Application of shakedown theory in track substructure design

Tracks require high performance of earth structures against excessive residual settlement under repeated train loads. In the current design standards, the quality of soil materials and compaction control are strictly prescribed based on empirical knowledge and scale tests; however, construction costs become relatively high accordingly. A more rational design method based on shakedown theory is presented here. 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 optimisation programme. It is found the shakedown limit is dependent on the ratio of train velocity to shear wave velocity for a given earth structure. The maximum admissible train loads for the cases with different design velocities can be predicted by modifying the quasi-static shakedown limit with an attenuation factor.