Hydro-mechanical Model for Slope Stability Assessment: A polygonal stabilization-free discretization

Meshfree Snow Modelling using a Modified Cam-Clay Approach

Snow is a complex geomaterial whose macroscopic response is governed by density, temperature, and the topology of its evolving microstructure. Its mechanical behavior spans elastic, plastic, viscous, and failure dominated regimes, imposing significant challenges for numerical methods, which intends to simulate large deformations, evolving free surfaces, and complex boundary interactions. This work presents the first integration of a Modified Cam-Clay constitutive formulation for snow into a purely meshfree strong-form collocation framework based on the Generalized Finite Difference Method. The main methodological contribution is a numerical coupling that combines a global implicit mixed formulation for pressure and velocity with a constitutive return-mapping algorithm. The hydrostatic pressure contribution is obtained from a Poisson equation and subsequently corrected through the Modified Cam-Clay return-mapping procedure, while the deviatoric response is treated semi-implicitly using a numerical viscosity formulation. This partitioned treatment of the volumetric and deviatoric stress contributions enables stable simulations with comparatively large time steps while producing smooth spatial pressure fields. As a result, forces on complex boundary geometries can be evaluated accurately. Numerical results of this coupling illustrate the algorithmic stability of the framework, the effective imposition of boundary conditions, and the suitability of local spatial refinement. The feasibility of applying the framework to vehicle-snow interaction through rigid-body coupling is also illustrated. The presented formulation provides a robust basis for future simulations of dynamic snow loading on vehicle structures.

A semi-implicit double-point Material Point Method for both free-surface flow and seepage in deformable porous media

A new semi-implicit, two-phase, double-point formulation of the Material Point Method (MPM) for soil–water interaction with seepage and free-surface flows under large deformation is presented in this paper. The approach advances the water phase implicitly while keeping the soil phase explicit, enabling stable, efficient time integration in problems that involve rapid seepage and strong free-surface motion. The proposed framework models high-Reynolds-number interphase drag through a non-linear Darcy’s law implemented for the first time within an incremental fractional step MPM formulation without enlarging the implicit solve. This methodology also enhances the numerical stability for fast flows and wave breaking via a hyperelastic constitutive treatment of slightly compressible viscous water, and mitigates spurious oscillations through a new stabilisation approach for the velocity. Robustness of soil–water interface is achieved by combining nodal-based, free-surface detection, suited for higher-order spline functions with smooth porosity–permeability transitions that avoid constitutive divergence at sharp material boundaries. Validation against laboratory benchmark cases reported in the literature, including pure-water dam break, dam-break seepage through a porous barrier, two granular-collapse tsunami experiments, and a dam-break wave over a movable granular bed, shows accurate and stable free-surface evolution, pressure time histories, seepage fronts, and wave-gauge records. Using an advanced critical-state soil model (NorSand) further improves the reproduction of granular flow kinematics. The results demonstrate that the proposed formulation is a reliable and computationally efficient tool for geotechnical hazards involving intense soil–water coupling, seepage, sediment transport and free water.

Contact-based inverse analysis for nonlinear material identification in spatially heterogeneous solids

This study presents a contact-based isogeometric Finite Element Model Updating (FEMU) framework for identifying spatially varying constitutive parameters of nonlinear solids. The formulation considers large quasi-static deformations of hyperelastic 3D solids and thin shells due to mechanical contact. The proposed inverse approach utilizes full-field displacement measurements available at least on the free surface and, in the case of pure Dirichlet boundary conditions, the resultant contact forces as well. The nonuniform material parameter fields are discretized using low-order Lagrange interpolation independent of the isogeometric analysis mesh, providing control over the inverse problem size and potential discontinuities in the material. The FEMU least-squares objective is minimized using a trust-region reflective algorithm - a local gradient-based optimization approach. Computational efficiency is enhanced through the analytical derivatives of the objective and a material continuation strategy. The proposed framework is evaluated through three numerical examples based on synthetically generated data: a Canham shell strip on a rigid foundation, indentation of a Koiter shell model of the human abdominal wall, and indentation of a Neo-Hookean block. The examples verify the ability of the proposed method to reconstruct inhomogeneous material via mechanical contact. Analytical derivatives improve the computational efficiency and facilitate conducting sensitivity and identifiability analyses of the material parameters. The presented approach is non-destructive and can be used for various inverse problems, such as in-vivo biomechanics of soft tissues and laboratory material characterization.

Torsional dynamics of end-bearing pile in non-homogeneous soil: variational approach coupled with Ritz solution

ABSTRACT An analysis is developed for torsional dynamics of end-bearing pile foundations embedded in inhomogeneous soil deposits. The inhomogeneity of the soil deposit is incorporated in the analysis through an algebraic expression that can simulate linear, parabolic, and hyperbolic variation of shear modulus with depth. In the analysis, the pile is modelled as a one-dimensional elastic continuum, while the soil is a three-dimensional viscoelastic continuum. The Extended Hamilton’s Principle is employed to derive the governing differential equations describing pile and soil motions, which are solved employing Bessel functions and Ritz procedure, respectively. The accuracy of the analysis is verified against existing solutions in the literature. The proposed framework is further employed to study the influence of inhomogeneity. From the study, it is found that the effect of soil inhomogeneity on dynamic torsional stiffness, wave propagation, and pile-twist distribution cannot be neglected, especially for softer (pile-soil stiffness ratio greater than 500) soil deposits.

Evaluation of the Performance of a Finite Volume Physics-Based Model for Soil Erosion Simulation

Having reliable tools for characterizing rainfall-induced soil erosion is fundamental to the effective management of agroforestry systems in order to increase resilience against climate change. Physics-based models provide a robust, comprehensive and widely applicable framework to quantify runoff generation and soil erosion during intense rainfall events in agroforestry catchments. In this work, we propose a novel hydro-erosive model to simulate hydrodynamical flow and bed mobilization, movement and deposition. This hydro-erosive model solves the two-dimensional shallow water equations (SWE-2D) with hydrological source terms for runoff generation, coupled with the 2D depth-averaged solid transport and the soil surface evolution equations. The partial differential system is solved using a finite volume method. Alternative Integral/Differential Bed Slope and explicit upwind/implicit pointwise friction term discretization options can be used to improve performance in terms of numerical stability and conservation. The behavior of different discretization options in this hydro-erosive model is evaluated through an analytical hillslope verification, a benchmark V-catchment rainfall–runoff test and a laboratory dam-break experiment over an erodible bed. The results show that the Differential Bed Slope formulation combined with the upwind friction discretization provides the most accurate and conservative predictions. Also, an Upwind Bed Updating method for integrating soil surface elevation change is compared with the cell-centered integration of the bed change term by suppressing non-physical oscillations without compromising computational efficiency. Overall, the proposed open-source hydro-erosive model provides a reliable and computationally efficient framework for high-resolution simulations of rainfall-induced soil erosion and represents a valuable tool for environmental and agroforestry applications, but appropriate calibration and mesh resolution are required to ensure reliable predictions.

Crack propagation in porous materials with an adaptive ordinary state-based peridynamics and quadtree-based scaled boundary finite element method coupling