Ultrasonic tomography to study localised deformation in sandstone

Full-field measurements are essential in the study of the behaviour of heterogeneous materials or phenomena. In particular the development of localised deformation cannot be fully studied using standard techniques, where measurements of loads and displacements are only made at the boundaries, as such measures will only be nominal or conventional after localisation (after Desrues & Viggiani, 2004). Thus displacement field measurements have been developed both in 2D (e.g., stereophotogrammetry, digital image correlation using photographs) and 3D (volumetric digital image correlation using x-ray tomography images) to characterise localised deformation. However such approaches, whilst providing a powerful tool to characterise localised phenomena, can only provide data on the kinematics and not on associated property changes (e.g., elastic properties), which are to be expected, e.g., due to compaction and related porosity reduction or grain crushing. We have shown previously (Hall et al., 2005) how ultrasonic tomography might be used for full-field measurement of the ultrasonic velocities, and thus elastic properties, in laboratory specimens of geomaterials. Ultrasonic tomography is an inverse method that involves measurements of the times for propagation of an ultrasonic signal (travel-times) between pairs of emitting and receiving transducers. The combination of many such measurements, for a set of intersecting ‘ray-paths’ between emitting and receiving transducers placed in different positions over the sample, allows, by inversion, a map of the variations in propagation velocity in the sample to be determined, in a least-squares sense. Ultrasonic velocities are a function of the elastic properties and density of the material, therefore ultrasonic tomography provides access to the spatial variations of the elastic property in a test sample. Combining such analysis with strain fields, e.g., from digital image correlation of photographs or x-ray tomography, could allow improved understanding of the link between strain and elastic property evolution to advance constitutive models. In this work we present new ultrasonic tomography results acquired using two arrays of 64 transducer elements providing data over 64x64 intersecting raypaths, which provides unprecedented (for geomaterials) ultrasonic tomography resolution. This analysis has been carried out for a set of sandstone specimens after triaxial compression tests under a range of different confining pressures. The specimens are cylinders with two opposing flattened faces to provide contact surfaces for the ultrasonic transducer arrays. Notches were made in these flattened faces to enforce the expected shear bands to develop in the middle of the sample and in the direction perpendicular to the velocity measurements. Initial results indicate the resolution of the localised shear-bands as zones of reduced velocity, which is likely associated with crack formation and grain crushing since the deformation is largely compactant.