  A semi-implicit two-phase double-point Material Point Method (MPM)
formulation, based on the incremental fractional-step method to model large
deformation geotechnical problems has been derived. The semi-implicit
formulation has two advantages compared with the explicit approach: the time
step is independent of the water phase, and the pore pressure field is more
stable. The semi-implicit MPM models based on the incremental fractional-step
method available in the literature consist of modelling the soil and water
mixture using a single set of material points only, in order to save
computational time. In this study, we further derive this formulation with two
sets of material points to represent the soil and water phases separately. The
stress oscillations that are frequently found in the water and soil phases are
stabilised with this approach. A new stabilisation method is developed based on
the modified F-bar method. The proposed method is validated with two numerical
examples under small and large deformations, respectively. After that, Nor-Sand
constitutive soil model is used to simulate landslides. Numerical examples show
an excellent performance of the proposed coupled MPM and the stabilisation
method. The formulation with two sets of material points yields significantly
different but more reliable results in the landslides analysis, compared with
the single-point approach. Additionally, this research shows that the
additional computational cost caused by the additional water material points is
acceptable. Therefore, it is recommended to use two sets of material points for
certain large deformation geotechnical problems.
