Avalanche action on rigid structures: Back-analysis of ... · Avalanche action on rigid structures: Back-analysis of Taconnaz deflective walls' collapse in February 1999 P. Berthet-Rambaud

hnology 47 (2007) 16–31www.elsevier.com/locate/coldregions

Cold Regions Science and Tec

Avalanche action on rigid structures: Back-analysis of Taconnazdeflective walls' collapse in February 1999

P. Berthet-Rambaud a,b,⁎, A. Limam a,c, P. Roenelle a,b, F. Rapin a,d,J.-M. Tacnet a,d, J. Mazars a,e

a French research network RNVO “Natural Hazards and Structures Vulnerability”b CETE-LRPC, French Civil Works Ministry, 25 av. F Mitterrand 69674, Bron, France

c URGC-INSA, 20 Av. Albert Einstein 69621 Villeurbanne, Franced Cemagref, UR ETNA, BP76, 38400 Saint-Martin d'Hères, France

e Laboratoire 3S, BP 53 38041 Grenoble cedex 9, France

Abstract

Knowledge about action undergone by an obstacle impacted by an avalanche is still insufficient to allow civil engineers todesign really efficient and resistant structures. The main difficulty is to take into account the mutual interactions that occur betweenthe structure and the flow and the influence of the obstacle on the avalanche action itself. An original back-analysis principle isproposed to obtain information on avalanche action from real destructive event and to ensure that the result is effectively what isundergone by the structure and not only what could be generated by the phenomenon. In that way, the destruction of two deflectivewalls in Taconnaz site by the 11th of February 1999 exceptional avalanche is studied with several parts: firstly, a large siteinvestigation program is conducted to gather observations including material specimen's tests and to exhibit two collapse scenarios.Then, laboratory experiments are performed to confirm failure mechanisms. Finally, numerical simulations used a rigorous three-dimensional finite elements model and a realistic representation of the concrete behaviour to evaluate the effective resistance of thestructures under different conditions, including quasi-static, cyclic and dynamic influences.© 2006 Elsevier B.V. All rights reserved.

Keywords: Avalanche action; Pathologies; Back-analysis; Reinforced concrete structures; Damage model; Finite element model

1. Introduction

The action of a snow-avalanche and its effects onstructures are still badly known. If pressure values haveeffectively been measured experimentally, it is too rarelyin the case of real structures: even nowadays, the influenceof the obstacle presence on the avalanche flow is regularlynot correctly taken into account and the corresponding

⁎ Corresponding author. Fax: +33 4 72 14 33 42.E-mail address: [email protected]

(P. Berthet-Rambaud).

0165-232X/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.coldregions.2006.08.004

action is consequently badly estimated. Then, design rulesand current practices do not include dynamic specifica-tions, whereas it obviously should, as more adequatecalculation tools exist nowadays.

Therefore, the back-analysis of damages generated bysnow avalanches is very valuable to improve the know-ledge on the flow pressure characteristics (Margreth andAmmann, 2004), which clearly constitutes the currentlimit for safer infrastructures. Moreover, considering areal situation is particularly useful for taking effectivelyinto account the mutual influence between the flow andthe obstacle and to treat with large structures: this inverse

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http://dx.doi.org/10.1016/j.coldregions.2006.08.004

17P. Berthet-Rambaud et al. / Cold Regions Science and Technology 47 (2007) 16–31

concept ensures that the result is what was effectivelyundergone by the structure.

This study is based on a real event at Taconnaz nearChamonix (France) and includes several parts: after adescription of the site and of the event, it presentsdocumentations and on site investigations before labora-tory experiments and numerical simulations. The objec-tive is here to show that an indirect civil engineering pointof view can also efficiently bring new knowledge aboutsnow avalanche's action for a better design of structuressubjected to such a phenomenon.

2. Current knowledge about avalanche's action forcivil engineers

Several studies about avalanche's action on struc-tures exist (Lang and Brown, 1980; Schaerer andSalway, 1980) and propose pressure measurementsand values. However, it remains difficult to exploitthese data for the design of structures potentiallysubjected to avalanche flows. Measurements are mainlyavailable directly as sensors results and what is missingis a specific analysis useful for civil engineers who needrather typical and general data project instead ofcomplete and precise information about one single andpast avalanche. Consequently, it is still admitted that theavalanche action is proportional to the referencedynamic pressure (ρ: snow density, V: flow speed):

P ¼ 12qV 2 ð1Þ

But this famous formula from hydraulics' theory doesnot apply exactly in the case of snow and avalanchewithout additional hypothesis and provides only a singlehomogeneous average pressure level. Then and evenadmitting that we can define correctly the right “average”speed and the right “average” density, there are stilldisagreements about the factor to apply to this referencepressure depending on the situation: avalanche type,normal or tangential load, ability of the obstacle to deviatethe avalanche, etc. For example, French and Swiss rulesmake a different use of Eq. (1) concerning densetangential load or aerosol pressure.

However, the main problem is that this formula comesfrom hypothesis, which do not intrinsically include thepresence of an obstacle (the impacted structure) includingits relative and original characteristics: shape, profile, size,etc.

The obstacle introduces a particularity in the flow. Itdisturbs the avalanche action distribution: the pressure issurely not spatially uniform and the impact against thestructure modifies its temporal evolution, eventually with

prejudicial dynamic effects. The knowledge of thesemutual influences and interactions between the flow andthe obstacle is also crucial to introduce a realistic load casein the structure design and then to use an adapteddimensioning and assessment method. That means inparticular that avalanche's action and structures cannot bestudied separately for such an interaction problem. Theresponse itself of a rigid and resisting structure during therush is negligible but the influence of its presence must beabsolutely taken into account to evaluate correctly thecorresponding action.

3. Concept and objectives of the back-analysis

In order to obtain realistic characteristics of the actionof a snow-avalanche on a structural obstacle, it isnecessary to adapt the information sources: directmeasurements of avalanche impacts on infrastructuresare very few. For example, using pressure sensors fixedsimply on shaped supports in the flow will not be totallyrealistic for civil engineering because it will not take intoaccount this crucial influence of the obstacle presence.In that way, maximum values from classic pressuresensor measurements could perhaps be compared to theresult of Eq. (1) multiplied by a correct factor but shouldnot be used as static action for structures design. Inparticular, the creation of a snow accumulation againstthe upstream side of the obstacle and the vertical orlateral flow deviations due to this obstacle needs toevaluate pressure from a representative situation.Moreover, what is important is not the equivalent staticpressure that can be potentially generated punctually bythe flow but the pressure that is effectively undergone bythe structure including its temporal effects.

Finally, one of themain ideas is not just to consider thatthe action is independently due to the avalanche flow butto understand that the obstacle presence participatesquantitatively and qualitatively to this action. Usingspecific and back-analysis tools based on on-siteobservations coupled with numerical modelling andlaboratory experiments, real events study constitutesalso a powerful information source of what is effectivelyundergone by a structure, then useful to elaborate realisticand proved-correct load cases.

This indirect approach generates new difficulties dueto the complexity of the problem (dynamics, non-linearmaterial, geometry). It can be difficult to exhibit the onlyright scenario leading exactly to the real studiedconsequences. But, it provides at least additionalinformation for experts: in the current situation withavailable knowledge level, confirmed information aboutthe spatial distribution and the temporal evolution of the

18 P. Berthet-Rambaud et al. / Cold Regions Science and Technology 47 (2007) 16–31

undergone action would be already a great improvementfor civil engineers.

4. Taconnaz site

In the French Alps, in the vicinity of the “Mont-Blanc” peak, Taconnaz avalanche path is situated in theintermediary part of Chamonix Valley below Taconnazglacier. Avalanches that can be rated as the mostimportant in France regularly sweep it.

Along its lengthwise profile (Fig. 1), a serac wallseparates two large potential starting zones. A large partof the complete track can also be situated over theglacier. A high moraine confines the down part of thetrack (down to the beginning of the deposition area at1250 m ASL).

Different cottages (Taconnaz, Vers-le-Nant, La Côte-du-Mont) are built on the alluvial fane at approximatelythe altitude of 1050 m ASL. At these locations, the slopeangle is still pronounced (17%=9.6°) and positive.

Thus, after several destructions and insufficiency ofprevious dams, a large avalanche protection system wasbuilt at the beginning of the 1990s. Closing the run-outzone, this complete protection system stretches from1250 m to 1180 m ASL and includes different obstacles,each with a particular function (Fig. 2): The 11 deflectivewalls are massive structures laid out in two ranges tospread the flow when entering in the protection system.Then, four lines of braking mounds are placed inquincunx to break the flow energy and speed. Threesuccessive platforms can finally stock the snow depositwith as extreme protection, lateral and frontal dams. Themain catching dam rises up to 14 m.

The deflective walls made of reinforced concrete arealso subjected directly to coming avalanches. Initially,they were designed and dimensioned for a linearpressure profile representative of a dense flow (between

Fig. 1. Lengthwise profile of Taconnaz

180 kPa at the top and 300 kPa at the bottom) under anaverage direction of 30° with the plane of the main wall(Fig. 15). Geometry and main dimensions of thesedeflective walls are given on Fig. 3.

Two foundation plates to take care of the slope of thesite support the main wall. The reinforcement is verystrong in particular for the uphill face but it is to be notedthat the downhill belt and the uphill belt are not linkedtogether by transverse reinforcement. To make thesestructures heavier, rock block masonry corresponding toa several tons ballast was added behind the wall with aprofiled shape to be hidden from the avalanchedirection.

5. February 11th, 1999 avalanche (Rapin andAncey, 2000)

At the beginning of January 1999, the snow cover inthe northern Alps was shallow scarcely reaching 50 cm innorth facing slope at 2000 m of altitude. At the end ofJanuary, 150 cm of fresh snow within 4 days weremeasured at the extremity of Chamonix Valley (altitude1470mASL). After several sunny windy and cold days, anew stream struck the Alps on 6th February. The tempe-rature was particularly cold. In the Chamonix centre(altitude 1050 m ASL), the snowfall reached 140 cm offresh snow, which corresponds to a 40 year period ofreturn. The corresponding snowpack structure included:

– a great quantity of cold recent snow with lowcohesion, settling under its own weight (meandensity close to 110 kg/m3);

– a weak layer probably existing at the base of thisrecent snow in spite of the strong winds whichpreceded the episode from the 6th to 10th;

– deep layers made up mainly of plane faces or depthhoar.

path (Rapin and Ancey, 2000).

Fig. 3. Geometry of Taconnaz deflective walls.

Fig. 2. General view and simplified plan of Taconnaz protection system.


In these conditions, the avalanche risk was announcedas very extreme by the local meteorological centre.

Thus in 3 days, seventeen major avalanches reacheddown the bottom of the Chamonix Valley. Among them,the avalanche of Montroc occurred on February 9th (12people killed, 17 houses destroyed) and on the 11th,approximately at 4 a.m., a big avalanche arrived atTaconnaz and concluded this terrible avalanches series.

This Taconnaz avalanche could not be directlyobserved but French experts tried then to exhibit arealistic scenario interpreting all available indicators. Inparticular, very big volumes of snow formed largedeposits outside of the protection system: 80000 m3

including ice blocks from the glacier as large as 1 m3

had flowed over the lateral dam and 220000 m3 jumpedover the last catching dam. Theses volumes are to becompared with the 530000 m3 measured inside theprotection system. There, the deposit surface appearedglobally regular and clearly white with flow tracksparallel to the main axis of the system. It included manyrock blocks, from one to several cubic meters. Snowheights were very different depending on the location:very thick along the frontal dam (until 15 m— platform3 was almost full), the deposit was only 1 or 2 m thick inthe central part (around the braking mounds and onplatforms 1 and 2). After the avalanche, all deflectivewalls and lateral dams were distinctly visible and notburied as if the flow just went through these obstacles.

From all observations, experts' conclusion is that thisavalanche started on the glacier: A large serac was broken

along the ice cliff (elevation 3200 m ASL) and releasedthe flow. Due to the high slopes and the fresh snow allalong, a big aerosol arose, its speed increased very quicklyand exceeded 80 m/s. After the glacier and a distancecovered of 1.5 km, the avalanche turned left along themoraine, grasping all the snow cover and rocks. Then, theaerosol part went up the opposite side of the path overmore than 90 m in elevation (broken trees).

When it entered in the protection system, the flow wasvery quick including a thick powder part and a flowingdense part with an important ice block volume ratio(evaluation of 30%). The main aerosol part of theavalanche was globally parallel to the main axis of the


protection system, went through all upstream obstacles(deflective walls and braking mounds), reached rapidlyand overflowed the frontal dam. This explains especiallythe deposit and snow heights distribution. In the sametime, due to trajectory complexity with different con-sequences for dense or powder parts, experts identifiedalso two secondary north-direction avalanche waves withhigher density, which finally went along or even jumpedthe lateral dam to make external destructions.

Considering its run-out distance, the return period ofthis avalanche was estimated at about 26 years whereasthis period is only 9 or 10 years considering the globalvolume. In fact, the Taconnaz path can either generatevery large dense flows with important volumes (overtwo million cubic meters — the protection system wasforeseen to stock about 800000 m3 but only in case ofdense avalanches) or very quick powder avalancheswith longer run-out distances. The 1999 avalanche wasalso quite different from Taconnaz usual events, whichled to the protection system design and dimensioning.

The main illustrations of the violence of this event arethe generated damages: Parts of the forest in three loca-tions and a ski lift were destroyed, some houses weretouched by air blast and damaged, but fortunately nobodywas injured. The upstream faces of some breakingmoundswere partly disordered but the most impressive damagesconcerned two of the deflective walls, which werecompletely broken. These two deflective walls are thosesituated at the right (in the direction of propagation)extremity of each range, wall no. 9 for the upper one andno. 11 for the lower one (Fig. 2). All other deflective wallsand especially the closest ones (no. 6 and no. 10) can show

Fig. 4. Deflective wall no. 9 a

some individual cracks or punctual impacts but were notdestroyed in 1999 and are still standing nowadays. Thefirst explanation for this crucial difference is to considerthat the main part of the avalanche (which was mainlyaerosol and not dense as foreseen initially for the systemdesign) entered in the protection system rather shifted to itsnorth side. Secondly and because of the different deflec-tive walls orientation (“inverse funnel” arrangement), thisparticular trajectory parallel to the main system axis led toa more prejudicial action direction (quasi-orthogonal) forextremity deflective walls. It is also to be noted that someconcrete blocks coming inevitably from the deflectivewalls destruction were found outside of the protectionsystem near its frontal dam: with the deposit character-istics, this confirm that these structures were destroyed bythe main part of the avalanche as described before.

6. Civil engineering on site investigations

Firstly just after the avalanche, it seemed roughly thatthese two deflective walls were destroyed by the sameway with the same consequences and final state: theirupper corner is like cut and lies on the ground some20 m downstream, carried there by the flow (Fig. 4).Concerning rebars, some are severed but many of themare free in the air like combed by the flow. An importantcoating concrete part is also pulled out (Fig. 5).

After a documentation step to gather all availableinformation from design and works period, precise on-site investigations were performed by the CETE ofLyon, Service of the French Civil Works Ministry expertin construction pathologies (CETE, 2002).

nd its pulled out corner.

Fig. 5. Combed rebars and coating concrete.

Table 1Laboratory tests results on rebars (CETE, 2002)

Test no. Wall no. σ elast 0.2%(MPa)

σ max(MPa)

Elongation(%)

1 11 Rupture 738 0.42 11 Rupture 761 0.63 11 Rupture 748 0.64 11 Rupture 762 0.55 9 591 621 7.56 9 535 617 10.5


Firstly, materials specimens were extracted in differentlocations of the two damaged structures and then in-vestigated through conventional laboratory tests: thesetests results established the very good quality of concrete(about 58MPa formaximumcompression stress, coherentwith initial tests and 30 GPA for Young modulus). Thisquality is confirmed by aggregate fractures along concretecracks. Verification about rebars confirmed also that thereinforcement was correctly placed at the building time.

This first step shows at least that the deflective wallswere correctly constructed according to design documentsand were still in a good structural state just before theavalanche (for example with no freezing influence forconcrete).

However, laboratory investigations on rebars showedalso a difference between wall no. 9 (upper range) and no.11 (lower range). All the reinforcement specimens for testcame from rebars outside of concrete after the avalancheand enough far from their potential rupture zones. For wallno. 9, tests showed that these reinforcement specimenshad kept their original mechanical characteristics after theavalanche, whereas for wall no. 11, rebars lost completelytheir elasticity capacity as if they were subjected to ageneral elongation during the rush (Table 1).

The second important difference between walls no. 9and no. 11 was that the entire structure no. 11, including itsfoundations plates and the rockmasonry ballast, was founddisplaced of about 2 m downhill, creating a deep troughuphill and causing a 7° general inclination of the wall. Thistranslation did not cause foundations failure or rupture

initiation between the wall and plates: as it was not sodeeply grounded (some decimetres), the complete structureonly slipped “on” the ground. Then, fracture and cracksinvestigations confirmed the necessity of two differentscenarios to explain the initiation of the walls collapse.

Indeed, if the two still-standing parts of the wallsshow both bending cracks parallel to the main fracture,wall no. 11 appears much more damaged also with ahorizontal cracks network on the upstream face andtypical compression fractures at extremity on the backside (Figs. 6 and 7). Concerning this last wall, the mainfracture is circular with a bending crack network ofabout 1.5 m wide along it. This fracture follows globallythe rock masonry upper limit. Horizontal cracks aredistributed along a 2.5 m wide and 7 m long horizontalband. Some particular cracks (vertical or inclined) showthe influence of the two foundation plates. Concerningwall no. 9, the crack network consists only in a 2 m widebending cracks band along the main fracture, which do

Fig. 6. Wall no. 11 final state.


not follow the rock masonry limit. Some hard impactsare also visible, due surely to the upstream location ofthis deflective wall (deflective walls no. 9, no. 6, no. 5and no. 1 show more impacts than the others).

Equivalent differences are found examining the twopulled out corners: for structure no. 9, this part isobviously more destroyed (inversely to the respectivestill-standing parts) on the two sides with nomore coating

Fig. 7. Wall no. 9

concrete, whereas the corner of structure no. 11 is stillquite in good state (Fig. 8). Their positions downhill totheir initial respective location confirmed the trajectory ofthe destructive avalanche part (see Section 5).

Finally the CETE study proposes two scenarioscoherent to explain these differences that occurred duringthe same avalanche: wall no. 11 was simply destroyed bya distributed pressure on the uphill wall face as commonly

final state.

Fig. 8. Pulled out corner, respectively no. 11 (a) and 9 (b).


considered for avalanche solicitation. All observationsmade for this wall are consistent with this conclusion andits destruction is supposed to be caused by a pressure levelhigher than its resistance capacity including the influenceof the rock masonry support.

For wall no. 9, observations are finally quite differentas if the load was spatially limited, at least initially, to the

Fig. 9. Several tons rock found

upper corner of the structure: this scenario is based on theinfluence of a localized impact. This last conclusion isnot so astonishing considering that the ice part in theavalanche and moreover that big rock blocks areregularly carried by avalanches: several 10-ton blockshave already been found in the protection systemespecially in 1999 (Fig. 9). Finally, all observations for

in the protection system.

Fig. 10. Reduced scale deflective wall.


wall no. 9 are also consistent with this scenario andcollapse is supposed to be initiated by this impact.

7. Quasi-static laboratory tests

To support this first conclusion, laboratory tests werethen foreseen in particular to investigate initial failure

Fig. 11. Laborator

mechanisms. As a dynamic test was not possible, a quasi-static test was performed, considering that the behaviourof a rectangular wall submitted to normal pressure isnowadays still insufficiently knownwith a limited numberof experimental and numerical studies (Mazars, 1998).

When non-linear response is of interest, the behav-iour of this type of structure is influenced by the

y test bench.

Fig. 12. Crack pattern at ultimate state.


interaction between bending and shear. The macro typeof modelling, generally adopted by engineering ap-proach for design, will have some inherent difficulties inaccurately reproducing the ultimate behaviour which isstrongly dependant on the damage propagation andassociated stress redistribution which constitutes herethe main parameters. To investigate the simplifyingassumptions made in design, and to provide experimen-tal data in this particular field, these experimental testsare conducted on a 1/6 reduced laboratory scale modelof the reinforced concrete deflective wall of Taconnaz(Fig. 10).

The geometry of the model is defined according to thereal structure without the two foundations plates andsimplifying the wall shape itself. This leads to a reducedspecimen having the following dimensions: 1.60 mheight, 2.47 m long, and the thickness of the wall is0.25 m. The chosen boundary conditions are a simplifi-cation of the real situation: the footing is clamped with asingle foundation. The reinforcement ratio is identical tothe one of the real structure, and the characteristics of thesteels rebar (length, shape, overlapping) are respected.The model is completely equipped with strain gaugespositioned on the concrete wall and on the steel rebars;displacement transducers provide the horizontal deflec-tion of the vertical wall at different locations and levels.These different transducers allow us to catch the crackinitiation, its localisation and propagation, the appearanceof rebar yielding and the associated load redistribution.

In parallel, experiments are conducted to characterizeconcrete and especially to determine its quasi-staticcompressive strength under conditions of uniaxial stress.Cylindrical specimens 220mm long and 110mmdiameterare subjected to unconfined compression, at a nominalstrain rate of 10−3 s−1 following the ASTM standardsC39-96. The quasi-static compressive strength of approx-imately 65 MPa is found to be 12% higher than the one ofthe concrete in reality and these two different concretes areconsidered as equivalent.

Finally, the test principle consists a uniform pressureload applied by loading cushions on the total externalfaces of the wall: this load is gradually incremented untilthe ruin (Fig. 11).

From the test it is observed that concrete crackingstarted in the lower portion of the wall, near the junction tothe footing and around the anchorage system. The crackspropagated perpendicularly to the surface of the verticalwall in accordance with bending effect, but progressivelyan inclination is observed. At the bearing capacity onehuge fissure, with an inclination of 45°, propagates sud-denly and drastically, and conducts to the ruin of thestructure (Fig. 12).

The load deflection curve (Fig. 13) shows that, at theonset of cracks apparition, a decrease of the structure'srigidity is observed. The local behaviour observed on thesteel reinforcements with strain gauge measurement con-firms cracks initiation for a load intensity of 0.1 MPa. Thereinforcements rebars remained elastic until the collapse, inaccordance with a non-ductile global behaviour.

At the compressed side of the wall structure, no damageof the concrete material is observed and the maximal strainobtained is less than 0.002, which corresponds to thecrushing deformation obtained at the ultimate load for theconcrete characterisation under uniaxial compression tests.

In order to exploit and analyse these particular tests, asimple model (Merabet and Reynouard, 1999) that in-tegrates the most characteristic features of reinforced con-crete under monotonic loading is used. This model is basedon the plasticity theory for uncracked concrete and adoptsthe concept of a smeared crack approach with orthogonalfixed cracks and assumes a plane stress condition.

The simulation (Limam, 2005) reproduces the mostimportant characteristics of the quasi-static behaviour ofthis type of structural element. The type of failure (fragileinstead of ductile) is also well simulated and useful

Fig. 14. PRM modelling of the concrete behaviour (Pontiroli, 1995).

Fig. 13. Experimental load deflection curve obtained for the wall structure.


information about the behaviour of the deflective wallsubmitted to normal pressure during different load stagesis obtained. Finally, this laboratory test and its analysisconfirm that the specimen behaviour is mainly governedby shear with a fragile and non-ductile ruin.

8. Numerical simulation

After on-site investigations and laboratory experi-ments, a numerical approach applied to the two realdeflective walls is used to quantify the avalanche effectsmore accurately and to evaluate action dynamics in-fluences. To be useful, tools used must be able to rig-orously take into account the real geometry of the structureand moreover to model correctly the real behaviour ofmaterials. In thatway, a finite element analysis is proposedincluding a stress–strain relationship that allows a realisticrepresentation of the concrete behaviour under dynamicloads and its corresponding damages. A long use of thisnumerical tool, in particular for falling rock problem orseismic conditions ensures the accuracy of the calculations(Berthet-Rambaud, 2004).

8.1. Numerical tools

The numerical simulations are based on a rigorousthree-dimensional modelling of the structure using thefinite elements code Abaqus. The explicit solver of thiscode allows highly non-linear transient dynamic analysisof phenomena like impacts. Abaqus offers also thepossibility of managing several interactive entities, for

example to simulate a block collision. The analysis can,therefore, introduce the impact in a way similar to thereality, managing only the impact characteristics.

The deflective wall is modelled with volumetric finiteelements including different degrees of mesh refinementaccording to the real geometry. The reinforcement isrepresented independently by bar elements, which areembedded in the concrete part of the model to ensure aperfect bond between reinforcement and concrete.

For this first simulation campaign, the structure isassumed perfectly fixed to the ground and the rock

Fig. 15. Avalanche and normal pressure.

Fig. 16. Simplified pressure time profile.


blocks masonry volume is represented by a rigid shell incontact with the downhill face of the wall with the samereal contact surface. The behaviour of this system isgoverned numerically by four linear springs linked tothis shell, distributed and calibrated to obtain realisticnormal displacements at the interface wall-masonryvolume. The order of magnitude of these displacementsis assumed to be about 5 mm corresponding to theseparation distance observed between the wall and themasonry volume for the two damaged structures afterthe avalanche on deflective walls no. 9 and no. 11.

Then, for an accurate simulation of the structuralresponse due to a snow-avalanche, it is necessary to usea realistic representation of the materials' behaviourunder dynamic and cyclic loadings. For the concrete, thebehaviour properties must include some phenomenasuch as decrease in material stiffness due to cracking,stiffness recovery related to closure of cracks, andinelastic strains concomitant to damage.

The stress–strain relationship is represented in thisnumerical analysis by the PRM (Pontiroli–Rouquand–Mazars) (Pontiroli, 1995; Rouquand and Pontiroli, 1995)damagemodel that uses a scalar damage variableD, whichis the damage indicator. The one-dimensional expressionof the stress–strain relationship is given by Eq. (2):

ðr−rftÞ ¼ Eoð1−DÞðe−eftÞ ð2Þ

where Eo is the Young modulus, σft is the crack closurestress in tension and εft is the irreversible straincorresponding to σft. A similar expression is used withtensors to describe the three-dimensional states.

D includes damages due to compression and tension;its value varies from 0 (for uncracked material) to 1 (formacro-cracked material). The variation of D is governedby the equivalent strain (Mazars, 1986):

fe ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXi¼1;3

heii2þs

ð3Þ

where ⟨·⟩+ denotes the positive part and εi are theprincipal strains. The damage variable D is calculatedthrough the damage indicators in tension (Dt) and incompression (Dc):

D ¼ abt Dt þ ð1−atÞbDc ð4Þ

The damage evolution is given by:

Da ¼ 1− 1−Aað Þ eofe −Aae−Baðfe−eoÞ ð5Þ

with α=c, t; σft and εft are calculated with:

rft ¼ Eoð1−DcÞðeft−efcÞ þ Eoefc ð6Þeft ¼ eft0 1−Dcð Þ− Dc

1−Dcefc ð7Þ

σfc and εfc are considered as material parameter data.The damage threshold εo depends on the strain rate ε· in

order to model the strain rate effect under dynamicloading. A typical stress–strain response produced by thismodel for a uniaxial alternate loading in multi tension-compression steps is given in Fig. 14. The threedimensional version of this model (used in the numericalsimulations) is implemented in Abaqus—explicitly usingan external Fortran subroutine. The regularization

Fig. 17. Cyclic and dynamic loadings influence on Taconnaz deflectivewalls behaviour.

Fig. 18. Damage distribution under uniform pressure.


technique (Hillerborg et al., 1976) is used in order to avoidmesh dependency.

The stress–strain relationship for the reinforcingbars is considered as simply elastic plastic. The materialparameters are identified from previous laboratorymaterials tests to ensure the most realistic materialrepresentation.

8.2. Numerical collapse definition

Numerically, it is then necessary to define quantita-tively the collapse initiation of the structure. Indeed, it isobvious on site to conclude that the two deflective wallsare broken but from a numerical point of view, especiallywith a finite element representation, the question israther: When does the rupture initiate and happen? Thisproblem is quite difficult to solve particularly forcomplex three-dimensional geometries and combinationof non-linear materials (steel and concrete). A goodindicator is also necessary. Using a damage model, thisrupture could be linked to a certain damage level ofconcrete or to the displacement evolution of a particularand representative point. The problem is then to detectcorrectly the good initiation time and to be able to have aconsistent and quantitative approach. We finally chooseto consider the “first” plasticization of a main rebar in thestructure. This solutionmay not be perfect but has at leasta mechanical basis and this first plasticization oftenrepresents the beginning of irreversible damages thatlead irremediably to the final collapse of the structure.The objective is also here to model correctly thebehaviour of the structure until the beginning of itscollapse and to consider that the next phase is not thedestruction of the structure.

8.3. Numerical results

First simulations consist in determining the effectiveresistance capacity of Taconnaz deflective walls underorthogonal distributed pressure. Indeed, the originalFrench civil engineering design rules for concretestructures including different safety factors and finally,resistance capacity of the real structure cannot bedirectly linked to initial design hypothesis. Moreoverin the case of the 1999s avalanche (see Section 5), itseems clear that the flow direction was more prejudicialthan those used for initial design, being closer to theorthogonal direction of the wall of destroyed structures.

To determine this effective resistance capacity understatic conditions, pressure is uniformly and incremen-tally applied on the uphill face of the wall until thedefined-rupture of the structure. This uniformity hy-pothesis is prudently chosen for simplicity all the morein cases the avalanche load seems to be higher at thebottom of the flow (and this design hypothesis was usedat Taconnaz; Fig. 15) but could also be lower at the topin particular when the structure is overflowed. In fact, allintermediary situations could even exist in this last case,between the first avalanche impact and a stabilizedoverflow. This should also take into account a dynamicevolution of the spatial load distribution (Berthet-Rambaud et al., 2004). To ensure the static of thesimulation, the solicitation rate is tested to verify that nodynamic influence happened numerically. Finally, asolicitation rate of 400 kPa/s is used.

Without the rock volume behind the wall, the normalstatic resistance capacity is evaluated at 160 kPa and thiscapacity reaches 220 kPa including the rock volume.These static calculations show first that the resistancecapacity of the structure depends of course on thepresence of the rock volume but also confirm that thiscapacity is quite greater than initial dimensioning

Fig. 19. Damage distribution under rock impact.


hypothesis: in the orthogonal direction of the wall, thishypothesis was a linear pressure profile between 45 kPaat the top and 75 kPa at the bottom (Fig. 15, thesenormal values are obtained from the avalanche pressureand direction was evaluated by experts using a sin2 30°factor). In that way, this numerical tool providesimportant information for example for risk managementabout the real capacity of protection system.

The next calculations concern the influence of thedynamics of the flow. The problem is that research hasnot yet fully apprehended the action of the snowavalanche and answers for real structures in the flow aremissing. Finally, the temporal evolution of the ava-lanche action in such a case is not yet clearly known.

For this present study and without reliable availableprofiles, a simple in-time profile with two parameters isused: the time t of the maximum pressure and the value Pocorresponding to the pressure stage (Fig. 16).

Po is chosen inferior to the static resistance capacityof 200 kPa and t varies from 10−1 to 10−4 s. Dynamiccalculations show finally that the rupture can happenprematurely due to dynamics' influence. It underlinesthe necessity to take into account the dynamics of thephenomena for such structures subjected to snowavalanches or to other natural hazards like falling rocks.

Another prejudicial aspect of avalanche action is itscyclic and very quick temporal evolution: numericalsimulations confirm that dynamic and cyclic load, even ifmaximum pressures remain inferior to the static resistancecapacity of the structure, can lead after a few cycles to anincreasing damaging until the total collapse of thestructure (Fig. 17). Concerning the mechanically dissym-metric behaviour of the wall (due to a very differentreinforcement ratio in downhill and uphill rebars layers),pressure releases can even generate inverse damages dueto the elastic spring back of the wall.

Using damage model for concrete, it is also possible todetermine the weakest zones in the structure: applying auniform pressure (scenario for wall no. 11), damagedistribution on the wall is illustrated on Fig. 18. It is veryclose to the real fracture.

The same simulation is also possible introducing ablock impact (scenario for wall no. 9): to perform thissimulation, we choose a representative numerical con-crete block of about 5 m3, 12 tons with an impact speed of30 m/s (5400 kJ of kinetic energy). The contactmanagement parameters come from block impact studiesin (Berthet-Rambaud, 2004). In that case, results show(Fig. 19) that the upper corner of the wall is much moredestroyed (in particular with damages on the back face)and rebar plasticization happens locally during impact.

Finally, this numerical approach appears as a verypowerful way to model structure's behaviour forphenomena like snow-avalanches. It allows taking intoaccount complex geometry and dynamic loadings and canbe used to complete back analysis approach or simply toperform a numerical experimentation to improve protec-tion design. In Taconnaz case, it confirms the two collapsescenarios for each deflective wall.

9. Conclusions

The 11th of February 1999 destructive avalanche atTaconnaz near Chamonixwas a great opportunity to studyin real conditions interactions between a snow avalancheand an obstacle and as a consequence on rigid structures.Without no direct observation or reliable information, thisstudy is based on the back analysis of the final state of twodestroyed deflective walls. This analysis used on siteinvestigations, laboratory experiments and numericalsimulations to propose two collapse scenarios for wallsno. 9 and no. 11. The consistency of observations and tests


is confirmed by numerical calculations and generalconclusions can be drawn from this event to improveprotection design and generally conception of structuressubjected to snow avalanches:

– Cyclic and dynamic aspects of avalanche's actionabsolutely need to be taken into account, as they areparticularly prejudicial for rigid structures. Numeri-cal mechanical tools are nowadays available tomodel such a situation and development of adaptedengineering tools is still necessary in this domain.

– Knowledge about avalanche's action against struc-tures is still insufficient and it is necessary to continuewith appropriate experimentations in order to obtainreliable space–time pressure profiles of what is reallyundergone by a structure submitted to a snow-ava-lanche and usable by civil engineers. It includes alsothe temporal evolution of the spatial load distribution,for example when the structure is overflowed. Thesame indirect principle can be used here to developoriginal and efficient experiments: instead of pressuresensors, this means to introduce representative ex-perimental structures in the flow and to study theirbehaviour during the avalanche rush. The mainadvantage is to limit the complexity due to real struc-tures impacted by an exceptional event with realisticobstacles on a controlled and known site. Secondly, itallows multiplying data cases in correct conditions.Since 2002 new experiments are developed using thisconcept on the French full-scale avalanche experi-mental site in Lautaret Pass (Berthet-Rambaud et al.,2003). They concern both vertical structures likewalls and in a close future, slabs to simulate roadprotection galleries.

– Then, avalanche's action cannot be limited to adistributed pressure. In many cases, it is possible tofind rock blocks, ice blocks or trees in the flow that cangenerate localised impacts with potential damagingconsequences. The difficulty is to take them correctlyinto account when dimensioning the structure: asupplementary static force is not sufficient for designbecause it will not be as prejudicial as in reality withdynamics consequences. Some recent developmentsare interesting concerning rock impacts on concreteslab, either with analytical (Delhomme et al., 2005) ornumerical approaches (Berthet-Rambaud, 2004).

– Concerning reinforced concrete structures, reinforce-ment design is very important and even a priority: itmust not be neglected especially to resist to shear andpunching effects.

– Numerical tools can also provide interesting informa-tion for risk management: various conditions can be

tested to evaluate effective resistance capacities. Usinga damage model for concrete, it is also possible toexhibit potential fractures and weakest zones ofstructures, eventually to reinforce them (Limam andHamelin, 1998).

Finally, some additional conclusions can be specif-ically drawn for Taconnaz deflective walls. First of all, itis obvious that the avalanche direction is crucial: thehypothesis of a 30° angle between the wall and the flowdirection dramatically decreased the action to take intoaccount for design whereas in that case, walls orienta-tions are different and (1999 event confirmed this), theflow direction is sometimes difficult to predict (espe-cially for major avalanches in long and complex path).Applying directly the avalanche pressure profile (Fig. 15)to the wall would have surely changed the global resultwith a more appropriate dimensioning.

Of course, it must be also recalled that initial designhypothesis applied only for dense avalanches and 1999aerosol surely increased dynamics importance. However,the lack of transverse reinforcement was also a terribleweak point of these deflective walls: if advancedcalculations including impacts and dynamic loads arenot always possible, it is at least necessary to correctly andsufficiently (over)-reinforce concrete with an adequaterebars network able to resist not only bending but alsoshear and punching effects. This reinforcement quality isthe crucial basis for concrete structures subjected todynamic and cyclic loadings!

Six years after this event, the protection system remainsas it was on February 12th, 1999. Indeed, in spite of twodestroyed deflective walls and some modified brakingmounds, its main protection capacities are still fulfilled andseveral important avalanches occurred during this periodwithout any problem. However and to update the referencescenario after 1999, French experts made proposals toimprove Taconnaz protection system: they consist espe-cially more efficient dams, repaired and additional moundsand two platforms (instead of three) with a positive slope.These modifications have to be studied more preciselyduring the coming months. Concerning the two destroyeddeflectivewalls, questions remain to find the best technicalsolution with acceptable financial costs: it seems to bedifficult to repair but it is more difficult to replace and, asthe deflective function is not the main one, efforts are nowfocused on the other parts.

As a general conclusion, back-analysis of destructiveevents can be very useful to improve avalanche actionknowledge and protection design to be able to refinedimensioning hypothesis and to make sure that futurestructures will resist for what they were planned for. Of


course, it can never prevent that one day the avalanche willbe stronger than ever before.

Acknowledgements

The authors acknowledges the financial support ofthe RGC&U “Civil Engineering and Urbanism net-work” within the framework of the PRANE program(structures subjected to the action of snow).

References

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Avalanche action on rigid structures: Back-analysis of ... · Avalanche action on rigid structures: Back-analysis of Taconnaz deflective walls' collapse in February 1999 P. Berthet-Rambaud