Blind matching of crushed sand particles via branch and bound

Particle breakage of granular materials plays an important role in its microstructure change and macroscopic behavior under external loads. However, measuring the breakage degree of individual particles in a deformed sand specimen still remains a challenge in geomechanics research. This paper presents a novel method that can track and match fragments to the mother particle from which they break off by searching a limited number of candidate particles. Integrating the branch-and-bound search algorithm with the Standard Iterative Closest Point (Standard ICP) algorithm, this method is applied to process and analyze the X-ray tomography data of 9 Leighton Buzzard sand particles, which each was crushed in a single particle crushing test. Firstly, a total of 62 fragments were collected, mixed up and sorted according to its volume (in the descending order). Secondly, the local bending energy algorithm was used to identify the fracture surfaces of each fragment that were resulted from the mechanical crushing of sand particles. Then the branch-and-bound algorithm was employed to determine the lower and upper bounds of cubes and sub-cubes by efficiently searching the 3D translation and rotation spaces. Finally, a trial matching of each fragment to each of the 9 original particles was made to identify the corresponding mother particle and its location in the mother particle. The effectiveness and efficiency of the proposed tracking method was demonstrated by the matching of 62 fragments to their corresponding mother particles.