ECCOMAS 2024

Semi-implicit Material Point Method with Fractional-step Method for Unsaturated Soil

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

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The heavy rainfall induces hazardous landslides through water seepage. This process reduces the suction and translates the soil condition from unsaturated to saturated. To simulate such seepage failure, the material point method (MPM) has made a remarkable progress. Nevertheless, most of the previous MPM developments for unsaturated soil have employed explicit time integration, which causes pore water pressure oscillations due to the large bulk modulus of water, resulting in large computational costs. Alternatively, semi-implicit MPMs equipped with the so-called fractional-step method have been proposed by several scholars to overcome these problems by solving the pressure Poisson’s equation for incompressible water. 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 behaviour 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, which suppresses the numerical instability and improves computational efficiency. Additionally, we adopt the incremental pressure Poisson’s equation to avoid splitting error, which is occurred by splitting the momentum balance equation in the standard fractional-step method, and employ the sub-grid method for supressing the so-called odd-even oscillations in the steady-state. 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, and validation analysis is carried out for simulating a model experiment of seepage failure.