The dominant mechanism of riverbank cantilever failure is soil erosion of the bank toe and near bank zone. This paper demonstrates that the shape of the riverbank cantilever failure depends on the properties of the soil and the fluctuation of the river water level (RWL). With a stable RWL, a riverbank with higher resistance force leads to failure with larger and deeper overhang erosion width. When RWL rises, a less cohesive soil bank will be eroded over a larger width and riverbank failure will occur earlier. With a low rate of rising RWL, riverbank failure may happen in a type of mass failure. With a high rate of rising RWL, a riverbank will fail in a type of overhang riverbank failure, with the soil erosion rate being the main affected factor.
On the basis of the generalized physical model of the riverbank, the experiments were conducted to study the mechanisms of riverbank failure under the coupling effect of seepage flow and river flow. The experimental setup was specially designed, as well as test point location, parameters and procedures, and the main influencing factors were analyzed affecting riverbank failure based on the failure types, the variations of pore water pressure and soil displacement. The results indicated that the coupling effect has different influences on the bank failure in three aspects: the failure type, the process and the extent. In addition, the river flow played a more important role than the seepage flow in the coupling effect on the bank failure.
We prove that groups acting geometrically on delta-quasiconvex spaces contain no essential Baumslag-Solitar quotients as subgroups. This implies that they are translation discrete, meaning that the translation numbers of their nontorsion elements are bounded away from zero.