Much of our effort in numerical analysis within geotechnical engineering is devoted to evaluating the likelihood of failure in a given boundary value problem (BVP). However, certain problems occasionally require studying the post-failure behaviour of the mobilised soil mass and its resulting consequences. These large deformation analyses exceed the capabilities of conventional finite element formulations, requiring the use of specialised numerical techniques, such as the material point method (MPM), which can mitigate mesh distortion issues. However, since MPM is based on the same principles as the finite element method (FEM), it shares many of its limitations, including volumetric locking and the hourglass effect, as well as additional challenges, such as stress oscillations due to material points crossing element boundaries. Furthermore, when combined with a constitutive description exhibiting softening, MPM can lead to non-objective results with a pathological dependence on the adopted mesh and poor convergence properties. Within this context, the present work addresses the importance of regularisation in MPM for the objective simulation of localised deformations in the presence of brittle materials. A nonlocal approach was incorporated within an existing MPM framework and applied to the simulation of a number of simple BVPs with a softening material. As in conventional FEM simulations, results without regularisation showed a more brittle global response and larger strains and displacements as the element size was reduced. Furthermore, and particularly relevant for studying the consequences of a given collapse, run-out distances were shown to depend on the mesh resolution. On the other hand, regularised simulations exhibited consistent behaviour, with a global response and a configuration of localised deformations that were approximately independent of the employed mesh. However, it was demonstrated that stress oscillation issues must also be addressed when softening is considered to prevent numerical instabilities. ... Read more

This paper investigates the implementation of a nonlocal regularisation of the material point method to mitigate mesh-dependency issues for the simulation of large deformation problems in brittle soils. The adopted constitutive description corresponds to a simple elastoplastic model with nonlinear strain softening. A number of benchmark simulations, assuming static and dynamic conditions, were performed to show the importance of regularisation, as well as to assess the performance and robustness of the implemented nonlocal approach. The relevance of addressing stress oscillation issues, due to material points crossing element boundaries, is also demonstrated. The obtained results provide relevant insights into brittle materials undergoing large deformations within the MPM framework. ... Read more

Chalk is present in a large area of the East and South coast of the UK where renewables are now being installed. In most cases they are founded on displacement piles, whose design uses empirical methods or partial (wished-in-place) simulations. Installation effects such as grain crushing and pore pressure generation are conservatively estimated (if considered at all), as the change of chalk properties around the pile due to pile installation cannot be easily quantified. In this work it is shown how advanced numerical modelling can be used to guide the design of the foundations in these complex soils. ... Read more