthickness

    T

    - T

    Daytime curling: top of slab heats relative to thebottom during a warm day

    Weight of slabpulls downward

    Tension on bottomof slab

    Analytical solutions for stresses exist for simple cases

    However, thermal gradients are often nonlinear

    Slab-base interaction plays a significant role in response

    Loss of contact between slab and base layer Shear stresses develop at slab-base interface

    Analysis of Thermal Gradients

    slabthickness

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    EverFE idealizes gradients as linear, bilinear or tri-linear Equal vertical spacing assumed between each T

    2Elements

    3Elements

    1Element

    Temperature VariationsUsed in FE Analysis

    Analysis of Thermal Gradients

    Bilinear Gradient:

    Specified TemperatureVariation

    slabthickness

    Analysis of Thermal Gradients

    Trilinear Gradient:

    1Element

    Temperature VariationsUsed in FE Analysis

    Specified TemperatureVariation

    3Elements

    2Elements

    slabthickness

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    Analysis of Thermal GradientsQuick parametric study

    Re-run our single-slab model Consider positive (+5oC/-5oC) and negative (-5oC/+5oC) gradients Consider both bonded and unbonded base with no shear transfer

    Results of Analyses:

    Maximum Principal Stress (MPa)

    Bonded Unbonded

    Positive 1.45 0.94

    Negative 1.22 0.86

    Analysis of Thermal Gradients

    Effect of thermal gradient nonlinearity

    Re-run our single-slab model with nonlinear gradients, unbonded base

    Positive gradient Negative gradient

    Results:

    1.71 MPa for positive (82% increaseover linear gradient)

    0.47 MPa for negative (45% decreaseover linear gradientplus peak stress is at mid-thickness of slab!)

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    Analysis of Slab ShrinkageShrinkage can be simulated as an equivalent thermal gradient

    Example:

    Consider a uniform shrinkage of -0.0001 mm/mm

    Coeff. of thermal expansion = 1.1x10-5/oC

    Equivalent T = -0.0001/1.1x10-5/oC = -9.09oC

    -9.09oC Re-run our single-slab model assuming:

    No slab-base shear transfer A rough HMA base (E= 2000 MPa, kSB = 0.27 MPa/mm,

    0 = 0.25mm)

    Analysis of Slab ShrinkageResults of Simulation

    No slab-base shear transfer

    x= +/-0.25mm at x = 0mm, 5000mm

    No stresses are developed in slab

    BOS Stresses

    max = 0.32 MPa

    With slab-base shear transfer

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    Early-Age Effects Concrete pavements sometimes crack during curing

    Primary causes are thermal and/or shrinkage gradientsthat occur prior to concrete gaining full tensile strength

    Shrinkage cracks innew pavement

    Early-Age EffectsSimple example of how this can be studied with EverFE

    Re-run our single-slab model founded on CTB

    Consider a negative (-5oC/+5oC) thermal gradient

    Unbonded base with no shear transfer

    Examine effect of curing time on ratio of slab stress:slab MOR

    Assumptions:

    MOR = E= (usual ACI equations, psi)

    Assume these relationships are valid for cure times of 128 days Type I cement, published relationship between time and

    Examine effect of curing time on ratio of slab stress:slab MOR

    cf

    6c

    f

    000,57c

    f

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    Early-Age EffectsDetails of Analysis Parameters

    Age-strength relationship

    1.0 5.5 11100 1.172.5 10.3 15230 1.60

    4.0 13.8 17580 1.859.0 20.7 21530 2.27

    28.0 27.6 24870 2.62

    Age E MOR

    days MPa MPa MPa

    cf

    Early-Age EffectsResults of Analysis

    TOS stresses

    Displaced shape 0 5 10 15 20 25 300.30

    0.35

    0.40

    0.45

    0.50

    Maxstress/MOR

    Time (days)

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    Workshop Topics Introduction

    Overview of Finite-Element Concepts

    Generation and Solution of a Simple Model

    Slab-Base Interaction

    Analysis of Thermal Gradients and Slab Shrinkage

    Modeling Dowel Joint Load Transfer

    Modeling Aggregate Interlock Joint Load Transfer

    Example of a More Complex Simulation

    Obtaining EverFE and Program Architecture

    Dowel Joint Load TransferThe challenge: How do we model this?

    separation ofslab and subgrade

    dowel

    wheel load

    high stresson subgrade

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    Dowel Joint Load Transfer Early models used springs at transverse joints

    Other models used beams on elastic foundations

    Primarily 2D models with

    plate elements

    Both 2D models with plateelements and 3D models

    Dowel Joint Load Transfer

    Challenges for idealizing dowels in 3D FE models:

    Dowel-slab interaction and dowel looseness are difficult to treat

    Conventional discretizations require slab and dowel nodes to coincide

    slab mesh lines

    Plan View

    dowels

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    Dowel Joint Load TransferOur solution is the embedded dowel element

    solidelement

    Beam element is constrained to

    displace compatibly with theembedding solid element

    dowels

    slab mesh linesImmediate Benefit:

    Dowel Joint Load Transfer

    Specification of dowels in EverFE

    Dowels can be equally spaced Dowels can be located in wheelpaths Dowels can be manually located by specifying y-coordinate Each row of slabs can have different dowel placements

    Example of dowel placement

    Start a new model with say 2 rows x 3 columns of slabs Go to dowel panel Try different methods of dowel placement

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    Dowel Joint Load TransferTreatment of Dowel-Slab Interaction with EverFE

    Rigorous treatment Either bonded or unbonded Can be severe nonlinearity

    Dowel Looseness

    gap

    length

    gap

    Less rigorous treatment Model remains linear Allows intermediate bond levels

    Dowel-Slab Support Modulus

    Kz = modulus ofdowel support diameter

    Dowel LoosenessSignificance:

    Has been studied experimentally and numerically Small gaps (< 0.50mm) can greatly reduce joint load transfer

    Treatment by EverFE:

    Embedded element formulation is very advantageous Treated as a nodal contact problem Multiple embedded beam elements are used for each dowel

    multipleelements

    singleelement

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    914 mm

    1220

    mm 12 - 6.35 mm dowels

    10 kN

    rubber pad

    k= 0.09 MPa/mm

    51mm

    grease and drinking straw

    Laboratory Tests of Hammons (1997)

    unbonded CTB

    Dowel Looseness

    VerticalDisplacement(mm)

    0.2

    0.4

    0.6experimentalno CTB

    Distance from Joint (mm)

    0-200 100-100-400

    model, no looseness

    model, gap = 0.08 mm

    Dowel Looseness

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    Distance from Joint (mm)

    0-200 100-100-400

    Ve

    rticalDisplacement(mm)

    0.2

    0.4

    0.6

    model, k= 0.09 MPa/mm, gap = 0.08mm

    experimentalwith CTB

    Dowel Looseness

    model, k= 0.07 MPa/mm,gap = 0.08 mm

    Dowel LoosenessExample for 2-slab system:

    Slabs are 4600mm long x 3600mm wide x 250mm thick

    Founded directly on dense liquid, k = 0.03 MPa/mm

    E= 28000 MPa, = 0.20, density = 0

    Center an 80-kN axle with 2 wheels transversely, left of joint

    Set linear aggregate interlock stiffness to 0

    Use 11 evenly spaced 32mm diameter dowels at the joint

    Choose dowel looseness, de-select bonded, Emb = 225 mm

    Set GapB to 125mm (1/2 embedded length)

    We will vary GapA: (0 to 0.4mm in 0.05mm increments)

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    Dowel LoosenessResults of Analysis

    Gap l u LTE(mm) (mm) (mm) (%) (MPa)

    0.00 0.467 0.467 100 0.8650.05 0.528 0.528 81 1.0190.10 0.578 0.384 66 1.1210.15 0.622 0.344 55 1.267

    0.20 0.646 0.323 50 1.3090.30 0.660 0.310 47 1.3230.40 0.664 0.306 46 1.326

    Dowel-Slab Support ModulusBackground:

    More traditional method of idealizing dowel-slab interaction

    Dowel-slab interface idealized with distributed springsResults in a linearly elastic model

    Can specify varying degrees of bond and dowel locking

    Example:

    Consider the same example we just analyzed

    Specify dowel-slab support modulus in lieu of dowel loosenessVary modulus from 1 to a very large value, say 1x10-6

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    Dowel-Slab Support ModulusResults of Analysis

    Kz l u LTE(MPa) (mm) (mm) (%) (MPa)

    1e6 0.474 0.471 99 0.9121e4 0.505 0.457 90 1.182

    5000 0.517 0.447 86 1.223500 0.612 0.357 58 1.310

    100 0.771 0.200 26 1.3621 0.969 0.004 0 1.417

    Dowel Misalignment/Mislocation

    Inaccurately cut transverse joints mislocated dowelsImproperly placed dowels dowel misalignment

    Elevation View

    z

    Actual

    position q

    s

    Intendedposition

    x

    Plan View

    Intendedposition

    ActualPosition qr

    y

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    Dowel Misalignment/MislocationTreatment by EverFE

    Embedded dowel element permits implementation Straightforward when dowel-slab support modulus is specified A different solver must be used when modeling looseness

    Example with EverFE

    Consider the same example we just analyzed Vary x from 0 100mm with Kz = 2000 (LTE = 79% at x = 0) Study effect of x on response

    Dowel Misalignment/MislocationResults of Analysis:

    0 78.6 1.26 3789 135.720 78.6 1.26 3787 136.1

    40 78.6 1.26 3783 137.260 78.2 1.27 3770 139.580 77.9 1.27 3745 143.7

    100 77.3 1.27 3703 150.2

    x LTE Dowel Bearing(mm) (%) (MPa) Shear Stress

    (N) (MPa)

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    Transverse Ties

    Can be independently specified for each longitudinal joint

    Modeled with same embedded elements used for dowels

    Can model tie-slab support and restraint moduli

    Assumed evenly spaced along each joint

    First tie is placed at tie spacing from left-hand joint

    Transverse Ties

    4600mm (typ)

    3600mm

    1800mm

    Model Properties 250mm slab on dense liquid 12-32mm dowels give 80% LTE

    at transverse joint Tied shoulder

    13mm diameter, 750mm long ties Corner axle load and thermal

    gradient considered in analyses

    Example to Illustrate Tie Effectiveness

    80 kN axle

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    Transverse Ties

    650 670 690 710 730 750

    0.7

    0.9

    1.1

    1.3

    1.5

    Tie Spacing (mm)

    Maxim

    um

    PrincipalStress(MPa)

    Slab stress with NO ties:

    Axle load: 1.33 MPa Thermal: 0.746 MPa Axle+thermal: 1.39 MPa

    Axle load

    Axle + thermal

    Thermal

    Transverse TiesObservations and Conclusions:

    Ties can dramatically reduce slab stresses due to corner loads

    Tie effectiveness strongly depends on its proximity to joint

    700 mm spacing Max. stress = 0.719 MPa

    710 mm spacing Max. stress = 1.38 MPa

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    Workshop Topics Introduction

    Overview of Finite-Element Concepts

    Generation and Solution of a Simple Model

    Slab-Base Interaction

    Analysis of Thermal Gradients and Slab Shrinkage

    Modeling Dowel Joint Load Transfer

    Modeling Aggregate Interlock Joint Load Transfer

    Example of a More Complex Simulation

    Obtaining EverFE and Program Architecture

    Aggregate InterlockThe challenge: How do we model this?

    aggregateinterlock

    wheel load

    Interaction of two rough crack surfaces Seasonal joint opening significantly affects load transfer

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    Aggregate InterlockUsual FE Treatment of Aggregate Interlock:

    Springs at Transverse Joints

    Simple, traditional approach Model remains linear No effect of joint opening

    Coulomb Friction

    Shear depends on normal stress Any joint opening => no shear

    EverFEs Two-Phase Model

    aggregate particles

    crack

    Relies on Walravens Model

    concrete is two-phase medium

    aggregate particles are rigid spheres paste is rigid-plastic

    cracks follow aggregate boundaries

    particles bear on paste, at point of slip

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    ( )Fy pu x yA A=

    ( )Fx pu y xA A= +

    Particle Equilibrium:

    pu

    Fx

    Fy

    pu pu

    =

    aggregate

    particle

    deformed

    paste

    embedment

    crack

    opening

    EverFEs Two-Phase Model

    EverFEs Two-Phase Model

    Two-phase model parameters

    1) pu = ultimate strength of cement paste

    2) = paste-aggregate coefficient of friction (0.4 0.5)

    ccpuf0.8= Walraven suggests

    fcc = 1.25fc (units are MPa)

    3) aggregate volume fraction (usually 0.7 0.8)

    4) Maximum aggregate size (typically 18 or 20 mm)

    5) Initial joint opening (seasonally variable)

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    EverFEs Two-Phase ModelInitial joint opening is a critical parameter

    Greatly affects nonlinear aggregate interlock model Affects contact between joint faces

    initial jointopening

    04

    8

    12

    16

    20

    0 0.5 1.0

    ShearStress

    Relative Vertical Displacement

    increasing

    jointo

    pening

    directeffect

    EverFEs Two-Phase Model

    Tests by Colley and Humphrey (1967) Finite Element Idealization

    Zero

    StiffnessTwo-Phase

    Model

    2743 mm

    1219mm

    Loading PL

    Joint FillerPre-cracked

    178m

    m

    229m

    m

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    EverFEs Two-Phase Model

    178 mm Slab

    1 2 3

    Joint Opening (mm)

    0

    20

    40

    60

    80

    100

    Two-phasemodel

    Experimental

    data

    020

    40

    60

    80

    100

    1 2 3

    Joint Opening (mm)

    229 mm Slab

    LTE(%)

    EverFEs Two-Phase ModelExample for 2-slab system:

    Slabs are 4600mm long x 3600mm wide x 250mm thick

    Found directly on dense liquid, k = 0.03 MPa/mm

    E= 28000 MPa, = 0.20, density = 0

    Center an 80-kN axle with 2 wheels transversely, left of joint

    No dowels at the joint

    Specify nonlinear aggregate interlock model

    pu = 50 MPa = 0.4 volume fraction = 0.75 Dmax = 20mm

    Examine effect of joint opening on response

    Same asdoweledmodel

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    0.1 0.489 0.486 99 0.8630.5 0.519 0.456 88 1.2271.0 0.568 0.406 71 1.271

    1.5 0.632 0.343 54 1.3012.0 0.707 0.267 38 1.3303.0 0.860 0.114 13 1.3864.0 0.963 0.012 1 1.414

    JointOpening l u LTE

    (mm) (mm) (mm) (%) (MPa)

    EverFEs Two-Phase ModelResults of analysis:

    EverFEs Two-Phase Model

    Practical use of two-phase model:

    Recent research has validated this type of model

    However, the model is not perfect:

    It assumes no fracture of coarse aggregate(Walraven suggests scaling down pu to account for this)

    EverFE does not account for smooth surface at sawcut

    (Will tend to overestimate joint shear transfer)

    Estimating parameters is difficult

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    Linear Aggregate Interlock ModelSprings at transverse joints

    Simple approach Model remains linear Joint opening has no effect

    Example for 2-slab system

    0.0 0.974 0.000 0 1.4180.1 0.647 0.328 51 1.3600.5 0.538 0.436 81 1.2901.0 0.518 0.456 88 1.238

    10.0 0.493 0.481 97 0.997100.0 0.488 0.486 99 0.852

    JointStiffness l u LTE

    (MPa/mm) (mm) (mm) (%) (MPa)

    Workshop Topics Introduction

    Overview of Finite-Element Concepts

    Generation and Solution of a Simple Model

    Slab-Base Interaction

    Analysis of Thermal Gradients and Slab Shrinkage

    Modeling Dowel Joint Load Transfer

    Modeling Aggregate Interlock Joint Load Transfer

    Example of a More Complex Simulation

    Obtaining EverFE and Program Architecture

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    Effect of Slab-Base ShearTransfer and Dowel Locking

    Low: kSB 0 (bond-breaker)

    Intermediate: kSB = 0.035 MPa/mm, = 0.60 mm (ATB)

    High: kSB = 0.416 MPa/mm, = 0.25 mm (HMAC)0

    0

    Prior studies have identified critical parameters:

    Interface shear stiffness (kSB) and elastic limit ( ) Dowel-slab bond (dowel locking)

    Interface properties for given base types (Zhang and Li 2001):

    0

    250 mm thick slab 150 mm thick base 32 mm dowels,no looseness

    Material properties:

    E= 28,000 MPa= 0.20= 2,400 kg/m3

    = 1.1x10-5/oC

    Parametric Study FE Model

    4600 mm

    3600mm

    doweled joints

    60,300 DOF3,024 brick elements slab

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    Parametric Study Loads

    UniformShrinkage

    T

    10 oC

    + Gradient+ Shrinkage

    + T T

    6 oC

    14 oC

    Gradient+ Shrinkage

    T T

    14 oC

    6 oC

    Slab Displacements and Stresses

    Displacementsdue to

    T T

    Max. principalstresses due to T T

    500 XMagnification

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    Selected Maximum Stresses (kPa)

    DowelType

    T

    + T T

    T T

    LoadCase

    T+ T T

    T T

    Low Int. High

    Degree of Slab/BaseShear Transfer

    Locked

    Unlocked

    0870688

    159973818

    5941180991

    0872689

    118906669

    5911510547

    StressLocation

    BottomBottom

    Top

    BottomBottom

    Top

    Discussion of Results for TT

    Negative prestrain gradientproduces curling, tension on top

    Dowel restraint uniformlyincreases tension

    Shear stresses at bottom of slabdecreasetension on top of slab =

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    Effect of Dowel Restraint for + TT

    0 400 800 1200 1600 20000.9

    1.1

    1.3

    1.5

    Dowel Axial Restraint Modulus (MPa)

    Max.

    PrincipalStress(MPa)

    High Slab/BaseShear Transfer

    IntermediateSlab/BaseShear Transfer

    Discussion of Results for + TT

    Positive prestrain gradientproduces tension on bottom

    Shear stresses at bottom of slabincreasetension on bottom of slab

    Dowel restraint restricts relative

    slip between slab and base

    With high base/slab sheartransfer, restricted slip decreasestension due to base-slab shear

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    Workshop Topics Introduction

    Overview of Finite-Element Concepts

    Generation and Solution of a Simple Model

    Slab-Base Interaction

    Analysis of Thermal Gradients and Slab Shrinkage

    Modeling Dowel Joint Load Transfer

    Modeling Aggregate Interlock Joint Load Transfer

    Example of a More Complex Simulation

    Obtaining EverFE and Program Architecture

    Obtaining EverFE

    1. Get a cashiers check for $5000 made out to Bill Davids

    Go to http://www.civil.umaine.edu/EverFE Download EverFE2.23.exe Run EverFE2.23.exe on your computer You can now run EverFE using the new

    desktop icon, or from the Programs menu Questions to [email protected]

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    Program ArchitectureBasic architecture of software

    User Interface

    (Tcl/Tk/vtk)

    FE meshing code

    (compiled C++)

    FE solver

    (compiled C++)

    What you see

    Nonlinear agg.

    interlock

    (compiled C++)

    What does the hard work

    Program Architecture

    Directory structure

    Top-level directory

    Aggregate interlock data

    Project definitions/results

    Help file and manual

    Finite-element solver

    Tcl/Tk code

    Tcl/Tk libraries

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    Program ArchitectureHow Project Data is Stored

    Each project has a file with a .prj extension, and a subdirectory The .prj file is a placeholder to allow the project to be recognized The subdirectory contains project definition, FE input/output

    Why is this important?

    These files are simple ASCII text files, but can get large If you want to archive a project to save disk space, you simplymove the .prj file and entire subdirectory to another storage device

    At any time in the future, you can copy the .prj file andsubdirectory back to EverFE2.23/data, and it will be recognized

    Thank You