DSpace at VNU: Effect of deformation of prefabricated vertical drains on discharge capacity

Geosynthetics International, 2010, 17, No Effect of deformation of prefabricated vertical drains on discharge capacity H H Tran-Nguyen1 , T B Edil2 and J A Schneider3 Assistant Professor of Bridge and Highway Engineering, Department of Civil Engineering, Ho Chi Minh City University of Technology, 268 Ly Thuong Kiet Street, B6 Building, District 10, Ho Chi Minh City, Vietnam, Telephone: +84 1390 0663, Telefax: +84 3863 7002, E-mail: tnhhung@hcmut.edu.vn or tnhhung@gmail.com Professor of Geological Engineering, Department of Civil and Environmental Engineering, University 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 Assistant Professor of Geological Engineering, Department of Civil and Environmental Engineering, 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 Additionally, if soils with a higher hydraulic conductivity, such as 10À8 m/s occur at a site, 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] INTRODUCTION Deformation of PVDs by folding, crimping, bending, buckling or kinking resulting from large consolidation settlements may reduce the discharge capacity significantly 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 1072-6349 # 2010 Thomas Telford Ltd 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 capacity 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 431 432 Tran-Nguyen, Edil and Schneider The discharge capacity of a manually deformed PVD varies significantly with the type of PVD and the deformed shape Lawrence and Koerner (1988) investigated 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 decreased 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 investigated 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 investigators 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 photographs 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 consolidation 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 focused on: 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; measuring the discharge capacity of such deformed PVDs directly using the PVD-S apparatus under different hydraulic gradients; and investigating the controlling factors that may affect discharge capacity, such as hydraulic gradient, percentage consolidation settlement, flexural stiffness of the PVD, and soil type 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 Effect of deformation of prefabricated vertical drains on discharge capacity 433 Pneumatic air cylinders LVDT for vertical displacement Movable top piston, δ ϭ 127 mm PVD 100 ϫ (4Ϫ6) mm 325 Travel length of the piston Top reservoir P6 P5 P4 P3 750 P2 PVD 200 425 Soil specimen P1 320 (b) Bottom reservoir 320 (a) Figure Features of the PVD-S apparatus (a) main dimensions of PVD-S apparatus (mm); (b) arrangement of piezometers PVD 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 reservoirs 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 crosssection of 120 mm 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 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 immediately 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 capacity 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- Geosynthetics International, 2010, 17, No 434 Tran-Nguyen, Edil and Schneider tions of the two reservoirs The hydraulic gradient is calculated by dividing the head difference by the embedded 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 piezometers, 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 consolidation stage Therefore the discharge measured from this study is free of siltation effects Each discharge capacity measurement took about 60 Duration of consolidation 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 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 performance 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 The properties of the soil specimens prepared for the tests in their initial condition, and measured after the tests, are summarized in Table 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 Table Properties of the soils % Finer (sieve no 200) Clay fraction , ìm (%) Liquid limit (%) Plasticity index (%) Specific gravity pH a Specific surface areaa (m2 /g) cv b (m2 /s (m2 /yr)) ky c (m/s) Friction angle, ö9 (degrees) Kaolinite 100 80 49 25 2.59 4.2–4.5 10 1.6 10À9 25 Craney Island 80 73 80 55–60 2.71 NA NA 10À8 (1.89) 10À9 (0.13) 4.8 10À10 30 Soil a From manufacturer Normally consolidated coefficient of consolidation c Mean hydraulic conductivity for tests performed k decreases with void ratio e (or applied effective stress), and is approximated as k ¼ 10À10 m/s for Kaolinite and k ¼ 1.5 10À10 m/s for Craney Island clay b Table Physical properties of the soils in the tests Stage Confining medium Initial Kaolinite Final Craney Island Kaolinite Craney Island PVD Water content (%) Void ratio Degree of saturation (%) Unit weight (kN/m3 ) Dry unit weight (kN/m3 ) A B C D B A B C D B 86.5 90.0 90.5 87.0 92.0 40.0 38.6 38.2 38.5 38.8 2.24 2.33 2.34 2.22 2.56 1.04 1.00 0.99 1.01 1.05 100 100 100 100 98 100 100 100 100 100 14.6 14.5 14.5 14.8 14.4 17.5 17.6 17.7 17.6 18.0 7.8 7.6 7.6 7.9 7.5 12.5 12.7 12.8 12.7 12.9 Geosynthetics International, 2010, 17, No Effect of deformation of prefabricated vertical drains on discharge capacity 435 Table Properties of the PVDs tested (from manufacturers, except flexural stiffness) PVD A Dimensions Filter sleeve Core Flexural stiffness Discharge capacity Thickness (mm) Width (mm) AOS (O95 ) (ìm) Permittivity (sÀ1 ) k (m/s) Material Shape ASTM D1388 (ìJ/m) Straight (m3 /s) Kinked at 350 kPa (m3 /s) B 3.6 100 140 0.5 NA PP Continuous channel 74 111 10À6a) NA 3.2 100 180 0.7 3 10–4 PP Grooved 40 100 10À6(b) NA C D 98 , 75 1.7 1.5 10–3 PP Monofilament 34 90 10À6(c) 80 10À6 5.5 96 , 75 NA 1.5 10–3 PE Studded 2.4 10À6(d) 2.4 10À6 a At 241 kPa Not mentioned c At 350 kPa d At 750 kPa, i ¼ 0.1 NA: not available b 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 qw ¼ Q i (1) 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 substantially affect the discharge capacity To check these different interpretations, hydraulic gradients were varied from 0.1 to when measuring discharge capacity, as shown in Figure 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 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 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 (between 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 as a function of percentage settlement åv , defined as åv ¼ Vertical settlement 100% Inital height of soil specimen (2) Tests on PVD B were performed in both Kaolin and Craney Island dredgings All PVDs initially had similar discharge capacities, at approximately 120 10À6 m3 /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 shows the degree of discharge capacity reduction as a function of percentage settlement for a hydraulic gradient of 0.1 Results are similar for other hydraulic gradients tested The degree of discharge capacity reduction, Rq , in percent is defined as  qw,åv >0  Rq ¼ À 100% (3) qw,åv ¼0 where qw,åv ¼0 is the initial discharge capacity, that is, at a percentage settlement of 0, and qw,åv >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% Geosynthetics International, 2010, 17, No 436 Tran-Nguyen, Edil and Schneider 140 140 120 εv ϭ 0% Discharge capacity, qw (m3/s) (ϫ10Ϫ6) Discharge capacity, qw (m3/s) (ϫ10Ϫ6) εv ϭ 0% εv ϭ 30% εv ϭ 41.3% 100 80 60 40 20 120 εv ϭ 29% 100 εv ϭ 39.1% 80 60 40 20 0.1 0.1 Hydraulic gradient, i (a) Hydraulic gradient, i (b) 140 140 120 εv ϭ 29.3% 100 εv ϭ 38.2% εv ϭ 0% Discharge capacity, qw (m3/s) (ϫ10Ϫ6) Discharge capacity, qw (m3/s) (ϫ10Ϫ6) εv ϭ 0% 80 60 40 20 0.1 120 εv ϭ 32.6% 100 80 60 40 20 εv ϭ 22.1% 0.1 Hydraulic gradient, i (d) Hydraulic gradient, i (c) 140 Discharge capacity, qw (m3/s) (ϫ10Ϫ6) εv ϭ 0% 120 εv ϭ 25.6% εv ϭ 40.4% 100 80 60 40 20 0.1 Hydraulic gradient, i (e) Figure 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 at 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 capacity, 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 and with respect to different types of PVDs, although not shown, were similar at other gradients Geosynthetics International, 2010, 17, No Effect of deformation of prefabricated vertical drains on discharge capacity 3.0 PVD A, Kaolinite Normalized discharge capacity, qw,i /qw,1 Normalized discharge capacity, qw,i /qw,1 3.0 2.5 2.0 1.5 1.0 437 PVD B, Kaolinite 2.5 2.0 1.5 1.0 0.1 0.1 Hydraulic gradient, i (b) Hydraulic gradient, i (a) 3.0 Normalized discharge capacity, qw,i /qw,1 Normalized discharge capacity, qw,i /qw,1 3.0 PVD C, Kaolinite 2.5 2.0 1.5 1.0 0.1 PVD D, Kaolinite 2.5 2.0 1.5 1.0 0.1 Hydraulic gradient, i (c) Hydraulic gradient, i (d) Normalized discharge capacity, qw,i /qw,1 3.0 PVD B, Craney Island 2.5 2.0 1.5 1.0 0.1 Hydraulic gradient, i (e) Figure 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 3.3 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 condition The flexural stiffness of the PVDs was measured by adapting ASTM standard D1388 for measuring the flexural stiffness of geosynthetics ASTM D1388 involves measuring 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 Geosynthetics International, 2010, 17, No 438 Tran-Nguyen, Edil and Schneider Discharge capacity, qw (m3/s)(ϫ10Ϫ6) 140 PVD A, Kaolinite PVD B, Kaolinite PVD C, Kaolinite PVD D, Kaolinite PVD B, Craney Island 120 100 80 60 40 20 0 10 20 30 40 Percentage settlement, εv (%) 50 Figure Discharge capacity of the four PVDs tested under a hydraulic gradient of 0.1 as a function of percentage settlement 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 continuous 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 properties of the individual drainage channels in the crosssection 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 Rq of 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 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 Degree of reduction of discharge capacity, Rq (%) 100 80 60 40 PVD A, Kaolinite PVD B, Kaolinite 20 PVD C, Kaolinite PVD D, Kaolinite PVD B, Craney Island 0 10 20 30 Percentage settlement, εv (%) 40 50 Figure Degree of reduction of discharge capacity under a hydraulic gradient of 0.1 as a function of percentage settlement Correspondingly, 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 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 Geosynthetics International, 2010, 17, No Effect of deformation of prefabricated vertical drains on discharge capacity 439 Discharge capacity, qw (m3/s) (ϫ10Ϫ6) 140 (a) (b) 120 PVD B, Kaolinite PVD B, Craney Island 100 80 60 40 20 0 (c) 10 20 30 40 Percentage settlement, εv (%) (a) 50 Degree of reduction of discharge capacity, Rq (%) 100 (d) B, Kaolinite B, Craney Island 80 60 40 20 (e) 0 Figure 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 Although 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 consolidation occurred at a rate approximately half that of Kaolinite 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 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 10 20 30 40 Percentage settlement, εv (%) (b) 50 Figure (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 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 t¼ Th D2e ch (4) where Th is a dimensionless time factor, ch is the horizontal coefficient of consolidation of the soil [k/ (ªw mv )], and De is 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): Geosynthetics International, 2010, 17, No 440 Tran-Nguyen, Edil and Schneider 3.0 ln ð1 À U Þ F ð nÞ À8 ln ð1 À U Þ Fw nị ẳ Th ẳ (5a) Th,w (5b) 2.5 F nị ẳ ln nị n2 3n2 À À 4n2 n2 À Th,w /Th 2.0 where F(n) is a factor accounting for the well spacing, and Fw (n) adds the influence of well resistance in that expression The influence of a smear zone is not addressed in this paper, because of the way experiments were performed; 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 1.5 1.0 PVD A, Kaolinite PVD B, Kaolinite PVD C, Kaolinite PVD D, Kaolinite PVD B, Craney Island Example 0.5 (6a) % ln ð nÞ À 10 100 1000 Available discharge capacity, qw (m3/yr) (a) 104 3.0 The addition of well resistance to Equation 6a results in the expression (e.g Hansbo 1981) ! ! kh Fw ð nÞ % ln nị ỵ z2LDR zị (6b) qw 2.5 2.0 Th,w /Th 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 ! ! 2ð k h L (6c) Fw ð nÞ % ln nị ỵ DR qw PVD A, Kaolinite PVD B, Kaolinite PVD C, Kaolinite PVD D, Kaolinite PVD B, Craney Island Example 1.5 1.0 0.5 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 ln ð1 À U Þ Fw nị ẳ Th ln U Þ F ð nÞ À Á ð2ð=3ÞL2DR k h =qw Fw nị ẳ1ỵ ẳ F nị ln ð nÞ À 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 capacity and hydraulic conductivity measured in the five tests in this study, as well as an example with a particularly higher hydraulic conductivity (1 10À8 m/s) but the same discharge performance of PVD B in Craney Island dredgings A hypothetical drainage length of 20 m is used together with a spacing of 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 10 20 30 40 Percentage settlement, εv (%) (b) 50 Figure Increase in time for consolidation (Th,w /Th ) due to well resistance for a 20 m drainage length PVD with m spacing in a triangular pattern at a hydraulic gradient of 0.1: (a) as a function of available discharge capacity; (b) as a function of settlement: Example calculation used k 1028 m/s with discharge capacity based on PVD B in Craney Island soil; others used the experimentally measured values for each soil and PVD suggest that the required discharge capacity should be greater than 100 to 150 m3 /yr (3.2 10À6 to 4.8 10À6 m3 /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 reductions 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 10À8 m/s as in the example, signifi- Geosynthetics International, 2010, 17, No Effect of deformation of prefabricated vertical drains on discharge capacity cant increases in consolidation times due to well resistance are calculated for percentage settlements in excess of 30% The relationships between discharge capacity, soil hydraulic conductivity, drain geometry and spacing, and increases in consolidation time due to well resistance are specific for a given set of parameters: therefore sitespecific performance testing, such as that in the PVD-S device, is recommended SUMMARY AND CONCLUSIONS A prefabricated vertical drain-soil (PVD-S) device was developed and used to simulate the consolidation process of a soft cylindrical element of soil with a PVD at its center Five experiments were conducted, four using Kaolinite and one using Craney Island dredgings as the confining soil, with four types of PVD The following conclusions are put forward, based on the experimental results kh LDR mv n ¼ De /dw Q qw qw1 qw i qw,åv qw,åv ¼0 Rq S Th Th,w The discharge capacity for design cannot be based on the discharge capacity of a straight PVD alone for sites where large settlement is expected The discharge capacity is dependent on hydraulic gradient, as a result of non-laminar flow occurring during the discharge capacity measurements The effects of non-laminar flow were observed in all tests performed using hydraulic gradients between 0.1 and Soil and drain type strongly control the deformation patterns of PVDs during consolidation, but minimal effects on discharge capacity were observed The required discharge capacity is strongly dependent on soil type, and proportional to the horizontal coefficient of consolidation and the amount of settlement for a given load Previous recommendations of a required discharge capacity of 100 m3 /yr are considered appropriate for the soils and drains tested in this study However, this is not a general recommendation, and it should be updated based on soil conditions and drain type, as well as drain geometry and installation pattern, preferably based on the results of performance testing NOTATIONS Basic SI units are given in parentheses cv ch De dw F(n) Fw (n) i k vertical coefficient of consolidation (m2 /s) horizontal coefficient of consolidation (m2 /s) PVD influence zone (m) PVD equivalent diameter (m) factor accounting for well spacing without well resistance (dimensionless) factor accounting for well spacing with well resistance (dimensionless) hydraulic gradient (dimensionless) hydraulic conductivity (m/s) t U z ªw åv 441 horizontal hydraulic conductivity (m/s) PVD length (m) coefficient of volume compressibility (m2 /N) factor (dimensionless) discharge volume of water (m3 /s) PVD discharge capacity (m3 /s) PVD discharge capacity under a hydraulic gradient of (m3 /s) PVD discharge capacity under any hydraulic gradient less than (m3 /s) PVD discharge capacity at åv (m3 /s) PVD discharge capacity at åv ¼ (m3 /s) degree of reduction of discharge capacity (dimensionless) PVD spacing (m) horizontal time factor without well resistance (dimensionless) horizontal time factor with well resistance (dimensionless) time (s) degree of consolidation (dimensionless) depth of a layer (m) unit weight of water (N/m3 ) percentage settlement (dimensionless) soil internal friction angle (degrees) REFERENCES Aboshi, H., Sutoh, Y., Inoue, T & Shimizu, Y (2001) Kinking deformation of PVD under consolidation settlement of surrounding clay Soils and Foundations, 41, No 5, 25–32 Ali, F H (1991) The flow behavior of deformed prefabricated vertical drains Geotextiles and Geomembranes, 10, No 3, 235–248 Barron, R A (1948) Consolidation of fine-drained soils by drain wells Transactions of American Society of Civil Engineers, 113, No 2346, 718–754 Bergado, D T., Manivannan, R & Balasubramaniam, A S (1996) Proposed criteria for discharge capacity of prefabricated vertical drains Geotextiles and Geomembranes, 14, No 9, 481–505 Bo, M W., Chu, J & Choa, V (2003) Soil Improvement: Prefabricated Vertical Drain Techniques, Thompson, Singapore Chai, J.-C., Miura, N & Nomura, T (2004) Effect of hydraulic radius on long-term drainage capacity of geosynthetics drains Geotextiles and Geomembranes, 22, No 1–2, 3–16 Chang, D T T, Liao, J C & Lai, S P (1994) Laboratory study of vertical drains for a ground improvement project in Taipei Proceeding of the 5th International Conference on Geotextiles, Geomembranes and Related Products, Singapore, September 1994, Vol 2, pp 807–812 Chu, J., Bo, M W & Choa, V (2004) Practical considerations for using vertical drains in soil improvement projects Geotextiles and Geomembranes, 22, No 1–2, 101–117 Chu, J., Bo, M W & Choa, V (2006) Improvement of ultra-soft soil using prefabricated vertical drains Geotextiles and Geomembranes, 24, No 6, 339–348 Cline, M J & Burns, S E (2003) Evaluation of Wick Drain Performance in Virginia Soils, Virginia Department of Transportation, Federal Highway Administration, Washington, DC, USA Hansbo, S (1981) Consolidation of fine-grained soil by prefabricated drains Proceedings of the 10th European Conference on Soil Mechanics and Foundation Engineering, Stockholm, Sweden, 1981, Vol 3, pp 677–682 Hansbo, S (1983) How to evaluate the properties of prefabricated drains Geosynthetics International, 2010, 17, No 442 Tran-Nguyen, Edil and Schneider Proceedings of the 8th European Conference on Soil Mechanics and Foundation Engineering: Improvement of Ground, Balkema, Rotterdam, The Netherlands, Vol 2, pp 621–626 Holtz, R D (1989) Behavior of bent prefabricated vertical drains Proceedings of the 12th International Conference on Soil Mechanics and Foundation Engineering, Rio de Janeiro, Brazil, Vol 3, pp 1657–1660 Holtz, R D., Jamiolkowski, M B., Lancellotta, R & Pedroni, R (1991) Prefabricated Vertical Drains: Design and Performance, CIRIA Ground Engineering Report, Butterworth-Heinemann Ltd, London Kim, S S., Shin, H Y., Han, S J & Kim, B I (2003) The estimation of discharge capacity for vertical drain materials using composite discharge capacity apparatus Proceedings of the 13th International Offshore and Polar Engineering Conference, Honolulu, Hawaii, USA, May 2003, pp 568–572 Kremer, R., De Jager, W., Maagdenberg, A., Meyvogel, I & Oostveen, J (1982) Quality standards for vertical drains Proceedings of the 2nd International conference on Geotextiles, Las Vegas, USA, August 1982, Vol 2, pp 319–324 Kremer, R (1983) Discussion to specialty session Proceedings of the 8th European Conference on Soil Mechanics and Foundation Engineering, Helsinki, Finland, May 1983, Vol 3, pp 1235–1237 Kremer, R H J., Oostveen, J P., van Weele, A F., De Jager, W F J & Meyvogel, I J (1983) Quality of vertical drainage Proceedings of the 8th European Conference on Soil Mechanics and Foundation Engineering: Improvement of Ground, Helsinki, Finland, May 1983, Vol 2, pp 721–726 Lawrence, C A & Koerner, R M (1988) Flow behavior of kinked strip drains Proceedings of the Symposium on Geosynthetics for Soil Improvement, Nashville, TN, USA, May 1988, ASCE Geotechnical Special Publication No 18, pp 22–35 Miura, N., Chai, J C & Toyota, K (1998) Investigation on some factors affecting discharge capacity of prefabricated vertical drain Proceedings of the 6th International Conference on Geosynthetics, Atlanta, GA, USA, April 1998, Vol 2, pp 845–850 Miura, N & Chai, J C (2000) Discharge capacity of prefabricated vertical drains confined in clay Geosynthetics International, 7, No 2, 119–135 Oostveen, J P (1983) Discussion to specialty session Proceedings of the 8th European Conference on Soil Mechanics and Foundation Engineering, Helsinki, Finland, May 1983, Vol 3, pp 1152–1154 Rixner, J J., Kraemer, S R & Smith, A D (1986) Prefabricated Vertical Drains, Federal Highway Administration Report FHWA/ RD-86/168, Vols I, II and II, Federal Highway Administration, Washington, DC, USA Sasaki, S (1981) Report of Experimental Test for the Prefabricated Drain Geodrain, Tokyo Construction Co., Tokyo Stark, T D., Williamson, T A., Fowler, J., Pezza, D & Gibbons, Y (1999) Prefabricated vertical-drain test section in Craney Island dredged material management area Journal of Performance of Constructed Facilities, ASCE, 13, No 1, 8–16 The Editor welcomes discussion on all papers published in Geosynthetics International Please email your contribution to discussion@geosynthetics-international.com by 15 June 2011 Geosynthetics International, 2010, 17, No ... International, 2010, 17, No Effect of deformation of prefabricated vertical drains on discharge capacity 3.0 PVD A, Kaolinite Normalized discharge capacity, qw,i /qw,1 Normalized discharge capacity, ... conductivity of 10À8 m/s as in the example, signifi- Geosynthetics International, 2010, 17, No Effect of deformation of prefabricated vertical drains on discharge capacity cant increases in consolidation... type strongly control the deformation patterns of PVDs during consolidation, but minimal effects on discharge capacity were observed The required discharge capacity is strongly dependent on soil