discharge capacity of prefabricated vertical drains confined in clay

Technical Paper by N. Miura and J.C. Chai
DISCHARGE CAPACITY OF PREFABRICATED
VERTICAL DRAINS CONFINED IN CLAY
ABSTRACT: This paper reports the long-term discharge capacities of four types of
prefabricated vertical drains (PVDs) confined in clay. The results indicate that under
clay confinement, the PVD discharge capacities significantly reduced with time. The
discharge capacity reduction may be caused by creep deformation of the PVD filter or
clogging of the drainage channels. PVD filter creep test results indicated that, for the
conditions considered, creep deformation was limited, which implies that clogging is
the main cause of the discharge capacity reduction. Hydraulic shocks were applied,
which partially unclogged the PVD, recovering a significant amount of the discharge
capacity. The higher the PVD hydraulic gradient and the larger the shape factor of the
drainage channel (defined as the drainage area per channel divided by its perimeter
length), the less discharge capacity reduction with time. However, there was no clear
trend regarding the effect of the apparent opening size, O 95 , of the filter on long-term
discharge capacity. Based on the test results, an empirical equation was proposed for
estimating the long-term clay-confined discharge capacity by using short-term rubber
membrane-confined test results. Regarding long-term discharge capacity, it is recommended
that a PVD with a larger drainage area per channel (approximately 3 mm 2 )and
a larger drainage channel shape factor (larger than 0.4 mm) should be selected.
KEYWORDS: Prefabricated vertical drain, Discharge capacity, Geotextile, Filter,
Creep, Deformation.
AUTHORS: N. Miura, Professor and Director, Institute of Lowland Technology,
Saga University, 1 Honjo, Saga, 840-8502, Japan, Telephone: 81/952-28-8576,
Telefax: 81/952-28-8190, E-mail: miuran@cc.saga-u.ac.jp; and J.C. Chai, Associate
Professor, Department of Civil Engineering, Saga University, 1 Honjo, Saga,
840-8502, Japan, Telephone: 81/952-28-8580, Telefax: 81/952-28-8190, E-mail:
chai@cc.saga-u.ac.jp.
PUBLICATION: Geosynthetics International is published by the Industrial Fabrics
Association International, 1801 County Road B West, Roseville, Minnesota
55113-4061, USA, Telephone: 1/651-222-2508, Telefax: 1/651-631-9334.
Geosynthetics International is registered under ISSN 1072-6349.
DATES: Original manuscript received 17 January 2000, revised version received 25
April 2000 and accepted 28 April 2000. Discussion open until 1 January 2001.
REFERENCE: Miura, N. and Chai, J.C., 2000, “Discharge Capacity of Prefabricated
Vertical Drains Confined in Clay”, Geosynthetics International, Vol. 7, No. 2, pp.
119-135.
GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2
119

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
1 INTRODUCTION
Prefabricated vertical drains (PVDs) are widely used to accelerate the consolidation
of soft clay deposits under preloading. Discharge capacity is one of the factors affecting
the behavior of PVDs (Hansbo 1981). Most PVD discharge capacity tests were conducted
by confining a PVD specimen in a rubber membrane; however, discharge capacity
tests with rubber membrane confinement do not represent field conditions. In the
field, a PVD is confined by clay, which is normally remolded during PVD installation.
Under field conditions, clay particles may enter the PVD drainage channels, and the
consolidation settlement of the improved subsoil may cause folding of the PVD. These
factors will affect the discharge capacity of PVDs. Miura et al. (1998) conducted a series
of laboratory tests investigating the discharge capacity of PVDs. The following factors
were studied: (i) confinement condition (confined by a rubber membrane or clay); (ii)
folding of the PVD; (iii) air bubbles trapped in the drainage channels; and (iv) variation
of the discharge capacity with time under clay confinement. For the conditions investigated,
it was found that the discharge capacity of the clay-confined PVD was much lower
than that of the rubber membrane-confined PVD, and, in the case of clay
confinement, the discharge capacity continuously decreased with time. Chai and Miura
(1999) reported test results on the discharge capacity of PVDs, as well as creep deformation
of PVD filters. The mechanism of PVD discharge capacity reduction with time under
clay confinement was also investigated. For the two types of PVDs tested, it was
concluded that the deformation (including creep) of the PVD filter contributed less than
20% of the discharge capacity reduction for the conditions investigated. More than 80%
of the reduction was attributed to clogging, which was caused by soil particles entering
the PVD core drainage channels and bio-films forming inside the drainage channels.
The clay-confined PVD test data reported by Miura et al. (1998) and Chai and Miura
(1999) were for two types of PVDs tested under a low hydraulic gradient (approximately
0.08). The following points were not clarified: (i) is the conclusion drawn applicable
to other PVDs? and (ii) what are the important factors affecting the long-term clay-confined
discharge capacity? Also, in practice, the following questions need to be answered.
Is it possible to estimate the long-term clay-confined discharge capacity using
short-term rubber membrane-confined test results (e.g. those tests conducted by
manufacturers)? And, what type of PVD will have a higher long-term clay-confined
discharge capacity? The objective of the present study is to attempt to answer these
questions.
In the present paper, the laboratory discharge capacity test results of four types of
commonly used PVDs in Japan are reported. The creep deformation and apparent opening
size of the filter, as well as the effect of hydraulic gradient on the long-term clayconfined
discharge capacity, are investigated. An empirical method for estimating the
long-term clay-confined discharge capacity of PVDs is presented. Suggestions are provided
for the selection of PVDs in engineering practice based on the test results of the
present study.
120 GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
2 DISCHARGE CAPACITY OF CLAY-CONFINED PVD SPECIMENS
2.1 Test Method and Materials Used
The device used for clay-confined PVD discharge capacity tests is illustrated in Figure
1. The apparatus includes a cylindrical cell with a diameter of 200 mm and height
of 600 mm. The maximum PVD specimen length that can be tested with this device is
approximately 400 mm. The PVD is confined by a 100 mm-diameter remolded soil column
contained in a rubber membrane. The soil column simulates remolded soil around
the PVD, i.e. the smear zone. A detailed description of the test procedure can be found
in the paper by Chai and Miura (1999). The primary test setup procedures are summarized
as follows:
1. Install the PVD specimen in the bottom pedestal, which is connected to the inlet water
flow system.
2. Fix the rubber membrane in the bottom pedestal and place the cylindrical mold (inner
diameter of 100 mm) into position.
Head difference, ∆H
Confining pressure
100 mm
Clay
PVD
Rubber membrane
Cross section of PVD specimen
Specimen
200 to 400 mm
Figure 1.
Apparatus used to measure the discharge capacity of PVD specimens.
GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2
121

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
3. Place the remolded clay (at a water content approximately equal to the liquid limit)
into the mold layer-by-layer until the desired height is attained.
4. Install the top pedestal and connect the PVD specimen to the outlet water flow system.
Fix the rubber membrane to the top pedestal.
5. Apply a suction of approximately 10 kPa to the specimen and remove the mold.
6. Apply the confining pressure and gradually release the suction.
7. Set the desired hydraulic gradient.
8. Allow the clay to consolidate under a given confining pressure. After the clay consolidates,
measure the discharge capacity.
Four types of PVDs commonly used in Japan were tested. The four PVDs have different
core structures (Figure 2) and filters (Table 1). Both rubber membrane-confined
(approximately 0.9 mm thick) and clay-confined tests were conducted. To simulate
long-term field behavior, the clay-confined tests were approximately three months long
(except for one test). A micro pump was used to recirculate the water (tap water, not
de-aired) during the tests. The tests were conducted in an air-conditioned room with the
temperature typically within the range of 18 to 26_C. The pump motor was not placed
in the water to ensure that it would have no effect on the water temperature. Most tests
were conducted at a confining pressure, σ, of 49 kPa. Assuming an earth pressure coefficient
of 0.5, 49 kPa represents the horizontal earth pressure under an embankment
approximately 5 m high, or the initial horizontal earth pressure at a depth of approximately
10 m in the ground. Remolded Ariake clay, which consisted of 57.0% clay,
41.7% silt, and 1.3% sand particles, was used (liquid limit of 105.0% and a plastic limit
of 42.8%).
For the test apparatus used (Figure 1), an amount of head loss is associated with the
hose connecting the inlet and outlet water tanks, which should be considered when interpreting
the test results. To calibrate the head loss, a test without a PVD specimen and
soil column was conducted. In this case, the water flowed from the inlet water tank to
the outlet water tank through the hoses and cylindrical chamber only. The head difference,
∆H, between the inlet and outlet water tanks was varied, and the corresponding
amount of water flow, Q, was measured. The Q versus ∆h relationship for this test device
is plotted in Figure 3. This curve was used to correct the test results according to
the following procedure:
Table 1.
Physical properties of the prefabricated vertical drain (PVD) filters.
Property
PVD filter
PVD A PVD B PVD C PVD D
Mass/unit area (g/m 2 ) 50 37 50 154
Thickness (mm) 0.21 0.12 0.21 0.44
Polymer Polyester Polyolefin Polyester Polypropylene
Manufacturing
process
Continuous filament
(heat-bonded)
Short fibre
(heat-bonded)
Continuous filament
(heat-bonded)
Short fibre
(heat-bonded)
122 GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
PVD A
Unit drainage
channel
PVD B
Unit drainage
channel
1.8
2.0
2.4
Filter
Core
94
2.4
40 drainage channels
1.5
Initial drainage area = 108 mm 2
97
3.6
70 drainage channels
1.3 Initial drainage area = 200 mm 2
PVD C
Unit drainage
channel 1.7
2.7
1.0
94
3.6
39 drainage channels
Initial drainage area = 199 mm 2
1.0
99
PVD D
3.1
Unit drainage 3.3
56 drainage channels
channel
1.4 0.8 Initial drainage area = 224 mm 2
0.8
Dimensions in mm
Figure 2.
Core structures of the tested PVD specimens.
1. From a measured amount of water flow, the corresponding head loss in the hoses,
∆h, was obtained from Figure 3.
2. To calculate the head loss, ∆H - ∆h, within a PVD specimen, ∆h was subtracted from
the total head difference, ∆H, used during the test.
3. The corrected hydraulic gradient, i, within the PVD specimen was calculated as
(where L is the length of the PVD specimen):
i =
∆H − ∆h
L
(1)
GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2
123

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
Head loss within test apparatus, ∆h (mm)
30
20
10
∆h = 0.000526Q 1.588
0
0 200 400 600 800 1000
Rate of water flow, Q (m 3 /year)
Figure 3.
Correction curve for the head loss of the test apparatus.
4. For ease of comparison, the results were further linearly converted to a fixed hydraulic
gradient, which was approximately the average value of the corrected hydraulic
gradients.
2.2 Test Results for Low Hydraulic Gradient
The hydraulic gradient, i, within a PVD may also have an influence on discharge
capacity. Conceptually, the higher the i value, the less the clogging effect. Laboratory
tests should be conducted with an i value close to field conditions; however, to measure
the field hydraulic gradient within a PVD is not practical. Also, since the hydraulic gradient
varies with time, as well as with soil conditions, embankment loading, and
construction scheme, it is difficult to define a single hydraulic gradient value. Chai and
Miura (1999) conducted finite element analyses for three embankments on PVD-improved
subsoil. In the analyses, the effect of the PVD was simulated using one-dimensional
drainage elements (Chai et al. 1995). The numerical results indicated that, at the
end of construction, the maximum hydraulic gradient within the PVDs was in the range
of 0.1 to 0.3. Considering that the value of i will decrease during the consolidation process,
most clay-confined tests were set with a hydraulic gradient of approximately 0.08
in the present study.
Figures 4a to 4d present the clay-confined test results for PVDs A, B, C, and D, respectively.
In Figures 4a to 4d, the left ordinate is the ratio of the clay-confined discharge
capacity, Q C , divided by the short-term (approximately two days) rubber
membrane-confined discharge capacity, Q R . The pattern of the variation of Q C /Q R with
124 GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
(a)
(b)
Discharge capacity ratio, Q C / Q R
(c)
Discharge capacity ratio, Q C / Q R
1
0.8
0.6
0.4
0.2
Elapsed time, t (days)
1
0.8
100
0.6
0.4
0.2
0 0 0
0 100 200 300 0
1
0.8
0.6
0.4
0.2
PVD A
σ =49kPa
i =0.08
Predicted
Discharge capacity recovery
due to partial unclogging
PVD C
σ =49kPa
i =0.08
Predicted
Discharge capacity recovery
due to partial unclogging
0
0
0 100 200 300
Elapsed time, t (days)
150
50
400
(d)
1
0.8
300
200
0.6
0.4
100
0.2
0
PVD B
σ =49kPa
i =0.08
PVD D
0
100 200 300
Elapsed time, t (days)
σ =49kPa
i =0.08
Predicted
Predicted
300
200
100
0
100 200 300
Elapsed time, t (days)
600
400
200
Rate of water flow, Q C (m 3 /year)
Rate of water flow, Q C (m 3 /year)
Figure 4. Discharge capacity-elapsed time curves for a low hydraulic gradient, i = 0.08,
and a confining pressure, σ = 49 kPa: (a) PVD A; (b) PVD B; (c) PVD C; (d) PVD D.
elapsed time will be used to develop an empirical equation for predicting the long-term
clay-confined discharge capacity using the short-term rubber membrane-confined test
results in Section 2.3. The right ordinate is the rate of water flow. Test results, for PVDs
A and B, that were reported by Chai and Miura (1999) are included here for comparison.
It can be seen that, for the four PVDs tested, the discharge capacities all decreased significantly
with time. The recovery of discharge capacities in Figures 4a and 4c was due
to the application of hydraulic shocks, which is discussed later in this section. Since the
four types of PVDs tested have different core structures and filters, it can be stated that,
under the adopted conditions, the reduction of discharge capacity with time is a com-
GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2
125

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
mon phenomenon and should be considered when designing soft subsoil improvements
using PVDs.
The following phenomena have been considered for the reduction of PVD discharge
capacity with time: (i) creep deformation of the filters; and (ii) clogging due to clay particles
entering the drainage channels of the PVD core and possible formation of biofilms
(Chai and Miura 1999). Creep tests for the PVD filters were conducted. The creep
test device is illustrated in Figure 5. The filter was tested in the direction corresponding
to the transverse direction of the PVDs. The tested specimens were 200 mm wide and
400 mm long. To avoid necking of the specimen, a clamp was fixed in the middle of
the specimen. The creep test results are summarized in Figure 6. It can be seen that the
PVD B filter is weaker than PVD A and C filters. To relate the deformation (including
creep) of a filter with the reduction of the cross-sectional area of the drainage channel,
the following assumptions were made:
1. As illustrated in Figure 7, the deformed shape of the filter is a circular arc.
2. The confining pressure is balanced by the tensile force, T, in the filter in the y direction
(Figure 7).
400 mm
Filter specimen
Weight
200 mm
Middle clamp to
restrict necking
of the specimen
Bar to prevent
swinging of the
specimen
Ruler
Side view
Front view
Figure 5.
Illustration of the PVD filter creep test apparatus.
126 GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
Elapsed time, t (logarithmic scale)
(a)
Tensile strain, ε (%)
0
10
20
30
40
1hour
PVDs A and C
1 week
1day
1month
1year
191 N
241 N
341 N
391 N
(b)
0
Tensile strain, ε (%)
10
20
30
40
PVD B
141 N
Failure
91 N
41 N
64 N
(c)
Tensile strain, ε (%)
0
10
20
30
40
PVD C
241 N
341 N
441 N
641 N
Figure 6. Creep test results for the PVD filters (specimen width = 200 mm): (a) PVDs A
andC;(b)PVDB;(c)PVDD.
GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2
127

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
y
x
Confining
pressure,
F=Bσ
Tsinα
Tensile force, T
α
Core
B
Deformed filter
(circular arc)
Figure 7.
Calculation of the reduction of the drainage area.
By varying the value of α (Figure 7) (and therefore, the radius of the arc), balance
between the confining pressure and the mobilized tensile force in the filter can be obtained
(trial and error). The reduction of the cross-sectional area of the drainage channel
is a function of the filter deformation behavior and the geometry of the drainage channel.
Based on the test results, the relationships between confining pressure and the reduction
of the cross-sectional area of the drainage channels were calculated and are
shown in Figures 8a to 8d for PVDs A to D, respectively. Figure 8 indicates that under
a confining pressure of 49 kPa, deformation (including creep) of the filter reduces the
cross-sectional area of the drainage channel by approximately 5% for PVDs A and C,
and approximately 20% for PVDs B and D. Comparing the amount of reduction after
one day, one month, and one year (extrapolated), it can be seen that under a confining
pressure of 49 kPa, most of the cross-sectional area reduction is due to short-term deformation
and the creep deformation is small. The PVD D filter is strong, but the perimeter
length of the filter sleeve is longer than the perimeter length of the core, and the
core is weaker. In particular, the extra length of the filter sleeve contributed approximately
15% to the reduction of the cross-sectional area of the drainage channel. The
test results indicate that PVD filter deformation is not a dominating factor for discharge
capacity reduction.
For PVDs A and C, before terminating the clay-confined tests, hydraulic shockswere
applied by firmly stepping on the inlet hose or rapidly varying the head difference. By
doing so, the fine particles (or bio-films) were partially pumped out of the drainage
channels of the PVD core. Then, the discharge capacities were recovered to a value corresponding
to that of approximately one week of elapsed time (Figures 4a and 4c). This
indirectly indicates that clogging of the PVD core is the main mechanism reducing the
discharge capacity with time. It was observed that, during application of the hydraulic
shocks, flocculated fine particles were forced out of the PVD drainage channels and deposited
on the wall of the outlet hose. Also, after the discharge capacity test, the filter
was analyzed using electron-microscope photographs. There were bio-films on the
drainage-channel side of the filter (Chai and Miura 1999). Air bubbles trapped in the
drainage channels were also considered a possible cause of the discharge capacity re-
128 GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
(a)
Reduction of cross-sectional area, R A (%)
0
20
40
60
(b)
Confining pressure, σ (kPa)
100 200 300 400
0
PVD A
20
40
After 1 day
After 1 month
After 1 year (extrapolated)
60
Confining pressure, σ (kPa)
100 200 300 400
PVD B
(c)
(d)
Reduction of cross-sectional area, R A (%)
0
20
40
60
Confining pressure, σ (kPa)
100 200 300 400
PVD C
0
20
40
60
Confining pressure, σ (kPa)
100 200 300 400
PVD D
Figure 8. Relationship between confining pressure and the reduction of the drainage
area:(a)PVDA;(b)PVDB;(c)PVDC;(d)PVDD.
duction with time. Miura et al. (1993) reported that trapped air bubbles caused a reduction
of the PVD discharge capacity under rubber membrane confinement. With further
investigation, it was found that when maintaining unfolded inlet and outlet hoses, the
effect of trapped air bubbles was a minor factor influencing PVD discharge capacity
GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2
129

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
(Miura et al. 1998). Furthermore, no air bubbles were forced out when the hydraulic
shocks were applied for the tests on PVDs A and C.
The filter opening size and geometry of the drainage channels may have an effect
on the clogging phenomenon. The apparent opening size (O 95 , the filter opening diameter
such that 95% of the openings are smaller that that size) of the four filter types was
measured using glass beads according to ASTM D 4751. The apparent opening size distributions
of the four filters are given in Figure 9, and the O 95 values are listed in Table
2. Even though it is not generally agreed upon to use O 95 values to represent the opening
size of nonwoven geotextiles, i.e. filters (Giroud 1996), it is believed that O 95 values
are a useful index for comparing the relative size of the 5%-larger geotextile openings.
Table 2.
The O 95 values of the PVD filters and the geometry of a unit drainage channel.
Test
no.
PVD
O 95 of
filter (µm)
Geometry of unit
drainage channel
Cross-sectional
area (mm 2 )
Shape
factor (mm)
t filt d f ti C
Q C
Area reduction due
to filter deformation
(%)
Q R
3months
1 PVD A 52 2.70 0.41 3.1 0.108
2 PVD B 78 2.86 0.41 15.4 0.117
3 PVD C 52 2.57 (3.91) 0.41 (0.48) 4.6 0.105*
4 PVD D 213 3.98 0.47 21.5 0.230
Notes: The number outside the parentheses is the average value of larger and smaller channels, and the
number in parentheses is for the larger channel only (Figure 2). *Extrapolated value.
Percent passing by weight (%)
100
80
60
40
20
PVDs A and C
PVD B
PVD D
0
0 100 200 300
Apparent opening size (µm)
Figure 9.
Apparent opening size distribution of the PVD filters.
130 GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
The size of a drainage channel is expressed as its cross-sectional area. A parameter
called the shape factor is introduced to represent the shape of a drainage channel. The
shape factor of a drainage channel is defined as the ratio of the cross-sectional area divided
by the perimeter length of the cross section. To develop a relationship between
the drainage channel size/shape factor and the degree of discharge capacity reduction,
an arbitrary discharge capacity ratio at three months, (Q C /Q R ) 3months , was adopted. For
the PVDs tested, cross-sectional area, shape factor of the drainage channel, area reduction
due to filter deformation (t = 1 month and σ = 49 kPa), and the value of
(Q C /Q R ) 3months are given in Table 2. The following observations can be made with regard
to the data in Table 2: (i) there is no clear trend regarding the relationship between apparent
opening size, O 95 , of the filter and (Q C /Q R ) 3months ; (ii) it appears that the geometry
of the drainage channel has an effect on the value of (Q C /Q R ) 3months . PVD D has the largest
(Q C /Q R ) 3months value, and, accordingly, it has the largest drainage area per channel
and the largest shape factor.
2.3 Effect of Hydraulic Gradient
For PVDs A, B, and D, clay-confined discharge capacity tests were conducted using
a higher hydraulic gradient (i ≈ 0.4) . The Q C /Q R values are compared in Figures 10a
to 10c, respectively. As expected, for the PVDs tested, there was less reduction in the
discharge capacity for higher i values. For example, at t = 2 months and i = 0.08, the
clay-confined discharge capacity was approximately 18, 20, and 23% of the rubber
membrane-confined short-term values for PVDs A, B, and D, respectively. For the i =
0.4 case, the corresponding values are approximately 35, 46, and 55%, respectively.
The discharge capacity ratios for i = 0.4 are approximately twice the corresponding values
for i = 0.08.
In the field, after construction and during the consolidation process, the hydraulic
gradient within the PVD will reduce. Reduction ofthe hydraulic gradient promotesPVD
clogging and reduces the PVD efficiency. This factorshould be considered whendesigning
soft subsoil improvements using PVDs, especially when the designed consolidation
period is long.
3 ESTIMATION OF THE LONG-TERM CLAY-CONFINED DISCHARGE
CAPACITY OF PVDs
The long-term clay-confined discharge capacity test is time consuming and not a
routine test. Based on the test results of the present study, an empirical equation is proposed
to estimate the long-term clay-confined discharge capacity, Q C , by using the
short-term rubber membrane-confined discharge capacity, Q R . It is assumed that the
effect of confining pressure is approximately the same for the rubber membrane- and
clay-confined tests. Also, as discussed in Section 2.2, creep deformation may not be a
significant factor under working conditions. Only two variables, elapsed time, t, and
hydraulic gradient, i, are considered in the following proposed equation:
Q C = Q R
i
C s (t∕t c ) + i
(2)
GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2
131

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
(a)
(b)
(c)
Discharge capacity ratio, Q C / Q R
Discharge capacity ratio, Q C / Q R
Discharge capacity ratio, Q C / Q R
1
0.8
0.6
0.4
0.2
0
0
1
0.8
0.6
0.4
0.2
100 200 300
0
0
1
100 200 300
PVD D σ =49kPa
0.8
i =0.4(measured)
i =0.08(measured)
0.6
Predicted
0.4
0.2
PVD A
PVD B
σ =49kPa
i =0.4(measured)
i =0.08(measured)
Predicted
σ =49kPa
i =0.4(measured)
i =0.08(measured)
Predicted
0
0 100 200 300
Elapsed time, t (days)
Figure 10. Effect of the hydraulic gradient on the discharge capacity ratio values: (a) PVD
A; (b) PVD B; (c) PVD D.
132 GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
where: t c = time constant (= 1 day, which was introduced to balance the units); and C s
= constant. Although different soils and PVDs may have different C s values, for simplicity,
C s = 0.01 is recommended for making a preliminary prediction. The calculated/
predicted discharge capacity ratio values for C s = 0.01 are included in Figures 4a to 4d
and Figures 10a to 10c as solid lines. Generally, Equation 2 gives a reasonable prediction
of long-term clay-confined discharge capacities. For PVD B and a higher hydraulic
gradient, i = 0.4, the prediction of Q C is poor. To improve the accuracy of the calculated
Q C value, the C s value may be varied according to soil conditions, filter type, and the
geometry of the drainage channel. Presently, there is not enough information to establish
a general relationship between C s and these influencing factors. Qualitatively, the
larger the creep deformation of the filter, the smaller the cross-sectional area, and, the
smaller the drainage channel shape factor, the larger the C s value. Therefore, for PVDs
with a strong filter (for example, the PVD A filter), a larger drainage-channel shape factor
will cause less reduction of the discharge capacity with time. A larger square (ideally
circular) drainage channel will provide better performance than a rectangular drainage
channel with the same cross-sectional area. All of these factors should be considered
when selecting a PVD.
4 CONCLUSIONS
The following conclusions have been made regarding the present study:
1. Long-term clay-confined discharge capacity tests were conducted for four types of
PVDs commonly used in Japan. The results indicate that, for all of the PVDs tested,
the discharge capacity significantly reduced with time. It is suggested that this factor
be considered when designing soft subsoil improvements using PVDs.
2. The two factors considered for the reduction of discharge capacity with time are
creep deformation of the PVD filter and clogging of the PVD drainage channels. The
PVD filter creep tests indicated that creep deformation of the filter only causes less
than a 20% reduction of the cross-sectional area of the drainage channel, which implies
that clogging is a dominating factor for the following reasons:
S The application of hydraulic shocks partially cleared up the clogging and significantly
recovered the discharge capacity of the PVDs.
S Increasing the hydraulic gradient within the PVD (i.e. reduce the clogging potential),
reduced the amount of discharge capacity reduction with time.
S The PVD with a larger drainage channel and a larger shape factor (drainage area
per channel divided by its perimeter length) showed less discharge capacity reduction
because the drainage channel is not easily clogged.
However, there is no clear trend between the apparent opening size of the filter, O 95 ,
and the discharge capacity reduction with time for the cases investigated.
3. Since the long-term clay-confined discharge capacity test is not a routine test, an empirical
equation was proposed to estimate the long-term clay-confined discharge capacity
of PVDs by using a short-term rubber membrane-confined test result.
GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2
133

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
4. For practical purposes, it is suggested that, regarding the long-term discharge capacity,
a PVD with a larger drainage area per channel (approximately 3 mm 2 ) and a larger
drainage channel shape factor (greater than 0.40 mm) should be selected.
ACKNOWLEDGMENTS
This research was partly supported by Kinjo Rubber Co., Ltd., Osaka, Japan. The
authors would like to express their appreciation to N. Nomura, Director of the Technical
Department of Kinjo Rubber Co., Ltd., for his helpful suggestions and comments.
Thanks are also extended to K. Toyota and H. Yamasaki, graduates of Saga University,
Japan, for conducting some of the laboratory tests and assisting in figure preparation.
REFERENCES
ASTM D 4751, “Standard Test Method for Determining Apparent Opening Size of a
Geotextile”, American Society for Testing and Materials, West Conshohocken, Pennsylvania,
USA.
Chai, J.C. and Miura, N., 1999, “Investigation of Factors Affecting Vertical Drain Behavior”,
Journal of Geotechnical and Geoenvironmental Engineering, Vol. 125, No.
3, pp. 216-226.
Chai, J.C., Miura, N., Sakajo, S. and Bergado, D.T., 1995, “Behavior of Vertical Drain
Improved Subsoil Under Embankment Loading”, Soils and Foundations, Vol. 35,
No. 4, pp. 49-61.
Giroud, J.P., 1996, “Granular Filters and Geotextile Filters”, Geofilters ’96: comptes
rendus, Lafleur, J. and Rollin, A., Editors, École Polytechnique, Proceedings of the
conference Geofilters’96 held in Montreal, Quebec, Canada, May 1996, pp. 565-680.
Hansbo, S., 1981, “Consolidation of Fine-Grained Soils by Prefabricated Drains”, Proceedings
of the Tenth International Conference on Soil Mechanics and Foundation
Engineering, Balkema, Vol. 3, Stockholm, Sweden, June 1981, pp. 677-682.
Miura, N., Chai, J.C. and Toyota, K, 1998, “Investigation on Some Factors Affecting
Discharge Capacity of Prefabricated Vertical Drain”, Proceedings of the Sixth International
Conference on Geosynthetics, IFAI, Vol. 2, Atlanta, Georgia, USA, April
1998, pp. 845-850.
Miura, N., Park, Y.M. and Madhav, M.R., 1993, “Fundamental Study on the Discharge
Capacity of Plastic Board Drain”, Journal of Geotechnical Engineering,JSCE,Vol.
35, No. 3, pp. 31-40. (in Japanese)
134 GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2

MIURA AND CHAI D Discharge Capacity of Prefabricated Vertical Drains Confined in Clay
NOTATIONS
Basic SI units are given in parentheses.
B = width of drainage channel (m)
C s = a constant (Equation 2) (dimensionless)
F = confining load (N/m)
i = hydraulic gradient (dimensionless)
L = length of specimen (m)
O 95 = filter opening size such that 95% of pores are smaller than that size,
i.e apparent opening size of filter (m)
Q = rate of water flow during discharge capacity test (m 3 /s)
Q C = confined in-clay discharge capacity (m 3 /s)
Q R = confined in rubber membrane discharge capacity (m 3 /s)
(Q C /Q R ) 3months
= discharge capacity ratio after three months (dimensionless)
R A = reduction of cross-sectional area (%)
T = tensile force in filter (N/m)
t = time (s)
t c = time constant = 1 day
x = horizontal distance (m)
y = vertical distance (m)
α = inclination angle (_)
∆H = total head difference (m)
∆h = head loss within hose system of test apparatus (m)
ε = tensile strain (dimensionless)
σ = confining pressure (N/m 2 )
GEOSYNTHETICS INTERNATIONAL S 2000, VOL. 7, NO. 2
135