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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!