A Stochastic Dynamical Model of Slope Creep and Failure

• Published in: Geophysical research letters Vol. 50; no. 11
• Main Authors: Lei, Qinghua, Sornette, Didier
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 16.06.2023; Wiley
• Subjects: Acceleration; Additives; Catastrophic events; catastrophic failure; Deformation; Distribution; Dynamic models; finite-time singularity; Geological hazards; Intermittency; Kesten process; landslide; Landslides; Landslides & mudslides; Mitigation; Modelling; Nonlinear feedback; Numerical simulations; Probability density function; Probability density functions; Probability distribution functions; Probability theory; Random variables; Simulation; Slope; slope creep; Slopes; Solifluction; Statistical analysis; Stochastic models; Stochastic processes; Stochasticity; Tertiary; Time series; Velocity distribution; Norway; Switzerland
• ISSN: 0094-8276; 1944-8007; 1944-8007
• DOI: 10.1029/2022GL102587

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. Plain Language Summary Landslides that threaten life and property often exhibit complex temporal evolutions. Some landslides may creep slowly over a long period of time, while others can accelerate rapidly or even collapse catastrophically. It remains difficult to understand and/or predict their behavior. In this work, we develop a novel stochastic dynamical formulation that can realistically reproduce the displacement time series of landslides in natural systems. It can simulate the progressive deformation of a slowly creeping slope as well as mimic its rapid acceleration with/without catastrophic failure. The ever‐present fluctuations in natural systems can also be captured in this stochastic modeling framework. By conducting synthetic numerical simulations capable of resembling many of the observed essential features of real landslides, we develop quantitative insights into the mechanisms that drive their complex temporal evolutions. Recommendations for landslide hazard forecasting and mitigation are further provided. Key Points A slope approaching failure tends to exhibit a phase transition from secondary to tertiary creep The stochastic Kesten process reproduces the phenomenology of intermittent bursts and inverse gamma velocity distribution of secondary creep A nonlinear stochastic dynamical process captures the tertiary creep of a slope evolving into a slow or catastrophic landslide