ISSN 1408-7073 RMZ - MATERIALS AND GEOENVIRONMENT PERIODICAL FOR MINING, METALLURGY AND GEOLOGY RMZ - MATERIALI IN GEOOKOLJE REVIJA ZA RUDARSTVO, METALURGIJO IN GEOLOGIJO RMZ-M&G, Vol. 55, No. 1 pp. 1-146 (2008) Ljubljana, February 2008 Historical Review More than 80 years have passed since in 1919 the University Ljubljana in Slovenia was founded. Technical fields were joint in the School of Engineering that included the Geologic and Mining Division while the Metallurgy Division was established in 1939 only. Today the Departments of Geology, Mining and Geotechnology, Materials and Metallurgy are part of the Faculty of Natural Sciences and Engineering, University of Ljubljana. Before War II the members of the Mining Section together with the Association of Yugoslav Mining and Metallurgy Engineers began to publish the summaries of their research and studies in their technical periodical Rudarski zbornik (Mining Proceedings). Three volumes of Rudarski zbornik (1937, 1938 and 1939) were published. The War interrupted the publication and not until 1952 the first number of the new journal Rudarsko-metalurški zbornik - RMZ (Mining and Metallurgy Quarterly) has been published by the Division of Mining and Metallurgy, University of Ljubljana. Later the journal has been regularly published quarterly by the Departments of Geology, Mining and Geotechnology, Materials and Metallurgy, and the Institute for Mining, Geotech-nology and Environment. On the meeting of the Advisory and the Editorial Board on May 22nd 1998 Rudarsko-metalurški zbornik has been renamed into "RMZ - Materials and Geoenvironment (RMZ -Materiali in Geookolje)" or shortly RMZ - M&G. RMZ - M&G is managed by an international advisory and editorial board and is exchanged with other world-known periodicals. All the papers are reviewed by the corresponding professionals and experts. RMZ - M&G is the only scientific and professional periodical in Slovenia, which is published in the same form nearly 50 years. It incorporates the scientific and professional topics in geology, mining, and geotechnology, in materials and in metallurgy. The wide range of topics inside the geosciences are welcome to be published in the RMZ -Materials and Geoenvironment. Research results in geology, hydrogeology, mining, geotechnology, materials, metallurgy, natural and antropogenic pollution of environment, biogeochemistry are proposed fields of work which the journal will handle. RMZ - M&G is co-issued and co-financed by the Faculty of Natural Sciences and Engineering Ljubljana, and the Institute for Mining, Geotechnology and Environment Ljubljana. In addition it is financially supported also by the Ministry of Higher Education, Science and Technology of Republic of Slovenia. Editor in chief Table of Contents - Kazalo Internal oxidation of Cu-C and Ag-C composites Notranja oksidacija Cu-C in Ag-C kompozitov Čevnik, G., Kosec, G., Kosec, L., Rudolf, R., Kosec, B., Anžel, I. Composition and morphology of diborides in Al-Ti-B alloys after annealing at 1873 K Sestava in morfologija diboridov v zlitinah Al-Ti-B po žarjenju na 1873 K Zupanič, F....................................................................................................................... 7 Tool for programmed open-die forging - case study Orodje za programsko vodeno prosto kovanje - študija primera Bombač, D., Fazarinc, M., Kugler, G., Turk, R......................................................... 19 A laboratory test for simulation of solidification on Gleeble 1500D thermo-mechanical simulator Laboratorijski test simulacije strjevanja na termo-mehanskem simulatorju Gleeble 1500D Bradaskja, B., Koruza, J., Fazarinc, M., Knap, M., Turk, R...................................... 31 Comparative test of active and passive multichannel analysis of surface waves (MASW) methods and microtremor HVSR method Primerjalni test aktivne in pasivne večkanalne analize površinskih valov (MASW) ter metode mikrotremorjev (HVSR) Gosar, A., Stopar, R., Rošer, J..................................................................................... 41 Application of seismic tomography in investigations of the motorway alignment in the Šentvid tunnel area Uporaba seizmične tomografije pri raziskavah AC trase na območju predora Šentvid Rošer, J., Stopar, R., Gosar, A..................................................................................... 67 Surveying for geophysical exploration, using a single-frequency global navigation satellite system receiver capable of 30 cm horizontal kinematical positioning uncertainty Uporaba enofrekvenčnega sprejemnika GNSS s 30 cm negotovostjo v kinematičnem načinu dela za terenske geofizikalne preiskave Dimc, F., Mušič, B., Osredkar, R.................................................................................. 85 1 The possibility of using homogeneous (projective) coordinates in 2D measurement exercises Možnost uporabe homogenih (projektivnih) koordinat v dvodimenzionalnih merskih nalogah Ganić, A., Vulić, M., Runovc, F., Habe, T. ................................................................... 111 How we calculate volume with the use of "NTF" method Kako izračunamo volumen z uporabo metode "NTF" Durgutović, A., Vulić, M.............................................................................................. 127 Strokovna literatura Professional literature Kos, M............................................................................................................................ 135 Author s Index, Vol. 55, No. 1 ................................................................................................................................................................136 Instructions to Authors ........................................................................................................................................................................................137 Template ............................................................................................................................................................................................................................................140 Internal oxidation of Cu-C and Ag-C composites Notranja oksidacija Cu-C in Ag-C kompozitov Gabrijela Cevnik1,3, Gorazd Kosec2,3, Ladislav Kosec3, Rebeka Rudolf 4, Borut Kosec3, Ivan Anžel 4 1METAL Ravne d.o.o., Koroška cesta 14, SI-2390 Ravne na Koroškem, Slovenia; E-mail: gcevnik@metalravne.com 2ACRONI d.o.o., Cesta Borisa Kidriča 44, SI-4270 Jesenice, Slovenia; E-mail: gorazd.kosec@acroni.si 3University of Ljubljana, Faculty of Natural Sciences and Engineering, Aškerčeva cesta 12, SI-1000 Ljubljana, Slovenia; E-mail: kosec@ntf.uni-lj.si, borut.kosec@ntf.uni-lj.si 4University of Maribor, Faculty of Mechanical Engineering, Smetanova ulica 17, SI-2000 Maribor, Slovenia; E-mail: rebeka.rudolf@uni-mb.si, ivan.anzel@uni-mb.si Received: December 3, 2007 Accepted: January 11, 2008 Abstract: The internal oxidation in copper-carbon and silver-carbon composites occurs when they are exposed to air or oxygen at high temperature. Solubility of carbon in copper or in silver is very low. The kinetics of oxidation at high temperature and activation energy were determined and the mechanism of internal oxidation was analysed. The kinetics of internal oxidation was determined for both cases and it is depended from the diffusion of oxygen following parabolic time dependence according to Wagner's theory. The activation energy for Cu-C composite is 70.5 kJ/mol, and for Ag-C composite is 50.1 kJ/mol, what is in both cases close to the activation energy for the volume diffusion of oxygen in copper or in silver. In both cases gas products are formed during the internal oxidation of composites. In the internal oxidation zone pores, bubbles occur. The carbon oxidates directly with the oxygen from solid solution as long there is a contact, which breaks down with the presence of gas products. Then the oxidation occurs over the gas mixture of CO and CO2. Izvleček: Pri visokih temperaturah kompoziti bakra in srebra z ogljikom na zraku ali v kisiku reagirajo po mehanizmu notranje oksidacije. Topnost ogljika v trdnem bakru in trdnem srebru je zelo majhna. Analizirali smo kinetiko oksidacije kompozitov, določili aktivacijsko energijo in mehanizem notranje oksidacije. Kinetika oksidacije je pri obeh skupinah materialov odvisna od difuzije kisika in sledi parabolični odvisnosti od časa v skladu z Wa-gnerjevo teorijo. Aktivacijska energija procesa je za kompozit Cu-C enaka 70,5 kJ/mol, za kompozit Ag-C pa 50,1 kJ/mol, kar je blizu aktivacijski energiji za volumsko difuzijo kisika v trdnem bakru oziroma srebru. Pri oksidaciji kompozita nastajajo plinski produkti. Oksidacija ogljika poteka neposredno s kisikom iz trdne raztopine, ko pa se zaradi nastanka plinske faze stik prekine, pa preko plinske zmesi CO in CO2. Key words: internal oxidation, internal oxidation zone (IOZ), composite, copper, silver, diffussion, kinetics Ključne besede: notranja oksidacija, cona notranje oksidacije (CNO), kompozit, baker, srebro, difuzija, kinetika Introduction Internal oxidation is a general term for the process taking place under the surface of alloys and including the selective reaction of a less noble composite constituent with oxygen[1,2]. The phenomenon of internal oxidation was first noticed in copper alloys with silicon, nickel, tin, manganese and zinc, but it is also seen in silver alloys with additions of less noble alloy constituents[3]. The oxidation of these alloys results in the zone with a typical heterogeneous composition, the so called internal oxidation zone (IOZ)[45]. The internal oxidation is a phenomenon that includes several elementary processes with oxygen transmission as the most important factor of growth and morphological characteristics of the oxidized zone. Conditions for the process of internal oxidation are[4,6]: • larger electronegativity of alloy constituent from the basic metal, • larger oxygen solubility in basic metal, and • higher diffusion rate of oxygen in basic metal in comparison with the diffusion rate of alloy constituent. Special examples require additional condi- tions like the maximal concentration of alloy constituent, oxidation temperature and partial oxygen pressure in atmosphere. All these influence the transmission process from the internal to external oxidation or passivation. Theoretical principles The first theoretic analysis being the principle of further research was made by Wagner[4] who used his own principle mathematic pattern for the caluclation of process kinetics to explore typical examples of internal oxidation in different alloys. The discussed examples of oxidation of Cu-C and Ag-C composites belong to the examples of internal oxidation of two-phase alloys. Copper and silver dissolve a small portion of carbon in both liquid and solid state, and do not create compouds with carbon. Therefore their composites are two-phase composites and consist of a matrix and carbon particles. Copper and silver meet the conditions that are necessary for internal oxidation: • both metals are more noble than carbon, • oxygen solubility in both metals is relatively high, and с с с с ООО ООО ООО о о о о Figure 1. Internal oxidation mechanism of two-phase alloys when there is no dissolution of alloy component during oxidation Slika 1. Mehanizem notranje oksidacije dvofazne zlitine za primer, ko se legirni element ne raztaplja med oksidacijo Figure 2. Mechanism of a two-phase alloy internal oxidation when there is a dissolution of the alloy component during oxidation Slika 2. Mehanizem notranje oksidacije dvofazne zlitine za primer, ko se legirni element raztaplja med oksidacijo • diffusion rate of oxygen exceeds the diffusion rate of carbon. Internal oxidation of two-phase alloys and composites runs according to one of Kap-teijn and Meijering mechanisms[6,7] or follows the mechanism that is a combination of both[8] (Figures 1 and 2). Experimental work For testing purpose, samples made of copper with 1 and 2 m.% carbon and samples made of silver with 1, 2, 5 and 10 m.% carbon were prepared[9-11]. Cu-C and Ag-C composites were made using the process of powder metallurgy. Mixtures of metal and graphite powder were compacted in a rigid hydraulic tool on the hydraulic press. They were subjected to sintering under vacuum and then to hot isostatic process. As a result, materials reached a practically theoretic density with no porosity. Cu-C composits were oxidized in a mixture of Cu2O and Cu powders so that the oxygen partial pressure equalled Cu2O dissociation pressure. Therefore, no copper oxide was created on the surface of Cu-C composites and internal oxidation was released. In case of Ag-C composites, internal oxidation was released also in the air or in pure oxygen as silver oxide disintegrates completely already at temperatures around 453 K [12]. We cut samples from both materials and prepared them for a metallographic analysis using an optical microscope (OM) and scanning electronic microscope (SEM). Results and discussion After the internal composite oxidation, the zone of internal oxidation (IOZ) consists of a matrix and scattered oxide particles (bubbles, pores) of composite constituent. A comparison of morphological characteristics of the internally oxidized zone in different composites shows essential differences in the size, form and distribution of oxide particles in the matrix. We noticed no resi- dues of porosity at the microscopic level. We found that the thermodynamic condition for the internal oxidation is met in the Cu-C and Ag-C composites. Metallographic characteristics of internally oxidized Cu-C composites show that internal oxidation is running primarily with a direct carbon oxidation (Figure 3). Metallographic characteristics of internally oxidized Ag-C composites show that oxidation of these type of composites is probably running directly out of a solid solution (Figures 4 and 5). On the basis of kinetics of growth of the internal oxidation zone (Figures 6 and 7) we calculated the activation energy of process. The activation energy for Cu-C compositesis 70.5 kJ/mol which is close to the activation energy for a volume diffusion of oxygen in copper between 1023 and 1323 K that amounts to 67.2 kJ/mol. For Ag-C composites, the calculated activation energy is 50.1 kJ/mol which is close to the activation energy for a volume diffusion of oxygen in silver between 1023 and 1173 K that amounts to 46.1 kJ/mol. In both examples, the activation energies are very close to the activation energy for a volume diffusion of oxygen in copper and in silver. This makes us conclude that kinetics of the internal oxidation in both composite groups primarily depends upon oxygen diffusion. Conclusions Ag-C and Cu-C composites meet all necessary conditions for internal oxidation. They Figure 3. Microstructure of internally oxidized Cu-2m.% C composite (1323 K, 23h, oxygen) Slika 3. Mikrostruktura notranje oksidiranega kompozita Cu-2m.% C (1323 K, 23h, kisik) Figure 4. Microstructure of internally oxidized Ag-10m.% C composite (1123 K, 4h, oxygen) Slika 4. Mikrostruktura notranje oksidiranega kompozita Ag-10m.% C (1123 K, 4h, kisik) Figure 5. Microstructure of internally oxidized Ag-5m.% C composite (1123 K, 4h, oxygen) Slika 5. Mikrostruktura notranje oksidiranega kompozita Ag-5m.% C (1123 K, 4h, kisik) Time (h) Figure 6. Kinetics of the internal oxidation of Cu-1m.% C and Cu-2m.% C composites at 1323 K in Cu-Cu2O mixture Slika 6. Kinetika notranje oksidacije kompozi-tov Cu-1m.% C in Cu-2m.% C pri 1323 K v Cu-Cu, O zmesi N o o,s Time (h) Figure 7. Kinetics of internal oxidation of Ag-5m.% C composite Slika 7. Kinetika notranje oksidacije kompozi-ta Ag-5m.% C are typical two-phase composites and gas products are the result of internal oxidation. The internal oxidation of Cu-C composites is running primarily with a direct carbon oxidation. The kinetics of oxidation parabo-lically depends upon time and is controlled by oxygen diffusion in solid copper. Arising pores are unstable and get spheroidized. In case of Ag-C composites, we noticed some similarity between the geometry of pores and carbon particles only with small concentrations of carbon (0.5 to 2 m.% C). Differences are obvious with large carbon concentrations. In the discussed example, oxygen diffusion in silver is the most essential parameter for the control of oxidation kinetics. Carbon oxidation is carried out directly with oxygen out of solid solution and - when the creation of gas phase this contact is interrupted - over a gas mixture of CO and CO2. Povzetek Notranja oksidacija Cu-C in Ag-C kom-pozitov Kompoziti bakra in srebra z ogljikom v kisiku ali na zraku reagirajo pri visokih temperaturah po t.i. mehanizmu notranje oksidacije. Topnost ogljika v trdnem bakru in trdnem srebru je zelo majhna. Analizirali smo kinetiko oksidacije kompo-zitov, določili aktivacijsko energijo in mehanizem notranje oksidacije. Kinetika oksidacije je tako pri kompozitih Cu-C kot tudi pri kompozitih Ag-C odvisna od difuzije kisika in sledi parabolični odvisnosti od časa v skladu z Wagneijevo teorijo. Aktivacijska energija procesa je za kompo-zite Cu-C enaka 70,5 kJ/mol, za kompozite Ag-C pa 50,1 kJ/mol, kar je zelo blizu akti-vacijski energiji za volumsko difuzijo kisika v trdnem bakru oziroma srebru. Pri oksidaciji kompozita nastajajo plinski [5] produkti. Oksidacija ogljika poteka neposredno s kisikom iz trdne raztopine, ko pa se zaradi nastanka plinske faze stik prekine, pa preko plinske zmesi CO in CO [6] V okviru predstavljenega dela so bili izdelani in analizirani kompoziti Cu-C z 1 oziroma 2 m.% C ter kompoziti Ag-C z 1, 2, 5 in 10 m.% C. Vsi kompoziti obravnavani v prispevku so bili izdelani po postopkih metalurgije prahov. Z uporabo optične in elektronske presevne mikroskopije so bile izvedene me-talografske analize vzorcev obeh navedenih skupin kompozitnih materialov. References [1] Rapp, A. (1965): Kinetics, Microstruc- tures and Mechanism of Internal Oxydation - Its Effect and Prevention in High Temperature Alloy Oxydation. Corrosion.; Vol. 21, pp. 382-401. [2] HaGAN, s.p., Polizzotti, A., Luckman, G. (1985): Internal Oxydation of Binary Alloys. SIAM Journal of AppliedMatherials.; Vol. 45, No. 6, pp. 956-971. [3] Gesmundo, F., Viani, F., Niu, Y. (1996): The Internal Oxidation of Two-Phase Binary Alloys Under Low Oxidant Pressures. Oxidation of Metals.; Vol. 45, No. 1-2, pp. 5176. [4] Wagner, C. (1959): Reaktionstypen bei der Oxydation von Legierungen. Zeitschrift für Elektrochemie.; Vol. 63, pp. 722-782. [7] [8] [9] [10] [11] [12] Kosec, L., Kosec, B., Horvat, s. (1999): Internal Oxidation of Binary Silver-Sulphur Alloys. Metall.; Vol. 53, No. 7-8, pp. 383-385. Kapteijn, J., Meijering, J.L. (1973): Internal Oxidation of Two-Phase Alloys. Zeitschrift für Metallkunde.; Vol. 64, No. 8 , pp. 578-580. Meijering, J.L. (1971): Internal Oxidation in Alloys. Advances in Materials Research.; Vol. 5, Ed. Herman H., Wiley-Interscience. Anžel, i., Kneissl, A.c., Kosec, L. (1999): Internal Oxidation of Rapidly Solidified Ternary Copper Alloys; Part I: A New Model of Dispersoids Formation. Zeitschrift für Metallkunde.; Vol. 90, No. 8, pp. 621-629. Anžel, i., Kneissl, A.c., Kosec, L. (1999): Internal Oxidation of Rapidly Solidified Ternary Copper Alloys; Part II: An Experimental Study. Zeitschrift für Metallkunde.; Vol. 90, No. 8, pp. 630-636. Bizjak, M., Kosec, L. (2000): Phase Transformations of Al-Fe and Al-Fe-Zr Rapidly Solidified Alloys. Zeitschrift für Metallkunde.; Vol. 91, No. 2, pp. 160-164. Rudolf, R., Kosec, L., Križman, A., Anžel, I. (2006): Microstructure Analysis of Internally Oxidized Cu-C Composite. Metallurgy.; Vol. 45, No. 2, pp. 79-84. Kosec, G., Kosec, L., Anžel, i., Gon -tarev, V., Kosec, B., Bizjak, M. (2005): Internal Oxidation of Silver Alloys with Tellurium, Selenium and Sulphur. Metallurgy.; Vol. 44, No. 1, pp. 37-39. Composition and morphology of diborides in Al-Ti-B alloys after annealing at 1873 K Sestava in morfologija diboridov v zlitinah Al-Ti-B po žarjenju na 1873 K Franc Zupanič 1 'University of Maribor, Faculty of Mechanical Engineering, Smetanova ulica 17, SI-2000 Maribor, Slovenia; E-mail: franc.zupanic@uni-mb.si Received: January 13, 2008 Accepted: February 26, 2008 Abstract: In the investigation, Al-Ti-B alloys with different Ti/B ratios were annealed at 1873 K for 10 hours. Under this condition diboride particles were in contact with molten aluminium. During annealing considerable growth of remaining unmelted diboride particles took place. The composition of diboride particles shifted extremely close to the composition of pure TiB2 regardless of the Ti/B ratios in the alloys, indicating that in equilibrium almost pure TiB2 coexisted with a melt. Diboride particles were bound with well-defined crystal facets. Types and relative size of the facets depended on the Ti/B ratio. It is strongly indicated that an excess of Ti (B) in the melt over that needed to form TiB2 stabilizes crystal planes having planar arrangement of Ti (B) atoms. Izvleček: V tej raziskavi smo več zlitin Al-Ti-B, ki so imele različna razmerja Ti/B, žarili 10 ur pri 1873 K. V teh razmerah so bili delci diborida v kontaktu z aluminijevo talino. Med žarjenjem so diboridni delci močno zrasli. Njihova sestava se je v vseh raziskanih zlitinah močno približala sestavi čistega TiB2, kar kaže, da je v termodinamskem ravnotežju s talino praktično čisti TiB2. Diboridni delci so bili obdani s kristalnimi fasetami. Vrsta in relativna velikost faset je bila močno odvisna od razmerja Ti/B. Obstajajo trdni dokazi, da presežek Ti (B) nad vrednostjo, ki je potrebna za tvorbo TiB2, stabilizira kristalne ravnine, ki imajo ravninsko razporeditev Ti (B) atomov. Key words: Al-Ti-B alloys, diboride phase, high-temperature annealing, morphology, microstructure Ključne besede: Al-Ti-B zlitine, diboridna faza, visokotemperaturno žarjenje, morfologija, mikrostruktura Introduction It is believed that particles of the diboride phase (Al,Ti)B2 present in Al-Ti-B alloys play the most important role in the grain-refining process in aluminium alloys[1,2]. Therefore, they were the subject of several investigations[1-5]. The results show that during manufacturing of Al-Ti-B alloys by an aluminothermic synthesis the diboride phase is formed with compositions ranging from that of the stoichiometric AlB2 to that of the stoichiometric TiB2[1-3]. All di-borides, pure AlB2 and TiB2, as well as the mixed diboride (AfT^ x)B2 (0 < x < 1) posses the same crystal structure (space group P6/mmm, Ref. 6) and very similar lattice parameters (see Figure 1). On this ground it was suggested that the mixed diboride phase (AlxTij x)B2 represents a thermody-namically stable phase in the aluminium- rich corner of the Al-Ti-B ternary system[7]. However, some experimental results do not support this assumption[2,8]. Johnsson and Jansson [2] found out that the composition of the mixed diboride moved toward the compositions of pure TiB2 and AlB2 during holding in liquid aluminium. In addition, it was discovered that during synthesis of Al-Ti-B alloys by arc melting almost pure AlB2 and TiB2 formed. Furthermore, the formation of the mixed diboride (AlxTi1-x) B2 from pure diborides AlB2 and TiB2 did not take place even after exposure for 1000 h at 1073 K[8]. However, 1073 K is relatively low temperature since it amounts only 0.3 Tm of TiB2, where Tm indicates melting temperature of pure TiB2: 3498 K[9]. This could mean that even if the mixed boride would be a ther-modynamically stable phase, the transfor- Figure 1. Crystal structures of diborides found in the ternary system Al-Ti-B. The diborides possess crystal structures belonging to the same space group P6/ mmm. The lattice parameters are similar, mixed diboride having lattice parameters between those for AlB2 and TiB2. The crystal structure has layered form with alternate stack of planar hexagonal metal layers (m) and hexagonal boron layers (b). Slika 1. Kristalne zgradbe diboridov v ternarnem sistemu Al-Ti-B. Kristalne zgradbe diboridov spadajo v isto prostorsko skupino P6/mmm. Mrežni parametri so podobni. Mrežni parametri zmesnega diborida so med parametri čistega AlB2 in TiB2. Zgradba diborida je plastna, sestavljena iz izmeničnih heksago-nalnih kovinski plasti (m) in heksagonalnih borovih plasti (b). mation of pure AlB2 and TiB2 to the mixed diboride (AlxTi1-x)B2 might be suppressed by kinetic reasons. Annealing of Al-Ti-B alloys containing both pure AlB2 and TiB2 is not possible at much higher temperatures that should allow completion of the transformation in shorter times, because AlB2 would transform via a peritectic reaction to the liquid phase and a-AlB12 above 1253 K[10]. As a consequence, the diboride phase can be studied at higher temperatures only in equilibrium with other phases. In this work some Al-Ti-B alloys with different Ti/B ratios were heated to 1873 K. This temperature exceeded 0.5 Tm of TiB2, therefore in these conditions kinetic obstacles for achieving heterogeneous equilibrium between diboride phase and aluminium melt should be eliminated. The main purpose of the work was to determine the composition of the diboride phase coexisting with the liquid phase in order to contribute new information for the constitution of the ternary system Al-Ti-B. In addition, special attention was paid to the influence of Ti/B ratio on the morphology of diboride particles. Experimental Table 1. Composition of the investigated Al-Ti-B alloys prepared by an aluminothermic reduction of Ti from KTiF and B from KBF, 2 6 4 Tabela 1. Sestava preiskanih zlitin Al-Ti-B, ki so bile izdelane z aluminotermično redukcijo Ti iz K TiF, in B iz KBF, 2 6 4 Alloy Zlitina Ti / wt.% Ti / mas.% B / wt.% B / mas. % Ti/B weight ratio masno razmerje Ti/B Ti + B / wt.% Ti + B / mas. % A8 8.55 1.93 4.43 10.48 A6 7.34 2.86 2.56 10.2 A7-1 3.73 2.77 1.34 6.5 A7-2 3.14 2.85 1.1 5.99 alumina vessel. The annealing took place in a high temperature furnace ASTRO in an argon atmosphere. Heating and cooling rates were 60 K/min, whereas the holding time at 1873 K was 10 hours. Metallographic preparation Samples for the light (LM) and ning electron microscopy (SEM) prepared using standard metallographic techniques[13]. The samples were polished directly before analyses with energy dispersive spectroscopy (EDS) to remove possible etching products and oxide layers on the investigated surface. scan- were Annealing of alloys In this investigation samples of Al-Ti-B alloys were manufactured by an alumino- thermic reduction of Ti and B from KTiF 2 6 and KBF4 salts, respectively. The chemical compositions of the alloys are given in Table 1. Details of alloy preparation can be found elsewhere[12]. Before annealing at 1873 K the samples were put into small alumina crucibles situated inside a covered For investigation of the morphology of di-boride particles deep etching was applied using two different etchants: (1) a solution consisting of 50 % HCl and water, and (2) a methanol-iodine solution (30 ml methanol, 3 g tartaric acid and 1 g iodine). Satisfying results were obtained after 10-15 min etching in the HCl solution and 1 -2 hours etching in the methanol-iodine solution. It is important to stress that the mor- phology of diboride particles in each alloy was the same regardless of the applied etchant. This strongly indicates that both etchants dissolved only aluminium matrix and, what is of utmost importance, did not attack diboride particles. Energy dispersive spectroscopy EDS was performed in a scanning electron microscope SIRION 400 NC (FEI Company), equipped with an energy dispersive analyser INCA 350 (Oxford Analytical). Boron was mainly determined qualitatively, whereas titanium and aluminium were determined quantitatively in all observed phases. We used titanium and aluminium standard spectra obtained from pure titanium and aluminium, as well as from pure diborides AlB2 (large AlB2 particles in binary Al-B alloy) and TiB2 (from pure arc-melted TiB2). X-ray diffraction The phase composition of alloys was determined using an X-ray diffractometer Philipps PW 1710. The general diffraction curves were recorded at a scanning rate of 0.025 °/s (Bragg angle) scan range from 5° to 70° and the detailed diffraction curves with 0.025 °/10 s with a scan range between 33.5° and 35° (around the (100) diboride peak). The results of X-ray diffraction were primarily used for the determination of the diboride lattice parameters. It was found out that lattice parameters a and c of the diboride phase can be calculated reliably if positions of at least five diffraction peaks can be determined. In some cases only (100) peak was well defined. In this case only the value of a-axis could be calculated. The composition of the diboride phase -the atomic fraction of aluminium on the metallic sublattice of diboride phase CAl -was estimated on the basis of two criteria: - the deviation of the lattice parameter a from that of pure TiB2[3]: CAl =—^-100 % (1) aTiB2 aAlB2 - the deviation of the axis ratio c/a from that of pure TiB2[4]: c / a - (c / a)TiB CAl - , ™2—100 % (2) (C / a)AlB2 - (C / a)T Results and discussion The compositions of Al-Ti-B alloys were chosen so that the diboride phase should exists in the equilibrium with the liquid phase at the annealing temperature (1873 K). During heating of Al-Ti-B alloys all other phases present initially (e.g. Al3Ti, a-AlB12, AlB2) were melted completely, only the titanium-rich diboride remained partly unmelted. To estimate the quantity of unmelted TiB2 the solubility product proposed by Sigworth[14] was used: log (wTi)(wB)2 = 8.526-16,043/T (3) where T means temperature in K, and wTi and wB contents of Ti and B (in wt.%) in the melt, respectively. Table 2 shows the results. It is obvious that 4-7.2 % TiB2 remained unmelted. Since the solubility product defined by equation (3) may be too Table 2. Concentration of titanium and boron in the liquid phase and the quantity of unmelted TiB2 at 1873 K using equation (3) Tabela 2. Koncentracija titana in bora v talini in količina nestaljenega TiB2 pri 1873 K, izračunana z uporabo enačbe (3) Alloy Ti dissolved in the melt / wt.% B dissolved in the melt / wt.% estimated initial quantity of TiB2 / wt.%o unmelted TiB2 at 1873 K / wt.% A8 5.22 0.42 6.2 4.8 A6 2.40 0.62 9.2 7.2 A7-1 0.53 1.32 5.4 4.7 A7-2 0.36 1.59 4.6 4 high, the amount of unmelted TiB2 is to be slightly higher. Morphology of diboride particles The size of the diboride particles in the initial state (after aluminothermic reduction) rarely exceeded 1 ^m (Figure 2). In alloys with hypostoichiometric and stoichiomet-ric composition (Ti/B < 2.21) agglomerates of diboride particles in Al-rich solid solution could be observed. In alloys with hiperstoichiometric composition, in addition to boride agglomerates also Al3Ti particles were present. However, during annealing at 1873 K very large hexagonal plates of the titanium-rich diboride formed. The height of the plates often exceeded 5 ^m and their edge 10 ^m (Figures 3 and 4). All diboride particles were bound with very well defined crystal faces; however their morphology was not the same in all investigated alloys. In the alloy A7-1 having an excess of B over that needed for formation of TiB2 (Ti/B) = 1.34, the basal {0001} facets dominate (Figure 4a). Note also traces of the prismatic {1010} and pyramidal facets. It is not possible to determine the Miller-Bravais indices of these pyramidal planes by inspection of deep-etched specimens only. However, it seems possible that their indices could be {hk 01}, h > l, h = -k. In the near-stoichiometric alloy A6 (Ti/B = 2.56) two additional types of facets were observed (Figure 4b): prismatic {1120} and pyramidal {1121} facets. In the alloy A8 having an excess of Ti over that to form TiB2 (Ti/B = 4.43), the diboride particles were bound by basal {0001} and prismatic {1010}facets (Figure 4c). To explain the influence of Ti/B ratio on the observed morphology of the diboride particles we must take a closer look to the atomic arrangements in the following crystallographic planes: {0001}, {1010}, {1120}, {1121} and {2201}. In the {0001} planes, boron and titanium atoms form alternate planar layers (Figure 1). Thus, the outer layer in the contact with the liquid phase could be occupied only by boron or only by titanium atoms. In the family of {1010}planes only titanium atoms can be arranged in a planar array, whereas the arrangement of boron atoms cannot be planar (Figure 5 a). In both {1120} and {1121} families of planes it is not possible to get the planar outer layer occupied by only one kind of atoms, but in each case with both boron and titanium atoms (Figure 5a). On the other hand, boron atoms can be arranged in a planar manner, therefore the facets of this plane dominate in alloy A7-1. Figure 2. Secondary electron micrographs of a) alloy A7-1 and b) alloy A8. The arrows indicate diboride agglomerates. Slika 2. Mikroposnetek z vrstičnim elektronskim mikroskopom (sekundarni elektroni) zlitin: a) A7-1 in b) A8. Puščici kažeta na diboridne agregate. Figure 3. Secondary electron micrographs of a) alloy A7-1 and b) alloy A8. The arrow indicates AlB2 particle. D indicates TiB2. Slika 3. Mikroposnetek z vrstičnim elektronskim mikroskopom (sekundarni elektroni) zlitin a) A7-1 in b) A8. Puščica kaže na delec AlB2. D pomeni TiB2. Figure 4. Secondary electron micrographs of diboride particles in the investigated alloys after deep-etching: a) Alloy A7-1, b) alloy A6 and c) alloy A8 after exposure for 10 hours and 1873 K (1: (0001), 2: (1010), 3: (1120), 4: (1121), arrow in a: (hk 01), h > l, h = -k) Slika 4. Mikroposnetek z vrstičnim elektronskim mikroskopom (sekundarni elektroni) zlitin dibo-ridnih delcev v preiskovanih zlitinah po globokem jedkanju: a) Zlitina A7-1, b) zlitina A6 and c) zlitina A8 po desetih 10 urah pri 1873 K (1: (0001), 2: (1010), 3: (1120), 4: (1121), puščica na sliki a: (hk 01), h > l, h = -k) RMZ-M&G 2008, 55 According to this analysis it is very likely that diboride particles in the alloys with an excess of titanium are bound with {0001} and {1010} planes, because in these planes titanium alloys are arranged in planar array. Similarly, in the alloys with an excess of boron {0001} planes dominate, since in these planes boron atoms form planar layers. On the other hand, {1120} and {1121} planes that contain both titanium and boron atoms are very important in the alloy A6 having near-stoichiometric composition. The above presented evidence indicates that an excess of Ti (B) tends to stabilize crystal planes with the planar arrangements of Ti (B) atoms. Composition of the diboride phase The results of EDS analyses showed that even after 1000 s live time aluminium peaks could not be resolved in EDS spectra of diboride particles present in the alloy A8. On the X-ray diffraction curve only two peaks arising from the diboride phase were identified thus it was not possible to reliably calculate its lattice parameters. Only the length of the a-axis from the position of (100) diboride phase was calculated. Using equation (1) we determined CAl = 1.67 at.% Al on the metallic sublattice. It is believed that in this case the results of EDS analysis were more reliable. Thus, apparently pure TiB2 existed in the equilibrium with the liquid phase (Table 3). EDS showed also that in the alloy A6 no aluminium peak could be resolved in spectra of diboride particles - similarly as in the alloy A8. On the other hand, several well-defined peaks arising from both Cu Kaj and Cu Ka2 radiation could be easily resolved (Figure 6). The calculated lattice Figure 5. Arrangement of atoms in some planes of TiB2. In a) TiB2 crystal is bound by traces of {1010} and {1120} planes (projection perpendicular to (0001) plane. In b) planar arrangement of titanium and boron atoms in (0001) plane is shown. Slika 5. Razporeditev atomov v nekaterih ravninah TiB2. Na sliki a) je TiB2 kristal obdan z ravninama {1010} in {1121} (projekcija pravokotna na ravnino (0001). Na sliki b) je prikazana ravninska ureditev titanovih in borovih atomov v ravnini (0001). parameters coincided completely with the lattice parameters of pure TiB2. The aluminium content computed by equations (1) and (2) amounts 0 at.% Al. Therefore, the results of EDS analysis, as well as the results of XRD clearly indicate that in this alloy almost pure TiB2 exists in the equilibrium with the melt (Table 3). melt during cooling below 1173 K. The lattice parameters of the titanium-rich and aluminium-rich diborides corresponded closely to the lattice parameters of pure TiB2 and AlB2. Also in these alloys the experimental results showed that almost pure TiB2 existed in the equilibrium with the melt at 1873 K (Table 3). Both alloys A7-1 and A7-2 existed at 1873 K in the two-phase liquid + diboride region. On EDS spectra of some diboride particles very small aluminium peaks could be observed. The calculations gave us the result CAl « 0,3 at.% Al. This is close to the detection limit of the EDS. On X-ray diffraction curves peaks arising from the diffraction of Cu Ka1- and Cu Ka2-radiation on the lattice planes of both AlB2 and TiB2 could be observed. Of course, AlB2 was not present at 1873 K, but has crystallized from the During annealing at 1873 K the size of diboride particles increased considerably. In can be shown by a simple calculation that one such particle have formed from several thousands to several ten thousands of particles that were initially present in the microstructure. It is the most probable that diboride particles shown in Figures 3 and 4 had formed by a process similar to the Ostwald ripening; smaller particles have dissolved and the larger particles have grown. Therefore, for the attainment of the equilibrium composition of the diboride phase diffusivity inside particles is less important than the attachment/detachment kinetics during dissolution/growth of the diboride particles. Since under isothermal conditions diboride particles grow slowly, it is believed that he interface attachment/ detachment kinetics should be fast enough to maintain the equilibrium composition of the diboride phase. On the basis of this discussion and the results of X-ray diffraction and EDS analyses we may conclude that at 1873 K apparently pure TiB2 existed in the equilibrium with the liquid phase regardless of the Ti/B ratio. Conclusions During annealing at 1873 K considerable growth of unmelted diboride particles took place. They probably grew by a process similar to Ostwald ripening. The composition of diborides was extremely close to the composition of pure Figure 6. The results of X-ray diffraction. The shape and the position of the (100) diboride peak in different alloys after 10 hours exposure at 1873 K. In alloy A7-1 also peaks arising from AlB2 that had formed during cooling could be seen. Arrows indicate the positions of (100) peaks of pure TiB2 and pure AlB2 by diffraction of Cu Ka1 radiation. Slika 6. Rezultati rentgenske difrakcije. Oblika in položaj vrhov (100) diborida v različnih zlitinah po 10 urah žarjenja pri 1873 K. V zlitini A7-1 se pojavi tudi vrh AlB2, ker AlB2 nastane pri ohlajanju. Puščici kažeta vrhova (100) čistega TiB2 in čistega AlB2 pri difrakciji Cu Ka1. Table 3. Aluminium content on the metallic sublattice of the diboride phase according to the results of XRD and EDS Tabela 3. Vsebnost aluminija na kovinski pod-mreži diboridne faze skladno z rezultati XRD in EDS alloy cal / at.% Al (equation 1) cal / at.% Al (equation 2) cal / at.% Al (EDS) remark pripomba A8 1.5 - 0 TiB2 A6 0 0 0 TiB2 A7-1 0 0 0.3 TiB2 A7-1 100 98.8 99.8 AlB2 TiB2 regardless of the Ti/B ratios in the investigated alloys. Therefore all evidence strongly suggests that at 1873 K almost pure TiB2 existed in the equilibrium with the liquid phase in all investigated alloys. Diboride particles were bound with well-defined crystal facets. Types and relative size of the facets were dependent on the Ti/B ratio. An excess of Ti (B) tended to stabilize crystal planes with the planar arrangement of Ti (B) atoms. In the alloy A8 with an excess Ti over that needed to form TiB2 {0001} and {1010} planes dominated, whereas in alloy A7-1 and A7-2 having an excess of boron {0001} planes dominate, since in these planes boron atoms form planar layers. On the other hand, {1120} and {1121} planes that contain both titanium and boron atoms are very important in the alloy A6 having near-stoichiometric composition. Povzetek Sestava in morfologija diboridov v zlitinah Al-Ti-B po žarjenju na 1873 K Delci diboridne faze (Al,Ti)B2 imajo pomembno vlogo pri udrobnitvi kristalnih zrn v aluminijevih zlitinah. Kadar zlitine Al-Ti-B izdelamo z aluminoternično sintezo imajo diboridi spekter sestav, ki se razteza od sestave čistega AlB2 do sestave čistega TiB2. V literaturi še vedno obstajajo razhajanja ali sta v sistemu Al-Ti-B ter-modinamsko stabilna čista diborida AlB2 in TiB2 ali pa zmesni diborid (Al,Ti)B2. V tej raziskavi smo raziskovali vzorce zlitine Al-Ti-B, ki smo jih izdelali z aluminotermično redukcijo Ti in B iz soli KTiF, in KBF. Zlitine Al-Ti-B so imele 2 6 4 različno razmerje Ti/B. Zlitine smo nato žarili 10 ur pri 1873 K. Ta temperatura presega 0,5 T t TiB2 (Tt je temperatura tališča v kelvinih), zato so difuzijski procesi dovolj hitri, da se lahko vzpostavi ravnotežje v sorazmerno kratkem času. Pri 1873 K so bili delci diborida v kontaktu z aluminijevo talino. Med žaljenjem so diboridni delci močno zrasli. Z analizo EDS in rentgensko difrakcijo (XRD) smo ugotovili, da se je njihova sestava v vseh raziskanih zlitinah močno približala sestavi čistega TiB2. To kaže, da je v termo-dinamskem ravnotežju s talino praktično čisti TiB . Ugotovili smo tudi, da so bili diboridni delci obdani s kristalnimi fasetami. Vrsta in relativna velikost faset je bila močno odvisna od razmerja Ti/B. V zlitini A8, v kateri je bil presežek titana glede na idealno stehiometrično razmerje (2,21:1) so bili diboridni delci obdani s fasetami osnovne ploskve {0001} in prizmatičnimi ravninami {1010}. V zlitini s skoraj stehiometrično sestavo (Ti/B = 2,56) sta se pojavile še fasete dveh dodatnih ravnin: prizmatič-ne {1120} in piramidne {1121}. V zlitini A7-1, ki je imela presežek B (Ti/B = 1,34) je prevladovala faseta osnovne ravnine {0001}. Z analizo rezultatov in primerjavo faset z razporeditvijo atomov v diboridu smo ugotovili, da presežek Ti nad vrednostjo, ki je potrebna za tvorbo TiB2, stabilizira kristalne ravnine, ki imajo ravninsko razporeditev Ti atomov. Podoben učinek ima B, ki stabilizira ravnine, v katerih so atomi B razporejeni v ravnini. References [1] Wang, C., Wang, M., Yu, B., Chen, D., Qin, P., Feng, M. and Dai, Q. (2007): The grain refinement behavior of TiB2 particles prepared with in situ technology. Materials Science and Engineering A.; Vol. 459, Issues 1-2, pp. 238-243. [2] Johnsson, M., Jansson, K. (1989): Study of Al1 xTixB2 particles extracted from Al-Ti-B alloys. Z. Metallkd.; Vol. 89, pp. 394-398. [3] Kiussalaas, R. (1986): Relation be- tween phases present in master alloys of the Al-Ti-B type. Chemical Communications. Stockholm University. [4] Stolz, u.K., Sommer, F., predel, B. (1995): Phase equilibria of aluminium-rich Al-Ti-B alloys - solubility of TiB2 in aluminium melts. Aluminium.; Vol. 71, pp. 350-355. [5] Feng, c. F., Froyen, L. (1997): Incor- poration of Al into TiB2 in Al matrix composites and Al-Ti-B master alloys. Materials Letters.; Vol. 32, pp.275-279. [6] Pohl, A., Kizler, P., Telle, R., Aldin- ger, F. (1994): EXAFS studies of (Ti,W)B2 compounds. Z. Metallkde.; Vol. 85, pp. 658-663. [7] Hayes, F. H., Lukas, H. L., Effenberg, G., Petzow, G. (1989): Themody-namic calculation of the Al-rich corner of the Al-Ti-B system. Z. Metallkde.; Vol. 80, pp. 361-365. [8] Zupanič, F., Spaić, S., Križman, A. (1998): Contribution to the ternary system Al-Ti-B. Part 1: The study of diborides present in the aluminium corner. Materials Science and Technology.; Vol. 14, pp. 601-607. [9] Massalski, T. B. (1990): Binary alloys phase diagrams. ASM International.; pp. 544-548. [10] Massalski, T. B. (1990): Binary alloys phase diagram. ASMInternational.; pp. 123-125. [11] Zupanič, F., Spaić, S., Križman, A. (1998): Contribution to the ternary system Al-Ti-B. Part 1: The study of alloys in the triangle Al-AlB2-TiB2. Materials Science and Technology.; Vol. 14, pp. 1203-1212. [12] Zupanič, F., Spaić, S. (1999): Metall (Berl. West). Vol. 53, No. 3, pp. 125-130. [13] Petzow, G. (1994): Atzen. 6. Aufla- ge. Gebrüder Borntraeger, Berlin Stuttgart. [14] Sigworth, G. K. (1984): The grain-re- fining of aluminium and phase relationships in the Al-Ti-B system. Metall. Trans. A.; Vol. 15A, pp. 272-282. Tool for programmed open-die forging - case study Orodje za programsko vodeno prosto kovanje - študija primera David Bombač ', Matevž Fazarinc ', Goran Kugler ', Radomir Turk 1 University of Ljubljana, Faculty of Natural Sciences and Engineering, Department of Materials and Metallurgy, Aškerčeva cesta 12, SI-1000 Ljubljana, Slovenia; E-mail: david.bombac@ntf.uni-lj.si, matevz.fazarinc@arnes.guest.si, goran.kugler@ntf.uni-lj.si, rado.turk@ntf.uni-lj.si Received: November 26, 2007 Accepted: January 13, 2008 Abstract: An open-die forging process as referred to in the following assumptions is a process where plastic material is compressed in one main axis only and the spread into the two other main axes is not limited. In view of present competitive markets modern open-die forging plants are highly dynamic production plants and vastly explore possibilities of programmed forging. Computer aided technology tools for programmed forging is the basis for innovative and cost effective technology planning which consider the performance limits of forging equipment and material in order to achieve the optimum productivity. Izvleček: Proces prostega kovanja, ki je obravnavan v tej študiji, je postopek, kjer je material tlačno deformiran v eni smeri, v ostalih dveh pa se prosto širi. Na današnjem izredno konkurenčnem trgu so obrati prostih kovačnic izredno dinamični obrati in široko izkoriščajo možnost programiranega kovanja. Računalniško podprta tehnološka orodja za programirano kovanje so osnova za inovativno in cenovno učinkovito planiranje proizvodnje. Ta preuči meje zmožnosti stiskalnice in mejne vrednosti materiala, ter na podlagi teh določi optimalne pogoje preoblikovanja. Key words: hot forming, open-die forging, programmed forging, pass schedule, forging simulation Ključne besede: vroče preoblikovanje, prosto kovanje, programirano kovanje, plan vtikov, simulacija kovanja Introduction In metal forming, open-die forging is a metal forming process in which a work-piece is usually pressed between flat dies with a series of compressive deformation steps and manipulated and/or rotated. The open-die forging process as referred to in the following assumptions is a process where plastic material is compressed in one main axis only and the spread into the two other main axes is not limited. It has not lost its importance in recent times and is for steel manufacturing carried out under hot working conditions when the metal is deformed plastically above its recrystal-lization temperature. The open-die forging plants consist of a forging press and one or two rail-bound manipulators. The dies or tools are small compared with the overall sizes of the forgings. The process is carried out incrementally, where only a part of the workpiece is being deformed at each stage. The principle of such an incremental forging process is simply the compressing or upsetting of the material step-by-step until it reaches the final target shape. In the further development of this type of forming operation, the requirements are for accuracy of load prediction and metal flow[1-3]. In view of present competitive markets modern open-die forging plants are highly dynamic production plants and vastly explore possibilities of programmed forging. Apart from the pure production speed, the main focus today is on the achievement of minimum forging tolerances and a consistent level of quality. In the past procedures in open-die forging were based on the individual forgemaster's experience and observation of each forging stroke to determine both elongation and sideways spreading. An experienced forge master can develop a geometrical pass schedule quite easily, however; the optimization of a pass schedule to minimize forging time is quite difficult as it involves the consideration of numerous factors which influence the production rate. Computer aided technology tools for programmed forging is the basis for innovative and cost effective technology planning which consider the performance limits of forging equipment and material in order to achieve the optimum productivity. It must consider all of the important factors including spread behaviour, die geometry and the speeds of the press and manipulators. The required pressing force relative to the material resistance is calculated as a function of the instantaneous temperature and compared to the maximum available press force. Optimization of the pass schedules in the open-die forging technology and activities for successful implementation of the computer aided forging technology demand close cooperation between forging plants and science. Technology developed in cooperation must be constantly maintained and adapted to the latest technological breakthroughs. Theoretical framework for programmed forging The open-die forging as mentioned before is incremental process where after one forging pass on a square bar the side faces take on an irregular shape, commonly termed barrelling, which is due to frictional constraint at the tool faces and to the influence of the adjacent undeformed portion of the bar. The influence of the machine operator experience on the monitoring of the process must be decreased in order to ensure reproducible process that increases productivity and improve quality of the forgings hence reducing machine operator experience related fluctuations. Moreover computer aided forging technology enables judgment of the characteristic forging capabilities of the plant and their influence on the productivity[4]. However the machine operator has ability to initiate corrections to the programmed forging schedule any time if it is necessary. Pass schedule calculation is determination of relevant process data for processing a defined end piece from initial ingot. Such calculation is very demanding due to complexity of open-die forging process. For instance to enable a mutual harmonisation between forging press and manipulator a proper description of the material being pressed between two flat dies is required. Moreover material does not only deform in the forging direction but also towards the manipulator. In order to fully exploit capabilities of forging equipment manipulator feeding rate or manipulator bite has to be determined. This can be achieved by employing the empirical formula proposed by Tomlinson and Stringer[3] which is based on assumption of constant volume during plastic deformation and describes the relationship between manipulator feeding rate, material shape and reduction for steel. The change of length and width of a forging can be described by a spread factor and the reduction ratio. From practical experience with programmed forging it is known that the influence of reduction ratio on the spread is negligible[4]. To compute the forging pass schedules for bars and predict the changes of shape as well as other important parameters during the forging process empirical formulae have been proposed. The pass procedure for the forging of final shape depends on initial and final cross section shape of bar and are: 1) from square stock to a square bar, 2) from square to round, 3) from round to square and round to round, where same forging principle is used. Breakdown procedure is as follows 1) square to square process goes through next shapes: square - rectangular - square where the reduction ratio can be varied every second pass. A square forged down to a rectangular section with a certain reduction ratio, turned 90° and forged down again with the same reduction ratio and the same bite ratio, turns automatically into a new square with smaller size. To obtain sharp corners of bar decrease of the reduction ratio is required. 2) The process square to round follows the same breakdown routine square - rectangular - square, ending in four passes with an octagon, which have about 7 % more area than the final round. Finish to the round is made in a swaging die. 3) Forging pass schedule of round to square and round to round follows the same forging principle. Forging of rectangular cross sections requires a different technology, where shape factor of h/w (height/width) plays important role leading to a variation of the spread factor. For example rectangular bars where a shape factor exceeds 1/6 results in the normal forging range practically no spread but only elongation[4]. Figure 1. Material flow for open-die forged products Slika 1. Tok materiala pri prostem kovanju Ingots are extensively used as forging stock in the open-die forging of large components. In Figure 1 typical steelmaking material flow from electric arc furnace to forging press is shown. Whenever ingots are used it is often mandatory to adopt a forging procedure that will remove the cast structure in the finished forging. Another important aspect of calculation and optimisation of apt pass schedule is to be aware of limits of ingots, products, materials and technology. When all properties are collected and stored to databases we can start calculating efficient pass schedule. Use of computer aided technology, as depicted in Figure 2 for development and optimization of pass schedules in open- die forging requires some input of forging know-how. This applies particularly to the reduction factor which has to take care of the shape of the ingot, surface conditions, and brittleness of the material and in most cases must be varied with the dropping forging temperature. Also important is the bite ratio which defines the depth of deformation and grain change in the forging. Grater bite ratio is better but leads to increase of forging force, which is limited with equipment. Results and discussion HFS software fundamentals for calculation of pass schedules are models where some of them are physically based e.g. temperature. Other models are deductions flnfi 2 fupliurjül) Mrjdpulu'.'ji 1 П M j, u pillalo: 2 l upiiLiii u!. ! ITjL-H L VII E к: и у.ч гл Figure 2. Modern open-die forging plant with additional PC for virtual aided technology Slika 2. Moderen obrat kovačnice za prosto kovanje z dodatnim računalniškim vodenjem tehnologije from experience e.g. material spreading. In software database also technological characteristics of the forging equipment e.g. maximum press force, press velocity and acceleration, manipulator velocity and acceleration, etc are stored. Users of HFS software have possibility and are limited to change only input data that are stored in input databases as follows. Ingot database where all geometrical characteristics of ingots are stored. Product database allows users to specify and store shape and dimensions of products. In materials database physical characteristics regarding hot workability, radiation and thermal properties for desired materials are stored. Technological database includes data linked to technological parameters used accord- ing to specific forging schedule e.g. shape and size of forging tool. For accurate pass schedule calculation user must constantly update parameters stored in input databases. Specifically important are parameters influencing calculation of temperature e.g. density, specific heat and radiation coefficient. Figure 3a shows influence on temperature calculation regarding specific heat, whereas in Figure 3b depicts influence of radiation coefficient on temperature respectively. Figure 3 shows that lowering specific heat coefficient decreases calculated temperature, on the other hand lowering radiation coefficient increases calculated temperature. All calculations plotted in Figure 3 were performed using upseted 24t ingot and material AISI H13. Figure 3. Influence of (a) specific heat and (b) radiation coefficient on temperature after passes while forging flat product from upseted 24t ingot to product dimensions of 1000x500 Slika 3. Vpliv (a) specifične toplote pri konstantnem tlaku cp in (b) koeficienta sevanja na potek temperature po različnih vtikih pri kovanju ploščatega izdelka iz 24t nakrčenega ingota za izdelek 1000x500 Figure 4. Graphical presentation of forging pass schedule for billet dimensions 1000x400; a) calculated pass schedule and b) acquainted forge masters pass schedule Slika 4. Grafični prikaz plana vtikov za gredice dimenzije 1000x400; a) izračunan plan in b) izmerjen plan kovaških mojstrov Table 1. Detailed characteristics of pass schedules for billet dimensions 1000*400 Tabela 1. Natančen prikaz planov vtika za gredico z dimenzijami 1000*400 Calculated pass schedule Acquainted pass schedule Step Height Width Bite Rotation Step Height Width Bite Rotation 1 1450 1450 189.43 90 1 1450 1450 150 90 2 1260 1464.07 164.61 90 2 1300 1450 150 90 3 1299.46 1299.46 169.76 90 3 1300 1300 100 90 4 1129.69 1339.02 139.02 90 4 1200 1300 150 180 5 1200 1164.22 152.1 90 5 1050 1300 150 180 6 1012.13 1236.74 132.23 180 6 900 1300 50 90 7 879.9 1268.24 114.95 180 7 1250 900 150 90 8 764.95 1295.32 99.93 180 8 750 1250 50 90 9 665.01 1317.36 117.36 90 9 1200 750 150 90 10 1200 700 91.53 90 10 600 1200 50 90 11 609.09 1220.84 79.57 180 11 1150 600 60 90 12 529.51 1238.28 38.28 90 12 540 1150 30 90 13 1200 533.68 34.7 90 13 1120 540 40 90 14 498.99 1207.66 65.19 180 14 500 1120 20 90 15 433.8 1221.09 159.53 90 15 1100 500 40 90 16 1061.57 451.5 42.74 90 16 460 1100 20 90 17 408.76 1070.83 42.05 90 17 1080 460 40 90 18 1028.78 413.58 10 90 18 420 1080 60 90 19 403.58 1028.78 6 90 19 1020 420 10 90 20 1022.78 403.58 2 90 20 410 1020 10 90 21 401.58 1022.78 6 90 21 1010 410 5 90 22 1016.78 401.58 1.58 90 22 405 1010 5 90 23 400 1016.78 6 90 23 1005 405 3 90 24 1010.78 400 0 90 24 402 1005 3 90 25 400 1010.78 6 90 25 1002 402 2 90 26 1004.78 400 0 90 26 400 1002 2 90 27 400 1004.78 4.78 90 27 1000 400 0 90 28 1000 400 28 400 1000 HFS simulator allows prediction and verification of pass schedules for automatically and manually operated open-die forging technology. To certify and confirm calculations of recently developed virtual aided tool for simulation of hot open die forging, HFS, a comparison of calculated and industrial pass schedules is necessity. For later pass schedules of most experienced forge masters from industry were selected. Industrial equipment used to validate accuracy of developed software package was a forging plant with 25/30 MN forging press and one railbound forging manipulator. The calculated forging plan shows good correlation with the acquainted forging plan as one can see from comparison of Figure 4a and Figure 4b and Figure 5 a and Figure 5b. The bite rate is much more equally distributed through the passes. The 180° rotation of the billet is more often used compared to acquainted plan. This results in a straighter billet because the de- formation is more evenly distributed. The HFS calculated forging plan also takes into account the spread of billet in the direction normal to forging direction as can be seen as the increase of dimension in direction square to forging direction in Figure 3a and in Figure 4a. Detailed values for forging pass schedule for billet with dimensions 1000x400 are given in Table 1 and for billet with dimensions 1000x500 in Table 2. In Tables 1 and 2 the calculated pass schedule appears to be as good as that of the best forge master and in some cases even better regarding number of pass steps to obtain final dimensions. HFS also calculates spreading later used for press management and much more accurate and therefore the calculated dimensions for height and width are given in decimal numbers. Forge masters pass schedule does not consider spreading and the values were measured by press control program and are therefore rounded. Step number Figure 5. Graphical presentation of forging pass schedule for billet dimensions 1000x500; a) calculated pass schedule and b) acquainted forge masters pass schedule Slika 5. Grafični prikaz plana vtikov za gredice dimenzije 1000x500; a) izračunan plan in b) izmerjen plan kovaških mojstrov Table 2. Detailed characteristics of pass schedules for billet dimensions 1000*500 Tabela 2. Natančen prikaz planov vtika za gredico z dimenzijami 1000*500 Calculated pass schedule Acquainted pass schedule Step Height Width Bite Rotation Step Height Width Bite Rotation 1 1450 1450 200 90 1 1450 1450 150 90 2 1250 1494.48 197.62 90 2 1300 1450 150 90 3 1296.86 1296.86 180.64 90 3 1300 1300 200 90 4 1116.22 1339 139 90 4 1100 1300 0 90 5 1200 1150.94 160.32 90 5 1300 1100 150 90 6 990.62 1238.72 138 180 6 950 1300 150 180 7 852.63 1271.57 118.77 180 7 800 1300 50 90 8 733.87 1299.52 102.22 180 8 1250 800 150 90 9 631.65 1322.03 122.03 90 9 650 1250 30 90 10 1200 644.21 45.54 90 10 1220 650 70 90 11 598.67 1210.37 83.39 180 11 580 1220 60 90 12 515.28 1228.71 171.15 90 12 1160 580 50 90 13 1057.56 534.22 24.94 90 13 530 1160 40 90 14 509.27 1057.56 28.38 90 14 1120 530 15 90 15 1029.17 511.95 10 90 15 515 1120 40 90 16 501.95 1029.17 6 90 16 1080 515 10 90 17 1023.17 501.95 1.95 90 17 505 1080 40 90 18 500 1023.17 6 90 18 1040 505 0 90 19 1017.17 500 0 90 19 505 1040 20 90 20 500 1017.17 6 90 20 1020 505 0 90 21 1011.17 500 0 90 21 505 1020 10 90 22 500 1011.17 6 90 22 1010 505 0 90 23 1005.17 500 0 90 23 505 1005 5 90 24 500 1005.17 5.17 90 24 1000 505 5 90 25 1000 500 25 500 1000 0 90 26 1000 500 0 90 27 500 1000 A case study comparison was made between a calculated and measured pass schedule for two different billet sizes. The calculated pass schedule shows good correlations with the measured one and is in some cases even better than that of the best forge masters, resulting in less passes needed for reaching the end dimensions of the forged billet. The bite rate in calculated pass schedule is much more evenly distributed between the passes thus resulting in more evenly distributed deformation and should provide better material properties and minimise the risk of an onset of cracks. Ability of HFS is also spread calculation of a billet. This can be later on used for a complete automation of a forging press leading to minimisation of the cost of open-die forging process and increase the yield. Conclusions Efforts to increase productivity and improve quality of technological processes are of a high importance in open-die forging. The investments costs of open-die forging equipment are high and profitability depends to large extent on intensive and flexible use. Automatic forging sequences ensure higher productivity and better quality of products. The developed software for open-die forging HFS allows the calculation of pass schedules and gives support for selection and verification of optimal pass schedule. Technology engineer using the HFS program has a good control over open-die forging process, thus resulting in an opportunity to select optimal process parameters for each product and material. Accuracy of calculated pass schedules largely depends on accurate initial data needed in HFS software. Analysis and detailed comparison of data obtained online in open-die forging plant and calculated offline using HFS software shows good agreement. We believe that are possible further technological optimizations of pass schedules and therefore savings when technologists familiar with open-die process and equipment abilities when HFS in used. Povzetek Orodje za programsko vodeno prosto kovanje - študija primera Poizkusi za povečanje produktivnosti in izboljšanje kvalitete tehnoloških procesov so izrednega pomena v obratih prostega kovanja. Cene investicij za opremo, ki je potrebna za prosto kovanje so izredno visoke zato je dobičkonosnost odvisna predvsem od razširjenosti in fleksibilnosti uporabe. Avtomatizirni postopki kovanja zagotavljajo večjo produktivnost in boljšo kvaliteto končnih izdelkov. Z razvita programsko opremo HFS je moč izračunati plan vtikov in s tem nudi oporo pri optimalni izbiri plana. Tehnolog, kateremu je v pomoč HFS, ima dobro kontrolo nad procesom prostega kovanja. Tako se lahko osredotoči na izbiro optimalnih parametrov za vask proizvod in material. Natančnost izračuna s programom HFS pa je v veliki meri odvisna od natančnsti začetnih podatkov v programu. Narejena je bila študija primera med izračunanim in izmerjenim planom vtika za dve različni dimenziji gredic. Izračunan plan kaže dobro ujemanje s planom, ki je bil izmerjen pri ekipi najboljših kovaških mojstrov. V nekaterih primerih je ta celo boljši, saj je bilo potrebnih manj vtikov za dosego končnih dimezij. Stopnja odvzema je pri izračunanem planu bolj enakomerno razporejena med prevleki. S tem je dosežena tudi bolj enakomerna razporeditev deformacije med prevleki, kar ima za posledico boljše materialne lastnosti in preprečuje vrjetnost nastanka razpok. Program HFS izračunava in upošteva tudi širjenje gredice. Vse te lastnosti je moč uporabiti kasneje za avtomatizacijo preše za prosto kovanje. To bi zmanjšalo stroške prostega kovanja in povečalo končni izplen. References [1] Aksakal, B., Osman, F.H., Bramley, A.N. (1997): Upper-bound analysis for the automation of open-die forging. Journal of Materials Processing Technology.; Vol. 71, pp. 215-223. [2] Choi, S.K., Chun, M.S., Van Tyne, C.J., Moon, Y.H. (2006): Optimization of open die forging of round shapes using FEM analysis. Journal of Materials Processing Technology.; Vol. 172, pp. 88-95. [3] Tomlinson, A., Stringer, J.D. (1959): Spread and elongation in flat tool forging. Journal of Iron Steel Institute.; Vol. 193-2, pp. 157-162. [4] Phanke, H.J. (1983): Grundlagen des programmierten Schmidens. Stahl und Eisen.; Vol. 103, pp. 547-552. A laboratory test for simulation of solidification on Gleeble 1500D thermo-mechanical simulator Laboratorijski test simulacije strjevanja na termo-mehanskem simulatorju Gleeble 1500D Boštjan Bradaskja ', Jurij Koruza2, Matevž Fazarinc2, Matjaž Knap2, Radomir Turk2 1ACRONI d.o.o., Cesta Borisa Kidriča 44, SI-4270 Jesenice, Slovenia; E-mail: bostjan.bradaskja@acroni.si 2University of Ljubljana , Faculty of Natural Sciences and Engineering, Departmant of Materials and Metallurgy, Aškerčeva cesta 12, SI-1000 Ljubljana, Slovenia; E-mail: jurij.koruza@ntf.um-lj.si, matevz.fazarinc@ntfuni-lj.si, matjaz.knap@ntf.uni-lj.si, rado.turk@ntf.uni-lj.si Received: November 18, 2007 Accepted: January 7, 2008 Abstract: A highly repeatable solidification test was developed. It was designed to study the effect of process parameters on solidified micro and macrostruc-tures. Different cooling rates were used for solidification and cooling of S 355 J2 construction steel. It was observed that cooling rate has a substantial influence on final grain size and on columnar-to-equiaxed transition zone (CET). Within the interval of constant thermal gradient, different macro-and micro-structural features have been provided, which consequently enables the study of dynamics of precipitation dependence on solidification processing parameters. Izvleček: Razvit je bil visoko ponovljiv test strjevanja. Razvit je bil kot orodje, za preučevanje vpliva procesnih parametrov na lito mikro in makrostrukturo. Za strjevanje konstrukcijskega jekla S 355 J2 so bile uporabljene različne ohlajevalne hitrosti. Opažen je bil močan vpliv ohlajevalne hitrosti tako na končno velikost zrn, kot tudi na mejno plast med stebričastimi in ekviaksi-alnimi zrni. Znotraj intervala, kjer je bil temperaturni gradient konstanten, so bile s pomočjo različnih ohlajevalnih hitrosti, v vzorcih dobljene različne mikro in makrostrukturne značilnosti, kar omogoča študij dinamike izločanja v odvisnosti od parametrov strjevanja. Key words: solidification test, macrostructure, cooling rate, Gleeble Ključne besede: test strjevanja, makrostruktura, ohlajevalna hitrost, Gleeble Introduction The solidification of molten steel is one of the most important processes in the processing path of steel manufacturing. The microstructure that derives from the solidified ingot or slab has a large influence on the characteristic of the produced material and process path that follows. The micro and macrostructures in ingots usually show spatial variations of features and properties. This can be simulated with combination of computer simulation of ingot/slab cooling and high temperature testing with controlled solidification and cooling of the specimens. The high temperature experiments on the Gleeble testing machine that were found in literature are mainly focused on characteristics of metal in the mushy zone or the mechanical properties of solidified specimens for continuous casting application and do not deal with the development of microstructure. The investigations have not been focused on influence of process parameters on development of micro and macrostructure. In these tests, the solidification process was only the first stage followed by tensile mechanical loading and no observations of solidified structure were made. Seol et al.[1,2] were studying the behavior of material under tensile loading of in-situ melted and solidified cylindrical specimens. The tensile strength and ductility of carbon steels was measured in the temperature range of mushy zone. Also the stress - strain relations in austenite and 5-ferrite phase regions at various temperatures and strain rates were analyzed. Na et al.[3] used the Gleeble system to investigate cracking occurrence during continuous casting of steels by tensile testing. In this work effects of carbon content, strain rate and sampling orientation on hot ductility were investigated. Glowacki et al.[4] used tensile test to study the deformation behavior of steel within the mushy zone. Suzuki et al.[5-7] employed different methods of laboratory simulation of continuous casting and direct rolling of steels with special emphasis on embrittlement in dependence to chemical composition, thermal history, strain rate and fracture mode. Nevertheless some investigations were made on development of solidified mi-crostructure of aluminum alloys, using the Gleebe system, by Kostrivas and Lippold [8]. Although the testing procedure was similar, the difference between the physical properties of aluminum and steel brings up new problems and requires some different approaches. Because of the above mentioned reasons it was decided that a highly repeatable solidification test should be developed with accurate knowledge and control of the temperature field in the specimen. The test was developed using a Gleeble 1500D thermo-mechanical simulator. This machine enables simultaneous, computer guided, thermal and mechanical loading of the specimen, within a very precise range. The main goal was to track the development of micro and macrostructure in dependence to testing parameters. Experimental procedure and material The laboratory test for controlled solidification has been developed using Gleeble 1500D thermo-mechanical simulator, which has been equipped with specially developed additional parts for solidification simulation. Cylindrical specimens, 110 mm long with a diameter of 10 mm, as shown in Figure 1 were used for the experiments. A 10 mm screw-thread was engraved on each side of the specimen which enabled the fixation of the specimen into the jaws with aim to perform tensile and compression loadings. To support the melt zone a 30 mm quartz crucible with a 1 mm wall thickness has been placed around the center part of the specimen. Quartz material was used because of its high temperatures endurance, small linear coefficient of thermal expansion and negligible diffusion with the specimen material. Crucibles have been furnished with axially running 2 mm slot for insertion of the thermo couples and also to provide an opening for exiting gasses. To decrease the radial thermal gradient, refractory material was placed over the crucible. Additionally two special water-cooling ribs made from coroer were placed on each side of the specimen, to attain sufficient thermal gradient in axial direction. Varying the position of the ribs enabled the control of the axial thermal gradient and consequently the width of the melting zone. Schematic plan of placing of the specimen is shown on Figure 2. Temperature was controlled by 0.35 mm thick S-type (Pt10wt%Rh-Pt) thermocouple, spot-welded in the middle of the specimen and isolated with alumina tubes. An additional thermocouple stand was applied to prevent the motion of the leading thermocouple and to assure the correct temperature measurements during the upset of liquid phase. In order to minimize the surface oxidation and consequently the detachment of the welded thermocouple, all experiments were conducted in protective Ar atmosphere. Before setting up the temperature program for the test, Thermo-Calc software was used to define the liquidus and solidus temperature of the material studied. The specimen was heated with the heating rate of 15 K/s up to 100 K below liquidus temperature. The heating rate was then decreased to 1 K/s for better control of temperature near the incitine tcirmcraturc. If necessary, the TC JL TC JL 10.0 30.0 TC _y —Ф10.0 _t „_110.0 Figure1. Cross section of the specimen Slika 1. Shematski načrt preizkušanca aditional water-coolcd copper rib refractory material main water-cooled coopcrjaw 10.0 15,5 12,0 ЗОЙ 12.0 15.5 10.0 ---у- -у--- 2,5 2.5 Figure 2. Schematic plan of the mounted specimen Slika 2. Shematski načrt namestitve preizkušanca quartz crucible temperature was raised manually to attain the desired width of the melted zone. For stabilization of melted zone the specimen was held at the liquidus temperature for 30 - 40 seconds. Afterwards it was cooled with a predefined cooling rate between 1 K/s and 10 K/s. During the cooling an adequate mechanical program was applied with the movement of the main jaws to compensate solidification shrinkage and to prevent formation of cracks. Value of stroke depends on the material properties and the width of the melt zone. After the whole volume has been solidified, a constant compression loading was applied to prevent appearance of cracks caused by further temperature shrinkage of material. In order to evaluate the developed equipment the construction steel, S 355 J2, with chemical composition listed in Table 1, was selected. After the tests, the solidified samples were sectioned longitudinally and axially along their mid-plane for metallographical observation. To reveal the macrostructure and microstructure, 10 % HNO3 and 2 % HNO3 etching agents were used, respectively. The etched specimens were examined by means of optical microscopy using Olympus SZX12 binocular and Olympus BX51M optical microscope. Results and discussion The axial thermal gradient was adjusted by setting two additional cooling ribs at different positions from the center of the specimen. By this way the solidification conditions (steepness of the gradient) can be controlled. Figure 3 represents the measured axial temperature difference at different positions of cooling ribs: 17.5, 20.0 and 25.0 mm from each side of the center of the specimen. Thermocouples were spot Table 1. Chemical composition of the S 355 J2 steel in wt. % Tabela 1. Kemijska sestava jekla S 355 J2 v ut.% Element C Si Mn P S Al Nb wt. % 0.15 0.45 1.03 0.012 0.001 0.028 0.019 £ 800 t 700 4- H p l soočil £ 500 Ć 400 300 200 100 g ё '5 = g i г ß .s < 1 1 1 KOSIH oii o: in L1 conimi! r 17,5 nini ns: 2 5 mm » - - ■ ■ - / Л o 200 loo eoo eoo looo 1200 1400 leoo Temperature [°C] Figure 3. Comparison of axial temperature difference measured between the center part of the specimen and 15 mm from the center along the axis of the specimen, using different placements of the water-cooled copper ribs (17.5, 20, and 25 mm from the center of the specimen) Slika 3. Primerjava temperaturnih razlik izmerjenih med sredino vzorca ter 15 mm od sredine vzorca v osni smeri vzorca, v odvisnosti od postavitve dodatnih hladilnih reber (postavitev 17,5, 20 in 25 mm od sredine vzorca) welded on the surface of the specimen as could be seen on Figure 2. The specimen was isolated with refractory material. The effect of the refractory material on the radial temperature difference between the surface and the center of the specimen was measured for the isolated and unisolated specimen. The results are shown in Figure 4. This difference was measured using the same technique as described by Glowacki et al.[4]. With isolation the heat loss through the surface was minimized and consequently more directional solidification achieved. Four isolated specimens were melted and solidified using different cooling rates, 1 K/s, 3 K/s, 5 K/s and 10 K/s. For comparison, one experiment without isolation and with cooling rate of 3 K/s was carried out. The obtained macrostructures in axial and radial cross-section are presented in Figure 5a-d for isolated specimens and in Figure 5e for un-isolated specimen. Position of the cooling ribs was the same in all experiments that is 17.5 mm from the center on each side as shown on Figure 2. The width of the melted zone was between 12 and 15 mm and was surrounded by 5 to 8 mm wide heat affected zones on each side. Figure 4. Comparison of the measured radial temperature difference between isolated and un-isolated specimens Slika 4. Primerjava radialne temperaturne razlike med izoliranim in neizolira-nim vzorcem Figure 5. Longitudinal and axial cross-section of the isolated specimens with cooling rates 1 °C/s, 3 °C/s, 5 °C/s, 10 °C/s from a) to d) respectively and an un-isolated specimen e) with cooling rate 3 °C/s Slika 5. Vzdolžni ter prečni prerez vzorcev s pripadajočo mikrostrukturo: a) hitrost ohlajanja 1 °C/s, b) hitrost ohlajanja 3 °C/s, c) hitrost ohlajanja 5 °C/s, d) hitrost ohlajanja 10 °C/s, e) hitrost ohlajanja 3 °C/s. Vzorci od a) do d) so bili izolirani, vzorec e) je bil strjen brez izolacije Lower cooling rates caused the formation of columnar grains which can be observed in the macrostructures presented in the Figure 5a-d. These grains start to form on the solid material on the edge of the melted zone and grow into the center of the melt, in the opposite direction of the heat flow. With increase of the cooling rate the solidification time shortens which resulted in increased number of smaller sized grains (Figure 5a-d). Above a certain threshold of cooling rate, as seen in Figure 5d, a relatively large amount of latent heat is momentarily set free. The heat flow is not sufficient thus the cooling rate of the remained liquid in the center of the specimen is reduced. Therefore the center of the specimen is solidified with a slower cooling rate. Consequently the observed solidified structure consists of two different grain structures where the CET zone is clearly seen. The first grains are columnar and are more numerous than those obtained from the specimens solidified with slower cooling rate. The second type of grains is more globular type and is solidified last. These grains did not solidify directionally. In order to investigate the effect of the isolation on macro- and microstructure, one specimen was solidified without isolation. The cooling rate was 3 °C/s and the mac-rostructure is shown on Figure 5e. Because of the large radial heat loses due to radiation the solidification was not directional and there was also a large shrinkage cavity. The surface was solidified prior to the center of the specimen and the lack of the material appears because it could not be compensated by compression loading. The grain size does not differ from that obtained from the specimen which was solidified with isolation. Conclusions A solidification test was developed, using thermo-mechanical simulator Gleeble 1500D which enables simultaneous computer guided mechanical and thermal loading. Additional cooling ribs were used to control the axial thermal gradient. With varying the position of these ribs different temperature fields were obtained. The radial temperature difference was minimized by means of refractory material, placed around the quartz crucible. With an additional test without refractory material it was proven that solidification was not unidirectional and a large shrinkage cavity was observed. A comparison between four samples solidified and cooled with different cooling rates was made. It was observed that cooling rate has a substantial influence on final grain size. With increasing the cooling rate the grains are found to be smaller. CET zone was also observed in the sample that was cooled with the highest cooling rate. Povzetek Laboratorijski test simulacije strjevanja na termo-mehanskem simulatorju Gleeble 1500D Razvit je bil test za strjevanje kovinskih materialov. Test je bil razvit kot dodatek termo-mehanskemu simulatorju metalurških stanj, Gleeble 1500D, ki omogoča simultano računalniško vodenje temperaturnega in mehanskega programa obremenjevanja vzorca. Z dodatnimi, vodno hlajenimi, bakrenimi, hladilnimi rebri je bil kontroliran aksialni temperaturni gradient. S premikanjem le-teh je moč doseči različna temperaturna polja. Radialni temperaturni gradient je bil zmanjšan z uporabo ognjevzdržnega materiala, ki je obdajal kvarčno cevko. Z dodatnim testom, ki je bil izveden brez ognje-vzdržnega materiala, je bilo pokazano, da strjevanje ni potekalo usmerjeno, oziroma ni bilo enoosno. Narejena je bila primerjava med štirimi vzorci, strjenimi in ohlajenimi z različnimi ohlajevalnimi hitrostmi. Opaženo je bilo, da ima ohlajevalna hitrost močan vpliv na končno velikost zrn. Z povečevanjem ohla-jevalne hitrosti so zrna postajala manjša, v vzorcu, ki je bil ohlajen z najvišjo hitrostjo, pa je moč opaziti prehodno cono med stebričastimi in ekviaksialnimi kristali. References [1] Seol, D.J., Won, Y.M., Oh, K. H., Shin, Y.C. and Yim, C.H. (2000): Mechanical Behaviour of Carbon Steels in the Temperature Range of Mushy Zone. ISIJ International; Vol. 40, No. 4, pp. 356-363. [2] Seol, D. j., Won, Y.M., Yeo, T., Oh, K.H., Park, J.K. and Yim, C. H. (1999): High Temperature Deformation Behavior of Carbon Steel in the Austenite and 5-Ferrite Regions. ISIJ International.; Vol. 39, No. 1, pp. 91-98. [3] Na, W., Zijiu D., Weichang, C., Yan, Z. (1989): Hot Ducility of Continuous Casting Carbon Steel. SPT3.; vol. 10-12, Vienna. [4] Glpwacki, M., Malinowski, Z., Hojny, M., Jedrzejczyk, D. (2004): The phisical and mathematical modelling of plastic deformation of samples with mushy zone. Inverse Problems, Design and Optimization Symposium. Rio de Janeiro, Brazil. [5] Suzuki, H.G., Nishimura, S. and Ya- maguchi, S. (1988): Physical Simulation of the Continuous Casting of Steel. The International Symposium on Physical Simulation of Welding, Hot Forming and Continuous Casting held in Ottawa. Canada. [6] Suzuki, H.G., Nishimura, S. and Yamagutchi, S. (1984): Improvement of Hot Ductility of Continuously Cast Carbon Steels. Transactions ISIJ.; Vol. 24, pp. 54-59. [7] Suzuki, H.G., Nishimura, S. and Yamagutchi, S. (1982): Charac- teristics of Hot Ductility in Steels. Transactions ISIJ.; Vol. 22, pp. 48-56. [8] Kostrivas, A. and Lippold, j.c. (2000): A Method for Studying Weld Fusion Boundary Microstructure Evolution in Aluminum Alloys. Welding Research Supplement. pp. 1-8. Comparative test of active and passive multichannel analysis of surface waves (MASW) methods and microtremor HVSR method Primerjalni test aktivne in pasivne večkanalne analize površinskih valov (MASW) ter metode mikrotremorjev (HVSR) Andrej Gosar1,2, Robert Stopar3, Janez Rošer2 'Environmental Agency of the Republic of Slovenia, Seismology and Geology Office, Dunajska cesta 47, SI-1000 Ljubljana, Slovenia, E-mail: andrej.gosar@gov.si ^University of Ljubljana, Faculty of Natural Sciences and Engineering, Aškerčeva cesta 12, SI-1000 Ljubljana, Slovenia; E-mail: janez.roser@ntf.uni-lj.si 3Geoinženiring d.o.o., Dimičeva ulica 14, SI-1000 Ljubljana, Slovenia; E-mail: robert.stopar@geo-inz.si Received: December 5, 2007 Accepted: January 15, 2008 Abstract: Shallow shear-wave velocity structure is important for seismological ground motion studies and for geotechnical engineering, but it is quite difficult and expensive to derive by using conventional geophysical techniques. Multichannel analysis of surface waves (MASW) and microtremor methods are therefore a valuable alternative developed in the last decade. A test of active and passive MASW and microtremor HVSR method was conducted in the southern part of Ljubljana which is characterised by soft sediments and strong seismological site effects. Land streamer which allows fast movement of geophones array in the field was successfully applied for the first time. Shear-wave velocities in the range 50-200 m/s were obtained in the 25 m thick layer of Quaternary sediments overlying Palaeozoic bedrock. The correspondence of velocity profiles obtained with different methods was satisfactory. Active MASW proved most useful in a case of target depth which does not exceed 30 m and passive MASW for greater depths. The advantage of microtremor HVSR is that it yields direct estimate of the fundamental resonance frequency of the sediments. Izvleček: Hitrost strižnih seizmičnih valov v površinskih plasteh je pomembna za seizmološke analize nihanja tal ob potresu in v geotehniki, vendar pa jo je dokaj težko in drago določiti z uveljavljenimi geofizikalnimi metodami. V zadnjem desetletju pa so razvili nove metode večkanalne analize površinskih valov (MASW) in spektralnih razmerij mikrotremorjev (HVSR). V južnem delu Ljubljane, za katerega so značilni mehki sedimenti in izra- ziti lokalni seizmološki vplivi na potresne valove, smo izvedli test aktivne in pasivne MASW metode ter metode mikrotremorjev. Pri tem smo prvič uporabili »land streamer«, ki omogoča hitro premikanje geofonov na terenu. V 25 m debeli plasti kvartarnih sedimentov, ki prekrivajo paleozojsko podlago smo ugotovili hitrosti strižnih valov v razponu 50-200 m/s. Ujemanje hitrostnih profilov določenih z različnimi metodami je bilo zadovoljivo. Pokazalo se je, da je aktivna MASW metoda najbolj uporabna na območjih, kjer ciljna globina ne presega 30 m, pasivna MASW metoda pa tudi pri večjih globinah. Prednost metode mikrotremorjev (HVSR) je, da daje neposredno oceno osnovne resonančne frekvence sedimentov. Key words: multichannel analysis of surface waves (MASW), microtremors, horizontal-to-vertical spectral ratio (HVSR), Rayleigh waves, shear-wave velocity, Ljubljana Moor Ključne besede: večkanalna analiza površinskih valov (MASW), mikrotrem-orji, spektralno razmerje horizontalne in vertikalne komponente (HVSR), Rayleighovi valovi, hitrost strižnih valov, Ljubljansko barje Introduction Determination of a shallow shear-wave velocity structure is important for any quantitative microzonation study in seismic hazard assessment. The soil classification is according to Eurocode 8 standard for the design of earthquake resistant structures (Eurocode 8, 2003) based primarily on average shear-wave velocity in the upper 30 m of the soil profile (VS3(). If this is not available, the results of the Standard Penetration Test (NSPT) or shear modulus (cj are also used. All are directly linked to a material's stiffness. From the seismologi-cal point of view the shear-wave velocity is the best indicator. Besides determination of a ground type the shear-wave velocity is a critical input parameter for any numerical ground motion simulation and estimation of site amplification. Since it is directly related to the shear modulus, it is also very important in geotechnical engineering and environmental studies. The conventional approaches for near-surface shear-wave velocity investigations have been shear-wave seismic refraction method and down-hole velocity measurement in boreholes. Seismic signals from these surveys consist of wavelets with frequencies usually higher than 30 Hz. Application of both methods is relatively expensive in terms of field operation, data analysis and overall costs to be adequately included in microzonation studies. Usually such studies should cover large urbane areas and therefore require a pattern of measurements which is dense enough for a given geological setting to be representative. The obvious drawback of a down-hole method is the high cost of drilling. Seismic refraction method is also time consuming because it should be conducted separately using longitudinal- (P) and shear- (S) waves using two sets of geophones (vertical and horizontal) and different ways of signal generation by a sledgehammer. The P-waves are needed to determine the depth Comparative test of active and passive multichannel analysis. 43 structure and the S-waves to obtain relevant velocities for seismological site characterisation. In noisy urban environment, it is often difficult to generate enough strong signal to be effective. In the last decade a new method called Multichannel Analysis of Surface Waves (MASW) was developed (park et al., 1999; Wightman et al., 2002) which has several advantages in comparison to conventional seismic refraction and borehole measurements in determination of a shallow shear-wave velocity structure. It is based on the study of the dispersion of surface seismic (mainly Rayleigh) waves. These waves have much lower frequencies (e. g. 1-30 Hz) than body waves used in conventional seismic investigations. The sampling depth of a particular frequency component of surface waves is in direct proportion to its wavelength. This property makes the surface wave velocity frequency dependent, i. e. dispersive. The shear-wave velocity structure can be therefore obtained by the inversion of surface-waves dispersion curve (Xia et al., 1999), depending how the surface waves are generated active and passive MASW techniques are known (park et al., 2007). In active MASW method the surface waves are generated through an impact source like a sledgehammer, similar as in refraction seismic method. On the other hand the passive MASW method utilizes surface waves generated passively (seismic noise) by natural (tidal motion, sea waves, wind, rivers) or artificial (traffic, industry) activities. Ambient vibrations (seismic noise of natural and artificial origin) are used also in microtremor method. In this method mi- crotremors are recorded with single three-component seismometer and analyzed in a frequency domain. Spectral ratio between the records on horizontal and vertical component yield fundamental frequency of soft sediments deposited over hard bedrock. The method is therefore called Horizontal to Vertical Spectral Ratio (HVSR) method. It is used mainly in quantitative microzo-nation to identify the areas where the danger of resonance between sediments (soil) and buildings exist. This method does not provide directly shear-wave velocity structure, but this can be derived by modelling of spectral ratio curve if necessary. For the Ljubljana (the capital of Slovenia) region a new quantitative microzonation based on microtremor measurements in a very dense grid of 200 m x 200 m (Figure 1) is in preparation (Gosar , 2007b). Particular attention is given to the southern part of Ljubljana, which is built on very soft lacustrine and marsh deposits of the Ljubljana Moor where strong site effects can be expected. Most of this area is based on preliminary data classified as Eurocode 8 ground type S1 (Zupančič et al., 2004). For S1 and S2 ground types Eurocode 8 standard does not give soil factors but prescribes site investigations to derive the amplification factor. Therefore we decided to perform a comparative test of two different MASW methods and microtremor method to asses their applicability for further investigations in this area. The test site was located near Ljubljanica river on Dolgi breg (Figure 1). For this location the depth to the bedrock (approx. 25 m) is known from nearby borehole and from geophysical measurements (Figure 2). In addition Standard Spectral Ratio (SSR) analysis of Figure 1. Location map of seismic measurements at Dolgi breg in the southern part of Ljubljana. Triangles indicate planed microtremor measurements. Slika 1. Položaj seizmičnih meritev na Dolgem bregu v južnem delu Ljubljane. Trikotniki označujejo načrtovane meritve mikrotremorjev. 0 1 2 km Figure 2. Profile across the Ljubljana Moor (Quaternary sediments) and Golovec hill (Permian and Carboniferous sandstones, conglomerates and shales) with the location of measurements at Dolgi breg Slika 2. Profil prek Ljubljanskega Barja (kvartarni sedimenti) in Golovca (permski in karbonski peščenjaki, konglomerati in skrilavci) z lokacijo meritev na Dolgem bregu earthquake data was available (Gosar & živčić, 1998) which allowed comparison of site amplification. Seismogeological setting Ljubljana, the capital of Slovenia is situated in a young sedimentary basin filled with Quaternary deposits. According to the seismic hazard map of Slovenia for 475-years return period (Lapajne et al., 2001), a relatively high seismic hazard is characteristic of the area with design ground acceleration values of 0.20-0.25 g for a rock site. At the same time this is the most densely populated area of Slovenia with more than 300.000 inhabitants. The strongest earthquake in the history of the city occurred in 1895, when Ljubljana was hit by M=6.1 earthquake which caused extensive damage of VIII-IX MCS maximum intensity. Strong site effects were characteristic of the southern part of Ljubljana, which is built on very soft lacustrine and marsh de- posits of the Ljubljana Moor. The topography of the basins bedrock is here very rugged and its depth ranges from 0 m to 200 m (Figure 2). It is composed of Permian and Carboniferous sandstones, conglomerates, shales and Triassic dolomites. The Quaternary sediments are very heterogeneous, composed of clay, gravel, sand, lacustine chalk and peat. The uppermost layers are very soft. The existing microzonation of Ljubljana was prepared in 1970 (Lapajne , 1970) using the nowadays outdated methodology of Medvedev (1965) to be used with the old seismic hazard intensity map of Slovenia which is given in MSK scale. The quantitative parameters to calculate "intensity increments" were obtained from P-wave seismic refraction measurement, but according to the methodology of Medvedev, no S-wave velocity information was collected. After the preparation of a new seismic hazard map of Slovenia (Lapajne et al., 2001) which specifies design ground acceleration for rock or firm soil, a need arose for a new microzonation prepared according to Eurocode 8 and specifying soil factors (Eurocode 8, 2003). The first attempt of a new microzonation of Ljubljana to be used in disaster prevention only, and not for earthquake resistant design, was prepared exclusively from existing data (Zupančič et al., 2004). The majority of the southern part of Ljubljana was classified in this map as ground type S1 and minor parts in the border shallower parts as ground type E. The main weakness of used existing data is a lack of shear-wave velocity information, because only at three locations S-wave refraction seismic data were available to calculate soil factors for ground type S1. Methodology Active MASW The active MASW was introduced by Park et al. (1999). It adopts the conventional seismic refraction mode of survey (Figure 3a) using an active seismic source (usually sledgehammer) and a linear receiver array, collecting data in a roll-along mode. It utilizes surface waves, mainly horizontal travelling fundamental-mode Rayleigh waves, directly from impact point to receivers. Rayleigh waves are characterized by elliptical and retrograde particle motion. Its amplitude decreases exponentially with depth (Figure 3b). Different types of waves are recorded with multichannel array including: direct and refracted arrivals, air waves, reflections, fundamental and higher modes of Rayleigh waves, back-scattering of surface waves and ambient noise. Dispersion nature of different types of waves is imaged through a 2D wave-field transformation into dispersion image (Xia et al., 2004). Certain noise wavefields such as back- and side-scattered surface waves and several types of body waves are automatically filtered out during this transformation (Park et al., 2007). From the dispersion image a dispersion curve of the fundamental mode of Rayleigh waves is picked, which is then inverted for a 1D Vs profile (Xia et al., 1999; Roth & Holin -Ger , 1999). Multiples of them recorded in a roll-along mode can be used to prepare a 2D Vs map. Typical field configuration consists of 24-channels connected to engineering seismograph (Figure 3a). Low-frequency geo-phones (e. g. 4.5 Hz) are recommended. Although the highest sensitivity is obtained with conventional geophones equipped with spikes, a land streamer (Figure 4) is a very good alternative on a flat ground, because of significant convenience in field operation. Maximum depth of investigation (Zmax) is usually in 20-30 m range. However, it can vary with different sites and different strength of active sources used. Length of the receiver spread (xT) is directly related to the longest wavelength (Xmax) that can be analyzed and is connected to the maximum depth of the investigation. On the other hand, receiver spacing (dx) is related to the shortest wavelength (Xmin) and therefore to the shallowest resolvable depth of investigation. The source offset (x1) controls the degree of the record contamination by the near-field effects (Park et al., 2006). Computer b) Figure 3. a) Schematic representation of active MASW measurements. b) Particle motion for Rayleigh waves showing amplitude decrease with depth (after Sheriff & Geldart , 1995). Slika 3. a) Shematski prikaz aktivnih MASW meritev. b) Gibanje delcev pri Rayleighjevem valovanju, ki kaže upadanje amplitude z globino (po Sheriff & Geldart, 1995). Figure 4. Land streamer with 24 vertical geophones and a sledgehammer as a seismic source; on a small insert a detail of geophone mount is shown Slika 4. Land streamer z 24 navpičnimi geofoni in kovaško kladivo kot seizmični vir; majhna slika prikazuje izvedbo pritrditve geofona When using sledgehammer or weight drop as a source a vertical stacking of multiple impacts can suppress ambient noise significantly. Passive MASW The main disadvantage of active MASW is the maximum depth of investigation which is usually 20-30 m. The amount of active-source energy needed to gain a few more Hz at the low-frequency end of the dispersion image, and thereby to increase investigation depth by several tens of meters, often rises several orders of magnitude, rendering efforts with an active source impractical and uneconomical (Park et al., 2007). On the other hand, passive surface waves generated by natural (tidal motion, sea waves, wind, rivers) or artificial (traffic, industry) activities are usually of a low frequency (1-30 Hz) with wavelengths ranging from few km (natural sources) to a few tens or hundreds of meters (artificial sources), providing a wide range of penetration depths. This method was originally developed in Japan and called microtremor survey method (okada, 2003) and adopted a smaller number (usually less than ten) of receivers. It is sometimes called also Mi-crotremor Array Measurements or MAM (Hayashi et al., 2006). Louie (2001) first introduced linear refraction microtremor arrays (ReMi method). These methods were later developed as passive MASW method, which uses 24 or more geophones to fully exploit the advantages of multichannel recording and processing (Park et al., 2007). It therefore has an increased resolution in the analysis of both the modal nature and azimuthal properties of surface waves. The passive MASW method employs a 2D geophone array such as a cross (Figure 8) or circular layout to record passive surface waves. Other array types as triangular or square are also common, but it is recommended that they have a symmetric shape. Any asymmetry can bias a result toward a specific direction of incoming surface waves that do not necessarily coincide with the actual direction of major surface-wave energy. Array dimension is directly related to the longest wavelength (Xmax) that can be analyzed and is connected to the maximum depth of the investigation. On the other hand, minimum receiver spacing is related to the shortest wavelength (Xmin) and therefore to the shallowest resolvable depth of investigation. The typical depth of investigation for passive MASW is up to 100 m. Data processing and analysis is similar as in active MASW and includes three steps: 1) generation of the dispersion image (phase velocity-frequency chart), 2) extraction of the dispersion curve from the image and 3) inversion of 1D shear-wave velocity profile from the dispersion curve (Park et al., 2006). Some techniques like ReMi use slowness instead of phase velocity. It is often useful to combine dispersion images from active and passive sets for two reasons: to enlarge the usable bandwidth of dispersion (and therefore the depth range) and to better identify the modal nature of dispersion trends (Park et al., 2005). Microtremor HVSR The microtremor HVSR method is in the last decade widely used for microzona-tion and site effects studies (e. g. Gosar, 2007a, 2007b). However, the theoretical basis of HVSR method is still debated and different explanations have been given. "Body waves" explanation is based on S-wave resonance in soft sediments layer with minor or neglecting influence of surface waves. More widely accepted is the "surface waves" explanation that HVSR is related to the ellipticity of Rayleigh waves which is frequency dependent (Bard, 1999). HVSR exhibits therefore a sharp peak at the fundamental frequency of the sediments, if there is a high impedance contrast between the sediments and the underlying bedrock. Criticism of the HVSR method was often related to the fact that there is no common practice for data acquisition and processing. Attempts to provide standards were only recently been made (SESAME, 2004). It is widely accepted today that the frequency of the HVSR peak reflects the fundamental frequency of the sediments. Its amplitude depends mainly on the impedance contrast with the bedrock and cannot be used as a site amplification. However, a comparison with results of standard spectral ratio method has shown that the HVSR peak amplitude underestimates the actual site amplification (Bard , 1999; SESAME, 2004). HVSR also does not provide any estimate of the actual bandwidth over which the ground motion is amplified. The main advantages of HVSR method are therefore simple and low-cost measurements and direct estimates of the resonance frequency of sediments without knowing the geological and S-velocity structure of the underground. Any knowledge about the thickness or/and velocity of sediments and the comparison of HVSR results with other methods and with the observed earthquake damage can significantly improve the reliability of the results. Microtremor HVSR method does not provide directly shear-wave velocity structure, but this can be derived by modelling of spectral ratio curve if necessary. It is usually based on the search for the model whose theoretical HVSR response best matches the observed HVSR by random perturbation of model parameters within preselected limits (Herak , 2007). Data acquisition and analysis A comparative test of three different methods was performed at Dolgi breg near Ljubljanica river on the Ljubljana Moor (Figures 1 and 2). This site was selected for several reasons: a) the depth to the bedrock (approx. 25 m) is known from nearby borehole and geophysical measurements, b) the thickness of soft sediments is inside the depth penetration of active MASW method (less than 30 m), c) strong acoustic impedance contrast between sediments and bedrock is known from previous mi-crotremor measurements (Gosar, 2007b) and d) at a nearby location earthquake data were recorded which allows Standard Spectral Ratio (SSR) analysis (Gosar & živčić, 1998) for comparison. Data acquisition parameters for all three methods are summarized in Table 1. Active and passive MASW measurements were performed using 24 channel ABEM Terraloc Mk6 seismograph with 24 bit digitiser. Because active MASW and mi- Table 1. Summary of data aquisition parameters Tabela 1. Povzetek parametrov zajema podatkov Survey type Active MASW Passive MASW Microtremor HVSR Source 8 kg sledgehammer noise noise Seismograph ABEM Terraloc Mk6 ABEM Terraloc Mk6 Tromino Geophones 4.5 Hz (land streamer) 4.5 Hz (spike coupling) three-component electrodynamic Receiver array 24 channel linear 24 channel cross Array dimension (xT) 23 m 55 m Receiver spacing (dx) 1 m 5 m Source offset (x1) 5 m Receiver array move 5 m measur. at 5 points Sampling frequency 2000 Hz (0.5 ms) 500 Hz (2 ms) 128 Hz Recording time 2 s 32 s 20 min No. of records 20 20 5 crotremor HVSR methods are both sensitive to noise introduced by wind, were the measurements realized on a calm day without wind. Active and passive MASW data were processed and analysed using SurfSeis software (Park et al., 2006) and microtremor HVSR data using Grilla software (Micromed , 2006). Active MASW Active MASW measurements were performed along a walking path covered with compacted sand. The 4.5 Hz vertical geophones (24) were mounted on a "land streamer" (Figure 4) designed at Geoinženiring which allows fast movement of the receiver array between measuring points without planting the geophones equipped with spikes into the ground. Land streamer is composed of small sledges equipped with screws to mount geo-phones, linked with textile ribbon which allows pulling the whole array to a new position. The distance between geophones was 1 m, the source offset 5 m and the array move between subsequent records 5 m. A sledgehammer was used as a source and 10 hits vertically stacked at each point. This produced a clear surface waves signal over the total recording length of 2 s (Figure 5). Together 20 records were measured along a 100 m long profile. Data were processed in the following way. After data conversion from SEG-2 to KGS format the field geometry was encoded into the header of seismic traces. Dispersion images were calculated separately Figure 5. Seismogram example of active MASW measurements Slika 5. Primer seizmograma aktivnih MASW meritev a.) 6 10 15 20 2b 30 35 Frequency (Hz) Figure 6. Dispersion images of two active MASW measurements: a) example with only fundamental mode of surface waves visible, b) example with higher modes of surface waves at frequencies >8 Hz Slika 6. Disperzijski sliki dveh aktivnih MASW meritev: a) primer z vidno le osnovno obliko površinskih valov, b) primer z višjimi oblikami površinskih valov pri frekvencah >8 Hz. 400 350 300 Ш. 250 "5 ° 200 Qt S3 150 n a. 100 50 0 10 15 20 25 Frequency (Hz) 30 35 40 Figure 7. Dispersion curves of twenty active MASW measurements (thin black lines) with average curve (thick grey line) Slika 7. Disperzijske krivulje dvajsetih aktivnih MASW meritev (tanke črne črte) s povprečno krivuljo (debelejša siva črta) for all 20 records using frequency range 1-40 Hz and phase velocity range 10-400 m/s. The dominant frequency of surface waves was around 5 Hz. A very good signal to noise ratio was obtained for all records (Figure 6). The dispersion (Figure 6a) of the fundamental mode of surface waves is therefore very clear in the frequency range from 3 to 35 Hz with a steep decrease of phase velocity in the range 2-7 Hz down to minimum phase velocity of around 70 m/s, followed by a slight increasing of the phase velocity up to 32-35 Hz. In some of dispersion images (Figure 6b) some higher modes of surface waves are clearly visible above 8 Hz. After the definition of the bounds (lower and upper limits of phase velocities for the dispersion curve to be extracted) was the automatic picking algorithm successful in extraction of the dispersion curve due to good signal to noise ratio. The total number of points constituting the dispersion curve was set to 30 with equal-wavelength frequency interval used to make the frequency interval more dense at low and coarse at high frequencies. Dispersion curves for all 20 records are together with average curve shown in Figure 7. They are very similar, there is some discrepancy only in the initial part (low frequency) of the curves. One-dimensional (1D) inversion of dispersion curves was performed using a gradient based iterative solution to the weighted equation (Xia et al., 1999) using LevenbergMarquardt method. A variable model (the thickness of layers is increasing with depth) of ten layers was applied. The maximum depth defined by the size of the array and the lowest frequency of dispersion curve was around 30 m. The stopping criteria for inversion was maximum 12 iterations or Figure 8. Cross geophone array used for passive MASW measurements Slika 8. Križna geofonska razvrstitev uporabljena za pasivne MASW meritve RMS error in phase velocity lower than 5. P-wave velocity was fixed to S-wave velocity using the Poisson ratio of 0.4. The average result of inversion for all 20 records is together with ± one standard deviation shown in Figure 14a. The variability of the results was quite small, because of the similarity of dispersion curves. It becomes greater only below the sediments/bedrock boundary which is clearly defined at around 25 m as a steep increase of S-velocity from around 200 m/s to 350 m/s. Passive MASW Passive MASW measurements were performed using symmetric cross-array (Figure 8) on a land covered with grass. The 4.5 Hz vertical geophones equipped with spikes were planted in equidistance with 5 m spacing in N-S and E-W direction. The array dimension in each direction was 55 m, which roughly determines the maximum depth of investigation. Together 20 records of 32 s length (Figure 9) were measured without moving the geophone array. Figure 9. Seismogram example of passive MASW measurements Slika 9. Primer seizmograma pasivnih MASW meritev Data were processed in the following way. After data conversion from SEG-2 to KGS format the field geometry was encoded into the header of seismic traces. Dispersion image was calculated separately for all 20 records and the dispersion images than stacked together (Figure 10). The frequency range of calculation was 1-25 Hz and phase velocity range 10-300 m/s. A signal to noise ratio is obviously lower in passive than in active measurements. Nevertheless is the fundamental mode of surface waves quite clear in the frequency range 3-14 Hz, whereas higher modes prevail above 14 Hz. Dispersion curve was extracted in the frequency range 2-14 Hz using the same parameters as in active MASW. Both dispersion curves, average for active MASW and for passive MASW, are shown in the Figure 11. The shape of both curves is similar with a clear bend at around 7 Hz, but the curve of passive MASW is slightly shifted towards lower frequencies and lower phase velocities. In the frequency range 8-14 Hz is the passive MASW dispersion curve almost flat and shows a phase velocity of around 30 m/s. For one-dimensional (1D) inversion of dispersion curve the same method was applied as in active MASW using a variable model (the thickness of layers is increasing with depth) of 13 layers to obtain a comparable layer thicknesses in upper 30 m as in active MASW. The maximum depth defined by the size of the array and the lowest frequency of dispersion curve was around 56 m. The stopping criteria for inversion was maximum 12 iterations or RMS error in phase velocity lower than 5. P-wave velocity was fixed to S-wave velocity using the Poisson ratio of 0.4. The result of the inversion is shown in Figure 14b. 6 10 15 Frequency (Hz) Figure 10. Dispersion image of passive MASW measurements Slika 10. Disperzijska slika pasivnih MASW meritev Figure 11. Dispersion curves of active (average) and passive MASW measurements Slika 11. Disperzni krivulji aktivnih (povprečje) in pasivnih MASW meritev Microtremor HVSR Microtremor measurements were performed by using five portable seismographs Tromino (Micromed) composed of three orthogonal electrodynamic velocity sensors, 24 bit digitizer and recording unit with flash memory card. All parts are integrated in a common case to avoid electronic and mechanical noise that can be introduced by wiring between equipment parts. Good ground coupling on soft soils was obtained by using long spikes mounted at the base of the seismograph. Seismographs were deployed along the same 100 m long profile as used for active MASW measurements with 25 m spacing between instruments. The recording length was 20 minutes, which allows spectral analysis down to 0.5 Hz. HVSR analysis was performed in the following way. Recorded time series were visually inspected to identify stronger transient noise. Each record was then split into 30 s long non-overlapping windows for which amplitude spectra in a range 0.5-64 Hz were computed using a triangular window with 5 % smoothing and corrected for sensor transfer function. HVSR was computed as the average of both horizontal component spectra divided by the vertical spectrum for each window. From the colour coded plot of HVSR functions for all 40 windows, the windows including strong transient noise were identified in order to be excluded from further computation. At the end, the average HVSR function with a 95 % confidence interval was computed. All five HVSR curves are shown in Figure 12. They all show a sharp peak related to the fundamental frequency of sediments at 1.5 Hz (range 1.4-1.6 Hz). The amplitude of the peak which is less stable parameter Figure 12. HVSR curves of five microtremor measurements Slika 12. Krivulje HVSR petih meritev mikrotremorjev Frequency (Hz) Figure 13. Results of modelling of average microtremor HVSR curve Slika 13. Rezultat modeliranja povprečne krivulje HVSR iz meritev mikrotremorjev of HVSR analysis is from 9.5 to 13 (average 10.5) what is an indication of a strong acoustic impedance contrast between sediments and bedrock. Average curve calculated from all five HVSR curves is shown in Figure 13. The obtained fundamental frequency and HVSR amplitude is comparable to the results of Standard Spectral Ratio (SSR) analysis performed at nearby Rakova jelša, where seismograms of two regional earthquakes were recorded. Their amplitude spectra was divided by the spectra of the records of same earthquakes measured at a rock site on a Golovec hill to obtain a SSR. The dominant frequency of amplification obtained was around 2 Hz and the maximum amplification around 12 (Gosar & živČić, 1998). One-dimensional modelling of the average HVSR curve was performed using ModelHVSR program (Herak, 2007) which computes the theoretical P- and S-wave transfer function (amplification) of a layered, viscoelastic model for vertical incident P- and S-waves and use it for the calculation of a theoretical HVSR curve. Since only seismic impedances and travel times through layers have an influence on defining a transfer function, both depths and velocities can not be resolved at the same time. Therefore we used the same layer thicknesses as in active MASW inversion and keep them constant in a modelling procedure. For a starting model we also took velocities obtained by the inversion of active MASW measurement and then in a random model perturbation allowed a maximum 25 % variation of Vp and Vs. The number of random tries was 1000. The results are shown in Figure 13 as: measured average HVSR curve, curve which corresponds to the starting model and a curve which corresponds to the final model shown in Figure 14c. The fit between measured and calculated HVSR curve in terms of frequency and amplitude is very good, but there is a difference in the width of the peak. Results The one-dimensional shear-waves velocity profiles obtained with three different methods are shown in Figure 14. Despite determination of the depth of sediments/ bedrock boundary is not the strong part of applied methods, is it clearly reflected at around 25 m in both profiles obtained by active MASW and microtremor HVSR as a sharp increase of S-velocity from around 200 m/s to 350-400 m/s. Passive MASW is less sensitive to the strong contrast of acoustic impedance and therefore is this boundary not so clear. However is the increase of S-velocity to around 300 m/s below the depth of 26 m already indicative for a bedrock. Comparison of all three velocity profiles inside the sediments shows the following: a) all the profiles start with thin (1-2 m thick) low-velocity layer followed by 1-1.5 m thick higher velocity layer (120-150 m/s); since the passive MASW was recorded on a grass is the soft surface layer there thicker in comparison to active MASW measurements recorded on a path built of compacted sand, Figure 14. Shear-wave velocity profiles from a) active MASW (with ± one standard deviation), b) passive MASW and c) microtremor HVSR modelling Slika 14. Profili hitrosti strižnih valov za a) aktivni MASW (z ± enim standardnim odklonom), b) pasivni MASW in c) modeliranje krivulje HVSR iz mikrotremorjev b) in the depth range 2-7.5 m there is a low velocity layer (50-120 m/s), c) in the depth range 7.5-25 m is the velocity according to active MASW and microtremor HVSR quite stable (150210 m/s), while according to passive MASW there is a gradual increase of velocity from 150 to 250 m/s. The S-velocities from dispersion of surface waves for the upper five meters are comparable to the velocities from shallow seismic refraction measurements performed at geologically similar location at Park Svoboda, also in the southern part of Ljubljana, where the velocities between 95 and 180 m/s were measured in the first five meters (Živanović & Stopar, 1995). The parameter widely applied in seismic microzonation, also the main parameter for ground type classification in Eurocode 8 standard (Eurocode 8, 2003), is average shear-wave velocity in upper 30 m (vs30). It is computed according to the following expression where hi and V denote the thickness (in m) and shear-wave velocity (in m/s) in the i-th formation of layer, in a total of N, existing in the top 30 metres. Since the shear-wave velocity in the bedrock can not be well defined with applied methods we computed equivalent average velocity for the total thickness of sediments (around 25 m) and obtained the following values: • active MASW - 145 m/s, • passive MASW - 120 m/s, • microtremor HVSR - 120 m/s. Considering only this parameter to define the ground type in Eurocode 8, can be the investigated site classified as ground type D (vs<180 m/s). But if we consider also a description of the stratigraphic profile, it is more likely ground type S1 (vs<100 m/s) described as: deposits consisting - or containing a layer at least 10 m thick - of soft clay/silts with high plasticity index and high water content. Conclusions Performed investigations with three different methods have shown that they are all effective in the determination of a shallow shear-waves velocity profile, but there are also some important differences between them. Obtained one-dimensional velocity profiles are similar to acceptable extent. The average shear-wave velocity in the 25 m thick layer of sediments is between 120 m/s and 145 m/s. The value obtained by active MASW (145 m/s) is 20 % greater than the values obtained by passive MASW and microtremor HVSR modelling (120 m/s). We found no explanation for this, but the difference is not too big to have a considerable influence on the determination of the ground type in seismic microzonation. The ground at investigated site can be therefore according to Eurocode 8 classified as type D or more likely S1, if we consider also a description of the stratigraphic profile. Comparison of active and passive MASW has shown that if the depth of investigation does not exceed 30 m much more clear dis- persion image of surface waves is obtained with active method and is therefore preferable. A possible solution to increase the usable frequency range of dispersion would be to combine dispersion images obtained from active and passive measurements at the same location with different geophone arrays (Park et al., 2005) or using even the same linear array along a road where the traffic represents strong enough source of surface waves (Park et al., 2006). In the later case a long record is used triggered by a single hit of a sledgehammer. Initial part of the record is then processed as active and the remaining part as passive MASW. Land streamer array of geophones was tested for the first time and proved very efficient for active MASW measurements along a two-dimensional profile. The only condition is that the surface of the ground is flat enough to assure near-vertical position of geophones. In a case of expected lateral variations of velocity, two-dimensional measurements have additional advantages with respect to passive measurements. Microtremor HVSR method yield directly the fundamental frequency of the sediments overlying the bedrock which itself is a very valuable parameter of any microzo-nation, because it provides an estimate of the danger of soil-structure resonance. S-velocity profile can be derived by modelling of HVSR curve only if a reliable constraint on the thickness of the sediments can be done. If this is a case, as shown in our test, also microtremor data can provide a good estimate of one-dimensional S-velocity profile. Moreover, applicability of microtremor HVSR method highly depends on a strength of the impedance contrast between sediments and bedrock. On the contrary, MASW methods provide velocity profiles also for sites with gradual increase of velocity with depth. Povzetek Primerjalni test aktivne in pasivne večkanalne analize površinskih valov (MASW) ter metode mikrotremorjev (HVSR) Hitrost strižnih seizmičnih valov v površinskih plasteh je pomembna za seizmološke analize nihanja tal ob potresu in v geotehniki, vendar pa jo je z uveljavljenimi geofizikalnimi metodami dokaj težko in drago določiti. V zadnjem desetletju pa so razvili nove metode večkanalne analize površinskih valov (MASW) in spektralnih razmerij mikrotremorjev (HVSR). MASW metoda temelji na disperziji površinskih (predvsem Rayleighjevih) valov, ki imajo precej nižje frekvence (1-30 Hz) kot prostorski seizmični valovi. Pri aktivnem MASW generiramo seizmične valove z udarci kladiva, pri pasivnem MASW in pri metodi mikrotremorjev pa uporabljamo seizmični nemir naravnega in umetnega izvora, ki je stalno prisoten v okolju. V južnem delu Ljubljane, za katerega so značilni mehki sedimenti in izraziti lokalni seizmološki vplivi na potresne valove, smo izvedli test aktivne in pasivne MASW metode ter metode mikrotremorjev. Testno območje se nahaja na Dolgem bregu ob Ljubljanici, kjer je debelina kvartarnih sedimentov okoli 25 m. Pri aktivnem MASW smo prvič uporabili geofone pritrjene na posebnih nosilcih povezanih s trakom (»land streamer«), ki omogoča hitro premikanje linearne razvrstitve 24-ih geofonov v medsebojni razdalji 1 m. Pri pasivnem MASW smo uporabili križno razvrstitev 2 x 12 geofonov v medsebojni razdalji 5 m. Meritve mikrotremoijev pa smo izvedli s posebnimi trikomponentni-mi seizmografi. Pokazalo se je, da je aktivna MASW metoda najbolj uporabna na območjih, kjer ciljna globina ne presega 30 m, pasivna MASW metoda pa tudi pri večjih globinah. Prednost metode mikro-tremorjev (HVSR) je, da daje neposredno oceno osnovne resonančne frekvence sedi-mentov. Pri slednji smo hitrostni profil določili z eno-dimenzionalnim modeliranjem spektralnega razmerja obeh vodoravnih glede na navpično komponento zapisa. V 25 m debeli plasti kvartarnih sedimentov v katerih prevladujeta glina in pesek smo ugotovili hitrosti strižnih valov v razponu 50-200 m/s, v podlagi iz paleozojskega peščenjaka, konglomerata in skrilavca pa 350-400 m/s. Pod 1-2 m debelo površinsko nizkohitrostno plastjo je 1-1,5 m debela višjehitrostna plast (120-150 m/s). V globini 2-7,5 m sledi nižjehitrostna plast (50120 m/s). Med 7,5 m in 25 m je hitrost po aktivnem MASW in mikrotremoijih dokaj stalna (150-210 m/s), po podatkih pasivnega MASW pa postopoma narašča od 150 do 250 m/s. Ujemanje hitrostnih profilov določenih z različnimi metodami je bilo zadovoljivo. Povprečna hitrost sedimentov v vrhnjih 30 m (vs30), ki se po standardu Eurocode 8 uporablja za klasifikacijo tal v potresni mikrorajonizaciji, je med 120 in 145 m/s. To bi uvrstilo obravnavana tla v vrsto D (v<180 m/s). Če pa upoštevamo še dodaten opis stratigrafskega profila, pa je bolj ustrezna uvrstitev v Sj (vs<100 m/s) saj profil vsebuje debelejšo plast zelo mehkih glinenih sedimentov z visoko vsebnostjo vode. Acknowledgments The authors are indebted to Ivan Majhen for the construction of a land streamer and to Sandi Kmetič for his help in field measurements. References Bard, p.y. (1999): Microtremor measurements: a tool for site effect estimation? The effects of surface geology on seismic motion. Editors: (Irikura, K., Kudo, K., Okada, H. and Sasatami, T.), Balkema, pp. 1251-1279. Hayashi, k., Inazaki, t., Suzuki, h. (2006): Buried incised-channels delineation using microtremor array measurements at Soka and Misato Cities in Saitama Prefecture. Bull. Geol. Surv. Japan.; Vol. 57/9-10, pp. 309-325. Gosar, a., živčić, m. (1998): Ojačanje nihanja tal zaradi lokalne geološke zgradbe na južnem obrobju Ljubljane (Rakova jelša). Potresi v letu 1997.; pp. 59-66. Gosar, a. (2007a): Microtremor HVSR study for assessing site effects in the Bovec basin (NW Slovenia) related to 1998 Mw5.6 and 2004 Mw5.2 earthquakes. Engineering geology.; Vol. 91, pp. 178-193. Gosar, a. (2007b): Raziskave vpliva lokalne geološke zgradbe na potresno nihanje tal in ranljivosti objektov z mikrotremorji. Geologija.; Vol. 50/1, pp. 65-76. Herak, m. (2007): ModelHVSR 3.3 user manual. University of Zagreb, 6 pp. . Eurocode 8 (2003): Design of structures for earthquake resistance. Part 1: General rules, seismic actions and rules for buildings. European Committe for Standardization. Lapajne, J. (1970): Seizmična mikrora-jonizacija Ljubljane. Geofizikalne raziskave 1969-1970. Geološki zavod Ljubljana, 16 pp. (unpublished report). Lapajne, J., Sket Motnikar, B., Zupančič, P. (2001): Karta potresne nevarnosti Slovenije - projektni pospešek tal. Agencija RS za okolje. Louie, L.N. (2001): Faster, Better: Shear-wave velocity to 100 meters depth from refraction microtremor arrays. Bul. 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(1999): Inversion of source-generated noise in highresolution seismic data. The Leading Edge; Vol. 18/12, pp. 14021406. SESAME (2004): Guidelines for the implementation of the H/V spectral ratio technique on ambient vibrations: measurements, processing andinterpretation.; 62 pp. . Sheriff, R.E., Geldart, L.P. (1995): Exploration seismology. Cambridge University Press, 592 pp. Wightman, W.E., Jalinoos, F., Sirles, P., Hanna, K. (2002): Multichannel Analysis of Surface Waves Method. http://www.cflhd.gov/agm/ engApplications/Pavements/414 MultichannelAnalysisSurfWaves-Method.htm Xia, J., Miller, R.D., Park, C.B. (1999): Estimation of near-surface shear-wave velocity by inversion of Rayleigh waves. Geophysics.; Vol. 64, pp. 691-700. Xia, J., Miller, R.D., Park, C.B., Ivanov, J., Tian, G., Chen, C. (2004): Utilization of high-frequency Rayleigh waves in near-surface geophysics. The Leading Edge.; Vol. 23/8, pp. 753-759. Zupančič, P., Sket-Motnikar, B., Gos -ar, A., Prosen, T. (2004): Karta potresne mikrorajonizacije mestne občine Ljubljana. Potresi v letu 2002.; pp. 32-54. živANOvič, m., Stopar, R. (1995): Geofizikalne raziskave lokacij monitoringa močnih potresov na območju mesta Ljubljane. Geoinženiring, 14 pp. (unpublished report). Application of seismic tomography in investigations of the v motorway alignment in the Šentvid tunnel area Uporaba seizmične tomografije pri raziskavah AC trase •s/ na območju predora Šentvid Janez Rošer ', Robert stopar2, Andrej Gosar1,3 'University of Ljubljana, Faculty of Natural Sciences and Engineering, Aškerčeva cesta 12, SI-1000 Ljubljana, Slovenia; E-mail: janez.roser@ntf.uni-lj.si 2Geoinženiring d.o.o., Dimičeva ulica 14, SI-1000 Ljubljana, Slovenia; E-mail: robert.stopar@geo-inz.si ^Environmental Agency of the Republic of Slovenia, Dunajska cesta 47, SI-1000 Ljubljana, Slovenia; E-mail: andrej.gosar@gov.si Received: December 19, 2007 Accepted: January 12, 2008 Abstract: The motorway tunnel Šentvid construction area has a very demanding geotechnical structure. On the basis of previous investigations, it was not possible to exactly define the best locations of merging caverns with ramp tunnels. That is why initially an exploration gallery has been constructed, in which different geological, geomechanical and geophysical investigations have been carried out. The goal of geophysical investigations was to obtain seismic parameters to define geomechanical rock mass characteristics in the region of planned merging caverns. Final solution is the velocity field of longitudinal and transversal seismic waves in the investigated region. Dynamic elastic moduli distribution of rock mass was also computed from seismic parameters. Seismic velocity fields and the distribution of dynamic elastic moduli well define areas of more compact rock mass. Izvleček: Območje AC predora Šentvid je v geotehničnem smislu zelo zahtevno. Ker na podlagi predhodno izvršenih preiskav ni bilo mogoče natančno določiti lokacij kavern dveh priključnih predorov, je bil najprej izdelan raziskovalni rov, v katerem so bile izvedene različne geološke, geomehanske in geofizikalne raziskave. Cilj geofizikalnih raziskav je bil s pomočjo seizmičnih parametrov določiti geomehanske lastnosti posameznih kamnin v območjih načrtovanih priključnih kavern. Končni rezultat je hitrostno polje longitudinalnega in transverzalnega seizmičnega valovanja preiskovanega območja ter iz njiju izračunani dinamični elastični moduli hribine. Seizmična tomografija je dobro opredelila območja kompaktnejše kamnine, kar odražajo tako hitrosti longitudinalnega in transverzalnega valovanja kot tudi dinamični elastični moduli. Key words: geophysics, seismic tomography, Šentvid tunnel, dynamic elastic moduli Ključne besede: geofizika, seizmična tomografija, predor Šentvid, dinamični elastični moduli Introduction The Šentvid tunnel is part of the motorway bypass of Ljubljana, section Šentvid - Koseze, which connects Ljubljana with Gorenjska motorway part. There were several attempts to establish motorway bypass in the past years, but all the suggested solutions were postponed because of their pretentiousness. Due to the unbearable traffic situation the investigations for tunnel construction finally commenced in 1999. The twin-tube tunnel system Šentvid is divided into four units (Figure 1): two lane tunnel, ramp tunnels, merging caverns and three lane tunnel. The length of all tubes is approximately 3000 m and excavation profiles vary from 81 m2 in ramp tunnels to 300 m2 in merging caverns (Žigon et al., 2004). Due to outstanding dimensions of planning caverns and variable geological conditions, additional investigations were required to exactly define locations of the merging caverns. To satisfy all the requests an exploration gallery has been constructed (Figure 1). Additional geophysical investigations were performed in several stages. In October 2004 the surface seismic refraction profiling was performed as the starting point for further seismic investigation activities. After the construction of the exploration gallery had finished in 2005, the seismic investigations between the surface, the exploration gallery and the boreholes were performed. The scope of the survey was characterization of the geotechnical conditions in the motorway tunnel Šentvid Figure 1. Alignment of the Šentvid tunnel and the exploration gallery Slika 1. Trasa predora Šentvid in raziskovalnega rova Table 1. Geomechanical parameters of Permian and Carboniferous layers Tabela 1. Geomehanski parametri permokarbonskih plasti Geomechanical parameters Layers of dark grey siltstone and clayed shalestone Layers of light grey sandstone and dark grey micaceous siltstone Tectonic clay and breccia RMR class IV (35 points) class III (42 points) class V (< 20 points) oc [MPa] 1.00 2.50 - 3.30 0.04 - 0.06 Ф [°] 25 - 28 27 - 30 18 - 22 Фгег [ ] 22 - 25 24 - 27 15 - 19 c [MPa] 0.40 0.36 - 0.46 0.00 v [/] 0.26 - 0.27 0.25 - 0.26 0.29 - 0.31 E [GPa] 1.70 - 3.10 2.10 - 4.10 0.11 construction area. The goal of geophysical investigation activities was to use seismic parameters to define geomechanical rock mass characteristics in the region of planned merging caverns. modulus of elasticity, ф - angle of internal friction, фгег - residual friction angle, c - cohesion and v - Poisson's ratio (Fifer Bizjak et al., 2003). Geomechanical parameters are summarized in Table 1. Geological conditions The Šentvid tunnel alignment passes through Permian and Carboniferous sediments that include sandstone, siltstone and claystone, which are disintegrated from surface to about 30 m deep. In the tunnel area siltstone is prevalent. The region has undergone intense tectonic deformations, presumably during several deformation phases (Čadež et al., 2004). Tectonised zones consist of shalestone and highly tectonised clay. Rock masses were characterized in terms of RMR (Rock Mass Rating). The following parameters for each different rock type were determined in laboratory: ac - uniaxial compressive strength of rock mass, E - The lithological layers are generally sheared parallel to their schistosity. Fault gouge and fault breccias of all lithologies occur in association with faults and shear planes. The lateral continuity of the lithological layers is inconsistent due to frequent displacements along intersecting faults (Čadež et al., 2004). Hydrogeological conditions in tunnel area are suitable and are classified as poorly permeable and small groundwater extractions (from 0.1 to 1.0 l/s per m of tunnel tube) are expected (Brenčič , 2000). In the tunnel area two hydrogeological units were defined: weathered and disintegrated rock in portal area and the interior rock mass. Both units differ in permeability and porosity. Field investigations First phase investigations for Šentvid tunnel commenced in 1991. Later additional investigations began in 1999. In December 1999 the tunnel region was geologically and hydrogeologically mapped. In this phase five structural and nine geomechani-cal boreholes were drilled, which were all geologically monitored and cored. In boreholes seismic down-hole surveys, presio-metric tests, SPT and slug tests were performed. Laboratory investigations of the mineralogical and geomechanical properties of characteristic rock samples were also done. sectional images. Due to computing power progress the tomographic method became very useful in astronomy, followed by great success in medicine and also in geophysics. The main restrain in geophysical tomography is that geometric factors are less determinable and that the investigation plain is mostly accessible only from two directions. Seismic tomography is used to image the interior of the Earth, for determining the elastic properties of the rock masses involved in geotechnical engineering and is particularly suitable for detecting and characterizing local structures, such as faults, fractures, cavities and other discontinuities. In October 2004 surface seismic refraction investigations started. On the basis of those results further geophysical investigations were planned. When the construction of the exploration gallery was finished at the beginning of 2005, geophysical measurements in the exploration gallery and between gallery, surface and boreholes were performed. Seismic investigations included surface refraction measurements along the tunnel alignment (10 linear arrays), tomography between the exploration gallery and the surface (5 linear arrays), tomography between the exploration gallery and the boreholes (2 linear arrays) and tomography between the right and left gallery (2 linear arrays). For processing of tomographic data, the investigated area is divided into square grid, where cell dimensions depend on the seismic ray coverage (Figure 2). It is essential for a successful solution that every cell is intersected by multiple rays from different angles. Travel time of the seismic ray between the source and the receiver is equal to the sum of travel times through every single cell. Consider that the source of seismic wave motion is in point M (x, y) and the receiver (geophone) is in point N (x, y). Travel time of the signal is then written as (Figure 2): M ,N — I 1 -ds Seismic tomography The mathematical basis for tomographic imaging was laid down by Johann Radon already in 1917. He showed that a form of an object could be obtained from its cross- After discretisation: J-columns re reiver \N S — cell (t.j) 'N source boreholes Г Figure 2. Velocity field in matrix form (Cosma et al., 1984) Slika 2. Slika hitrostnega polja v matrični obliki (Cosma et al., 1984) Tomographic inversion By the tomographic inversion, the information obtained from field measurements is transformed to a model of the structure of the rock. Tomographic data sets often consist of many measurements. The result is that matrices can be large, sparse, and difficult to invert directly. A variety of computational methods have been developed to implement matrix inversions, such as generalized simulated annealing algorithm (SeisOpt , 2002) and simultaneous iterative reconstruction technique - SIRT (Jackson and Tweeton , 1994), which are both iterative solvers. These two methods were used to reconstruct the seismic velocity models in Šentvid tunnel tomography. The generalized simulated annealing algorithm performs repeated forward model- RMZ-M&G 2008, 55 ling, where new models are conditionally accepted or rejected based on a probability criterion. This criterion allows the algorithm to escape from non-unique, local, travel-time minima to achieve a unique, globally optimized model of subsurface velocity structure (SeisOpt , 2002). Another processing was performed by using the inversion algorithm based on the SIRT method. It updates an initial model through repeated cycles of forward travel time computation. Then the curved-ray inversion was performed. In the curved-ray tomography inversions the starting velocity model plays a crucial role, because the routine can be trapped in local minima misidentifying the global minimum solution (Dines and Lytle , 1979). Seismic data acquisition First we performed seismic refraction survey on the surface. Above the right exploration gallery there were 6 geophone arrays and above the left exploration gallery 4 arrays. Every array is composed of 24 geophones which record the seismic waves. Distance between receivers (4.5 Hz geophones) was 4 m. Three 24-channel digital seismographs with sample rate of 0.1 ms were used. The main purpose of refraction survey was to establish a reasonable starting model for tomography between the exploration gallery and the surface. The propagation of longitudinal (P) waves as well as transversal (S) waves was measured with all surface arrays. Because of a different kind of seismic noise (particularly traffic) and large source-receiver distances, a more powerful source was needed. Therefore explosive was used as a seismic source. It was placed in approximately 1 m deep boreholes spreading along the seismic profile. In this manner we successfully acquired refraction data from a depth of up to 50 m (Stopar, 2005). As a source of transversal wave motion we used a sledgehammer and specially designed wooden plank. The same shot-points as for surface refraction were then used also for tomographic survey between the surface and the exploration gallery. Geophones were installed in the ceiling of the exploration gallery as shown in Figure 3. Seismic profile in the right exploration gallery consists of three linear arrays (72 geophones) and in the left exploration gallery of two arrays (48 geophones). The distance between geophones was also 4 m. Figure 3. Vertical and horizontal geophone mounted on the ceiling of exploration gallery Slika 3. Vertikalni in horizontalni geofon pritrjena na stropu raziskovalnega rova Figure 4. Tomography ray-density coverage for seismic rays between the right exploration gallery, the surface and the borehole PŠ-15 Slika 4. Gostota seizmičnih žarkov pri tomografiji med desnim rovom, površino in vrtino PŠ-15 Tomography was performed also between the right and the left exploration galleries. Geophones were located in the left gallery and the shot-points in a short section of the right exploration gallery and cross-passage (Figure 10). For the shot-points we drilled shallow boreholes (approximately 1 m) in which we inserted explosive. To improve tomographic velocity fields in the lateral direction, tomography between boreholes and the exploration gallery was also conducted. The geophones were in the same locations in the ceiling as for tomography between the exploration gallery and the surface. Shot-points locations for tomography in the right exploration gallery were inside the borehole PŠ-15. The borehole PŠ-15 was 72 m deep. The shot-points in this borehole were at depths of 72 m, 55 m, 50 m, 45 m, 35 m and 27 m. The shot-points locations for tomography between the left exploration gallery and the boreholes PŠ-14 and PŠ-17 were in the borehole PŠ-17 at depths of 83 m, 78 m, 66 m, 53 m, 43 m, 33 m and 23 m. In the borehole PŠ-14 an obstruction occurred so that it was only possible to reach a depth of 50 m. Therefore the shot-points in PŠ- 14 were at depths of 50 m, 40 m, 30 m and 25 m. Figure 4 represents tomography ray-density coverage for seismic rays between the right exploration gallery, the surface and the borehole PŠ-15. The boreholes PŠ- 15 and PŠ-17 were out of the exploration gallery alignment for 15 m and 17 m, respectively (Figure 1). Thus corrections of the measured travel times were made. Figure 5. A representative seismic record with first arrivals picks obtained with explosive source on the surface and receivers in the exploration gallery Slika 5. Značilen seizmični posnetek s prvimi prihodi seizmičnega signala pridobljen s proženjem eksploziva na površini in sprejemniki v raziskovalnem rovu Seismic data analysis and modelling A total of 10176 travel times were recorded. Figure 5 shows a representative example of seismic records with corresponding picks of first arrivals of seismic waves, obtained with seismic tomography between the exploration gallery and the surface. Initial data processing involved tomo-graphic inversion based on a nonlinear optimization method using a generalized simulated annealing algorithm. The preliminary velocity data from the surface refraction seismic, interval velocities from the boreholes PŠ-14, PŠ-15 and PŠ-17 and the lithological data were used as constraints in the starting model. The final velocity model of the P waves acquired from tomography data between the surface, the right exploration gallery and the borehole PŠ-15 with 17901 nodes (81 by 221) and cell dimensions of about 1.5 m in both directions, is shown in Figure 6a. For seismic tomography of the S waves between the surface and the right exploration gallery, the tomographic calculations were carried out on a regular rectangular grid that occupied an area of about 330 m (horizontal) by 100 m (vertical), with 588 nodes (14 by 42) spaced at intervals of about 8 m in both directions (Figure 7). Next, a more detailed processing by the use of the inversion algorithm based on the SIRT was performed. For seismic P-wave tomography between the surface, the right exploration gallery and the borehole PŠ-15 the tomographic calculations were carried out on a regular rectangular grid that occupied an area of about 300 m (horizontal) by 100 m (vertical), with 1220 nodes (20 by 61) spaced at intervals of about 5 m in both directions (Figure 6b). Figure 8 represents the final velocity model of the P waves acquired from tomography data between the surface, the left exploration gallery and the boreholes PŠ-14 and PŠ-17. The model consists of 700 nodes (25 by 28) spaced at intervals of about 7 m and 6 m in the x and y directions, respectively. In order to build a reasonable initial model for the curved-ray inversion, we started by inverting the travel time data with a straight-ray approximation using an initial velocity model obtained from the surface refraction data. A smoothed version of the updated model, obtained after 16 straight-ray iterations, was then used as a starting model for the successive curved-ray iterations. Before running new iterations, however, several explicit global and node constraints were incorporated into the model. Global constraints were imposed specifying the maximum and minimum allowable velocities, which equal to 6000 and 340 m/s (the P-wave velocity in the air), respectively. Node constraints, which force the solution to match known boundary values, were applied with a fuzzy logic approach (Jackson and Tweeton , 1994) using measured specimen velocities and other supplemental site information. Constraining the grid node is mainly where low ray-coverage imposed by source-to-receiver geometry, improved mathematical resolution by reducing the ill-conditioning of the inversion. For seismic tomography of the S waves between the surface and the left exploration gallery the tomographic calculations based on the SIRT technique was also performed. Due to a bad signal-to-noise ratio in the S wave data we had to use a smaller amount of data. That is why the model consists of 121 nodes and the cell dimensions are approximately 28 by 10 m (Figure 9). The tomographic calculations of the P waves data between the right and the left exploration gallery were carried out on a regular rectangular grid with 450 nodes (45 by 10) spaced at intervals of about 6.7 m and 5.5 m in x and y directions, respectively (Figure 10). From the relation between the longitudinal and the transversal wave velocity, the dynamic elastic moduli were calculated. For the calculations we also needed the rock density data. The data were obtained from observations, laboratory and in situ measurements and are shown in Table 2 (Likar and Čadež , 2006). Calculations were based on a regular rectangular grid that occupied an area of about 340 m (horizontal) by 110 m (vertical), with 588 nodes (42 by 14) spaced at intervals of about 8 m in both directions. Rock density distribution inside the grid was determined with linear interpolation based on the range of wave velocity inside individual cells. We consider that higher seismic velocity corresponds to higher rock density and vice versa. Results and discussion Tomography between the right exploration gallery, the surface and the borehole PŠ-15 With the tomography between the right exploration gallery, the surface and the borehole PŠ-15 we acquired the exact data above the right tube of the Šentvid tunnel (Figure 6). From the result of modelling based on a nonlinear optimization method a low P velocity zone (velocities under 3000 Table 2. Rock density in the Šentvid tunnel area the more compact rock masses correspond Tabela 2. Gostota kamnin na območju predora to P velocities of about 4000 m/s. Šentvid Lithology Ф (g/cm3) Intercalations of meta-sandstone and meta-siltstone, meta-sandstone typically prevailing 2.65 Meta-siltstone with meta-sandstone layers/lenses, locally with slate layers 2.55 Slate, locally with meta-sandstone/ meta-siltstone layers 2.45 Fault breccia, fault gouge 2.30 m/s), which extends from the surface to the depth of about 30 m and indicates disintegrated rock, may be distinguished (Figure 6a). This low velocity zone is thicker on the side adjacent to the Celovška street, where parts of highly tectonised materials (probably shaly claystone) are anticipated. The second zone, characterized by P-wave velocities over 4000 m/s at distances of about 220 to 340 m, represents a more compact rock mass. With the use of the inversion algorithm based on the SIRT we acquired a more detailed P-wave distribution (Figure 6b). Up to distance of about 120 m we have disintegrated material, which resulting in low velocity zone. From that distance further a higher velocities are present, which corresponds to compact rock mass, presumably sandstone. In the vicinity of the shot-points on the surface are, due to higher resolution, noticeable abnormal areas with P-wave velocity around 3000 m/s. Individual curved shapes may indicate some geological structures, especially fault zones and incidental lithological layers. Low velocity zone in the right gallery, from 120 to 150 m, indicates highly tectonised zone. In general, We obtained similar results from a tomo-graphic S waves velocity image (Figure 7). Zone of the compact rock (S velocity over 1500 m/s) coincides with the results obtained from the tomographic P waves velocity image between the right exploration gallery, the surface and the borehole PŠ-15. Due to difference in cell dimensions between the S wave velocity model (cell size 8 by 8 m) and the P wave velocity model (cell size 1.5 by 1.5 m), the values of S wave velocity above the right exploration gallery are less reliable. From those models we can deduce that rock materials above the right tunnel tube is mostly tectonised, a minor zone of a compact rock is only in the lower right part of the tomogram, at distances of about 200 m to 320 m. Tomography between the left exploration gallery, the surface and the boreholes PŠ-14 and PŠ-17 Figure 8 presents the result of the tomography between the left exploration gallery, the surface and the boreholes PŠ-14 and PŠ-17. As expected, lower P wave velocities (lower than 2000 m/s) are on the surface, where soil and weathered rock are present. With depth the velocity increases and in the central part of the tomogram, around elevation of 370 m, it exceeds 4000 m/s. This material corresponds to seismic compact rock mass. Relatively low seismic velocities (P velocity under 3500 m/s) appear at the beginning of the left exploration gallery, i.e. up to the distance of 140 m. This corresponds to a more tectonised rock, but also indicates a fault zone. At a distance of about 180 m in the left gal- woctr^ ar (» wevn 50 70 BO 80 im 110 120 IX 140 150 ISO ITO 1Ю 190 2M 210 220 230 240 250 250 270 230 290 300 Э10 3ZO 330 MO 350 360 3'0 420 30 TO BO 90 100 11D 120 130 140 150 130 170 130 190 2H3 210 230 230 240 350 260 270 250 290 300 310 320 330 340 350 360 370 Figure 6. Tomographic P waves velocity image between the right exploration gallery, the surface and the borehole PŠ-15: a) nonlinear optimization method, b) SIRT method Slika 6. Slika hitrosti P valov pridobljenih s tomografijo med desnim raziskovalnim rovom, površino in vrtino PŠ-15: a) nelinearna optimizacijska metoda, b) SIRT metoda 60 70 BO 00 1 m 110 130 1M 140 130 150 170 130 1« 200 210 220 230 240 360 260 270 230 2B0 300 310 020 Э30 340 J50 360 Figure 7. Tomographic S waves velocity image between the right exploration gallery, the surface and the borehole PŠ-15 (nonlinear optimization method) Slika 7. Slika hitrosti S valov pridobljenih s tomografijo med desnim raziskovalnim rovom, površino in vrtino PŠ-15 (nelinearna optimizacijska metoda) W ;x:.:y of P *3Mes Hl 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 250 240 260 260 270 260 290 300 310 320 <*rji *->: II Figure 8. Tomographic P waves velocity image between the left exploration gallery, the surface and the boreholes PŠ-14 and PŠ-17 (SIRT) Slika 8. Slika hitrosti P valov pridobljenih s tomografijo med levim raziskovalnim rovom, površino in vrtinama PŠ-14 in PŠ-17 (SIRT) Vefotìty оГ S wflvuü 60 70 60 SO 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 260 290 300 310 disiarci Mill Figure 9. Tomographic S waves velocity image between the left exploration gallery, the surface and the boreholes PŠ-14 and PŠ-17 (SIRT) Slika 9. Slika hitrosti S valov pridobljenih s tomografijo med levim raziskovalnim rovom, površino in vrtinama PŠ-14 in PŠ-17 (SIRT) Figure 10. Tomographic P waves velocity image between the right and the left exploration gallery (SIRT) Slika 10. Slika hitrosti P valov pridobljenih s tomografijo med desnim in levim raziskovalnim rovom (SIRT) lery we find more favourable conditions. The P wave velocities over 4000 m/s correspond to a compact rock, most likely to sandstone. The overburden height in the left exploration gallery is higher than in the right exploration gallery. For that reason seismic data from tomography above the left exploration gallery did not have sufficient resolution to correctly image the low velocity zone at the beginning of the left gallery. From the tomographic S waves velocity image (Figure 9) similar result was obtained. Because water does not influence propagation of the transversal waves, low velocity surface layers could be even thicker. Nevertheless, higher S velocities (above 1500 m/s) indicate more compact rock mass. In modelling of the S wave velocity field above the left exploration gallery only half the amount of data as for P waves velocities was used. Thus the S wave velocity image resolution is smaller than the resolution of the P wave velocity image (Stopar, 2005). Tomography between the right and the left exploration gallery The final velocity model of the P waves acquired from tomography data between the right and the left exploration galleries is shown in Figure 10. In the first 80 m from the cross-passage, the velocity model is rather reliable. From that point further the image of P wave velocity is unreliable, due to almost parallel seismic rays. At the start of the left exploration gallery a low velocity zone, with velocity varying from 3000 to 3500 m/s, was found. According to geological data acquired during the exploration gallery construction that low velocity zone correlates with highly tectonised claystone and siltstone. Velocity increases in the direction along the left exploration gallery, where one of the merging caverns is planned. Although that velocity is relatively high, the materials in this area are moderately tectonised. At tomography between the right and the left exploration galleries we do not have to deal with surface soil and weathered materials. Thus the P wave velocities are higher than the values Figure 11. An example of obtained dynamic elastic moduli - values of dynamic Poisson's ratio above left exploration gallery Slika 11. Primer pridobljenih dinamičnih elastičnih modulov - vrednosti dinamičnega Poissonovega količnika nad levim raziskovalnim rovom Figure 12. An example of obtained dynamic elastic moduli - values of dynamic Young's modulus above the right exploration gallery Slika 12. Primer pridobljenih dinamičnih elastičnih modulov - vrednosti dinamičnega Youngovega modula nad desnim raziskovalnim rovom obtained with tomography between the laboratory measurements a larger volume surface and the exploration gallery. Higher of the material is taken into consideration. disintegration of material is also a consequence of the exploration gallery construction. Conclusions Seismic dynamic elastic moduli We determined that values of dynamic Pois-son's ratio vary from 0.24 to 0.48 (Figure 11). Higher values of dynamic Poisson's ratio near the surface are a consequence of saturated weathered and disintegrated material. The values of the dynamic Young's modulus vary from 1000 to 20000 MPa as shown in Figure 12. Compared to laboratory acquired Young's moduli for different rock types (Table 1), the calculated dynamic Young's moduli are one magnitude greater. The dynamic shear modulus varies from 200 to 7000 MPa and the dynamic bulk modulus varies from 100 to 40000 MPa. A larger anomaly appears along the right exploration gallery at distance of approximately 220 m, where values of the dynamic elastic moduli are higher. According to the seismic velocity data, the data from boreholes and other geological information, we can deduce that rock mass here is less tectonised. Taking mutual relations between dynamic elastic moduli and P and S wave velocities into account, the similarity of geological structures in all the images is not surprising. The ratio between the static and dynamic elastic moduli depends on the type of material and is usually smaller than one. The real meaning of the dynamic elastic moduli is that we can use them to distinguish between geotechnically good and weak rock masses, because in contrast to The goal of geophysical investigations was to obtain seismic parameters to define geomechanical rock mass characteristics in the region of planned merging caverns. Final solutions are the P and S wave velocity fields with additional dynamic elastic moduli calculations. All the solutions well indicate areas of a more compact rock mass. The real value of acquired data is that it presents "in-situ" conditions along the tunnel alignment. Seismic measurements between the surface and the exploration gallery were, difficult to perform due to large distances, several communications, urban noise and construction works in the exploration gallery. In spite of all that, the seismic P wave propagation signal was of good quality, only the signal data of the S wave propagation was less satisfactory, especially those from the most distant shot-points. The tomographic velocity models of the P waves present a satisfying complementary solution for locating merging caverns. The S wave velocity results of the tomography between the surface, the exploration gallery and the boreholes are not so good than the P wave velocity results. Reasons for that could be in a less accurate determination of the transversal waves arrivals, in a smaller amount of information due to worse signal-to-noise ratio and also because the variations of geomechanical parameters have a more significant effect on transversal than on longitudinal waves. Nevertheless the velocity fields of longi- tudinal and transversal waves and the dynamic elastic moduli distribution well indicate areas of a more compact rock mass. mično refrakcijsko profiliranje in seizmično tomografijo med površino, vrtinami in raziskovalnim rovom. Rezultati seizmičnih preiskav v in nad Povzetek raziskovalnim rovom predora Šentvid odražajo predvsem mehanske lastnosti pre- Uporaba seizmične tomografije pri iskovane kamnine v nadkritju predora. raziskavah AC trase na območju pre- Vrednost pridobljenih podatkov je v tem, dora Šentvid da predstavljajo "in-situ" podatek vzdolž zveznih profilov. Glede na to, da velik del Predmet geofizikalnih raziskav je bilo vrednosti hitrosti longitudinalnega valova- območje izgradnje predora Šentvid. Šent- nja izvedenih raziskav seizmične tomogra- viški hrib bo avtocesta prečkala v obliki fije dosega 3000 m/s in več, lahko govori - dveh ločenih predorskih cevi s priključ- mo o hribini. Izjema so površinske plasti, nima cevema, poseg pa je zaradi neugo- ki zlasti v smeri proti severnemu portalu dne geološke zgradbe zelo zahteven. Ker dosegajo tudi debelino več deset metrov. na podlagi predhodno izvršenih preiskav Posamezne nižje hitrostne anomalije so ni bilo mogoče natančno določiti lokacij posledica pretrte kamnine ali prelomnih priključnih kavern, je bil najprej izdelan con. Seizmične raziskave so dobro podale raziskovalni rov, v katerem so bile izve- območja kompaktnejše kamnine, kar od- dene različne geološke, geomehanske in ražajo tako slike hitrosti longitudinalnega geofizikalne raziskave. Cilj geofizikalnih in transverzalnega valovanja kot tudi slike raziskav je bil, s pomočjo seizmičnih pa- dinamičnih elastičnih modulov. Predvideni rametrov, določiti geomehanske karakteri- lokaciji priključnih kavern sta bili na osno- stike posameznih kamnin v območjih na- vi dodatnih raziskav, med katere sodijo črtovanih priključnih kavern. Geofizikalne tudi geofizikalne, potrjeni. raziskave so vključevale površinsko seiz- References BRENčič,M.(2000):Hidrogeološkoporočilo za predor Šentvid. Geološki zavod Slovenije, Ljubljana, unpublished report, 45 p. cosma, c., Ihalainen, M., Korhonen, R. (1984): The Crosshole Seismic Method. Report ofphase II. of development programme. Helsinki, 36 pp. Čadež, F., Kleberger, j., Genser, W., pöschl, I. (2004): Sentvid Motorway Tunnel - Interim Results from Slovenia's Most Recent Exploration Gallery. 7. mednarodno posvetovanje o gradnji predorov in podzemnih prostorov, zbornik referatov. Uredila: Kostiov, L. in Likar, J., Ljubljana: Društvo za podzemne in geotehnične konstrukcije in Univerza v Ljubljani, pp. 50-56. Dines, k. A. and Lytle, j.R. (1979): Computerized Geophysical Tomography. Proceedings of the IEEE.; Vol. 67, No. 7, pp. 1065-1073. Fifer Bizjak, k., petkovšek, B., pet -Rica, R. (2003): Geološke in geomehanske raziskave za predor Šentvid. Gradbeni vestnik.; Vol. 52, pp. 15-21. Jackson, M.j., Tweeton, D.R. (1994): MI-GRATOM - Geophysical tomography using wavefront migration and fuzzy constraints. USBM Report of Investigation 9497. United states department of the interior, Bureau of mines, 35 p. Likar, j., Čadež, j. (2006): Verification analysis of the stability of large underground caverns in the three-lane road tunnel Šentvid. FLAC and Numerical Modeling in Geo-mechanics - 2006, proceedings of the 4th international FLAC symposium, Spain, pp 71 - 77. Seisopt@2d (2002): Ver. 3.0, Seismic Refraction Tomography software copyright Optim, Inc., University of Nevada, Reno, Nevada. Stopar, r. (2005): Poročilo o geofizikalnih preiskavah na območju predora Šentvid (levi in desni raziskovalni rov). Geoinženiring d.o.o., Ljubljana, unpublished report, 16 p. žigon, a., žibert, m. in Jemec, p. (2004): Projektiranje predorskega sistema Šentvid. 7. mednarodno posvetovanje o gradnji predorov in podzemnih prostorov, zbornik referatov. Uredila: Kostiov, L. in Likar, J., Ljubljana: Društvo za podzemne in geotehnične konstrukcije in Univerza v Ljubljani, pp. 125147. Surveying for geophysical exploration, using a single-frequency global navigation satellite system receiver capable of 30 cm horizontal kinematical positioning uncertainty Uporaba enofrekvenčnega sprejemnika GNSS s 30 cm negotovostjo v kinematičnem načinu dela za terenske geofizikalne preiskave Franc Dimc ', Branko Mušič 2, Radko osredkar3 'University of Ljubljana, Faculty of Maritime Studies and Transportation, Pot pomorščakov 4, SI-6320 Portorož, Slovenia; E-mail: franc.dimc@fpp.uni-lj.si 2University of Ljubljana, Faculty of Arts, Department of Archaeology, Zavetiška 5, SI-1000 Ljubljana, Slovenia; E-mail: branko.music@ff.uni-lj.si 3University of Ljubljana, Faculty of Computer and Information Science, Tržaška cesta 25, SI-1001 Ljubljana, Slovenia; E-mail: radko.osredkar@fri.uni-lj.si Received: January 7, 2008 Accepted: February 25, 2008 Abstract: Some preliminary tests of various types of inexpensive Global positioning system (GPS) receivers were performed in order to assess the utility of the technique to geophysical surveying conditions. A 30 cm basic kinematical accuracy of the fixes was sought. Different sources of positioning errors are analyzed under different, realistic conditions in the field (multipath, satellite obscuration, etc) and the influence of the sampling rate and phase data processing on the relative accuracy for static and kinematical positioning analyzed. It is demonstrated that under favorable conditions a 30 cm relative uncertainty of the kinematical positioning is achievable and that under conditions where a degradation of the GPS fixes occurs during the scans, it is possible to a certain extent, by post-processing of the measurement data, to compensate for the errors and to refine the positioning results. Izvleček: V članku so predstavljeni začetni preizkusi različnih vrst cenejših sprejemnikov GPS, opravljenih z namenom ugotoviti uporabnost radio-navigacijske satelitske tehnike za geofizikalne preiskave. Preizkuse smo začeli z namenom ugotavljanja, če je natančnost določitve položaja 30 cm dosegljiva. Na terenih smo analizirali različne vzroke napak (večpotje, zas-trtost satelitov) in vpliv pogostnosti odčitavanja in obdelave faze na relativno natančnost statičnih in kinematičnih preizkusov. Pokazali smo, da je v dobrih pogojih relativna natančnost 30 cm dosegljiva in da je v določenih pogojih možno z naknadno obdelavo odčitkov (kompenzacijo napak) rezultate popraviti. Key words: GPS tracking, kinematic measurements, geophysical exploration Ključne besede: sledenje z GPS, kinematične meritve, geofizikalne raziskave Introduction The idea behind the construction of an inexpensive single frequency GPS system that is simple to use arises from the need for flexibility and effectiveness of geophysical surveys. A sufficient degree of flexibility can only be assured by the complete autonomy of the team in the planning and executing of fieldwork through the positioning of identified anomalous areas. This is the data layer in integral bases, which in archaeo-geophysical prospection represents the basis for the planning of further systematic and detailed geophysical research on identified sites through the application of the multi-method approach (see: mušič & Horvat, 2007; mušič et al., 2008). GPS equipment (receivers) is relatively cheap, is easily portable, offers real-time fixes and thus makes kinematical positioning possible (Wang et al., 2002). Neither does its application require specialist skills. It makes GPS positioning technology well suited for autonomous geophysical prospection (Gaffney , 2003), in particular in large-scale evaluation projects, where total detailed survey is not as important as establishing background levels and acquiring a good understanding of the effects of the geology and pedology. Its efficient application is of crucial importance for surveys in the regions where geodetic fixed points for terestrial position meaurements are not accessible. The nominal accuracy of the GPS positioning can be greatly improved by advanced signal processing and post processing, which means that a 30 cm accuracy of kinematical relative positioning (Van Sickle , 2001), deemed sufficient for the autonomous use of the GPS for geophysical prospection, is attainable. It is characteristic of GPS positioning methods that the accuracy of relative positions fixes is usually considerably better than the accuracy of absolute position fixes. After a comprehensive post-processing efforts a very accurate static positioning by single frequency GPS receiver it is also possible (Beran , 2007). We have thus attempted to improve the performance of relatively inexpensive GPS receivers by use of reference points of known position in the field. We were concerned solely with horizontal positioning, which is of primary importance, leaving the more difficult problem of vertical positioning to a future project. In the autonomous mode with a single frequency receiver, the position of a reference point is first measured as accurately as possible. A roving receiver then continuously corrects its position outputs by calculating its pseudo range by using single pseudo range differences (DGPS) obtained from a nearby monitoring static GNSS station on a known location, from a network of such stations, or from geostationary satellites known also as SBAS (Van Sickle , 2001). Kinematical sub-meter accuracy as determined by a single receiver was also stud- ied. This requires time triggering and/or event triggering of the logging process, and a synchronization of the process with position output acquisition. In the kine-matical acquisition mode, if there is insufficient time for the settlement of the position outputs, the positioning device must still ensure sufficient continuous accuracy. When settlement of geophysical results takes minutes, instead of seconds, semi-kinematical positioning is possible. This requires the surveyor to return to a reference measurement point after a certain period of time. Positioning and accuracy of positioning by GPS When at least four satellites are in view of the receiver, it is possible to calculate a three dimensional position from the received data. The computation of position is influenced by the propagation of the signals from the satellites through the atmosphere, and stability of the satellite clocks. Weak satellite signals, coded for higher accuracies, are distinguished from the noise with correlation techniques. In addition to time signals, the GPS receiver also receives Table 1. Some of the frequently used abbreviations Tabela 1. Seznam pogosteje uporabljanih kratic CP Carrier phase. A phase of a signal that carries the information DGPS An augmentation system whereby radionavigation signals arc monitored at a known position and the corrections so determined are transmitted to users in the coverage area. DOP A dimension!ess number that accounts for the contribution of relative satellite geometry to errors in position determination. GNSS Generic term for satellite navigation systems. GNSS-1 covers GPS and GLONASS augmented with additional ranging, differential and integrity signals (eg EGNOS, MSAS, WAAS). G PR Ground Penetrating Radar HDOP The factor by which a two-dimensional fix in a horizontal plane is degraded by geometrical considerations. RMS The variability of a measurement such as a single line of position in one dimension; with no bias also an estimate of the standard deviation of the errors. 2DRMS Twice the root-mean-square of the radial distances from the true position to the observed positions obtained from a number of trials Should contain 95% of observed positions. TPS Total positioning station UERE User equivalent range error. Any error contributing to the error budget of a stand-alone satellite navigation receiver, expressed as an equivalent error in the range between the user's receiver and satellite. Total UERE is the root sum square of the individual errors. UTM Universal Transverse Mercator, a projection whereby a meridian as line of contact between projection plane and Earth surface are used V DOP The factor by which the one-dimensional vertical accuracy of a fix is degraded by geometrical considerations. navigation signals comprising positions of satellites and their operational status. Receivers can operate in an autonomous mode or as rovers. Higher accuracies can normally be achieved by also taking into account the corrections transmitted by a primary positioning receiver station, located at a known position. Single, double and triple difference methods diminish some of the errors generated either by the primary station and/or the rover and the satellites (Van Sickle , 2001). Equipment manufacturers normally state the accuracy of positioning of their products with respect to certain conditions (signal to noise ratio) of reception, and this is considered as the greatest possible absolute accuracy that can be achieved by a device. However, nominal accuracy does not depend solely on the stated conditions, but to a much larger extent on processing and post processing of the satellite data available to the receiver. In satellite positioning it is impossible to completely exclude all the environmental factors that may influence the results. They result in an accuracy interval, which is related to the experimental standard deviation (estimated position error, also known as (d)RMS error) (USM, 1999). Since more variables (dimensions) are observed, the accuracy is noted in each dimension separately. Two dimensional (2DdRMS) is calculated for two variables. The compound error of positioning is the result of all the contributing factors: inaccurate satellite ephemeris data and inaccurate clock corrections sent, changes of propagation delays due to ionosphere density fluctuations with solar or geomagnetic activity and signals reflected from highly conductive surfaces resulting in multipath signals at the receiver position, disturbing the processing of the directly received signals and receiver thermal noise. Processing methods (phase averaging, estimation filter scenarios) of the raw signals also influence the accuracy of the results. Reducing the influence of the limited receiver view of satellite constellation (dilution of precision, DOP: HDOP - horizontal DOP, VDOP - vertical DOP) during signal processing yields the final positioning error, the so called "user equivalent range error" (UERE) (de Jong et al., 2001). The precision of a position measurement output (known as the fix) depends both upon the measurement geometry, as represented by the DOP values, and range errors caused by signal strength, ionospheric effects, and multipath errors. The latter depend upon physical surroundings of the measuring point, i.e. to terrain relief, near-by buildings or other highly reflective surfaces (water bodies), or foliage plants (Lachapelle at al., 1994). Multipath errors cause systematic variations of GPS fixes, while other sources of errors cause random, chaotic or bias type of variations. Overall uncertainty of positioning of a point is thus calculated as a product of the accuracy (experimental deviation of the measurements) and DOP (Van Sickle , 2001). The positioning accuracy of a moving receiver (rover) is in general not equal to the uncertainty of a stationary fix and should at a certain areas be determined separately. For this purpose a reference trajectory (charted path, on-site measured distances) is established and marked on the measurement site. Deviations of fixes from the reference trajectory are measured while tak- ing the velocity of the rover into account. Uncertainty of kinematical positioning is defined (USM, 1999) as the standard deviation from the mean value or the true value if known. It has been calculated in our work from the distances of fixes against a reference trajectory marked on the ground. GNSS ACCURACY REQUIRED FOR GEOPHYSICAL PURPOSES A basic requirement of geophysics is determined as a 30 cm uncertainty in kine-matical positioning. A positioning system should satisfy the demands of geophysical fieldwork, such as real-time position output acquisition with the specified accuracy. A special concern in geophysical field work is the accuracy with which the user can return to an already measured position with the same navigation system. In evaluating the positioning results, it should be understood that accurate static positioning does not necessarily lead to accurate kine-matical positioning. Obstacles obscuring or reflecting the signals from satellites, and the pattern of positions of obstacles in the field, often change the conditions of reception along the positioning trajectory, causing multipath errors. When using a low-cost GPS receiver, measurement errors, i.e. multipath and antenna variations in carrier phase, are much more likely to cause problems than with high performance receivers. Kinematical accuracy is determined from the root mean square differences between the position outputs and the nearest point on the reference trajectory. It strongly depends on the velocity of the roving receiver and capabilities of Figure 1. Test GPS equipment Slika 1. GPS oprema za preizkusne meritve the GPS software. In our work velocities up to 3 m/s have been considered. In testing the viability of a GPS based positioning sytem for geophysical fieldwork the following equipment was used (see Figure 1): • Single frequency GPS receivers: R1 Allstar (12 channels, 1 Hz), R2 Allstar (12 channels, 5 Hz), Novatel , R3 GPSmap C60, Garmin, • antenna: Aero AT 575-70, (gain: 26 dB), Canadian Marconi Company, • total station: TPS 1100 (Leica), • GSM modem: Fastrack M1206B-on, Wavecom, • logger: laptop computer, • log software: Starview, • processing data: Matlab (Mathworks), in case of more than one geodetic point available, a transformation from GPS data to local geodetic system was used. For the comparison reasons two more GPS receivers which were not involved in the fieldwork are also taken into consideration: R4 FlexPak-V1, NovaTel and R5 SR 20, Leica Geosystems. The lowest RMS can be achieved by the R5 (0.3 m, after CP post- Table 2. Test sites with brief descriptions Tabela 2. Oznake preizkusnih terenov s kratkimi opisi Sile label De s cripti on SI sports field, predefined geometry S2 archaeological site Veselov Cvinger, near Stična S3 a car park in front of a building in Ankaran S4 the surroundings of the geodetic point at Malija S5 an archaeological site Dolge n jive, near Vrhnika S6 an archaeological site Tanagra, Greece processing) whereas the highest 2DRMS is get by the commercial R3 (static 2.5 m). Under good receiving conditions the experimentally observed RMS values might become very similar, however in atmosphere changing conditions for example a benefits of R5 would result in lower RMS as of R3. Comparison of the prices to the price of R3 as the etalon price (1 EP) gives the following sequence: R2 as already obsolete device (1.9 EP), R4 (5 EP) and R5 (from 10 EP up to 13 EP). Results and discussion Test sites and equipment types In order to test the positioning capabilities and accuracy of a GPS system, several types of equipment were tested at 5 different and well defined testing areas: the Adria sports field at Ankaran (site S1), an archaeological site at Veselov Cvinger, near Stična (site S2), a car park in front of a building in Ankaran (site S3), the surroundings of the geodetic point at Malija (site S4), and an archaeological site of Nauportus at Dolge njive, near Vrhnika (site S5) (see: mušič & Horvat, 2007; mušič et al. 2008). The third archaeological site is Tanagra (Greece) (site S6) (see: bintliff et al., 2000, 2002; Bilc, 2003; mušič et al., 2004). The different locations have considerably different topological and signal propagation characteristics: Site S1 (a sports field) has simple geometry and is topologically well defined, site S2 is an exposed location on a ridge, signals at site 53 are especially prone to multipath errors and signal losses due to obscuration, site 54 (geodetic reference point of the 1st degree) has a well defined position and low multipath variations, however it is exposed to interference and other errors, and site S5 is an archaeological site close to a river. A summary of the static positioning measurement results on the sites is given in Table 3. It can be seen that uncertainty of fixes is decreased by the absence of multi-path errors as well as open sky, and by the use of DGPS. Uncertainty was calculated for three locations: Site S2 where moderate multipath error was observed (point No. 1, was used further as a reference point at this site, as it is also a geodetic point), a location at site S3 with obvious multi-path errors, and a location at site S4, again with moderate multipath errors and additional sources of error, whose effects can only partially be resolved by data analysis. Variations of HDOP strongly influence the uncertainty. Average HDOP of experiment No. 2 was 1.24 while for experiment No. 3 Table 3. Statistical parameters of static measurements Tabela 3. Statistične značilnosti statičnega določanja položaja lixp. No. Sile Receiver Mode No. of fixes Absolute static uncertainty (m) 1 S2 R2 DGPS 7201 1.2 2 S3 R2 GPS 438855 4.5 3 S3 R2 GPS 1921488 3.4 4 S4 R3 GPS 3903 2.3 5 S4 R2 GPS 12148 2.1 6 S4 R2 DGPS 7739 1.7 it was 1.12. In the absence of loss of data due to cycle slips, the numbers of fixes is simply the product of measurement time (in seconds), and the data acquisition rate (number of fixes per second, 1 for R3 and 5 for R2). Static positioning measurements The measurements of static positioning at sites S2 and S3 are presented in Figure 2. Measurements were performed continuously for 5 consecutive days at S3 (Figure 2.a). Accuracy was determined as dRMS and was 2.96 m. The details of transformed angle/length ratio resolution are shown around a geodetic point, chosen as (0,0) position. The repeatability of observations at S2 with receiver R2 (DGPS) are shown in Figure 2.b. Measurements were performed over two days, separated by 42 days. Repeatability of positioning at points No. 2, No. 3 and No. 4 from the reference point (No. 1, with relative position 0 m) is shown. The relative experimental standard deviation of distances for points No. 2, No. 3, and No. 4 are 23 cm, 30 cm and 29 cm respectively, with a standard deviation of the reference point from its true position of 32 cm. It should be pointed out, that the large excursions of data in Figure 2.b do not represent settling times of the measurements, but real excursions of the instrument fixes from the points under consideration, caused by the movement of the experimenter from one point to another. The largest source of the uncertainties in this case are not the multipath errors, but the unfavourable position of the sites chosen (S2, S3), which have a reduced view of the satellites, not insuring optimal number of satellites in view. Data in Figure 2.b demonstrate that fixes, relative to a reference point, under unfavourable measuring conditions (obscuration of satellites) do not satisfy the accuracy requirements. However, even under such conditions the average accuracy of fixes is 8 cm from the requirement. These results cannot be directly compared to uncertainties presented in Table 3, as the relation between accuracy and uncertainty involves the variable HDOP. Assesment of kinematic uncertainty The results of assessment of kinematical uncertainty, relative to reference lines of 30.00 m and 41.30 m lengths, marked on the ground, are presented in Figure 3 and Figure 4 respectively. Measurements were performed by two receivers R1 and R2 on three different sites S1, S4 and S6. It can be observed from Figure 3 that in all cases 0 2000 4000 6000 6000 10000 12000 14000 16000 2.b Time (s) Figure 2. Results of static positioning at S3, centered with geodetic procedure (2.a) and repeatability of a distance from the reference point during fieldwork at S2 (2.b) Slika 2. Rezultati določanja položaja točke na terenu S3, osredinjeni z geodetsko izmero (2.a) in ponovljivosti določanja razdalje do referenčne točke na terenu S2 (2.b) Table 4. Statistical parameters of the 'line following' kinematical measurements on sites S1, S4 and on archaeological site S6 Tabela 4. Statistične značilnosti kinematičnih preizkusov sledenja ravni črti na terenih S1, S4 in arheološkem najdišču S6 Site Conditions Receiver No. of fixes No. о Г walks Relative kinematical uncertainty fem) Sl Multipath RI 3475 101 - 6 ± 317 S! Mul tipati R2 24551 132 5 ± 104 S4 higher HDOP R2 10740 50 1 ±41 S4 lower HDOP R2 10755 50 I ±26 S4 moderate HDOP. DGPS R2 6867 36 2± 29 S6 moderate 11DOP R2 6Ä. CÜ V У rXy Xx ли, 4 J M (-i л К у "кх Хх )м 'Lb) 1 ы \ ч / kx {О X, (2) V A line is defined in almost the same way as a point, the one difference being that the line is treated as a set of all points that equal the set of three (v u w). For example, if (3 2 -2) defines a line, then (-3/2 -1 1) is the notation for that same line. In other words, a line is an ordered set of three numbers, denoted as (v u w), which do not equal zero all at the same time, in which case (yv ум yw) would be the same line for any given у Ф 0 [1]. Incidence relation Given point P and line l - where P and l are short for (y x m) and (v u w), respectively -we say that the two are incident to one another (incidence relation being descriptive of the relation simply summed up as the point lying on the line i.e. the line going "through" the point) in the case, the following is true: {P ■ l} = {l ■ P} = yv + xu + mw = vy + ux + wm = 0 [2]. The principle of duality The axiom of geometry says that there is exactly one line that is in incidence with two different points P1 and P2, i.e. exactly one line goes through both different points. If we exchange the term "line" with the term "point" in the above axiom, we get a geometrical theorem that states there is exactly one point that is in incidence with two different lines lj and l2 - in other words, two different lines intersect at exactly one point in space. The afore-mentioned axiom and theorem are said to be mutually dual, i.e. points and lines are mutually dual spatial elements, while the "running" and intersecting of lines are mutually dual operations[3]. For different points P1(y1 x1 m) and P2(y2 x2 m2); yl Ф X • y2, x1 Ф X • x2 , m1 Ф X • m2 there is always an ordered set of three elements, (v u w), for which the following need most definitely apply: yv + xu + mlw = 0 y2v + x2u + m2w = 0 (3) And for two different lines, in our particular example ^ (v1 u1 w1) and l2 (v2 u2 w2); v1 Ф / v2, u1 Ф / • u2 , w1 Ф / • w2; there is always an ordered set of three elements, (y x ш), for which the following need apply: vyy + u1x + w1 ш = 0 v2y + u2x + w2 ш = 0 (4) Thus, homogeneous systems of equations are combined with the following expression: (5) Then we are able to beget the formula of the point or line: (6) Each set of three question. therefore represents a solution to the system under The coordinates of the point or line follow: Ci {:} ;}, 11 11, С i tì tt Й (7) A point or a line pertaining to a projective plane can be multiplied by any number X or /i , as long as the value is not equal to zero, which then gives us the actual coordinates of this same point or line: (8) For a point, this would be: And for a line: (v и н')=A. И со, y2 У, xi У1 X2 > (9) (10) The ideal point and line The parallels (coefficient of site k = k = k) l and l2 with formulas Y = k]X + n and Y = k2X + n2 are given. For X, we enter values X = , and for Y values Y = ю , then multiplying the equations with ю, which in turn gives us the formulas of lines using homogeneous coordinates: y = kx + пю and y = kx + п2ю (11) Considering that the lines are parallel, we are interested in the set of three, (v u w), such that it must correspond to both formulas. By subtracting the equations we get: ю(п1 - n2) = 0. As n1 Ф n2, then ю = 0 and the equations y = kx + пгю and y = kx + п2ю are reduced into y = xk. Since we are dealing with homogeneous coordinates, we can say that x = 1. From this, we come to the conclusion thaty = k. Thus, we obtain a set of three, (k 1 0), which does indeed correspond to both equations. If the lines lj and l2 are parallel to the y-axis, then the formulas of the lines in homogeneous coordinates have the form x = юх1 and x = юх2. In this case, the set of three (0 1 0) corresponds to both formulas. To summarize, the set of three, (k 1 0), corresponds to a formula of the forms y = kx + п1ю and y = kx + п2ю only when k = ^ = k2, or when the lines are parallel and the coefficient of site equals k. The set of three (0 1 0) corresponds to all formulas of the form x = юх1 that describe the parallels of the y-axis. A bouquet of parallel lines (all parallel lines are of the same class and form organised heaps of parallel lines denoted as "bouquets") defines a point Рда in projective plane that has been defined as an ideal point. The bouquet P consists of all lines that are parallel to a certain line l. The equation pertaining to line l is Y = kX + n, or X = Xp if it is parallel to the y rather than the x-axis. The line l belongs to bouquet Px exactly when the set of three (k 1 0) corresponds to the equation of line l in its homogeneous coordinates, and to pencil Px exactly when what corresponds to this equation is this set of three: (0 1 0). Consequentially, we can have the set of three (k 1 0) in the former case, and the set of three (0 1 0) in the latter case for homogeneous coordinates of the ideal point Px. Since we may multiply homogeneous coordinates with any number that is different than zero, we may say that the set of three (y x 0) represents the homogeneous coordinates of one ideal point, where y and x are any given elements different from zero. In this way, we have adjusted our homogeneous coordinates (y x ю) so that they befit each and every point of our projective plane. The point with such coordinates also lies in the Euclidean plane if ю Ф 0, and is an ideal point when ю = 0 [4]. Two ideal points define the ideal line l q The solution of the system are the very coordinates of our ideal line l o or, if: (12) (13) (14) The set of three (0 0 1) represents the coordinates of an ideal line such that all ideal points lie on it. The ideal line and angle of site An ideal point represents the intersection of a group of all lines that are parallel to one another in finite space. A specific ideal point upon an ideal line belongs to each group of parallel lines that in finite space represent a so-called »angle of site« between the lines of a certain class and the positive end of the x-axis. The coordinates of the line that goes through the points Pl(yl xl ml) and P2(yl + d cos ф xl + d sin ф m2), where ф is the so-called angle of site are enclosed within the line PlP2 and the positive side of x-axis, and d represents the distance between the points Pl and P2, which would be: (v u w) = / (x1(a>2 - m) - d cos фт1 y(ml - m2) + d sin фт2 d(y cos ф - x1 sin ф)) (15) If : m2 = m = l => (v u w) = / (-d cos ф d sin ф d(y cos ф - x1 sin ф)) (16) or, when: (m2= ml= l A dФ 0 A dФ да A / =d) => (v u w) = (- cosф s^ (yl cosф - xl sinф)) (17) The set (v u w) = (- cos ф sin ф (yl cos ф - xl sin ф)) represents the coordinates of the line that is notated using polar coordinates. The intersection of the line given with polar coordinates and the ideal line (0 0 1) is the ideal line, now denoted using polar coordinates: 4i n

(y x m ) = (sin ф cos ф 0) (19) The notation y xm mj = (sin ф cos ф 0) at the same time alos represents standardised coordinates of said ideal line, for which the following is valid: (20) where: 118 Ganić, A., Vulić, M, Runovc, F., Habe, T. Should the lines lj in l2 enclose the angle a , and the line l} is defined through the ideal point (sin ф; cos ф; 0), then the ideal point of line l2 is defined as (sin (ф;+a) cos (ф; + a) 0), where ф;+a is the angle of site of the line l2: sŠV«, 91 Figure 1. The angle between our two lines and angles of site Slika 1. Kot med premicama in smerna kota Intersection An intersection is both a measurement and calculation method, with the aid of which the coordinates of a new point can be calculated from measured angles or (outer) directions upon given points of the existing triangulation network. A given new point is determined as an intersection of several outer directions that are controllably oriented at each standpoint. The coordinates of points L(Yl XL) and R(Yr Xr) are given. Observation: We are observing the direction from two given points (L and R) towards the new point M. Angle a is observed from the point L between points M-left and R-right, and angle ß from point R between points L-left and M-right. Based on the given and observed information, we must establish the coordinates of the unknown point M, which would translate into us looking for XM and YM: Figure 2. Intersection Slika 2. Zunanji urez The connecting line LM denotes the line left, RM the line right, and LR the line left-right. The lines left and left-right are bisected via one another in point L and enclose the angle a, while the lines right and left-right do the same in point R, therefore enclosing the angle ß. By establishing the ideal point Lm of the line left and the ideal point Rm of the line right, the lines left and right have been accurately established. Thus, we have also established their intersection M, which represents the coordinates of the point we are seeking. L denotes the ideal point on the line left,, R the ideal point on the line right and LR the да ^ 7 да A c-7 да ideal point on the line left-right. Points Lm and Rm are obtained with the help of the ideal point LRm, which is established through the bisection of line left-right with the ideal line. When the point LRm is standardised (transformed into a format such as (sin ф cos ф 0)), we can, with the help of the latter, as well as with the help of angles a and ß, determine the points L and R on the line l . i да да да 1. Establishing the line left-right - The coordinates of point L are (yL = YL xL = XL 1) - The coordinates of point R are (y = YR = Yr + Xr + d sin и R xr = X = XL + d cos uR 1) Therefore, the following is true: The formula of the line left-right is: XL + d- cosv, 1 or, its coordinates: YL+d-sinv," XL+d-ca&vl 1 Yl 1 Yl +d sinv/ >; xL У L xL t L Ri H d smvj d cosvL 2. Establishing the ideal point on the line left-right The line left-right is bisected with the ideal point (0 0 1): The coordinates of the ideal point are denoted as follows: 0 1 Уш. = 1 r£ 1 Y, +ds inv* 1 YL 1 0 » У L 1 rf sinv* У, d sinv ,R ^-cosvf = —d -sinv* 1 У,. 1 Yl +d-sinv/1 = 0 (23) (24) (25) (26) (27) (28) (29) (30) The point LRm = A( - d sin uRR - d cos uR 0) is standardised, which means that it is multiplied by factor: I X = JyLK2+xLK2+aLK2 Consequentially, we transform the notation LRx = A( - d sin uR- d cos uR 0) into LRк A( + sin uR + cos uTR 0). L V-W +-W —=>Ы^ =X (-d-sìnvf -d-cosvf о) (31) к = J ^ - siri v * J + (il -cos v )* T^>LR. =x(-đ srnv* -rf cosvf 0) к = LR„=X(-d-sinv/ - d - cosv 1 0) К = = -pL=>Iff -(/• cosv* (A TF K ' So, finally, the standardised ideal point is: or: LR, - (+ sin (v* + kit ) +COS ^I + kn ) o) 3. Establishing the ideal points on the lines left and right (a) Ideal point L of the line left (32) (33) (34) (35) (36) (37) The line left-right encloses, along with the positive side of x-axis, the angle uR, and with M= uRT - the line left, the angle a. The angle of site of the line left is uM = uR - a and the ideal line is of the form: L = ( sin (uR - a) cos (uR - a) 0) (38) (b) Ideal point R of the line right The coefficient of site of the line right is uM = uR + ß and the ideal line is of the form: R = ( sin (uR + ß) cos № + ß) 0) (39) 4. Establishing the lines left and right (a) Establishing the line left: The line left goes through the points L and L: "left "hp sin v f ■ cos a - cosv * ■ si n a cosv," - cosa + sinv* - sina 0 X ^lefi cosvI-cosa +sinv*-sina О '■left I = 0 (40) vkfi ' X, 0 sinv*-cosa-cosv* sina 1 1 = cosv * ■ cosa +sinvf -sin a = cos(y*-o. (41) = -sinv* ■ cosa-cosv"'Sina = -sin(y*-a) (42) sinv, -cosa-cosv, sina cosv, -cosa+sinv, -sina L • i v у ' hfl л hfl (43) = -У,ф -cos (v* -a У Х,ф ■ sin (v" -a ) Coordinates of the line left: (b) Establishing the line right The line right is defined by the points R and Rw: vrighl cosv', -cos ß -smvj -sin ß 0 Л. ,„., I = cosv^ -cosß -sinv„ ■ sin = COS^^ + ß ) (45) (46) 0 sinv^ cos ß + cosvj£ - sin ß 1 I = -sinv^ 'Cosß + cosvjJ 'Kinß =-sin(vj + ß) (48) Coordinates of the line right: 5. Establishing the unknown point M The point M is defined as the intersection of the lines LM = L L and RM = R R: = 0 (50) М = (у,ч % ©„)= / «M Wleß li- Г "ад ytefi V- »w \ ''righi Wrtghl f i .':>.';' [1] (51) Figure 3. Intersection with projective coordinates Slika 3. Zunanji urez s projektivnimi koordinatami Conclusions In projective geometry, the lines have their own coordinates inasmuch as points do. A point is defined as an ordered set of three numbers (y x ш), which are not allowed to simultaneously take on the value of zero, seeing as the latter would make (ly Ix 1ш) the same point for any given l Ф 0. We can obtain an infinite number of ordered sets of coordinates of a given point from the non-homogeneous coordinates of that same point, just as well as we can obtain only one ordered pair of numbers from homogeneous coordinates. A line, much like a point, is an ordered set of three numbers, (v u w), which must not all equal zero at the same time, seeing as that would again make (pv pu pw) the same line for any given ц Ф 0. The set (v и w) = (x-x2 y-y2 y1x2-y2x1) represents the coordinates of the line that are denoted using rectangular coordinates, whilst the set (v и w) = (- cos ф sin ф y1 cos ф - x1 sin ф) represents the coordinates of the line that is denoted using polar coordinates. By using projective coordinates, the establishment of the intersection R(Y X) of two lines - the line l, defined by the points A1(Y1 X) and A2(Y2 X2), and the line l2, on which the points B1(Y1 X) and B2(Y2 X2) lie - is very simple, and is defined using the help of nine second order determinants: First, the coordinates of lines lt and l2 are established, for which six of secondary-order determinants need to be calculated: (52) (53) The intersection R, as the intersection of lines ^ and l2, is established with the calcula- tion of another three secondary-order determinants: ц = 1 *>R = (y X (o)= u, w, i 'i W, v, V, V, w, R=(y x ш)= > ± !\ = (y X l)= (у X) I (O CO (54) (55) The projective plane, as has already been mentioned, originates from the Euclidean plane when we assume ideal points and an ideal line. Thus, the point with coordinates (y X a) lies in the Euclidean plane if a Ф 0, and a = 0 to render our point ideal. Two different ideal points define the ideal line (0 0 1), on which all ideal points lie. The notation (sin ф cos ф 0) represents these coordinates of our ideal point, from which we can find the angle which a given line encloses in partnership with the positive side of the x-axis. If the line l l and the positive side of the first axis enclose the angle ф p and both 11 and l2 enclose the angle a, then the ideal point of the line l2 can be determined as (sin^;+a) cos^;+a) 0), where ф2 = ф+a is the angle of site of the line l2. Via the introduction of ideal points and an ideal line, we are able to avoid the process of calculation of lengths and angles of site in 2D measurement exercises (the practical example here being the one depicted using intersections). The coordinates of an unknown point may always be established as the intersection of two lines, defined by the given and ideal points. Povzetek Možnost uporabe homogenih (projektivnih) koordinat v dvodimenzionalnih merskih nalogah V projektivni geometriji imajo poleg točk tudi premice koordinate. Točka je definirana kot urejena trojka števil (y x a), ki niso vse hkrati enake nič, s tem da je (ky Ax Xa) ista točka za katerikoli X Ф 0. Iz nehomogenih koordinat neke točke dobimo neskončno urejenih trojk homogenih koordinat iste točke, iz homogenih koordinat neke točke pa lahko dobimo eno samo urejeno dvojico števil. Premica je urejena trojka števil (v u w), ki niso vse hkrati enake nič, s tem da je (pv ци ц-w) ista premica za katerikoli ц Ф 0. Trojka (v u w) = (x-x2y-y2yl x2- y2 x1} predstavlja koordinate premice zapisane s pravokotnimi koordinatami, trojka (v u w) = (- cos ф sin ф yl cos ф - xl sin ф) pa koordinate premice zapisane s polarnimi koordinatami. Z uporabo projektivnih koordinat je določitev presečišča R(YX) dveh premic, premice ll, ki ju določata točki Al(Yl X) in A2(Y2 X2) ter premice l2 na kateri ležita točki Bl(Yl X1 ) in B2(Y2X2) zelo enostavna, saj se presečišče določi s pomočjo devetih determinant drugega reda: Najprej se določijo koordinate premic l l in l2 za kar je potrebno rešiti šest determinant drugega reda: Presečišče R, kot presek premic l1 in l2 pa je odrejeno z rešitvijo še treh determinant drugega reda: ^ II Vi? W V V fi [i = 1 => R = (y X to)= f W, V, V, 1/, V «2 W1 W1 V2 V2 U2 R=(y X