A unified model for estimating the permanent deformation of sand under a large number of cyclic loads

How to accurately estimate the permanent deformation of soils due to large number cycles of cyclic loads is essential in many engineering projects, such as offshore wind turbine foundation and high-speed railway. It is still a challenging issue, although many works have been carried out. In this study, a series of cyclic triaxial tests with different levels of initial mean effective stress, relative density, initial static stress ratio, and cyclic stress ratio were performed on saturated Toyoura sand. Test results clearly showed that the vertical permanent strain increased with increasing cyclic stress ratio and initial mean effective stress. Moreover, the shear strain amplitude during the initial loading of the first load cycle was used to describe the intensity of soil particles rearrangement which is the mechanism of permanent deformation. A unique relationship between the shear strain amplitude and the vertical permanent strain was established. A four-parameter model was subsequently proposed for estimating the permanent strain of sand under cyclic loading, which inherently considered all the main influencing factors. Finally, the comparison between the estimation and the measurement in laboratory tests convincingly illustrates the adequacy of the proposed model in estimating the permanent deformation of sand under cyclic loading.