Study of the effect of lateral inhomogeneities on the propagation of Rayleigh waves in an elastic medium

by Nasseri-Moghaddam, Ali

The use of geophysical testing methods has considerable potential to be a cost effective and accurate technique to assess near-surface soil conditions. Multi channel analysis of surface waves (MASW) test is a geophysical non-intrusive test that uses the dispersive characteristic of Rayleigh waves to estimate low strain shear modulus and damping coefficient of near-surface soil. Also, this technique is used to detect underground voids. Recently, MASW technique has gained more attention, partly because of its ease of use and partly because of the significant improvements in data acquisition systems. The theories of MASW test consider the effect of horizontal soil layering, though the effect of lateral inhomogeneities (i. e. cavities and voids), inclined layering and inverse layering (i. e. a layered system in which the top layers are stiffer than the bottom ones) are not addressed properly in these theories.

The objective of this dissertation is to investigate the effect of lateral inhomogeneities on the propagation of Rayleigh waves in an elastic half-space excited by a transient loading. The results can be applied to locate underground cavities using MASW test and to improve the MASW analysis techniques. In lieu of theoretical solutions, two and three dimensional numerical models are constructed to simulate the MASW test. To assure the quality of the obtained data, numerical models are calibrated with Lamb solution. Voids with different sizes and embedment depths are inserted in the medium. Responses along the surface as well as inside the medium are recorded and analyzed in time, frequency, spatial and frequency-wave number domains. Different material types and sources are used to generalize the results. Afterwards, the combined effect of void and layered systems on the surface responses are studied. To verify the results, experimental field and laboratory data are presented and the trends are compared to the numerical results.

It is found that the void starts to vibrate in response to the Rayleigh wave excitation. Due to the vibration of the void energy partitioning occurs. Part of the incident energy is reflected in the form of Rayleigh wave. Another part is converted to body waves, and spread into the medium. The transferred part of the energy is attenuated and has smaller amplitudes. Finally, a part of energy is trapped in the void region and bounces back and forth between the void boundaries, until it damps. The trapped energy is associated to higher modes of Rayleigh waves and excited Lamb waves. The effect of trapped energy is seen as a region in the vicinity of the void with concentrated energy, in frequency domain. The extents of this region depends on the void size, and the frequency content of the incident energy. Thus, in some cases it is possible to correspond the size of the model to the extents of the region with energy concentration.

A new technique is proposed to determine the location of a void, and estimate its embedment depth. The technique is called Attenuation Analysis of Rayleigh Waves (AARW), and is based on the observed damping effect of the void on the surface responses. For verification, the results are compared to experimental field and laboratory data. The observations are in good agreement with the observed numerical results. Further, the AARW technique showed to be a promising tool for void detection.