Observation of rock fragment ejection in post-failure response

Rockburst is a dynamic energy phenomenon accompanying the failure of hard rock in the form of brittle fractures [1–3]. Surplus energy is released when the accumulated elastic strain energy of rock is greater than the consumptive energy required for fracturing during its quick post-failure. This freed energy often takes radiant forms, such as acoustic energy, electromagnetic energy, and thermal energy [2,4,5], as well as physical forms, such as fragments being thrown in the laboratory, or an ejective rockburst in the field [6–11]. Of these types of releases, the fragments with kinetic energy always result in dangerous engineering accidents due to their abrupt impacts at high speeds [12–17]. To reduce bursting disasters in underground engineering, a great deal of effort has been put forth to explain the rockburst mechanism, predict ejection behavior, and design corresponding protective support techniques, etc. [18–24]. Conventional wisdom indicated that knowledge of the ejection velocity of the burst rock fragments is the key to further predicting rockburst risks and designing a corresponding protective support system [25–28]. For example, Kaiser and Cai underlined that rock ejection with a velocity of up to 3 m/s required a specially integrated yielding support system [28]. Simulated rockburst experiments in an underground tunnel in South Africa were successfully conducted to measure the ejection velocity of rock fragments directly. The results indicated that the in situ rock fragments were ejected from the tunnel wall with velocities in the range of 0.6 m/s to 2.5 m/s, thereby providing useful clues for rockburst's prevention technique in deep mining [29,30]. As expected, high experimental costs, rigorous site requirements (i.e., hard rock and high geostress) and complicated preparatory work for such field experiments have limited the application of in-situ rockburst measurements. Laboratory observations of rock ejections serve as a convenient and reasonable alternative method [31–33]. Petukhov noted that violent fracture of rock specimen in a compression machine could represent a laboratory simulation for dynamic rock failure during a burst in the field [32,34]. Visual observations of fragment ejection velocity in a laboratory are important not only to understand further the outbreak behavior of fragments in post-failure of hard rock but also to assess the bursting properties of rock in actual engineering. High-speed filming, which records instantaneous behavior by taking successive photographs over a short time interval, has been used in dynamically mechanical experiments as an accurate tool for observing impact failure [33,35,36]. Unfortunately, the highspeed camera has few applications in the documentation of ejection performance rock specimens under quasi-steady compression conditions. As a result, these filming methods warrant further research. In this article, we present a method to observe the ejection velocity of rock fragments under laboratory uniaxial compression tests with the help of a high-speed camera. Also shown in this article is an algorithmic program developed to calculate the initial speed and throwing angle of ejected rock fragments. This work