Forward Modeling Of Zigzag Dispersion And Pavement Systems Dispersion Curves

Rayleigh wave prospecting is a new near-surface geophysical method. It has been widely used in geo-technical site investigation and non-destructive testing, because a dispersion curve corresponding to the structure of strata can be obtained quickly by this method, and its operation is easy and economic. It has also high precision in near-surface prospecting.Why there are zigzag dispersion curves and how to calculate the Rayleigh dispersion curves quickly for pavement systems are studied in this paper.After the review of the development of Rayleigh surface wave, the author has deduced the dispersion equation of guided waves propagating in stratified half-space based on the transfer matrix approach, and calculated the Rayleigh phase velocities and group velocities of some models consisting of two/three homogeneous layers. According to the results, we know that the dispersion curves do not intersect with each other forever, but two adjacent dispersion curves probably have intersection trend with the frequency increasing. A new kinds of mode has also been found by the author, namely the truncation mode. Its dispersion curve has been divided into two detached parts. For a heterogeneous elastic solid consisting of two homogeneous layers, threehomogeneous layers whose shear wave velocities increasing with depth, or three homogeneous layers whose interlayer has high velocity, if there are multi-mode dispersion curves, the phase velocity Vr of the first mode will close up to the Rayleigh wave velocity of the bottom layer when frequency f-0Hz, and Vr of the first mode will close up to the Rayleigh wave velocity of the top layer when f. Therefore the dispersion curves obtained in the field are primarily consisted of the first mode. For a heterogeneous elastic solid consisting of three homogeneous layers whose interlayer has low velocity, the phase velocity Vr of the first mode will also close up to the Rayleigh wave velocity of the bottom layer when frequency f- 0Hz, but Vr of the first mode will close up to the shear wave velocity of the interlayer when f , and there is a cut-off frequency at high frequency region for the first mode and Vr close up to the compressional velocity of interlayer when interlayer is liquid. Consequently the dispersion curves obtained in investigation consist of multimode guided waves. The zigzag dispersion curves will occur because of jump among modes.Second, when models consisting of two/three layers have multimode guided waves, the author has calculated their vertical displacements at the free surface, and analyzed the relationship with the central frequency of source. According to the modeling results, the maximal displacement curve consists of different modes when there is a low velocity interlayer.Therefore, the signals detected in those conditions consist of multimode guided waves, and the zigzag dispersion curves will be obtained because the energies of guided waves are discontinuous between each other. If there is not a low velocity interlayer, the maximal displacement curve is the curve of the first mode. According to the comparison with geotechnical site investigation data, our analytical method is right. The displacements of guided waves have also close relationship with sources. For example, the displacements will change when the source central frequency has been changed. It indicates that we should select an appropriate central frequency so that we can receive effective signals in the field exploration.Finally, the author has discussed how to calculate the dispersion curves of pavement systems. Imagine there is a semi-infinite layer whose material properties are same with the top layer under the sub-grade, so the complex roots become real roots, and we can calculate the guided waves dispersion curves in real domain by transfer matrix approach. According to the comparing results with theoretical dispersion curve calculated from peaks of vertical flexibility coefficient, the new method is feasible. Furthermore, the maximal displacement curve of pavement systems consists of...