Analytical Solution for Estimating the Stress State in Backfill Considering Patterns of Stress Distribution
Publication: International Journal of Geomechanics
Volume 19, Issue 1
Abstract
Large underground voids created by removal of ore are usually backfilled with mill tailings. The stress state in the backfill must be estimated to ensure safety. Most of the existing analytical solutions for estimating stress at any depth within mine fills had adopted the assumption of uniform vertical stress. However, this assumption does not make for a valid hypothesis. This paper presents an analytical solution to estimate the stress state in vertical backfilled stopes with stress patterns of distribution in the fill considered. The trajectory of minor principal stress in the fill from the centerline to the wall was assumed to be either a circular-arc, parabola, or catenary. The direction of the minor principal stress at the centerline was vertical to the centerline, and the direction along the rock mass was determined using the geometrical relationship of Mohr’s stress circle. The stress states of the differential flat elements in the backfill were analyzed through equilibrium considerations. Then, the analytical solution for estimating the stress state in the backfill was obtained. A series of examples are presented and compared with existing analytical solutions and numerical results carried out in ABAQUS (version 6.13). A nonuniform stress distribution across the backfill width is also presented. The vertical normal stress component at the centerline was greater than that along the wall. The stress state in the backfill was affected by the friction angle and cohesive strength of the backfill soils, friction angle at the wall interface, and trajectory of the minor principal stress. A discussion is presented after the comparison of numerical and analytical results and addresses the limitations of the proposed analytical solutions.
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Acknowledgments
Many people and organizations contributed to the success of this project. The financial support from the National Key Basic Research Program of China (973 Program; Grant 2015CB057801), National Science Fund for Distinguished Young Scholars of China (NSFC Grant 51725802), and National Natural Science Foundation of China (NSFC Grants 51238009 and 51338009) are gratefully acknowledged.
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Published In
International Journal of Geomechanics
Volume 19 • Issue 1 • January 2019
Copyright
© 2018 American Society of Civil Engineers.
History
Received: Dec 15, 2017
Accepted: Jul 13, 2018
Published online: Nov 13, 2018
Published in print: Jan 1, 2019
Discussion open until: Apr 13, 2019
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