Long-term cyclic loading applied to clay at stress levels lower than the critical cyclic stress leads to soil deformation without inducing damage. The Monismith model is well-known for its simplicity and ability to describe the trend of cumulative plastic strain under cyclic loading. However, the simulated cumulative plastic strain increases indefinitely with the number of cycles until damage occurs. At lower cyclic stress levels, the cumulative plastic strain tends to be stabilized with an increasing number of cycles, ultimately limits the applicability of the model. To address this issue, a series of axial-torsional bi-directional cyclic loading tests are conducted on saturated clay using a hollow cylinder torsional shear apparatus. An empirical three-parameter mathematical prediction model is proposed by analyzing the development of cumulative generalized shear strain based on test results. The relationships of model parameters a with plasticity index, frequency, generalized shear stress, and mean effective stress; b with plasticity index, and c with frequency and plasticity index are presented as functional expressions. Finally, the predicted results of the empirical model are compared with test results to verify its effectiveness, providing a basis for calculating cumulative deformation in clay under long-term low cyclic stress levels.
