Development of a computational method for inverting dynamic moduli of multilayer systems with applications to flexible pavements




Xu, Qinwu

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Most existing computational methods for inverting material properties of multilayer systems have focused primarily on elastic properties of materials or a static approach. Typically, they are based on a two-stage approach: (I) modeling structural responses with a computer program, and (II) estimating layer properties mathematically using the response outputs determined in stage I without interactions with the governing state partial-differential-equation (PDE) of stage I. This two-stage approach may not be accurate and efficient enough for inverting larger scale model parameters. The objective of this research was to develop a computational method to invert dynamic moduli of multilayer systems with applications to flexible pavements under falling weight deflectometer (FWD) tests, thereby advancing existing methods and fostering understanding of material behaviors. This research first developed a finite-element and Newton-Raphson method to invert layer elastic moduli using FWD data. The model improved the moduli seeds estimation and achieved a satisfactory accuracy based on Monte Carlo simulations, addressing the common back-calculation issue of no unique solutions. Consequently, a time-domain finite-element method was developed to simulate dynamic-viscoelastic responses of the multilayer systems under loading pulses. Simulation results demonstrated that the dynamic-viscoelastic-damping-coupled model could emulate structural responses more accurately, thereby advancing existing simulation approaches. By using the dynamic-viscoelastic-response model as one computation module, this research led to the development of a PDE-constrained Lagrangian optimization method to invert dynamic moduli and viscoelastic properties of multilayer systems. The Lagrangian function was used as an objective function, with a regularization term and governing-state PDE constraint. Both the first-order (gradient) and second-order variation (Hessian matrix) of the Lagrangian were computed to satisfy necessary and sufficient optimality conditions, and Armijo rule was modified to determine a stable step length. The developed method improved computation speed significantly, and it is superior for large-scale inverse problems. The model was implemented for evaluating flexible pavements under FWD tests and for inverting the master curve of dynamic moduli of the asphalt layer. Independent computer coding was developed for all numerical methods. The computational methods developed may also be applied to other multilayer systems, such as tissues and sandwich structures at different time and length scales.



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