An Improvement of Vermeer-de Borst Constitutive Model for Numerical Simulation of the Shear Behavior of Rockfills
Author
Abstract
The most important features and phenomena of the deformation behavior of rockfills are stress-dependent stiffness, hardening and dilative (or contractive) behaviors, as well as breakage, rotation and redistribution of particle size. An elasto-plastic constitutive model has been suggested by Vermeer and de Borst to simulate the shear behavior of soils, concretes and rocks. This research has tried to improve this model for numerical simulation of the shear behavior of rock fills. The improvement of the model has been performed through proposing new mobilized dilation and friction angles functions and new relationships for some parameters. For validation, a series of large-scale triaxial tests performed on the rockfill shell of Masjed-e-Soleyman dam have been simulated with the improved model. The results show that the improved Vermeer-De Borst model has a good accuracy to simulate the shear behavior of rockfills numerically.
Keywords
1. Marsal, R. J., “Large Scale Testing of Rock Fill Materials”, Journal Soil Mechanic and Foundation Division, ASCE, Vol. 93, No. 2, pp. 27-43, 1967.
2. Marschi, N. D., Chan, C. K., and Seed, H. B., “Evaluation of Properties of Rockfill Materials”, Journal Soil Mechanic and Foundation Division, ASCE , Vol. 98, No. 1, pp. 95-114, 1972.
3. Charles, J. A., and Watts, K. S., “The Influence of Confining Pressure on the Shear Strength of Compacted Rockfill”, Geotechnique, Vol. 30, No. 4, pp. 353-367, 1980.
4. Indraratna, B., Wijewardena, L. S. S., and Balasubramaniam, A. S., “Large-Scale Triaxial Testing of Greywacke Rockfill”, Geotechnique, Vol. 43, No. 1, pp. 37-51, 1993.
5. Abbas, S. M., “Testing and Modelling the Behavior of Riverbed and Quarried Rockfill Materials”, Ph.D Thesis. Delhi, India: Indian Institute of Technology, 2003.
6. Varadarajan, A., Sharma, K. G., Venkatachalam, K., and Gupta, A. K., “Testing and Modeling Two Rockfill Materials”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 129, No. 3, p. 206-218, 2003.
7. Gupta, A. K., “Triaxial Behaviour of Rockfill Materials”, Electronic Journal Geotechnical Engineering, Vol. 14 (Bund. J), pp. 1-18, 2009.
8. Aghaei, A., Soroush, A., and Rayhani, M., “Large-Scale Triaxial Testing and Numerical Modeling of Rounded and Angular Rockfill Materials”, Scientia Iranica, Transaction A: Civil Engineering, Sharif University of Technology, Vol. 17, No. 3, pp. 169-183, 2010.
9. Soroush, A., and Jannatiaghdam, R., “Behavior of Rockfill Materials in Triaxial Compression Testing”, International Journal of Civil Engineering, Technical Note, pp. 153-161, 2012.
10. Vasistha. Y., Gupta, A. K., and Kanwar, V., “Medium Triaxial Testing of Some Rockfill Materials”, Electronic Journal Geotechnical Engineering, Vol. 18 (Bund. D), pp. 923-964, 2013.
11. Xiao, Y., Liu, H., Chen, Y., and Jiang, J., “Strength and Deformation of Rockfill Material Based on Large-Scale Triaxial Compression Tests. I: Influences of Density and Pressure”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 140, No. 12, 10.1061/(ASCE)GT.1943-5606.0001176, 2014.
12. Xiao, Y., Liu, H., Chen, Y., and Jiang, J., “Strength and Deformation of Rockfill Material Based on Large-Scale Triaxial Compression Tests. II: Influence of Particle Breakage”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 140, No. 12, 10.1061/(ASCE)GT.1943-5606.0001177, 2014.
13. Khoiri, M., Ou, C. Y., and Teng, F. C., “A Comprehensive Evaluation of Strength and Modulus Parameters of a Gravelly Cobble Deposit for Deep Excavation Analysis”, Engineering Geology, Vol. 174, pp. 61-72, 2014.
14. Honkanadavar, N., and Sharma, K., “Testing and Modeling the Behavior of Riverbed and Blasted Quarried Rockfill Materials”, International Journal of Geomechanics, ASCE, Vol. 14, No. 6, 10.1061/(ASCE)GM.1943-5622.0000378, 2013.
15. Gupta, A. K., “Effect of Particle Size and Confining Pressure on Breakage and Strength Parameters of Rockfill Material”, Electronic Journal of Geotechnical Engineering, Vol. 14 (Bund. H), pp. 1-12, 2009.
16. Honkanadavar, N. P., Gupta, S. L., and Ratnam, M., “Effect of Particle Size and Confining Pressure on Shear Strength Parameter of Rockfill Materials”, International Journal of Advanced Civil Engineering and Architecture Research, Vol. 1, No. 1, pp. 49-63, 2012.
17. Gupta, A. K., “Effects of Particle Size and Confining Pressure on Breakage Factor of Rockfill Materials using Medium Triaxial Test”, Journal of Rock Mechanics and Geotechnical Engineering, Vol. 8, No. 3 , 2016.
18. Xiao, Y., Liu, H., Ding, X., Chen, Y., Jiang, J., and Zhang, W., “Influence of Particle Breakage on Critical State Line of Rockfill Material”, International Journal of Geomechanics, ASCE, Vol. 16, No. 1, 10.1061/(ASCE)GM.1943-5622.0000538, 2016.
19. Gupta, A. K., “Constitutive Modeling of Rockfill Materials”. Ph.D Thesis, Delhi, India: Indian Institute of Technology, 2000.
20. Varadarajan, A., Sharma, K. G., Abbas, S. M., and Dhawan, A. K., “Constitutive Model for Rockfill Materials and Determination”, International Journal of Geomechanics, ASCE, Vol. 6, No. 4, pp. 226-237, 2006.
21. Seif El Dine, B., Dupla, J. C., Frank, R., Canou, J., and Kazan, Y., “Mechanical Characterization of Matrix Coarse-Grained Soils with a Large-Sized Triaxial Device”, Canadian Geotechnical Journal, Vol. 47, No. 4, pp. 425-438, 2010.
22. Kulhawy, F. H., and Duncan, J. M., “Stresses and Movements in Oroville Dam”, Journal Soil Mechanic and Foundation Division, ASCE, Vol. 98, No. 7, pp. 653-665, 1972.
23. Escuder, I., Andreu, J., and Reche, M., “An Analysis of Stress-Strain Behaviour and Wetting Effects on Quarried Rock Shells”, Canadian Geotechnical Journal, Vol. 42, No. 1, pp. 51-60, 2005.
24. Veiskarami, M., Ghorbani, A., and Alavipour, M. R., “Development of a Constitutive Model for Rockfills and Similar Granular Materials Based on the Disturbed State Concept”, Frontiers of Structural and Civil Engineering, Vol. 6, No. 4, pp. 365-378, 2012.
25. Xu, M., and Song, E., “Numerical Simulation of the Shear Behavior of Rockfills”, Computers and Geotechnics, Vol. 36, No. 8, pp.1259-1264, 2009.
26. Xiao, Y., Liu, H., Chen, Y., and Jiang, J. “Testing and Modeling of the State-Dependent Behaviors of Rockfill Material”, Computers and Geotechnics, Vol. 61, pp. 153-165, 2014.
27. Vermeer, P. A., and De Borst, R., “Non-Associated Plasticity for Soils, Concrete and Rock”, Heron, Vol. 29, No. 3, pp. 1-64, 1984.
28. Zhao, X. G., and Cai, M., “A Mobilized Dilation Angle Model for Rocks”, International Journal of Rock Mechanics & Mining Sciences, Vol. 47, pp. 368-384, 2010.
29. Jafarpour, M., Rahmati, H., Nouri, A., Chan, D., and Vaziri, H., “Determination of Mobilized Strength Properties of Degrading Sandstone”, Soils and Foundations, Vol. 52, No. 4, pp. 658-667, 2012.
30. Schanz, T., and Vermeer, P. A., “Angle of Friction and Dilatancy of Sand”, Geotechnique, Vol. 45, No. 1, pp. 145-151, 1996.
31. Wong, R. C., “Mobilized Strength Components of Athabasca Oil Sand in Triaxial Compression”, Canadian Geotechnical Journal, Vol. 36, No. 4, pp. 718-735, 1999.
32. Itasca Consulting Group, “FLAC; Fast Lagrangian Analysis of Continua”, Minneapolis, Minnesota, USA, 2011.
33. Duncan, J. M., and Chang, C. Y., “Nonlinear Analysis of Stress and Strain in Soils”, Journal of Soil Mechanics and Foundation Division, ASCE, Vol. 96, No. 5, pp. 1629-1653, 1970.
34. Rowe, P. W., “Stress-Dilatancy, Earth Pressure and Slopes”, Journal of Soil Mechanics and Foundation Division, ASCE, Vol. 89, No. 5, pp. 37-36, 1963.
35. Salim, W., and Indraratna, B., “A New Elastoplastic Constitutive Model for Coarse Granular Aggregates Incorporating Particle Breakage”, Canadian Geotechnical Journal, Vol. 41, No. 4, pp. 657-671, 2004.
36. MahinRoosta, R., and Alizadeh, A., “Simulation of Collapse Settlement in Rockfill Material Due to Saturation”, International Journal of Civil Engineering, Vol. 10, No. 2, pp. 93-99, 2012.
37. Ramamurthy, T., and Gupta, K. K., “Response Paper to How Ought One to Determine Soil Parameters to be Used in the Design of Earth and Rockfill Dams”, International Proceedings of Indian Geotechnical Conference, New Delhi, India, Vol. 2, pp. 15-19, 1986.
38. Moshanir Power Engineering Consultants, “Review on Additional Laboratory Tests on Materials of Masjed-e-Soleyman Dam”, Tehran, Iran, 1986.
2. Marschi, N. D., Chan, C. K., and Seed, H. B., “Evaluation of Properties of Rockfill Materials”, Journal Soil Mechanic and Foundation Division, ASCE , Vol. 98, No. 1, pp. 95-114, 1972.
3. Charles, J. A., and Watts, K. S., “The Influence of Confining Pressure on the Shear Strength of Compacted Rockfill”, Geotechnique, Vol. 30, No. 4, pp. 353-367, 1980.
4. Indraratna, B., Wijewardena, L. S. S., and Balasubramaniam, A. S., “Large-Scale Triaxial Testing of Greywacke Rockfill”, Geotechnique, Vol. 43, No. 1, pp. 37-51, 1993.
5. Abbas, S. M., “Testing and Modelling the Behavior of Riverbed and Quarried Rockfill Materials”, Ph.D Thesis. Delhi, India: Indian Institute of Technology, 2003.
6. Varadarajan, A., Sharma, K. G., Venkatachalam, K., and Gupta, A. K., “Testing and Modeling Two Rockfill Materials”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 129, No. 3, p. 206-218, 2003.
7. Gupta, A. K., “Triaxial Behaviour of Rockfill Materials”, Electronic Journal Geotechnical Engineering, Vol. 14 (Bund. J), pp. 1-18, 2009.
8. Aghaei, A., Soroush, A., and Rayhani, M., “Large-Scale Triaxial Testing and Numerical Modeling of Rounded and Angular Rockfill Materials”, Scientia Iranica, Transaction A: Civil Engineering, Sharif University of Technology, Vol. 17, No. 3, pp. 169-183, 2010.
9. Soroush, A., and Jannatiaghdam, R., “Behavior of Rockfill Materials in Triaxial Compression Testing”, International Journal of Civil Engineering, Technical Note, pp. 153-161, 2012.
10. Vasistha. Y., Gupta, A. K., and Kanwar, V., “Medium Triaxial Testing of Some Rockfill Materials”, Electronic Journal Geotechnical Engineering, Vol. 18 (Bund. D), pp. 923-964, 2013.
11. Xiao, Y., Liu, H., Chen, Y., and Jiang, J., “Strength and Deformation of Rockfill Material Based on Large-Scale Triaxial Compression Tests. I: Influences of Density and Pressure”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 140, No. 12, 10.1061/(ASCE)GT.1943-5606.0001176, 2014.
12. Xiao, Y., Liu, H., Chen, Y., and Jiang, J., “Strength and Deformation of Rockfill Material Based on Large-Scale Triaxial Compression Tests. II: Influence of Particle Breakage”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, Vol. 140, No. 12, 10.1061/(ASCE)GT.1943-5606.0001177, 2014.
13. Khoiri, M., Ou, C. Y., and Teng, F. C., “A Comprehensive Evaluation of Strength and Modulus Parameters of a Gravelly Cobble Deposit for Deep Excavation Analysis”, Engineering Geology, Vol. 174, pp. 61-72, 2014.
14. Honkanadavar, N., and Sharma, K., “Testing and Modeling the Behavior of Riverbed and Blasted Quarried Rockfill Materials”, International Journal of Geomechanics, ASCE, Vol. 14, No. 6, 10.1061/(ASCE)GM.1943-5622.0000378, 2013.
15. Gupta, A. K., “Effect of Particle Size and Confining Pressure on Breakage and Strength Parameters of Rockfill Material”, Electronic Journal of Geotechnical Engineering, Vol. 14 (Bund. H), pp. 1-12, 2009.
16. Honkanadavar, N. P., Gupta, S. L., and Ratnam, M., “Effect of Particle Size and Confining Pressure on Shear Strength Parameter of Rockfill Materials”, International Journal of Advanced Civil Engineering and Architecture Research, Vol. 1, No. 1, pp. 49-63, 2012.
17. Gupta, A. K., “Effects of Particle Size and Confining Pressure on Breakage Factor of Rockfill Materials using Medium Triaxial Test”, Journal of Rock Mechanics and Geotechnical Engineering, Vol. 8, No. 3 , 2016.
18. Xiao, Y., Liu, H., Ding, X., Chen, Y., Jiang, J., and Zhang, W., “Influence of Particle Breakage on Critical State Line of Rockfill Material”, International Journal of Geomechanics, ASCE, Vol. 16, No. 1, 10.1061/(ASCE)GM.1943-5622.0000538, 2016.
19. Gupta, A. K., “Constitutive Modeling of Rockfill Materials”. Ph.D Thesis, Delhi, India: Indian Institute of Technology, 2000.
20. Varadarajan, A., Sharma, K. G., Abbas, S. M., and Dhawan, A. K., “Constitutive Model for Rockfill Materials and Determination”, International Journal of Geomechanics, ASCE, Vol. 6, No. 4, pp. 226-237, 2006.
21. Seif El Dine, B., Dupla, J. C., Frank, R., Canou, J., and Kazan, Y., “Mechanical Characterization of Matrix Coarse-Grained Soils with a Large-Sized Triaxial Device”, Canadian Geotechnical Journal, Vol. 47, No. 4, pp. 425-438, 2010.
22. Kulhawy, F. H., and Duncan, J. M., “Stresses and Movements in Oroville Dam”, Journal Soil Mechanic and Foundation Division, ASCE, Vol. 98, No. 7, pp. 653-665, 1972.
23. Escuder, I., Andreu, J., and Reche, M., “An Analysis of Stress-Strain Behaviour and Wetting Effects on Quarried Rock Shells”, Canadian Geotechnical Journal, Vol. 42, No. 1, pp. 51-60, 2005.
24. Veiskarami, M., Ghorbani, A., and Alavipour, M. R., “Development of a Constitutive Model for Rockfills and Similar Granular Materials Based on the Disturbed State Concept”, Frontiers of Structural and Civil Engineering, Vol. 6, No. 4, pp. 365-378, 2012.
25. Xu, M., and Song, E., “Numerical Simulation of the Shear Behavior of Rockfills”, Computers and Geotechnics, Vol. 36, No. 8, pp.1259-1264, 2009.
26. Xiao, Y., Liu, H., Chen, Y., and Jiang, J. “Testing and Modeling of the State-Dependent Behaviors of Rockfill Material”, Computers and Geotechnics, Vol. 61, pp. 153-165, 2014.
27. Vermeer, P. A., and De Borst, R., “Non-Associated Plasticity for Soils, Concrete and Rock”, Heron, Vol. 29, No. 3, pp. 1-64, 1984.
28. Zhao, X. G., and Cai, M., “A Mobilized Dilation Angle Model for Rocks”, International Journal of Rock Mechanics & Mining Sciences, Vol. 47, pp. 368-384, 2010.
29. Jafarpour, M., Rahmati, H., Nouri, A., Chan, D., and Vaziri, H., “Determination of Mobilized Strength Properties of Degrading Sandstone”, Soils and Foundations, Vol. 52, No. 4, pp. 658-667, 2012.
30. Schanz, T., and Vermeer, P. A., “Angle of Friction and Dilatancy of Sand”, Geotechnique, Vol. 45, No. 1, pp. 145-151, 1996.
31. Wong, R. C., “Mobilized Strength Components of Athabasca Oil Sand in Triaxial Compression”, Canadian Geotechnical Journal, Vol. 36, No. 4, pp. 718-735, 1999.
32. Itasca Consulting Group, “FLAC; Fast Lagrangian Analysis of Continua”, Minneapolis, Minnesota, USA, 2011.
33. Duncan, J. M., and Chang, C. Y., “Nonlinear Analysis of Stress and Strain in Soils”, Journal of Soil Mechanics and Foundation Division, ASCE, Vol. 96, No. 5, pp. 1629-1653, 1970.
34. Rowe, P. W., “Stress-Dilatancy, Earth Pressure and Slopes”, Journal of Soil Mechanics and Foundation Division, ASCE, Vol. 89, No. 5, pp. 37-36, 1963.
35. Salim, W., and Indraratna, B., “A New Elastoplastic Constitutive Model for Coarse Granular Aggregates Incorporating Particle Breakage”, Canadian Geotechnical Journal, Vol. 41, No. 4, pp. 657-671, 2004.
36. MahinRoosta, R., and Alizadeh, A., “Simulation of Collapse Settlement in Rockfill Material Due to Saturation”, International Journal of Civil Engineering, Vol. 10, No. 2, pp. 93-99, 2012.
37. Ramamurthy, T., and Gupta, K. K., “Response Paper to How Ought One to Determine Soil Parameters to be Used in the Design of Earth and Rockfill Dams”, International Proceedings of Indian Geotechnical Conference, New Delhi, India, Vol. 2, pp. 15-19, 1986.
38. Moshanir Power Engineering Consultants, “Review on Additional Laboratory Tests on Materials of Masjed-e-Soleyman Dam”, Tehran, Iran, 1986.
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