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Technical Note

A comprehensive method for analyzing the effect of geotextile layerson embankment stability

A. Tolooiyan a,*, I. Abustan a, M.R. Selamat a, Sh. Ghaffari b

a School of Civil Engineering, Universiti Sains Malaysia (USM), Engineering Campus, Pulau Pinang, Malaysiab Soil and Water Engineering, P.O. Box 3185838143, Karaj, Tehran, Iran

a r t i c l e i n f o

Article history:

Received 28 March 2008

Received in revised form

20 November 2008

Accepted 21 November 2008

Available online 20 February 2009

Keywords:

Embankment

Water condition

Geotextile

Mathematical model

Stability

Finite element method

a b s t r a c t

Commercial software is used widely in slope stability analyses of reinforced embankments. Almost all of

these programs consider the tensile strength of geotextiles and soilgeotextile interface friction.

However, currently available commercial software generally does not consider the drainage function of

nonwoven geotextile reinforcement. In this paper, a reinforced channel embankment reinforced by

a nonwoven geotextile is analyzed using two methods. The first method only considers the tensile

strength and soilgeotextile interface friction. The second method also considers the drainage function.

In both cases, the reinforced embankment is modeled in rapid drawdown condition since this is one of

the most important conditions with regard to stability of channel embankments. It is shown that for this

type of application, modeling a nonwoven geotextile reinforced embankment using commercial software

which neglects the drainage function of the geotextile may be unrealistic.

2009 Elsevier Ltd. All rights reserved.

1. Introduction

When it happens, embankment collapse can be disastrouscausing serious loss of life, money and time. Reconstructingcollapsed embankments can be very costly and from a purely

economic standpoint, it would be more beneficial to reinforce theembankment so that it does not fail rather than reconstruct.Nowadays advances in technology in material science have

produced geosynthetic materials for usage in various aspects ofcivil engineering.

Geosynthetic materials that are used widely in embankments toincrease stability (Bergado and Teerawattanasuk, 2008; Brianon

and Villard, 2008; Chen et al., 2008; Li and Rowe, 2008; Rowe and

Taechakumthorn, 2008; Sarsby, 2007). Geotextile layers increasethe embankment stability by virtue of two primary functions:

tensile reinforcement (as in the cases cited above) and as a drainageelement reducing pore pressures.

Most analyses of geotextile reinforced embankments considerthe effect of the tensile stiffness of the geotextiles but generally

do not consider the drainage function of nonwoven geotextilereinforcement. While this is suitable for most applications, in thecase of nonwoven geotextile reinforced channel embankments this

may represent a significant oversight. Thus the objective of thispaper is to examine the effect of ignoring and considering thedrainage function for a channel embankment subject to rapid

drawdown.

2. Current numerical procedure

Lemonnier et al. (1998), analyzed the effect of geotextile rein-forcement on the stability of embankments by a mathematicaldisplacement method presented by Gourc et al. (1986), where byonly the tensile strength of the geotextile was taken into consid-

eration in the analysis. Sharma and Bolton (2001), Bergado et al.(2002), and Hinchberger and Rowe (2003), utilized different

commercial and non-commercial FEM models to analyze thestability of geotextile reinforced embankments. In all of theseinvestigations, tensile strength and soilgeotextile interface frictionwere taken into consideration, while ignoring the geotextiledrainage ability. Nagahara et al. (2004) used FEM to analyze the

effect of the drainage ability of geotextiles on stability of embank-ments. Nagahara and colleagues reported that the measured hori-zontal deformation of the case study embankment was much

smaller than estimated by FEM due to the neglecting soilgeo-textile interface friction in their FEM analysis. Iryo and Rowe (2005)firstly used FEM to model the drainage ability of geotextile, then,after estimating the water surface in embankment, they used

* Corresponding author.

E-mail address: [email protected] (A. Tolooiyan).

Contents lists available at ScienceDirect

Geotextiles and Geomembranes

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / g e o t e x m e m

0266-1144/$ see front matter 2009 Elsevier Ltd. All rights reserved.

doi:10.1016/j.geotexmem.2008.11.013

Geotextiles and Geomembranes 27 (2009) 399405
mailto:[email protected]://www.sciencedirect.com/science/journal/02661144http://www.sciencedirect.com/science/journal/02661144mailto:[email protected]


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a limit equilibrium method to consider the tensile strength of thegeotextile.

The FEM can be used to compute stresses and displacements inearth structures and soil masses. The method is particularly usefulfor soilstructure interaction problems, in which structuralmembers interact with a soil mass (USACE, 1995). In complex

conditions, it is often difficult to anticipate failure modes, particu-larly if reinforcement or structural members such as geotextiles,concrete retaining walls, or sheet piles are included (USACE, 2003).Another important input to the stability analyses for reinforced

slopes is the load in the reinforcement and FEM can provide usefulguidance for establishing the load that will be used ( USACE, 2003).The capabilities of FEM, led to it being used by many researchers toinvestigate the behavior of reinforced embankments e.g. Rowe

(1982, 1984), Rowe and Soderman (1984), Humphrey and Holtz(1989), Hird and Kwok (1989), Rowe and Mylleville (1990), Bergadoet al. (2002), etc. However, Rowe and Mylleville (1994) explainedthat careful consideration must be given to the type of FEM and

constitutive relationships that will be used to model the discretecomponents of the reinforced embankments.

2.1. Serious limitations of mathematical models in modeling

geotextile

While commercial software such as Plaxis Ver.7.2 (1998), MStabVer.9.8 (2004), Geostab 2004 (2004), Stedwin Ver.2.6 (1999) andPcstabl Ver.6 (1999) are widely used to analyze geotextile rein-

forced embankment, those just consider the geotextile tensilestrength and/or soilgeotextile interface friction. In some cases ofreinforced embankment analysis, the results may be unrealisticbecause the drainage function of geotextile is ignored by the

previously mentioned commercial software.

2.2. Equations to evaluate geotextile tensile strength and soil

geotextile interface friction

To evaluate the soilgeotextile interface in FE analysis theMohrCoulomb equation can be used as it is widelyemployed in FEmodeling of soilstructure interfaces. This equation is able toconsider both cohesion and friction angle of interfaces.

The equation for considering geotextile tensile strength is

usually strain energy equation that is shown in Eq. (1).

Pa

ZL0

EA

2

du

dx0

2dx0 (1)

wherePa is the strain energy, EA is the axial rigidity, L is the lengthof geotextile, u is the axial displacement along the geotextile, andx0

is the distance along the geotextile.

2.3. Necessity of equations associated with water in reinforcedembankment components

In analyzing the embankment, one of the most important issues

is pore water pressure since pore water pressure whether positiveor negative has a direct effect on the stability and safety factor ofembankment. Therefore realistic pore water pressure conditionsneed to be considered explicitly in the analysis.

2.4. Water flow in reinforced embankment components

Richards (1931) derived the governing equation for transient

water flow within an unsaturated material from Darcys law andContinuity. For the two dimensional homogeneous anisotropic

material, the equation is as Eq. (2).

kxv

2h

vx2 ky

v2h

vy2

vQ

vt mwgw

vh

vt(2)

where h is the total hydraulic head, kx, ky are the unsaturatedhydraulic conductivities for the x- and y-directions, mw is the slope

of the water volume characteristic curve, gw is the unit weight ofwater, Q is the volumetric water content, and t is the time.

2.5. Water storage in reinforced embankment components

Both the soil and geotextile consists of a collection of solidparticles and interstitial voids. The pore spaces or voids could befilled either with water or air, or with a combination of both. In

saturated materials (soil and/or geotextile), all the voids are filledwith water and the volumetric water content of the materials isequal to the porosity of the soil according to Eq. (3).

Q nS (3)

where Q is the volumetric water content, n is the porosity, and Sisthe degree of saturation (in saturated materials equal to 1.0 or100%)

In unsaturated materials, the volume of water stored withinthe voids depends on the negative water pressure (suction). Thewater content is not constant and therefore so a function isrequired to describe how the water contents changes with

different stresses in the materials. The volumetric water contentfunction describes the capability of materials to store water underchanges in pore water pressures (Krahn, 2004). A typical functionof volumetric water content and pore water pressure is shown in

Fig. 1.The volumetric water content function describes what portion

(or volume) of the voids remains water-filled as the materials

drains. The three main features that characterize the volumetricwater content function are the air-entry value (AEV), the slope ofthe function for both the positive and negative pore water pressure

(mw), and the residual water content (Qr). The air-entry value (AEV)corresponds to the value of negative pore water pressure when thelargest voids or pores begin to drain freely. It is a function of themaximum pore size in a soil and is also influenced by the pore-sizedistribution within a soil. Soils with large and uniformly shaped

pores have relatively low AEVs (Krahn, 2004). Another key featureof the volumetric water content function is the residual volumetricwater content (Qr), which represents the volumetric water contentof a soil where a further increase in negative pore water pressure

does not produce significant changes in water content (Krahn,2004).

Fig. 1. Volumetric water content (storage) function (Krahn, 2004).

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As shown in Fig. 1, the slope of the volumetric water contentversus pore water pressure has different slopes (mw) in positive and

negative pore water pressure regions. The value of the slope in thepositive pressure range is the coefficient of volume compressibility,and in physical terms, it describes how much a saturated soilvolumewill swell or shrinkfor a given change in pore pressure. This

coefficient can be back-calculated from consolidation test data(Krahn, 2004).

mw 1

E(4)

where E is the elasticity modulus.

Van Genuchtens (1980) predictive method for measurement ofa volumetric water content function in negative pore water pres-sure has been used in many studies and its validity has beenexamined for a wide range of soils. Iryo and Rowe (2004) also used

this model to investigate infiltration into a soil column containinga nonwoven geotextile layer and found that it works well formodeling the unsaturated reaction of the nonwoven geotextile.Therefore, this method could be used in modeling to describe the

hydraulic properties of both soil and the geotextile.

Q Qr Qs Qrh

1 Ja

nim (5)

where Q is the volumetric water content, Qr is the residual volu-metric water content,Qs is the saturated volumetric water content,

J is the negative pore water pressure, and a, n, m are the curvefitting parameters.

Rawls et al. (1982), and Carsel and Parrish (1988) conductedsubstantial experimental work and obtained the Van Genuchten

model parameters for different soil textural groups according to theUSDA soil classification system. As a result of this work, laboratoryparticle size analysis can be directly related to the modeledparameters. Further, for geotextile, the Van Genuchten model

parameters could be taken from the typical values evaluated frompublished data compiled by Iryo and Rowe (2003).

2.6. Hydraulic conductivity in reinforced embankment components

In a saturated soil, allthe pore spacesbetween the solid particlesare filled with water. Once the air-entry value is exceeded, airenters the largest pores and the air-filled pores become non-

conductive conduits to flow and increase the tortuosity of the flowpath. As a result, the ability of the soil and geotextile to transportwater (the hydraulic conductivity) decreases. As pore water pres-sures become increasingly more negative, more pores become air-

filled and the hydraulic conductivity decreases further. By thisdescription, it is clear that the ability of water to flow througha profile depends on how much water is present in the soil, which is

represented by the volumetric water content function (Krahn,2004).

The hydraulic conductivity function for an unsaturated soil canbe developed using Van Genuchten method. Van Genuchten (1980)offered the following closed form equation to describe the

hydraulic conductivity of soil as a function of suction, as seen inEq. (6).

kw ks

h1

aJn1

1

aJn

mi21 aJn

m2

(6)

where ks is the saturated hydraulic conductivity, a, n, m are thecurve fitting parameters, J is the required suction range, and n is

equal to 1/(1m).

From Eq. (6), the hydraulic conductivity function of soil orgeotextile could be estimated once the saturated conductivity and

the two curve fitting parameters, a and m are known.Van Genuchten showed that the curve fitting parameters could

be estimated graphically based on the volumetric water contentfunction of the soil and suggested that the best point to evaluate

these parameters is the halfway point between the residual andsaturated water content of the volumetric watercontent function. IfQp be the volumetric water content at the halfway point of thevolumetric water content function, and Jp be the suction at thesame point, then the slope Sp of the function could be calculated as

Eq. (7) (Krahn, 2004).

Sp 1

Qs Qr

dQpdlog Jp (7)

Van Genuchten proposed Eqs. (8) and (9) to estimate the parame-ters m and a, when Sp is calculated.

m 1 exp0:8Sp

(8)

where Sp is between 0 and 1.

m 1 0:5755

Sp

0:1

S2p

0:025

S3p(9)

where Sp > 1.

After calculating m, a could be estimated by Eq. (10).

a 1

J

2

1m 1

1m(10)

2.7. Analysis associated with drainage ability of geotextile

By applying Eqs. (2)(10) to both the soil and geotextile, it ispossible to obtain water storage and hydraulic conductivity inembankment components and subsequently estimate the mannerof water flow in reinforced embankments. It follows that the effect

of geotextiles as a drain layer could be taken into consideration inanalysis of reinforced embankment. In this research, the finiteelement computer program SEEP/W Ver. 5.18 (GEO-SLOPE Inter-

national Ltd., 2002a) was used to solve Eqs. (2)(10).

Table 1

Specifications of nonwoven geotextile.

Material property Value

Thickness (mm) 2.5

Unit weight (kN/m3) 1.11

Hydraulic conductivity in plane direction (m/s) 2.72E3

Hydra uli c conduc ti vi ty in c ross plan e dir ection (m/s) 7E2

Elasticity modulus (kPa) 33,000

Maximum tensile strength (kN/m) 21

Table 2

Soil characteristics and soilgeotextile interface specifications.

Specification Value

Water content (percentage) 32

Dry unit weight (g/cm3) 1.43

Poisson Ratio 0.38

Specific gravity 2.71

Hydraulic conductivity (m/s) 4.29E7

Elasticity modulus (kPa) 12,500

Soil cohesion in saturated condition (kPa) 10.571

Soil f riction angle in saturat ed condition (degree) 50.06

Soilgeotextile interface cohesion in saturated condition (kPa) 15.491

Soilgeotextile interface friction angle in saturated condition (degree) 52.21

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2.8. Analysis associated with geotextile tensile strength

and soilgeotextile interface friction

In this research, Eq. (1) was used in a linear-elastic mode tomodel the effect of tensile strength of geotextile. The finite elementcomputer program SIGMA/W Ver. 5.18 (GEO-SLOPE InternationalLtd., 2002b) was used to solve Eq. (1). To estimate the elasticity

modulus of a particular kind of nonwoven geotextile, appropriatetests were done according to ASTM D4632 (2003) in the compositematerial laboratory of USM. The specifications of this particular

nonwoven geotextile are mentioned in Table 1.To analyze the strain, stress and shape change in embankment

components, an elasticplastic model was used by utilizing SIGMA/W Ver. 518. Also, this model can consider the soilgeotextile

Fig. 2. Situation of the geotextile layers in reinforced channel embankment.

Fig. 3. Slip surface of reinforced embankment during rapid drawdown, analyzed by proposed method.



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interface friction by very fine meshes in the soilgeotextile inter-face. The friction angle and cohesion between the soil and geo-textile were determined using direct shear tests in the geotechnical

laboratory of USM. The geotextile layers were cut to square piecesof 100 mm by 100 mm and then it was glued using epoxy glue tothe top of a piece of hard wood having the same dimensions(100 mm by 100 mm). This procedure was used previously by

Mahmood et al. (2002). The soil used was classified as Silt Loamand Lean Clay with Sand in USDA and Unified Soil ClassificationSystem, respectively. Soilgeotextile interface specifications andcharacteristics of the soil are mentioned in Table 2.

3. Modeling reinforced channel embankment

Different size of three node triangular meshes with three inte-gration points was employed to model the embankment, althoughground surface and the geotextile layers were formed by very finefour node quadrilateral meshes with four integration points. In

seepage analysis, the left and right boundaries were modeled by

infinite elements however in stressstrain analysis the embank-ment bounded with zero displacement along edges. As a multi-

joined analysis, the stressstrain distribution FEM analysis was

conducted by SIGMA/W. In parallel, the FEM analysis was con-ducted by SEEP/W to model pore water pressure distribution in theembankment material.Finally, the FE results of SIGMA/Wand SEEP/

W were jointly imported into the SLOPE/W (GEO-SLOPE Interna-tional Ltd., 2002c) to analyze the embankment stability and safetyfactor.

To estimate the effect of reinforcement and to compare between

the conventional analysis and the proposed analysis method,a channel embankment was simulated using three methods duringrapid drawdown condition. Firstly, the channel embankment wasanalyzed without reinforcement (non-reinforced embankment).

Secondly, with the same rapid drawdown condition, a geotextile

reinforced embankment was analyzed by using the conventional

method and the geotextile tensile strength and soilgeotextileinterface friction were considered together. Thirdly, with the samerapid drawdown condition and reinforcing method, the reinforcedembankment was analyzed by using the proposed method that

considered geotextile tensile strength, soilgeotextile interfacefriction, and the drainage ability of the geotextile, together. Beforerapid drawdown, the water level in the channel was 3 m. In 8 h thewater level was dropped down about 2.5 m and the water level in

the channel reached 0.5 m. In all of the three mentioned analyses,

Fig. 4. Water table at 3 h and 8 h after start of rapid drawdown, analyzed by conventional method (a) and proposed method (b).

Fig. 5. Maximum effective stress at 3 h after start of rapid drawdown, analyzed by

conventional method (a) and proposed method (b).



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embankment stability was calculated at 3 h after the start of rapiddrawdown. USACE (2003) emphasize that the minimum required

safety factor of earth slope should be 1.30 during rapid drawdowncondition.

3.1. Stability safety factor of reinforced and non-reinforced

embankment

Analysis of the non-reinforced embankment gives a stabilitysafety factor equal to 1.26. According to USACE (2003), thisembankment might be unstable during rapid drawdown condition,indicating reinforcement is needed to prevent instability.

To reinforce the embankment, as shown in Fig. 2, three layers ofneedle-punched nonwoven geotextile with 1.5 m length and 1 mdistance in between were laid inside the embankment. The

reinforced embankment was analyzed by the aforementionedconventional method under the rapid drawdown condition.Analysis of the reinforced embankment gave a stabilitysafety factorequal to1.29. The increase in safety factor in the reinforcedembankment is due to the effect of tensile strength and soilgeo-

textile interface friction.To find the more complete effect of geotextile, the reinforced

embankment was analyzed by the proposed method with the samerapid drawdown condition. A safety factor of 1.33 was obtained

from the analysis which considered the drainage property of thegeotextile. This factorof safety meets the USACE (2003) guideline inembankment stability which requires a minimum value of 1.3 forrapid drawdown conditions. The slip surface of the reinforced

embankment, analyzed by the proposed method is shown in Fig. 3.

Fig. 4(a) and (b) show the water table at 3 h and 8 h after start ofrapid drawdown analyzed by conventional and proposed method,respectively. Comparing the water table in Fig. 4(a) and (b), shows

that geotextile layers drain the embankment internal water duringthe rapid drawdown and the embankment becoming lighter. Fig. 5shows the result of stressstrain analysis at 3 h after start of rapid

drawdown. Different effective stress at the right side of embank-ment is due to the different pore water pressure condition analyzedby the conventional and proposed method.

Fig. 6 shows the safety factor of non-reinforced embankment

and reinforced embankment analyzed by conventional andproposed method. Although all the reinforcing and rapid draw-down conditions are exactly the same in both analyses, theproposed complete method offered the highest safety factor. This

highlights the benefit of accurately modeling both the

reinforcement and drainage functions of needle-punchednonwoven geotextile as demonstrated in the proposed method.

4. Conclusion and results

Conventionalanalysesof a needle-punched nonwoven geotextile

reinforced channel embankment which only considers the effect ofthe tensile stiffness and strength of the geotextile on embankmentstabilityunderestimated the stabilitycompared to analysesthat alsoconsidered the drainage function of the geotextile. The proposed

analysis method which considers both functions provides a morerealistic methods of assessing the stability of needle-punchednonwoven geotextile reinforced channel embankments subjectedto

rapid drawdown.

Acknowledgements

The first author would like to express his sincere appreciation toDavid Igoe, Tom Doyle and Paul Doherty PhD researchers fromUniversity College Dublin for their help in reviewing this paper.

References

ASTM D4632, 2003. Standard test method for grab breaking load and elongation ofgeotextiles. In: Annual Book of ASTM Standards, vol. 04.13, pp. 4952.

Bergado, D.T., Long, P.V., Murthy, B.R.S., 2002. A case study of geotextile-reinforcedembankment on soft ground. Geotextiles and Geomembranes 20, 343365.

Bergado, D.T., Teerawattanasuk, C., 2008. 2D and 3D numerical simulations ofreinforced embankments on soft ground. Geotextiles and Geomembranes 26(1), 3955.

Brianon, L., Villard, P., 2008. Design of geosynthetic-reinforced platforms spanninglocalized sinkholes. Geotextiles and Geomembranes 26 (5), 416428.

Carsel, R.F., Parrish, R.S., 1988. Developing joint probability distributions of soil

water retention characteristics. Water Resources Research 24, 755769.Chen, Y.-M., Cao, W.-P., Chen, R.-P., 2008. An experimental investigation of soil

arching within basal reinforced and unreinforced piled embankments. Geo-textiles and Geomembranes 26 (2), 164174.

Geostab Version 2004, 2004. Geos Ingenieurs Conseils S.A. Parc dAffaires Inter-national, Archamps, France.

Gourc, J.P., Ratel, A., Delmas, Ph., 1986. Design of fabrics retaining walls: thedisplacement method. In: Proceedings of Third International Conference onGeotextiles and Geomembranes, Vienna, Austria, Session 3A/1, pp. 289294.

Hinchberger, S.D., Rowe, R.K., 2003. Geosynthetic reinforced embankments on softclay foundations: predicting reinforcement strains at failure. Geotextiles andGeomembranes 21, 151175.

Hird, C.C., Kwok, C.M., 1989. Finite element studies of interface behaviour in rein-forced embankments on soft ground. Computers and Geotechnics 8 (2),111131.

Humphrey, D.N., Holtz, R.D., 1989. Effect of surface crust on reinforced embank-ments. In: Proceedings of Geosynthetics 89 Conference, San Diego, USA, pp.136147.

Iryo, T., Rowe, R.K., 2003. On the hydraulic behavior of unsaturated nonwoven

geotextiles. Geotextiles and Geomembranes 21, 381404.

Fig. 6. Increment of safety factor due to reinforcement, analyzed by the conventional and the proposed method.



7/7

Iryo, T., Rowe, R.K., 2004. Numerical study on infiltration into soilgeotextilecolumn. Geosynthetics International 11 (5), 377389.

Iryo, T., Rowe, R.K., 2005. Infiltration into an embankment reinforced by nonwovengeotextiles. Canadian Geotechnical Journal 42 (4), 11451159.

Krahn, J., 2004. Seepage Modeling with SEEP/W. Geo-Slope International Ltd.,Alberta, pp. 14, 7179.

Lemonnier, P., Soubra, A.H., Kastner, R., 1998. Variational displacement method forgeosynthetically reinforced slope stability analysis: I. Local stability. Geotextilesand Geomembranes 16, 125.

Li, A.L., Rowe, R.K., 2008. Effects of viscous behaviour of geosynthetic reinforcement

and foundation soils on embankment performance. Geotextiles and Geo-membranes 26 (4), 317334.

Mahmood, A., Zakaria, N., Ahmad, F., 2002. Studies on geotextilesoil interface shearbehavior. Electronic Journal of Geotechnical Engineering. Available online:http://www.ejge.com/2000/Ppr0013/Ppr0013.htm (accessed 02.02.07).

MStab Version 9.8, 2004. Slope Stability Software for Soft Soil Engineering. DelftGeoSystems B.V., Delft, Netherlands.

Nagahara, H., Fujiyama, T., Ishiguro, T., Ohta, H., 2004. FEM analysis of high airportembankmentwith horizontal drains. Geotextiles and Geomembranes 22, 4962.

Pcstabl Version 6, 1999. General Solution of Slope Stability Problems. PurdueUniversity, West Lafayette, Indiana, USA.

PLAXIS Version 7.2, 1998. Finite Element Code for Soil and Rock Analysis. Balkema,Rotterdam, Netherlands.

Rawls, W.J., Brakensiek, D.L., Saxton, K.E., 1982. Estimating soil water properties.Transactions of the ASAE 25 (5). 13161320 and 1328.

Richards, L.A., 1931. Capillary conduction of liquids through porous mediums.Journal of Applied Physics, 1, 318333.

Rowe, R.K., 1982. The analysis of an embankment constructed on a geotextile. In:Proceedings of Second International Conference on Geotextiles, vol. 2, LasVegas, Nevada, USA, pp. 677682.

Rowe, R.K., 1984. Reinforced embankment: analysis and design. Journal ofGeotechnical Engineering Division, ASCE 110 (2), 231247.

Rowe, R.K., Mylleville, B.L.J., 1990. Implications of adopting an allowable geo-synthetic strain in estimating stability. In: Proceedings of the Fourth Interna-tional Conference on Geotextiles, Geomembranes and Related Products, TheHague, pp. 131136.

Rowe, R.K., Mylleville, B.L.J., 1994. Analysis and design of reinforced embankmentson soft or weak foundations. In: Bull, John W. (Ed.), Chapter 7 in Soil StructureInteraction: Numerical Analysis and Modelling. E & FN Spon Chapman Hall,London, pp. 230260.

Rowe, R.K., Soderman, K.L., 1984. Comparison of predicted and observed behaviourof two test embankments. Geotextiles and Geomembranes 1, 143160.

Rowe, R.K., Taechakumthorn, C., 2008. Combined effect of PVDs and reinforcementon embankments over rate-sensitive soils. Geotextiles and Geomembranes 26(3), 239249.

Sarsby, R.S., 2007. Use of Limited Life Geotextiles (LLGs) for basal reinforcement ofembankmentsbuilt on soft clay. Geotextilesand Geomembranes 25 (45), 302310.

SEEP/W Ver.5.18, Software Manual, 2002. GEO-SLOPE International Ltd., Calgary,Alberta, Canada.

SIGMA/W Ver.5.18, Software Manual, 2002. GEO-SLOPE International Ltd., Calgary,Alberta, Canada.

SLOPE/W Ver.5.18, Software Manual, 2002. GEO-SLOPE International Ltd., Calgary,Alberta, Canada.

Sharma, J.S., Bolton, M.D., 2001. Centrifugal and numerical modelling of reinforcedembankments on soft clay installed with wick drains. Geotextiles and Geo-membranes 19, 2344.

Stedwin Version 2.6, 1999. Slope Stability Analysis System. Purdue University, WestLafayette, Indiana, USA.

U.S. Army Corps of Engineers, 1995. Geotechnical Analysis by the Finite Element

Method, Engineer Technical Letter 1110-2-544. Department of the Army,Washington, DC, pp. A/1A/39.

U.S. Army Corps of Engineers, 2003. Engineering and Design Slope Stability, Engi-neer Manual No. 1110-2-1902. Department of the Army, Washington, DC, pp. 3/13/5, C/39C/40.

Van Genuchten, M.Th., 1980. A closed-form equation for predicting the hydraulicconductivity of unsaturated soils. Soil Science Society of America Journal 44,892898.

Nomenclature

Pa: strain energyE: elasticity modulusA: cross section areaEA: axial rigidityL: length of geotextileu: axial displacement along the geotextile

x0: distance along the geotextileh: total hydraulic headkw: unsaturated hydraulic conductivitykx: unsaturated hydraulic conductivities in x-directionky: unsaturated hydraulic conductivities in y-directionmw: slope of the water volume characteristic curvegw: unit weight of waterQ: volumetric water contentt: timen: porosityS: degree of saturation

AEV: air-entry valueQr: residual water contentQs: saturated volumetric water contentJ: negative pore water pressurea, n, m: curve fitting parametersks: saturated hydraulic conductivityQp: volumetric water content at the halfway point of the volumetric water content

function

Jp: suction at the halfway point of the volumetric water content functionSp: slope of volumetric water content function at the halfway point

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