An improved thermo-parameters method for dynamic shakedown analysis of railway subgrade

To ensure the safety and stability of train operation, a reasonable evaluation of long-term durability of railway subgrade subjected to large number of cyclic train loads is necessary. With the concept of controlling safety margins against excessive inelastic deformation, shakedown theory provides an effective approach for the analysis of long-term performance of geotechnical structures. In this paper, an improved thermo-parameters method (TPM) is proposed to carry out dynamic shakedown analysis on the railway subgrade. Mathematically, the method is formulated as an optimization problem, in which the objective function is the dynamic shakedown limit and variables are the shakedown residual stresses defined through the distribution of hypothetical thermal stress field and further described by the Non-Uniform Rational B-Splines (NURBS) surface. The presented solution procedure was incorporated to the finite element (FE) model and numerical examples were presented to demonstrate its effectiveness for different cases. An in-situ test conducted in a fill section of railway subgrade was used for numerical modeling and further result validation. The results indicated that the dynamic shakedown limits varied with the loading frequency and showed smaller values than the quasi-static shakedown limit, especially at the natural frequency of structure. The current findings may be beneficial to the further understanding of the long-term durability and stability of subgrade under dynamic loading, and provide useful information for the shakedown design of the railway subgrade.