A LINEAR STABILITY ANALYSIS OF BIFURCATION PHENOMENA OF SUBMARINE LANDSLIDE

Abstract

 Large-scale submarine landslides can magnify the tsunami amplitude generated by earthquakes and cause severe damage to offshore infrastructures such as submarine cables and pipelines. It is, therefore, important to reveal the mechanism of submarine landslides and the kinematic behavior during the sliding process of submarine slopes. The authors, so far, have conducted laboratory model experiments to understand the kinematic characteristics of submarine landslides. It has been revealed that submarine landslide motions can be classified into three types based on the time histories of the slide velocity. In particular, in the case of the large landslide, it exhibited creep behavior in which the landslide velocity increased exponentially after a steady-state with the constant velocity. In the present study, we discuss those different types of landslide as a bifurcation problem from the steady-state slide and perform a linear stability analysis considering the nonlinear friction law. The main objective of this analysis is to find out the dominant parameters involved in the transition of the submarine landslide from the steady-state to the massive landslide. The results of the linear stability analysis show that the nonlinear system bifurcates into three cases depending on the change in the shear stress acting on the sliding surface after the onset of the slide: two stable cases and one unstable case. In particular, in cases where the system becomes unstable, it was found that the shear stress that is lower than that in the initial steady-state can lead to large landslides. Furthermore, time histories of the slide velocity and the displacement were calculated numerically for each case. The results showed that the slide velocity patterns observed in the experiments, and those calculated were well matched qualitatively. The results of the linear stability analysis mathematically support the idea proposed by the authors that submarine landslide behavior can be classified into three patterns.