Theoretical dynamic displacement analysis for rock bolt with surrounding rock-soil body

To analyze rock-bolt dynamic mechanics, one theoretical model has been put forward based on several assumptions. At the interface of the bolt and surrounding rock-soil body, the coupling of a linear spring and a damper is used for the bolt system. The coefficient k of the spring and the damper coefficient ? are key parameters between the rock-soil body and bolt. The elastic and viscoelastic kinematic equations are established, and the displacement control equations are binary second-order partial-differential equations that can be simulated by numerical methods. One example shows the displacement curves with input waves; the displacement decays with different distributions. The curves of different times were simulated, and it was found that as the ratio value of the coefficient k of the spring and elastic modulus E increases, the displacement-decay-ratio speed increases per unit length. The same is true for the ratio values of the damper coefficient ? and elastic modulus E. The theoretical model can also be used to solve the impact-force problems.