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Enhancement of the Material Point Method for fluid-structure interaction and erosion

Final Report Summary - GEO FLUID (Enhancement of the Material Point Method for fluid-structure interaction and erosion)

Economic activities, population growth, falling land levels and climate change are generating increasing pressure on habitable space in deltas, river basins and coastal areas throughout the world. Advanced technologies and developments in engineering fields (e.g. geotechnical and hydraulic engineering) enable to reclaim new land, which requires bigger and better defensive structures like breakwaters, revetments and scour protections. From an engineering point of view, realising structures in coastal areas and river basins is much more challenging than building on land. Often, extensive research including complex and expensive physical experiments on scale models is needed to determine an optimal unique solution for the site-specific conditions. As an alternative, one can use computer software to assess a structure's impact on the environment and its behaviour. However, numerical models that accurately take into consideration large soil deformations while correctly capturing both the behaviour of soil and water and, most importantly, the interaction between both media under the influence of varying currents, are not available.

In this project, the researcher has extended and generalised a promising numerical method (i.e. the material point method (MPM)) with a high potential for solving fluid-structure interaction problems. In the field of geomechanics, the interaction between the soil skeleton and pore fluid is considered, but as yet this has not been done in combination with the contact to free-surface water. The aims of the MPM extension was to:

(1) correctly capture the interaction between fluids and structures; and
(2) enable the modelling of erosion and sediment transport in open channel flows.

To achieve the first aim, the Navier-Stokes equations for describing the motion of a viscous fluid were implemented in the MPM. Several fluid flow problems were modelled with the extended MPM, which proved the ability of the method to solve free-surface problems. The results have been validated with analytical solutions (if available) and some experimental results. Solid-fluid interaction problems, like the floating body in water and the dropping of a heavy body into water, have been modelled successfully. The process of installation of a geo-container on the bottom of a water reservoir has been successfully simulated.

In the second part of the research work, the MPM has been applied to model state transition and erosion phenomena which are observed in soil-fluid interaction problems. To model these phenomena, the MPM has been extended containing two sets of particles, i.e. for the solid and fluid phase. The appropriate governing equations have been formulated. The model introduced here can be applied in the case of a granular material like sand or gravel. In first instance, the extended MPM has been applied to undrained analyses for which analytical solutions are available for validation. In the next step, more complex problems were considered such as seepage flow through porous material, a collapsing submerged sand column and the fluidisation of soil and sedimentation of granular material suspended in water. Furthermore, the analysis of a scour process - i.e. the process in which soil is eroded and subsequently transported by flowing water, and finally deposited at other locations - has been successfully modelled by the MPM. The problem of a slope attacked by water has been analysed. The erosion and transport phenomenon have been simulated by the method.

By using a straightforward constitutive model of the porous medium in combination with an extensive implementation of the kinematic and equilibrium equations in the MPM, complex geomechanical problems were solved. The research results have been implemented in a two-dimensional (2D) MPM code (provided as background) and described in a technical report.

The extended MPM is a promising computational tool for modelling the phenomena related to soil-fluid interaction and erosion problems. The impact of the extended MPM is threefold. Firstly, it can be used for the design of so-called geo-containers, which are large geotextile bags filled with a soil material. This will increase the effectiveness of geo-containers for repairing damaged dikes or constructing temporary dams. Secondly, the extended MPM allows for the modelling of the breaching phenomenon which is very important for dredging processes, e.g. for the case of using suction pipes. Thirdly, outcomes of erosion and scour can be predicted by the MPM analysis. In this way, the region possibly impacted by a flooding and related events can be estimated by the method, which can help prepare evacuation plans or to protect the threatened area. In conclusion, the extended and generalised MPM is an economic supplement for expensive model and field tests, and therefore an encouraging innovation in coastal and river engineering. In fact, it is an outstanding scientific achievement unequalled in the field of geotechnical engineering.

This project has enabled the researcher to enter a new field of numerical modelling of fluid-structure interaction problems and erosion in particular. Furthermore, he strengthened secondary skills. His participation in meetings and workshops was beneficial to both the researcher and Deltares, possibly leading to future (joint) research and consulting activities.