Workshop Slides EVERFE

(1)

EverFE Workshop

Sacramento, CA March 11, 2004 Bill Davids, PhD, PE University 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

(2)

JPCP Is a Complex Structure

I-90 in Washington State

Dowel Retrofit

Contraction Joint

Failure Modes in JPCP

(3)

Failure Modes in JPCP

Corner Break

Failure Modes in JPCP

Transverse Joint Faulting

(4)

Failure Modes in JPCP

Shrinkage Cracking

Mechanistic-Empirical Design

of JPCP

1. Estimate design parameters (thickness, joint spacing, etc.) 2. Predict response

under axle loads, temperature changes, etc.

3. Assess effect of

stresses on fatigue life and durability Not OK 4. Plans and Specs, Bid, Construct OK Construction Problems?

(5)

Neg. gradient Pos. gradient

2. Linear thermal gradients through the slab thickness

Predicting Response of JPCP

Usually 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

(6)

What is EverFE?

• Software for the 3D Finite Element (FE) analysis of JPCP • Incorporates specialized strategies for modeling important

response 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 Model

Basic 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

(7)

Workshop Objectives

1. Familiarize you with EverFE’s 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 can’t 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

(8)

Finite-Element Concepts

Mathematical definition:functional method for solving partial differential equations

Our definition:well-established numerical technique 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

(9)

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 Concepts

FE Procedure in a Nutshell:

• Divide a structure into discrete inter-connected “finite elements” that meet at “nodes”

• Make each finite element responsible for defining an approximate 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 unknown displacements, recover stresses, etc.

(10)

Finite-Element Concepts

Simple 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 x f dx u d EA =

Finite-Element Concepts

Finite-element discretization and solution

element nodes

stress

exact solution

(11)

Finite-Element Concepts

How does each element represent the solution?

1D linear element

nodal displ. interpolated displ.

1D quadratic element

constant stress linearly varying

stress

Finite-Element Concepts

Basic Element Types in Structures and Solid Mechanics

2D Elements Beam/Truss Element

Plate/Shell Elements

t

(12)

Finite-Element Concepts

History of FE Modeling of Concrete Pavements

• Earliest models treated slabs as plates on elastic solids • ILLISLAB, JSLAB, etc. released in late 1970s, early 1980s

Modeling of multiple slabs with 2D plate elements Methods for handling joint load transfer

• Researchers began using existing general-purpose 3D codes

Detailed models of doweled joints Treatment of slab-base interaction

• EverFE was first released in 1998

Development 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

(13)

Finite-Element Concepts

What is the peak tensile stress in a large slab with: 40 kN wheel load applied at the edge, r = 228 mm Slab properties: t = 254 mm, E = 27,600 MPa, v = 0.20 Subgradek = 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 405mm

square contact area (equivalent area to circle) Critical questions:

• How large a slab to model?

(14)

Finite-Element Concepts

Finite-Element Solution:

Start with a large slab (5000mm x 5000mm) Study the effect of mesh refinement on solution

2 x 2 elements 5000mm 5000 mm 24 x 24 elements increase # of elements

Examine the effect of model size on solution

Finite-Element Concepts

0 10 20 30 0.6 0.8 1 1.2 1.4 1.6 Westergaard

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

M a x im u m S tre ss (M P a )

Effect of Mesh Refinement on Results

2 elements through thickness

1 element through thickness

(15)

Discretization 12 u12 24 u24 Stress (MPa) 1.48 1.43 2 Elements through thickness

What if we change our discretization slightly?

Load is centered in element: • Element captures linear

variation in stress • Element can’t see peak

stress! 13 u13 25 u25 1.23 1.33

Finite-Element Concepts

Effect of Model Size on Results

1000 3000 5000 7000 9000 0.5 0.7 0.9 1.1 1.3 1.5 M a x im u m S tre ss (M P a ) Slab Size (mm)

(16)

Workshop Topics

• Introduction

• Obtaining EverFE and Program Architecture

Generating an EverFE Model

16-noded interface element

20-noded brick element

8-noded dense liquid element x

y z

beam elements for dowels and transverse ties

(17)

Generating an EverFE Model

Example 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 kN axle 5000mm 3600m m slab bonded CTB

Workshop Topics

• Introduction

(18)

Slab-Base Interaction

The 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 Interaction

EverFE’s 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 in slab

base

corresponding pairs of nodes

permanently tied if base is bonded (linear)

(19)

Slab-Base Interaction

EverFE’s treatment of shear stresses at interface

slip, Interface elements relate

slip to shear stress

0

δ

k_SB

Defining parameters

Shear stress-slip relation:

S h e a r stre ss

Applies onlywhen slab and base

remain in contact

Slab-Base Interaction

Background on shear stress-slip relation

Shear stress is caused by several mechanisms Classical friction

Interlock (interaction of two rough surfaces) Adhesion (chemical bond)

This elastic-plastic model has seen recent use in literature Rasmussen and Rozycki (2001)

Zhang and Li (2001)

(20)

Slab-Base Interaction

What are typical values for kand ₀?

Data reported by Rasmussen and Rozycki (2001): Base Type

Rough HMA Smooth HMA Rough Asphalt Stabilized Smooth Asphalt Stabilized

Cement Stabilized Granular k_SB (MPa/mm) 0.270 0.068 0.200 0.065 4.100 0.027 0 (mm) 0.250 0.510 0.510 0.640 0.025 0.510

Slab-Base Interaction

Quick 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 k_SBon peak tensile stress

k_SB 0.0 0.5 1.0 2.0 5.0 10.0 50.0 2.53 2.25 2.14 2.01 1.83 1.71 1.51 Notes

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

(21)

Workshop Topics

• Introduction

Analysis of Thermal Gradients

Corners of slab curl upward s lab th ic k nes s - T + T

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

Weight of slab pulls downward

(22)

Analysis of Thermal Gradients

Center of slab lifts upward s lab th ic k nes s T - T

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

Weight of slab pulls 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

s lab th ic k nes s

(23)

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

2 E lem ents 3 E lem ents 1 E lem ent Temperature Variations Used in FE Analysis

Analysis of Thermal Gradients

Bilinear Gradient: Specified Temperature Variation s lab th ic k nes s

Analysis of Thermal Gradients

Trilinear Gradient: 1 E lem ent Temperature Variations Used in FE Analysis Specified Temperature Variation 3 E lem ents 2 E lem ents s lab th ic k nes s

(24)

Analysis of Thermal Gradients

Quick parametric study

• Re-run our single-slab model

• Consider positive (+5o_C/-5o_{C) and negative (-5}o_C/+5o_{C) 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 gradient

(25)

Analysis of Slab Shrinkage

Shrinkage 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_/o_C

•Equivalent T = -0.0001/1.1x10-5_/o_{C = -9.09}o_C

-9.09o_C •Re-run our single-slab model assuming:

• No slab-base shear transfer

• A rough HMA base (E = 2000 MPa, k_SB= 0.27 MPa/mm, 0= 0.25mm)

Analysis of Slab Shrinkage

Results of Simulation No slab-base shear transfer

x = +/-0.25mm at x = 0mm, 5000mm No stresses are developed in slab

BOS Stresses

σmax= 0.32 MPa

(26)

Early-Age Effects

• Concrete pavements sometimes crack during curing • Primary causes are thermal and/or shrinkage gradients

that occur prior to concrete gaining full tensile strength

Shrinkage cracks in new pavement

Early-Age Effects

Simple example of how this can be studied with EverFE

• Re-run our single-slab model founded on CTB

• Consider a negative (-5o_C/+5o_{C) 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 1–28 days • Type I cement, published relationship between time and

• Examine effect of curing time on ratio of slab stress:slab MOR ’ c f ’ 6 f_c ’ 000 , 57 f_c

(27)

Early-Age Effects

Details of Analysis Parameters

Age-strength relationship 1.0 5.5 11100 1.17 2.5 10.3 15230 1.60 4.0 13.8 17580 1.85 9.0 20.7 21530 2.27 28.0 27.6 24870 2.62 Age E MOR

days MPa MPa MPa ’ c f

Early-Age Effects

Results of Analysis TOS stresses Displaced shape 0.300 5 10 15 20 25 30 0.35 0.40 0.45 0.50 M a x st re ss/ M O R Time (days)

(28)

Workshop Topics

• Introduction

Dowel Joint Load Transfer

The challenge: How do we model this?

separation of slab and subgrade

dowel wheel load

high stress on subgrade

(29)

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 plate elements 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

(30)

Dowel Joint Load Transfer

Our solution is the embedded dowel element

solid

element Beam element is constrained to

displace compatibly with the embedding solid element

dowels

slab mesh lines

Immediate 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

(31)

Dowel Joint Load Transfer

Treatment 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

K_z = modulus of

dowel support ×diameter

Dowel Looseness

Significance:

• 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 multiple

elements single

(32)

914 mm 1220 m m 12 - 6.35 mm dowels 10 kN rubber pad

k

= 0.09 MPa/mm 51 m m

grease and drinking straw

Laboratory Tests of Hammons (1997)

unbonded CTB

Dowel Looseness

V e rt ic al Di spl a ce m e n t ( mm) 0.2 0.4 0.6 experimenta_{no CTB} l

Distance from Joint (mm) 0 -200 -100 100 -400 model, no looseness model, gap = 0.08 mm

Dowel Looseness

(33)

Distance from Joint (mm) 0 -200 -100 100 -400 V e rt ic al Di spl a ce m e n t ( mm) 0.2 0.4 0.6

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

experimental with CTB

Dowel Looseness

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

Dowel Looseness

Example 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, ν= 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)

(34)

Dowel Looseness

Results of Analysis Gap l u LTE (mm) (mm) (mm) (%) (MPa) 0.00 0.467 0.467 100 0.865 0.05 0.528 0.528 81 1.019 0.10 0.578 0.384 66 1.121 0.15 0.622 0.344 55 1.267 0.20 0.646 0.323 50 1.309 0.30 0.660 0.310 47 1.323 0.40 0.664 0.306 46 1.326

Dowel-Slab Support Modulus

Background:

More traditional method of idealizing dowel-slab interaction Dowel-slab interface idealized with distributed springs Results 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 looseness

(35)

Dowel-Slab Support Modulus

Results of Analysis K_z _l _u LTE (MPa) (mm) (mm) (%) (MPa) 1e6 0.474 0.471 99 0.912 1e4 0.505 0.457 90 1.182 5000 0.517 0.447 86 1.223 500 0.612 0.357 58 1.310 100 0.771 0.200 26 1.362 1 0.969 0.004 0 1.417

Dowel Misalignment/Mislocation

Inaccurately cut transverse joints mislocated dowels Improperly placed dowels dowel misalignment

Elevation View z ∆ Actual position β q s Intended position x ∆ Plan View α Intended position Actual Position q r y ∆

(36)

Dowel Misalignment/Mislocation

Treatment 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 K_z= 2000 (LTE = 79% at x = 0)

• Study effect of x on response

Dowel Misalignment/Mislocation

Results of Analysis: 0 78.6 1.26 3789 135.7 20 78.6 1.26 3787 136.1 40 78.6 1.26 3783 137.2 60 78.2 1.27 3770 139.5 80 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)

(37)

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 ½ tie spacing from left-hand joint

Transverse Ties

4600mm (typ) 3600m m m 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

(38)

Transverse Ties

650 670 690 710 730 750 0.7 0.9 1.1 1.3 1.5 Tie Spacing (mm) Max im u m Pr inc ipa l Str e s s ( M Pa)

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 Ties

Observations 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

(39)

Workshop Topics

• Introduction

Aggregate Interlock

The challenge: How do we model this?

aggregate interlock wheel load

• Interaction of two rough crack surfaces

(40)

Aggregate Interlock

Usual 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

EverFE’s Two-Phase Model

aggregate particles crack

Relies on Walraven’s 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

(41)

(

)

F_y =σ_pu A_x −µA_y

(

)

F_x =σ_pu A_y +µA_x Particle Equilibrium:

σ

pu

F

_x

F

y

τ

pu

=

µσ

pu aggregate particle deformed paste embedment crack opening

EverFE’s Two-Phase Model

Two-phase model parameters

1) _pu= ultimate strength of cement paste

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

cc pu =8.0 f

σ • Walraven suggests

• f_cc= 1.25f’_c (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)

(42)

EverFE’s Two-Phase Model

Initial joint opening is a critical parameter

• Greatly affects nonlinear aggregate interlock model • Affects contact between joint faces

initial joint opening 0 4 8 12 16 20 0 0.5 1.0 Shear Str e ss

Relative Vertical Displacement inc rea sin_g joi nt o peni ng direct effect

EverFE’s Two-Phase Model

Tests by Colley and Humphrey (1967) Finite Element Idealization

Zero

Stiffness Two-Phase_Model

2743 mm 1219 m m Loading PL Joint Filler Pre-cracked 178 m m 229 m m

(43)

EverFE’s Two-Phase Model

178 mm Slab 1 2 3 Joint Opening (mm) 0 20 40 60 80 100 Two-phase model Experimental data 0 20 40 60 80 100 1 2 3 Joint Opening (mm) 229 mm Slab LT E ( % )

EverFE’s Two-Phase Model

Example 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, ν= 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 as

doweled model

(44)

0.1 0.489 0.486 99 0.863 0.5 0.519 0.456 88 1.227 1.0 0.568 0.406 71 1.271 1.5 0.632 0.343 54 1.301 2.0 0.707 0.267 38 1.330 3.0 0.860 0.114 13 1.386 4.0 0.963 0.012 1 1.414 Joint Opening _l _u LTE (mm) (mm) (mm) (%) (MPa)

EverFE’s Two-Phase Model

Results of analysis:

EverFE’s 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 puto account for this)

• EverFE does not account for smooth surface at sawcut (Will tend to overestimate joint shear transfer)

(45)

Linear Aggregate Interlock Model

Springs 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 1.418 0.1 0.647 0.328 51 1.360 0.5 0.538 0.436 81 1.290 1.0 0.518 0.456 88 1.238 10.0 0.493 0.481 97 0.997 100.0 0.488 0.486 99 0.852 Joint Stiffness l u LTE (MPa/mm) (mm) (mm) (%) (MPa)

Workshop Topics

• Introduction

(46)

Effect of Slab-Base Shear

Transfer and Dowel Locking

Low:k_SB§0 (bond-breaker)

Intermediate:k_SB= 0.035 MPa/mm, = 0.60 mm (ATB) High:k_SB= 0.416 MPa/mm, = 0.25 mm (HMAC)δ0

0

δ

Prior studies have identified critical parameters: • Interface shear stiffness (k_SB) and elastic limit ( ) • Dowel-slab bond (“dowel locking”)

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

0 δ •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_/o_C

Parametric Study FE Model

4600 mm

3600 m

m

doweled joints

60,300 DOF

(47)

Parametric Study Loads

Uniform Shrinkage – T – 10 o_C + Gradient + Shrinkage + T – T – 6 o_C – 14 o_C – Gradient + Shrinkage – T – T – 14 o_C – 6 o_C

Slab Displacements and Stresses

Displacements due to – T – T Max. principal stresses due to – T – T 500 X Magnification

(48)

Selected Maximum Stresses (kPa)

Dowel Type – T + T – T – T – T Load Case – T + T – T – T – T

Low Int. High

Degree of Slab/Base Shear Transfer Locked Unlocked 0 870 688 159 973 818 594 1180 991 0 872 689 118 906 669 591 1510 547 Stress Location Bottom Bottom Top Bottom Bottom Top

Discussion of Results for

– T–T

• Negative prestrain gradient produces curling, tension on top •Dowel restraint uniformly

increases tension

• Shear stresses at bottom of slab

(49)

Effect of Dowel Restraint for

+ T–T

0 400 800 1200 1600 2000 0.9 1.1 1.3 1.5

Dowel Axial Restraint Modulus (MPa)

Ma x . P rin cip a l S tre ss (MP a ) High Slab/Base Shear Transfer Intermediate Slab/Base Shear Transfer

Discussion of Results for

+ T–T

• Positive prestrain gradient produces tension on bottom • Shear stresses at bottom of slab

increase tension on bottom of slab •Dowel restraint restricts relative

slip between slab and base •With high base/slab shear

transfer, restricted slip decreases tension due to base-slab shear

(50)

Workshop Topics

• Introduction

Obtaining EverFE

1. Get a cashier’s 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]

(51)

Program Architecture

Basic 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

(52)

Program Architecture

How 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 simply

move the .prj file and entire subdirectory to another storage device • At any time in the future, you can copy the .prj file and

subdirectory back to EverFE2.23/data, and it will be recognized