Abstract
The interface between granular bodies and structures is analysed with the finite element method and a micro-polar hypoplastic constitutive model. Quasi-static shearing of an infinitely long and narrow granular strip between two rigid walls of different roughness under conditions of free dilatancy and constant vertical pressure is investigated. The constitutive model can reproduce the essential features of granular bodies during shear localization. To model the different roughness of the interface, micro-polar boundary conditions are proposed taking into account the asperity of the wall roughness and grain diameter. Some emphasis is given to the influence of the wall roughness on the thickness of shear zone and the mobilization of wall friction.
Similar content being viewed by others
References
Tejchman J., Wu W.: Experimental and numerical study of sand-steel interfaces. Int. J. Numer. Anal. Methods Geomech. 19(8), 513–537 (1995)
Tejchman J., Bauer E.: FE-simulations of a direct and a true simple shear test within a polar hypoplasticity. Comput. Geotech. 21(1), 1–16 (2005)
de Gennaro V., Frank R.: Elasto-plastic analysis of the interface behavior between granular media and structure. Comput. Geotech. 29, 547–572 (2002)
Tejchman J.: Influence of a characteristic length on shear zone thickness in hypoplasticity with different enhancements. Comput. Geotech. 31(8), 595–611 (2004)
Maier, T.: Numerische Modellierung der Entfestigung im Rahmen der Hypoplastizität. PhD Thesis, University of Dortmund (2002)
Pena A.A., Herrmann H.J., Lizcano A., Alonso-Marroquin F.: Investigation of the asymptotic states of granular materials using a discrete model of anisotropic particles. In: Garcia-Rojo, R., Herrmann, H.J., McNamara, S. (eds) Powders and Grains., pp. 697–700. Taylor and Francis, London (2005)
Thornton C., Zhang L.: A numerical examination of shear banding and simple shear non-coaxial flow rules. Philos. Mag. 86(21–22), 3425–3452 (2006)
Alonso-Marroquin F., Vardoulakis I., Herrmann H.J., Weatherley D., Mora P.: Effect of rolling on dissipation in fault gouge. Phys. Rev. E 74, 1–10 (2006)
Potyondy J.G.: Skin friction between various soils and construction materials. Geotechnique 4, 339–353 (1961)
Sondermann W.: Spannungen und Verformungen bei bewehrter Erde. Mitteilungen des Institutes für Grundbau, Universität Braunschweig, Braunschweig (1983)
Desai C.S., Drumm E.C., Zaman M.M.: Cyclic testing and modeling of interfaces. J. Geotech. Eng. ASCE 111, 6 (1985)
Boulon, M.: Numerical and physical modeling of piles behaviour under monotonous and cyclic loading. In: Modelling Soil–Water–Structure Interactions, pp. 285–293. Balkema (1988)
Hassan, A.H.: Etude experimentale et numerique du comportement local et global d’une interface sol granulaire structure. Phd Thesis, Grenoble University (1995)
Neuffer, F., Leibnitz, A.: Über den Gleitwiderstand zwischen Erdstoffen und Bauwerksflächen. In: Bericht aus der Bauforschung, pp. 37. Heft (1964)
Yoshimi, Y., Kishida, T.: Friction between sand and metal surface. In: Proceedings of the 10th ICSMFE, vol. 1, pp. 831–834 (1981)
Huck, P.J., Saxena, S.K.: Response of soil-concrete interface at high pressure. In: Proceedings of the 10th ICSMFE, vol. 2, pp. 141–144 (1981)
Löffelmann F.: Theoretische und experimentelle Untersuchungen zur Schüttgut-Wand-Wechselwirkung und zum Mischen und Entmischen von Granulaten. Publication Series of the Institut für Mechanische Verfahrenstechnik, Universität Karlsruhe, Karlsruhe (1989)
Brumund W.F., Leonards G.A.: Experimental study of static and dynamic friction between sand and typical construction materials. J. Test. Eval. 1, 162–165 (1973)
Kishida H., Uesugi M.: Tests of the interface between sand and steel in the simple shear apparatus. Geotechnique 37, 45–52 (1987)
Uesugi, M.: Friction between Dry Sand and Construction. PhD thesis, Tokyo Institute of Technology (1987)
Becker M., Lippmann H.: Plane plastic flow of granular model material. Arch. Mech. 29, 829–846 (1977)
Haaker, G.: Measurement of wall friction and wear in bulk solids handling. In: Proceeding of the International Conference On Silos-Forschung und Praxis, Tagung 88, Karlsruhe, pp. 389–405 (1988)
Fakharian K., Evgin E.: An automated apparatus for three-dimensional monotonic and cyclic testing of interfaces. Geot. Test. J. ASTM 19(1), 22–31 (1996)
Lerat P.: Etude de l’interface sol-structure dans les milieux granulaires a’ l’aide d’un nouvel appareil de cisaillement annulaire. These de Doctorat de l’Ecole Nationale des Ponts et Chausse’es, Paris (1996)
Vesic A.S.: bearing capacity theory from experiments. J. Soil Mech. Found. Eng. ASCE 99, 575–577 (1973) Discussion
Wernick E.: Tragfähigkeit zylindrischer Anker in Sand unter besonderer Berücksichtigung des Dilatanzverhaltens. pp. 75. Publication Series of the Institute for Rock and Soil Mechanics, University Karlsruhe, Karlsruhe (1978)
Tejchman J.: Scherzonenbildung und Verspannungseffekte in Granulaten unter Berücksichtigung von Korndrehungen. Publ. Ser. Inst. Soil and Rock Mech. (University Karlsruhe) 117, 1–236 (1989)
Unterreiner P., Vardoulakis I., Boulon M., Sulem J.: Essential features of a cosserat continuum in interfacial localisation. In: Chambon, R., Desrues, J., Vardoulakis, I. (eds) Localisation and Bifurcation Theory for Soils and Rocks, pp. 141–155. Balkema, Amsterdam (1994)
Unterreiner, P.: Contribution a l’etude et al la modelisation numerique des sols cloues: application au calcul en deformation des ouvrages de soutenement. PhD thesis, Ecole Nationale des Ponts et Chaussees (1994)
Vardoulakis I., Shah K.R., Papanastasiou P.: Modelling of tool-rock shear interfaces using gradient-dependent flow theory of plasticity. Int. J. Rock Mech. Min. Sci. Geomech. 29(6), 573–582 (1992)
Tejchman J.: Shearing of an infinite narrow granular layer between two boundaries. In: Mühlhaus, H.B. (eds) Bifurcation and Localisation Theory in Geomechanics, pp. 95–103. Swets & Zeitlinger, Lisse (2001)
Huang W., Bauer E., Sloan S.W.: Behaviour of interfacial layer along granular soil-structure interfaces. Struct. Eng. Mech. 15(3), 315–329 (2003)
Lade P.V.: Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces. Int. J. Solid Struct. 13, 1019–1035 (1977)
Vermeer P.: A five-constant model unifying well-established concepts. In: Gudehus, G., Darve, F., Vardoulakis, I. (eds) Proceedings of the International Workshop on Constitutive Relations for Soils, pp. 175–197. Balkema, Amsterdam (1982)
Pestana J.M., Whittle A.J.: Formulation of a unified constitutive model for clays and sands. In. J. Num. Anal. Meth. Geomech. 23, 1215–1243 (1999)
Desrues J., Chambon R.: Shear band analysis for granular materials: the question of incremental linearity. Ingen. Arch. 59, 187–196 (1989)
Darve F., Flavigny E., Megachou M.: Yield surfaces and principle of superposition revisited by incrementally non-linear constitutive relations. Int. J. Plast. 11(8), 927–948 (1995)
Kolymbas D.: A rate-dependent constitutive equation for soils. Mech. Res. Comm. 6, 367–372 (1977)
Wu W.: Hypoplastizität als mathematisches Modell zum mechanischen Verhalten granularer Stoffe. pp. 129. Publication Series of the Institute of Soil and Rock Mechanics, University Karlsruhe, Karlsruhe (1992)
Gudehus G.: A comprehensive constitutive equation for granular materials. Soils Found. 36(1), 1–12 (1996)
Bauer E.: Calibration of a comprehensive hypoplastic model for granular materials. Soils Found. 36(1), 13–26 (1996)
von Wolffersdorff P.A.: A hypoplastic relation for granular materials with a predefined limit state surface. Mech. Cohesive Frict. Mater. 1, 251–271 (1996)
Wang C.C.: A new representation theorem for isotropic functions. J. Rat. Mech. Anal. 36, 166–223 (1970)
Tejchman J., Wu W.: FE-investigations of non-coaxiality and stress-dilatancy rule in dilatant granular bodies within micro-polar hypoplasticity. Int. J. Numer. Anal. Methods Geomech. 33(1), 117–142 (2009)
Chambon R.: Une classe de lois de compartement incrementelement non lineaire pour les sols non visqueux, resolution de quelques problemes de coherences. C.R. Acad. Sci 308, 1571–1576 (1989)
Wu W., Niemunis A.: Failure criterion, flow rule and dissipation function derived from hypoplasticity. Mech. Cohesive Frict. Mater. 1, 145–163 (1996)
Herle I., Gudehus G.: Determination of parameters of a hypoplastic constitutive model from properties of grain assemblies. Mech. Cohesive Frict. Mater. 4(5), 461–486 (1999)
Wu W., Kolymbas D.: Hypoplasticity then and now. In: Kolymbas, D. (eds) Constitutive Modeling of Granular Materials, pp. 57–105. Springer, Heidelberg (2000)
Tamagnini C., Viggiani C., Chambon R.: A review of two different approaches to hypoplasticity. In: Kolymbas, D. (eds) Constitutive Modeling of Granular Materials, pp. 107–145. Springer, Heidelberg (2000)
Niemunis A., Herle I.: Hypoplastic model for cohesionless soils with elastic strain range. Mech. Cohesive Frict. Mate. 2, 279–299 (1997)
Bauer E., Huang W., Wu W.: Investigations of shear banding in an anisotropic hypoplastic material. Int. J. Solids Struct. 41, 5903–5919 (2004)
Tejchman J., Niemunis A.: FE-studies on shear localization in an anisotropic micro-polar hypoplastic granular material. Granul Matter 8(3–4), 205–221 (2006)
Tejchman J., Wu W.: Modeling of textural anisotropy in granular materials with stochastic micro-polar hypoplasticity. Int. J. Non-linear Mech. 42, 882–894 (2007)
Gudehus G.: Seismo-hypoplasticity with a granular temperature. Granul. Matter 8, 93–102 (2006)
Tejchman J., Wu W.: FE-investigations of shear localization in granular bodies under high shear rate. Granul. Matter 11(2), 115–128 (2009)
Tejchman J.: Effect of grain crushing on shear localization in granular bodies within micro-polar hypoplasticity. Using DEM. Arch. Hydro-Eng. Environ. Mech. 57(1–2), 3–30 (2010)
Herle I., Kolymbas D.: Hypoplasticity for soils with low friction angles. Comput. Geotech. 31, 365–373 (2004)
Masin D.: A hypoplastic constitutive model for clays. Int. J. Numer. Anal. Meths. Geomech. 29, 311–336 (2005)
Huang W.-X., Wu W., Sun D.A., Sloan S.: A simple hypoplastic model for normally consolidated clay. Acta Geotech. 1, 15–27 (2006)
Oda M.: Micro-fabric and couple stress in shear bands of granular materials. In: Thornton, C. (eds) Powders and Grains, pp. 161–167. Balkema, Rotterdam (1993)
Pasternak E., Mühlhaus H.-B.: Cosserat continuum modelling of granulate materials. In: Valliappan, S., Khalili, N. (eds) Computational Mechanics: New Frontiers for New Millennium, pp. 1189–1194. Elsevier, Amsterdam (2001)
Mühlhaus H.-B.: Continuum models for layered and blocky rock. In: Hudson, J.A., Fairhurst, Ch. (eds) Comprehensive Rock Engineering, vol. 2, pp. 209–231. Pergamon Press, Oxford (1990)
Schäfer H.: Versuch einer Elastizitätstheorie des zweidimensionalen ebenen Cosserat-Kontinuums. In: Berlin, W. (eds) Miszellaneen der Angewandten Mechanik, Festschrift Tolmien, Akademie- Verlag, Berlin (1962)
Günther W.: Zur Statik und Kinematik des Cosserat-Kontinuums. Abhandlungen der Braunschweigschen Wissenschaftlichen Gesellschaft 10, 195–213 (1958)
Tejchman J., Gudehus G.: Shearing of a narrow granular strip with polar quantities. Int. J. Num. Anal. Methods Geomech. 25, 1–28 (2001)
Tejchman J.: Modelling of shear localisation and autogeneous dynamic effects in granular bodies. Publ. Ser. Inst. Soil Rock Mech. (University Karlsruhe) 140, 1–353 (1997)
Tejchman J.: FE modeling of shear localization in granular bodies with micro-polar hypoplasticity. In: Wu, W., Borja, R. (eds) Springer Series in Geomechanics and Geoengineering, Springer, Berlin (2008)
Bathe K.-J.: Finite Element Procedures in Engineering Analysis. Prentice-Hall, Englewood Cliffs (1982)
Widulinski L., Kozicki J., Tejchman J.: Numerical simulation of a triaxial test for sand using a discrete element method. Arch. Hydro Environ. Eng. 56(3–4), 3–26 (2009)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tejchman, J., Wu, W. FE-investigations of micro-polar boundary conditions along interface between soil and structure. Granular Matter 12, 399–410 (2010). https://doi.org/10.1007/s10035-010-0191-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10035-010-0191-x