Non-linear rotational waves and complex rotation patterns in a chain of blocks with elbowing

Block elbowing, the process in which rotating blocks push neighbouring blocks apart, influences both geological deformation and the stability of mining excavations in blocky rock masses. A clearer understanding of elbowing is essential for improving rock mass modelling and maintaining the safety of engineering structures. To this end, we analyse a chain of stiff blocks connected by springs, with one or two end active (driving) blocks – the blocks whose rotation is externally induced. All other - passive blocks - have translational and rotational degrees of freedom. The results show that block rotation is sequential (starting from driving blocks) producing a rotational wave with strongly configuration-dependent rotational patterns.

Opposite to a single driving block system, a double-driving block system exhibits more complex behaviour, as the active blocks may rotate in the same direction (Case I) or in opposite directions (Case II). In Case I passive blocks can exhibit anticlockwise rotation that is opposite to the clockwise rotating driving blocks, while in Case II all passive blocks do not rotate at all.

Further deformation patterns arise from block geometry, introduced by varying block corner rounding to represent spheroidal weathering. The results reveal a transition from reversible to irreversible passive block kinematics. Reversible responses include either clockwise rotation followed by full recovery or no rotation. The boundary between these types of block behaviour is defined by a linear relationship between the active-passive and passive-passive contact friction coefficients, with the intercept related to block corner rounding. In contrast, irreversible kinematics characterised by residual rotation emerge only for highly rounded blocks. This irreversible behaviour is restricted to short block chains and disappears in chains of five blocks suggesting a critical size of the Cosserat like zone with independent rotational degrees of freedom. This study provides new insights for modelling the stability and long-term evolution of blocky rock masses.