Simplified analytical solution for stress concentration ratio of piled embankments incorporating pile–soil interaction

Piled embankments have been extensively used for high-speed rail over soft soils because of their effectiveness in minimizing differential settlement and shortening the construction period. Stress concentration ratio, defined as the ratio of vertical stress carried by pile heads (or pile caps if applicable) to that by adjacent soils, is a fundamental parameter in the design of piled embankments. In view of the complicated load transfer mechanism in the framework of embankment system, this paper presents a simplified analytical solution for the stress concentration ratio of rigid pile-supported embankments. In the derivation, the effects of cushion stiffness, pile–soil interaction, and pile penetration behavior are considered and examined. A modified linearly elastic-perfectly plastic model was used to analyze the mechanical response of a rigid pile–soil system. The analytical model was verified against field data and the results of numerical simulations from the literature. According to the proposed method, the skin friction distribution, pile–soil relative displacement, location of neural point, and differential settlement between the pile head (or cap) and adjacent soils can be determined. This work serves as a fast algorithm for initial and reasonable approximation of stress concentration ratio on the design aspects of piled embankments.