Complex Dynamics of Landslides with Time Delay Under External Seismic Triggering Effect

Abstract

In present paper, model of infinite creeping slope with Dieterich-Ruina rate-and state-dependent friction law is analyzed using methods of nonlinear dynamics. The model is examined under the variation of two parameters: time delay t _d and initial shear stress s ₀. Time delay describes the memory effect of the sliding surface and it is generally considered as a function of history of sliding. Initial stress parameter is periodically perturbed, corresponding to long duration shear seismic wave, or it could be generated by non-natural sources such as traffic vibrations. The co-action of the observed parameters is estimated for two different regimes of sliding, namely β < 1 and β > 1, where β denotes the ratio of long-term to short-term (immediate) stress change. The results of the analysis indicate that the most complex dynamics occurs for β < 1, when a possible Ruelle-Takens-Newhouse route to chaos is observed, with a transition from equilibrium state, through periodic and quasiperiodic motion to deterministic chaos. For β > 1, system exhibits chaotic dynamics for t _d  = 0.1 and for δ _s  ≤ 0.18. These results correspond well with the previous experimental observations on clay and siltstone with low clay fraction, indicating that the motion along the sliding surface is velocity-strengthening (β < 1).