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