Aula 10c - Geotecnique (Consoli Fahey 2009)

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Consoli, N. C. et al. (2009). Ge´otechnique 59, No. 5, 471–476 [doi: 10.1680/geot.2007.00063]
471
TECHNICAL NOTE
Effect of relative density on plate loading tests on fibre-reinforced sand
N. C. CONSOLI* , M. D. T. CASAGRANDE† , A. THOME´‡, F. DALLA ROSA* and M. FAHEY§
Plate load tests were carried out on un-reinforced sand
and sand reinforced with fibres, compacted at relative
densities (DR) of 30%, 50% and 90%. For the reinforced
sand, 24 mm long polypropylene fibres were added, a
concentration of 0.5% by dry weight. The analysis of the
results indicates that the soil load-settlement behaviour is
significantly influenced by the fibre inclusion, changing
the kinematics of failure. The best performance was
obtained for the densest (DR = 90%) fibre-sand mixture,
where a significant change in the load-settlement beha-
viour was observed at very small (almost zero) displace-
ments. However, for the loose to medium dense sand (DR
= 30% and 50%), significant settlements (50 mm and 30
mm respectively) were required for the differences in the
load-settlement responses to appear. The settlement re-
quired for this divergence to occur could best be repre-
sented using a logarithmic relationship between
settlement and relative density. The overall behaviour
seems to support the argument that inclusion of fibres
increases strength of sandy soil by a mechanism that
involves the partial suppression of dilation (and hence
produces an increase in effective confining pressure, and
a consequent increase in shear strength).
KEYWORDS: bearing capacity; failure; footings/foundations;
reinforced soils; sands
Des tests sous charge sur plaque ont e´te´ effectue´s sur du
sable non renforce´ ainsi que sur du sable renforce´ a` la
fibre de verre, compacte´s avec des densite´s relatives (DR)
de 30%, 50% et 90%. Au sable renforce´, on a ajoute´ des
fibres de polypropyle`ne de 24 mm, avec une concentra-
tion de 0,5% en poids sec. L’analyse des re´sultats indique
que l’inclusion des fibres influe de fac¸on significative sur
le comportement de la charge/au tassement du sol, en
modifiant la cine´matique de la rupture. Les me´langes
fibres /sable les plus denses (DR 90%) permettent d’ob-
tenir les performances les meilleures, et pre´sentent une
variation significative du comportement de tassement
sous charge avec des de´placements extreˆmement limite´s
(quasiment nuls). Toutefois, avec le sable meuble ou
moyennement dense (DR 30% et 50%), un tassement
significatif est ne´cessaire pour voir apparaıˆtre les diffe´r-
ences dans les re´ponses au tassement sous charge. La
meilleure fac¸on de repre´senter le tassement requis pour
que se produise la divergence est le rapport logarithmi-
que entre le tassement et la densite´ relative. Le compor-
tement ge´ne´ral semble appuyer la the`se d’apre`s laquelle
l’inclusion de fibres renforce la re´sistance du sol sablon-
neux sous l’effet d’un me´canisme comportant la suppres-
sion partielle de la dilatation (en re´alisant ainsi une
augmentation de la pression de confinement, et, en con-
se´quence, une augmentation de la re´sistance au cisaille-
ment).
INTRODUCTION
Field tests are uncommon in the area of fibre-reinforcement
of soils. Consoli et al. (2003) were among the first to
demonstrate the improvement in behaviour in an in situ plate
load test on a silty sand soil resulting from inclusion of
fibres in the soil. The plate load tests carried out by Consoli
et al. (2003) on the fibre-reinforced soil were performed to
relatively high bearing pressures, and gave a noticeably
stiffer response than that carried out on the non-reinforced
soil. Other important work was performed by Crockford et
al. (1993), who evaluated the gain in the lifetime of a
pavement resulting from fibre inclusion. Regarding labora-
tory tests, Gray & Ohashi (1983) studied the mechanics of
fibre-reinforcement in cohesionless soils, and showed that
inclusion of fibres increased peak shear strength and ducti-
lity of soils under static loads. A number of factors such as
fibre content, orientation of fibres with respect to the shear
surface, and the elastic modulus of the fibres were each
found to influence the contribution of fibres to the shear
strength. Later work by many researchers (e.g. Maher &
Gray, 1990; Consoli et al., 1998, 2002, 2005, 2007a, 2007b;
Zornberg, 2002, Michalowski & Cerma´k, 2003, Heineck et
al., 2005), has improved understanding of the mechanisms
involved and the parameters affecting the behaviour of fibre-
reinforced soils under static loading conditions in the labora-
tory.
The present work is aimed at examining the influence of
relative density on the behaviour of plate load tests bearing
on a compacted fibre-reinforced sand stratum, when com-
pared with a non-reinforced sand layer. It is not expected
that fibre-reinforced sand would ever be used in practice at
low relative density, as this would be a very inefficient use
of fibre reinforcement. Tests at low relative density were,
however, included in this study to help in understanding the
mechanism of how the fibres interact with the dilational
tendencies of the material to produce the extra strength. This
study includes an investigation of the performance of the
plate tests at large displacements and the determination of
the amount of settlement required for the fibres to have an
effect on the load–settlement response. The results presented
are part of a comprehensive joint testing programme being
Manuscript received 11 April 2007; revised manuscript accepted 26
September 2008. Published online ahead of print 10 December 2008.
Discussion on this paper closes on 2 November 2009, for further
details see p. ii.
* Department of Civil Engineering, Federal University of Rio
Grande do Sul, Av. Osvaldo Aranha, 99, 3 andar, 90035-190, Porto
Alegre, Rio Grande do Sul, Brazil.
† Department of Civil Engineering, Catholic University of Rio de
Janeiro, Rio de Janeiro, Brazil.
‡ Faculty of Engineering and Architecture, University of Passo Fundo,
Campus I da UPF, Bairro Sa˜o Jose´, Rio Grande do Sul, Brazil.
§ School of Civil & Resource Engineering, The University of
Western Australia, 35 Stirling Highway, Crawley, Western Australia,
Australia.
carried out by the Federal University of Rio Grande do Sul
(UFRGS) and the University of Passo Fundo (UPF), located
in southern Brazil, to verify the improvement in the behav-
iour of shallow foundations on sandy soil owing to fibre
reinforcement.
EXPERIMENTAL PROGRAMME
Materials
The sand used in the testing was obtained from the region
of Osorio near Porto Alegre, in southern Brazil. The soil is
classified in ASTM D 2487-93 (ASTM, 1993) as non-plastic
uniform fine sand (SP) and the specific gravity of the solids
is 2.63. Mineralogical analysis showed that sand particles are
predominantly quartz. The grain size is entirely fine sand
with an effective diameter (D50) of 0.16 mm, and uniformity
and curvature coefficients of 1.9 and 1.2, respectively. The
minimum and maximum void ratios are 0.6 and 0.9, respec-
tively.
Polypropylene fibres were used throughout this investiga-
tion to reinforce the soil. Their average dimensions were
24 mm in length and 0.023 mm in diameter, with a specific
density of 0.91, a tensile strength and elastic modulus of
120 MPa and 3 GPa, respectively, and a linear strain at
failure of about 80%. The fibre content used in the experi-
ments was 0.5% of the dry sand weight. Consoli et al.
(2007a, 2007b) and Vendruscolo (2003) demonstrated that a
fibre content of 0.5% and a length of 24 mm were about the
minimum that made a significant difference to the measured
strength. In addition, fibre contents above 0.5% and lengths
above 24 mm cause difficulties regarding obtaining homo-
geneity of the soil–fibre mixture. Hence this was chosen as
a logical fibre content to use in the footing experiments.
In previous triaxial testing reportedby Vendruscolo
(2003), it was shown that at DR of 40% and 90%, the
strength of the same sand, reinforced with 0.5% fibre
content, could be represented by a linear Mohr–Coulomb
failure line with �9 of 418 and 478, respectively, and
cohesion intercept of 24 and 35 kPa, respectively. The
equivalent parameters for the unreinforced sand at DR of
40% and 90% were �9 of 358 and 418, respectively, and zero
cohesion intercept for both cases. Vendruscolo also found
that initial stiffness was not affected by fibre inclusion.
Plate load tests
The plate load tests were carried out using a 0.30 m
diameter smooth circular rigid steel plate, 25.4 mm in thick-
ness, resting on the top of non-reinforced and fibre-
reinforced sand. The soil material was prepared by mixing
dry sand with fibres in a rotating drum mixer, and then
adding water to achieve a water content of 12%. Adding
water was necessary to prevent segregation of the sand and
fibre, so a water content close to the optimum water content
value (OMC), as determined by Standard (Proctor) compac-
tion tests, was used. While this was necessary from a
practical point of view, it would have been preferable from a
theoretical point of view to have conducted the tests on
either completely dry soil or completely saturated soil, as
this would have eliminated the (unknown) suctions resulting
from the partially saturated condition. It should also be
noted, however, that compaction at similar moisture content
would most likely be carried out in practice, so in this sense,
the preparation procedure was appropriate.
The tests were conducted on samples compacted within a
wooden box, 2.8 m 3 2.8 m in plan dimensions, and 1.4 m
high, with a soil thickness of 1.2 m, which is equivalent to
4 times the plate diameter. The soil was placed in 12
consecutive lifts, each 0.1 m thick, with each layer being
compacted using a vibratory plate, to relative densities of
either 30%, 50% or 90%.
The load was applied through a system comprising a
hydraulic jack, a reaction beam and a load platform, and
measured using a calibrated load cell. The loading system
had a capacity of 200 kN. The displacements of top of the
plate were measured using three linear variable differential
transducers (LVDTs) spaced equally around the periphery of
the plate (see Fig. 1(b)). Another LVDT was positioned
100 mm outside the edge of the plate, to determine the
external displacements of the soil surface. The LVDTs were
fixed to a reference beam and supported on external supports
in such a manner as to ensure a stable reference for the
displacement measurements. The data from the load cell and
LVDTs were logged by a data acquisition system. Pressure
cells were inserted in the side walls of the box at mid-
height. These registered only insignificant stress changes
during the tests, showing that the square box was sufficiently
large to have no effect of finite box size.
The load was applied in equal increments of not more
than one-tenth of the estimated ultimate bearing capacity.
Each increment was maintained for at least 30 min, and until
the following criterion was achieved
Ln � Ln�1 < 0:05 Ln � L1ð Þ (1)
where Ln is the average LVDT reading (on the top of the
plate) at a specified time t (15 s, 30 s, 1 min, 2 min, 4 min,
8 min, 15 min, 30 min, 1 h and so on, after stage loading
Reaction system
Hydraulic piston
Reference beam
LVDT
Plate Load cell
Sand/fibre-reinforced sand
Pressure cell
(a)
Load cell
Plate
LVDT
(b)
Fig. 1. Test set-up: (a) cross-section and (b) plan view
472 CONSOLI, CASAGRANDE, THOME´, DALLA ROSA AND FAHEY
application), Ln�1 is the immediately-previous reading, and
L1 is the first reading of the stage of loading taken just after
stage loading appliance, according to Brazilian standard
NBR-12131 (1991), which is in accordance with the stan-
dard ASTM D 1194-94 (1998). When the LVDTs reached
their limit, they were reset at the end of a loading stage,
allowing settlement measurements greater than 50 mm.
RESULTS AND ANALYSIS
The results obtained from the tests in non-reinforced and
fibre-reinforced sand are shown in Figs 2 and 3, respectively.
In each case, results are shown for relative densities of 30%,
50% and 90%. For the non-reinforced cases in Fig. 2, it is
possible to observe that increasing the relative density from
30% to 50% results in a higher load capacity at each
settlement level, but increasing from 50% to 90% results in
an even more dramatic increase, as already well established
in the literature (e.g. Ve´sic, 1975). A similar pattern was
observed for fibre-reinforced sand (Fig. 3), although even
more pronounced. Thus, from Fig. 3, the load required for
5 mm settlement for DR ¼ 90% was approximately 22 times
that for DR ¼ 30%, while for non-reinforced sand, the
equivalent ratio was approximately 6. In addition, inclusion
of fibres in the sand has resulted in a change in the shape of
the load–displacement curves: the non-reinforced cases (Fig.
2) show reasonably well-defined ultimate loads (‘failure’),
but the fibre-reinforced cases (Fig. 3) show loads continuing
to increase at the ends of the tests for all three relative
densities, even where the total settlements were substantial.
The response could therefore be described as being more
‘ductile’ or as showing ‘strain hardening’ characteristics.
Views of the plate and surrounding soil at the completion
of the tests with DR ¼ 50% are shown in the photographs in
Figs 4(a) and 4(b) for non-reinforced and fibre-reinforced
sand, respectively. In Fig. 4(a) it can be seen that the plate
had a vertical ‘punching failure’ penetration in the sand
(Ve´sic, 1975), which usually occurs in loose sands. Radial
fissures in the sand around the plate can also be seen in this
figure. For the equivalent fibre-reinforced case shown in Fig.
4(b), a somewhat different pattern can be observed. This
consists of a conically shaped depression zone extending
outwards and upwards from the edge of the plate. This
suggests that displacements in this zone are vertical, redu-
Load: kN
0 20 40 60 80 100 120 140 160 180
V
er
tic
al
 d
is
pl
ac
em
en
t: 
m
m
0
50
100
150
200
250
DR: 30%
DR: 50%
DR: 90%
Fig. 3. Load–settlement behaviour observed for fibre-reinforced
sand
(a)
(b)
(c)
Fig. 4. Failure mechanisms obtained for (a) sand with DR
50%; (b) fibre-reinforced sand with DR 50%; and (c) fibre-
reinforced sand with DR 90%
Load: kN
0 20 40 60 80 100 120 140 160 180
V
er
tic
al
 d
is
pl
ac
em
en
t: 
m
m
0
50
100
150
200
250
DR: 30%
DR: 50%
DR: 90%
Fig. 2. Load–settlement behaviour observed for non-reinforced
sand
EFFECT OF RELATIVE DENSITY ON PLATE LOADING TESTS ON FIBRE-REINFORCED SAND 473
cing with distance from the plate edge, and not punching
failure. There was no evidence of radial fissures, although a
circular fissure can be seen at a radius about 80 mm greater
than that of the plate, coinciding approximately with the
extremity of the depression zone. Deformation patterns
similar to these were also observed for the tests at DR ¼
30%.
In contrast, for the non-reinforced sand at DR ¼ 90%,
heave in the sand surface around the plate was observed as
the plate penetrated the soil, showing characteristics of
generalised failure (Ve´sic, 1975) with well-defined slip sur-
faces. Fig. 4(c) shows the situation at maximum load for the
fibre-reinforced case with DR ¼ 90%. The maximum load
applied in this test (which had still not reached failure) was
about 50% greater than the ‘failure’ load for the equivalent
non-reinforced case; nevertheless, it can be seen from this
figure there is no tendency for generalised failure in this
case.
DISCUSSION
As already mentioned, the failure patterns in the non-
reinforced cases can be classified in the terminologyof
Ve´sic (1975) as ‘punching shear’ for the medium dense (and
loose) case and as ‘generalised failure’ for the very dense
case. Inclusion of fibres in the sand resulted, however, in a
radical change in failure mechanisms observed, for both
loose and dense mixtures. This behaviour is attributed to
interaction between the fibres and the sand around and
below the plate. It is important to emphasise the importance
of relative stiffness of the fibre reinforcement and the sand
(loose, medium dense or very dense conditions) on the
behaviour of the composite.
The triaxial tests of Vendruscolo referred to previously
show that inclusion of fibres results in a strength gain that
can be characterised by an increase in c9 (cohesion intercept)
and �9 on a Mohr–Coulomb strength diagram. The increase
in bearing capacity could probably be explained on the basis
of this strength increase. The increase in foundation stiffness
could not, however, be so simply explained, as Vendruscolo
(2003) and Heineck et al. (2005) present results showing
that initial stiffness of this same sand is unchanged by fibre
insertion. Thus, rather than thinking in terms of increases in
c9 and �9, an alternative approach is to consider mechanics
of how the fibres act to increase strength (and stiffness).
Figure 5 shows a direct comparison of the plate settle-
ments for non-reinforced and fibre-reinforced sand for DR ¼
30%, and similar comparisons are shown in Figs 6 and 7 for
DR ¼ 50% and 90% respectively. The vertical displacements
observed 100 mm from the plate edge are also presented in
these figures. A relevant fact is related to displacements
measured outside the plate, which showed a considerable
modification due to the change in DR and the introduction
of fibre. For all relative densities studied, expansion of the
sand outside of the plate is reduced because of the fibre
reinforcement. In the case of loose to medium dense sand
(DR ¼ 30% and 50%), the fibre-reinforced sand is pulled
down with the plate in the same direction as the plate
movement, and in the case of DR ¼ 90%, the vertical
upwards heave expansion is drastically reduced, even for
loads 50% higher than the non-reinforced soil failure load.
It has been shown by many authors (e.g. Maher & Gray,
1990, Zornberg, 2002, Heineck et al, 2005) that the fibres in
fibre-reinforced sand actually work in tension and not in
shear. The tensile restraint produced by the fibres tends to
act to increase the effective confining pressure, which in-
creases the frictional component of the strength. In effect,
the fibres tend to act to suppress dilation (e.g. Michalowski
& Cerma´k, 2003) in dense sands, such that shear deforma-
tion occurs in a manner analogous to undrained shearing; in
this latter case, the tendency for dilation results in genera-
tion of negative pore pressure, and hence an increase in
effective stress, which acts to suppress dilation. The degree
to which dilation is suppressed by the fibres is probably
quite low, but, as will be shown later, it is still sufficient to
give a significant increase in effective stress, and hence in
shear strength and stiffness.
In these tests, the plate load–settlement plots for the non-
reinforced and fibre-reinforced loose sand at DR ¼ 30%
shown in Fig. 5 start to diverge only after a considerable
amount of deformation has occurred, that is point A, corre-
sponding to a settlement of about 50 mm. This is consistent
with the fact that dilation only tends to occur (if at all) for
such low relative densities after considerable shearing has
occurred. The same applies for the medium dense (DR ¼
50%) cases shown in Fig. 6, although here the divergence
starts at a lower settlement (about 30 mm; point B). In
contrast, the equivalent plots for the very dense cases (DR ¼
90%) in Fig. 7 show strong divergence from very early in
the test (at almost zero settlement; point C), consistent with
the fact that dilation for very dense sands tends to occur
almost right from the start of shearing.
Sand*
Fibre Sand*�
Sand†
Fibre Sand� †
200 40 60 80 100 120 140 160 180
Load: kN
V
er
tic
al
 d
is
pl
ac
em
en
t: 
m
m
�100
�50
0
50
100
150
200
250
300
A
Fig. 5. Load–settlement behaviour for DR 30%.
�Readings in
the plate; †readings out of the plate
B
Sand*
Fibre Sand*�
Sand†
Fibre Sand� †
200 40 60 80 100 120 140 160 180
Load: kN
V
er
tic
al
 d
is
pl
ac
em
en
t: 
m
m
�100
�50
0
50
100
150
200
250
300
Fig. 6. Load–settlement behaviour for DR 50%.
�Readings in
the plate; †readings out of the plate
C
Sand*
Fibre Sand*�
Sand†
Fibre Sand� †
200 40 60 80 100 120 140 160 180
Load: kN
V
er
tic
al
 d
is
pl
ac
em
en
t: 
m
m
�100
�50
0
50
100
150
200
250
300
Fig. 7. Load–settlement behaviour for DR 90%.
�Readings in
the plate; †readings out of the plate
474 CONSOLI, CASAGRANDE, THOME´, DALLA ROSA AND FAHEY
The three points of divergence between the load–
settlement curves for the non-reinforced and reinforced
cases, that is points A, B and C from Figs 5, 6 and 7
respectively, are plotted as settlement against relative density
in Fig. 8. As a first approach, a linear relationship can be
fitted to these points (see Fig. 8). Conceptually, however, a
logarithmic relationship, also shown in Fig. 8, might be a
more appropriated representation, given that asymptotic
behaviour is suggested for relative densities above 90%. A
logarithmic relationship, when extrapolated to very low rel-
ative density, would imply that very large settlement would
be required for any difference between non-reinforced and
fibre-reinforced cases to become evident. This is consistent
with the ‘dilation suppression’ idea discussed above, because
at very low relative density, there is very little tendency for
dilation to occur, and, even if it does, it only occurs after
very large strains.
The relationships between peak and residual friction
angles, dilation angles and confining stress were investigated
by Bolton (1986) for a wide range of sands. Defining the
relative density index, IR, as
IR ¼ DR Q � ln p9ð Þ � R (2)
where p9 is the mean effective confining pressure (in kPa),
and Q and R are constants, he showed that the effect of p9
on maximum dilation angle łmax could be approximated as
łmax (s) ¼ 6IR (3)
for plane strain shearing. Similarly, for triaxial conditions,
the effect of p9 on dilatancy could be expressed as
� d �v
d �1
¼ 0:3IR (4)
Thus, for p9 ¼ 100 kPa, these relationships suggest plane
strain łmax values of 7.98, 13.28 and 23.78 for DR values of
0.3, 0.5 and 0.9 respectively (i.e. 30%, 50% and 90%). If p9
is increased to 200 kPa, however, the corresponding values
of łmax are 6.78, 11.18 and 20.08. From this, it can be
reasoned that in fibre-reinforced sands of these relative
densities, with initial p9 ¼ 100 kPa, a relatively minor sup-
pression of dilation (by 1.28, 2.18 and 3.78, respectively) is
achieved by doubling p9, which would also achieve a similar
suppression of dilatancy in triaxial conditions. From this
rather crude analysis, it can therefore be reasoned that the
fibres only have to achieve a modest reduction in dilatancy
to have a significant effect on p9, and hence a significant
effect on shear strength and on stiffness, which is also
dependent on p9. Thus, a relatively minor suppression of
dilatancy brought about by the fibres acting in tension
would be sufficient to cause a significant change in the
load–settlement behaviour in a plate bearing test. Note
that, according to equation (2), complete suppression of
dilation for sand in plane strain, with DR ¼ 90% requires
p9 . 7 MPa!
Finally, a complete understanding of how exactly the
fibres act to improve the behaviour so much has not been
reachedyet and perhaps a comprehensive answer will
require detailed micro-mechanics analysis, or discrete ele-
ment method (DEM) modelling.
CONCLUDING REMARKS
The following observations and conclusions are made
regarding the influence of the relative density on the behav-
iour of plate tests bearing on polypropylene fibre-reinforced
and non-reinforced sandy soil.
(a) From the plate load tests carried out in the present
research, it can be concluded that inclusion of fibres in
the sand caused a dramatic change in plate load–
settlement behaviour, when compared with the non-
reinforced sand, conferring on the composite material
superior strength and stiffness characteristics compared
with non-reinforced sand.
(b) The inclusion of fibres changes the failure mechanisms
observed for non-reinforced sand. The interaction
among the sand grains and the fibres, which occurred
for all relative densities considered, depends on the
relative density of the material. In the case of loose to
medium dense sand (DR ¼ 30% and 50%), the fibre-
reinforced sand in a zone outside the plate edge is
pulled down with the plate, avoiding punching failure.
For the dense case (DR ¼ 90%), the fibres have the
effect of reducing the heave outside the plate edge,
even for loads 50% greater than the failure load for the
non-reinforced sand. Another detail observed that
confirms the fibre-reinforced sand mobilisation outside
the plate area is that the radial fissures that are manifest
in non-reinforced sand have disappeared for the fibre-
reinforced sand, independent of the relative density.
(c) The effect of fibre inclusion was found to be more
pronounced for higher densities. At all relative
densities, the fibre-reinforced tests showed higher
overall stiffness, and higher bearing capacity. The
amount of settlement required before the load–
settlement curves for the non-reinforced and fibre-
reinforced tests start to diverge depends heavily,
however, on relative density (50 mm for DR ¼ 30%,
30 mm for DR ¼ 50%, and almost zero for DR ¼ 90%).
The relationship between these diverging-point settle-
ments and DR could be reasonably fitted by a
logarithmic relationship, given that asymptotic behav-
iour is suggested for relative densities bigger than 90%.
(d ) The effect of fibre inclusion on bearing capacity and
stiffness, and the sensitivity of that effect to relative
density seems to fit with the idea that fibres have the
effect of tending to suppress dilation, which increases
the mean effective stress p9 and hence increases the
strength and stiffness of the soil.
(e) This work demonstrates that fibre-reinforced sand has
the ability to maintain strength (or even continue to
increase strength) with ongoing deformation, suggesting
a very ductile material. Thus, this material might
potentially be used in other earthworks, such as part of
cover liners of municipal solid waste landfills, which
can potentially undergo large differential settlements, as
well as in embankments over organic soft soils, which
undergo excessive deformation owing to consolidation.
Linear relationship
Logarithmic relationship
A
B
C
0 10 20 30 40 50 60 70 80 90 100
Relative density: %
S
et
tle
m
en
t: 
m
m
120
100
80
60
40
20
0
Fig. 8. Plate settlement at which load–settlement curves for the
non-reinforced and fibre-reinforced cases diverge (points A, B
and C from Figs 5, 6 and 7 respectively)
EFFECT OF RELATIVE DENSITY ON PLATE LOADING TESTS ON FIBRE-REINFORCED SAND 475
ACKNOWLEDGEMENTS
The authors wish to express their gratitude to PRONEX/
FAPERGS (Process No. 04/0841.0) and to CNPq (the
Brazilian Council of Scientific and Technological Research)
for the financial support to the research group. This research
was partly carried out at UWA (Gledden Fellowship).
NOTATION
c9 cohesion intercept
DR relative density
IR relative density index
Ln average LVDT reading (on the top of the plate) at a specified
time t
Ln�1 average LVDT reading immediately-previous to Ln
L1 first LVDT reading of the stage of loading taken just after
stage loading appliance
p9 mean effective confining pressure
�v volumetric strain
�1 distortional strain
�9 friction angle
łmax maximum dilation angle
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476 CONSOLI, CASAGRANDE, THOME´, DALLA ROSA AND FAHEY
	INTRODUCTION
	EXPERIMENTAL PROGRAMME
	Materials
	Plate load tests
	Equation 1
	Figure 1
	RESULTS AND ANALYSIS
	Figure 2
	Figure 3
	Figure 4
	DISCUSSION
	Figure 5
	Figure 6
	Figure 7
	Equation 2
	Equation 3
	Equation 4
	Figure 8
	CONCLUDING REMARKS
	ACKNOWLEDGEMENTS
	NOTATION
	REFERENCES
	American Society for Testing and Materials 1993
	American Society for Testing and Materials 1998
	Bolton 1986
	Brazilian standard NBR-121311991
	Consoli 1998
	Consoli 2002
	Consoli et al. 2003
	Consoli 2005
	Consoli 2007a
	Consoli et al. 2007b
	Crockford et al. 1993
	Gray & Ohashi 1983
	Heineck et al, 2005
	Maher & Gray, 1990
	Michalowski & Cermák, 2003
	Vendruscolo 2003
	Vésic 1975
	Zornberg, 2002