Creep damage model of weak interlayer based on fractional order integral

The soft interlayer, often considered the "weak link" of slopes, poses a significant threat to slope stability. This study focuses on the Permian carbonaceous shale soft interlayer commonly found in Southwest China. The creep characteristics of the soft interlayer were investigated, and a graded shear creep test was conducted in addition to conventional shear tests to analyze the shear deformation behavior of the soft interlayer comprehensively. The long-term strength of the soft interlayer was determined using the steady-state creep rate method. Building upon the Riemann-Liouville fractional order integral theory and statistical damage theory, an improved model based on the traditional Nishihara model was developed. The accuracy of the model was verified using the adaptive differential evolution algorithm in combination with the weak interlayer shear creep test curve, followed by a parameter sensitivity analysis. The results demonstrate that the improved model adequately describes the three stages of creep in the weak interlayer. The creep curve is influenced by the differential order., the shape parameter m, and the proportional parameter F-0. Parameter m reflects the brittle characteristics of the soft interlayer, while parameter F-0 characterizes its physical and mechanical strength. The research results can provide a theoretical basis for disaster prevention monitoring and stability analysis of slopes with weak interlayer.