Abstract
Axi-symmetric evolutions can occur in the lab and in situ, they are important for validation, design and technologies. Using again attractors in the large, this chapter is less a report on successful applications than an outline of what could further be done. Axial symmetry can arise with suitable initial and boundary conditions and can get lost with bifurcations towards critical phenomena. Axi-symmetric solutions will also serve as a support of interpolations for evolutions with two symmetry planes (Sects. 15.1 and 15.2).
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References
Alshibli K.A., Sture S., Costes N.C., Frank M.L., Lankton M.R., Batiste S.N., and Swanson R.A. Assessment of localized deformations in sand using X-ray computed tomography. Geotech. Test. J., 23(3):274–299, 9 2000.
Bak P., Tang C., and Wiesenfeld K. Self-organized criticality: An explanation of 1/f noise. Phys. Rev. Lett., 59(4):381–384, 1987.
Cox A. D., Eason G., and Hopkins H.G. Axially symmetric plastic deformation in soils. Phil. Trans. Roy. Soc., 254:1–45, 1961.
Cudmani R. Anwendung der Hypoplastizität zur Interpretation von Drucksondierwiderständen in nicht-bindigen Böden. Geotechnik, 19(4):266–273, 1996.
Cudmani R. and Sedlacek G. Analytische und numerische Standsicherheitsanalyse der Schlitzwandherstellung in einem weichen marinen Ton in Oslo, Norwegen. Geotechnik, 29(3):272–288, 2006.
Desrues J., Chambon R., Mokni M., and Mazerolle F. Void ratio evolution inside shear bands in triaxial sand specimens studied by computed tomography. Géotechnique, 46(3):529–546, 1996.
Gudehus G. and Nübel K. Evolution of shear bands in sand. Géotechnique, 54(3):187–201, 2004.
Hicher P.Y. and Wahyudi H. Microstructural analysis of strain localisation in clay. Comput. Geotech., 16:205–222, 1994.
Huber G. and Wienbroer H. Vibro-viscosity and granular temperature of cylindrical grain skeletons-experiments. In M.J. Herrmann, R. Garcia-Rojo and S. McNamara, editors, Powders and Grains 05, pages 287–290. Balkema, Rotterdam, 2005.
Jenike A.W. Steady gravity flow of frictional-cohesive solids in converging channels. J. Appl. Mech., 31:5–11, 3 1964.
Mandl G. Mechanics of Tectonic Faulting, Models and Basic Concepts. Elsevier, Amsterdam, 1988.
Persson B.N.J. Sliding Friction - Physical Principles and Applications. Springer, Berlin, 2 edition. 2000b.
Rendulic L. Ein Grundgesetz der Tonmechanik und sein experimenteller Beweis. Der Bauingenieur, 18(31/32):459–467, 8 1937.
Roscoe K.H. The influence of strains in soil mechanics. Géotechnique, 20(2):129–170, 1970.
Stazhevskii S.B. On the contribution of ring structures to the stress-strain state of the lithosphere and to metallogeny. Fysicheskaya Mesomechanika, 8:65–70, 2005. In Russian.
Stazhevskii S.B. Ring structures as a source of seismicity. Fysicheskaya Mesomechanika, 9:23–32, 2006. In Russian.
Vielsack P. and Hartung A. An example for the orbital stability of permanently disturbed non-smooth motions. Zeitschr. Angew. Math. Mech., 79(6): 389–397, 1999.
Wieghardt K. Ueber einige Versuche an Strömungen in Sand. Ing.-Archiv, 20:109–115, 1952.
Cudmani R. Statische, alternierende und dynamische Penetration in nichtbindigen Böden. PhD thesis, Institute Soil Mechanics and Rock Mechanics, University of Karlsruhe, Heft 152, 2001.
Cudmani R. and Sturm H. An investigation of the tip resistance in granular and soft soils during static, alternating and dynamic penetration. In Proceedings of the International Conference on Vibratory Driving and Deep Soil Compaction, pages 221–231. 2006.
Cudmani R., Huber G., and Gudehus G. A mechanical model for the investigation of the vibro-drivability of piles in cohesionless soils. In A. Holeyman et al., editor, Proceedings of the International Conference on Vibratory Driving and Deep Soil Compaction, pages 45–52. Louvain, 2002.
Deman F. Achsensymmetrische Spannungs- und Verformungsfelder in trockenem Sand. PhD thesis, Institute of Soil Mechanics and Rock Mechanics University of Karlsruhe, Heft 62, 1975.
Dierssen G. Ein bodenmechanisches Modell zur Beschreibung des Vibrationsrammens in körnigen Böden. PhD thesis, Institute of Soil Mechanics and Rock Mechanics, University of Karlsruhe, Heft 133, 1994.
Haar A. and von Karman Th. Plastic deformations in soils. Nachr. Ges. Wiss. Gött., page 204, 1909.
Higo Y. Instability and Strain Localization Analysis of Water-saturated Clay by Elasto-viscoplastic Constitutive Models. PhD thesis, Soil Mechanics, Department of Civil Engineering, Kyoto Unversity, 2003.
Hvorslev M. J. Ueber die Festigkeitseigenschaften gestörter bindiger Böden. Number 45. Danmarks Naturvidenskabelige Samfund, Ingeniorvidenskabelige Skrifter A, 1937.
Janssen H.A. Versuche über Getreidedruck in Silozellen. Zeitschr. d. Vereines deutscher Ingenieure, 1045, 1895.
Kudella P. Mechanismen der Bodenverdrängung beim Einpressen von Fluiden zur Baugrundverfestigung. PhD thesis, Institute of Soil Mechanics and Rock Mechanics, University of Karlsruhe, Heft 132, 1994.
Kuntsche K. Materialverhalten von wassergesättigtem Ton bei ebenen und zylindrischen Verformungen. PhD thesis, Institute of Soil Mechanics and Rock Mechanics, University of Karlsruhe, Heft 91, 1982.
Mahutka K.-P., König F., and Grabe J. Numerical modelling of pile jacking, driving and vibratory driving. In T. Triantafyllidis, editor, Numerical Modelling of Construction Processer in Geotechnical Engineering for Urban Environment, pages 235–246. Bochum, 2006.
Mazurkiewicz B.K. Skin friction on model piles in sand. Technical Report 25, Danish Geotechnical Institute, Copenhagen, 1968.
Meier T. Application of Hypoplastic and Viscohypoplastic Constitutive Models for Geotechnical Problems. PhD thesis, Institute of Soil Mechanics and Rock Mechanics University of Karlsruhe, 2009.
Rebstock D. Hypoplastic simulation of piles and column foundations. In H. Brandl and F. Kopf, editors, 16th Eur. Young Geot. Engineers Conf., pages 303–312. Vienna, 2004.
Rebstock D. Versagensmechanismen von Pfählen unter zyklischer Belastung. 29. Baugrundtagung 2006, Forum für junge Geotechnik- Ingenieure, 2006. available online.
Rebstock D. Stressing and Relaxation of Sand. PhD thesis, Institute of Soil Mechanics and Rock Mechanics, University of Karlsruhe, 2010, under preparation.
Rübel S. Evolution of State and Shape of Viscous Formations. PhD thesis, 2010, under preparation.
Schwarz P.Beitrag zum Tragverhalten von Verpressfählen mit kleinem Durchmesser unter axialer zyklischer Belastung. PhD thesis, Lehrst. und Prüfamt für Grundbau, Bodenmech. und Felsmech. der TU München, München, 2002.
Senneset K., Janbu N., and Svano G. Strength and deformation parameters from cone penetration tests. In Proceedings on the 2th European Symposium Penetration Testing, pages 863–870. Rotterdam, 1982.
Tejchman J. Modelling of Shear Localisation and Autogeneous Dynamic Effects in Granular Bodies. PhD thesis, Institute of Soil Mechanics and Rock Mechanics, University of Karlsruhe, Heft 140, Habilitation, 1997.
Wernick E. Tragfähigkeit zylindrischer Anker in Sand unter besonderer Berücksichtigung des Dilatanzverhaltens. PhD thesis, Institute of Soil Mechanics and Rock Mechanics, University of Karlsruhe, Heft 75, 1978.
Winter H. Fliessen von Tonböden: Eine mathematische Theorie und ihre Anwendung auf den Fliesswiderstand von Pfählen. PhD thesis, Institute of Soil Mechanics and Rock Mechanics, University of Karlsruhe, Heft 82, 1979.
Wu W. Hypoplastizität als mathematisches Modell zum mechanischen Verhalten granularer Stoffe. PhD thesis, 1992.
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Gudehus, G. (2011). Axi-symmetric evolutions. In: Physical Soil Mechanics. Advances in Geophysical and Environmental Mechanics and Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36354-5_14
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