Characteristics of inverse dispersion curve of Rayleigh wave in pavement shallow structure with engineering application

The inverse dispersion curve depicts the dispersion characteristics of inverse layered models, in the layer velocity decreases with depth. To reveal the inverse dispersion characteristics of Rayleigh-wave propagation in pavement, we established a method to determine the dispersion curve of Rayleigh-wave multimodal coupling superposition in pavement structure by decomposing the contribution of multi-mode phase velocity to the vertical displace-ment of road surface, which was verified by the velocity-stress finite difference scheme. On this basis, further comparative calculations found that the generalized reflection and transmission coefficient method for solving the Rayleigh wave fundamental dispersion curve can fully demonstrate the dispersion characteristics of the coupling superposition of multi-mode dispersion curves of Rayleigh wave in pavement structure, which is suitable for the calculation of Rayleigh-wave inverse dispersion characteristics. Meanwhile, the analysis of dispersion characteristics shows that when the frequency is higher than 5000 Hz, the phase velocities are determined by surface materials. In the low frequency band with frequency <10 Hz, the phase velocities are determined by soil-based deepest materials. And with the increase of the thickness of the intermediate layer, the phase velocity range of dispersion curve moves to the low frequency. In this regard, through sensitivity calcu-lation, an optimization method for Rayleigh wave testing and inversion of elastic modulus of pavement structural layers was established by combining Levenberg-Marquardt and adaptive genetic algorithm. Through the comparative test on the scale model of three-layer pavement structure in laboratory, the results show that the elastic modulus of each layer of pavement structure can be successfully evaluated from the inverse dispersion characteristics of Rayleigh wave in pavement structure.