Second Best Paper - Alfaro and Pathak

8/14/2019 Second Best Paper - Alfaro and Pathak

1/14

Dilatant stresses at the interface of granular fills andgeogrid strip reinforcements

M. C. Alfaro1 and Y. P. Pathak2

1 Associate Professor, Department of Civil Engineering, University of Manitoba, Winnipeg, MB R3T 5V6,

Canada, Telephone: 1 204 474 8155, Telefax: 1 204 474 7513, E-mail: [email protected] Assistant, Department of Civil Engineering, University of Manitoba, Winnipeg, MB R3T 5V6,

Canada, Telephone: 1 204 474 8072, Telefax: 1 204 474 7513, E-mail: [email protected]

Received 22 May 2004, revised 25 April 2005, accepted 23 May 2005

ABSTRACT: Design guidelines for geosynthetic-reinforced soil walls recommend the use of

densely compacted granular soils as select fills. The prevailing construction practices employ two

reinforcement layouts. In one, geosynthetics are laid out continuously throughout the length of

reinforced area ( sheet reinforcement): this layout is usually associated with wrap-around and

modular block-type facing units. In the other, geosynthetics are laid out discretely (strip

reinforcement): this is usually associated with panel-type facing units. These two reinforcement

layouts interact differently with densely compacted granular fills, which are inherently dilatant.

Sheet reinforcement corresponds to a free dilatancy condition whereas strip reinforcement

corresponds to a restrained dilatancy condition. The effect of restrained dilatancy results in an

increase in normal stresses or mobilization of dilatant stresses at the soil reinforcement interface

during reinforcement pullout and in turn generates additional localized compressive stresses in the

surrounding granular fill. This has a generally positive influence because it enhances the pullout

resistance of the reinforcement and also raises the effective stresses, resulting in an increase in the

shear strength of the granular fill and thus improving the internal stability of reinforced soil walls.

This paper presents an extension to earlier work by Alfaro et al. on the pullout interaction

mechanisms of geogrid strip reinforcements. It examines the mobilization of dilatant stresses at the

soilreinforcement interface during reinforcement pullout. The study shows that it is essential to

take into account the influence of dilatant stresses in the internal stability analysis of reinforced

soil walls that use geogrid strip reinforcements.

KEYWORDS: Geosynthetics, Geogrid, Restrained dilatancy, Granular soil, Soil geosynthetic

interaction, Reinforced soil

REFERENCE: Alfaro, M. C. & Pathak, Y. P. (2005). Dilatant stresses at the interface of granular

fills and geogrid strip reinforcements. Geosynthetics International, 12, No. 5, 239252.

1. INTRODUCTION

Current internal stability analyses of geosynthetic-rein-

forced soil walls consider two reinforcement failure

modes: (1) rupture due to tensile over-stressing in the

high-stress zone within the reinforced soil mass, and (2)

pullout or slippage of the reinforcement in the low-stress

zone within the reinforced soil mass. The recommended

method of analysis to determine the arrangement and

number of reinforcement layers is based on the tie-back

wedge method of limit equilibrium analysis. In this

approach the factor of safety of each layer of reinforce-

ment against over-stressing and pullout is referenced to an

internal Rankine active plane propagating from the toe of

the wall at an angle 45 + /28 to the horizontal, where is the internal friction angle of the reinforced soil. The

design tensile load in each layer of reinforcement based

on the contributory area about each reinforcement layer

must be in excess of the allowable long-term design load

of the reinforcement. The pullout resistance in each layer

of reinforcement is dependent on the interface normal

stress, the anchored length of reinforcement beyond the

failure plane, and the soil geosynthetic interaction. Fac-

tors that influence soil geosynthetic interaction include

the mechanisms of interaction, the physical and mechani-

cal properties of the soil, and the mechanical properties,

shape and geometry of the geosynthetic reinforcement

(Lopes 2002). Soil geosynthetic reinforcement interaction

is usually evaluated in the laboratory by direct shear test

and pullout test.

There are three main soil geosynthetic reinforcement

interaction mechanisms, as illustrated in Figure 1 (Jewellet al. 1984): (1) skin friction along the reinforcement; (2)

soil-to-soil shear; and (3) passive thrust in the form of

Geosynthetics International, 2005, 12, No. 5

2391072-6349 # 2005 Thomas Telford Ltd


2/14

punching shear on the transverse members of reinforce-

ment. The interaction mechanism for planar geosynthetic

reinforcements such as geotextiles is purely through skin

friction. Interaction parameters for geotextile reinforce-

ments are conveniently evaluated by performing direct

shear tests. For geosynthetic grid reinforcements such as

geogrids, the passive thrust of transverse members of the

grids and the soil-to-soil shear are also considered, if

relative movements occur in the soil at the apertures of the

grids. The interaction parameters related to geogrids are

evaluated using pullout tests.

Most design guidelines (e.g. Elias et al. 2001; AASHTO

2002) recommend the use of densely compacted granular

soils as select fills because of their strength, stiffness,

good drainage, and ease of construction. The prevailing

construction practices employ two reinforcement layouts:

(1) sheet reinforcement and (2) strip reinforcement. Insheet reinforcement layout, geosynthetic reinforcements

are laid out continuously throughout the length of the

reinforced area (full coverage): this is usually associated

with wrap-around and modular block-type facing units, as

shown in Figure 2a. In strip reinforcement layout, the

geosynthetic reinforcements are laid out discretely (partial

coverage): this is usually associated with panel-type facing

units, as shown in Figure 2b. These two reinforcement

layouts interact differently with densely compacted gran-

ular fills, which are inherently dilatant. Sheet reinforce-

ment corresponds to the condition of free dilatancy

whereas strip reinforcement corresponds to the condition

of restrained dilatancy (Alfaro et al. 1995; Sobolevsky

1995). The outcome of restrained dilatancy is the develop-

ment of increased normal stresses or the mobilization of

dilatant stresses that enhance the pullout resistance of the

reinforcement.

Investigators (Lo 1998, 2003; Wang and Richwien

2002) have proposed simplified analytical models to

evaluate the pullout resistance of strip reinforcements in

dilatant soils. These models were validated through the

apparent interface friction coefficient derived from pullout

force measurements. The apparent interface friction coef-

ficient is calculated as (Schlosser and Elias 1978)

f F

2BLen(1)

where F is the pullout force, B is the strip width, Le is the

effective length of the pullout strip, and n is the averagenormal stress acting at the reinforcement level. The

resulting apparent interface friction coefficient was found

generally to be greater than unity, which was attributed to

the increase in normal stress through a mechanism of

restrained dilatancy. Increases in normal stresses at the

soilreinforcement interface are generally not known, but

Hayashi et al. (1997, 1999) attempted to measure the

normal stresses directly near the interface. These measure-

ments, together with a selected analytical model found in

the literature, were used in this paper to study the

mobilization of dilatant stresses at the interface during

pullout of geogrid strip reinforcements, and to investigate

their influence on the internal stability of reinforced soil

walls.

2. CONDITIONS OF FREE AND

RESTRAINED DILATANCYThe condition of free dilatancy is illustrated in Figure 3a.

A geosynthetic reinforcement placed at a certain level

Slip planesTransverse

member(b)

(a)

b

Figure 1. Soil geogrid interaction mechanisms (re-plotted

from Jewell et al. 1984): (a) shear between soil and plane

surfaces; (b) soil bearing on reinforcement surfaces

(a)

(b)

Figure 2. Two types of geosynthetic reinforcement layout: (a)

sheet reinforcement; (b) strip reinforcement

240 Alfaro and Pathak



3/14

within a densely compacted granular fill is subjected to a

normal stress, n. The application of pullout force, F,generates shear in the soil at the vicinity of the interface,

which is accompanied by grain repacking. Shearing of soil

can be generated by one or more of the interaction

mechanisms described earlier: skin friction along the

reinforcement, soil-to-soil shear, and passive thrust on the

transverse members of reinforcement. Associated with soil

shearing of densely compacted granular fill is the volume

increase, or what is called dilatancy. For the sheet

reinforcement layout, dilatancy in the process of shearing

does not influence the value of the applied normal stress,

n. Soil dilatancy would only cause uplifting of thebackfill soil lying uppermost.

The condition of restrained dilatancy is illustrated in

Figure 3b. Geosynthetic reinforcement is placed under the

same situation as before. The application of pullout force

leads to the mobilization of shear at the vicinity of the

interface, and generates soil dilatancy. But for strip

reinforcement, dilatancy will be restrained by the sur-

rounding non-dilating soil, which induces an increase in

normal stress or dilatant stress, n, at the soilreinforce-ment interface (Sobolevsky 1995; Hayashi et al. 1996).

This dilatant stress generates an increase in the interface

shear resistance and subsequent enhancement of the pull-out resistance.

Early reinforced soil structures utilized narrow metallic

strip reinforcements (Schlosser and Elias 1978) and, more

recently, high-tenacity polyester straps (Lo 2003). Geogrid

strip reinforcements were also used in lieu of metallic strip

reinforcements (e.g. Jones 2002). The width of geogrid

strip can range from 200 mm to 1000 mm, which is larger

than that commonly used for metallic strips (about

100 mm). Alfaro et al. (1995) have shown that, as the strip

becomes wider, combined free and restrained dilatancy

conditions can develop (Figure 4). The free dilatancy

condition develops at the middle portion, and the re-

strained dilatancy develops at both edges of the strip

reinforcement. An expedient assumption of this conceptual

mechanism is setting the extent at which restrained

dilatancy develops at the edge of strip (represented by

width Be in Figure 4). Plausible support for this assump-

tion comes from the results of pullout tests conducted with

various strip widths, B. Studies (Ochiai et al. 1992; Farrag

et al. 1993) show that, as B increases, the pullout

resistance decreases. Here, pullout resistance is defined as

the pullout force per width of geogrid (F/B) measured at a

specific condition of displacement. Our interpretation of

these studies implies that the effect of restrained dilatancy,

which developed dilatant stresses and thus enhanced pull-

out resistance at the soilreinforcement interface, was

averaged out over the entire width of the strip even thoughit was localized only at a certain extent of the strip edge

(see Figure 5). Distributing the effect of restrained

Initial conditions Stress conditions during shear

Reinforcement

H

n5 H

n

2d

d

d

n

n

F

n5 H

Initial conditions

n

H

Reinforcement

d< 0d< 0

Stress conditions during shear

nn

nn

F

(a)

(b)

Figure 3. Stress conditions in reinforced soil (re-plotted from Hayashi et al. 1996): (a) free dilatancy condition in sheet

reinforcement layout; (b) restrained dilatancy condition in strip reinforcement layout

Dilatant stresses at the interface of granular fills and geogrid strip reinforcements 241



4/14

dilatancy to the whole portion of the strip, even if the free

dilatancy condition applies in the middle portion, will

result in a decrease of pullout resistance with increasing

strip width.

The development of the restrained dilatancy condition

for strip reinforcements has practical implications in

optimizing the width of the geogrid strip. The use of

narrow rather than wide geogrid strip has both technical

and economical implications in relation to the pullout

resistance that can be achieved in a geogrid strip. The

mobilization of dilatant stress, n, at the soilreinforce-ment interface will also result in additional compressive

stresses in the surrounding granular soil. This has a direct

positive effect in the vicinity of the strip reinforcements because it raises the effective stresses, resulting in an

increase in the shear strength of the granular fill and thus

improving the internal stability of the reinforced soil walls.

By exploiting the superposition of additional compressive

stresses within the granular fill, geogrid strip reinforce-

ments can be positioned in both vertical and horizontal

directions, providing optimal design spacing (Sobolevsky

1995). However, it is recognized that the development of

dilatant stresses at the soilreinforcement interface is

associated with a decrease in compressive stresses away

from the reinforcements (Hayashi et al. 1997; Milligan

and Tei 1998). Any additional stresses generated by super-

position at zones away from the reinforcements may be

compensated for by that decrease in compressive stresses.

Future studies can be undertaken to incorporate this effect

in a 3D numerical analysis of reinforced soil structures

with strip reinforcement layouts.

3. PULLOUT TEST DATA

3.1. General

Before discussing the mobilization of dilatant stresses, it

may be of interest to describe briefly the pullout test data

that partly form the basis of this particular study. The testset-up, procedures and materials used in the pullout tests

will be briefly described here; the details can be found in

Non-dilating

zone

Dilating zone

Shear stress

occurs at

border between

dilating zone

and non-dilating

zone

Dilating zone

Non-dilating

zone

Restrained dilatancy interaction

Applied

normal stress

n

n

Be B2 2Be Be

Free dilatancy interaction

n

n

B< 2Be

(a) (b)

(c) (d)

Increase in

normal stress

Figure 4. Conceptualized pullout interaction mechanisms of strip reinforcement (re-plotted from Alfaro et al. 1995): shear

stress and strain mobilized around (a) wide strip, (b) narrow strip; distribution of normal stress on (c) wide strip, (d) narrow

strip

Strip reinforcement

Be

B

Be

n

n

Figure 5. Idealized distribution of normal stress at soil

reinforcement interface for wide strip




5/14

Alfaro et al. (1995) and Hayashi et al. (1997, 1999). The

pullout box is 1500 mm long by 600 mm wide by 400 mm

deep. The test apparatus is capable of performing pullout

tests following both the American standard test method

(ASTM D 6706) and the Japanese standard test method

(as described in Hayashi et al. 1994). Friction between the

soil and the side walls of the box was minimized by using

lubricated rubber membranes. This was verified by instal-ling pressure cells across the width of the box near the

reinforcement level. Pressure cell readings indicated simi-

lar measured values at the center and near the side wall

locations, demonstrating effective reduction of wall fric-

tion. The pressure cell readings at different applied normal

stresses also allowed calibration of the pressure cells when

placed within the soil. This was important, because the

measured normal stresses were generally greater than the

applied normal stresses (air pressure plus overburden soil

pressure). With greater cell stiffness relative to the

surrounding soil, a stress concentration or arching effect

occurred on the pressure cells, resulting in measured

normal stresses that were higher than those that were

applied (Dunnicliff and Green 1988; Lazebnik and Tsinker

1998). The normal stresses in the vicinity of the soil

reinforcement interface during reinforcement pullout were

measured with 450 mm-diameter miniature earth pressure

cells (Kyowa Electronic Instruments 1993). Load cells

were used to measure the applied pullout force. Linear

variable differential transformers (LVDTs) were used to

measure the junction (or node) displacements along the

length of the geogrid reinforcement length, and the soil

dilatancy during pullout load. Measuring junction displa-

cements along the reinforcement length allows for proper

interpretation of the interface load transfer and also provides proper evaluation of the pullout resistance.

The granular fill used is a well-graded sandy gravel

with the following grain size properties: average particle

size, d50 4.74 mm; uniformity coefficient, Cu 15; andcoefficient of curvature of the gradation curve, Cc 1.67.The maximum and minimum dry unit weights are

19.10 kN/m3 and 14.32 kN/m3 respectively. Triaxial tests

carried out by Inaba (1994) on the compacted soil

indicated that the internal friction angle, , is about 438

for a relative density of 90%. For the material and stress

range of 20100 kPa, the corresponding shear modulus,

G, is estimated to be about 7 MPa. Tensar SR-80, a

uniaxial geogrid normally used for reinforced soil walls

and steep slopes, was employed as the geogrid strip

reinforcement specimen. The shape and geometry of the

geogrid used are shown in Figure 6.

3.2. Free dilatancy test set-up

The condition of free dilatancy is simulated in the

laboratory using a reinforcement width that is slightly less

than the width of the pullout box (width of strip, B 580 mm; width of pullout box, Bo 600 mm; B/Bo ! 1).The free dilatancy condition is representative for this type

of test set-up, as the lubricated side walls do not induce a

restraining effect. Soil dilatancy associated with soil

shearing at the interface would only cause uplifting of the

backfill soil lying above the reinforcement. Relationships

between measured soil dilatancy, v, and shear displace-ment, h, for various applied normal stresses are given inFigure 7. A schematic of measurement locations is also

given in the figure. The shear displacements in Figure 7

represent the average of the two junction displacements at

locations encompassing the point where dilatancy was

measured. It can be seen that soil dilatancy is suppressed

at higher applied normal stresses. This implies that

dilatant stresses, n, resulting from the restrained dila-tancy condition are expected to diminish with increasing

applied normal stresses, n. The measured soil dilatancywith shear displacements from the free dilatancy test set-

up will be used later to provide an expression for the

mobilization of dilatant stress.

3.3. Restrained dilatancy test set-up

The condition of restrained dilatancy is simulated in the

laboratory using a reinforcement width that is much

smaller than the width of the pullout box (width of strip,

B 300 mm; width of pullout box, Bo 600 mm; B/Bo 0.50). The restrained dilatancy condition is representa-tive for this type of test set-up because dilatancy will be

restrained by the surrounding non-dilating soil, which

induces dilatant stresses, n, at the soilgeogrid inter-

Rollwidth(transverse)

Roll

length

(longitudinal)

Transverse members (junctions)

16 mm 16 mm

6.4 mm

Ribs

160 mm

1.4 mm 3.9 mm max

3.6 mm minTypical dimensions

Figure 6. Geometry of geogrid used in pullout test




6/14

face. The results indicate that, for the type of geogrid and

granular fill used, the restrained dilatancy condition begins

to cover the whole strip when the strip width B % 200 to300 mm or Be % 100 to 150 mm (Alfaro et al. 1995;Hayashi et al. 1997). This was determined by conducting

pullout tests at various strip widths and by subsequently

distinguishing the pullout resistance due to restrained

dilatancy from that due solely to the free dilatancy

condition. The pullout resistance due to restrained dila-

tancy begins to decrease with decreasing B: that is, when

Be at both ends of the strip begins to merge (see Figure 8).

Hayashi et al. (1997, 1999) measured the changes in

dilatant stresses with shear displacements directly using pressure cells placed near the interface of a geogrid strip

with width B 300 mm. Only one applied normal stress(n 20 kPa) was investigated, but the data should

provide information on the mobilization of dilatant stres-

ses with shear displacements. Figure 9 shows the position-

ing of the pressure cells. Four pressure cells, positioned

across the width of the box, represent one section along

the length of the geogrid specimen. Three sections were

identified as follows: Section I is right in front of a

transverse member (junction); Section II is further away in

front of a transverse member; and Section III is right at

the back of a transverse member. Sections II and III are

both located at the ribs of the geogrid, whereas Section I

is located right in front of the transverse member or junction. The junction is defined as the point at which the

ribs are interconnected in order to provide structure and

dimensional stability; the rib is the continuous elements of

the geogrid (ASTM D 6706).

4. MOBILIZATION OF DILATANTSTRESSES AT SOILGEOGRIDINTERFACE

4.1. Measured dilatant stresses

Figures 10a and 10b show the changes in measured

normal stress during reinforcement pullout. Figure 10a

corresponds to the test set-up in which the reinforcement

width is much less than the width of the pullout box (B/Bo, 1; strip reinforcement layout, condition of restrained

dilatancy). Figure 10b corresponds to the test set-up in

which the reinforcement width is slightly less than the

width of the pullout box (B/Bo ! 1; sheet reinforcementlayout, condition of free dilatancy). The two cases have

shown similar negative changes in measured normal stress.

However, in general, higher positive changes in measured

normal stress were observed for B/Bo , 1 than for B/Bo! 1. This demonstrates the effect of restrained dilatancy

as illustrated in the preceding section of this paper. It isrecognized that positive changes in normal stress are

measured for the condition of free dilatancy (Lopes 2002).

This is most likely attributed to the 3D nature of geogrids

that have apertures. The effect of restrained dilatancy in

the context of this paper can then be estimated from the

difference between the changes in measured normal stress

of the two conditions.

An interesting observation about the results in Figure

10 is the general trend of an increase changes in measured

positive normal stress in front of the junction and then a

decrease with shear displacements for pressure cell read-

ings at Section I (pressure cells located in front of thegeogrid junction). This trend is related to the horizontal

distance of the transverse member (junction) relative to

the position of the pressure cells. Note that displacements

of junctions were monitored during the reinforcement

pullout using tell-tales. As the junction approaches the

pressure cell location at Section I, the normal stress

increases, but once it passes that location the dilatant

stress begins to decrease. Conversely, the pressure cells at

Sections II and III, which are located in the ribs of the

geogrid, recorded negative values. A reasonable explana-

tion for the decreasing normal stresses at the rib locations

during reinforcement pullout comes from the study of

soil geogrid interaction by Milligan et al. (1990) usingphotoelastic stress patterns, as shown in Figure 11. Recall

the interactions mechanisms in Figure 1, where the

20.5

0

0.5

1.0

1.5

2.0

2.5

3.0

Verticaldisplacement,

v(mm)

Shear displacement, h (mm)

Location of normal displacement measurements

Reinforcement junction

150 mm

250 mm

a

0 10 20 30 40

b

n5 20 kPa

n5 30 kPa

n5 40 kPa

6 5 4 3 2 1

Figure 7. Measured soil dilatancy against shear displacement

during geogrid pullout for various applied normal stresses

(re-plotted from Alfaro et al. 1995)

Strip reinforcement

B< 2Be

Be Be

n

n

Figure 8. Idealized distribution of normal stress at soil

reinforcement interface for narrow strip




7/14

transverse members of the geogrid reinforcement induced

punching shear in front of the transverse members during

pullout. The punching shear in front of the transverse

members can be viewed as the zone where there is an

intense development of dilatant stresses. As for the non-

development of dilatant stresses at the rib locations, this

observation may be explained by the behavior of anchor

plates in sand reported by Rowe and Davis (1982). It was

shown in their theoretical investigation through the velo-

city fields that, when anchor plates were pulled, there was

flow of soil into the back of the anchors; in the case of a

geogrid this is at the ribs or the back of the transverse

members. The tendency of soil to flow into the back of

the transverse member during geogrid pullout results in

decreasing normal stress at the ribs.

4.2. Mobilized dilatant stresses from measured soil

dilatancy

Dilatant stresses are not normally measured in standardpullout tests (e.g. ASTM D 6706). However, soil dilatancy

measurements are easily incorporated in such a test.

Measured soil dilatancy with shear displacements can be

used to determine the mobilized dilatant stresses with

shear displacements. Simple analytical models are avail-

able in the literature to provide an expression for the

mobilized dilatant stresses at the interface during pullout

of soil nails. Milligan and Tei (1998) developed an

analytical model for estimating the average dilatant stress,

n, at the interface of a soil nail:

n 4G

2r hr (2)

where G is the shear modulus of the soil, r is the radius of

the nail, r is the radial expansion of the soil in thesheared zone around the nail (in the context of this paper

r is soil dilatancy), and h is the thickness of the shearedzone. The value of h has been found to be a function of

the mean particle size of the soil, d50, and the angle of soildilatancy, (Milligan and Tei 1998). Another form ofequation was given by Luo et al. (2000):

20

Position

no. 2

Position

no. 4

Position

no. 3

Position

no. 1

110 190 130 130 40

Pressure cellsRubber membranewith silicone grease

Wall of pullouttest box

(Note: All dimensions are in mm)

(a)

Pullout

direction

I IIIII

Pressure

cells3 @ 42.5

Section no. Position no.

No. 3

No. 1

No. 4

No. 2

Transverse members

(junctions) no.

Geogrid 170

1500

40

130

130

190

110

Bo

321 4 5 6

CL

A

CL

Geogrid-B-

-Bo5 600-

(b)

A

B

Figure 9. Schematic showing locations of pressure cells (re-plotted from Hayashi et al. 1997): (a) plan: (b) cross-section AA




8/14

n 2Gr

r

(3)

The equation developed by Luo et al. (2000) to estimate

dilatant stresses will result in about the same estimate as

that by Milligan and Tei (1998). The former is simpler, as

it does not require the value of the thickness of the

sheared zone. As the shearing of soil is related mainly to

the interface area, it is therefore reasonable to convert the

circular section of the nail to an equivalent rectangular

section of the strip with the same perimeter as that of the

circular section (Luo et al. 2000). Neglecting the thickness

of reinforcement, the dilatant stress, n, at the interfaceof strip reinforcement can be approximated by

n 2Gv

B(4)

where v is the vertical displacement (soil dilatancy) of

the soil during pullout of the geogrid strip under freedilatancy (unrestrained) conditions, and B is the width of

the strip. Sobolevsky (1995) has a similar expression:

2160

2120

280

240

0

40

80

120

160

200

240

280

320

360

Geogrid

Pullout direction

Section II

rel

Section I

rel

0 20 40

40200

Changesinmeasuredn

ormalstress(kPa)

Relative horizontal displacement of pressure cell and junction 2, rel (mm)

(a)

Pressure cell position no. 2



Transverse member (junction 2)

Section III

rel

0 20 40

100 80 60 40 20 0 20 40 60 80 100

2160

2120

280

240

0

40

80

120

160

200

240

280

320

360

Changesinmeasurednormalstress(kPa)

100

Relative horizontal displacement of pressure cell and junction 2, rel (mm)

(b)

80 60 40 20 0 20 40 60 80 100

Section II

rel

40200

Section I

rel

0 20 40

Section III

rel

0 20 40

Geogrid

Pullout directionTransverse member (junction 2)

Pressure cell position no. 2Pressure cell position no. 3


Figure 10. Measured change in normal stresses against horizontal displacements of transverse member relative to location of

pressure cells for n 20 kPa (re-plotted from Hayashi et al. 1997): (a) strip reinforcement layout; (b) sheet reinforcement

layout

Figure 11. Photoelastic stress patterns during pullout of

geogrid reinforcement (after Milligan et al. 1990)




9/14

n 2Gv

1 B(5)

where is the Poissons ratio of the soil and is a factorfor conversion from circular cross-section to rectangular

cross-section of reinforcement, which is a function of

length and width of sheared area.

For simplicity, Equation 4 will be used in estimating themobilization of dilatant stresses. Recall that relationships

between soil dilatancy and shear displacement vary with

applied normal stress, as shown in Figure 7. A polynomial

equation representing these relationships can be expressed

as follows:

v a2h bh (6)

where v is the soil dilatancy, h is the shear displace-ment, and the coefficients a and b are fitting parameters

that vary with the applied normal stresses. Values of these

fitting parameters are determined from pullout tests

simulating the free dilatancy condition (see Figure 7). Thevalues are summarized in Table 1. Substituting Equation 6

in Equation 4 results to an expression for the mobilization

of dilatant stresses with shear displacements:

n 2G

Ba2h bh

(7)

It should be noted that, in geosynthetics testing, the

pullout test is considered to be a performance test. This

means that it is necessary to determine the interaction

properties (i.e. the vh relationships) of geosyntheticsand soil materials in association with site-specific environ-

ments. Evaluation of the dilatant stress from vhrelationships under free dilatancy follows the same line of

thought as Goodman (1980) applied in rock mass disconti-

nuities. The relationships between shear stress and shear

displacement (h relationships) under restrained condi-tions had been estimated from vh relationships underfree dilatancy conditions.

Figure 12 shows the relationships between dilatant

stresses and shear displacements for various applied

normal stresses using Equation 7. Also shown in the

figure are the measured dilatant stresses under an applied

stress, n 20 kPa (the difference of the changes inmeasured normal stress between Figures 10a and 10b).

Overall, the tendency of increasing dilatant stresses with

shear displacements using the analytical model developed

by Luo et al. (2000) seems to be reasonable. No attempt

has been made to capture the decrease in dilatant stress

after reaching the peak value at large shear displacements

(. 25 mm). The mobilization of dilatant stress was ver-

ified further by converting the mobilized dilatant stress

(peak value) into an equivalent apparent interface friction

coefficient and comparing the resulting value with the

value recommended by AASHTO (2002) for metallic strip

reinforcements. To do this, the equation given by Alfaro et

al. (1995) to estimate the pullout force of strip reinforce-

ment is used:

F 2BLen tan 4Ben tan (8)

where F is the pullout force, B is the strip width, Le is the

effective length of the pullout strip, n is the normal stressacting at the interface, is the interface friction angle, Beis the width at the edge of strip where dilatant stress is

developed, andn is the dilatant stress. The first term ofthe equation is the pullout capacity from the free dilatancy

condition. The second term is from the effect of the

restrained dilatancy condition through the development of

dilatant stress. Using Equation 8 and appropriate material

properties derived in Alfaro et al. (1995), the estimated

pullout force for a strip reinforcement located at about

1 m from the top of the wall (n % 20 kPa) is

F 2 3 0:3 3 1:17 3 203 tan 328 4

3 0:15 3 1:17 3 1603 tan 328 79 kN

The apparent interface friction coefficient can then becalculated using Equation 1:

f 79

23 0:33 1:173 20 5:6

This value is about three times higher than the value given

in the AASHTO guidelines, but conforms with field

pullout test results by Runser et al. (2001), whose values

of fback-calculated from measured pullout force ranged

from 4 to 6.8 for reinforcements located a few meters

below the top surface of the wall.

Although dilatant stresses are produced at relatively

lower applied stresses (less than 100 kPa), they have

implications especially for reinforcements at upper levelsof the wall, because the internal stability at these levels is

likely to be governed by reinforcement pullout rather than

Table 1. Fitting parameters for measured dilatancy against

shear displacements

n (kN/m2) a b

20 0.0007 0.008530 0.0006 0.001

40 0.0005 0.0109

250

0

50

100

150

200

250

300

350

Dilatantstress,

n

(kPa)

Shear displacement, h (mm)

Measured (n5 20 kPa)

Calculated (n5 varies)

0 10 20 30 40

n5 20 kPa

n5 30 kPa

n5 40 kPa

Figure 12. Mobilization of dilatant stresses with shear

displacements for various applied normal stresses




10/14

reinforcement rupture. The mobilization of dilatant stres-

ses at the interface enhances the pullout resistance of the

reinforcement and induces localized additional compres-

sive stresses in the surrounding granular fill, and thus

influences the internal stability of reinforced soil walls.

5. INFLUENCE OF DILATANT STRESSESON INTERNAL STABILITY OFREINFORCED SOIL WALLS

Pullout of reinforcements from the granular fill mobilizes

dilatant stresses within the reinforced zone. The maximum

shear displacements associated with reinforcement pullout

occur along the internal Rankine active plane (potential

failure plane shown in Figure 13). Therefore it is in the

vicinity of this plane where the maximum dilatant stresses

are expected to be mobilized at each reinforcement layer.

The mobilization of dilatant stresses at the soilreinforce-

ment interface induces localized compressive stresses in

the surrounding granular fill, the distribution of which can

be approximated using a solution of a uniform strip

loading within a soil mass. No analytical solution is

readily available for determining compressive stresses

within the soil for this type of loading, but a classical

solution for point load acting in the interior of an infinite

elastic body as shown in Figure 14 is available. This

solution can be written in Cartesian coordinates (Davis

and Selvadurai 1996) as follows:

z P

4m

nz

R3

3z3

R5

(9)

where R ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

z2 x2 y2p

, m (1 ), n (1 2), is the Poissons ratio of the soil, and the rest of the terms

are as shown in Figure 14. Integrating Equation 9 results

in an expression to calculate the compressive stresses due

to line loading within the soil mass, Q (load per unit

length):

z

11

Q dy

4m

nz

R3

3z3

R5

Q

4m

nz

x2 z2

2z3

x2 z2 2

" #(10)

Equation 10 can be integrated to calculate the compressive

stresses due to strip loading, q (load per unit area), as

shown in Figure 15:

z

x2

x1

q dx 4m

nz

x2 z2

2z3

x2 z2 2

" #(11)

If we let x z tan and q n, the result of theintegration can be written in a simpler trigonometric form:

z n

4mn

d 2

cos2 d

!(12)

Interface shear

stress,

Distribution of interface

shear stress along

reinforcement length

Potential failure plane

Reinforcement length, L

45 1/2

max

Figure 13. Interface shear stress distribution along reinforce-

ment length

y

z

2P

x

Infinite

elastic

body

Figure 14. Point load acting in the interior of an infinite

elastic body using Kelvins solution (after Davis and

Selvadurai 1996)

2x

z

z

x

z

d

x

B

Infinite

elastic

body

q

x dx

Q 5qdx

`

Figure 15. Induced normal stress components in an infinite

elastic body (soil) due to strip loading acting in the interior of

body




11/14

z n

4 1 2 1 sin cos 2

(13)

Equation 13 represents stresses within the soil mass due to

dilatant stress, n. Using the superposition concept of

elastic theory, these stresses can be added to the overburden pressures and the stresses induced by surcharge

loading (if any).

Two cases were investigated to show the influence of

dilatant stresses on the granular fill. In Case 1 B 300 mm: the dilatant stresses are imposed throughout the

width of the geogrid strip (full restrained dilatancy condi-

tion, B 2Be: see Figure 8). In Case 2 B 1000 mm: thedilatant stresses are acting only at a certain extent of the

edges of the geogrid strip (Be 150 mm). This is the caseof combined free and restrained dilatancy conditions (see

Figure 5). Figure 16 shows the isobars of additional

compressive vertical stresses for Case 1, and Figure 17

shows them for Case 2. Note that the isobars are the samefor different elevations of reinforcement layers. However,

their magnitudes vary as the dilatant stress decreases with

decrease in reinforcement elevation. It can be seen that the

narrower strip width is more effective in inducing addi-

tional compressive stresses in the soil mass. If dilatant

stresses can reach up to 100 kPa, the superposition of

isobars can result in considerable additional compressive

stresses in the soil mass that are worthy of considerationin the internal stability analysis of geosynthetic-reinforced

soil walls.

A typical reinforced soil wall as shown in Figure 18

was analyzed to illustrate the influence of dilatant stresses

on the internal stability of reinforced soil walls. A uniform

surcharge equal to 10 kPa was assumed, and the reinforce-

ment layout in Case 1 above was used (full restrained

dilatancy condition). The total vertical stress distribution

along the height of the wall is shown in Figure 18.

Dilatant stresses at the interface increase the interface

normal stresses and subsequently the pullout resistance.

These values decrease with reinforcement locations from

top to bottom of the wall, until the elevation where the

applied normal stresses completely suppress the develop-

ment of dilatant stresses.

The stress conditions within the reinforced zone are

examined through the stress path of a soil element at the

vicinity of the soilreinforcement interface. Soil elements

without and with mobilization of dilatant stresses are

considered (soil elements A and B respectively in Figure

19). Note that reinforcement pullout is associated with

lateral movements of the wall and thus reduction of

horizontal stress. Assuming there is no change in the

intermediate principal stress (2), and the vertical and

horizontal stresses are the major and minor principalstresses respectively (1 and 3), the stress path followedfor soil element A will be

0

0.5

1.0

1.5

2.0

2.5

3.0

Depth,z

(m)

0 0.5 1.0 1.5 2.0

Horizontal distance (m)

Horizontal spacing 5 0.6 m on centres

Vertical spacing 5 0.6 m

Figure 16. Normalized vertical dilatant stress (z/n) iso-

bars mobilized from geogrid strip width B 300 mm

0

0.5

1.0

1.5

2.0

2.5

3.0

Depth,z

(m)

0 0.5 1.0 1.5 2.0

Horizontal distance (m)

Horizontal spacing 5 0.6 m on centres

Vertical spacing 5 0.6 m

Figure 17. Normalized vertical dilatant stress (z/n) iso-

bars mobilized from geogrid strip width B 1000 mm




12/14

q 1 2 3 0 0 3 3

p 1

31 2 3

1

30 0 3

1

33

and thus stress path q/ p will have a negative slope. The

stress path followed for soil element B will be

q 1 2 3 n 0 3

n 3

p 1

31 2 3

1

3n 0 3

1

3n 3

It is expected that the absolute value ofn will be higherthan that of3 so that the stress path of soil element B(q/ p) will have a positive slope. Moreover, the mobili-

zation of dilatant stresses enhances the pullout resistance

of the reinforcements and in turn reduces pullout displace-

ments and lateral movements of the wall. This means thatthe reduction in lateral stress 3 for soil element B islower than the corresponding reduction for soil element A.

It can be seen in Figure 19 that soil element B has a stress

path with an increasing mean effective stress, whereas soil

element A has a stress path with a decreasing mean

effective stress. Even if the absolute value ofn is lowerthan that of 3, the stress path for soil element B isalways to the right of the stress path for soil element A.

This implies that the presence of dilatant stresses increases

the mean effective stresses (and therefore the shear

strength) of the granular fill and thus enhances the internal

stability of the wall. These particular influences were also

shown in a finite element analysis carried out by Otaniet al. (1992).

It is recognized that the analysis presented here regard-

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

0

Geogrid strip

(width 5 0.3 m)

q5 10 kPa

Depth,z

(m)

Dilatant stress

Surcharge

Geostatic stress

L5 geogrid length

45 1/2

5 20 kN/m3

5 43

1

3

0 40 80 120 160Normal stress, n (kPa)

Figure 18. Typical geogrid-reinforced soil wall with total vertical stress distributions

Mean effective stress,p

Deviatoric

stress, q

M

1ve2ve

A2

A1

A B

Critical-state line

Initial stress state

15 0

3

15n

3

Figure 19. Stress paths for soil element within reinforced

zone with and without restrained dilatancy effect




13/14

ing the influence of dilatant stress on the internal stability

of reinforced soil walls is simplistic. The internal stability

of reinforced soil walls is strongly coupled and interactive.

Pullout of reinforcements results in lateral movements and

produces shear displacements at the soil reinforcement

interface. The mobilization of dilatant stresses enhances

pullout resistance of the reinforcement, increases the

strength of the granular fills, and in turn reduces pulloutdisplacements and lateral movements of the wall. In terms

of improvement towards a more realistic analysis of the

stress and strain conditions in the reinforced soil zone,

numerical modeling that incorporates the appropriate

stress path of the soil and the coupled and interactive

behavior within the reinforced soil is recommended.

6. CONCLUDING REMARKS

A study was undertaken of the mobilization of dilatant

stresses at the interface between soil and reinforcement

during pullout of geogrid strip reinforcements. Mobiliza-

tion of dilatant stresses using the measured soil dilatancy

was represented through a simple analytical model avail-

able in the literature. The mobilization of dilatant stresses

at the soilreinforcement interface can result in additional

localized compressive stresses in the surrounding granular

fill. This can have a positive influence, because it

enhances the pullout resistance of the geogrid strip

reinforcement and raises the effective stresses, resulting in

an increase in the shear strength of the granular soil in the

vicinity of strip reinforcements. It is therefore essential to

take the influence of dilatant stresses into account in the

internal stability analysis of reinforced soil walls using

geogrid strip reinforcements.

NOTATIONS

Basic SI units are given in parentheses.

a, b fitting parameters (dimensionless)

B width of geogrid specimen (m)

Be width along edge of reinforcement influenced

by restrained dilatancy (m)

Bo width of pullout box (m)

Cc coefficient of curvature of soil particle size

distribution curve (dimensionless)Cu coefficient of uniformity of soil particle size

distribution (dimensionless)

d50 average particle size (m)

F pullout force (N)

f apparent interface friction coefficient

(dimensionless)

G shear modulus of soil (N/m2)

H overburden height (m)

h thickness of sheared zone (m)

K coefficient of earth pressure (dimensionless)

Ka coefficient of earth pressure in active state

(dimensionless)

K0 coefficient of earth pressure at rest(dimensionless)

M slope of critical-state line (dimensionless)

P applied point load (N)

p mean normal stress (N/m2)

Q load per unit length (N/m)

q strip load per unit area, surcharge load,

deviatoric stress (N/m2)

r radius of nail (m)

x x-coordinate, horizontal distance (m)

y y-coordinate (m)z z-coordinate, depth (m)

, , angles of rotation (degrees) unit weight of soil (N/m3)

rel relative horizontal displacement between

pressure cell location and junction (m)

h shear displacement of soil (m)r radial expansion of soil in shear zone around

a soil nail (m)

v vertical displacement of soil due to dilatancy(m)

Poissons ratio of soil (dimensionless)b bearing stress of soil on reinforcement

surfaces (N/m2)

n applied normal stress (N/m2)

n dilatant stress (N/m2)

napp applied normal stress (N/m2)

nmeas pressure cell reading (N/m2)

x horizontal stress (N/m2)

vo initial vertical stress (N/m2)

z vertical stress (N/m2)

1 major principal stress (N/m2)

2 intermediate principal stress (N/m2)

3 minor principal stress (N/m2)

soil internal friction angle (degrees)

angle of dilatancy (degrees) conversion factor from circular cross-section

to rectangular cross-section of reinforcement

(dimensionless)

REFERENCES

AASHTO (2002). Standard Specifications for Highway and Bridges, 7th

edn. Washington, DC: American Association of State Highway and

Transportation Officials.

ASTM D 6706-01. Standard Test Method for Measuring Pullout

Resistance in Soil. West Conshohocken, PA: American Society for

Testing and Materials.

Alfaro, M. C., Hayashi, H., Miura, N. & Watanabe, K. (1995). Pullout

interaction mechanism of geogrid strip reinforcement. Geosynthetics

International, 2, No. 4, 679698.

Davis, R. O. & Selvadurai, A. P. S. (1996). Elasticity and Geomechanics.

New York: Cambridge University Press.

Dunnicliff, J. & Green, G. E. (1988). Geotechnical Instrumentation for

Monitoring Field Performance. New York: John Wiley & Sons.

Elias, V., Christopher, B. R. & Berg, R. R. (2001). Mechanically

Stabilized Earth Walls and Reinforced Soil Slopes: Design and

Construction Guidelines, FHWA-NHI-00-043. Washington, DC:

Federal Highway Administration.

Farrag, K., Acar, Y. B. & Juran, I. (1993). Pullout resistance of geogrid

reinforcements. Geotextiles and Geomembranes, 12, No. 3,133159.

Goodman, R. E. (1980). Introduction to Rock Mechanics, 2nd edn. New

York: John Wiley & Sons.Hayashi, S., Makiuchi, K., Ochiai, H., Fukuoka, M. & Hirai, T. (1994).

Testing methods for soil geosynthetic frictional behaviour: Japa-

nese standard. Proceedings of the 5th International Conference on




14/14

Geotextiles, Geomembranes and Related Products, Singapore,

411414.

Hayashi, S., Alfaro, M. C. & Watanabe, K. (1996). Dilatancy effects of

granular soil on the pullout resistance of strip reinforcement.

Proceedings of the International Symposium on Earth Reinforce-

ment, Fukuoka, pp. 3944.

Hayashi, S., Watanabe, K., Shahu, J. T., Hirai, T. & Alfaro, M. C.

(1997). Mechanism and evaluation of pullout resistance of strip

geogrid reinforcements. Proceedings of the International Sympo-

sium on Mechanically Stabilized Backfill, Denver, CO, pp.

223233.

Hayashi, S., Shahu, J. T. & Watanabe, K. (1999). Changes in interface

stresses during pullout tests on geogrid strip reinforcement.

Geotechnical Testing Journal, 32, 3238.

Inaba, Y. (1994). Soil-Geogrid Reinforcement Interaction, Special Study

Report. Department of Civil Engineering, Saga University, Japan.

Jewell, R. A., Milligan, G. W. E., Sarsby, R. W. & Dubois, D. (1984).

Interaction between soil and geogrids. Proceedings of the

Symposium on Polymer Grid reinforcement in Civil Engineering,

London, pp. 1830.

Jones, C. J. F. P. (2002). Reinforced soil: vertical retaining walls. In IGS

Mini Lecture Series, Chapter 10. Easley, SC: International

Geosynthetics Society, on CD-ROM.

Kyowa Electronics Instruments (1993). Soil Pressure Transducer Series.

Kyowa Electronics Instruments Co. Ltd, Chofu, Japan.

Lazebnik, G. E. & Tsinker, G. (1998). Monitoring of SoilStructure

Interaction: Instruments for Measuring Soil Pressures. New York:

Chapman & Hall.

Lo, S. R. (1998). Pullout resistance of polyester straps at low overburden

stress. Geosynthetics International, 5, No. 4, 361382.

Lo, S. R. (2003). The influence of constrained dilatancy on pullout

resistance of strap reinforcement. Geosynthetics International, 10,

No. 2, 4755.

Lopes, M. L. (2002). Soilgeosynthetic interaction. In Geosynthetics and

Their Applications (ed. S. K. Shukla), Chapter 2. London: Thomas

Telford, pp. 5579.

Luo, S. Q., Tan, S. A. & Yong, K. Y. (2000). Pullout resistance

mechanism of a soil nail reinforcement in dilative soils. Soils and

Foundations, 40, No. 1, 4756.

Milligan, G. W. E. & Tei, K. (1998). The pullout resistance of model soil

nails. Soils and Foundations, 38, No. 2, 179190.

Milligan, G. W. E., Earl, R. F. & Bush, D. I. (1990). Observations of

photo-elastic pullout tests on geotextiles and geogrids. Proceedings

of the 4th International Conference on Geotextiles, Geomembranes

and Related Products, Vienna, 754751.

Ochiai, H., Hayashi, H. & Otani, J. (1992). Evaluation of pullout

resistance of geogrid reinforcement in soils. Proceedings of the

International Symposium on Earth Reinforcement, Kyushu, pp.

141146.

Otani, J., Ochiai, H. & Hayashi, S. (1992). Restraining effect of geogrid

reinforced soil in finite element analysis. Proceedings of the

International Symposium on Earth Reinforcement, Kyushu, pp.

147150.

Rowe, R. K. & Davis, E. H. (1982). The behaviour of anchor plates in

sand. Geotechnique, 32, No. 1, 2541.

Runser, D. J., Fox, P. J. & Bourdeau, P. L. (2001). Field performance of a

17-m high reinforced soil retaining wall. Geosynthetics Interna-

tional, 8, No. 5, 367391.

Schlosser, F. & Elias, V. (1978). Friction in reinforced earth. Proceedings

of the ASCE Symposium on Earth Reinforcement, Pittsburgh, pp.

735763.

Sobolevsky, D. Y. (1995). Strength of Dilating Soil and Load-Holding

Capacity of Deep Foundations. Rotterdam: A. A. Balkema.

Wang, Z. G. & Richwien, W. (2002). A study of soilreinforcement

interface friction. ASCE Journal of Geotechnical and Geoenviron-

mental Engineering, 128, No. 1, 9294.

The Editors welcome discussion in all papers published in Geosynthetics International. Please email your contribution to

[email protected] by 15 April 2006.



Second Best Paper - Alfaro and Pathak

Documents

Transcript of Second Best Paper - Alfaro and Pathak