Microsoft Word - numero 14 articolo 5 N B. Pol Co bar AB nu int pap cra As arr ph dis ava KE IN cro hyp Ela inv the me stu on Th lite of Co tha ver var inv C Numeric M. Chiaia litecnico di Tor rso Duca degli rbara.frigo@p BSTRACT. U merically by trinsically dy per, we mod ack propaga ssuming that rest fracture hilosophy for stributed alo alanches to p EYWORDS. F NTRODUCTIO aused b between mechan own (Mode I pothesis of a astic Fracture vestigate is re e second mec echanism (Mo udied by mean the theory of he snowpack erature. By tak crown fractur onsidering the at increasing i ry different a riability cause vestigates the C cal study a, B. Frigo rino, Departm li Abruzzi, 24 polito.it Under the hy y means of L ynamical, an del dynamic ation throug t the weak l propagation r the use of ng the snow propagate w Fracture mec ON by the snow n a thick, stro nisms: it start I), fracture at perfectly bri e Mechanics presented by chanism of dr ode II fractur ns a numerica f crack arreste is considered king into acco re propagatio e spatial varia its spatial vari approaches, s es lower pro possible redu y of frac ment of Structu 4, 10129 Tor ypothesis of Linear Elast nother aspec crack propa gh the prese layer is almo n, into the fr f artificial di w slope area: with less cata chanics; Sno stratifications ong and stiff ts with fractu t the flanks ttle phenome [1, 2]. Since y dynamic fra ry slab avalan re propagation al simulations ers. d like a linear ount kinetic e on and their s ability of the iability would such as cellu obability for uction of the B. M. Chiaia et cture arr ural and Geote rino, Italy f a perfectly tic Fracture ct to investi agation into ence of wea ost collapse framework o scontinuities the target is strophic effe ow avalanche s, the snowp f slab and coh ure at the we (Mode II an enon, avalanc e, however, t acture propag nches trigging n between we s to analyse it r–elastic plat energy and th tability have b physical and d lead to lowe ular automata catastrophic e propagation t alii, Frattura ed rest on echnical Engin brittle phen Mechanics igate is repr a dry snow ak zones dis d, we simul of Dynamica s (void) into s to split a la ects. e; Crack arre ack can be s hesive basal la ak layer on t nd Mode III) che triggering the real phen gation. In the g: the fracture eak layer and ts possible ar te (2D proble hanks to the u been investig mechanical p er release prob a [4] and sta avalanches n of crown fr d Integrità Strutt snow co neering, nomenon, av (LEFM). Sin resented by slab and we stributed alo late the effic al Fracture M o the snowp arge avalanch esters; Active chematized a ayer. The slab the bed surfa and fracture g is usually inv nomenon is e framework o e at the crow snow slab), t rest based on em) with phy use of the FE gated in contin properties of bability for sn tistical mech is the same racture by the turale, 14 (2010) over valanche trig nce, howeve dynamic fra e investigate ong the exte ciency of ar Mechanics. W pack able to he slab into e protection as a sandwich b avalanche r ace (Mode II) e at the stau vestigated nu intrinsically d of Fracture M wn. As a conse the secondary n Dynamic El ysical parame EM software nuous (natura f snow cover, now avalanch hanics [5] mo . To suppor e theory of C 0) 45-51; DOI: 10 ggering can er, the real p acture propa the possibil ension of th rtificial voids We put forw perform as smaller slab . h structure: a release pursui ) following b uchwall (crush umerically by dynamical, an Mechanics, th equence of th y Mode I crac lastic Fractur eters chosen FRANC 2D al) snow cove some studie hes. Although odels, the ide rt this percep Crack Arrester 0.3221/IGF-ESIS. be investiga phenomeno agation. In lity to arrest he snow slo s in the slab ward here a n s crack arres bs, causing sm a thin weak l its a sequenc by fracture at hing). Under means of Lin nother aspec he paper anal he first trigge ck propagatio re Mechanics according to [3], several p er. es have sugge h the studies h ea that increa ption, the pa rs applied on .14.05 45 ated on is this the ope. b to new sters mall layer ce of t the the near ct to lyses ering on is and the paths ested have ased aper n the mailto: barbara.frigo@polito.it http://www.gruppofrattura.it http://dx.medra.org/10.3221/IGF-ESIS.14.05&auth=true B. M 46 sno the alo Th ava dis TH spe In the cra cur ene ene dif pro cur ene wh and Co con wh pro spe For inte W M. Chiaia et alii ow cover. Dy e presence of ong the extens he use of crac alanche slab i continuities ( HE PRINCIPL hen t and r (shad eed. Figure 1 a quasi-static e energy avail ack arrests. Fi rve, it eventu ergy that can ergy has been fference betw operty, where rves represen ergy balance m d t )(G here, as usual, d Ek is the kin onsidering the nditions can b )(tKI  here v is the opagation (dyn eed by means r an infinite b ensity factor )(I tK  W i, Frattura ed In ynamic crack f discontinuou sion of the sn ck arresters is into smaller s (void) into the LE OF CRAC the driving fo rapid crack pr ded area in Fi : Balance of en c case, a crack lable for an i ig. 1b illustrat ually crosses t be converte n dissipated. T ween KIa and eas KIa depen ting KI and G must be mod d dE dA dU dA dF  , F is the wor netic energy. e stage of cr be written as: )(vKID crack speed namic crack-res s of optical m body or short and the dyna )0()( IKvk tegrità Struttural propagation us weak zone now slope. s a first step slabs, causing e snowpack – CK ARREST orce G for cr ropagation oc ig. 1a) is conv nergy for: (a) fr k is stable if t incremental e tes a simple c the R curve. ed into fractu The apparent KIA is gover nds on geom G values. If th dified to includ dA Ek rk done by ex rown fracture d, KI the ins sistance), whic methods. t propagation mic energy re le, 14 (2010) 45 into a dry sn es (equipped towards a ne g small avalan – the snow crack rack extension ccurs (Fig. 1. verted into ki (a) racture propag the driving fo extension of crack arrest. T Arrest does ure energy. Ar arrest toughn rned by the etry. Figs. 1a he crack drivi de kinetic ene xternal forces e, the govern tantaneous s h depends on n periods, KI(t elease rate can 5-51; DOI: 10.322 now slab is m with differen ew idea of ac nches to prop k arresters- dis n exceeds the a). According inetic energy. gation, (b) unst orce G is less a rapidly pro The fracture not occur at rrest occurs b ness, KIa, is t kinetic energ a and 1b com ing force inco ergy, so, the d s, A is the fra ning equation stress intensit n the crack v (t) is not equa n be expresse 21/IGF-ESIS.14.0 modelled to as nt shapes and ctive avalanch pagate with l tributed alon e material cra g to the first The magnitu table crack pro s than or equa opagating cra initiates whe t this point, b below the re therefore less gy created du mpare materia orporates the dynamic defin acture surface n for Mode I ty factor and velocity and c al to the static ed in the form 05 sess the poss d geometries he protection less catastrop ng the snow sl ack resistance law of therm ude of the kin (b) opagation and a al to the mat ack falls below n KI = KIc. I because the s sistance curv than the true uring crack p al resistance w effect of kin nition of ener e area, U is t I crack propa d KID is the an be measur c stress intens m: sibility of crac of artificial v n: the target i phic effects th lope release a e R, the struc modynamics, t netic energy d arrest (Anderso terial resistanc w the materi If the structur structure still ve, after most e material res propagation; K with quasi-sta etic energy, th rgy release rat the elastic def agation unde material res red as a func sity factor. Th ck arrest thro voids) distribu is to split a l hanks to artif area. cture is unsta the excess en dictates the cr on, 1995). ce R. Similarl ial resistance, re has a fallin l contains kin t of the avail istance, KIA. KIA is a mat atic driving fo he Griffith-Ir te is [6]: (1) formation en er elasto-dyna (2) sistance to c ction of the c he dynamic st (3.a) ough uted arge ficial able, ergy rack ly, if , the ng G netic lable The terial force rwin ergy amic rack rack tress http://www.gruppofrattura.it http://dx.medra.org/10.3221/IGF-ESIS.14.05&auth=true wh fun dim the wh Wi of stre NU Co eve red stif the the cer Wi pro con acc C )( gG t  here KI(0) and nctions of cra mensions. Sin e form: At)( G here : )( vA ith the same a width of dr ength). UMERICAL S rack arr stress c possibil onsidering som en advantage duces the stre ff stringer ele e nearest rivet e beneficial e rtain geometri ith the use of opagation, sev nsidered like cording to Ta C )0()( Gg v d G (0) are th ack speed v. nce G = K2/ E E tK vA I )( )( 2 11            h c v r approach and ry slab avalan SIMULATION rest can be a concentration lity is to redu me experimen ous that the ess intensity f ment betwee ts are very clo effect of a sin ical arrangem f the FEM so veral paths o a linear–elast ab. 1 [2]. Slope Snow Weak Snow Snow E Snow Weak G Weak Mode IIc he static stres Eq. 3.a is va E, it is possib  1     hv d assuming th nche depend N OF DYNAM attained in th n and introdu uce the stress ntal results fo crack passes factor. The st en the two clo ose to the cra ngle hole itse ment of holes. oftware FRA of crown frac tic square she Paramete angle: α w slab height: H k layer height: w slab density: w slab elastic E w slab Poisson k layer shear Gw k layer peak st e II fracture c Tabl B. M. Chiaia et ss intensity fa alid as long a ble to combin he arrest of fra ding on slab MIC FRACTU hree different uction of resi intensity fact or riveted she s between riv tringer is mo osest rivets te ack. Then the elf is negligib ANC 2D [3], cture propaga et (100m x 10 er H h ρ modulus: n’s ratio: ν r modulus: trength: τp energy: G le 1: Typical va t alii, Frattura ed actor and the as the length ne Eqns. 3.a a acture propag parameters URE ARREST t ways: reduc dual compre tor by forcing et structures, vet holes: th re effective in ends to keep t e stringer is ve ble, the best r based on the ation and the 00m), with un Typical valu 38° 0.5 m 10 mm 200 kg m-3 1 MPa 0.2 0.1 MPa 2 kPa 0.2 J m-2 alues for snow d Integrità Strutt e energy relea of crack pr and 3.b, obtai gation, Jamies (slab thickne T IN DRY SNO ction of the c ssive stresses g the crack to , we know tha he stringer tak n doing so w the crack clo ery effective i results are ob e maximum c eir stability h nit thickness ue Ran 30-4 0.3-1 1-15 3 100-300 0.5-10 0.1- 0.1-0.6 0.3-6 0.1-0.3 w slab and weak turale, 14 (2010) ase rate, respe opagation is ining the rela son and John ess, slab tens OW AVALAN crack tip stre s [8]. In the o runs into a at if stringers kes load from when the rive sed. If the cr in the reducti btained when circumferentia have been inv (1m), and wit nge Ref 45° 1 m mm 0 kg m-3 0 MPa -0.4 6 MPa [1 kPa [1 3 J m-2 k layer [2]. 0) 45-51; DOI: 10 ectively, g and small compa ationship betw nston [7] deriv sile strength NCHES ess intensity, case of snow weaker part o s are attached m the cracke ets are closer ack passes be ion of crack t n the crack p al stress crite vestigated. Th th physical pa ference [9] [9] [9] [9] [9] [9] 0, 11] 0, 11] [12] 0.3221/IGF-ESIS. (3.b) d k are unive ared to specim ween KI and (4) (5) ve the expres and basal sh reduction of w avalanches, of the snowp to the plate, ed skin and t to the crack: etween two h tip stresses. S passes betwee erion for frac he snow cove arameters cho .14.05 47 ersal men G in sion hear f the the pack. it is thus : the holes ince en a cture er is osen http://www.gruppofrattura.it http://dx.medra.org/10.3221/IGF-ESIS.14.05&auth=true B. M 48 For at t coh ado As in mo Sev and arr or sto Th dis frac infl Th (Fig M. Chiaia et alii r simplicity, t the top of th hesive behavi opted (see Eq a preliminary the horizon onotonically in veral simulati d different ar esters: for ex a single and p opping and ca he first interes continuous li cture when th fluence of cra he optimal con g. 4a). In a m i, Frattura ed In the condition he slab, have iour has been qns. 1 – 5). (a Figu (b) Cr y test, a simu ntal direction ndicating uns ons have bee rrangements o ample a cont parallel discon ancelling the p sting result is inear crack a he crack ove ck arrester is Figure ndition (i.e. a model slab (1 tegrità Struttural s of no horiz been conside n considered a) ure 2: (a) Schem rown fracture p ulation of the and then r stable fracture en conducted of crack arres tinuous single ntinuous line presence and obtained ana arresters (Fig. rpasses the s not enough a 3: (a) Crown f linear sharp decrea 100 m x 100 m le, 14 (2010) 45 zontal displace ered. An initi in the simula me of snowpac propagation on e slab without rotates slight e propagation afterwards to sters in the sn e linear crack ar crack arres the effects of alysing the pl 3). We note nowpack bet and the fractu (a) fracture propag crack arrester ase of KI, see m) with a cen 5-51; DOI: 10.322 ement at the ial flaw was i ations, and th (b) ck with induce n the snowpack t crack arrest tly. The KI n (Fig. 2). o study the in now cover. A arrester (with sters. In all th f the crack ar lot of Stress I e a little drop tween two pa ure restarts its gation on the s s; (b) Plot of K Fig. 4b), was ntral area (30 21/IGF-ESIS.14.0 lateral sides o mposed at on he dynamic va ed initial flaw o k. (c) Plot of K ters was carrie value, depen nfluence of d About the latt h width and l hese simulatio rresters. Intensity Fac p of the KID w arallel rows o s propagation snowpack with KID vs. crack s obtained for m x 40 m) w 05 of the slab, an ne lateral sid alues of the f on the left bord KID vs. crack le ed out. Crow nding on th different starti ter, we tested length equal t ons, the crack ctor vs. Crack which indent f discontinuo n. (b) h parallel discon length. r a quincunci weakened by nd of no verti e of the slab fracture param (c) der. ength. wn fracture pr e fracture g ing position o different geo to : 2m x 5m k overpasses t k length in th tifies a tempo ous crack arre ntinuous al crack arres the presence ical displacem . The absenc meters have b ropagates init growth, incre of the initial ometries of cr and 0.1m x 5 the voids with he case of par orary stop of esters: the sp ster configura e of a quincun ment ce of been tially eases flaw rack 5m), hout rallel f the patial ation ncial http://www.gruppofrattura.it http://dx.medra.org/10.3221/IGF-ESIS.14.05&auth=true arr wa bet Fig cre wh unt F DI act ava due for slab Th the the sto T angement of s totally inter tween the firs g. 5a and 5b s eates a “influe hich avoids th til another inf Figure 4: (a) C Figure 5: (a) Cr ISCUSSION A he simu that, to indepen tive avalanche alanches from e to Mode II r the use of a b into smaller he idea of the e trees as natu e stability of t opping its pro T f circular or h rrupted. Note st and the sec show that, va ence area” (wh he coalescenc fluence area i Crown fracture rown fracture p AND CONCL ulations show increase spa ndent avalanch e protection. m triggering, b propagation artificial disco r slabs, causin e implementat ural arresters: the snowpack opagation ins hexagonal arr e the transitio cond vertical c arying the pos hose radius, i ce of the crac is reached. e propagation w propagation wi LUSION the effectiven atial variabilit hes. So, we c Usually, the but it is not s in the weak l ontinuities (vo ng small avala tion of snow : the tree slow k. Moreover t side of the w B. M. Chiaia et resters (holes on from unsta column of ho sitions of the in our simulat ck tip within (a) with a quincun (a) ith a quincunci ness of these ty helps to s can suppose t e long term c so infrequent layer. Thanks oid) distribute anches to pro w crack arreste ws the flow o the perimeter wood, the cr t alii, Frattura ed with radius able fracture oles (Figs. 4a e initial crack, tions, can be the hole. Aft ncial circular cra ial hexagonal c e arresters to r stabilize the s that the use o control struct in big slopes s to the snow ed along the opagate with l ers arises from of snow avala r of the fores rack is heade d Integrità Strutt equal to 3 m condition to and 4b). the simulatio estimated as ter a minimu ack arrester arr crack arrester a reduce substa slope, eventu of crack arre tures for sno s that fracture w crack arreste snow slope a less catastrop m three in sit anches and pr st is a natural d downhill. T turale, 14 (2010) m), fracture pr a stable one, ons give simi being approx um point (B), (b) rangement. (b) (b) arrangement. (b antially the cr ually splitting sters is a first ow avalanches e in the crow ers, we put fo area: the targe hic effects. tu observation revents the re obstacle for The second 0) 45-51; DOI: 10 ropagation in , with crack a ilar results: ea ximately twice the KI facto ) Plot of KID v b) Plot of KID rack driving f g a major ev t step toward s in the uppe wn can bypass orward here a et is to split a ns. The first elease of aval the fracture i observation 0.3221/IGF-ESIS. n the snow co arrest that oc ach crack arre e the hole rad or increases a vs. crack length vs. crack lengt force. This me ent into sma ds a new idea er zones prev s the protecti a new philoso a large avalan is the analysi lanches thank in the snowp comes from .14.05 49 over curs ester dius) again h. th. eans aller, a for vent ons, ophy nche is of ks to pack: the http://www.gruppofrattura.it http://dx.medra.org/10.3221/IGF-ESIS.14.05&auth=true B. M 50 foll top sno the tria wo In pro num voi pre inv bef AC T M. Chiaia et alii lowing statem pography of t owpack [13]. e wind deflect angular shape ork as a crack conclusion, c opagation of merical inves ids) snowpac eliminary resu vestigation tak fore definite c CKNOWLEDG he finan Italia/Fr by RegioT i, Frattura ed In ment: sponta the slope: the Studying the tors with a cr e inside the sn arresters. (b) Wind de Figure considering th a weak layer stigations in c cks. The use ults testify the king into acc conclusions w GMENTS ncial support rancia (Alpi 2 one Piemonte tegrità Struttural aneous crow e concave an e methods of ross shape (Fi nowpack of t (a) Figure 6: (a) W eflectors on the (a) 7: (a) Snow-gri pr he snowpack r cracking ha continuous (n of crack arre e effectivenes count directly will be drawn. t provided by 2007-2013) is e and Italian M le, 14 (2010) 45 wn fractures nd convex rip f defence aga ig. 6) in the r the release ar Wind deflector e ridge of Lava ipper element. rotected by Sno as a linear–el as been cons natural) and d esters is a fir ss of the activ y Mode II arr . y Progetto S s gratefully ac Ministry of W 5-51; DOI: 10.322 follow the s pples of the s ainst avalanch ridge of the av rea [14, 15]. O r with a cross s ancher – Morge (b) Example o ow-grippers (w lastic plate (2 sidered. The discontinuou rst step towar ve crack arres rest on the w trategico RIS cknowledged. Work and Soc 21/IGF-ESIS.14.0 same path. T slope induce hes, we have valanche basi Obviously, th (b) shape (Photo b ex (AO) – basi (b) of release area www.incofil.com 2D problem), path of the us (equipped w rds a new id st concept fo weak plane an SKNAT - O . The research cial Security. 05 This is due tension and identified tw in and (ii) the ese defence s by Frigo, 2003) in (Photo by C of the avalanc m). the Mode I c crack has be with a differe dea for active or dry snow a nd the cohesi biettivo coop h activity is f to the morp compression wo typologies e snow-grippe structures mu ). Ceriani, 2000). che basin crown fractur een investigat ent shapes an e avalanche p avalanches. O ive nature of perazione ter funded by gra phology and n zone inside of structures ers (Fig. 7) wi ust be adapte re after comp ted by mean nd geometrie protection. Th Obviously, fur f snow is nee rritoriale euro ant co-suppo the e the s: (i) ith a d to plete s of es of hese rther eded opea orted http://www.gruppofrattura.it http://dx.medra.org/10.3221/IGF-ESIS.14.05&auth=true RE [1] [2] [3] [4] [5] [6] [7] [8] [9] [10 [11 [12 [13 [14 [15 EFERENCES D. M. McC B. Chiaia, P P. Wawrzyn 3.1, Cornell K. Kronhol B. Chiaia, B T. L. Ander J. B. Jamies D. Broek, E J. Schweizer 0] P. M. B.Föh 1] B. Jamieson 2] H. O. K. K 3] D. M. McC 4] F. Sivardièr 5] R. Fromm, S lung, J. Geop P. Cornetti, B. nek, A. Ingra l University (1 lm, K. W. Bir B. Frigo, Journ rson, Fracture on, C. D. Joh Elementary E r, Cold Reg. S hn, C. Campo n, C.D. Johns Kirchner, G. M lung, P. Scha re, Neige et A L. Rammer, phys. Res. 84( . Frigo, Cold affea, FRANC 1993). rkeland, Geop nal of Statisti e Mechanics F hnston, Canad Engineering Fr Sci. Technol., onovo, G. Kr ston, Annals o Michot, J. Sch aerer, The Av Avalanches (A Sperimentazi B. M. Chiaia et (B7) (1979) 35 Reg. Sci. Tec C 2D – A tw physical Rese cal Mechanic Fundamental dian Geotech racture Mech , 30 (1999) 43 rüsi, Annals o of Glaciology weizer, Scrip alanche Hand ANENA), (20 ione snowgrip t alii, Frattura ed 519. chnol. 53 (200 wo dimensiona earch Letters, cs: Theory and ls and Applica hnical Journal hanics, Martin 3. of Glaciology, y, 32 (2001) 59 ta Materialia, dbook, The M 04) 107. pper sullo Sch d Integrità Strutt 08) 170-178. al crack prop 32 (2005) L1 d Experimen ations, Secon l, 29 (1992) 61 nus Nijhoff Pu , 26 (1998) 1. 9. 46 (2002) 42 Mountaineers hmittenhöhe. turale, 14 (2010) pagation simu 19504. t, (2009) P02 nd Edition, CR 1. ublishers (198 25. Book, Seattle . Scheda tecni 0) 45-51; DOI: 10 ulator, User’s 056. RC Press (19 86). e WA, USA ( ica Snowgrip 0.3221/IGF-ESIS. Guide – Ver 95). (1993). per (2003). .14.05 51 sion http://www.gruppofrattura.it http://dx.medra.org/10.3221/IGF-ESIS.14.05&auth=true << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.4 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /CMYK /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams false /MaxSubsetPct 100 /Optimize true /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments true /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /ARA /BGR /CHS /CHT /CZE /DAN /DEU /ESP /ETI /FRA /GRE /HEB /HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 5.0 i kasnijim verzijama.) /HUN /ITA /JPN /KOR /LTH /LVI /NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.) /NOR /POL /PTB /RUM /RUS /SKY /SLV /SUO /SVE /TUR /UKR /ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.) >> /Namespace [ (Adobe) (Common) (1.0) ] /OtherNamespaces [ << /AsReaderSpreads false /CropImagesToFrames true /ErrorControl /WarnAndContinue /FlattenerIgnoreSpreadOverrides false /IncludeGuidesGrids false /IncludeNonPrinting false /IncludeSlug false /Namespace [ (Adobe) (InDesign) (4.0) ] /OmitPlacedBitmaps false /OmitPlacedEPS false /OmitPlacedPDF false /SimulateOverprint /Legacy >> << /AddBleedMarks false /AddColorBars false /AddCropMarks false /AddPageInfo false /AddRegMarks false /ConvertColors /ConvertToCMYK /DestinationProfileName () /DestinationProfileSelector /DocumentCMYK /Downsample16BitImages true /FlattenerPreset << /PresetSelector /MediumResolution >> /FormElements false /GenerateStructure false /IncludeBookmarks false /IncludeHyperlinks false /IncludeInteractive false /IncludeLayers false /IncludeProfiles false /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe) (CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /DocumentCMYK /PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged /UntaggedRGBHandling /UseDocumentProfile /UseDocumentBleed false >> ] >> setdistillerparams << /HWResolution [2400 2400] /PageSize [612.000 792.000] >> setpagedevice