VGeST - Virtual Geoscience Simulation Tools

Stresses in armour units

GGS (an EPSRC- and Industry-funded project 2010-2014)


Full Title: GGS – Forces and Stresses on Gigantic Granular Systems for Coastal Engineers

The project is funded by EPSRC (EP/H030123/10) together with Artelia Group and Baird Associates. We use FEMDEM modelling technology to investigate the behaviour of armour unit systems at the scale of unit interactions and at the scale where the solid material as a whole is performing as a granular system. Rubble-mound rock and concrete armoured structures are a special case of granular media – what we have termed ‘Gigantic Granular Systems’. 

Amour units; AccropodeTM seen in coast protection and Core-locTM in a breakwater

To size units for ‘hydraulic stability’ against wave action, designers implicitly accept scaled laboratory tests and empirical formulae from best practice manuals such as CIRIA/CUR/CETMEF (2007), use unit designers’ guidance, and follow world-wide precedent practice. The assumption is that units are designed to have minimal movement so they should not break, but some movement is inevitable. Many imaginative large offshore schemes, including Nuclear Power stations, are shelved because of an inability to quantify risk. Cube-like units in double layers or excessively massive single layer systems are still deployed. The coastal structure research problem, discussed by experts such as Burcharth, Melby, Phelp and others, has long been recognised as one of determining distributions of static and dynamic stresses at full-scale. To obtain such stress information has proved very challenging in experimental studies which at best will give measurements only at the locations where sensors are placed. One major advantage of numerical studies is therefore the ability to visualise the complete internal stress distribution within all the solids. The GGS project is a first step to solving this problem. Numerical modelling has successfully placed full-scale units correctly. 

Breakwater armour layer system modelled with FEMDEM: 8 m cubed Core-locTM units placed on rock under layer

Statistical analysis tools have been developed to quantify heterogeneity and packing density in the initial construction. Settlement, dynamic and static stresses are now being investigated for various shapes and sizes of units where elastic-plastic constitutive models and 3D fracture models are being integrated within FEMDEM.

FEMDEM simulation and demonstration of location of maximum contact forces

The GGS project scope extends only as far as the examination of solids interactions where the disturbance is provided by prescribed forces or vibrating boundary conditions. Complete granular system response under more realistic disturbances, i.e. by extreme hydraulic wave loadings, is the main modelling goal of our team so that progressive ‘hydraulic damage’ by excessive unit displacements is combined with ‘structural damage’ and breakage of units as they settle or dislodge. Below, we show an example of FEMDEM modelling capability; the unit positions are shown superimposed before and after a major vibration disturbance has been applied.

Position of 8 m3 Core-locTM unit packs before and after a disturbance, modelled with FEMDEM

Settlement and Transient Stress Development in ACCROPODETM units

A loose pack of 8m3 concrete units is subjected to a shake test on a smooth slope at full-scale using the FEMDEM code Y3D.

Results of simulations examining dynamic and static stress levels, settlement and factors of safety for CORE-LOCTM and ACCROPODETM units were described in two conference papers presented in Yokohama, Oct 2011, at Coastal Structures ‘11, where the above simulation was discussed. 

Wave Proxy Research

In June 2012, in addition to simulating vibration disturbances where the underlayer and surrounding container walls move, the result of disturbance forces more similar to those applied by wave action have been simulated. An oscillatory velocity field has been applied parallel to the armour layer slope and drag forces computed and applied to the units within the zone influenced by wave action. Buoyancy and reduced submerged friction can also be applied. The intial packing density shown here is well below that recommended for practical applications. The unit movements modelled by the FEMDEM code Y3D can be seen to concentrate in the ‘wave disturbance zone’. This is a very simplistic model but it illustrates the potential to model expected movements given a prescribed water velocity distribution and a drag force formulation. These developments follow from recent research into two-way coupling by Xiang, Vire, Pain and others.

Simulation of displacements after six waves in low packing density CORE-LOC layer

It is also possible to observe various parameters during the simulated wave action and displacement of units. In the movie shown at the link below, the maximum contact force is captured where high magnitude is given by the hot colours.

 forces and movement during wave action

The research shown below was reported in 2009 and was undertaken by Dr. Jiansheng Xiang at Imperial College under the supervision of  Dr. J-P Latham.  

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:



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.  

Vcross VRcross

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.  


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., Xiang, J. and Baird, W.F.  2011 A numerical investigation of the influence of friction and vibration on laboratory scale armour unit layers. Proceedings of International Conference on Coastal Structures, Yokohama, Japan. September 6-8, 2011.  

Xiang J., Latham J.-P., Zimmer, D., Baird, W.F., Fons, M. 2011. Modelling breakwater armour layers and the dynamic response of armour units. Proceedings of International Conference on Coastal Structures, Yokohama, Japan. September 6-8, 2011.  

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.