A $u$-$p_w$ SPH framework with mechanical-hydraulic boundary treatment in GeoDualSPHysics for large-deformation geomechanics
Abstract: Pore-water pressure changes the effective stress and deformation of saturated geomaterials, while skeleton deformation generates pressure and drives drainage. Resolving this feedback together with hydraulic boundary conditions is necessary for simulations that connect consolidation to large post-failure movement. This paper presents a hydromechanical extension of GeoDualSPHysics using a single-layer displacement-pore-water-pressure ($u$-$p_w$) smoothed particle hydrodynamics (SPH) framework. An explicit pressure-rate equation combines volumetric compression and Darcy diffusion, and the resulting pore pressure feeds back into the skeleton momentum balance. The implementation extends the existing modified dynamic boundary condition (mDBC) infrastructure to carry hydraulic ghost values alongside mechanical boundary data. Prescribed pressure at drained surfaces is combined with impermeable walls and impermeable loaded contacts, with separate control of loading and drainage activation. The formulation is assessed through one-dimensional consolidation, two-dimensional flexible-strip loading, and the three-dimensional Cryer problem. The Cryer simulations reproduce the non-monotonic central pressure response over four Poisson ratios, with normalized pressure root-mean-square errors of 0.012-0.030. The consolidation tests also expose remaining settlement and late-time pressure discrepancies. Applications to 5 m and 8 m sensitive-clay slopes illustrate sequential retrogressive failure and large deformation. The contribution is the integration of hydraulic feedback and boundary handling within GeoDualSPHysics; the results establish an initial verification basis while identifying remaining accuracy and convergence questions.