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Geotextiles and Geomembranes 24 (2006) 116128

A simple method to evaluate the pullout resistance of extruded geogrids

embedded in a compacted granular soil

Nicola Moraci, Domenico Gioffre`

Universita Mediterranea di Reggio Calabria, Dip. MECMAT, via Graziella Loc. Feo di Vito, I-89060 Reggio Calabria, Italy

Received 28 February 2005; received in revised form 26 September 2005; accepted 15 November 2005

Available online 10 January 2006

Abstract

Pullout tests are necessary in order to study the interaction behaviour between soil and geosynthetics in the anchorage zone; hence, the

resulting properties have direct implications on the design of reinforced soil structures.

Several experimental studies showed the influence of different parameters (reinforcement stiffness, geometry and length, applied

vertical effective stress, and geotechnical properties of soil) on the peak and on residual pullout resistance.

On the basis of the results of the tests carried out by Moraci and Recalcati [2005. Factors affecting the pullout behaviour of extruded

geogrids embedded in a compacted granular soil. Geotextiles and Geomembranes, submitted for publication], a new theoretical method

was developed to determine the peak and the residual pullout resistance of extruded geogrids embedded in a compacted granular soil.

The method is capable of evaluating both the bearing and the frictional components of pullout resistance, taking into account the

reinforcement extensibility and geometry as well as the non-linearity of the failure envelope of backfill soil. The comparison between

theoretical and experimental results was favourable, thus confirming the suitability of the proposed approach.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Soil dilatancy; Reinforcement extensibility; Pullout resistance; Skin friction; Bearing resistance

1. Introduction

The main interaction mechanisms affecting the pullout

resistance of extruded geogrids are the skin friction,

between soil and reinforcement solid surface, and the

bearing resistance, that develops against transversal

elements (Fig. 1).

The pullout resistance of a geogrid, assuming that the

different interaction mechanisms act at the same time with

maximum value and that they are independent of each

other, may be evaluated using the following equation:

PR PRS PRB, (1)

where PRS is the skin friction component of pullout

resistance and PRB the bearing component of pullout

resistance.

The frictional component of pullout resistance, for a

geogrid of length LR and unit width WR (Fig. 2), may be

evaluated from the following expression:

PRS 2aSLRt 2aSLRs0n tan d, (2)

where s0n is the normal effective stress, d the skin friction

angle between soil and geogrid, t the shear stress acting at

soilreinforcement interface and aS the fraction of geogrid

surface area that is solid.

To evaluate the bearing component of pullout resistance,

Jewell (1990) proposed the following expression:

PRB LR

S

aBs

0bB, (3)

where S is the spacing between geogrid bearing members,

LR=S the number of geogrid bearing members, aB thefraction of total frontal area of geogrid available for

bearing, B the bearing member thickness and s0b the

effective bearing stress on the geogrid bearing members.

For granular soils, the bearing stresses s0b on geogrid

bearing members are linked to the soil shear strength angle,

ARTICLE IN PRESS

www.elsevier.com/locate/geotexmem

0266-1144/$- see front matter r 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.geotexmem.2005.11.001

Corresponding author. Tel.: +39 0965875263; fax: +39 0965875201.

E-mail addresses: [email protected] (N. Moraci),

[email protected] (D. Gioffre` ).
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the initial stress state, the interface roughness and the

reinforcement depth in relation to the sizes of the bearing

members (Rowe and Davis, 1982). For punching failure

mechanism, the ratio s0b=s0n depends only on soil shear

strength angle and may be defined as following (Jewell

et al., 1985):

s0b

s0n ep=2f

0 tan f0 tanp

4

f0

2 . (4)

For general shear failure mechanism, the ratio s0b=s0n

may be defined as follows:

s0bs0n

ep tan f0

tanp

4f0

2

. (5)

According to Jewell (1996), the Eqs. (4) and (5) represent

a lower bound and an upper bound for the bearing

component of resistance in pullout conditions.

In order to evaluate the bearing component of pullout

resistance, Matsui et al. (1996) and Bergado and Chai

(1994) proposed other relationships.

ARTICLE IN PRESS

Nomenclature

d skin friction angle between soil and geogrid

(deg.)

aB fraction of total frontal area of geogrid avail-

able for bearing (dimensionless)s0b effective bearing stress on the geogrid bearing

members (kN/m2)

s0n normal effective stress (kN/m2)

aS fraction of geogrid surface area that is solid

(dimensionless)

Ab area of each rib element (mm2)

Ar node embossment area (mm2)

At bar portion between two nodes area (mm2)

B bearing member thickness (mm)

Br node thickness (mm)

Bt thickness of the bar portion between two nodes

(mm)

Beq strip of uniform thicknessCaS reduction coefficient of geogrid area where skin

friction develops (aS)

d50 average grain size (mm)

fb soilgeosynthetic pullout interaction coefficient

(dimensionless)

L reinforcement length in the anchorage zone (m)

LR specimen length (m)

nt number of geogrid bearing members

ntb number of nodes in a transversal element

PR pullout resistance (kN/m)

PRB bearing component pullout resistance (kN/m)

PRR residual pullout resistance (kN/m)

PRS skin friction component pullout resistance(kN/m)

PRRS skin friction component pullout resistance

under residual conditions (kN/m)

S spacing between geogrid bearing members

(mm)

U uniformity coefficient (dimensionless)

wopt optimum water content (%)

Wr node width (mm)

Wt width of the bar portion between two nodes

(mm)

f0 soil shear strength angle (deg.)

f0cv soil shear strength angle at constant volume

(deg.)f0p peak shear strength angle (deg.)

gdmax maximum dry unit weight (kN/m3)

mRS=GSY soilgeosynthetic residual interface apparent

coefficient of friction (dimensionless)

mS/GSY soilgeosynthetic peak interface apparent coef-

ficient of friction (dimensionless)

Fig. 2. Definition of terms for a geogrid (Jewell, 1990).

Fig. 1. The two mechanisms for bond between reinforcement and soil(Jewell et al., 1985).

N. Moraci, D. Gioffre / Geotextiles and Geomembranes 24 (2006) 116128 117


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In particular, Matsui et al. (1996) proposed an equation

based on a Prandtls mechanism, as shown in Fig. 3:

s0bs0n

ep tan f tanp

4f0

2

cos

p

4f0

2

1 sin f0 sinp

4

f0

2 . 6

The comparison between the values s0b=s0n obtained

through expression (6) and the pullout test results

performed by the authors on steel grid reinforcement

(diameter 6 mm) embedded in granular soil (f0 37:31)showed a good agreement (Fig. 4).

Assuming that there was an uniform distribution of

shear stress applied along the whole surface of reinforce-

ment, Jewell (1990) obtained a general theoretical relation-

ship to evaluate the pullout resistance of a geogrid:

PR 2aSLRs0n tand

LR

S

aBBs

0b

2fbLRs0n tanf

0, 7

where fb is the interaction coefficient in pullout conditions.

This coefficient can be evaluate based on geometrical

parameters of the reinforcement and on the soil shear

strength characteristics (Jewell, 1990).

Others studies (Palmeira, 2004; Palmeira and Milligan,

1989) emphasized the influence of scale, shape and

interference effects.

The scale effects are related to the ratio between the

transverse element thickness (B) of the reinforcement and

soil grain size D50 and to the ratio between the spacing

between geogrid bearing member (S) and soil grain sizeD50. These effects are relevant if B/D50p10 (Fig. 5,

Palmeira and Milligan, 1989) and if S/D50 is less than 3

(Jewell et al., 1985).

The shape effects are related to the geometry of the

reinforcement transverse elements. Jewell (1996), in order

ARTICLE IN PRESS

Fig. 3. Assumed failure surface for the evaluation of s0b (Matsui

et al., 1996).

Fig. 4. Comparison between proposed equation and available pullout test

data of anchor and grid reinforcements (Matsui et al., 1996).

100

75

50

25

00 20 40 60 80 100 120

Pullout displacement (mm)

Bearingres

istanceperunitwidth

ofreinforcement(kN/m)

Normal pressure

= 98.1kPan

Grid geometry

225x150x6 (mm)

N

N= 1

N= 2

N= 3

Fig. 5. Scale effect on bearing capacity (Palmeira and Milligan, 1989).

N. Moraci, D. Gioffre / Geotextiles and Geomembranes 24 (2006) 116128118


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to take into consideration the shape effects, suggested using

a shape coefficient that can be assumed to be equal to 1.0 in

the case of a circular shape and equal to 1.2 in the case of

rectangular shape.

Milligan et al. (1990), by means of photo-elastic studies,

showed that the bearing action reduced the friction

between the soil and the reinforcement (interference effect).This means that, under similar conditions, the fraction of

the ultimate pullout load due to skin friction may be

considerably smaller than that due to bearing, and smaller

than the value produced between grid area available for

friction, normal stress and the skin friction coefficient

between the soil and grid.

As the ratio between the distance between grid bearing

members and bearing member thickness increases, the

interference between these members will decrease to an

extent that they will behave as a series of isolated bearing

members being pulled out of the soil mass. Palmeira (2004)

observed metal grids embedded in dense sand and saw that,

for S/B ratios of above 40, the grid bearing members

behaved in isolation, under the experimental conditions

adopted.

As mentioned above, the passive failure surfaces that

developed against bearing members cause a reduction of

the skin friction component of the pullout resistance. This

effect can be taken into account in terms of reduction of

geogrid area where skin friction develops (aS). For this

reason a reduction coefficient, CaS, may be introduced.

The limits of theoretical expression used to evaluate the

soilgeosynthetic pullout interaction coefficient, fb, have

been investigated by different researchers (Palmeira and

Milligan, 1989; Wilson-Fahmy and Koerner, 1993; Moraciand Montanelli, 2000; Ghionna et al., 2001). In particular,

previous experimental studies (Palmeira and Milligan,

1989; Moraci and Montanelli, 2000; Ghionna et al.,

2001) have shown that the values of fb are largely

influenced by the reinforcement geometry, extensibility

and soil dilatancy. Thus, it is important to develop a new

theoretical expression that is able to include the evaluation

of all the parameters that influence the mobilization of the

interaction mechanisms (frictional and passive) during

pullout, as emphasized by previous works (Moraci et al.,

2002, 2003, 2004; Moraci and Recalcati, 2005). In the

present paper, on the basis of the test results obtained by

Moraci and Recalcati (2005), a new theoretical method was

developed to evaluate the pullout resistance of extruded

geogrids embedded in a compacted granular soil. The

method is able to evaluate both the passive and the

frictional components of pullout resistance taking into

account the reinforcement extensibility and geometry, as

well as, the non-linearity of the failure envelope of the

backfill soil.

2. The method

Test results obtained by Moraci and Recalcati (2005)

showed the influence of different parameters (reinforce-

ment stiffness and structure, embedded length and vertical

effective stress) on the pullout behaviour of mono-oriented

extruded geogrids embedded in a compacted uniform

medium sand.

In particular, it was found that the dilatancy of the soil

at the interface is the phenomenon that most influences the

pullout resistance and the interface apparent coefficient offriction (mS/GSY). Due to the dilatancy effects, the apparent

coefficient of skin friction mobilized at low vertical

effective confining pressures is higher than that at high

confining pressures.

Experimental results (Moraci and Recalcati, 2005) also

showed that the reinforcement extensibility influences the

peak pullout resistance. In particular, extensibility effects

were more evident in long reinforcements and in high

vertical confining stresses. In residual conditions, the

extensibility effects were negligible.

Test results (Moraci and Recalcati, 2005) also showed an

increase in peak and residual pullout resistance, and

therefore in the mobilized interface apparent coefficient

of friction, while increasing the competent bearing area of

each node, upon which the bearing mechanisms are

mobilized.

The decrease of the pullout resistance after the peak is

related to both reinforcement length and confining stress.

Finally, the apparent coefficient of friction mobilized in

residual conditions depends only on the applied vertical

stress and geogrid geometry; in these conditions mRS=GSYdoes not depend on reinforcement length.

In the case of long reinforcements and high effective

vertical stresses, reinforcement extensibility induces a

progressive mobilization of the elementary interactionmechanisms (skin friction and bearing resistance).

Vice versa, in short reinforcements (independent of

vertical effective stresses) and in long reinforcements

(subjected to low vertical effective stresses) the longitudinal

strains are small. In such cases, the reinforcement behaves

in a rigid way rigid and the interaction mechanisms are

effectively activated at the same time along the whole

length of the reinforcement.

Different experimental studies (Matsui et al., 1996;

Palmeira, 2004) showed that, for the characteristic

displacement field of pullout tests, the bearing stress, after

the displacement corresponding to the maximum value,

remains almost constant with any increase in displacement

(Figs. 6 and 7).

In order to separate the two components of the pullout

resistance, it is possible to perform pullout tests on geogrid

specimens where a portion of transverse reinforcing

elements are removed (Alagiyawanna et al., 2001; Alfaro

et al., 1995; Matsui et al., 1996; Palmeira and Milligan,

1989). Due to their structure, the bearing resistance of

the geogrids used in this study, develops both at the

node embossments and at the transverse bars. With

this reinforcement form it is not possible to deter-

mine experimentally the two components of pullout

resistance.

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In order to validate the previous findings, which may

explain the different behaviour of the three geogrids used in

the research (in terms of pullout resistance and in terms of

apparent coefficient of friction), the following approach

was used:

1. The use of a simple Eq. (8) for the determination of the

pullout resistance in geogrids and soils for which the

scale effects are negligible (i.e. S=B larger than 40 andS/D50 larger than 1000):

PR 2CaSaSLRs0n tan d ntntbAbs

0b, (8)

where CaS is the reduction coefficient of geogrid area

where skin friction develops, nt LR=S the number ofgeogrid bearing members, ntb the number of nodes in a

transversal element, Ab At Ar the area of each rib

element (including the single node and the bar portion

between two nodes) where the bearing resistance can be

mobilized (Fig. 8) and s0b the bearing stress evaluated by

Eq. (6) according to Matsui et al. (1996).

2. To take into account the particular structure of the

elements on which the bearing resistance mobilizes, the

soil dilatancy effects (non-linearity of the failure

envelope of back fill soil) and the geogrid extensibility.

3. The comparison between theoretical (Moraci and

Recalcati, 2005) and experimental values of the pullout

resistance under different conditions.

Pullout tests have been performed on three different

HDPE extruded mono-oriented geogrids (described asGG1, GG2 and GG3, respectively) (Moraci and Recalcati,

2005). The three geogrids show similar geometrical

characteristics when viewed in plan. They have the same

number of tensile elements per unit width and longitudinal

rib pitch, and similar elliptical aperture shape. On the

contrary, the three geogrids have a different cross-sectional

shape with major differences in rib and bar thickness.

A more detailed analysis of the transversal bar geometry

has shown a non-uniform shape with greater thickness at

the rib intersection. The bearing interaction mechanisms

develop both at the node embossments and at the

transverse bars. Therefore, the node embossment and the

transverse bar geometry have been carefully determined to

evaluate the bearing resistance surfaces.

The results of this analysis are reported in Table 1, where

Wr and Br are the node width and thickness, respectively,

Wt and Bt are the width and thickness of the bar portion

between two nodes, respectively (Fig. 8), and Ab is the area

of each rib element (including the node embossment and

the bar portion between two nodes At Ar) where the

bearing resistance can be mobilized.

The complex geometry of the transverse bars, including

the areas Ab in the same transverse element, was assumed

to be equivalent to that of a strip of uniform thickness (Beq)

(Fig. 9).

ARTICLE IN PRESS

Fig. 7. Load displacement curve for an isolated bearing member

(Palmeira, 2004).

Fig. 8. Schematic cross-section AA of the geogrid bar.

Table 1

Structural characteristics of the different geogrids (for symbol see Fig. 8)

Geogrid Wr (mm) Wt (mm) Br (mm) Bt (mm) Ab (mm2)

GG1 11.26 6.6 3.80 3.57 66.35

GG2 11.86 6.0 4.65 4.48 82.03

GG3 12.36 5.5 5.16 4.85 90.45

2.5

2.0

1.5

1.0

0. 5

0. 0 5 10 15 20 25

B/ D50

square section

round section

B

('

/'

)s/('/

'

)

b

n

b

n

Fig. 6. Relationship between bearing resistance and pullout displacement

(Matsui et al., 1996).



6/13

A granular soil was used in the tests. The soil was

classified as uniform medium sand with a uniformity

coefficient U d60=d10 1:5 and an average grain sized50 0:22 mm. Standard Proctor compaction tests gave amaximum dry unit weight gdmax 16:24kN=m

3at an

optimum water content wopt 13:5%.Direct shear tests, performed at an initial unit weight

equal to 95% ofgdmax (obtained at a water content of 9%),

yielded high single values of the peak shear strength angle

f0p, in the range 481 (for s0v 10 kPa) to 421 (for

s0v 100 kPa). The shear strength angle at constant

volume, f0cv, was 341.

The soil shear strength angle used to determine of the

skin friction component of the pullout resistance based on

previous experimental researches on smooth HDPE

geomembranes was assumed to have a value of d equal

to 1/3 f0 (Fannin and Raju, 1993; Raju, 1995). In order to

take into account the reinforcement extensibility, the

following assumptions were made:

1. In long reinforcements (LR 0:921:15 m) and higheffective vertical stresses, the reinforcement extensibility

induces a progressive mobilization of the two elemen-

tary interaction mechanisms. Under these conditions,

the skin friction was evaluated using an average value of

the shear strength angle between the peak and the

constant volume values, assuming a non-linear failure

envelope for the backfill soil.

2. In short reinforcements (LR 0:4 m), independent ofthe applied vertical effective stresses, and in long

reinforcements (subjected to low vertical effective

stresses), the longitudinal strain is small. In such cases,

the reinforcement behaves as a rigid material and the

interaction mechanisms are activated simultaneously

along the whole reinforcement. Under these conditions,

the peak shear strength angle can be used to evaluate

both components of the pullout resistance, assuming a

non-linear failure envelope for the backfill soil and a

suitable stress level.

On the basis of the experimental results obtained by

Matsui et al. (1996) and Palmeira (2004), the bearing

resistance component of pullout resistance was evaluated

using the peak shear strength angles corresponding to the

different vertical effective stresses, in order to take into

account the non-linearity of the failure envelope (due to

dilatancy effects) of the backfill soil.

Eq. (8) permits the evaluation of the residual pullout

resistance PRR. In this case in order to evaluate the skin

friction component of pullout strength, the soil shear

strength angle at constant volume f0cv was used.

In order to evaluate the reduction of the skin friction

component induced by the passive failure surfaces devel-

oped on bearing members, a reduction coefficient, CaS, of

the geogrid area, where skin friction develops (aS), was

used. This value, derived from the assumption that the

maximum extensions of passive failure surfaces are equal

to 40 times the thickness of the equivalent bearing members

(Fig. 9), is given by

CaS Seff

S

S 40nBeq

S. (9)

This reduction is only applied under residual conditions.

3. Experimental validation of proposed method

In order to validate the proposed method, the theoretical

values of the peak and residual pullout resistances obtained

using Eq. (8) were compared with the experimental

results obtained by Moraci and Recalcati (2005) reported

in Table 2.

Tables 35 show the peak (PexpR ) and residual (P

expRR)

experimental pullout resistances, calculated by the present

method (PtheorR and PtheorRR ), the theoretical values of the

peak and residual skin friction resistance (PtheorRS

and PtheorRRS

)

and the ratio between the skin friction resistance and

pullout resistance both at the peak and in residual

conditions (PtheorRS =PexpR and P

theorRRS =PR

expR ).

Figs. 1012 show (in the different reinforcement lengths)

the comparison between experimental and theoretical

values of the peak pullout resistances, evaluated for the

different applied vertical effective confining stresses. The

skin friction component of the peak pullout resistance is

small in comparison to the bearing component. On the

basis of the theoretical analysis (Eq. (8)), the skin friction

component PRS 2aSLRs0n tan d represents less than

20% of the peak pullout resistance. In particular, the

values vary between 9% and 19%, for GG1, and between

ARTICLE IN PRESS

Fig. 9. Assumed equivalent geometry.



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8% and 19% for GG2 and GG3 (Tables 35). The lower

values are related to the lower vertical effective stress and

to short reinforcements; the higher values are related to

the higher vertical effective stresses and to long reinforce-

ments. Figs. 1315 show the same comparison in terms of

residual pullout resistance.

ARTICLE IN PRESS

Table 3

Theoretical and experimental peak (PR) and residual (PRR) pullout resistance (kN/m) for geogrid GG1

LR(m)

s0v (kPa) PexpR (kN/m) P

theorR (kN/m) P

theorRS (kN/m) P

theorRS =P

expR

(%)

PexpRR (kN/m) P

theorRR (kN/m) P

theorRRS (kN/m) P

theorRRS =P

expRR

(%)

0.40 10 9.62 7.33 0.87 9.06 5.63 6.61 0.15 2.70

0.40 25 20.26 14.29 2.08 10.28 13.29 12.59 0.38 2.87

0.40 50 30.95 22.78 3.98 12.85 18.93 19.57 0.76 4.02

0.40 100 39.79 37.03 7.58 19.04 26.43 30.98 1.52 5.76

0.90 10 16.62 14.88 1.96 11.79 12.14 13.27 0.34 2.82

0.90 25 34.55 29.10 4.69 13.56 29.79 25.28 0.86 2.88

0.90 50 52.53 45.51 7.89 15.02 50.34 39.33 1.71 3.40

0.90 100 a 74.28 15.36 a a 62.34 3.42 a

1.15 10 20 18.66 2.50 12.52 14.76 16.59 0.44 2.97

1.15 25 37.13 36.51 5.99 16.14 34.32 31.62 1.09 3.19

1.15 50 62.79 57.10 10.08 16.06 62.79 49.21 2.19 3.491.15 100 a 93.28 19.63 a a 78.02 4.38 a

aSpecimen failure.

Table 4


LR(m)


theorR (kN/m) P

theorRS (kN/m) P

theorRS =P

expR

(%)

PexpRR (kN/m) P

theorRR (kN/m) P

theorRRS (kN/m) P

theorRRS =P

expRR

(%)

0.40 10 13.42 9.11 1.12 8.37 8.44 8.19 0.20 2.33

0.40 25 24.76 17.78 2.69 10.86 15.43 15.59 0.49 3.18

0.40 50 41.17 28.38 5.13 12.45 24.04 24.23 0.98 4.08

0.40 100 56.59 46.19 9.77 17.26 37.51 38.38 1.96 5.23

0.90 10 21.32 18.51 2.53 11.86 15.43 16.42 0.44 2.86

0.90 25 39.99 36.23 6.04 15.11 32.14 31.29 1.10 3.44

0.90 50 70.07 56.68 10.18 14.52 62.46 48.71 2.21 3.54

0.90 100 103.91 92.65 19.81 19.07 103.91 77.26 4.42 4.25

1.15 10 26.96 23.20 3.23 11.98 19.53 20.54 0.56 2.89

1.15 25 51.43 45.46 7.72 15.01 44.00 39.15 1.41 3.20

1.15 50 75.62 71.13 13.00 17.19 75.62 60.95 2.82 3.73

1.15 100 a 116.37 25.32 a a 96.69 5.64 a

aSpecimen failure.

Table 2

Peak (PR) and residual (PRR) pullout resistance (kN/m) measured in the tests (Moraci and Recalcati, 2005)

Geogrid Specimen

length (m)

Normal stress s0v

10 (kPa) 25 (kPa) 50 (kPa) 100 (kPa)

PR PRR PR PRR PR PRR PR PRR

GG1 0.40 9.62 5.63 20.26 13.29 30.95 18.93 39.79 26.43

GG1 0.90 16.62 12.14 34.55 29.79 52.53 50.34 78.44a

GG1 1.15 20.00 14.76 37.13 34.32 62.79 62.79 72.48a

GG2 0.40 13.42 8.44 24.76 15.43 41.18 24.04 56.59 37.51

GG2 0.90 21.32 15.43 39.99 32.14 70.07 62.46 103.91 103.91

GG2 1.15 26.96 19.53 51.43 44.00 75.62 75.62 106.91a

GG3 0.40 12.84 7.36 22.72 13.64 37.68 25.18 58.68 49.04

GG3 0.90 19.85 15.48 41.80 34.69 72.95 61.27 97.59 97.59

GG3 1.15 24.35 19.61 47.75 43.79 81.77 81.77 115.19 115.19

aSpecimen failure.



8/13

Thus, the following conclusions can be drawn. The skin

friction component of residual pullout resistance is also

small in comparison to the bearing component. On the

basis of the theoretical analysis (Eq. (8)), the skin friction

PRS 2CaSaSLRs0n tan d component represents less than

6% of the residual pullout resistance (Tables 35). Such

small values are due to the reduction of the skin friction

component caused by the bearing failure surfaces (inter-

ference effects).

Figs. 1012 show that the proposed method is in close

agreement with the experimental data. In particular, an

underestimation of the peak pullout resistance was

observed which was more evident for short reinforcements.

This situation could be attributed to the local increment of

the vertical effective stress due to the constrained dilatancy,

which is not considered in the simple proposed model. For

short reinforcements (LR 0:40m), the percentagedifferences between experimental results and theoretical

values in terms of peak pullout resistance, ranges between

7% and 32%; for long reinforcements (LR 0:9021:15 m), such differences are quite small (0% and 19%)(Table 6).

Similar results were obtained in terms of residual pull-

out resistance. In this case, the method agrees well with

the experimental data (Figs. 1315). In short reinforce-

ments, the differences between the experimental results

and the theoretical values vary between 1% and 26%

(Table 6).

ARTICLE IN PRESS

Table 5


LR(m)


theorR (kN/m) P

theorRS (kN/m) P

theorRS =P

expR

(%)

PexpRR (kN/m) P

theorRR (kN/m) P

theorRRS (kN/m) P

theorRRS =P

expRR

(%)

0.40 10 12.84 9.79 0.99 7.68 7.36 8.98 0.17 2.34

0.40 25 22.72 19.00 2.36 10.37 13.64 17.08 0.43 3.16

0.40 50 37.68 30.14 4.50 11.94 25.18 26.50 0.86 3.42

0.40 100 58.68 48.73 8.57 14.61 49.04 41.88 1.72 3.51

0.90 10 19.85 19.84 2.22 11.17 15.48 18.01 0.39 2.51

0.90 25 41.8 38.59 5.30 12.69 34.69 34.26 0.97 2.79

0.90 50 72.95 60.21 8.93 12.24 61.27 53.22 1.94 3.16

0.90 100 97.59 97.70 17.39 17.82 97.59 84.20 3.88 3.97

1.15 10 24.35 24.86 2.83 11.65 19.61 22.52 0.50 2.52

1.15 25 47.74 48.39 6.78 14.19 43.79 42.85 1.24 2.83

1.15 50 81.77 75.51 11.41 13.95 81.77 66.58 2.48 3.03

1.15 100 115.15 122.61 22.22 19.29 115.19 105.35 4.95 4.30

100

80

60

40

20

0

0 20 40 60 80 100 120 140

Pullout failure

LR

=1.15m

LR

=0.90m

LR

=0.40m

GG1 - peak

experimental theoretical

PR

[kN/m]

v[kPa]

Fig. 10. Comparison between experimental and theoretical values of peak

pullout resistance for GG1.

120

80

40

0

0 20 40 60 80 100 120 140

Pullout failure

LR

=0.40m

LR

=0.90m

LR

=1.15m

GG2 - peak


PR

[kN/m]

v[kPa]





9/13

For the tests in which confined tensile failure occurs the

method gives higher values of pullout resistance than in-air

tensile resistance evaluated at the same pullout test rate

(Moraci and Recalcati, 2005). Thus, the method is also

useful in the evaluation of the combination of s0v and LRthat produces confined reinforced pullout failures.

To evaluate the soilgeosynthetic interface apparent

coefficient of friction, mS/GSY, the following equation

can be used:

mS=GSY PR

2LRs0v

2aSLRs0n tan d ntntbAbs

0b

2LRs0v. (10)

The analysis was performed both in terms of the peak

and the residual soilgeosynthetic interface apparent

coefficient of friction.

ARTICLE IN PRESS

160

120

80

40

0

0 20 40 60 80 100 120 140

Pullout failure

LR

=0.40m

LR

=0.90mLR =1.15m

GG3 - peak


PR

[kN/m]

v[kPa]



100

80

60

40

20

0

0 20 40 60 80 100 120 140

Pullout failure

LR

=0.40m

LR

=0.90m

LR

=1.15m

GG1 - residual


PR

[kN/m]

v[kPa]

Fig. 13. Comparison between experimental and theoretical values of

residual pullout resistance for GG1.

120

80

40

0

0 20 40 60 80 100 120 140

Pullout failure

LR

=0.40m

LR

=0.90m

LR

=1.15m

GG2 - residual


PR

[kN/m]

v[kPa]



160

120

80

40

0

0 20 40 60 80 100 120 140

Pullout failure

LR

=0.40m

LR

=0.90m

LR

=1.15m

GG3 - residual


PR

[kN/m]

v[kPa]





10/13

Figs. 1618 show the trends of the experimental and

theoretical values of the peak pullout interface apparent

coefficient of friction mS=GSY, as a function of the vertical

effective applied stress, for the three different reinforce-

ment specimen lengths used.

In all cases, it is possible to observe a reduction in the

mobilized peak pullout interface apparent friction coeffi-

cient with an increase in the applied vertical effective stress.

Moreover, it is possible to note that the lower values of

mS/GSY are given with the longer reinforcement specimens.

These results are due to two different phenomena:

The first, of greater importance, is related to soil dilatancy

that develops in conjunction with the three-dimensional

passive failure surfaces that arise at the node embossments

and at the geogrid transverse reinforcing elements. Due to

soil dilatancy, which decreases with an increase in the

confining vertical effective stress, two main effects

develop: the first is due to the different work made to

expand the dilatancy surface at different vertical effective

confining stresses; the second effect is due to the

restriction of the dilatancy connected to the nearby soil

stiffness (constrained dilatancy), which produces a local

increment of the effective confining stress.

The second effect, of less intensity, is due to theextensibility of the reinforcement which modifies the

interface tangential stress distribution and the corre-

sponding pullout strength.

ARTICLE IN PRESS

Table 6

Percentage differences between experimental results and theoretical values

LR (m) s0v (kPa) GG1 GG2 GG3

PtheorR

PexpR

P

exp

R

%Ptheor

RRP

expRR

P

exp

RR

%Ptheor

RP

expR

P

exp

R

%Ptheor

RRP

expRR

P

exp

RR

%Ptheor

RP

expR

P

exp

R

%Ptheor

RRP

expRR

P

exp

RR

%

0.40 10 24 17 32 3 24 22

0.40 25 29 5 28 1 16 25

0.40 50 26 3 31 1 20 5

0.40 100 7 17 18 2 17 15

0.90 10 10 9 13 6 0 16

0.90 25 16 15 9 3 8 1

0.90 50 13 22 19 22 17 13

0.90 100 11 26 0 14

1.15 10 7 12 14 5 2 15

1.15 25 2 8 12 11 1 2

1.15 50 9 22 6 19 8 19

1.15 100 6 9

Specimen failure.

1.4

1.2

0.8

0.6

0.4

0 20 40 60 80 100 120 140

1

S/GSY

GG1 - peak

v[kPa]

experimental Lr = 0.40 m theoretical Lr = 0.40 m

theoretical Lr = 0.90 m


experimental Lr = 0.90 m



soilgeosynthetic interface apparent coefficient of friction for GG1.

2

1.6

1.2

0.8

0.4

0 20 40 60 80 100 120 140

S/GSY

GG2 - peak

v[kPa]










11/13

Moraci and Recalcati (2005) compared the experimental

results of the tests carried out on the three different

geogrids, with the same anchorage lengths and normal

stress, so that they were not influenced by the reinforce-

ment extensibility and the dilatancy effects. They observed

that the experimental results, interpreted as a function of

the different longitudinal tensile stiffnesses, do not show a

specific correlation. Vice versa, the test results confirmed

that the values of the soilgeosynthetic peak interface

apparent coefficient of friction, mS/GSY, are mainly influ-

enced by the structural characteristics (geometry and

shape) of the geogrids. In particular, the maximumpercentage differences of the values of mS/GSY are close to

the percentage differences of the competent bearing areas

(Ab) between geogrid types against which the passive

resistance is mobilized (Fig. 19). Figs. 2022 show the same

curves obtained in terms of the residual soilgeosynthetic

interface apparent coefficients of friction mRS=GSY.

The experimental results obtained by Moraci and

Recalcati (2005) showed that the residual pullout interface

apparent coefficient of friction does not depend on the

reinforcement length but only on the applied confining

stress.

Comparison of the results obtained for the three

different geogrids shows that mRS=GSY depends on geogrid

geometry. The differences between the predicted and the

experimental values range from 0% to 32% under peak

conditions and from 1% to 26% under residual ones.

The results indicate that the proposed model is suitable

to predict the interface apparent coefficient of friction,

particularly in the case of extensible reinforcements. In the

case of rigid reinforcements, the proposed method under-

estimates the interface apparent coefficient of friction.

ARTICLE IN PRESS

2

1.6

1.2

0.8

0.4

0 20 40 60 80 100 120 140

S/GSY

GG3 - peak

v[kPa]








2

1.6

1.2

0.8

0.4

0

1.6

1.2

0.8

0.4

0

0 20 40 60 80 100 120

LR

=0.40 m L

R=

0.90 m

LR

=1.15 m

GG3

GG2

GG1

GG3

GG2

GG1

GG3

GG2

GG1

Normal stress v[kPa]

0 20 40 60 80 100 120


0 20 40 60 80 100 120


S/GSY

S/GSY

1.6

1.2

0.8

0.4

0

S/GSY

Fig. 19. Peak interface apparent coefficient of friction vs. s0 for different geogrids (Moraci and Recalcati, 2005).



12/13

4. Conclusions

Comparison between the theoretical and experimental

permits the following conclusions to be drawn:

The proposed method (which takes into account theeffects of soil dilatancy, reinforcement extensibility,

geogrid structure and geometry, vertical effective

stresses and reinforcement length) predicts the experi-

mental data well, both in terms of the pullout resistance

and in terms of the interface apparent coefficient of

friction, especially for extensible reinforcements.

In the case of extruded geogrids embedded in compacteduniform medium sand, the skin friction components of

the peak pullout resistance are small in comparison to

the bearing component. The skin friction componentrepresents less than 20% of the peak pullout resistance.

The skin friction components of the pullout resistance

are small in comparison to the bearing component, in

residual conditions.

The proposed method can be used also to evaluate thecombination of s0v and LR relating to the confined

reinforcement pullout failure.

References

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0.9

0.8

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RS/GSY

GG1 - residual

v[kPa]







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GG2 - residual

v[kPa]






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