Study on the fatigue properties and constitutive model of siltstone under the coupled action of dry‒wet cycles and cyclic loads

To study the fatigue properties of siltstone under the coupled action of dry‒wet cycles and cyclic loads, uniaxial fatigue tests were conducted on rock samples. The results show that the fatigue stress‒strain curve of siltstone exhibits a "sparse-dense-sparse" characteristic. The trend of the variation in peak strain can be divided into three stages: the initial stage, the isokinetic stage, and the acceleration stage. With an increasing number of dry‒wet cycles, upper stress limit, or stress amplitude or with a decreasing loading frequency, a rock sample will have a more significant plastic deformation during the failure process, and its failure life will be shortened. Additionally, to construct a constitutive equation under the coupled action of dry‒wet cycles and cyclic loads, a fractional-order viscoelastoplastic fatigue model was established by introducing a Scott-Blair fractional-order element to replace the Newton damper in the Nishihara model. The cyclic loads were decomposed into static loads and cyclic loads with an average stress of zero. Based on the theory of viscoelastic mechanics, energy storage compliance and energy consumption compliance were introduced, and a compliance correction coefficient α was proposed. A constitutive equation under cyclic loads with zero average stress was established. To consider the impact of dry‒wet cycles, a dry‒wet correction coefficient Dn was also proposed. Finally, the constitutive equation of siltstone under the coupled action of dry‒wet cycles and cyclic loads was derived. The model can effectively describe the nonlinear characteristics of rock fatigue deformation and entire failure process. The experimental data verify the rationality of the model.