A Fractional Calculus-Based Constitutive Model for the Coupled Stress Relaxation of Rock Bolts in Saturated Clay and Parameter Sensitivity Analysis

The long-term relaxation of bolt prestress is a critical issue threatening the safety of geotechnical engineering such as slopes and foundation pits, while traditional integer-order models are inadequate for accurately describing their nonlinear time-dependent behavior in saturated clay. Based on fractional calculus theory, this paper establishes a constitutive equation for the coupled stress relaxation of rock bolts and saturated clay. By introducing the Riemann-Liouville fractional derivative and the two-parameter Mittag-Leffler function, the memory effect and continuous relaxation characteristics of the material are theoretically characterized. To achieve high-precision identification of the model parameters, a strategy coupling an Adaptive Hybrid Differential Evolution (AHDE) algorithm with the Levenberg-Marquardt (L-M) algorithm is proposed. The validity of the developed constitutive model was verified through application and parameter identification using monitoring data from rock bolts in the slope engineering of the Guangxi Friendship Pass Port. The results demonstrate that the proposed model can accurately replicate the entire stress relaxation process (R²=0.9517). Parameter sensitivity analysis further clarified the influence mechanisms of key parameters such as the fractional order and viscosity coefficient, providing a systematic method and reference for the theoretical analysis and engineering investigation of long-term prestress relaxation in rock bolts.