Galerkin solution of Winkler foundation-based irregular Kirchhoff plate model and its application in crown pillar optimization

Abstract

Irregular plates are very common structures in engineering, such as ore structures in mining. In this work, the Galerkin solution to the problem of a Kirchhoff plate lying on the Winkler foundation with two edges simply supported and the other two clamped supported is derived. Coordinate transformation technique is used during the solving process so that the solution is suitable to irregular shaped plates. The mechanical model and the solution proposed are then used to model the crown pillars between two adjacent levels in Sanshandao gold mine, which uses backfill method for mining operation. After that, an objective function, which takes security, economic profits and filling effect into consideration, is built to evaluate design proposals. Thickness optimizations for crown pillars are finally conducted in both conditions that the vertical stiffness of the foundation is known and unknown. The procedure presented in the work provides the guidance in thickness designing of complex shaped crown pillars and the preparation of backfill materials, thus to achieve the best balance between security and profits.