HYDRAULIC EFFICIENCY OF POROUS STRUCTURES USED FOR NEARSHORE

DAMPING OF WAVES

Selim M. Sayah1; Jean-Louis Boillat2; and Anton J. Schleiss3

ABSTRACT

Adequate basis for the design of soft and porous shore protection measures for

shallow coastal zones are still lacking. By means of experiments, the interaction of

brushwood fences with incident waves was investigated and their damping effect,

quantified by the transmission coefficient, was analyzed. The analysis used five

dimensionless variables based on the freeboard of the structure, its height and

porosity, the wave number and the wave steepness. It was first proven that the

response of the structure changes in relation to its immersion condition: its efficiency

decreases rapidly when it is totally submerged. While the freeboard, the porosity and

the wave steepness play a major role regarding the structure’s wave damping

efficiency, the effect of its height and the wave number is shown to be insignificant.

Using a parametric approach this experimental study provides a better understanding

of the behaviour of the brushwood fences and, as a result, helps to establish

technical recommendations for their dimensioning.

1 Ph.D., Chief Engineer, e-mail: selim.sayah@lombardi.ch, Laboratory of Hydraulic

Constructions, now at Lombardi Engineering Ltd., Via R. Simen 19, 6648 Minusio,

Switzerland.

2 Ph.D., Senior Research Associate, e-mail: jean-louis.boillat@epfl.ch, Laboratory of

Hydraulic Constructions, Ecole polytechnique fédérale de Lausanne, 1015 Lausanne,

Switzerland.

3 Professor, Director, e-mail: anton.schleiss@epfl.ch, Laboratory of Hydraulic

Constructions, Ecole polytechnique fédérale de Lausanne, 1015 Lausanne,

Switzerland.

CE Database keywords: Porous media; Wave attenuation; Protective structures;

Breakwaters; Damping

1 INTRODUCTION

Brushwood fences are most commonly used in lakes and nearshore sea regions

to provide reliable, soft, and cheap shore protection measures to mitigate shore

erosion and enhance sedimentation by breaking incident wave energy (Iseli et al.

1995). They are especially effective in shallow areas where hydrodynamic forces,

generated by wind and currents, are not very significant. They mainly consist of two

elements (Fig. 1). The first one, designed to insure structural stability, is composed of

two parallel rows of wooden piles (average spacing of piles is typically 0.6 m). The

second middle element is constituted of wooden porous branches, often called

“fascines”, inserted in a cylindrical bundled manner. This porous media is responsible

for the dissipation of incident waves. The average porosity of fascines varies

between 10% and 80% (Sayah et al. 2004). Beside their soft aspect, brushwood

fences provide many other advantages such as fast, easy and cheap construction, as

well as a relatively good wave damping ratio. In lakes, where aquatic activities are

practiced nearshore, they are able to attenuate incident waves, thus reducing wave

reflection that might increase nearshore wave heights (Ostendorp et al. 1995).

In the North Sea, such measures are also widely used to protect the foundation

of shore protection dikes against erosion by providing a porous medium that is very

effective as a wave damping screen (Mai et al. 1999).

(a) (b)

Fig. 1: Brushwood fences (or Christmas trees) used as soft shore protection agent

against wave impact and sediment loss: (a) in Swiss lakes; (b) in Louisiana’s wetland

Moreover, in the late eighties the Louisiana Department of Natural

Resources/Coastal Engineering Division (LDNR/CED 1998) established a program

called Louisiana Christmas Tree that intends to maintain Louisiana's coastal

wetlands and fight against its erosion by building similar structures. Real Christmas

trees are collected from private houses and used instead of fascine as brushwood

fences mainly to reduce wave energy while allowing the movement of water and

sediments. This program is ongoing and Christmas trees are used every year to

rebuild new fences or nourish old ones.

Although widely used, appropriate design criteria for such shore protection structures

are still lacking. Experience has shown that many implementations in lakes have not

provided the expected results due to the lack of sound scientific knowledge related to

their efficiency in wave damping as a function of local hydrodynamic conditions

(Sayah and Mai 2007). This paper aims to provide comprehensive framework for the

dimensioning of brushwood fences by means of experimental tests carried out on a

downscaled physical model.

2. EXPERIMENTAL SET-UP AND TESTS ON PHYSICAL MODEL

Physical tests were conducted in the wave tank at the Laboratory of Hydraulic

Constructions-LCH of the Swiss Federal Institute of Technology - Lausanne. The

tank is 10 m long, 6 m wide, and 1.3 m deep. A pneumatic wavemaker was used to

generate monochromatic unidirectional waves. A realistic typical bathymetry found

commonly in the shallow zones of the major confined water bodies in Switzerland

was designed inside the wave tank. The brushwood fences model (Fig. 2a) with an

average scale of 1:10 consisted of building the fascine (the main porous media of the

brushwood fences) by enrobing a highly porous material with a geotextile. It can be

assumed that the overall porosity of the fascine is approximately the same as the

geometrical porosity of the geotextile. The experimental work involved three series of

tests carried out on a fixed bed (excluding sediment transport). Three different

porosities of the structure were tested: P1=0.16, P2=0.36, and P3=0.62, each for

three different heights h=0.7, 1.0, and 1.25 m (full scale values). The transmission

coefficient KT (=HT/H in Fig. 2b) was measured for several wave periods and several

water depths (d in Fig. 2b).

(a) (b)

Fig. 2: Experimental model of the brushwood fences (a) and parameters considered

for the study (b)

Before carrying out the main test, primary analysis was done in order to compare the

different elements used for the construction of the physical model of brushwood

fences and check their hydraulic response with regards to the hydraulic behaviour of

real scale brushwood fences. This initial analysis is based on the calculation of the

minor head-loss coefficient due to the presence of the structure in a straight pipe. For

this purpose, a specific installation was built. The physical model was mounted in a

fixed cylindrical instrument installed within the pipe. For each water flow value, the

pressure upstream and downstream of the model was measured using twin tube

hydraulic piezometers. The flow in the pipe was measured simultaneously by an

electromagnetic flowmeter and an ultrasonic water level gauge fixed over an elevated

water recuperation tank at the end of the pipe where a triangular weir served to

calculate the flow. The flow values during tests varied between 4 and 12 l/s. For each

configuration, local head-losses generated by the presence of the model were

measured for four different flow values.

Fig. 3a compares the effect of the three selected geotextile porosities (P1 to P3) and

the effect of the model width (b in Fig. 2b) using the dimensionless Reynolds head-

loss coefficient as follows (Idelcik, 1960):

g

vhs

2

2Re

(1)

where is the density of water, v the measured flow velocity, g the acceleration

due to gravity, and sh the measured local head-losses. The influence of the

presence of the geotextile could be clearly seen. Although the width of the structure

does not seem to have a significant effect, the measured head-loss values are not

proportional to the porosity of the structure. This could be explained by the increase

of the drag coefficient due to the very small grid of the geotextile P1.

The hydraulic response of the above-described materials was compared to some

experimental results carried out with real brushwood fences at the Franzius-Institut

für Wasserbau und Küsteningenieurwesen of Hannover University in Germany (von

Lieberman et al. 1997). During the tests a real model of brushwood fences (S1

configuration in Fig. 3b) was used having a fixed width of b=0.25 m. It was tested in a

channel 0.98 m wide, 1 m high and 22 m long. Water levels were measured in front

and behind of the model, for different flow values. In order to make a comparison

between the tests carried out with a downscaled model and full scaled model, the

minor head-losses due to the presence of the structure are expressed as a function

of the flow velocities during the tests (Fig. 3b). It can be seen that the range of the

head-loss of the laboratory model covers the entire range of the head-loss related to

the real full scale model for similar flow velocities. This proves that the response of

the material used to construct the small model is comparable to the real material of

the brushwood fences under the same hydraulic conditions (Sayah 2006).

Unfortunately, no full scale tests were carried out at Hannover University for other

widths and porosities.

HLP1 HLP2 HLP30

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Rey

nold

s H

ead-

Loss

Coe

ffic

ient

R

e [

-] 2.5cm5cm7cm10cm

0.1 0.2 0.3 0.4 0.5 0.60

0.5

1

1.5

2

Flow Velocity [m/s]

Minor Head-Loss hs [m]

b=2.5cmb=5cmb=7cmb=10cmHLP1HLP2HLP3S1

(a) (b)

Fig. 3: (a) Reynolds head loss coefficient of the physical model of the geotextile

structure used as brushwood fences for three different porosities P1, P2 and P3; (b)

Comparison of the minor head losses of the physical model with prototype values

(S1).

3 INTERACTION OF THE BRUSHWOOD FENCES WITH REGULAR WAVES

In the following, the results of the physical experiments focus on the transmission

coefficient of a brushwood fence; a sensitivity analysis for the effect of different

variables on this coefficient is performed. The results are based on regular wave

measurements before and after the obstacle. The wave heights are measured by two

couples of ultrasonic wave gauges situated at the seeward and leeward sides of the

fence. Concerning the investigation of the selected dimensionless variables, several

points should be noted:

The main goal of this investigation is to define the general trends linking the

analysed dimensionless variables to the transmission coefficient. These trends

used only to understand the effect of the selected variable on the transmission

coefficient, are not to be considered as final results.

The investigation for each variable is performed while keeping the other variables

constant; therefore, the possible interaction of different variables is not included.

Hence, these results should be considered as an intermediate step aimed at

identifying the trends of the transmission coefficient in relation to the various

variables adopted in the analysis.

A multivariate analysis investigating the relationship of the transmission

coefficient to all the variables, simultaneously, is the only way to obtain more

accurate and relevant results. However, since the basic trends for each variable

are still unknown, it is important to identify these trends separately first. The

second stage would be to group all the variables together and to take into

consideration the effects of simultaneous variations of several variables.

3.1 EFFECT OF THE FREEBOARD OF THE STRUCTURE Rc/Hi

The relative freeboard is an important dimensionless variable that relates incident

wave heights (Hi) with the structure height and water depth (d). The freeboard Rc is

the difference of these last two variables. It has been used by many researchers in

several applications related to breakwater efficiency in damping incoming waves,

such as Mai et al. (1999), Daemrich et al. (2001) and Calabrese et al. (2003).

Additionally, these studies included the relative freeboard in the calculation of the

transmission coefficient.

The experimental results for the average height of h=10 cm are illustrated in

Fig. 4. It can be seen from the curve fitting plotted for different porosities that the

transmission coefficient, KT=Htransmitted/Hincident, decreases almost linearly when the

relative freeboard Rc/Hi increases.

-2 -1.5 -1 -0.5 0 0.5 1 1.5 20

0.10.20.30.40.50.60.70.80.9

11.11.21.31.41.5

Rc/H

i [-]

KT [-] d=12.5cm

d=10 cmd=7 cmd=5 cmBest fit95% prediction bounds, 0.12

-2 -1.5 -1 -0.5 0 0.5 1 1.5 20

0.10.20.30.40.50.60.70.80.9

11.11.21.31.41.5

Rc/Hi [-]

KT [-] p=0.62p=0.36p=0.16

(a) (b)

Fig. 4: Transmission coefficient KT as a function of the relative freeboard Rc/Hi: (a)

results for the intermediate porosity of 0.62; (b) best-fit curve for the three tested

porosities according to Eq. 2 and Table 1 for h=10 cm

When the relative freeboard is lower than -1 (a negative value indicates that the

structure is totally submerged), KT seems to reach a maximum constant value. This

indicates that the structure rapidly loses its efficiency in wave damping when it is

submerged. In all cases, the maximum value of KT when the structure is submerged

seems to be comprised between 0.7 and 1.1 (with respect to the prediction bounds).

For Rc/Hi higher than 1, KT reaches an almost constant value.

Fig. 4 reveals that a low porosity of brushwood fences increases wave damping.

Nevertheless, wave damping does not seem to increase proportionally when the

porosity decreases, indicating a nonlinear relation between porosity and KT.

The best-fit curves suggested by Fig. 4b are given by the following Eq. 2:

dH

Rc

H

Rb

H

RaK

i

c

i

c

i

cT

23

(2)

where the different fitting coefficients are obtained using the values of Table 1:

porosity a b c d 95% Prediction bounds

0.62 0.01 0.02 0.12 0.76 ±0.12

0.36 0.01 0.01 0.12 0.67 ±0.13

0.16 0.01 0.00 0.14 0.57 ±0.13

Table 1 : Average values of the cubic fitting coefficients in Eq. 2 for each porosity

value

The cubic best-fit curves plotted in Fig. 4b are valid to the interval -2≤Rc/Hi≤2.

The shape of the curves reveals the effect of a variable porosity on the transmission

coefficient. The discrepancy between the curves for different porosities is higher

when the structure is emerging (Rc≥0) in comparison to a totally submerged

condition. This indicates that the porosity gradually loses its importance when the

structure is totally submerged, as expected.

Hence, the cubic fitting of the entire collected data suggests that the structure

response to the incoming waves is depending on the water depth. When the

structure is totally submerged, KT seems to vary differently as a function of the

relative freeboard in comparison to the condition when the structure is emerging. This

indicates that a more adequate data treatment would be required to separate the

conditions related to the two water depths.

In reference to the first observation, a separate analysis is suggested in the next

sections where two series of data are considered. The first series is the ‘s’ series,

when the structure is completely submerged, and the second is the ‘e’ series related

to an emerging structure.

3.2 EFFECT OF THE WAVE PERIOD Hi/gT2

The variation of KT with the wave steepness Hi/gT2 for different structure heights

and porosities is investigated in this section. This normalized wave steepness has

been used by many researchers, for instance Herbich (1990) and Rao et al. (1999).

In fact, it is a direct expression of the wave steepness since it does not use the water

depth in order to calculate the wave length.

0 1 2 3 4 5 6 7 8

x 10-3

00.10.20.30.40.50.60.70.80.9

11.11.21.31.41.5

Hi/gT2 [-]

KT [-] p=0.62p=0.36p=0.16

0 1 2 3 4 5 6 7 8

x 10-3

00.10.20.30.40.50.60.70.80.9

11.11.21.31.41.5

Hi/gT2 [-]

KT [-] p=0.62p=0.36p=0.16

(a) (b)

Fig. 5: Transmission coefficient KT calculated as a function of the relative wave

steepness Hi/gT2 for the three tested porosities according to Eq. 3 and Table 2 for

h=10 cm (a) emerged structure ‘e’ series (b) submerged structure ‘s’ series.

The best-fit curves are given in Fig. 5. They show that KT decreases linearly

when Hi/gT2 increases. This is in agreement with the findings in the papers

mentioned above. The decreasing trend of KT when Hi/gT2 increases can be

explained by considering the velocity of wave generated currents. As the wave

steepness increases, the wave frequency increases as well, resulting in an increase

in currents velocity and acceleration. When a wave reaches the porous structure, the

currents velocity and acceleration suddenly change, causing reduction in energy due

to the turbulence produced by the sudden change in the water motion and by the

interaction with the structure. Hence, the steeper the wave, the more intense is the

turbulence, and the greater the loss, resulting in lower KT.

The results of the evolution of KT as a function of the wave steepness for the

lowest porosity of 0.16 confirm the above mentioned behaviour. In fact, when the

porosity is very low, the energy reduction increases rapidly with wave frequency due

to the increased drag coefficient. The best-fit curves illustrated in Fig. 5 can be

reproduced using Eq. 3.

bgT

HaK i

T 2

2 (3)

The values of the coefficients a and b depend mostly on the porosity of the structure.

They are given in Table 2 for the application range 0<Hi/gT2<0.008.

Porosity

Series ‘e’

(emerging structure)

Series ‘s’

(submerged structure)

a b a b

0.62 3.59 0.73 -12.53 0.89

0.36 -12.05 0.67 -15.83 0.83

0.16 -25.55 0.51 -24.21 0.70

Table 2: Average values of the linear fitting coefficients in Eq. 3 for each experimental

configuration.

3.3 EFFECT OF THE POROSITY OF THE STRUCTURE

As mentioned previously, the porosity of the brushwood fences seems to have a

significant influence on its efficiency regarding the transmission coefficient. Although

the effects of the other dimensionless variables were analyzed for different porosities,

the separate influence of the porosity has not yet been addressed. Therefore, the aim

of this section is to understand the influence of the porosity on wave transmission

using the three different porosities considered during the experimental tests.

A direct relationship between KT and p is depicted in Fig. 6 for the two domains, Rc≥0

(emerging structure) in Fig. 6a and Rc≤0 (submerged structure) in Fig. 6b. In each

domain, the values of KT are plotted for each porosity and each structure height.

Each point plotted in Fig. 6 corresponds to a single test run. Two straightforward

conclusions can be given:

The average values of KT for each porosity are different for each domain.

The increase of KT is not proportional to the increase of the porosity of the

structure. Fig. 6a suggests that when p is multiplied by about 4 (p=0.16/p=0.62)

the transmission coefficient is multiplied only by about 2.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.10.20.30.40.50.60.70.80.9

11.11.21.31.41.5

p [-]

KT [-] h=0.7mh=1.0mh=1.25mPower Fitting95% prediction bounds, 0.22

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.10.20.30.40.50.60.70.80.9

11.11.21.31.41.5

p [-]

KT [-]

h=0.7mh=1.0mh=1.25mPower Fitting95% prediction bounds, 0.32

(a) (b)

Fig. 6: Transmission coefficient KT calculated as a function of the porosity of the

brushwood fences for different structure heights (a) Rc≥0 (emerging structure); (b)

Rc≤0 (submerged structure)

In order to evaluate the best trends describing the relationship between KT and p,

several fitting curves are tested. The power fitting corresponds to the highest

correlation factor and lowest 95% prediction bounds as shown in Fig. 6 according to

Eq. 4:

bT paK )( (4)

where a and b are coefficients given in Table 3:

Series ‘e’

(emerging structure)

Series ‘s’

(submerged structure)

a b a b

0.86 0.17 0.22 0.35

Table 3: Average values of the power fitting coefficients in Eq. 4 for each

experimental configuration

Such law was also proposed by D’Angremond et al. (1996) where the authors

suggested a power relationship directly related to the width of the structure. It must

me mentioned that in the present case the porosity of the structure (the physical

model) replaces the real width of the brushwood fences.

4 PROPOSED EMPIRICAL RELATIONSHIP AND FINAL ANAYLSIS

On the basis of the above mentioned investigations, a direct relationship for the

calculation of the transmission coefficient is proposed in this section. This is

accomplished by using the three main identified variables: the freeboard of the

structure, its porosity, and the wave steepness. The proposed formulation is based

on a specifically developed Gauss Newton Algorithm which was able to solve more

than 500 non-linear equations relating the selected variables. The best correlation

corresponds to Eq. 5 where the 95% prediction bounds are equal to 0.24 and the

linear regression corresponds to tan 0.97 (Fig. 7).

204.02 4.1269.011.0)(01.0

gT

Hp

H

R

H

RK ic

i

cT

i

(5)

0 0.5 1 1.50

0.5

1

1.5

KT,mes[-]

KT,cal[-] Linear regression, tan=0.97

95% prediction bounds, 0.24

Fig. 7: Comparison between the measured and calculated transmission coefficients

The proposed relationship is applicable under the following three constraints:

The relative freeboard Rc/Hi should be within the interval [-2; +2].

The porosity should be reasonably higher than 0.

The wave steepness Hi/gT2 should be within the interval [0.001; 0.008].

This range of application corresponds to the intervals of the experimental tests.

Additionally, Eq. 5 is recommended only for porosities above 0.1. In reality,

brushwood fences with such low porosity value are almost impossible to construct.

However, when they are filled with sediment, their porosities could tend to zero. In

this case, the transmission coefficient will tend to zero (when the diffracted waves are

not considered and when the structure is emerging).

5 CONCLUSIONS

The efficiency of brushwood fences using a downscaled model of 1:10 has been

investigated in a wave tank under several hydrodynamic conditions. Using three

different porosities with a range large enough to cover realistic values, the

transmission coefficient of three heights of the structure has been measured for six

water levels each. Incoming wave heights and periods generated in the wave tank

were close to prototype conditions.

This first stage investigation was carried out using the direct results of the

experimental tests in order to understand and evaluate qualitatively and semi-

quantitatively the effect of each selected dimensionless variable on wave

transmission. This analysis revealed the following:

The response of the structure is different with regards to its immersion condition.

When the structure is submerged, every dimensionless variable had a different

effect on the transmission coefficient in comparison to the condition when the

structure emerges.

The relative freeboard, wave steepness, and porosity played a major role in the

response of the structure regarding wave damping. The direct effect of the

relative height and wave number was not significant and could be neglected.

A non-linear relationship has to be considered when the effect of the relative

freeboard and the porosity of the structure on the transmission coefficient is

evaluated. Nevertheless, the wave steepness seems to have a linear influence on

wave transmission.

6 ACKNOWLEDGMENT

The authors are grateful to the Swiss Innovation Promotion Agency (CTI) for the

financial support of the present research under the grant N° KTI 5670.1, together with

other research partners.

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