JMS, Vol. 44, No. 1, 2008

GEOMECHANICS

ROCK MASS DEFORMATION MODELING USING THE NON-ARCHIMEDEAN ANALYSIS
S. V. Lavrikov, O. A. Mikenina, and A. F. Revuzhenko*

The non-Archimedean space is a multi-scale one. The paper shows that this face is applicable to developing mathematical models of rocks exhibiting a hierarchy of structural levels. A closed model, considering anisotropy and weakening of a rock mass, is constructed. The equations in terms of displacements and the resultant internal force vector are derived. The authors have obtained the numerical solution to the problem on deformation of a rock mass around extended galleries, and showed how the areas of weakening and residual strength evolve. The energy flow lines are plotted.

Non-Archimedean space, rock mass, stresses, strains, energy flow lines

REFERENCES
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2. A. F. Revuzhenko, S. B. Stazhevskii, and E. I. Shemyakin, «On the deformation mechanism of loose material under large-scale shears,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (1974).
3. M. Onami, et al., Introduction to Micromechanics [Russian translation], G. Ya. Gunn (Ed.), Metallurgiya, Moscow (1987).
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6. S. Aldeverio, Yi. Fenstad, R. Hueng-Kron, and T. Lindstrom, Non-Standard Methods in Stochastic Analysis and Mathematical Physics [Russian translation], Mir, Moscow (1990).
7. M. Devis, Applied Non-Standard Analysis, Wiley, New York (1977).
8. F. Klein, Elementary Mathematics from the Higher Mathematics Standpoint. Geometry [in Russian], Nauka, Moscow (1987).
9. V. A. Uspenskii, What is a Non-Standard Analysis? [in Russian], Nauka, Moscow (1987).
10. A. F. Revuzhenko, Non-Archimedean Space as the Basis of the Mathematical Apparatus in Rock Mechanics [in Russian], D. D. Ivlev and N. F. Morozov (Eds.), Fizmatlit, Moscow (2006).
11. A. F. Revuzhenko, Mechanics of Elastic-Plastic Media and the Non-Standard Anaysis [in Russian], NGU, Novosibirsk (2000).
12. N. I. Muskhelishvili, Some Fundamental Problems of Mathematical Theory of Elasticity [in Russian], Edition 5, Nauka, Moscow (1966).
13. A. F. Revuzhenko, «Rocks as a medium with internal sources and flows of energy. Report 1,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 4 (1990).
14. S. V. Lavrikov and A. F. Revuzhenko, «Model of deformation of pillars with consideration of the effects of energy storage and weakening of the materials,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 6 (1994).
15. N. A. Umov, Selected Works [in Russian], Gostekhizdat, Moscow — Leningrad (1950).
16. A. Lyav, Mathematical Theory of Elasticity [in Russian], NKI SSSR, Moscow — Leningrad (1935).
17. V. I. Kramarenko and A. F. Revuzhenko, «Energy flows in medium under deformation,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 6 (1988).

DEFORMATION OF QUASI-PLASTIC SALT ROCKS UNDER DIFFERENT CONDITIONS OF LOADING. REPORT II: REGULARITIES OF SALT ROCK DEFORMATION UNDER TRIAXIAL COMPRESSION
V. M. Zhigalkin*, V. N. Semenov, O. M. Usol’tseva, P. A. Tsoi, V. A. Asanov**, A. A. Baryakh**, I. L. Pan’kov**, V. N. Toksarov**, and A. V. Evseev

The paper reports on the test data on the elastic-plastic deformation of mottled sylvinite and rock salt under trialxial compression conditions. The basic regularities are established for variations of strain and strength parameters of salt rocks depending upon the structure and shape of specimens and the loading rates.

Mechanical tests, physico-mechanical properties, complete strain diagrams

REFERENCES
1. A. A. Baryakh, S. A. Konstantinova, and V. A. Asanov, Salt Rock Deformation [in Russian], Gorny Inst., Ekaterinburg (1996).
2. V. M. Zhigalkin, O. M. Usol’tseva, V. N. Semenov, P. A. Tsoi, V. A. Asanov, A. A. Baryakh, I. L. Pan’kov, and V. N. Toksarov, « Deformation of quasi-plastic salt rocks under different conditions of loading. Report I: Deformation of salt rocks under uniaxial compression,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 6 (2005).
3. G. D. Ushakov, Apparatus and Processes for Rock Deformation Investigations [in Russian], Nauka, Novosibirsk (1977).
4. A. N. Stavrogin and B. G. Tarasov, Experimental Physics and Mechanics of Rocks [in Russian], Nauka, St. Petersburg (2001).

NUMERICAL MODELING OF FLUID FLOW AND. A. HYDRAULICALLY INDUCED FRACTURE PROPAGATION
A. M. Lin’kov

The paper proposes an efficient method for the joined solution to the problems on fluid flow and hydraulic fracture extension.

Hydraulic fracturing, fluid flow, fracture extension, numerical modeling

REFERENCES
1. V. V. Zubkov, V. F. Koshelev, and A. M. Lin’kov, «Numerical modeling of hydraulic fracture initiation and development,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 1 (2007).
2. Yu. P. Zheltov and S. A. Khristianovich, «Hydraulic fracturing in an oil-bearing pool,» Izv. AN SSSR, OTN, No. 5 (1955).
3. J. Geertsma and F. de Klerk, «A rapid method of predicting width and extent of hydraulically induced fractures,» J. Pet. Tech., December (1969).
4. T. K. Perkins and L. F. Kern, «Widths of hydraulic fractures,» J. Pet. Tech., Sept. (1961).
5. R. D. Carter, «Derivation of the general equation for estimating the extent of the fractured area,» in: Appendix to «Optimum fluid characteristics for fracture extension,» by G. C. Howard and C. R. Fast, Drill. and Prod. Prac. API. (1957).
6. G. C. Howard and C. R. Fast, «Hydraulic fracturing,» Monograph Series, Dallas: Soc. Petrol. Eng. (1970).
7. R. P. Nordgren, «Propagation of a vertical hydraulic fracture,» Soc. Pet. Eng. J., Aug. (1972).
8. O. P. Alekseenko and A. M. Vaisman, «Certain aspects of a two-dimensional problem on the hydraulic fracturing of an elastic medium,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (1999).
9. K. G. Nolte, «Fracture design based on pressure analysis,» Soc. Pet. Eng. J. Paper SPE 10911, Feb. (1988).
10. C. Wright, «Rate step-down analysis — a diagnostic for fracture entry,» in: Reservoir Stimulation, M. J. Economides and K. G. Nolte (Eds.), Chapter 9 (2000).
11. A. M. Lin’kov, V. V. Zubkov, and M. A. Kheib, «A method of solving three-dimensional problems of seam workings and geological faults,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 4 (1997).
12. A. M. Lin’kov, Complex Boundary Integral Approach of the Elasticity Theory [in Russian], Nauka, Saint Petersburg (1999).
13. D. I. Garagash and E. Detournay, «Plane-strain propagation of fluid-driven fracture: small toughness solution,» ASME, J. Appl. Mech., 72 (2005).
14. D. I. Garagash, «Plane-strain propagation of a hydraulic fracture during injection and shut-in: asymptotic of large toughness,» Eng. Fract. Mech., 73 (2005).
15. S. L. Mitchell and A. P. Pierce, «An asymptotic framework for analysis of hydraulic fracture: the impermeable fracture case,» ASME, J. Appl. Mech., 74 (2007).
16. A. M. Lin’kov, «Numerical modeling of three-dimensional problems of rock mechanics,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 1 (2006).

FORMATION OF TENSILE FRACTURES IN THE STRESS CONCENTRATION ZONE IN GYPSUM
S. V. Suknev

The paper studies the influence of a gypsum material composition on the characteristic of formation and extension of tensile fractures in the zones of tensile stress concentrations in gypsum samples under compression. The experimental results are compared with the data of on a limiting pressure calculated by the traditional and gradient failure criteria. The parameters of the gradient criterion for the studied materials are determined.

Failure, fracture, hole, stress concentration, scale effect, stress gradient, non-local criteria

REFERENCES
1. A. J. Durelli and R. H. Jacobson, «Brittle-material failures as indicators of stress-concentration factors,» Exp. Mech., 2, No. 3 (1962).
2. E. Z. Lajtai, «Brittle fracture in compression,» Int. J. Fract., 10, No. 4 (1974).
3. B. J. Carter, «Size and stress gradient effects on fracture around cavities,» Rock Mech. and Rock Eng., 25, No. 3 (1992).
4. H. Hyakutake, T. Hagio, and H. Nisitani, «Fracture of FRP plates containing notches or a circular hole under tension,» Int. J. Pressure Vessels and Piping, 44, No. 3 (1990).
5. S. Imamura and Y. Sato, «Fracture of a graphite solid cylinder with a transverse hole in tension,» J. Coll. Eng. Nihon Univ. Ser. A., 28 (1987).
6. H. Nisitani and H. Noguchi, «Tensile fracture criterion of high strength steel specimens with a circumferential notch,» Trans. J. Soc. Mech. Eng. Ser. A., 52, No. 477 (1986).
7. A. Seweryn and Z. Mroz, «A non-local stress failure condition for structural elements under multiaxial loading,» Eng. Fract. Mech., 51, No. 6 (1995).
8. S. E. Mikhailov, «A functional approach to non-local strength condition and fracture criteria,» Eng. Fract. Mech., 52, No. 4 (1995).
9. L. P. Isupov and S. E. Mikhailov, "A comparative analysis of several nonlocal fracture criteria, « Arch. Appl. Mech., 68, No. 9 (1998).
10. S. V. Suknev, «Local strength criterion,» Probl. Proch., No. 4 (2004).
11. S. V. Suknev, «Gradient strength criterion,» in: Cold Resistance of Materials and Structural Elements: Results and Prospects [in Russian], Nauka, Novosibirsk (2005).
12. S. V. Suknev and M. D. Novopashin, «Criterion of normal tension crack formation in rocks under compression,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 2 (2003).
13. M. A. Legan, «Interaction between gradient criteria of local strength in the stress concentration zone and the linear fracture mechanics,» Prikl. Mekh. Tekh. Fiz., No. 4 (1993).
14. S. V. Suknev, V. K. Elshin, and M. D. Novopashin, «Experimental investigation into processes of crack formation in rock samples with hole,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 5 (2003).
15. L. I. Sedov, Continuum Mechanics [in Russian], 2, Nauka, Moscow (1984).

REVIEW OF ROCK MASS RATING CLASSIFICATION: HISTORICAL DEVELOPMENTS, APPLICATIONS, AND RESTRICTIONS
C. O. Aksoy

Historical development of the rock mass rating (RMR) system, first developed and later reviewed by Bieniawski, and contributed by other researchers, is presented. The advanced version of RMR classification and the scope of its application are specified.

Rock mass, Bieniawski’s classification, score estimation

REFERENCES
1. Z. T. Bieniawski, «Engineering classification of jointed rock masses,» Trans. South African Institute Civil Engineering, 15 (1973).
2. N. R. Barton, R. Lien, and I. Lunde, «Engineering classification of rock masses for the design of tunnel supports,» Rock Mechanics, 6, No. 4 (1974).
3. E. Hoek, «Strength of the rock and rock masses,» ISRM News Journal, 2, No. 2 (1995).
4. A. Palmström, «RMi-a rock mass characterization system for rock engineering purposes,» PhD Thesis, Oslo University, Norway (1995).
5. A. Palmström, «On classification systems,» in: Proceedings of Workshop on Reliablity of Classification Systems a Part of the International Conference «GeoEng-2000», Melbourne (2000).
6. R. Ulusay and H. Sonmez, Engineering Properties of Rock Masses, [in Turkish], The Chamber of Geology Engineering of Turkey, Ankara, Turkey (2002).
7. H. Lauffer, «Gebirgsklassifizierung für den stullenbau,» Geologie und Bauwesen, 24 (1958).
8. J. A. Franklin and R. Chandra, «The slake durability test,» Int. J. Rock Mech. & Min. Sci., No. 9 (1972).
9. H. J. Oliver, «Swelling properties and other related mechanical parameters of Karro strata as encountered in the orange-fish tunnel,» in: Proceedings of the 15th Annual Congress of Geological Society of South Africa (1973).
10. Z. T. Bieniawski, «Geomechanics classification of rock masses and its application in tunneling,» in: Proceedings of the 3rd Conference of International Society of Rock Mechanics, Denver (1974).
11. Z. T. Bieniawski, «Rock mass classification in rock engineering,» in: Proceedings of the Symposium on Exploration for Rock Engineering, Cape Town, Balkema (1976).
12. Z. T. Bieniawski, «The geomechanics classifications in rock engineering applications,» in: Proceedings of the 4th Congress on Rock Mechanics, ISRM, Montreux (1979).
13. Z. T. Bieniawski, «Rock mass classification as a design aid in tunneling,» Tunnels and Tunelling, July (1988).
14. Z. T. Bieniawski, Engineering Rock Mass Classifications, John Wiley and Sons (1989).
15. ISRM. The Complete ISRM Suggested Methods for Rock Characterization, Testing and Monitoring: 1974–2006. Suggested Methods Prepared by the Commission on Testing Methods, International Society for Rock Mechanics, R. Ulusay and J. A. Hudson (Eds.), Compilation Arranged by the ISRM Turkish National Group, Ankara, Turkey (2007).
16. J. S. Schrier, «The block punch index test,» Bul. Int. Assoc. Eng. Geology, 38 (1988).
17. R. Ulusay and C. Gokceoglu, «The modified block punch index test,» Can. Geotechn. J., 34, No. 6 (1997).
18. R. Ulusay and C. Gokceoglu, «An experimental study on the size effect in block punch index test and its general usefulness,» Int. J. of Rock Mech. and Min. Sci., 35, Nos. 4 and 5 (in NARMS’98-ISRM International Symposium, Cancun-Mexico) (1998).
19. R. Ulusay and C. Gokceoglu, «A new test procedure for the determination of the block punch index and its possible uses in rock engineering,» ISRM News J., 6, No. 1 (1999).
20. R.Ulusay, C.Gokceoglu, and S. Sulukcu, «Draft ISRM suggested method for determining block punch strength index (BPI),» Int. J. Rock Mech. and Min. Sci., 38 (2001).
21. S. Sulukcu and R. Ulusay, «Evaluation of the block punch index test with particular reference to the size effect, failure mechanism and its effectiveness in predicting rock strength,» Int. J. Rock Mech. and Min. Sci., 38 (2001).
22. D. H. Laubscher, «Geomechanics classification of jointed rock masses-mining applications,» Trans. Inst. Min. Met. (1977).
23. D. H. Laubscher, «Design aspects and effectiveness of support system in different mining conditions,» Trans. Inst. Min. Met. (1984).
24. E. Unal, R. Ulusay, and I. Ozkan, Rock Engineering Evaluations and Rock Mass Classification at Beypazari Trone Site, METU Project No: 97–03–05–02–02 (1997а).
25. E. Unal, R. Ulusay, and I. Ozkan, Rock Engineering Evaluations and Rock Mass Classification at Beypazari Trone Field: Borehole TS-3 Site, Project No: 97–03–05–01–06, METU Ankara (1997b).
26. B. Singh and R. K. Goel, Rock Mass Classification: A Practical Approach in Civil Engineering, Elsevier (1999). 27. H. Lauffer, «Zur gebirgsklassifizierung bei frasvortrieben,» Felsbau, 6, No. 3 (1988).
28. R. K. Goel and J. L. Jethwa, «Prediction on support pressure using RMR classification,» in: Proceedings of the Indian Geotechnical Conference, Surat, India (1991).
29. Z. T. Bieniawski, «Determining rock mass deformability: Experience from case histories,» Int. J. Rock Mech. Min. Sci., 15 (1978).
30. J. L. Sefarim and J. P. Pereira, «Consideration of the geomechanics classification of Bieniawski,» in: Proceedings of the International Symposium on Engineering Geology and Underground Constructions, Lisbon, Portugal, 1 (1983).
31. G. A. Nicholson and Z. T. Bieniawski, «A non-linear deformation modulus based on rock mass classification,» Int. J. of Min. and Geol. Eng., No. 8 (1990).
32. R. Ulusay, «Geotechnical evaluations and deterministic design consideration from pit-wall slopes at Eskihisar (Yatagan-Mugla) strip coal mine,» Ph. D. Thesis, METU, Geological Engineering Dept. Ankara, Turkey (1991).
33. R. Ulusay and C. Aksoy, «Assessment of failure mechanism of highwall slope under spoil pile loadings at a coal mine,» Eng. Geology, 38 (1994).
34. C. O. Aksoy, T. Onargan, T. Gungor, K. Kucuk, and M. Kun, The Evaluation of Excavation and Support System between Goztepe and F. Altay Stations of Second Stage of Izmir Metro Project, DEUEF, DEU-MAG, Izmir (2006).
35. T. Onargan and C. O. Aksoy, Report on the Evaluation of the Excavation of Type Second Station Tunnel and Application in Project on the Second Stage of Izmir Metro Project, DEUEF, Izmir (2006).
36. M. K. Verman, «Rock mass-tunnel support interaction analysis,» Ph. D. Thesis, University of Roorkee, Roorkee, India (1993).
37. E. Hoek and E. T. Brown, Underground Excavations in Rock, Inst. of Mining and Metallurgy, Stephen Austin and Sons Ltd., London, 106 (1980).
38. E. Unal and I. Ozkan, «Determination of classification parameters for clay-bearing and stratified rock mass,» in: Proceedings of the 9th International Conference on Ground Control in Mining, West Virginia University, Morgantown (1990).
39. E. Unal, Modified Rock Mass Classification: M-RМR system, Milestone in Rock Engineering, The Bieniawski Jubilee Collection, Balkema, Rotterdam (1996).
40. R. N. Singh and D. R. Gahrooee, «Application of rock mass weakening coefficient for stability assessment of slopes in heavily jointed rock mass,» Int. J. of Surface Mining, Reclamation and Environment, No. 3 (1989).
41. R. Ulusay, I. Ozkan, and E. Unal, «Characterization of weak, stratified and clay-bearing rock masses for engineering applications,» in: Proceedings of the Fractured and Jointed Rock Masses Conference, L. R. Mayer, N. G. W. Cook, R. E. Goodman and C. F. Trans (Eds.), Lake Tahoe, California (1995).
42. H. Sonmez and R. Ulusay, «Modification to the geological strength index (GSI) and their applicability to stability of slopes,» Int. J. of Rock Mechanics and Mining Science, 36, No. 6 (1999).
43. E. Unal, I. Ozkan, and R. Ulusay, «Characterization of weak rock, stratified and clay-bearing rock masses,» in: ISRM Symposium:EUROCK’92 Rock Characterization, Chester, UK, J. A. Hudson (Ed.), British Geotechnical Society, London (1992).

ROCK FAILURE

NUMERICAL MODELING OF DEFORMATION AND FAILURE OF SANDSTONE SPECIMENS
Yu. P. Stefanov

The author has simulated behavior of geomaterials based on the modified models of Drucker — Prager — Nikolaevski and Rudnicki. It is shown how fractures extend under stresses applied on a section of a specimen surface. The characteristic patterns are obtained for deformation localization in low porosity and high porosity sandstone under biaxial compression, and the stress-to-strain curves are plotted.

Plasticity, failure, dilatancy, compaction, fractures, deformation, modeling

REFERENCES
1. D. Drucker and W. Prager, «Soil mechanics and plastic analysis of limit design,» Quaterly Applied Mathematics, 10, No. 2 (1952).
2. V. N. Nikolaevski, «Mechanical properties of soils and theory of plasticity,» in: Mechanics of Deformable Solids [in Russian], 6, VINITI AN SSSR, Moscow (1972).
3. V. N. Nikolaevski, Geomechanics and Fluid Dynamics [in Russian], Nedra, Moscow (1996).
4. J. F. Labuz, S.-T. Dai, and E. Papamichos, «Plane-strain compression of rock-like materials,» Int. J. of Rock Mech. and Min. Sci. & Geomech., Abstr., 33, No. 6 (1996).
5. W. Zhu and T. Wong, «The transition from brittle faulting to cataclastic flow. Permeability evolution,» Journal of Geophysical Research, 102, No. B2 (1997).
6. R. A. Schultz and R. A. Siddharthan, «General framework for the occurrence and faulting of deformation bands in porous granular rocks,» Tectonophysics, No. 411 (2005).
7. A. El. Bieda, J. Sulema, and F. Martineau, «Microstructure of shear zones in Fontainebleau sandstone,» Int. J. of Rock Mech. and Min. Sci. & Geomech., 39 (2002).
8. J. Fortin, S. Stanchits, G. Dresen, and Y. Gue?guen, «Acoustic emission and velocities associated with the formation of compaction bands in sandstone,» Journal of Geophysical Research, 111, B10203, doi:10.1029/2005JB003854 (2006).
9. R. J. Cuss, E. H. Rutter, and R. F. Holloway, «The application of critical state soil mechanics to the mechanical behaviour of porous sandstones,» Int. J. of Rock Mech. and Min. Sci. & Geomech., 40 (2003).
10. J. W. Rudnicki, «Shear and compaction band formation on an elliptic yield cap,» Journal of Geophysical Research, 109, B03402, doi:10.1029/2003JB002633 (2004).
11. E. Grueschow and J. W. Rudnicki, «Elliptic yield cap constitutive modeling for high porosity sandstone,» International Journal of Solids and Structures, 42 (2005).
12. F. L. DiMaggio and I. S. Sandler, «Material models for granular soils,» J. of Eng. Mech., ASCE, 97, No. EM3 (1971).
13. A. F. Revuzhenko, Mechanics of Granular Media, Springer, (2006).
14. Yu. P. Stefanov, «Numerical investigation of deformation localization and crack formation in elastic brittle-plastic materials,» Int. J. Fract., 128, No. 1 (2004).
15. M. M. Nemirovich-Danchenko, «Hypoelastic brittle medium model: application to calculation of deformation and failure of rocks,» Fizich. Mesomekh., 1, No. 2 (1998).
16. Yu. P. Stefanov, «Deformation localization and failure in geomaterials. Part I: Numerical modeling,» Fizich. Mezomekh., No. 5 (2002).
17. Yu. P. Stefanov, «Some features of numerical modeling of the elastic brittle-plastic material behavior,» Fizich. Mezomekh., 8, No. 3 (2005).
18. Yu. P. Stefanov and M. T’erselen, «Modeling the behavior of high porosity geomaterials in the course of formation of localization compaction bands,» Fizich. Mezomekh., 10, No. 1 (2007).
19. M. Wilkins, «Calculation of elastoplastic flows,» in: Methods in Computational Physics, B. Alder (Ed.), 3, Academic, New York (1964).
20. J. W. Rudnicki and J. R. Rice, «Condition for localization of plastic deformation in pressure sensitive dilatant materials,» J. Mech. and Phys. Solids, 23, No. 6 (1975).
21. K. A. Issen and J. W. Rudnicki, «Conditions for compaction bands in porous rock,» J. Geophys. Res., 105, No. 21 (2000).

DETECTION OF FEATURES OF. A. RUPTURE STRUCTURE IN WALLS OF AN OPEN PIT IN TERMS OF THE MURUNTAU OPEN PIT
A. G. Bagdasar’yan, B. G. Lukishov, V. N. Rodionov*, and A. S. Fedyanin**

In terms of the Muruntau open pit, the paper addresses the possibility of formation of a rupture structure in host rock, based on the analysis of its surface manifestations.

Rocks, defects, blocks structure, block sizes, strain rate, fracture

REFERENCES
1. V. N. Rodionov, «Dissipative structures in rock mechanics,» Usp. Mekh., 4, No. 2 (1979).
2. V. N. Rodionov and I. A. Sizov, «Appearance on nonuniformity of the stress state as a result of fracture of rocks,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 4 (1981).
3. V. N. Rodionov, A. G. Bagdasar’yan, and V. M. Kol’tsov, «Correlations between the granular compositions of an exploded rock mass and other manifestations of the rock mass structure,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 5 (1982).
4. V. N. Rodionov and I. A. Sizov, «Model of a solid with the dissipative structure for rock mechanics,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 6 (1988).
5. V. N. Rodionov, I. A. Sizov, and V. M. Tsvetkov, Foundations of Rock Mechanics [in Russian], Nauka, Moscow (1986).
6. V. N. Rodionov and A. G. Bagdasar’yan, «Surface irregularities and structure of rock in place,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (1985).

MINERAL MINING TECHNOLOGY

MINE STABILITY WITH APPLICATION OF SUBLEVEL CAVING SCHEMES
A. M. Freidin, S. A. Neverov, A. A. Neverov, and P. A. Filippov

The paper expounds results gained in mathematical modeling of stress state of a rock mass under mining by sublevel caving with areal-frontal and frontal ore drawing schemes. Stability of underground excavations in the course of applying the compared methods is evaluated in terms of the Sheregesh deposit. The authors recommend on supporting the openings at the ore drawing-off level.

Technology, stress state, modeling, stability

REFERENCES
1. V. N. Oparin, et al., World-Wide Experience of Underground Mining Automation [in Russian], N. N. Mel’nikov (Ed.), SO RAN, Novosibirsk (2007).
2. V. R. Imenitov, Mining Operations in Underground Ore Development [in Russian], Nedra, Moscow (1984).
3. A. M. Freidin, P. A. Filippov, S. P. Gaidin, E. N. Koren’kov, and S. A. Neverov, «Prospects of technical re-equipment of underground mines of the metallurgy complex in West Siberia,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 3 (2004).
4. A. M. Freidin and S. A. Neverov, «Modeling of area-end ore drawing under caved rocks,» Fiz.-Tekh. Probl. Razrab. Polezn. Iskop., No. 5 (2005).
5. A. M. Freidin, E. N. Koren’kov, P. A. Filippov, et al., «Russian Federation Patent No. 2208162. Ore development with sublevel caving,» Byull. Izobret., No. 19 (2003).
6. S. A. Neverov, A. M. Freidin, and A. A. Neverov, «Russian Federation Patent No. 2301335. Underground ore development by sublevel caving,» Byull. Izobret., No. 17 (2007).
7. A. B. Fadeev, Finite Element Method in Rock Mechanics [in Russian], Nedra, Moscow (1987).
8. B. V. Shrepp, V. I. Boyarkin, V. A. Kvochin, et al., «Problems of deep mining at the deposits of Gornaya Shoria and Khakasia,» in: Production Problems of Deep Ore Development [in Russian], IPKON AN SSSR, Moscow (1979).
9. B. V. Shrepp, «Geomechanical estimate of mining conditions at deep level of the Sheregesh deposit,» Bezop. Truda Prom., No. 7 (1995).
10. D. M. Kazikaev, Rock Mechanics in Underground Ore Mining [in Russian], MGGU, Moscow (2005).

PROCEDURES FOR GEOTECHNICAL CHARACTERIZATION AND ECONOMICAL FEASIBILITY STUDIES — APPLICATION TO AN UNDERGROUND MARBLE EXPLOITATION
M. Matilde Costa e Silva and P. Falcão Neves

For marble underground excavation it is important to develop a collection of procedures, rules and models in order to collect information to build a database, making it usable and available to all users so that they can make decisions. The information must be based on technical and economic criteria, during the lifetime of the excavation and after the close down of the mining activities. The importance of geotechnical characterization in the economical evaluation of underground mining of dimension stone is so emphasized. A sensitivity analysis of the economic indicators with the variation of the geotechnical and ornamental parameters is performed. The results of an economic feasibility study of an underground exploitation of marble at Pardais, Vila Vi?osa, are presented.

Geotechnics, economical feasibility, marble, quarry, management procedures

REFERENCES
1. M. M. Costa e Silva and P. Falcão Neves, «Management procedures for an underground excavation of marble,» ISRM International Symposium on Rock Mechanics for Mountains Regions, EUROCK 02, SPG (2002). 2. Manual de Rocas Ornamentales, ITGE, Madrid, (1998). 3. Projecto de execução de uma exploração subterrânea de mármores em Pardais, Vila Viçosa, IGM (2000). 4. L. J. Krajewski and L. P. Ritzman, Operations Management, Addison-Wesley Publishing Company (1993). 5. L. Cabral, Economia Industrial, McGraw Hill de Portugal, Lisboa (1994).

MINERAL DRESSING

MODIFIED REAGENT MODE IN PORPHYRY COPPER-MOLYBDENUM ORE FLOTATION
V. A. Bocharov, L. S. Khachatryan*, V. A. Ignatkina, and Zh. Baatarkhuu**

Test data on the selective reagent modes at bulk flotation cycle and modified carboxymethylcellulose (CMC) at a selection cycle for the bulk copper-molybdenum concentrate. The selected reagent mode at a bulk flotation cycle with industrial kerosene and Beraflot as collectors and OPSB as a frother made it possible to recover 87 % of copper and 82 % of molybdenum into a rough bulk concentrate. Tests with CMC application at the selection cycle revealed a potential opportunity to reduce 1.5 — 2.0 times the summary sodium sulfide consumption, to cut down running costs of pulp and depressant heating, and to improve molybdenum recovery with no negative effect on other parameters of the bulk concentrate selection.

Flotation, sulfide concentrate, sulfide minerals, collectors

REFERENCES
1. Zh. Baatarkhuu, Sh. Gezegt, S. Davaanyam, et al., «Experience of copper-porphyry ore flotation,» Gorn. Zh., No. 2 (1998).
2. S. Gereltuyaya, Zh. Baatarkhuu, and S. Davaanyam, «Choice of a selective collector for pyrite and development of technological mode for collective flotation circuit,» in: Development of New Machinery and Technologies in Mongolia, Erdenet, Mongolia (1998).
3. S. Davaanyam, I. Sh. Sataev, Zh. Baatarkhuu, et al., Process for copper-molybdenum ore beneficiation with S-703G collector,» Tsv. Met., No. 8 (2000).
4. Zh. Baatarkhuu, «Effect of genetic-morphological properties of copper-porphyry ores on their dressing technology,» Gorn. Zh., No. 1 (2001).
5. V. A. Bocharov, L. S. Khachatryan., V. A. Ignatkina, and G. A. Lapshina, Investigation into Process for Copper-Molybdenum Separation, Based on Application of the Modified Organic CMC Depressant [in Russian], Fondy MISiS, Moscow (2005).
6. V. A. Bocharov, G. S. Agafonova, and L. S. Khachatryan, «Intensive CMC salt-based processes for dressing rebellious ores and products,» Gorn. Zh., No. 1 (1988).
7. V. A. Chanturia, T. V. Nedosekina, M. I. Mantsevich, and I. N. Khramtsova, «Effect of dimethyldithiocarbamata on interaction of pyrrhotite with butylxanthate,» Tsv. Met., No. 10 (2002).
8. V. A. Bocharov, V. A. Ignatkina, G. A. Lapshina, et al., «Studies of collectors for flotation of gold-bearing ores,» Tsv. Met., No. 1 (2005).
9. V. A. Ignatkina, V. A. Bocharov, V. V. Stepanova, and T. I. Kustova, «Studies of modified dithiophosphates in the sulfide copper, iron, zinc, and gold mineral flotation,» Obog. Rud, No. 6 (2005).

EFFECT OF THE PHYSICAL-CHEMICAL FACTORS ON FLOTATION PERFECTION OF MAGNETITE CONCENTRATES
T. N. Gzogyan and S. L. Gubin*

The paper describes the laboratory studies aimed at comprehensive analysis and establishment of the optimal parameters for preparation of a pulp for reverse cation flotation when producing a low-silica iron ore concentrate. The kinetics of the process is investigated with application of a collecting agent and depressing agents for iron minerals.

Cation flotation, parameters, collecting agent, flotation kinetics, separation selectivity, flotation velocity

REFERENCES
1. S. V. Dudenkov, L. Ya. Shubov, L. A. Glazunov, et al., Theoretical and Practical Bases for Application of Flotation Reagents [in Russian], Nedra, Moscow (1969).
2. O. S. Bogdanov, A. K. Podnek, V. Ya. Khainman, et al., «Issues of the flotation theory and technology,» Trudy Inst. Mekhanobr., Issue 124, Leningrad (1959).
3. V. A. Glembotskii, Foundations of the Physico-Chemistry of Flotation Processes [in Russian], Nedra, Moscow (1980).
4. G. S. Berger, Floatability of Minerals [in Russian], Gosgortekhizdat, Moscow (1962).
5. O. S. Bogdanov and N. S. Mikhailova, «Action mechanism of anionic and cation collecting agents during flotation of iron minerals,» in: Proceedings of the 5th Science-and-Technical Session of the Mekhanobr Institute [in Russian], Leningrad (1966).
6. S. L. Gubin and V. M. Avdokhin, «Magnetite concentrate flotation by cation collectors,» Gorn. Zh., No. 7 (2006).

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