3D strain mapping in rocks using digital volumetric speckle photography technique

Abstract

Speckle photography technique is a versatile displacement/deformation mapping technique that can be applied to almost any material. It has its genesis in the laser speckle interferometry technique whereby the natural speckles created by illuminating an optically rough surface using a coherent laser beam are used as displacement gauging elements. It evolves into the white light speckle photography technique whereby a random pattern of any type is used as a displacement measurement transducer. With the advent of digital cameras and ubiquitous usage of computers, the digital version of the technique is developed. Up to now, the technique is essentially limited to 2D applications. Recently, we extended the technique into the 3D domain by using the volumetric imaging capabilities of CT or MRI. In this paper, we apply this technique to measuring the internal deformation of rocks. It so happens that certain rocks have natural density variation at various places such that when imaged by CT these impurities can be treated as 3D speckles. The elements of volumetric speckle photography technique are as follows. A reference volumetric image of the rock is recorded by a micro-CT scan and stored as a reference. Under load, the deformed CT image of the rock is also recorded. Both volume images are divided into subsets of certain voxel arrays. Each corresponding pair of the subsets is “compared” via a two-step 3D Fourier transform analysis. The result is a 3D map of displacement vectors representing the collective displacement experienced by all the speckles within the subset of voxels. The strain distribution of the entire rock specimen can then be calculated using appropriate displacement strain relations. The application of this technique to strain mapping of red sandstone and argillite rocks is presented.