Limited laboratory studies have investigated the cyclic behavior of sands under plane strain state, despite the current extensive applications of the plane strain hypothesis in modeling the behavior of subgrade soils beneath long road embankments. This study aims to explore the traffic-induced deformation behavior of sand under plane strain state and compare it to the conventional triaxial stress state. A series of one-way high-cyclic tests were performed on Fujian sand under both states using a true triaxial apparatus, considering different cyclic stress levels, consolidation stresses, consolidation anisotropies, and relative densities. In the plane strain scenario, the deformation of the specimen in the direction of intermediate principal stress was restricted when the cyclic major principal stress was applied. The test results indicate that during long-term cyclic loading, the sand exhibits substantially lower accumulated axial and volumetric strains when subjected to plane strain state as opposed to the conventional triaxial state. The reduction effect of plane strain state on the accumulated axial strain was found to be distinctively correlated with the strain levels, regardless of the cyclic stress amplitude and relative density. A practical formula was developed to estimate the difference in accumulated axial strain between the plane strain and triaxial states. Additionally, the intermediate principal stress of specimens under plane strain state was observed to oscillate cyclically in accordance with the one-way vertical cyclic stress. The intermediate principal stress coefficient, triggered by vertical cyclic loading, is more pronounced under high deformation, with its magnitude dependent on the specific loading conditions.

In order to study accumulated deformation characteristic of Yellow River silt under long-term cyclic loading, a series of dynamic triaxial test was conducted. The effects of confining pressure, relative density, loading frequency and cyclic stress ratio on accumulated deformation behavior were studied. The results show that the accumulated strain increases as the confining pressure and cyclic stress ratio increase. The increment of relative density and loading frequency will restrain the increase of accumulated strain. Based on test results, accumulative strain prediction model that can reflect the effects of confining pressure, relative density, loading frequency and cyclic stress ratio was proposed. By comparing the measured curve and the predicted curve of accumulated strain, it can be concluded that the prediction model developed in this study is applicable for the Yellow River silt. These findings offers some insight into the deformation estimation and prediction of subgrade with Yellow River silt.