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.

STABILITY OF PLACED BLOCK REVETMENTS

Conference Paper · April 2007

DOI: 10.1142/9789812709554_0424

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INFLUENCE OF WAVE STEEPNESS ON STABILITY OF PLACED

BLOCK REVETMENTS

Mark Klein Breteler1, 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 1 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,

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 = 2 /(gTp); Tp = wave period at the peak of the spectrum (s); g = acceleration of gravity (m/s2); = slope angle (o)

Figure 2 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:

Small scale flume tests: pressure on the slope

quantification of load characteristics numerical calculation of stability

large-scale stability tests

conclusions

= p/( g) + z With: p = pressure (Pa); = pressure potential (m); = density of water (kg/m3) and z = vertical coordinate (m)

Figure 3 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 3

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

Figure 4 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

pressure transmission through filter

high pressure head

low pressure head

on the slope uplift

pressure head on the slope breaking wave (water surface)

filter cover layer geotextile

D

, Z

impact

on slope

in filter

X revetment

local minimum

uplift

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 8 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

Figure 5 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:

Wave run-down:

trough

impact

tan k50-80%k x

front

b min tan f

Wave impact:

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, 5 m wide and 7 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 3 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 7

Figure 6 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 7 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:

1 sop = 0.0068; op = 3.4: 0.5 < Hs < 1.1 m

2 sop = 0.0045; op = 4.3: Hs = 1,0 m

3 sop = 0.0033; op = 5.0: 0,5 < Hs < 0.9 m

4.5 m

15 cm Hydroblocks

8.8 m sand 5.5 cm filter 20-40 mm

geotextile sand-cement (represenents clay layer)

concrete (dummy slope)

concrete (dummy slope)

+6.5 m

+2.0 m

+0.0 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 8

Figure 7 Installation of the pressure cells in the concrete blocks (Hydroblock) (left), and breaking wave in Delta Flume (s op = 0.0067) (right).

0

2

4

6

8

10

H s

no damage damage

Figure 8 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 1

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

0.0

0.2

0.4

0.6

0.8

1.0

wave steepness H s /L op (-)

N imp

relative number of impacts relative number of pressure fronts

Figure 9 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 9 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 Tp/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

0.0

0.5

1.0

1.5

2.0

2.5

3.0

/H s

small scale, slope 1:4 small scale, slope 1:3 large scale, slope 1:3.5

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 9 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