# MPM-DREDGE project -- Description

## Introduction

The aim of the MPM-DREDGE project is to develop, validate and demonstrate a numerical tool for the modelling and simulation of dredging applications. It is aimed to solve the numerical issues associated with large deformations and fluid pressures that occur in the interaction between soils and fluids. This effort will result in a joint computer code that combines earlier pioneering work of the two participants (University of Cambridge and Deltares) in the field of soil-fluid interaction. During the MPM-DREDGE project new methodologies will be developed, the advanced code is going to be intensively validated using benchmark problems and will be demonstrated for dredging applications. A major impact of the new software and of the joint effort of the participants through a collaboration in the MPM-DREDGE project is expected as expressed by the dredging industry.

Economic activities, population growth, falling land levels and climate change are generating increasing pressure on available resources of (renewable) energy and habitable space in deltas, river basins and coastal areas throughout the world. Advanced technologies and developments in engineering fields enable to shift boundaries for exploration and exploitation of oil, gas and wind energy further off coast, and to develop ports and reclaim new land. The latter requires bigger and better defensive structures like breakwaters, revetments and scour protections. In order to be able to protect economically vital and at the same time vulnerable areas against flooding and erosion, today and tomorrow, the dredging industry is forced to persist in pushing back frontiers. From an engineering point of view, realising structures in this type of hostile environments is much more challenging than building on land. During their construction and use, these structures are not only affected by wind and gravity. They are also constantly exposed to waves, currents and changing seabed characteristics caused by important processes like erosion and deposition. Moreover, the conditions are very site-specific, meaning that standard solutions are often not applicable. Dedicated materials and construction techniques are to be used and a dedicated numerical tool is needed to determine an optimal unique solution.

Dredging is the maritime recovery, transportation and deposition of natural geomaterials (soil and rock) by special dredging vessels. In this way dredging supports aforementioned issues through e.g. port development, land reclamation, oil and gas exploration and exploitation, offshore wind farms, etc. The impact of the European dredging industry is visible worldwide, e.g. the construction and extension of the Suez canal and the Panama canal and for instance land reclamation for airports in Hong Kong, Singapore, Sydney, Macao and Qatar. This list may be extended with coastal protection projects, wind farms, etc. With a 66% share of dredging in worldwide open markets, the European dredging industry is an economic engine for Europe. Its annual turnover is more than € 7 billion and despite the downturn in the global economy it is still growing. The direct employment within the four largest European dredging companies alone exceeds 25,000 people and the indirect employment is estimated to be twice as large. About 70% of all operations of these companies take place outside Europe, yet almost 90% of return flows back to Europe. The above facts illustrate the importance of dredging for the European community. To maintain its competitive edge, the European dredging industry is re-investing in research and developments. Indeed, significant technological improvements stem from sound engineering judgement and in-depth research in both specialised vessel construction and soil-fluid interaction.

One approach in investigating soil-fluid interaction is the performance of physical experiments. However, considering the extreme costs of these often large scale experiments, the dredging industry cannot perform those on a regular basis. With the advent of computers and computational mechanics it has become feasible to develop numerical tools for the simulation of dredging operations. In particular the pioneering work of the University of Cambridge (academic project participant) and Deltares (commercial international centre for applied research) constitutes a sound basis for the numerical simulation of soil-fluid interaction. Both institutes have recognised the high potential of the so-called material point method (MPM) for solving soil-fluid interaction problems, as reflected by the work of e.g. Bandara (2013) and Vermeer (2008).

In Figure 1 an example of the result of such a MPM simulation is shown in which the large soil deformations of a river levee are illustrated.

*Figure 1: Simulation of slope failure (deviatoric shear strain) using the material point method (MPM).*

Originally, the material point method was developed at Los Alamos National Laboratory (USA) by Harlow (1964), who studied fluid flow by material points moving through a fixed grid. Subsequently, this method has been applied in particular to solids and contact problems between solids (Sulsky, 1994, 1995, 2007; Bardenhagen, 2000, 2002; Ionescu, 2006). The extension into geomechanical applications originated from Wieckowski (1998, 2004) and Coetzee (2004, 2005). At this moment, numerical simulations allow to consider stiff structures dropped into open water. In contrast, numerical models that allow for the simulation of large soil deformations, while correctly capturing both the behaviour of soil and water as well as their interaction are hardly available. Recently, attempts have been made by both institutions. Within Deltares Van Esch (2011), Jassim (2012) and Wieckowski (2012) have done pioneering work. Independently such work was also carried out at the University of Cambridge by Abe (2012) and Bandara (2013).

The dredging industry recognises that the above work is very promising. They realise that existing computer codes cannot handle most practical problems and, moreover, that such numerical methods have not been validated yet for their field of interest. At the same time, also considering the complexity of such simulations, the University of Cambridge and Deltares recognise that further development of their computer codes is very demanding. For this reason, it is decided to combine forces and work together on a joint computer code that will be tailored for the simulation of dredging related problems, and to demonstrate that the code can be applied to dredging practice. The MPM-DREDGE project facilitates this collaboration by linking the fundamental scientific research at the University of Cambridge to the applied scientific work and experimental research at Deltares. On the other hand, the validation and practical application of the material point method is of high interest for the future users of the numerical tools, which are the four largest European dredging companies: Boskalis, Dredging International, Jan de Nul and Van Oord.

The MPM-DREDGE project focuses on three major applications related to the demands of the dredging industry:

- the dropping of geocontainers,
- the modelling of liquefaction and
- the modelling of erosion processes including scouring around offshore structures.

This, and the availability of results from large scale experiments on geocontainers and liquefaction for validation and verification of numerical simulations, motivate the focus on these applications in the MPM-DREDGE project. Without a proper validation and verification, the dredging industry cannot be expected to apply such a new numerical method in the dredging practice.

## Project aims and objectives

The aim of the MPM-DREDGE project is to develop, validate and demonstrate a joint three-dimensional computer code for modelling large deformation problems for soil-fluid interaction, including generation and dissipation of (excess) pore pressures, with special dedication to dredging applications. From the scientific point of view, the MPM-DREDGE project involves major development and extension of the material point method (MPM) which will result in a joint computer code. However, the MPM-DREDGE project is not restricted to code development only, but is also aimed to validation and demonstration of its practical applicability which involves, amongst others, the use of available scale model tests. Real field applications will be considered through intensive collaboration between (dredging) industry and academia. The approach is problem driven, i.e. the numerical tools are developed in order to solve challenging problems of practical importance for the supporting partners in the dredging business.

The main focus of the MPM-DREDGE project will be on the modelling of soil-fluid interaction problems related to the following three dredging applications:

- (A.1) Dropping of geocontainers with interaction between pore water and open water
- (A.2) Liquefaction and marine slope slides including the dredging of soils
- (A.3) Erosion and scour around offshore and near-shore structures

The scientific and technological objectives of the MPM-DREDGE project are:

- (O.1) Development of a joint three-dimensional dynamic MPM computer code
- (O.2) Implementation of Navier-Stokes equations in 3D computer code
- (O.3) Development of multiple particle sets to distinguish each phase of a material
- (O.4) Modelling the interchange of particles between different domains
- (O.5) Connection and interchange between pore water and open water
- (O.6) Interaction of water and soil, boundary/interface conditions
- (O.7) Investigation of non-uniform flow during large deformation and failure including the involvement of inertia effects
- (O.8) Implementation of advanced flow formulation, e.g. Forchheimer equation
- (O.9) Implementation of a soil erosion model that utilises both soil and water particles
- (O.10) Investigation of initiation of slope liquefaction and development of constitutive model formulation applicable for MPM implementation
- (O.11) Validation of implementations with benchmark problems and experiments
- (O.12) Application to engineering problems of dropping of geocontainers, liquefaction of slopes and erosion processes
- (O.13) Training of geotechnical engineers and scientists in advanced numerical analysis using the dynamic MPM software
- (O.14) Dissemination of results to scientists and geotechnical professionals through publications and workshops
- (O.15) Dissemination of results to broader (engineering) public through website including a discussion/exchange forum on internet
- (O.16) Outreach activities for general public

## Applications

#### Dropping of geocontainers

Geocontainers are large bags of highly permeable geomembranes containing up to several hundred cubic meters of water-saturated soil, see Figure 2. They are dumped by a split barge onto the riveror seafloor and thereby experience very large deformations. The application of these geotechnical structures in the core of a breakwater or a river dam is a cost-effective alternative for the dumping of gravel or stone. Experiments have been carried out by Deltares on small geocontainers to study their impact on the river- or seafloor as well as the stability of geocontainers under wave loading (Bezuijen, 2000, 2004, 2009). Subsequently, publications by Wieckowski (1998, 2004) have triggered Deltares to model geocontainers by the MPM. So far, the free fall of an impermeable geocontainer in open water has been successfully modelled. Considering an impermeable geocontainer, the major challenge of modelling the interaction between pore water and open water remains to be done within the proposed project. Here it should be emphasised that real geocontainers are permeable, requiring full modelling of interaction of pore water and open water. Another remaining challenge is the use of an advanced constitutive model for the soil. Here it should be realised that a geocontainer is subjected to both large cyclic deformations and large local changes of density. As a consequence, the stiffness, the friction angle and the permeability of the soil will change significantly during the installation process.

*Figure 2: Dumping of a geocontainer from a barge (left), dike constructed from geocontainers (right).*

Considering large (dynamic) changes of soil permeability, it is also important to reconsider Darcy’s law which describes the flow in porous media. Darcy's law, which is an expression of conservation of momentum, was initially determined experimentally, but has since been derived from the Navier- Stokes equations via homogenization. Darcy's law is also used to describe oil, water, and gas flows through petroleum reservoirs. It should be realised that Darcy's law is only valid for slow, viscous flow. Fortunately, most groundwater flow cases fall in this category. Typically, any flow with a Reynolds number less than one is clearly laminar, and it would be valid to apply Darcy's law. Experimental tests have shown that flow regimes with Reynolds numbers up to 10 may still be Darcian, as in the case of groundwater flow. However, for very short time scales, a time derivative of flux may be added to Darcy's law, which results in valid solutions at very small times. The main reason for doing this is that the regular groundwater flow equation (diffusion equation) leads to singularities at constant head boundaries at very small times. This form is more mathematically rigorous, but leads to a hyperbolic groundwater flow equation. Such equation is more difficult to solve and is only useful at very small times, typically out of the realm of practical use; however it may be significant for the proposed research. Moreover, for very high velocities in porous media, inertial effects can also become significant. Sometimes an inertial term is added to the Darcy's equation, known as Forchheimer term. This term is able to account for the non-linear behaviour of the pressure difference versus velocity data (Bejan, 1984), where an additional term is introduced which is known as inertial permeability. Darcy's law is valid only for flow in continuum region. For a flow in transition region, where both viscous and Knudsen friction are present, a new formulation is used, which is known as binary friction model (Pant, 2012), where the Knudsen diffusivity of the fluid in porous media is introduced.

#### Liquefaction

Flow slides of slopes may be natural or human-induced geo-hazards. Natural flow slides of submerged slopes with surfacing loose sand layers often severely damage flood defences, as e.g. occurred along the coast of the Dutch province of Zeeland during the last few centuries (Silvis, 1995). These natural flow slides were induced mainly by the steepening of the submerged loose sandy slopes by scour due to tidal flow. In geological times natural flow slides of loose fine sediments, composing the slopes of the continental margins, occurred repeatedly. Such flow slides are caused by the steepening of the slope gradient by both tectonic movements and on-going sedimentation processes and naturally triggered by vibrations by earthquakes and nowadays possibly also by offshore activities. The slides can then eventually involve large volumes of seafloor material and flow along large distances towards the deeper ocean floor, destroying anything along their paths, as sub-sea cables, pipelines and bottom-based installations for exploration of oil and gas, and due to their large volume they can even induce tsunamis. Human-induced flow slides can occur due to e.g. deepening of waterways and harbours, strengthening of flood defences, hydraulic mining of sand and gravel and offshore construction. Also heavy construction, like tanks for storing fluids, and severe vibrations near the crests of sensitive submerged slopes may induce flow slides. Dredging activities of submerged loose sandy slopes easily trigger flow slides as well. For the dredging industry the predictability of liquefaction is important to avoid damage to both the designed slope and the dredging equipment, although controlled liquefaction is also a wanted event during the mining of sand.

Flow slides can be initiated by both liquefaction of loosely packed sand layers in the underwater slopes and by retrogressive erosion of more densely packed sand layers (breaching). The damage caused by the liquefied slope failures is often considered more important than the subsequent flow. However, flow slides occurring along the slopes of the continental margins can initiate turbidity currents (Mastbergen, 2003), destroying sub-sea cables, pipelines and bottom-based offshore installations and even inducing tsunamis. Immediately following the occurrence of undrained instability, the unstable volume of loose sediments starts to move down the slope, building up kinetic energy by transferring the conserved mechanical part of its lost potential energy, while heating the soil through friction by the lost mechanical part. As the flow rate of the liquefied soil increases along its path down the slope, the liquefied soil may start to mix with the surrounding water (known as fluid entrainment), further increasing its apparent fluidity. When reaching the bottom of the slope the liquefied soil decelerates as the horizontal bed forces it to flow horizontally, causing an increasing shear resistance, a loss of pore water and an increase of soil density, until finally the flow slide stops. The alternating stress and deformation, induced in saturated loose soils by severe earthquake loading, can cause additional pore pressure generation, accelerating the occurrence of undrained instability and the initiation of a flow slide, even if the initial mobilized friction level is still significantly below that of the undrained instability limit.

The current project will contribute to the modelling of liquefaction and water entrainment by improving both the design and construction of submerged loose sandy slopes by the dredging industry; and establishing the suitability of such slopes along deep open water for heavy industrial activities near their crests. The capabilities and limitations of the MPM will be assessed in terms of physical clarity of formulation, quality of simulation, computational robustness and ease of parameter determination for the description of the phenomena.

To validate the MPM approach, results of large scale model laboratory tests which were performed in a liquefaction tank on submerged model slopes will be used. The slopes in these experiments were loaded to failure by liquefaction by: 1) steadily increasing the steepness of the slope by tilting the liquefaction tank, 2) dredging at the toe of the slope at a range of dredging rates. Advanced constitutive models for the mechanical behaviour of loose saturated sands will be implemented in MPM. Finally, the practical applicability of the developed knowledge and software tools is demonstrated by comparing predictions of dredging projects with appropriate field observations, which will be obtained in collaboration with the dredging industry.

#### Erosion and scouring

The third application of the proposed project is the modelling of scour and erosion in open channel flows by the MPM. It forms an extremely important issue in many areas of river and environmental engineering and related areas (see Figure 3). For example, riverbed erosion can lead to instabilities of embankment slopes and undermining of bridge foundations, thereby favouring structural failure. Consequently, the assessment of erosion is highly relevant for the breaches of river embankments during floods. In fact, erosion is one of the main causes of environmental damage in floods.

*Figure 3: Coastal erosion in The Netherlands (left) and dune erosion test in water flume at Deltares (right).*

Scour and erosion occur in the contact zone between soil and open water, where the conventional concepts of soil mechanics, such as the existence of a soil skeleton, do no longer apply. Instead there is a mixture zone between the open water and the soil skeleton. The transition from a firm skeleton to a flowing mixture is the crux in modelling scour and erosion. Up to now research on this topic has been highly experimental and resulting empirical laws will have to be embedded in the numerical approach. Pioneering numerical solutions for these types of problems have been reported using mainly finite difference and finite volume schemes in Eulerian and Arbitrary Lagrangian- Eulerian (ALE) grids for solving both the fluid flow and the sediment equations. An alternative approach, which simplifies many of the difficulties of the above methods is the MPM.

Within Deltares, this MPM approach has been tested in a simple 2D code. Within the current project this preliminary study will be extended to a 3D code, which is obviously essential for analysing scour around 3D offshore structures. It is also essential for the study of progressive dike breaches. It is acknowledged that full modelling of scour and erosion with validation of the model and demonstration of possibilities and limitations cannot be entirely accomplished within the time frame of the proposed project. But considerable advancements will be made.

## Project Tasks

#### Work Package 1: Code development

- Task 1.1: Soil-water coupling and boundary interface modelling
- Task 1.2: Soil constitutive modelling for cyclic loading, partial saturation and fluid entrainment and soil erosion modelling
- Task 1.3: Joint dynamic MPM code

#### Work Package 2: Validation and applications

- Task 2.1: Dropping of geocontainers
- Task 2.2: Liquefaction and slope slides
- Task 2.3: Erosion and scouring

#### Work Package 3: Knowledge exchange, dissemination and publicity

- Task 3.1: Knowledge exchange
- Task 3.2: Workshops, training courses and secondments
- Task 3.3: Management tasks