1. BACKCALCULATION OF AIRFIELD PAVEMENT STRUCTURES BASED ON WAVE PROPAGATION THEORY Kunihito MATSUI (Tokyo Denki University) Yoshiaki OZAWA (Century-techno Inc.) Kazuya TAKEHARA (Tokyo Denki University) 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

2. CONTENTS Brief description of wave propagation equations Time domain backcalculation procedure Pavement sections FWD tests were conducted Backcalculation results Comparison of measured and computed deflections Complex modulus Strain responses after backcalculation 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

3. Pavement model Definition of stresses in the axisymmetric coordinate 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22 Impulse

4. Wave propagation expression by FEM Mass matrixDamping matrix Stiffness matrixForce vector A typical damping model Stiffness proportional damping Density proportional damping 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

5. Wave Propagation in Viscoelastic Media Density c Density proportional damping (1a) (1b) 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

6. Strain-displacement relationship,,, (2a) (2b) (2c) 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

7. Stress-strain relationship for Voigt Model (3) 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

8. Boundary Conditions at Surface where (4) 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

9. Matching measured and computed deflections 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

10. Pavement of FWD test site Point I.DLayer 1Layer 2Layer 3Layer 4Files LRS C01 (Section1) 20’ by 20’ PCC Slab H = 11 inch P306 Econo=crete H = 6.125 inch P154 material H = 8.375 inch Low Strength Sub- grade GRAPHA & GRAPHB LRS/LFS Trans Area Slab 1 C01 12.5’ by 20’ PCC slab H=17.125 in P209, H varied from 8.375 to 23.5 inch Low Strength Sub-grade GRAPHC & GRAPHD LFS A09 @ C/L (Section2) P401 asphalt, H = 5 inch P401, Asphalt stabilized base, H=4.875 inch P154 sub- base, 29.625 inch Low Strength Sub- grade GRAPHE & GRAPHF, (No loading area) LFS F11, Lane 2 (Section2) P401 Asphalt, H = 5 inch P401, Asphalt stabilized base, H=4.875 inch P154 sub- base, 29.625 inch Low Strength Sub- grade GRAPHG & GRAPHH (Loading area) LFC F13, Lane 2 (section 3) P401 Asphalt, H = 5 inch P209, Crushed Stone, H = 7.75 inch P154 sub- base, H = 36.375 in Low Strength Sub- grade GRAPHI & GRAPHJ (Loading area) LFC A09 @ C/L (Section 3) P401 Asphalt, H = 5 inch P209, Crushed Stone, H = 7.75 inch P154 sub- base, H = 36.375 in Low Strength Sub- grade GRAPHK & GRAPHL (No loading area) HFC @ C/L (Section 4) P401 Asphalt, H = 5.25 inch P209, Crushed Stone, H = 10.875 inch High strength Sub-grade GRAPHM & GRAPHN (No loading area) HFC Lane 2 (Section4) P401 Asphalt, H = 5.25 inch P209, Crushed Stone, H = 10.875 inch High strength Sub-grade GRAPHO & GRAPHP (Loading area) 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22 (1) (*) (2) (3) (4)

11. 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

12. Backcalculation results 1 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

13. Backcalculation results 2 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

14. Backcalculation results 3 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

15. Backcalculation results 4 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

16. Backcalculated Layer Damping(MPa s) 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

17. Complex modulus Magnitude of complex modulus Complex modulus varies with frequency 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

18. Magnitude of complex modulus 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22 (Section 3 : Loading area)

19. Computed and measured deflections (Section 1) 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

20. Horizontal strain at loading and no loading area (Section 2) (at bottom of As stabilized layer) 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

21. Vertical strains at loading and no loading area (Section 2) (At the top of subgrade) 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

22. Conclusions PCC modulus is about 24,500 MPa, Econocrete modulus about 13,000 MPa. Soft subgrade modulus runs from 90 MPa to 120 MPa. Stiff subrade modulus is from 300 MPa to 380 MPa. Damping coefficients are roughly less than 1 % of layer moduli in magnitude. 2010 FAA Technology Transfer Conference, Atlantic City, NJ, USA April 19-22

23. Other observations When subgrade strength is low, layer moduli of upper layers reduce after repeated loading. When subgrade strength is high, layer moduli of upper layers increase and subgrade modulus reduces after repeated loading. Is it because of densification of upper layers when subgrade is stiff? Advantage of analytical solution is that responses (displacements, stresses and strains) can be easily computed anywhere.