A Unified Shakedown Limit Equation for Pavements and Railways Under Repeated Traffic Loads

In 1943, Terzaghi proposed a simple, unified equation for determination of the bearing capacity of soils considering static surface loads. From then, this classical equation and its later extensions have been widely used in the design of various foundations against instantaneous failure. With the fast development of transportation industry, researchers have been interested in the evaluation of shakedown limits of pavements and railways under repeated traffic loads, which are much smaller than Terzaghi’s bearing capacity. Noting that various shakedown limits for different problems share some common trends and key factors, this paper proposes a simple, unified shakedown limit equation, in a format analogous to Terzaghi’s equation. The shakedown limit equation includes three terms, which represent the contributions from cohesion, self-weight of the underlying soil, and self-weight of any superficial rigid layers, respectively. Numerical results indicate that the coefficient in the cohesion term Ncsd depends on the soil friction angle; while the coefficient in the self-weight term Nγsd is controlled by soil friction angle and a dimensional factor γa/ c. Values of Ncsd and Nγsd for a typical rolling point contact problem also explain the different contribution ratios from the soil self-weight to the shakedown limits of pavement and railway problems.