| Computerized tomography (CT) has long been used successfully in different areas of science and engineering. X-ray tomography and MRI in diagnostic medicine, and geographical imaging, usually used for characterizing the subsurface of earth, are well-known examples. For experimental determination of stress fields, transmission photoelasticity has been well established and successfully applied in solid bodies. However, for the determination of stress fields in particulate media, especially in granular soil medium, very little research has been conducted. Here, based on CT principles, a non-destructive technique is presented for the determination of stress fields in granular soil medium. This technique is based on crosshole seismic probing, which is usually used by geophysicists for geophysical imaging. In this technique, a set of seismic energy sources and a set of sensors are distributed on different boundaries of the soil region of interest. The measured propagation delay between each source-receiver pair, usually called the "travel-time", is used to infer the stress field.; The wave velocity field in granular soil medium is essentially anisotropic and heterogeneous. In conjunction with the borehole technique, two different mathematical models have been presented to approach the problem. One is based on the states of stress at each point in the domain as the principal unknowns to be determined, and the other is based on defining the stress field as a mathematical expression with a certain number of unknown parameters. Both models lead to a constrained nonlinear least squares problem. However, the first turned out to be technically unmanageable due to the highly nonlinearity of the governing equations and the large number of unknowns involved, while the latter proved to be not only manageable but also an efficient approach. To demonstrate the merits of this approach for the determination of stress field of granular soil, a number of test cases corresponding to different boundary conditions are presented where the stress fields are reconstructed from travel-times which are produced numerically. |
