A nodal integration-based particle finite element method for poro-elastoplastic modelling of saturated soils using mathematical programming

  • Wang, Liang (ETH Zürich)
  • Zhang, Xue (University of Liverpool)
  • Geng, Xueyu (University of Warwick)
  • Lei, Qinghua (ETH Zürich)

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We develop a novel numerical model combining the nodal integration technique and the second order cone programming (SOCP) based particle finite element method for effective stress analysis of saturated porous media subject to large deformation. In this computational framework, a generalised Hellinger-Reissner variational principle is adopted to reformulate the governing equations for saturated soil dynamics into a min-max optimisation problem. With the finite element discretisation, nodal integration over cells and an implicit time integration scheme, the discretised min-max problem is further transformed into a standard SOCP problem that can be resolved efficiently using the advanced primal-dual interior point method. By doing so, the proposed model acquires several advantages in effective stress analysis: (i) linear triangular element is used without volumetric locking issues because of the strain smoothing technique; (ii) no regularisation technique is needed to stabilise the fields of stress or pore water pressure due to the adopted mixed variational principle; and (iii) no variable mapping operation is required after remeshing owing to the nodal integration scheme. The proposed model is validated against available analytical and numerical solutions and applied to the long-term deformation of an embankment with stone column improvement. The model captures the long-term mechanical behaviour of soils in real-time and tracks the movement of structures, demonstrating its potential for efficiently simulating the long-term behaviour of soils with large deformation in practice.