Rock slope failure preparation paced by total crack boundary length

The study addresses how rock slope failures initiate and evolve during the poorly observed preparation phase, when cracks nucleate, grow, and coalesce to form a failure plane. While the activation phase of slope failures has been extensively studied, the preparatory cracking that determines timing, volume, and mobilization mechanism remains elusive due to limited observability within natural hillslopes. Seismic and acoustic emissions from rock cracking can provide indirect, high-resolution insight into subsurface processes, but signals often have low signal-to-noise ratios. This work leverages a unique dataset from the Illgraben catchment (Swiss Alps) to detect and quantify crack activity using a hidden Markov model, and to link the observed precursory crack evolution to a simple physical model that identifies the dominant control on failure plane development immediately prior to failure.

Prior studies have documented the high societal and geomorphic impact of slope failures and the role of external triggers such as earthquakes and rainfall. The activation (runout) phase is well characterized by seismic and numerical approaches, but the preparation phase is less understood. Laboratory and field studies have shown that crack growth emits detectable seismic and acoustic signals, and machine-learning methods based on hidden Markov models have been successfully used for event detection in seismic records. Previous modeling commonly treats cracks as one-dimensional features affecting damage accumulation and time-to-failure through subcritical crack growth influenced by environmental conditions (humidity, temperature). However, an explicit role for the total crack boundary length as a two-dimensional control parameter in natural slope-scale failure preparation has not been emphasized. This study builds on and extends these strands by detecting low-SNR cracking in situ and interpreting its temporal evolution through a mechanistic framework.

Study site and instrumentation: The Illgraben catchment (∼10 km², 1900 m relief) in Switzerland experiences frequent rockfalls and slides. From 2012 to 2014, up to ten Nanometrics Trillium Compact 120 s broadband seismometers (sampled at 200 Hz with Digos DataCube loggers) were deployed. Three stations (STA4, STA5, STA6) were within a few hundred meters of a 10,000 m³ rockslide that occurred on 2013-01-02, with STA6 located ∼180 m from the detachment area.

Event detection via hidden Markov models: Event detection and classification used ASESS (Advanced Seismic Event Spotting System) in Python 3.8 with ObsPy. Workflow steps: (i) waveform parametrization, (ii) model training, (iii) event detection. Thirty features related to spectral, complex trace, and polarization properties were computed in 256-sample windows sliding by 1 s; two low-weight features (normalized envelope and its derivative) were dropped via PCA, retaining 28 features (22 for synthetic tests excluding polarization). Data were bandpass filtered 1–30 Hz to target mass-wasting signals and avoid microseisms and teleseismic effects.

Event classes and training: Four classes were defined: crack (short, 1–20 Hz, impulsive onset), slope failure (detachment plus downslope disintegration; short to minutes, high energy), debris mobilization (mobilization of loose material without initial rupture; emergent, lower energy than slope failure), and tectonic earthquakes (to avoid confusion). For geomorphic classes, the hour 2013-01-02 10:00–11:00 UTC served as training for temporary background and event models; a separate hour around a local earthquake (2013-01-05 07:00–08:00 UTC) trained the tectonic class. To account for nonstationary noise, a new background model was estimated for each day using that day’s 24 h record; classification combined fixed event models with the preceding day’s background model.

Post-processing and spatial filtering: Detections were refined by applying a log-normal likelihood threshold of −70; duration thresholds (cracks: 0.5–5 s; slope failure/debris mobilization: >5 s); and network-coincidence constraints requiring detection at STA6 and at least one of STA4/STA5. Events were located using a signal envelope migration approach in R (package eseis): deconvolution, detrending, 1–30 Hz filtering, envelope computation, cross-correlation-derived envelope time delays, distance-to-time conversion using an apparent velocity of 500 m s−1 with 30 m DEM topographic correction, and probabilistic source grids. Only events within a spatial filter area encompassing the main rockslide were retained.

Performance assessment: Synthetic tests injected empirical crack signals into white and pink noise to quantify true/false positive rates versus SNR. A confusion matrix was built by comparing 7 h of visually inspected STA6 records (2013-01-01 20:00 to 2013-01-02 03:00 UTC) against machine detections to evaluate class confusion.

Physical model for crack evolution: Assuming (1) cumulative crack number N(t) ∝ fractured area A(t)=Af/Atot, (2) dA/dt = l v with constant crack propagation velocity v, making the total crack boundary length l the controlling variable, and (3) boundary conditions for l(A) that increase from near zero, peak, then decrease to near zero as rock bridges vanish, the simplest function l(A) = A(1 − A/Atot)/τ was used. Combining yields a logistic (sigmoidal) solution for cumulative crack number: N(t) ≈ Atot / [1 + exp(b − t)], with b an integration constant. Fits used scipy.optimize.curve_fit. A variant allowing non-constant velocity (v = v0 e^{t/τ0}) was tested; it did not improve fit quality at first order.

• 1592 crack events were identified in the 20 days before and 10 days after the 2013-01-02 rockslide using the HMM detection across six stations.
• No clear external trigger was present in the five days prior: no precipitation or earthquake activity; air temperature fluctuated around freezing in the preceding weeks and was −2 °C at failure time.
• Cumulative crack number N(t) was approximately linear (R² = 0.989) during the two weeks before the event, then transitioned to an S-shaped (sigmoidal) pattern in the final 27 hours.
• The logistic model N(t) ≈ Atot / [1 + exp(b − t)] fit the last 27 hours extremely well (R² = 0.998), with example parameters r ≈ 0.1, Atot ≈ 0.97, b ≈ 4.3 (figure fit), indicating the total crack boundary length as the dominant control on late-stage failure plane development.
• Parameter r values between 0.1 and 0.15 correspond to 2.7–4 hours as the characteristic timescale of the sigmoidal growth phase, implying a potential maximum warning time of about one day once the sigmoidal phase begins.
• A sharp increase in slope failure and debris mobilization detections occurred at the main rockslide time, with a second debris mobilization step two days later coincident with air temperature rising above 5 °C.
• The analysis supports a transition from distributed, externally modulated cracking to localized, internally controlled damage accumulation on the impending failure plane.

The results demonstrate that immediately prior to a major slope failure, the cracking dynamics are governed by an internal state parameter—the total crack boundary length—rather than by external forcings. The observed transition from linear to sigmoidal growth in cumulative crack number marks a switch from distributed, externally influenced crack initiation to localized, internally controlled damage accumulation and coalescence on the failure plane. The excellent fit of a logistic model derived from simple mechanistic assumptions indicates that explicitly treating cracks as two-dimensional areal features, and tracking the evolution of total crack boundary length, is essential to capture pre-failure dynamics. This framework clarifies why many failures lack clear external triggers: external factors modulate subcritical stress states but do not necessarily control the final approach to failure, which is paced by internal damage evolution. In practical terms, continuous seismic monitoring with automated HMM-based crack detection can identify the onset of the sigmoidal phase, providing a physically grounded early-warning indicator with lead times potentially on the order of hours to a day.

This study combines dense seismic monitoring and hidden Markov model event detection with a simple mechanistic model to reveal that total crack boundary length is the first-order control on failure plane development in the hours preceding a rockslide. The cumulative crack activity in the Illgraben case transitioned from linear to sigmoidal growth in the final 27 hours, and a logistic model fit this evolution with high fidelity, highlighting an internally paced approach to failure. Conceptually, cracks should be treated as two-dimensional areal features, not one-dimensional, to capture pre-failure dynamics. Operationally, detecting the onset of sigmoidal crack-rate increase could underpin early warning, with potential lead times of up to about one day. Future work should investigate how lithology, climate, and site conditions control the characteristic timescale parameter, generalize the approach to diverse settings, and integrate real-time detection and modeling into operational landslide early warning systems.

• Single-case study at Illgraben limits generalizability; replication across sites and lithologies is needed.
• Crack signals often have low SNR; despite HMM advantages, false positives/negatives are possible, and only a short interval was visually cataloged for confusion assessment.
• Event location uses assumptions (apparent velocity 500 m s−1, DEM-based corrections) and a broad spatial filter; location uncertainties remain.
• The mechanistic model assumes constant crack propagation velocity in its simplest form; while a non-constant velocity variant was tested, parameter trade-offs and limited improvement suggest model simplifications that may not capture all physics.
• Effective early warning depends on instrument proximity and network configuration comparable to this study; performance at greater distances or noisier environments may degrade.