Geotextiles and Geomembranes 22 (2004) 329–358 Modeling of the confining effect due to the geosynthetic wrapping of compacted soil specimens Atsushi Iizuka a, *, Katsuyuki Kawai a , Eun Ra Kim b , Masafumi Hirata c a Department of Architecture and Civil Engineering, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501, Japan b Graduate School of Science and Technology, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501, Japan c Geotechnical Engineering Division, Research Institute of Toyo Construction Co. Ltd., 1-25-1 Naruohama, Nishinomiya 663-8142, Japan Received 21 January 2003; received in revised form 8 January 2004; accepted 18 January 2004 Abstract This paper presents the modeling of the composite soil-geosynthetic structure and discusses the effect of the reinforcement arising from the confining of the deformation of the soil by geosynthetics. A series of compressive shear tests for compacted sandy soil specimens, wrapped in geosynthetics, is carried out for the purpose of quantitatively examining the effect of the geosynthetic reinforcement arising from the confining of the deformation of compacted soils during shearing. Furthermore, an elasto-plastic modeling for compacted soil and a rational determination procedure for input parameters, needed in the elasto-plastic modeling, are presented. In this paper, the subloading yielding surface is introduced to the elasto-plastic modeling in order to describe the irreversible deformation characteristics of compacted soil during shearing. Since compacted soil is essentially unsaturated and its mechanical behavior is influenced by the suction working in the compacted soil media, the suction effect is taken into account in estimating of the degree of compaction. Finally, an elasto-plastic finite element simulation is conducted and the geosynthetic-reinforcement effect is presented. r 2004 Elsevier Ltd. All rights reserved. Keywords: Compacted soil; Suction effect; Geosynthetic reinforcement; Elasto-plastic modeling ARTICLE IN PRESS *Corresponding author. Tel.: +81-78-803-6029; fax: +81-78-803-6069. E-mail address: [email protected] (A. Iizuka). 0266-1144/$ - see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.geotexmem.2004.01.001
Transcript
Geotextiles and Geomembranes 22 (2004) 329–358
Modeling of the confining effect due to thegeosynthetic wrapping of compacted soil
specimens
Atsushi Iizukaa,*, Katsuyuki Kawaia, Eun Ra Kimb,Masafumi Hiratac
aDepartment of Architecture and Civil Engineering, Kobe University, 1-1 Rokkodai, Nada,
Kobe 657-8501, JapanbGraduate School of Science and Technology, Kobe University, 1-1 Rokkodai, Nada, Kobe 657-8501, JapancGeotechnical Engineering Division, Research Institute of Toyo Construction Co. Ltd., 1-25-1 Naruohama,
Nishinomiya 663-8142, Japan
Received 21 January 2003; received in revised form 8 January 2004; accepted 18 January 2004
Abstract
This paper presents the modeling of the composite soil-geosynthetic structure and discusses
the effect of the reinforcement arising from the confining of the deformation of the soil by
geosynthetics. A series of compressive shear tests for compacted sandy soil specimens,
wrapped in geosynthetics, is carried out for the purpose of quantitatively examining the effect
of the geosynthetic reinforcement arising from the confining of the deformation of compacted
soils during shearing. Furthermore, an elasto-plastic modeling for compacted soil and a
rational determination procedure for input parameters, needed in the elasto-plastic modeling,
are presented. In this paper, the subloading yielding surface is introduced to the elasto-plastic
modeling in order to describe the irreversible deformation characteristics of compacted soil
during shearing. Since compacted soil is essentially unsaturated and its mechanical behavior is
influenced by the suction working in the compacted soil media, the suction effect is taken into
account in estimating of the degree of compaction. Finally, an elasto-plastic finite element
simulation is conducted and the geosynthetic-reinforcement effect is presented.
0266-1144/$ - see front matter r 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.geotexmem.2004.01.001
1. Introduction
Geosynthetic-reinforced soil structures consist of two elements: one is compactedsoil and the other is geosynthetics. The reinforcement effect should not beinterpreted as the strength and the rigidity of the soil itself being merelysupplemented by geosynthetic reinforcement, but should be understood as that thesoil and the geosynthetics behave as a composite material. The strength and therigidity of geosynthetic-reinforced soil structures do not appear as mere summationsof the strength and the rigidity levels of the soil and the geosynthetic. They are aresult of the mechanical interaction between the soil and the geosynthetic. Ohta et al.(1997, 2002) constructed a series of trial embankments that were reinforced bygeosynthetics and tried to examine the geosynthetic-reinforcement effect. Fig. 1presents one of the geosynthetic-reinforced trial embankments, which has anoverhanging slope, constructed in Kanazawa, Japan in 1993. Photo 1 shows asnapshot of the embankment. The geosynthetic-reinforced embankment wasdesigned based on the conventional design method, but it showed surprisinglyhigher levels of strength and rigidity as a unified composite material than expected.This strongly motivated the authors to investigate the mechanical interactionbetween compacted soil and geosynthetics. In this paper, the authors focus on theconfining effect by geosynthetics. Compacted soil has dilative characteristics undershearing just like overconsolidated clay. If geosynthetics are properly placed in thecompacted soil media, the geosynthetics will work to prevent the dilation of thecompacted soil when the soil is sheared by an applied load. Then, the effectivestresses in the compacted soils will increase resulting in the gaining of the strengthand the rigidity of the compacted soil as a whole. Such a confining effect bygeosynthetics is investigated in this paper through a series of laboratory model testsand numerical simulations.
The dilatancy characteristics of compacted soil depend on the degree ofcompaction. Therefore, it is necessary to quantitatively express the degree of
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Fig. 1. Geosynthetic-reinforced trial embankment in 1993.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358330
compaction. The equivalent preconsolidation stress is herein introduced from thesimilarity of its mechanical properties to overconsolidated clay. Furthermore,compacted soil is essentially unsaturated and its mechanical properties vary not onlywith the water content but also with the suction. In this paper, therefore, the authorsquantitatively express this influence arising from unsaturated conditions as suctionchanges in the compacted soil media. A simple method to consider it in specifyingthe equivalent preconsolidation stress is proposed.
As far as the mechanical behavior of geosynthetic-reinforced soil structures isfocused in this paper, the effect of geosynthetic reinforcement cannot be discussedonly from the viewpoint of the (limit) equilibrium of forces as treated in theconventional design method. It is necessary to discuss the geosynthetic-reinforce-ment mechanism under the theoretical framework whereby the constitutiveequations for both compacted soil and geosynthetics have been prepared as amediator between the equilibrium of forces and strain compatibility. In this paper, todescribe the mechanical properties of compacted soil, the authors employ the elasto-plastic constitutive model to which the subloading surface concept proposed byHashiguchi (1989) is introduced. The geosynthetic material can be simply modeled tobe an elastic material based on the extension test results.
2. Soil used and preparatory laboratory tests
The soil used in experiment is Pleistocene sand named Omma sand, sampled fromTaiyogaoka in Kanazawa, Japan. The specific gravity of the soil particles is 2.74, thegrain size distribution includes a gravel fraction (2 to 75mm) of 2%, a sand fraction(75 mm to 2mm) of 80%, a silt fraction (5 mm to 75 mm) of 11%, and a clay fraction(less than 5 mm) of 7%. The uniformity coefficient is 21.8 and the maximum grainsize is 9.5mm.The compaction curve of the soil is shown in Fig. 2, obtained fromProctor’s method (JIS A1210), in which the optimum water content is found to be18.8%. For the preparatory laboratory tests, two kinds of soil specimens wereprepared: one was undisturbed (compacted) samples which were taken from the trial
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Photo 1. View of additionally loaded trial embankment reinforced by geosynthetics.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358 331
embankment body (Photo 1) compacted by vibration roller for 0.1m spreadingdepth and the other was completely remolded (disturbed/loosened) samples of whichthe water contents were adjusted to the prescribed values (w ¼ 7 and 25%) asstraddling the optimum water content of 18.8%.
A series of shear box tests (SBT) were carried out. Both the disturbed and theundisturbed samples were subjected to shear under a condition of constant volumeafter the completion of Ko-consolidation with vertical pressures of 39.2, 78.4, 156.8,and 313 kPa. The test results are summarized in Fig. 3 for the disturbed (very loose)samples and in Fig. 4 for the undisturbed (compacted) samples. The upper figuresindicate the compression curves in the Ko-consolidation and the lower ones show theeffective stress paths in the shear process under a condition of constant volume.Comparing Figs. 3 and 4, the similarity with saturated clay for both compressibilityand dilatancy characteristics can be recognized. Namely, the disturbed (compacted)samples behave like overconsolidated clay in contrast of the behavior of thedisturbed (loose) samples which act like normally consolidated clay.
The mechanical behavior, particularly the dilatancy characteristics of theoverconsolidated clay, is determined by the overconsolidation ratio, OCR, whichis specified by the preconsolidation vertical stress and the effective current verticalstress. Similarly, in case of the compacted soil, if the equivalent preconsolidation stress
can be estimated in association with the preconsolidation stress in the over-consolidated clay, it can be employed as an index which quantitatively expresses thedegree of compaction in the compacted soil. Based on such an idea, thedetermination procedure for the equivalent preconsolidation stress and the equivalent
OCR of the in-situ compacted soil has been proposed, that is, the equivalentpreconsolidation stress is determined by the intersection of the compression lines ofthe disturbed and the undisturbed samples with the same water content for thee � log s0v relation. For details, see Ohta and Hata (1977), Ohta et al. (1978), andOhta et al. (1986). We employ their idea of the equivalent preconsolidation stress tocharacterize the compacted soil in this paper. However, compacted soil is essentiallyunsaturated. The mechanical behavior of unsaturated soil, in general, cannot beidentified only with the water content. It strongly depends on the suction. It is knownthat the mechanical behavior of unsaturated soil varies with the suction if the water
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8 10 12 14 16 18 20 22 24 26 281.45
1.50
1.55
1.60
1.65
ρd max = 1 .615 t/m3
w opt = 18 .8 %
Dry
den
sity
, ρd
(t/m
3 )
Water content,w (%)
Fig. 2. Compaction curve for Omma sand.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358332
content stays the same. Therefore, the consideration of suction is desired forcharacterizing the mechanical behavior of unsaturated compacted soil. In this paper,a simple method, which is available for the practical use, of estimating the suctionvalue possibly remaining in the compacted soil, and a determination procedure forthe equivalent preconsolidation stress, considering the suction, are presented.
3. Quantification of the suction effect in compacted soil
A series of static compaction tests was carried out in the laboratory to measure thesuction value remaining in the compacted soil for Omma sand. The disturbedsample, for which the water content was adjusted to a prescribed value, was set in theoedometer box. Firstly, an air pressure of 98 kPa was applied to avoid cavitation inthe pore water measurement system. After that, the unsaturated specimen wasstatically compacted (loaded) at a constant strain rate while monitoring the appliedload and the pore water pressure through the ceramic disk placed at the bottom ofthe specimen. The suction value was calculated as the difference between the pore airpressure and the pore water pressure. After the specimen was compacted to the
Fig. 3. Mechanical properties of the disturbed samples from SBT: (a) Virgin compression lines of the
disturbed (remolded) soil specimens, (b) shear properties of the disturbed (remolded) soil specimens.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358 333
prescribed degree of compaction (a prescribed dry density), the load was removedand the changes of suction with time were continuously measured until the suctionsettled down to a certain constant value. For the details on the test apparatus and thetesting procedure, see Kawai et al. (2003a, b). Typical test results are shown in Fig. 5,
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100 200 300 400 500 600
-10
0
10
20
30
40
50
60
ρd=1.40 (g/cm3)
w=10.99(%)
Leaving
Unloading
Loading
Time (min)
Suc
tion,
s (
kPa)
Fig. 5. Suction change with loading history.
0 100 200 300 400 500 6000
100
200
300
400
w = 16.8% w = 14.6% w = 16.0% w = 16.1%
Sample 2
0 100 200 300 400 500 6000
100
200
300
400
w = 15.4% w = 15.5% w = 12.8% w = 15.1%
Sample 1
She
ar s
tres
s , τ
(kP
a)
She
ar s
tres
s , τ
(kP
a)
Effective normal stress , σv' (kPa) Effective normal stress , σv' (kPa)
101 102 103
0.8
1.0
1.2
1.4
Sample 1w = 15.4%w = 15.5%w = 12.8%w = 15.1%
Voi
d ra
tio, e
Effective normal stress , σv' (kPa) 101 102 103
Effective normal stress, σv' (kPa)
0.8
1.0
1.2
1.4
Sample 2w = 16.8%w = 14.6%w = 16.0%w = 16.1%
Voi
d ra
tio, e
(a)
(b)
Fig. 4. Mechanical properties of the undisturbed compacted samples from SBT: (a) Swelling lines of the
undisturbed compacted soil specimens, (b) shear properties of the undisturbed compacted soil specimens.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358334
in which the dry density at the completion of compaction is 1.40 g/cm3 and the watercontent is 10.99%. The final suction value remaining in the compacted soil wasmeasured to be 22.5 kPa.
The obtained data are plotted on a plane of the suction and the degree ofsaturation, which is equivalent to the water retention relation of the compactedOmma sand, as shown in Fig. 6. Alternatively, Fig. 7 indicates the relationshipbetween the water content and the suction. Fig. 8 is obtained by reading the watercontent and the dry density at every suction value from Fig. 7 and drawing down thesuction contour. Fig. 8 provides not only the compaction curve, but also the suctiondistribution as additional information related to the compaction curve (Fig. 2) on theplane of the water content and the dry density.
According to Karube and Kato (1989) and Karube et al. (1989), volumetricchanges in unsaturated soil can be expressed as
de ¼ �ldp
p þ f ðsÞð1Þ
in which e is the void ratio, l is the gradient of the virgin compression line(l ¼ 0:434Cc), p is the mean net stress, and f ðsÞ is the scalar function expressing thesuction effect. Eq. (1) can be rewritten as the e and sv relation, since the K0 value canbe regarded as a constant in the virgin compression state, that is
de ¼ �ldsv
sv þ *fðsÞð2Þ
in which sv is the vertical net stress. Kawai et al. (2003a) simplified Eq. (2) andproposed an integrated form as
e ¼ e0 � l lnsv þ s
sy0 þ as; ð3Þ
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0 20 40 60 80 100 120 1400
20
40
60
80
100
Suction, s(kPa)
Deg
ree
of s
atur
atio
n,S
r(%
) ρd=1.55g/cm3
ρd=1.50g/cm3
ρd=1.40g/cm3
Fig. 6. Relation between suction and the degree of saturation.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358 335
when the suction changes are not dominant during monotonic loading. Herein, s isthe suction, and e0 and sy0 are the void ratio and the vertical net stress at thereference, respectively. Eq. (3) implies that the virgin compression lines of theunsaturated soil in the e and sv spaces are parallel to every suction value and theirintervals are determined by parameters sy0 and a: Herein, an examination is made asto whether or not Eq. (3) is satisfied for the test data of unsaturated Omma sand. Thevirgin compression lines obtained from the K0 consolidation tests are provided inFig. 3(a). The suction value corresponding to each datum set of water content andinitial dry density (or initial void ratio) of the soil samples subjected to theconsolidation tests in Fig. 3(a) is estimated from the water content, the dry density,and the suction relation of Omma sand shown in Fig. 8. Since the suction values areestimated to be 4 and 25 kPa for the water contents of 25% and 7%, respectively, thevirgin compression lines in Fig. 3(a) are rewritten in the e and sv þ s relation shown
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120
100
80
60
40
20
00 10 15 20 25 30
Water content, w(%)
Suc
tion,
s(kP
a)
ρd=1.55g/cm3
ρd=1.50g/cm3
ρd=1.40g/cm3
Fig. 7. Relation between water content and suction relation.
0 10 15 20 25 300.4
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
1.70
Sr = 80(%
)
Sr =90(%
)
Sr =100(%
)
10100 80 60 40 20 8 6 s=4 kPa 2Dry
den
sity
, ρd
(g/c
m3 )
Water content, w (%)
Fig. 8. Suction distribution and compaction curve.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358336
in Fig. 9. According to Fig. 9, the compression lines of the disturbed Omma sand arefound to be parallel to every suction value except for the beginning portion that hasnot yet reached the virgin compression line in Fig. 3(a). Parameters sy0 and a inEq. (3) can be determined as follows. Matyas and Radhakrishina (1968) showed thatthe void ratio contour could be uniquely drawn as straight lines on the plane of theapplied net stress and the suction. As seen in Eq. (3), all straight contour lines witheach value of initial void ratios intersect at a point. Using the estimated datum setsfor the void ratio and the vertical net stress at suction values of 4 and 25 kPa fromFig. 9, an attempt is now made to draw the void ratio contour on the plane of thevertical net stress and the suction. Herein, the term for the vertical effective stress isused for the vertical net stress, because the vertical net stress means the consolidationstress here. Since two points can be plotted on the plane of the effective vertical(normal) stress and the suction for each value of initial void ratio (equivalent to theinitial dry density) from Fig. 9, the straight contour lines for each initial dry densitycan be drawn by connecting every two points, as shown in Fig. 10. In Fig. 10, all
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1 10 100 1000
0.8
1.0
1.2
1.4
1.6
σv+ s (kPa)
Voi
d ra
tio, e
s=4kPa
s=25kPa
Fig. 9. Compression lines considering suction.
10000 8000 6000 4000 2000 0
120
100
80
60
40
20
0
1
a
1.2
1.70
1.60
1.55
ρdy=1.45 (g/cm3)ρdy=1.5 1.4
1.35 1.
3
Suc
tion,
s(k
Pa)
Effective normal stress, σv (kPa)
Fig. 10. Relation between vertical stress and suction.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358 337
straight lines intersect at a point. When the gradient of each straight contour line isexpressed as 1=a; the intersection is geometrically found to be the point of ðsv; sÞ ¼ðsy0=ð1þ aÞ;�sy0=ð1þ aÞÞ; in which sy0 is the value of sv at s ¼ 0 and parameter a inEq. (3) is found to be expressed as a ¼ 1þ a: Thus, parameters sy0 and a in Eq. (3)are determinable from Fig. 10. In the case of Omma sand, sy0 and a are estimated tobe 20.0 kPa and 2.56 (a ¼ 1:56) for the specimen of s ¼ 25 kPa, respectively. Sincethe dry density can be expressed from Eq. (3) as
rd ¼Gsrd0
Gs � rd0l lnððsv þ sÞ=ðsy0 þ asÞÞð4Þ
in which Gs is the specific gravity and rd0 is the dry density at the reference, therelationship between the void ratio and the vertical applied stress can be convertedinto a relationship between the dry density and the vertical applied stress. Once therelationships for the suction, the dry density (or void ratio) and the vertical appliedstress are presented, the virgin compression curves on the plane of the dry densityand the effective vertical stress can be more closely estimated with every suctionvalue than these in Fig. 3(a). The obtained relations are summarized in Fig. 11 as themutual relationships among the compaction curve, the compression (consolidation)curves, the dry density contour, and the water retention characteristics by explicitlyconsidering the suction. The first quadrant gives a conventional compaction curve,which shows relationship between density and water content. The second quadrantgives the compression curves of dry density from Eq. (4). The third quadrant is theyield line expressed in Fig. 10. The fourth quadrant shows relationship between
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3000 2500 2000 1500 1000 500 0
s(kPa)
80
15
2
60
40
20
10864
σv(kPa)
0 10 15 20 25 300.0
1.3
1.4
1.5
1.6
1.7
100 80 60 40 20
10 8 6 s=2(kPa)s=4(kPa)
0ρ
d(g/cm3)
w(%)
s(kPa)
Sr =80(%
)
Sr =90(%
)
Sr =100(%
)
1.2
1.60
1.55
1.50
ρ dy=1
.45(
g/cm
3 )
1.40
1.35 1.
3
120
100
80
60
40
20
0
ρd=1.55g/cm3
ρd=1.50g/cm3
ρd=1.40g/cm3
Fig. 11. Relations among water content, dry density, applied stress, and suction.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358338
water content and suction and depends on dry density. The equivalent preconsolida-tion vertical stress, considering suction, is then determinable from Fig. 11. Fig. 12explains the way to estimate the preconsolidation stress from Fig. 11. In the 1stquadrant, the suction value remaining in the compacted soil can be determined whenthe dry density gd and the water content w are given, for example, the suction s3 forK in Fig. 12. Since normally compression lines (equivalent to the compression linesof NC samples) for various suction values are provided in the second quadrant, theequivalent preconsolidation stress can be specified by a crossing point with thecompression line of the compacted sample (equivalent to the swelling line of OCsample), for example, the equivalent preconsolidation stress svy3 for the compactedsoil in which the suction value of s3 remains, as shown in Fig. 12. If the suction valueremaining in the compacted soil is smaller, the estimated equivalent preconsolidation
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s1s2s3s4s5
s=0
ρd
σvy3 σvy2σv
s
w
Sr =100(%
)
Sr =90(%
)
Sr =80(%
)
s1s2s3s4s5s6s7
Compression test after soaking
s5
s3
s2
Compression test ats=s3
dρ
dρ
Fig. 12. Estimate process of equivalent preconsolidation stress.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358 339
stress results in being smaller as demonstrated in Fig. 12 (J and W in the secondquadrant). Thus, the suction effect can be taken into consideration in estimate of thepreconsolidation stress. And also, it is found that this consideration of suction effectis consistent to the knowledge for unsaturated soil reported in the past. Namely,yielding lines in the third quadrant is consistent to yielding points for unsaturatedsoil shown by Matyas and Radhakrishina (1968) and the relationship betweensuction and water content in the fourth quadrant is equivalent to the water retentionrelation of unsaturated soil.
4. Compressive shear test on compacted soil wrapped by geosynthetics
4.1. Model test procedure
The Omma sand, of which the water content was adjusted to a prescribed value,was uniformly compacted by a 3.5 kg rammer up to a designated degree ofcompaction while being wrapped in geosynthetics, as shown in Fig. 13. The soil isspread to a thickness of 40 to 80mm for each compaction. The compacted soilspecimen (300mm in diameter by 400mm in height) was wrapped in geosyntheticsand laid on the uniaxial loading apparatus, as shown in Fig. 14. It was then subjectedto compressive shear, see Iizuka et al. (2002). Table 1 summarizes the preparedcompacted soil specimens for the tests. The number of compactions and thethickness were varied with the specimen as shown in Table 1. Some specimens with alower degree of compaction (Tests 6 to 8 in Table 1) were also prepared for thepurpose of investigating the influence on the geosynthetic-reinforcement effect due tothe difference in the dilatancy characteristics of compacted soils. In order to measurethe extension forces working on the geosynthetics, the strain gauges (limit strain:5%, uniaxial type, 120O, base: 4.2� 1.5mm, grid: 1.0� 0.65mm) are herein tightlypasted on the geosynthetics, as shown in Fig. 13. In the experiment, the verticaldisplacement of the specimens and the extension stress working on the geosyntheticswere measured with the applied vertical load, as seen in Fig. 14. Compressive shearwas performed at a sufficiently slow rate in order to satisfy the condition that thevolume of the specimen is changeable (drained condition). As for the geosyntheticmaterials used in the experiment, the uniaxial extension tests were carried out tomeasure the stiffness and the ultimate strength of the geosynthetics. Fig. 15 shows
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Fig. 13. Preparation of the test specimens.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358340
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Load cell (capacity:20 ton)
Hydraulic jack
(capacity:20 ton, stroke:150 mm)
Measurement ofdisplacement
Specimen
Strain gauges
Compression
12345678
Fig. 14. Compressive shear apparatus.
Table 1
Prepared compacted soil specimens for compressive shear test
Test No. Degree of compaction (the number of
compaction)� (layers)
Water content
w (%)
Dry density rd(g/cm3)
2 50� 10 18.1 1.53
3 50� 10 17.6 1.56
4 50� 10 17.3 1.60
5 50� 10 17.1 1.54
6 30� 6 16.6 1.43
7 30� 6 17.0 1.43
8 25� 5 16.8 1.45
9 50� 10 16.5 1.55
0 2 100
20
40
60
80
100
120
93.9 kN/m
Axial strain rate 1%/min
Load
(kN
/m)
Axial strain (%)4 6 8
Fig. 15. Stress–strain relation of geosynthetics.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358 341
the stress–strain relation of the geosynthetic materials obtained from the uniaxialextension tests. The extension strength is 93.9 kN/m, the cross-sectional area is3.2� 10�4m2 and Young’s modulus is 4.86� 106 kPa. The geosynthetic could bemodeled as a linearly elastic material, as shown in Fig. 16. It is noted that thegeosynthetics used in the experiment is a textile coated by vinyl chloride, which iswoven by aramid-polyester fiber in lattice shape. Photo 2 indicates a snapshot takenduring the tests.
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σ
ε
EGeosynthetics cannotwork for compression
Geosynthetics yieldsat this stresst
: Young’s modulus
Fig. 16. Geosynthetics model (bar element).
Photo 2. View of compressive shear tests: (a) initial figure of test, (b) compressive displacement of 80mm
(Test 6).
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358342
4.2. Test results
The load and displacement relations obtained from the compressive shear tests areshown in Fig. 17. It is found that the well-compacted soil specimens (higher degree ofcompaction) indicated by black symbols (’, m, K and .) show higher rigidity thanthe relatively poorly compacted soil specimens indicated by white symbols (W, Jand U). Fig. 18 shows the extension forces working on the geosynthetics at locationsNos. 2 and 4, see Fig. 14. It can be seen that the higher the initial degree ofcompaction is, the larger the extension force working on the geosynthetics gets withthe displacement. The effect of confining the deformation of the soil specimen bygeosynthetics can be more obviously recognized when the initial degree ofcompaction of the specimen is higher. Namely, the geosynthetics work moreremarkably to prevent the dilative deformation of the soil specimen when thecompaction degree of the specimen is higher. It can be concluded that thereinforcement effect by geosynthetics is closely related to the dilatancy characteristics
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0 20 40 60 800
20
40
60
80
100
120 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9Lo
ad (
kN)
Displacement (mm)
Fig. 17. Relation between load and displacement.
0 20 40 60 800
5
10
15
20
25
30Strain gauge No. 2 Test 2
Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9F
orce
(kN
)
Displacement (mm)0 20 40 60 80
Displacement (mm)
0
5
10
15
20
25
30Strain gauge No.4
Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9F
orce
(kN
)
(a) (b)
Fig. 18. Development of the axial forces working on the geosynthetics with displacement: (a) At strain
gauge No. 2, (b) at strain gauge No. 4.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358 343
of the soil, since well-compacted soil specimens (higher degree of compaction) tendto dilate more during shear.
Fig. 19 shows the distribution of the extension forces working on the geosyntheticsalong the circumference of the specimens, when the compressive displacementreaches each of 10, 20,y, and 80 cm. It can be seen that the distribution of extensionforces along the circumference of the specimen is almost uniform regardless of thelocation. Herein, note that the case of the well-compacted specimens is representedby Test 5, the case of the relatively poorly compacted specimens is represented byTest 6, respectively, and y ¼ 0 denotes the location at the top of specimen.
Changes in circumferential length and cross-sectional area during compression areindicated in Figs. 20 and 21. The circumferential length of the specimen graduallyincreases regardless of the initial compaction degree. On the contrary, the cross-sectional area of the specimen decreases regardless of the initial compaction degree inall of the tests.
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0 20 40 60 80 100 120 140 160 1800
5
10
15
20
25
30
35
40
θ d=10 d= 50 d=20 d= 60 d=30 d=40
d : Displacement (mm)
Test 5
For
ce (
kN)
θ (degree)0 20 40 60 80 100 120 140 160 180
0
5
10
15
20
25
30
35
40
θ d=10 d= 50 d=20 d= 60 d=30 d= 70 d=40 d= 80
d : Displacement (mm)
Test 6
For
ce (
kN)
θ (degree)(a) (b)
Fig. 19. Extension forces working on the geosynthetics along the circumference of the specimen: (a) Well-
C : Circumferential lengthCI : Initial circumferential length
Test 5 Test 6 Test 7 Test 8 Test 9
C /
CI
Displacement (mm)
Fig. 20. Changes in circumferential length.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358344
5. Finite element simulations of compressive shear tests
5.1. Condition of analysis and preliminary elastic simulation
A series of finite element simulations of the compressive shear model tests wascarried out. Fig. 22 shows the finite element modeling of the tests, in which a 4 nodequadrilateral constant strain element is employed. To simulate the compressive sheartests, the displacement is vertically given to the specimen at a strain rate of 1.0%/minas indicated in Fig. 22. First, as a preliminary simulation, the compacted soil isassumed to be a linearly elastic material that has no irreversible dilatancycharacteristics associated with shearing. Also, based on the uniaxial extension testresults for geosynthetics (Fig. 15), the geosynthetic wrapping of the soil specimenis modeled by the linear elastic bar elements shown in Fig. 16, whose propertiesare a Young’s modulus of E¼ 4:86� 106 kPa, a cross-sectional area ofA¼ 3:20� 10�4 m2, and a tensile strength of Nf ¼ 93:9 kN/m. In the computation,it is assumed that the bar elements (modeling the geosynthetics) do not resist theaxial compression, as indicated in Fig. 16.
Fig. 23 compares the load and displacement relation obtained from theexperiments with the computed ones, in which three values of Young’s modulusfor compacted soil are chosen, as shown in the figure, but Poisson’s ratio is assumedto be 0.33 in all cases. The case of E ¼ 6000 kPa seems to effectively explain the loadand displacement relation of the well-compacted specimen, Test 5. Changes in thecross-sectional area and the circumferential length of the specimen are compared inFigs. 24 and 25, respectively. A Young’s modulus of 6000 kPa is used in thecomputation, while Poisson’s ratio is varied from 0.2 to 0.499 with each case. As forthe cross-sectional area of the specimen in Fig. 26, all the cases seem to be able todescribe the tendency that the experiments show (the cross-sectional area decreaseswith loading). However, as for the circumferential length of the specimen as shownin Fig. 25, only the case of n ¼ 0:499 can explain the experimental results of Test 5.The assumption of n ¼ 0:499 theoretically means an almost incompressible condition
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0 20 40 60 800.85
0.90
0.95
1.00
1.05
A : Cross sectional areaAI : Initial cross sectional area
Test 5 Test 6 Test 7 Test 8 Test 9
A /
AI
Displacement (mm)
Fig. 21. Changes in cross-sectional area.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358 345
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0 20 40 60 800
50
100
150
(ν=0.33)
E : Young's modulus
E=5000(kPa)
E=6000(kPa)
E=4000(kPa)
Experimental data (Test 5) F.E.results (elastic model)
Load
(kN
)
Displacement (mm)
Fig. 23. Relation between computed load and displacement (elastic).
0 20 40 60 800.85
0.90
0.95
1.00
1.05
E=6000 kPa
Displacement (mm)
A/A
1
A: Cross sectional area
A1: Initial area
ν =0 .2
ν =0 .33
ν =0 .4
ν =0 .499 Experimental data(Test5)
Fig. 24. Computed cross-sectional area (elastic).
Fig. 22. Finite element mesh.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358346
and is not acceptable as Poisson’s ratio of the soil materials in engineering practice.Fig. 26 compares the computed distribution of extension forces working on thegeosynthetics with the measured ones in Test 5. It can be concluded that the elasticassumption, which does not consider the dilatancy characteristics during compres-sive shearing for the compacted soil, cannot explain the geosynthetic-reinforcementeffect observed in the model tests.
5.2. Elasto-plastic finite element simulation
If a more logical consistency is pursued, the elasto-plastic constitutive equation forunsaturated soil should be employed for modeling the compact soil. However,although some nonlinear constitutive models for unsaturated soil have beenproposed (Karube, 1987; Alonso et al., 1990; Kohgo et al., 1993; Honda et al.,
F.E.M exp. d=20.0 mm d=40.0 mm d=60.0 mm d : Displacement
(b)
Fig. 26. Computed extension forces working on the geosynthetics along the circumference of the specimen
(elastic): (a) E ¼ 6000 kPa and v ¼ 0:333 for Test 5, (b) E ¼ 6000 kPa and v ¼ 0:499 for Test 5.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358 347
2000 and so forth), they are still in the development stage and have some difficultiesin expressing the mechanical behavior inside the normal yielding surface. Moreover,some additional parameters have to be determined to describe the unsaturatedcharacteristics. This is a considerable obstacle to their practical use at the presentstage.
In this paper, therefore, a conventional elasto-plastic constitutive model, proposedby Sekiguchi and Ohta (1977), is employed and the subloading surface conceptoriginally proposed by Hashiguchi (1989) is introduced to secure the descriptionability inside the normal yielding surface, see Appendix A. The constitutive model bySekiguchi and Ohta (1977) can be regarded as an extension of the original Cam-claymodel, but is distinguished from it in its ability to describe the mechanical behaviorarising from the initially induced anisotropy and the stress reorientation. Thedetermination procedure for the input parameters needed in Sekiguchi and Ohtaconstitutive model has been well established (Iizuka and Ohta, 1987; Ohta et al.,1988, 1989, 1991, 1992, 1994) through a lot of practical case studies using a finiteelement code, DACSAR, into which Sekiguchi and Ohta model has been installed(Iizuka and Ohta, 1987and Mestat, 2001).
5.2.1. Input parameter specification and the calibration of the modeling
The input parameters needed for the computation are determined from thecompression and the shear test results for the disturbed sample (Figs. 3(a) and (b)).Stress ratio ðt=s0vÞf at the critical state in the case of direct shearing, such as shearbox tests under a condition of constant volume, can be derived by simultaneouslysolving the critical state condition, b ¼ 0 in Eq. (A.6), and the undrained (constantvolume) condition, ’evð¼ ’ee
v þ ’epvÞ ¼ 0; of Sekiguchi and Ohta model as (Ohta et al.,
1993 and Morikawa et al., 1997)
ts0v
� �f
¼1þ 2K0
3ffiffiffi3
p M : ð5Þ
With the help of the empirical relation of K0¼ 1� sin f0 (Jaky, 1944), critical stateparameter M can be expressed by ðt=s0vÞf since M¼ ð6 sin f0Þ=ð3� sin f0Þ: Theexperimental value of ðt=s0vÞf is given in Fig. 3(b) and little difference is found in thecritical state lines with the water content. However, two possible critical state linescan be drawn, as shown by the solid lines in Fig. 3(b), depending on which point, thefinal or the kink points, on the effective stress path should be taken as the criticalstate. Herein, the kink point of the effective stress path is chosen as the critical statepoint, and critical state parameter M is then determined to be 1.42. The compressionindex, l (¼ 0:434Cc), can be directly determined as 0.12 from Fig. 3(a) since it isknown that the gradient of the virgin compression line from the K0 consolidation inthe e � ln s0v relation and that from the isotropic consolidation in the e � ln p0
relation coincide with each other (e.g., Mitachi and Kitago, 1976). Swelling index k isestimated to be 0.023 from the empirical relation of M ¼ 1:75ð1� k=lÞ by Karube(1975), because the swelling index required as an input parameter by the constitutivemodel is the gradient of the isotropic swelling line and it differs from that of the K0
swelling line shown in Fig. 4(a). The equivalent preconsolidation vertical stress is
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determined from Fig. 27 with each water content. The lateral axis of the effectivenormal stress is rewritten with a logarithm scale, and the K0 swelling data in Fig. 4(a)are plotted in Fig. 27 together with the virgin compression line with each suctionvalue in Fig. 11. Since the suction value of the compacted soil with the water contentcan be estimated from the suction contour in Fig. 11, the value of the equivalentpreconsolidation vertical stress is given as each intersection of the K0 swelling lineand the virgin compression line with each suction value. Thus, the obtainedequivalent preconsolidation vertical stress, s0v0; is 882 kPa for a water content of15.4% (s ¼ 7:0 kPa), 1904 kPa for 15.5% (s ¼ 8:5 kPa), 536 kPa for 12.8%(s ¼ 10:0 kPa), and 1549 kPa for 15.1% (s ¼ 8:5 kPa). The equivalent OCR iscalculated as s0v0=s
0vi from the equivalent preconsolidation vertical stress and the
current effective vertical stress. The coefficient of the current earth pressure at rest,Ki; is estimated from the empirical relation of Ki ¼ ðOCRÞnK0 and n ¼ 0:42 afterLadd et al. (1977). Poisson’s ratio, n; is assumed to be 0.33.
The theoretical effective stress paths computed from Sekiguchi and Ohta modelwith the subloading surface using the above-determined input parameters, arecompared in Fig. 28 with the experimental results of Fig. 4(b), in which parameter,m; defined in Eq. (A.4), is assumed to be 1.0 and 0.1. The theoretical paths computedfrom Sekiguchi and Ohta model without the subloading surface (original model bySekiguchi and Ohta) are also compared. It cannot be said that the computedprediction explains the shear behavior of compacted soil well. At least, however, itcan successfully express the dilatancy characteristics of compacted soil and in thecase of m ¼ 1:0; seems to give a better prediction for compacted Omma sand.
5.2.2. Computed results
Likewise, for the compressive shear model tests, the equivalent preconsolidationvertical stresses of the compacted specimens can be estimated from Fig. 29,considering the suction effect. The virgin compression lines of Omma sand, with eachsuction value being expected to remain in the compacted soil, are transcribed fromFig. 11. Since it was very difficult to evaluate the initial effective vertical stress levels
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10000 1000 1001.2
1.3
1.4
1.5
1.6
1.7s(kPa)
1008060
Effective normal stress, σv (kPa)
Sample 1 w=15.4% w=15.5% w=12.8% w=15.1%
2
40
201086 4 0
ρ d(g
/cm
3 )
Fig. 27. Estimate of equivalent preconsolidation stress for SBT.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358 349
in the specimen just before the compressive shear in the model test, however; it wasdecided that the equivalent preconsolidation vertical stress would be determined asthe value corresponding to the initial dry density of each specimen, as shown inFig. 29, without considering the slope of the swelling line. Therefore, it would resultin somewhat underestimating the equivalent preconsolidation vertical stress. Theestimated equivalent preconsolidation vertical stress levels are tabulated in Table 2.The initial effective vertical stress, in reality, would not be uniform inside thespecimen, but would be distributed in the specimen. Then, the effective overburdenpressure estimated at the center of the specimen is employed in the computation as arepresentative value.
Fig. 30 compares the computed load and displacement relation with theexperimental results. The black symbols, FEM 5 and FEM 9, denote the cases ofwell compacted specimens (high degree of compaction), corresponding to Tests 5
ARTICLE IN PRESS
10 100 1000 100001.2
1.3
1.4
1.5
1.6
1.7
1.8s(kPa)
806040
20
1086
40
Effective normal stress, σv(kPa)
Dry
den
sity
, ρd
(g/c
m3 )
Test 5 Test 6 Test 7 Test 8 Test 9
Fig. 29. Estimate of the equivalent preconsolidation stress for the compressive shear tests.
Sample 1
shea
r st
ress
,τ(k
Pa)
effective normal stress, σ 'v (kPa)
F.E.result Experimental data
m=1
m=0.1
Original SO model
400
300
200
100
05004003002001000
Fig. 28. Computed stress paths of the compacted soil.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358350
and 9, respectively, while the white symbols, FEM 6, FEM 7, and FEM 8, representthe cases of relatively poorly compacted specimens (relatively low degree ofcompaction), corresponding to Tests 6, 7, and 8, respectively. Although a completeagreement between the computed and the measured results cannot be seen, it isfound that at least the computed results explain the influence due to the difference incompaction degrees. In computed results, the changes in slope of the load and
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0 20 40 60 800
20
40
60
80
100
120 m=1 FEM 5 FEM 6 FEM 7 FEM 8 FEM 9 Experimental data
Load
(kN
)
Displacement (mm)Displacement (mm)0 20 40 60 80
0
20
40
60
80
100
120Original SO model
FEM 5 FEM 6 FEM 7 FEM 8 FEM 9 Experimental data
Load
(kN
)
0 20 40 60 800
20
40
60
80
100
120m=0.1
FEM 5 FEM 6 FEM 7 FEM 8 FEM 9 Experimental data
Load
(kN
)
Displacement (mm)
(a) (b)
(c)
Fig. 30. Relation between computed load and displacement (elasto-plastic): (a) Sekiguchi and Ohta’s
original model, (b) subloading model with m ¼ 1:0; (c) subloading model with m ¼ 0:1:
Table 2
Estimated equivalent preconsolidation stress for compressive shear
Simulation case Initial effective vertical
stress svi0 (kPa)
Equivalent preconsolidation
vertical stress sv0 0 (kPa)Corresponding
model test case
FEM5 3.54 1430 Test 5
FEM6 3.26 386 Test 6
FEM7 3.27 380 Test 7
FEM8 3.33 536 Test 8
FEM9 3.54 1757 Test 9
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358 351
displacement curves are seen. They are due to the yielding from an elastic region.However, it is found that introducing the subloading surface inside the normalyielding surface brings a smoother development of the load and displacement curves,similar to the experimental results. As for choosing parameter m; which controls theaccessibility rate of the subloading surface to the normal yielding surface, as definedin Eq. (A.4), the case of m ¼ 1:0 seems to yield a better prediction. But, steepdevelopment of the load with displacement is not simulated well. The amount ofdilative deformation produced by the constitutive model with a subloading surfacemight be still insufficient. It is left as a question to the authors and further research isrequired. Figs. 31 and 32 compare the computed cross-sectional area andcircumferential length of the specimen with the measured results (Test 5). Thecomputed predictions explain the measured results well.
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0 20 40 60 800.85
0.90
0.95
1.00
1.05
Displacement (mm)
A/A
1
A: Cross sectional areaA1: Initial area
Original SO model m = 1 m = 0.1Experimental data (Test 5)
Fig. 31. Computed cross-sectional area (elasto-plastic computation).
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358352
Fig. 33 indicates the computed development of the axial forces working on thegeosynthetics with the displacement at the locations of strain gauges Nos. 2 and 4(see Fig. 14) being compared with the measured results. In addition, Fig. 34 showsthe computed distribution of axial forces along the circumference of the specimen,for which the case of a high degree of compaction (Test 5, FEM 5) is shown inFig. 34(a) and the case of a relatively low degree of compaction (Test 6, FEM 6) isin Fig. 34(b). The elasto-plastic modeling with the subloading surface is found to wellexplain the measured results, in spite of the fact that the elastic modeling for thecompacted soil cannot explain the experiment, as shown in Fig. 26.
6. Conclusion
This paper presents the modeling of geosynthetic-reinforced compacted soil anddiscusses the effect of the reinforcement arising from the confining of the
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0 20 40 60 80 100 120 140 160 1800
10
20
30
40Test 5
m =1
θ
For
ce (
kN)
θ (degree)
F.E.M exp. d=20.0 mm d=40.0 mm d=60.0 mm
d : Displacement
0 20 40 60 80 100 120 140 160 1800
5
10
15
20 m =1
Test 6
θ
For
ce (
kN)
θ (degree)
F.E.M exp.d=20.0 mmd=40.0 mmd=60.0 mm d : Displacement
(b)(a)
Fig. 34. Computed extension forces working on the geosynthetics along the circumference of the
Fig. 33. Computed development of the extension forces working on the geosynthetics (elasto-plastic
computation): (a) At strain gauge No. 2, (b) at strain gauge No. 4.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358 353
deformation of the compacted soil by geosynthetics. A series of compressive sheartests for compacted sandy soil specimens, wrapped in geosynthetics, is carried out.And the numerical modeling of geosynthetic-reinforced compacted soil is presented.Herein, in order to describe the irreversible dilatancy characteristics of compactedsoil, the Sekiguchi and Ohta elasto-plastic constitutive model with the subloadingyielding surface is introduced for compacted soil from the mechanical similarity withover-consolidated clay. Furthermore, compacted soil is essentially unsaturated andits mechanical behavior is influenced by the suction remaining in the compacted soilmedia. In this paper, an estimate method of compaction degree considering thesuction effect is proposed. Major conclusions are summarized as follows.
The degree of compaction for compacted soil is expressed by the equivalentpreconsolidation stress and its estimate method considering not only the watercontent but also the suction remaining in the unsaturated compacted soil is proposedas a diagram for practical use, shown in Fig. 11.
In order to describe the irreversible deformation characteristics of compacted soil,the subloading surface is introduced inside the normal yielding surface of Sekiguchiand Ohta elasto-plastic constitutive model. And a determination procedure of inputparameters for compacted soil is presented.
A series of compressive shear tests for compacted soil specimens, wrapped ingeosynthetics, is carried out and the geosynthetic-reinforcement effect is measured.The extension force acting in the geosynthetic reinforcement increases withcompressive shearing of compacted soil specimen so as to prevent the deformationof the specimen. It results in increasing the effective stress levels in the compacted soilmedia and gaining the rigidity and strength of the specimen.
A series of finite element simulations for the compressive shear tests is carried out.It is shown that the elastic modeling for compacted soil cannot explain thereinforcement effect in the compressive shear test for compacted soil, wrapped ingeosynthetics. At least, it is necessary to introduce the elasto-plastic modeling, whichcan describe the dilatancy characteristics of compacted soil.
In this paper, only a one sandy soil, Omma sand, is used in a series of experiments.The validity of the conclusions for other sands remains to be established.
Acknowledgements
The authors acknowledge Emeritus Professor D. Karube of Kobe University andProfessor H. Ohta of Tokyo Institute of Technology for their continuousencouragement during this research. The authors would also like to express theirappreciation to Messrs T. Yamakami of Kanazawa University and M. Maeda andY. Yokota of Maeda Kohsen Co. Ltd. for their help in conducting some of the tests.This research was financially supported in part by the Ministry of Education,Culture, Sports, Science and Technology. Also, this study presented here wassupported in part by the Twenty-First Century Center of Excellence (COE) Program‘‘Design Strategy towards Safety and Symbiosis of Urban Space’’ awarded toGraduate School of Science and Technology, Kobe University.
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Appendix A. Elasto-plastic modeling of compacted soil
In this paper, a conventional elasto-plastic constitutive model, proposed bySekiguchi and Ohta (1977), is employed for compacted soil. And the subloadingsurface concept originally proposed by Hashiguchi (1989) is introduced to expressthe elasto-plastic behavior including the dilatancy characteristics of compacted soilinside the normal yielding surface.
The normal yielding function of Sekiguchi and Ohta model (Sekiguchi and Ohta,1977) is expressed as
f ¼l� k1þ e0
lnp0
p00
þ DZ� � epv ¼ 0 ðA:1Þ
in which D is the coefficient of dilatancy proposed by Shibata (1968), epv is the plasticvolumetric strain, and l (¼ 0:434Cc) and k (¼ 0:434Cs) are compression and swellingindices, respectively. Parameters l; k and D have a theoretical relation with criticalstate parameter M as M ¼ ðl� kÞ=Dð1þ e0Þ (Ohta, 1971). Z� is the generalizeddeviatoric stress parameter defined as
Z� ¼
ffiffiffi3
2
rs
p0 �s0
p00
�������� ðA:2Þ
in which s is the deviatoric stress tensor, subscript 0 denotes the value at thereference, and | � | is the Euclid norm. After Hashiguchi (1989), subloading surface fsis similar to the normal yielding surface and can be defined using similarity ratio R as
fs ¼l� k1þ e0
lnp0
p00
þ DZ� � epv þl� k1þ e0
ln R
� �¼ 0 ðA:3Þ
in which similarity ratio R determines the scale of the subloading yielding surfaceagainst the normal yielding surface and is defined as p0= %p0 using the current effectivemean stress, p0 at the subloading yielding surface and its conjugate effective meanstress, %p0 at the normal yielding surface. The evaluation law of similarity ratio R isassumed as
’R ¼ UR ’epj j ¼ �m
Dðln RÞ ’epj j for ’epa0 ðA:4Þ
after Hashiguchi (1989), in which m is the newly introduced material parametercontrolling the accessibility rate of the subloading surface to the normal yieldingsurface. Herein, note that the scalar function, UR is defined in the region of 0oRp1and satisfies UR ¼ N when R ¼ 0 and UR ¼ 0 when R ¼ 1: The conceptual diagramof the subloading surface is shown in Fig. 35. Since the current effective stress alwaysstay on the subloading surface, the consistency condition can be described as ’fs ¼ 0:Therefore, assuming the associated flow rule as ’ep ¼ Lqfs=qr0 and introducing thegeneralized Hooke’s law for describing the elastic region as ’r0 ¼ De ’ee ¼ Deð’e � ’epÞ;the plasticity multiplier of L is determined as
L ¼1
h
qfs
qr� ’r ¼
1
H
qfs
qr�De ’e ðA:5Þ
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in which h ¼ trðqfs=qrÞ � mMðln R=RÞ ðqf =qsÞ�� ��; H ¼ h þ qfs=qr �De qfs=qr; ’e is the
strain increment tensor, ’r0 is the effective stress increment tensor, and superscripts eand p denote the elastic and the plastic components, respectively. The stress andstrain expression of Sekiguchi and Ohta model with the subloading surface isobtained as
’r0 ¼ De �ðKb1 þ 3Gðg � g0Þ=Z
�Þ#ðKb1 þ 3Gðg � g0Þ=Z�Þ
b2K þ 3G þ p0=Dðb� mM ðln R=RÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib2=3þ 3=2
qÞ
264
375’e ðA:6Þ
in which De is the fourth-order elastic stiffness tensor, 1 is the unit tensor, g isthe deviatoric stress ratio tensor (g ¼ s=p0), b is the accessibility function to thecritical state (b ¼ M � ð3=2Z�Þg � ðg � g0Þ), K is the elastic bulk modulus(K ¼ ðð1þ e0Þ=kÞp0), G is the elastic shear modulus (G ¼ 3ð1� 2nÞK=ð2ð1þ nÞÞ=K ;n: Poisson’s ratio), and # denotes the operator of the tensor multiplier. The loadingð’epa0Þ or the unloading ð’ep ¼ 0Þ can be judged by the plasticity multiplier as
Lo0: unloading;
L ¼ 0 : neutral;
L > 0 : loading:
ðA:7Þ
Thus, the obtained stress and strain relation is implemented in the finite elementcode, DACSAR (Iizuka and Ohta, 1987) and is used in the computation. Note thatthe input parameters needed for the computation are l (the compression index), k(the swelling index), D (the coefficient of dilatancy) or M (the critical stateparameter) and m (the parameter controlling the accessibility of the subloadingyielding surface to the normal yielding surface) as the material constant, and e0 (thevoid ratio just after completion of the consolidation which is usually taken as thereference state). The state parameters are K0 (the coefficient of earth pressure at rest),s0v0 (preconsolidation vertical stress), Ki (the coefficient of current earth pressure atrest) and s0vi (the initial effective vertical stress).
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q
p ′
K0-line
preconsolidation stress
normal yield surface
subloading surface
Fig. 35. Subloading surface.
A. Iizuka et al. / Geotextiles and Geomembranes 22 (2004) 329–358356
References
Alonso, E.E., Gens, A., Josa, A., 1990. A constitutive model for partially saturated soils. Geotechnique
40 (3), 405–430.
Hashiguchi, K., 1989. Subloading surface model in unconventional plasticity. International Journal of
Solids and Structures 25, 917–945.
Honda, M., Iizuka, A., Kawai, K., Karube, D., 2000. Stress–strain relationship for unsaturated soil.
Journal of Geotechnical Engineering JSCE 659/III–52, 153–164 (in Japanese).
Iizuka, A., Ohta, H., 1987. A deformation procedure of input parameters in elasto-viscoplastic finite
element analysis. Soils and Foundations 27 (3), 71–87.
Iizuka, A., Hirata, M., Yokota, Y., Ohta, H., Kim, E.R., Kubo, T., 2002. Compressive shear tests of
compacted soils wrapped by geosynthetics. Proceedings of the 7th International Conference on
Geosynthetics, Nice, Vol. 3, 1133–1136.
Jaky, J., 1944. The coefficient of earth pressure at rest. Journal of the Union of Hungarian Engineers and
Architects, pp. 355–358 (in Hungarian).
Karube, D., 1975. Unstandardized triaxial testing procedures and related subjects for inquiry. Proceedings
of the 20th Symposium on Geotechnical Engineering, Tokyo, pp. 45–60 (in Japanese).
Karube, D., 1987. A constitutive equation of unsaturated soils. Proceedings of Symposium on Mechanical
Properties of Unsaturated Soils, Tokyo, pp. 59–68 (in Japanese).
Karube, D., Kato, S., 1989. Yield functions of unsaturated soil. Proceedings of the 12th International
Conference on Soil Mechanics and Foundation Engineering, Rio de Janeiro, Vol. 1, 615–618.
Karube, D., Katsuyama, J., Nishiumi, K., Niwa, N., 1989. Yield function of unsaturated soils under
triaxial compression. Journal of Geotechnical Engineering JSCE 406/III–11, 205–211 (in Japanese).
Kawai, K., Iizuka, A., Kim, E.R., Nagareta, H., 2003a. Suction changes during compaction and their
effects on the compressive yield stress. Journal of Geotechnical and Geoenvironmental Engineering
ASCE, submitted for publication.
Kawai, K., Nagareta, H., Hagiwara, M., Iizuka, A., 2003b. Suction change of compacted soils during
statically compaction. Proceedings of the 2nd Asian Conference on Unsaturated Soils-Geotechnical
and Geoenvironmental Aspects, Osaka, pp. 429–434.
Kohgo, M., Nakano, M., Miyazaki, T., 1993. Verification of the generalized elasto-plastic model for
unsaturated soils. Soils and Foundations 33 (4), 64–73.
Ladd, C.C., Foott, R., Ishihara, K., Schlosser, F., Poulos, H.G., 1977. Stress-deformation and strength
characteristics. Proceedings of the 9th International Conference on Soil Mechanics and Foundation
