Formulation of a three dimensional analytical solution to evaluate stresses in backfilled vertical narrow openings

The mechanical response of backfill in narrow openings is significantly influenced by its interaction with the surrounding walls. Previous work conducted on backfilled trenches and mining stopes indicates that the theory of arching can be used to estimate earth pressures in narrow, vertical backfilled openings. In this paper, a 3D analytical solution is proposed to evaluate the state of stress along the boundaries of the openings. The proposed solution, based on a generalized version of the Marston approach, is compared with numerical modeling and laboratory experimental results taken from the literature. A discussion follows on some particular features and limitations of the analytical solutions.