×

zbMATH — the first resource for mathematics

Stress-dilatancy based modelling of granular materials and extensions to soils with crushable grains. (English) Zbl 1122.74359
Summary: Stress-dilatancy relations have played a crucial role in the understanding of the mechanical behaviour of soils and in the development of realistic constitutive models for their response. Recent investigations on the mechanical behaviour of materials with crushable grains have called into question the validity of classical relations such as those used in critical state soil mechanics.
In this paper, a method to construct thermodynamically consistent (isotropic, three-invariant) elasto-plastic models based on a given stress-dilatancy relation is discussed. Extensions to cover the case of granular materials with crushable grains are also presented, based on the interpretation of some classical model parameters (e.g. the stress ratio at critical state) as internal variables that evolve according to suitable hardening laws.

MSC:
74E20 Granularity
74L10 Soil and rock mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hardin, Journal of Geotechnical Engineering 111 pp 1177– (1985)
[2] Lade, Journal of Geotechnical Engineering 122 pp 309– (1996)
[3] The influence of particle breakage and state on the behaviour of sands. In International Workshop on Soil Crushability, IWSC’99, Yamaguchi, Japan Geotechnical Society; Japan, 2000.
[4] Nakata, Soils and Foundations 41 pp 39– (2001) · doi:10.3208/sandf.41.2_39
[5] Laboratory studies of a weakly bonded artificial soil. Ph.D. Thesis, Imperial College of Science Technology and Medicine, University of London, 1987.
[6] Aversa, Rock Mechanics and Rock Engineering 31 pp 25– (1998)
[7] Airey, Journal of Geotechnical Engineering 119 pp 1379– (1993)
[8] Nova, European Journal of Mechanics - A/Solids 11 pp 135– (1992)
[9] Conceptual bases for a constitutive model for bonded soils and weak rocks. In Hard Soils-Soft Rocks, et al. (eds). Balkema: Rotterdam, Athens, Greece, 1993.
[10] Lagioia, Géotechnique 45 pp 633– (1995)
[11] Nova, International Journal for Numerical and Analytical Methods in Geomechanics 27 pp 705– (2003)
[12] Cotecchia, Géotechnique 47 pp 523– (1990)
[13] Rouainia, Géotechnique 50 pp 153– (2000)
[14] Stability of subvertical cuts in pyroclastic deposits. In Proceedings of Geoeng 2000, Melbourne, Australia, 2000.
[15] Castellanza, Revue Francaise de Genie Civil 6 pp 1169– (2002) · doi:10.1080/12795119.2002.9692738
[16] Al-Douri, International Journal for Numerical and Analytical Methods in Geomechanics 25 pp 49– (1994)
[17] Lateral loading response of piles in calcareous sediments. In OTRC ’99 Conference, American Society of Civil Engineers: Austin, TX, 1999; 17-36.
[18] Drivability and performance of model piles driven into cemented calcareous sand. In Stresswave 2000, VI International Conference on the Application of Stress-Wave Theory to Piles, Sao Paulo, Brazil, Balkema: Rotterdam, 2000; 47-52.
[19] Cecconi, International Journal for Numerical and Analytical Methods in Geomechanics 25 pp 1525– (2001)
[20] McDowell, Géotechnique 48 pp 667– (1998)
[21] Cecconi, International Journal for Numerical and Analytical Methods in Geomechanics 26 pp 1531– (2002)
[22] Soil Behaviour and Critical State Soil Mechanics. Cambridge University Press: Cambridge, U.K., 1990. · Zbl 0743.73023
[23] A coarse grained weak rock with crushable grains: the Pozzolana Nera from Roma. In Constitutive Modelling and Analysis of Boundary Value Problems in Geotechnical Engineering’, (ed.). Hevelius, Benevento, Napoli: Italy, 2003; 158-185.
[24] Roscoe, Géotechnique 8 pp 22– (1958)
[25] Roscoe, Géotechnique 9 pp 71– (1959)
[26] Rowe, Proceedings of Royal Society of London A 269 pp 500– (1962)
[27] Theoretical meaning and observed values of deformation parameters for soil. In Stress-Strain Behaviour of Soils, (ed.). Henley-on-Thames: U.K., 1972.
[28] Critical State Soil Mechanics. McGraw Hill: London, 1968.
[29] Numerical Analysis and Simulation of Plasticity, Handbook of Numerical Analysis, vol. VI. Elsevier Science: Amsterdam, 1998; 183-499. · Zbl 0930.74001
[30] Moreau, Comptes Rendus Acad. Sc., Paris 271 pp 608– (1970)
[31] Cours de Méchanique des Milieux Continus. Masson: Paris, 1973.
[32] Halphen, Journal de Mécanique 14 pp 39– (1975)
[33] Germain, Journal of Applied Mechanics 50 pp 1010– (1983)
[34] Thermomechanics of Plasticity and Fracture. Cambridge University Press: Cambridge, 1992. · Zbl 0753.73001 · doi:10.1017/CBO9781139172400
[35] Reddy, Applied Mechanics Reviews 47 pp 429– (1993)
[36] Plasticity: Mathematical Theory and Numerical Analysis. Springer: New York, 1999. · Zbl 0926.74001
[37] Modaressi, International Journal for Numerical and Analytical Methods in Geomechanics 18 pp 133– (1994)
[38] A Study of Plasticity Theories and Their Applicability to Soils. Ph.D. Thesis, Cambridge University, 1981.
[39] Houlsby, Computers and Geotechnics 1 pp 3– (1985)
[40] Collins, Proceedings of Royal Society of London Series A 453 pp 1975– (1997)
[41] Houlsby, International Journal of Plasticity 16 pp 1017– (2000)
[42] Collins, International Journal for Numerical and Analytical Methods in Geomechanics 26 pp 1313– (2002)
[43] Convex Analysis. Princeton University Press: Princeton, 1970. · Zbl 0932.90001 · doi:10.1515/9781400873173
[44] Inelastic Analysis of Structures. Wiley: Chichester, 2002.
[45] On the generalised stress-strain behaviour of ?wet? clay. In Engineering Plasticity, (eds). Cambridge University Press: Cambridge, U.K., 1968. · Zbl 0233.73047
[46] Lade, International Journal of Solids and Structures 13 pp 1019– (1977)
[47] Nova, Archiwum Mechaniki Stosowanej 29 pp 445– (1977)
[48] Nova, International Journal for Numerical and Analytical Methods in Geomechanics 3 pp 255– (1979)
[49] Sinfonietta classica: an exercise on classical soil modelling. In Constitutive Equations for Granular Non-Cohesive Soils, (eds). Balkema: Rotterdam, Cleveland, 1988.
[50] Baker, International Journal for Numerical and Analytical Methods in Geomechanics 8 pp 167– (1984)
[51] Thermomechanics of Evolving Phase Boundaries in the Plane. Clarendon Press: Oxford, 1993. · Zbl 0787.73004
[52] Gutierrez, Soils and Foundations 40 pp 49– (2000) · doi:10.3208/sandf.40.2_49
[53] van Eekelen, International Journal for Numerical and Analytical Methods in Geomechanics 4 pp 89– (1980)
[54] Lagioia, Computers and Geotechnics 19 pp 171– (1996)
[55] Herle, Mechanics of Cohesive-Frictional Materials 4 pp 461– (1999)
[56] Miura, Soils and Foundations 37 pp 89– (1997) · doi:10.3208/sandf.37.2_89
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.