Application of shakedown theory in the design of earth structures for tracks under repeated train loads

Tracks require high performance of earth structures against excessive residual settlement under repeated train loads. In the current design standards, good quality of soil materials and compaction control are strictly prescribed based on empirical knowledge and scale tests; however, construction cost becomes relatively high accordingly. A more rational design method based on shakedown theory is presented in this paper. This method makes use of the lower-bound shakedown theorem and models the soils as Mohr-Coulomb materials. By calculating the analytical load-induced dynamic elastic stress field in a three-dimensional half-space and introducing a self-equilibrated residual stress field, the maximum magnitude of surface pressure on the soil foundation (i.e. shakedown limit) against long-term residual settlement is calculated through an optimization program. It is found the shakedown limit is dependent on the ratio of train velocity to shear wave velocity for a given earth structure. The shakedown limits for cases with different train velocities are compared with the design pressure from track analysis.