Revisiting the analytical solutions for ultimate bearing capacity of pile embedded in rocks

Abstract

This paper investigates the validity and shortcomings of the existing analytical solution for the ultimate bearing capacity of a pile embedded in a rock mass using the modified Hoek–Brown failure criterion. Although this criterion is considered a reference value for empirical and numerical calculations, some limitations of its basic simplifications have not been clarified yet. This research compares the analytical results obtained from the novel discontinuity layout optimization (DLO) method and the numerical solutions from the finite difference method (FDM). The limitations of the analytical solution are considered by comparing different DLO failure modes, thus allowing for the first time a critical evaluation of its scope and conditioning for implementation. Errors of up to 40% in the bearing capacity and unrealistic failure modes are the main issues in the analytical solution. The main aspects of the DLO method are also analyzed with an emphasis on the linearization of the rock failure criterion and the accuracy resulting from the discretization size. The analysis demonstrates DLO as a very efficient and accurate tool to address the pile tip bearing capacity, presenting considerable advantages over other methods.

Keywords

• Discontinuity layout optimization (DLO)
• Analytical solution
• Bearing capacity
• Deep foundations
• Hoek–Brown failure criterion
• Finite difference method (FDM)