Real Concrete Units:

AccropodeTM Units, Le Havre, France

Accropode IITM Units, S Korea (Courtesy CLI)

Stress development at instant during a drop test collision of Accropode IITM Unit simulated with VGeST FEMDEM tools

For faceted and angular concrete units and rock blocks used in armour layers, FEMDEM provides excellent shape representation and deformability for static and dynamic problems. It also provides a powerful tool for examining stress chains within granular packs of armour units, e.g. showing where units in the toe of a structure are carrying excessively high stresses while other units are carrying very little.

Virtual Concrete Units:

Vcross

VRcross

Two virtual units were designed with the purpose of providing a non -commercial test case. They are termed the Vcross (33 tonnes) and VRcross units (42 tonnes) the latter having the corners substantially reinforced and a greater mass but the same square cross section for the base of the cross arms.

Cut plane showing maximum tensile stress of 3.89 MPa at instant of maximum stress 4.6 ms after drop test collision of Vcross Units, Vcrossmovie (see Latham et al. 2009).  Total destruction of unit arms due to tensile failure would be expected.

Maximum tensile stress of 3.49 MPa at instant of maximum stress 4.8 ms after drop test collision of Vcross Units. Same impact velocity, greater mass, local spalling and crushing damage only to the VRcross unit.

The drop test simulation continues with the block bouncing off the anvil into the air.  The FEMDEM method has been extended to multibody systems such as realistic rock dumping and packing relevant to armour layers.

Reference

Latham, J.-P., Mindel, J., Xiang, J., Guises, R., Garcia, X., Pain. C.,Gorman, G., Piggott, M., Munjiza, A., 2009. Coupled FEMDEM/Fluids for coastal engineers with special reference to armour stability and breakage.  Geomechanics and Geoengineering, Volume 4, Issue 1, 797-805. dx.doi.org/10.1080/17486020902767362

This research was undertaken by Dr. Julian Mindel during his PhD studies at Imperial College under the supervision of Dr. J-P Latham and Prof. Chris Pain, with assistance from AMCG’s Dr. Gareth Collins, Dr. Gerard Gorman, Dr. Matt Piggott and Dr.Jiansheng Xiang.

Wave breaking is shown here in a 3D model. Below we apply the model so the wave interacts with a structure.

Waves breaking on coastal structures were first modelled by Julian Mindel using ‘Fluidity’ superimposed on solids. The resolution given by mesh refinement between units enables drag forces to be calculated with greater realism. The vertical drag force as the wave breaks over and then acts to uplift the units due to buoyancy forces is shown below.  The simulation utilizes the superimposed mesh two-phase method (see fluid-solid interaction) and was run on one processor.

Velocity profiles for one moment just after wave impact are shown in the figure below.

It is also possible to deposit packs of armour units using DEM methods to create granular packs through which wave action can be studied.

The two-way coupling has been validated and an example of coupled DEM/Fluids modelling was shown, see colliding spheres fluid-solid interaction simulation.

Reference

Dr. Julian Mindel PhD Thesis

The code capabilities can be compared with the popular benchmark experiment of a collapsing water column with obstruction.  The figure shows the experiment on the left with the equivalent stage of the simulation in blue on the right, note how closely the violent flows are captured.

Multi-fluid (air and water) interface modelling on 3D unstructured finite element meshes has been achieved using a compressive advection scheme to ensure interface sharpness to the limit of the local resolution. This is of particular interest when modelling breaking waves. A functional-based mesh enhancement by movement (Arbitrary Lagrangian Eulerian) method was implemented to improve efficiency, aid interface sharpness achieved by the compressive scheme, and exploit Lagrangian benefits (Mindel et al. 2007). Surging, plunging, spilling waves have been created using different smooth foreshore slope angles, the videos below show plunging and spilling waves resolved by mesh adaptivity.

The plunging simulation shows the violent plunging tongue and air-water mixing with bubbles eventually surfacing. This level of detail is achievable because of the adaptive mesh technology which can be seen to refine where the greater resolutions are required. This work was presented by Mindel at the 5th Coastal Structures Conference, Venice 2007. Two close-up snapshots of the wave breaking simulation are shown below.

Validation study (MARIN/Kleefsman data set)

The classic experimental validation data set for the challenging CFD problem of a 3D domain with a collasing water column producing a wave striking a vertical rectangular block obtained in the MARIN experimental facility was reported by Kleefsman.  Recent 3D simulation of the six-second experiment by Mindel produced the pressure sensor results shown below, which are within 10% of the experimentally determined peak pressure transient of the observed sensor readings (smoother line of graph is sensor).

References

Dr Julian Mindel PhD Thesis 2009

Mindel, J.E., Collins, G.S., Latham, J.-P., Pain C.C. and Munjiza, A. 2007. Towards a numerical wave simulator using the two-fluid interface tracking approach combined with a novel ALE scheme. Proceedings of the Fifth International Conference on Coastal Structures, Venice, Italy, July 2-4, 2007. Published by World Scientific Publishing Co. Pte. Ltd. 2009, 1465-1476.

Sea-level rise and increased storminess present huge challenges to coastal engineers worldwide. The seaward slope of many breakwaters and shoreline defence structures consists of thousands of interlocking units of concrete or rock, making up a massive granular defence against wave attack. The units are placed freely to form an armour layer which is intended to both dissipate wave energy and remain structurally stable.

Design guidance on the mass and shape of these units is based on empirical equations derived from Froude scale physical model tests. The two main failure modes for concrete armour layers are displacement (hydraulic instability) and breakage (structural instability), which are strongly coupled. Breakage mechanisms cannot all be faithfully reproduced under scaled physical models.

Fundamental understanding of the forces governing such wave-structure interaction remains poor and unit breakages continue to perplex the designers of concrete armour units. Designers of breakwaters, coastal structures and wave energy devices predict and optimise performance and survivability in storm conditions using wave tanks as their main methodology. Very large tank facilities approaching prototype scale are expensive and smaller scale models can be unreliable due to force relations not scaling correctly. For a better understanding of wave energy turbulence, block movement, and internal stresses within armour units in breakwaters with the possibility of 15m high waves numerical models have enormous potential.

A growing research effort in coastal structure resilience and performance is turning to numerical modelling of armour layer systems where the main tools are DEM, FEMDEM and CFD. The coupling of the solids modelling (DEM and FEMDEM codes developed within the VGW project) to the generic multiphase adaptive unstructured mesh  code “Fluidity” has recently been achieved and validation results have been excellent. To prepare Fluidity for wave modelling, interface tracking for free surface flows and waves, previously non-existent in Fluidity, were developed first by Julian Mindel. Limitations often found with volume of fluids (VOF) approaches in 3D were overcome by developing a completely different basis for modelling air-water and solid-fluid interfaces. (see interface tracking). The breakage of armour units in a simple drop test simulation was modelled with the Y2D FEMDEM code (Latham et al. 2008). A new 3D FEMDEM code with quadratic tetrahedral elements has been added to VGeST, enabling dynamic stresses to be modelled (Xiang, Munjiza and Latham 2009).  Coupling of the solids and fluids was validated for one way coupling of flow through backed beds and placed in the context of wave structure interaction modelling technology for the testing of coastal structures and wave energy devices (Latham et al. 2009).  Stress chains in particulate systems (Guises et al. 2009) have also been investigated which has implications for how armour unit systems transmit forces and stresses. These can also be seen dynamically in 3D simulations of rock silo filling. Development and application of numerical modelling to coastal engineering is further highlighted on proceeding pages.

References

Latham, J.-P., Munjiza, A., Mindel, J., Xiang, J., Guises, R., Pain, C.C., Gorman, G. and Garcia, X. 2008. Modelling of massive particulates for breakwater engineering using coupled FEMDEM and CFD. Particuology 6,  572–583. doi:10.1016/j.partic.2008.07.010

Xiang, J., Munjiza, A. and Latham, J.-P., 2009. Finite strain, finite rotation quadratic tetrahedral element for the combined finite-discrete element method. International Journal for Numerical Methods in Engineering. 79(8), 946-978. doi: 10.1002/nme.2599

Latham, J.-P., Mindel, J., Xiang, J., Guises, R., Garcia, X., Pain. C.,Gorman, G., Piggott, M., Munjiza, A., 2009. Coupled FEMDEM/Fluids for coastal engineers with special reference to armour stability and breakage.  Geomechanics and Geoengineering, Volume 4, Issue 1, 797-805. dx.doi.org/10.1080/17486020902767362

Guises, R., Xiang, J., Latham, J.-P., Munjiza, A. 2009. Granular packing: Numerical Simulation and Characterization of the Effect of Particle Shape, Granular Matter, Vol 11, 281-292  doi:10.1007/s10035-009-0148-0

Mindel (2008) PhD Thesis