BEHAVIOR OF FABRIC- VERSUS FIBER-REINFORCED SAND

By Donald H. Gray,1 A. M. ASCE and Talal Al-Refeai2

ABSTRACT: Triaxial compression tests were run to compare the stress-strain re­sponse of a sand reinforced with continuous, oriented fabric layers as opposed to randomly distributed, discrete fibers. The influence of various test parame­ters such as amount of reinforcement, confining stress, and inclusion modulus and surface friction were also investigated. Test results showed that both types of reinforcement improved strength, increased the axial strain at failure, and in most cases reduced post-peak loss of strength. At very low strains (<1%) fabric inclusions resulted in a loss of compressive stiffness. This effect was not observed in the case of fiber reinforcement. The existence of a critical confining stress was common to both systems. Failure envelopes for reinforced sand par­alleled the unreinforced envelope above this stress. Strength increase was gen­erally proportional to the amount of reinforcement, i.e., the number of fabric layers or weight fraction of fibers, up to some limiting content. Thereafter, the strength increase approached an asymptotic upper limit. Fiber-reinforced sam­ples failed along a classic planar shear plane, whereas fabric-reinforced sand failed by bulging between layers.

INTRODUCTION

A variety of tensile inclusions ranging from low-modulus, polymeric materials to relatively stiff, high-strength metallic inclusions have been used to reinforce soils. These tensile inclusions come in many forms ranging from strips and grids to discrete fibers and woven and non-woven fabrics.

The main purpose of this paper is to report the results of comparison tests on the stress-deformation response of a dry sand reinforced with continuous, oriented fabric layers as opposed to discrete, randomly dis­tributed fibers. Oriented fabric layers or geotextiles are widely used in engineering practice in a variety of reinforcement applications (3,7,10,15). Reinforcement with randomly distributed, discrete fibers has attracted considerable attention in concrete technology (16). Very little informa­tion has been reported, on the other hand, on the use of this technique for reinforcing soils.

A secondary objective of the paper is to describe the influence of var­ious inclusion properties, soil properties, and test variables on the stress-deformation response of fabric- or fiber-reinforced sand. Finally, the pa­per explores the feasibility of fabric or fiber reinforcement to improve the performance of granular trenches or columns used to stabilize foot­ings in weak clays (12).

REVIEW OF LITERATURE

C o n t i n u o u s , Or iented Fabric Layers M o s t e n g i n e e r i n g fabrics or geotex t i les i n w i d e s p r e a d u s e a r e m a d e

'Prof., Dept. of Civ. Engrg., Univ. of Michigan, Ann Arbor, MI 48109. 2Asst. Prof., Dept. of Civ. Engrg. , King Saud Univ., Riyadh, Saudi Arabia. Note.—Discussion open until January 1, 1987. To extend the closing date one

month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on August 28, 1985. This paper is part of the Journal of Geotechnical Engineering, Vol. 112, No. 8, August, 1986. ©ASCE, ISSN 0733-9410/86/0008-0804/$01.00. Pa­per No. 20860.

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from polymeric materials or fibers. Typical polymers are polypropylene, polyester, polyethylene, and polyamide. The two most common types of geotextiles are woven and nonwoven fabrics. The former are manu­factured from two sets of parallel filaments or yard oriented in two mu­tually perpendicular directions. Nonwovens consist of a mat of fibers of either continuous or discrete length filaments, arranged in a random pat­tern and bonded together mechanically, thermally, or chemically.

A number of investigators (2,13,14) have conducted strength tests on sand specimens reinforced with fabric inclusions. The fabric inclusions were placed horizontally in the direction of the major principal plane. In general, results have shown that ultimate strength increased with in­creasing layers of fabric and that axial deformation tended to increase with decreasing spacing between fabric layers (increased number of lay­ers). Results of these tests have also shown that the strain required to reach peak strength increased and that the tendency towards brittle be­havior or loss of post-peak strength in dense sand was markedly re­duced by the presence of reinforcement. Furthermore, results showed that larger strains were required to reach peak stress in reinforced loose, as opposed to dense, sand.

Randomly Distributed, Discrete Fibers A considerable amount of research has been conducted on fiber re­

inforcement of soil using regular arrays of oriented fibers (4,18). Very few papers have been published, on the other hand, on randomly dis­tributed, discrete fiber reinforcement (6) in soils. Unlike geotextiles, such fibers are not currently marketed for soil reinforcement purposes. Short fibers consisting of steel and fiberglass are available commercially, how­ever, as admixes for fiber reinforcement of concrete.

Lee, et al. (11), reported the results of a single triaxial test on sand reinforced with firwood shavings. Their results showed that small amounts of fiber markedly increased both the strength and rigidity of the sand. Andersland and Khattak (1) presented the results of triaxial tests on a kaolin clay reinforced with paper pulp (cellulose) fibers. The specimens were consolidated from a slurry mix. The addition of fibers increased both the stiffness and undrained strength of the kaolinite.

Hoare (6) reported the results of laboratory compression and CBR tests on a sandy gravel reinforced with very small amounts (less than 2% by weight) of random fibers. Compaction tests showed that the fibers in­creased the resistance to densification. When a constant compactive ef­fort was applied to a range of samples with increasing fiber content, the strength either increased hardly at all or actually decreased. This was caused by the concommitant increase in porosity that occurred with in­creasing fiber content. An increase in soil porosity or void ratio would tend to negate any increase in strength from fiber reinforcement.

THEORETICAL DEVELOPMENT

Fabric Reinforcement Several investigators (2,14,17,19) have reported the results of triaxial

and plane strain compression tests on cylindrical samples of dry sand containing thin, horizontal layers of tensile reinforcing material. The re-

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suits of these triaxial tests on fabric-reinforced sand have been inter­preted in two different yet related ways.

Equivalent Confining Stress Concept.—Yang (19) hypothesized on the basis of his tests that tensile restraint in the reinforcement induced an "equivalent confining stress" increase, Acx3 . Accordingly, from the Mohr-Coulomb formulation for the strength of a cohesionless material, it fol­lows that

K ) K = (03 + ^)KP (1) in which (alf)R = major principal stress at failure in reinforced sand; tr3 = applied confining stress on the sample; Kp = tan2 (45 + 4>/2); 4> = friction angle of the unreinforced sand.

Pseudo-Cohesion Concept.—Schlosser and Long (17) proposed that the reinforcements induced an anisotropic or pseudo cohesion cR that was a function of their spacing and tensile strength. Thus, the strength of the reinforced composite is given by

(<rlf)R = <r3Kp + 2cRVK„ (2)

The anisotropic of pseudo cohesion (cR) was computed from a force-equilibrium analysis of a reinforced composite. The following expres­sions can be derived:

Horizontal reinforcement: cR = (3) 2AH V ;

a f[K„cos2p - s i n 2 p ] Inclined reinforcement: cR = — (4)

2AHWp

in which af = force per unit width of reinforcement at failure; AH = spacing between reinforcements; and (3 = angle of inclination of rein­forcement counterclockwise from the major principal plane.

Comparison of Eqs. 1 and 2 indicates a correspondence between Acr3 and cR, i.e.,

°V VK: CR = — ^ • (5)

Comparison of Eqs. 3 and 5, in turn, shows the following:

aF Aa3 = — (6)

AH W

Thus, the tensile resistance of the reinforcement (aF/AH) is directly equal to the equivalent confining stress increase (Acr3). If the reinforcements break, af is replaced by the tensile strength (RT) of the fabric. On the other hand, if they merely stretch, the usual case with highly extensible, low-modulus fabrics, aF is equal to the tensile strain in the fabric times its modulus.

Fiber Reinforcement Comparable models have not been developed for predicting strength

increases from randomly distributed, discrete fibers in soil. Force-equi-

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FIG. 1.—Model for Oriented Fiber Reinforcement In Sand: (a) Perpendicular Fi­bers; and {b) Inclined Fibers

librium models have been developed, however, for oriented, fiber arrays (4,18). Models for individual fibers, initially oriented either perpendic­ularly or inclined to the shear surface in a sand are shown in Fig. 1. Shearing stress that develops in the sand mobilizes tensile resistance in the fibers via friction at the fiber-sand interface. Shearing action in the sand causes the fibers to distort as shown; as a result the tensile resis­tance in the fibers is directed into a normal component, which increases the confining stress on the failure plane and a tangential component that directly opposes shear. The predicted strength increase from regular ar­rays of multiple, oriented fibers is given by the following equations:

Perpendicular fibers: ASR = tR(sin 6 + cos 0 tan c}>)

Inclined fibers: ASR = fR[sin (90 - i|/) + cos (90 - t|/) tan <M

in which <\i = tan~J

k + (tan 0~\

(7)

(8)

(9)

and SR = shear strength increase from fiber reinforcement; tR = mobi­lized tensile strength of fibers per unit area of soil; § = angle of internal friction of sand; 6 = angle of shear distortion; i = initial orientation angle of fiber with respect to the shear surface; k = shear distortion ratio (k = x/z); z = thickness of shear zone; and x = horizontal shear displacement.

The mobilized tensile strength per unit area of soil (tR) is the product of the tensile stress in the fiber at the shear plane and the area ratio or concentration of fibers in the shear plane:

tn = AR

°R (10)

in which aR = tensile stress developed in the fibers at the shear plane; and AR/A = fiber area ratio.

Orientation Effects Predictive models for strength increases from either fabric or fiber re­

inforcement with oriented arrays take into account the initial angle of inclination with respect to the failure plane. Both types of models predict that maximum strength increase occurs where the reinforcements are oriented in the direction of maximum principal tensile strain (4,9). This

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Initial Orientation of Fiber

Rientorcemenl.i - degrees

ASr,= t H [ s i n ( 9 0 - ^ ) +

cos(90-^)tand>]

FIG. 2.—Theoretical Influence of Initial Orientation of Reinforcements with Re­spect to Failure Surface: (a) Fabric Layers; and (b) Fibers

.'CK

0.3

'0.2

2 UJ a: u

X <5 0.1 z UJ ir i-co

< LU x CO

bJ o CD u

< rr LU > <

-0.1 -

#2 REED FIBERS

L = 4 .9cm , / A = 0 . 4 5 6 %

SINGLE PLANE OF STIFF, ROUGH REINFORCEMENT

(from Jewel 1,1980)

INITIAL FIBER ORIENTATION,!- DEGREES

FIG. 3.—Influence of Initial Fiber Orientation on Observed Shear Strength In­creases in Dry Sand

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translates into horizontal reinforcements in the case of triaxiai compres­sion tests on fabric-reinforced sands and reinforcements initially inclined approximately 60° to the shear plane in the case of oriented fiber rein­forcement in dry sand (<$> = 30°) in a direct shear test. Fig. 2 shows the theoretically predicted influence of initial orientation based on Eqs. 4, 8, and 9. These predictions have been verified experimentally (4,10) in the case of oriented fiber reinforcement, as shown in Fig. 3.

In the case of randomly distributed fibers it can be shown from sta­tistical analysis (16) that the most probable orientation of randomly dis­tributed fibers with respect to a shear failure surface in a sand is 90°. Gray and Ohashi (4) corroborated this prediction by running a test in which fibers were inserted at random angles with respect to the shear surface in a direct shear test. The failure envelope for randomly oriented fibers virtually coincided with the envelope for perpendicular fibers.

EXPERIMENTAL PROGRAM

Material Properties Triaxiai compression tests were run on reinforced samples of a dry

dune sand from Muskegon, Michigan. This sand is a clean, uniform, medium-grained sand that has been used in previous reinforcement studies (4,5) at the University of Michigan. Properties of the sand are summarized in Table 1.

Commercially available geotextiles with a range of mechanical and rheological properties were selected for fabric reinforcement (see Tables 2 and 3). Both woven and nonwoven fabrics were tested. Fiberglas 196 (boat cloth) was included as well in order to test a fabric with a relatively high tensile modulus and low surface friction. The latter was determined from interface friction tests for sand sliding on a fabric surface.

Both natural and synthetic fibers were used in the study of randomly distributed, discrete fiber reinforcement. The fibers varied from 13 to 38 mm in length and from 0.3 to 1.75 mm in diameter. The synthetic fibers are made of glass and are available commercially as admixes for fiber-reinforced concrete. Properties of the fibers are summarized in Table 4.

The glass fibers used in the testing program were supplied by the manufacturer in standard lengths of 13, 25, and 38 mm. These synthetic fibers are considerably denser and stiffer than the natural reed fibers, but they also have much lower surface friction properties. The reed fi­bers were cut from long fibers to the same lengths as the glass fibers. Although the lengths of the two types of fibers were the same, the glass

TABLE 1.—Properties of Muskegon Dune Sand

Effective grain

size, D10

(1)

0.28 mm

Median grain diam­

eter, D50

(2)

0.41 mm

Coefficient of uni­

formity, C„ (3)

1.50

Specific gravity of solids, Gs

(4)

2.65

Maximum void

ratio, emax

(5)

0.78

Minimum void

ratio, emln

(6)

0.50

Angle of internal friction (triaxiai test)

(7)

39° (Dr = 86%) 32° (Dr = 21%)

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TABLE 2.—Physical Properties of Geotextiles

Fabric (1)

GEOLON 400

GEOLON 200

TYPAR 3601

TYPAR 3401

FIBERGLAS 196

Manufacturer (2)

Nicolon Corp

Nicolon Corp

Dupont

Dupont

Baymills

Filament (3)

Polypropylene multifilament

Polypropylene tape

Polypropylene multifilament

Polypropylene multifilament

Glass yarn monofilament

Fabrication process

(4)

woven

woven

nonwoven

nonwoven

woven

Nominal thickness

(mm) (5)

0.74

0.46

0.46

0.38

1.09

Weight (g/m2) . (6)

220

136

203

136

1,153

TABLE 3,—Mechanical Properties of Geotextiles

Fabric

(D GEOLON 400 GEOLON 200 TYPAR 3601 TYPAR 3401 FIBERGLAS 196

Tensile" strength (lbs/in.)

(2)

250 x 175b

160 225 130

318 x 273

Elongation at break (%)

(3) 15 X 15

25 63 62

8 X 10

Mullen burst (psi) (4)

420 375 263 170 —

Secant Modulus0

(lbs/in.) 5% (5)

922 356 60 23

2,742

10% (6)

1,085 340 73 29

3,975 (@ 8%) aASTM D-1682 Method 16 at 12 in./min constant rate of extension. bWarp and fill directions, respectively. cWarp direction. Note: 1 lb/in. = 0.175 kN/m; 1 psi = 6.89 kPa.

TABLE 4.—Fiber Properties

Fiber (1)

#1 Reed" #2 Reed Glass fiberb

Diameter (mm) (2)

1.25 1.75 0.30

Specific gravity (3)

0.58 0.58 2.70

Tensile strength kg/cm2 x 103

(4)

0.34 0.34

12.76

Tensile modulus kg/cm2 x 10"

(5)

1.5 1.5

71.4

"Common basket reed (Phragmites communis). bNo. 204 filament strands produced by Owings Corning Glass.

fibers had much larger aspect ( length/diameter) ratios because of their smaller diameters.

Triaxial Compression Tests Fabrics.—A standard Geonor triaxial apparatus was used for testing

fabric-reinforced sand. All tests were carried out on cylindrical samples

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':;'•}'/; 1

AH/2

1

T £& H/2

-r AH

AH/2 J.

• . . %

— ' — • —

AH/2

AH

A H / 2

N=1 N = 2 N = 3

FIG. 4.—Fabric Layer Positions in Triaxial Test Specimens

with a diameter of 36 mm and a height of 80 mm. The reinforcements consisted of circular disks of fabric, which were cut from fabric sheets by rotating a heated, sharpened aluminum tube (35-mm I.D.) on fabric placed on a wood block.

The sand was tested in both dense (e = 0.54) and loose (e = 0.72) conditions. These void ratios corresponded to relative densities of 86% and 21%, respectively. For reinforced sand samples, the specimens were built up layer by layer with circular disks of fabric placed at predeter­mined intervals. The number of reinforcement layers varied from 1 to 6. The spacing between consecutive layers was kept equal and double the distance from the ends, as shown schematically in Fig. 4. The triaxial specimens were loaded to failure under five different confining pres­sures (0.5, 1, 2, 3, and 4 kg/cm2).

The equivalent confining stress increase (Aa3) from fabric reinforce­ment was determined from the observed increase in major principal stress at failure according to the following relationship:

Aa3 = a3 l~n (11)

in which Acr3 = equivalent confining stress increase; Aav = increase in major principal stress at failure; and crlf = major principal stress at failure for the unreinforced sand.

The reinforcement or pseudo cohesion (cR) was calculated from Eqs. 5 and 11 according to the following:

CR = (12)

Fibers.—Triaxial compression tests on sands reinforced with short fi­bers were carried out on the same size specimens used for the fabric-reinforced sand. Tests on sand reinforced with the longer fibers (38 mm), on the other hand, were performed on 71-mm diameter and 180-mm high samples.

Mixing is a critical factor in the case of discrete, randomly oriented fiber reinforcement. Blade or paddle-type mixers will not work as they tend to drag and ball up the fibers. Vibratory mixers tend to float the fibers up. A special oscillatory or helical action mixer was used to avoid

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these problems. But even this type of mixer has limitations on the max­imum weight fraction of fiber that can be uniformly and randomly dis­tributed in the mix. The degree of randomness in the mixture was de­termined by visual inspection.

Segregation tends to occur when a dry, fiber-sand mixture is trans­ferred to a triaxial mold prior to testing. It was necessary to moisten the sand slightly in order to avoid segregation while transferring the mix and forming the samples. A water content of 10% was selected for this purpose. This moisture content provided enough apparent cohesion to prevent segregation during the formation of the samples. Furthermore, this moisture content did not significantly affect the stiffness and stress-deformation properties of Muskegon dune sand. The sand contains no fines and is sufficiently coarse (see Table 1) that capillary effects were unimportant at this moisture content. This was checked by control tests on unreinforced samples of the sand at a moisture content of 10%.

Both intergranular porosity and amount and type of compaction affect the response (6) of a fiber-reinforced soil. The greater the fiber content, the greater compactive effort required to maintain a given porosity. On the other hand, an increase in compactive effort also results in greater fiber entanglement and distortion, which also affects the response of fiber-reinforced soil. A decision was made, therefore, to keep the inter­granular porosity constant and adjust the compactive effort as neces­sary. An intermediate void ratio of 0.62 (Dr = 57%) was selected because it was easily achieved for most of the fiber concentrations. Reported void ratios are based on the weight of mineral solids rather than total solids. Compaction was achieved by lightly tamping successive layers of moist sand-fiber mix with a tamper consisting of a circular disk attached to a steel rod. The disk had a diameter slightly less than the mold to mini­mize any shear distortion and reorientation during placement of the mix­ture.

Test Variables.—A number of soil, fiber, and test parameters were systematically varied in order to examine their influence on the stress-deformation response and strength of reinforced sand. These test pa­rameters are summarized in Table 5 for fabric- and fiber-reinforced sand.

Strain rate is an important consideration in the case of reinforcement with polymeric fabrics, which are subject to creep and stress relaxation. In order to study strain-rate effects several preliminary triaxial tests were run on samples reinforced with three layers of each fabric under a wide range of strain rates between 0.03%/min and 1.56%/min at a constant

TABLE 5.—Test Parameters

Fabric reinforcement (1)

Sand relative density Confining stress No fabric layers and spacing Strain rate Fabric modulus and surface friction

characteristics

Fiber reinforcement (2)

Confining stress Fiber weight fraction Fiber aspect ratio Compactive effort Fiber modulus and surface friction

characteristics

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confining stress of 2 kg/cm2. All fabrics tested were insensitive to changes of strain rate up to 1%/min. A strain rate of 0.40%/min was chosen for all subsequent triaxial tests reported herein.

TEST RESULTS

Reinforcement with randomly distributed, discrete fibers resulted in both striking similarities and significant differences in constitutive be­havior compared to reinforcement with continuous, oriented fabric lay­ers. These differences and similarities in constitutive behavior are sum­marized herein.

Similarities in Constitutive Behavior Increasing amounts of reinforcement, greater number of fabric layers

(N), or larger weight fraction of fibers (co ) increased peak strength and reduced post-peak loss in strength of dense sand at high strains, as shown in Fig. 5. The existence of a critical confining stress is common to both systems. Failure envelopes for reinforced sands parallel the unreinforced envelope above this stress, as shown in Fig. 6. The lower the surface roughness or interface friction, e.g., Fiberglass 196, the greater is the critical confining stress. For example, the threshold or critical confining stress was approximately 1 kg/cm2 for the rough-textured fabrics, whereas it exceeded 4 kg/cm2 for the smooth fiberglass cloth.

Strength increase is generally proportional to the amount of reinforce­ment, i.e., the number of fabric layers or weight fraction of fibers, up to some limiting content, as shown in Fig. 7. In the case of fiber rein-

FIG. 5.—Stress-Strain Relationships from Triaxial Compression Tests on Rein­forced Muskegon Dune Sand: (a) Oriented, Fabric Layers; and (6) Random, Dis­crete Fibers (N = Number of Fabric Layers, a>, = Weight Fraction of Fibers

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Soil Only Qeolon 400 Geolon 200 Typar 3601 Typar 3401 F. Glass 196

(a) a 3 (Kg/cm2) Confining Stress o$ (Kg/cm2)

FIG. 6.—Failure Envelopes from Triaxial Compression Tests on Reinforced Mus­kegon Dune Sand: (a) Oriented, Fabric Layers; and (b) Random, Discrete Fibers (I/O, = Fiber Aspect Ratio)

forcement [Fig. 7(b)] the strength versus fiber-content relationship was also affected by aspect ratio (I/O,) or the ratio of fiber length (/) to fiber diameter (il). At higher reinforcement contents, the strength increase tended to approach an asymptotic upper limit. This behavior was ob­served in all cases for the fabrics but was only checked experimentally for the plastic fibers at an aspect ratio of 84.

Yang (19) presented a semi-empirical equation that relates the equiv­alent confining stress increase (cr3) to the reinforcement spacing ratio (AH/ d) in a triaxial test. The equation has the following form:

(a)

e = .5

$ Geolon

O Typar

Number Of Layers

4 0 0

3401

6

» S

t F

ailu

re

i 5

I -= £

I

S

El

CO

**

Glass Fiber

/ *

J "'' / /

1/ i/a /** » "

O 125

0 1 2 3 4 S

(W W| (%)

„ * - * -

6 7

FIG. 7.—Strength Increase as Function of Amount of Internal Reinforcement in Triaxial Compression Tests on Muskegon Dune Sand: (a) Oriented, Fabric Layers; and (to) Random, Discrete Fibers

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Geolon 200

Theo re t i ca l (a f te r Yang 1972 )

%L I est Resul ts

0.0 O.S 1.0 1.5 2.0 2.5

AH/d

FIG. 8.—Relationship between Spacing/Diameter Ratio and Strength Ratio for Fabric-Reinforced Sand

Q~3 + Arj 3

f j 3 /AH" (13)

in which CT3 = initial confining stress; AH = spacing between reinforce­ment layers; d = triaxial specimen diameter; and C,m = empirical con­stants.

Fig. 8 shows the curve predicted by Eq. 13 and experimental results of triaxial tests on a sand reinforced with layers of a woven geotextile. Similar results were observed with other fabrics. The experimental re­sults and theoretical curve compare fairly well at large spacing ratios, but diverge at ratios less than 0.5. These results indicate that reinforce­ments placed at spacing ratios (AH/d) more than unity have little effect.

In the case of fiber reinforcement, it was observed that the strength, as expressed by the major principal stress at failure for a given fiber and aspect ratio, was proportional to the weight fraction (see Fig. 7). Cross plots of these curves also showed that strength varied linearly with as­pect ratio for a given weight fraction, and that the slope of these curves increased with larger fiber concentrations. These cross plots are shown in Fig. 9 for both the reed and glass fibers. The graphical plots in Fig. 9 are useful because they reveal the combinations of fiber type, aspect ratio, and weight fraction that will yield a desired strength increase. Fig. 9 also shows the efficiency of "rougher" reed fibers relative to the "smooth" glass fibers. For example, at equal weight fractions and aspect ratios (e.g., 1% and 40, respectively) the reed fibers are considerably more effective. The vertical dashed lines terminated by arrows in Fig. 9

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Glass Fiber

# 1 Reed

Wf %

0 20 40 60 80 I00 120 140

Jt/0.

FIG. 9.—Major Principal Stress at Failure for Fiber-Reinforced Sand as Function of Aspect Ratio at Different Fiber Weight Fractions

indicate the difference in strength at equal aspect ratio (l/il) and weight fraction (u^). This comparison is based on extrapolated data for the reed fibers.

Differences in Constitutive Behavior Despite many similarities in their constitutive behavior some funda­

mental differences were observed between sands reinforced with ran­dom fibers as opposed to oriented fabric layers. Major differences in con­stitutive behavior are summarized in Table 6 and in Figs. 10 and 11.

In addition to these differences in constitutive behavior there are also practical differences in the way the reinforcements can be incorporated into a sand. Geotextiles must be placed layer by layer, usually by hand, between successive lifts of sand. Random fiber reinforcement, on the other hand, is a variant of admixture stabilization. The sand-fiber mix is

TABLE 6.—Major Differences in Constitutive Behavior

Property or behavior

(1) Mode of failure

(Fig. 10) Stiffness (Fig. 11) Orientation effect

Type of Reinforcement

Continuous, oriented fabric (2)

Bulging between layers Decreases at low strains Horizontal fabric layers (initially

oriented parallel to the major principal plane or in the direc­tion of major principal tensile strain) yield the largest strength increases (Ref. 4).

Discrete, random fibers (3)

Classic, planar failure Increases at all strains Random fiber placement

yields results similar to those observed with aligned fibers initially oriented 90° to the fail­ure plane (Ref. 5).

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FIG. 10.—Mode of Failure Observed during Triaxial Compression Tests on Rein­forced Muskegon Dune Sand: (a) Oriented, Fabric Layers; and (b) Random, Dis­crete Fibers

Typar 360I as=2Kg/cm

e=.54

(a) <b)

Gloss Fiber t?5= 2 Kg/cm

e=.62

i /f l 34

12S

Wf % .5 2

o a a m

Axial Strain (%) Axial Strain {%)

FIG. 11.—Normalized Secant Modulus versus Strain in Reinforced Muskegon Dune Sand: (a) Oriented, Fabric Layers; and (b) Random, Discrete Fibers

simply placed in lifts and tamped sufficiently to yield the desired void ratio.

These two types of placement conditions would likely affect both labor and construction requirements. These requirements in turn could influ­ence the feasibility and cost effectiveness of either method for such ap­plications as reinforced granular columns or trenches for stabilizing weak clay soils.

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REINFORCED GRANULAR TRENCHES AND COLUMNS

The load-carrying capacity of soft soils can be improved by using gran­ular piles, also known as stone columns (8), as shown in Fig. 12. The two-dimensional plane-strain version of a granular pile is a granular trench. Madhav and Vitkar (12) have investigated the latter problem and have derived analytical expressions for the ultimate bearing capacity of footings on such stabilized soils. They presented bearing capacity factors for various combinations of parameters considered, e.g., the ratio of trench-to-footing width, the ratio of granular trench cohesion to external soil cohesion, etc.

The effectiveness of a granular trench or column can be improved still further by internal reinforcement with randomly distributed fibers or ori­ented fabric layers. The results reported herein can be used to gage the degree of improvement. The bearing capacity factors Nc, Ny, and Nq for a strip footing on weak clay stabilized with a granular trench have been evaluated (12) for a range of conditions in the ratios A/B and cx/c2. Sub­script 2 refers to the weak soil and subscript 1, to the granular trench. Significant increases in the bearing capacity factors were predicted (12) for all ratios of A/B greater than zero when the ratio Ci/c2 approaches unity.

The cohesion C\ can be provided by intrinsic cohesion, i.e., the pres­ence of a clay binder in the granular medium, or by pseudo cohesion cR from internal reinforcement. The main difference in these two types of cohesion is that the latter depends upon confining stress for full mobi­lization.

The results presented herein suggest that by adding the right amount of either fabric or fiber reinforcement to a granular trench or column it should be possible to match the cohesion of the surrounding soil, in other words, to achieve the higher Nc value for the case Ci/cz = 1. Fig. 7 shows that either three layers of geotextile (AH/d = 0.74) or 1% by weight of glass fibers with an aspect ratio of 125 would provide an in­crease in major principal stress at failure {uif) or 4 kg/cm2 (392 kPa) in a sand column subjected to an average confining stress (<r3) of 2 kg/cm2

(196 kPa). This increase in major principal stress at failure corresponds

H-— B — —&A

n u i u i i

Weak clay

Granular pile

or trench

L

•

t

Weak clay

h>— A —H

FIG. 12.—Granular Trench or Column for Stabilising Weak Clay Soils

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(Eq. 11) to a pseudo cohesion (cR) of approximately 0.96 kg/cm2 (94 kPa). Thus, for all expected values of cohesion c2 in a surrounding weak clay soil it should be possible to at least match this cohesion by internal re­inforcement in the granular trench or column.

CONCLUSIONS

Triaxial compression tests were run on a dry sand reinforced with ran­domly distributed, discrete fibers and oriented, continuous fabric layers. Test results showed that both types of reinforcement systems increased strength and modified the stress-deformation behavior of sand in a sig­nificant manner. The following main conclusions emerged from the study:

1. Continuous, oriented fabric inclusions markedly increased the ul­timate strength, increased the axial strain at failure, and in most cases limited reductions in post-peak loss of strength.

2. At very low strains (<1%) fabric inclusions produced a loss in com­pressive stiffness of triaxial specimens. The loss in stiffness was more pronounced when the number of layers or the tensile modulus of the fabric was greater.

3. Fabric reinforcements placed at spacing/diameter ratios greater than one had little effect on strength.

4. Discrete, randomly distributed fibers increased both the ultimate strength and the stiffness of reinforced sand. The decrease in stiffness at low strains, observed with fabric inclusions, did not occur with the fibers.

5. The increase in strength with fiber content varied linearly up to a fiber content of 2% by weight, and thereafter approached an asymptotic upper limit. The rate of increase was roughly proportional to the fiber aspect ratio.

6. At the same aspect ratio, confining stress, and weight fraction, rougher (not stiffer) fibers tended to be more effective in increasing strength.

7. Internal fabric or fiber reinforcement of a granular trench used to stabilize a weak clay soil should substantially increase the bearing ca­pacity of a strip footing placed on the soil.

ACKNOWLEDGMENT

The study described in this paper was supported by a research grant from the Air Force Office of Scientific Research, Grant No. AFOSR-84-0189.

APPENDIX.—-REFERENCES

1. Andersland, O. B., and Khattak, A. S., "Shear Strength of Kaolinite/Fiber Soil Mixtures," Proceedings, International Conference on Soil Reinforcement, Vol. I, Paris, France, 1979, pp. 11-16.

2. Broms, B. B., "Triaxial Tests with Fabric-Reinforced Soil," Proceedings, Inter­national Conference on Use of Fabrics in Geotechnics, L'Ecole Nationale des Ponts et Chaussees, Vol. Ill, Paris, France, 1977, pp. 129-133.

3. Giroud, J. P., "Geotextiles and Geomembranes," Geotextiles and Geomembranes

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Journal, Vol. 1, No. 2, Feb., 1984, pp. 5-40. 4. Gray, D. H., and Ohashi, H., "Mechanics of Fiber Reinforcement in Sand,"

Journal of the Geotechnical Engineering Division, ASCE, Vol. 109, No. GT3, Pa­per 17780, Mar., 1983, pp. 335-353.

5. Gray, D. H., Athanasopoulos, G., and Ohashi, H., "Internal/External Fabric Reinforcement of Sand," Proceedings, 2nd International Conference on Geo-textiles, Vol. Ill, Las Vegas, Nev., 1982, pp. 611-616.

6. Hoare, D. J., and "Laboratory Study of Granular Soils Reinforced with Ran­domly Oriented Discrete Fibers," Proceedings, International Conference on the Use of Fabrics in Geotechnics, L'Ecole Nationale des Ponts et Chaussees, Vol. I, Paris, France, 1977, pp. 47-52.

7. Holtz, R. D., and Broms, B. B., "Wall Reinforced by Fabrics," Proceedings, International Conference on the Use of Fabrics in Geotechnics, L'Ecole des Ponts et Chaussees, Vol. I, Paris, France, 1977, pp. 113-117.

8. Hughes, J. M., and Whithers, N. J., "Reinforcement of Soft Cohesive Soil with Stone Columns," Grand Engineering, Vol. 7, 1974, pp. 42-49.

9. Jewell, R. A., "Some Factors which Influence the Shear Strength of Rein­forced Sand," CUED/D-Soils/TR85, Cambridge University Engineering De­partment, Cambridge Univ., England, 1980.

10. Koerner, R. M., and Welsh, J. P., Construction and Geotechnical Engineering Using Synthetic Fabrics, Wiley and Sons, N.Y., 1980, 265 pp.

11. Lee, K. L., Adams, B. D., and Vagneron, J. J., "Reinforced Earth Retaining Walls," Journal of Soil Mechanics and Foundations Division, ASCE, Vol. 99, SM10, Oct., 1973, pp. 745-764.

12. Madhav, M. R., and Vitkar, P. P., "Strip Footing on Weak Clay Stabilized with a Granular Trench or Pile," Canadian Geotechnical Journal, Vol. 15, 1978, pp. 605-609.

13. McGown, A., and Andrawes, K. Z., "The Influence of Non-Woven Fabric Inclusions on the Stress-Strain Behavior of a Soil Mass," Proceedings, Inter­national Conference on the Use of Fabrics in Geotechnics, L'Ecole des Ponts et Chaussees, Vol. I, Paris, France, 1977, pp. 161-166.

14. McGown, A., Andrawes, K. Z., and Al-Hasani, M. M., "Effect of Inclusion Properties on the Behavior of Sand," Geotechnique, Vol. 28, No. 3, Mar., 1978, pp. 327-346.

15. Mitchell, J. K., and Schlosser, F., "Mechanism, Behavior and Design Meth­ods for Earth Reinforcement," General Report, Proceedings, International Conference on Soil Reinforcement, Vol. I, Paris, France, 1979, pp. 25-74.

16. Namaan, T., Moavenzadah, F., and McGarry, F., "Probabilistic Analysis of Fiber Reinforced Concrete," Journal of Engineering Mechanics Division, ASCE, Vol. 100, No. EM2, Feb., 1974, pp. 397-413.

17. Schlosser, F., and Long, N. T., "Recent Results in French Research on Rein­forced Earth," Journal of the Construction Division, ASCE, Vol. 100, No. C03, Mar., 1974, pp. 223-237.

18. Waldron, L. J., "Shear Resistance of Root-Permeated Homogeneous and Stratified Soil," Soil Science Society of America Proceedings, Vol. 41, 1977, pp. 843-849.

19. Yang, Z., "Strength and Deformation Characteristics of Reinforced Sand," dissertation presented to the University of California, at Los Angeles, Calif., in 1972, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.

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