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The role of initial coherence and path materials in the dynamics of three rock avalanche case histories Aaron, Jordan; McDougall, Scott; Moore, Jeffrey R; Coe, Jeffrey A; Hungr, Oldrich Feb 7, 2017

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RESEARCH Open AccessThe role of initial coherence and pathmaterials in the dynamics of three rockavalanche case historiesJordan Aaron1*, Scott McDougall1, Jeffrey R. Moore2, Jeffrey A. Coe3 and Oldrich Hungr1AbstractBackground: Rock avalanches are flow-like landslides that can travel at extremely rapid velocities and impactsurprisingly large areas. The mechanisms that lead to the unexpected mobility of these flows are unknown anddebated. Mechanisms proposed in the literature can be broadly classified into those that rely on intrinsiccharacteristics of the rock avalanche material, and those that rely on extrinsic factors such as path material. In thiswork a calibration-based numerical model is used to back-analyze three rock avalanche case histories. The results ofthese back-analyses are then used to infer factors that govern rock avalanche motionResults: Our study has revealed two key insights that must be considered when analyzing rock avalanches. Resultsfrom two of the case histories demonstrate the importance of accounting for the initially coherent phase of rockavalanche motion. Additionally, the back-analyzed basal resistance parameters, as well as the best-fit rheology, aredifferent for each case history. This suggests that the governing mechanisms controlling rock avalanche motion areunlikely to be intrinsic. The back-analyzed strength parameters correspond well to those that would be expected byconsidering the path material that the rock avalanches overran.Conclusion: Our results show that accurate simulation of rock avalanche motion must account for the initiallycoherent phase of movement, and that the mechanisms governing rock avalanche motion are unlikely to beintrinsic to the failed material. Interaction of rock avalanche debris with path materials is the likely mechanism thatgoverns the motion of many rock avalanches.BackgroundRock avalanches are a class of extremely rapid, flow-likelandslides that can impact people and property far fromtheir source. Beginning with the work of Heim (1932),many researchers have noted an apparent increase inrock avalanche mobility with increasing volume (Heim1932; Scheidegger 1973; Hsu 1975; Li 1983; Corominas1996; Legros 2006; Whittall et al. 2016). This observation isbased on plots of volume vs. angle of reach (defined as theinclination from horizontal of the line connecting the high-est point on the failure scarp to the distal end of the de-posit), suggesting that higher volume events have greatermobility. However, the mechanism(s) that contribute(s) tothis apparent volume-mobility trend remain debated (e.g.Hungr and Evans, 2004).A number of theories have been proposed to explainthe apparent correlation between mobility and volumeof rock avalanches. Many of these theories are reviewedby Legros (2002) and Hungr & Evans (2004). The theor-ies can be broadly grouped into mechanisms that aredue to intrinsic characteristics of the rock avalanche ma-terial and those that rely on extrinsic factors such aspath material. The following recently published theoriesdemonstrate that the debate surrounding rock avalanchemovement mechanisms is still ongoing. These include: Johnson et al. (2016) showed results of discreteparticle models that predict an increase of mobilitywith increasing volume. They propose that thisphenomenon arises from acoustic waves propagatingthrough the particle assembly that reduce* Correspondence: jaaron@eos.ubc.ca1Department of Earth, Ocean and Atmospheric Sciences, University of BritishColumbia, 2020 - 2207 MainMall, Vancouver, British Columbia V6T 1Z4,CanadaFull list of author information is available at the end of the articleGeoenvironmental Disasters© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, andreproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link tothe Creative Commons license, and indicate if changes were made.Aaron et al. Geoenvironmental Disasters  (2017) 4:5 DOI 10.1186/s40677-017-0070-4intergranular stresses, consistent with the theory ofacoustic fluidization (e.g. Melosh 1979). Manzanal et al. (2016) proposed that rock avalanchesdilate upon failure, however; as fragmentationproceeds, the reduction in grain size results in aswitch from dilative to contractive behaviour,resulting in generation of pore-air pressures. Lucas et al. (2014) proposed a velocity weakeningrheology, and showed that a consistent set ofparameters could reproduce field observations fromthree rock avalanche case histories. They noted thattheir rheology is consistent with the mechanism offlash heating. Bowman et al. (2012) presented geotechnicalcentrifuge experiments that suggest a positivecorrelation between degree of fragmentation andrunout length. Their experiments used a bilinear pathwith a high angle sloped portion (70°). Blasio & Crosta(2015) demonstrated that a steep path combined withisotropic fragmentation can increase centre of massdisplacement; however, the effect disappears for slopeangles typical of rock avalanche paths. Coe et al. (2016) and Aaron & Hungr (2016a) bothinvoked low basal friction due to entrainment andoverriding of saturated soil to explain the dynamicsof the West Salt Creek rock avalanche and theAvalanche Lake rock avalanche, respectively. In bothcases, this hypothesis was supported by field evidenceof entrained path material at the base of the deposit.Due to the uncertainty about the governing mechanismscontributing to rock avalanche motion, the developmentof mechanistic models remains challenging. Instead, manyresearchers use semi-empirical models (e.g. Hungr 1995).In these models, the governing equations are derivedbased on conservation of mass and momentum; however,the parameters that govern the simulations are not truematerial properties. Instead, these parameters are empir-ical and derived based on back-analysis of full-scale casehistories. These models typically treat the rock avalancheas a frictional fluid, which ignores the effects of the ini-tially coherent stage of rock avalanche motion (Aaron &Hungr 2016b).Over the past two decades, there has been a proliferationof models developed based on a semi-empirical approach(Bouchut et al. 2003; Pitman et al. 2003; McDougall &Hungr 2004; Pirulli 2005; Pastor et al. 2009; Huang et al.2012; Cascini et al. 2014; Dai et al. 2014). These modelswork well in a back-analysis context; however, they haveonly been applied to forecast potential runout in a few pub-lished cases (e.g. Nicol et al. 2013; Loew et al. 2017). Thechallenge of performing forward-analysis with these modelsis that it remains difficult to relate successful back-analysesto potential failures. This is the biggest challenge that mustbe overcome before semi-empirical runout models can beroutinely used in practice, and arises from the fact thatthere are likely multiple mechanisms that govern mobilityand the conditions contributing to these mechanisms areusually not known a priori.The purpose of this study is to investigate factorsgoverning rock avalanche motion using two dynamicmodels. We show that many characteristics of rock ava-lanche motion can be explained by considering the disin-tegration process and the slide path materials. We firstprovide a description of the dynamic models used forthis investigation in the following section, then describeresults of our back-analyses of three large-volume rockavalanches.Description of the dynamic modelsTwo dynamic models, entitled the flexible block model(Aaron and Hungr, 2016b) and Dan3D (McDougall, 2006;Hungr and McDougall, 2009) are used in the presentwork. These models each describe different phases of rockavalanche motion. The flexible block model is appropriatefor simulating the initially coherent portion of rockavalanche motion, while Dan3D is used to simulate therock avalanche motion after it fragments and becomesflow-like. The key aspects of these two models are de-scribed in the following sections.Flexible block modelThe flexible block model is a dynamic model developedto simulate the initially coherent phase of motion exhib-ited by many rock avalanches. In this model, the land-slide is treated as a flexible block that translates androtates over a user-defined, three-dimensional rupturesurface. Movement is initiated by an unbalanced gravita-tional force accelerating the failed material from rest.Deformation is not permitted in the horizontal direc-tions; however, vertical deformation is allowed in orderto ensure that the flexible block remains on the rupturesurface. The governing equations solved by this modelare shown in Eqs. 1, 2 and 3. A detailed derivation ofthese equations is presented by Aaron & Hungr (2016b).The flexible block model uses an orthogonal coordinatesystem with the z-axis oriented vertically.mbody  _vx ¼ Fx ð1Þmbody  _vy ¼ Fy ð2ÞIz  _ωz ¼ Tz ð3ÞWhere mbody is the mass of the flexible block, _vx ; _vyare the x and y translational accelerations, Fx, Fy are thenet forces acting on the flexible block in the x and y di-rections, Iz is the moment of inertia of the flexible blocktaken about the z-axis, _ωz is the angular accelerationAaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 2 of 15about the vertical z-axis, and Tz is the net torque actingabout the z-axis.The net force and torque on the flexible block are cal-culated by discretizing the failed mass into a system ofcolumns. The number of columns used to represent thefailed mass can either be chosen by the user or selectedautomatically based on the resolution of the input top-ography files. As shown in Fig. 1, the forces resolved oneach column are the column weight and the basal resist-ance force which acts opposite the direction of motion.The net forces acting on each column are summed toderive the net force and torque acting on the assemblageof columns. This algorithm is summarized in Fig. 2. Thisprocedure is similar to simple 3D limit-equilibriummethods (methods which neglect internal forces); how-ever, instead of solving for a factor of safety, the methodsolves for translational and angular accelerations. In thecurrent version of the model, internal forces are neglected,so the model should not be used to simulate stronglycompound failures.Dan3DThe governing equations solved by Dan3D are summa-rized in Eqs. 4 and 5 (McDougall 2006). Only the finalform of the equations used in the model are presented; adetailed derivation is presented by Hungr & McDougall(2009). These equations are depth-averaged and derived inFig. 1 Forces acting on a column of material in the flexibleblock model. W is the weight of the column, and T is the basalresistance forceFig. 2 Flowchart of the flexible block model algorithm. The three steps that describe the flexible block model are highlighted. t fluidize is a userspecified parameterAaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 3 of 15a Lagrangian coordinate system, with the x-coordinatealigned with the local direction of motion and the z-coordinate oriented in the bed-normal direction.ρhDvxDt¼ ρhgx−kxσz∂h∂xþ τzx−ρvxE ð4ÞρhDvyDt¼ ρhgy−kyσz∂h∂yð5ÞWhere ρ is the density, vx,y are the depth-averaged xand y velocities, h is the flow depth, gx,y are the x and ycomponents of gravity, kx,y are the x and y horizontalstress ratios (ratio of lateral stress to bed normal stress)calculated based on Savage-Hutter theory (Savage andHutter, 1989), σz is the bed normal stress, τzx is the basalresistance, and E is the entrainment rate.A free-body diagram that shows the forces acting on aslice of material oriented in the direction of motion isdisplayed in Fig. 3. The first term on the right hand sideof Eqs. 4 and 5 represents the gravitational stress (thedownslope component of the W force in Fig. 3), whilethe second term represents the longitudinal pressuregradient (P force in Fig. 3). The basal resistance stress (Tforce in Fig. 3) and momentum loss due to entrainment(E force in Fig. 3) only occur in the x-direction due tothe fact that the x-coordinate is aligned with the localdirection of motion. The entrainment rate (E) and dens-ity, as well as the parameters that govern kx,y and τzx, areuser-specified.When performing a back analysis with Dan3D, the pa-rameters that are commonly calibrated are the internalfriction angle (used to calculate kx,y) and parameters as-sociated with the user-specified basal rheology (used tocalculate τzx). The entrainment rate is sometimes a cali-brated parameter, although it is common to evaluate thisparameter based on known estimates of initial and finalvolumes (McDougall & Hungr, 2005).Three rheologies are commonly used in Dan3D simu-lations to calculate τzx. The frictional rheology is shownin Eq. 6:τzx ¼ −σz tan ∅bð Þ ð6Þwhere σz is the bed-normal effective stress and ∅b isthe calibrated apparent friction angle, which includespore-pressure effects. The Voellmy rheology (e.g. Hungr &McDougall, 2009), given in Eq. 7 is similar to the frictionalrheology, with an additional velocity-dependent term:τzx ¼ −σz f þ ρgv2xξ ð7Þwhere f is the friction coefficient (equivalent to tan (∅b))and ξ is the turbulence parameter. Both f and ξ are cali-brated parameters. The Bingham rheology (e.g. Hungr &McDougall, 2009), given by Eq. 8, does not assume thatthe basal resistance is proportional to the bed-normal ef-fective stress:τ3zx þ 3τyield2þ μBinghamvxh τ2zx−τ3yield2¼ 0 ð8Þwhere τyield is the yield stress and μBingham is the viscosity;both of these parameters are calibrated.In the analysis that follows, the equations are simpli-fied by ignoring centripetal acceleration and entrainmentterms and using the frictional rheology to calculate thebasal resistance stress. This allows for the derivation ofsimplified equations that demonstrate the behavior ofDan3D. Only the x-direction equation of motion is con-sidered for this analysis. By making these assumptions,the equation of motion reduces to:DvxDt¼ g sin αð Þ þ gk ∂h∂x−g tan ∅bð Þ cos αð Þ ð9Þwhere α is the slope angle.Through algebraic rearrangement, this equation canbe put in the following form:DvxDt¼ gcos αð Þ tan αð Þ− tan θð Þð Þ þ gk∂h∂xð10ÞThe first term on the right hand side captures thegravitational acceleration and basal resistance to move-ment, similar to a block sliding down an inclined plane.The second term on the right hand side expresses theacceleration due to internal pressure gradients. It is thisterm that differentiates equivalent fluid models fromrigid body models, such as lumped mass models (Heim,Fig. 3 Conceptual free-body diagram of a slice of material orientedin the direction of motion in Dan3D. W is the weight; T is the basalresistance; P is the internal force due to free surface gradients; and Eis the inertial resistance due to entrainmentAaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 4 of 151932). From Eq. 10, it can be seen that Dan3D simulatestwo mechanisms that drive landslide motion. The masswill accelerate when the slope angle is greater than thefriction angle, as in the initial path of many rock ava-lanches, or when there is a strong enough free-surfacegradient (∂h∂x in Eq. 10 and P force on Fig. 3), as in manyflowslides. Equation 10 also demonstrates that when africtional rheology is used and the free surface gradientis small, the mass will only decelerate when the slopeangle is less than the friction angle.Dan3D-FlexDan3D and the flexible block model have been coupledin order to simulate extremely rapid, flow-like landslidesthat have an initially coherent phase of motion (Fig. 2).The coupled model is called Dan3D-Flex, and has beenused to simulate a large number of rock avalanche casehistories (e.g. Aaron & Hungr 2016b; Castleton et al. 2016;Grämiger et al. 2016; Moore et al. 2017). To couple thetwo models, the solution algorithm switches from the flex-ible block model to Dan3D at a user-specified time. Asshown in Aaron & Hungr (2016a, b), this parameter canbe chosen to correspond with the expected fragmentationmechanism. The geometry and velocity of the flexibleblock during the final time step are used as the initial con-ditions for the Dan3D simulation.MethodThree rock avalanche case histories have been back-analyzed using Dan3D-Flex. These cases were selectedto investigate two primary factors that must be consid-ered when analyzing the runout of rock avalanches: (1)disintegration process and (2) the slide path materials.All three cases have similar volumes; however, they differ ininitiation mechanism and path materials. Back-analyzingthese events provides a way to quantify the effects of thesefactors.Two of the three cases were run using both the flex-ible block model (with Dan3D-Flex) and ignoring theinitially coherent portion of motion (with Dan3D). Bycomparing the results of these cases, the necessity ofusing the flexible block model in accurately simulatingrock avalanche motion can be assessed.To explore the effects of path materials, the shearstrength distribution required to reproduce fieldobservations was assessed for all three cases using the cali-bration methodology described in Aaron et al. (2016). Inthis methodology, quantitative fitness metrics are used toassess the quality of a simulation. These metrics can ac-count for a variety of simulation constraints including im-pact area, velocity and deposit distribution. For each of thecase histories, a wide range of parameter combinationswere evaluated. This ensured that we explored the en-tire parameter space and achieved the best possible par-ameter fitness to all available back-analysis constraints.We hypothesize the following. If all three cases can beback analyzed using the same rheology and similar back-analyzed strength parameters, then it is possible that asingle volume-dependent failure mechanism governs rockavalanche motion, and that mobility can be explained witha general theory that is not site-specific. However, if therheology and back-analyzed parameters are different forthese cases, then it is more likely that different site-specific mobility mechanisms govern the runout of rockavalanches.ResultsThe best-fit parameters, defined as the parameters thatbest reproduce all simulation constraints (e.g. impactarea, deposit distribution and velocity), for each of thethree case histories are summarized in Table 1. Individualdescriptions of the case histories follow in the subsequentsections.West Salt CreekThe West Salt Creek rock avalanche occurred on May25th, 2014, and claimed the lives of three people. Thislandslide released from the northern flank of GrandMesa, in western Colorado. The event had a complex,two-stage failure mechanism. The first stage included re-activation of an ancient slump block in a unit consistingof shales and marlstones, with an estimated total volumeof rock displaced by the slump of 54 Mm3 (White et al.2015; Coe et al. 2016). It is thought this reactivation wastriggered by a rain-on-snow event (White et al., 2015).The second phase of the failure consisted of rapidevacuation of a rock avalanche from the toe of the dis-placed slump block (Coe et al. 2016). The rock avalanchehad a source volume of approximately 12 Mm3. Thehypothesized initiation mechanism of the rock avalanche,based on Coe et al. (2016), is shown in Fig. 4.Table 1 Back-analyzed basal resistance parameters for each of the three case historiesCase History SZ-∅b (°) P-∅b (°) P-ξ (ms-2) P-τyield (KPa) P-μBingham (KPa*s)West Salt Creek – – – 32 7Bingham Canyon 10 26 – – –Rautispitz 18 10 300 – –The basal rheologies used are summarized in Eqs. 6, 7 and 8. SZ refers to source zone, and P refers to pathAaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 5 of 15White et al. (2015) identified a prehistoric landslidethat travelled part of the way down West Salt Creek.White et al. (2015) also noted that the debris of the 2014event underwent rapid slaking (in the months followingthe event), which has transformed the shales and marl-stones into disaggregated, loose clasts of fine-graineddebris. Coe et al. (2016) hypothesized that the surficialsediments present in the West Salt Creek channel likelyconsisted of a mixture of alluvium and landslide de-posits. Based on these observations and hypotheses, it ispossible that, after failure, the rock avalanche overranloose fine-grained sediments that had a high degree ofsaturation from the high precipitation and snowmeltthat preceded the rock avalanche.As can be seen in Fig. 5, the rock avalanche over-topped a 40 m high ridge, and superelevated throughthree bends along the runout path. Based on these su-perelevations, White et al. (2015) estimated runout vel-ocities of 37 m/s, 25 m/s and 9 m/s at the three bends(from upstream to downstream, respectively) using theforced vortex equation (e.g. Chow, 1959). Coe et al.(2016) also provided dynamic constraints on the motionof the rock avalanche through interpretation of radiatedseismic signals; they estimated that the slide was travel-ling at an average velocity of 21 m/s.Lidar data were collected after the event to constrainthe post-slide geometry. Pre-event topographic dataare available on a 10-m spaced grid. Based on these,the deposit distribution is well-constrained and we de-rived an accumulation/depletion map (Fig. 7). Imme-diately down slope of the slump block there is littlechange in the topography, indicating that either therewas no deposition in this zone, or there was erosion ofpath materials that were later replaced by depositionof rock avalanche debris. Significant deposition beginstowards the distal end of the channelized portion ofthe path. We estimate the volume of material thatovertopped the ridge is between 100,000 m3 and150,000 m3 (Fig. 7).Fig. 5 Overview of the West Salt Creek Rock Avalanche (Photo: J Coe)Fig. 4 Failure mechanism for the West Salt Creek Rock Avalanche hypothesized by Coe et al. (2016). Panel a shows the topography before failure.The geometry after the slump (green line on panel b and c) was derived from a Dan3D-Flex analysis. Panel d shows the topography after the rockavalanche had vacated the source zone. The section line is shown on Fig. 7Aaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 6 of 15A back-analysis of the West Salt Creek Rock Ava-lanche was conducted based on the failure mechanismdescribed by Coe et al. (2016). The 3D rupture surfaceof the slump block was input into Dan3D-Flex, and africtional rheology was used to simulate initial rotationalfailure. We used 7015 columns to represent the failedmass, and the mass was kept rigid throughout the entiresimulation. The friction angle was adjusted by trial-and-error until the back-tilted portion at the top of the slopebest matched the post-slide LiDAR surface. The resultsof this back-analysis are shown in Fig. 4. The back scarpof the rock avalanche is visible on the post-slide LiDAR,and this was combined with the final Dan3D-Flex geom-etry to create a 3D rupture surface for the second phaseof motion (i.e. initiation of the rock avalanche). Thisprocess is shown schematically in Fig. 4. Our reconstruc-tion resulted in a modelled rock avalanche source vol-ume of 12 Mm3, very close to that estimated from theaccumulation/depletion map.Initially, we used the Voellmy rheology to parameterizethe basal resistance force. The best fit results, obtainedby testing 400 different parameter combinations, areshown in Fig. 6. As can be seen in Fig. 7, no combinationof friction coefficient and turbulence parameter can simul-taneously reproduce the overtopping of the ridge andthe distal runout extent. Additionally, when material ispredicted to overtop the ridge, it does not deposit inthe correct location.Fig. 6 Final deposit depth and predicted impact area when basal resistance is parameterized with the Voellmy rheology. The red outline showsthe observed impact area. A minimum deposit depth value of 0.3 m is necessary due to the solution method used by Dan3DFig. 7 West Salt Creek Rock Avalanche accumulation and depletion map. Coe et al. (2016) noted that the estimated vertical error of the digitalelevation data is ± 4.72 m. The section line refers to Fig. 4Aaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 7 of 15To overcome these shortcomings, we next tested theBingham rheology. This rheology is appropriate to simu-late rapid shearing of fine-grained material, which in thepresent case represents the saturated, fine-grained ma-terial along the valley floor that was overridden by therock avalanche. The material within the body of the rockavalanche had high frictional strength (Coe et al., 2016).The results of a sensitivity analysis using the Binghamrheology are shown in Fig. 8. As can be seen in Fig. 8, aτyield =32 KPa and μbingham = 7 KPa*s provides the bestcompromise between simulating both the impact areaand deposition on the 40-m high ridge (based on the ac-cumulation depletion map, we expect that the volumedeposited on the ridge is between 100,000 m3 and150,000 m3). The simulation results for this best-fit com-bination are shown in Fig. 9; we obtained good agree-ment between field observations and model results, bothin terms of impact area and deposit thickness distribution.Runout velocities predicted by the model are approxi-mately 30% higher than the maximum velocities estimatedby White et al. (2015); however, they broadly agree withthe average velocity estimated by Coe et al. (2016).There are two reasons for the improved results whenbasal resistance is parameterized with the Bingham rhe-ology. The first is that centripetal accelerations do notincrease basal resistance (as in the Voellmy rheology); sothe flowing mass expends less momentum overtoppingthe ridge. The second is that deposition is now con-trolled by both flow depth and slope angle, as opposedto the frictional and Voellmy rheologies, where depos-ition is controlled by slope angle alone. This allows themass to deposit both on the steep overtopped ridge, aswell as at the distal toe. These two factors provide strongjustification for the use of the Bingham rheology tosimulate the West Salt Creek rock avalanche.Bingham CanyonThe Bingham Canyon rock avalanches were a series oftwo rock avalanches that occurred on April 10th, 2013,in Utah, USA, at the Bingham Canyon mine (Fig. 10).The mine is one of the largest in the world, and debrisfrom the two landslides filled the pit bottom with wasteand destroyed heavy equipment. Most of the data associ-ated with this event is privately owned, and is currentlyunavailable for researchers. The analysis presented hereis based on public data sources and an aerial topographicsurvey described by Moore et al. (2017).Both Bingham Canyon rock avalanches initiated alonga highly persistent basal fault dipping 21° due west(Fig. 10). This fault extends from the toe of the sourcearea to near the crown. Only a small volume of materialwas deposited in the source zone, which indicates thatthe ultimate strength along the basal fault was very low.Fig. 8 Results of the sensitivity analysis used to determine the best-fit Bingham parameters for the West Salt Creek rock avalanche. Impact areafitness is calculated using a dimensionless number that measures the misfit between a user specified impact area and the simulated impact area.Lower numbers indicate better fitness (a value of zero indicates perfect agreement between observed and simulated impact area). The best compromisebetween simulating the observed impact area and deposit distribution is found for τyield =32 KPa and μbingham = 7 KPa*s. Volume is in m3Aaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 8 of 15Fig. 9 Predicted impact area and simulated deposit depths when basal resistance is parameterized with the best fit Bingham rheology. The redoutline shows the observed impact area. A minimum deposit depth value of 0.3 m is necessary due to the solution method used by Dan3DFig. 10 Overview of the Bingham Canyon rock avalanche. Very little material is left on the rupture surface in the source zone, and there does notappear to be any runup at the distal toe. Modified from Pankow et al. (2014)Aaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 9 of 15In Fig. 10, it can be seen that two different types of deb-ris are visible in the deposit. The grey debris consists ofbedrock that failed during the first rock avalanche, whilethe predominantly orange debris is composed of a higherproportion of waste rock, which failed as the second rockavalanche.Moore et al. (2017) constructed a post-event digitalelevation model (DEM) based on their aerial topographicsurvey. A pre-event DEM was then derived from thepost-event DEM based on a manual reconstruction guidedby high-resolution, pre-event aerial photographs. Thistopographic reconstruction resulted in a total estimatedvolume of the two rock avalanches of 52 Mm3. Moore etal. (2017) estimated that 30 Mm3 failed during the firstrock avalanche and 22 Mm3 failed during the second rockavalanche.The back-analysis presented here was first summarizedby Moore et al. (2017). The present work focuses on thevalues determined for the back-analyzed parameters inthe context of rock avalanche movement mechanisms,as well as highlighting the necessity of simulating ini-tially coherent motion using Dan3D-Flex. We used 3609columns to represent the phase 1 sliding mass, and 4001columns to represent the phase 2 sliding mass. For thephase 1 simulations, the rigid motion distance was se-lected to correspond with fragmentation occurring whenthe mass vacates the source zone and interacts with therugged topography on the benches. For the phase 2 sim-ulations, it was selected to correspond with the phase 2sliding mass impacting the scarp vacated by the phase 1debris. The basal resistance force was parameterizedusing two frictional rheologies, one in the source zoneand one for the pit walls and floor (Fig. 11). The twofriction angles that govern these rheologies were thencalibrated. Two field observations proved critical whencalibrating these rheologies. Firstly, the strength of thebasal fault in the source zone had to be low enough sothat all the material vacated the planar rupture surface.Secondly, Fig. 10 shows that there was very little runupon the distal pit wall, indicating that the mass did notenergetically runup and fall back into the pit.The best-fit results using Dan3D-Flex are shown inFig. 11a. These simulations use a friction angle of 10° inthe source zone and 26° along the runout path (Table 1).As noted by Moore et al. (2017), this parameter combin-ation reproduces velocity estimates based on field mea-surements of superelevation and runup. These simulationsreproduce the two key field observations noted above: (1)little volume is simulated to remain on the planar rupturesurface, and (2) no runup is simulated at the toe.The best-fit results of a back analysis for the first rockavalanche not using the flexible block model are shownin Fig. 11b. Excessive spreading around the source zone ispredicted by the model, resulting in a poor reproductionof the observed impact area. The runout distance is alsounderpredicted when the same friction angles are used asin the Dan3D-flex simulations. Selecting a lower frictionangle that reproduces the distal runout distance leads toeven more excessive lateral spreading.RautispitzThe Rautispitz rock avalanche is a prehistoric landslidethat occurred in the Glarner Alps of eastern Switzerland.This rock avalanche was recently analyzed by Nagelisenet al. (2015), and cosmogenic nuclide surface exposuredating indicated an age of 12.6 ± 1 ka. The Rautispitzrupture surface is a 33° dip slope. The rock avalancheinitiated as a planar sliding failure with volume of ap-proximately 91 Mm3. After the rock avalanche traverseddown the source slope, it ran up the opposing valley walland spread out over the valley floor (Fig. 12). Landslidedeposits dammed the Sulzbach River, creating LakeObersee and projected a tongue of debris that travelledseveral kilometers down to the village of Naefels (Fig. 12)(Nagelisen et al., 2015).A Dan3D back analysis of the Rautispitz rock avalanchewas conducted by Nagelisen et al. (2015); however, thisanalysis was performed before the creation of Dan3D-Flex. Thus, due to the inability of simulating an initiallycoherent phase of motion, Nagelisen et al. (2015) insteadhad to use varying internal strength, a topographic wallaround the source zone, and high basal resistance outsidethe observed impact area in order to limit undue lateralspreading.To overcome these deficiencies, the back analysis wasrerun using Dan3D-Flex. The topography files used werethose created by Nagelisen et al. (2015), who used apost-event DEM to derive an estimate of the pre-eventrupture surface. Two material types were used in theback analysis: (1) the frictional rheology was used in thesource zone, and (2) the Voellmy rheology was used forthe valley floor. A friction angle of 18° was assigned onthe source slope (Table 1), consistent with the mechanismof extreme polishing of a planar feature due to high bed-normal stresses (Cruden & Krahn 1978). The rigid motiondistance for Dan3D-Flex was selected to correspond to thelocation where most of the material had vacated the rup-ture surface, assuming the likely fragmentation mechanismfor this rock avalanche was interaction with ruggedtopography (De Blasio 2011). We used 11,790 columnsto represent the failed mass.The best-fit results of our new back-analysis are shownin Fig. 13. The results are similar to those obtained byNagelisen et al. (2015); however, the crucial differencebetween these and the present results is the modelparameterization. It was found necessary to use two dif-ferent rheologies in order to simultaneously reproducethe proximal and distal deposits (Table 1); however, noAaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 10 of 15extra parameters (or unreal topographic barriers) wereneeded to limit lateral spreading.DiscussionThe three back analyses demonstrate that the accuracyof rock avalanche runout models can be greatly improvedby accounting for the initially rigid phase of motion. Theseback analyses also show that the basal shear strength andresulting dynamic behavior can be explained by the char-acter of the path materials.The necessity of accounting for the initial, coherentphase of landslide motion in runout models manifests it-self differently in each of our three analyzed case histories.For the Rautispitz rock avalanche, reasonable simulationresults could be attained without the flexible block model;however, this required a parameterization that would bedifficult to predict a priori. As shown by Nagelisen et al.(2015), attaining reasonable results using the unmodifiedversion of Dan3D required assigning a high friction angleoutside the observed impact area in order to limit lateralspreading. In effect, the user prescribed the amount of lat-eral spreading that is allowed, as opposed to letting thenumerical model predict this behaviour. This is undesir-able because it removes one of the major advantages ofsimulating landslide motion over three-dimensionalterrain. As shown in Fig. 13, Dan3D-Flex enabled aFig. 11 Simulation results for the two rock avalanche phases of the Bingham Canyon slide (a). Simulation results for the first rock avalanchewhen the flexible block model is not used (b); here a large amount of material spills out to the north of the source zone, which is inaccurate. Thered outline shows the source zone, the light blue outline shows the final deposit extent and the dark blue line shows the observed impact area.The minimum deposit depth value was specified as 1 m (a minimum deposit depth is necessary due to the solution method used by Dan3D)Aaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 11 of 15Fig. 13 Rautispitz calibrated results using Dan3D-Flex. The use of Dan3D-Flex enabled a model parameterization that could be anticipated beforethe event happened. The black outline shows the observed impact area, and a minimum deposit depth of 5 m was usedFig. 12 Mapped release and deposit area extents for the Rautispitz rock avalanche (Nagelisen et al. 2015); inset photo from Rautispitz summitlooking north over deposits near Lake Obersee. Coordinates are in meters of the Swiss grid system; map grid interval = 1 kmAaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 12 of 15simple parameterization of basal resistance, comparableto that used for previously successful back analyses ofrock avalanches. Therefore, these results can be used toaid forward-analysis. The use of the flexible blockmodel to simulate the initially coherent stage of motionis consistent with the movement mechanism governingthis stage of motion, and the one additional parameter(the distance travelled as a coherent block) can be assesseda priori based on pre-failure topography (Aaron andHungr, 2016b).As shown in Fig. 11, a reasonable simulation of theBingham Canyon rock avalanches is impossible withoutthe flexible block model. No parameterization of basalresistance is able to restrict the initial rock avalanchemotion to the low-strength basal fault in the sourcezone. The use of the flexible block model enables morerealistic simulation of this event, as the initial failuremechanism is appropriately reproduced. The distancetravelled as a flexible block for the first rock avalanchecorresponds to the assumption that the failed mass frag-mented when it spilled out of the rupture surface anddown the steep, benched pit wall. For the second rockavalanche, the flexible block distance corresponds tofragmentation induced by impact with the steep scarpleft behind after the first rock failure. Thus, the userspecified flexible block distance for this case could beforecast a priori to correspond to these mechanisms.For West Salt Creek, the flexible block model is not ne-cessary once the rock avalanche initiates; however, in orderto simulate the complex failure process hypothesized byCoe et al. (2016), Dan3D-Flex is needed to reproduce theinitial rotational slump and the initiation of the rock ava-lanche. Without this capability, it would be difficult to de-termine the initial geometry of the long runout portion andtest the Coe et al. (2016) failure mechanism. If 3-D limitequilibrium analyses were able to determine the failuremechanism of the West Salt Creek landslide, Dan3D-Flexcan be used to assess the initial failure volume of the poten-tial rock avalanche. Forecasting such a mechanism a priori,however, remains challenging.Although similar in volume, the case histories analyzedin this study have vastly different best-fit basal resistanceparameters. The Bingham Canyon rock avalanche is bestsimulated using two frictional rheologies, one in thesource zone and one along the path. The best-fit frictionangles are 10° and 26°, respectively. The low frictionangle in the source zone likely corresponds to extremepolishing of the planar basal rupture surface due toshearing under high normal stress (Cruden & Krahn1978; Aaron and Hungr, 2016a). The friction angle alongthe path corresponds closely to that expected for dryfragmented rock (~30°, Hsu (1975)).The Rautispitz rock avalanche is best simulated usinga frictional rheology in the source zone and a Voellmyrheology for the path. Similar to Bingham Canyon, a lowback-analysed friction angle was assumed in the sourcezone, likely corresponding to shearing from peak to ul-timate strength. The back-analyzed Voellmy parameterscorrespond to rapid undrained loading of loose saturatedsediments (Hungr and Evans, 2004).For West Salt Creek, comparing Figs. 6, 7 and 9 dem-onstrates that the avalanche could not be well simulatedusing a Voellmy rheology. Simultaneous reproduction ofthe runout distance and hill overtopping were only ob-tained by incorporating a basal rheology governed by aconstant yield stress and velocity-dependent resistance.This rheology (Bingham) is appropriate for liquefied,fine-grained materials (Jeyapalan, 1981). The reason thatthis rheology worked well for this case is that the WestSalt Creek rock avalanche likely overrode and liquefiedthe clayey colluvium that mantled the pre-failure path. Asimilar style of event was documented by Geertsema etal. (2006).Back-analyzed resistance parameters required to repro-duce the observed field characteristics of the three studiedcase histories are well explained by the path materials, andit is likely that interaction with path materials is the mech-anism governing the runout behavior of many rock ava-lanches. It is unlikely that any single intrinsic mechanismcan explain the contrasting basal shear strength of theWest Salt Creek rock avalanche and the Bingham Canyonrock avalanches. Any such mechanism should act similarlyfor both events; however, after vacating the rupture sur-face, the Bingham Canyon rock avalanches did not exhibitexcessive mobility, whereas the West Salt Creek rock ava-lanche was highly mobile and not governed by frictionalmechanics. Comparison of these two cases demonstrates aspectrum of rock avalanche behavior, corresponding tohigh- and low-strength path materials. The only volume-dependent mechanism needed to explain their behavior isthe reduction in friction angle along the basal surface dueto shearing under high normal stress. This fact, combinedwith the interaction with path material, is likely a mechan-ism that governs the runout behavior of many large-volume rock avalanches.ConclusionThrough back-analysis of three rock avalanche case his-tories, we have demonstrated the importance of account-ing for the initially coherent phase of motion in dynamicmodels. We also derived the basal shear resistance alongthe runout path required to reproduce bulk characteristicsof each of the three cases, and used these results to infermechanisms of rock avalanche mobility. The present workcannot conclusively prove nor disprove any of the rockavalanche mobility theories. It is likely that multiple mech-anisms influence rock avalanche motion; however, thepresent work demonstrates that the path materials canAaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 13 of 15exert a strong influence on mobility. Our back-analysis re-sults can be used to derive new observations to furthertest existing mobility theories. Any successful, universaltheory of rock avalanche mobility must be able to accountfor the fact that the Bingham Canyon rock avalanche ex-perienced high frictional resistance along the runout path,the Rautispitz rock avalanche experienced low frictionalresistance on the runout path, and that the basal resistanceof the highly mobile West Salt Creek rock avalanche can-not be explained by frictional mechanics alone. The au-thors consider it unlikely that any rock avalanche intrinsicmechanism will be able to explain these three contrastingobservations.AcknowledgementsThis work was supported by a graduate scholarship provided by The NaturalSciences and Engineering Research Council of Canada, as well as scholarshipsprovided by the Department of Earth, Ocean and Atmospheric Sciences at TheUniversity of British Columbia. We thank Francis Rengers, Rex Baum, Janet Slateand two anonymous reviewers for their constructive comments that improvedthe manuscript.Authors’ contributionsJA carried out the analysis and drafted the manuscript. SM helped with thenumerical modelling and helped draft the manuscript. JM collected data andperformed some of the analysis for Bingham Canyon and Rautispitz. JCcollected data and provided guidance on the analysis of the West Salt Creekrock avalanche. OH helped draft the manuscript. All authors read andapproved the final manuscript.Competing interestsThe authors declare that they have no competing interests.Author details1Department of Earth, Ocean and Atmospheric Sciences, University of BritishColumbia, 2020 - 2207 MainMall, Vancouver, British Columbia V6T 1Z4,Canada. 2Department of Geology and Geophysics, University of Utah, 115South 1460 East, Salt Lake City, UT 84112, USA. 3U.S. Geological Survey,Denver Federal Center, MS 966, Denver, Colorado 80225, USA.Received: 19 October 2016 Accepted: 28 January 2017ReferencesAaron, J and Hungr, O. 2016a. Dynamic analysis of an extraordinarily mobile rockavalanche in the Northwest Territories, Canada. Canadian GeotechnicalJournal 53:899–908.Aaron, J and Hungr, O. 2016b. Dynamic simulation of the motion of partially-coherent landslides. Engineering Geology 205: 1–11.Aaron J, Hungr, O, & McDougall, S. 2016. Development of a systematic approachto calibrate equivalent fluid runout models. 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On the prediction of the reach and velocity of catastrophiclandslides. Rock Mechanics 5: 231–236.White, J, Morgan, M & Berry, K. 2015. The West Salt Creek Landslide : ACatastrophic Rockslide and Rock/Debris Avalanche in Mesa County, Colorado,Colorado Geological Survey Bulletin 55, 45 p.Whittall, JR, Eberhardt, E & McDougall, S. 2016. Runout analysis and mobilityobservations for large open pit slope failures. Canadian Geotechnical Journal(accepted).Submit your manuscript to a journal and benefi t from:7 Convenient online submission7 Rigorous peer review7 Immediate publication on acceptance7 Open access: articles freely available online7 High visibility within the fi eld7 Retaining the copyright to your article    Submit your next manuscript at 7 springeropen.comAaron et al. Geoenvironmental Disasters  (2017) 4:5 Page 15 of 15

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