Rock slope failure preparation paced by total crack boundary length

Slope failures are significant natural hazards causing substantial damage and loss of life globally. They are a two-phase process: a preparation phase involving crack growth and coalescence to form a failure plane, followed by an activation phase where the mass moves. While the activation phase is relatively well-understood, the preparation phase is less so, hindering accurate prediction of failures. Rock cracking emits seismic signals detectable in the field, offering indirect information on internal processes. This study leverages a high-signal-to-noise ratio seismic dataset from the Illgraben catchment in Switzerland, known for frequent rock falls and slides, to analyze crack activity leading up to a large rockslide event on January 2nd, 2013. A machine learning approach based on hidden Markov models is used to optimize crack detection and analyze the temporal evolution of crack formation prior to the rockslide, aiming to identify key parameters controlling the failure plane development and improve early warning systems.

Previous research on rock slope failure has focused heavily on the activation phase, with various models addressing factors like rainfall, seismic activity, and material properties triggering failure. However, understanding the preparatory phase is crucial for effective prediction. Studies utilizing acoustic and seismic monitoring have shown promise in detecting crack initiation and propagation, but often face challenges in discerning signals from background noise. The use of machine learning techniques, such as hidden Markov models, is a relatively recent advancement in the field, offering improved capabilities for automated event detection and classification in noisy seismic data. Existing models often treat cracks as one-dimensional entities, neglecting the crucial role of the two-dimensional geometry and the total crack boundary length in failure plane evolution. This study builds upon these previous works by applying advanced signal processing and machine learning techniques to a high-quality dataset, focusing on a quantitative analysis of the temporal dynamics of crack development in the critical period immediately preceding slope failure.

The study utilized seismic data from a network of nine broadband seismometers deployed in the Illgraben catchment. Three instruments were positioned close to the rockslide site (January 2nd, 2013), providing high-resolution data. A hidden Markov model (HMM)-based machine learning technique, implemented in the ASESS (Advanced Seismic Event Spotting System) software, was employed to detect and classify seismic events within the data. The HMM approach allowed for the identification of crack events, slope failures, and debris mobilization events, even with low signal-to-noise ratios (SNR). The algorithm's performance was assessed using synthetic data with varying SNR levels to quantify the accuracy of event detection. The temporal evolution of crack events was analyzed, specifically focusing on the period leading up to the major rockslide. A mechanistic model was developed to explain the observed crack rate evolution. The model assumes: 1) a proportionality between the cumulative number of cracks and the fractured area of the failure plane, 2) the rate of change of the fractured area is proportional to the total crack boundary length and crack propagation velocity, and 3) the total crack boundary length initially increases with crack growth, then decreases as cracks coalesce and form a continuous failure plane before final failure. These assumptions resulted in a differential equation that was solved analytically, generating a sigmoidal exponential function fitted to the observed cumulative crack number. The model parameters were evaluated, and the influence of non-constant crack propagation velocity was tested. Event location was determined through signal migration techniques using at least two of the three stations closest to the rockslide. Events outside the area of the main event were excluded using a spatial filter. The analysis focuses on the period leading up to the 2013 rockslide to understand the transition from distributed cracking to localized damage accumulation.

The study identified 1592 crack events in the 20 days before and 10 days after the January 2nd, 2013 rockslide. The analysis revealed a clear temporal evolution of crack activity. Initially, the cumulative number of cracks (N(t)) increased linearly, indicating a stochastic, distributed crack initiation phase. However, in the 27 hours before the rockslide, the cumulative crack number exhibited an S-shaped pattern, indicating a transition to a localized crack damage phase. A mechanistic model, incorporating the total crack boundary length as a primary control parameter, successfully fitted the observed S-shaped curve with a high R-squared value (0.998). This strongly supports the hypothesis that the total crack boundary length is the key factor governing the acceleration of failure plane formation in the hours preceding the rockslide. The model's parameters suggest a rapid failure plane development timescale of 2.7–4 hours once the internal failure mechanism is triggered. The lack of clear external triggers (precipitation or seismic activity) in the days preceding the rockslide supports the idea that internal processes, governed by the crack boundary length, were dominant in driving the event. The success of the 2-D model highlights that considering the areal extent of cracks and their boundary length is crucial for understanding slope failure dynamics at the hillslope scale. The study also uses a confusion matrix, and synthetic data testing to evaluate the accuracy and reliability of event detection using HMMs. The synthetic tests show that true positive detection remains high even for low SNR signals, validating the reliability of the HMM methodology in detecting the subtle crack-related seismic signals. The confusion matrix, based on a visual inspection of a subset of the data, helps to quantify the accuracy of the automated classification by ASESS.

The findings significantly advance our understanding of rock slope failure by demonstrating the crucial role of total crack boundary length in the final stages of failure plane development. The transition from a linear to an S-shaped crack rate, captured by the mechanistic model, signifies a shift from externally driven, distributed cracking to an internally controlled, localized damage accumulation phase. The successful fit of the model emphasizes that considering the two-dimensional nature of cracks, and their boundary length as a state parameter, is essential. This contrasts with traditional one-dimensional crack models. The lack of clear external triggers for the rockslide highlights the importance of internal processes in driving failure. This has significant implications for early warning systems, suggesting that monitoring internal crack development, rather than relying solely on external triggers, may be more effective. The relatively short timescale (hours to a day) of the sigmoidal phase in the crack rate emphasizes the necessity for real-time monitoring.

This study provides strong evidence that the total crack boundary length acts as a primary control parameter during the final stages of rock slope failure preparation. The developed mechanistic model accurately captures the observed S-shaped crack rate pattern, highlighting the significance of treating cracks as two-dimensional features. The lack of clear external triggers in this case underscores the dominant role of internal processes in driving the event. The findings have important implications for developing improved early warning systems for slope failures, suggesting that real-time monitoring of crack propagation, potentially using seismic data analysis coupled with HMM techniques, holds great promise for predicting impending events. Future research could explore the controls on the timescale of failure plane development, including lithological and climate factors. This could lead to more accurate estimates of warning times and improved risk assessment.

The study is based on a single event in the Illgraben catchment. While the high-quality data and detailed analysis provide compelling results, further research is needed to confirm the generalizability of these findings across different geological settings and climate regimes. The mechanistic model relies on several simplifying assumptions, such as constant crack propagation velocity, which may not perfectly reflect the complexity of real-world conditions. The accuracy of event detection and classification by the HMM method is evaluated using synthetic data and a limited visual inspection of the real data. A more extensive validation across different datasets would further strengthen the results. The spatial resolution of the event location algorithm might introduce uncertainty into the interpretation of the spatial distribution of crack events.