Semi-Implicit MPM for Seepage Failure Analysis

  • Hidano, Soma (Tohoku University)
  • Yamaguchi, Yuya (FUJITSU LTD)
  • Takase, Shinsuke (Hachinohe Institute of Technology)
  • Moriguchi, Shuji (Tohoku University)
  • Kaneko, Kenji (Hachinohe Institute of Technology)
  • Terada, Kenjiro (Tohoku University)

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Heavy rainfall induces hazardous landslides by soil water infiltration. In this process, the shear resistance of soil is decreased by the transition from unsaturated to saturated states. To simulate such catastrophic failure, particle methods have recently become popular, and, among them, the material point method (MPM) has accomplished a remarkable progress in the area of computational geomechanics. In comparison with other particle methods, the MPM uses an Eulerian mesh to solve the set of governing equations and does not require search for neighbor particles. This advantage makes the implementation of parallelization easy. In addition, many previous research products devised for the finite element method (FEM) can be reused for the MPM. Nevertheless, most of the previous MPM developments for unsaturated soil suffer from two demerits, when explicit time integration is adopted. One is the pore water pressure oscillation caused by using the large water bulk modulus, and the other is the large computational cost, which is needed due to not only the large bulk modulus or the low permeability of water. Alternatively, semi-implicit MPMs equipped with the so-called fractional-step method have been proposed by several scholars to overcome these problems. However, few studies have so far been made to deal with large deformation of slopes made of unsaturated soil. In this study, we develop a semi-implicit MPM to properly express the mechanical behavior of unsaturated soil based on Biot’s mixture theory. The new contribution of this study is the incorporation of the fractional-step method into the MPM to solve the pore water pressure implicitly using the pressure Poisson's equation, which suppress the numerical instability and improves computational efficiency. Moreover, the time increment can be chosen without considering the magnitude of water permeability because the interaction between solid and liquid phases is evaluated using the intermediate velocity. Several numerical examples are presented to demonstrate the capability and performance of the proposed method. In particular, validation analysis is carried out for simulating a model experiment of seepage failure.