Triggering inverse rotation in 1D model of blocky rock mass

The weak connections between individual blocks in blocky rock mass lead to the possibility of block rotations. Rotation of non-spherical blocks pushes the adjacent blocks away; the phenomenon termed elbowing [1]. Furthermore, rotations in both directions create the lateral displacements in the same direction such that the behaviour becomes non-linear of absolute value type. In order to investigate the resulting pattern of elbowing blocks, we considered a simple one-dimensional structure (chain) of stiff square blocks holding together by springs. Only the end block (driving block) with a fixed centroid position is rotated, while each passive block has two degrees of freedom: translational and rotational. A one-dimensional physical model, analytical model, and numerical model (using the commercial discrete element software UDEC) are developed. It was observed that the passive blocks do not consistently rotate in the same direction as the driving block; instead, when the driving block reaches a certain critical angle, it triggers the change of the direction of rotation and the blocks start inverse rotation. We define the angle of the driving block, when the rotation of the passive blocks returns to zero, as the ‘angle of interior zero’. It was found that this angle is influenced by the magnitude of contact friction and the number of blocks. The result demonstrates the complexity of block motion pattern even in such a simple blocky system.

[1] Pasternak, E., Dyskin, A.V., Estrin, Y. (2006) Deformations in transform Faults with rotating crustal blocks. Pure Appl. Geophys. 163 2011-2030.

Acknowledgement: The authors are grateful to Dr I. Shufrin and the School of Engineering workshop for the help with designing and manufacturing of an initial version of the experimental device.