INFLUENCE OF WAVE STEEPNESS ON STABILITY OF PLACED BLOCK REVETMENTS

Block revetments are vulnerable for pressure fluctuations on the slope during wave attack. Especially gradients that occur during wave impacts and during maximum wave rundown are important. This research focuses on the influence of wave steepness on the hydraulic load on the block revetment. Small scale model tests have been performed to investigate the hydraulic loads on a smooth slope (wave pressures; wave impacts). The results of these measurements have been analyzed with a Matlab program and the numerical model Zsteen, which is capable of calculating block motion as a function of the pressure distribution in time and space on the slope. Largescale tests in the Delta Flume of Delft Hydraulics have been used to verify the conclusions. The comparison of small scale and largescale results also gave insight in the scale effects involved.

See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/301430744 INFLUENCE OF WAVE STEEPNESS ON STABILITY OF PLACED BLOCK REVETMENTS Conference Paper · April 2007 DOI: 10.1142/9789812709554_0424 CITATION READS 17 3 authors, including: Mark Klein Breteler Deltares 41 PUBLICATIONS 74 CITATIONS SEE PROFILE All content following this page was uploaded by Mark Klein Breteler on 04 May 2016 The user has requested enhancement of the downloaded file Proceedings of 30th ICCE conference, San Diego USA, 2006 INFLUENCE OF WAVE STEEPNESS ON STABILITY OF PLACED BLOCK REVETMENTS Mark Klein Breteler 1, Robert ‘t Hart2 and Theo Stoutjesdijk3 Block revetments are vulnerable for pressure fluctuations on the slope during wave attack Especially gradients that occur during wave impacts and during maximum wave rundown are important This research focuses on the influence of wave steepness on the hydraulic load on the block revetment Small scale model tests have been performed to investigate the hydraulic loads on a smooth slope (wave pressures; wave impacts) The results of these measurements have been analyzed with a Matlab program and the numerical model Zsteen, which is capable of calculating block motion as a function of the pressure distribution in time and space on the slope Large-scale tests in the Delta Flume of Delft Hydraulics have been used to verify the conclusions The comparison of small scale and large-scale results also gave insight in the scale effects involved INTRODUCTION Placed block revetments are constructed to withstand the wave forces on dikes, especially in regions where rip rap is not locally available, such as the Netherlands The blocks are placed adjacent to each other on a filter layer to form a relatively closed and smooth surface, which is easy to walk on (see Figure 1) The wave forces due to wave run-up and run-down will be only small, because of the smooth surface On the other hand, the uplift forces due to pressure fluctuations in the breaking waves are a considerable threat to the stability Figure Example of block revetment during construction In the past years extensive research on the stability of block revetments has been conducted by Delft Hydraulics in co-operation with GeoDelft, WL | Delft Hydraulics, P.O.Box 177, 2600 MH Delft, the Netherlands; Ministry of Transport, Public Works and Water Management, Delft, the Netherlands; GeoDelft, P.O.Box 69, 2600 AB Delft, the Netherlands 2 commissioned by Rijkswaterstaat (Ministry of Transport, Public Works and Water Management) Recently a series of small scale and large scale model tests were performed to investigate the influence of the wave steepness (or breaker parameter) on the stability of block revetments: Wave steepness: sop = Hs/Lop Breaker parameter: op = tan / sop With: Hs = Significant wave height at the toe of the structure (m); Lop = deep water wave length = /(gTp2); Tp = wave period at the peak of the spectrum (s); g = acceleration of gravity (m/s2); = slope angle (o) Small scale flume tests: pressure on the slope quantification of load characteristics large-scale stability tests numerical calculation of stability conclusions Figure Overview of research Experimental research on the stability of block revetments is hindered by scale effects These are partly due to conflicting scale rules for the waves (Froude) and the flow in the filter layer under the blocks (Reynolds) The flow in the filter layer determines the uplift pressure on the cover layer which jeopardizes the stability and is therefore of crucial importance Furthermore scale effects occur in the wave impacts (Bullock et al, 2001) Since large-scale tests are extremely expensive, the research has been carried out with small scale tests, numerical calculations and a limited number of large-scale tests Each of these three parts of the research contribute to the conclusions (see Figure 2) The small scale tests have been performed to measure the pressure distribution in time and space on the slope These have led to a quantification of a number of selected load characteristics The small scale tests have also been used as input for the numerical calculations with Zsteen (Stoutjesdijk 2003) This finite element method calculates the uplift pressure on the cover layer by calculating the pressure distribution in the filter Furthermore it calculates the block motion and therefore gives insight in the stability of the revetment In this way we can cope with the conflicting scale rules of Froude and Reynolds Furthermore we have carried out large-scale tests in the Delta Flume of Delft Hydraulics in which we have measured the hydraulic load on the slope and the stability of the revetment This has given the necessary insight in the scale effects involved in wave impacts, and allowed us to verify the results regarding the stability of the revetment THEORY The stability of block revetments is especially jeopardized by pressure gradients on the slope For practical reasons we focus on the pressure potential (pressure head), , instead of the pressure, p: = p/( g) + z With: p = pressure (Pa); = pressure potential (m); (kg/m3) and z = vertical coordinate (m) = density of water impact on slope in filter , Z uplift local minimum revetment X Figure Pressure potential (pressure head) distribution on the slope and in the filter during wave impact (schematised) Especially at moments when the pressure potential has a local minimum, an uplift pressure will occur giving an uplift force on the blocks This is because of the fact that the pressure potential in the filter underneath the cover layer will be a damped representation of the pressure distribution on the slope This is shown in Figure Since the filter layer is full of water, which can be regarded as almost incompressible, the pressure potential on top of the cover layer will be transmitted instantaneously to the filter layer (see Figure 4) This means that the pressure potential in the filter is primarily influenced by the pressure potential on the cover layer at that specific moment, and is hardly influenced by previous moments pressure head on the slope breaking wave (water surface) high pressure head uplift low pressure head on the slope cover layer filter geotextile D b subsoil pressure transmission through filter Figure Pressure transmission through the filter layer during the moment of maximum wave rundown (schematised) (similar process as during wave impacts) The block motion, however, will be related to the product of the pressure potential difference across the cover layer (net uplift pressure potential) and the duration of this This product equals the uplift impuls, which can be held responsible for the block motion This theory has been checked thoroughly in previous research (e.g Hofland et al 2005) Previous research (Klein Breteler 2000) has shown that block revetments can be subdivided into two basic types of structures: revetments with a rather open cover layer, typically with a relative open area between the blocks (joints and gaps) of to 15% low permeability revetments, such as rectangular blocks placed close together with very small joints, typically with a relative open area of less than 3% The revetments built in present-days in the Netherlands are primarily of the open type, because the rather open cover layer releases the uplift pressure more easily and therefore is more stable than the low permeability revetments The open revetments are more vulnerable to wave impacts, and hardly respond to the load during wave rundown For the low permeability revetments this is the other way around Since both revetment types still exist in the Netherlands, research is focused on both types This means that two types wave loading are distinguished: the pressure front during wave rundown (just before wave impact occurs) the pressure distribution during wave impact b tan front f 0,9 xs Wave run-down: impact Wave impact: imp tan x k50-80%k max Bimp trough Figure Some characteristics of the pressure potential distribution on the slope during wave rundown and during wave impact Based on these considerations a number of decisive load characteristics have been identified, such as: during wave rundown: maximum pressure potential in the front, relative to the minimum ( b) minimum pressure potential in the front, relative to the stil water level ( min) maximum pressure potential gradient in the front: / x = tan f (with x = horizontal coordinate (m)) during wave impact: peak pressure potential in the wave impact: max maximum pressure potential relative to the adjacent pressure potential in the trough next to the impact ( imp), duration of the wave impacts (timp), width of the wave impacts (Bimp), pressure potential gradient in the impact ( / x) The analysis of the measurements was focused on characteristics such as these Some of the results of the measurements and conclusions will be presented in this paper SMALL SCALE MODEL TESTS The small scale tests in the Schelde Flume of Delft Hydraulics have been carried out with a slope of 1:3 and 1:4, which is typical for Dutch dikes The surface of the slopes was smooth and impermeable The slope was equipped with 47 pressure cells that measured the pressure potential on the slope during the wave action The sampling frequency of these instruments was 2kHz The presently carried out tests had a wide range of wave characteristics with relatively low wave steepness (rather long waves): wave height: 0.07 < Hs < 0.22 m wave period: 2.8 < Tp < 6.3 s wave steepness: 0.001 < sop < 0.017 breaker parameter: 2.4 < op < 7.3 The data of earlier research with waves of normal steepness (0.020 < sop < 0.040) were added for the present analysis Since a very detailed measurement of the pressure distribution on the slope was necessary, a very small spacing between the instruments was used The pressure cells were placed in the wave impact area at a distance of 22 mm Unfortunately, the housing of the pressure cells didn't allow such small spacing, and therefore the instruments were placed into two arrays The distance between the two arrays was 20 mm Below and above the impact area a larger spacing was used, which allowed the instruments to be placed in one array The lowest pressure cell was situated approximately 40 cm below the still water level (SWL) and the highest was approximately 25 cm above SWL Most tests were conducted with 0.1 < Hs < 0.2 m LARGE SCALE MODEL TESTS The stability of the block revetments was investigated in the large scale model facility of Delft Hydraulics: the Delta flume The flume is more then 220 m long, m wide and m deep The wave generator is capable of making waves with a significant wave height of up to 1.7 m with individual waves of up to m At the end of the flume an 8.8 m high dike was constructed with a slope of 1:3.5, and a block revetment of 15 cm thick on a filter layer (see Figure 6) The block revetment was an open type with a relative open area of 13% This type of block revetments is vulnerable for wave impact, but not for the pressure front during wave rundown The shape of the blocks can be seen in Figure 15 cm Hydroblocks 4.5 m +2.0 m concrete (dummy slope) +6.5 m concrete (dummy slope) 5.5 cm filter 20-40 mm geotextile sand-cement (represenents clay layer) 8.8 m sand +0.0 m Figure Cross-section of large scale model in the Delta flume (schematised) The structure was equipped with 21 pressure cells on the cover layer to measure the wave load, and 13 pressure cells in the filter The pressure cells are shown in Figure They were installed in metal cylinders in the blocks with a thin metal plate with holes to protect the instruments against stones that are washed across the surface of the revetment The stones are used to fill in the gaps and mobilise the interaction between the concrete blocks Because of this protection plate some damping of the highest peak pressures during impacts could occur, but without the protection the pressure cells would not survive the impacts of the stones on the slope The filter layer was a broken granite layer of 5.5 centimetres thick with a grain size of 20 to 40 mm (D15 = 22 mm) The blocks formed a 15 cm thick layer and had a rather low density of 1952 kg/m3 Various test series were performed with different wave steepnesses: sop = 0.0068; op = 3.4: 0.5 < Hs < 1.1 m sop = 0.0045; op = 4.3: Hs = 1,0 m sop = 0.0033; op = 5.0: 0,5 < Hs < 0.9 m In each test series the wave height was increased step-by-step until damage to the revetment occured, or until the maximum capacity of the flume was reached Since the tests have been conducted with rather long waves, the maximum capacity of the flume was limited due to the limited stroke of the wave board Results of the tests are given in Figure Figure Installation of the pressure cells in the concrete blocks (Hydroblock) (left), and breaking wave in Delta Flume (sop = 0.0067) (right) 10 Hs/( D) (-) trend no damage damage 0 breaker parameter op (-) Figure Test results of the large scale model tests On the vertical axis the ratio of the wave height and weight of the cover layer is given, while on the horizontal axis the breaker parameter is used, with =( b )/ = relative density of the blocks (-); b = density of the blocks (kg/m3) and D = cover layer thickness (m) As was expected, the stability of the block revetment was higher at a low wave steepness of 0.0033 compared to the test series with sop = 0.0068 If the wave steepness decreases the number of wave impacts decrease and also the maximum impact pressure decreases This is discussed in more detail in the next paragraph, together with the trend line given in Figure 8 ANALYSIS OF THE RESULTS The measured pressure potential on the slope as a function of time and space was first analysed with a Matlab programme to find the characteristics of the hydraulic load in all individual waves The large difference between the load in each wave made it necessary to perform a statistical analysis In this paper the attention is focused on the 2% exceedance values, relative to the number of incoming waves The measurement files have been reduced to a sample frequency of 100 Hz, to allow the analysis within a reasonable computational time Since the results will be used for the determination of the stability of block revetments, very small duration loads are usually insignificant A large uplift pressure of say ms will not be able to lift a block out of the revetment, since inertia and the permittivity of the filter will not allow for this The permittivity (discharge through the filter) is important because the flow of water through the filter should be able to push out the block The influence of the permeability of the filter limits the velocity of the lifted block, meaning that a short duration load can only result in a very small motion of the block Nimpact/N Nfront/N (-) 1.0 0.8 0.6 relative number of impacts 0.4 relative number of pressure fronts 0.2 0.0 0.000 0.005 0.010 0.015 wave steepness Hs/Lop (-) 0.020 Figure Relative number of the waves in which a pressure front and an impact has been identified The Matlab programme first determines each individual wave and identifies in each wave the moment of the wave impact and of maximum wave rundown, when the pressure front is steepest The programme is able to identify almost all impacts, but has some difficulty with very small impacts (with a low maximum pressure, which is even lower than under the crest of the incoming wave height) The small wave impacts, however, are less important for the stability of the block revetments Figure shows one of the result of the analysis of the small scale tests: the number of identified wave impacts and pressure fronts On the vertical axis the number of wave impacts and pressure fronts have been divided by the number of incoming waves, N The Figure shows that in 90 to 100% of the waves a pressure front has been identified The number of impacts is, however, much smaller For waves with a wave steepness of sop > 0,015 more than 60% of the waves have an impact The relative number of impacts is decreasing with decreasing wave steepness throughout the range of tests, especially for 0.002 < sop < 0.010 For relatively long waves of sop = 0.005 only 20% of the waves will give an impact In Figure 10 the height of the pressure front b is given with an exceedance frequency of 2% On the vertical axis this height is made dimensionless by dividing it by the wave height Hs On the horizontal axis the wave steepness is given (sop = Hs/(2 Tp2/g)) Note that in this Figure not only the small scale tests have been given, but also the large-scale tests on the slope of 1:3.5 The Figure clearly shows that the dimensionless pressure front height b/Hs measured in the small scale tests is approximately equal to the large-scale tests results The value of b/Hs increases with decreasing wave steepness, meaning that the longer waves impose a larger load on the structure Since this pressure front is decisive for the stability of the low permeability block revetments, it is expected that these revetments will have a lower stability for relatively long waves (small wave steepness) This increase can be neglected for sop > 0.015, but is very significant for sop < 0.010 front height B2%/Hs (-) 3.0 2.5 2.0 small scale, slope 1:4 1.5 small scale, slope 1:3 1.0 large scale, slope 1:3.5 0.5 0.0 0.000 0.010 0.020 0.030 wave steepness Hs/Lop (-) 0.040 Figure 10 Dimensionles height of the pressure front as a function of the wave steepness The influence of the wave steepness on the dimensionless maximum pressure head, imp/Hs, is shown in Figure 11 The trend with the wave steepness is most clear for the small scale tests It shows that there is hardly any influence of the wave steepness as long as sop > 0.006, while in Figure it was shown that the number of impacts is still increasing significantly with increasing wave steepness for sop > 0.006 An observer along the flume would notice that a decreasing wave steepness influences the way the waves break 10 More and more waves will not break with an impact but will rush up and down the slope From Figure and 11 it is concluded that this change of the way the waves are breaking on the slope does not result in a smaller wave impact pressure for sop > 0.006 It primarily results in a smaller number of impacts Figure 11 also shows a large difference in dimensionless wave impact pressures between the small scale tests and the large-scale tests The dimensionless wave impact pressure is much larger in the small scale tests Apparently there is an important effect of the scaling The problem of scaling the wave impacts is extremely difficult to solve in a scientifically sound manner Many scientists in the past have tried this, but without much success A recent overview of the various attempts has been given by Bullock et al (2001) Therefore an empirical approach has been chosen to be able to find practical answers to the question of the quantification of the wave load to calculate the stability of block revetments The simple Froude scaling doesn't work, as shown in Figure 11, because various phenomena involved are not included in this scaling law An important aspect of the fluid is the occurrence of air bubbles which has a large influence on the compressability of the water In large-scale tests the bubbles are relatively small and stay much longer in the water than in small scale tests That makes the water more compressible and results in lower impact pressures with a longer duration of the impact 4.0 small scale, slope 1:4 imp2%/Hs (-) 3.0 small scale, slope 1:3 2.0 large scale, slope 1:3.5 1.0 0.0 0.000 0.005 0.010 0.015 wave steepness Hs/Lop (-) 0.020 Figure 11 Dimensionles wave impact pressure as a function of the wave steepness The size of the bubbles is influenced by the surface tension, which is taken into account in the Weber number (Doorn 1979): We u2L w 11 with: = density of the water (kg/m3), u = characteristic flow velocity (m/s), L = characteristic length (m), w = surface tension of water ( 0,073 N/m) The characteristic flow velocity during wave attack on the slope is proportional to (gHs) The characteristic length is the wave height This results in the following modified Weber number: We ' gH s2 w The Weber number governs the effect of bubbles in the water and should be included in the scaling of the tests It is assumed that a part of the process is primarily influenced by the Weber number and and another part is primarily influenced by the Froude number Therefore a combination of Froude and Weber scaling is introduced The dimensionless impact pressure potential is with this combined Froude and Weber scaling as follows: imp Hs gH s2 a w with: imp = maximum pressure potential on the slope relative to the minimum pressure potential seaward of the wave impact (m); a = empirical coefficient (-) The empirical coefficient a determines the amount of Weber scaling The larger the influence of the compressability (bubbles in the water) on a certain aspect of the wave impact, the larger the empirical coefficient a will be If a = normal Froude scaling results In Figure 12 the same test results are presented as in Figure 11, but now with the combined Froude/Weber scaling of the maximum pressure potential, with a = 0.2 From the Figure it is clear that the scaling problems have now disappeared The large-scale test with sop = 0.003 is still a little below the results of the small scale tests, but this is due to the very small amount of wave impacts that occurred during this test This has influenced the accuracy of the test For other aspect of the wave impacts the value of a can be larger or smaller, or even negative (such as for the impact duration) From Figure 12 it is concluded that a decreasing wave steepness (or increasing breaker parameter) will given a decreasing maximum wave impact pressure for relatively long waves This means that the hydraulic load will decrease and consequently the stability will increase with increasing breaker parameter This matches the trend of the large-scale tests given in Figure 12 15.0 small scale, slope 1:4 small scale, slope 1:3 large scale, slope 1:3.5 10.0 imp2%/Hs ( gHs2/ a w) (-) 20.0 5.0 0.0 0.000 0.005 0.010 0.015 wave steepness Hs/Lop (-) Figure 12 Dimensionles maximum Froude/Weber scaling with a = 0.2 wave impact 0.020 pressure with combined STABILITY OF THE REVETMENT The stability of the revetments cannot be measured in the small scale model, because of conflicting scaling rules Therefore the measured pressure distribution as a function of time and space of the small scale tests has been used as input for the numerical model Zsteen, which calculates the uplift pressure on a block revetment for each sample of the measurements (Stoutjesdijk 2003) The consecutive moments with a large uplift pressure are combined to calculate the block motion The results of the calculations is dependent on the type of block revetment In this paragraph the attention is focused on open revetments with a relative open area between the blocks of 13%, comparable with the block revetment in the large-scale tests Figure 13 Results of the numerical calculations and the trendline from extrapolation of the old formula for < op < 2.5 13 Figure 13 gives an impression of the results of the calculations In the Figure a line is drawn which is the extrapolation of the trend of the old formulas which had an applicability of < op < 2.5 This line is the maximum Hs/ D for design purposes, and its trend shows a decreasing stability of the revetment for an increasing breakerparameter (decreasing wave steepness) The trend of the calculation results matches the trend of the results of the large scale model tests (Figure 8) and also matches the conclusion from Figure 12, in which it was shown that the maximum impact pressure decreases with decreasing wave steepness The latter is equivalent to an increasing stability with an increasing breaker parameter, for op > CONCLUSIONS The analysis of the results of the small scale model tests has given detailed insight in the relation between the wave load and the wave steepness This has resulted in the conclusion that for relatively long waves ( op > 2.5) the decisive wave load: increases with increasing breaker parameter for low permeability revetments decreases with increasing breaker parameter for open block revetments This trend is confirmed by the numerical calculations with Zsteen and the large-scale tests in the Delta Flume of WL | Delft Hydraulics The combined use of small scale model tests, a numerical model and a limited number of large scale model tests made it possible to draw reliable conclusions regarding the stability of block revetments, without the necessity of a large amount of expensive large-scale tests The hypothesis of a combined Froude/Weber scaling is a promising empirical method of dealing with scale effects in wave impacts for practical applications REFERENCES Hofland, B and M Klein Breteler (2005); Accuracy of Zsteen during wave impacts (in Dutch); Delft Hydraulics, report H4455, April 2005 Bullock, G.N., A.R Crawford, P.J Hewson, M.J.A Walkden and P.A.D Bird, The influence of air and scale one wave impact pressures Coastal Engineering Journal 42 (2001) 291-312 Doorn, Th van (1979); Scale effects in wave impacts on a slope (in Dutch); Delft Hydraulics, report M1057, augustus 1979 Stoutjesdijk, T.P (2003); Final report on stability criterion in Zsteen (in Dutch); GeoDelft CO-405120/36, may ‘03 Klein Breteler, M (2000); Large scale tests on block revetments (in Dutch), Delft Hydraulics, report H3272, may 2000 View publication stats ... 0.020 0.030 wave steepness Hs/Lop (-) 0.040 Figure 10 Dimensionles height of the pressure front as a function of the wave steepness The influence of the wave steepness on the dimensionless maximum...Proceedings of 30th ICCE conference, San Diego USA, 2006 INFLUENCE OF WAVE STEEPNESS ON STABILITY OF PLACED BLOCK REVETMENTS Mark Klein Breteler 1, Robert ‘t Hart2 and Theo Stoutjesdijk3 Block revetments. .. breaking waves are a considerable threat to the stability Figure Example of block revetment during construction In the past years extensive research on the stability of block revetments has been conducted