Fractal rock slope dynamics anticipating a collapse

Area of Science:

• Geophysics
• Rock Mechanics
• Complex Systems

Background:

• Rock slope failures pose significant geohazard risks.
• Understanding slope dynamics is crucial for risk assessment and mitigation.
• Previous studies often simplified slope behavior, neglecting complex fluctuation patterns.

Purpose of the Study:

• To analyze the time series of dilatometric measurements of relative displacements on sandstone slopes.
• To differentiate the dynamics between stable and unstable rock slopes.
• To characterize the statistical properties of residual displacements after meteorological influences are removed.

Main Methods:

• Dilatometric measurements of relative displacements on rock cracks.
• Time series analysis of displacement data from stable and unstable sandstone slopes.
• Statistical analysis of residuals, including correlation analysis and probability distribution fitting.

Main Results:

• Inherent rock slope dynamics exhibit limited nonlinearity.
• Residual fluctuations in stable slopes show short-range correlations and non-Gaussian, fat-tailed behavior.
• Unstable slopes display self-affine dynamics characteristic of fractional Brownian motion with long-range power-law correlations and power-law probability distributions.

Conclusions:

• The distinct fluctuation dynamics (short-range vs. long-range correlations) can differentiate stable from unstable rock slopes.
• The observed self-affine dynamics and power-law distributions in unstable slopes suggest critical phenomena preceding failure.
• Further research into these complex dynamics can improve predictive models for rock slope stability.