Abstract
The paper deals with numerical investigations of a deterministic and statistical size effect in granular bodies during shearing of an infinite layer under plane strain conditions and free dilatancy. For a simulation of the mechanical behavior of a cohesionless granular material during a monotonous deformation path, a micro-polar hypoplastic constitutive was used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. To describe a deterministic size effect, the calculations were carried out with an uniform distribution of the initial void ratio for four different heights of the granular layer: 5, 50, 500 and 2,000 mm. To investigate a statistical size effect, the distribution of the initial void ratio in infinite granular layers was assumed to be spatially correlated. As only primary stochastic calculations were performed, single examples of different random fields of the initial void ratio were generated. For this purpose a conditional rejection method was used.
Similar content being viewed by others
References
Wernick, E.: Tragfähigkeit zylindrischer Anker in Sand unter besonderer Berücksichtigung des Dilatanzverhaltens. Publication Series of the Institute for Rock and Soil Mechanics, University Karlsruhe 75 (1978)
Tatsuoka F., Goto S., Tanaka T., Tani K. and Kimura Y. (1997). Particle size effects on bearing capacity of footing on granular material. In: Asaoka, A., Adachi, T., and Oka, F. (eds) Deformation and Progressive Failure in Geomechanics., pp 133–138. Pergamon, New York
Tejchman J. (2004). FE-simulations of a direct wall shear box test. Soils Found. 44(4): 67–81
Bazant Z.P. and Chen E.P. (1997). Scaling of structural failure. Appl. Mech. Rev. 50(10): 593–627
Bazant Z. and Planas J. (1998). Fracture and size effect in concrete and other quasi-brittle materials. CRC Press LLC, Boca Raton
van Vliet, M.R.A.: Size effect in tensile fracture of concrete and rock. PhD thesis, University of Delft (2000)
Chen, J., Yuan, H., Kalkhof, D.: A nonlocal damage model for elastoplastic materials based on gradient plasticity theory. Report Nr.01–13, Paul Scherrer Institute, 1–130 (2001)
Le Bellego C., Dube J.F., Pijaudier-Cabot G. and Gerard B. (2003). Calibration of nonlocal damage model from size effect tests. Eur. J. Mech. A Solids 22: 33–46
Weibull W. (1951). A statistical theory of the strength of materials. J. Appl. Mech. 18(9): 293–297
Carpinteri, A., Chiaia, B., Ferro, G.: Multifractal scaling law: an extensive application to nominal strength size effect of concrete structures. In: Mihashi, M., Okamura, H., Bazant, Z.P. (eds.) Size Effect Of Concrete Structures. E&FN Spon, 173, 185 (1994)
Bazant Z. and Pang S.D. (2006). Computational structural reliability—a major challenge and opprtinity for concrete and other quasibrittle structures. In: Meschke, G., Mang, H. and Bicanic, N. (eds) Computational Modelling of Concrete Structures, EURO-C 2006., pp 845–856. Taylor and Francis, London
Vorechovsky M. and Matesova D. (2006). Size effect in concrete specimens under tension: interplay of sources. In: Meschke, G., Mang, H. and Bicanic, N. (eds) Computational Modelling of Concrete Structures, EURO-C 2006., pp 905–914. Taylor and Francis, London
Tejchman J. (2004). Influence of a characteristic length on shear zone formation in hypoplasticity with different enhancements. Comput. Geotech. 31(8): 595–611
Regueiro R.A. and Borja R.I. (2001). Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity. Int. J. Solids Struct. 38(21): 3647–3672
Gutierrez M.A. and Borst R. (1998). Energy dissipation, internal length scale and localization patterning—a probabilistic approach. In: Idelsohn, S., Onate, E. and Dvorkin, E. (eds) Computational Mechanics., pp 1–9. CIMNE, Barcelona
Fenton G.A. and Griffiths D.V. (2002). Probabilistic foundation settlement on spatially random soil. J. Geotech. Geoenviron. Eng. 128(5): 381–389
Niemunis, A., Wichtmann, T., Petryna, Y., Triantafyllidis, T.: Stochastic modeling of settlements due to cyclic loading for soil-structure interaction. In: Proc. Int. Conf. Structural Damage and Lifetime Assessment, Rome, 1–8 (2005)
Tejchman J. and Bauer E. (1996). Numerical simulation of shear band formation with a polar hypoplastic model. Comput. Geotech. 19(3): 221–244
Tejchman J. and Gudehus G. (2001). Shearing of a narrow granular strip with polar quantities. J. Numer. Anal. Methods Geomech. 25: 1–18
Tejchman J. and Niemunis A. (2006). FE-studies on shear localization in an anisotropic micro-polar hypoplastic granular material. Granular Matter 8(3–4): 205–220
Walukiewicz H., Bielewicz E. and Górski J. (1997). Simulation of nonhomogeneous random fields for structural applications. Comput. Struct. 64(1–4): 491–498
Górski, J.: Non-linear models of structures with random geometric and material imperfections simulation-based approach. Monography, vol. 68. Gdansk University of Technology (2006)
Przewłócki J. and Górski J. (2001). Strip foundation on 2-D and 3-D random subsoil. Probab. Eng. Mech. 16: 121–136
Rechenmacher A.L. and Finno R.J. (2004). Digital image correlation to evaluate shear banding in dilative sands. Geotech. Test. J. 27(1): 13–22
Rechenmacher A.L. (2006). Grain-scale processes governing shear band initiation and evolution of sands. J. Mech. Phys. Solids 54: 22–45
Slominski C., Niedostatkiewicz M. and Tejchman J. (2006). Deformation measurements in granular bodies using a particle image velocimetry technique. Arch. Hydroeng. Environ. Mech. LIII(1): 71–94
Pena A.A., Herrmann H.J., Lizcano A. and Alonso-Marroquin F. (2005). Investigation of the asymptotic states of granular materials using a discrete model of anisotropic particles. In: Garcia-Rojo, H. (eds) Powders and Grains., pp 697–700. Taylor and Francis, London
Gudehus G. (1996). A comprehensive constitutive equation for granular materials. Soils Found. 36(1): 1–12
Bauer E. (1996). Calibration of a comprehensive hypoplastic model for granular materials. Soils Found. 36(1): 13–26
von Wolffersdorff P.A. (1996). A hypoplastic relation for granular materials with a predefined limit state surface. Mech. Cohesive Frictional Mater. 1: 251–271
Wang C.C. (1970). A new representation theorem for isotropic functions. J. Rat. Mech. Anal. 36: 166–223
Wu W. and Niemunis A. (1997). Beyond failure in granular materials. Int. J. Numer. Anal. Methods Geomech. 21: 153–174
Wu W. and Niemunis S.A. (1996). Failure criterion, flow rule and dissipation function derived from hypoplasticity. Mech. Cohesive Frictional Mater. 1: 145–163
Herle I. and Gudehus G. (1999). Determination of parameters of a hypoplastic constitutive model from properties of grain assemblies. Mech. Cohesive Frictional Mater. 4(5): 461–486
Wu, W., Kolymbas, D.: Hypoplasticity then and now. In: Kolymbas, D. (ed.) Constitutive Modeling of Granular Materials, pp. 57–105. Springer, Heidlberg (2000)
Tamagnini C., Viggiani C. and Chambon R. (2000). A review of two different approaches to hypoplasticity. In: Kolymbas, D. (eds) Constitutive Modeling of Granular Materials., pp 107–145. Springer, Heidlberg
Maier, T.: Numerische Modellierung der Entfestigung im Rahmen der Hypoplastizität. PhD Thesis, University of Dortmund (2002)
Oda M. (1993). Micro-fabric and couple stress in shear bands of granular materials. In: Thornton, C. (eds) Powders and Grains., pp 161–167. Balkema, Rotterdam
Pasternak E. and Mühlhaus H.-B. (2001). Cosserat continuum modelling of granulate materials. In: Valliappan, S. and Khalili, N. (eds) Computational Mechanics—New Frontiers for New Millennium., pp 1189–1194. Elsevier, Amsterdam
Schäfer, H.: Versuch einer Elastizitätstheorie des zweidimensionalen ebenen Cosserat-Kontinuums. Miszellaneen der Angewandten Mechanik, Festschrift Tolmien, W., Berlin, Akademie-Verlag (1962)
Tejchman J. and Herle I. (1999). A class A prediction of the bearing capacity of plane strain footings on granular material. Soils Found. 39(5): 47–60
Florian A. (1992). An efficient sampling scheme: Updated latin hypercube sampling. Probab. Eng. Mech. 2: 123–130
Groen, A.E.: Three-dimensional elasto-plastic analysis of soils. PhD Thesis, Delft University, pp. 1–114 (1997)
Tejchman J. (2006). Effect of fluctuation of current void ratio on the shear zone formation in granular bodies within micro-polar hypoplasticity. Comput. Geotech. 33(1): 29–46
Tejchman, J., Górski, J.: Deterministic and statistical size effect during shearing of granular layer within a micro-polar hypoplasticity. Int. J. Numer. Anal. Methods Geomech. (2006, in print)
Tejchman, J., Górski, J.: FE-investigations of a deterministic and statistical size effect in granular bodies within micro-polar hypoplasticity. In: Proceedings of 20th Canberra International Physics Summer School and Workshop on Granular Materials. The Australian National University, Canberra, 4–8 December 2006
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tejchman, J., Górski, J. FE-investigations of a deterministic and statistical size effect in granular bodies within a micro-polar hypoplasticity. Granular Matter 9, 439–453 (2007). https://doi.org/10.1007/s10035-007-0041-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10035-007-0041-7