Propagation of the Longitude Stress Wave through a Filled Fracture Considering Cyclic Loading/Unloading Behaviours

Modelling the response of the filled fracture to the stress wave is of great significance for the prediction and prevention of rock mass instability under dynamic loads. An actual stress wave has varied frequencies, amplitudes, and multiple cycles, which makes the filled fracture suffer from cyclic loading/unloading actions. As a result, its mechanic properties such as the stiffness are progressively altered, which can prominently influence stress wave propagation in a feedback manner. However, existing analytical methods face challenges in modelling this dynamic process. Here, we conducted cyclic compression tests on simulated filled fractures. The filled fracture first produced compression-hardening deformation with stiffness increasing. When unloaded, its stiffness was abruptly enhanced compared with the loading case. This enhanced stiffness could be memorized when reloaded till the compressive stress exceeded the historical maximum, after which the filled fracture produced compression-hardening deformation again. Constitutive equations were proposed to characterize the above compressive stress-closure relation and were accurately validated by experimental results. On this basis, we established an analytical model for the propagation of the longitude stress wave through a filled fracture considering cyclic loading/unloading behaviours. It could well reproduce the experimental result on propagation of the stress wave with two main merged pulses through an artificially filled fracture. Parametric studies were conducted to systematically examine the influences of the cyclic loading/loading process, amplitude, and frequency. It was found that cyclic loading/unloading actions to the filled fracture could be memorized and accumulated to a maximum extend, which prominently affected subsequent stress wave propagation.