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Estimating the permanent strain of granular materials in embankments subjected to cyclic loading is a major challenge for transport engineering projects. In practice, the development of permanent strain can be divided into two periods, postcompaction and secondary cyclic compression. In this study, the existing literature on prediction of permanent strain is reviewed in detail, and the key advantages and limitations of each model are presented and discussed. Based on the gaps identified in the existing literature, a new model for predicting the permanent strain of granular materials under low cyclic loadings is proposed. This model defines two new terms, "representative cycle number" and "reference strain line," to distinguish the postcompaction and secondary cyclic compression periods accurately. Specifically, the new model correlates the stress states, first with the accumulated strain at the end of the postcompaction period, and then with the strain rate in the secondary cyclic compression period, with good accuracy. This model eliminates the requirement for static compression tests, which are normally needed for the existing models. The new model also avoids the determination of resilient modulus, which is not a competent definitive parameter for evaluating the performance of granular materials. Further, the new model is validated by predicting the permanent strain development of two types of granular materials that are adopted in pavement subgrade and railway subgrade, respectively, in cyclic triaxial tests. The new model is applied in a trial for predicting the long-term settlement of a full-scale physical model of railway embankment under cyclic loading. The results indicate that the new model can effectively capture and accurately predict the permanent strain of testing materials under various stress states and testing conditions. It is also proved that the practical value of the new model is promising. The effects of moisture content, particle size distribution, and compaction degree were not considered, and further studies are recommended to investigate these factors. [ABSTRACT FROM AUTHOR]

Therefore, HT ht plays a similar role for granular materials as CSR for soft soils ([11]) in the identification of the shakedown ranges. 5(b) and 8(b) of the original paper, a characteristic curve between HT ht and the shakedown range indicator, HT ht can be well established. With the fitting parameters determined and the boundary values of HT ht , the corresponding boundary values for HT ht can be accurately calculated. [Extracted from the article]