The existing fatigue models are not sensitive to load cycles and do not consider the effect of osmotic pressure. To study the strain characteristics and fatigue constitutive model of limestone under osmotic pressure and cyclic disturbance coupling, 300 cycles of loading and unloading tests under different osmotic pressures were carried out and the evolution characteristics of irreversible accumulative deformation curve were analyzed. Then, an improved Nishihara fatigue model was established based on the theoretical results of rheological model by introducing the nonlinear function into Nishihara model. The results show that the irreversible cumulative deformation under different osmotic pressures experiences three evolutionary processes of initial deformation stage, stable deformation stage, and accelerated deformation stage with increasing cycle indexes, showing the typical fatigue deformation characteristics. The axial deformation at initial deformation stage increases significantly, the stable deformation stage shows approximately linear growth and accounts for 40% to 73% of total cycle indexes, and the accelerated deformation stage shows a sudden increase indicating the overall instability of limestone. The nonlinear function is introduced into the Nishihara fatigue model based on rheological theory, and a fatigue deformation model that can reflect the entire process of irreversible accumulative deformation curve is established. The physical meanings of model parameters are discussed, and the relationships between model parameters and cycle indexes are inverted. The model parameters have good convergence and verify the rationality and applicability of the fatigue constitutive model based on experimental data. The results have reference value for revealing the fatigue characteristics of rock under osmotic-cyclic stress coupling.
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