CO-383990/8
Febmary 1999
Geosystems
CO-383990/8
Febmary 1999
Bez
The survey was performed for:
Dienst Weg- en Waterbouwkunde
P.O. box 5044
2600 GA Delft
DEPARTMENT STRATEGIC RESEARCH
projectmanager: A. Bezuijen
projectsupervisor: Dr. H. den Adel
D E L F T G E O T E C H N I C S Stieltjesweg 2, 2628 CK DELFT
P.O. Box 69, 2600 A B DELFT Telephone 31 - 15 -2693500
Telefax 31 - 15 - 2610821 Postal account 234342 Bank MeesPierson N V
Title and sub-title: Geosystems
Department: Strategic research
Project: Geosystemen
Project manager(s): A. Bezuijen
Project supervisor(s): Dr. H . den Adel
Name and address of client: RWS
Reference chent: ir. K.W. Pilarczyk Dienst Weg- Waterbouwkunde
Postbus 5044
2600 GA Delft Copies sent: 2
Type report: fmal
Simamary of report:
Literature on geosystems has been evaluated with the goal to come to a state of the art report with respect to the dimensioning of geosystems.
Existing calculation models have been examined and compared with the results of measurements. Some extensions have been made on existing models to calculate the stresses in the geotextile of a geocontainer during impact and to improve the model of Higuchi.
Dimensioning of a geocontainer is still difficult since the knowledge of the critical loading during opening and impact is still limited, resulting in inaccurate models, whereas experiments present inconclusive results. Some upperbound approximations for design are presented.
This report is an extension of the report CO-369280/43 of November 1997. The influence of air and the degree of filling of the geocontainer is investigated, as well as the stability and the influence of stones in the bottom under the geocontainer on the loading of the geotextile. Furthermore the experiments performed by ACZ on geocontainers have been evaluated.
Comments:
Keywords: Distribution: RWS, D W W
Geosystems, Geocontainers
Saved under title: e:\ioso\so\bez\geosys.wp No. of pages: 80, incl. appendices
Version: Date: Prepared by: Signature: Checked by: Signature:
1 Bez Adel
2 November 1997 Bez Adel
CO-383990/08 February 1999
T A B L E OF CONTENTS
1 Introduction 1 1.1 General 1 1.2 Geotubes and geocontainers 2
2 Opening of the barge 3 2.1 Introduction 3 2.2 Required circumference of the geotextile 3
2.3 Tension in geotextile during fnst opening 4
2.3.1 Container filled with slurry 5 2.3.2 Container filled with sand V 2.4 Tension in geotextile during opening 8
2.4.1 Literature 9 2.4.2 Possible improvements 10
2.4.3 Failure mechanism 11 2.4.4 Failure of sand 12 2.5 Tension just before the container leaves the barge 15
2.6 Analysis of Fowlers article 17 2.7 Influence of length circumference 19
2.8 Conclusions 23 3 Loading during impact 25
3.1 Dumping velocity 25
3.1.1 Theory 25 3.1.2 A C Z experiments 28
3.2 Stress and strain in geotextiele during impact geocontainer filled with slurry 32
3.2.1 Calculations of Palmerton 32 3.2.2 Analytical calculations 35 3.3 Example calculations impact 38 3.4 Deformation during impact of geocontainer filled with sand 39
3.5 Influence of air 41 3.5.1 Air in the f i l l during dumping 41
3.5.2 Influence of air in fill on deformation of container during impact 43
3.5.3 Stress in geotextile during dumping due to air 45
3.6 Impact not parallel to the sea bottom 46
3.7 Influence of subsoil 47
3.7.1 Soft subsoil 47 3.7.2 Stress and strain in geotextile due to bumps in the sea bed 47
4 Shape geocontainer after dumping 51 4.1 Timoshenko's method 52
4.2 Extensions 54 4.2.1 Elastic foundations 54
4.3 Shortcomings 56 4.4 Mechanisms for dry sand 56
4.5 Mechanism for wet sand 57 4.6 Calculations compared with measurements 57
Deformations due to lateral forces and wave attack 5.1 Deformations in container due to lateral forces 5.2 Stability under wave attack
63 63 67 Scaling mles
6.1 Geometrical scaling
6.2 Velocity, time, stresses and forces 6.3 Different scaling rules?
69 69 69 70
Design rules 73
Conclusions and recommendations 75
References 77 Literature Geotubes 1.1 Description of M i k i 1.1.1 Allowable forces 1.1.2 Measurements 91 91 91 92 Stability of structures 2.1 Sandbags 2.1.1 Description of tests 2.1.2 Consequences for design 2.2 Geotextile as dune protection
95 95 95 95 95
CO-383990/08 February 1999
1 Introduction
1.1 General
In contract nr. DWW-1213 of October 14th 1996 D W W commissioned Delft Geotechnics to perform research on geosystems (Geotubes and Geocontainers).
3 Phases were envisaged, a complementary literature study, checking and, i f necessary, improving of existing calculation methods and the integration of developed knowledge in design rales. After finishing the work under this contract, it appeared that not all aspects of geocontainers were covered. Therefore, an additional contract was signed between D W W and Delft Geotechnics. Contract nr. DWW-1448 of June 23th, 1998 and the proposal CO-383990/03 decribe this additional work. This report presents the results of these 2 contracts.
Literature on geocontainers focuses on the forces on the geotextile during dumping and impact on the subsoil. During these phases, the maximum forces are exerted on the geotextile and for dimensioning, it is necessary to be able to estimate these forces. Literature shows that ruptures in geotextiles during placement may happen.
The problem for this part of the study is, that the behaviour of falling ground is normally not studied in soil mechanics. Usually it is studied how to prevent movements of soil. How falling soil, for example in a sandbag, behaves is usually no object for study, but is now the aim to describe the behaviour of the geocontainer.
Literature on geotubes focuses not on the dumping, as for geocontainers, but on the stability of geotubes on a slope or under wave attack. Large-scale model tests have been performed to measure the stabihty under wave attack.
This report describes the state of the art in the dimensioning both geocontainers and geotubes. I t concentrates on the geocontainers, since geocontainers provide the design engineer with more pitfalls than geotubes. The various phases in the placing of geocontainers are shown in Figure 1. The numbers i n this figure refer to the paragraphs where the situation shown is dealt with.
The report is stractured in the following way:
In Chapter 2 the stresses caused by the process of opening the barge are dealt with. The stresses in the geotextile during free fall and impact on the sea bottom are dealt with i n Chapter 3. Chapter 4 considers the end shape of a geocontainer when filled with a slurry or sand. Chapter 5 shows deformations due to lateral loadmg and due to wave attack after placement. Scaling rales for model tests are discussed i n Chapter 6. Conclusions what calculation methods can be used as design rales are presented in Chapter 7. Chapter 8 gives conclusions and recommendations. In the report it is described which models are available for the various phases. Furthermore it is
of soil I Figure 1: Various phases in the placement of geocontainers with a qualitative sketch of the
resulting forces on the geotextile. Numbers indicate the paragraphs where the situation shown is dealt with.
described which models can be used to come to a design. It w i l l appear that only a few models are based on a f u l l understanding of the physical phenomena. In most cases, the solutions presented are approximations. I f possible, upper bound solutions are presented. More research will provide a better understanding of the physics of dumping soil, which can lead to an
optimahsation of the design. Although design models are presented, it should be noted that these structures rely largely on quality assessment and workmanship. No design can take into account bad quality of seems, sharp edges on barges or debris on the subsoil.
1.2 Geotubes and geocontainers
The body of this report deals with geocontainers. Some hterature about geotubes is deah with in the appendixes. Furthermore, the results of some stability tests are dealt with in the appendix. However, the stability of the sand in the structure is dealt with in Chapter 5.
CO-383990/08 February 1999
2 Opening of the barge
2.1 Introduction
The constmction of a geocontainer starts with placement of the geotextile in the barge, the dumping of material and closing of the geocontainer. These stages do not lead to a large loading of the geotextile. The furst loading of the geotextile is when the barge starts to open and the geotextile across the opening is stretched. The next loading that has to be considered, is when the barge has opened further and there is a considerable free hanging part of the geotextile, across the opening of the barge. This free hanging part is loaded with the soil of the container. The two stages of loading during the opening are dealt with in this chapter.
First a geometrical calculation is presented to calculate the required perimeter of the geotextile, then the tensile stresses in the geotextile during various stages of opening are presented. The chapter ends with a geometrical calculation to show the influence of the circumference on the minimum necessary opening of the barge. In these calculations the influence of permeability of the geotextile and it's content is not taken into account. It is assumed that dumping goes rather quickly and that therefore the drainage of water from the geocontainer during dumping will only be limited.
2.2 Required circumference of the geotextile
The circumference of the geotextile must be sufficiently large to allow the deformation needed for the geocontainer to pass through the opening with a given split b^ and a given cross-sectional area of material in the geocontainer: A,. The more deformation during dumping is wished the longer the circumference has to be. Den Adel et al. [den Adel 1996] have described the desired length. Their calculation method is presented below, see also Figure 2 and Figure 3.
The requked circumference of geotextile sheet, S during dumping, is given by:
When the geocontainer hits the bottom, it reshapes. The originally vertically orientated cone transforms into a cylinder and fmally reshapes into a horizontally orientated ellipse (Figure 3). The real shape on the bottom. Figure 3 will be more close to a rectangular one for low filling grade ((jj^i), while more close to the semi-oval shape for a high filling grade. Therefore the maximum height of geocontainer, a^, in the fmal position w i l l be:
1(1 -f^ï6^i)<a,<^{l-V1-14<P(1)J (^'^^
())f5ii is tiie filling-grade ratio (<1) and (p=AJS^, where A„ is the maximum area of the cross-section of the split barge. This equation provides a tool for estimation of the average number of geo-containers, required for a given stmcture.
i I I U ' ^ >l
Figure 2: Sketch of the deforma- Figure 3: Various phases in the tion during release. dumping process.
The formula's (2.1) and (2.2) show that a certain circumference is necessary to allow release at a certain opening, but that a larger chrcumference leads to a lower hight a^ of the container.
2.3 Tension in geotextile during first opening
The situation dealt with in this paragraph is shown in Figure 4. It is the situation at the moment the barge starts to open. A t this moment the bottom part of the geocontainer is stretched. The geotextile must overcome the friction forces. The contribution of elastic deformation in the geotextile is also calculated but appears to be negligible compared to the opening of the barge.
CO-383990/08 February 1999
This aspect is not deaU with in literature. In literature the calculation of stresses in the geotextile started in the next phase. Since the loading can be substantial, depending on the friction between the barge and the geotextile and the angle between the sides of the barge, this aspect is calcu-lated.
2.3.1 Container filled with slurry
Assume that the geocontainer is filled with slurry that behaves more or less like a hquid. Only normal stress is transferred from the slurry to the geocontainer. The forces on the sides of the barge are sketched in Figure 4. This figure shows that vertical equilibrium of forces lead to:
F„cose + \xF„ sine = Q.5G (2-3) As the geotextile shdes over the barge the friction between the barge and the geotextile can be
written as:
| i F „ = r (2.4) where:
F„ : the force perpendicular on the bottom of the barge (kN/m) T : friction force between barge and geotextile (= - the maximum tensile force in the
geotextile) (kN/m)
G : the weight of the geocontainer resting on the barge (kN/m) 1^ : the friction between the geotextile and the barge. (-) 0 : angle see Figure 4
The opening of the barge creates a tensile force in the geotextile (T):
r=o.5
COS0 +sin0
(2.5)
Figure 4 Forces on geotextile at the beginning of the opening of the barge when container is filled with slurry.
As the opening increases, 6 increases, but G decreases due to uplift pressure and because the weight of the slurry is partly carried by the free haning geote-xtile. Considering these contributions, as w i l l be described later in this report, it appeared that when equation (2.5) is used for the start of the opening of the barge, a result close to the maximum T is obtained. For engineering purposes, it is sufficient to increase the result of equation (2.5)
with 10% to find the maximum tensile strength due to the opening of the barge.
As an example, the opening a barge filled with slurry with a cross-sectional area of 22 m^ is calculated (see Appendix 1). Assuming a n of 0.5 and a density of the slurry of 15 kN/m and a starting angle 6 of 23 degrees. In this situation, the maximum loading on the geotextile is approximately 75 kN/m.
Resuhs of this formula can be compared with measurements of Fowler near New York. [Fowler 1995] The analysis of this article is described in Section 2.6 in this chapter. From this analysis it appears that the measured tensile force at the moment the geocontainer leaves the barge, is approximately 75 kN/m, but using formula (2.5) i t appears that at the beginning of the openmg the tensile force is 100 kN/m.
As is shown in Figure 4 there is an equilibrium of the vertical forces, but not of the horizontal ones The horizontal forces are determined by the deformation behaviour of the f i l l material. I f this is very stiff the horizontal stress will be zero, at the centre of the bai-ge during opening. For slurry, that behaves as a liquid the horizontal stress wiU be equal to the hydrostatic pressure. Sand has an intermediate behaviour as will be described in next section. The friction as it is described here is a more or less worst case approximation. I f the fiU material has some stiffness, the horizontal stresses will decrease during opening, leading to lower friction. See the calculation example in the next section.
Influence of hydrostatic pressure
Figure 5: Forces on geotextile at the beginning of the opening of the barge when con-tainer is filled with slurry.
If the slurry behaves as a liquid, then there w i l l also be a horizontal force. This becomes clear i f only half of the container is considered, see Figure 5.
The forces on the container are shown in the situation when the side of the barge starts to move outward with respect to the container. The lower part of the figure shows the forces in this situation. Vertical equilibrium leads again to Equation (2.3).
Horizontal equilibrium using Equation (2.4) leads to the equation:
CO-383990/08 February 1999
This means that there is a fixed relation between the force F , and the tension in the geotextile. This seems not logical because F, is determined by the hydrostatic pressure. However, this equation is vahd only i f the geocontainer does not reach the vertical part of the barge. I f it does reach that vertical side, the horizontal force from that side has to be subttacted. I f it does not reach that vertical side. Equation (2.6) wiU be obtained by adjusting the position where the container is stiU connected with the barge. As it is shown in Figure 5, the tension i n the geotextile wiU l i f t the geotextile from the lowest part of the barge.
It should be noted, that even is a part of the geotextile is lifted from the barge, that Equation (2.3) and (2.4) still holds.
2.3.2 Container filled with sand
When the container is filled with sand, or another material with a mechanical shear strength that cannot be neglected, the situation becomes more complicated. In this situation, a shear stress can be fransferred from the f i l l material to the geotextile. Since the container is stretched the
horizontal forces wiU be small, equal to the active stress as long as the angle of the barge (9) is smaller than the friction angle of the geotextile and the sand. The shearing force that is exerted from the sand to the geotextile can be written as, see Figure 6:
r^=O.5Gsin0-F^cose (^"^^ and the horizontal force (F,) is determined by the earth pressure in the container and can be
writ-ten as:
With:
In this formulas is:
iVx=tan2(45+0.5(|))
G F.
c (t)
the shearing force exerted on the geotextile by the sand the weight of the geocontainer
the horizontal force
the volumetric weight of the container the height of the container
coefficient of passive resistance
cohesion of the material in the geocontainer friction angle (2.9) (kN/m) (kN/m) (kN/m) (kN/m^) (m) (-) (kPa) (deg)
I f the angle of the barge (9) becomes larger than the friction angle between the sand and the geotextile, then the sand will have the tendency to slide down. However, this wiU not happen.
because the sand from the other half of the barge wiU have the same tendency. Consequently, the horizontal force is no longer determined by the equation for the active earth pressure as men-tioned above. It is determined by the equilibrium of both sides of the barge. For this situation the equations read: F = G (tane-sin(|)) (2.10) l+tan0 sin^ F„=Gcos0-F^sin0 r =F„ sind) (2.11) (2.12) hi this last situation, the sand will slide with respect to the geotextile. Normally this w i l l not be the case, although it can happen when the friction between the geotextile and the bai-ge is large.
The total force on the geotextile determining the tension, is the combination of the shearing force exerted by the sand and the shearing force exerted by the barge. Normally these are in opposite direction, which results in a smaller tension for this situation than in the situation of a slurry.
Using the same example as for the slurry, for a container of 3 m high, but now filled with sand with a friction angle of 30 degrees (the same friction angle between the geotextile and the sand) and a volumetric weight of 16 kN/m^ it is found that the tension in the geotextile at the
beginning of the opening of the barge is 55 kN/m (using the same 10% marge).
2.4 Tension in geotextile during opening
Section 2.3 deals with the forces during the first opening of the barge. I n this section the forces WiU be calculated at the moment the barge has opened further. The model of Higuchi gives a
solution at which opening angle the geocontainer starts to fall through the opening. This is not a straightforward calculation. The resuh depends on the stress distribution in the container during the various phases of the dumping process. Results depend to a great extend to the assumed stress distribution. Therefore first the model of Higuchi (including some improvements as suggested by Lindenberg and Den Adel), wiU be described briefly, afterwards various comments w i l l be given and consequences discussed. Figure 6: Forces on geotextile at the beginning of the
ope-ning of the barge when container is filled with sand.
CO-383990/08 February 1999
2.4.1 Literature
Various calculation methods are presented in literature that calculate the tensile forces on the geotextile at the moment the geocontainer slides through the opening of the barge, hi this section this literature w i l l be described, hi the next sections, some possible improvements wiU be men-tioned.
In "Altematieve systemen; Geocontainers" CO-365930 [Den Adel, 1996] and in "Design aspects of Geotubes and Geocontainers" [Pilarczyk, 1997] calculation methods are presented to predict the loading on a geotextile when dumped from a split barge, just before it leaves the split barge. The method is an improved version of the method which has been derived by Higuchi [Tsunoda,
1995].
given in the Appendix.
The method as presented by Den Adel is
similar. However, T as described by Den b Adel is not the tension force in the
geotextile, but the total force parallel to
\ ^
Fah slope of the barge.
X e / 1.
The method is based on the following assumptions:
1. The soil in the container is
^ /|^ /|\ /|^ 1< ^0 >1
divided into i parts, see rigure /. pig^-e 7: Sketch used in the Higuchi model. The middle part with width bo is
not directly supported by the barge. This part is supported by the geotextile and the fric-tion forces between that part of the soil and the parts still supported by the barge. The loading on the geotextile (T) is determined by the loading on the soil above the opening (its weight minus the friction and the hydrostatic uplift force) and the opening angle 9 of the barge. A large opening angle means that the geotextile is dkected towai'ds a more vertically direction and therefore it can resist a vertical directed loading with less tension in the geotextile compared with the same loading on a more horizontal dkected geotextile.
The friction angle between the soil part in the middle and the two still supported parts is determined by the friction angle and the horizontal earth pressure. The horizontal earth pressure is calculated, as a factor Ko of the vertical earth pressure.
The calculation resuhs in a tension on the geotextile (T), see assumption 2, a force
parallel to the bottom of the barge (F), composed of the tension (T) and the component of weight of the soil parallel to the slope, and the friction force (nF„, with \i the friction
coefficient between steel and the geotextile and N the force normal to the sides of the barge) that has to be overcome before sliding of the geotextile occurs. In case F>|iF„ the container w i l l shde out of the barge. Here F=|iF„ is assumed (no acceleration).
5. It is assumed that the soil in the triangles left and right of the opening of the barge will not deform.
Mr. R. 't Hart from the Dutch Public Works Department has commented to this model. He mentioned that a equilibrium calculation is made on the base of suggested failure planes that cannot be the active failure planes during failure. Furthermore it is mentioned that a very stiff geotextile will slide directly at the frrst opening of the barge.
Mr. J. Lindenberg (Dutch Public Works Department) has commented this model as weU. His main comments regard the assumption that friction between the geocontainer and the spht barge is still very high, whereas the split barge has been opened until the unsupported length b^. When the friction between the geocontainer and the split barge is still too high, the elongation i n the geotextile, surrounding the geocontainer, must be of the order of bg. Since Mction between the geocontainer and the split barge is not yet exceeded by the tensile stress, the elongation must entirely take place between the two sides of the split barge. The strain wiU be very high, of the order of 100%. In his view such a high strain would lead to tearing the geocontainer just between the two sides of the split barge. This aspect has been elaborated in Section 2.3.
Studying the model more shortcomings can be mentioned:
When the container leaves the barge the soil is in a passive condition (the diameter of the container decreases), leading to a KQ larger than 1 instead of smaller than 1.
The curvature of the unsupported part of the geotextile is not determined by the angle of the split barge. The curvature is determined by the loading.
Arching can be found in granular material
2.4.2 Possible improvements
Based on the original model, but taking into account its shortcomings and the comments, a model is suggested using on the following assumptions.
The loading on the unsupported part of the geotextile is determined with a formula of Terzaghi that is also used i n calculations for the face stability of tunnels. It is originally derived to describe the influence of arching in a soil layer that has partly a yielding support. To use this formula in this situation, the soil above the geotextile must settle with respect to the soil i n the still supported part.
CO-383990/08 February 1999 Atan(|) h l - e x p --^Atan(}) bo c h Y X
the pressure loading on the geotextile the width of the opening of the split barge the cohesion of the soil in the split barge
the height of the soil above the opening in the split barge the specific weight of the soil
soil pressure coefficient angle of friction (2.13) (kPa) (m) (kPa) (m) (kN/m^) (-) (rad)
It is assumed that q3 is constant over the opening and perpendicular to the geotextile. This approximation is valid for slurry at a small opening of the barge. For sand and for larger openings it w i l l not be valid. The situation for larger openings is elaborated in Section 2.5. The curvature of the geotextile in that case will be a part of a circle. The curvature of the geotextile (r) is presented by:
T_
9.
r = — (2.14)
With:
T the tension force in the geotextile (kN/m)
For a given the minimum tension force equals:
2
The friction between the geocontainer and the two sides of the split barge must be sufficiently low to allow for sliding. This is necessary when the barge opening increases, as was mentioned by Lindenberg and discussed in Section 2.3.
2.4.3 Failure mechanism
In the calculation method described by den Adel and Pilarczyk the possible friction (F) is calculated and compared with the tension (T) that is caused by the unsupported part of the geotextile in the opening bo. A t the critical barge opening, the opening at which the geotextile starts to slide out of the barge, the tension is equal to the friction. I f the barge is opened further, the tension exceeds the friction and the geotextile is pulled out of the barge.
In the example of Den Adel this happened at an opening of 19 degrees and an opening width of 2.21 m. A t that moment the tensile force in the geotextile was calculated to be 57 kN/m for ^=0.4. However, using the formulation of Terzaghi (Equation (2.13)) and assuming that there w i l l be a circular shape of the geotextile leads using Equation (2.15) to much lower tensile
force is luglier tlian the passive earth strength, then failure will occur. In fact the last sentences imply a simplification. The upward directed force F„ w i l l lead to failure earlier than a purely horizontal force. However, this value is taken as a fust approximation.
The passive earth resistance is the vertical stress multiplied by the coefficient of passive earth pressure. In this case, the vertical stress in the soil above the free hanging part of the geotextile is not in all cases determined by density of the soil and the height of the container. Friction and arching decrease the vertical stress. There are two limits to the vertical stress:
the stress cannot be higher than the weight of the soil.
the vertical stress at the bottom, above the foe hanging part of the geotextile, is not to exceed the stress corresponding to the maximum possible tension in the geotextile.
To calculate the last criterion, is not calculated according to the formula of Terzaghi. It is calculated from the maximum tension T on the geotextile that w i l l result in shding and from this the vertical pressure is calculated using the formula:
27L (2.18)
This formula again implies a half-circular curvature of the geotextile.
When the effective stress at the bottom is known, the stress distribution is sketched as is shown in Figure 9. It is assumed that gravity determines the increase of the effective stress at the top of the container until it is equal to the maximum stress q,. This leads to the following equation for the resistance of the sand against deformation, i.e. the maximum force per unit length:
/ . ' ' - • • (2.19)
In this formula, the fkst part within the minus operation is the part according to gravity only, which is valid i f the vertical effective stress is not reduced by arching. The second part is valid if the maximum allowable stress in the geotextile is lower than the vertical effective stress without stress reduction due to friction and arching.
In this formula: Kp : the passive earth pressure coefficient.
Figure 9: Distribution vertical effective stress m geocontainer during opening.
CO-383990/08 February 1999
stresses in ttie geotextile. Using the same example as used by Den Adel, but with these equations, lead to a tensile force of only 17 kN/m. As a result slippage of the geotextile is no longer criti-cal, but the failure of sand in the geotextile becomes critical.
This resuh appears to be i n line with the dumping of geocontainers, as it is recorded on several video's. I f large tension i n the geotextile initiates failure, then it can be expected that the geotextile at the top of the geocontainer is stretched at the beginning of the dumping. However, this does not appear from the video. It seems as i f failure of the sand in the geotextile initiates the dumping.
The next paragraph wiU describe a model to calculate this failure of sand in the geocontainer.
2.4.4 Failure of sand
Just before the geocontainer is dumped, it will move downward. A t that moment, the sand deforms in order to pass through the opening. The sand has to overcome the passive resistance. The situation is sketched in Figure 8. It is assumed that the free hanging part of the container has a cross-section of a half circle. Such a shape needs the minimum tension to counteract the weight of the free hanging part of the container and therefore the container wiU adjust to this shape before it falls out of the container.
The forces on the barge have to counteract the weight of the geocontainer. Figure 8 can be used to study the forces on the geocontainer. From it can be concluded that:
= 2F„cos0 + 2iiF„sin0 + 21(1 - cos0) (216)
or: 1G^ - T(l - COS0)
F = —
" COS0 + j i s i n 0
(2.17)
Figure 8: Sketch for calculations with improved model.
Where:
G,ff : the effective weight of the
container (kN/m) F„ : the stress perpendicular to the
geotextile (kN/m)
The (l-cosG) comes in because this is the vertical force that the barge exerts on the geotextile to change the direc-tion of the geotextile at the opening edge. The horizontal part of this force (=F„ sin9) squeezes the sand. I f this
Using tiiese formulas, the driving horizontal force (F^sinB) and the resistive force can be calculated. The result is presented in Figure 10, for the example presented in the Appendix. In this figure a somewhat lower value of the passive earth resistance was chosen. According to the standard formulation, as given by Terzaghi and Peck (1967), Kp should be 3 for a friction angle of 30 degrees. Here a value of 2 is chosen since, as mentioned before, the stress is not purely horizontal.
S t a b i l i t y s a n d i n g e o c o n t a i n e r
200
0 10 20 30 40 50
Opening of the barge in degrees
Figure 10: Loading and strength of a geocontainer during opening of the barge. (nu=n, the friction coefficient, 17 degrees opening corresponds with bo= 2m).
This figure presents not the tensile force in the geotextile, but the horizontal force per unit length in the sand. The loading is the horizontal part of F„, F„sin0. F„ is calculated with equation (2.17) and the strength F, is described with equation (2.19). Due to the sliding of the geocontainer, the sand is squeezed, leading to a horizontal force per meter barge length. This force is compared with the maximum passive resistance of the sand as calculated with equation (2.17).
As soon as 0 = 15° (for \x = 0.18) or 0 = 25° (for |a = 0.4) the passive strength becomes smaller than the driving force (in both cases F, = F„sina=110 kN/m) and the container will slide down from the barge. At that moment the tensile stress in the geotextile is approximately 50 kN/m. The method as presented here has still some shortcomings. Palmerton (1996) has shown with a Distinct Element numerical code that there is also a distinct influence of the length of the
CO-383990/08 February 1999
If the ratio between cross sectional area and cross-sectional length is 1/D with D the width of the container then only a circular shape is possible. Tension stresses in the geotextile will prevent any other shape, but of course, tension stresses w i l l be very high.
Another shortcoming is that the tension is calculated assuming that the geotextile curvature will be the curvature of a circle with a diameter equal to the opening width of the barge. However, it appears possible that the diameter is larger, see Figure 11. In such a situation, the tension can also be larger, as will be described in the next paragraph.
Figure 11: Sketch for calculations just before leaving the barge.
2.5 Tension just before the container leaves the barge
Just before the container leaves the barge a large part of the fill material w i l l be supported by the geotextile, see Figure 11. The weight of the f ü l has to be supported by the tension in the geotextile. This is in fact the same situation as w i l l be dealt with in the Leshchinsky model, only the direction of gravity is different. The Leshchinsky model describes the tension in a geotextile after placing of the geocontainer, see Chapter 4 (Sections 4.1 until 4.3). It is assumed that the tension is constant all over the geotextile. Theory and equations w i l l be dealt with in Chapter 4. Using the same approach.
it is possible to solve the equations for the free hanging part of the geotextile. As an example, the resulting shape of a container is shown in Figure 12. This result was obtained by numerical integration of equa-tion (4.3) for a 2-dimensional case. In this calculation the barge had an opening (bo) of 4.5 m and the geotextile hangs for 4 m out of the barge (hi,=4 m in Figure 11). The pressure on the f i l l material (from the material above 4 m, h,, in Figure 11) is only very small. The volumetric weight of the material is 8 kN/m^ the under water weight of wet sand, and the tension in the geotextile is 80 kN/m.
Deformation tube!
\
/
1
width (m)
Figure 12: Shape of free hanging part of tube just before dumping. Result of calculation. First case.
Using tiiis modei, it appeared tliat high tension stresses are found in the geotextile. Figure 13 shows the resuhs of a calculation for the situation that was simulated by Palmerton (opening at dumping 2.44 m, length of catenary 19.8 m, bulk density 1300 kg/m^). Using the model described above, a much larger stress i n the geotextile was found than reported by Palmerton. Palmerton reported 2% strain in a geotextile with an E-modulus of 2100 kN/m, corresponding with a tension of 42 kN/m. Using the numerical model described here, a tension of approximately 90 kN/m is found. With the same E-modulus this corresponds with a strain of 4.3%. These values are approximately, since the pressure exerted by the fill material stiU in the barge is not exactly
known.
The shape found in the calculation con-esponds with the shape reported by Palmerton, compare Figure 13 with Figure 20. In this last graph only the part lower than z=7.3 m is vahd, since for higher values of z, the width is smaller than the opening width of the barge.
The reason for this discrepancy is that a static approach is used, for a dynamic situation. A t the maximum opening of the barge, the container is sliding down and there is no equilibrium. I n this stage of the dumping process every obstacle obstructing the falling w i l l lead to high tensile forces and most likely to rup-ture.
From the calculations of Palmerton i t appears that the maximum tension is found at a lower width of the free hanging part of the geotextile (9.1 instead of 19.8 m). For this situation the tensile stress, calculated with the method described here, is much lower, only approxi-mately 35 kN/m^ much better in agreement with the value given by Palmerton.
Figure 13: Calculation example of the
shape of the free hanging part of the These resuhs show the problem with this calculation container just before dumping, method. It can only be used i f there is knowledge Palmerton case. about the geometry (the width of the free hanging part,
the opening width), the pressure distribution in the f i l l material and the moment that sliding occurs.
However, it shows that high tensile stresses are possible. These high tensile stresses can be prevented by reducing the friction between the geotextile and the barge as much as possible and by increasing the length of the geotextile to facilitate deformations.
D e f o r m a t i o n t u b e
0 I — 1 1 '
0 1 2 3 4
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2.6 Analysis of Fowlers article
Fowler et al. describe an experiment with a 4000 yard^ (3058 m^) geocontainer, filled with soft dredged material. In this paragraph a comparison wiU be made between the experimentally obtained data and the simple model as described i n chapter 5 of the study by Den Adel [Adel,
1996] and modified in Section 2.3 of this study.
The geocontainer i n his article consists of two geotextiles. The inner one is a non woven, the outer one is a polyester woven geotextile. The outer container is assumed to carry the tensile loads, the function of the inner container is to confine the dredged material. Fowler has provided the geocontainer with two pressure transducers, measuring the inside and outside pressure, as well as six longitudinal and six transversal strain gauges. The geocontainer is filled with dredged material, having a density of 84 pounds per foot^ (corresponding to a density of 1330 k g / m l The container is dumped by means of a spht barge. When it is filled, its draft is approximately
17 feet (5.18 m). The inner dimensions of the split barge are 41 feet (12.5 m) wide. Information relating to the depth is not provided. However it can be derived from the length of sloping sides of the spht bai-ge (24.5 feet, 7.47 m) and the inner width. The radius, which approximates the path of the two sides of the split barge, when it is opened, is not provided either; it can be deduced from the following pieces of mformation: when the split barge has been opened approxi-mately 11 feet (3.35 m), the angle of the sloping side of the split barge is approxiapproxi-mately 47.5°. The split barge is coated with a HPDE liner in order to reduce friction between the geocontainer and the split barge. The angle of friction between the liner and the geotextile is reported to be approximately 10°, leading to a coefficient of friction, j i , of 0.18.
The initial angle of the split barge, OQ, is derived from the inner length of the split barge and its sloping sides, being approximately 33°. The radius R, describing the path of the splh barge when it is opened, is derived by bearing i n mind that an opening of the split barge being approximately
11 feet (3.35 m) corresponds to an opening angle of 14.5° (47.5° minus 33°) of the split barge. The radius is approximately 22 feet (6.70 m).
The tensile strength has been measured in warp en weft, being approximately 5000 pounds per 4 inches (1250 pii) at 0.13 strain. The tensile strength is therefore roughly 220 kN/m'.
From the hnear part of the stress strain relation, the effective stiffhess of the geotextile can be derived from: 180 kN/m' at a strain of 0.1, leading to:
F = 1.8 X 10^ 6 (2.20) where F is the force in N and e the strain as a decimal fraction (0.1 means 10% strain).
Fowler describes that the readings of transversal strain gauges are at their peak values, during the process of opening the split barge. During free fall, strain decreases considerably. When the impact at the bottom of the ocean occurs, there is no rise in transversal strain reported either. Fowler reports roughly 0.04 strain, leading to tensile forces in the geotextile of approximately 80 kN/m'.
In Figure 14 the tensile force in the geotextile (T) is plotted as a sohd line against the opening of the split barge (bg), according to the theory developed by Den Adel. The friction force per meter between the geotextile and the liner of the spht barge, calculated at a coefficient of friction of |i=0.18, is indicated by triangles. When these lines intersect, the tensile force in the geotextile equals the friction force. At this opening of the split barge the geocontainer is likely to start free faU. For ^=0.18 this is at bo= 2.8 m, corresponding with an opening angle of approximately 8 degrees. For |j=0.4 this is at 6.6 m and opening angle of 20 degrees. The tensile forces i n the geotextile are approximately 75 kN/m' and 115 kN/m respectively.
h = 6.3 [m] 0) S 0) 'Ö5 c
Opening of the scow [m]
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The measured and the calculated values of the forces are in good agreement. It can be concluded that the model, as quahtatively described in Section 2.4.1, is i n agreement with measured tensile forces, when a geocontainer filled with dredged material is being dumped. For a geocontainer filled with material, which has intemal friction, the remarks as made i n the previous sections of this report still hold.
Furthermore a careful analysis of the observed data wiU leam even more about the processes which govem dumping.
When the split barge is opened, the extemal pressure, i.e. the water pressure in the split barge around the geocontainer, rises within a short period to 13 feet. The cause for this is that water flows into the barge, levelling the pressure difference caused by the draft of the spht barge. The water pressure inside the geocontainer rises as weU, remarkably fast, even too fast compared to the extemal pressure. Both intemal and extemal pressure rise to a value roughly as expected for the draft of the spht barge. However, when the spht barge has been opened roughly 5 feet, the intemal pressure starts slowly to decrease to half the value corresponding to the draft. It seems like pressures less than the hydrostatic pressure are being generated. The reason for this process is not known.
The measured strain increases smoothly to its maximum value. There are no sharp increases or decreases in the strain to be observed. There are two possible explanations for this phenomenon.
The geocontainer slides down slowly and regularly along the sides of the split barge The geocontainer might be stuck somewhere, but tensile forces are not transmitted unattenuated through the geotextile.
The latter is hard to explain i n this specific case. When a geocontainer is filled with a material that displays intemal friction, tensile forces can be dissipated by friction between the geotextile and the material inside. This is not a valid argument when the geocontainer is filled with soft dredged material. So the geocontainer has to slide down smoothly.
2.7 Influence of length circumference
In the Sections 2.3 until 2.6 the forces were determined using the weight of the contents of the container and the interaction of this contents with the barge. From the resuhs of these calculation it was decided whether or not shding occurs. However, there can also be some interaction with the geotextile. The geotextile limits the possible shapes of the container, because the circumfer-ence has a certain length. A geocontainer is a closed volume and that also means that not aU forms are possible. For further discussion we assume a ckcle as a reference shape.
The relation between area and circumference of the circle can be written as:
With: ^ S : circumference of the circle(m)
O : area of the circle (m)
Neglecting the possible strain i n the geotextile, this relation also means that i f the ratio between the
circumference and the root of the area obeys the relation mentioned above, the shape can only be a circle. Every other shape can only be made i f the circumference is larger.
Dumping a geocontainer with a rela-tion between cross-secrela-tional area and circumference of the cross-section as given i n equation (2.21) is hardly possible, because the geocontainer cannot deform. The longer S, for a
given area O, the more flexible is the geocontainer to leave the barge through a relative small opening. This aspect of the dumping is thus independent from the friction between the geocontainer and the barge. Even i f there is no friction at aU, stiU a minimum opening bo is necessary to release the geocontainer.
The shape of the geocontainer just before dumping is shown i n Figure 15, as was already shown in Figure 11 (this shape is based on numerical calculations of Palmerton see Section 3.2.1). To calculate the minimum opening that is necessary for releasing the geotextile the geocontainer is schemed to the dashed line. It is easy to calculate the area enclosed by this line and its circumfe-rence, since these line enclosed one rectangle with length (h^+h) and width \ i n the middle and two rectangular triangles with sides h^ and \tmQ at both sides of barge. The area (A) of this body can be written as:
Figure 15: Container just before dumping and ap-proximation for calculation. A is the area
of the container.
ht (2.22)
CO-383990m ^^^''"^^ ' ' ' '
the ckcumference (S) as:
(2.23)
During releasing of the geocontainer the deformation necessary to obtain the shape shown in Figure 15 leads to an increase of the necessary circumference when compared with the starting situation with bo and h equal zero and a shape that is composed of 2 triangles. Normally there is some slack in the geotextile and therefore there is a possibihty for deformation. Without friction
Figure 16: Example calculation for A=22 m ^ 80=22 and R=3.4 m showing the necessary ckcumference to release a geocontainer for different opening sizes.
in the container itself (slurry) and between the container and the barge, the container wiU deform until the slack i n the geotextile is used and the geotextile fits without any slack around the contents of the container. For every opening bo the equilibrium w i l l be determined by the circumference of the cross-section. As will be shown, there is a minimum ckcumference for every opening bo as a function of A and the angle 9 that is necessary to allow releasmg of the geotextile. Qualitatively it is clear from Figure 15 that for a small opening bo, h must be very large to get the required cross-sectional area and the geocontainer can only be released through such a smaU opening i f S is very large. The maximum S for releasing the geocontainer at a certain opening bo can be found by determining the maximum i n S as a function of h. At that
moment the condition dS/dh=0 must be satisfied. Using the equations for S and A it can be derived:
ds ^ ^>> (2.24) dhu sine &otane
and the maximum circumference is reached as:
h ^ 0 . 5 ( 1 ^ + 1 ) (2.25) &o cose
When the area of the geocontainer is Imown, equation (2.22) can be used with equation (2.25) to calculate h. Using this resuh in equation (2.23), the S necessary to release the geotextile for the given value of bo can be calculated. Figure 16 shows a resuh of such a calculation, using A=22 m ^ 60=22 degrees (the value of Q when the barge is closed) and a radius of 3.4 m between the opening of the barge and axis over which it opens, see also Appendix 1. The resuh shows clearly that a very long circumference is necessary for a smaU bo and that this decreases when the barge opens. The circumferences for a square, a circle and the two triangles that form the barge when closed are presented for comparison.
The resuhs of this method were compared with the resuUs that were obtained by Palmerton with the ScowDropSim program. The parameters used by Palmerton were: A=17.5 m ^ 00=36.4 degrees and R=5.9 m. For such a situation the method described here leads to an opening bo of 2.15 m before the container is released. Palmerton found a smaller opening of only 1.46 m. However, he simulates a very stretchable geotextile whh a stiffhess of 35 kN/m while he calculated a maxunum loading of 61 kN/m, which would correspond with a strain of more than
170%. I f on average the geotextile circumference is increased 30% due to the strain, then the calculation as presented here is in agreement with the calculation of Palmerton.
A rough estimate for the tension in the geotextile can also be made, by assuming a hydrostatic pressure in the container (using the volumetric weight of the slurry). With this assumption the tension in the geotextile can be written as:
T = 0.5b,(y-yjih,^h^ (2-26)
where:
Y3 : the volumetric weight of the slurry ( k N / m )
Y,^ : the volumetric weight of water ( k N / m ) The method described here leads to a h and h^ (see Figure 15) at critical opening of 5.66 and 1.5
m respectively. The slurry had a density of 16 k N / m l This leads with equation (2.26) to a tension T of 48 kN/m. This is lower than was found by Palmerton (61 kN/m) in his numerical simulation. The discrepancy is caused to a large extend by the discrepancy in critical opening (inserting the value of ^ found by Palmerton leads to a value of 51 kN/m for the tensile strength).
CO-383990/08 February 1999
2.8 Conclusions
Models to calculate the tension in the geotextile of a geocontainer during dumping ai-e stih rather crude. Different assumptions lead to quite a different range of values of the maximum tension as well as different phases that ai-e critical. Based on the present knowledge it seems reasonable to assume that the moment of first opening of the barge is critical for the tension in the geotextile. At that particular moment, the tensile stresses can be calculated quite easily. This is confffmed by
some of the experiments, but some others seem to show that maximum strain is found when the barge has opened further. However, no strain gauges were placed at the centre of the bottom of the container, where theoretically this maximum could be expected.
Using distinct element calculations, Palmerton [Palmerton 1996] has found that the strain in the geotextile, was close to the maximum value at the moment the opening starts, see Figure 20. This value was only exceeded by some cychc effects and the dynamic effects when the container left the barge and during impact.
Using the Leshchinsky model, but with the gravity force in the opposite direction then usual in this model (see Chapter 4), it is possible to predict the shape of the free hanging part of the geotextile. This is not the shape of a circle, hi addition tension can be calculated i f the width of the opening and the length of the free hanging part is known. However, this is mostly not the case.
The analytical calculation methods do not include dynamic effects, therefore the peaks i n the strain that occur during releasing and dumping of the container are not taken into account. These peaks i n the strain appear to be dominant in the case the container is filled with slurry without friction nor cohesion. In case the container is filled with sand, the influence of the impact on the strain i n the container appears to be of less importance [Fowler 1994].
Calculations based on friction and based on limited allowable deformation of the shape container due to the length of the circumference of the cross-section are presented, hi reality both these phenomena w i l l be present. To estimate the loading on the geotextile, i t is necessary that both calculations are made. The calculations based on friction will be determining when there is a large friction. The calculations based on limited allowable deformation of the shape of the container wiU be determining in case of a slurry and a limited friction between container and barge.
CO-383990/08 February 1999
3 Loading during impact
Impact on the bottom may be the major loading on the geotextile. It is therefore essential to have a calculation method available to estimate this loading. Some influences of the impact, the non-hydrostatic pressure distribution and the influence on the shape of the container wiU be discussed in the next chapter because they use the calculation method that is described there. In this
chapter, attention wiU be focused on the magnitude of the loading. To calculate the loading the dumping velocity must be estimated first. Therefore, the velocity of the falling container and the impact are dealt with in this chapter.
3.1 Dumping velocity
3.1.1 Theory
The position and velocity of a falling container is elaborated by [Adel 1996]. The governing differential equation can be written as:
VP f^=V{p-9^)8 -^A^p^Cy (3.1
where:
V : the volume of the container (m^) A j : the surface perpendicular to the flow (m^)
p = (l-n)Pg + nsp,^: the volumetric weight of the contents of the container (kg/m^)
n : the porosity (") s : the degree of saturation (-)
p„ : the volumetric weight of the grains (kg/m^) p^^ : the volumetric weight of the water (kg/m) V : the velocity of the geocontainer (m/s)
: the drag coefficient (-)
t : time (s) In these formula the parameter A^ and p are difficult to determine. A^ depends on the filling
grade of the container and the deformation that occurs before the container leaves the barge. As a first approximation a circular cross-section can be assumed, from which the diameter can be calculated as the cross-sectional area is known, or the width of the barge. With this procedure A^ wih be overestimated, leading to a velocity that is too low. However, as wiU be shown in the next paragraph result i n velocities that are in most cases in agreement with measurements, p depends heavily on the amount of air entrapped in the geocontainer. I f the geocontainer is very permeable p will increase change during dumping. I f the container is filled with fine sand or silt the air entrapped i n the material w i l l not be replaced by the water and the density of the grain air mixture has to be calculated.
The container is released at t=0 with a velocity v(0)=0. This leads to the solution:
v(0
= V, l - e x p 5-1+exp -2-2V P-Pw \ ^S<^D Pw 8 2VThe position of the container as a function of time reads:
zit) = fv(t)dt = V^T l . h l
1 +exp -2-i
= '^V _£_
Where:
z(t) : depth of container at time t v(t) : the velocity as a function of time v„ : the equilibrium velocity
X : the characteristic time ( i f t / T = l , then v(t)/v„=0.76)
(3.2) (3.3) (m) (m/s) (m/s) (s)
Using the following transformations:
(3.4)
where h^ is the depth where the container hits the bottom, a dimensionless relation between v' and h' can be derived:
^/ ^ 1 -exp(2/tO+exp(/;OVexp(2/iO-l exp(2/z')-exp(ft')Vexp(2/jO -1
(3.5)
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>
h'
Figure 17: Relation between v' and h'.
Den Adel proved with these equations, that for a typical container of 500 m^' it wiU take 22.5 m of water depth to reach 95% of the final falling velocity.
Palmerton found in his simulations (which w i l l be described more in detail in next paragraph) a maximum dumping velocity of 12 ft/s at 47 f t below the bottom of the split barge. This
corresponds to 3.65 m/s at 14.3 m water depth. The other parameters used for the container are mentioned in Table 1.
The situation described by Palmerton, (see Table 1) is simulated with the analytical formula's presented in this section. Using the maximum opening of the barge to calculate the height of the container and the foUowing parameters can be applied:
V / A =6.5 m, Cd=1, p=1300 kg/m^ p,,=1000 kg/m\ g=9.81 m/sl \=9.3 m, which lead to a velocity v at the bottom of 5.0 m/s. This is in reasonable good agreement with the measurements, where 4.6 m/s was found, and even better than the simulation of Palmerton. The water depth of
container wiien free fall started. Looldng at the results of Palmerton this was at 9.3 m Parameter valu
0
dimen-sion
above the bottom.
3.1,2 A C Z experiments 3.1,2 A C Z experiments opening velocity 0.06 m/s
barge 3.7 m Measurements on the dumping velocity have max opening 1.22 m also been reported by van Oord [Oord 1995] amplitude water level 5 s
period amplitude 1300 kg/m^ Den Adel [Adel 1996] has estimated the density container 1 deg. value A j from figures from [Oord 1995] and friction in soil 0 kPa found A^=75 m^. Using again Cj,=l the cohesion 10 deg. measured values at the bottom can be com-friction geotex./barge 1292 3
m pared with the calculated ones. The results Volume tube 53.6 m are presented in Table 2.
length of 1 - The calculated values are different from the geocontainer ones presented in [Adel 1996]. It appeared drag coefficient (C^) that there was a mistake in the original
calculations.
Table 2 shows that measured and calculated Table 1: Parameters used in distinct element y^j^^g reasonable agreement. The
calculation by Palmerton.
-15 -10 -5 0 5 10 15
X ( m )
Figure 18: Position of the container at various time steps during dumping. Based on ACZ measurements.
CO-383990/08 February 1999
calculated values being a somewhat higher than the measured values. It is likely that some air was entrapped i n the container. The calculated velocity is in agreement with the measured one when 10, 17 and 9% air was entrapped for the tests 1, 2 and 3 respectively. This also means that when using the first test as an example 10% air inclusion leads to a reduction of the dumping velocity from 5.2 to 4.4 m/s, a reduction of 15%. Since the kinetic energy is proportional to the square of the velocity, the reduction in kinetic energy is 28%.
Test h P V V
[ml [kg/m^J [m^] [m/s] [m/s]
1 14.2 1600 170 4.4 5.2
2 9.8 1600 130 3.3 4.5
3 12.7 1500 135 3.6 4.2
Table 2: Measured (v^,,^) and calculated (v,^,) velocities at the bottom. Measurements from [Oord 1995].
time (s)
Figure 19: Position of geocontainer (S in plot) and pore pressures (P) as measured during experiments ftom ACZ.
Based on the report [Oord, 1995], the experiments have been analysed. Experiment 2 was most suitable because this experiment was the only one with instrumentation and without failure of the geocontainer. The data of the experiment have been digitised and from that the position of the container during dumping is calculated. The position of the container at various time steps is shown i n Figure 18. In this figure, the same scale was chosen for the horizontal and vertical axis. It is clear that the container did not faU in a horizontal position. As one side hhs the bottom a more horizontal position occurs. The depth is determined by numerical integration of the given velocity of the container. The problem is that the depth as calculated does not agree with the actual dumping depth. The calculated depth is higher. A possible reason for that is rotation of the container during dumping. The depth was measured with steel wires, connected at the top of the container. At the end of the dumping, the container was placed up side down. When the container rotates, the wires wiU be puUed around the container, leading to a larger measured depth than in reality. This phenomenon becomes clear when the measured position is compared with the measured pressure, see Figure 19. In this figure the Y-axis at left and right side are chosen in a way that the lines of pressure should coincide with the lines of displacement i f only hydrostatic pressures were present. Now it appears that after dumping the measured increase in hydrostatic pressure is corresponding with an increase in depth of 8 m, while a dumping depth of nearly 16 m is measured. A small part of this discrepancy is caused by the decrease in draught of the spht barge, but according to the report this is only 0.9 m.
The results described above means that the actual average velocity of the container is roughly only halve the velocity that was measured. The exact velocity is not known, since the rotation during dumping is not known. Due to this, it is tricky to compare measured velocities with calculated ones. The increase i n pressure with time (Figure 19) suggests larger maximum velocities than those measured with wires.
Assuming a maximum velocity that is only half the measured velocity must be 4, or the density must be lower than presented in Table 2. Both options are not very reaUstic. A Cp of 1 is, according to theory, already a rather high value and using = 1 and adjusting the density to get comparable values for the measured and calculated velocity leads to very low densities. These values are not reaUstic because even dry sand i n a loose state has a higher density. Therefore it has to be concluded that the resuUs up to now are inconclusive.
Other reasons for the difference between calculations and measurements can be:
1. In reahty the dumping height is lower, see e.g. the lower left plot in Figure 20, although some corrections are made to make an estimate as good as possible.
2. Probably the height of the container is less than the value used in the formulas presented by Den Adel.
4. The value of the friction coefficient is taken too low. I t is difficult to estimate the friction coefficient, because the falling container has a very high Reynolds number (1.5.10') and the shape of the container is not known accurately. However, according to theory the
CO-383990/08 February 1999
friction coefficient is expected to be lower for these high Reynolds numbers.
From these results, it can be concluded that it is still difficult to come to an accurate predic-tion of the faUing velocity. The method presented seems to result in too high values for the velocity. More measurements are necessary to come to a more accurate prediction of the falling velocity.
It is also not straightforward to
determine the dumping velocity in a test. This is mostly done by changes in pore pressure measured on the container. This is a sound method as long as the container falls parallel to the bottom and does not rotate. However, both non parallel S . O 10.0 15.0 20.0 2 5 . 0 30.0 35.0 40.0 45.0 5 0 . 0 55.0
TIHE - s e c
Figure 21: Strains in geotextile calculated by distinct ele-ment program during opening barge (2-45 s) and impact (48 s)
falling and rotation do occur in practice.
3.2 Stress and strain in geotextiele during impact geocontainer filled with slurry
3,2.1 Calculations of Palmerton
Detailed numerical calculations on the process of releasing a geocontainer from a barge and the impact on the subsoil were performed by Palmerton [Palmerton, 1996]. He uses a distinct element method. From [Palmerton, 1997] it became clear, that a special program ScowDropSim was developed to simulate the dropping.
The slurry in the container is divided into a large number of crrcular discs (a 2-dimensional approach is used). In the calculations the interaction between the adjacent discs and between the discs, the suiTounding geotextile and the barge is described. A t the moment of impact also the interaction with the bottom is described.
CO-383990/08 February 1999
geocontainer, See Table 1. Only a very low friction angle (1 degree) and no cohesion was used. A friction angle of 10 degrees was used for the friction between the geotextile and the split barge waUs. The dumping process as simulated in the calculations is visuahsed in Figure 20. Maximum strain in the geotextile was found during impact at the bottom, see Figure 21, being nearly 5%.
The distinct element calculations are quite complicated and require a huge amount of calculation time. It is therefore of interest to compare these resuhs with the results of more simple models in order to investigate whether or not these more simple models can be used as a design method. A similar comparison was aheady done for the dumping velocity (see Section 3.1). Here it will be evaluated for the strain with help of analytical calculations as described in Section 3.2.2. The maximum strain during dumping is a function of the circumference of the geocontainer. I f for the given cross-section the circumferential length of the geotextile is longer, then the maximum strain decreases.
A peak strain during dumping of 4.8% was found in a first simulation. Furthermore, it was found that increasing the circumferential length of the geotextile by adding 4.5 m (15 feet) at the lower end of the geocontainer leads to a reduction of the peak strain to 2.6%.
Various simulations with Palmerton's computer code are described in [Palmerton, 1997]. This article shows the influence of intemal friction in the fill material of the container and the friction between container and split barge on the shape of and stresses in the container during dumping. Addhionally the influence of a sloping bottom and a water flow are investigated. The paper also presents some more details about the computer code ScowDropSim that is used.
The fact that the computer code is specially developed for this application means that the code is optimized for this problem. However, it also means that it will be difficuh to get additional output and that developments depend on one person.
A l l calculations show a considerable increase in the cross-sectional area of the container when it leaves the barge. This area decreases again at the moment the container hits the bottom. It seems as i f the permeability of the geotextile and the soil in the container is not taken into account properly. The limitations of the permeability of the geotextile and the soil in the container generally w i h prevent such large volume variations. Therefore, the influence of the permeability on the volume of the geocontainer has to be included in the model.
The influence of friction between container and barge and the intemal friction on the stresses in the geotextile is investigated in example calculations. However, the resuhs do not allow a firm conclusion. As it is stated by Palmerton: " . . i t is useful to show that the membrane tension response as the GFC (GeoFabric Container) goes through the splh barge exit and bottom impact process is quhe complicated. It is very difficult to identify definitive trends between the chosen frictional parameters and the tension response, although it appears that lower (j) values may lead to less membrane tension at bottom impact. However, the example with 5=(t)=0° shows a rather
high tension value at impact. This is probably due to that this GFC fell through the water column in a much slenderer (and taller) configuration: when impact occurred, the height of the sediment was greater than in other cases. There are too many variables (6,(1) and the ocean bottom slope angle) to infer trends on the tension response with the limited information".
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3.2.2 Analytical calculations
Den Adel [Adel 1996] also presents a formula to calculate the maximum strain during impact. This formula is based on the assumption of purely elastic deformation. The kinetic energy is converted completely to elastic energy i n the geotextile. No energy dissipation by deformation of the soil or slurry in the container or of the subsoil beneath the container is taken into account. The formula reads:
p A vL% E S (3.e
Where:
(kg/m^)
P : the density of the slurry (kg/m^)
A : the cross-sectional area of the geotextile
V b o t t : the velocity at the bottom
(m)
t g : the thickness of the geotextile (m)
E : Young's modulus (Pa)
S : the circumference of the geotextile (m)
E : the peak strain in the geotextile (-)
Using Equation (3.6), the parameters of Table 1 and using the velocity of 3.6 m/s as found in the simulation of Palmerton, a peak shain of 10% was found. This is a much higher peak strain than the 4.8% found by Palmerton in his simulations. Assuming no dissipation at aU, Equation (3.6) clearly overestimates the maximum loading on the geotextile even for slurry.
In this formula, an increase in length of the geotextile around the container wiU lead to a
decrease in the peak strain. However, there is only a smaU influence of this length (the strain e is proportional to 1/V(S), where S is the length). In reahty, the influence wiU be larger because an increase in the circumference of the geotextile wiU lead to more deformation of the container and as a resuh also more dissipation is possible.
As a furst estimate to calculate the influence of friction, the contribution of the friction between the geotextile and subsoil is calculated. Just as the geotextile at the bottom of the geocontainer is pressed on the subsoil, during the impact, it w i l l also be stretched due to the increase in tension. This wiU lead to a friction loss. Equation (3.6) is an energy conservation equation. Therefore, the friction loss has to be added to the right hand side of this formula, resulting in:
l p A v ' = h,ESe'^PÖB' (3.7) 2 ^ 2 *
where:
B : half of the width of the geocontainer that touches the subsoil during impact. (m)
P : the pressure on the bottom during impact (kPa) 6 : the friction coefficient between the geotextile and the subsoil (-)
