Fragmentation energy in rock avalanches - Université Laval · Fragmentation energy in rock...

Fragmentation energy in rock avalanches1

Pascal Locat, Réjean Couture, Serge Leroueil, Jacques Locat, andMichel Jaboyedoff

Abstract: Fragmentation is one of the mechanisms involved in rock avalanches. Quantifying the associated energy dur-ing a rock avalanche can help to assess the influence of fragmentation on post-failure mass movements. In this paper,in situ block size distributions of the intact rock mass and the debris deposits are presented and analyzed for nine rockavalanches, five in the Canadian Rocky Mountains and four in the European Alps. Degrees of fragmentation are esti-mated from these data. Two methods are examined to assess fragmentation energy, one based on the comminution the-ory, and one on the blasting energy used in the mining industry. The results show that, for the studied rock avalanches,there is a relationship between the reduction in diameter ratio, Rr = D50/d50 (where D50 and d50 are the mean diameterof the intact rock mass and the mean diameter of the debris, respectively), and the potential energy per unit volumenormalized with respect to the point load strength of rock (γHG/σc), where γ is the unit weight of the material, HG isthe vertical distance between the centres of gravity of the mass at the start and end positions, and σc is the point loadstrength). For the cases studied, fragmentation energy calculations average 20% of the potential energy. An empiricalrelationship between Rr and γHG/σc has been established and is used in the definition of a disintegration index (ID).This index seems to reflect the physics of the disintegration process, since it accounts for the fact that the reduction indiameter ratio is a function of the dissipated energy and the strength of the rock. These factors have long been knownto affect fragmentation but have never been presented in a coherent manner for rock avalanches.

Key words: rock avalanches, disintegration, fragmentation energy, Canadian Rocky Mountains, European Alps.

Résumé : La fragmentation est un des mécanismes opérant lors d’avalanche rocheuses. La quantification de l’énergieassociée à ce mécanisme permettrait d’apprécier l’influence de celui-ci sur la phase post-rupture d’une avalanche ro-cheuse. Dans cet article, les distributions des tailles des blocs du massif rocheux et des débris sont présentées et com-parées pour neuf cas d’avalanches rocheuses : cinq dans les montagnes Rocheuses canadiennes et quatre dans les Alpeseuropéennes. Des degrés de fragmentation ont pu être estimés. Pour évaluer l’énergie de fragmentation, deux méthodeson été examinées : l’une est basée sur l’énergie de concassage et l’autre est basée sur l’énergie de sautage utilisée dansle domaine minier. Les résultats obtenus portent à croire qu’il y aurait une relation entre l’indice de réduction de taille(Rr = D50/d50) et l’énergie potentielle par unité de volume, normalisée par la résistance au double poinçonnement(γHG/σc). Les énergies de fragmentation calculées pour les neuf cas étudiés donne en moyenne 20 % de l’énergie po-tentielle. Une relation empirique entre Rr et γHG/σc est proposée, et est par la suite utilisée pour définir un indice dedésintégration (ID). Cet indice reflète la physique du processus de désintégration puisqu’il considère que l’indice de ré-duction de taille est fonction de l’énergie dissipée et de la résistance de la roche. Ces facteurs connus depuis longtempsn’avaient jamais été présentés d’une façon cohérente pour des cas d’avalanches rocheuses.

Mots clés : avalanches rocheuses, désintégration, énergie de fragmentation, Rocheuses canadiennes, Alpes européennes.Locat et al. 851

Introduction

Rockslide and rockfall avalanches (Cruden and Varnes1996) are among the most spectacular and catastrophic natu-ral events that affect landscapes, populations, and infrastruc-ture in all mountainous areas around the world (Voight 1978;Evans and DeGraff 2002). Simple rockfalls usually concern

small volumes of material, which rapidly descend steepslopes, with little or no interaction between the elements, andaccumulate as talus cones at angles near the basic frictionangle of the material (Eisbacher and Clague 1984; Evansand Hungr 1993). On the other hand, a rock avalanche orlarge rockfall can be defined as the rapid detachment ofmore than 105 m3 (Rochet 1987) of a relatively intact rock

Can. Geotech. J. 43: 830–851 (2006) doi:10.1139/T06-045 © 2006 NRC Canada

830

Received 24 January 2005. Accepted 20 March 2006. Published on the NRC Research Press Web site at http://cgj.nrc.ca on3 August 2006.

P. Locat2 and S. Leroueil. Department of Civil Engineering, Laval University, Sainte-Foy, QC G1K 7P4, Canada.R. Couture. Geological Survey of Canada, 601 Booth Street, Ottawa, ON K1A 0E8, Canada.J. Locat. Department of Geology and Engineering Geology, Laval University, Sainte-Foy, QC G1K 7P4, Canada.M. Jaboyedoff. Quanterra, Ch. Tour-Grise 28, 1007 Lausanne, Switzerland.

1Earth Science Sector Contribution Number 20060135.2Corresponding author (e-mail: [email protected]).

mass, after a catastrophic failure along a well-defined rup-ture surface leading to a rockslide (Eisbacher and Clague1984). This is followed by an extremely rapid “disintegratedmotion” (Erismann and Abele 2001; Pollet and Schneider2004), with many interactions between rock debris that in-volve shearing, swelling, punching, and stripping processes(Pollet 2004).

The most remarkable feature of dry rock avalanches,widely discussed in previous works (Heim 1932; Scheidegger1973; Hsü 1975; Davies 1982; Hungr 1990; Nicoletti andSorisso-Valvo 1991; Corominas 1996), is the marked increasein the horizontal component of the overall travel distance (Lin Fig. 1) as the volume increases from about 105–106 m3 to109 m3 (Fig. 2). Displaced material changes from a frictionalbehaviour, characterized by a travel angle (tan–1(H/L), whereH is the horizontal travel distance) of about 32° or more( /H L ≥ 0.6), to a fluid-like behaviour, with H/L reaching val-ues as low as 0.1 (of about 6°). The travel distance of a debrismass is controlled by numerous factors such as volume(Davies and McSaveney 1999), rock material properties(Rochet 1987; Davies and McSaveney 1999), type of slopefailure (Eisbacher 1979; Hungr 1981; Friedmann et al. 2003),runout surface shape and roughness (Nicoletti and Sorisso-Valvo 1991; Corominas 1996), and other possible mecha-nisms reducing the basal or internal friction (Hungr 1990).

Fragmentation, defined as the size reduction of rock parti-cles by crushing during mass movement, is a major process

in rock avalanches and should be considered in the factorsinfluencing the mobility (Cruden and Hungr 1986; De Matos1988; Strom 1994; Schneider et al. 1999; Davies et al. 1999;Erismann and Abele 2001; Davies and McSaveney 2002;Pollet 2004). Few studies have focused on fragmentationcharacterization (Cruden and Hungr 1986; Couture et al.

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Fig. 1. Definition of the geometrical parameters cited in the text (modified from Couture 1998). D, diameter of block; H and L, totalvertical and horizontal travel distances, respectively, measured from the crown of the starting zone to the tip of the debris mass, whichdefines the Fahrböshung (travel angle = tan–1(L/H)); HG and LG, vertical drop and horizontal displacement, respectively, of the centreof gravity from the initial position (CoGi) to the final position (CoGf); Ld, deposition length; Le, excessive horizontal travel distance(Hsü 1975); v50, block volume at 50% passing of the computed block volumes distribution from the deposition zone; V50, block vol-ume at 50% passing of the computed block volumes distribution from the starting zone. The open circles bisected by horizontal andvertical broken lines are centres of gravity of the detached and debris masses.

Fig. 2. Plot of H/L versus volume for rock avalanches. Thelower and upper broken lines represent rock avalanches thatshow maximum and minimum mobility, respectively, with re-gards to their volume (modified after Hsü 1975).

1998, 1999; Pollet 2004), however, and few numerical mod-els have tried to integrate the fragmentation process duringthe post-failure stage (Davies and McSaveney 2002; Stead etal. 2003; Eberhardt et al. 2004).

Vaunat and Leroueil (2002) combine all mechanisms thatcontrol the post-failure mass movement in the mobility in-dex (I), which is defined as follows:

[1] I H L= ′/( tan )φ

where H and L are the total vertical and total horizontal dis-tance, respectively, measured from the crown of the startingzone to the tip of the debris (Fig. 1); and ′φ is the effectiveangle of internal friction. This latter index can be decom-posed as follows:

[2] I I I I I I I I= +( )U C D F E geo field

where IU is the undrained index representing the loss instrength just after failure; IC is the consolidation index ex-pressing the change in strength during movement due toconsolidation or incorporation of water during the move-ment; ID is the disintegration index; IF is the failure indexand is related to stress conditions at failure; IE is the elonga-tion index and represents the effect of change in mass andmostly the change in contact area; Igeo is the geometrical in-dex and corrects the length measured between the centres ofgravity to the lengths L and H suitable for risk estimation;and Ifield represents the effect on mobility of the characteris-tics of the surface below the starting zone. The disintegrationindex ID is the amount of potential energy consumed byremoulding or fragmentation of the material inside the mov-ing mass:

[3] I E ED D P/=

where ED is the disintegration energy, and EP is the potentialenergy.

No procedure to evaluate the disintegration energy or thedisintegration index in rock avalanches has been proposed inthe literature. The aim of the present work is to add informa-tion about fragmentation in rock avalanches by the charac-terization of the particle-size reduction, from the startingzone to the deposition zone (see Fig. 1), of nine well-documented rock avalanches and to propose a procedure toestimate fragmentation energy consumed in rock avalanchesusing empirical relations developed in the mining industry.

During a rock avalanche with non-channelized runout andwithout any obstacles, the following equation summarizesthe energy balance during a time increment ∆t (modifiedfrom Müller, in Heim 1932):

[4] ∆ ∆ ∆ ∆ ∆E t E t E t E t E tT P K F D( ) ( ) ( ) ( ) ( )= + + + = 0

where ET, EP, EK, EF, and ED are the total energy, potentialenergy, kinetic energy, friction energy, and disintegration en-ergy, respectively (e.g., loosening and fragmentation ener-gies).

Following eq. [4], the energy consumed by disintegrationof the ruptured mass reduces the overall available energyand should reduce the kinetic energy and mobility. On theother hand, crushing and grinding mechanisms increase thevolume of fine material (fine sand, silt, and clay), especiallyin the basal sheared zones (Vankov and Sassa 2000). This

leads to a decrease of the pore space and, if water is avail-able, to the generation of high pore pressures inside or at thebase of a moving mass. This can help the mass to flow andthus increases mobility (Hutchinson 1986; De Matos 1988;Sassa 1988; Wang and Sassa 2003; Sassa and Wang 2005).

The next sections summarize rock avalanche fragmenta-tion theories, the artificial fragmentation used in the miningindustry, the methodology adopted to characterize rock ava-lanches and assess fragmentation, and the analysis of thefragmentation for nine rock avalanches, four in the EuropeanAlps and five in the Canadian Rocky Mountains.

Fragmentation processes and associatedenergy

Turcotte (1997, p. 28) wrote the following: “Fragmenta-tion involves the initiation and propagation of fractures andit is a highly non-linear process requiring complex modelseven for the simplest configuration.” Fracture process energyis linked to the length of the crack extension and to the newsurfaces created (Bieniawski 1967). For rock avalanches,evaluation of fragmentation and calculation of the relatedenergy are simplified by evaluating the particle-size reduc-tion between the intact mass and the debris. Energy requiredfor fragmentation can then be calculated using empirical re-lations developed in the mining industry for blasting andcrushing rock materials. The next sections present general in-formation about rock fragmentation in rock avalanches andempirical relations to calculate the fragmentation energy.

Fragmentation in rock avalancheObservations of cuts in several rock avalanche debris de-

posits, such as the one at Frank slide (Cruden and Hungr1986; Couture 1998), illustrate that fragmentation is a majormechanism in rock avalanches. De Matos (1988) suggeststhat natural fragmentation in rock avalanches should be in-fluenced by (i) the depth of the debris mass (i.e., verticalstress produced by its own weight); (ii) the duration of theevent; (iii) the mineralogical composition of rock, textures,and grain size; (iv) the density of discontinuities and defectswithin the rock mass (joints, flaws, weak minerals, etc.); and(v) the presence of water. This latter point is reinforced bythe fact that water can help to fracture the rock mass whenhydraulic pressures are high (Sartori et al. 2003). This hasbeen observed during the early stages of the Randa rockfall,where a series of rock and water bursts was observed andfilmed at the base of the cliff (Sartori et al. 2003). Waterwithin the mass movement could also make the grindingprocesses easier. Tourenq (1970) showed with laboratorytests, such as the Deval test, that wearing of the rock mate-rial increases in the presence of water. Kanda et al. (1988)observed in laboratory bending tests on glass material thatthe wet strength is lower than the dry strength and that cracklength in water is 10% greater than that in air. Bond (1955)also noted that dry grinding requires about 33% more energythen wet grinding.

Another factor is the speed of mass movement. It shouldcontrol the impact velocities between particles and, in thesame way, the effectiveness of the fragmentation (Harris1966). Grady and Kipp (1987) showed, for oil shale, that anincrease in the strain rate decreases the average size of the

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fragments produced. Harris (1966) mentioned that in crushermills, the machine must reach a threshold velocity to reachan efficient fragmentation, which corresponds to a powerthreshold. He reported that the optimum velocity fell in therange of 40–120 m/s, depending on how the blow is deliv-ered and on the initial size of the crushed material. Thisrange of velocity is in the same order of magnitude as thoseindicated for extremely rapid mass movements as defined byCruden and Varnes (1996).

As the volume of fine materials increases during the massmovement, the effectiveness of the fragmentation processesdecreases. As noted by Harris (1966) for crusher mills,deep-bed crushing without removal of the fines is the leasteffective comminution process and needs a lot more energythan crushing with screening of the fines. In rock ava-lanches, shocks between coarser particles would be dampedby the presence of fines.

Smoothness of the limit between the inclined and horizon-tal portions of the transition zone of a rock avalanche pathprofile (Fig. 1) controls the degree of deceleration and thepressures generated within the mass movement (Hungr1981; Strom 1999). This should have an effect on the disin-tegration. Also, geomorphic control (Nicoletti and Sorisso-Valvo 1991) of the mass movement by channelization(Mitchell et al. 2002) or impact against the opposite wall ofa valley (Erismann and Abele 2001) would have an effect onthe degree of fragmentation.

Thus, fragmentation in a rock avalanche involves verycomplex processes, and it is probably impossible to accu-rately evaluate the corresponding energy. Empirical approachesdeveloped in the mining industry for calculating fragmenta-tion energy can be applied to rock avalanches, however.

BlastingMost of the time, mining engineers follow empirical rules

to adjust the quantity of explosive energy needed to blast agiven volume of rock materials. As early as 1725, Belidor(1725) showed that charge weight, i.e., energy, is propor-tional to both the volume excavated and the surface area ofthat volume (Persson et al. 1993). Since that time, many pa-rameters were identified as influencing the efficiency of theblast. After Gama (1995, 1996), they can be divided intothree groups: (i) explosive parameters, which depend on thetype of explosive, such as detonation pressure, available en-ergy, gas volume, and density; (ii) charge loading parame-ters, such as charge weight, type and point of initiation, anddecoupling; and (iii) rock mass properties, such as cohesion,density, dynamic compressive strength, dynamic tensilestrength, and structure.

In the present work, the equivalent blast energy has beenevaluated using the concept of rock mass fragmentability,termed K by Gama (1995, 1996). Fragmentability is definedas “the threshold of specific energy of the explosive thatmay break the rock mass to just separate blocks along theirweakest links, and inducing no further fragmentation”(Gama 1996, p. 210). Using this concept, Gama (1995) pro-posed that the explosive energy required for reducing blocksize by blasting in jointed rock mass can be calculated as

[5] W K S SB b a1/ 2( / )=

where WB is the work (in kW·h per tonne of rock) needed toblast rock material; and Sa and Sb are the size of the blocksafter and before blasting, respectively. According to eq. [5],if WB < K, there is no fragmentation. If WB = K, then Sa =Sb, which means that explosive energy is used only to sepa-rate blocks along their discontinuities but without reducingtheir size. According to Gama (1995), average values of Kfor three rock types are 0.128 for basalt, 0.112 for granite,and 0.092 for limestone (in kW·h per tonne of rock).

CrushingFragmentation by crushing, also called comminution in

the literature, has been studied since the “first theory ofcomminution” was developed by Rittinger (1867, cited inBond 1952). Rittinger postulated that the work needed tofragment a solid by crushing or grinding is proportional tothe area of the new surfaces created and hence inversely pro-portional to the produced diameter. Kick (1885, cited inBond 1952) proposed the “second theory of comminution”in which the fragmentation work is considered proportionalto the reduction in volume of the particles.

Bond (1952) observed that crushing and grinding are con-cerned with both surface and volume and proposed the“third theory of comminution”. This theory is a unificationof the first two theories. Bond considered that the workneeded to break particles of a certain size is initially propor-tional to their volume but becomes proportional to the areaas new surfaces are created.

Bond (1955, p. 196) defined rock breakage as follows:“Rock breakage is produced by deforming the rock, com-monly under pressure, until the resulting stress locally ex-ceeds the breaking strength and crack tips forms, usually onthe surface. The surrounding strain energy then flows to thenew crack, which is thereby extended to split the rock.When the rock breaks, or the strain is otherwise released, themechanical energy input is transformed into heat.”

For practical use in fragmentation by crushing or grindingmachines, Bond (1952) established that the energy requiredfor fragmentation is

[6] W W d DiC = −− −10 801 2

801 2( )/ /

where WC is the work (in kW·h/t) to crush rock materialfrom a grain-size distribution characterized by D80 (in µm)to a new grain-size distribution characterized by a smallerdiameter, d80 (in µm); and Wi is the Bond work index, whichdepends on the type of material (Table 1). Values in Table 1were determined empirically from laboratory impact crush-ing tests and plant and pilot mill tests on the same materials(Bond 1952).

LimitationsBefore using eqs. [5] and [6] for evaluation of fragmenta-

tion energy in rock avalanches, some limitations have to bepointed out.

Fragmentability (K) in eq. [5] was determined from exper-imental field test results from blasts in different masses ofrock. Fragmentation by blasting depends on the dynamicproperties of the intact rock and the spatial distribution andproperties of the discontinuities (Scoble et al. 1996). Frag-mentation also depends on the type of explosive, distancefrom the blast hole, and geometry of the blast pattern with

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respect to the rock mass structure (Persson et al. 1993;Gama 1995). After blast initiation, some part of the energyis used to loosen and heave the mass. It is important to keepin mind that blasting is used to break rock materials intocoarse particle size. Use of eq. [5] for energy calculationmust then be restricted to material diameters of a few tens ofcentimetres.

Bond’s work index (Wi) (eq. [6] and Table 1) was deter-mined in the laboratory with different crusher machines,where a part of the energy is lost in machine wearing anddeformation. Also, crushers have a limited feed size. Itshould then be considered that a diameter of a few metres isover the acceptable feed diameter for crushing. Also, in thepresent work, the percent passing size has been fixed at 50%(d50) instead of the 80% (d80) proposed in eq. [6]. This isvalid if the shape of the block size distribution curves and, inparticular, the coefficients of uniformity (Cu = D60/D10) ofthe initial and final block size distributions are the same,which is assumed for all the rock avalanches studied here.

Considering a block of limestone with three initial diame-ters (D50) of 10, 5, and 1 m, graphical representations ofeqs. [5] and [6] in Fig. 3 show that all are in the same rangeof fragmentation energies. The influence of the initial diam-eter (D50) on energy calculated with eq. [6] is negligiblewhen the crushed material diameter is less than 0.1 m. Onthe other hand, energy calculated from the blasting formula(eq. [5]) is influenced by the initial diameter. Energy ishigher for large diameters (10 and 5 m) and lower for diame-ters smaller than approximately 1 m, in comparison with thecrushing energy. This could be explained by the fact that thelarger the diameter, the larger the quantity of energy neededto heave and break the material. The crushing formula(eq. [6]) is also based on size reduction. If there is no reduc-tion in diameter, there is no energy consumed. On the otherhand, with the blasting formula (eq. [5]) the energy con-sumed can be calculated even if there is only loosening ofthe mass, i.e., heaving of the rock mass along the preexistingdiscontinuities inducing no further fragmentation.

Methodology

Rock avalanche characterizationRock avalanche data used hereafter were collected by

three of the authors (Couture 1998; Locat 2001; Jaboyedoff2003) following the methodology detailed in Couture et al.(1999). In summary, this methodology can be divided intofour major steps: (i) gathering documentation; (ii) fieldwork;(iii) laboratory testing; and (iv) analysis related to stability,mobility at the post-failure stage, and energy balance.

The first step is to collect available information on re-corded historical events, geological and structural aspects,geomorphology, former reports, and any iconographic docu-ments. Topographic maps, digital terrain model (DTM), airphotographs, and climatic data represent the basic elementsgathered during this step.

Fieldwork consists of mapping and scan line surveys, pho-tographic sampling of the debris mass, and determination ofphysical and mechanical properties of the rock material.Geological formations and their limits are defined with thehelp of topographic maps, geological maps, and air photo-graphs. Detailed surveys in the detachment, transition, anddeposition zones confirm the outlines of these zones. Thisalso serves to identify features such as impact traces on treesin the transition zone and inverse grading or alignments ofridges on top of the debris. Compressive strengths of rocksand joints are evaluated in situ using the Schmidt hammertest. Roughness of joints, discontinuities, and the failureplane are evaluated using a joint roughness profiler. Stereo-graphic representation of data uses the lower hemisphereprojection of an equal-area stereonet.

A structural mapping survey is performed in the detach-ment zone to assess the mean block size of the intact rockmass. This consists of linear surveys, where direction, dip,trace length, and position of all joints and discontinuities en-countered along a line in an observation window are mea-sured (Hadjigeorgiou et al. 1995). Ideally, it should be donein three orthogonal directions at sites where the fracturingcharacteristics of the rock mass are well exposed. In the lab-oratory, scan line data are analyzed with a three-dimensionaljoint set model, STEREOBLOCK, to evaluate block sizedistribution based on stereological principles and on statisti-cal analysis of joint sets (Hadjigeorgiou et al. 1995). Thismodel makes the assumption that the blocks are of sphericalform. Then, diameter (D) is related to block volume (V) bythe following equation:

[7] D = 2(3V/4π)1/3

In some cases, structural mapping surveys were impossi-ble because of inaccessibility of the starting zone. In thesecases, photographs of the rock wall were used to compute

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Material Wi (kW·h/t)

Clay 6.9Limestone 13.8Quartz 15.0Granite 16.6Oil shale 17.4Flint 28.7

Table 1. Average work index (Wi) values forvarious materials (modified after Bond 1952).

Fig. 3. Graphical representation of eqs. [3] and [4] for initialblock size (D50) of 10, 5, and 1 m, fragmented to a given diame-ter of d50.

the block size distribution of the rock mass. Diameter wascalculated from the image analysis system used to computeblock size distribution. Volume-distribution curves werethen calculated with eq. [7].

Photographic sampling of the debris mass uses a methoddeveloped by the Canada Centre for Mineral and EnergyTechnology (CANMET) (Doucet and Lizotte 1992) for themining industry and applied to rock avalanches(Hadjigeorgiou et al. 1996; Couture et al. 1996, 1998; Cou-ture 1998). It uses a graduated frame or a known size ele-ment as scale, such as a ball or a 1 m × 1 m frame, withphotographs taken as much as possible perpendicular to thedeposit to avoid distortions. The image analysis system canthen measure the diameter of each block using the scale inthe photograph as a calibration. At the end, output data areconverted into a Rosin–Rammler distribution (Rosin andRammler 1933) with a Fortran program, TANGO (Doucetand Lizotte 1992), in the form of ln(ln(1/R)) and ln(x),where R is the percent size retained, and x is the diameter offragments. The best-fitting line is determined by the least-squares method. Regression parameters n, which is the uni-formity coefficient (slope of the regression line), and xc,which is the characteristic size of the distribution taken atthe inflection point of the curve (passing 63.2%), are thenused to calculate the size distribution using the followingRosin–Rammler equation:

[8] R = exp[–(x/xc)n]

With the particle-size distributions of the mass before(eq. [7]) and after (eq. [8]) the rock avalanche, eqs. [5] and[6] can be used to assess the fragmentation work per tonneof material.

Laboratory tests were conducted at Laval University Lab-oratory of Mines and Metallurgy on rock samples collectedat the site of the rock avalanches. Basic friction angle wasdetermined on saw-cut specimens following the direct sheartest procedure of the International Society for Rock Me-chanics (1981). Compressive strength was determined fol-lowing the point load test procedure (International Societyfor Rock Mechanics 1985). When it was possible to visuallyidentify bedding on specimens, load was applied bothperpendicular and parallel to bedding. This test provides anestimation of the fracture toughness for characterizingcomminution potential (Bearman et al. 1989; Bearman 1999).

Evaluation of energy components

Potential energyThe potential energy is the available thermomechanical

energy of a body that depends on its mass, the gravitationalacceleration, and the drop of its centre of gravity from ahigher starting point to a lower ending point. For a rock ava-lanche, the potential energy can be expressed as (Erismannand Abele 2001)

[9] EP = HG γ V

where EP is the total potential energy, HG is the vertical dis-tance between the centres of gravity (CoG) of the mass atthe start and end positions (Fig. 1), γ is the unit weight of thematerial, and V is the volume of the failed mass. Positions ofthe centres of gravity were found on the rock avalanche

cross sections by digitizing the contours of the detachedmass and the debris mass and by applying the method pro-posed by Bourke (1988).

Fragmentation energyThe degree of fragmentation can be characterized by the

reduction ratio termed Rr and defined as

[10] Rr = D50/d50

where D50 and d50 are the mean diameter of the intact rockmass and the mean diameter of the debris, respectively.When particle-size distributions define an envelope, the me-dian point of the envelope was taken as D50 or d50 of the ma-terial used for calculations. Equation [10] is used hereafterto compare fragmentation without an energy term. Equiva-lent fragmentation energy by blasting (EB, in joules) is cal-culated as

[11] EB = 3600WBV ρ

where WB is the explosive work calculated from eq. [5], V isthe volume of the rock avalanche (in m3), ρ the density ofthe rock material (in kg/m3), and 3600 is a conversion factor(to convert from kW·h/t to joules). Equivalent fragmentationenergy by crushing (EC, in joules) is calculated as

[12] EC = 3600WCV ρ

where WC is the crushing work calculated from eq. [6].

Studied rock avalanches

The rock avalanches studied here are situated in the Cana-dian Rocky Mountains (Fig. 4) and the European Alps(Fig. 5). Most of the cases studied have already been pre-sented in the literature, but some additional structural andparticle-size information was collected for the present study.The following paragraphs only summarize general informa-tion concerning these cases, and the reader can refer to pa-pers cited in the text for more detailed descriptions. The listof the studied cases with very general information is pro-vided in Table 2. Relevant details and energy calculation re-sults obtained for each rock avalanche are listed in Table 3.Reference to Fig. 1 should be made for definition of the geo-metrical parameters used for rock avalanche descriptions.

Rock avalanches in the Canadian Rocky Mountains

Frank slideThe Frank rockslide avalanche (FR) occurred at 4:10 a.m.

on 29 April 1903, killing at least 70 people (McConnell andBrock 1904). This rockslide avalanche is located at 49°36′N,114°25′43′′W (Fig. 4), in the southeastern part of the FrontRange of the Rocky Mountains in Alberta. The failure sur-face mainly followed the bedding planes of the eastern flankof the Turtle Mountain anticline (Cruden and Krahn 1973;Jones 1993; Benko and Stead 1998), dipping at 40° in a dipdirection of 65° (broken line in Fig. 6b). The slide involvedabout 30 Mm3 of limestone from the Mississippian RundleGroup (Norris 1993; Mossop and Shetsen 1994). Total verti-cal (H) and horizontal (L) distances are about 760 and3500 m, respectively (Fig. 6a).

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Five discontinuity sets were identified by structural map-ping at the top and on the southwest side of Turtle Mountain(solid lines in Fig. 6b). Mean dip and dip direction for dis-continuity sets are 60°/023° for S1, 57°/151° for S2,56°/201° for S3, and 70°/076° for S4 (Fig. 6b). Mean strikeand dip of bedding are 46° and 282° (Fig. 6b). Note thatthese values correspond to the west side of the Turtle Moun-tain anticline. Dip varies from about 10° on top of the moun-tain to about 60° on the side. Block size distribution wascomputed in STEREOBLOC from two scan lines mappednear the starting zone. The computed mean block size diam-eter (D50) is 2.25 m (V50 in Fig. 6c).

Debris mass covered up to 3 km2 and ran up to 120 mover the slightly inclined opposite side of the valley (seeFig. 6a). Fluvial materials from the Crowsnest River wereincorporated and splashed on both sides of the moving mass.A narrow stretch of fines, over 100 m wide, surrounds thedeposit and was termed “splash zone” by Cruden and Hungr(1986). A cross section within the debris mass was createdby the reconstruction of the Canadian Pacific Railway (CPR)line (Fig. 6a). This window over the 15 m height of the de-bris depth exposes the inverse grading very well. From thebase to the top, Cruden and Hungr defined by standard siev-ing and photographic sampling techniques four zones calledbase (d50 ≈ 3.5 cm), middle (d50 ≈ 8.3 cm), coarse (d50 ≈30 cm), and top (d50 ≈ 110 cm). The cross section in Crudenand Hungr shows that the thickness of each zone is approxi-mately 5 m for the base, 3 m for the middle, 4 m for thecoarse, and 3–5 m for the top. For a comparison with the ob-

servations of Cruden and Hungr, five photographic sampleswere taken in the same sector. The fine materials were notconsidered by the photographic sampling technique usedhere. The results defined an envelope that varies from 0.40to 1.40 m (v50 in Fig. 6c). It can be seen that the envelopecompares well with the top and coarse particle-size distribu-tions obtained by Cruden and Hungr. The value of d50 is cal-culated from combined data from Cruden and Hungr and thepresent study (Fig. 6c). This gives a middle value of 0.25 m(v50 in Fig. 6c). In addition to the data gathered along theCPR exposure, two low-level air photograph survey lineswere conducted by helicopter over the debris surface fromthe distal margin of the debris to the Crowsnest River (Cou-ture et al. 1998). Analyses of 17 photographic samples fromboth lines show a gradual decrease in mean grain size fromabout 3.0 m at the proximal part of the deposit to about0.9 m at the far end of the deposit (Couture et al. 1998).

Slide MountainThe Slide Mountain rockslide avalanche (SM) took place

on the eastern border of Jasper National Park at 53° ′ ′′5 50 N,117°3 ′ ′′8 24 W (Fig. 4), about 40 km northeast of the town ofJasper, Alberta. About 13 Mm3 of limestone from the UpperDevonian Palliser Formation (Mossop and Shetsen 1994)avalanched from the southwest slope of the mountain, whichdips at 55° in a dip direction of 210°, and filled the FiddleRiver valley (Fig. 7a). The failure surface essentially fol-lowed the bedding plane, which is curved, dipping at about60° at the top to 15° at the level of the Fiddle River (Evans

© 2006 NRC Canada


Fig. 4. Location map of the studied Canadian rock avalanches (see Table 2).

et al. 1997). Total vertical and horizontal travel distances are450 and 1650 m, respectively (Fig. 7a).

Structural data were collected on outcrops near the riverand on the top of the mountain. Four discontinuity sets weremapped, namely S1, S2, S3, and bedding. The dip and dipdirections are 67°/279° for S1, 40°/049° for S2, 62°/127° forS3, 61°/197° for the top of the bedding (Sot), and 18°/220°for the base of the bedding (Sob; see Fig. 7b). S1 and S2control the lateral walls of the starting zone. Scan line map-ping was conducted on an outcrop of the Palliser Formationat the edge of Highway 16, about 25 km west of the slide(Fig. 4). Four scan lines were mapped. Mean computedblock diameter varies between 7.0 and 15.6 m (Fig. 7c). Themiddle value used for calculation is 10.6 m (V50 in Fig. 7c).

Thick beds of limestone from the Palliser Formation influ-ence these high values.

Debris covers an area of 1.3 Mm2 and ran up to 120 mover the gently inclined opposite side of the valley. Expo-sures in the debris mass along the Fiddle River show largesubangular blocks in a matrix of fine particles. Although in-verse grading is not well developed, concentration of largerblocks on the top of the deposit is observed. The base of thedebris mass lies directly on bedrock, and both sides of thedeposit are bordered by thin sheets of glacial and fluvial ma-terials, confirming that valley deposits were incorporatedwithin the moving mass. An aerial view of the depositionzone shows a crown of coarse material that surrounds a cen-tral forested zone. The latter can be explained by the pres-

© 2006 NRC Canada

Locat et al. 837

Fig. 5. Location map of the studied European rock avalanches (see Table 2).

Site Material V (×106 m3) H (m) L (m)

Frank Slide (FR) Limestone 30 760 3500Slide Mountain (SM) Limestone 13 420 1650Queen Elizabeth (QE) Limestone 45 950 2645Jonas Creek north (JCN) Quartzite 2.4 860 2800Jonas Creek south (JCS) Quartzite 4.9 900 1830Claps de Luc (CL) Limestone 2 370 800La Madeleine (LM) Schist 90 1250 4500Charmonétier (CH) Amphibolite 0.13 520 600Arvel (AR) Limestone 0.61 250 350

Note: H and L, total vertical and horizontal travel distances, respectively, measured from the crown of thestarting zone to the tip of the debris mass; V, volume of slide material.

Table 2. General information on rock avalanches considered in the study.

© 2006 NRC Canada


Cha

ract

eris

tic

FR

SM

QE

JCN

JCS

CL

LM

CH

AR

Det

ache

dvo

lum

e(×

106

m3 )

3013

452.

44.

92

900.

130.

61S

ourc

ear

ea(×

106

m2 )

0.56

0.26

0.54

0.16

0.25

0.20

1.30

0.02

0.06

Dep

osit

area

(×10

6m

2 )2.

441.

280.

931.

080.

500.

402.

060.

040.

03M

ean

thic

knes

sof

the

sour

ce(m

)55

6550

1520

1016

08

26M

ean

thic

knes

sof

the

depo

sit

(m)

1525

603

1215

6015

10H

oriz

onta

ltr

avel

dist

ance

,L

(m)

3500

1650

2645

2800

1830

800

4500

600

350

Ver

tica

ltr

avel

dist

ance

,H

(m)

760

420

950

860

900

370

1250

520

250

Fahr

bösc

hung

(°)

12.3

14.0

20.3

17.1

26.5

24.8

15.5

40.9

37.4

Exc

essi

vetr

avel

dist

ance

,L

e(m

)22

8497

811

2514

2439

020

825

00na

na

Dep

osit

ion

leng

th,

Ld

(m)

2300

1130

1800

1880

700

425

500

400

310

Run

up(m

)12

012

019

010

030

130

nana

Ver

tica

ldr

opof

the

CoG

,H

G(m

)43

013

546

648

566

318

369

039

310

7

Hor

izon

tal

disp

lace

men

tof

the

CoG

,L

G(m

)15

4942

187

815

8912

8630

918

5047

511

7

Type

ofro

ckL

imes

tone

Lim

esto

neL

imes

tone

Qua

rtzi

teQ

uart

zite

Lim

esto

neS

chis

tA

mph

ibol

ite

Lim

esto

neD

ensi

ty(k

g/m

3 )26

0026

0026

0026

1426

1426

0026

0026

0026

50P

oint

load

com

pres

sive

stre

ngth

(MPa

)a93

7575

480;

320

480;

320

238

7016

4;77

163

Bas

icfr

icti

onan

gle

(°)

3836

4334

3442

3535

39M

ean

bloc

ksi

zedi

stri

buti

onD

etac

hmen

tzo

ne,

D50

(m)

2.25

10.6

010

.60

0.60

0.60

7.20

2.50

1.00

0.80

Dep

osit

ion

zone

,d 5

0(m

)0.

251.

600.

830.

400.

904.

900.

120.

300.

50

EP

(J)

3.3×

1014

4.5×

1013

5.4×

1014

3.0×

1013

8.3×

1013

9.3×

1012

1.6×

1015

1.3×

1012

1.7×

1012

EB

(J)

7.9×

1013

2.9×

1013

1.4×

1014

2.5×

1012

3.4×

1012

2.1×

1012

3.5×

1014

2.1×

1011

6.6×

1011

EC

(J)

5.3×

1013

8.1×

1012

4.6×

1013

7.7×

1011

01.

9×10

112.

6×10

141.

4×10

112.

0×10

11

EB

(%of

EP)

2464

268

422

2216

39

EC

(%of

EP)

1618

93

02

1711

12

Rr

(D50

/d50

)9.

06.

612

.81.

50.

71.

420

.73.

31.

5

Not

e:A

bbre

viat

ions

for

the

rock

slid

eav

alan

ches

asin

Tab

le2.

na,

not

avai

labl

e.a W

here

two

valu

esar

egi

ven,

the

firs

tis

the

poin

tlo

adpe

rpen

dicu

lar

toth

ebe

ddin

gpl

anes

and

the

seco

ndis

the

poin

tlo

adpa

ralle

lto

the

bedd

ing

plan

es.

Tab

le3.

Cha

ract

eris

tics

and

ener

gyca

lcul

atio

nsof

the

five

Can

adia

n(F

R,

SM

,Q

E,

JCN

,an

dJC

S)

and

four

Eur

opea

n(C

L,

LM

,C

H,

and

AR

)ro

cksl

ide

aval

anch

esco

nsid

ered

inth

est

udy.

ence of finer material in which shrubs and trees can takeroot. Fiddle River has cut through the debris, forming asteep-sided gorge 20–40 m deep. Four photographic samplesfrom this exposure were taken and analyzed. The value ofd50 varies between 1.2 and 2.0 m (Fig. 7c). The middle valueused for calculation is 1.6 m (v50 in Fig. 7c).

Queen ElizabethThe Queen Elizabeth rockslide avalanche (QE) took place

on the southwest side of the sharp-crested Queen ElizabethRanges at 52°5 ′ ′′2 36 N, 117°4 ′2 W (Fig. 4), about 25 km eastof the town of Jasper (Evans et al. 1997). A peculiar failuremode across bedding was identified here and termed “break-out” by Evans et al. (1997). About 45 Mm3 of limestonefrom the Upper Devonian Palliser Formation (Mossop andShetsen 1994) ran down the slope, which dips at about 35°with a dip direction of 220°, and created a landslide-dammed lake in the main valley, which has since beeninfilled with sediment. Total vertical and horizontal (farthestend of the deposit) travel distances are about 950 and2645 m, respectively (Fig. 8a). Note that the cross section inFig. 8a shows a horizontal travel distance of about 1700 m,which is the horizontal distance between the crown of thestarting zone and the highest point on the opposite slope,

which is not the farthest end of the deposit. As shown inFig. 1, the QE rockslide avalanche is less mobile than othersof the same volume.

Structural mapping allowed the identification of three dis-continuity sets, namely S1, S2, and bedding. The dip and dipdirection are 86°/306° for S1, 44°/063° for S2, and 52°/221°for bedding (Fig. 8b). Two faults divide the slope and wouldhave divided the failed mass into three parts (Fig. 8a). De-formation of strata indicates an inverse thrust movement ofthe faults. Scan line mapping was conducted on an outcropof the Palliser Formation, at the edge of Highway 16, about25 km west of the slide (Fig. 3). Four scan lines weremapped. Mean computed block diameter varies between 7.0and 15.6 m (V50 in Fig. 8c). For calculation, the middle pointof the envelope for the Pallisser Formation was used. Thisgives a D50 value of 10.6 m.

Debris ran up to 190 m on the steep opposite side of thevalley. A ridge and hollow aligned parallel to the valleywalls are observable on the surface of the deposit. Thiscould have been produced by the rapid deceleration of themoving mass induced by the impact on the opposite slope.No vertical exposure inside the debris mass is available. Onthe debris surface, the size and shape of the blocks are ap-proximately 1 m3 and angular, respectively. Eight photo-

© 2006 NRC Canada

Locat et al. 839

Fig. 6. Frank rockslide avalanche (FR): (a) cross section; (b) stereonet; (c) particle-size distributions. Geology after Cruden and Krahn(1973), and debris thickness estimated after a cross section in McConnell and Brock (1904).

graphic samples were taken over the deposit. Analysis ofthese photographs gave a grain-size distribution with d50varying from 0.60 to 1.20 m (Fig. 8c). The value used forcalculation is 0.83 m (v50 in Fig. 8c).

Jonas Creek, north and southThis site is characterized by two well-defined rockslide

avalanches, namely the Jonas Creek north (JCN) and JonasCreek south (JCS) rockslide avalanches. Both ran down thewest side of Jonas Ridge Mountain (Cruden 1976; Bruce1978; Bruce and Cruden 1980), which dips in this sector atabout 33° with a dip direction of 225°. The site is at52°2 ′ ′′6 00 N, 117°2 ′ ′′4 30 W (Fig. 4), about 65 km southeast ofthe town of Jasper, along Highway 93 in Jasper NationalPark. The material involved in these rock avalanches con-sists of massive and hard, light brown to pink weatheredquartzite with thin shale lenses interbedded from the LowerCambrian Gog Group (Hughes 1955; Mossop and Shetsen1994). Fieldwork done in the area (Bruce and Cruden 1980;Locat 2001) revealed little evidence of shale lenses in eitherthe slope surface or the debris. The volumes estimated byBruce and Cruden (1980) for JCN and JCS are 2.1 and4.5 Mm3, respectively. Estimations made by the authors give2.4 and 4.9 Mm3 for JCN and JCS, respectively (Table 3),slightly greater than those of Bruce and Cruden. Total verti-cal and horizontal travel distances are 850 and 2900 m, re-

spectively, for JCN, and 900 and 2000 m, respectively, forJCS (Figs. 9a and 9b). It is interesting to note that for thesame material and environmental conditions, with less thanhalf of the volume and a shorter vertical drop than JCS, JCNtravelled horizontally about 1000 m more than JCS. Volumementioned in the description of JCS was calculated from thedimensions of the starting zone, considering one singleevent. Air photograph analyses over the debris zone of JCSsuggest at least two distinct pulses of debris, however. Also,impact against drumlinoid forms in the valley observed onair photographs could have reduced the mobility of JCS.

Failure planes followed the bedding, dipping at about 32°in a dip direction of about 226°. As noted by Bruce andCruden (1980), bedding is slightly curved, with dip increas-ing from 28° in the lower part of the failure surface to 39°near the back scarp. In addition to the bedding, five disconti-nuity sets were identified in the starting zones, namely S1,S2, S2*, S3, and S3* (Fig. 9c). The dip and dip direction are68°/069° for S1, 73°/126° for S2, 71°/304° for S2*,82°/223° for S3, and 62°/022° for S3*. Sets S2 and S2* areapproximately orthogonal to sets S1, S3, and S3* and con-trol at small scale the initial shape and dimensions of the ini-tial blocks and at a larger scale the lateral margins and backscarp of the starting zones. Bedding varies in thickness from0.1 to over 1.0 m, and joint spacing is about 0.65 m. Blocksize distribution was obtained by photographic analyses of

© 2006 NRC Canada


Fig. 7. Slide Mountain rockslide avalanche (SM): (a) cross section; (b) stereonet; (c) particle-size distributions (modified after Evans etal. 1997).

the north lateral wall of the south starting zone. Mean calcu-lated block diameter (D50) is about 0.6 m (V50 in Fig. 9d).

No cross section in the deposit is available. All photo-graphic samples were taken at the surface of the debris.Even if debris thickness is small (about 3–6 m for JCN),very few fine materials were observed at the margin and be-tween the debris. Eight photographic samples were analyzedfor JCN. Mean diameters (d50) vary from 0.2 to 1.0 m(Fig. 9d). For calculation, the middle point of the envelope is0.4 m (v50 in Fig. 9d). Four photographic samples were ana-lyzed for JCS, and mean diameters (d50) vary in that casefrom 0.7 to 1.1 m (Fig. 9d). For calculation, the middle pointof the envelope is 0.9 m (v50 in Fig. 9d). Note that the debrissize distributions in Fig. 9d are about 1.5 times the mean di-ameter of the intact rock mass. Two hypotheses can explainthis: (i) there was not enough energy to break rock piecesalong all the joints during the mass movement, and (or)(ii) there is an inverse grading similar to that found at Frankslide. The fact that no splash zone was identified on the airphotographs and in the field survey (i.e., few fines material)combined with the fact that quartzite strength is very high

(see Table 3) points to the first hypothesis. In any case, frag-mentation was certainly very limited.

Rock avalanches in the European Alps

Claps de Luc, Drôme, FranceThe Claps de Luc rockslide avalanche (CL) took place at

44°2 ′ ′′2 12 N, 5°1 ′ ′′6 12 E (Fig. 5) along the Drôme River,France (Couture et al. 1997). Road D93 crosses the debrismass. In the year 1442, 2 Mm3 of thickly bedded limestone,Tithonian in age (Upper Jurassic), detached and slid alongthe stratification, fragmenting into metre-sized blocks thatspread on both sides of a rock spur (Fig. 10a). Total verticaland horizontal travel distances are 370 and 800 m, respec-tively (Fig. 10a).

Three discontinuity sets were mapped in the starting zone,namely S1, S2, and bedding (Fig. 10b). The dip and dip di-rection are 84°/282° for S1, 53°/002° for S2, and 38°/174°for bedding. The starting zone is slightly curved, with dipvarying from 30° at the base to 45° at the top. Discontinuityspacing varies between 1.50 and 4.35 m. Three scan lines

© 2006 NRC Canada

Locat et al. 841

Fig. 8. Queen Elizabeth rockslide avalanche (QE): (a) cross section; (b) stereonet; (c) particle-size distributions (modified after Evanset al. 1997).

were examined along the wall of the starting zone. A com-puted distribution gave a mean block size (D50) of 7.25 m(V50 in Fig. 10c).

The debris is very coarse and angular with no trace of finematerials. In that case, the grain-size distribution was ob-tained directly by analysis of magnified, high-resolution ae-

rial photography over the deposition zone. Mean block sizeof the debris (d50) is 4.2 m (v50 in Fig. 10c).

La Madeleine, Savoie, FranceThe La Madeleine rockslide avalanche (LM) is situated

near the Italian border in the Maurienne Valley, France, at

© 2006 NRC Canada


Fig. 9. Jonas Creek north (JCN) and Jonas Creek south (JCS) rockslide avalanches: (a) JCN cross section; (b) JCS cross section;(c) JCN and JCS stereonets; (d) JCN and JCS particle-size distributions.

45°17 41′ ′′N, 6°57 52′ ′′E (Fig. 5) (Couture et al. 1997, 1999).More than 90 Mm3 of lustrous schist from the Upper Creta-ceous Liguro-Piémontaise stratigraphic unit collapsed bysliding along the schistosity, damming the Arc River andcreating a temporary lake. Total vertical and horizontaltravel distances of the mass displacements are about 1250and 4500 m, respectively (Fig. 11a). Remaining lacustrinesediments that deposited in the lake were dated at more than7000 years old (Couture et al. 1997).

Thick-bedded schist was observed at the base and top ofthe starting zone. Discontinuity spacing varies from 23 to46 cm. Four discontinuity sets were mapped from three dif-ferent sectors in the starting zone (Fig. 11b). The most per-sistent discontinuity set is the schistosity, with a mean dipand dip direction of 14°/252°. Other discontinuity sets areS1 (85°/105°), S2 (87°/178°), S2* (85°/203°), and S3(85°/318°). Mean block size (D50) established from two scanlines mapping in the massive part of the starting zone isabout 2.5 m (V50 in Fig. 11c). Pollet (2004) mapped 11 scanlines in the starting zone and on lateral margins usingSIMBLOC. Considering a cubic shape (D = V1/3), the result-ing value of D50 is 1 m.

The surface of the deposition zone is hummocky andstrewn with boulders with a volume of up to 15 000 m3

(Pollet 2004). With time, deep gorges were carved in the de-

bris by the Arc River, revealing the internal structures of thedeposit such as inverse grading, block alignment, flow struc-tures (Couture 1998), and shattered blocks with “jigsaw”fracture patterns (Pollet 2004). Between boulders, thecrushed schist matrix, cemented by carbonate in someplaces, can reach particle sizes as low as the grain size ofclay (Pollet 2004). Mean particle-size diameter (d50) com-puted from 13 photographic samples varies between 0.07and 0.30 m (Fig. 11c). The middle point of the envelopeused for calculation is 0.12 m (v50 in Fig. 11c). Pollet (2004)combined the photographic sampling technique, standardsieving, and the use of a laser particle counter with field es-timation of the volumetric proportions of the debris. He esti-mated that 5% of the material has a diameter greater than1 m, 41% is from 1 to 0.1 m in diameter, and 54% consti-tutes the matrix (diameter < 0.1 m). This is in agreementwith observations made by Couture (1998).

Charmonétier, Isère, FranceThe Charmonétier rockslide avalanche (CH, Fig. 5) took

place at 45°01 50′ ′′N, 6°0 ′ ′′2 08 E on the northeastern flank ofthe Massif de Taillefer, accessible by Road N91 between thecities of Grenoble and Briançon, France (Couture et al.1997). On 24 August 1987, after heavy rainstorms, a rockmass, consisting of amphibolites, averaging 0.13 Mm3, de-

© 2006 NRC Canada

Locat et al. 843

Fig. 10. Claps de Luc rockslide avalanche (CL): (a) cross section; (b) stereonet; (c) particle-size distribution (modified after Couture etal. 1997).

tached and travelled down in the ravine of Charmonétier,cutting Road D219. Total vertical and horizontal travel dis-tances are 600 and 520 m, respectively (Fig. 12a).

Four discontinuity sets were mapped in the starting zone(Fig. 12b). Foliation (F1), dipping at 26° with a dip directionof 023°, controls the failure plane, and discontinuity sets S2(80°/104°), S3 (76°/192°), and S4 (88°/058°) control the lat-eral walls and back scarp of the starting zone. Five scanlines mapped in the starting zone were used to estimate theblock size distribution. Mean block size is about 1 m (V50 inFig. 12c).

The major part of the debris was deposited at the end ofthe ravine of Charmonétier, forming a talus cone with an an-gle averaging 34°. Although the rockslide started more orless as a rockslide avalanche, the debris mass has a rock-fall-deposited shape. In the transition zone, soft deposits fromamphibolite alteration with an average particle size of 1 cmwere eroded over a depth of about 1.5 m and incorporatedwithin the moving mass. Four photographic samples wereanalyzed. Mean particle size (d50) varies from 0.06 to 0.40 m(Fig. 12c). The middle point of the envelope used for calcu-lations is 0.29 m (v50 in Fig. 12c).

Arvel, Vaud, SwitzerlandOn 14 March 1922, about 0.6 Mm3 of limestone fell down

in a cloud of dust from the Arvel cliff (AR) on the alluvialplain of the Rhône River, near the town of Villeneuve in theVaud Canton, Switzerland (Choffat 1929; Jaboyedoff 2003).The scar of the AR rockslide avalanche is situated at45 01 50° ′ ′′N, 6 02 08° ′ ′′E, about 30 km southeast of Lausanne

and about 700 m east of Highway A9 (Fig. 5). This rock av-alanche could be considered as a cliff collapse or as arockslide on a steep failure plane. The saturated alluvial ma-terials at the bottom of the slope were pushed forward by themass movement like a carpet (Choffat 1929). An open-pitquarry, in operation prior to the event, probably favored thedestabilization of the rock face by exploiting the toe of theslope. A quarry is still in operation today tens of metresfrom the sector of the 1922 rock avalanche (Jaboyedoff2003). The infrastructure struck by the rock avalancheincludes sheds, roads, a cable car, a railway, and a waterchannel. Total vertical and horizontal travel distances char-acterizing the event are 248 and 363 m, respectively(Fig. 13a). In a very detailed study, Choffat (1929) reportedthat on the day before the event woodsmen observed that amajor discontinuity dipping above the rock face (85°/286°)was opening. This observation prompted the authorities toevacuate the quarry. A few hours before the event, rockbursts were observed near the base of the rock face. Thecliff collapsed along the opened discontinuity noted previ-ously.

In the starting zone, the rock mass is mainly made up ofcalcarenite from the Lower Jurassic formations (alternationof limestone and marls) of the Préalpes medians plastiquesnappe (Jaboyedoff 2003). Beds dip at about 35° in a south-southeast direction within the Arvel slope area (set So with adip and dip direction of 37°/145°, Fig. 13b). Dip and dip di-rection of the slope were about 78°/276° prior the event(broken lines in Figs. 13a and 13b). Lateral margins and theshape of the debris blocks were controlled by five joint sets,

© 2006 NRC Canada


Fig. 11. La Madeleine rockslide avalanche (LM): (a) cross section; (b) stereonet; (c) particle-size distribution (modified after Coutureet al. 1997 and Pollet 2004).

namely S1–S5. The dip and dip directions were 76°/036° forS1, 37°/315° for S2, 60°/225° for S3, 40°/30° for S4, and85°/286° for S5. Block size distribution was computed fromphotographic sampling of the north side of the starting zone(Fig. 13c) and gives a D50 value of about 0.8 m (V50 inFig. 13c).

In general, the debris is made up of large blocks. About67% of the debris accumulated as a talus cone at the toe ofthe cliff, and 33% spread into the valley (Fig. 13a). The de-bris was divided into the southern, central, and northern sec-tions (Choffat 1929). The largest blocks were located in thenorthern part of the rockslide avalanche, near the slope.Some blocks had a volume of about 500 m3, and the largest(8000 m3) was found at the toe of the cliff. In general, fewfine materials were observed. When observed, fine materialwas described as a mix of dust, earth material, and gravel(Choffat 1929). A tendency to observe finer material withdepth in the talus cone was also noted by Choffat (1929).This indicates that larger blocks fell at the end of the move-ment on the top of the talus cone material, which absorbedmost of the impact energy. Photographic analyses were per-formed on old photographs published by Choffat. The meansize of the debris seems to be about 0.5 m (v50 in Fig. 13c).The particle-size distribution curve shown in Fig. 13c in-cludes some of the very large blocks mentioned earlier. Thisexplains why the distribution of the debris is better graded

than the distribution of the intact mass (Cu intact < Cu de-bris). Choffat observed that a fall height of 10 m is enoughto fragment a falling rock mass. Based on this observation,he calculated that approximately 11% of the potential energywas used for the disintegration of the entire mass of the rockavalanche.

Data interpretation

The previous descriptions illustrate that the rock ava-lanches studied herein differ in terms of rock type, volume,geomorphic control, and block size distributions of the start-ing and deposition zones. Their main characteristics areshown in Table 3. Volumes range from about 0.1 × 106 to100 × 106 m3 and, as shown in Fig. 2 in a H/L versus vol-ume diagram, the studied rock avalanches do not behave dif-ferently from others reported by Hsü (1975). Most of therock avalanches studied here failed along their major discon-tinuity sets: beddings (FR, SM, JCN, JCS, CL) or foliations(CH, LM). However, AR collapsed along a major disconti-nuity across the stratification, and QE had a composite fail-ure surface along and across bedding.

Figure 14 presents the degree of fragmentation or reduc-tion ratio (eq. [10]) as a function of H/L, approximately themobility index I H L= ′/ tan φ = (eq. [1]). There is no clearrelationship between these two parameters for the rock ava-

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Locat et al. 845

Fig. 12. Charmonétier rockslide avalanche (CH): (a) cross section; (b) stereonet; (c) particle-size distribution (modified after Couture etal. 1997).

lanches studied here. Rock avalanches with essentially thesame mobility can have a different reduction ratio value (Rr),which is the case for JCN, SM, QE, FR, and LM. On theother hand, rock avalanches with a similar reduction ratiovalue (Rr) show different travel distances, and hence mobil-ity, such as in the case of JCN, JCS, AR, CH, and CL. Theabsence of a relationship could possibly be due to the vol-ume of rock involved.

A comparison between the reduction ratio value (Rr) andvolume is presented in Fig. 15 and shows that the rock ava-lanches studied here can be separated into two main groupswith respect to their volume: (i) those with volumes lessthan about 5 Mm3 and with little fragmentation (CH, AR,CL, JCN, and JCS), and (ii) those with larger volumes andgreater fragmentation (SM, FR, QE, and LM). Both groupshave a typical deposit architecture, namely clast supportedfor the first group and matrix supported for the secondgroup, with inverse grading in some cases (FR, LM). Thiscontrast in type of debris deposit between large and smallrock avalanches has already been reported by McSaveney etal. (2000). In general, the reduction ratio seems to increasewith an increase in the volume, but CH is inconsistent withthis trend. Indeed, CH shows the smallest volume and high-est reduction ratio of the first group. This may indicate that

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Fig. 13. Arvel (AR) rockslide avalanche: (a) cross section; (b) stereonet; (c) particle-size distribution (modified after Choffat 1929).

Fig. 14. Relationship between reduction ratio (Rr = D50 /d50) andmobility represented as H/L.

volume does not correlate directly with the degree of frag-mentation in rock avalanches. On the other hand, CH has agreat height (520 m; Table 3) compared with its volume, andthis may indicate that the height, and thus the energy, playsa significant role in the fragmentation process. Also, for thecase of CH, factors such as saturated conditions, which fa-cilitate the grinding processes (Tourenq 1970), and achannelized runout, which maintains the interaction betweenblocks within the moving mass for a longer period of timethan in the case of a nonchannelized mass movement, mayhave contributed to an increase in fragmentation efficiency.

If eq. [9] is rearranged, γHG becomes the potential energy(EP) per unit of volume (V) for a rock avalanche:

[13] γH E VG P= /

Figure 16 shows Rr = D50 /d50 as a function of γHG. Ingeneral, after a threshold γHG, the reduction ratio increaseswith an increase in γHG, but again some discrepancies canbe noted. A comparison between LM and JCS rock ava-lanches highlights the fact that, for the same value of γHG,the reduction ratio of LM is more than 20 times the reduc-tion ratio of JCS. This is likely due to the fact that the com-pressive strength of the quartzite from JCS, defined here asthe point load strength, is about eight times greater than thatfound in the lustrous schist of LM (see Table 3).

Figure 17 shows the reduction ratio (Rr = D50 /d50) as afunction of the potential energy per unit volume (γHG) nor-malized by the point load strength (σc). This illustrates theempirical relation between the degree of fragmentation (Rr),the available energy, and the strength of rock. A linear re-gression over the nine points gives the following empiricalequation, with a regression coefficient (R2) of 0.94:

[14] γ σH D dG c 50 500.006 0.012( /= +[ )]

This relation is based on the potential energy and not onthe fragmentation energy. As indicated by eq. [4], the poten-tial energy in rock avalanches is also dissipated into friction.

Note that D50/d50 = 1 corresponds to a threshold energy offragmentation. An analogy to crushing and blasting pro-cesses can be made because the fragmentation, energy, andstrength of the material are related. In eq. [5], thefragmentability (K) is an empirical factor related to the na-ture of the rock mass. In eq. [6], the work index of Bond(1952) is an empirical factor related to the strength of therock (Table 1). Equations [11] and [12] give the fragmenta-tion energy calculated on the basis of eqs. [5] and [6] andcan be compared with the available potential energy for thestudied cases.

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Locat et al. 847

Fig. 15. Relationship between reduction ratio (Rr = D50 /d50) andvolume for studied rock avalanches.

Fig. 16. Relationship between reduction ratio (Rr = D50 /d50) andpotential energy per unit of volume (γHG).

Fig. 17. Relationship between reduction ratio (Rr = D50 /d50) andthe disintegration index (ID = γHG /σc).

Figure 18 shows the fragmentation energies in percentageof EP, estimated from eq. [11] for blasting energy and fromeq. [12] for crushing energy, as function of the reduction ra-tio (Rr = D50 /d50). Fragmentation energy estimated by blast-ing (eq. [11] and Fig. 18a) varies between about 5% (JCS)and 65% (SM) of EP. The median value is at about 25% ofEP. Fragmentation energy estimated by crushing (eq. [12]and Fig. 18b) varies between 0% and 18% of EP. The me-dian value is at about 15% of EP. Recall that for blasting(eq. [5]), as the initial size (D50) of the rock material in-creases, the energy needed to blast this material increases(Fig. 3); the highest value of 65% for SM can be explainedby the large D50 value (10.6 m) combined with a relativelylow energy per unit volume, when compared with other rockavalanches in this study (Fig. 16). The lowest values, whichare represented by JCS and JCN in Fig. 18, can be explainedby their low reduction ratio, due to hardness of the material,and the high energy per unit volume (Fig. 16), when com-pared with the other rock avalanches studied herein. Anotherpossible explanation for low values is limitations of the mea-suring method. For JCS and JCN, only one scan line wasmade to define D50 in the starting zone. Parts of the startingzone with larger block sizes could be missing. Also, photo-graphic sampling in the deposition zone was done only atthe surface of the debris, since a cross section was not avail-able at these sites. The d50 size must be taken as an upperbound value. If the results of calculations listed in Table 3for JCS and SM are excluded, the fragmentation energieslisted in Table 3 give a mean value of about 20% of EP. Thisvalue can be used in combination with eq. [14] for evaluat-ing the disintegration energy in rock avalanches. Based onthe nine cases studied herein, the disintegration energy (ED)can be expressed as

[15] ED = 0.2γHG = 0.2{σc[0.006 + 0.012(D50/d50)]}

The disintegration index (eqs. [2] and [3]) can be assessedfor rock avalanches using eq. [15], after the following equa-tion:

[16] I E E HD D P G c0.2 0.006= =/ ( / ){ [γ σ+ 0.012(D d50 50/ )]}

This gives an indication of the part of potential energydissipated into disintegration inside the moving mass. Ac-cording to eqs. [15] and [16], there may be no fragmentation(Rr = 1), but ED and ID ≠ 0. In that case, we assume that en-ergy was dissipated by heaving and bulking of the mass. ForRr < 1, the quantity of energy obtained can be considered asthe loosening energy used to partially heave the mass alongonly a part of the discontinuities. This can be observed if thepotential energy is below the threshold value to obtain frag-mentation, especially for small-volume rockslides. For thecase of AR, Choffat (1929) noted that a fall height of about10 m was needed to disintegrate a part of the rock mass.This corresponds to approximately 11% of EP available inthe case of AR. Considering simple collapse of the masswithout fragmentation for AR, i.e., for Rr = 1 and a pointload strength of 170 MPa (Table 3), the disintegration index(ID) would be about 22% of EP, using eqs. [3] and [15].Considering field variability of the strength, a difference ofabout 11% between the approximation made by Choffat andthe calculation made with eq. [16] seems acceptable.

Limitations of the approach usedThere are several limitations associated with the evalua-

tion of the intact block size distribution. Block size distribu-tion of the intact rock mass is determined from material nearthe failure zone, which is not the material directly involvedin the avalanche. Also, the analyzed volumes are generallyvery small relative to the overall rock avalanche volumesvarying between 0.2% for CH and 0.0003% for LM. Also,the STEREOBLOC software assumes a spherical blockshape to simplify computation. This results in an underesti-mation of the diameter for an equivalent convex solid(Hadjigeorgiou et al. 1995).

As for the block size distribution of the debris, the follow-ing comments are made. For rock debris photographic sam-pling of a blasted bench, Palangio and Franklin (1996)suggest at least eight images for each blast, with preferablymore than 400 fragments per image. In the case of photo-graphic sampling of rock avalanche debris, the area to besampled is much larger than the area of a blasted bench. Inthat case, this technique should involve many photographicsamples to be representative. For some of the rock ava-lanches presented herein, the number of photographs takenand fragments observed are under these minimums due tofield conditions. Moreover, when images are taken over thesurface of the deposits, inverse grading as for FR or LM in-duces an underestimation of the degree of fragmentation.Where no cross sections in the debris are available, the frag-mentation ratio should be considered as a minimum. Also,the degree of fragmentation at the surface of deposits mayvary with the distance from the proximal to the distal partsof the deposits, as reported by Couture et al. (1998) for theFrank slide. This is why in many cases the block size distri-butions of the debris are presented as an envelope instead ofa single curve.

The amount of fines is underestimated with this techniquebecause large particles hide the smaller particles. This re-sults mainly in an overestimation of the mean size of the dis-

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Fig. 18. Relationship between disintegration energy, in percent-age of the dissipated potential energy (Table 3), and the reduc-tion ratio (D50 /d50) for (a) the blasting energy γHG (eq. [11]),and (b) the crushing energy (eq. [12]).

tribution and an underestimation of the variability of thedistribution (Maerz and Zhou 2000). The limit of the smallerparticle size observable on a photographic sample dependson the scale at which the photograph is taken. For this study,minimum measurable size varied between 1 and 5 cm. Toimprove the resolution of fines, standard sieve tests shouldbe carried out using the fine portion of the deposit and fittedto the coarser portion as a function of the percentage of thearea covered by the fines (Cruden and Hungr 1986; Pollet2004). This was not done for this study.

Also, methods used for defining the fragmentation energy(from crushing and blasting) are highly empirical and ap-proximate. The results and conclusions of the present studyare thus also approximate.

Conclusions

Nine rock avalanches from the European Alps and Cana-dian Rocky Mountains have been examined in the presentstudy. For each case, the block size distribution was deter-mined for the intact rock and the debris, and the correspond-ing disintegration energy was estimated on the basis ofapproaches developed in the mining industry in relation toblasting and crushing. The results show the following:(1) For the nine cases studied, there exists an empirical

relationship between the reduction in diameter ratio,Rr = D50/d50, and the potential energy per unit volumenormalized with respect to the point load strength of therock (γHG/σc) (Fig. 17; eq. [14]).

(2) The disintegration energy is approximately 20% of thepotential energy for the cases studied.

(3) The empirical relationship can be used to define the dis-integration index, ID, proposed by Vaunat and Leroueil(2002). Due to the limitations of the approach used, therelationship established in this study is approximate butseems to reflect the physics of the disintegration processand indicates that the reduction in diameter ratio wouldbe a function of the dissipated energy and the strengthof the rock. These factors have long been known to af-fect fragmentation but had never been presented in a co-herent manner for rock avalanches.

More data are needed to confirm the relationships pro-posed in this study. Further studies should be done, prefera-bly on rock avalanches where cross sections in the debrismass are available.

Acknowledgements

The authors would like to thank the Fonds pour la Forma-tion de Chercheurs et l’Aide à la Recherche (FCAR), theNatural Sciences and Engineering Research Council of Can-ada (NSERC), and the Geological Survey of Canada fortheir financial support. Special thanks is extended to ParksCanada for providing access to sites in Jasper National Parkin the Canadian Rocky Mountains and to all the people whohave been involved in this project. Dr. O. Hungr and twoanonymous reviewers provided constructive critique, whichresulted in a substantial improvement of the paper.

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