【正文】 Development of a dynamic model for a cone bolt To ensure safety in underground excavations, it is important that the support systems used are capable of resisting the dynamic loads produced, for example, by rock bursts. In this paper, a dynamic simulation model for a cone bolt is proposed based on an experimental study. Drop weight tests were performed on resinbased cone bolts. These experiments revealed that the bolt has two energy absorption mechanisms: sliding in the resin and plastic deformation. To simulate this behaviour, a two degreesoffreedom lumpedmass model is proposed. Experimentally, the proportions of sliding and plastic deformation were found to vary significantly from one test to another. To account for this variability, two methods are proposed to determine the value of the parameters governing the sliding of the bolt in the resin, whereas a dynamic forceelongation model is used to simulate the plastic deformation. Comparing the results of a simulation to experimental data proved that the constitutive elements of the model are appropriate to simulate the dynamic response of the cone bolt. 1. Introduction Nowadays, underground excavations can be as deep as 5000 such levels, the rock mass can be highly stressed causing an increase in the frequency and severity of rock bursts. During a rock burst of moderate to major severity, the ejected rock mass can reach velocities between 3 and 10 m/s with corresponding energy levels varying from 10 to 501cJ/mz [1].Because of the dynamic nature of these phenomena, it is important to know the dynamic behaviour of rock reinforcement elements in order to properly design the support system. To study the subject, the mechanical and mining engineering departments of McGill University are collaborating with CANMET Mining and Mineral Sciences Laboratories (MMSL) in Ottawa. The work conducted so far through this collaboration has had three main objectives: (1)to validate the testing apparatus available at CANMETMMSL, (2) to determine the influence of the testing parameters on the response and performance of a cone bolt and (3) to develop a model to simulate the dynamic behaviour of a cone bolt. The first two objectives were reported in [2,3], whereas this article focuses on the third one, ., modelling the dynamic behaviour of a cone bolt. The dynamic models proposed in the literature for rock support elements can be divided in two main categories: lumpedmass and dynamic deformation models. Thompson et al. [4] used a lumpedmass model to simulate dynamic tests based on the momentum transfer principle [5 ]. Using this principle, the rock bolt to be tested is dropped simultaneously with the loading mass. When the freefalling elements have reached the desired velocity, the anchor of the bolt is rapidly stopped and the inertia of the loading mass dynamically loads the tested reinforcing element. In their model, the loading mass, the bolt anchor and other ponents of the setup were discretized as punctual masses connected in series by springs and dampers. However, the use of springs and dampers to connect each element might not be the most appropriate choice to model each interaction, especially the bolt ploughing through the resin. A lumpedmass model was also used by Tannant et al. [6 ] to simulate the axial strain response measured in mechanically anchored rock bolts during in situ dynamic loads were produced by explosives but their magnitude was always below the yield limit of steel. On the other hand, dynamic deformation models are based on the theory of strain (or stress) waves in solids [7,8]. Yi and Kaiser [9,10] performed drop weight tests on a clamped steel rod to simulate a mechanically anchored bolt. The bolts were loaded elastically or plastically depending on the drop weight , the model developed simulates only the propagation of elastic waves [11].The duration and amplitude of the simulated strain wave were found to be in good agreement with the experimental data. In order to study the local strain distribution along of the bolt, Ansell [12一 14] performed dynamic tests using an approach similar to the momentum transfer principle of Player et al. [5]. However, the loading mass used was lighter and the impact velocity was faster. To simulate the observed strain distribution, Ansell used two different techniques based on the theory of strain waves: a graphodynamical method proposed by Fischer [15一 18] and a numerical scheme, the Godunov39。 It is also important to mention that the angle of the cone has a significant influence on the performances of the cone bolt。 therefore, it is also important to characterize the steel plastic behaviour. Quasistatic properties The quasistatic yield limit and ultimate strength of steel are available from the manufacturer and equal to 517 MPa (107 kN) and 745 MPa (155 kN), respectively. To verify these values and to characterize the strain hardening behaviour, pullout tests were conducted on four cone bolts. The tested bolts were installed in steel samples tubes following the same procedure used for dynamic tests (see Section ). The forceelongation curves obtained for the four bolts were similar so only one test is illustrated in Fig. 5. From this test, the yield limit and ultimate strength can be evaluated as 125 and 185 kN, respectively, proving that the values of the manufacturer were quite conservative. . Dynamic properties For a bar under quasistatic uniaxial tension, the state of stress and strain is usually assumed to be uniform through its cross section and length. However, in the case of an impact, it is possible to have localized plasticity [13] as well as an increase of the yield limit and ultimate strength of steel pared to its quasistatic values [25]. Both of these effec