predictionofporesizecharacteristicsofneedle-punched...

Research ArticlePrediction of Pore Size Characteristics of Needle-PunchedNonwoven Geotextiles Subjected to Uniaxial Tensile Strains

Lin Tang1 Qiang Tang 2 Aolai Zhong1 and Hanjie Li1

1Department of Civil Engineering Harbin Institute of Technology at Weihai Weihai 264209 China2School of Rail Transportation Soochow University Suzhou 215000 China

Correspondence should be addressed to Qiang Tang tangqiangsudaeducn

Received 15 March 2020 Revised 17 May 2020 Accepted 26 May 2020 Published 23 June 2020

Academic Editor Guoqing Cai

Copyright copy 2020 Lin Tang et al )is is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

A modified theoretical model has been proposed to predict the pore size characteristics of nonwoven geotextiles under certainuniaxial tensile strains considering the difference between the out-of-plane Poissonrsquos ratio and the in-plane Poissonrsquos ratio ofgeotextiles )e pore size distributions (PSDs) and O95 subjected to different levels of uniaxial tensile strains in two needle-punched nonwoven geotextiles have been investigated by the dry sieving test )e variation of the fibre orientation with tensilestrains and the corresponding effect on pore sizes has been evaluated by image analysis )e out-of-plane Poissonrsquos ratio and thein-plane Poissonrsquos ratio of geotextiles have been examined A comparison has been made between the predictions of the originaland the modified models It is shown that the modified model can more accurately predict the decreasing rate of the PSDs O95and O98 than the original one)e corrected theoretical O95 and O98 under certain strains can provide a reference for the filtrationdesign under engineering strains )e fibres reorientating to the loading direction result in the increase of the directionalparameter with increasing tensile strains which leads to the decrease of pore sizes )e theoretical PSDs are sensitive to thevariation of directional parameter

1 Introduction

Nonwoven geotextiles are widely used as filtration anddrainage materials in various fields [1] To ensure the re-tention of the soil without influencing the flow of seepagewater the design of geotextiles needs to meet several criteriaincluding retention permeability and anticlogging capa-bilities which are often based on the relationship betweenthe characteristic pore sizes O95 or O98 and soil grain sizes[1ndash7] )e filtration applications of geotextiles are typicallysubjected to tensile strains and result in noticeable variationsof pore size and permeability in nonwoven geotextiles[8ndash14] However unstrained pore sizes are commonly testedand used in design which induces the failure in the engi-neering application [8ndash14] )erefore accurate determina-tion of pore sizes at certain tensile strains is essential in thefiltration design of nonwoven geotextiles

)ere is still limited theoretical model to predict theeffect of uniaxial tensile strain on the pore sizes in geotextiles

[13 14] Based on the Poisson Polyhedron)eory which canpredict a radius distribution of circles inscribed in thepolygons a series of theoretical models of pore size distri-butions (PSDs) of unstrained nonwoven structures andnonwoven geotextiles have been established [15ndash20] )emodels have also been extended for uniaxial and biaxialtensile strain conditions [13 21] Silva et al [22] have de-veloped image-based technique for measuring pore sizedistributions of nonwoven geotextiles depending on thetheory Furthermore a three-dimensional structure of ab-sorptive glass mat separator has been established based onthe theory [23] Many kinds of porous media have beenemployed in the experiments to prove the validity of thesemodels including nonwoven heat-bonded geotextiles hy-brid needle punched nonwoven geotextiles spunbondednonwoven geotextiles thermally bonded nonwoven struc-tures and glass mat [12 13 15ndash23] )e fibre orientationdistribution is an important parameter in the model whichneeds to be estimated by image analysis [17ndash20] Due to the

HindawiAdvances in Civil EngineeringVolume 2020 Article ID 8839519 12 pageshttpsdoiorg10115520208839519

fact that the microscopes can typically focus on limitedlayers of the fibres the samples employed in the literaturewere relatively thin which were generally less than 250 gm2

[13ndash23] If the sample is relatively thick the fibres in deeplayers will be blurry and cannot be evaluated with an opticalmicroscope

In the theoretical models of PSDs a nonwoven structureor geotextile is assumed to be an isotropic material [13ndash21]which means the in-plane and out-of-plane Poissonrsquos ratiosare taken as the same value Also the directional parameterKα at different levels of uniaxial tensile strains was not givenin the literature [13ndash21])e strained Kαwas calculated froman equation instead of the statistical work of reorientatedfibres [13 17] And limited experiments of nonwovengeotextiles have been carried out in validating or improvingthe theoretical model

When it comes to the experiments about the influence ofthe uniaxial tensile strain on the pore sizes or permeability ofnonwoven geotextiles the results are still scant [8ndash14]Fourie and Kuchena [8] demonstrated that tensile strain canlead to dramatic decreases in the flow rate through soil-geotextile systems for needle-punched nonwoven geo-textiles Edwards and Hsuan [11] reported that the needle-punched geotextile shows a decrease in flow rate whereasthe heat-set nonwoven geotextile experiences an increasewhen subjecting to uniaxial tensile loads )e PSDs of threeneedle-punched geotextiles tested by Wu and Hong [24]decrease with uniaxial tensile strains in wet sieving testsAnd the results of Wu et al [10] illustrated the pore size andthe mean flow rate through two heat-bonded nonwovengeotextiles increase with the increase in uniaxial tensilestrain It seems that the uniaxial strain results in the decreaseof pore sizes for the needle-punched geotextiles and theopposite trend was observed for heat-bonded nonwovengeotextiles More experiments still need to be done to verifythe conclusions [8ndash14 24]

)erefore in this study an existing model of PSDssubjected to uniaxial tensile strains has been modifiedconsidering the difference between the in-plane and out-of-plane Poissonrsquos ratios of geotextiles Two needle-punchednonwoven geotextiles were employed in dry sieving tests(ASTM D4751-16(A)) [4] to estimate the PSDs underuniaxial tensile strains )e directional parameters Kα atdifferent levels of uniaxial tensile strains have been obtainedfrom the image analysis of the fibres reorientation Also thein-plane and out-of-plane Poissonrsquos ratios of geotextiles havebeen estimated Comparisons have been made between thepredictions of the modified model and the original modelwith the experimental results )e modified model can moreaccurately predict the decreasing tendency of PSDs and thecorrected O95 and O98 under certain strain can be used as areference in design

2 Theoretical Model

21 Original Model Depending on an unstrained poremodel of Rawal et al [12 13 17ndash20] a theoretical model ofthe PSDs subjected to uniaxial tensile strains is shown asfollows )e cumulative probability Ff(d) of a particle with

diameter d passing through the layers of nonwoven is shownin the following equations [13 17ndash20]

Ff(d) 1 minus 1 + ω d +ω2d2

21113888 1113889e

minus ωd1113890 1113891

N

(1)

where

ω 4Vf(ε)Kα βf1113872 1113873

πDf

(2)

N Tg

Df

(3)

Vf(ε) Vf

(1 + ε)(1 minus ]ε)2 (4)

Kα βf1113872 1113873 1113946(π2)minus α

minus (π2)minus αcos βf

11138681113868111386811138681113868

11138681113868111386811138681113868 χ βf1113872 1113873dβf (5)

Vf μ

Tgρh

(6)

where ω is the coverage parameter N is the number oflayers Vf is the total fibre volume fraction ε is the uniaxialtensile strain Kα is the directional parameter χ(βf) is theorientation distribution function of fibres and βf is theorientation angle of fibres subjected to strains Df is the fibrediameter ] is Poissonrsquos ratio of the nonwoven μ is the initialmass per unit area Tg is the nonwoven thickness ρh is thefibre density )e details of the parameters were explained inthe literature [12 13 17ndash20]

22 Modified Model In equation (4) the uniaxial tensilebehaviour of a nonwoven geotextile is taken as a plane stressproblem And the out-of-plane Poissonrsquos ratio and the in-plane Poissonrsquos ratio are taken as the same parameter ]

According to the experimental results in the previousliterature and this study the out-of-plane Poissonrsquos ratio ofnonwoven geotextiles seems to be smaller than the in-planePoissonrsquos ratio [13 18 24ndash27] Rawal and Agrahari [13]demonstrated that the in-plane Poissonrsquos ratios in machinedirection range between 238 and 381 for two thermallybonded nonwovens )e relationship of in-plane Poissonrsquosratio and longitudinal strain was determined by Rawal et al[18] and the in-plane Poissonrsquos ratio can increase from 21 to40 with increasing strains )e in-plane Poissonrsquos ratio of anonwoven geotextile tested by Shukla et al [25] remains 175from zero to 10 strain Kutay et al [26] reported that thelateral strain is always greater than the axial strain for aneedle-punched nonwoven geotextile and Poissonrsquos ratio atfailure is equal to 21 In the literature the in-plane Poissonrsquosratios are at least equal to or larger than 10

When it comes to the out-of-plane Poissonrsquos ratioVerma et al [27] tested the out-of-plane Poissonrsquos ratio oftwo needle-punched polypropylene nonwoven NW1 andNW2 Both of the out-of-plane Poissonrsquos ratios of the twogeotextiles range between 021 and 037 when the strains

2 Advances in Civil Engineering

increase from 0 to 10 Also the decrease of thickness ofthree nonwoven geotextiles (referred to as GT1 GT2 andGT3) with increasing uniaxial strain was tested by Wu andHong [24] as shown in Figure 1 )e decrease of thethickness with tensile strains is approximately linear Hencein this study the experimental data are linearly fitted andthe slopes of the fitted lines k are used to calculate the out-of-plane Poissonrsquos ratio ]perp shown as follows

]perp minus εt

ε

k

t0 (7)

where εt is the strain in the thickness and ε is the in-planeuniaxial tensile strain t0 is the unstrained thickness of ageotextile And the ]perp for GT1 GT2 and GT3 are calculatedto be 017 036 and 014 respectively as shown in Figure 1which are smaller than the in-plane Poissonrsquos ratio in theliteratures [13 18 25 26]

In this study equation (4) is modified to the followingequation

Vf(ε) Vf

(1 + ε) 1 minus ]perpε( 1113857 1 minus vε( 1113857 (8)

where v is the in-plane Poissonrsquos ratio which should bedetermined depending on the direction of the uniaxialtensile strain ε And the total fibre volume fraction isinfluenced by the in-plane lateral strain as well as the strainin the thickness of geotextiles

)us the modified model of PSDs subjected to uniaxialtensile strains combines equations (1)ndash(3) (5) (6) and (8)

In the filtration criteria of geotextiles O95 is a commonlyused characteristic pore size it indicates that 95 of thepores are smaller than that size [1 4] whereas the theoreticalO95 read from the theoretical PSD cannot fit perfectly withthe value of experimental O95 in the literatures [13 17ndash20] Ifa strained theoretical O95 needs to be used in the filtrationdesign under a certain engineering strain the differencebetween the theoretical and experimental O95 should becorrected )e experimental O95 of an unstrained geotextilecan be easily tested before applications or be given by themanufactures Hence the difference between the unstrainedexperimental and theoretical O95 can be used to correct theerror of the strained theoretical O95 as long as the decreasingrate can be accurately predicted )en when the uniaxialtensile strain is ε the strained O95 used in design can becalculated as follows

O95corrected(ε) O95 exp(0) minus O95theo(0) + O95theo(ε) (9)

where O95corrected(ε) is the corrected theoretical O95 underthe strain ε which may be used in the filtration designcriteria O95exp(0) is the experimental O95 of unstrainedgeotextile samples O95theo(0) is the O95 read from thetheoretical PSD under the strain 0 and O95theo(ε) is theO95 read from the theoretical PSD under the strain ε

3 Experimental Procedure

31 Materials Used To verify the rationality of the modifiedmodel dry sieving test was adopted to test the changes in the

PSDs of two needle-punched nonwoven geotextiles underuniaxial tensile strains Due to the fact that the fibre ori-entation needs to be estimated by image analysis relativelythin samples were employed )e geotextiles were desig-nated as NW100 and NW200 which indicated that themasses per unit area of the two geotextiles were approxi-mately 107 gm2 and 225 gm2 Details of the geotextiles usedare described in Table 1

32 Apparatus and Procedure Rowe and Mylleville [28]demonstrated that the strain imposed on geotextiles in thedirection perpendicular to the long axis of the embankmentcan be as much as 10 Izadi et al [29] noted that the strainsin a geotextile due to impact loadings were in the range of35ndash5 Won and Kim [30] mentioned that there is a 6strain in a geotextile of a 5m high soil wall and Schimelfenyget al [31] found a larger than 7 strain for a geotextile inwarp and fill directions of a containment dyke Fourie andAddis [9] concluded that most of the decrease of filtrationopening size has already occurred under the application ofthe smallest load According to the fact that the strain levelsrecorded in the literatures are smaller than 10 the uniaxialtensile strains of 3 5 and 10 were selected to study theinfluence of strains on pore sizes)e test procedures were asfollows

(1) A universal tensile test apparatus was used to formstrained geotextile specimens for the dry sieving test)e tensile loads were applied along the machinedirection during testing When a geotextile specimenwas stretched to a designated strain the specimenwas secured by clamps as shown in Figure 2(a) )einternal diameters of the clamps are 200mm whichcan be fitted on the 200mm diameter sieves )e sizeof an unstrained specimen used for dry sieving test isillustrated in Figure 2(b) )en the clamped

GT1GT2GT3

Linear fit of GT1Linear fit of GT2Linear fit of GT3

νperp = 036

νperp = 017

νperp = 014

10

15

20

25

ic

knes

s (m

m)

5 10 15 200Tensile strain ()

Figure 1 Variations in geotextile thickness with tensile strains(data sourced from reference [24])

Advances in Civil Engineering 3

geotextile specimens were cut free from the appa-ratus Grids were drawn on the specimens beforetesting as an indicator for the tensile strain and thestrain reversal after cutting

(2) )e microscopic image of the clamped specimen wastaken by a microscope )e fibres were recognizedmanually by drawing straight lines on the fibresusing AutoCAD as presented in Figure 2(c) Andthe statistical work was done by calculate the pro-portion of lines for 10degorientation angle interval withrespect to the machine direction 0deg [12 13 17ndash20]And then the directional parameter Kα was

calculated by equation (5) More than 120 fibres wereinvolved in the statistical work of each image

(3) )e thickness of the clamped geotextile specimenwas tested under 2 kPa normal pressure by thicknesstesting instrument (ASTM D5199-12) [32] which isused to calculate the out-of-plane Poissonrsquos ratio)e standard deviations of the thickness of samplesunder a certain strain range from 3 to 23 μm )evariations of geotextile thickness with tensile strainsare illustrated in Figure 3 And equation (7) is used togive the out-of-plane Poissonrsquos ratios of NW100 andNW200 which are 017 and 031 respectively

(a)

380

380

250

280

100

100

Clamp

Unit mm

(b)

(c)

60

100

60

100

A

C

G B

D

E H F

Unit mm

Clamp

(d)

Figure 2 Preparation of strained geotextile specimen (a) Photograph of strained geotextile specimen secured by clamps (b) Schematic ofan unstrained specimen for the dry sieving test (c) Measurement of fibre orientations (d) Schematic of unstrained specimen for the in-planePoissonrsquos ratio test

Table 1 Properties of nonwoven geotextiles and structures

NW100 NW200Mass per unit area (gm2) 107 225)ickness (μm) 863 1690Density of fibre (gcm3) 132 132Diameter (μm) 23 23Out-of-plane Poissonrsquos ratio 017 031In-plane Poissonrsquos ratio (machine direction) 117 116


(4) Apply commercially available antistatic spray uniformlyto the geotextile And the clamped geotextile was fittedwith a pan and a cover and was fixed on a mechanicalsieve shaker to conduct dry sieving tests (ASTMD4751-16(A)) [4] Spherical glass beads ranging in size from0033mm to 0425mm were utilized

(5) )e in-plane Poissonrsquos ratio of geotextiles was testedby image analysis in the machine direction )e sizeof an initial specimen used for in-plane Poissonrsquosratio test is illustrated in Figure 2(d) )e geotextilespecimen was clamped to create a 100mmtimes 100mmsquare test area A 60mmtimes 60mm square wasdrawn on the specimen Giroud [33] mentioned thatthe Poissonrsquos ratio derived from the lateral strain atmid-length of the specimen tends to be over-estimated Hence the average lateral strain of linesAB CD and EF of the marked square was used tocalculate the in-plane Poissonrsquos ratio as equations(10)ndash(12) )e standard deviations of in-planePoissonrsquos ratio are 0003 for NW100 and 005 forNW200 respectively

ε1 AprimeBprime minus AB( 1113857AB +(CprimeDprime minus C D)C D +(EprimeFprime minus EF)EF1113874 1113875

3

(10)

ε2 GprimeHprime minus GH

GH (11)

] minusε1ε2

(12)

where ε1 is the average lateral strain and ε2 is the longitudinalextension strain AprimeBprime and AB are the strained length andinitial length of the line AB )e same goes for the othermarked lines

4 Results

41 Fibre Orientation )e machine direction of the geo-textiles was set as 0deg in the statistics which is also the di-rection for the loading in the tensile test Figure 4 illustratesthe microstructures of the unstrained and strained (10)NW100 specimens )e histograms of the relative frequencyof fibres for NW100 and NW200 under designated strainsare given in Figure 5 With the strain increasing the ran-domly distributed fibres reorientate to the loading directionin Figure 4 which agrees with the histograms of relativefrequency of fibres for NW100 as shown in Figure 5 )erelative frequency at 0deg increases from 014 to 024 forNW100 and from 008 to 016 for NW200 when the strainincreases from 0 to 10 For NW100 there is an increasetrend for the relative frequency of fibres around 0deg especiallyfrom minus 20deg to 20deg In Figure 5(a) the relative frequency offibres for NW100 at 0deg is a little bit larger than the otherswith the relative frequency of the other directions com-paratively uniform )at agrees with the conclusion thatmost of nonwoven geotextiles are preferentially orientated[12 13] For NW200 the relative frequency of fibres for theunstrained NW200 is comparatively uniform in Figure 5(e)With an increase of strain from 0 to 10 the relativefrequency of fibres increased from 009 to 012 for minus 10deg angleand from 001 to 005 for 10deg angle respectively

)e directional parameter Kα is defined as the averagedistance between the bonds projected on the planar direc-tion [17ndash20])eKα at designated tensile strains is calculatedfrom equation (5) which is the integral of the product of|cos βf| and the corresponding relative frequency of fibresfor βf from minus 90deg to 90deg as given in Table 2 )e Kα of bothsamples increases with uniaxial tensile strains When thestrain increases from 0 to 10 the Kα increases from 063to 076 for NW100 and from 063 to 072 for NW200

A parametric study is performed to calculate the poresize distributions for different values of Kα as shown inFigure 6 When the Kα increases from 06 to 08 by 33 forthe two samples under 0 strain the PSDs of NW100 andNW200 move towards the direction of small pore sizes )eO95 read from the theoretical PSDs decreases from 319 to238 μm by 34 for NW100 and from 223 to 170 μm by 31for NW200 )e larger the Kα is the smaller the theoreticalpore sizes will be )e theoretical pore size is sensitive to thevariation of Kα Hence the accurate determination of Kα iscritical to the prediction of pore size under tensile strains)e theoretical results also agree with the phenomenon thatthe fibres reorientation to one direction results in narrowerspace between the fibres and the decrease of the pore sizes

42 Pore Size Distribution )e experimental PSDs areplotted by the cumulated frequency of the pore size versusthe pore size as presented in Figure 7 )e experimentalPSDs of both NW100 and NW200 move towards the di-rection of small pore sizes with increasing strain demon-strating the decrease of pores of different sizes )e shapes ofthe PSD curves for NW100 and NW200 do not vary reg-ularly under different strains Depending on the physical

NW100NW200

νperp = 017

νperp = 031

2 4 6 8 100Tensile strain ()

800

1000

1200

1400

1600

1800

ic

knes

s (microm

)

Figure 3 Variations in thickness with tensile strains of NW100and NW200


(a) (b)

Figure 4 Microstructures of an NW100 geotextile specimen (a) 0 strain (b) 10 uniaxial tensile strain

NW100 0

000

005

010

015

020

025

Rela

tive f

requ

ency

ndash60 ndash40 ndash20 0 20 40 60 80ndash80Fibre orientation angle (deg)

(a)

NW100 3

000

005

010

015

020

025

Rela

tive f

requ

ency


(b)

NW100 5

000

005

010

015

020

025

Rela

tive f

requ

ency


(c)

NW100 10

000

005

010

015

020

025

Rela

tive f

requ

ency


(d)

000

003

006

009

012

015

018NW200 0

Rela

tive f

requ

ency


(e)

NW200 3

000

003

006

009

012

015

018

Rela

tive f

requ

ency


(f )

Figure 5 Continued


properties of the geotextiles the theoretical PSDs are cal-culated from the original model [12 13 18ndash20] and themodified model labelled as ldquo)eo-Ordquo and ldquo)eo-Mrdquo re-spectively in Figure 7 Both kinds of the theoretical PSDsdecrease with increasing strains )e distances between twoadjacent theoretical curves of themodifiedmodel are smallerthan that of the original one Evaluating the predictionaccuracy of the two models is difficult because the shapes ofPSDs of the two models cannot fit perfectly with the

experimental PSDs Hence the characteristic pore sizes O95were determined from the PSDs to quantify the variations

O95 is not very susceptible to the effect of static electricityin dry sieving tests which may result in the uptrend of thePSDs in the area of small pores and influence the results ofsmall characteristic pore sizes [1 4] )erefore the O95 wereread from the theoretical and experimental PSDs to comparethe predictions of two models )e difference between thetheoretical and experimental O95 at 0 strain was used tocalculate the corrected O95corrected(ε) by using equation (9))e experimental O95 and O95corrected(ε) are illustrated inFigure 8 )e experimental O95 values of NW100 andNW200 decline with strains )e decreasing tendency of O95predicted by the modified model agrees better with theexperimental O95 than the original model )e originalmodel overestimates the decreasing rate for both NW100and NW200 It may be attributed to the fact that the originalmodel overestimates the out-of-plane Poissonrsquos ratio

5 Discussion

Rawal and Agrahari [13] validated their model through theimage analysis of two thermally bonded nonwoven struc-tures labelled as TB1 and TB2 )e physical properties ofTB1 and TB2 are tabulated in Table 3 )e experimental andtheoretical PSDs of the original model are read from thesemi-logarithmic figures When the figure has a linear scaleon the x-axis the distances between adjacent theoreticalPSDs are obviously larger than those of the experimentalresults as illustrated in Figures 9(a) and 9(c) Also thedistances between the strained experimental PSDs and thecorresponding theoretical ones cannot be neglected)e O98values subjected to uniaxial tensile strains were given in theliterature If the theoretical O98 of the original model iscorrected by equation (9) and compared with the experi-mental results the theoretical O98 drops faster with in-creasing strains than the experimental result as shown inFigure 10 which is consistent with the overestimation of thedecreasing rate of NW100 and NW200 Furthermore the

000

003

006

009

012

015

018

Fibre orientation angle (deg)

Rela

tive f

requ

ency

NW200 5

ndash80 ndash60 ndash40 ndash20 0 20 40 60 80

(g)


003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 10

(h)

Figure 5 Histograms of relative frequency of fibres subjected to different uniaxial tensile strain (a) NW100 0 (b) NW100 3 (c) NW1005 (d) NW100 10 (e) NW200 0 (f ) NW200 3 (g) NW200 5 (h) NW200 10

Table 2 Directional parameter Kα at different levels of strains

Strain () NW100 NW2000 063 0633 068 0655 071 06910 076 072

NW100 0 Kα = 06NW100 0 Kα = 08

NW200 0 Kα = 06NW200 0 Kα = 08

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency

100 200 300 400 5000Pore diameter (μm)

Figure 6 Parametric study of Kα at 0 strain


theoretical PSDs are larger than the experimental ones forNW100 NW200 TB1 and TB2

)e out-of-plane Poissonrsquos ratios of TB1 and TB2 werenot considered in the test )e thicknesses of TB1 and TB2are comparatively small which are 044mm and 043mmrespectively )e out-of-plane Poissonrsquos ratios of the thinnerspecimen in the literature of Wu and Hong [24] and thisstudy are both 017 If the out-of-plane Poissonrsquos ratios forTB1 and TB2 are assumed to be 017 the theoretical PSDspredicted by the modified model are given in Figures 9(b)and 9(d) And the corresponding corrected O98 by usingequation (9) are shown in Figure 10 )e distances betweentwo adjacent modified theoretical PSDs are more next to thatof the experimental results than the original model in

Figure 9 And the modified model can give a better pre-diction of the decreasing rate of the O98 in Figure 10

Although the out-of-plane Poissonrsquos ratios for TB1 andTB2 are assumed the results indicate that the considerationof the out-of-plane Poissonrsquos ratio may lead to more accuratepredictions )e prediction of the values of O95 and O98 bythe model is not terribly accurate whereas the decreasingrate predicted by the modified model is acceptable and thevalues of O95 and O98 can be corrected depending on theprecisely measured unstrained values )en the O95 under acertain strain can be predicted from the modified model andmay be used in the filtration criteria In this study only tworelatively thin nonwoven geotextiles have been tested tovalidate the model Additional experiments on thicker

0 theo-O3 theo-O5 theo-O10 theo-O

0 exp3 exp5 exp 10 exp

NW100

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy

100 200 3000Pore diameter (μm)

(a)

0 theo-M3 theo-M5 theo-M10 theo-M


NW100

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(b)



NW200

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(c)



NW200

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(d)

Figure 7 Experimental and theoretical PSDs of dry sieving test (a) Experimental and theoretical PSDs of the original model for NW100 (b)Experimental and theoretical PSDs of the modified model for NW100 (c) Experimental and theoretical PSDs of the original model forNW200 (d) Experimental and theoretical PSDs of the modified model for NW200


NW100

ExpTheo-OTheo-M

100

120

140

160

180

200

220

240

O95

(microm

)


(a)

NW200

ExpTheo-OTheo-M

60

80

100

120

O95

(microm

)


(b)

Figure 8 Experimental and theoretical O95 tested by dry sieving test (a) NW100 (b) NW200

Table 3 Properties of nonwoven structures [13]

TB1 TB2Mass per unit area (gm2) 30 30)ickness (mm) 044 043Density of fibre (gcm3) 138 138Diameter (μm) 166a 28a

Kα 081 077Out-of-plane Poissonrsquos ratio 017b 017b

In-plane Poissonrsquos ratio in machine direction290 (4) 381 (4)264 (8) 292 (8)238 (12) 261 (12)

Note a)e diameters of fibres were calculated depending on the parameters given in the literature [13] TB1 and TB2 were produced by blending the homofiland bicomponent polyester fibres in equal proportions by weight hence the diameter of fibres is taken as the average diameter of the two fibres as mentionedby Rawal and Agrahari [13] bAssumed value

0 theo-O 4 theo-O8 theo-O12 theo-O

0 exp 4 exp8 exp12 exp

TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()

100 200 300 400 500 600 7000Pore diameter (microm)

(a)



TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(b)

Figure 9 Continued


nonwoven geotextiles and other test methods of pore sizemeasurement are required to verify the conclusion More-over other loading directions except for the machine di-rection should be examined

6 Conclusions

In this study the existing model of pore size distributionsof nonwoven geotextiles subjected to uniaxial tensilestrains has been modified considering the effect of the out-

of-plane Poissonrsquos ratio )e experimental PSDs movetowards the direction of small pore sizes with increasingstrain indicating the decrease of pore sizes )e shapes ofthe experimental PSDs do not vary regularly with strains)e modified model can more accurately predict the de-creasing rate of O95 and O98 And the original model mayoverestimate the decreasing rate and the value of O95 andO98 )e corrected O95 predicted by the modified modelunder a designated strain can provide a reference for thefiltration design



TB2

0

20

40

60

80

100Cu

mul

ativ

e fre

quen

cy (

)

200 400 600 800 10000Pore diameter (microm)

(c)



TB2

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(d)

Figure 9 Experimental and theoretical PSDs of TB1 and TB2 (a) Experimental and theoretical PSDs of the original model for TB1 (b)Experimental and theoretical PSDs of the modified model for TB1 (c) Experimental and theoretical PSDs of the original model for TB2 (d)Experimental and theoretical PSDs of the modified model for TB2 (data of experimental and theoretical PSDs of the original model sourcedfrom reference [13])

TB1 expTheo-OTheo-M

5 10 150Tensile strain ()

80

160

240

320

O98

(microm

)

(a)

TB2 expTheo-OTheo-M

300

400

500

600

700

800

900

O98

(microm

)


(b)

Figure 10 Experimental and theoretical O98 of image analysis (a) TB1 (b) TB2 (experimental O98 sourced from reference [13])


)e randomly distributed fibres reorientate to theloading direction with the increasing uniaxial tensile strain)e relative frequencies of fibres at the loading directionincrease from 014 to 024 for NW100 and from 008 to 016for NW200 when the strain increases from 0 to 10 Alsothere is an increase trend for the relative frequency of fibresaround the loading direction )e larger the uniaxial tensilestrain is the larger the Kα is and the smaller the theoreticalpore size will be which agrees with the experimental results)e theoretical PSD is sensitive to the change of Kα Whenthe Kα increases by 33 the O95 read from the theoreticalPSDs decreases by 34 for NW100 and by 31 for NW200

)e experimental results indicate that the out-of-planePoissonrsquos ratio of nonwoven geotextiles is smaller than thein-plane Poissonrsquos ratio )e out-of-plane Poissonrsquos rationeeds to be taken into consideration in the model of geo-textiles Additional experiments are required to verify theconclusions

Data Availability

)e data used to support the findings of the study are in-cluded in the article

Conflicts of Interest

)e authors declare no conflicts of interest

Acknowledgments

)is research was funded by the National Natural ScienceFoundation of China (51708160) Chinese ScholarshipCouncil (CSC No 201906125022) Research and InnovationFoundation (2018) the Shandong Taishan Scholars SpecialFund the Shandong Provincial Natural Science FoundationChina (ZR2015PE006) the Fundamental Research Funds forthe Central Universities (HITNSRIF2017018) and theScientific Research Foundation of Harbin Institute ofTechnology at Weihai (HIT(WH)201423)

References

[1] R M Koerner Designing with Geosynthetics Prentice-HallNew Jersey NJ USA 1998

[2] J P Giroud ldquoQuantification of geosynthetic behaviorrdquoGeosynthetics International vol 12 no 1 pp 2ndash27 2005

[3] J P Giroud ldquoReview of geotextile filter criteriardquo in Pro-ceedings of the Proceedings of the First Indian GeotextilesConference Indian Institute of Technology Bombay IndiaFebruary 1988

[4] American Society for Testing Materials ASTM D4751-16ASTMTest Method for Determining the Apparent Opening Sizeof a Geotextile American Society for Testing MaterialsPhiladelphia PA USA 2016

[5] European Committee for Standardization ENISO12956Geotextiles and Geotextile-Related Products-Determination ofthe Characteristic Opening Size European Committee forStandardization Brussels Belgium 1999

[6] Canadian General Standards Board CANICGSB-148 1-10Fifth Draft Method 10 Method of Testing Geotextiles

Filtration Opening Size of Geotextiles Canadian GeneralStandards Board Ottawa Canada 1991

[7] Y Jiao J He P Y Zhou and Z Q Cao ldquoPotential offlocculant-aided soil slurry dewatering in land reclamationlaboratory investigationsrdquo Advances Civil Engineeringvol 2018 Article ID 8040193 6 pages 2018

[8] A B Fourie and S M Kuchena ldquo)e influence of tensilestresses on the filtration characteristics of geotextilesrdquo Geo-synthetics International vol 2 no 2 pp 455ndash471 1995

[9] A B Fourie and P C Addis ldquo)e effect of in-plane tensileloads on the retention characteristics of geotextilesrdquo Geo-technical Testing Journal vol 20 pp 211ndash217 1997

[10] C-S Wu Y-S Hong and R-H Wang ldquo)e influence ofuniaxial tensile strain on the pore size and filtration char-acteristics of geotextilesrdquo Geotextiles and Geomembranesvol 26 no 3 pp 250ndash262 2008

[11] M Edwards and G Hsuan ldquoPermittivity of geotextiles withbiaxial tensile loadsrdquo in Proceedings of the 9th InternationalConference on Geosynthetics pp 1135ndash1140 Guaruja BrazilMay 2010

[12] A Rawal A Kochhar and A Gupta ldquoBiaxial tensile behaviorof spunbonded nonwoven geotextilesrdquo Geotextiles and Geo-membranes vol 29 no 6 pp 596ndash599 2011

[13] A Rawal and S K Agrahari ldquoPore size characteristics ofnonwoven structures under uniaxial tensile loadingrdquo Journalof Materials Science vol 46 no 13 pp 4487ndash4493 2011

[14] X-W Tang L Tang W She and B-S Gao ldquoPrediction ofpore size characteristics of woven slit-film geotextiles sub-jected to tensile strains film geotextiles subjected to tensilestrainsrdquo Geotextiles and Geomembranes vol 38 pp 43ndash502013

[15] G Lombard A Rollin and C Wolff ldquo)eoretical and ex-perimental opening sizes of heat-bonded geotextilesrdquo TextileResearch Journal vol 59 no 4 pp 208ndash217 1989

[16] Y H Faure J P Gourc and P Gendrin ldquoStructural study ofporometry and filtration opening size of geotextilesrdquo inEosynthetics Microstructure and Performance I D Peggs Edpp 102ndash119 American Society for Testing and MaterialsWest Conshohocken PA USA 1990

[17] A Rawal P V Kameswara Rao S Russell and A JeganathanldquoEffect of fiber orientation on pore size characteristics ofnonwoven structuresrdquo Journal of Applied Polymer Sciencevol 118 no 5 pp 2668ndash2673 2010

[18] A Rawal A Priyadarshi N Kumar S V Lomov andI Verpoest ldquoTensile behaviour of nonwoven structurescomparison with experimental resultsrdquo Journal of MaterialsScience vol 45 no 24 pp 6643ndash6652 2010

[19] A Rawal ldquoStructural analysis of pore size distribution ofnonwovensdaggerrdquo Journal of the Textile Institute vol 101 no 4pp 350ndash359 2010

[20] A Rawal and H Saraswat ldquoPore size distribution of hybridnonwoven geotextilesrdquo Geotextiles and Geomembranesvol 29 no 3 pp 363ndash367 2011

[21] L Tang S T Sun X W Tang and R X Zhang ldquoAnalysis ofpore size distributions of nonwoven geotextiles subjected tounequal biaxial tensile strainsrdquo in Springer Series in Geo-mechanics and Geoengineering pp 842ndash846 Springer BerlinGermany 2016

[22] R A Silva R G Negri and D de Mattos Vidal ldquoA newimage-based technique for measuring pore size distribution ofnonwoven geotextilesrdquo Geosynthetics International vol 26no 3 pp 261ndash272 2019

[23] A Rawal P V K Rao and V Kumar ldquoDeconstructing three-dimensional (3D) structure of absorptive glass mat (AGM)


separator to tailor pore dimensions and amplify electrolyteuptakerdquo Journal of Power Sources vol 384 pp 417ndash425 2018

[24] C S Wu and Y S Hong ldquo)e influence of tensile strain onthe pore size and flow capability of needle-punched non-woven geotextilesrdquo Geosynthetics International vol 23 no 6pp 422ndash434 2016

[25] S K Shukla N Sivakugan and S Mahto ldquoA simple methodfor estimating Poissonrsquos ratio of geosynthetics at zero strainrdquoASTMGeotechnical Testing Journal vol 32 pp 181ndash185 2009

[26] M E Kutay M Guler and A H Aydilek ldquoAnalysis of factorsaffecting strain distribution in geosyntheticsrdquo Journal ofGeotechnical and Geoenvironmental Engineering vol 132no 1 pp 1ndash11 2006

[27] P Verma M L Shofner A Lin K B Wagner andA C Griffin ldquoInducing out-of-plane auxetic behavior inneedle-punched nonwovensrdquo Physica Status Solidi (B)vol 252 no 7 pp 1455ndash1464 2015

[28] R K Rowe and B L J Myleville ldquoImplications of adopting anallowable geosynthetic strain in estimating stabilityrdquo inProceedings of the Fourth International Conference on Geo-textiles Geomembranes and Related Products vol 1pp 131ndash136 Hague Netherlands May 1990

[29] E Izadi T Decraene S De Strijcker A Bezuijen andD Vinckier ldquoA laboratory investigation on the impact re-sistance of a woven geotextilerdquo Geotextiles and Geo-membranes vol 46 no 1 pp 91ndash100 2018

[30] M-S Won and Y-S Kim ldquoInternal deformation behavior ofgeosynthetic-reinforced soil wallsrdquo Geotextiles and Geo-membranes vol 25 no 1 pp 10ndash22 2007

[31] P Schimelfenyg J Fowler and D Leshchinsky ldquoFabricreinforced containment dyke New Bedford superfund siterdquoin Proceedings of the Fourth International Conference onGeotextiles Geomembranes and Related Products vol 1pp 149ndash154 Hague Netherlands May 1990

[32] ASTM International ASTM D5199-12 Standard Test Methodfor Measuring the Nominal Fickness of Geosynthetics ASTMInternational West Conshohocken PA USA 2012

[33] J P Giroud ldquoPoissonrsquos ratio of unreinforced geomembranesand nonwoven geotextiles subjected to large strainsrdquo Geo-textiles and Geomembranes vol 22 no 4 pp 297ndash305 2004


fact that the microscopes can typically focus on limitedlayers of the fibres the samples employed in the literaturewere relatively thin which were generally less than 250 gm2

[13ndash23] If the sample is relatively thick the fibres in deeplayers will be blurry and cannot be evaluated with an opticalmicroscope

In the theoretical models of PSDs a nonwoven structureor geotextile is assumed to be an isotropic material [13ndash21]which means the in-plane and out-of-plane Poissonrsquos ratiosare taken as the same value Also the directional parameterKα at different levels of uniaxial tensile strains was not givenin the literature [13ndash21])e strained Kαwas calculated froman equation instead of the statistical work of reorientatedfibres [13 17] And limited experiments of nonwovengeotextiles have been carried out in validating or improvingthe theoretical model

When it comes to the experiments about the influence ofthe uniaxial tensile strain on the pore sizes or permeability ofnonwoven geotextiles the results are still scant [8ndash14]Fourie and Kuchena [8] demonstrated that tensile strain canlead to dramatic decreases in the flow rate through soil-geotextile systems for needle-punched nonwoven geo-textiles Edwards and Hsuan [11] reported that the needle-punched geotextile shows a decrease in flow rate whereasthe heat-set nonwoven geotextile experiences an increasewhen subjecting to uniaxial tensile loads )e PSDs of threeneedle-punched geotextiles tested by Wu and Hong [24]decrease with uniaxial tensile strains in wet sieving testsAnd the results of Wu et al [10] illustrated the pore size andthe mean flow rate through two heat-bonded nonwovengeotextiles increase with the increase in uniaxial tensilestrain It seems that the uniaxial strain results in the decreaseof pore sizes for the needle-punched geotextiles and theopposite trend was observed for heat-bonded nonwovengeotextiles More experiments still need to be done to verifythe conclusions [8ndash14 24]

)erefore in this study an existing model of PSDssubjected to uniaxial tensile strains has been modifiedconsidering the difference between the in-plane and out-of-plane Poissonrsquos ratios of geotextiles Two needle-punchednonwoven geotextiles were employed in dry sieving tests(ASTM D4751-16(A)) [4] to estimate the PSDs underuniaxial tensile strains )e directional parameters Kα atdifferent levels of uniaxial tensile strains have been obtainedfrom the image analysis of the fibres reorientation Also thein-plane and out-of-plane Poissonrsquos ratios of geotextiles havebeen estimated Comparisons have been made between thepredictions of the modified model and the original modelwith the experimental results )e modified model can moreaccurately predict the decreasing tendency of PSDs and thecorrected O95 and O98 under certain strain can be used as areference in design

2 Theoretical Model

21 Original Model Depending on an unstrained poremodel of Rawal et al [12 13 17ndash20] a theoretical model ofthe PSDs subjected to uniaxial tensile strains is shown asfollows )e cumulative probability Ff(d) of a particle with

diameter d passing through the layers of nonwoven is shownin the following equations [13 17ndash20]

Ff(d) 1 minus 1 + ω d +ω2d2

21113888 1113889e

minus ωd1113890 1113891

N

(1)

where

ω 4Vf(ε)Kα βf1113872 1113873

πDf

(2)

N Tg

Df

(3)

Vf(ε) Vf

(1 + ε)(1 minus ]ε)2 (4)

Kα βf1113872 1113873 1113946(π2)minus α

minus (π2)minus αcos βf

11138681113868111386811138681113868

11138681113868111386811138681113868 χ βf1113872 1113873dβf (5)

Vf μ

Tgρh

(6)

where ω is the coverage parameter N is the number oflayers Vf is the total fibre volume fraction ε is the uniaxialtensile strain Kα is the directional parameter χ(βf) is theorientation distribution function of fibres and βf is theorientation angle of fibres subjected to strains Df is the fibrediameter ] is Poissonrsquos ratio of the nonwoven μ is the initialmass per unit area Tg is the nonwoven thickness ρh is thefibre density )e details of the parameters were explained inthe literature [12 13 17ndash20]

22 Modified Model In equation (4) the uniaxial tensilebehaviour of a nonwoven geotextile is taken as a plane stressproblem And the out-of-plane Poissonrsquos ratio and the in-plane Poissonrsquos ratio are taken as the same parameter ]

According to the experimental results in the previousliterature and this study the out-of-plane Poissonrsquos ratio ofnonwoven geotextiles seems to be smaller than the in-planePoissonrsquos ratio [13 18 24ndash27] Rawal and Agrahari [13]demonstrated that the in-plane Poissonrsquos ratios in machinedirection range between 238 and 381 for two thermallybonded nonwovens )e relationship of in-plane Poissonrsquosratio and longitudinal strain was determined by Rawal et al[18] and the in-plane Poissonrsquos ratio can increase from 21 to40 with increasing strains )e in-plane Poissonrsquos ratio of anonwoven geotextile tested by Shukla et al [25] remains 175from zero to 10 strain Kutay et al [26] reported that thelateral strain is always greater than the axial strain for aneedle-punched nonwoven geotextile and Poissonrsquos ratio atfailure is equal to 21 In the literature the in-plane Poissonrsquosratios are at least equal to or larger than 10

When it comes to the out-of-plane Poissonrsquos ratioVerma et al [27] tested the out-of-plane Poissonrsquos ratio oftwo needle-punched polypropylene nonwoven NW1 andNW2 Both of the out-of-plane Poissonrsquos ratios of the twogeotextiles range between 021 and 037 when the strains



]perp minus εt

ε

k

t0 (7)



Vf(ε) Vf












GT1GT2GT3


νperp = 036

νperp = 017

νperp = 014

10

15

20

25

ic

knes

s (m

m)








(a)

380

380

250

280

100

100

Clamp

Unit mm

(b)

(c)

60

100

60

100

A

C

G B

D

E H F

Unit mm

Clamp

(d)








3

(10)


GH (11)

] minusε1ε2

(12)


4 Results





NW100NW200

νperp = 017

νperp = 031


800

1000

1200

1400

1600

1800

ic

knes

s (microm

)



(a) (b)


NW100 0

000

005

010

015

020

025

Rela

tive f

requ

ency


(a)

NW100 3

000

005

010

015

020

025

Rela

tive f

requ

ency


(b)

NW100 5

000

005

010

015

020

025

Rela

tive f

requ

ency


(c)

NW100 10

000

005

010

015

020

025

Rela

tive f

requ

ency


(d)

000

003

006

009

012

015

018NW200 0

Rela

tive f

requ

ency


(e)

NW200 3

000

003

006

009

012

015

018

Rela

tive f

requ

ency


(f )

Figure 5 Continued





5 Discussion


000

003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 5


(g)


003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 10

(h)



Strain () NW100 NW2000 063 0633 068 0655 071 06910 076 072

NW100 0 Kα = 06NW100 0 Kα = 08

NW200 0 Kα = 06NW200 0 Kα = 08

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency

100 200 300 400 5000Pore diameter (μm)









NW100

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(a)



NW100

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(b)



NW200

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(c)



NW200

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(d)



NW100

ExpTheo-OTheo-M

100

120

140

160

180

200

220

240

O95

(microm

)


(a)

NW200

ExpTheo-OTheo-M

60

80

100

120

O95

(microm

)


(b)









TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(a)



TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(b)

Figure 9 Continued



6 Conclusions





TB2

0

20

40

60

80

100Cu

mul

ativ

e fre

quen

cy (

)


(c)



TB2

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(d)


TB1 expTheo-OTheo-M


80

160

240

320

O98

(microm

)

(a)

TB2 expTheo-OTheo-M

300

400

500

600

700

800

900

O98

(microm

)


(b)





Data Availability




Acknowledgments


References







































]perp minus εt

ε

k

t0 (7)



Vf(ε) Vf












GT1GT2GT3


νperp = 036

νperp = 017

νperp = 014

10

15

20

25

ic

knes

s (m

m)








(a)

380

380

250

280

100

100

Clamp

Unit mm

(b)

(c)

60

100

60

100

A

C

G B

D

E H F

Unit mm

Clamp

(d)








3

(10)


GH (11)

] minusε1ε2

(12)


4 Results





NW100NW200

νperp = 017

νperp = 031


800

1000

1200

1400

1600

1800

ic

knes

s (microm

)



(a) (b)


NW100 0

000

005

010

015

020

025

Rela

tive f

requ

ency


(a)

NW100 3

000

005

010

015

020

025

Rela

tive f

requ

ency


(b)

NW100 5

000

005

010

015

020

025

Rela

tive f

requ

ency


(c)

NW100 10

000

005

010

015

020

025

Rela

tive f

requ

ency


(d)

000

003

006

009

012

015

018NW200 0

Rela

tive f

requ

ency


(e)

NW200 3

000

003

006

009

012

015

018

Rela

tive f

requ

ency


(f )

Figure 5 Continued





5 Discussion


000

003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 5


(g)


003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 10

(h)



Strain () NW100 NW2000 063 0633 068 0655 071 06910 076 072

NW100 0 Kα = 06NW100 0 Kα = 08

NW200 0 Kα = 06NW200 0 Kα = 08

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency

100 200 300 400 5000Pore diameter (μm)









NW100

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(a)



NW100

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(b)



NW200

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(c)



NW200

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(d)



NW100

ExpTheo-OTheo-M

100

120

140

160

180

200

220

240

O95

(microm

)


(a)

NW200

ExpTheo-OTheo-M

60

80

100

120

O95

(microm

)


(b)









TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(a)



TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(b)

Figure 9 Continued



6 Conclusions





TB2

0

20

40

60

80

100Cu

mul

ativ

e fre

quen

cy (

)


(c)



TB2

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(d)


TB1 expTheo-OTheo-M


80

160

240

320

O98

(microm

)

(a)

TB2 expTheo-OTheo-M

300

400

500

600

700

800

900

O98

(microm

)


(b)





Data Availability




Acknowledgments


References










































(a)

380

380

250

280

100

100

Clamp

Unit mm

(b)

(c)

60

100

60

100

A

C

G B

D

E H F

Unit mm

Clamp

(d)








3

(10)


GH (11)

] minusε1ε2

(12)


4 Results





NW100NW200

νperp = 017

νperp = 031


800

1000

1200

1400

1600

1800

ic

knes

s (microm

)



(a) (b)


NW100 0

000

005

010

015

020

025

Rela

tive f

requ

ency


(a)

NW100 3

000

005

010

015

020

025

Rela

tive f

requ

ency


(b)

NW100 5

000

005

010

015

020

025

Rela

tive f

requ

ency


(c)

NW100 10

000

005

010

015

020

025

Rela

tive f

requ

ency


(d)

000

003

006

009

012

015

018NW200 0

Rela

tive f

requ

ency


(e)

NW200 3

000

003

006

009

012

015

018

Rela

tive f

requ

ency


(f )

Figure 5 Continued





5 Discussion


000

003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 5


(g)


003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 10

(h)



Strain () NW100 NW2000 063 0633 068 0655 071 06910 076 072

NW100 0 Kα = 06NW100 0 Kα = 08

NW200 0 Kα = 06NW200 0 Kα = 08

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency

100 200 300 400 5000Pore diameter (μm)









NW100

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(a)



NW100

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(b)



NW200

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(c)



NW200

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(d)



NW100

ExpTheo-OTheo-M

100

120

140

160

180

200

220

240

O95

(microm

)


(a)

NW200

ExpTheo-OTheo-M

60

80

100

120

O95

(microm

)


(b)









TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(a)



TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(b)

Figure 9 Continued



6 Conclusions





TB2

0

20

40

60

80

100Cu

mul

ativ

e fre

quen

cy (

)


(c)



TB2

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(d)


TB1 expTheo-OTheo-M


80

160

240

320

O98

(microm

)

(a)

TB2 expTheo-OTheo-M

300

400

500

600

700

800

900

O98

(microm

)


(b)





Data Availability




Acknowledgments


References









































3

(10)


GH (11)

] minusε1ε2

(12)


4 Results





NW100NW200

νperp = 017

νperp = 031


800

1000

1200

1400

1600

1800

ic

knes

s (microm

)



(a) (b)


NW100 0

000

005

010

015

020

025

Rela

tive f

requ

ency


(a)

NW100 3

000

005

010

015

020

025

Rela

tive f

requ

ency


(b)

NW100 5

000

005

010

015

020

025

Rela

tive f

requ

ency


(c)

NW100 10

000

005

010

015

020

025

Rela

tive f

requ

ency


(d)

000

003

006

009

012

015

018NW200 0

Rela

tive f

requ

ency


(e)

NW200 3

000

003

006

009

012

015

018

Rela

tive f

requ

ency


(f )

Figure 5 Continued





5 Discussion


000

003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 5


(g)


003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 10

(h)



Strain () NW100 NW2000 063 0633 068 0655 071 06910 076 072

NW100 0 Kα = 06NW100 0 Kα = 08

NW200 0 Kα = 06NW200 0 Kα = 08

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency

100 200 300 400 5000Pore diameter (μm)









NW100

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(a)



NW100

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(b)



NW200

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(c)



NW200

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(d)



NW100

ExpTheo-OTheo-M

100

120

140

160

180

200

220

240

O95

(microm

)


(a)

NW200

ExpTheo-OTheo-M

60

80

100

120

O95

(microm

)


(b)









TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(a)



TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(b)

Figure 9 Continued



6 Conclusions





TB2

0

20

40

60

80

100Cu

mul

ativ

e fre

quen

cy (

)


(c)



TB2

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(d)


TB1 expTheo-OTheo-M


80

160

240

320

O98

(microm

)

(a)

TB2 expTheo-OTheo-M

300

400

500

600

700

800

900

O98

(microm

)


(b)





Data Availability




Acknowledgments


References






































(a) (b)


NW100 0

000

005

010

015

020

025

Rela

tive f

requ

ency


(a)

NW100 3

000

005

010

015

020

025

Rela

tive f

requ

ency


(b)

NW100 5

000

005

010

015

020

025

Rela

tive f

requ

ency


(c)

NW100 10

000

005

010

015

020

025

Rela

tive f

requ

ency


(d)

000

003

006

009

012

015

018NW200 0

Rela

tive f

requ

ency


(e)

NW200 3

000

003

006

009

012

015

018

Rela

tive f

requ

ency


(f )

Figure 5 Continued





5 Discussion


000

003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 5


(g)


003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 10

(h)



Strain () NW100 NW2000 063 0633 068 0655 071 06910 076 072

NW100 0 Kα = 06NW100 0 Kα = 08

NW200 0 Kα = 06NW200 0 Kα = 08

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency

100 200 300 400 5000Pore diameter (μm)









NW100

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(a)



NW100

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(b)



NW200

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(c)



NW200

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(d)



NW100

ExpTheo-OTheo-M

100

120

140

160

180

200

220

240

O95

(microm

)


(a)

NW200

ExpTheo-OTheo-M

60

80

100

120

O95

(microm

)


(b)









TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(a)



TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(b)

Figure 9 Continued



6 Conclusions





TB2

0

20

40

60

80

100Cu

mul

ativ

e fre

quen

cy (

)


(c)



TB2

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(d)


TB1 expTheo-OTheo-M


80

160

240

320

O98

(microm

)

(a)

TB2 expTheo-OTheo-M

300

400

500

600

700

800

900

O98

(microm

)


(b)





Data Availability




Acknowledgments


References









































5 Discussion


000

003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 5


(g)


003

006

009

012

015

018


Rela

tive f

requ

ency

NW200 10

(h)



Strain () NW100 NW2000 063 0633 068 0655 071 06910 076 072

NW100 0 Kα = 06NW100 0 Kα = 08

NW200 0 Kα = 06NW200 0 Kα = 08

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency

100 200 300 400 5000Pore diameter (μm)









NW100

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(a)



NW100

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(b)



NW200

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(c)



NW200

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(d)



NW100

ExpTheo-OTheo-M

100

120

140

160

180

200

220

240

O95

(microm

)


(a)

NW200

ExpTheo-OTheo-M

60

80

100

120

O95

(microm

)


(b)









TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(a)



TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(b)

Figure 9 Continued



6 Conclusions





TB2

0

20

40

60

80

100Cu

mul

ativ

e fre

quen

cy (

)


(c)



TB2

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(d)


TB1 expTheo-OTheo-M


80

160

240

320

O98

(microm

)

(a)

TB2 expTheo-OTheo-M

300

400

500

600

700

800

900

O98

(microm

)


(b)





Data Availability




Acknowledgments


References












































NW100

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(a)



NW100

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(b)



NW200

00

02

04

06

08

10

Cum

ulat

ive f

requ

ency


(c)



NW200

00

02

04

06

08

10Cu

mul

ativ

e fre

quen

cy


(d)



NW100

ExpTheo-OTheo-M

100

120

140

160

180

200

220

240

O95

(microm

)


(a)

NW200

ExpTheo-OTheo-M

60

80

100

120

O95

(microm

)


(b)









TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(a)



TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(b)

Figure 9 Continued



6 Conclusions





TB2

0

20

40

60

80

100Cu

mul

ativ

e fre

quen

cy (

)


(c)



TB2

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(d)


TB1 expTheo-OTheo-M


80

160

240

320

O98

(microm

)

(a)

TB2 expTheo-OTheo-M

300

400

500

600

700

800

900

O98

(microm

)


(b)





Data Availability




Acknowledgments


References






































NW100

ExpTheo-OTheo-M

100

120

140

160

180

200

220

240

O95

(microm

)


(a)

NW200

ExpTheo-OTheo-M

60

80

100

120

O95

(microm

)


(b)









TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(a)



TB1

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(b)

Figure 9 Continued



6 Conclusions





TB2

0

20

40

60

80

100Cu

mul

ativ

e fre

quen

cy (

)


(c)



TB2

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(d)


TB1 expTheo-OTheo-M


80

160

240

320

O98

(microm

)

(a)

TB2 expTheo-OTheo-M

300

400

500

600

700

800

900

O98

(microm

)


(b)





Data Availability




Acknowledgments


References







































6 Conclusions





TB2

0

20

40

60

80

100Cu

mul

ativ

e fre

quen

cy (

)


(c)



TB2

0

20

40

60

80

100

Cum

ulat

ive f

requ

ency

()


(d)


TB1 expTheo-OTheo-M


80

160

240

320

O98

(microm

)

(a)

TB2 expTheo-OTheo-M

300

400

500

600

700

800

900

O98

(microm

)


(b)





Data Availability




Acknowledgments


References








































Data Availability




Acknowledgments


References






































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