investigating the controlling factors that may affect discharge capacity, such as hydraulic gradient, percentage consolidation settlement, flexural stiffness of the PVD, and soil type..
Trang 1Effect of deformation of prefabricated vertical drains
on discharge capacity
H H Tran-Nguyen1, T B Edil2 and J A Schneider3
Minh City University of Technology, 268 Ly Thuong Kiet Street, B6 Building, District 10, Ho Chi Minh
City, Vietnam, Telephone: +84 9 1390 0663, Telefax: +84 8 3863 7002, E-mail: tnhhung@hcmut.edu.vn
or tnhhung@gmail.com
of Wisconsin-Madison, 1415 Engineering Drive, Madison, WI 53706, USA, Telephone: +1 608 262
3225, Telefax: +1 608 890 3718, E-mail: edil@engr.wisc.edu
University of Wisconsin-Madison, 1415 Engineering Drive, Madison, WI 53706, USA,
Telephone: +1608 262 3491, Telefax: +1 608 890 3718, E-mail: jamess@cae.wisc.edu
Received 24 March 2010, revised 20 September 2010, accepted 20 September 2010
ABSTRACT: The effects of deformation on PVD discharge capacity remain discrepant among
investigators This study investigates the discharge capacity behavior of deformed PVDs using a
laboratory performance test Four different PVDs were tested, and two different soils were used for
confinement The reduction of the discharge capacity of PVDs varied with the type of PVD and
percentage settlement, and reached up to 99% at a maximum percentage settlement of 41%
Hydraulic gradient also appreciably affects discharge capacity, owing to the non-steady-state flow in
the core of the PVD Soil type impacts on the deformation pattern of PVDs, but its effect on
discharge capacity appears to be slight in this study Soil type, however, has a significant influence
on required discharge capacity For a 20 m long drain in example calculations, one of the PVDs
would result in restriction of water flow and cause significant increases in time for consolidation
significant increases in consolidation time could occur at percentage settlements in excess of
approximately 30% for all drains tested
KEYWORDS: Geosynthetics, Soft clays, Consolidation, Prefabricated vertical drain, PVD, Deformation,
Hydraulic gradient, Discharge capacity
REFERENCE: Tran-Nguyen, H H., Edil, T B & Schneider, J A (2010) Effect of deformation of
prefabricated vertical drains on discharge capacity Geosynthetics International, 17, No 6, 431–442
[doi: 10.1680/gein.2010.17.6.431]
1 INTRODUCTION
Deformation of PVDs by folding, crimping, bending,
buckling or kinking resulting from large consolidation
settlements may reduce the discharge capacity
signifi-cantly or totally (Kremer et al 1983; Ali 1991; Aboshi et
al 2001; Bo et al 2003; Chu et al 2006) The amount
and nature of deformation are thought to be functions of
the deformational resistance of PVD, the type of PVD, the
compressibility of the soil, and the vertical stress applied
on the soil Even though many researchers have studied
the deformation of PVDs, the effects of deformation on
discharge capacity are still inconclusive (Holtz et al
1991; Aboshi et al 2001; Chu et al 2006)
Two methods have been widely used in investigating the
effect of PVD deformation on discharge capacity In the first, the deformation of the PVD is manually induced by bending it to a specified shape, and discharge capacity tests are run by placing the deformed PVD in a soil or membrane for lateral confinement (i.e index tests) In the second method, the PVD is allowed to deform naturally with consolidation settlement in a soil, and the discharge capa-city is measured while the deformed PVD is in the soil (i.e performance test) The first method imposes an artificial deformation on the PVD: consequently it may not simulate general field conditions, and could under- or overestimate the discharge capacity However, it does provides rapid test results The second approach is more comparable to in situ conditions, and thus can be considered more representative
of field conditions, but it is time-consuming
Geosynthetics International, 2010, 17, No 6
431
1072-6349 # 2010 Thomas Telford Ltd
Trang 2The discharge capacity of a manually deformed PVD
varies significantly with the type of PVD and the
deformed shape Lawrence and Koerner (1988)
investi-gated the discharge capacity of several types of PVD
under a hydraulic gradient of 1.0 using a simple kinking
device They reported that the discharge capacity
de-creased in the range 9–72% with a single 908 wedge
Holtz et al (1991) showed that the discharge capacity of
PVDs under a hydraulic gradient of 1.0 with induced
sinusoidal deformation was reduced considerably at 20%
applied settlement Chang et al (1994) used an apparatus
similar to a triaxial test device to measure the discharge
capacity of PVDs with the induced shape of letters U or V
under a maximum confining pressure of 294 kPa They
showed that the reduction of the discharge capacity of six
PVDs tested under hydraulic gradients of 0.46, 0.87, 1.31,
and 1.74 was between 20% and 92% Bergado et al
(1996) used their modified triaxial test device and
investi-gated the discharge capacity of various PVDs intensively
under many initial deformation modes With two clamps
plus 30% bending, the discharge capacity of PVDs under
hydraulic gradients of 0.25, 0.5 and 1.0 diminished by
34% to 99%, depending on the type of PVD Cline and
Burns (2003) used a simple device that can create a single
908 folding They reported that the reduction of discharge
capacity of PVDs wrapped in plastic membranes under a
hydraulic gradient of 1.0 varied from 17% to 34%
The effects of naturally deformed PVD on discharge
capacity remain discrepant, even though several
investiga-tors agree that the discharge capacity reduces significantly
when the vertical strain is larger than 15% Sasaki (1981)
and Hansbo (1983) reported that the folding of a PVD at a
relative vertical strain of 15% in a large-scale laboratory
test had no effect on the discharge capacity Miura et al
(1998) reported that folding (without kinking) of PVDs
does not influence discharge capacity up to a vertical
strain of 20% Contrary to these findings, Kremer et al
(1982), Kremer (1983), and Oostveen (1983) indicated
that folding of PVDs due to large vertical strains severely
diminishes the discharge capacity However, no direct
discharge capacity data were presented, except for
photo-graphs of extremely folded PVDs Kremer (1983) found
that the discharge capacity of a PVD sample excavated
from a two-year test area was shut off Based on this,
Kremer (1983) stated that large folding of a PVD can cut
off the discharge capacity completely, and when the
relative vertical strain is larger than 15%, the reduction of
the discharge capacity has to be taken into account
Significant reduction of discharge capacity for vertical
consolidation strains in excess of 15% is widely reported
Ali (1991) used a consolidation cell (0.5 m in diameter)
with a 0.5 m high kaolinite specimen to investigate the
discharge capacity of PVDs deformed naturally by
con-solidation settlement That study found that the discharge
capacity of PVDs at a hydraulic gradient of 0.5 under a
vertical pressure of 120 kPa reduced substantially, in the
range 47–99%, under a relative compression of 30% The
reduction varied with the stiffness of the PVD: the stiffer
the filter sleeve, the higher was the discharge capacity
Aboshi et al (2001) used a half consolidation cell (0.3 m
inside diameter) with a PVD in the center of the cell to test undisturbed soil samples That study found that a crook or kink in the PVD shut off the discharge capacity completely Kim et al (2003) used a consolidation cell (0.5 m in diameter) to investigate the discharge capacity
of a PVD under consolidation settlement They found that the discharge capacity of the PVD at a hydraulic gradient
of 0.50 was reduced by about 89% of its initial discharge capacity at the end of consolidation when the PVD had experienced a vertical load of 245 kPa, but it was unclear how much settlement took place Chu et al (2006), using
a 495 mm diameter consolidation cell, investigated the discharge capacity of a PVD embedded in a very soft soil under a vertical pressure of 110 kPa They reported that the discharge capacity reduced up to 84% at a vertical strain of 46% by the end of the consolidation stage The discharge capacity was measured by the constant-head method under a hydraulic gradient of 0.5 Their PVD was extremely bent, but not kinked, at the end of the test In summary, the literature indicates that a vertical strain in excess of 20% can significantly affect PVD discharge capacity
To gain a better understanding of the effects of deformation on PVD discharge capacity, this study fo-cused on:
1 developing a consolidation cell apparatus (the PVD-S apparatus), and employing it to generate natural deformation of PVDs embedded in soil, simulating the in situ conditions as closely as possible;
2 measuring the discharge capacity of such deformed PVDs directly using the PVD-S apparatus under different hydraulic gradients; and
3 investigating the controlling factors that may affect discharge capacity, such as hydraulic gradient, percentage consolidation settlement, flexural stiffness
of the PVD, and soil type
2 TEST PROGRAM
2.1 Test apparatus The PVD-S apparatus, which is an aluminum cylinder of 0.32 m inside diameter and 0.75 m high, was used to simulate the consolidation process of soft soils with a prefabricated vertical drain (PVD) at the center of the cylinder (Figure 1) The PVD-S allows a maximum percentage settlement of 41%, which is a typical value in very soft soils, inducing significant deformations in the PVD The discharge capacity of the PVD can be measured intermittently throughout the test by circulating water through it by means of two reservoirs fitted to its two ends A set of six piezometers are arranged in different radial directions from the center, located at a distance of 0.2 m from the bottom, to measure pore water pressure (PWP) during consolidation (Figure 1b) Combined with the settlement data, this allows verification of the progress
of primary consolidation
The primary objective of the PVD-S device is to investigate the reduction of the discharge capacity of a
Geosynthetics International, 2010, 17, No 6
Trang 3PVD that deforms naturally with progressing consolidation
settlement This is considered a performance test, because
the PVD is tested in contact and interacting with the
surrounding soil, as opposed to an index test, in which the
deformed PVD would be tested directly, without soil
confinement The PVD-S apparatus is designed to force
predominantly radial flow rather than vertical flow Water
is squeezed out of the soil specimen only through the PVD
installed in the center of the cylinder Water in the soil
mass travels only in the radial direction, reaches the PVD,
and drains out vertically into the top and bottom
reser-voirs Rubber membranes are placed at the top and bottom
to prevent water draining in the vertical directions The
volume of water drained can be measured for comparison
with the settlement
2.2 Test procedure
The mandrel, which is a rectangular metal box with
cross-section of 120 mm 3 15 mm and 900 mm long, holding a
PVD inside, was placed in the center of the cylinder
before placing the soil in the cylinder The mandrel
prevents both the PVD from deforming and the soil
specimen from consolidating in the radial direction during
placement of the soil The soil was placed in the cylinder
in layers up to a height of 700–720 mm, and agitated by a vibrator to remove any air trapped during filling One end
of the PVD was terminated in the bottom reservoir, whose valves are closed during soil placement The mandrel was withdrawn after placing the soil, followed by the loading piston The top end of the PVD terminated in the top reservoir, attached at the center of the loading piston A set of six piezometers was installed on the side wall Approximately 1 h passed before the top part of the cell was assembled, during which time it was observed that the gap created by the withdrawal of the mandrel was filled with the soft soil A discharge capacity test using the constant-head method in the PVD was carried out imme-diately after assembling the top part of the cell A nominal pressure of 12.5 kPa was applied to keep the piston from uplifting during the discharge test These discharge capa-city data are considered to correspond to the discharge capacity of a straight PVD The initial discharge capacity test was performed under hydraulic gradients of 0.10, 0.25, 0.50, 0.75 and 1.0 by circulating water from the bottom reservoir to the top reservoir Different hydraulic gradients were used to observe whether the flow through the PVD was non-laminar or laminar The different hydraulic gradients were generated by adjusting the
eleva-320
Movable top
piston,δ⫽ 127 mm
P2
P4 P5
P3
PVD
v the piston
LVDT for vertical
displacement
PVD 100 ⫻ ⫺ (4 6) mm
Pneumatic air
cylinders
320
Bottom reservoir
P1
P6
Soil specimen
Top reservoir
(b)
(a) Figure 1 Features of the PVD-S apparatus (a) main dimensions of PVD-S apparatus (mm); (b) arrangement of piezometers
Effect of deformation of prefabricated vertical drains on discharge capacity 433
Geosynthetics International, 2010, 17, No 6
Trang 4tions of the two reservoirs The hydraulic gradient is
calculated by dividing the head difference by the
em-bedded length of the PVD in the soil specimen When the
soil reached the end of primary consolidation, based on
the settlement and PWP data collected from the
piezo-meters, a discharge capacity test was conducted again
under various hydraulic gradients The experiment was
continued in this manner, with incremental increases of
the vertical pressure to 25 kPa, 50 kPa, 100 kPa, 200 kPa
and 400 or 490 kPa The discharge capacity test was
conducted at the end of each consolidation stage Water
was circulated along the core of the PVD to wash fine
particles infiltrated into the PVD core during the
consoli-dation stage Therefore the discharge measured from this
study is free of siltation effects Each discharge capacity
measurement took about 60 min Duration of
consolida-tion was 5–14 days for each loading increment, depending
on soil type The total time to complete the test was 4–5
weeks
Chu et al (2004) reported a large reduction (,60%) in
discharge capacity over 4 weeks Time effects were not
part of the scope of this study; however, creep effects are
considered to be negligible relative to the deformations
induced in the PVD (Miura and Chai 2000) The discharge
capacities of most PVDs are affected by lateral pressures
of 150 kPa or more (Rixner et al 1986) For this study,
the lateral pressure generated from the vertical pressure
was estimated to be less than 150 kPa, except for the last
loading increment, with a maximum pressure of 490 kPa
Thus it is expected that the discharge measured in this study was slightly affected by lateral pressure The tests were performed at room temperature (i.e 22–248C)
2.3 Test materials Two soils were used: Hydrite R Kaolinite (a low-plasticity clay) and Craney Island dredgings (a high-plasticity clay) Hydrite R Kaolinite is commercial kaolin in powder form, and was prepared as slurry at an approximate water content of 90%, which is almost twice its liquid limit Craney Island dredgings were sampled in Craney Island, Virginia, from an island of stored dredgings PVD per-formance in Craney Island dredgings was described in detail by Stark et al (1999) The testing described in Stark
et al (1999) was performed in the south-central portion of the north containment area, whereas the tests in this study used a slightly different material The Craney Island samples studied in this test series were collected from the upper meter of sediment from the southwest corner of the south containment area A single homogenized sample was prepared by mixing seven buckets of the soil samples The compositional properties of the soils are given in Table 1 The properties of the soil specimens prepared for the tests in their initial condition, and measured after the tests, are summarized in Table 2 Four types of widely used PVDs covering a range of construction were tested (four with Hydrite R Kaolin and one with Craney Island) The properties of the PVDs are shown in Table 3
Table 1 Properties of the soils
(sieve no.
200)
Clay fraction
Liquid limit (%)
Plasticity index (%)
Specific gravity
(degrees)
(1.89)
Craney
Island
(0.13)
Table 2 Physical properties of the soils in the tests
medium
(%)
saturation (%)
Unit weight
Dry unit weight
Geosynthetics International, 2010, 17, No 6
Trang 53 FACTORS WITH POTENTIAL
EFFECTS ON DISCHARGE CAPACITY
3.1 Hydraulic gradient
Discharge capacity, qw, is defined as the volume of water
per unit time that can conduct along the core of a PVD in
the axial direction under a unit hydraulic gradient (Hansbo
1983) It is given by
qw¼Q
where Q is the discharge volume of water along the PVD
per unit time (m3/s), and i is the hydraulic gradient
Assuming that Darcy’s law is valid, qw should be constant
with hydraulic gradient
Bo et al (2003) indicated, based on several research
reports, that hydraulic gradient i can affect discharge
capacity measurement, and should be measured at its in
situ value However, it is difficult to estimate the in situ
value of i in the PVD Bo et al recommended that a
hydraulic gradient of 0.50 should be used for discharge
capacity measurements By contrast, Holtz et al (1991)
concluded that the hydraulic gradient does not
substan-tially affect the discharge capacity To check these
differ-ent interpretations, hydraulic gradidiffer-ents were varied from
0.1 to 1 when measuring discharge capacity, as shown in
Figure 2 The discharge capacity decreases with increasing
hydraulic gradient Therefore the flow in the core of the
PVD is not laminar, even at small hydraulic gradients
Non-laminar flow and air bubbles affect the discharge
capacity of the PVD
The small hydraulic diameter of the channels within
each PVD, and the relatively high flow rates, result in
high Reynolds numbers, and thus non-laminar flow As
the hydraulic gradient reduces, the Reynolds number
decreases, but the conditions are still turbulent Figure 3
shows the discharge capacity normalized to the discharge
capacity at a hydraulic gradient of unity as a function of
soil type, drain type, and deformation of the drain It may
be inferred from Figure 3 that the discharge capacity at low gradients may be underpredicted by a factor of 1.5 to 2.5, if it is based on a unit hydraulic gradient Although not tested in this study, it can also be inferred that discharge capacities at gradients greater than unity may be overpredicted While the use of a hydraulic gradient of 0.5 (e.g Bo et al 2003) tends to minimize errors, it should be acknowledged that the hydraulic gradient (be-tween 0.1 and 1) has a large influence on the discharge capacity
3.2 Percentage settlement The discharge capacity of the four PVDs tested using a hydraulic gradient of 0.1 is shown in Figure 4 as a function of percentage settlementv, defined as
v¼ Vertical settlement Inital height of soil specimen3 100% (2) Tests on PVD B were performed in both Kaolin and Craney Island dredgings All PVDs initially had similar discharge capacities, at approximately 120 3 106m3/s PVDs A, B and C had a relatively linear decrease in discharge capacity with increasing percentage settlement, but PVD D had a much more rapid drop in discharge capacity for initial strains up to 10%
Figure 5 shows the degree of discharge capacity reduc-tion as a funcreduc-tion of percentage settlement for a hydraulic gradient of 0.1 Results are similar for other hydraulic gradients tested The degree of discharge capacity reduc-tion, Rq, in percent is defined as
Rq¼ 1qw,v >0
qw,v¼0
where qw,v¼0 is the initial discharge capacity, that is, at a percentage settlement of 0, and qw,v>0 is the discharge capacity at any other percentage settlement In agreement with previous studies, significant levels of reduction in discharge capacity are observed All PVDs, except PVD
A, showed a reduction in discharge capacity of 90–99.5%
Table 3 Properties of the PVDs tested (from manufacturers, except flexural stiffness)
PVD
NA: not available.
Effect of deformation of prefabricated vertical drains on discharge capacity 435
Geosynthetics International, 2010, 17, No 6
Trang 6at a percentage settlement of approximately 40% PVD A
had much better performance, but still had a reduction in
discharge capacity of 70% at a percentage settlement of
40% For the cases of PVD D in Kaolinite and PVD B in
Craney Island dredgings, reductions in discharge capacity
of greater than 98% were observed This could be
consid-ered as essentially a complete cut-off of discharge capa-city, although the actual flow rates through the drain and the flow rates through the soil will be compared later to assess drain performance The behavior observed in Figures 4 and 5 with respect to different types of PVDs, although not shown, were similar at other gradients
20
40
60
80
100
120
140
εv⫽ 30%
εv⫽ 41.3%
qw
qw
qw
qw
qw
Hydraulic gradient, i
0 20 40 60 80 100 120 140
εv⫽ 29%
εv⫽ 39.1%
Hydraulic gradient, i
0
20
40
60
80
100
120
140
0%
εv⫽ 29.3%
εv⫽ 38.2%
Hydraulic gradient, (c)
i
0 20 40 60 80 100 120 140
εv⫽ 22.1%
εv⫽ 32.6%
Hydraulic gradient, i
(d)
0 20 40 60 80 100 120 140
εv⫽ 25.6%
εv⫽ 40.4%
Hydraulic gradient, (e)
i
Figure 2 Discharge capacity of the four PVDs tested as a function of hydraulic gradient and percentage settlement: (a) PVD A, Kaolinite; (b) PVD B, Kaolinite; (c) PVD C, Kaolinite; (d) PVD D, Kaolinite; (e) PVD B, Craney Island
Geosynthetics International, 2010, 17, No 6
Trang 73.3 PVD structure and flexural stiffness
The discharge capacity behavior of different PVDs is
believed to be dictated by their flexural stiffness and the
structure of their cores at the same consolidation
condi-tion The flexural stiffness of the PVDs was measured by
adapting ASTM standard D1388 for measuring the
flexur-al stiffness of geosynthetics ASTM D1388 involves meas-uring the amount of bending under self-weight and the mass per unit area PVD A and D have the highest and lowest flexural rigidity, respectively, as shown in Table 3
1.0
1.5
2.0
2.5
3.0
PVD A, Kaolinite
qqw,
qqw,
qqw,
qqw,
qqw,
Hydraulic gradient, (a)
i
1.0 1.5 2.0 2.5 3.0
PVD B, Kaolinite
Hydraulic gradient, i
(b)
1.0
1.5
2.0
2.5
3.0
PVD C, Kaolinite
Hydraulic gradient, (c)
i
1.0 1.5 2.0 2.5 3.0
PVD D, Kaolinite
Hydraulic gradient, (d)
i
1.0 1.5 2.0 2.5 3.0
PVD B, Craney Island
Hydraulic gradient, (e)
i
Figure 3 Normalized discharge capacity of the four PVDs tested against hydraulic gradient (data at each hydraulic gradient are for all percentage settlements: (a) PVD A, Kaolinite; (b) PVD B, Kaolinite; (c) PVD C, Kaolinite; (d) PVD D, Kaolinite; (e) PVD B, Craney Island At each gradient the data points indicate reduction in normalized discharge capacity with increasing percentage settlement
Effect of deformation of prefabricated vertical drains on discharge capacity 437
Geosynthetics International, 2010, 17, No 6
Trang 8Correspondingly, the Rq of PVD A is the lowest and the
Rq of PVD D is the highest at comparable percentage
settlement These results agree well with the findings of
Ali (1991), Bergado et al (1996), Chai et al (2004) and
Miura and Chai (2000), that the more flexible the core of
the PVD, the greater the reduction in qw A stiffer PVD
can tolerate high deformation of the surrounding soil
while maintaining sufficient continuous flow channels in
its core
If the core structure of a PVD provides more space for
water flow, it will have a higher discharge capacity PVD
A with continuous channels and PVD B with a grooved
core prevent the filter sleeve from intruding easily into the
core, and thus provide and maintain available spaces for
water flow during consolidation The 3D monofilament
core of PVD C, in which monofilaments are arranged in a 3D layout, creating individual channels, appears to provide
a large space for water flow Water can also travel between channels, unlike the continuous or grooved channels However, the monofilament is not as stiff as the contin-uous or grooved channel to prevent the filter sleeve squeezing into the drainage channel The studded core of PVD D can provide a punching effect on the filter sleeve, owing to the high stress concentration at the corners of the sharp studs (Ali 1991), and consequently the filter sleeve can easily intrude into the drainage channels to diminish the area for water flow Miura and Chai (2000) and Chai
et al (2004) studied the long-term qw of PVDs in a clay confinement They carefully measured the hydraulic prop-erties of the individual drainage channels in the cross-section of the PVDs they tested They concluded that the discharge capacity is reduced less with a PVD having a larger drainage channel and a larger hydraulic diameter
Rqof the PVDs tested in this study is consistent with these reports, as it decreased gradually from PVD A, B, C to D 3.4 Deformation patterns of PVDs
Figure 6 shows photographs of the deformed PVDs after completion of the tests The PVDs were highly deformed after 32–40% settlement (at the end of the tests), although the deformation modes vary among the PVDs Many kinks and crimps can be seen, and are more significant for PVD
C and D These kinks are believed to be the main obstruction to flow, and cause a large reduction of the discharge capacity All PVDs were tested under the same model configuration, but displayed different deformed shapes, reflecting their construction
3.5 Soil type
To assess the dependence of the reduction in discharge capacity on soil type, the discharge capacity of PVD B was tested in two soils: Kaolinite and Craney Island dredgings Figure 7a shows the degree of discharge capacity reduction varying with percentage settlement, and Figure 7b shows the reduction in normalized discharge capacity with increasing percentage settlement Both figures show data for a hydraulic gradient of 0.1 Similar conclusions are drawn for other hydraulic gradients tested When compared with the percentage settlement, the discharge capacity and reduction in discharge capacity are quite similar for both soils types using PVD B This is surprising, in view of the differences in deformation patterns observed in Figure 6b and 6c To reach the maximum percentage settlement of approximately 40%, the Kaolinite specimen was loaded to 400 kPa and the Craney Island dredgings to 490 kPa, indicating similar compression characteristics Both soils had an initial void ratio near 2.4 (Table 3), and both have a clay fraction close to 75% The largest difference in material behavior
is the friction angle of the soils, which evidently had little effect on the relationship between settlement and reduction
in PVD discharge capacity Additional soils with a wider range of grain sizes and compression characteristics need
to be tested to assess the influence of soil type on reduction in discharge capacity
0
20
40
60
80
100
120
140
PVD A, Kaolinite PVD B, Kaolinite PVD C, Kaolinite PVD D, Kaolinite PVD B, Craney Island
qw
Percentage settlement,εv(%) Figure 4 Discharge capacity of the four PVDs tested under a
hydraulic gradient of 0.1 as a function of percentage
settlement
0
20
40
60
80
100
PVD A, Kaolinite PVD B, Kaolinite PVD C, Kaolinite PVD D, Kaolinite PVD B, Craney Island
Rq
Percentage settlement,εv(%) Figure 5 Degree of reduction of discharge capacity under a
hydraulic gradient of 0.1 as a function of percentage
settlement
Geosynthetics International, 2010, 17, No 6
Trang 9Although the mechanical properties of Craney Island
dredgings and Kaolinite were quite similar in these tests,
the water flow characteristics were significantly different
Craney Island dredgings required 37 days to reach a
settlement of 40%, whereas Kaolinite required only 21
days Therefore the average volume of water flowing into
the PVD from Craney Island dredgings during
consolida-tion occurred at a rate approximately half that of
Kaoli-nite The required discharge capacity of a drain in Craney
Island dredgings would therefore be less than that required
for Kaolinite, leading to lower well resistance: this is
addressed in the next section
4 REQUIRED DISCHARGE CAPACITY
The discharge capacity of a PVD should have a minimum
value that is much larger than the discharge rate of water
in the soil mass surrounding it, in the influence zone
towards the PVD As the discharge capacity of the drain
becomes close to that of the surrounding soil, the time for
consolidation will increase, owing to well resistance Well resistance is typically characterized as a function of kh/qw, the ratio of the horizontal hydraulic conductivity of the soil to the discharge capacity of the drain (divided by the square of the discharge length of the drain) (e.g Holtz et
al 1991) The time, t, for consolidation is quantified according to
t¼ThD
2 e
where Th is a dimensionless time factor, ch is the horizontal coefficient of consolidation of the soil [k/ (ªwmv)], and Deis the equivalent diameter of the influence zone (i.e 1.05 times the PVD spacing for a triangular installation pattern) The degree of consolidation, U, is related to the normalized time factor (e.g Holtz et al 1991):
(a)
(b)
(c)
(d)
(e) Figure 6 Deformation patterns of the four PVDs tested at
the termination of the tests (no scale): (a) PVD A, Kaolinite;
(b) PVD B, Kaolinite; (c) PVD B, Craney Island; (d) PVD C,
Kaolinite; (e) PVD D, Kaolinite
0 20 40 60 80 100 120 140
PVD B, Kaolinite PVD B, Craney Island
qw
Percentage settlement, (%)
(a)
0 20 40 60 80 100
B, Kaolinite
B, Craney Island
Percentage settlement, (%)
(b)
Rq
Figure 7 (a) Discharge capacity of PVD B in Kaolinite and Craney Island dredgings as a function of percentage settlement; (b) degree of discharge capacity reduction as a function of percentage settlement
Effect of deformation of prefabricated vertical drains on discharge capacity 439
Geosynthetics International, 2010, 17, No 6
Trang 10Th¼ln 1ð UÞF nð Þ
Th,w¼ln 1ð UÞFwð Þn
where F(n) is a factor accounting for the well spacing, and
Fw(n) adds the influence of well resistance in that
expres-sion The influence of a smear zone is not addressed in
this paper, because of the way experiments were
per-formed; however, one can expect that the addition of a
smear zone would result in an even lower required
discharge capacity than these results indicate The general
expression for F(n) was presented by Barron (1948) as
F nð Þ ¼ ln nð Þ n
2
n2 1
3n2 1 4n2
ln nð Þ 3
4
(6a)
The addition of well resistance to Equation 6a results in
the expression (e.g Hansbo 1981)
Fwð Þ ln nn ð Þ 3
4
þz 2Lð DR zÞ kh
qw
(6b)
where LDR is the drainage length for the well, and z is the
depth of a layer To assess the average degree of
consolidation across an entire drain, Fw(n) is expressed as
Fwð Þ ln nn ð Þ 3
4
þ2
3 L
2 DR
kh
qw
(6c)
The influence of well resistance increases as the
discharge capacity decreases, and quantification of the
influence of Fw(n) can be addressed using the ratio of
Equation 5b using Fw(n) (Equation 6c) and Equation 5a
using F(n) (Equation 6a) to give
Th,w
Th
¼ln 1ð UÞFwð Þn
8
8
ln 1ð UÞF nð Þ
¼Fwð Þn
F nð Þ ¼ 1 þ
2=3
ð ÞL2
DR kh=qw
ln nð Þ 3=4
(7)
Figure 8a gives the ratio of the time factors (Th,w/Th) as
a measure of the delay in consolidation time due to well
resistance, as a function of the available discharge
capa-city and hydraulic conductivity measured in the five tests
in this study, as well as an example with a particularly
higher hydraulic conductivity (1 3 108m/s) but the same
discharge performance of PVD B in Craney Island
dred-gings A hypothetical drainage length of 20 m is used
together with a spacing of 1 m in a triangular pattern in
all cases These values represent realistic and more critical
field conditions for well resistance Significant increases
in time for consolidation are observed in some cases for
qw less than 100 m3/yr The example with high hydraulic
conductivity soil indicates that the normalized time for
consolidation could be as high as 2.6 times These
analyses are in agreement with previous studies, which
suggest that the required discharge capacity should be greater than 100 to 150 m3/yr (3.2 3 106 to 4.8 3
106m3/s) to maintain acceptable performance (Rixner et
al 1986; Holtz 1989; Holtz et al 1991; Chang et al 1994; Bo et al 2003; Chu et al 2004)
The data are also plotted in Figure 8b as the increase in normalized consolidation time due to well resistance against percentage settlement Although significant reduc-tions in discharge capacity are measured, there is a minimal increase in time for consolidation for all cases except PVD D This is due largely to the low hydraulic conductivity in Kaolinite and Craney Island dredgings If the reduction in discharge capacity for Craney Island dredgings is compared with a soil with a hydraulic conductivity of 1 3 108m/s as in the example,
signifi-0 0.5 1.0 1.5 2.0 2.5 3.0
PVD A, Kaolinite PVD B, Kaolinite PVD C, Kaolinite PVD D, Kaolinite PVD B, Craney Island Example
Th,w
Th,w
Available discharge capacity, (m /yr)
(a)
0 0.5 1.0 1.5 2.0 2.5 3.0
PVD A, Kaolinite PVD B, Kaolinite PVD C, Kaolinite PVD D, Kaolinite PVD B, Craney Island Example
Percentage settlement, (%)
(b)
Figure 8 Increase in time for consolidation (Th,w/Th) due to well resistance for a 20 m drainage length PVD with 1 m spacing in a triangular pattern at a hydraulic gradient of 0.1: (a) as a function of available discharge capacity; (b) as a
Island soil; others used the experimentally measured values for each soil and PVD
Geosynthetics International, 2010, 17, No 6