1. JOINT LOAD TRANSFER EFFICIENCY OF RIGID PAVEMENT CONSIDERING DYNAMIC EFFECTS UNDER A SINGLE MOVING LOAD Xinhua YU, Yumin ZHOU, Zhiming TAN Tongji University, PRC Edward H Guo SRA International, USA FAA 2010, Atlantic, New Jersey, April 20-22, 2010

2. OUTLINE (1)Observation from Field and Tests (2)Conceptual Analysis of the Dynamic Modeling (3)Findings

3. Does Low LTEs Cause Early Slab Cracks? (I) Ioannides and Korovesis, 1990, 1992 Winter

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

5. Does Low LTEs Cause Early Slab Cracks? (III)

6. 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

7. 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

8. Differences Between Models (III) Reality – Strain history when a four wheel gear across a joint LTE(S) is temporarily defined by

9. Differences Between Models (IV) Evaluation Using HWD (FWD) Machine LTE(S) calculated from the measured LTE(W)

10. Differences Between Models (V) Ioannides and Korovesis, 1990, 1992 Static Modeling in Existing Analysis

11. 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

12. Model in this Paper

13. Conceptual Analysis (I) 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. A B LTE=

14. 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)

15. Findings I - Parameters L /mB /mh /ml b /mE /MPau 540.20.1300000.15 pavement damping C s =0.008~1.2MN·s/m 3 foundation reaction modulus k=40~90 MN/m 3 foundation damping C k =0.002~0.2 MN·s/m 3

16. Findings II - Strains and Deflections at Specified Points i, e 1,e 2 (1- C s =0.008MN·s/m 3, 2- C s =0.4MN·s/m 3, 3- C s =1.2MN·s/m 3 ) Higher damping, lower responses, higher speed, lower responses

17. Findings III - Time lag of peak strain at point e 1 ΔX (=Δt∙v) (1- C s =0.008MN·s/m 3, 2- C s =0.4MN·s/m 3, 3- C s =1.2MN·s/m 3 ) The higher pavement damping, the more delay the calculated peak responses

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

19. Findings V - LTE(S) versus Moving Speed v (1- C s =0.008MN·s/m 3, 2- C s =0.4MN·s/m 3, 3- C s =1.2MN·s/m 3 ) (k w = 0) (k w =3000 MN/m 3 ) LTE(S) seems no longer equal to 0 while speed v great than 0 and the joint shearing stiffness k w =0.

20. Findings VI - LTE(S) versus LTE(w) – Dynamic Model (1- C s =0.008MN·s/m 3, 2- C s =0.4MN·s/m 3, 3- C s =1.2MN·s/m 3 )

21. Findings VII – Effects of Foundation modulus k (C s =0, v=5m/s) k /MN/m 3 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

22. Findings VIII – Effects of Foundation damping C k (C s =0, v=5m/s) C k /MN · s/m ε loaded /10 -6 LTE(S) /% 0.00223845.5 0.0223946.0 0.223945.9 The influence of foundation damping C k on LTE(S) is quite small

23. 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 C s, 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 C s ; The joint load transfer efficiency is insensitive to the reaction modulus k and damping C k of concrete pavement foundation.

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