Rock Slope Failures Research Articles

Modeling Brittle Failure in Rock Slopes Using Semi‐Lagrangian Nonlocal General Particle Dynamics

ABSTRACTThe nonlocal general particle dynamics (NGPD) has been successfully developed to model crack propagation and large deformation problems. In this paper, the semi‐Lagrangian nonlocal general particle dynamics (SL‐NGPD) is proposed to solve brittle failure in rock slopes. In SL‐NGPD, the interaction between particles due to deformation is calculated in the initial configuration, while the friction contact interaction from discontinuities is calculated in the current configuration. The Van der Waals force model is utilized for friction contact. The bond‐level energy‐based failure criterion is developed to predict tensile/compressive‐shear mix‐mode cracks. The artificial viscosity and damage correction are used to enhance the numerical stability and accuracy when modeling brittle failure. The SL‐NGPD paradigm is numerically implemented through adaptive dynamic relaxation and predictor–corrector schemes for stable numerical solutions. The stability and accuracy of SL‐NGPD are verified by simulating compression tests. Thereafter, the crack coalescence patterns of double‐flaw specimens are investigated to understand the triggering failure mechanism of jointed rock slopes. Finally, the progressive failure process of the rock slope with step‐path joints is simulated to demonstrate its validity and robustness in modeling brittle failure in rockslides. The numerical results illustrate that the proposed SL‐NGPD is promising and performant for analyzing brittle failure problems in geotechnical engineering.

Early warning and dynamics of compound rockslides: lessons learnt from the Brienz/Brinzauls 2023 rockslope failure

AbstractPrediction of rockslope dynamic evolution and catastrophic failure remains a fundamental challenge for scientists and practitioners, even though this topic has been studied for decades. Here we report about a case in the Swiss Alps, which has received worldwide attention, not only because a village was evacuated on May 12, 2023, and traffic corridors were progressively closed prior to the slope collapse, but also because this site had been studied and monitored with unprecedented detail during many years before failure. In 2023 the structural and dynamic evolution of the 2 million m3 suspended compound rockslide at Brienz/Brinzauls was closely monitored with diverse ground-based systems and continuously modeled with Voight’s creep law. Substantial deviations from this classical failure model were observed, which are in most cases not related to variations in external driving factors, but diverse internal strength degradation processes. This led to a systematic analysis of Voight’s model uncertainty and the development of an early warning system which includes supplementary early warning parameters to the classical velocity thresholds. We show how to treat the spatial and temporal variations of velocity thresholds and when they reach their applicability limit in a real-time early warning model. The unstable compartment at Brienz/Brinzauls progressively collapsed in the night of June 15, 2023, and generated a series of dry granular flows and rock mass falls, which just stopped at the Brienz settlement boundary.

How water, temperature, and seismicity control the preconditioning of massive rock slope failure (Hochvogel)

Abstract. The anticipation of massive rock slope failures is a key mitigation strategy in a changing climate and environment requiring a precise understanding of pre-failure process dynamics. Here we exploit >4 years of multi-method high-resolution monitoring data from a large rock slope instability close to failure. To quantify and understand the effect of possible drivers (water from rain and snowmelt, internal rock fracturing, and earthquakes), we correlate slope displacements with environmental data, local seismic recordings, and earthquake catalogues. During the snowmelt phase, displacements are controlled by meltwater infiltration with high correlation and a time lag of 4–9 d. During the snow-free summer, rainfall induces accelerations with a time lag of 1–16 h for up to several days without a minimum activation rain sum threshold. Rock fracturing, linked to temperature and freeze–thaw cycles, is predominantly near the surface and unrelated to displacement rates. A classic Newmark analysis of recent and historic earthquakes indicates a low potential for immediate triggering of a major failure at the case site, unless it is already very close to failure. Seismic topographic amplification of the peak ground velocity (PGV) at the summit ranges from a factor of 2–11 and is spatially heterogeneous, indicating a high criticality of the slope. The presented in-depth monitoring data analysis enables a comprehensive rockfall driver evaluation and indicates where future climatic changes, e.g. in precipitation intensity and frequency, may alter the preconditioning of major rock slope failures.

Rock slope stability analysis of a limestone quarry in a case study of a National Cement Factory in Eastern Ethiopia

Rock slope failures pose significant challenges in geotechnical engineering due to the intricate nature of rock masses, discontinuities, and various destabilizing factors during and after excavation. In mining industries, such as national cement factories, multi-benched excavation systems are commonly used for quarrying. However, cut slopes are often designed with steep angles to maximize economic benefits, inadvertently neglecting critical slope stability issues. This oversight can lead to slope instability, endangering human lives and property. This study focuses on analyzing the stability of existing quarry cut slopes, estimating their final depth, and conducting a parametric study of geometric profiles including bench height, width, face angle, and rump width. Kinematic analysis helps identify potential failure modes. The results reveal that the existing quarry cut slope is prone to toppling, wedge failure, and planar failure with probabilities of 42.68%, 19.53%, and 14.23%, respectively. Numerical modeling using the finite element method (Phase2 8.0 software) was performed under both static and dynamic loading conditions. The shear reduction factor (SRF) of the existing quarry cut slope was 1.01 under static loading and 0.86 under dynamic loading. Similarly, for the estimated depth, the SRF was 0.82 under static loading and 0.7 under dynamic loading. These values indicate that the slope stability falls significantly below the minimum acceptable SRF, rendering it unstable. The parametric study highlights the face angle of the bench as the most influential parameter in slope stability. By adjusting the bench face angle from 90° to 75°, 70°, and 65°, the SRF increased by 31.6%, 35.4%, and 37.9%, respectively. Among these, a 70° bench face angle is recommended for optimal stability with a SRF of 1.27 under static loading and 1.18 under dynamic loading.

Progressive failure and quantitative stability analysis of rock slope with cross-type discrete fracture network using spring-based smoothed particle hydrodynamics method

The propagation and coalescence of discontinuous cross-type joints are often the primary drivers of rock slope failures. Due to the inherent randomness of these joints, identifying suitable methods to accurately characterize progressive failure and quantitatively assess the stability of slopes with cross-type joints is particularly challenging. To address this, a Discrete Fracture Network-Spring Based-Smoothed Particle Hydrodynamics (DFN-SB-SPH) method is proposed, which considers cross-type DFN generation, rock matrix heterogeneity, cracking, block contact, and deposition within a unified SPH framework. In this approach, damage and contact of blocks are achieved by introducing a fracture sign to enhance the kernel function and applying Newton's law to the damaged particles to realize the point to point contact. A uniaxial compression test on rock samples with double fissures is carried out to verify the accuracy of the proposed method. The influence of joint density, geometric parameters (i.e., trace length, dominate dip angle) of cross joints, and rock mass heterogeneity on the failure characteristics of RSCD are investigated. The results revealed that the DFN-SB-SPH model possesses robust capabilities for crack tracking, mass movement, and contact slipping along fracture surfaces. Moreover, DFN generation, heterogeneous characterization, shear and tensile fractures within a single SPH framework without mesh distortion are realized. Five typical failure modes calculated by DFN-SB-SPH are primarily determined by the combination of joint dip angles and trace lengths. Furthermore, the dip angle, trace length, joint density, and rock mass heterogeneity significantly alter the stability of RSCD with sensitivity coefficients for factor safety of 27.7 %, 44.6 %, 72.9 % and 35.0 %, respectively. Higher dominant dip angles (above 60°) lead to significantly longer run-out distances for RSCD compared to lower angles (below 30°) once instability occurs. The sudden rise in major principal stress at the slope's top and toe, along with the shift of tensile stress concentration towards the middle, predicts the stages of crack propagation and sliding in slope failure.

Pseudo-dynamic viscoelastic stability analysis of anti-dip bedding rock slopes

Earthquakes contribute to the failure of anti-dip bedding rock slopes (ABRSs) in seismically active regions. The pseudo-static method is commonly employed to assess the ABRSs stability. However, simplifying seismic effects as static loads often underestimates rock slope stability. The development of a practical stability analysis approach for ABRSs, particularly in slope engineering design, is imperative. This study proposes a stability evaluation model for ABRSs, incorporating the viscoelastic properties of rock, to quantitatively assess the safety factor and failure surface under seismic conditions. The mathematical description of the pseudo-dynamic method, derived in this study, accounts for the viscoelastic properties of ABRSs and integrates the Hoek–Brown failure criterion with the Kelvin-Voigt stress-strain relationship of rocks. Furthermore, to address concurrent translation-rotation failure in ABRSs, upper bound limit analysis is utilized to quantify the safety factor. Through a comparison with existing literature, the proposed method considers the effect of harmonic vibration on the stability of ABRSs. The obtained safety factor is lower than that of the quasi-static method, with the resulting percentage change exceeding 5%. The critical failure surface demonstrates superior positional accuracy compared to the Aydan and Adhikary basal planes, with minimal error observed between the physical model test and the numerical simulation test. The parameter sensitivity analysis reveals that the inclination of ABRSs exhibits the highest sensitivity (Sk) value across the three levels of horizontal seismic coefficient (kh). The study aims to devise an expeditious calculation approach for assessing the stability of ABRSs during seismic events, intending to offer theoretical guidance for their stability analysis.

Study on deformation characteristics of toppling failure of anti-dip rock slopes under different soft and hard rock conditions

For the widespread exposure of toppling deformation phenomena in anti-dip engineering slopes such as hydropower, transportation, and mining, especially deep-seated toppling, these large-scale deep-seated toppling deformations reaching depths of hundreds of meters have become significant geotechnical engineering problems that restrict large-scale engineering construction and require urgent solutions. There are significant differences in the failure characteristics and mechanisms of anti-dip rock slopes under different soft and hard rock conditions. This study, starting from the failure characteristics and mechanisms under different soft and hard conditions of rocks, summarizes two types of toppling deformation: ductile bending deep toppling (DBDT) and brittle fracture shallow toppling (BFST). The UDEC method is used to preliminarily explore the threshold of rock mechanical parameters for these two types of toppling, with 80 MPa (UCS, uniaxial compressive strength) mechanical parameters serving as the preliminary threshold. The results indicate that hard rock undergoes BFST, whereas soft rock undergoes DBDT. The rock mechanical parameters of 100 MPa (UCS) and 20 MPa (UCS) were selected to study the evolution process and mechanism of DBDT and BFST deformations, respectively. Numerical simulation results have innovatively revealed the mechanical behavior characteristics between rock layers during the process of toppling deformation. Because toppling deformation mainly originates from interlayer displacement deformation and intra-layer tensile deformation of rock layers, the interlayer mechanical characteristics are of great significance for understanding the mechanism of toppling deformation. This research can provide a theoretical basis for the stability assessment and development utilization of anti-dip rock slopes and toppled slopes.

Predisposing, triggering and runout processes at a permafrost‐affected rock avalanche site in the French Alps (Étache, June 2020)

AbstractAlthough numerous recent studies have explored the relationship between permafrost degradation and rock slope failure, there is still a need for in‐depth investigations to develop relevant hazard assessment approaches. We investigate the predisposing, triggering and propagation processes of a rock avalanche (c. 225,000 m3) that occurred in Vallon d'Étache (France) on 18 June 2020, whose scar was coated by ice and water. Weather records and energy balance models show that the rock avalanche occurred right after the warmest spring and winter since at least 1985, but also right after the spring with the highest water supply anomaly (snowmelt and rainfall). Measured ground surface temperature and geoelectrical surveys reveal that relatively ice‐rich permafrost could exist in the NW face (release area) while it is inexistent below the SE face, contradicting certain permafrost maps. Heat transfer simulations suggest that the rock avalanche occurred during a transition from cold to warm permafrost conditions at failure depth (30 m), with a temperature increase of up to 0.6°C per decade since 2012 (when considering potential snow cover effect), and current temperature ranging between −3 and −1°C, depending on the applied model forcing. This warming certainly contributed to predispose slope to failure. In addition, the shift towards warm permafrost and water infiltration potentially enhancing permafrost degradation along fractures through heat advection or favouring the development of high hydrostatic pressures may have played as triggering factors. Finally, propagation simulations show that the rock avalanche involved several phases with different rheological properties due to the incorporation of snow and material segregation within the deposit. These new insights at various scales highlight the complexity of the triggering and propagation processes of rock slope failure occurring in high mountains, a significant part of which can be linked to snow effects on ground temperature, water supply and rheological properties.

Numerical simulation of wedge failure of rock slopes using three-dimensional discontinuous deformation analysis

Numerical simulation of wedge failure of rock slopes using three-dimensional discontinuous deformation analysis

Schmidt-hammer exposure-age dating of seven paraglacial rock-slope failures in the Bolungarvík-Suðureyri area (Westfjords, Iceland)

Many rock-slope failures (RSF) impact Iceland's Westfjords morphology. Five RSF areas, totalling seven RSFs, were studied in the western fjords around Bolungarvík-Suðureyri: Óshólar, Minni-Hlið, Meira-Hraun, the Vatnadalur valley and part of the Sunddalur valley.The aim of this article is to provide chronological data of the RSFs and to subsequently obtain a better chronosequence of post-glacial events, none of which have yet been dated in the Westfjords. More particularly, we discuss a paraglacial hypothesis of their occurrence.For this purpose, the Schmidt-hammer exposure-age dating (SHD) method is used on the RSF deposits, and the rebound values obtained from the impacted blocks are converted to age estimates using radiocarbon ages obtained from the different sites in order to calculate a SHD age calibration. Then, we establish a chronology of the setting up of the events. In this way, seven RSFs have been dated and different chronological generations of deposit emplacement have been exhibited for some of them. Thus, various periods of instability affected mountain slopes. The Óshólar RSF is thought to have been deposited firstly at around 12,500 cal BP, the Minni-Hlið RSF at ∼9800 cal BP, the Meira-Hraun RSF at ∼8700 cal BP, the Vatnadalur RSFs at ∼9000 cal BP, ∼ 6900 cal BP, and ∼ 4300 cal BP, and the Sunddalur RSF at ∼9600 cal BP. These RSFs therefore correspond to so-called paraglacial events, which took place at the beginning of deglaciation of the area during the first half of the Holocene.

Was there a low-altitude Younger Dryas Stadial glacier in south-east Wales? Re-interpretation of landforms and palaeo-climatic inferences

A glacial origin for cirque-like hollows cut into the western escarpment of the Usk valley near Abergavenny, South Wales has become widely accepted. Associated supposed extensive moraine ‘festoons’ have been depicted merging and contemporaneous with Last Glacial Maximum (LGM) deposits formed by ice occupying the adjacent Usk valley. We re-interpret these festoons as the product mainly of rock slope failures (RSFs) emanating from the hollows. A cirque glacier origin is preferred to account for a compact double-ridge feature in one of the hollows. The equilibrium-line altitude (ELA) of the reconstructed glacier (357 m) is >60 m lower than all similarly small, presumed Younger Dryas Stadial (YDS; c., 12.9–11.7 ka) glaciers elsewhere in South Wales. To test whether this glacier nevertheless might date from the YDS, we apply three approaches to reconstruct annual palaeo-precipitation amounts at the ELA, two based on relationships between accumulation and ablation for modern glaciers and the third on a simple degree-day model (DDM) using likely climatic characteristics for this event. The DDM can be tailored to represent the recognised large-amplitude YDS annual temperature range rather than the much smaller one experienced by modern glaciers, making it our preferred approach. Although conditions along the Usk valley escarpment during the LGM would have been well suited to cirque glacier formation, the DDM approach, using the large-amplitude annual temperature ranges, suggests that a YDS age might also be possible. The results have implications for re-assessing the likely ages of some former small glaciers in South Wales.

Investigating the toppling failure of anti-dip rock slopes containing non-persistent cross-joints via a strength-based fracture method

The toppling failure of anti-dip rock slopes is significantly affected by crack propagation from non-persistent cross-joints (NPCJs). In this study, a strength-based localized maximum stress (SLMS) criterion is adopted to model the toppling failure process caused by crack propagation in anti-dip rock slopes containing a set of NPCJs via the finite element method. The crack initiation sequence from NPCJs and the toppling evolution of anti-dip slopes under different stratum dips and slope angles, as well as the influences of stratum dips and slope angles on toppling evolution, are investigated. Variations in the displacements during the toppling of the slope and the influence of toppling on the displacements are analyzed. Additionally, variations in the magnitude and distribution area of interlayer friction between rock layers during the toppling evolution process and the effects of toppling on the evolution of interlayer friction are examined. The results indicate that the toppling process of the anti-dip slope containing NPCJs involves three stages: crack initiation and propagation from the NPCJs, the development of interlayer tensile and shear cracks, and toppling failure of the rock layers. The stability of anti-dip slopes containing NPCJs is greatly affected by the stratum dip and slope angle. The horizontal displacements and interlayer crack aperture increase nonlinearly with the development of toppling evolution, and the magnitude of the increase gradually increases. Moreover, the magnitude and distribution area of interlayer friction vary with the development of toppling evolution. The maximum interlayer friction gradually increases, but the distribution area of friction decreases.

An analytical solution to predict slip-buckling failure of bedding rock slopes under the influence of top loading and earthquakes: Case studies of Hejia landslide and Tangjiashan landslide

An analytical solution to predict slip-buckling failure of bedding rock slopes under the influence of top loading and earthquakes: Case studies of Hejia landslide and Tangjiashan landslide

Block-flexure toppling failure of rock slopes using an equivalent deformation compatibility method

Block-flexure toppling constitutes the predominant form of toppling failure in rock slopes. Although it has been extensively studied, the current theoretical models are often oversimplified by treating rock layers as rigid bodies that diverge from actual conditions. The proposed Equivalent Deformation Compatibility Method (EDCM) offers a fresh approach to assess the stability of rock slopes prone to block-flexure toppling. EDCM posits that blocky rock layers, with their inability to withstand significant bending and role in merely transferring forces, can be modeled as intact layers with a reduced modulus. The method simplifies the complex issue of analyzing discrete and continuous rock layers to the study of layered soft and hard rock, establishing deformation compatibility equations subsequently. Validation of the EDCM was achieved through numerical models, physical model testing, and application to an actual slope. The factor of safety (FS) for slopes corresponds with the results from both models and the actual slope, demonstrating the method's applicability for evaluating susceptibility to block-flexure toppling. When applying the EDCM, it is advised to set the elastic modulus reduction coefficient for blocky layers at a value below 0.1.

Numerical Simulations for Deformation and Failure of Layered Rock Slopes and Their Support Design by Particle Flow Code

Numerical Simulations for Deformation and Failure of Layered Rock Slopes and Their Support Design by Particle Flow Code

Numerical study on flexural toppling failure of rock slopes using the finite discrete element method

Numerical study on flexural toppling failure of rock slopes using the finite discrete element method

Massive sediment pulses triggered by a multi-stage 130 000 m3 alpine cliff fall (Hochvogel, DE–AT)

Abstract. Massive sediment pulses in catchments are a key alpine multi-risk component. Substantial sediment redistribution in alpine catchments frequently causes flooding, river erosion, and landsliding and affects infrastructure such as dam reservoirs as well as aquatic ecosystems and water quality. While systematic rock slope failure inventories have been collected in several countries, the subsequent cascading sediment redistribution is virtually unaccessed. For the first time, this contribution reports the massive sediment redistribution triggered by the multi-stage failure of more than 130 000 m3 from the Hochvogel dolomite peak during the summer of 2016. We applied change detection techniques to seven 3D-coregistered high-resolution true orthophotos and digital surface models (DSMs) obtained through digital aerial photogrammetry later optimized for precise volume calculation in steep terrain. The analysis of seismic information from surrounding stations revealed the temporal evolution of the cliff fall. We identified the proportional contribution of > 600 rockfall events (> 1 m3) from four rock slope catchments with different slope aspects and their volume estimates. In a sediment cascade approach, we evaluated erosion, transport, and deposition from the rock face to the upper channelized erosive debris flow channel, then to the widened dispersive debris flow channel, and finally to the outlet into the braided sediment-supercharged Jochbach river. We observe the decadal flux of more than 400 000 m3 of sediment, characterized by massive sediment waves that (i) exhibit reaction times of 0–4 years in response to a cliff fall sediment input and relaxation times beyond 10 years. The sediment waves (ii) manifest with faster response times of 0–2 years in the upper catchment and over 2 years in the lower catchments. The entire catchment (iii) undergoes a rapid shift from sedimentary (102–103 mm a−1) to massive erosive regimes (102 mm a−1) within single years, and the massive sediment redistribution (iv) shows limited dependency on rainfall frequency and intensity. This study provides generic information on spatial and temporal patterns of massive sediment pulses in highly sediment-charged alpine catchments.

Mapping release and propagation areas of permafrost-related rock slope failures in the French Alps: A new methodological approach at regional scale

Rock slope failure (RSF) from permafrost-affected rockwall is an emerging threat for human lives and infrastructure which raises a need for RSF hazard assessments in the alpine environment. This study proposes the first mapping approach to RSF release and propagation areas in the French Alps.By analysing a unique RSF database (1389 recent events in the Mont Blanc massif), we determine three levels of RSF Susceptibility Indexes (RSI) to map the potential release areas. We highlight a strong correlation between RSF and permafrost: 99 % of RSFs occurred from rockwalls with a Mean Annual Rock Surface Temperature (MARST) ≤ 3 °C and 35 % with MARST from −2 to 0 °C.The release area maps (34 km2 to 284 km2 depending on the RSI) are entered into a simple propagation model (RockavELA), using a dimensionless area-based energy line principle (i.e. reach susceptibility) to map propagation areas of potential RSFs. Three propagation limits are proposed, fitting the propagation characteristics of another RSF database containing 3497 events observed across the European Alps with heterogeneous propagation substrates, and merged with 48 additional events from high mountains in the French Alps. RockavELA reproduced the runout extent of 20 high mountain RSFs with <50 % of frontal and lateral error. Output maps show little sensitivity to the propagation limits (<25 % difference between the high and low propagation limits).This work is a preliminary step to identify potential hazard hot spots in the French Alps, and proposes a novel approach that could be applied in other mountain ranges.

Back-analysis of the paraglacial slope failure at Grewingk Glacier and Lake, Alaska

The relationship between rock-slope failure and glacier retreat is complex, and paraglacial failures often lack clearly identified triggers. To better understand the role of glacier retreat in rock-slope failures, we analysed the processes that led to the October 1967 Grewingk landslide in Kachemak Bay State Park on the Kenai Peninsula, Southcentral Alaska. The rock material collapsed onto the glacier toe and into its pro-glacial lake and produced a tsunami wave that swept the outwash plain. On the day of the failure, rainfall and snowmelt were well within normal ranges, and seismic records show no significant shaking. Three years prior to the 1967 failure, the slope withstood the second largest earthquake ever recorded (Great Alaskan earthquake, MW 9.2). We reassessed the volume of the failure by differencing pre- and post-digital terrain models and found a value of 20–24 × 106 m3, which is four times smaller than a previous estimate. The back analysis of the Grewingk landslide is based on remote sensing data and field measurements including aerial satellite image analysis, detailed surveying and understanding of the structural geology, a kinematic analysis, and runout modelling. Our research provides an example of a major paraglacial failure that lacks an obvious trigger and points to several geological factors and changing environmental conditions that likely promote such failures. This study further indicates that the Grewingk landslide, pre-conditioned by the geometry of faults and joints, may have reached a critical stability state due to internal processes and the potential combined effects of seismic activity and glacier retreat prior to the collapse.

An approach for determination of lateral limit angle in kinematic planar sliding analysis for rock slopes

Planar sliding is one of the frequently observed types of failure in rock slopes. Kinematic analysis is a classic and widely used method to examine the potential failure modes in rock masses. The accuracy of planar sliding kinematic analysis is significantly influenced by the value assigned to the lateral limit angle γlim. However, the assignment of γlim is currently used generally based on an empirical criterion. This study aims to propose an approach for determining the value of γlim in deterministic and probabilistic kinematic planar sliding analysis. A new perspective is presented to reveal that γlim essentially influences the probability of forming a potential planar sliding block. The procedure to calculate this probability is introduced using the block theory method. It is found that the probability is correlated with the number of discontinuity sets presented in rock masses. Thus, different values of γlim for rock masses with different sets of discontinuities are recommended in both probabilistic and deterministic planar sliding kinematic analyses; whereas a fixed value of γlim is commonly assigned to different types of rock masses in traditional method. Finally, an engineering case was used to compare the proposed and traditional kinematic analysis methods. The error rates of the traditional method vary from 45% to 119%, while that of the proposed method ranges between 1% and 17%. Therefore, it is likely that the proposed method is superior to the traditional one.