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Hard structural planes mainly exist in rock slopes and their creep characteristics largely determine slope stability. Traditional models have some shortcomings in describing the creep characteristics of hard structural planes, such as poor adaptability and unclear physical meaning of parameters. In order to overcome these shortcomings, based on the creep failure mechanism of hard structural planes, an element combination model is adopted in the study. In the instantaneous deformation stage, the plastic deformation proportional coefficient n is introduced based on the strain rebound theory of loading-unloading tests. In the attenuation creep stage, the hardening coefficient C and creep index m are introduced. In the viscoelastic-plastic failure stage, the weakening factor k is introduced. By improving traditional elements, a new piecewise nonlinear constitutive relationship of hard structural planes is established and then the creep equation is obtained with integration method. The adaptability of the established model and the way to solve parameters are analyzed and the correctness of the model is proved theoretically. The data of creep tests of the prefabricated serrated interpenetrated green sandstone structural plane and the concealed non-interpenetrated marble structural plane are further fitted and verified, yielding a fitting result exceeding 0.95, thereby indicating a strong correlation. By optimizing the whole creep process of the hard structural plane in stages and demonstrating the difference in the creep mechanism of the hard structural plane at different depths in a rock mass in the high and low stress fields in the form of piecewise function, the physical meaning of the improved model is clearer. In addition, the improved model allows the higher accuracy of nonlinear characteristics in attenuation creep stage and acceleration creep stage and provides the theoretical basis for the stability analysis of rock slopes. [ABSTRACT FROM AUTHOR]