Prevabricated Vertical Drain (PVD)

PREVABRICATED VERTICAL DRAIN
(PVD)
Ref: Deformation analysis in soft ground improvement by JinChun Cai
and John P Carter, 2011
Vacuum history
 Vacuum preloading method was first proposed by
professor Kjellman in 1952, small field test was
performed.
 China researchers start the research of vacuum method
in 1957, the vacuum below membrane is relative low.
 From 1980, in practical project, China realized the stable
vacuum pressure below membrane over 80Kpa or even
more.
 Also In 1982, as reported, in Japan project, the stable
vacuum pressure reached over 80Kpa.
Vacuum system
 Vacuum preloading consists of a vertical drains and
horizontal drainage system on top (usually using sand
layer with perforated pipe).
 The horizontal pipe inside the sand layer connected to a

vacuum pump. To maintain air tightness, cover the whole
system by geo-membrane with the ends of which be
placed at the bottom of a trench, then filled with low
permeable soil.
 Negative pressure is created by vacuum pump.

In the negative pressure field, water outflow of soil by
pressure difference, soil consolidates.
Schematic illustration of a PVD
A unit cell of vertical drain consolidation
PVD usually install in square or triangular

pattern with spasing S, and re is calculated:
re = 0.564 S Square pattern

re = 0.525 S Triangular patterm
FAKTOR WAKTU UNTUK KONSOLIDASI
Akibat drainasi vertikal : Akibat drainasi radial :

Tv = cvt Tv = cht
d2 4R2
S S
S d
S
R R
rd rd
R = 0.564S R = 0.525S 2rd

Pola bujur sangkar Pola segitiga 2R
Blok-blok silindris
Barron’s solution
where
t = the time after an instantaneous increase of the total vertical stress,
u = the excess pore water pressure at any point and at any given time t;
r = theradial distance of the considered point from the centre of the
soil cylinder; and
ch = the coefficient of consolidation in the horizontal direction.
where
and where n = re/rw

Hanbo’s solution
Hansbo 1981:
where μ represents the effect of the spacing between the PVDs as well as the effects
of smear and well resistance. It can be expressed as:
For an average well resistance, μ can be expressed as:
Where s = rs/rw, l = the drainage length of a PVD,

kh = the horizontal hydraulic conductivity of the native soil containing the PVD,
ks = the horizontal hydraulic conductivity of the smear zone.
Equivalent Drain Diameter
Rixner at all, 1986
where w and td are the width and thickness of the PVD, respectively. Equation (above) has
been widely used in practice and was also subsequently verified by the independent
finite element analyses conducted by Chai and Miura (1999).
Discharge Capacity of a PVD
Discharge Capacity of a PVD (2)
Miura et all, 1988 investigated factors:

(a) Confining the drain in clay (compared with confining the drain by a rubber membrane);
(b) The effect of possible air bubbles trapped in the drainage pathways;
(c) The effect of folding of the drain; and
(d) The long-term discharge capacity
The main findings from these tests are as follows.

(a) For the cases investigated, the discharge capacity observed when confining the drain in
clay for one week (i.e., a relatively short term) was only about 20% of the
corresponding value when the drain was confined by a rubber membrane. One long-
term test, which lasted for about 5months, indicated that the discharge capacity also
reduced significantly with elapsed time.
(b) Air bubbles trapped in the drainage pathways of the drain reduced the discharge
capacity by about 20%.
(c) The folding of the drain (with no kinking) combined with a vertical strain up to 20% did
not have much effect on the discharge capacity, supporting the conclusion drawn earlier
by Hansbo (1983).
Cf values for various clay deposits
The apparatus
Illustration of discharge capacity test device

Physical properties of the PVDs
Water flow versus elapsed time for
long term discharge capacity tests
(after Chai and Miura 1999)
Creep effect
Creep test results (after Chai and Miura 1999)

Concept used to calculate the reduction of
drainage area (after Chai and Miura 1999)
Reduction in cross sectional area
The reduction in cross sectional area

due to deformation (including creep)
of the filter was 4 and 17% for
PVD(A) and PVD(B), respectively.
Relationship Confining pressure (kPa) between reduction of

cross-sectional area and confining pressure (after Chai and Miura 1999)
Smear Effect (2)
Two parameters are needed to characterize the smear effect, namely the
diameter of the smear zone (ds) and the hydraulic conductivity ratio (kh/ks),
ds can usually be estimated as:
ds = (2 to 3) dm
where dm = the equivalent diameter of the cross-sectional area of a mandrel.
where subscript l represents the value determined in the laboratory,

Cf is the hydraulic conductivity ratio between field and laboratory
values. In some cases, (kh/ks)l = (kh/kv)l.
Smear Effect (3)
Modelling the smear zone around a drain (after

Chai and Miura 1999)
Smear Effect (4)
Comparison of average degree of consolidation for different assumption

regarding the shape of the smear zone (after Chai and Miura 1999)
Cf values for various clay deposits
Optimum Thickness of Unimproved Sub-layer (Hc)
Carilo 1942: Uvh = 1 − (1 − Uv) (1 − Uh)

where Uvh = the average degree of consolidation of the PVD-improved subsoil layer,
Uh = the average degree of consolidation of the layer due to radial drainage only (due
to the presence of the PVDs)
Uv = the average degree of consolidation of the layer due to vertical drainage alone.
Chai et al. 2001): Uv = 1 − exp(−CdTv)
where Tv = cvt/h2 is the time factor for vertical consolidation, cv = the coefficient of
consolidation in the vertical direction, h = the vertical drainage path length and Cd = a constant.
Illustration of improved and

unimproved layer
Effect of Cd on the degree of consolidation
(after Chai et al. 2001)
Unimproved layer
Hai etall., 2009 … H<20 m

Two-Dimensional Modelling of PVD-Improved
Soil
Methods for modelling PVD improved subsoil in two-dimensional (2D) plane strain analysis
can be classified into 4 groups.
 The first group represents the individual PVDs by solid elements and reproduces the
axisymmetric (unit cell) and plane strain responses by matching the times for 50%
consolidation by adjusting the value of the hydraulic conductivity inthe horizontal direction
assumed for plane strain (Shinsha et al. 1982; Indraratna and Redana 1997).
 The second group adopts a macro element in the FEM program to represent the hydraulic
behaviour of a PVD (Sekiguchi et al. 1986).
 The third group employs discrete 1D drainage elements to represent individual PVDs
(Hird et al. 1992; Chai et al. 1995).
 The fourth group combines the drainage effects of the PVDs and the natural soil in the
vertical direction by assuming an equivalent hydraulic conductivity in the vertical direction
for a single solid medium (Chai et al. 2001).
Approach of Shinsha et al.
where B = the half drain spacing in the plane strain model,

khp = the matched horizontal hydraulic conductivity for the plane strain case,
Thp = the time factor corresponding to the given degree of consolidation for
plane strain conditions calculated using Terzaghi’s 1D consolidation
theory with a drainage path length of B.
Illustration of S 2B modelling the effect of PVDs in plane strain analysis

One-Dimensional Drainage Elements
Hird et al. (1992) adopted a discrete one-dimensional (1D) drainage element to model
the effects of a PVD installed in soil.
where F1, F2, d, u and t = increments of nodal force, nodal flow, nodal displacement,
nodal pore water pressure and time, respectively; K = the material stiffness matrix;
L = the link (or coupling) matrix and Φ = the hydraulic conductivity matrix.
One-Dimensional Drainage Elements
Hird et al. (1992) applied Hansbo’s (1981) solution to a plane strain vertical drain.
Plane strain
unit cell
Comparison of the results of axisymmetric and matched
plane strain analyses (after Hird et al. 1992)
Modelling PVDs Using Equivalent Solid Elements
Comparison of the average degree of Comparison of normalized excess pore water

horizontal consolidation at the bottom of pressure distribution in the horizontal direction
the PVD (modified from Chai et al. 1995) (modified from Chai et al. 1995)
Axisymmetric and plane strain unit cell models (after Indraratna and
Redana 1997)
Equivalent Vertical Hydraulic Conductivity, kve
One and two way drainage conditions (after

Chai et al. 2001)
Verification of the Method
For brevity and convenience, the equivalent vertical hydraulic conductivity method
will be referred to in the following as the ‘simple method’.
Assumed 1-D
subsoil conditions (after Chai
et al. 2001)
Assumed subsoil and drain parameters
Comparison of theaverage degree of Comparison of excess pore water pressure
consolidation of uniform subsoil (after Chai et distribution of uniform subsoil (after Chai et al.
al. 2001) 2001)
Modelling a Large Scale Laboratory Test
Large scale consolidometer (after Saowapakpiboon et al. 2010). (a) Sketch;

(b) Photo of actual device
Comparison of Measurements and Numerical Simulations
The laboratory model tests were simulated using the finite element method in order to back-
analyze the parameters related to the drain performance, e.g., the smear zone parameter,
kh/ks, etc. (Saowapakpiboon et al. 2010), as well as to evaluate the effectiveness of the
various methods for modelling PVD performance. The soil sample was simulated by the
Modified Cam clay model (Roscoe and Burland 1968) and the model parameters
determined from laboratory test results are listed in Table below.
FEM meshes (after Saowapakpiboon et al. 2010). (a) Radial drainage
model; (b) Equivalent kev model
Comparison of the settlement – time curves Comparison of excess pore water pressures at
(measured data from Saowapakpiboon et al. the transducer location (measured data from
2010) Saowapakpiboon 2010)
FEM Modelling and Model Parameters
Cross-section of
embankment and location of
field instrumentation (after
Chai et al. 2001)
Finite element mesh in the analysis (after Chai et al. 2001)
Model parameter for subsoil in the test site in eastern China
Parameters related to the behaviour of PVD

Comparison of Results
Comparison of the settlement curves (after Chai

et al. 2001)
Calculated excess
pore water pressure variations
(after Chai et al. 2001)
Lateral displacement profiles (after Chai et al.
2001)
Settlement versus elapsed time
curves (Measured data from
Miyakoshi et al. 2007 modified
from Chai et al. 2010);
(a) Section-A; (b)Section-B;

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PREVABRICATED VERTICAL DRAIN

 The horizontal pipe inside the sand layer connected to a

 Negative pressure is created by vacuum pump.

PVD usually install in square or triangular

re = 0.564 S Square pattern

Akibat drainasi vertikal : Akibat drainasi radial :

R = 0.564S R = 0.525S 2rd

and where n = re/rw

For an average well resistance, μ can be expressed as:

Where s = rs/rw, l = the drainage length of a PVD,

Rixner at all, 1986

Miura et all, 1988 investigated factors:

The main findings from these tests are as follows.

Illustration of discharge capacity test device

Creep test results (after Chai and Miura 1999)

The reduction in cross sectional area

Relationship Confining pressure (kPa) between reduction of

where subscript l represents the value determined in the laboratory,

Modelling the smear zone around a drain (after

Comparison of average degree of consolidation for different assumption

Carilo 1942: Uvh = 1 − (1 − Uv) (1 − Uh)

Illustration of improved and

Hai etall., 2009 … H<20 m

where B = the half drain spacing in the plane strain model,

Illustration of S 2B modelling the effect of PVDs in plane strain analysis

Comparison of the average degree of Comparison of normalized excess pore water

One and two way drainage conditions (after

Large scale consolidometer (after Saowapakpiboon et al. 2010). (a) Sketch;

Parameters related to the behaviour of PVD

Comparison of the settlement curves (after Chai

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