Nederlands-Vlaams Onderzoekscentrum voor Kustconstructies
Dutch-Flemish Centre for Coastal Structures Research

Nederlandse versie

Research lines

Stability of concrete elements

In the present stability formulae for concrete elements the stability is calculated using a method based on armour stone. The additional friction because concrete elements hook into each other is added as a surcharge on the weight. This is fundamentally incorrect. For gentle shorelines the weight is determining, but for steep slopes the friction resistance. However, the friction also depends on the weight of the blocks above the block considered. So a stability formula is needed where apart from the weight also the friction and the force due to block on top are included. This force is a function of the block weight, the slope angle, the number of blocks and the friction between blocks and the filter layer. 

For cube-type of elements (normal cubes or Antifer) pattern placing leads to much higher stability. Research by Robin van Buchem has shown that the constant in the Van der Meer stability formula is indeed a function of the packing density. 

In order to understand this process one needs to have a good value of the friction. This work has been done by Marco de Lange. 

Phases of the research:

Relevante Nevlock studies:

The influence of the wave height distribution on the stability of single layer concrete armour units
Van de Koppel 2012 Static and dynamic loads on the first row of interlocking, single layer armour units
Van der Linde 2009 Stability of single layer armour units on low crested-breakwaters
De Lange, M 2010 Extraction Force Xbloc: Model Tests
Van Buchem, R.V. 2009 Stability of a single top layer of cubes
Van Zwicht, B.N.M. 2009 Effect of the concrete density on the stability of Xbloc armour units
De Rover, R.A. 2007 Breakwater stability with damaged single layer armour units

Toe structures
The stability of toe structures with various types of foreshores is still a point of discussion. Worldwide there is no agreement on the way of computing the stability, especially in case of a "non-standard" foreshore. in the past basic research on this matter has been done by Gerding and by Docters van Leeuwen. The data of Doctors van Leeuwen did not fit well into the whole scheme, and are therefore disregarded by many authors. However, a good design method should be as such that also her data fit into the scheme. Later Van der Meer adapted the Gerding formula and extended it for shallow water. This extension has been confirmed by the tests of Ebbens. Also Baart and Dijkstra did work on toe stability. However, they all used a "black-box" approach, i.e. the stability of a given type of toe depends on wave height and wave period in front of the structure. However Baart showed that a much better approach is to determine the hydraulic boundary conditions at the toe (i.e.using an appropriate numerical model) and then determine the stone stability using an appropriate stone stability formula (i.e. an Izbash type formula, but including effects of turbulence and pressure gradients). Hofland and Hoan have given some ideas for the development of such formulas, however their work focussed on permanent flow, while under aa wave we have an oscillating flow.

The measurements of Nammuni-Krohn show that the linear wave theory is not too bad for predicting the flow velocities. However some correction is needed. The following steps are foreseen to develop a new toe formula:

Relevant Nevlock studies:
Nammuni-Krohn, J. 2009 Flow velocity at rubble mound breakwaters
Ebbens, R.E. 2009 Toe structures of rubble mound breakwater: stability in depth limited conditions
Dijkstra, O.P.J. 2008 Armour layer stability on a bermed slope breakwater
Baart, S.A. 2008 Toe structure for rubble mound breakwaters: analysis of toe bund design tools and a method for toe rock stability description
Hoan, N.T. 2008 Stone stability under non-uniform flow
Hofland, B, 2005 Rock and roll : turbulence-induced damage to granular bed protections
Van den Berk, M. 1999 Stability of toe and slope structures of rubble mound breakwaters
Docters van Leeuwen, L. 1996 Toe stability of rubble-mound breakwaters
Gerding, E. 1993 Toe structure stability of rubble mound breakwaters

Other relevant studies:
Baart, S, Ebbens, R., Nammuni-Krohn, J., Verhagen, H.J. [2010] Toe rock stability for rubble mound breakwaters
Van der Meer, J.W., d’Angremond, K. and Gerding, E., (1995), Toe structure stability of rubble mound breakwaters, proceedings of ICE 1995, London, p. 308-321

Wave height at the toe

For the the calculation of toe stability and slope stability the wave condtion near the toe is determining. Because of reflection by the structure, this wave height cannot be measured easily in a flume. usually an array of three wave gauges are used and then from comparing the data the incoming and reflective wave are separated. But for steep structures this is not very constistent, because a set of gauges is not a single point. It is worthwhile to investigate this problem using a VOF model in which very simple the wave height with and without structure can be calculated for exactly the same wave conditions. In nearly all generic tests the Jonswap has been used. All formulas are calibrated for this formula. At this moment one assumes that
H2% and Tm-1,0 are the two parameters determining the stability of the breakwater. In how far this is also correct for completely different spectral shapes is still matter of investigation. Research by Hovestad has shown that identical values of H and T near the toe can cause different damage in case of different foreshores. So maybe there is another parameter also relevant.
Phases of the research:

Relevant Nevlock studies:

Hovestad, M. 2005 Breakwaters on steep foreshores


There is a tendency to place a berm in front of a breakwater in ordet to decrease the requried height of the structure. This is relevant for coastal protection in front of urban or recreational develoments. In that case the visual contact with the sea is very relevant. However, there are no good design rules for berms on (normal) breakwaters. Some work has been done on berm breakwaters, but a berm breakwater is a different concept.
Relevant for the design is that the wave impact on the structure changes (surging may become plunging), and also the interlock between elements may decrease. There is a relation with the research on toe stability. An extensive study has been done in 1986, but since then much more is known about wave impacts in general. The tests of Dijkstra gave more insight, but it proved that in all the tests of Dijkstra the lower part of the slope was determining the strength. Because of the selected test cases, there were no clear findings regarding the upper part of the slope. Also it became clear that the berm width is relevant, but the number of tests was too small to come to final conclusions.
Steps in research:
  • do more tests with a varying range of berm width
  • do tests in which especially the upper slope is attacked by waves
  • investigate the effect of various berm types with a VOF model
  • translate this in a simple design rule

Relevant Nevlock studies:
Dijkstra, O.P.J 2008 Armour layer stability on a bermed slope breakwater

Relevant other studies:
Vermeer, A.C.M. 1986 Stability of rubble mound berms and toe constructions. Report on literature survey and model investigation [in Dutch]. Report no M2006, WL|Delft Hydraulics, Delft.


A lot is already known about overtopping. However, we lack still som knowledge regardingovertopping over semi-permeable structures, especially under prototoype conditions. Field tests give some diferent results than scale model tests. For impermeable slopes we have rather good black-box formulas, and also computation with Swash and VOF models works well. Overtopping for permeable strucures with Swash is still impossible, and with VOF models not well calibrated. So, some more work on the (mathematical) modelling of overtopping over semi-permeable structures is needed. This is especially true in relation to the forces by overtopping on semi-permeable structures, like the crown walls of breakwaters.
Steps in in research:
  • validate and improve Swash for overtopping in case of permeable breakwaters
  • validate Swash for overtopping with high waves, calibrate with protoptype tests
  • validate VOF models for computing the overtopping over and the force on breakwater crown walls. 

Relevant Nevlock studies:
Martinez Pez 2013 Validation of Swash for wave overtopping
Oosterloo 2013 Influence of very oblique waves on wave overtopping
Suzuki et al. 2012 A numerical study on the effect of beach nourishment on wave overtopping in shallow foreshores
Krom 2012 Wave overtopping at rubble mound breakwaters with a non-reshaping berm
Lioutas 2012 Spatial distribution of overtopping
Kester, D van 2009 Spatial distribution of wave overtopping
Dijk, B. van 2001 The rear slope stability of rubble mound breakwaters
Bosman, G. 2009 Velocity and flow depth variations during wave overtopping

Relevant other studies:
Van Gent, M. 2003 Wave overtopping events at dikes. Proc 28th int conf coastal engg, Cardiff, 7–12 Jul 2002. World Scientific, Singapore
Van Gent, M. and Puzueta, B. 2005 Rear-side stability of rubble mound structures. Proc int conf coastal engg, Lisbon, 19–24 Sep 2004. World Scientific, Singapore

Interface stability

Geometrically open filters are much more economic than geometrically closed filters. However, the design of such filters is still problematic.  In CUR framework a report has been made by Verheij. In this report a new formula is presented, however this formula did not have a proper calibration. Because of this need Van de Sande performed a number of tests, resulting in proof of concept of the formula, as well as a slight adaptation of the coefficients of the formula. However, he also found that in case of very turbulent flow (for example a propeller jet) may have different effect. Papadopoulos investigated the stability of open filters under the toe of a breakwater, so under an oscillating flow. This investigation showed that more data are needed to come to final conclusions before geometrically open filters can be applied without problems under breakwater toes.

Next steps in research:
  • Develop a formula to determine the effect of turbulence on the required thickness of an open filter
  • Execute tests in the lab to measure the interface stability in case of turbulence
  • Evaluate the data of Papadopoulos and develop and execute relevant tests to measure erosion under an open filter in wave conditions

Relevant Nevlock Studies
Papadopoulos 2012 Scour below the toe of breakwaters
Van de Sande 2012 Stability of open filter structures
Caus 1998 Imperfecte filterconstructies onder golfbrekers
Booij 1998 Erosie onder een geometrisch open filter

Relevant other studies
Verheij et al 2012 Interface stability of granular material under currents
CUR 233 (Verheij & Hoffmans) 2011 Interface stability of granular filters


In the Van der Meer formula the permeability of the layers under the armour is represented by the "notional permeability". In practice the use of that value is somewhat complicted, because P cannot be calculated but has to be determined from the four diagrams Van der Meer has presented in his thesis. Also it is not known what is the effect of a geotextile inside a structure. Some designers require always a value of P=0.1 when applying a geotextile, in order to be on the safe side. It is questionable if this is really needed, but proof is difficult because the effect of a geotextile cannot be determined in scale tests. An other point of discussion is the effect of filling layers. Sometimes some filler is added between layers in order to create a temporary work way. Does such a horizontal layer with lower permeability indeed decrease the value of P?

Phases of the research:
  • Development of conceptual models in which the permeability is included
  • Make calculations with the conceptual model on de basis of tests (among others the tests of Van der Meer
  • Additional tests in the lab

Relevante Nevlock studies:
Jumelet, D 2010 The influence of core permeability on armour layer stability
Vilaplana Domingo, A. 2010 Evaluation of the volume-exchange model with Van der Meer laboratory tests results
Van Broekhoven, P.J.M. 2011 The influence of armour layer and core permeability on the wave run-up
Kik, R. 2011 The notional permeability of breakwaters: experimental research on the permeability factor P
Kik 2012 Notional Permeability
Kluwen, J. 2012 Physical model tests of the notional permeability on breakwaters
Mellink, B.A. 2013 Numerical and experimental research of wave interaction with a porous breakwater

Propeller Jets

An ongoing problem is the stability of bed protections under influence of propeller induced currents. Especially the effect of bow thrusters is causing a lot of problems for designers. Therefore additional research is needed. In the period 2000/2005 some basic knowledge was acquired on propeller interaction. Several types of mathematical models have been applied, however the success was not very great until this moment. Nowadays a very promising approach is the use of OpenFoam for this types of load, but there are still a lot of open questions. 

Fases in het onderzoek:

  • Het opzetten van een Deft model met daarin een schip en een (boeg) schroefstraal en berekenen wat de stroming en turbulentie nabij de bodem zijn; het kalibreren van het model aan de hand van de metingen van Van Veldhoven, Nielsen en Van Blaaderen.
  • Het aanpassen van de formules van Jongeling Hofland en/of Hoan zodanig dat de stabiliteit in een turbulente schroefstraal bepaald kan worden.
  • Het uitvoeren van een experiment om de bovengenoemde formule te toetsen.

Relevante Nevlock studies:

Van Veldhoven, V.J.C.G.L. 2002 Vooronderzoek schroefstraal Op een talud met breuksteen: stroomsnelheden en steenstabiliteit
Schokking, L.A. 2002 Bowthruster-induced Damage
Nielsen, B.C. 2005 Bowthruster-Induced Damage: A physical model study on bowthruster-induced flow
Van Blaaderen, E.A. 2006 Modelling bowthruster induced flow near a quay-wall
Van der Laan, T 2005 Het ontwikkelen van een model voor boegschroefstralen bij verticale kademuren
Van Doorn, R. 2012 Bow Thruster Currents at Open Quay Constructions on Piles
Van den Brink. A.J.W. 2014 Modelling scour depth at quay walls due to thrusters
de Jong, J. 2014 Modeling thrusters with openFoam
Roelse, F. 2014 Stability of slope material affected by bow thrusters at open quay structures

Transport ot stones by currents and waves

The formulas of Shields and Izbash give an indication for the stability of stone in normal current. Jongeling, Hofland and Hoan have extended these formulas for application in case of an arbitrary turbulence. Also a change has been made to describe the stability instead of number of stones displaced by the entrainment rate. This allows to describe the transport of stone quantities also with this parmeter, so effectively an improvement of the Paintal formula

The mentioned equations are valid for (turbulent) flow. The effect of waves has not been included. For non-breaking waves the formula of Sleath is used, but also this formula has limitations. Some research ahas been done by Terrile and Tromp, but this has not yet lead to a practical design formula. new research on near bed structures van Van de Heuvel has improved our knowledge, but there are still questions related to scaling factors for the physical model tests applied.

Also for the stability of stones in high turbulent, high velocity currents (e.g. propeller jets) this is a promising approach, but no practical solution exists yet.

Phases of the research:

Relevante Nevlock studies:
Van den Heuvel, P. 2013 The effect of multiple storms on near bed structures
Forschelen, P. 1999 Transport van granulair bodemmateriaal: Een onderzoek naar transport bij lage hydraulische belasting
Tromp, M. 2004 Influences of fluid accelerations on the threshold of motion
Terrile, E. 2004 The threshold of motion of coarse sediment particles by regular non-breaking waves
Terrile, E; Reniers, A; Stive, M; Tromp, M; Verhagen, H.J. 2006 Incipient motion of coarse particles under regular shoaling waves; Coastal Engineering (53) pp81-92
Hoan, N.T. 2008 Stone stability under non-uniform flow
Saers, W. 2005 Erosion of rubble mound near-bed structures under irregular waves
Hofland, B, 2005 Rock and roll : turbulence-induced damage to granular bed protections
van den Bos, J.P. 2006 Design of granular near-bed structures in waves and currents
Dessens, M. 2004 The influence of flow acceleration on stone stability
de Ruijter, R. 2004 Turbulence structures affecting stone stability in backward-facing step flow: experiments by means of Particle Image Velocimetry
Bijman, W. 2000 Transport van stortsteen door golven en stroming

Marginal stone quality

In many cases in practise the available stone from a nearby quarry is cheap, but of quality below standard. Good quality stone can be imported from far away and is therefore quite expensive. This problem can be solved by using heavier blocks than the ones described by the design formulas. But it is not known how much surcharge should be accounted for in these situations Good design guidelines for the application of "inferior" rock is lacking. This is the first step in this research, there are not yet previous Nevlock reports who studied this problem. 





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The Dutch-Flemish Centre for Coastal Structures Research is a cooperation between Delft University of Technology, Ghent University and the contractors Van Oord, Royal Boskalis Westiminster, BAM and Deme. The goal is to initiate joint research in the field of construction for coastal protection, like breakwaters, bed protection, dike revetments, etc. For information:
Postal address: TU-Delft-Sectie Waterbouwkunde - Postbus 5048 - NL2600GA Delft - Netherlands