Shakedown analysis and its application in pavement and railway engineering

This paper has been prepared in memory of Professor Scott Sloan. It first presents a brief review of the development of shakedown analysis methods for pavement and railway engineering problems. In particular, it describes a new lower-bound method using the concept of critical residual stress fields and an upper-bound method using a nonlinear programming technique, which were developed by the authors, and then extended and applied to solve various shakedown problems in pavement and railway engineering. Moreover, this paper summarises and compares shakedown solutions for pavement and railway engineering problems, whilst highlighting the key factors that influence the shakedown limits. In addition, this paper proposes a simple, unified shakedown limit equation for pavements and railways under repeated moving surface loads. The equation includes three terms, which represent the resistances from cohesion, self-weight of the underlying soil, and self-weight of any superficial rigid layers, respectively, in a format analogous to Terzaghi's bearing capacity equation. Numerical results indicate that the coefficient in the cohesion term N_c^sd depends on the soil friction angle; while the coefficient in the self-weight term N_γ^sd is controlled by the soil friction angle and a dimensional factor γa/c. Values of N_c^sd and N_γ^sd for a typical rolling point contact problem are also presented and interpreted, which explain the different contribution ratios from the soil self-weight to the shakedown limits of pavement and railway problems.