A Dynamic Damage Model for the Rock-Shed Roof Under the Rockfall

The dynamic response of the rock-shed roof under the rockfall is a complicated mechanical process, which mainly includes the following three deformation stages, e.g. the elastic compression, plastic damage compression and elastic resilience stages of the rock-shed roof. However, the existing models based on Hertz elastic-perfectly plastic contact theory cannot perfectly reflect the above mechanical process. Therefore, on basis of the classical Hertz contact theory, the damage of the rock-shed roof induced by the rockfall is firstly introduced to consider its effect on the material elastic modulus, and then the revised Hertz contact theory considering the damage is proposed. Secondly, in view of the existing calculation method of the maximum rockfall impact force based on the theorem of impulse, a new calculation method is proposed by combining the revised Hertz contact theory. Thirdly, according to the dynamic mechanical response process of the rock-shed roof under the rockfall and in view of the revised Hertz contact theory, a dynamic damage model for the rock-shed roof under the rockfall is proposed, which can perfectly illustrate the variation law of the impact force with the deformation of the rock-shed roof during the rockfall. Finally, the proposed model is verified with other models for the maximum rockfall impact force. In all, the proposed model can perfectly describe the dynamic mechanical behavior of the rock-shed roof under the rockfall, which can be referred for the engineering design.