Three dimensional discontinuous deformation analysis (3D DDA) and its application to the rock slope toppling

Numerical simulations are very important to the disaster preventions in rock slope engineering, and many researchers pay attention to the developments and applications of numerical analysis methods in this field recently, because of the developments of computer science. In order to simulate the behaviors of rock slopes with discontinuities more precisely, the numerical method is required to consider the effects of distributions of discontinuities, terrains, contacts among blocks and the large displacements in three dimensions. In this paper, both the theory of three dimensional discontinuous deformation analysis(3D DDA) and its application to simulate rock slope failure problems are discussed. DDA belongs to the discrete numerical analysis methods, and the contact judgment and contact force computation should be concerned. The contact forces are produced when blocks contact to each other. Usually, normal contact spring is employed to calculate the normal contact forces to prevent blocks from penetrating to each other during contacts, and the normal contact spring is deleted when blocks are leaving. In addition, the failure along discontinuous surfaces can be simulated easily by applying the Mohr-Coulomb failure criterion. The appropriate contact spring arrangement in 3D DDA follows the criterion of no-penetration and no-tension to obtain correct contact forces during contacts. The new approach has been successfully applied to simulate a rock slope toppling at Amatoribashi-nishi site in Japan. The simulation results are quite good in agreement with the video pictures obtained from the field. It is believed that the simulation is very helpful on investigation of the failure mechanism and process, and can provide useful knowledge to study the similar events in future.