Polyphase rock slope failure controlled by pre-existing geological structures and rock bridges

Even after decades of intensive research, assessing rock slope stability remains a challenge. One reason for this is the spatial variability of rock bridges (RBs) related to non-persistent, pre-existing geological structures, especially as the detection of RBs is generally limited to the post-failure period. Thus, the identification and classification of RBs and their inclusion in numerical studies are demanding, yet essential, since even small quantities of RBs can be decisive for rock slope stability. In our study, we demonstrate how brittle RB failure and pre-existing geological structures control the mechanisms of a polyphase rock slope failure. Therefore, we present a case study in the Austrian Alps, where three rock falls with a failure volume of 30,000 m3 occurred in 2019. Based on detailed process reconstructions, high-resolution terrain models, and comprehensive geological and rock mechanical investigations, we derived high-quality input for our distinct element model (DEM). By applying asymmetric Voronoi tessellation in the DEM, we modelled the coalescence of pre-existing geological structures by brittle RB failure. As a result, we identified toppling as the predominant failure mechanism at the study site. Distinctive geological structures decisively affected the failure mechanism. However, the toppling failure was only reproducible by incorporating RBs in the DEM in their pre-failure position. Finally, we found that joint persistence, and consequently the presence of potential RBs, controls which initial rock fall failure mechanism was developed. In conclusion, we state that the initial toppling failure of the Hüttschlag rock falls is controlled by non-persistent geological structures in interplay with RBs.


Introduction
Rock falls are a landslide process characterised by the detachment of a rock mass or individual blocks from an unstable rock slope (Cruden and Varnes 1996;Hungr et al. 2014).Rock fall investigations gain importance as landslides impose an ever more significant hazard to people and infrastructure in alpine realms (Zangerl et al. 2008) due to rising population, touristic activity, and housing sprawl.Thereby, rock falls are one of the most prevalent mountain hazard processes (Crosta et al. 2015).
Rock slope failure can occur in variable mechanisms, e.g.falling, sliding, toppling, or a combination of these mechanisms (Cruden and Varnes 1996;Hungr et al. 2014).For toppling, Goodman and Bray (1976) defined subclasses, i.e. block-, flexural-, or block-flexure-toppling, in 2D.These were expanded and refined to the third dimension in numerical models by Brideau and Stead (2010).However, the initial failure mechanisms on an unstable rock slope should be distinguished from the deformation mechanism underlying the running-out, as the former may significantly differ from the latter (Poisel and Preh 2004;Ma and Liu 2022).Identifying both mechanisms underlying the initial failure as well as the running-out is a critical step in hazard assessment and management, since they control the choice of adequate monitoring techniques and mitigation measures applied.
A critical predisposition factor that determines if and in what kind of mechanism a rock slope fails are brittle geological structures, i.e. pre-existing discontinuities, and their orientation relative to the slope (e.g.Wyllie and Mah 2004;Brideau and Stead 2012).Accordingly, a structural control of slope instabilities is often addressed in the literature (e.g.Agliardi et al. 2001Agliardi et al. , 2013;;Gschwind et al. 2019;Truttmann et al. 2021).These brittle structures can develop according to stress conditions during tectonic processes (e.g.Fossen 2010) or as geologically young structures, such as sheeting joints at shallow depths (Hencher et al. 2011).The European Eastern Alps and its tectonic units were formed by two Alpine orogenies (Schmid et al. 2004).During these tectonic events, the rocks composing these tectonic units inherited structural features on multiple scales and with variable characteristics (Twiss and Moores 2007;Fossen 2010).Accordingly, these structures may result from brittle and at higher temperatures also from ductile and semi-ductile deformation phases and can critically influence slope instabilities by the formation of weakness zones (Stead and Wolter 2015).
Reducing slope stability analysis to brittle structures, i.e. pre-existing discontinuities, would also neglect the critical role of intact rock bridges (RBs).RBs affect rock slope strength and brittle RB failure can critically influence slope kinematics (Donati et al. 2023).Consequently, the identification, classification, role, and measurement of these intact RBs have been one focus of discussion within the landslide community for decades (e.g.Terzaghi 1962;Einstein et al. 1983;Stead and Eberhardt 2013;Tuckey and Stead 2016;Elmo et al. 2022;Elmo 2023).In a simplified manner, RBs can be classified according to their position relative to preexisting, brittle discontinuities.If a discontinuity shows intact areas within its plane, these are referred to as in-plane RBs (Einstein et al. 1983).They can furthermore be distinguished according to their position and function during slope failure either as in-plane basal or in-plane lateral release (Elmo et al. 2018).If two brittle discontinuities enclose an intact rock mass, they are herein addressed as rock bridge volumes (RBVs).Depending on the geometry of the overlapping discontinuities enclosing the RBV relative to the direction of failure, they are herein either regarded as positive or negative RBVs (Fig. 1).
A simple kinematic analysis, which is commonly performed to identify possible rock slope failure mechanisms (Wyllie and Mah 2004), assumes fully persistent, planar discontinuities.That, in turn, excludes all RBs.However, Shang et al. (2017) have proven the existence of in-plane RBs by a forensic excavation technique, and even small quantities of RBs may have a considerable impact on the stability of rock slopes (Tuckey and Stead 2016).Whilst advances in the identification of in-plane RBs at shallow depths were achieved by thermal imaging (Guerin et al. 2019), we generally lack the tools to identify and thus measure RBs prefailure (Elmo 2023).Also, the mechanism of rock slope failure itself may be controlled by the spatial variability and size of RBs, and brittle RB failure may provide kinematic freedom for specific failure mechanisms.For instance, Donati et al. (2019) demonstrated that the brittle fracture propagation in a sedimentary rock mass was decisive in providing a toppling slope failure.Donati et al. (2023) further emphasised that the accumulation of rock slope damage due to slope instabilities, despite its importance, still receives relatively little attention in slope stability studies.Einstein et al. (1983) formulated two modes of RB failure, i.e. tensile failure (Mode 1) and shear failure (Mode 2).Which mode develops essentially depends on the normal stress levels in a rock slope.Accordingly, critical failure paths form in RBs during failure.These failure paths start from a nucleus, i.e. the tips of pre-existing micro-cracks and -flaws.Starting from these nuclei, tensile failure (wing cracks), shear failure (secondary cracks), or a combination of these propagate to coalesce and evolve to a fully persistent rupture surface (e.g.Bobet and Einstein 1998;Basu et al. 2013).Such pre-existing micro-cracks and flaws within a metamorphic rock mass can be tectonically inherited (Fossen 2010).
Therefore, the term intact rock mass bridge (Stead and Eberhardt 2013) may be appropriate, when a rock mass incorporating fractures of various scales (i.e.micro to macro) separates major pre-existing discontinuities.In numerical studies, it is not possible to consider all inherent micro-and meso-scale fractures of a rock mass due to the constraints in computing power.Therefore, it is necessary to perform up-scaling procedures, which in turn lead to the incorporation of simplified synthetic rock mass bridges into numerical studies (Elmo et al. 2022).
Various approaches and simplifications have evolved to model brittle RB failure (Stead et al. 2001).Some of these Fig. 1 Rock bridge (RB) terminology used in this paper-modified from Einstein et al. (1983), Stead andEberhardt (2013), andElmo et al. (2022).Note that the negative RBV imposes an asperity and tapered the block (Elmo et al. 2018), and the actual failure path to develop within the RBVs can only be revealed in the course of or after slope failure (Elmo 2023) apply a hybrid finite-discrete approach, e.g.ELFEN (Rockfield 2017), or a distinct element modelling (DEM) approach, e.g.UDEC (Itasca 2018).In some publications using UDEC, the tessellation of intact rock blocks in random polygonsreferred to as Voronoi elements-was applied to investigate brittle failure paths.This was done on the grain-scale, e.g.Chen et al. (2015), or on the slope scale, e.g.Spreafico et al. (2017).However, this method requires a cautious calibration of the Voronoi contacts (Stead and Wolter 2015).Gao and Stead (2014) introduced a modified approach referred to as 'Trigon Method'.In this approach, the Voronoi elements are split into triangular elements.As a result, the model output produced more realistic fracture patterns and block displacements.The Trigon method was applied by, e.g.Zheng et al. (2018), for slope failures related to flexural toppling.In our study, we followed the classic Voronoi approach.However, by applying asymmetric Voronoi tessellation, we refined it for our purpose.In doing so, we took the main anisotropy of the modelled metamorphic rock mass-i.e. the foliation and schistosity-into account.Based on results derived from direct shear tests, we calibrated the shear strength properties assigned to the Voronoi contacts.By this approach, we modelled brittle RB failure between pre-existing structures in a highly anisotropic rock mass.
For this purpose, we selected a rock fall case study in Hüttschlag (Salzburg, Austria) in the Eastern European alps, where three rock falls with a failure volume of circa 30,000 m 3 occurred in the year 2019.Rock slope failure occurred from a source-area with distinctive pre-existing brittle, semi-ductile, and ductile structural features.Fortunately, none of the past rock falls caused any casualties.However, due to potential future rock falls at the study site, it is not only of scientific but also of public interest to investigate the mechanisms and processes underlying the rock slope failure.We conducted our study in a three-staged research strategy: (i) Unravelling the polyphase rock fall process by highresolution unmanned aerial vehicle photogrammetry (UAV-P) in combination with video analysis and photographic event documentation, in order to reconstruct the initial failure mechanism and identify the position of failed RBs on the rock slope.(ii) Conducting holistic geological investigations to identify the structural inventory of the rock fall site and to characterise the outcropping lithologies.Together with rock mechanical laboratory analysis, this provided broad input parameters for the DEM and enabled us to calibrate the shear strength properties assigned to the Voronoi contacts.(iii) Investigating the effect of the pre-existing structural inventory and RBs on the initial failure mechanism by using the DEM method with asymmetric Voronoi tessellation.
By applying this research strategy on the Hüttschlag rock falls, we demonstrate the control of the distinctive structural inventory and intact RBs on the initial failure mechanism of a polyphase rock fall process.

The Hüttschlag rock fall site
The rock falls investigated in this paper (Fig. 2a) occurred in the municipality of Karteis/Hüttschlag (47°10.0′N, 13°16.3′E) located in the alpine Großarl valley, Salzburg, Austria (Fig. 2b).The Großarl valley was mapped geologically in great detail by Exner (1956), who allocated the outcropping lithologies to the cretaceous (Piller et al. 2004) Penninic unit of the Bündner schists (classic term: Bündnerschiefer) of the Eastern Tauern Window.Schmid et al. (2013) proposed an updated nomenclature for these units.Therein, the rocks of the study site are regarded as part of the Glockner Nappe System, which is the largest Penninic nappe of the Tauern Window (Pestal et al. 2009).It comprises calcareous micaschists and subordinate meta-pelites derived from the Valais Ocean, together with intercalated greenschist rock.In the Großarl valley, the schistosity of these lithologies generally dips north-northeast at a moderate dip-angle (Exner 1956;Pestal and Hejl 2005;GBA 2021).
At the study site, the Großarl valley is surrounded by steeply to almost vertically inclined rock slopes, which strike sub-parallelly to the alignment of the valley.Sections of steep rock slopes are interrupted by moderately inclined plateaus forming a stepped terrain (Fig. 2c).One of these rock slopes just above the valley bottom located south-east of the settlement Karteis/Hüttschlag failed by three main rock fall events in the year 2019: the first on the 25 th of March, the second on the 15 th of July, and the third on the 24 th of October.
The rock fall debris reached the agricultural land on the valley bottom (Fig. 2a).The distalmost deposited blocks stopped just before a pedestrian and cycle path beside the river Großarl, which separates the rock fall site from the main road of the valley.From the highest point of the scarp area at 1263 m a.s.l. to the distalmost deposited blocks at 1010 m a.s.l.(∆h = 253 m), the rock fall material covered a horizontal distance of 300 m, resulting in a fahrböschung angle (Heim 1932) of 40.1°.The rock fall debris of all rock fall events added up to a cumulative deposition volume of approx.41,000 m 3 .Individual blocks show edge lengths of up to 10 m, resulting in volumes of up to 300 m 3 (Fig. 2d).
In the scarp area, an overhanging rock mass (herein referred to as 'metastable rock nose') of approx.6000 m 3 deformed considerably by forming an extension fracture.However, it remained on the rock slope in metastable conditions after the last event (Fig. 2e).It shows clear evidence for possible future rock fall events.Above all, the presence of the large extension fracture at the back of the metastable rock nose, which shows an aperture of 4 to 5 m near the surface with narrowing towards the bottom, supports this assumption.

Workflow and data overview
In accordance with the previously defined research strategy, we present a workflow, which was applied in this study (Fig. 3).
The purpose of the workflow is to lead to the fulfilment of the objectives of this paper, and to enable the reader to assess the added value of the methods used and results obtained.Each element in the workflow is addressed in more detail in the subsequent sections: 'Process reconstruction,' 'Geological characterisation,' 'Rock mechanical laboratory analysis,' and 'Distinct element modelling (DEM) series'.The abbreviations used in the workflow are listed in its figure caption.
An overview of the data used in this study is presented in Table 1, showing the acquisition date and type, sources, resolutions, and purposes for this paper.

Event documentation
After each of the three rock falls in Hüttschlag, high-resolution photographic event documentations were acquired by helicopter.They allowed us to qualitatively assess the post-failure geometry on the rupture surface of the unstable rock slope after each event and to unravel the polyphase character of the rock fall process.Additionally, we identified the location of structures existing prior to failure, i.e. pre-existing discontinuities, and where brittle failure paths developed in intact RBs in the course of the rock fall process.
Moreover, we obtained unique insights into the initial failure mechanism of the 1 st rock fall event on the 25th of March 2019 by analysis of an eye-witness video.This helped us to validate the output of our DEM described in the 'Distinct element modelling (DEM) series' section.

UAV-P
We applied UAV-P after the 3 rd rock fall event to quantitatively determine the complex post-failure topography of the rock fall site at high-resolution.UAV-P missions for landslide identification, monitoring, and assessment have become an applicable and ever-improving technique for engineering geological matters (Casagli et al. 2017;Giordan et al. 2018Giordan et al. , 2020)).
We processed 628 pictures acquired with a DJI Phantom 4 Real Time Kinematics (RTK) drone (DJI 2020) within the Agisoft Metashape Professional 1.8.0 (LLC 2022) photogrammetry software.We aligned the pictures acquired with the UAV with known centre coordinates from the RTK-GNSS together with 73 high-resolution, helicopter-borne photographs (without position information) focusing on the rock fall source-area.This yielded a high-resolution digital surface model and an orthophoto of the rock fall site after the third and latest rock fall event.
We compared the pre-failure ALS digital elevation model from 2007 with the post-failure UAV digital surface model from 2021 by the calculation of a digital elevation model of difference (DoD).In photogrammetric digital surface models, areas with vegetation show high position and geometric errors.Thus, we excluded vegetated areas from our DoD analyses.Based on non-vegetated stable reference areas, we assessed a level of detection (LoD), which is here defined as the second standard deviation of DoD values in stable reference areas (Fey et al. 2015): The DoD allowed us to detect terrain changes at high resolution in the rupture area, e.g. the initial failure mechanism of metastable areas.

Structural characterisation
To properly characterise the rock mass from which the rock falls occurred, we conducted geological field surveys comprising mapping of structural and lithological features.In addition, we acquired samples for further petrographic and microscopic investigations in the vicinity of the rock fall scarp (Fig. 4a).
Whilst field mapping, we classified discontinuities according to their orientation (Clar-Notation with (dip direction/dip angle) [°] used for all orientational data) and generic appearance (Hencher 2013).For an objective discontinuity characterisation, we conducted scanline recording as proposed by Priest (1993).Therefore, we chose three orthogonally orientated in situ scan-lines (Fig. 4b) with a total length of 90 m in the vicinity of the rock fall site (Fig. 4a).Due to working safety concerns, it was not feasible to conduct vertical in situ scan lines on the unstable rock slope.However, we mitigated a possible sampling bias by the scan-line inclination (covered vertical distance of 15 m).
(1) Based on this data, we identified discontinuity sets by stereographical analysis (equal area projection into the lower hemisphere used for all stereo-plots) by the DIPS 8.003 (Rocscience 2020) software.To statistically analyse these sets, we applied density probability distribution functions (Hudson and Priest 1979), in order to derive values for normal set spacing (χ) and total trace length (μ).For the analysis, we used the workflow and code published by Zangerl et al. (2022) within the GNU Octave (6.4.0) (Eaton et al. 2020) software.

Lithological characterisation
For a petrographic confirmation of the macroscopically mapped lithologies, orientated samples were processed for microscopic thin-section analysis and X-ray-diffractometry (XRD).We investigated the thin-sections on a Leica DM4500P polarisation microscope to classify the metamorphic rocks according to their mineralogy (MacKenzie et al. 2017) and to identify microstructures (Passchier and Trouw 2005).The X-ray-diffractometry (XRD) by a PANalytical X'Pert Pro (Waseda et al. 2011) complemented the petrographic investigations.
To determine the intact rock density, we performed non-destructive pycnometry on a micromeritics AccuPyc II 1340 gas (Helium) pycnometer.We conducted 17 measurements on five randomly selected samples from the rock fall material.The rock fall material was also used for the rock mechanical laboratory analysis described below ('Rock mechanical laboratory analysis').

Rock mechanical laboratory analysis
The rock mechanical properties of the rock mass are a key input of our DEM study, especially considering the necessity of calibrating the shear strength properties assigned to the Voronoi contacts (Stead and Wolter 2015).
By point load tests on 22 block specimens (specimen volume approx.200 cm 3 , Fig. 5a) with a Wille Geotechnik portable point load test apparatus (Fig. 5b) according to the ISRM (1985) procedure, we obtained the break load and consequently the point load index of the samples.Sample size correction was applied (Brook 1985) in order to calculate the unconfined compressive strength (UCS) of the intact rock by a ISRM (1985) proposed factor.
By direct shear tests (compare Voit et al. 2022) on the rock fall material, we approximated the Mohr-Coulomb failure criterion which is implementable into our DEM study ('Distinct element modelling (DEM) series').To identify the Mohr-Coulomb failure criterion comprising the friction angle φ (°) and cohesion c (MPa), it was necessary to identify pairs of normal stress σ n and shear stress τ acting on the specimens at the time of shear failure: For this purpose, we applied different levels of normal force F N (vertical load) and a shear force F S (horizontal force) to the upper, free part of the specimen (Fig. 5c) by two hydraulic cylinders (Fig. 5d).Whilst F N was kept on a constant level, F S was constantly increased until shearfailure occurred.We then determined the area of the failure surface (ranging from 290 to 660 cm 2 ) to calculate σ n and τ acting on the specimen at the time of failure.The direct shear test-specimens were irregular and larger (specimen volume approx.5000 cm 3 ) than for the point load tests.
We performed the direct shear tests in two phases.In Phase1, we tested the intact, irregular specimens, which incorporated pre-existing rock-fabric elements, i.e. (semi-) ductile features, brittle fractures, and the schistosity.Thus, we approximated the shear strength of an irregular, natural, and intact specimen.After Phase1, we sorted out specimens with strongly undulating failure surfaces that could not be identified beyond doubt.
In Phase2, the remaining specimens were readjusted to their position prior to failure, and the fully persistent shear fractures induced during Phase1 were tested again.Thereby, we approximated the Mohr-Coulomb failure criterion for fully persistent, pre-existing discontinuities, i.e. faults and joints.Accordingly, this Mohr-Coulomb criterion was assigned to pre-existing discontinuities in the DEM study ('Distinct element modelling (DEM) series').

Distinct element modelling (DEM) series
For the final stage of our research strategy, we used 2D numerical modelling based on the Universal Distinct Element Code (UDEC) 7.0 (Itasca 2018), which enabled us to investigate mechanical relations between pre-existing structures, brittle RB failure, and the rock fall process.
For our DEM study, we acknowledged the following simplifying assumptions and constraints.We accepted the rock fall failure mechanism as a 3D problem (Brideau and Stead 2010).However, by selecting a slope profile section for our 2D numerical model parallel to the lateral release surfaces provided by pre-existing discontinuities, we reduced the problem to a 2D phenomenon.Thereby, caution was required regarding the over-or underrepresentation of RBs when downscaling from 3D to 2D (Elmo et al. 2018).Furthermore, we neglected any tectonic stresses within the DEM by assuming that topographic stresses outweigh possible tectonic stresses, due to the overhanging pre-failure topography.
UDEC can model a rock mass consisting of deformable blocks (intact rock) separated by discrete contacts (pre-existing discontinuities) with different constitutive relationships.In this study, we assigned the linear-elastic constitutive relation to the blocks.Mohr-Coulomb contact (2) = tan( ) * σ n + c law was assigned to the contacts based on our results of the direct shear tests ('Rock mechanical laboratory analysis').However, UDEC does not allow new brittle failure paths to form in the elastic blocks, i.e. the growth of natural cracks and their coalescence.Thus, the brittle failure of intact RBs is neglected.To circumvent this constraint, we tessellated the elastic blocks (intact rock) into asymmetric Voronoi elements (Itasca 2018).In the DEM study, the Voronoi elements were implemented with an elongated axis (aspect ratio of 1.6) which was aligned according to the anisotropy of the rock, i.e. parallel to the schistosity.The maximum edge length of the Voronoi elements was 1.5 m and thus of a size considerably smaller than the original blocks.A small Voronoi element size reduces errors in the development of failure paths due to the Voronoi geometry (Gao and Stead 2014).Thus, we allowed the propagation of any brittle failure path along the pre-existing Voronoi contacts, if their tensile-or shear-strength properties were exceeded.
In this study, we conducted two main DEM campaigns.The first campaign served to back-calculate the rock fall process.In its course, we tested three variants of Mohr-Coulomb properties for the Voronoi contacts in individual model scenarios.To find these Mohr-Coulomb variants for each Voronoi model scenario, we used the results from the direct shear tests ('Rock mechanical laboratory analysis').The Phase1 results (intact specimen) were assumed as the upper limit and the Phase2 results (fully persistent fracture surface) as the lower limit for the Voronoi contacts.In between these limits, we defined three pairs of c and φ, i.e.V1, V2, and V3, which were each tested in an individual model scenario.We compared the output for each model scenario with observations from the UAV-P and graphical event documentation.Thereby, we tested these Voronoi model scenarios and adopted the properties that reproduced the process most accurately in the second modelling campaign.We then investigated the sensitivity of the rock fall process to the persistence of pre-existing discontinuities in a calibrated DEM.

Initial failure and deformation mechanisms of the polyphase rock fall process
We identified block toppling as the initial failure mechanism of the 1 st rock fall event on the 26 th of March 2019 by video analysis (Fig. 6a).In the video, we observed a failing rock mass column tilting downhill, with the highest velocities at the upper part and the lowest in the lower part of the block, clearly suggesting a rotational movement mechanism.This type of kinematics is further emphasised by the spatial occurrence of remnants of snow in the air during the failure event.During the progression of the event, a transition of the mechanism from toppling to falling occurred (Fig. 6a, compare frame 0.49 [s] to 0.79 [s]).Finally, the failed rock mass disappeared in rock dust, which hindered us from visually tracing the mechanism underlying the running-out in the video analysis.
However, the fresh rock mass exposed by this 1 st failure event is visible on the rupture surface by helicopter-borne photographs (Fig. 6b).These documentations were also acquired after the 2 nd (Fig. 6c) and 3 rd (Fig. 6d) rock fall event and prove the polyphase character of the rock fall.On the rock slope, we identified areas which were newly exposed due to these rock fall events by their bright green and unweathered colour (Fig. 6d).This differentiates them from the pre-failure rock surface, which was already exposed to weathering processes before failure and therefore showed a darker colour and some vegetation and lichen cover.The spatial distribution of weathered surfaces after the 1 st failure event allowed us to reconstruct the pre-failure topography of the slope.After the 1 st rock fall event, some remnants of the weathered surface were situated on the rupture surface just above the highlighted lithological boundary (Fig. 6b).Directly above this weathered area, an overhanging rock mass with vegetation cover was still in place on the rock slope, proving that the slope showed an overhanging pre-failure topography.
During the 2 nd event 112 days later, this weathered, overhanging rock mass failed.Moreover, the remnants of the prefailure surface above the tectonic boundary directly below it were erased as well (compare Fig. 6b-c).This upwardsdirected retrogressive failure propagation still preserved the overhanging topography of the slope.The 3 rd event occurred 101 days later.In its course, the failure propagation reached the top of the rock slope (Fig. 6d).
As visible in the event reconstruction (e.g., Fig. 6b-d), four discontinuity sets dominate the rupture surface.Set1 dips steeply to the south-west, i.e. parallel to the slope.Set2 dips to the north and Set3 to the south-east at a moderate dip angle.Finally, Set4 is sub-vertically inclined and strikes from northeast to south-west, i.e. normal to the slope.The helicopterborne documentations prove that in all three major events, these discontinuity sets were decisive: Set1 serves as the rear detachment, Set4 as lateral release, and the intersection of Set2 and Set3 as lateral boundaries and/or basal detachment of the failing rock masses.These sets are anticipated here and addressed in more detail in the structural characterisation in the subsequent chapter 'Geology of the study site'.
After each major event, a pre-existing discontinuity related to the slope parallel discontinuity Set1 dominates the lower half of the newly exposed rock slope, showing a plane, polished surface (e.g.Fig. 6d).However, the upper half of the newly exposed rock slope shows an undulating, rougher surface with abrupt changes in orientation.In between these rougher areas, pre-existing discontinuities of Set1 are daylighting in a stepped geometry.We infer that the rough surfaces in the upper part separating the individual Set1 discontinuities resemble failed RBs.They failed within the rock fall process itself and coalesced the daylighting discontinuities of Set1 to form a fully persistent detachment surface (Fig. 6d).
This observation allowed us to reconstruct the location of pre-existing discontinuities of Set1 prior to failure.Consequently, we determined where RBs had to fail in the course of the rock fall process.This provided valuable input for our DEM study as described in the 'Distinct element modelling (DEM)' section.
We studied terrain changes based on the pre-and postfailure topography from 2007 and 2021 by determining the DoD.Thereby, the rock fall site was divided into a source-, transfer-, and deposition-area (Fig. 7a).The outlined source-area covers 1500 m 2 and shows a volume loss of approx.30,000 m 3 , with the highest change in elevation of − 47 m (Fig. 7b).At its eastern edge, an extension fracture separates the metastable rock nose from the slope (compare Fig. 2e).Since this extension fracture widens from the bottom upwards to an aperture of 5 m on the surface, we infer an initial block toppling mechanism for the metastable rock nose.This block toppling mechanism is also suitable to reproduce the distinctive DoD pattern in the sourcearea (sketch in Fig. 7d).
The transfer area covering an area of approx.6500 m 2 separates the source-area from the deposition-area and is characterised by small positive and negative DoD values in the range of + 7 to − 9 m.On the one hand, the patches of negative DoD values in the transfer-area are allocated to entrainment by failing rock masses.On the other hand, the positive patches are attributed to the selective deposition of rock fall debris in the transfer-area.More volume was entrained than deposited, resulting in a volume loss of approx.5000 m 3 in the transfer-area.
The deposition-area shows a gain in volume of approx.41,000 m 3 and can furthermore be divided into a coherent body of rock fall debris at the foot of the slope (Fig. 7a), and individual blocks that separated from the rock fall debris travelled further and ploughed into the sedimentary valley fill (Fig. 7c).The maximum grain size of the components of the poorly sorted rock fall debris reached boulder to block size (Blair and McPherson 1999).It covered an area of 11,500 m 2 , showing the largest thickness of approx.10 m in its centre, declining towards the margins.Remarkably, the individual blocks show edge lengths of up to 10 m yielding volumes of up to 300 m 3 (B3 in Fig. 7c).The bouncing, rolling, and sliding mechanism of these blocks led to impact craters and plough-like traces (negative DoD values) on the talus and valley infill sediments.Although the running-out of the blocks was not caught on camera in the video analysis (Fig. 6a), these tracks allowed us to reconstruct the movement characteristics as bouncing (block B3, 25 m between impact craters), rolling (blocks B4 and B5), and finally sliding (B3, Fig. 7c).
The results and observations presented in this chapter, e.g.overhanging pre-failure topography and position of preexisting discontinuities and RBs, are used to provide input for the DEM study ('Distinct element modelling (DEM)').Additionally, the observed failure mechanisms and postfailure geometries of the polyphase rock fall process serve to validate the output of the DEM back calculation campaign.

Lithological analysis
A main lithological boundary visible on the rupture surface (Fig. 6d) divides the rock slope into an upper part Page 11 of 25 363 comprising greenschists and a lower part comprising calcmica-schists (Fig. 8a, b).The greenschists show a welldefined schistosity, which originates from phyllosilicates, i.e. some muscovite and mostly chlorite, with a preferred orientation.These phyllosilicates are aligned around idiomorph grains of amphibole (actinolite) (Fig. 8c).Subparallel to the schistosity a secondary foliation (Huet et al. 2020) can be observed, resulting from the alternating succession of chlorite-rich layers with layers composed mostly of plagioclase (albite) and some quartz.By the application of He-pycnometry, we derived a density for the greenschists of 2.928 ± 0.035 g cm 3 .
The calc-mica-schists in the lower part of the unstable rock slope show a well-defined schistosity too (Fig. 8c).However, in contrast to the greenschists, the schistosity is caused by the sub-parallel alignment of layers almost composed of muscovite only.These muscovite-rich layers alternate with calcite and quartz-rich layers yielding a secondary foliation.Furthermore, an opaque phase is present, presumably consisting of pyrite.In addition, east and north of the rock fall scarp, dark, schistose meta-pelitic rocks crop out.These meta-pelites are fine-grained and contain mostly calcite, muscovite, and quartz (Fig. 8c).
As indicated before, these lithologies have been incorporated in several deformation events from which they inherited distinctive ductile, semi-ductile, and brittle structural features.

Structural analysis
Based on discontinuity analysis and cross-cutting relationships, three tectonically inherited deformation phases, i.e.D1, D2, and D3, can be distinguished and assigned into a relative chronological order.The oldest visible deformation phase D1 is characterised by a micro-scale isoclinal folding of quartzite layers with a fold axis plane orientated subparallel to the schistosity.This isoclinal folding of D1 caused the development of a secondary foliation and of the schistosity.In their current position, the schistosity and foliation surfaces dip moderately towards the north, i.e. obliquely into the slope (Fig. 9a).
Semi-ductile shear bands of the younger D2 deformation phase are crosscutting the secondary D1 foliation.The D2 shear bands (Passchier and Trouw 2005;Huet et al. 2020) are related to Set2 and Set3 (Fig. 9b).In its current position, Set2 dips moderately towards the north, i.e. sub-parallel to the schistosity.Set3 dips moderately towards the south-east and the intersection of Set2 with Set3 yields a vector dipping into the slope at a mean dip angle of 30°.
The Set2 and Set3 shear bands of the D2 deformation phase are visible both on the micro-scale by structural mapping on thin-sections (Fig. 10a) and on the mesoscale by scanline recording (Fig. 10b).The Set2 shear bands appear in an en-echelon like pattern and enclose elements composed of multiple secondary foliation layers and the schistosity.These elements are deflected from their general orientation, which results in an offset from the adjoining element.The youngest, brittle deformation phase D3 crosscuts all structural features described before.D3 comprises joints, i.e. brittle fractures with no or only marginal displacement parallel to it, and faults, i.e. discrete discontinuities with brittle deformation parallel to it (Twiss and Moores 2007;Huet et al. 2020).These joints and faults are allocated to Set1 and Set4 (Fig. 9c).Furthermore, D3 structures were developed as reactivation along the pre-existing, semi-ductile, D2 shear bands.A total of four main discontinuity sets allocated to these deformation phases were identified (Fig. 9d).By application of scanline methods for each set, the mean orientation, the normal set spacing, and the full trace length were determined (Table 2).This lithological and structural characterisation served as a key input for our DEM study.To finalise the DEM input, we subsequently present the results from our rock mechanical investigations.

Rock mechanical investigations
The rock mechanical properties of the intact greenschist rock were studied by point load and direct shear tests.The test procedures are described in detail in the 'Rock mechanical laboratory analysis' section.Of the point load tests conducted normally to the schistosity, we declared 13 of the 22 test-runs as valid, due to the proper  2) on the a micro-and on the b meso-scale 363 Page 14 of 25 formation of the fracture surface (ISRM 1985).Of these, we calculated a size-corrected (Brook 1985) point load index of 3.04 ± 0.78 MPa and consequently an UCS of 60 ± 16 MPa.
By direct shear tests, we obtained pairs of normal σ n and shear stress τ for each specimen at the time of failure (Fig. 11a).Five shear tests were successfully performed on intact specimens (Phase1).On the new, fully persistent shear fractures induced during Phase1, eight additional shear tests were performed (Phase2).The covered range of normal stress during the test runs ranged from 138 to 415 kPa for Phase1 and from 222 to 1934 kPa for Phase2.
A linear regression performed on the σ n -τ-pairs of Phase1 yields a coefficient of determination R 2 p1 of 75%.According to the Mohr-Coulomb criterion, we calculated a friction angle φ p1 of 68.5° and a cohesion c p1 of 74.2 kPa (Fig. 11c).For Phase2, where fully persistent surfaces were tested, we obtained a friction angle φ p2 of 20.4° and a cohesion c p2 of 188.8 kPa.The linear regression fitted to the Phase2 results yields a R 2 p2 of 94%.Since fully persistent shear fractures were tested in Phase2, a value for c of 0 kPa was assumed.This yielded an adapted Mohr-Coulomb criterion, herein referred to as Phase2* (Fig. 11b), with a friction angle of 26.4°.This is  comparable to results for in situ shear tests on discontinuities in a rock comprising phyllosilicates published by Fishman (2004).Accordingly, the Mohr-Coulomb criterion obtained from the Phase2* results was assigned to pre-existing discontinuities in the DEM-study.However, the Mohr-Coulomb criterion for Phase1 delivered an unusually high value for φ and a relatively low value for c, with a moderate R 2 (= 0.75).In order to find the Mohr-Coulomb properties for the Voronoi contacts, we estimated three different variants of Mohr-Coulomb parameters from the data, i.e.V1, V2, and V3 (Fig. 11b).Thereby, we assumed the adapted Phase2* results (c and φ for a fully persistent discontinuity) as the lower limit and increased the values for φ and c stepwise, until the highest results for Phase1 were covered ('Distinct element modelling (DEM) series').
These three different variants of Mohr-Coulomb properties were subsequently assigned to the Voronoi contacts and tested in the back-calculation step of the DEM study ('Back calculation of the rock fall failure mechanism'), in order to find the Mohr-Coulomb properties reproducing the process most accurately.

Distinct element modelling (DEM)
For the 2D geomechanical modelling study, we used a slope profile derived from the ALS-based digital elevation model ( 2007) as pre-failure topography for all models.The slope profile trends northeast to southwest (30-210°), i.e. sub-parallel to the lateral release surface of Set4 (compare Fig. 6d).However, overhanging sections are not captured by the ALS method, due to the limitations of the acquisition type.Nevertheless, we could reasonably reconstruct the overhanging pre-failure topography (Fig. 12a), by the observations done in the process reconstruction, as shown in the 'Initial failure and deformation mechanisms of the polyphase rock fall process' section.

Back calculation of the rock fall failure mechanism
For the back calculation of the rock fall failure mechanism, the observed structural inventory described in the 'Geology of the study site' section was implemented into the corrected pre-failure topography (Table 3).
The structural input comprised five traces of the Set1 discontinuities that were exposed after the latest rock fall event and could also be detected in the UAV-P-derived postfailure topography (Fig. 12a).This resulted in a stepped, en-echelon pattern of the Set1 discontinuities.They dip out of the slope at dip angles ranging from 76 to 82°.Due to the geometry of the Set1 discontinuities, sections of intact rock are enclosed between the individual discontinuity traces, representing negative RBVs (Figs. 1 and 12b).As described in the 'Distinct element modelling (DEM) series' section, Voronoi tessellation was used to simulate intact RBs within the DEM.Accordingly, the area of Voronoi tessellation is outlined in Fig. 12b, and the geometry and orientation of the Voronoi elements are shown in the detailed view.Finally, the intersection vectors of the semi-ductile Set2 and Set3 are integrated, dipping into the slope at a dip angle of 30°.After implementing the structural inventory into the DEM, the boundary conditions were assigned to the model (Fig. 12c).
In the model runs, a linear elastic constitutive relationship was assigned to the blocks, i.e. the Voronoi elements, and different Mohr-Coulomb constitutive relationships were assigned to the contacts (Fig. 12d).The linear elastic properties of the Voronoi elements and the Mohr-Coulomb properties for the brittle discontinuities of Set1 were held constant (Table 4).By contrast, the Mohr-Coulomb properties assigned to the intersection vectors of the semi-ductile Set2 and Set3 and to the Voronoi contacts were varied, as shown in Fig. 12d, resulting in three different model scenarios, i.e.V1, V2, and V3 (Table 4).By comparing the output of each Voronoi model scenario with the in situ observations of the failure process, we identified the Mohr-Coulomb properties which reproduced the main features of the process most accurately.In doing so, we calibrated the properties for the Voronoi contacts according to the back calculation of the rock fall process.
In the back-calculation step, we observed the detachment of several rock mass columns from the rock slope for all Voronoi model scenarios V1, V2, and V3 (Fig. 13).The individual rock mass columns were distinguishable by different magnitudes of displacement.In general, the slope displacement was characterised by sub-horizontal displacement vectors dipping out of the slope, and by the displacement magnitude increasing upwards within the individual rock mass columns.These observations allowed us to allocate the initial failure mechanism in the DEM to block toppling, which is in accordance with the initial failure mechanism observable in the video record (Fig. 6a).
In model scenarios V2 and V3, the rock mass columns were separated by newly developed, brittle failure paths growing along the pre-existing Voronoi-contacts.Generally, these fractures originated at the upper tips of the implemented discontinuities of Set1, which provided a rear detachment for the failing rock mass columns.The new failure paths propagated obliquely upwards, finally intersecting with the slope surface.Removing the rock mass columns from the slope caused overhanging post-failure slope topographies.Where brittle RB failure occurred, the topography was characterised by new, rough rupture surfaces.Where pre-existing discontinuities were exposed, planar surfaces daylighted.This is in agreement with the post-failure geometry of the slope observed in nature (Fig. 6b-d).
In model scenario V2, the amount of joint plane separation increased upwards within each discontinuity trace related to Set1.This indicated that the aperture of the rear detachment traces opened upwards in the DEM, which supports the initial toppling failure and is in accordance with the deformation observed in nature at the extension fracture separating the metastable rock nose (Fig. 7b).
This was also observable in the Voronoi model scenario V3 for the upper four rear detachment discontinuity traces related to Set1 (Fig. 13).However, the lowest Set1 discontinuity in the V3 model scenario showed an opposite pattern in the joint plane separation, i.e. the magnitude of separation increasing downwards.Furthermore, the block separated by the lowermost Set1 discontinuity showed displacement vectors parallel to Set1, indicating a sliding mechanism, which was not observed in nature.
In contrast to the V2 and V3 model scenarios, the jointplane separation pattern increasing upwards was not detected for the Set1 traces in the V1 model scenario.Instead, a strong disintegration of the rock fall mass was observed, characterised by multiple fracture paths within the outermost rock mass column.The strong fragmentation in the V1 scenario is assumed to be too large to reproduce a coherent, failing rock mass column, as visible in the video record (Fig. 6a).
The differences between the individual Voronoi model scenarios V1, V2, and V3 were only minor and show that the range of Mohr-Coulomb properties derived from the direct shear tests are feasible to reproduce most of the phenomena observed in nature.Yet, the fragmentation in model scenario V1 is assumed to be too large, and the local planar sliding mechanism observed in scenario V3 was not detected Fig. 13 Output of the Voronoi model scenarios V1, V2, and V3: 1.Initial toppling mechanism, 2. Several rock mass columns detaching from the rock slope, 3. Brittle RB failure resulting in a rough, new surface, 4. Overhanging post-failure topography, 5. Local rock slide mechanism, 6. Metastable areas, 7. Strong fragmentation of the outermost rock mass column in nature.Given that the V2 model scenario reproduced all phenomena observed in nature, we integrated the V2 Mohr-Coulomb properties for the Voronoi contacts (c = 300 kPa and φ = 40°) into the second modelling campaign.In this campaign, the influence of joint persistence on the failure mechanisms is studied.

Influence of joint persistence on the failure mechanism
In the framework of the second modelling campaign, the geomechanical properties used in the V2 model scenario were adopted and held constant (Table 4).For simplification and unambiguous control of the model geometry, the Set1 discontinuities naturally occurring in an en-echelon pattern were reduced to one single, planar discontinuity, henceforth referred to as Set1-joint (Fig. 14).In doing so, the negative RBVs included and considered in the 'Back calculation of the rock fall failure mechanism' were neglected.In this second modelling campaign, variation was only performed concerning the length (persistence) of the implemented Set1-joint, acting as a rear/basal detachment discontinuity.
The origin of the Set1-joint was placed at the point, where the lowest en-echelon discontinuity implemented in the back-calculation study was daylighting on the foot of the slope (Fig. 14a).Starting from there, the length of the Set1-joint trace was increased stepwise, until it connected with the point where the uppermost en-echelon Set1 discontinuity was daylighting on top of the slope.Consequently, full persistence (100% of the entire length of the slope) was reached and the dip angle of the Set1-joint was reduced to 68° (Fig. 14e).
Firstly, the joint was inserted with a persistence of 50%, leading to a Voronoi-tessellated RBV to be left in the upper part of the rock slope (Fig. 14a).This caused the slope to fail in a toppling mechanism (a dip of displacement vector ~ 22°), comparable to the back calculation study.We also observed several rock mass columns detaching from the slope and new, brittle failure paths forming.The same failure mechanism, i.e. block toppling of several rock mass columns, was observed for a persistence of 60% (displacement vector ~ 28°, Fig. 14b) and 66% (displacement vector ~ 30°, Fig. 14c) respectively.
However, starting from 75% persistence, the displacement vectors changed to a steeper dip angle, essentially sub-parallel to Set1, indicating a sliding mechanism (Fig. 14d).The only part of the rock slope still showing a toppling mechanism was only found in the uppermost section of the slope, where the Set1-joint was not persistent.Applying 100% joint persistence with no RB related to the joint, a complete rock slide mechanism was reproduced (Fig. 14e).
The modelling study clearly showed the sensitivity of the initial failure mechanism to the persistence of the Set1-joint, and we found that above a persistence threshold of 66%, the failure mechanism transitioned from toppling to sliding.

Process classification
After the initial toppling failure of the 1 st event, the blocks transitioned into a falling process (Fig. 6a).It finished with the deposition of the main rock fall debris at the foot of the unstable rock slope.Due to the deposition of the rock fall debris as a coherent body in a small area adjoining the rock slope, an interaction between the blocks occurred most likely during the failure process (Fig. 7a).To some extent, this rather suggests a flow-like movement behaviour (Hungr et al. 2014).The mechanism underlying the running-out of the individual blocks-i.e.bouncing, rolling, and sliding-was distinctively traced by the DoD (Fig. 7c).Thus, the movement types within the process transition from initial toppling (source area), to falling Fig. 14 Results from the numerical model investigating the sensitivity of the initial failure mechanism to the persistence of the rear detachment discontinuity, block contour with displacement magnitude and displacement vector, a general dip of displacement vectors is sketched, a to e shows increasing persistence (transfer area), to bouncing, rolling, and finally sliding (deposition area), until the rock fall material came to a final standstill.A similar succession of movement types was also discovered by Ma and Liu (2022) in a combined case and modelling study.
Whilst the initial toppling failure of the 1 st event was caught on camera, we have no eye-witness video of the 2 nd or 3 rd event.However, the initial failure mechanism of the metastable rock nose was identified as toppling too.Furthermore, we found toppling to be the predominant failure mechanism in the back-calculation step of our DEM (Fig. 13).Thus, we infer that the initial failure mechanism of the 2 nd and 3 rd event was most likely toppling too.Still, a local planar sliding mechanism cannot be excluded, especially as the spatial distribution of RBs is highly variable, and we discovered discontinuity persistence as a factor controlling the failure mechanism (Fig. 14).
The cumulative failure volume of all three rock falls detected in the source area amounted to circa 30,000 m 3 .The additionally entrained volume in the transfer area amounted to circa 5000 m 3 .However, in the deposition area, we detected a volume of approx.41,000 m 3 , i.e. an increase of 17%.Such an increase in volume is expectable due to the fragmentation of the rock fall material.Since there is no high-resolution data available after each rock fall, the failure volume of each individual event can only be estimated.Assuming that all major rock fall events showed a roughly similar failure volume (estimated in the range of 5000 to 15,000 m 3 ) the fahrböschung angle of 40.1° fits well with published relations between failure volume and run-out (Scheidegger 1973;Fey et al. 2011).

The structural setting and control
Four discontinuity sets influenced the rock fall process, as visible on the rupture surface (Fig. 6d).These structures were inherited from at least three consecutive tectonic deformation phases, which were assigned into a relative chronological order.The oldest phase D1 resulted in the development of a strong anisotropy in the metamorphic rock mass (Fig. 15a).This anisotropy had a strong influence on the rock mechanical properties of the rock and was accounted for in the DEM by the inclination of the asymmetric, elongated Voronoi elements (Fig. 12).
The classification of the distinctive structures of the younger, semi-ductile D2 phase on the meso-and microscale (Fig. 15a) is more challenging.They would correspond to shear band boudins (Goscombe et al. 2004); however, the boudinaged element consists of packages of foliation (Fig. 10).Thus, the structure could be classified as an asymmetric foliation boudinage, which can occur on multiple scales (Fossen 2010).Still, such boudin structures may be confused with a C-S-C′ fabric in ductile shear zones (Rodrigues and Pamplona 2018).Regardless of the classification, the semi-ductile shear bands on the microscale can be considered as flaws within the rock, as identified within the microscopic thin-section analysis (Fig. 10).Such flaws may act as nuclei, from where fractures propagate to coalesce, forming a brittle, fully persistent failure surface (Bobet and Einstein 1998).
The faults and joints of the brittle D3 deformation phase cross-cut the D2 shear bands (Fig. 15b) and are related to two discontinuity sets (Set1, Set4) enclosing a right angle (Table 2).Although two sets of orthogonal joints must not necessarily reflect a change in the regional stress pattern (Bai et al. 2002;Twiss and Moores 2007), they are commonly found to form parallel to the direction of the highest principle stress (Fossen 2010).Thus, we do not exclude that the discontinuities of Set1 and Set4 are caused by two individual brittle deformation phases.However, no coherent cross-cutting evidence was found which would prove that these sets originated from two separate brittle deformation phases.Therefore, they are subsumed here in the brittle D3 phase.
To explain the current position of the discontinuities, we infer a youngest, rotational D4 deformation event that rotated all pre-existing structural features from the deformation phases D1, D2, and D3, to the north-east along a horizontal rotation axis by 30° (Fig. 15c).In course of this D4 event, the structural features inherited from the previous deformation phases would be rotated from a position according to the Anderson (1905) condition to their present orientation.
The tectonic origin for the brittle discontinuities is supported by the calcite filling in an extension fracture parallel to Set4 (Fig. 15b) and by their embedment in a coherent tectonic framework (Fig. 15c).However, we do not exclude that some of the brittle discontinuities, i.e. faults and joints, have been reactivated as sheeting joints (Twiss and Moores 2007;Hencher et al. 2011).This would be especially relevant for the prominent, slope-parallel discontinuities on the rupture surface related to Set1, although no infilling was found for the Set1 discontinuities.However, since these Set1 discontinuities are part of a coherent tectonic picture and occur in a stepped pattern with a dip-angle less steep than the dip of the pre-failure slope (Fig. 12a), we infer that the trace of the joint was at least tectonically pre-defined and may have been reactivated as a sheeting joint (Hencher 2013).
Kinematically, these four discontinuity sets allow either a sliding or a direct block toppling mechanism.Planar sliding requires a discontinuity set which dips out of the slope at a dip angle less steep than the slope itself.This is fulfilled by discontinuities of Set1 in combination with Set4 acting as lateral release structures for a rock slide.Yet, as stated before, a toppling (Hungr et al. 2014) failure was identified as the predominant failure mechanism for the Hüttschlag rock falls (e.g.Fig. 6a).Moreover, toppling was the main failure mechanism in the DEM back-calculation study (Fig. 13).
The kinematic conditions for block toppling are more complex, as a rear, lateral, and basal detachment is required (Brideau and Stead 2010).A general criterion for toppling is that the rear detachment surface dips steeply into the slope.However, field evidence and the UAV-P-derived postfailure topography clearly suggest that the rear detachment surface is provided by discontinuity planes related to Set1.They dip out of the slope at a dip-angle ranging from 76 to 82° (Fig. 12a).Whilst the kinematic conditions for block toppling are fulfilled in terms of lateral release (Set4) and basal detachment (intersection vector of Set2&3), no rear detachment surface dipping into the slope is provided.This rather suggests an initial sliding mechanism, than a direct block toppling mechanism and reveals a discrepancy with the failure mechanisms observed in nature.This discrepancy is discussed below.

Rock bridge control on the rock fall process
In our DEM, we modelled intact portions of the rock slope by asymmetric Voronoi tessellation.The Mohr-Coulomb properties for the Voronoi contacts were approximated by the direct shear tests ('Rock mechanical investigations').When testing fully persistent shear fractures (Phase2), the results showed a good R 2 (94%) and yielded a Mohr-Coulomb failure criterion comparable to literature values (Fishman 2004).However, the direct shear test results derived from intact specimens (Phase1) yielded a Mohr-Coulomb criterion with a moderate R 2 (75%) only (Fig. 11a).These more scattered results for the intact specimens were most likely due to the irregular test medium itself, i.e. a natural rock mass with pre-existing flaws, e.g.microcracks and (semi-)ductile features.Such flaws presumably reduced the shear strength of some specimens, depending on their orientation relative to the direction of the applied shear force (Huang et al. 2020).This additionally underlined the challenge of incorporating RBs into DEM studies, especially regarding up-scaling procedures (Elmo et al. 2022), and highlighted the necessity of calibrating the shear strength properties assigned to the Voronoi contacts (Stead and Wolter 2015).
We addressed this issue by conducting three different model scenarios, in which we assigned different Mohr-Coulomb criteria to the Voronoi contacts and compared the model output to the observations from the rock fall reconstruction ('Back calculation of the rock fall failure mechanism').The failure paths observed in our DEM studies originated from the upper tips of pre-existing geological discontinuities.These failure paths propagated along the contacts of Voronoi elements, which represented the schistosity by their elongated axis.As a result, they exactly reproduced the fracture patterns observed in nature (compare Fig. 13 to Fig. 6d).Still, minor deviations observed between the model scenarios allowed us to find the ideal properties for the Voronoi contacts, reproducing the process with the highest accuracy.This outlined the feasibility of the Voronoi calibration technique applied in this study, i.e. conducting direct shear tests on larger specimens, which incorporate natural irregularities, and calibrating the results within a back-calculation step of the DEM study.
The reconstructed geometry of Set1 resulted in a negatively stepped, en-echelon discontinuity pattern.This Page 21 of 25 363 geometry of Set1 caused negative RBVs to be enclosed between individual discontinuities (compare Zhou and Chen 2019) of the set (Fig. 16a).In all Voronoi model scenarios of the back calculation step of the DEM (Fig. 13), the lowermost part of the rock slope failed first-either in a toppling or sliding mechanism (block I in Fig. 16a).To allow kinematic freedom for block I, a critical failure path had to form in the RBV at its top.It originated from the upper tip of the lowest Set1-joint and propagated obliquely upwards to reach the surface.A similar fracture development was observed by Donati et al. (2019) for a toppling failure on a sandstone rock mass, which was undermined by clay erosion (Spreafico et al. 2017).
The block I failure caused an overhanging post-failure topography and exposed the lowest pre-existing Set1-joint and failed rock bridges (Fig. 16b).We distinguished these failed RBs from the pre-existing discontinuities by their strongly undulating, rough surfaces with abrupt changes in orientation (Fig. 6d).A similar approach was reported by Bolla and Paronuzzi (2020).The removal of block I caused the destabilisation of block II (Fig. 16b) in a retrogressive manner.
In order to provide kinematic freedom for block II, two critical brittle failure paths had to form in RBVs, to provide coalescence between the en-echelon arranged Set1 discontinuities and the surface.One in the negative RBV at the foot of block II and one in the RBV at its top.For a sliding failure of block II, the negative RBV at the foot of block II would have had to be sheared off.Thus, the negative RBV functioned as an asperity and tapered block II (Elmo et al. 2018).As a consequence, the rock mass column of block II moved outwards, i.e. to the left in Fig. 16b.Accordingly, a toppling failure developed, as observed in nature (Fig. 6a), reconstructed by UAV-P (Fig. 7b), and reproduced in the back-calculation step of the DEM study (Fig. 13).Then, the next adjoining rock mass column (block III in Fig. 16c) was destabilised in the same manner.
Removing block III induced an extension regime, resulting in the formation of an extension fracture separating the metastable rock nose (block IV) from the slope.However, the rock nose did not fail completely.A first explanation would be a geometrical condition of the en-echelon Set1 discontinuities, which provided a foundation for the metastable rock nose, even though all RBs failed.However, the rock on the bottom of the metastable rock nose on the rupture surface showed no signs of fracturing (Fig. 2e).A more plausible explanation is that there is sufficient RB support at the rock nose bottom (Fig. 16d).As stated by Tuckey and Stead (2016), even small quantities of RBs can substantially improve rock slope stability.This was also shown by Paronuzzi et al. (2016) for a rock wedge failure, which stability was critically influenced by a single RB, covering an area of less than 0.2% of all failure surfaces.This is most likely the case for the metastable rock nose of the Hüttschlag rock fall site.
The schematic failure propagation sketched in Fig. 16 is in accordance with the polyphase character of the rock fall process and the overhanging post-failure geometry of the failed rock slope observed in nature (Fig. 6).The time lag between the rock fall events in nature, i.e. 112 days between the 1 st and 2 nd rock fall event and 101 days between the 2 nd and 3 rd , may result from progressive failure along discontinuities (Kemeny 2005).This especially highlights the challenge of unravelling the timing and clear trigger factors of slope failures (Eberhardt et al. 2001).

Persistence control on the rock fall process
In our simplified DEM study in the framework of our second modelling campaign ('Influence of joint persistence on the failure mechanism'), we excluded negative RBVs by reducing Set1 to a single, planar discontinuity.Thereby, a Voronoi-tessellated RBV was left at the upper section of the rock slope (Fig. 14a).The RBV was progressively reduced and finally removed, by increasing the persistence of the Set1-joint stepwise.The location of the critical failure path developed in the RBV in the upper section of the rock slope was only revealed in the course of slope failure.This further highlighted the challenges in incorporating RBs into forward analysis, as the actual RB position is generally not detectable prior to failure (Elmo 2023).
At 100% and 75% persistence for the pre-existing Set1joint, a sliding mechanism was developed.Remarkably, below a threshold of 66% persistence, the failure mechanism changed back to toppling (Fig. 14).This showed that the toppling mechanism is not necessarily dependent on the block tapering by negative RBVs (Elmo et al. 2018) but may also be governed by a RBV in the upper section of the rock slope.However, the mechanism must be different, as the negative RBVs were removed here.This provided kinematic freedom for a sliding mechanism, if a critical failure path developed in the upper RBV, still connecting the rock mass to the slope.Nonetheless, a toppling mechanism was developed below 66% persistence of the Set1-joint (Fig. 14).A possible explanation is that failure of the rock mass along the Set1-joint resulted in the destabilisation of the RBV in the upper section of the rock slope.This may have caused a complex mechanical interaction between the failing rock masses, leading to toppling failure.

Conclusions
We classify the landslide process in Hüttschlag as an active, polyphase rock fall process, with toppling as the initial failure mechanism.The rock falls show a cumulative failure volume of 30,000 m 3 and a fahrböschung angle of 40.1°.The mechanism underlying the running-out of the main rock fall debris possibly included some flow-like movement behaviour.However, individual blocks showing volumes of up to 300 m 3 left that rock fall debris and travelled further by bouncing, rolling, and finally sliding.
Within the rock mass hosting the rock falls, we identified four pre-existing discontinuity sets and allocated these to distinctive, consecutive, structural deformation phases.The presence, persistence, and orientation of these brittle and semi-ductile discontinuity sets affected the rock fall process and provided detachment surfaces.Thus, they control the geometry and lateral expansion of the slope instability and allow to outline possible initial failure mechanisms.We emphasise this interconnection between tectonically inherited structural features of variable deformation characteristics and rock fall processes.By our DEM studies, we confirmed this structural impact and conclude: (a) A combination of detailed structural geological in situ surveys, lithological investigations, rock mechanical laboratory analysis, and UAV-P (RTK) missions provides a proper basis for a DEM study.(b) In the DEM, asymmetric Voronoi tessellation with calibrated shear strength properties for the Voronoi contacts allowed to reproduce all characteristic phenomena of the rock fall process observed in nature and to model RB failure by the development of new, brittle failure paths.(c) Negative RBVs enclosed by pre-existing, en-echelon arranged Set1 discontinuities imposed asperities to failing rock masses, forcing them to fail in a toppling mechanism.Without the tapering imposed by these asperities, a rock slide mechanism would have been feasible.This was demonstrated in a second DEM campaign, in which the en-echelon discontinuities of Set1 were reduced to a single, planar joint, thus excluding negative RBVs.From 75 to 100% persistence of the Set1-joint, a rock slide mechanism was reproduced in the DEM study.(d) Remarkably, the initial failure mechanism changed from sliding to toppling below a threshold of 66% persistence of the single, planar Set1-joint.Thus, which failure mechanism was developed in the second DEM campaign depended on the persistence of the single pre-existing Set1-joint.

Fig. 2
Fig. 2 Geographical setting and overview of the Hüttschlag study site after the 3 rd and latest rock fall event.a UAV-P-derived 3D model.b Location of the study site in Austria, c Topography of the Großarl valley with location and extent of the rock falls highlighted, d Block

Fig. 3
Fig. 3 Applied workflow used for this study.Abbreviations: DoD, digital elevation model of difference; DSM, digital surface model; Photo-Doc, photographic event documentation; UCS, uniaxial compressive strength

Fig. 4
Fig. 4 Type and location of applied methods.a Extent of the rock fall and area of data acquisition, location of sampling, outcrops, and of the scanlines SL1, SL2, and SL3 (orthophoto in the central area is based on UAV-P mission (see 'UAV-P') and the hillshade in the peripheral areas is derived from the digital elevation model 2007).b Orientation of the in situ scanlines and of the rupture surface within the equal area projection into the lower hemisphere

Fig. 5
Fig.5Rock mechanical laboratory analysis.a 22 greenschist samples cut into block specimens for point load tests(ISRM 1985).b Point load test setup for the sample HS-PL 1 within the apparatus with the schistosity orientated normally to the applied force (F B ). c Direct shear test set-up with the irregular specimen and the various components.d Structure of the force units for the direct shear tests with calottes to ensure proper force transmission on the specimen

Fig. 6
Fig.6Reconstruction of the rock fall process.a Frames derived from the video documentation of the 1 st failure event of the Hüttschlag rock falls; the red cross marks the same, steady tree-crown for orientational purposes; the green cross shows the position of a specific tree-crown on top of the failing rock mass columns and the blue cross shows its reconstructed positions from the previous frames, b situation after the 1 st event, the weathered surface below overhanging portions of the rock slope and above the tectonic contact is outlined by a dashed, turquoise line.c Situation after the 2 nd event, d situation after the 3 rd event with possible future rock fall mass ('metastable rock nose') highlighted and enlarged in the 3D UAV-P model from 2021

Fig. 7
Fig. 7 Digital elevation model of difference (DoD) of the Hüttschlag rock fall site, the DoD is transparent within the LoD of ± 0.1 m. a Overview of the source-, transfer-, and deposition-area.b Source-area with metastable rock nose and distinctive DoD pattern (I, II, III, IV)

Fig. 8
Fig.8Geology of the study site.a Geological map, b geological cross-section, and c selected pictures from the transmissive light microscopy for the respective lithologies with plane polarised light (PPL) and crossed polarised light (XPL) for the same area of the thin sections, Mineral abbreviations: Ac, actinolite; Alb, albite; cc, calcite; Chl, chlorite; Ep, epidote; Ms, muscovite; Qtz, quartz

Fig. 9
Fig.9Overview of the structural data: a D1 deformation phase-schistosity and foliation; b D2 semi-ductile deformation phase-shear bands; c D3 brittle deformation phase-joints and faults; d discontinuity sets in their current position, the schistosity was excluded when identifying the discontinuity sets

Fig. 11
Fig. 11 Mohr-Coulomb criteria based on the direct shear test a results from Phase1 and Phase2 with linear regressions.b Phase2* resembles an adapted Mohr-Coulomb criterion for Phase2 with c p2* = 0 kPa; it was assumed as lower limit for the Mohr-Coulomb criteria; three dif-

Fig. 12
Fig. 12 Set-up of the numerical model.a Correction of the pre-failure topography (ALS) and implementation of the major pre-existing structural inventory, b Voronoi-tessellated area and structural input, c overview of the complete model framework with boundary conditions and structural inventory, tectonic contact indicated for orientational purposes, d rock mechanical entities of the DEM and assigned constitutive relationships

Fig. 15
Fig. 15 Schematic depiction of the structural geological deformation events in interplay with the inherited discontinuity sets.a D2: semi-ductile deformation phase, Set2 and Set3.b D3: Brittle deformation phase with Set1 and Set4 in a right-angled position.c D4: Inferred rotation towards the northeast by 30°

Fig. 16
Fig. 16 Schematic sketch of the role of RBVs in the phased failure of the Hüttschlag rock falls, centre of gravity of the blocks is indicated with a red cross, a destabilisation of block I; note, that it is only in the course of failure that we know which part of the intact rock volume

Table 1
Overview of the data used in this study

Table 3
Consideration of all discontinuity sets in the 2D DEM

Table 4
Back calculation of the rock fall failure mechanism-input parameters and variation study with the V1, V2, and V3 model scenarios