Abstract
In soil mechanics, laboratory tests are typically used to classify soils or to test new material laws such as the barodesy model. The results of these tests provide the theoretical basis for subsequent simulations and analysis in geotechnical engineering (e.g., cuts, embankments, foundations). Simulation tools which are reliable as well as economical concerning the computing time are indispensable for applications. In this contribution we introduce two novel meshfree generalized finite difference methods—Finite Pointset Method and Soft PARticle Code—to simulate the standard benchmark problems “oedometric test” and “triaxial test”. One of the most important ingredients of both meshfree approaches is the weighted moving least squares method used to approximate the required spatial partial derivatives of arbitrary order on a finite pointset.
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Acknowledgments
This paper presents results of the joint research project “Untersuchung der Anwendbarkeit von netzfreien numerischen Simulationsmethoden auf Probleme der Geotechnik und Geomechanik” carried out by two groups in Kaiserslautern and in Innsbruck. 1. Kaiserslautern, Germany: The group consisting of Prof. Dr.-Ing. C. Vrettos, D. Chen (Division of Soil Mechanics and Foundation Engineering, University of Kaiserslautern), Dr. J. Kuhnert, Dr. I. Ostermann (Fraunhofer ITWM) is supported by the “Deutsche Forschungsgemeinschaft (DFG)”, Germany, project numbers VR 3/5-1 and KU 1430/7-1. 2. Innsbruck, Austria: The group consisting of Prof. Dr.-Ing. D. Kolymbas, C.-H. Chen, I. Polymerou, Dr. V. Šmilauer (temporarily) (Division of Geotechnical and Tunnel Engineering, University of Innsbruck) is supported by the “Fonds zur Förderung der wissenschaftlichen Forschung (FWF)”, Austria, project number I 547-N13.
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Ostermann, I., Kuhnert, J., Kolymbas, D. et al. Meshfree generalized finite difference methods in soil mechanics—part I: theory. Int J Geomath 4, 167–184 (2013). https://doi.org/10.1007/s13137-013-0048-7
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DOI: https://doi.org/10.1007/s13137-013-0048-7
Keywords
- Strong solution of coupled PDEs
- Barodesy model
- Weighted moving least squares (WMLS) method
- Finite pointset method (FPM)
- Soft PARticle code (SPARC)