A Fractional-Derivative-Based Constitutive Model for the Mechanical Behavior of Fully Grouted Rock Bolt Under Confined Pullout Creep

Fully grouted rock bolts have been extensively utilized in underground reinforcement. Numerous experimental and theoretical studies have been performed to examine the short-term strength of the fully grouted rock bolts under the normal pullout test. However, the creep behavior closely associated with the long-term strength of the rock-bolting system has been rarely examined. Here, we proposed a fractional-derivative-based constitutive model to simulate the observed creep stages of the fully grouted rock bolts under the confined pullout creep condition. The model leveraged the Abel dashpot to capture the nonlinear creep and an exponentially decaying damage function to represent the accumulated deterioration in the bolt–grout interfacial strength during creep. The proposed constitutive model was validated against a series of laboratory confined pullout creep tests. The tests covered confining pressures up to 3.0 MPa and sustained pullout loads ranging from 37 to 279 kN. The analytical curves agreed closely with the measurements (R2 > 0.98), indicating that the model can characterize the time-dependent pullout response of the tested bolt–grout system. Our study facilitates the underground reinforcement system design in the fields of civil and mining engineering where long-term rock-bolting service is required.