A Stochastic Dynamical Model of Slope Creep and Failure

Abstract

We propose a stochastic dynamical model to simulate slope secondary and tertiary creep phenomena. The slope secondary creep is represented by the Kesten process defined as a stochastic affine auto-regressive process involving both multiplicative and additive random variables. The Kesten process can realistically capture the co-existence of a background deformation and intermittent displacement bursts, which are together well characterized by an inverse gamma velocity distribution. The slope tertiary creep is modeled by a nonlinear stochastic dynamical equation embodying a nonlinear feedback mechanism and a nonlinear random effect, which can mimic the development of slow or catastrophic landslides. For catastrophic landslides, the probability density function of slope velocities tends to deviate from the inverse gamma distribution by populating the “dragon-king” regime, although sometimes they may grow undetectably in the “black-swan” regime. Our model provides a quantitative framework to understand, simulate, and interpret complex landslide displacement time series.