Simulation of insertion problems in partially saturated soils with the Particle Finite Element method

  • Monforte, Lluís (CIMNE)
  • Arroyo, Marcos (Universitat Politècnica de Catalunya)
  • Carbonell, Josep Maria (CIMNE)
  • Gens, Antonio (Universitat Politècnica de Catalunya)

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The paper presents a Particle Finite Element formulation [1,2] to simulate partially saturated porous media at large strains. A set of somewhat simplified governing equations is adopted, by assuming that the gas phase is permanently at atmospheric pressure and that air cannot be dissolved in the liquid phase. The weak form of the problem is discretized with linear interpolants for both, displacement and water pressure, and a fully implicit time-marching scheme is employed. The adopted combination of shape functions results in an unstable formulation at constant water content situations, rendering unphysical, spatial oscillations of the water pressure field. This numerical pathology is alleviated by adding a stabilization term to the mass balance equation. Moreover, a three-field mixed formulation, which introduces volume change as an additional field variable, is proposed, which successfully mitigates volumetric locking arising by the quasi-incompressible response predicted by the constitutive model. The constitutive response of the solid phase is described with a state-parameter dependent constitutive model (CASM), extended to partial saturation conditions by means of the Barcelona Basic model Loading-Collapse curve [3]. Meanwhile, the relation between suction and degree of saturation is modelled via a Van Genuchten equation. The proposed approach has been assessed against numerical benchmark examples, such as oedometer and triaxial tests, showing a good agreement with analytical and other numerical solutions. Finally, the performance of the developed formulation is illustrated in a more challenging problem, involving large deformations and contact: cone penetration testing in partially saturated soils. Special attention is paid to the relation between cone metrics and the initial state parameter for different degrees of saturation. REFERENCES [1] E. Oñate, S.R. Idelsohn, F del Pin, and R Aubry, “The particle finite element method – an overview”, Int. J. Comput. Methods., 1(2), 267-307 (2004). [2] J.M. Carbonell, L. Monforte, M.O. Ciantia, M. Arroyo and A Gens, “Geotechnical particle finite element method for modeling of soil-structure interaction under large deformation conditions”, Journal of Rock Mechanics and Geotechnical Engineering, 14(3), 967-983 (2022). [3] E.E. Alonso, A. Gens and A. Josa, “A constitutive model for partially saturated soils”, Géotechnique, 40(3), 405-430 (1990).