Artigos
Estudio y evaluación de los modelos matemáticos para la estimación de la dilatancia
Publicado 2015-12-03
Palavras-chave
- Arenamiento,
- Dilatancia,
- Estado crítico,
- Suelos granulares
Como Citar
Rondon, V. H., Fuentes, M. A., & Quintero, Y. A. (2015). Estudio y evaluación de los modelos matemáticos para la estimación de la dilatancia. REVISTA FUENTES, 13(2). https://doi.org/10.18273/revfue.v13n2-2015005
Resumo
El artículo muestra una revisión bibliográfi ca de los principales modelos que existen para el cálculo de la dilatancia en la roca. una vez explicado cada modelo, se procede a realizar el modelamiento matemático de ésta propiedad.
Esto se realiza mediante datos suministrados por la literatura, las cuales son: esfuerzos sometidos a la roca σ1,σ2,σ3, ángulo de fricción interna ∅, pendiente de la línea de estado critico M, el parámetro de estado , y otras constantes que se requieren para cada modelo. Una vez hechos los cálculos de la dilatancia en la roca, se procede a validar el modelamiento con datos reales, los cuales también son suministrados por la literatura. En éstas pruebas se midió la dilatancia real en dos tipos de arena, (Banding y Miga) y se realizaron 5 pruebas. Finalmente éstas mediciones se compararon con los cálculos realizados, y así llegar a la conclusión de que el mejor modelo para predecir el fenómeno dilatante de una roca es el de Li & Dafalias.
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Referências
1. Barden, L., Ismail, H. & Tong, P. 1969. Plane strain deformation of granular material at low and high pressures. Gkotechnique 19, No. 4,441452.
2. Billam, J. 1972. Some aspects of the behaviour of granular materials at high pressures. In Stress- strain behaviour of soils. DD. 69-80 (ed. R. H. G. Parry).
3. BiTech Publishers Ltd. pp. 55–62. Ishihara, K. 1993. Thirty-third Rankine Lecture: Liquefaction and flow failure during earthquakes. Géotechnique, 43(3): 349–415.
4. Blümel, M. & Bezat, F. A. 1998. Advanced control techniques for direct shear testing of jointed rock specimens.
5. Blümel, M., Button, E. A. & Pötsch, M. 2002. Steifigkeits- abhängigies Scherverhalten von Fels. Felsbau Rock and Soil Engineering 20(3): 22–32.
6. Brosch, F. J., Schachner, K., Blümel, M., Fasching, A. & Fritz, H. 2000. Preliminary investigation results on fabrics and related physical properties of an anisotropic gneiss. Journal of Structural Geology 22(11–12): 1773–1787.
7. Chen. Z. (s.f.). : “Analysis of a microcrack model and constitutive equations for time-dependent dilatancy of rocks”. Geophysical Journal International.
8. Collins, I.F 2005: “Elastic/plastic models for soils and sands”. Int. J. Mech. Sci. 47, 493–508
9. Cornforth, D. H. 1964. Some experiments on the influence of strain conditions on the strength of sand. Gkotechnique 14, No. 2, 143-167.
10. Dafalias, Y.F., Herrmann, L.R. 1986: “Bounding surface plasticity II: Application to isotropic cohesive soils”. J. Eng. Mech. 112(12), 1263–1291.
11. De Josselin de Jong, G. 1976. Rowe’s stress– dilatancy relation based on friction. Géotechnique, 26(3): 527–534.
12. Diego Guillermo Manzanal, 2008:“Modelo constitutivo basado en la teoría de la plasticidad generalizada con la incorporación de parámetros de estado para arenas saturadas y no saturadas”. Universidad politécnica de Madrid.
13. Dong, J.-J. & Pan,Y.-W. 1996.A Hierarchical Model of Rough Rock Joints Based on Micromechanics. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33(2): 111–123.
14. Foulis. Bishop, A. W. 1972. Shear strength parameters for undisturbed and remoulded soils specimens. In Stress-strain behaviour of soils, pp. 3-58 (ed. R. H. G. Parry).
15. Foulis. Bishop. A. W. & Green, G. E. 1965. The influence of end restraint on the compression strength of a cohe- sionless soil. GPotechniaue 15, No. 3,243-266.
16. Gao, Z.W., Zhao, J.D. 2012: “Constitutive modeling of artificially cemented sand by considering fabric anisotropy”. Computer and Geotechnics 41, 57–69.
17. Gajo, A. & Muir Wood, D. 1999. : “A kinematic hardening constitutive model for sands: the multiaxial formulation”. Int. J. Numer. Anal. Methods Geomech. 23, No. 5, 925–965.
18. Gentier, S., Riss, J. Archambault, G., Flamand, R. & Hopkins, D. 2000. Influence of fracture geometry on shear behaviour. Int. J. Rock Mech. Min. Sci. 37: 161–174.
19. Grasselli, G., Wirth, J. & Egger, P. 2002. Quantitative three- dimensional description of a rough surface and parameter evo- lution with shearing. Int. J. Rock Mech. Min. Sci. 39, 789–800.
20. Grupo geotecnia. (s.f.). : “Deformabilidad y resistencia de los suelos”. Universidad de Cantabria.
21. Hughes, J. M. O., Wroth, C. P. & Windle, D. 1977. Pressuremeter tests in sands. Ghotechnique 27, No. 4, 455477.
22. Horsfield, D., and Been, K. 1987. Computer controlled triaxial testing. In Proceedings of the 1st Canadian Symposium on Microcomputer Applications to Geotechnique, Regina, Sask. 22–23 October 1987.
23. Indraratna, B. & Haque, A. 2000. “Shear Behaviour of Rock Joints. Balkema: Rotterdam, Brookfield.
24. In Marr & Fairhurst (eds.), Nondestructive and Automated Testing for Soil and Rock Properties. ASTM STP 1350, Am. Soc. Test. Mat., 276–289.
25.Jefferies, M.G., and Been, K. 2000. Implications for critical state theory from isotropic compression of sand. Géotechnique, 50(4): 419–429.
26.Jefferies, M.G., and Shuttle, D. 2002. Dilation in general Cam- bridge-type models. Géotechnique, 52(9): 625–638.
27.Jefferies, M.G. 1997. Plastic work and isotropic softening in un- loading. Géotechnique, 47(5): 1037–1042.
28. Ken Been and Michael Jefferies, 2004”: Stress– dilatancy in very loose sand” NRC Research Press.
29. Koerner, R. M. 1970. Behaviour of single mineral soils in triaxial shear. J. Soil Mech. Fdns Div. Am. Sot. Civ. Engrs 96, SM4, 1373-1390.
30. Ladanyi, B. & Archambault, G. 1970. “Simulation of shear behavior of a jointed rock mass”. In Proc. 11th Symp. on Rock Mechanics: Theory and Practice, AIME, 105–125: NewYork.
31. Ladanyi, B. 1960. Etude des relations entre les contraintes et des d&formations lors du cisaillement des sols pulvtrulents. Annls Trau. Publ. Belg. No. 3, l-30.
32. Li, X.-S., Dafalias, Y. F., and Wang, Z.-L. 1999:“State-dependent dilatancy in critical-state constitutive modeling of sand.” Can. Geotech. J. (3) 64, 599–611.
33. Marachi, N. D., Chan, C. K., Seed, H. B. & Duncan, J. M. 1969.: “Strength and deformation characteristics of rockJill materials”. University of California Report TE-69-5, Berkeley.
34. Mateos García 1995. : “Determinación experimental de la función de dilatancia en un suelo granular denso”. J. Geogaceta (18) 150-152.
35. Nova, R., and Wood, D. M. 1979. : “A constitutive model for sandin triaxial compression.” Int. J. Numer. Analyt. Meth. Geomech., 255–278.
36. Pastor, M., and Zienkiewicz, O. C. 1986.: “A generalized plasticity, hierarchical model for sand under monotonic and cyclic loading.”
37. Proc., 2nd Int. Symp. on Numerical Models in Geomechanics, 131–150.
38. Pestana, J.M., Whittle, A.J., Gens, A. 2002.: “Evaluation of a constitutive model for clays and sands: Part II – clay behaviour”. Int. J. Numer. Anal. Meth. Geomech. 26, 1123–1146.
39. Reynolds, O. 1885: “On the dilatancy of media composed of rigid particles in contact. With experimental illustrations”. Phil. Mag. 20, 469–482
40. Roscoe & Burland 1968. : “On the generalized strain-strain behaviour of wet clay”. Engineering plasticity, J. Heyman and F.A.Cambridge University press, Cambridge UK 535-609
41. Rowe, P. W. 1962. : “The stress-dilatancy relation for static equilibrium of an assembly of particles in contact”, Proc. Roy. Soc., London, A269, 500-527.
42. Seywald, C. 2006. Investigations on the relationship between surface roughness and dilation of rock joints in direct shear. DiplomaThe- sis, Institute for Rock Mechanics andTunnelling, Graz University of Technology, Austria.
43. Schieg, T. 2006. Investigations on the shear behaviour of artificial rock joints. Diploma Thesis, Institute for Rock Mechanics and Tunnelling, Graz University of Technology, Austria.
44. Schofield, A.N. 1998: “The Mohr-Coulomb error. In: Proc. Symp. on Mechanics and Geotechnics”, LMS Ecole Polytechnique, Paris, vol. 23, pp. 19–27
45. Sridharan, A. and Prakash, K. 1995: Discussion on ‘Limitations of Conventional Analysis of Consolidation Settlement’, ASCE, J. of Geotechnical Engineering, 121 (6): 517.
46. Taylor, D.W. 1948. : “Fundamentals of soil mechanics”, john wiley and sons, Inc. New York.
47. Vaid, Y.P., and Sasitharan, S. 1992. The strength and dilatancy of sand. Canadian Geotechnical Journal, 29: 522–526.
48. Wood, D.M. 1990. Soil behaviour and critical state soil mechanics. Cambridge University Press, London, UK.
49. Wroth y Schofield 1963. : Ed. Mcgraw-Hill publishing Company Ltd.
50. Yamamuro, J.A., and Lade, P.V. 1997. Static liquefaction of very loose sands. Canadian Geotechnical Journal, 34: 905–917.
51. Yang, J. 2002. Non-uniqueness of flow liquefaction line for loose sand. Géotechnique, 52(10): 757–760.
2. Billam, J. 1972. Some aspects of the behaviour of granular materials at high pressures. In Stress- strain behaviour of soils. DD. 69-80 (ed. R. H. G. Parry).
3. BiTech Publishers Ltd. pp. 55–62. Ishihara, K. 1993. Thirty-third Rankine Lecture: Liquefaction and flow failure during earthquakes. Géotechnique, 43(3): 349–415.
4. Blümel, M. & Bezat, F. A. 1998. Advanced control techniques for direct shear testing of jointed rock specimens.
5. Blümel, M., Button, E. A. & Pötsch, M. 2002. Steifigkeits- abhängigies Scherverhalten von Fels. Felsbau Rock and Soil Engineering 20(3): 22–32.
6. Brosch, F. J., Schachner, K., Blümel, M., Fasching, A. & Fritz, H. 2000. Preliminary investigation results on fabrics and related physical properties of an anisotropic gneiss. Journal of Structural Geology 22(11–12): 1773–1787.
7. Chen. Z. (s.f.). : “Analysis of a microcrack model and constitutive equations for time-dependent dilatancy of rocks”. Geophysical Journal International.
8. Collins, I.F 2005: “Elastic/plastic models for soils and sands”. Int. J. Mech. Sci. 47, 493–508
9. Cornforth, D. H. 1964. Some experiments on the influence of strain conditions on the strength of sand. Gkotechnique 14, No. 2, 143-167.
10. Dafalias, Y.F., Herrmann, L.R. 1986: “Bounding surface plasticity II: Application to isotropic cohesive soils”. J. Eng. Mech. 112(12), 1263–1291.
11. De Josselin de Jong, G. 1976. Rowe’s stress– dilatancy relation based on friction. Géotechnique, 26(3): 527–534.
12. Diego Guillermo Manzanal, 2008:“Modelo constitutivo basado en la teoría de la plasticidad generalizada con la incorporación de parámetros de estado para arenas saturadas y no saturadas”. Universidad politécnica de Madrid.
13. Dong, J.-J. & Pan,Y.-W. 1996.A Hierarchical Model of Rough Rock Joints Based on Micromechanics. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 33(2): 111–123.
14. Foulis. Bishop, A. W. 1972. Shear strength parameters for undisturbed and remoulded soils specimens. In Stress-strain behaviour of soils, pp. 3-58 (ed. R. H. G. Parry).
15. Foulis. Bishop. A. W. & Green, G. E. 1965. The influence of end restraint on the compression strength of a cohe- sionless soil. GPotechniaue 15, No. 3,243-266.
16. Gao, Z.W., Zhao, J.D. 2012: “Constitutive modeling of artificially cemented sand by considering fabric anisotropy”. Computer and Geotechnics 41, 57–69.
17. Gajo, A. & Muir Wood, D. 1999. : “A kinematic hardening constitutive model for sands: the multiaxial formulation”. Int. J. Numer. Anal. Methods Geomech. 23, No. 5, 925–965.
18. Gentier, S., Riss, J. Archambault, G., Flamand, R. & Hopkins, D. 2000. Influence of fracture geometry on shear behaviour. Int. J. Rock Mech. Min. Sci. 37: 161–174.
19. Grasselli, G., Wirth, J. & Egger, P. 2002. Quantitative three- dimensional description of a rough surface and parameter evo- lution with shearing. Int. J. Rock Mech. Min. Sci. 39, 789–800.
20. Grupo geotecnia. (s.f.). : “Deformabilidad y resistencia de los suelos”. Universidad de Cantabria.
21. Hughes, J. M. O., Wroth, C. P. & Windle, D. 1977. Pressuremeter tests in sands. Ghotechnique 27, No. 4, 455477.
22. Horsfield, D., and Been, K. 1987. Computer controlled triaxial testing. In Proceedings of the 1st Canadian Symposium on Microcomputer Applications to Geotechnique, Regina, Sask. 22–23 October 1987.
23. Indraratna, B. & Haque, A. 2000. “Shear Behaviour of Rock Joints. Balkema: Rotterdam, Brookfield.
24. In Marr & Fairhurst (eds.), Nondestructive and Automated Testing for Soil and Rock Properties. ASTM STP 1350, Am. Soc. Test. Mat., 276–289.
25.Jefferies, M.G., and Been, K. 2000. Implications for critical state theory from isotropic compression of sand. Géotechnique, 50(4): 419–429.
26.Jefferies, M.G., and Shuttle, D. 2002. Dilation in general Cam- bridge-type models. Géotechnique, 52(9): 625–638.
27.Jefferies, M.G. 1997. Plastic work and isotropic softening in un- loading. Géotechnique, 47(5): 1037–1042.
28. Ken Been and Michael Jefferies, 2004”: Stress– dilatancy in very loose sand” NRC Research Press.
29. Koerner, R. M. 1970. Behaviour of single mineral soils in triaxial shear. J. Soil Mech. Fdns Div. Am. Sot. Civ. Engrs 96, SM4, 1373-1390.
30. Ladanyi, B. & Archambault, G. 1970. “Simulation of shear behavior of a jointed rock mass”. In Proc. 11th Symp. on Rock Mechanics: Theory and Practice, AIME, 105–125: NewYork.
31. Ladanyi, B. 1960. Etude des relations entre les contraintes et des d&formations lors du cisaillement des sols pulvtrulents. Annls Trau. Publ. Belg. No. 3, l-30.
32. Li, X.-S., Dafalias, Y. F., and Wang, Z.-L. 1999:“State-dependent dilatancy in critical-state constitutive modeling of sand.” Can. Geotech. J. (3) 64, 599–611.
33. Marachi, N. D., Chan, C. K., Seed, H. B. & Duncan, J. M. 1969.: “Strength and deformation characteristics of rockJill materials”. University of California Report TE-69-5, Berkeley.
34. Mateos García 1995. : “Determinación experimental de la función de dilatancia en un suelo granular denso”. J. Geogaceta (18) 150-152.
35. Nova, R., and Wood, D. M. 1979. : “A constitutive model for sandin triaxial compression.” Int. J. Numer. Analyt. Meth. Geomech., 255–278.
36. Pastor, M., and Zienkiewicz, O. C. 1986.: “A generalized plasticity, hierarchical model for sand under monotonic and cyclic loading.”
37. Proc., 2nd Int. Symp. on Numerical Models in Geomechanics, 131–150.
38. Pestana, J.M., Whittle, A.J., Gens, A. 2002.: “Evaluation of a constitutive model for clays and sands: Part II – clay behaviour”. Int. J. Numer. Anal. Meth. Geomech. 26, 1123–1146.
39. Reynolds, O. 1885: “On the dilatancy of media composed of rigid particles in contact. With experimental illustrations”. Phil. Mag. 20, 469–482
40. Roscoe & Burland 1968. : “On the generalized strain-strain behaviour of wet clay”. Engineering plasticity, J. Heyman and F.A.Cambridge University press, Cambridge UK 535-609
41. Rowe, P. W. 1962. : “The stress-dilatancy relation for static equilibrium of an assembly of particles in contact”, Proc. Roy. Soc., London, A269, 500-527.
42. Seywald, C. 2006. Investigations on the relationship between surface roughness and dilation of rock joints in direct shear. DiplomaThe- sis, Institute for Rock Mechanics andTunnelling, Graz University of Technology, Austria.
43. Schieg, T. 2006. Investigations on the shear behaviour of artificial rock joints. Diploma Thesis, Institute for Rock Mechanics and Tunnelling, Graz University of Technology, Austria.
44. Schofield, A.N. 1998: “The Mohr-Coulomb error. In: Proc. Symp. on Mechanics and Geotechnics”, LMS Ecole Polytechnique, Paris, vol. 23, pp. 19–27
45. Sridharan, A. and Prakash, K. 1995: Discussion on ‘Limitations of Conventional Analysis of Consolidation Settlement’, ASCE, J. of Geotechnical Engineering, 121 (6): 517.
46. Taylor, D.W. 1948. : “Fundamentals of soil mechanics”, john wiley and sons, Inc. New York.
47. Vaid, Y.P., and Sasitharan, S. 1992. The strength and dilatancy of sand. Canadian Geotechnical Journal, 29: 522–526.
48. Wood, D.M. 1990. Soil behaviour and critical state soil mechanics. Cambridge University Press, London, UK.
49. Wroth y Schofield 1963. : Ed. Mcgraw-Hill publishing Company Ltd.
50. Yamamuro, J.A., and Lade, P.V. 1997. Static liquefaction of very loose sands. Canadian Geotechnical Journal, 34: 905–917.
51. Yang, J. 2002. Non-uniqueness of flow liquefaction line for loose sand. Géotechnique, 52(10): 757–760.