Conceptual model for reinforced grass on inner dike slopes

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ComCoast

Conceptual model for reinforced

grass on inner dike slopes

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ComCoast

Conceptual model for reinforced

grass on inner dike slopes

This report has been prepared by - WL|Delft Hydraulics - Infram

- GeoDelft - TU Delft

This report is an initiative of the ComCoast project, co-financed by the EU-Interreg IIIb North Sea Programme.

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Work Package 3

Civil Engineering

Approach

Conceptual model for reinforced

grass on inner dike slopes

Background report

The report is written/edited by:

-

WL|Delft Hydraulics

-

Infram

-

GeoDelft

-

TU Delft

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1

1 1 Introduction

Introduction

1.1

1.1 1.1 Background

Background

ComCoast develops and demonstrates innovative solutions for flood protection in coastal areas. Within the WP3 project the strength will be demonstrated of a reinforced grass mat on the inner slope of a dike with respect to wave overtopping by carrying out a prototype test (Gerven et al, 2005). Therefore, a wave overtopping simulator has been built. This plunging apparatus will be used to test the strength of the grass with and without reinforcements. The development of a conceptual model allowing the prediction of the erosion of the grass is part of the WP3 project. CUR Bouw & Infra commissioned WL | Delft Hydraulics by letter dated July 25, 2006 with reference C136A_OB_06_16809 (order 3650) on the basis of the proposal dated July 13, 2007 (reference: ZWS19497/Q3657/sh) to make a conceptual model and to predict the erosion of the reinforced grass.

Parallel the Rijkswaterstaat project SBW (Strength and Loading upon Water Defences) aims to learn from prototype experiments in order to improve model relations for testing water defences. The SBW project counts three sub-projects: 1) Hydraulic Boundaries, 2) Field Measurements and 3) Failure Mechanism. Within the framework of the SBW-Failure Mechanism sub-project Wave Overtopping two failure mechanisms will be examined:

1.

Strength of grass without reinforcement;

2.

Shear failure of the grass/clay layer upon sand core (without reinforcement).

In a separate desk study conceptual models have been developed for the erosion of grass and the shear failure of the grass/clay layer (Van der Meer et al, 2007). Obviously, there is a strong link between both studies.

1.2

1.2 1.2 Project team

Project team

The study has been carried out by a team consisting of Mr. H.J. Verheij (WL | Delft Hydraulics), Mr. A. van Hoven and Mr. J. Lindenberg (GeoDelft), Dr. J.W. van der Meer (Infram) and Dr. A.L.A. Fraaij (TU Delft). WL | Delft Hydraulics was leading with Mr. H.J. Verheij in charge as the project manager of the study. Mr. F.C.M. van der Knaap conducted quality assurance of the report.

Furthermore, Ms. Syliva Hinostoza from Peru carries out her MSc graduation at the TU Delft and started September 2005. Her study will take approximately 6 months which unfortunately means that there are no possibilities to implement her study results in the desk study as discussed.

Mr. J. Koenis and Mr. C. Nijburg were the contact persons on behalf of CUR, whereas Dr. G.J.C.M. Hoffmans was the Rijkswaterstaat contact.

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2

2 2 Objective

Objective

The objective of the study is:

○ To describe a conceptual model for reinforced grass based for example on the model of Wilbert van den Bos, and

○ To make a prediction of the strength if possible of the reinforced grass.

The model of Wilbert van den Bos (2006) predicts the failure of weak spots in grass/clay layers. It is based on semi-empirical knowledge of the systematically scour research carried out in the sixties and seventies at Delft Hydraulics. The so-called EPM model (Erosie gevoelige Plekken Model, or model for spots susceptible for erosion) will be applied for the strength of grass with and without reinforcement (geo cells and/or geo grids). If necessary, a special component will be added for the geosynthetic strength. The prediction will be applied for the ComCoast tests with a reinforced grass mat whereby a geogrid has been placed 5 cm below the grass surface. It is assumed that the reinforced grass mat has the same characteristics as the grass mat without the geogrid. In other words: grass mat and clay are fully recovered since the geogrid was built in and the root system and the clay structure are not influenced or disturbed.

The activities have been carried out in close cooperation with the activities within the framework of the Rijkswaterstaat project SBW-wave overtopping/strength inner dike slope.

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3

3 3 Hydraulic load

Hydraulic load

In “Golfoverslag en sterkte binnentaluds van dijken – rapport predictiespoor SBW” (Van der Meer et al, 2007) the characteristics of the flow velocities, water depths and duration are addressed in detail. In this chapter an overview is presented.

In summary, analysing wave boundary conditions along the Dutch coasts, as used for the 5-yearly safety assessment, gives the following mean values which will be used to design the wave overtopping simulator applied for testing the inner dike slope with reinforced grass (see figure 3.1):

• Wave height: Hs = 2.0 m

• Peak period: Tp = 5.7 s (wave steepness sop = 0.04)

• Mean period: Tm = 4.7 s (Tp = 1.2 Tm)

Figure 3.1 – Sketch of the test set-up

During a storm of 6 hours about 120 waves will overtop during an average overtopping discharge of 1 l/s/m. The volumes follow an overtopping distribution. As an example the simulation of the overtopping volumes are presented in Figure 3.2 for 1 l/s per m. Similar figures can be presented for 0.1 l/s, 10 l/s and 30 l/s per meter.

0 200 400 600 800 1000 1200 0 10 20 30 40 50 60 70 80 90 100 110 120 130

Number of overtopping waves in ascending amount

o v er to p p in g v o lu m e p er w a v e (l it er s p er m w id th ) calculation simulation 1 l/s per m

56 waves with 50 l per m 50 waves with 150 l per m 10 waves with 400 l per m 6 waves with 700 l per m 3 waves with 1000 l per m

Figure 3.2 Calculated distribution of overtopping volumes and proposal for simulation. Mean discharge q = 1 l/s per m

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The overtopping volumes could be simulated as follows: • 56 waves with 50 l per m

• 50 waves with 150 l per m • 10 waves with 400 l per m • 6 waves with 700 l per m • 3 waves with 1000 l per m

Important aspects of the overtopping waves are the flow velocities and the thickness of the water layer can be detremined with the formulas of Schüttrumpf and Van Gent (Van der Meer et al, 2007). As an example in Figure 3.3 the maximum velocities for overtopping discharges of 1, 10 and 30 l/s per m at the outer crest line are shown. All three mean overtopping discharges give almost similar velocities for the same overtopping volumes per wave. Also from theoretical reasoning one would expect this, as the same overtopping volume itself is more or less independent from the mean overtopping discharge. An overtopping event with 1000 l/m in a 1 l/s per m discharge should behave similar as a 1000 l/m event in a 30 l/s per m discharge. The difference is of course that the larger discharge will have more of these events, but the event itself should not be too different, provided that the wave periods are more or less similar. 0 1 2 3 4 5 6 7 8 0 500 1000 1500 2000 2500 3000 3500 4000

overtopping volume V per wave (liters/m)

v el o ci ty u a t cr es t (m /s ) u (1 l/s) u (10 l/s) u (30 l/s)

Figure 3.3 Maximum velocities at the outer crest line as a function of the overtopping volume per wave; Hs = 2 m, Tp =5.7 s, tanα = 0.25

The flow velocity due to overtopping has a characteristic shape shown in Figure 3.4. The overtopping simulator is expected to simulate this shape. Tests have shown that this is possible (Van der Meer, 2006).

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Summarizing the flow simulator will produce flow velocities, and flow duration as function of the overtopping volume as presented in Table 3.1. In Table 3.2 the number of waves for each overtopping discharge is presented.

Table 3.1 Flow velocities and flow duration per overtopping volume Overtopping volume

(l/m)

flow velocity (m/s) range (m/s) flow time t1 (s)

50 2.0-2.5 1.5 – 3.0 1.5 – 2.5 150 2.9-3.2 2.5 – 3.5 1.5 – 2.5 400 4.1-4.3 3.5 – 5.0 2.0 – 3.0 700 4.8-5.1 4.2 – 5.7 2.5 – 3.5 1000 5.7 5.0 – 6.5 3.0 – 4.0 1500 6.2 5.5 – 7.0 3.0 – 4.0 2500 6.9 6.0 – 8.0 3.5 – 5.0 3500 7.6 6.5 – 8.5 3.5 – 5.0

Table 3.2 Number of waves as function of the discharge Overtopping volume (l/m) 0.1 l/s/m 1 l/s/m 10 l/s/m 30 l/s/m 50 3 56 369 - 150 3 50 200 687 400 2 10 240 325 700 1 6 - - 1000 3 44 206 1500 10 73 2500 5 25 3500 8

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4

4 4 Failure mechanism ero

Failure mechanism ero

Failure mechanism erosion of grass

sion of grass

4.1

4.1 4.1 Introduction

Introduction

Most inner dike slopes consist of a clay layer on a sand core with a cover of grass (Figure 4.1). The roots hold the clay aggregates together, but the number of roots diminishes with the depth. Subsequently, the strength of the grass cover decreases with increasing depth, but it is taken over by the cohesion and normal stresses according to the Mohr-Coulomb approach. Figure 4.2 demonstrates for a specific location the influence of the depth on the turf as well as the hyperbolic process of shear and direct stress as combined effects of grass in the upper layers and clay in the deeper layers. The minimum strength is at a depth of about 5 to 15 cm where the number of roots diminishes substantially.

Figure 4.1 Grass mat on a clay layer

A geogrid or geocell at for instance 5 to 10 cm below the surface will increase at that level the strength of the entire structure. It will prevent erosion of the underlying soil in the situation that the material above the geosynthetic has eroded. In other words, the presence of a geogrid or geocell stops the failure mechanism of erosion of the grass cover assuming well-functioning of the geogrid or geocell.

In reality the grass top layer is never fully intact or has a complete dense cover. There are local failures caused by soil fauna or open spots. Failures and open spots support erosion by giving a point of attack to the flow forces. Assuming open spots Van den Bos (2006) developed his EPM model based “spots susceptible to erosion” („Erosiegevoelige Plekken Model“). In Section 4.2 the modified model as developed in the SBW study will be presented.

This model is valid for the grass cover on top of the geosynthetic. Erosion of the soil material inside the geocell openings or from below the geogrid or geocell is a different failure mechanism. Within this study this mechanism has not been addressed, but probably it can be treated in a similar way as geosynthetics in erosion control applications. In this study a simplified approach has been followed by including an additional parameter for the influence of the presence of a geogrid or geocell in the critical flow velocity.

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Figure 4.2 Influence of density of roots on the shear stress (according to Hähne, 1991; in Schuppener, 1993)

Explanation: Scherspannung = shear stress; Normalspannung = effective normal stress; Tiefe = depth

Note that open spots will be assumed in the next sections, although at the proposed ComCoast tests in Delfzijl in principal no tests are scheduled with open spots. Obviously, an imperfect grass mat will be interesting because very often damage starts at open spots. It is recommended to incorporate in future tests also tests with open spots.

4.2

4.2 4.2 Prediction model

Prediction model

Van den Bos (2006) developed a model for a slope covered with a grass mat assuming spots without grass, the so called “spots susceptible to erosion” or EPM model. Indeed, the slope offers no grass at an open spot, so Van den Bos (2006) idealized a top soil layer with a hole with depth λ (Figure 4.3).

Figure 4.3 Spot susceptible to erosion (Van den Bos, 2006)

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(

)

2 max 1,7

0.7

_c m

U

t

y

k

α

λ

−

∆

=

∆

∑

(4.1) and

α

=

1.5 5r

+

₀ In which: ym = scour depth (m)

λ = 0.05 m; characteristic length equal to the maximum grass cover thickness (m) ∆t = time (s)

k = constant (m2_/s)

α = turbulence factor (-);

r0 = 0.05 – 0.25; relative turbulence intensity (-)

∆ = relative density (-)

Umax = maximum flow velocity (m/s)

Uc = critical flow velocity (m/s)

The critical flow velocity Uc can be determined on various manners. For instance, directly from Table 4.1,

or with the equations:

2 c c w

C

U

g

τ

ρ

=

(4.2) with 4

1,85 10

c E

c

τ

−

∗

=

(4.3) in which: C = Chézy coefficient (m0,5_/s)

τc = critical shear stress (Pa)

cE = strength parameter (m-1 s-1)

cE can be selected for the appropriate soil from Table 4.1. Note that the value of cE decreases with

increasing strength.

Table 4.1 shows constant values whereas Figure 4.2 showed that the strength depends on the depth. However, in order to determine the quality of the grass or the soil an expert’s opinion is required.

A constant value is acceptable for the top layer, but it is recommended to develop a depth-depending strength formula.

Table 4.1Characteristic strength parameters for grass, clay and sand soil Quality Strength factor

cE (m-1s-1)

critical shear stress τc (N/m2)

critical flow velocity Uc (m/s)

Grass Good 0,005 à 0,015 10-4 _{125 à 250} _{5 à 8}

Average 0,015 à 0,025 10-4 _{50 à 150} _{3 à 5}

Poor 0,025 à 0,035 10-4 _{25 à 75} _{2 à 4}

clay very good < 0,5 10-4 _{50 à 150} _{0,9 à 1,2}

Good 0,5 à 1 10-4 _{1,5 à 3} _{0,7 à 1,0}

structured 1 à 3 10-4 _{0,5 à 1,5} _{0,5 à 0,7}

Poor 3 à 5 10-4 _{0,3 à 0,5} _{0,3 à 0,5}

sand - > 10 10-4 _{0,1 à 0,2} _{0,15 à 0,3}

The figures in Table 4.1 are based on an analysis by Delft Hydraulics of the strength of a number of soils. This was done within the framework of activities related to the development of PC-Ring and a CUR study (CUR, 1996) to the erosion of unprotected river banks or canal banks. Results were used of research on grass dikes carried out in the Delta flume (Meijer & Verheij, 1998), the Scheldt wave basin (Verheij et al, 1995) and research by De Vroeg (de Vroeg et al, 2002) onto breach growth in dikes within the framework of Delft Cluster. The erosion was translated into strength parameters. This resulted in best guesses for the

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strength parameters and the critical shear stress, but on the basis of experimental results and expert judgement. The results have been summarized in Table 4.1.

Nevertheless, probably the best estimate for Uc, in stead of applying Table 4.1 or eq.(4.1) and (4.2), is by

using the Mirtskhoulava formula (Hoffmans & Verheij, 1987) which is based on the cohesion c of the soil and for this situation has been extended with the root cohesion CR (Van der Meer et al, 2007):

(

)

(

)

8.8 0.4 log 0.6 c s f R a h U gd C C d

ρ

  =   − + +   (4.4) with: Cf =0.035c in which: c = cohesion (kN/m2₎ CR = root cohesion (kN/m2) h = water depth (m)

d = thickness layer considered (m)

da = layer thickness equal to thickness of clay aggregate (m), da = 0,004 m

ρs = density saturated soil (kg/m3)

ρ = density water (kg/m3₎

g = gravity acceleration (m/s2₎

The EPM method can be easily compared with graphs as presented by CIRIA and which are also applied in the VTV (RWS, 2004). An example is shown in Figure 4.4.

Figure 4.4 Moment of failure by EPM (Van den Bos, 2006)

Up to now a method has been described without reinforcement. It is expected that the presence of a geosynthetic will prevent erosion of soil material below the geosynthetic. As said before a particular prediction method has not been derived within this study. However, it is also possible to add in eq.(4.4) a geosynthetic cohesion parameter Cgeo to the Mirtskhoulava formula to increase the strength:

(

)

(

)

8.8 0.4 log 0.6 c s f R geo a h U gd C C C d

ρ

  =   − + + +   (4.5)

So, equation (4.4) changes into (4.5) from the depth at which the reinforcement is present. From this depth the erosion will be retarded. Obviously, the mechanism of head-cut erosion as shown in Figure 4.3 and which is the basis of the EPM method, will not occur. The erosion of soil material will depend on the opening size op the geocell or geogrid (see Figure 4.5 for examples).

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Figure 4.5 Geogrids and Geocells

4.3

4.3 4.3 Shear failure along a planar parallel to the surface

Shear failure along a planar parallel to the surface

Although not a subject of this study some remarks will be made on shear failure along a planar. Ms Syliva Hinostoza from Peru who carries out her MSc graduation at the TU Delft, considers the stability of reinforced grass against planar sliding. Before discussing her first results, as she did not finish her MSc-study yet, an overview will be presented of the geotechnical aspects discussed in the SBW MSc-study (Van der Meer et al, 2007).

Within the SBW framework sliding of the top layer along a planar parallel to the slope was predicted in case of a non-reinforced grass slope. First, the Edelman-Joustra method was considered, secondly the Martin Young model, and thirdly, an advanced approach by using Plaxflow/Plaxis models. The Edelman-Joustra method is based on the stability of a soil layer with a thickness d (m) on a slope with an infinite length. It assumes saturated soil and groundwater flow parallel to the slope angle due to infiltration. The Edelman-Joustra formula written as reliability equation reads:

(

)

0

tan

0 c

Z

=

R

−

S

=

τ

−

τ

=

c

+

σ

φ

−

τ

(4.6) or

(

g

cos

w

cos ) tan

g

sin

Z

= +

c

γ

d

α γ

−

d

α

φ γ

−

d

α

in which: R = strength (N/m2₎ S = load (N/m2₎ τc = strength (N/m2) τ0 = load (N/m2)

σ = effective normal stress (N/m2₎

ϕ = angle of internal friction (0₎

c = cohesion (N/m2₎

γg = weight saturated soil (= ρsg ) (N/m3)

γw = weight water (N/m3)

α = slope angle (o₎

d = layer thickness (m)

Young (2005) extended the Edelman-Joustra model with the influence of roots (root cohesion CR; see also

eq.(4.4)) and the stress due to overflowing water. Both influences cannot be excluded in case of a limited thickness of the considered layer. The reliability equation with the added root cohesion (first term) and the shear stress due to overflowing water (last term) becomes:

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(

cos

tan

sin

)

(

cos

)

tan

sin

₂2

C

u

d

A

T

Z

w g w g r r

γ

α

γ

φ

α

γ

α

γ

θ

φ

θ

+

−

=

(4.7) where:

Tr = root tensile strength (N/m2)

Ar/A = root area ratio (-)

θ = angle of shear deformation (o₎

u = flowing velocity (m/s) C = Chézy coefficient (m0.5_/s)

Plaxis is a finite element model allowing computing stresses and deformations. The advantage of the model is that it is not necessary to assume a planar beforehand. Plaxflow provides insight in time-dependent groundwater flow and the degree of saturation of the flow.

Applying the various models with relevant data of the ComCoast test location without reinforcement, it was concluded that a planar sliding will not occur. At a depth where the number of roots decreases rapidly the stability shows a local minimum, which is in accordance with the results of Hähne (see Figure 4.2). Using a geogrid reinforcement at the ComCoast tests can have a positive effect on the sliding stability of the grass cover layer. Two mechanisms have to be considered:

1. Sliding of the top layer over the geogrid. The interface between soil and geogrid can be week in case of poor root penetration, a small friction angle between the soil and the geogrid and a disturbed soil structure at the boundary, caused by installation of the geogrid.

2. Sliding of a layer thicker than the geogrid depth. In this case two mechanisms can be distinguished: - Breaking or tearing of the geogrid.

- Pulling out of the geogrid from underneath the dike crest, if the embedding length and or depth are insufficient.

The first mechanism depends on the root penetration through the openings in the geogrid, the friction angle between soil and the geogrid and friction between the soil underneath, and on top of the geogrid, making contact through the geogrid openings. The sliding characteristics of the top layer – geogrid interface will develop in time, from the moment of installation. For the ComCoast test location the sliding resistance at the geogrid interface will be relatively small compared to the non-reinforced grass cover. The roots only had one growing season to grow through the geogrid openings and the friction angle between the geogrid and the soil will probably be less than the angle of internal friction in the undisturbed grass cover layer.

Sliding over the geogrid interface can be modeled by adjusting the friction terms to the Edelmann–Joustra criteria. The cohesion term can be replaced by a root cohesion term, where the root area ratio is adjusted to the geogrid situation. The angle of internal friction can be adjusted to cover both the friction angle between the soil and the geogrid plastic and the friction angle of the soil underneath and on top of the geogrid openings.

In case of the second mechanism, the geogrid adds an extra resisting force on the considered soil layer. The extra resisting force is maximized by the tensile strength of the geogrid and can be modeled by adjusting the Edelmann – Joustra criteria, if the slope length L (m) is considered:

( cos cos ) tan sin

geo geo c o g w g F Z R S c d d d L

τ

γ

α γ

α

φ γ

α

= − = + − = + + − − (4.8)

Provided mechanism 1 (superficial sliding along the geogrid – soil interface) can be prevented, the geogrid will provide extra stability of the grass cover layer.

Ms Syliva Hinostoza followed a little different approach and started with making an overview of the forces working on a reinforced inner dike slope. Figure 4.6 shows all forces working on a plane parallel of the slope including a geosynthetic.

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Figure 4.6 Balance of forces on a reinforced grass slope

Now consider the stability of a plane parallel of the slope:

SF = R / S (4.9)

In which;

SF = Safety Factor

R = forces increasing stability or strength (in general: resistance or strength) S = forces reducing stability or load (in general: load)

Relevant R forces are: • _{Clay: Fclay} • _{Roots: Froots}

• _{Geosynthetic: Fgeosynthetic} Relevant S forces are:

• _{Mass: Fmass}

• _{Flow above grass cover: Fflow} • _{Porous flow inside: Finside} Now the safety factors SF read:

F

_geogrid

h

L

d

α

θ

F

_RT

D

F

S

F

P

F

PV

F

_∆

_SR

τ

F

_PH

f

N

r

W

_S

I W ATER TUR F DIKE

r

f

_N

τ

∆

SR

F

S

F

W

_S

RT

F

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• no geosynthetic: _{no geosynthetic} stabilizing clay roots

destabilizing mass porous flow

F F F SF F F F F + = = + + (4.10)

• with geosynthetic: _{with geosynthetic} stabilizing clay roots geosynthetic

destabilizing mass porous flow

F F F F SF F F F F + + = = + + (4.11)

or _{with geosynthetic} _{no geosynthetic} geosynthetic

mass porous flow

F

SF SF

F F F

= +

+ +

Clearly, the influence of the geosynthetic can be observed.

Obviously, there exists a clear relationship with the Edelman-Joustra model, because in stead of eq.(4.9) we can also consider the reliability function according to eq.(4.6). In other words:

• no geosynthetic: R = τc = c + σ tan(ϕ) = f (Fstabilizing) = f (Fclay + Froots)

• with geosynthetic: R = c + σ tan(ϕ) = f (Fstabilizing) = f (Fclay + Froots + Fgeosynthetic)

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5

5 5 Prediction

Prediction

Applying eqs.(4.1) and (4.4) erosion of the grass cover can be predicted. As the ComCoast tests will be carried out with a geogrid with on top a grass mat with a thickness of 5 cm, even if those 5 cm has been eroded the reinforced slope has not failed because the geogrid is still present. Subsequently, failure must be defined if the geogrid allows erosion of material underneath the geogrid or ym > 0.06 m assuming a

geogrid thickness of 1 cm.

Note that in case of a non-reinforced grass mat failure should be defined if ym > 0.05 m.

The erosion for each wave can be computed and depending on the overtopping discharge more waves will overtop. For the prediction the following numbers are assumed (see also Chapter 3):

q = 0.1 l/s/m: 9 waves per 6 hour q = 1 l/s /m: 125 waves per 6 hour q = 10 l/s/m: 867 waves per 6 hour q = 30 l/s/m: 1324 waves per 6 hour

The critical flow velocity can be computed with the modified Mirtskhoulava formula including the geosynthetic factor Cgeo:

(

)

(

)

ρ

  =   − + + +   (4.5)

For the depth between z = 0 m and 0.05 m the value of Cgeo = 0 N/m2; for z > 0.05 m the value of Cgeo is

larger than 0 but the real value is unknown. We assume Cgeo = CR = 5 N/m2.

It should be noted that for the root cohesion CR a value of 5 kN/m2 has been applied taking into account

the discussion about the use of this parameter which requires also a lot of effort to be determined. Assuming average grass a minimum value for Uc is 3.0 m/s. Using furthermore k = 1.3 106 m2/s, α = 3

and ρs = 2000 kg/m3 for saturated soil the following scour in 6 hours per overtopping discharge can be

computed (using the figures in Tables 3.1 and 3.2 for the flow velocity for the relevant overtopping volume per wave):

q = 0.1 l/s/m: ym = 0 m (in 6 hour)

q = 1 l/s/m: ym = 0 m (in 6 hour)

q = 10 l/s/m: ym = 0 – 0.008 m (in 6 hour)

q = 30 l/s/m: ym = 0 – 0.013 m (in 6 hour)

It can be concluded that less than 5 cm will erode. Subsequently, the soil underneath the geogrid will not be exposed to overtopping waves. Thus, failure of the reinforced slope will not occur.

The available data mentioned in Chapter 3 do not allow estimating the allowable overtopping discharge resulting in a scour depth of 5 cm.

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6

6 6 Conclusions and recommendations

Conclusions and recommendations

A desk study has been carried out in order to develop a conceptual model for the erosion of inner dike slopes with reinforced grass cover. Based on the results the following can be concluded:

• The presence of a geosynthetic in a grass slope can be taken into account in the EPM method by increasing the critical flow velocity. In particular, a factor Cgeo has been added to the Mirtskhoulava

formula:

(

)

(

)

ρ

  =   − + + +  

• The value of Cgeo is unknown.

• Prediction of the failure of a reinforced grass cover did not result in a failure as the erosion is less than the thickness of the layer on top of the geosynthetic.

In summary, it is recommended to continue with the results obtained, because the elements for a prediction are available although a correct prediction is not possible yet. In this respect it is recommended to incorporate the failure mechanism of slope material underneath the geosynthetic which probably can be treated in a similar way as geosynthetics in erosion control applications.

The Mirtskhoulava formula is valid for the stability of individual elements, but probably there exists a relation with the Edelman-Joustra method for the stability against sliding based on the Mohr-Coulomb-relation. It is recommended to attempt to develop this relationship because it might link the stability of individual elements with the stability of soil layers.

Furthermore, it is recommended to develop depth-dependant strength parameters in accordance with the observed strength as shown in Figure 4.2: high strength at the surface due to roots, then decreasing to a depth of about 10 cm due to decreasing number of roots, and then increasing again due to clay properties.

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References

Bos, W. van den (2006): Erosiebestendigheid van grasbekleding tijdens golfoverslag. Afstudeeronderzoek TU Delft.

CUR (1996): Erosie van onverdedigde oevers CUR, rapport 96-7, Delft

Gerven, K.A.J. van et al (2005): Development of alternative overtopping resistant sea defences

Royal Haskoning, Nijmegen

Hoffmans, G.J.C.M. and H.J. Verheij (1987): Scour Manual A.A.Balkema Publishers, Rotterdam

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Van der Meer, J.W. et al (2007): Golfoverslag en sterkte binnentaluds van dijken Rapport Predictiespoor SBW, Infram, WL | Delft Hydraulics, Geodelft, rapport 05i028

Verheij, H.J. et al (1995): Onderzoek naar de sterkte van graszoden van rivierdijken WL|Delft Hydraulics, verslag Q1878, Delft.

Vroeg, J.H. de, et al. 2002. Processes related to breaching of dikes. Erosion due to overtopping and overflow. Delft Cluster, rapport DC-030202/H3803, Delft

Young, M.J. (2005): Wave overtopping and grass cover layer failure on the inner slope of dikes

Conceptual model for reinforced grass on inner dike slopes

ComCoast

Conceptual model for reinforced

grass on inner dike slopes

ComCoast

ComCoast

ComCoast

ComCoast

Conceptual model for reinforced

grass on inner dike slopes

Work Package 3

Civil Engineering

Approach

Conceptual model for reinforced

grass on inner dike slopes

Background report

Background report

Background report

Background report

The report is written/edited by:

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WL|Delft Hydraulics

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Infram

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GeoDelft

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TU Delft

Table of Contents

1

1

1

1 Introduction

Introduction

Introduction

Introduction

1.1

1.1

1.1

1.1 Background

Background

Background

Background

1.

2.

1.2

1.2

1.2

1.2 Project team

Project team

Project team

Project team

2

2

2

2 Objective

Objective

Objective

Objective

3

3

3

3 Hydraulic load

Hydraulic load

Hydraulic load

Hydraulic load

4

4

4

4 Failure mechanism ero

Failure mechanism ero

Failure mechanism ero

Failure mechanism erosion of grass

sion of grass

sion of grass

sion of grass

4.1

4.1

4.1

4.1 Introduction