Generalized stress field in granular soils heap with Rayleigh–Ritz method

Abstract

The stress field in granular soils heap (including piled coal) will have a non-negligible impact on the settlement of the underlying soils. It is usually obtained by measurements and numerical simulations. Because the former method is not reliable as pressure cells instrumented on the interface between piled coal and the underlying soft soil do not work well, results from numerical methods alone are necessary to be doubly checked with one more method before they are extended to more complex cases. The generalized stress field in granular soils heap is analyzed with Rayleigh–Ritz method. The problem is divided into two cases: case A without horizontal constraint on the base and case B with horizontal constraint on the base. In both cases, the displacement functions u(x, y) and v(x, y) are assumed to be cubic polynomials with 12 undetermined parameters, which will satisfy the Cauchy's partial differential equations, generalized Hooke's law and boundary equations. A function is built with the Rayleigh–Ritz method according to the principle of minimum potential energy, and the problem is converted into solving two undetermined parameters through the variation of the function, while the other parameters are expressed in terms of these two parameters. By comparison of results from the Rayleigh–Ritz method and numerical simulations, it is demonstrated that the Rayleigh–Ritz method is feasible to study the generalized stress field in granular soils heap. Solutions from numerical methods are verified before being extended to more complicated cases.

Keywords

• Generalized stress field
• Rayleigh–Ritz method
• Stress depression
• Variation of the function
• Principle of minimum potential energy