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Effects of Reinforcement Stiffness on Deformation of Reinforced Soil Structures under Sustained and Cyclic Loading

Uchimura,T. and Tatsuoka,F. Department of Civil Engineering, University of Tokyo uchimura@geot.t.u-tokyo.ac.jp Hirakawa,D. Department of Civil Engineering, Tokyo University of Science Shibata,Y. Ministry of Land, Infrastructure and Transport Government of Japan

ABSTRACT: The stiffness and residual deformation of geosynthetic-reinforced soil structure subjected to sustained concentrated vertical loading and a long-term vertical cyclic loading history was evaluated by per-forming small-scale model tests in the laboratory. Within the examined limit of reinforcement stiffness, the effects of reinforcement stiffness were utterly insignificant on the behaviour during unloading and reloading. When the vertical spacing was smaller than some limit, the deformation of backfill did not decrease noticea-bly with a decrease in the vertical spacing of reinforcement layers. Theses results suggest that it is not neces-sary to use metal reinforcement and the reinforced backfill property could be more important.

1 INTRODUCTION

To construct geosynthetic-reinforced soil structures allowing small instantaneous and residual deformations, such as bridge abutments, it is necessary to restrain the deformation of the backfill to a small value. It is gen-erally considered that the reinforcement materials can be classified to “extensible” reinforcements (e.g. geo-synthetics) and “inextensible” reinforcements (e.g. steel bars and strips), and soil structures reinforced with “extensible” materials has low stiffness and strength. However, this popular belief should be carefully exam-ined by experimental facts. The stiffness of reinforcement materials could be less essential to the stiffness of reinforced soil structures, because ordinary “extensible” geosynthetics have much higher stiffness than the backfill geo-materials.

The stiffness and residual deformation of geosynthetic-reinforced soil structures were evaluated by per-forming small-scale model tests in the laboratory. Sustained concentrated vertical loading and a long-term vertical cyclic loading history were applied. The backfill soil was a well-compacted well-graded gravel. A polymer geogrid and a metal grid were used as the reinforcement to evaluate the effects of reinforcement stiffness. Possible effects of the vertical spacing of reinforcement layers on the deformation characteristics of reinforced backfill were also evaluated by these model tests.

2 EFFECTS OF REINFORCEMENT STIFFNESS

2.1 Test methods Static and cyclic loading tests were performed on scaled models of reinforced soil bridge pier (Figures 1).

The pier models had 12 layers of geogrid with a vertical spacing of 5 cm and a cross-section of 35 cm x 35 cm. The periphery of each gravel layer, sandwiched by vertically adjacent geogrid layers, was protected by 5 cm-high and 2.5 cm-thick sandbags, which prevented the backfill from spilling out and confined the backfill. The backfill was a well-graded gravel (Dmax = 5mm, D50 = 2.52mm, Uc = 5.41, Dr = 90 %) compacted to a dry den-sity of 1.79 g/cm3. Two types of reinforcement were used: a polyester geogrid and a phosphor bronze grid (Figure 2). The polyester geogrid had nominal rapture strength of 39.2 kN/m and the maximum extensive strain of 22 % and stiffness of 507 kN/m, at a strain rate of 1 %/min. Each strand was 1 mm-wide and the ce-

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center-to-center spacing was 9 mm. The phosphor bronze grid consisted of 34 phosphor bronze strips (3.5 mm-wide, 0.2 mm-thick and 350 mm-long) for each direction having the center-to-center spacing of 20 mm. The stiffness was 5580 kN/m, which is 11 times larger than that of the polyester grid. Fine sand particles were glued to surface of the phosphor bronze grid to make the friction angle with the backfill material to be nearly the same as that of the polyester grid, around 40 degrees.

The vertical spacing between the reinforcement layers, 5 cm, was much smaller than that of real reinforced soil structures. However, as the particle size of the backfill materials and the aperture of the grids were also scaled, the dimensions may geometrically reasonably simulate typical prototype structures.

The pier models were vertically compressed in a strain control condition by using a gear system. The verti-cal compressive strains of the model were precisely measured by means of LDTs (local displacement trans-ducers) set on the side surfaces. The horizontal strains were measured at the middle height of the model in two directions orthogonal to each other by using laser displacement transducers with targets connected to the backfill just behind the sandbags.

Loadingplate

Backfillm aterial

M odel ofsandbags

Reinforcem ent

C om pressiveLoad

C om pressivestrain

Height: 60cm(5cm x 12layers)

C ross-section:35cm x 35cm

Vertical strainsm easured by LD Ts

Figure 1. Configurations of models.

209

9

1

1

3.5

3.5

20

1 0.2

a) Polyester b) Phosphor bronze

Unit: [mm]

a) Polyester b) Phosphor bronzeReinforcementCR* [%]TRR**Surface

19.61-

33.711

with Toyoura Sand

*CR = (covering ratio per each geogrid reinforcement layer)? 100 %**TRR = (total rigidity ratio of geogrid reinforcement)? 100 %

Figure 2. Configurations of reinforcements.

2.2 Results and discussions

Figures 3 and 4 show the results from two tests on models with reinforcement of polyester and phosphor bronze, which were loaded with the same procedures. At loading stage denoted as “a” to “s” in the figures, the vertical strain rate were variously changed step by step, within a range of 0.00472 %/min to 0.472 %/min, in order to observe the strain-rate dependency on the stress-strain behaviours, which is however out of scope of this paper. At sustained loading stage denoted as “s” to “y”, a constant vertical stress of 250 kPa was ap-plied for around 40 hours, while 100 cycles of unload/reload were applied with several stress amplitudes of 6.2, 12.4, 24.8, and 49.6 kPa. At several stages of unloading, denoted as “y” to “hh”, 100 cycles of cyclic load with amplitude of 12.4 kPa were applied.

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0

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a)

hh

gg ff

ee dd

cc bb

aaz

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x

Polyester+CHIBA Gravel

wvuts

rqp

on

ml

kj

ihgf

edcb

a

V

ertic

al st

ress

, σv [k

Pa]

Vertical strain, εv [%]

b-c, f-g, l-m, p-q: 4.72E-3 [mm/min]a-b, d-e, g-h, i-j, k-l, n-o, r-s, y-z, aa-bb, cc-dd, ee-ff, gg-hh:4.72E-2 [mm/min]c-d, e-f, m-n, o-p: 4.72E-1 [mm/min]j-k: stress relaxation (for 1 hour)h-i, q-r: creep (for 1 hour)s-t, x-y: creep (for 6 hours)t-u: cyclic loading, Amp.=6.2 kPa, 4.72E-2 [mm/min], 100 cyclesu-v, z-aa, bb-cc, dd-ee, ff-gg: cyclic loading, Amp.=12.4 kPa, 4.72E-2 [mm/min], 100 cyclesv-w: cyclic loading, Amp.=24.8 kPa, 4.72E-2 [mm/min], 100 cyclesw-x: cyclic loading, Amp.=49.6 kPa, 4.72E-2 [mm/min], 100 cycles

0 10 20 30 40 50 60 70 80

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b)

hh

ggff

eedd

ccbb

aaz

yxwvuts

rqp

on

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kj

ihg

fe

dcb

a

Ver

tical

stre

ss, σ

v [kPa

]

Elapsed time, t [hour]-10 0 10 20 30 40 50 60 70 80

-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.0 Polyester+CHIBA Gravel

rq

kjih

a

yxwvuts

Vertical strain, εv

Horizontal strain, εh

c)

Ver

tical

and

hor

izon

tal s

train

, εv a

nd ε h [%

]

Elapsed time, t [hour]

0 2 4 6 8 10 12 14 16 18 20

0.00

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0.06

i)

creep2

creep1

Compression

Res

idua

l stra

in a

t PL

stat

e, ∆ε

v [%]

Elapsed time during creep or cyclic loading at PL state, ∆t [hour]

Creep loading: 250 kPa for 6 hours creep1, point s-t in Fig 4-4-11a creep2, point x-y

Cyclic loading: 100 cycles, 4.72E-2 %/min cyclic1, ∆σv=6.2 kPa, point t-u cyclic1, ∆σv=12.4 kPa, point u-v cyclic1, ∆σv=24.8 kPa, point v-w cyclic1, ∆σv=49.6 kPa, point w-x

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.05

0.00

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-0.40Polyester+CHIBA Gravel

εh1(Com p.)εh2

εv (C om p.)

GRS Bridge Pier Model

εh2

εh1

e)

Hor

izon

tal s

train

, εh [%

]

Vertical strain, εv [%]

0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64

40

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200Polyester+CHIBA Gravel

(Eeq)v=195 MPa

(Eeq)v=338 MPa

(Eeq)v=421 MPa

(Eeq)v

=505 MPaf)

gg ff

ee dd

cc bb

aa z

Ver

tical

stre

ss, σ

v [kPa

]

Vertical strain, εv [%]

Figure 3. Loading test results on a model pier rein-forced with a polyester geogrid. (a) vertical compressive strain vs. vertical stress; (b) time history of vertical stress; (c) time history of vertical and horizontal strain; (d) time history of vertical strain increment at each sustained or cyclic loading stage; (e) vertical compressive strain vs. horizontal strain; (f) vertical strain vs. vertical stress at cyclic loading stages during unloading.

d )

Polyester + CHIBA Gravel

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0

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gg

small unloading/reloading cycles hh

ff

ee dd

cc bb

aa z

y

xwvuts

rqp

on

ml

kj

ihgf

ed

cba

Ver

tical

stre

ss, σ

v [kPa

]

Vertical strain, εv [%]

a)b-c, f-g, l-m, p-q: 4.72E-3 [mm/min]a-b, d-e, g-h, i-j, k-l, n-o, r-s, y-z, aa-bb, cc-dd, ee-ff, gg-hh:4.72E-2 [mm/min]c-d, e-f, m-n, o-p: 4.72E-1 [mm/min]j-k: stress relaxation (for 1 hour)h-i, q-r: creep (for 1 hour)s-t, x-y: creep (for 6 hours)t-u: cyclic loading, Amp.=6.2 kPa, 4.72E-2 [mm/min], 100 cyclesu-v, z-aa, bb-cc, dd-ee, ff-gg: cyclic loading, Amp.=12.4 kPa, 4.72E-2 [mm/min], 100 cyclesv-w: cyclic loading, Amp.=24.8 kPa, 4.72E-2 [mm/min], 100 cyclesw-x: cyclic loading, Amp.=49.6 kPa, 4.72E-2 [mm/min], 100 cycles

0 10 20 30 40 50 60 70 80

0

50

100

150

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300Phosphor bronze + Chiba Gravel

b)

hh

ggff

eedd

ccbb

aaz

yxwvuts

rqp

on

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kjih

gf

ed

cba

Ver

tical

stre

ss, σ

v [kPa

]

Elapsed time, t [hour]

0 10 20 30 40 50 60 70 80-0.3

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c)

hh

ggff

eedd

ccbbaa

zyxwv ut

srq

p on

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ihgf

edcba

Horizontal strain(average), εh

Vertical strain, εv

Ver

tcal

and

hor

izon

tal s

train

, εv a

nd ε h [%

]

Elapsed time, t [hour]

0 2 4 6 8 10 12 14 16 18 20

0.00

0.01

0.02

0.03

0.04

0.05

0.06Phosphor bronze + Chiba Gravel

Compression

d)

creep2

creep1

Creep loading: 250 kPa for 6 hours creep1, point s-t in figure 8a creep2, point x-y

Cyclic loading: 100 cycles, 4.72E-2 mm/min cyclic1, ∆σv=6.2 kPa, point t-u cyclic2, ∆σ

v=12.4 kPa, point u-v

cyclic3, ∆σv=24.8 kPa, point v-w cyclic4, ∆σv=49.6 kPa, point w-x

Res

idua

l stra

in a

t PL

stat

e, ∆ε v [%

]

Elapsed time during creep or cyclic loading at PL state, ∆t [hour]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.00.05

0.00

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εv (C om p.)

GRS Bridge Pier Model

Phosphor bronze + Chiba Gravel

εh2

εh1

Hor

izon

tal s

train

, εh [%

]

Vertical strain, εv [%]

e)

0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72

40

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140

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200Phosphor bronze + Chiba Gravel

(Eeq

)v = 203 MPa

(Eeq

)v = 349 MPa

(Eeq

)v = 383 MPa

(Eeq

)v =

501 MPa

f)

gg ff

ee dd

ccbb

aa z

Ver

tical

stre

ss, σ

v [kPa

]

Vertical strain, εv [%]

Figure 4. Loading test results on a model pier rein-forced with a phosphor bronze grid. (a) vertical compressive strain vs. vertical stress; (b) time history of vertical stress; (c) time history of vertical and horizontal strain; (d) time history of vertical strain increment at each sustained or cyclic loading stage; (e) vertical compressive strain vs. horizontal strain; (f) vertical strain vs. vertical stress at cyclic loading stages during unloading.

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The followings can be found from these results: 1) Clear viscous deformation due to sustained load and residual deformation due to cyclic loading were ob-

served, even though the backfill material was a non-cohesive well-graded gravel. 2) The relationships between the vertical stress and the vertical strain for the model reinforced with an “ex-

tensible” polyester geogrid was similar to the one reinforced with an “inextensible” phosphor bronze grid (e.g. compare Figures 3a and 4a).

3) The viscous and residual deformations for the model with a polyester geogrid were similar to those rein-forced with a phosphor bronze grid (e.g. compare Figures 3d and 4d).

4) The stiffness (average Young’s modulus) of the model structure measured by applying small-amplitude cyclic stresses at several stress levels during otherwise global unloading were similar for the models re-inforced with polyester geogrid and phosphor bronze grid (e.g. compare Figures 3f and 4f).

5) However, the horizontal strains for the model reinforced with a polymer grid was nearly twice as large as that for the model reinforced with a phosphor bronze grid (e.g. compare Figures 3e and 4e), while the vertical strains were nearly the same as each other.

It can be concluded from these results that the stiffness of the reinforcement was not essential to restrain the

deformation of reinforced soil structures within the examined range, even though the stiffness of the rein-forcement was different by a factor more than 10 times. The corresponding horizontal strain was however no-ticeably different.

3 EFFECTS OF VERTICAL SPACING BETWEEN REINFORCEMENT LAYERS

3.1 Test methods In order to investigate the effects of the total stiffness of the reinforcement, four models of reinforced soil

pier with a vertical spacing of 5 cm (single reinforcement layer) or 2.5 cm (double layers) between the rein-forcement layers (Figure 5) were tested. The backfill and the reinforcement were the same as the model rein-forced with polyester geogrid mentioned before. Two types of loading procedures were employed as shown in Figure 6. In the PLPS (preloading and prestressing) loading tests, the pier was preloaded to the 250 kPa, and it was sustained for 56 hours, then unloaded to 100 kPa, and finally 100 times of cyclic loads were ap-plied between 100 and 150 kPa. In the case without PLPS loading, the pier was loaded to 50 kPa, and 100 times of cyclic loads were applied between 50 and 100 kPa. These loading procedures simulated the esti-mated stress history of actual cases of a PLPS reinforced soil pier and a non-PLPS reinforced soil abutment, which were constructed for a railway bridge (Uchimura et. al. 2003b). In these tests, small cyclic stresses with amplitude of 5 kPa were applied at several stress levels in order to measure the average Young’s modulus of the structure. The strain rate was kept constant, 0.004 %/min, except for the sustained loading stages. The tensile strains in the reinforcement were measured by means of strain gages pasted at the center of the grid at the middle height in two directions orthogonal to each other.

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Reinforcem ent Backfill

35 cm

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2.5cm x

2 layers

Reinforcem ent Backfill

35 cm

(Sandbags w ere glued to reinforcem ent)

(Interm ediate reinforcem ent w as not glued)

0 20000 40000 60000 80000 1000000

50

100

150

200

250

300

PLPS loading

Non-PLPS loading Polyester

Ver

tical

stre

ss, σ

v [kP

a]

Elapsed time, t [sec]

Figure 5 Arrangement of reinforcement Figure 6 Time histories of applied load. (with and without PLPS loading.)

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3.2 Results and discussions Figure 7 shows the relationships between the vertical compressive stress and strain from the four tests.

Some scatter seen in these results (e.g. a model with single reinforcement layer showed higher stiffness than a model with double layers for non-PLPS loading) is probably due to a variation among the models. It seems that the difference in the behaviour between the models with single and double layers is within the range of the scatter. The secant modulus obtained from the cyclic loading states is as follows:

PLPS loading with single layer : 355 kPa PLPS loading with double layers : 345 kPa non-PLPS loading with single layer : 251 kPa non-PLPS loading with double layers : 234 kPa Figure 8 shows the average Young’s modulus of the structure measured by the small-amplitude cyclic load-

ings plotted against the vertical stress. It is clear that the Young’s modulus increased with an increase in the current vertical stress, and the vertical spacing of reinforcement layers had no effects on it.

Figure 9 shows the time histories of the vertical strain from the four tests. The residual strains caused by the cyclic loading were not affected by the difference in the vertical spacing of reinforcement layers. On the other hand, the horizontal strain (measured as the extension of geogrid) for the model with a single layer was almost twice as large as that with double layers in the case with PLPS loading (Figure 10a). The differences between the strains in the principal and transversal directions of the geogrid were due to a difference in the stiffness of strand in each direcion. In the case without PLPS loading, such trends were not clear probably due to a variation among the models (Figure 10b).

These results suggest that the vertical spacing of reinforcement layers is not essential to the vertical com-pressive stiffness of the reinforced soil structures within the examined range, while it affects the correspond-ing horizontal strains.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

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250

Non-PLPS loading,Single layers

Non-PLPS loading,Double layers

PLPS loading,Double layers

Polyester

PLPS loading,Single layer

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tical

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ss, σ

v [kP

a]

Vertical strain, εv [%]0 50 100 150 200 250 300

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Vertical stress (kPa)

Equi

vale

nt Y

oung

's m

odul

us (M

Pa)

Non-PLPS loading, single layer Non-PLPS loading, double layer PLPS loading, single layer PLPS loading, double layer

Figure 7 Vertical stress vs. vertical strain. Figure 8 Young’s modulus of structures.

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v [%

]

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PLPS loading,Single layer

Ver

tical

stra

in, ε

v [%

]

Elapsed time, t [sec] a) b)

Figure 9 a) Time histories of vertical strain; b) zoom up for the cyclic loading stage for PLPS loading.

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0 20000 40000 60000 80000 100000-0.35

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Principal direction

D ouble layers

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Single layers

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D ouble layers

Principal direction

H

oriz

onta

l stra

in, ε

h [%

]

Elapsed time, t [sec]

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0.00

D ouble layers

Principal direction

D ouble layers

T ransversal direction

Single layers

Principal direction

Single layers

T ransversal direction

Hor

izon

tal s

train

, εh [

%]

Elapsed time, t [sec]

a) b)

Figure 10 Time histories of horizontal strain measured by strain gages on geogrid:

a) PLPS laoding; b) non-PLPS loading.

4 CONCLUSIONS

It is usually considered that the effects of reinforcement stiffness could be significant on the deformation of reinforced backfill during primary loading and sustained loading applied during otherwise primary loading. However, within the examined limit of reinforcement stiffness, the effects of reinforcement stiffness were ut-terly insignificant on the behaviours. This result suggests that it is not necessary to use metal reinforcement, in particular when the reinforced backfill is preloaded and prestressed.

The vertical spacing between reinforcement layers should be small enough so that sufficiently large load could be applied to the backfill without damaging the backfill. However, when the vertical spacing is smaller than some limit, the deformation of backfill does not decrease noticeably with a decrease in the vertical spac-ing of reinforcement layers.

These results suggest that the total stiffness of the reinforcement larger than some limit may not be essential to the vertical compressive stiffness of the reinforced soil structures. It could be more effective to ensure bet-ter deformation characteristics of the backfill by selecting high quality backfill materials, controlling the com-paction quality, and if possible, improving the stiffness of the backfill by applying preload and prestress as proposed by Tatsuoka et. al. (1997) and Uchimura et. al. (2003a and b).

REFERENCES

Hirakawa,D., Uchimura,T., Shibata,Y. and Tatsuoka,F.: Time-Dependant Deformation of Geosynthetics and Geosynthetic-Reinforced Soil Structures, Proc. the 7th Int. Conf. on Geosynthetics, Nice, Vol.4, pp.1427-1430 (2002).

Tatsuoka,F., Uchimura,T., and Tateyama, M.: Preloaded and prestressed reinforced soil, Soils and Founda-tions, Vol.37, No.3, pp.79-94, (1997).

Uchimura, T., Tatsuoka, F. and Tanaka, I.: Long-term residual deformation of prototype geotextile-reinforced gravel structures, Proceedings of the 3rd International Symposium on Deformation Characteristics of Geomaterials (ISLyon 03), Vol. 1, pp. 1353-1361 (2003a).

Uchimura,T., Tateyama,M., Tanaka,I., and Tatsuoka,F. : Performance of a preloaded-prestressed geogrid-reinforced soil pier for a railway bridge, Soils and Foundations, Vol.43, No.6 (to appear) (2003b).