JOINT LOAD TRANSFER EFFICIENCY OF RIGID PAVEMENT CONSIDERING DYNAMIC EFFECTS UNDER A SINGLE MOVING LOAD

Xinhua YU, Yumin ZHOU, Zhiming TANTongji University, PRC

Edward H GuoSRA International, USA

FAA 2010, Atlantic, New Jersey, April 20-22, 2010

OUTLINE

(1)Observation from Field and Tests

(2)Conceptual Analysis of the Dynamic Modeling

(3)Findings

Does Low LTEs Cause Early Slab Cracks? (I)

Ioannides and Korovesis, 1990, 1992

Winter

Does Low LTEs Cause Early Slab Cracks? (II) 5

Does Low LTEs Cause Early Slab Cracks? (III)

The Maximum Strains vs. Number of PassesStrain Gage CSG17, Track 4

-100.00

-80.00

-60.00

-40.00

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

0 1000 2000 3000 4000 5000 6000

Number of Passes

Mic

ro S

tra

ins

Top

Bottom

Crack started

Crack completed

Survey Notes: The surface crack was occurred before pass 3938, 10:30 am, 3/29/2003 and a tiny crack was observed at that time

Differences Between Models (I)

FHWA

FAA

How to define Load Transfer Efficiency? (LTE)

LTE is a pending problem in dynamic modeling

Above two are equivalent only for static modeling

Differences Between Models (II)

• Fundamental differences exist between the model and field reality

• The model is static

– the speed of wheel is assumed to be zero

– the position of load is fixed on one side of the joint

• The reality is dynamic

– The wheels move with different speeds

– The position of the wheel changes at any moment

Differences Between Models (III)

Reality – Strain history when a four wheel gear across a joint

LTE(S) is temporarily defined by

Differences Between Models (IV)

Evaluation Using HWD (FWD) Machine

LTE(S) calculated from the measured LTE(W)

Differences Between Models (V)

Ioannides and Korovesis, 1990, 1992

Static Modeling in Existing Analysis

What is new in this paper?

– Dynamic model is used to replace the static model;

– The sensitivity of four parameters have been considered in analysis: Load speed, pavement damping, foundation reaction modulus and foundation damping

z

xo

kwE, u, h, Cs

k Ck

x

y

oP

v

i e1 e2

B

Lg

distance from edge lb

22 2

2( )

w wD w C kw h P x vt

t t

Model in this Paper

Conceptual Analysis (I)

22 2

2( )

w wD w C kw h P x vt

t t

22 2

2( )

w wD w C kw h P x vt

t t

Static Model

Dynamic Model

Makes the peak response decrease and delay in occurrence

Makes the peak load be shared by the unloaded slab. The higher the speed, the more will be shared.

ABLTE=

• Static model is a special case of dynamic model after two major conditions are satisfied:

• Damping = 0;• Load moving speed is zero;• Therefore, reliability of the dynamic

analysis can be verified by existing static analysis.

Conceptual Analysis (II)

Findings I - Parameters

L /m B /m h /m lb/m E /MPa u

5 4 0.2 0.1 30000 0.15

pavement damping

Cs=0.008~1.2MN·s/m3

foundation reaction modulus

k=40~90 MN/m3

foundation damping

Ck=0.002~0.2 MN·s/m3

Findings II - Strains and Deflections at Specified Points i , e1 ,e2

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50v /(m/s)

λ ε

123

0.2

0.4

0.6

0.8

1.0

0 10 20 30 40 50v /(m/s)

λ w

123

dynamic dynamicw

static static

w

w

(1- Cs =0.008MN·s/m3, 2- Cs =0.4MN·s/m3, 3- Cs =1.2MN·s/m3)

Higher damping, lower responses, higher speed, lower responses

Findings III - Time lag of

peak strain at point e1

x

y

oP

v

i e1 e2

B

Lg

distance from edge lb

¦ ¤t

¦Å_e1,v=0¦Å_e1,v¡ Ù0

Pv

e1

0.00

0.02

0.04

0.06

0.08

0.10

0 10 20 30 40 50v/ m/s

ΔX

/m

123

ΔX (=Δt∙v)

(1- Cs =0.008MN·s/m3, 2- Cs =0.4MN·s/m3, 3- Cs =1.2MN·s/m3)

The higher pavement damping, the more delay the calculated peak responses

Findings IV - Measured LTE(S) at FAA’s NAPTF

( ) 100% 100%unloaded unloaded

loaded unloaded loaded unloaded

LTE S

0.042( ) 100% 100% 43.3%

0.055 0.042unloaded

loaded unloaded

LTE S

Findings V - LTE(S) versus Moving Speed v

(1- Cs =0.008MN·s/m3, 2- Cs =0.4MN·s/m3, 3- Cs =1.2MN·s/m3)(kw= 0) (kw=3000 MN/m3)

LTE(S) seems no longer equal to 0 while speed v great than 0 and the joint shearing stiffness kw=0.

Findings VI - LTE(S) versus LTE(w) – Dynamic Model

(1- Cs =0.008MN·s/m3, 2- Cs =0.4MN·s/m3, 3- Cs =1.2MN·s/m3)

Findings VII – Effects of Foundation

modulus k (Cs=0, v=5m/s)

k /MN/m3 static LTE(S) /% dynamic LTE(S) /%

40 31.7 38.6

60 30.6 38.0

90 29.3 37.2

The influence of foundation reaction modulus k on LTE(S) is not significant

Findings VIII – Effects of Foundation

damping Ck (Cs=0, v=5m/s)

Ck /MN·s/m εloaded /10-6 LTE(S) /%

0.002 238 45.5

0.02 239 46.0

0.2 239 45.9

The influence of foundation damping Ck on LTE(S) is quite small

CONCLUSIONS

• The static model under-estimates the load transfer efficiency and over-estimates the risk for bottom-up cracks at concrete pavement joints;

• With increase of the load moving speed v, the joint load transfer efficiency LTE(S) increases;

• With increase of the pavement damping Cs, the joint load transfer efficiency LTE(S) increases;

• The ratio c (LTE(S) dynamic against LTE(S) static) varies in the range 1.0 to 2.0 mainly depending on variables v and Cs;

• The joint load transfer efficiency is insensitive to the reaction modulus k and damping Ck of concrete pavement foundation.

THANK YOU!