In this work, we present the application of a newly developed implicit second-order Material Point Method (MPM) on offshore geotechnical applications. The presented second-order MPM uses a special set of piecewise quadratic shape functions to circumvent the well-known issue of producing zero nodal mass contributions. To mitigate the effect of the standard MPM to produce highly oscillating stresses across cell interfaces, we have carried over our ideas obtained from the derivation of the second-order MPM to the Dual Domain Material Point (DDMP) Method, too. The resulting second-order DDMP Method produces a smoother stress distribution across the entire computational domain while being able to profit from the improved convergence rates of second-order finite elements. In a numerical example from geotechnical engineering applications, we illustrate the practical application of our enhanced Material Point and DDMP Methods by simulating a cone penetration. @en

The paper describes two new developments in the PLAXIS geotechnical finite element software. The first part involves some new developments related to the Material Point Method. Here, attention is given to user requirements, with special focus·on the di­vision of the geometry into different MPM and FEM domains, and on contact boundaries. The second part involves the development of a reliability analysis (or probabilistic analy­sis) module to deal with uncertainties in geo-engineering applications. In contrast to the use of (partial) safety factors on loads and materials, a reliability analysis determines the chance that an undesired event occurs (probability of failure). The paper gives some backgrounds of the calculation methods, and user input features and results are highlight­ed. @en

The Material Point Method (MPM) has been developed as a special finite element-based method for large deformation analysis, material flow and contact problems. When it comes to applications in soil, MPM can provide solutions where conventional FEM faces its limitations. Examples of geotechnical applications include landslides, silo filling and emptying, soil pushing and shoveling, as well as structure-soil penetration and installation problems (piles, anchors). In offshore geotechnics one can find several applications of the latter type where an MPM analysis can provide significant added value, such as for monopile penetration, (suction) anchor installation, spud can punch-through and trenching for pipelines and cables. In order to use MPM on a daily basis in practical applications, several numerical difficulties had to be overcome, such as inaccuracies, (numerical) instability, irregularities in strain and stress, contact formulation, boundary determination (applying boundary conditions), and last but not least, dealing with the required computing power. The latter is relevant, since MPM calculations are far more demanding than FEM calculations with a similar calculation grid. In this paper we highlight important numerical solutions that we have implemented for a practical use of MPM in geotechnical applications. Examples are the use of high-order elements and the Dual Domain Material Point method (DDMP) to smoothen strains and stresses, the use of an implicit integration scheme to stabilize calculations, the use of an augmented Lagrangian formulation to enhance the contact algorithm, and the use of dynamics and inertia to deal with local soil failure. Furthermore, the paper demonstrates a number of practical cases where MPM can provide added value in offshore geotechnical applications. @en

Material point method (MPM) is very suitable for modelling extreme deformation of materials, where the traditional finite element method (FEM) often encounters mesh distortion. However, FEM is more accurate and efficient than MPM for problems with small deformation. A large number of engineering applications involve modelling of contact interaction between two bodies where only one of them experiences large deformation. Examples are pile driving or spudcan penetration in soil mechanics, cutting, wear etc. Most of the work on contact modelling within MPM framework reports algorithms that simulate all contact bodies using MPM. One publication [1] presents explicit algorithm where one contact body is modelled with FEM, while the other with MPM.

In this work we present an algorithm for implicit modelling of such FEM/MPM contact interaction. The algorithm is based on minimization of the energy functional with constraint terms, formulated as in classical contact mechanics, using Augmented Lagrangian method [2]. However, instead of the distance function, we use level set function which zero contour tracks the boundary of the contact body modelled with MPM. Since the boundary of the FEM-based body is immersed into the MPM-based domain, the contact contribution is applied similar to fictitious domain methods [3]. The presented numerical examples validate the algorithm against the results, known from literature, as well as demonstrate its applicability for geomechanical calculations.@en