Design method for geotextile tubes considering strain –

Formulation and verification by laboratory tests using photogrammetry

S. Cantré*, F. Saathoff

Chair of Geotechnics and Coastal Engineering, University of Rostock,

Justus-von-Liebig-Weg 6, 18059 Rostock, Germany

Abstract

Geotextile tubes are usually made of at least one layer of high-strength woven geotextiles. However, if only

highly elastic materials are used, experience shows –comprehensibly– that the designed geometry and stresses,

derived from standard formulations or special computer software, both using small strain membrane theory,

essentially differ from reality. Therefore, an extended formulation, considering large strains, was developed

within the scope of a study on the structural and hydraulic design of geosynthetic dewatering tubes at the

University of Rostock. The solution was evaluated using a sensitivity analysis and verified in laboratory

experiments, where small-scale tubes were surveyed using a low-budget, high-precision photogrammetric

measurement technique. The new design method proved to produce good results. It should be used if the

construction is indeed a long tube and if the limit strain of the geotextile tubes exceeds 10% strain. Finally, the

results were compared to the existing methods for the structural design of geosynthetic applications, adding to

the discussion about attenuation factors in geotextile tube dewatering projects. For short-term applications

without refilling of the partly dewatered tubes, the product of attenuation and safety factors will usually not

exceed a value of two.

Keywords: Geotextile tubes, dimensioning, strains, laboratory testing, low-cost photogrammetry

1. Introduction

Geosynthetic containers have been increasingly used in hydraulic engineering (Alvarez et al. 2007, Shin and Oh

2007, Saathoff et al. 2007, Yan and Chu 2010) and sludge dewatering (Koerner and Koerner 2006,

Muthukumaran and Ilamparuthi 2006) projects during the past two decades. They come in a large variety of

shapes and sizes, starting from simple sandbags to large tubes of more than 100 m in length.

The existing mechanical dimensioning methods for geotextiles used as geotextile tubes are based on the

plane strain membrane theory (Liu 1981, Namias 1985, Leshchinsky et al. 1996, Plaut and Suherman 1998,

Ghavanloo and Daneshmand 2009). The linear membrane theory is based on Hook’s linear elastic material law

and a linear geometric deformation behaviour, generally applying to small deformations. If large deformations

are considered, the requirement of a linear constitutive law has to be dismissed. Therefore there is a need to

develop a design method for such materials.

Most geotextiles have non-linear material characteristics. It is known, that they possess thermo-visco-elasto-

plastic properties, which depend on direction and normal stress (Perkins 2000). These properties are usually

ignored in dimensioning processes using small strain solutions, while they have to be considered for large

strains. Therefore, an adequate solution needs to be formulated.

In this paper, the calculation methods of Namias (1985) and Plaut and Suherman (1998) are extended to

incorporate elastic strains. The solution was validated in laboratory experiments. The presented calculation

method is limited to tubes on rigid ground, which are filled on site. The plain strain state is still assumed.

However, for the plane strain state to be valid, geotextile tubes need to be long tubes, which is why a special

length-to-width ratio has been defined.

*Corresponding author. Tel.: +49 (0)381 4983704; fax: +49 (0)381 4983702

E-mail addresses: stefan.cantre@uni-rostock.de (Dr. S. Cantré), fokke.saathoff@uni-rostock.de (Prof. F. Saathoff)

2. Structural analysis of geotextile tubes

The design of hydraulically filled geotextile tubes is theoretically based on the surface tension of a water drop.

Calculation methods were originally developed to design membrane containers for both the storage (Timoshenko

1940, Namias 1985) and the transport of fluids (Wang 1984, Szyszkowski and Glockner 1987, Zhao 1995).

Based on the earliest publications on this topic, a design method for geotextile tubes was derived in the 1970s

(Liu 1981). This approach has been developed constantly, particularly regarding different loading conditions

(Plaut and Suherman 1998, Plaut and Klusman 1999), and eventually even finite element methods were applied

to analyse stacked tubes and three-dimensional systems (Seay and Plaut 1998, Huong 2001, Freeman 2002,

Cantré 2002, Kim 2003, Kim et al. 2004, Zhang and Tan 2006).

During the hydraulic tube filling process the filling material can be seen as an ideal fluid with the density

> 1g/cm3. During dewatering and consolidation the filling material solidifies, which may lead to an influence

in friction between filling material and geosynthetic shell. The relatively thin geosynthetic shell may be seen as a

membrane of equal density in a mathematical model. Regarding geotextile tubes as cylindrical membrane

structures in plane strain, the axial forces and the strains in both in-plane directions can be determined

considering Young’s modulus and Poisson’s ratio.

For large deformations, existing non-linearities need to be considered. For this, simple iterative methods can

be used or the differential equations for large deformations can be solved with boundary methods (Chen and

Zheng 2003) or finite element methods (Ibrahimbegovic and Gruttmann 1993).

In this paper the systems are limited to tubes resting on rigid ground which are filled on site. The maximum

membrane forces then occur during the filling process (Cantré 2002, Zhang and Tan 2006), and both the friction

forces and the solidification of the filling materials during dewatering can be ignored in the static analysis

(constant membrane forces). Model simplifications cause errors, which can be reduced if fine-grained filling

materials with low settling velocities are assumed. Then, the filling material can be considered a fluid over a

longer period of time.

2.1 Basic design method after Plaut and Suherman

The design method was developed using the solution of Plaut and Suherman (1998). For detailed information on

the basic solution, see the original publication. Only the governing equations are repeated here for a better

understanding. Fig. 1 shows the nomenclature of the geometry and forces at a differential membrane element.

The governing equations to determine the geometry and forces in the tube’s cross-section are the following:

( )bot atm

dT P P Y

dS

[1]

cos

dX

dS ; sin

dY

dS ; 0

dT

dS [2] [3] [4]

where T = tensile normal stress [kN/m], = tangential angle with respect to the

horizontal line [°], S = circumferential coordinate [m], Pbot = pressure at the bottom

of the tube [kPa], Patm = atmospheric pressure [kPa], = unit weight of the filling

material [kN/m³], Y = vertical coordinate (height) [m], X = horizontal coordinate

[m].

Fig.1: Cross-section and forces at the differential element after Plaut and Suherman (1998)

All values describing the geometry and membrane forces of the filled tube can be derived from the solution of

these differential equations. All values are defined as dimensionless reduced quantities in the X-Y plane referred

to the circumference C and – for stresses and pressures only – the density . These constants are also used as

boundary conditions. All dimensionless values are written in lower-case characters.

An integration parameter k was derived by Namias (1985) to solve the elliptic integrals E and K which result

from the rearrangement of the governing equations. This parameter depends on the unknown membrane force t

and can be determined using equation [5].

2 ( ) ( ) 1 0p E k K k [5]

where p = dimensionless pressure [ ], K(k) = complete elliptic integral of the first

kind, E(k) = complete elliptic integral of the second kind, k = integration parameter

[ ] (for more information see Plaut and Suherman 1998).

Therefore a third boundary condition is needed, e.g. the pressure at the top of the tube (Ptop) or the planned tube

height (H).

2.2 Recent design practice and problems

For the design process of geotextile tubes filled ashore on rigid ground, two commercial software products can

be used: GeoCoPS 3.0 (Leshchinsky and Leshchinsky 1996, Adama, 2009) and the combination of SOFFTWIN

and SOFFTCON (Palmerton 1998a/b). Because of the simplifications of the long tube used in these programs

(membrane theory and plane strain state), the ends of the tubes have to be considered separately.

Unfortunately the terms “geosynthetic tube” and “geotextile tube” are used for a large range of geosynthetic

container shapes. If a geosynthetic container with a small length-to-width ratio is called a tube, there will be

errors during the dimensioning process. Using the dimensioning methods presented here, the considerable

influence of the tube ends on the geometry and stresses are ignored. The mechanical influence of the ends of a

“short tube” together with an anisotropic geotextile, however, may even cause axial strains that exceed those in

circumferential direction (see Okamura et al. 2006).

3. Structural analysis considering strains

3.1 Theoretical background

High-strength geotextiles with low breaking elongation can be considered using the existing design methods.

Simple membrane theory describes the problem relatively well. Observations in projects using nonwovens with

large breaking elongation showed, however, that these geotextiles do not correspond to the computed results

very well, neither with respect to the designed cross-section nor the (elastic) strains. Therefore, geosynthetic

constitutive laws need to be included in the calculations. To calculate the tube geometry and the membrane

stresses within the tube, the method of Plaut and Suherman (1998) is extended by a nonlinear-elastic material

behaviour of the geosynthetics. For this, the small strain, large deformation theory was used, deliberately

ignoring visco-plastic influences and temperature-dependent properties.

With circumferential strains permitted, the circumference –previously assumed constant– changes, as do the

dimensionless values (including the tangential membrane force). The fit of circumference and tension force is

solved iteratively. First the membrane force T0 is computed using a predetermined circumference L0 (equation

[6]). The length modification using the constitutive law follows and then the new circumference L1 is calculated

(equation [7]). The incremental force between two iterations is used as the stop criterion.

2

0T t C [6]

0 1i iC C [7]

where T = membrane force [kN/m], t = non-dimensional membrane force [ ]; C0 = initial

circumference [m]; = density of the filling material [g/cm³], i = strain at interval i [%], i =

iteration index.

It is assumed that strains only appear along the “free” circumference C’ = C – B’, being the part of the tube’s

surface with no contact to the ground (although the consideration of strains along C is also possible). Only elastic

deformations are considered and the strains are considered to be constant (equation [9]), resulting from the

assumption of a constant circumferential stress. The governing differential equations [1] to [4] are extended by

equations [8] and [9].

2

0 0

1dS dC dC C

dT dT dT dE

[8]

0

d

dS

[9]

where = Poisson ratio [ ] and E = Young’s modulus [kN/m²].

Finally, equation [7] can be written as

0 0 1 0 1' 'i i i i iC C C B C C . [10]

where Ci = cross section in iteration step i [m]; C0 = circumference, unloaded [m]; B’i-1 = contact

width with the ground from previous iteration step [m]; C’i-1 = free circumference from previous

iteration step [m].

As a standard method to consider nonlinear-elastic material behaviour, an incremental approach was chosen

based on Kmiecik et al. (1993). Within each load increment the material behaviour is assumed to be linear-

elastic. The implementation of this method is described below.

Fig. 2: Stress-strain diagram and discretized points; list for computation

3.2 Programming

The solution was programmed using a standard programming language (MS Visual Basic 6.0). The equations of

Plaut and Suherman for a single, unloaded tube were implemented using three iteration methods:

- Solving the elliptic integrals of the linear-elastic membrane problem.

- Iterative determination of the stress-strain equilibrium.

- Incremental calculation of the material behaviour.

Since the complexity of the problem is of medium proportions and because of the high quality of recent

consumer PCs, simple numerical approaches can be used which lead to reasonable calculation times. After

inserting the initial boundary values, the other initial values are calculated. A secant method (regula falsi, Kerner

1987) was applied to iteratively determine the integration parameter k (solution from elliptic integrals E, K). The

method always converges and it can be quite fast if the start values are well chosen. Here, k is defined within the

open interval ]0,1[. For small boundary values of P and H, k approaches 1; otherwise, k approaches 0. The use of

a single initial estimation for k usually leads to a large computing time, especially if the chosen initial value

differs considerably from the solution. Therefore several explicit values were calculated and used as interval

boundaries to keep the computing time below ½ second (Pentium 4, 3.06 GHz, 512 MB RAM). The iteration

method leads to an accuracy level in the range of 10-5

k within the non-dimensional pressure interval ptop = [10-

5… 100]. The four elliptic integrals of the first and second kind are solved using Simpson’s rule. 250 net points

are needed to confirm a sufficient accuracy (10-10

k).

Then the strain analysis is performed. The tangential tensile force (t and T0) and the strain can be computed

directly from k (Plaut and Suherman 1998). During each iteration step the circumference changes according to

the strain. As a stop criterion the incremental force was chosen (ti - ti-1 < 10-5

, see Fig. 3). Linear elastic

geotextiles are considered using their Young’s modulus E and thickness. Nonlinear-elastic geotextile properties

are described incrementally based on a stress-strain relationship derived from tensile tests (e.g. a list of stress-

strain pairs as input, Fig. 2). In the presented solution up to 50 increments of constant Ei are used. The actual

circumference is computed iteratively using the basic equation [10]. For any number of linear intervals of the

stress-strain curve the new circumference is computed using equation [11].

0 1 1

1

' 'm

i i j i i

j

C C C C

[11]

where 1 2

01- ; 1... , 0j j

j

j

T Tj m T

E

(strain of bulk linear T--curve),

2

0

1

1- ; 1... , 0i mi

m

T Ti n T

E

(strain from final interval), j = control index for bulk

linear sections, and m = iteration index for strain sections in each iteration step i.

The bulk linear Young’s modulus is computed using equation [12].

1

1

j j

j

j j

T TE

[12]

The algorithm implemented in the program is shown in Fig. 3.

Initial values

L0, , and Ptop or H

Calculate first-stage values,

dimensionless

with respect to L0

Calculate the integration

parameter k (using the regula

falsi) until deviation < 10-12

Solve elliptic integrals with

Simpson‘s rule (N=250)

Calculate the tension force t

ti – ti-1< 10-5

Use variables and

constants from

data base

Elasticity properties

input manually or load from file

Calculate strains and the new

circumference in the plane

strain state

Calculate results,

display results

yes

no

Fig. 3: Computation algorithm

3.3 Sensitivity analysis

Based on the parameters circumference (C0), strain (), tangential tension (T), pressure (P), and height (H), the

influence of small parameter variations on the computed results were evaluated. The three initial parameters

Young’s modulus (E), density (), and circumference (C0) were varied ceteris paribus for different boundary

conditions, defined by default values of the pressure, or height. The basic settings for the parameter analysis

were chosen as follows:

- Young’s modulus E [kN/m²] 105

- Thickness d [mm] 1

- Poisson ratio [ ] 0.5

- Initial circumference C0 [m] 1 … 30

- Initial density Susp. [g/cm³] 1

- Pressure Ptop [kPa] 10

- Planned height H [m] 0.75 D0.

The variation of initial values is given in Table 1. The values were chosen in the range of practical applications.

The initial values were varied by 0.1%, 1% and 10% and their influence on the computed values was determined.

Table 1: Variation of values for the sensitivity analysis

Variable constant E for L0 = 1 E for L0 = 30 0 = 1 0 = 30 L0

Pressure Ptop 103 - 109 5*104 - 1010 0.8 – 2.0 0.8 – 2.0 1 - 37

Height 103 - 109 5*104 - 1010 0.8 – 2.0 0.8 – 2.0 1 - 37

As an example, the influence of circumferential deviations during calculation of the tension force is presented in

Fig. 4 for both constant pressure and height. The deviations of the circumference at constant pressure affect the

tension forces disproportionately, while the proportionality of the deviations at a given height strongly depends

on the chosen circumference. The larger the circumference, the smaller are the deviation consequences with

respect to C0. The dependency progression of circumference and pressure for a given height is of particular

interest. If both elasticity and pressure are given constant, the geometrical and force equilibrium for a defined

height can only be achieved after pressure progression, due to material expansion and an increase in the

circumference.

The sensitivity analysis shows that the program provides realistic results. In the three design cases studied

with respect to Ptop and H, deviations of the circumference have the largest disproportionate effect. In the case of

a given Ptop, the elastic modulus also plays a major role; this causes an extreme enlargement for elastic tubes,

because a tube with a much larger circumference is filled. However, with respect to H the density of the

suspension has a big influence on forces and strains. Table 2 summarizes the proportionalities for the constant

height H.

Table 2: Deviation of the calculation results due to the deviation of initial values (H = L0/*0,75)

Calculation Results

Initial Values F Ptop C T

E L0 = 1 m (fix) ~1 < 0.1a < 0.4a < 0.1a < 0.2a

L0 = 30 m (fix) < 1b < 0.2a < 1a < 0.2a < 0.2a

L0 = 1 m (fix) ~1 < 0.002b ~1 < 0.003b ~1

L0 = 30 m (fix) < 0.6c ~0.13 < 0.25c ~0.2 ~0.95

L0 L0 = variable < 2.2c < 0.6b < 4c < 1c < 2c

astrongly decreasing for decreasing elasticity

bslightly increasing for increasing initial values

cslightly decreasing for increasing initial values

(1 = proportionate, < 1 = subproportionate, > 1 = disproportionate)

(Bold: critical; bold&italic: critical only within a small range)

Fig. 4: Tensile force versus circumference (left: Ptop = constant, right: H = L0/*0.75)

4. Comparison with experimental data

An exact match of experimentally determined and numerically computed results is hardly possible. The

deviations of the parameters affecting the results are usually too large on both sides. Moreover, it is difficult to

decide which of the two methods describes the actual state more accurately (Monschau 1996). However, if the

results match well, both methods are usually assumed to be of high quality.

4.1 Experimental setup

The experimental data was derived in the laboratory using small-scale tubes (length 200 cm, diameter 20 cm).

Four different tube materials were used to represent the properties of different geotextiles:

(1) A non-permeable LDPE tube representing rigid geosynthetics (impermeable reference).

(2) A non-permeable latex tube to represent highly elastic geosynthetics (impermeable reference).

(3) A thin but strong woven textile (W2) representing rigid geotextiles.

(4) A thin flexible nonwoven (NW2) representing elastic nonwoven geotextiles.

The LDPE and latex tubes were filled with plain water while W2 and NW2 tubes were filled with a

soil/water mixture. Due to the small model size, all tube materials were very thin, which is why a contact-free

measurement system was chosen to measure the cross-sectional geometry and strains. The highly accurate low-

budget photogrammetric system (Fig. 5) included four digital cameras (1) to capture approximately half of a

tube’s (3) circumference during filling and dewatering while resting on a plane table (4). The photogrammetric

evaluation was performed using the bundle-block analysis software AUSTRALIS 6.0 while the actual strain

measurement based on the derived surface point data was programmed separately. A detailed description of the

measurement and evaluation system is presented in Thomas and Cantré (2009).

Fig. 5: Experimental Setup for the deformation analysis of (non-) permeable dewatering tubes in laboratory scale after

Thomas and Cantré (2009). 1: model tube; 2. reference coordinates; 3. plane table; 4. cameras.

Similar photogrammetric systems were used to measure strains on large NASA balloons (Welch et al. 2005) and

membrane roof structures (Lin et al. 2008). In the latter study, the accuracy of the photogrammetric network was

estimated close to ± 1.4 mm with a camera-to-object distance of 10 m. In the present study the camera-to-object

distance was approximately 1.5 m and the object accuracy was determined to be 0.025 mm, which is

approximately ten times more precise. This accuracy was necessary to detect strain differences of 1% strain

between every two measuring points (marker distance 40 mm).

Fig. 6: Cross sectional geometry: Calculated (with and without strain) and measured

4.2 Comparison of geometry measurements and calculations

The measured and calculated cross-sectional geometries match very well, especially in those experiments with

particularly accurate pressure values and elastic properties. A total number of 2285 diagrams were created using

a custom routine to compare the measured and calculated geometry (Fig. 6). The tube height H was chosen as a

reference value to describe the match of measured and calculated data. For all experiments both the absolute

deviation of the measured and computed height and their standard deviation were determined (Fig. 7).

Fig. 7: Average percentage deviations of the measured and calculated height

The best fit was derived during the initial filling stage. For NW2 the calculation overestimates the height only at

very high internal pressures. The largest average deviations were found for the highly elastic Latex material.

Here, particularly in the range of small internal pressures, the calculation overestimates the tube height by up to

7% (Fig. 7), although the tensile properties had been determined with the smallest deviation among the four

materials used.

Some of the deviations between measured and computed values can be explained with the use of a constant

Poisson ratio because for large deformations, the Poisson ratio is usually not constant. This may be considered

within the program algorithm; however, a strain-dependent Poisson ratio is usually not provided by the

geosynthetics manufacturers. In most cases, a mean value within the region of the expected strains should

comply.

4.3 Comparing strain measurements and calculations

The strains were evaluated according to different boundary conditions. To compare the measured and calculated

values, the average strain of each pressure step (mean value of all cross-sections) was plotted against the

pressure at the tube bottom. During the initial filling stage the average strain of the LDPE film experiments

deviate around +/- 0.3% strain (Fig. 8a). The deviations occur in the elastic region up to Pbot = 6 kPa. There is a

good match between computed and measured strains. The nonwoven NW2 showed a deviation of up to 3%

strain. The deviation decreases with increasing strains. In the region of Pbot ≈ 5 kPa, the occurring strains are

underestimated by the calculation algorithm. For Pbot > 7.5 kPa, however, the congruity is very good (Fig. 8b).

The deviation at low internal pressures may be due to the constant Poisson ratio. In reality, the influence of

lateral strain with small loads is considerably lower.

Fig. 8: Strains calculated and measured, LDPE and NW2

Fig. 9: Absolute strain deviation meas – cal for all materials

In Fig. 9 the absolute deviations of measured and computed strains are compared. The figure shows that the rigid

materials are reproduced well by the plane strain state and that the influence of the assumed constitutive

equations on the computed strains is very strong, at least for the NW2 and Latex materials. While the relative

deviations are very large for NW2, they are comparably small in the Latex material despite the large absolute

strain values. As is known from the sensitivity analysis, a 3% strain deviation has only little influence on the rest

of the computed magnitudes. Thus the dimensioning method can be considered very accurate despite the

deviations described.

5. Aspects for the structural design considering strains

5.1 Current design concept

The current design concept to determine the required tensile strength of geotextile tubes in Europe is based on

the limit state concept of the Eurocode (EC1 Actions on structures, EC7 Geotechnical design). In Germany, the

design of geosynthetic structures in ground engineering is implemented through EBGEO (2009), where the

acceptable tensile strength TR,D is determined by dividing the short-term strength by attenuation factors A1…4,

Adyn, Aadd (for additional influences), and a safety factor R (equation [13]).

,

,

1 2 3 4

R k

R D

R dyn add

TT

A A A A A A

[13]

For tube projects, the design tensile force is usually determined using a membrane approach, often by using one

of the computer programs GeoCoPS or SOFFTWIN (Adama, 2009, Palmerton, 1998a) and then applying the

above safety concept.

5.2 About the consideration of the long-term tensile strength in dewatering projects

There is a frequent discussion regarding whether the long-term tensile strength is necessary in the design of

geotextile tubes for dewatering purposes. Because of the dewatering process, the confined volume and thus the

tensile forces in the geosynthetic may reduce quickly. The following considerations add to the discussion.

If the filling material dewaters quickly and the geosynthetic filter is highly permeable, the filling-pressure-

induced stresses in the tube decrease very quickly. If the tube is only filled once, the influences of creep and both

chemical and biological impacts on the stability can be ignored. For highly permeable filling materials there is

usually no need for repeated filling, because the quick dewatering process leads to a filling ratio close to capacity

during the initial filling stage. Therefore, the design strength may be chosen close to the short-term strength.

However, if the tubes are sewn together, the seam strength is the limiting value. In this context, the authors hold

the opinion that, even if manufacturers propose better values, the design seam strength should be limited to 75%

of the minimal short-term geosynthetic strength. Using typical manufacturer values and the above explanations,

this may lead to an overall attenuation factor of < 2.

This process is different for very fine-grained materials that dewater with extensive filter cake formation or

that reduce the permeability of the geotextile through clogging and blocking phenomena. Table 3 contains an

example of the tensile stress reduction during the first four hours of the dewatering process with a fine-grained,

organic dredged material from Rostock, Germany (SM) and a nonwoven geosynthetic (NW1, O90 = 80 µm,

kv = 60 mm/s). For the example calculation a tube with a circumference of 10 m was assumed. The dewatering

data was derived from a pressure filtration experiment (Cantré, 2008). Two configurations were assumed: a 90%

filling of the tube (filling ratio) and a maximum filling height of 0.75 D (75% of the theoretical diameter).

Because of the low filtration velocity, the internal pressure needs several hours to reduce to a state with a

significant membrane stress reduction. However, this process is typically much faster than the loss of

geosynthetic strength caused by creep or degradation processes.

A refilling of the tubes can be useful if fine-grained materials with high initial water contents are dewatered.

Then the durability factors A1 and A4 should be considered. However, these factors may be reduced in

coordination with the geosynthetics manufacturer, because in dewatering projects the durability only refers to

several weeks or months, instead of several decades. Even for a permanent use of the tubes as a wrapping of

contaminated materials, creep and degradation processes do not play a major role, because the tension forces

inside the geosynthetic remain comparably small after dewatering. Finally, a design strength can be determined

that is also considerably smaller than the geosynthetic long-term strength.

Table 3: Example for the change of tension force by pressure reduction – results from pressure filtration tests

Case 1: L0 = 10 m; SM NW1, 50 kPa, 5 liters; filling ratio 90% (H = 0.68 D)

Time [h] v [cm/h] Q [m²/h] TC [kN/m] Dev. TC [%] F [%]

0 0 19.5 0 90

1 0.4 4E-2 18.7 -4.1 89.5

2 0.3 3E-2 18.2 -6.5 89.2

3 0.5 2.5E-2 17.7 -9.2 88.9

4

0.2 2E-2 17.4 -10.8 88.7

Case 2: L0 = 10 m; SM NW1, 50 kPa, 5 liters; H = 0.75 D (F = 94%)

Time [h] v [cm/h] Q [m²/h] TC [kN/m] Dev. TC [%] H [m]

0 0 29.0 0 10/*0,75

1 0.4 4E-2 27.5 -5.2 2.361

2 0.3 3E-2 26.5 -8.7 2.342

3 0.25 2.5E-2 25.7 -11.4 2.326

4 0.2 2E-2 25.1 -13.6 2.313

5.3 Considering longitudinal seams

With the strain measurements and calculations, it was proved that both the largest strains and the stresses occur

at the lower part of the tube where the largest curvature is located. For the first filling stage the strain differences

are, however, only in the range of a few per cent, which is unproblematic. For repeated filling, the sides of the

tube are stressed further, since the bending stiffness of the dewatered filling material has to be overcome. This

increases the strain differences between maximum and medium strain considerably. Therefore, seams and other

flaws should not be positioned at the sides of the tube. It is proposed to position the longitudinal seams – if any

exist – at the bottom so that the friction or adhesion (in the case of a membrane layer underneath) between the

geotextile and the ground reduce the membrane stress. Analogous considerations were made during the planning

of the artificial reef in Narrowneck, Australia (Saathoff et al. 2007). Should the seam be positioned at one side of

the tube, an additional safety factor should be used for the refilling stage. This factor needs to be developed in

the future within an analysis of the influence of the bending stiffness of different filling materials.

5.4 Design for large strains within the geotextile

Highly elastic geosynthetics can be designed using the methods explained above. However, only the tube’s

cross-section is considered. Based on practical experience, Lawson (2006) suggests adding a general strain value

of 11% during the design of geotextile tubes. This, however, is a very inexact method and it may lead to an

incorrect design – see the sensitivity analysis above. A general strain value of 11% would lead to a 16% increase

in the cross-sectional area at a planned height of 0.75 D. This may be an important planning parameter when

optimizing the size and number of tubes needed for a particular project.

At least some values of the geotextiles’ stress-strain relation are usually known, so the occurring strain can be

calculated with the newly developed method. The Poisson ratio, needed for calculations in the plane strain state,

needs to be determined or at least well estimated. If nonwovens are used as tubes for dewatering projects instead

of high-strength wovens, the predetermination of occurring strains is inevitable.

A drawback of the proposed design method is the limitation to the plane strain state. While modelling

succeeds very well for small-scale tubes, for continuous tubes with large diameters and biaxial elasticity,

considerable longitudinal strains and thus buckling phenomena can be foreseen. For isotropic geosynthetics,

however, the method is sufficiently exact.

5.5 Selecting an appropriate design method

To choose an appropriate design method, the most important question is whether the construction is a (long) tube

at all. Only in the case of a tube does the plane strain state apply. Here, the criterion to define a tube is the

length-to-width ratio. If the tube length L exceeds five times the maximum width (C0/2), the construction should

be considered a tube. Therefore the criterion is written as L/C0 > 2.5. The geotextile should also be

approximately isotropic. Then the calculation method can be chosen with respect to the material properties and

planned tube geometry; either the previously existing methods based on linear membrane theory or the new

method using a non-linear-elastic constitutive law (Fig. 10).

Fig. 10: Choosing the design tools for the tube cross section

6. Conclusions

The analysis and development of a calculation method for geosynthetic dewatering tubes on rigid ground, with

consideration of strains, led to a numeric solution based on the basic formulation of Plaut and Suherman (1998)

improved by the authors to include bulk linear material behaviour. The solution presented in this paper was

verified both experimentally and by a sensitivity analysis.

In the sensitivity analysis, input parameters and control values were varied. The programming proved to be

stable and always converging.

During the experimental analysis, small-scale tubes made of model textile and film materials were studied in a

photogrammetric measurement setup. The tubes were filled with water and a soil/water suspension, respectively.

The circumferential strains in the tube walls and the tube geometric shapes during filling and dewatering were

measured using four digital cameras and photogrammetric software. The results were then compared to those

derived using the new calculation method. The congruity of the results proved to be very good, so that both the

measurement method and the calculation method are of high quality. For geotextile tubes made of highly elastic

geotextiles, the new calculation method is valid.

Finally, some practical conclusions were derived from the tube analysis. The maximum strains proved to be

located at the lower side of the tube, a fact that should be considered when positioning longitudinal seams. The

design methods all rely on the linear membrane theory in the plane strain state. Therefore, the definition of the

tubes should be clarified within the respective literature with a specific length-to-width ratio. Only if the

structure is actually a long tube (L/C0 > 2.5) and the geotextile is close to an isotropic one, does the plane strain

state apply. Otherwise, the actual tube geometry and strains (in the field) cannot be calculated correctly with the

methods at hand. The choice of attenuation factors for the selection of geotextiles for dewatering projects is

dependent on the duration of the filling process including a potential refilling procedure. Due to the relatively

short loading time for the design strength needed to meet the maximum pumping pressure, the attenuation factor

for single dewatering tubes should not exceed a value of two.

Notation

Values and Factors

A = Attenuation factor

B’ = Contact width with the ground [m] (dimensionless: b’)

C = Circumference of the tube [m]

C’ = Free circumference of the tube C – B’ [m]

D = Theoretical diameter of the tube [m] (dimensionless: d)

E = Young’s modulus [kN/m²]

E(k), F(k) = Elliptic Integrals

F = Filling ratio

H = Tube height [m] (dimensionless: h)

k = Integration coefficient for the elliptic integrals [ ]

kV = Permeability normal to the plane [mm/s]

L = Length of the tube [m]

O90 = Characteristic opening size [µm]

P = Pressure at the bottom of the tube [kPa] (dimensionless: p)

S = Circumferential coordinate [m] (dimensionless: s)

T = Tensile normal stress, Membrane force [kN/m] (dimensionless: t)

Y = Vertical coordinate (height) [m] (dimensionless: y)

X = Horizontal coordinate [m] (dimensionless: x)

= Strain [%]

= Unit weight of the filling material [kN/m³]

R = Safety factor

= Tangential angle with respect to the horizontal line

= Poisson ratio [ ]

= Density of the filling material [g/cm³]

Indices

add = Additional

atm = Atmospheric (e.g. atmospheric pressure)

0 = Initial state

bot = Bottom (e.g. bottom pressure)

dyn = Dynamic

i = Iteration step

j = Control variable for bulk linear sections

m = Number of known strain parts in each iteration step i

top = Top of the tube (e.g. pressure at the top of the tube)

R = Resistance

k = Characteristic value

D = Design value

Abbreviations

NW1, NW2 = Nonwoven test materials

W2 = Woven test material

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Published in Geotextiles and Geomembranes 29(3):201-210. © 2010 Elsevier Ltd. DOI:10.1016/j.geotexmem.2010.10.009