ࡱ> .}q789:;<=>?@ABO s`ef`bjbj 177[| | |  ===8=L? r2hHM" N NN~\2]l^8e0g0g0g0g0g0g03hB6g0| fY>\@ffg0 NN ,2f` N| Ne0fe06| NH zC=~!D.B20r26X0686| \T^$a&cd:T^T^T^g0g0^T^T^T^r2ffff 4= =   1 UVOD U ovom diplomskom radu ispitivana je otpornost kamenog agregata na predrobljavanje. Kameni se agregati danas u industriji graevnih materijala koriste pri izradi cijelog niza proizvoda, ponajviae za proizvodnju betona i asfalta. Pri tom ine 75  85 % volumena asfaltne i betonske mjeaavine. Stoga je razumljiva va~nost ispitivanja svojstava kamenih agregata pri odreivanju njihove prikladnosti za te ili neke druge primjene u graevinarstvu. S obzirom na razne graevne konstrukcije u koje se ugrauje, kameni agregat je izlo~en i razli itim vrstama optereenja. Zahtjevi glede kvalitete kamenih agregata u danaanjoj graevinskoj praksi vrlo su visoki; agregat mora povoljno reagirati s vezivom (bitumen, cement i dr.), mora izdr~ati velika optereenja, udare i habanja, te zadr~ati povoljna svojstva tijekom vremena i pod utjecajem atmosferilija. Otpornost prema predrobljavanju je jedno od najva~nijih mehani kih svojstava kamenih agregata jer o njemu ovise stabilnost i trajnost graevina. Primarna metoda ispitivanja kamenog materijala na predrobljavanje prema EN 1097-2 je metoda "Los Angeles", dok se metoda "Impact" koristi kao alternativna metoda. U ovom radu kameni materijal je ispitivan prema obje metode i rezultati su razmotreni zasebno. OPI DIO 2.1 SVOJSTVA ESTICA I FUNKCIJA SVOJSTAVA Potrebe za ekonomi nom proizvodnjom i neprestani porast zahtjeva za kvalitetom tra~e uporabu strojeva i provedbu procesa na ato u inkovitiji na in, a od provedbe kontrole kvalitete provoenje u ato ranijoj fazi. Kvaliteta se mora zasnivati na samim elementima proizvodnog procesa. To nije zadatak samo proizvoa a i laboratorija za kontrolu kvalitete, ve on mora zapo eti provjerom sirovina i pokrivati sve faze odnosno stupnjeve proizvodnje. Ovakav sveobuhvatan pristup kontroli kvalitete pru~a priliku za preciznije otkrivanje izvora pogreaaka, te br~e reagiranje i provoenje potrebitih radnji da bi se one otklonile (1). U procesnom in~enjerstvu, stanje disperznosti je jedan od imbenika koji ima zna ajan utjecaj na svojstva proizvoda. Veliki broj proizvoda prolazi nekoliko puta kroz razli ite faze stanja disperznosti tijekom njihove proizvodnje. Svaki stupanj proizvodnje obuhvaa odreene ciljeve na ije dostizanje utje u svojstva estica ili proizvodna svojstva te karakteristike procesa. Proizvodna svojstva uklju uju slijedee parametre: - kemijski parametri - fizikalni parametri - tehnoloaki parametri (procesne i primjenske karakteristike). Za kemijski identi ne tvari fizikalni parametri su va~ni jer, u slu aju dispergiranih krutina, tehnoloaka svojstva ovise o parametrima estica odnosno fizikalnim parametrima koji se mijenjaju u skladu sa stupnjevima procesa. Rjeaavanje problema mogue je samo uz pomo fizikalnih parametara. Svojstva estica su primjerice veli ina i raspodjela, oblik, specifi na povraina, poroznost, fizkalna struktura, dok u tehnoloaka svojsta ubrajamo meljivost, te ljivost, stla ivost te te~nju aglomeriranju. Kao ato je spomenuto svojstva tvari ovise o svojstvima estica odnosno svojstvima disperznosti estica. Ovakvu funkcionalnu ovisnost Rumpf je nazvao funkcijom svojstava. Nakon laboratorijskih i tehni kih ispitivanja, za ato bolje razumjevanje i definiranje potrebno je proces razbiti na pojedina ne korake te ih analizirati zasebno. Takva zasebna analiza olakaava odluke o alternativnim na inima voenja procesa. Radi bolje preglednosti i razumljivosti pogodno je izraditi dijagram toka procesa iz kojeg se daju is itati osnovni parametri svakog dijela procesa:      Ponekad se te~i integralnom izra~avanju stanja disperznosti jednim brojem primjenom izabranih granulometrijskih vrijednosti jer olakaavaju postavljanje funkcije svojstava, odnosno matemati kog definiranja odnosa izmeu stanja disperznosti i tehnoloakih stanja sustava (procesnih i primjenskih). Granulometrijske zna ajke obi no su odreene veli ine estica, ali uz poznat faktor oblika to mo~e biti i specifi na povraina. Iznala~enje funkcije svojstava tra~i potpuno definiranje svojstava i parametara procesa kojim se doalo do veli ina nu~nih za njeno dobivanje. Proces dobivanja parametara za definiranje funkcije svojstava mo~emo prikazati jednostavnim dijagramom (primjer za metodu "Los Angeles"):      2.2 KARAKTERIZACIJA GRUBODISPERZNIH SUSTAVA Karakterizacija grubodisperznih sustava predstavlja opis primarnih svojstava estica kao ato su veli ina i raspodjela, oblik, mikrostruktura, osobine povraine te meusobni prostorni polo~aj estica(2). Stanje grubodisperznog sustava u praksi definiramo prikazivanjem sastava materijala i homogenosti mjeaavine te geometrijskih zna ajki grubodisperzne faze, odnosno njegovo granulometrijsko stanje. Struktura disperzne faze izra~ava se koli inskom raspodjelom zna ajke finoe. Kvantitativno definiranje koli inske raspodjele zna ajke finoe zahtjeva poznavanje raspodjele veli ine estica, tj. poznavanje kvantitativne raspodjele estica koje imaju jednake fizi ke karakteristike. Budui da su estice obi no nepravilnog oblika, mjere zna ajke finoe izra~avaju se naj eae ekvivalentnim promjerima kugle, ekvivalentnim promjerima kruga i statisti kim promjerima(2). Prvu grupu ine promjeri kugle koje imaju jednaka svojstva kao i sama estica (npr. volumen, povrainu itd.).U drugoj su grupi promjeri kruga koji imaju jednako svojstvo kao projicirani obris estice. Treu grupu veli ina, statisti ke promjere, dobiva se mjerenjem linearne dimenzije paralelne sa smjerom motrenja. Razli ite metode mjerenja veli ine definiraju razli ite zna ajke finoe i vrlo je va~no izabrati svojstvo relevantno za odvijanje procesa. Razvijen je cijeli niz metoda za mjerenje veli ina i raspodjele estica koje se uglavnom svode na mjerenje geometrijskih i sedimentacijskih zna ajki, te zna ajki naruaavanja elektri nog polja. Mjera koli ine ukazuje da li je raspodjela broj ana (r = 0) ili je masena, odnosno volumna ( r = 3). Koli inska raspodjela zna ajke finoe prikazuje se ili funkcijom gustoe raspodjele, qr(x) ili funkcijom raspodjele, Qr(x). Pojedine funkcije prevode se jedna u drugu integriranjem ili diferenciranjem, npr. dQr(x) = qr(x) (2).  EMBED PBrush  SLIKA 2.1: Funkcija raspodjele, qr(x) i kumulativna funkcija raspodjele, Qr(x) za razli ite na ine izra~avanja koli ine Realno je o ekivati da postoji minimalna i maksimalna veli ina estica, xmin i xmax, te da za x = xmin i x = xmax u estalost q(x) te~i nuli za stvarne raspodjele. Broj ana i masena/volumna raspodjela morale bi se teorijski pretvoriti jedna u drugu opom jednad~bom(2):  EMBED Equation.3   EMBED PBrush  SLIKA 2.2: Grafi ki prikaz funkcije gustoe raspodjele, qr(x) i funkcije raspodjele Qr(x). Brojne su matemati ke funkcije predlo~ene za aproksimiranje raspodjele veli ina. Npr.: Martinova, Gama, Rosin-Rammler-Spreling-Bennettova, Weinigova, Heywoodova, Griffithova, Gaudin-Schuhmannova, Gaudin-Meloyeva, Klimpel-Austinova, Beta, Harrisova, Rollerova, Normalna i Logaritam-normalana. Bilo koja funkcija predlo~ena za opis raspodjele veli ina estica trebala bi zadovoljititi dva kriterija: - da je primjerena rezultatima mjerenja , da postoji slaganje izmeu svojstva stvarne raspodjele veli ina estica i matemati kih svojstava funkcije. Prvi kriterij ispunjava veina funkcija, pa je est slu aj da se neka raspodjela mo~e aproksimirati s viae funkcija. Meutim, najairu primjenu za opisivanje raspodjele veli ina estica imaju logaritam  normalna (LN-) i Rosin  Rammler  Spreling  Bennettova (RRSB) funkcija raspodjele. LN  funkcija raspodjele(2):  EMBED Equation.3  Definirana je parametrom polo~aja (mjera centralne tendencije) x50 i parametrom raspraenosti (stupanj disperznosti estica oko mjere centralne tendencije sustava) s. x50 je median raspodjele tj. veli ina estice od koje je 50% manjih u sustavu. Parametar raspraenosti je standardna devijacija logaritma varijable x odnosno s = ln x84 / x16. Primjenjivost funkcije testira se ra unski ili pomou funkcionalnih mre~a LN  raspodjele. Takve mre~e imaju na ordinati nanesenu funkciju integrala vjerojatnosti, a na apscisi logaritam veli ine estice. Nalaze li se podaci mjerenja na pravcu, znak je da se raspodjela mo~e opisati predlo~enom funkcijom, odnosno izraziti njenim karakteristi nim veli inama. Konvencionalna metoda predvia o itanje medijana x50 iz standardizirane mre~e, a parametar raspraenosti odreuje se iz odnosa x84 i x16 ili o itava sa ruba mre~e. Iz podataka za  EMBED Equation.3  o itanih s obruba mre~e mo~e se izra unati specifi na povraina uz poznati faktor oblika f prema(2):  EMBED Equation.3  LN  funkcija raspodjele nalazi najveu primjenu u uvjetima opetovanih slu ajnih procesa RRSB  funkcija raspodjele glasi(2):  EMBED Equation.3  Ona je takoer dvoparametarska, a x63 je parametar polo~aja, a n je parametar raspraenosti. Osnova grafi kog prikazivanja je izraz(2):  EMBED Equation.3  Mogunost primjene funkcije testira se ra unski ili pomou standardiziranih funkcionalnih mre~a. Podaci mjerenja uneseni u mre~u nalaze se na pravcu, ukoliko se raspodjela pokorava toj eksponencijalnoj funkciji. Parametar polo~aja x63 o itava se iz standardizirane mre~e prema(2):  EMBED Equation.3 , a parametar raspraenosti izra unava iz nagiba pravca ili o itava s obruba mre~e. Iz podataka za  EMBED Equation.3  o itanih s obruba mre~e mo~e se uz poznati faktor oblika f izra unati specifi na povraina. RRSB  funkcija raspodjele nalazi najveu primjenu u procesima u kojima selektivni utjecaji i ograni avajui uvjeti smanjuju va~nost slu ajnih faktora. Kada raspodjele veli ina estica ipak odstupaju od tih dvoparametarskih funkcija, obi no se transformacijom:  EMBED Equation.3  uvode etveroparametarske raspodjele funkcija koje su odreene veli inama minimalne, odnosno maksimalne estice. Iz svega izlo~enog proizlazi da uspjeanost neke funkcije za opisivanje raspodjele veli ine estica, osim njene primjerenosti rezultatima mjerenja, ovisi u prvom redu o slaganju izmeu svojstava stvarne raspodjele veli ina estica i matemati kih svojstava funkcije. Funkcija predlo~ena za opisivanje raspodjele veli ina estica treba pri tomu zadovoljiti grani ne uvjete koji proizlaze iz stvarnog stanja sustava. Na temelju takvih predpostavki slijedi da se za opisivanje raspodjele veli ina estica najvea va~nost pridaje LN  funkciji raspodjele, ili njenoj viaeparametarskoj transformaciji. Za potpunu karakterizaciju geometrijskih svojstava grubodisperznog sustava potrebno je , uz definiranje raspodjele veli ina estica, opisati i njihov oblik. Izraziti oblik estice zna i prikazati obris estice, koji je rezultanta spojnice svih to aka na njenoj povraini. Nezavisan je o veli ini estice. Poradi velikog zna aja oblika estice na ponaaanje grubodisperznog sustava, javlja se potreba njegovog kvantificiranja. Na ini prikazivanja oblika estica, zasada joa neadekvatno razvijeni, dijele se na: verbalni opis, razli ito definirane faktore oblika, matemati ke funkcije, itd. Standardizirani verbalni opis predvia pojave ovih oblika: kugli ast, izometri an, plo ast do igli ast. Uz verbalni opis ve~u se ponekad odnosi izmeu glavnih izmjera: najvee du~ine, a1, najvee airine, a1 i najvee debljine, a3 (Slika 2.3.) (2).  SLIKA 2.3: Izra~avanje oblika estica glavnim izmjerama Faktori oblika su bezdimenzijske veli ine, izrazito ih je veliki broj, a obi no se definiraju kao odnosi mjerljivih svojstava estica, geometrijskih i dinami kih. Naj eai je Wadellov faktor sferi nosti, koji se izra~ava odnosom ekvivalentnih promjera(2):  EMBED Equation.3  Dinami ki faktor oblika izvodi se obi no aproksimiranjem neke realne estice dinami ki ekvivalentnim elipsoidom. Pretpostavlja se da se realne estice i elipsoid, pod istim vanjskim uvjetima, jednako ponaaaju u prostoru. Ponekad se dinami ki faktor oblika izra~ava odnosom stacionarnih brzina sedimentiranja estica nepravilnog oblika, vs,p i brzine sedimentiranja kuglica, vs,k:  EMBED Equation.3  Pri laminarnom opstrujavanju (Re < 0.5) dinami ki se faktor oblika mo~e izraziti kao omjer ekvivalentnih promjera:  EMBED Equation.3  Za izometri na tijela (kocka, oktaedar i tetraedar) vrijede slijedee relacije: (2)  EMBED Equation.3  Definiranjem oblika preko odreenih faktora te poznavajui raspodjelu veli ine estica i njezinu gustou, mogue je izra unati specifi nu povrainu koja je izrazito va~na kod definiranja parametara za dobivanje "funkcije svojstava":  EMBED Equation.3  (5) gdje je: ( - faktor oblika (d  gustoa estica x  veli ina estice 2.3 ENERGETSKI ODNOSI PRI DROBLJENJU Smanjivanje veli ine estica, odnosno predrobljavanje, u osnovi je razdvajanje estice u dva ili viae dijelova i stvaranje nove povraine (3). Predrobljavanje nekog kamenog agregata (ili openito nekog zrnatog sustava) dato je odnosom broja i veli ine zrna prije i poslije predrobljavanja, a sama otpornost prema predrobljavanju svojstvo je materijala dano ovisnoau stupnja predrobljivosti o broju i veli ini zrna u sustavu prije predrobljavanja (4). Za proces predrobljavanja, odnosno smanjivanja veli ine estica u bubnju potrebna je odreena energija. Nove povraine estica nastale procesom drobljenja vezane su uz energiju upotrijebljenu za to smanjivanje veli ine estica, ali se ta energija vrlo teako mjeri. Razlog tomu je ato se dio energije izgubi, odnosno izaziva druge procese u bubnju. Radi toga se u razmatranjima fenomena smanjivanja veli ine estica procesom drobljenja, svojstva materijala, kugli i bubnja aproksimiraju na na in da ne apsorbiraju energiju procesima kao ato su izdu~ivanje, kontrakcija ili zagrijavanje, koji nemaju za posljedicu lom estica. Rittinger (1867) je zaklju io da je energija utroaena u procesu smanjivanja estica proporcionalna novonastaloj povraini nakon procesa: Energija = K (nova povraina) = K (povraina nakon procesa  povraina prije procesa) = EMBED Equation.3  =  EMBED Equation.3  gdje su x1 i x2 ulazna i izlazna veli ina estica. Kick (1885) je zaklju io da se energija potrebna za provoenje "jednakih promjena u konfiguraciji na geometrijski sli nim tijelima jednakog tehnoloakog stanja mijenja u skladu s volumenom i te~inom tih tijela" (3). Deformacijska energija tijela proporcionalna je njegovom volumenu, a neposredno prije puknua vrstog tijela deformacijska energija je takoer proporcionalna volumenu. Prema tome, jedini ni volumen estica koje su u stanju neposredno od puknua sadr~e ovu deformacijsku energiju nezavisno od veli ine estica. Svaki put kad neka grupa estica jedini nog volumena zajedno doe do stanja neposredno od puknua, one sadr~e ovu istu energiju(3). Zaklju ujemo da je deformacijska energija pri maksimalnom naprezanju jednaka za jedini ni volumen u svakom stupnju usitnjavanja: ukupna deformacijska energija = K1 x broj stupnjeva smanjivanja Ako je prosje na ulazna veli ina estica x1, a izlazna veli ina estica xn u jedini nom volumenu, broj stupnjeva usitnjavanja je n, a opseg usitnjavanja za svaki stupanj je r, tada je :  EMBED Equation.3  i  EMBED Equation.3  ili ukupna deformacijska energija =  EMBED Equation.3 , tj.  EMBED Equation.3  Taplin je primjetio da Kickov zakon pokriva energiju potrebnu do to ke pucanja (loma), a Rittingerov zakon pokriva energiju stvarno potrebnu za lom nakon ato je estica dovedena do stanja deformacije u kojoj se lom dogaa, te da je omjer ove dvije koli ine energija povezan sa veli inom doti ne estice:  EMBED Equation.3  gdje je:  EMBED Equation.3 - energija potrebna za pripremu loma (Kick)  EMBED Equation.3 - energija potrebna za lom (Rittinger) x  veli ina estica Prema tome, kada je x velik Kickov zakon prevladava, a kada je x mali dominira Rittingerov zakon(3). Bond je razvio jednad~bu za sadr~aj energije materijala zasnovan na funkciji, recipro nom kvadratnom korjenu veli ine otvora kroz koju prolazi 80% materijala, prikazanu kao vrijednost Z-1/2 (u literaturi poznata i kao x80). Prema tome, za estice beskona ne veli ine ova funkcija je nula. Bond zaklju uje da se svaki proces usitnjavanja odnosno drobljenja mo~e smatrati meufazom u lomu estica beskona ne veli ine do beskona nog broja estica nulte veli ine. Energija koju posjeduje skupina estica proporcionalna je Z-1/2 (x80) i energiji svojstvenoj skupini estica odreenoj sa Z1 koja se predrobi u skupinu estica odreenu sa Z2 proporcionalna je razlici Z2-1/2 (x80,1) - Z1-1/2 . (x80,2). Takoer je proporcionalna energiji (W) potrebnoj za lom estica veli ine Z1 u estice veli ine Z2. Prema tome,  EMBED Equation.3  gdje je K specifi na konstanta materijala. U obliku ove jednad~be gdje je K zamjenjen s 10Wi, Wi se naziva Bondov indeks pa je:  EMBED Equation.3  Holmes je predlo~io modifikaciju Bondove jednad~be uvratavajui eksponent r umjesto Bondovih 1/2 , tako da ona glasi:  EMBED Equation.3  Vrijednosti r Holmes je utvrdio za razli ite materijale i oni su dati tabelarno u literaturi. Nekoliko je autora pokuaalo povezati Rittingerove, Kickove i Bondove izraze jednom opom jednad~bom, jedan od tih pokuaaja je i Holmesov:  EMBED Equation.3  gdje je: W  upotrijebljena energija (ili izvraeni rad) d  veli ina estice d0  po etna veli ina estice R  doseg smanjivanja  x SLIKA 2.4: Kumulativni prikaz podru ja zakonitosti U skladu s gore iznesenim teorijskim razmatranjima, razli iti su istra~iva i predlagali metode za usporeivanje na ina na koji se materijali mogu zdrobiti odnosno usitniti. U metodama koje su predlagali osnovna ideja je bila da se u proces ulazi sa materijalom poznate i odreene raspodjele veli ina estica. Jedan na in je da se odreuje upotrebljena energija za smanjivanje veli ine estica materijala do druge odreene raspodjele veli ina u to no odreenim uvjetima i specificiranoj opremi ili se nakon podvrgavanja materijala to no definiranom procesu drobljenja odreuje veli ina raspodjele estica(3). Prevoenje takvih rezultata u indeks predrobivosti odnosno meljivosti mogu je na nekoliko na ina. Jedan od njih je da se recipro na vrijednost tih rezultata naziva se otpornost prema predrobljvanju. Prvi je sa takvim razmatranjima zapo eo Stadtler koji je predlo~io da se sadr~aj energije razli itih nazivnih frakcija mo~e procjeniti prema Kickovom zakonu, posebno ako je raspon sita odreen tako da se zbog jednostavnosti ra unanja podvrgava geometrijskim odnosima. Prema tome, ako je svako sito u slogu povezano sa prethodnim i sljedeim, recimo korijenom od dva, tada to no odreeni opseg smanjivanja veli ine estica postoji izmeu svih sita u slogu(3). Prema Kickovom zakonu energija povezana sa n-tom veli inom otvora sita je n puta povezana sa prvom veli inom otvora sita u slogu. Carey i Stairmand su razvili ovu ideju odreujui stvarnu energiju povezanu sa raspodjelom veli ine estica materijala drobei materijal u jednostavnoj hidrauli koj preai. Konstruirali su graf za materijal iz kojega se energija mogla o itati za svaku veli inu estica te su, koristei isti na in kao i Stadtler, uspostavili vezu izmeu upotrijebljene energije i raspodjele veli ine estica. Drobljivost odnosno meljivost se u zadnje vrijeme odreuje ispitivanjima na pa~ljivo odabranim i definiranim aparaturama prema strogo propisanim pravilima. Hardgrove je razvio aparaturu na bazi mlina sa prstenima i kuglama u koji se stavlja 50 grama materijala veli ine estica izmeu 16 i 30 mesh ASTM, rotirajui prsten se optetreti sa 64 lb te se mlin zavrti 60 okretaja. Odrauje se te~ina (W) materijala koja prolazi kroz sito 200 ASTM , a Hardgrove index je 13 + 6.93W. Bond je razvio nekoliko metoda za odreivanje Bondovog radnog indeksa (Wi). Prva metoda je odreivanje pomou mlina to no odreenih dimenzija s punjenjem od 285 kuglica ukupne mase 20125 grama. U mlin se stavlja 700 cm3 uzorka veli ine estica manje od 3.33 mm. Mlin se okree 100 puta brzinom od 70 okretaja u minuti nakon ega se materijal prosijava na situ zadanog otvora koji je dio sloga. Ostatak na situ se nadopuni do 700 cm3 i vraa u mlin. Mlin se rotira onoliko puta koliko je potrebno da na kraju ciklusa sadr~i 28.6% prolaza kroz sito zadanog otvora. Postupak se nastavlja sve dok masa materijala koja prolazi kroz sito po jednom okretaju nije konstantna. Ona se naziva G u gramima i naziva se meljivost odnosno drobljivost. Ako je F veli ina otvora sita kroz koji prolazi 80 % materijala nakon ispitivanja, a P je veli ina otvora sita kroz koji prolazi masa G, tada je Bondov radni indeks za mokro mljevenje odnosno drobljenje:  EMBED Equation.3  Vrijednost Bondova radnog indeksa za suho mljevenje mo~e se dobiti uveanjem radnog indeksa za mokro mljevenje za 1.3 puta. Za mlinove sa aipkama Bondov radni indeks se dobiva ispitivanjem na standardiziranom mlinu u kojem je 21 aipka ukupne mase 33380 grama. Uzorak volumena 1250 cm3 i veli ine estica ispod 1.25 mm okree se brzinom 46 okretaja u minuti. Postupak odreivanja je isti kao za mlin sa kuglicama, te se Bondov radni indeks za mokro mljevenje izra unava iz slijedeeg izraza:  EMBED Equation.3  Bondov udarni test se izvodi sa dva jednaka ekia te~ine 30 libri koji su podeaeni tako da istovremeno udaraju u suprotne strane ispitivanog uzorka. Tijekom ispitivanja uzorak je postavljen tako da je njegov naju~i promjer (d) okrenut ekiima. ekii se di~u na zadanu visinu i puataju se da padnu na uzorak. Nakon toga podi~u se na sve veu visinu te udaraju uzorak dok se uzorak ne zdrobi. Ispituje se deset uzoraka i izra unava srednja vrijednost.  EMBED Equation.3  gdje je: I  otpornost na drobljenje udarom m( )  masa ekia h( )  krajnja visina ekia d  debljina uzorka Bondov radni indeks za mokro drobljenje odnosno mljevenje je:  EMBED Equation.3  gdje je  EMBED Equation.3  gustoa uzorka. Holmes je primjetio vezu izmeu P i G, gdje je P veli ina otvora sita kroz koju prolazi G, vrijednosti odreene standardiziranim Bondovim bubnjastim mlinovima:  EMBED Equation.3  tako da logaritamski prikaz  EMBED Equation.3  EMBED Equation.3  daje pravac. Koeficijent b Holmes je odredio za mnoge mineralne materijale, npr. kvarc 0.77, vapnenac 0.45, itd. Bond je predlo~io vezu izmeu njegovog radnog indeksa i Hardgrovog radnog indeksa:  EMBED Equation.3  ali ispitivanja na airokom rasponu mineralnih materijala pokazala su da je ova relacija samo pribli~no to na. U in~enjerskoj praksi ispitivanja otpornosti prema predrobljavanju kamenih agregata koji se koriste u graevinarstvu (cestogradnja, betonske konstrukcije) u meunarodnoj uporabi su metoda "Los Angeles" i metoda "Impact". Metoda "Los Angeles" potekla je iz SAD-a gdje je zbog svojih povoljnih karakteristika naiala na airoku primjenu kod utvrivanja otpornosti razli itih materijala na udarno  habajua optereenja. Drobljenje materijala je izazvano udaranjem i habanjem zrna o zrno, zrna o eli nu kuglu i zrna o bubanj. U odreenoj to ki okretanja bubnja agregat s kuglama udara u pre ku unutar bubnja koja ih di~e do trenutka kada pod utjecajem sile te~e oni padaju natrag na suprotnu stijenku bubnja, te tako dolazi do udaranja i habanja kamenog agregata. Los Angeles koeficijent, LA,(prema EN 1097  2) definira se kao postotak materijala koji prolazi kroz sito 1,6 mm nakon zavraetka ispitivanja. Stupanj otpornosti agregata prema predrobljavanju odreen metodom "Impact" zapravo predstavlja otpornost agregata prema predrobljavanju u dinami kim uvjetima ali, za razliku od metode "Los Angeles" , u situaciji kad zrna imaju meusobnu potporu i kad nije istovremeno prisutno i habajue optereenje na zrna agregata. Ispitivanje otpornosti na predrobljavanje metodom "Impact" je (prema EN 1097-2) predvieno kao alternativno metodi "Los Angeles" koja je referentna metoda. EKSPERIMENTALNI DIO METODA "LOS ANGELES" Oprema Ispitivanje metodom "Los Angeles" (EN 1097-2) obavlja se u eli nom bubnju ( 8.1), zatvorenom na oba kraja, iji je unutarnji promjer 7115 mm, a unutarnja du~ina 5085 mm (slika 1). Bubanj je montiran na dvije horizontalne osovine tako da se mo~e okretati oko svoje horizontalne osi s tim da osovine ne ulaze u bubanj. Na bubnju se nalazi otvor airine 150mm za ubacivanje kugli i ispitivanog uzorka. Za zatvaranje otvora postoji poklopac koji je tako izveden da nastavlja kontinuitet stijenke bubnja. Poklopac hermeti ki zatvara otvor kako bi se sprije io gubitak materijala zbog ispraaivanja. Tijekom rada poklopac je sa etiri vijka pritegnut uz bubanj. U bubnju je montirana pre ka du~ cijele izvodnice, airine 902 mm. Udaljenost pre ke od najbli~eg riba otvora bubnja ne smije biti manja od 380 mm u smjeru rotacije. Time se spre ava da materijal i kugle prilikom rotacije padaju na poklopac. Bubanj se pokree preko elektromotora koji je spojen na jednu od osovina. Broj anik vezan uz aparat broji okretaje bubnja te zaustavlja vrtnju (rad elektromotora) nakon ato bubanj napravi 500 okretaja. Brzina okretanja bubnja je od 31 do 33 okretaja u minuti. Ispod bubnja se nalazi metalna taca u koju se istresa ispitivani uzorak i kugle nakon zavraetka ispitivanja. Provedba ispitivanja Kumulativni uzorci svih frakcija (2/4, 4/8, 8/11, 11/16 mm) uzeti sa asfaltne baze Trstenik etvrtanjem su razdjeljeni na 6 uzoraka iste frakcije za ispitivanje. Tri uzorka svake frakcije odvojena su za ispitivanje metodom "Los Angeles", a tri uzorka za ispitivanje metodom "Impact". Prije odreivanja ulaznih granulometrija uzorci su oprani na situ 0,063 mm i osuaeni u suanici na (1055) C. 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Na svim uzorcima provedena je granulometrijska analiza na karakteristi nom slogu sita (0.09, 0.25, 0.71, 2, 4, 8, 11.2, 16 mm) iz kojih je rezultata izra unata ulazna povraina zrnja (PZU). Uzorci su zatim pojedina no ispitani metodom "Los Angeles". Uzorak se stavi u bubanj uz pripadajui broj i masu kugli za svaku frakciju (prema EN 1097  2, Dodatak A). Za frakciju 2/4 u EN 1097  2 nije naveden broj i masa kugli ve je te vrijednost utvrene za potrebe ovog ispitivanja ekstrapolacijom iz normom zadanih parametara za ostale frakcije. Broj anik se namjesti na 500 okretaja i uklju i rad elektromotora preko glavne sklopke. Po zavraetku 500 okretaja skine se poklopac otvora te se ispitani uzorak zajedno s kuglama istrese u metalnu tacu ispod bubnja. Nakon ispitivanja na uzorcima se provodi granulometrijska analiza na istom karakteristi nom slogu sita ( 0.09, 0.25, 0.71, 2, 4, 8, 11.2, 16 mm). METODA "IMPACT" Oprema Ispitivanje otpornosti na predrobljavanje metodom "Impact" (EN 1097  2) obavlja se na aparaturi koja se sastoji od fiksnog i pomi nog dijela (8.2). Fiksni dio se sastoji od postolja koje je u etiri to ke u vraeno na izdignutu betonsku plohu, te cilindri ne posude za uzorak unutarnjeg promjera (1700.1) mm, debljine stijenki (350.1) mm, visine 200 mm. Tu ak promjera stope (1681) mm se lagano pola~e na uzorak u posudi prije ispitivanja. Pomi ni dio aparata je eki mase (500.1) kg koji se di~e i spuata po vodilicama. Na vodilicama je obilje~ena visina 370 mm s koje se eki puata da pada. 3.2.2 Provedba ispitivanja Kako bi se osigurala usporedivost rezultata ispitivanja otpornosti na predrobljavanje metodom "Impact" i metodom "Los Angeles", ispitivanje metodom "Impact" je u tu svrhu modificirano. Po tri uzorka za ispitivanje izdvojena iz kumulativnog uzorka svake frakcije oprana su na situ 0.063 mm (prema EN 933 -1) i osuaena u suanici na (1055) C. Nakon pranja i suaenja svaki uzorak za ispitivanje je odvagnut na 30005 grama. Na svakom uzorku provedena je granulometrijska analiza na karakteristi nom slogu sita (0.09, 0.25, 0.71, 2, 4, 8, 11.2, 16 mm) iz kojih je rezultata izra unata ulazna povraina zrnja (PZU). Uzorci su zatim pojedina no ispitani metodom "Impact". Uzorak za ispitivanje se uspe u posudu za uzorak, izravna rukom, te se na njega se lagano polo~i tu ak. eki se ureajem za podizanje podigne na visinu 370 mm i pusti da slobodno padne na tu ak. Svaki uzorak se udari deset puta. Nakon 10 udaraca uzorci se vade i na njima se provodi granulometrijska analiza na istom karakteristi nom slogu sita (0.09, 0.25, 0.71, 2, 4, 8, 11.2, 16 mm). REZULTATI Kako bi se dobili relevantni rezultati ispitivanja kamenog agregata na predrobljavanje, kao ato je prethodno navedeno, ispitano je cijelo podru je (od 2mm do 16 mm) veli ina kamenog agregata eruptivnog porijekla koje se koristi u proizvodnji asfaltnih mjeaavina. Od svake nazivne frakcije (2/4, 4/8, 8/11, 11/16 mm) uzeto je ukupno aest uzoraka. Tri uzorka su ispitana po metodi "Los Angeles", a tri uzorka po metodi "Impact". Ukupno je ispitano 12 uzoraka po metodi "Los Angeles" i 12 uzoraka po metodi "Impact". Naknadno je zbog bolje interpretacije rezultata ispitano12 uzoraka nazivne frakcije 4/8 mm metodom  Los Angeles . Za svaki uzorak ispitan po obje metode rezultat je granulometrijska krivulja prije i nakon ispitivanja. Zbog bolje preglednosti granulometrijske krivulje za svaku nazivnu frakciju prije i poslje ispitivanja prikazane su tabli no (Tablica 2  13), te na istom dijagramu (Dijagram 1 - 12). U karakteristi an slog sita prilikom granulometrijske analize nakon ispitivanja po metodi  Los Angeles umetnuto je sito otvora 1.6 mm radi odreivanja Los Angeles koeficijenta prema EN 1097  2. LA koeficijent se izra~ava kao postotni omjer izmeu mase agregata koji je proaao kroz sito otvora 1.6 mm i po etne mase uzorka (Tablica 1). Tablica 1: Vrijednosti LA - koeficijenata Frakcija LA - koeficijentBroj uzorka123Sr. vrijed. 2/4  21,27 21,5 20,5 21,09 4/8  13,05 13,45 13,25 13,25 8/11  11,55 11,63 12,2 11,79 11/16  13,0 13,1 12,95 13,02 METODA  Los Angeles Tablica 2: Prikaz rezultata granulometrijske analize za nazivnu frakciju 2/4 mm SITA (mm)PRIJE PREDROBLJAVANJA Prolaz kroz sito,%POSLIJE PREDROBLJAVANJA Prolaz kroz sito, %Broj uzorkaBroj uzorka1231230.06300032,92,80.090,10,10,23,133,20.250,30,30,254,94,80.7111,11,3999,22.015,514,91535,735,8344.094,894,892,896,497968.099,599,598,899,899,999,511.2100100100100100100 Dijagram 1 METODA  Los Angeles Tablica 3: Prikaz rezultata granulometrijske analize za nazivnu frakciju 4/8 mm SITA (mm)PRIJE PREDROBLJAVANJA Prolaz kroz sito,%POSLIJE PREDROBLJAVANJA Prolaz kroz sito, %Broj uzorkaBroj uzorka1231230.0630002,83,12,90.090,30,20,33,23,53,30.250,70,60,84,85,150.711,31,11,28,18,48,22.02,92,72,517,517,817,64.014,914,11540,440,640,28.098,298,898,699,399,399,211.2100100100100100100  Dijagram 2 METODA  Los Angeles Tablica 4: Prikaz rezultata granulometrijske analize za nazivnu frakciju 8/11 mm SITA (mm)PRIJE PREDROBLJAVANJA Prolaz kroz sito,%POSLIJE PREDROBLJAVANJA Prolaz kroz sito, %Broj uzorkaBroj uzorka1231230.06300032,92,80.090,30,30,23,63,53,30.250,90,8154,94,70.711,51,51,57,47,272.02,22,32,312,612,2124.02,72,52,619,71918,58.019,520,1205756,555,211.290,291,291,29696,295,516.0100100100100100100 Dijagram 3  METODA  Los Angeles Tablica 5: Prikaz rezultata granulometrijske analize za nazivnu frakciju 11/16 mm SITA (mm)PRIJE PREDROBLJAVANJA Prolaz kroz sito,%POSLIJE PREDROBLJAVANJA Prolaz kroz sito, %Broj uzorkaBroj uzorka1231230.0630003,63,43,40.090,40,40,54,144,20.250,90,80,95,55,35,20.711,41,31,57,477,22.01,71,91,810,51010,24.01,92,52,215,114,214,98.034,63,9323131,211.210,212,711,153,752,95316.094,796,29798,69898,231.5100100100100100100 Dijagram 4  EMBED Excel.Chart.8 \s  METODA  Los Angeles Tablica 6: Prikaz rezultata granulometrijske analize za nazivnu frakciju 4/8 mm  6 kugli SITA (mm)PRIJE PREDROBLJAVANJA Prolaz kroz sito,%POSLIJE PREDROBLJAVANJA Prolaz kroz sito, %Broj uzorkaBroj uzorka1231230.0630002,832,90.0900,103,13,33,40.2500,10,14,24,440.7100,20,16,66,86,52.00,20,80,613,814,3144.08,39,5935,535,6348.09797989998,698,511.2100100100100100100 Dijagram 5 METODA  Los Angeles Tablica 7: Prikaz rezultata granulometrijske analize za nazivnu frakciju 4/8 mm  8 kugli SITA (mm)PRIJE PREDROBLJAVANJA Prolaz kroz sito,%POSLIJE PREDROBLJAVANJA Prolaz kroz sito, %Broj uzorkaBroj uzorka1231230.0630003,33,430.090,10,10,13,83,940.250,10,20,15,25,35,20.710,20,30,28,38,48,22.00,50,50,417,917,4174.08,45,8742,939,839,28.097,596,79799,599,19911.2100100100100100100 Dijagram 6  METODA  Los Angeles Tablica 8: prikaz rezultata granulometrijske analize za nazivnu frakciju 4/8 mm  10 kugli SITA (mm)PRIJE PREDROBLJAVANJA Prolaz kroz sito,%POSLIJE PREDROBLJAVANJA Prolaz kroz sito, %Broj uzorkaBroj uzorka1231230.0630004,34,54,20.090004,94,950.250006,76,660.710,10,10,210,710,4102.00,40,70,522,92222,54.09,88,8951,949,4498.097,897,297,699,599,599,311.2100100100100100100 Dijagram 7  METODA  Los Angeles Tablica 9: Prikaz rezultata granulometrijske analize za nazivnu frakciju 4/8 mm  12 kugli SITA (mm)PRIJE PREDROBLJAVANJA Prolaz kroz sito,%POSLIJE PREDROBLJAVANJA Prolaz kroz sito, %Broj uzorkaBroj uzorka1231230.0630004,94,54,20.090005,55,55,20.250007,67,27,10.710,10012,31211,52.00,50,30,426,426,225,94.08,29,2955,756,2558.097,197,497,299,799,599,511.2100100100100100100 Dijagram 8  METODA  Impact Tablica 10: Prikaz rezultata granulometrijske analize za nazivnu frakciju 2/4 mm SITA (mm)PRIJE PREDROBLJAVANJA Prolaz kroz sito,%POSLIJE PREDROBLJAVANJA Prolaz kroz sito, %Broj uzorkaBroj uzorka1231230.0630000,40,70,50.090,10,10,10,50,80,60.250,30,20,30,91,310.710,911,12,22,92,72.015,214,91520,421,9224.093,894,29596,496,7978.099,59899,199,899,799,811.2100100100100100100 Dijagram 9  METODA  Impact Tablica 11: Prikaz rezultata granulometrijske analize za nazivnu frakciju 4/8 mm SITA (mm)PRIJE PREDROBLJAVANJA Prolaz kroz sito,%POSLIJE PREDROBLJAVANJA Prolaz kroz sito, %Broj uzorkaBroj uzorka1231230.06300010,60,80.090,30,20,11,10,70,90.250,60,60,51,411,20.711,21,112,11,722.032,82,94,84,54,14.01514,91518,218,918,18.098,19897,298,197,99711.2100100100100100100 Dijagram 10  METODA  Impact Tablica 12: Prikaz rezultata granulometrijske analize za nazivnu frakciju 8/11 mm SITA (mm)PRIJE PREDROBLJAVANJA Prolaz kroz sito,%POSLIJE PREDROBLJAVANJA Prolaz kroz sito, %Broj uzorkaBroj uzorka1231230.0630000,50,40,50.090,10,10,10,60,50,60.250,70,60,81,111,20.711,31,21,42,42,222.02,22,22,34,84,244.02,932,86,96,66,68.02019,819,921,62221,411.2898787,489,489,689,516.0100100100100100100 Dijagram 11  EMBED Excel.Chart.8 \s  METODA  Impact Tablica 13: prikaz rezultata granulometrijske analize za nazivnu frakciju 11/16 mm SITA (mm)PRIJE PREDROBLJAVANJA Prolaz kroz sito,%POSLIJE PREDROBLJAVANJA Prolaz kroz sito, %Broj uzorkaBroj uzorka1231230.0630000,60,60,50.090,40,30,30,70,70,60.250,90,90,80,80,80,80.711,41,51,311,112.01,71,61,61,61,81,74.01,921,82,733,18.0333,26,28,17,511.210,210,210,120,32322,316.094,795969594,69531.5.0100100100100100100 Dijagram 12  EMBED Excel.Chart.8 \s  5 RASPRAVA Svojstvo kojim ~elimo okarakterizirati kameni agregat je otpornost prema smanjivanju veli ine estica, odnosno predrobljavanju dvama razli itim procesima: -procesom drobljenja u bubnju s to no definiranim brojem, masom i veli inom kugli, --procesom drobljenja udarnim optereenjem padajueg ekia to no odreene mase, visine pada i broja udara Otpornost prema predrobljavanju kamenog materijala ne smije ovisiti o granulometriji frakcija na kojima se odreuje to svojstvo ve bi trebala biti jednozna no vezana uz svojstva materijala od kojih su zrna na injena. Na neki se na in otpornost kamenog agregata prema predrobljavanju mo~e shvatiti i kao vrstoa agregata jer je ona funkcija vrstoe svakog pojedinog zrna u kamenom agregatu. Ovisno o polo~aju i obliku zrna u odnosu na vrstu i smjer naprezanja, drobljenje svakog zrna kontrolira njegova stati ka ili dinami ka tla na, smi na, vla na i savojna vrstoa. U graevinskoj konstrukciji ili u laboratorijskom uzorku naj eae istovremeno djeluju razli ita optereenja na svako zrno agregata. Uz navedene imbenike, odreivanje otpornosti prema predrobljavanju dodatno ote~ava i problem pravilnog prikaza rezultata nakon izvraenog drobljenja. Naj eae se mjeri koli ina agregata koja poslije drobljenja prolazi kroz neko sito manjih otvora od promjera najmanjih zrna prije drobljenja. Takvim na inom prikaza rezultata ne izmjeri se onaj dio uzorka koji se predrobio ali se nije dovoljno usitnio da proe kroz propisano mjerno sito, ato mo~e dovesti do pogreanih zaklju aka o kvaliteti kamenog materijala. Rezultati ispitivanja po metodi "Los Angeles" i metodi "Impact" egzaktno ne stavljaju u vezu broj i veli inu zrna prije i poslije ispitivanja. Dugogodianja praksa provoenja ispitivanja metodom "Los Angeles" pokazala su suprotno, tj. veliku zavisnost mjerenih vrijednosti predrobljavanja o granulometriji ispitivanih frakcija. Ta dugogodianja ispitivanja provoena su po 'staroj' metodi (HRN B.B8. 045), odnosno nije postojala direktna veza izmeu standardnih frakcija (0/4,2/4, 4/8, 8/11, 11/16,16/32 mm) i gradacija koriatenih za ispitivanje po metodi "Los Angeles". Novim normama EN 13043 i EN 1097-2 ta veza je 'uspostavljena' jer se uzorci za ispitivanje po metodi "Los Angeles" pripravljaju iz standardnih frakcija na standardnim sitima kvadrati nih otvora. Metoda "Impact" nije se prije provodila kao ispitivanje otpornosti materijala prema predrobljavanju kod standardnih frakcija, dok je to novim normama propisano. Da bi se dobili relevantni rezultati ispitivanja kamenog agregata na predrobljavanje, kao ato je prethodno navedeno, ispitano je cijelo podru je (od 2mm do 16 mm) veli ina kamenog agregata eruptivnog porijekla koje se koristi u proizvodnji asfaltnih mjeaavina. Velika pravilnost ovisnosti predrobljavanja o po etnom granulometrijskom sastavu materijala navodi na pokuaaj pronala~enja matemati ke funkcije koja opisuje tu ovisnost. U ovom radu to e se pokuaati napraviti preko ukupne povraine zrnja koja je zapravo mjera granulometrijskog sastava  ato je vei udio sitnih zrna ukupna povraina zrnja je vea i obratno. Iz rezultata granulometrijske analize za svaki pojedina ni uzorak ispitan po obje metode izra unata je povraina zrnja prije (PZU) i poslje (PZI) ispitivanja. Rezultati su prikazani tabli no za svaku metodu zasebno. Povraina zrna izra una se iz izraza:  EMBED Equation.3   EMBED Equation.3  gdje PZ  ukupna povraina zrnja (m2 ) ci  volumni udio pojedine frakcije kamenog materijala xi  promjer srednje veli ine zrna Ovaj izraz je izveden na temelju dviju aproksimacija: - volumen zrna kamenog agregata aproksimiran je volumenom kugle istog promjera - promjer srednje veli ine zrna u frakciji kamenog materijala odreenih granica veli ine zrna (xi , xi+1 ) izra~en je relacijom:  EMBED Equation.3  Volumni udio pojedine frakcije izra unava se iz rezultata granulometrijske analize gdje su rezultati dani u masenim postocima, preko izraza  EMBED Equation.3  gdje je WFi  maseni udio pojedine frakcije  EMBED Equation.3 - gustoa pojedine frakcije (s porama)  EMBED Equation.3 - srednja gustoa s porama koja se izra unava iz izraza:  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  Zbog ranije navedenih aproksimacija, teorijski odreena povraina zrnja kamenog agregata vjerovatno odstupa od to ne vrijednosti. Unato  tomu za sada se kao takva koristi budui se eksperimentom pokazalo da eventualne pogreake nebitno utje u na rezultat. 5.1 METODA "LOS ANGELES" Stavljanjem u omjer izra unatih povraina zrnja poslije (PZI) i prije (PZU) ispitivanja dobili smo podatak koliko se puta poveala povraina zrnja nakon predrobljavanja. Usporeujui podatke dobivene za frakciju 2/4 mm (6 kugli ukupne mase 260415 grama) i frakciju 11/16 mm (12 kugli ukupne mase 520820 grama) vidljivo je da je taj omjer kod frakcije 11/16 mm 2.7 puta vei nego kod frakcije 2/4 mm. Da bi se dobio podatak o promjeni povraine zrnja u odnosu na energiju prenesenu na agregat putem kugli u procesu drobljenja u bubnju, stavili smo u omjer broj kugli i prethodno izra unati omjer povraina zrnja poslje (PZI) i prije (PZU) ispitivanja u bubnju. Rezultati su prikazani u Tablici 14. Nakon izra unavanja dobiveni podaci uneseni su u dijagram (Dijagram 13) u kojem je na ordinati broj kugli kao mjera energije, a na apscisi omjer ukupne povraine zrnja poslje i ukupne povraine prije ispitivanja odnosno drobljenja. Iz dijagrama je vidljivo da omjeri gotovo linearno rastu od frakcije 2/4 mm iji je omjer najni~i do frakcije 11/16 mm iji je omjer najviai. Niske vrijednosti omjera za nazivnu frakciju 2/4 mm te visoke za frakciju 11/16 mm indiciraju zaklju ak da su sitnozrnati agregati otporniji na predrobljavanje od krupnozrnatih. Vidljivo je, takoer, da su vrijednosti izra unatih omjera za nazivne frakcije 4/8 mm i 8/11 mm vrlo bliske. Kako bi doali do boljih parametara za tuma enje ovog fenomena ispitana je jedna nazivna frakcija (4/8 mm) s etiri razli ita punjenja kugli. Ispitano je ukupno 12 uzoraka, tj. po tri uzorka za svako punjenje kugli (6, 8, 10 i 12 kugli to no odreene mase). Izra unate su povraine zrnja poslje (PZI) i prije (PZU) te njihov omjer stavljen u odnos sa brojem kugli. Rezultati su prikazani u Tablici 15. Nakon izra unavanja dobiveni podaci uneseni su u dijagram (Dijagram 14) u kojem je na ordinati broj kugli kao mjera energije, a na apscisi omjer ukupne povraine zrnja poslje i ukupne povraine prije ispitivanja odnosno drobljenja. Iz izlo~enih rezultata vidljivo je da su vrijednosti izra unatih  EMBED Equation.3  vrlo bliske za sva etiri razli ita punjenja kugli, odnosno povraina zrnja nakon predrobljavanja gotovo linearno raste s poveanjem mase odnosno broja kugli (Dijagram 14). Omjer  EMBED Equation.3  je  funkcija svojstva odnosno omjer koeficijenta promjene stanja i energije potrebne za tu promjenu U Tablici 4 date su vrijednosti LA  koeficijenta koji se izra~ava kao postotni omjer koli ine materijala koji je nakon procesa drobljenja u bubnju proaao kroz sito kvadrati nog otvora 1.6 mm i ukupne mase uzorka. Dobivene vrijednosti LA- koeficijenata indiciraju da se najviae predrobila frakcija 2/4 mm, dok su vrijednosti LA  koeficijenata ostalih frakcija prili no ujedna ene. Tablica 14: Obrada rezultata ispitivanja metodom Los Angeles na svim frakcijama Frakcija Broj kugli PZ (ulaz) (m2/100 cm2) PZ (izlaz) (m2/100 cm2) PZ(izlaz)/ PZ(ulaz) PZ(izl.)/PZ(ul.) Broj kugli EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  2/4 60,2878 0,28461,0454 1,04813,6324 3,68280,6054 0,61380,28671,05213,66970,61160,27941,04673,74620,6244 4/8 8 0,1594 0,15900,8647 0,86675,4247 5,45150,6781 0,68140,15740,87005,52730,69090,16020,86555,40260,6753 8/11 10 0,1212 0,11310,8584 0,85847,0825 6,97920,7083 0,69790,11890,84757,12780,71280,12920,86926,72750,6727 11/16 12 0,0893 0,08830,8691 0,8637 9,7324 9,77840,8110 0,81480,08820,86229,77550,81460,08750,85999,82740,8189 Prosje na masa pojedina ne kugle je 434 5 grama Dijagram 13  EMBED Excel.Chart.8 \s  Tablica 15: Obrada rezultata ispitivanja ispitivanja metodom Los Angeles na frakciji 4/8 mm Broj kugli PZ (ulaz) (m2/100 cm2) PZ (izlaz) (m2/100 cm2) PZ(izlaz)/ PZ(ulaz) PZ(izl.)/PZ(ul.) Broj kugli EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  60,1211 0,12810,8286 0,84656,8423 6,61561,1404 1,10250,13310,86866,52591,08760,13000,84226,47851,0797 8 0,1317 0,13140,9954 0,98757,5581 7,51330,9448 0,93920,13110,98167,48740,93590,13150,98557,49430,9368 10 0,1249 0,12651,1988 1,21979,5981 9,64160,9598 0,96410,12451,19859,62650,96260,13011,26199,70010,9700 12 0,1226 0,12481,3580 1,385011,0766 11,0960,9231 0,92470,12311,384711,24850,93740,12881,412210,96420,9137 Prosje na masa pojedina ne kugle je 434 5 grama Dijagram 14  EMBED Excel.Chart.8 \s  5.2 METODA "IMPACT" Za razliku od metode "Los Angeles" , kod metode "Impact" sila odnosno energija koja uzrokuje predrobljavanje materijala je uvijek ista. Zrna agregata su izlo~ena dinami kom udaru, a efekt habanja zrna o stijenke i zrna o zrno je puno manje izra~en nego kod metode "Los Angeles". Razmatranje rezultata ispitivanja zapo eto je stavljanjem u omjer izra unatih povraina zrnja poslje (PZI) i prije (PZU) ispitivanja da bi dobili podatak koliko se puta poveala povraina zrnja nakon predrobljavanja. Iz dobivenih koeficijenata vidljivo je da su poveanja povraine zrnja nakon predrobljavanja mnogostruko manja u odnosu na ispitivanja metodom  Los Angeles . Radi bolje preglednosti rezultati ovih razmatranja su prikazani u Tablici 16. Kod metode  Impact promatran je, za razliku od metode  Los Angeles , koeficijent promjene povraine zrnja prije i nakon predrobljavanja u odnosu na povrainu zrnja prije predrobljavanja (PZU) (Dijagram 15). Iz prikazanog dijagrama vidljivo je da se najmanje predrobila frakcija 2/4 mm, a najviae frakcija 11/16 mm. Takvi rezultati su bili o ekivani jer, kao ato je navedeno kod razmatranja ispitivanja metodom  Los Angeles , sitnozrnati agregati otporniji su na predrobljavanje od krupnozrnatih. Primjeuje se takoer da su koeficijenti promjene povraine zrnja prije i nakon predrobljavanja za nazivne frakcije 4/8 mm i 8/11 mm vrlo bliski ato indicira zaklju ak da je njihova otpornost prema predrobljavanju vrlo sli na. Tablica 16: Obrada rezultata ispitivanja metodom Impact na svim frakcijama Frakcija PZ (ulaz) (m2/100 cm2) PZ (izlaz) (m2/100 cm2) PZ(izlaz)/ PZ(ulaz) PZ (ulaz)/ PZ (izlaz) EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  EMBED Equation.3  2/40,2845 0,2829 0,4055 0,43481,4253 1,53720,7016 0,65390,28140,47571,69050,59150,28290,42321,49590,6685 4/8 0,1558 0,15760,2903 0,29711,8633 1,88460,5367 0,53060,15830,30221,90900,52380,15880,29881,88160,5314 8/11 0,1224 0,12220,2341 0,23481,9126 1,94810,5228 0,52040,11810,23021,94920,51300,12620,24021,98260,5254 11/16 0,0793 0,081460,1890 0,19052,3833 2,32320,4196 0,42750,08460,19242,27420,43970,08050,19022,31220,4232 Dijagram 15  EMBED Excel.Chart.8 \s  ZAKLJU AK Provedena su laboratorijska ispitivanja nazivnih frakcija kamenog agregata eruptivnog porijekla s ciljem iznala~enja egzaktnijeg na ina utvrivanja otpornosti kamenih agregata prema udarno  habajuim optereenjima po metodi  Los Angeles i metodi  Impact . Veliki nedostatak metode  Los Angeles je taj ato LA koeficijent ne prikazuje pravu otpornost prema drobljenju jer ne uzima u obzir promjene granulometrijskog stanja cijelog sustava ve samo jednog njegovog dijela. Tako se, uvidom u dobivene rezultate, mo~e zaklju iti da se najviae predrobila frakcija 2/4 mm ato nije to no. Pokazalo se da se uzorak, u pravilu, to viae predrobi ato mu je udio krupnijih zrna u granulometrijskom sastavu vei. Istra~ivanje provedeno u okviru ovog rada imalo je za cilj iznala~enje  funkcije svojstava , odnosno matemati ke ovisnosti promjene otpornosti prema predrobljavanju u odnosu na promjenu raspodjele ukupne povraine zrnja kao mjere granulometrijskog sastava. Razmatranjem dobivenih rezultata doalo se do zaklju ka da je omjer koeficijenta promjene stanja, odnosno promjene ukupne povraine zrnja, i energije potrebne za tu promjenu  funkcija svojstva , odnosno  EMBED Equation.3 . Zaklju eno je da takav koeficijent karakteristi an za ispitani materijal, te bolje izra~ava promjene granulometrijskih svojstava sustava prije i poslje ispitivanja prema metodi  Los Angeles jer obuhvaa promjene granulometrijskog stanja cjelokupnog sustava. Predla~e se da se taj koeficijent koristi kao izraz otpornosti kamenog agregata prema predrobljavanju metodom  Los Angeles . Ispitivanje otpornosti prema predrobljavanju metodom  Impact , za razliku od metode  Los Angeles , realnije oponaaa uvjete kojima je kameni agregat izlo~en u kolovoznim konstrukcijama jer zrna imaju meusobnu potporu . Razmatranjem dobivenih rezultata ispitivanja metodom  Impact vidljivo je da frakcije kamenog agregata pokazuju sli ne zakonitosti promjene ukupne povraine zrnja kao kod ispitivanja metodom  Los Angeles , ali bi za korelaciju rezultata bila potrebna detaljnija ispitivanja. LITERATURA (1) Polke, R.: Property functions for product development, 1. World Congress Particle Technology, Part I, Nurnberg (1986) 255 - 271 (2) Hraste, M.: Funkcije raspodjele veli ina estica, Kem. Ind, 41 (1992) 49 - 53 (3) Lowrison, G. C.: Crushing and Grinding, Butterworths(Co. Ltd, London 1974 (4) Ramljak, Z., Ladika, J., }enko, T.: Otpornost kamenog agregata prema predrobljavanju, Prvi hrvatski kongres o cestama, zbornik radova (1995) 567 - 570 (5) Hraste, M.: Mehani ko procesno in~enjerstvo, HINUS Zagreb 2003 EN 1097  2 Tests for mechanical and physical properties of aggregates  Part 2: Methods for the determination of resistance to fragmentation EN 13043 Aggregates for bituminous mixtures and surface treatments for roads, airfields and other trafficked areas PRILOZI 8.1 STROJ "LOS ANGELES"  EMBED PBrush  8.2 STROJ "IMPACT"   EMBED PBrush  }IVOTOPIS  Luka Krni roen je u `ibeniku 20. listopada 1975. U rodnom gradu zavraava osnovnu akolu i 1990. upisuje Prirodoslovno  matemati ku Gimnaziju u `ibeniku. Maturira s vrlodobrim uspjehom i 1995. upisuje Fakultet kemijskog in~enjerstva tehnologije u Zagrebu. Na drugoj godini studija pozvan je za demonstratora iz kolegija Opa i anorganska kemija. Nakon odsluaanih predavanja 2000. godine honorarno se zapoaljava u Cestograevnom laboratoriju Instituta graevinarstva Hrvatske na poslovima ispitivanja fizi ko  mehani kih i tehni ko  tehnoloakih svojstava kamenih agregata za uporabu u graevinarstvu, gdje izrauje diplomski rad.     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