Preloading and vertical drains
T. Stapelfeldt
Helsinki University of Technology
ABSTRACT: This report has been done at the Laboratory of Soil Mechanics and Foundation
Engineering of Helsinki University of Technology as part of the licentiate seminar of geotechnics
and it deals with the soil improvement by preloading techniques and the utilisation of vertical
drains.
The purpose of preloading and vertical drains is to increase the shear strength of the soil, to
reduce the soil compressibility and to reduce the permeability of the soil prior to construction and
placement of the final construction load and prevent large and/or differential settlements and
potential damages to the structures.
In this report preloading techniques and the usage of vertical drains are described. It introduces
installation methods of drains and possible influences of the drain efficiency. In addition, methods
for assessing the effectiveness of soil improvement are described.
1 INTRODUCTION
In times of urbanization, growth of population and associated developments, construction activities
are more and more focused on soils which were considered unsuitable in the past decades. These
soft soil deposits have a low bearing capacity and exhibit large settlements when subjected to
loading. It is therefore inevitable to treat soft soil deposits prior to construction activities in order to
prevent differential settlements and subsequently potential damages to structures.
Different ground improvement techniques are available today. Every technique should lead to
an increase of soil shear strength, a reduction of soil compressibility and a reduction of soil
permeability. The choice of ground improvement technique depends on geological formation of the
soil, soil characteristics, cost, availability of backfill material and experience in the past. According
to Bergado et al. (1996) they can be divided broadly into two categories. The first category includes
techniques which require foreign materials and utilisation of reinforcements. They are based on
stiffening columns either by the use of a granular fill (stone columns), by piling elements which are
not reaching a still soil stratum (creep piles) or by in situ mixing of the soil with chemical agents
(deep stabilisation). The second category includes methods which are strengthening the soil by
dewatering, i.e. preloading techniques often combined with vertical drains.
This report will focus on preloading techniques and utilisation of vertical drains. Preloading is
the application of surcharge load on the site prior to construction of the permanent structure, until
most of the primary settlement has occurred. Since compressible soils are usually characterized by
very low permeability, the time needed for the desired consolidation can be very long, even with
very high surcharge load. Therefore, the application of preloading alone may not be feasible with
tight construction schedules and hence, a system of vertical drains is often introduced to achieve
accelerated radial drainage and consolidation by reducing the length of the drainage paths.
T. Stapelfeldt, Preloading and vertical drains. 1
Although preloading and vertical drains are very close connected, in this work it is tried to treat
them separately. In chapter 2, the common methods of preloading are described. These methods are
conventional preloading, e. g. by means of an embankment, and vacuum induced preloading.
Chapter 3 focuses on the usage of vertical drains and mainly on prefabricated vertical drains.
The installation methods are described and the drain properties are introduced. Then, factors
influencing the drain efficiency, such as the smear zone, are discussed. Furthermore, the influence
zone of drains is described and theory of vertical drains is briefly presented.
In order to assess the effectiveness of soil improvement work, the degree of consolidation is
commonly used. The degree of consolidation can be calculated by different methods using field
measurements. In chapter 4 two of these methods are presented.
Preloading will not only cause settlement of the soft subsoil but also lateral displacements.
Chapter 5 deals with these issues.
2 PRELOADING TECHNIQUES
Preloading generally refers to the process of compressing the soil under applied vertical stress prior
to construction and placement of the final construction load. The two common preloading
techniques are conventional preloading, e. g. by means of an embankment, and vacuum induced
preloading.
2.1 Conventional preloading
The simplest solution of preloading is a preload, e. g. by means of an embankment. When the load
is placed on the soft soil, it is initially carried by the pore water. When the soil is not very
permeable, which is normally the case, the water pressure will decrease gradually because the pore
water is only able to flow away very slowly in vertical direction. In order not to create any stability
problems, the load must mostly be placed in two or more stages.
The principle is shown in Figure 1. If the temporary load exceeds the final construction load, the
excess refers to as surcharge load.
Figure 1: Preloading of subsoil
The temporary surcharge can be removed when the settlements exceeds the predicted final
settlement. This should preferably not happen before the remaining excess pore pressure is below
the stress increase caused by the temporary surcharge. By increasing the time of temporary
overloading, or the size of the overload, secondary settlement can be reduced or even eliminated
(see Figure 2). This is because by using a surcharge higher than the work load, the soil will always
be in an overconsolidated state and the secondary compression for overconsolidated soil is much
smaller than that of normally consolidated soil. This will benefit greatly the subsequent
geotechnical design (Chu et al., 2004).
T. Stapelfeldt, Preloading and vertical drains. 2
Load
Surcharge
Design load
Time
Settlement
„Final“ settlement for design load
Figure 2: Resulting settlement due to preloading
2.2 Vacuum preloading
Sometimes it is not feasible to place a fill embankment because the soft soil might be sometimes so
weak that even a common 1.5 m embankment might already cause stability problems. Then it can
be suitable to use the method of vacuum preloading.
In 1952 Kjellman was the first who introduced vacuum preloading to accelerate consolidation.
In vacuum consolidation the surcharge load is replace by atmospheric pressure.
In its simplest form the method of vacuum consolidation consists of a system of vertical drains
and a drainage layer (sand) on top. It is sealed from atmosphere by an impervious membrane.
Horizontal drains are installed in the drainage layer and connected to a vacuum pump. To maintain
air tightness, the ends of the membrane are placed at the bottom of a peripherical trench filled e. g.
with bentonite. Negative pressure is created in the drainage layer by means of the vacuum pump
(Figure 3). The applied negative pressure generates negative pore water pressures, resulting in an
increase in effective stress in the soil, which in turn is leading to an accelerated consolidation.
Figure 3: Vacuum system (after Masse et al., 2001)
T. Stapelfeldt, Preloading and vertical drains. 3
The common advantages of vacuum preloading are that there is no extra fill material needed, the
construction times are generally shorter and it requires no heavy machinery. Moreover, no
chemical admixtures will penetrate into the ground and thus it is an environmental friendly ground
improvement method (Chai, 2005).
Further advantages of the method are that isotropic consolidation eliminates the risk of failure
under additional loading of the permanent construction, there is no risk of slope instability beyond
boundaries and it allows a controlled rate and magnitude of loading and settlement (Masse et al.,
2001).
Possible problems associated with vacuum preloading are (Masse et al. 2001):
• To maintain an effective drainage system under the membrane that expels water and air
throughout the whole pumping duration.
• Keeping a non-water saturated medium below the membrane.
• To maintain an effective level of vacuum.
• To maintain a leak proof system in particular at the pumps / membrane connections and over the
entire membrane area.
• Anchoring and sealing of the system at the periphery.
• Reducing lateral seepage towards the vacuum area
According to Masse et al., (2001), unsuccessful attempts have been recorded in the past for
technological reasons. However, a major obstacle to development of vacuum based consolidation is
the lack of understanding of its basic principles.
2.3 Principles of preloading
Figure 4 illustrates schematically a vertical stress profile when a vacuum load (assuming 100 %
efficiency) is applied to the ground surface in comparison with initial conditions and conventional
surcharge.
Atmospheric pressure is generally a not varying parameter in geotechnics. Since soil stress
calculations are normally based on effective stresses, atmospheric pressure can be disregarded in
calculations. Considering atmospheric pressure, the effective stress state in initial conditions can be
written as follows:
σ´ = σ - u = (Pa + γ·h) – (Pa + γw·h)
(1)
where: σ´ = vertical effective stress, σ = total vertical stress, u = pore water pressure,
Pa = atmospheric pressure, γ = unit weight of soil, γw = unit weight of water and h = depth of soil
layer.
In case of a conventional surcharge, the total stress will increase due to the additional load and
thus, the effective stress will increase as well, whereas the pore water pressure remains unchanged.
In case of vacuum surcharge, the total vertical stress remains unchanged and the increase in
effective stress is due to a reduction of pore water pressure, i. e. applying negative pressure.
T. Stapelfeldt, Preloading and vertical drains. 4
Figure 4: Vertical stress profiles: (a) initial in situ conditions, (b) conventional surcharge and (c) vacuuminduced surcharge (after Elgamal and Adalier, 1996)
In terms of stress path distributions, the stress state can be described in triaxial space with mean
effective stress p´ and the deviator stress q, defined as:
q = σ ´1 −σ ´3
p´=
1
(σ ´1 +2σ ´3 )
3
(2)
(3)
where σ′1 and σ′3 are the principal normal stresses.
In Figure 5 different stress paths are described. Starting from an in situ stress state at point A, the
curve ABC describes the case of conventional preloading. When the fill is placed, it follows curve
AB with a possible failure if point B would cross the failure line Kf. Consolidation will take place
from B to C in the area of εh > 0 above the K0-line and hence, outward lateral deformation will
occur.
Line AD corresponds to oedometric consolidation. As for vacuum induced preloading, the stress
path follows the line AE. This is due to the fact that, during vacuum consolidation, the soil is under
quasi isotropic conditions and thus the principal normal stresses are equal. It can be seen that the
entire stress path is under the K0-line with the field of εh < 0 and hence under horizontal
compression or inward lateral displacement respectively.
T. Stapelfeldt, Preloading and vertical drains. 5
Figure 5: (p´, q) – diagram
3 VERTICAL DRAINS
3.1 General
Because of its low permeability, the consolidation settlement of soft clays takes a long time to
complete. To shorten the consolidation time, vertical drains are installed together with preloading
either by an embankment or by means of vacuum pressure. Vertical drains are artificially-created
drainage paths which are inserted into the soft clay subsoil. Thus, the pore water squeezed out
during consolidation of the clay due to the hydraulic gradients created by the preloading, can flow
faster in the horizontal direction towards the vertical drains. It is taken advantage of the fact, that
most clay deposits exhibit a higher horizontal permeability compared to the vertical. Subsequently,
these pore water can flow freely along the vertical drains vertically towards the permeable layers.
Therefore, the vertical drain installation reduces the length of the drainage path and, consequently,
accelerates the consolidation process and allows the clay to gain rapid strength increase to carry the
new load by its own (see Figure 6).
Figure 6: Preloading with vertical drains
In the 1930´s the first reasonable application of vertical sand drains was made in California. In
Sweden, during the same decade, Kjellman introduced the first prototype of a prefabricated vertical
drain made entirely of cardboard (Jamiolkowski et al., 1983). Subsequently, several types of
prefabricated vertical drains were developed which are basically consisting of a plastic core with a
T. Stapelfeldt, Preloading and vertical drains. 6
longitudinal channel wick functioning as a drain, and a sleeve of paper of fibrous material as a filter
protecting the core.
3.2 Types of vertical
In Table 1 different types of vertical drains with respect to their installation methods are shown.
Table 1: Types of vertical drains (after Holtz et al., 1991)
Drain type
Installation method
Drain
diameter [m]
Sand drain
Sand drain
Sand drain
Prefabricated
sand drains
(“sandwicks”)
Prefabricated
band-shaped
drains
Driven
or
vibratory
closed-end
mandrel
(displacement type)
Hollow stem continuousflight
auger
(low
displacement)
Jetted (non-displacement)
Driven
or
vibratory
closed-end
mandrel;
flight auger; rotary wash
boring (displacement or
non-displacement)
Driven
or
vibratory
closed-end
mandrel
(displacement or low
displacement)
Maximum
length [m]
0,15 - 0,6
Typical
spacing
[m]
1-5
≤ 30
0,3 - 0,5
2-5
≤ 35
0,2 - 0,3
0,06 - 0,15
2-5
1,2 - 4
≤ 30
≤ 30
0,05 - 0,1
(equivalent
diameter)
1,2 - 3,5
≤ 60
Sand drains are basically boreholes filled with sand. As for the displacement type of sand drains, a
closed mandrel is driven or pushed into the ground with resulting displacement in both vertical and
horizontal directions. The installation causes therefore disturbances, especially in soft and sensitive
clays, which reduces the shear strength and horizontal permeability.
The low- or non-displacement installations are considered to have less disturbing effects on the
soil. Drilling of the hole is done by means of an auger or water jets. In terms of jetting, however,
installation is very complex (Holtz et al., 1991).
Some disadvantages of sand drains are (Yeung, 1997):
• To receive adequate drainage properties, sand has to be carefully chosen which might seldom be
found close to the construction site.
• Drains might become discontinuous because of careless installation or horizontal soil
displacement during the consolidation process.
• During filling bulking of the sand might appear which could lead to cavities and subsequently to
collapse due to flooding.
• Construction problems and/or budgetary burdens might arise due to the large diameter of sand
drains.
• The disturbance of the soil surrounding each drain caused by installation may reduce the
permeability, the flow of water of water to the drain and thus the efficiency of the system.
• The reinforcing effect of sand drains may reduce the effectiveness of preloading the subsoil
The installation of prefabricated vertical drains is also done by a mandrel and it is a displacement
installation. Figure 7 shows a typical mandrel and the typical shape of a prefabricated drain. The
dimensions of the prefabricated drains are much smaller compared to sand drains (see Table 1) and
subsequently are the dimensions of the mandrel. Thus, the degree of soil disturbance caused by the
size of the mandrel during installations is lower.
T. Stapelfeldt, Preloading and vertical drains. 7
Figure 7: Typical mandrel and shape of a prefabricated drain (Mebradrain)
At the tip of the mandrel is detachable shoe or anchor made of a small piece of metal (see Figure
8). Sometimes it might also be a piece of drain itself (Holtz et al., 1991). The purpose of the anchor
is to prevent soil from entering the mandrel and plugging it during penetration. It also keeps the
drain at the desired depth as the mandrel is withdrawn.
Figure 8: Drain, mandrel and anchor plate (Cramer, undated)
3.3 Drain properties
3.3.1 Equivalent diameter for band-shaped drains
The conventional theory of consolidation with vertical drains assumes that the vertical drains are
circular in their cross-section. Since most of the prefabricated drains are rectangular in crosssection (band-shaped), the rectangular drain has to be converted into an equivalent cylindrical
shape. That implies that the equivalent diameter has the same theoretical radial drainage capacity as
the band-shaped drain. Hansbo (1979) suggested that both band-shaped and circular drains lead to
practically same degree of consolidation if their circumferences are equal. Hence, the equivalent
diameter (dw) of a band-shaped drain with width (a) and thickness (b) (see Figure 9) can be
expressed by:
dw =
2( a + b )
π
T. Stapelfeldt, Preloading and vertical drains. 8
(4)
Figure 9: A typical cross-section of a band-shaped drain (Holtz et al., 1991)
3.3.2 Discharge capacity
The purpose of using prefabricated vertical drains is to release the excess pore water pressure in
soil and discharge water. Therefore, the higher the discharge capacity of the vertical drains the
better the performance of them. The discharge capacity is required to analyse the drain (well)
resistance factor. However, well resistance is always less significant than drain spacing and the
disturbance (smear effect).
Once the water has entered the drain, it is still possible for the flow in the drain itself to be
reduced for a number of reasons. The discharge capacity depends on the following factors
(Bergado et al., 1996):
• Lateral earth pressure: By increasing lateral pressure, the filter passes into the core and
subsequently decreases the discharge capacity due to a reduction of the cross-sectional area
available for flow.
• Large settlements: During consolidation, the ground will be subjected to large settlements.
Thus, the drains tend to settle together with the ground which will result in bending of folding
of the drain (see Figure 10).
• Clogging of drain: In the initial filtering process of flow from the soil through the drain filter,
the displaced water will contain a small portion of fine particles. These may be deposited with
the core channels and may lead to clogging of the drain.
• Time: The discharge capacity may be reduced due to aging in the soil after installation, possibly
due to biological and chemical activities.
• Hydraulic gradient: The measured discharge capacity varies with different hydraulic gradients
and is smaller when a higher hydraulic gradient is used. This might be due to the loss of flow
energy as a result of turbulent flow at a high hydraulic gradient.
T. Stapelfeldt, Preloading and vertical drains. 9
Figure 10: Folded drain
3.3.3 Properties of the filter
In general, the drain material of a sand drain and the filter jacket of a prefabricated drain have to
perform two basic but contrasting requirements, which are retaining the soil particles and at the
same time allowing the pore water to pass through.
According to Hansbo (1979, 1994), the filter has to meet the following requirements:
• the permeability of the filter should be high enough not to influence the discharge capacity of
the drain system,
• on the contrary, the permeability of the filter should be low enough to retain fine soil particles.
The soil particles might penetrate through the filter into the core, which eventually might be
filled with soil and get clogged,
• the filter needs to be strong enough to withstand high lateral pressure in order not to be
squeezed into channel system of the core
• the filter should be strong enough not to break during installation, and
• the filter should not deteriorate with time because this would reduce the discharge capacity of
the drain.
An example of filter function is illustrated in Figure 11.
Figure 11: Example of filter function (Mebradrain)
T. Stapelfeldt, Preloading and vertical drains. 10
In order to meet the above mentioned requirements, there are basic filter design criteria that have to
be satisfied.
• Soil retention ability:
The first criterion is that the Apparent Opening Size (AOS) has to be sufficiently small so that it
can prevent clay particles from penetrating through the filter into drain. On the other hand, the AOS
cannot be too small as the filter has to provide a sufficient permeability. A commonly used
criterion is the following (Chu et al., 2004):
O95 ≤ ( 2 − 3 )D85
(5)
and
O50 ≤ ( 10 − 12 )D50
(6)
where:
O95 is the AOS of the filter (i.e. 95 % of the openings in the geotextile are smaller).
O95 ≤ 0,075 mm is often specified for vertical drains.
O50 is the size which is larger than 50 % of the fabric pores.
D85 is the particle diameter for which 85 % of the soil particles are smaller.
D50 is the particle diameter for which 50 % of the soil particles are smaller.
• Permeability:
The second criterion is that the permeability of the filter has to be sufficiently large. It should be at
least one order of magnitude higher than that of the soil. As the soil to be treated by prefabricated
vertical drains usually has a very low permeability, this requirement should be met in most cases
(Chu et al., 2004).
k f ≥ 10k S
(7)
where:
kf is the permeability of the filter and kS is the permeability of the soil.
• Mechanical properties of the filter and the core
Prefabricated vertical drains should have adequate strength to sustain the tensile stresses subjected
to it during the installation process. Theses forces are mainly tensile, partly from the drain’s self
weight and partly from friction between the drain and the installation equipment. According to
Kremer et al. (1983), the maximum tensile force develops when the mandrel accelerates and at the
start of the penetration or after slowing because of passing an obstacle or a resistant soil layer.
Therefore, the core, the strength of filter, strength of the entire drain and strength of the spliced
drain should be specified in both wet and dry conditions.
The drain is pulled from a rotating drum (which usually contains a considerable length of drain)
by the penetrating mandrel, while this drain is guided by one or more horizontally placed cylinders.
Thus, the drain has to be able to withstand certain tensile forces in combination with a minimum
curvature because of the orientation of the guides (cylinders). If vibratory equipment is used for
installation, the drain is also subjected to vibratory forces.
Recommendations in terms of tensile strength of the entire drain were given by Kremer et al.
(1983) which are based on tests on unused drain samples with a length of 350 mm. They are as
follows:
• The longitudinal tensile strength of any of the drain components should be at least 0,5 kN.
• The longitudinal strain at failure should be ≥ 2 % but ≤ 10 %.
• Any seams in the drain filter should have equal or better properties.
T. Stapelfeldt, Preloading and vertical drains. 11
The criteria of a tensile load of 0,5 kN and a strain ε = 2 % are based on estimates of the tensile
forces and strains in the drain which may occur during the installation procedure. The maximum
longitudinal strain of ε = 10 % is required in order to limit the deformation of the drain during
installation. Large deformations may lead to unwanted decreases in width or thickness of the drain.
Some results of tensile tests are illustrated Figure 12.
Figure 12: Results of tension tests on complete specimens of different drains (Kremer et al., 1983)
However, it is quite common nowadays to specify the tensile strength of the whole drain at both
wet and dry conditions to be larger than 1 kN at a tensile strain of 10 % (Chu et al., 2004).
That can be supported by field measurements carried out by Karunaratne et al. (2003). They
instrumented prefabricated vertical drains with strain gauges, as schematically shown in Figure 13.
Generally, the duration of the insertion of the mandrel for a typical prefabricated vertical drain
installation in a 25-30 m depth is about 20-25 s and additionally withdrawal is requiring another
30 s. For safety reasons, the installation speed was slowed down. Figure 13 illustrates the tension
measured by the two strain gauges. The tension measured in strain gauge A increased gradually
with installation depth to about 800 N during 93 s. The drain anchored at about 24 m depth and the
mandrel was held stationary for about 163 s. Tension still increased until the mandrel was
withdrawn although the drain was free to roll off from the drum. A sharp increase in tension up to
1000 N was then recorded as the mandrel was withdrawn, which dropped within the following 46 s.
Finally, the tension continued to decrease to a residual value, which practically stayed constant
until the end of monitoring. In contrast, the tension measured in strain gauge B was smaller
throughout the installation but began to increase even after cutting the drain.
A second test was carried out with normal installation speed. The measurements indicate the
almost the same results as in the first test until end of insertion. However, during withdrawal the
stain gauges cables were cut and no data could be recorded.
T. Stapelfeldt, Preloading and vertical drains. 12
Figure 13: Location of strain gauges and measurement of forces during installation and withdrawal of
mandrel (after Karunaratne et al., 2003)
3.4 Factors influencing the drain efficiency
3.4.1 Smear effect
The installation of vertical drains by means of a mandrel causes significant remoulding of the
subsoil, especially adjacent to the mandrel. Hence, a zone of smear will be developed with reduced
permeability and increased compressibility. In varved soils the finer and more impervious layers
will be dragged down and smeared over the more pervious layers (Barron, 1948). The smear zone
creates additional resistance which must be overcome by the excess water. This, in turn, will retard
the rate of consolidation.
The behaviour of permeability and compressibility within the smear zone is different than the
behaviour of the undisturbed soil, hence, the behaviour of soil stabilised with vertical drains can
not be predicted accurately if the effect of smear is ignored. Both Barron (1948) and Hansbo (1981)
modelled the smear zone by dividing the soil cylinder dewatered by the central drain into two
zones. The smear zone is the zone in the immediate vicinity of the drain and the other is the
undisturbed zone (see Figure 14).
Figure 14: Smear effect (Hansbo 1994)
T. Stapelfeldt, Preloading and vertical drains. 13
The degree of disturbance depends on several factors which are described below:
• Installation procedure:
Different relationships have been proposed to determine the size of the smear zone. For design
purposes Jamiolkowski and Lancellotta (1981) proposed that the diameter of the smear zone (ds)
and the cross sectional area of the mandrel can be related as:
ds =
(5 − 6) d m
2
(8)
where (dm) is the diameter of a circle with an area equal to the cross sectional area of the mandrel
or the cross sectional area of the anchor at the tip, which ever is greater. At this diameter, the
theoretical shear strain is approximately 5 % as shown in Figure 15.
Figure 15: Approximation of disturbed zone around the mandrel (from Bergado et al., 1996)
Based on laboratory investigations, Indraratna and Redana (1998) estimated the ratio of (ds / dm) to
be four to five.
• Soil structure:
For soil with pronounced anisotropy, the ratio of horizontal permeability to vertical permeability
(kh / kv) can be very high, whereas the ratio (kh / kv) becomes unity within the disturbed zone.
The ratio of horizontal to vertical permeability was also studied by Indraratna and Redana
(1998). It was measured that the coefficient of horizontal permeability becomes smaller towards the
drain but the coefficient of vertical permeability remains almost unchanged.
T. Stapelfeldt, Preloading and vertical drains. 14
Figure 16: Horizontal permeability (left; a), vertical permeability (left; b) and ratio of (kh / kv) (right) along
radial distance from central drain (Indraratna and Redana, 1998)
The ratio of (kh / kv) outside the smear zone approaches a value of 2, whereas inside the smear zone
the value has an average of 1,15. Thus it is close to unity and the permeability of the smear zone
can be put equal to the vertical permeability of the undisturbed zone.
• Size and shape of mandrel:
In general, the disturbances increase with increasing cross sectional area of the mandrel. Therefore,
in order to reduce disturbances, the mandrel size should be as close as possible to that of the drain.
Bergado et al. (1996) reported from a case study where the installation of drains was carried out
using a small mandrel in one half of the site and a large mandrel in the other half. The results
indicated a faster settlement rate and a slightly higher compression in the small mandrel area. That
would verify that a smaller smear zone was developed in the vicinity of the smaller mandrel.
3.4.2 Well resistance
The relevant features for the design and performance of vertical drains are their hydraulic properties: the discharge capacity of the cross-section and their filter permeability. If during the consolidation period the discharge capacity of the drain is reached, the overall consolidation process is
retarded. In such cases, the drains exhibit a resistance to water flow into them which known as well
resistance. It can develop and increase as the deterioration of the drain filter may lead to a
significant reduction of the cross-section. Furthermore, fine soil particles may pass through the
filter and decrease the area available for flow. Finally, folding of the drain because of large
settlements may result in a reduced discharge capacity (Holtz et al., 1991). It is suggested that as
long as the working discharge capacity of a prefabricated vertical drain exceeds 100-150 m³ / year,
the effect on consolidation due to well resistance may not be significant.
According to Chu et al. (2004), the well resistance is not only controlled by the factors
mentioned above, but also by the permeability of the soil and the maximum discharge length. As it
can be seen from Figure 17, the required discharge capacity is dependent on the maximum
discharge length and permeability of the soil. If the drainage length is changing, the required
discharge capacity may change significantly. The same occurs if the permeability is not determined
accurately. In these cases some drains may not be able to meet the requirements anymore.
T. Stapelfeldt, Preloading and vertical drains. 15
Figure 17: Required discharge capacity as a function of drain length and permeability of the soil
3.5 Influence zone of vertical drains
Vertical drains are commonly installed in square or triangular patterns as illustrated in Figure 18.
The influence zone of the drain (R) is a controlled variable, since it is a function of drain spacing
(S) as given by:
R = 0,546 ⋅ S
(9)
for drains installed in a square pattern and
R = 0,525 ⋅ S
(10)
for drains installed in a triangular pattern
The square pattern is more convenient to lay out and to control in the field. However, a triangular
pattern is usually preferred since it provides a more uniform consolidation between drains than the
square pattern (Holtz et al., 1991).
S
S
S
S
R
R
Drains
R = 0,546 S
R = 0,525 S
Square pattern
Triangular pattern
Figure 18: Plan of drain pattern und and zone of influence of each drain
T. Stapelfeldt, Preloading and vertical drains. 16
3.6 Theory of Vertical Drains
The basic theory of radial consolidation around a vertical drain system is an extension of the
classical one-dimensional consolidation theory.
Barron (1948) studied the two extreme cases of free strain and equal strain and showed that the
average consolidation obtained in both cases are nearly the same. The “free stain hypothesis”
assumes that the load is uniform over a circular zone of influence for each vertical drain, and that
the differential settlements occurring over this zone have no effect on the redistribution of stresses
by arching of the fill load. The “equal strain hypothesis” on the other hand assumes that the load
applied is rigid and equal vertical displacement in enforced at the surface, i.e. horizontal sections
remain horizontal. The solution for the second case is considerably simpler (Barron 1948).
3.6.1 Equal vertical strain hypothesis (Barron, 1948)
Barron developed a solution of the horizontal consolidation under ideal conditions using an
axisymmetric unit cell model (see Figure 19). The solution is based on the following assumptions:
• All vertical load are initially carried by excess pore pressure, thus the soil is saturated.
• The applied load is assumed to be uniformly distributed and all strains occur in vertical
direction.
• The zone of influence of the drain is assumed to be circular and axisymmetric.
• The permeability of the drain is infinite in comparison with that of the soil.
• Darcy’s law is valid.
Figure 19: Assumption soil cylinder under ideal conditions (Holtz et al., 1991)
For radial flow only, the differential equation governing the consolidation is given by:
∂u
 1 ∂u ∂ 2 u 
= ch 
+ 2
∂t
 r ∂r ∂r 
(11)
where u is the excess pore pressure at any point and at any time t, r is the radial distance of the
considered point from the centre of the drained cylinder and ch is the horizontal coefficient of
consolidation.
Under ideal conditions (no smear effect and no well resistance), the average degree of
consolidation for radial drainage is as follows:
 − 8Th 

U h = 1 − exp
 µ 
with
T. Stapelfeldt, Preloading and vertical drains. 17
(12)
Th =
ch t
De
(13)
n2
3n 2 − 1
ln(
n
)
−
n2 − 1
4n 2
(14)
and
µ=
where De is the diameter of the equivalent soil cylinder, dw is the equivalent diameter of the drain
and n (n = De / dw) is the spacing ratio.
3.6.2 Approximate equal strain hypothesis (Hansbo, 1981)
Hansbo (1981) derived an approximate solution for vertical drain based on the “equal strain
hypothesis” to take both a zone of smear with a reduced permeability and well resistance into
consideration.
By applying Darcy’s law, the rate of flow of internal pore water in the radial direction can be
estimated. The total flow of water from slice, dz, to the drain, dQ1, is equal to the change of flow of
water from the surrounding soil, dQ2, which is proportional to the change of volume of the soil
mass (see Figure 20).
Figure 20: A vertical drain including smear and well resistance (Holtz et al., 1991)
The average degree of consolidation is then given by
 − 8Tr 
U r = 1 − exp

 F 
(15)
where (in a simplified form)
k
n  k 
F = F ( n ) + Fs + Fr = ln  +  h  ln( s ) − 0 ,75 + πz( 2l − z 2 ) h
qw
 s   kw 
(16)
and F(n) is the drain spacing factor, Fs the smear effect, Fr the well resistance, kh is the horizontal
permeability, kw reduced permeability in the smear zone and s is given by s = rs / rw.
For smear effect only, the parameter is given by
T. Stapelfeldt, Preloading and vertical drains. 18
n  k
F = F ( n ) + Fs = ln  +  h
 s   kw

 ln( s ) − 0,75

(17)
In case of a perfect drain, the parameter reduces to
F = F ( n ) = ln(n ) − 0,75
(18)
4 ESTIMATION OF THE DEGREE OF CONSOLIDATION
The degree of consolidation is usually used as one of the criteria for assessing the effectiveness of
soil improvement work using the fill surcharge or vacuum preloading method. It is also often used
as a design specification (Chu and Yan, 2005). The degree of consolidation is normally calculated
as the ratio of the current settlement to the ultimate settlement. However, for a soil improvement
project, the ultimate settlement is unknown and has to be predicted.
There are different methods available to estimate the ultimate settlement and the degree of
consolidation. One of these methods is the Asaoka method:
The Asaoka method (Asaoka, 1978) is a method of settlement observation for one-dimensional
consolidation in which earlier observations are used to predict the ultimate primary settlement. If
necessary, the in situ coefficient of consolidation can also be backcalculated after the analysis. The
main advantage of this method is its simplicity. In common settlement analysis conditions such as
the initial distribution of the excess pore pressure, the drain length, the final vertical strain of soils
and the coefficient of consolidation are considered to be given in advance of the analysis. It is
known that these estimations are quite uncertain. For the Asaoka method neither determination of
soil properties nor measuring of the field pore pressure behaviour is needed.
Asaoka showed that one-dimensional consolidation settlements at certain time intervals could
be described as a first order approximation:
Sn = β 0 + β1 ⋅ S n −1
(19)
where S1, S2, …, Sn are settlements observations. Sn denotes the settlement at time tn. The time
interval ∆t = (tn - tn-1) is constant. The first order approximation should represent a straight line on a
(Sn vs Sn-1)-co-ordinate. The values of β0 and β1 are given by the intercept of the fitted straight line
with the Sn - axis and the slope. The ultimate primary settlement can be calculated with the
expression:
S ult =
β0
1− β1
(20)
which also describes the intercepting point with a 45°-line because Sult is given by Sn=Sn-1.
According to the above mentioned, the graphical method can be described as follows (see Figure
21):
• From the time/settlement curve take a series of Sn values.
• From those values plot the points on a (Sn vs Sn-1) co-ordinate.
• Find the values β0 and β1 and the intercepting point with the 45°-line to determine the ultimate
primary settlement.
T. Stapelfeldt, Preloading and vertical drains. 19
Figure 21: Asaoka method
Besides one-dimensional consolidation, the Asaoka method assumes a constant load and
homogeneous soil. If these assumptions are not fulfilled observational data may have an initial or
final upward curvature like Figure 22 shows.
Figure 22: Possible initial and final upward curvature (Holtz et al. 1991)
Tan and Chew (1996) showed in their article that settlement data from 0-30 % consolidation give
low estimates of ultimate primary settlement and overestimates of the coefficient of consolidation.
Results from 30-60 % consolidation underestimate the ultimate primary settlement by about 10 %
and overestimates the coefficient of consolidation by about 30%. Only data beyond 60 %
consolidation give accurate values of ultimate primary consolidation and the in situ coefficient of
consolidation. The Asaoka method is also strongly dependent on the used time interval.
T. Stapelfeldt, Preloading and vertical drains. 20
In case of staged construction and when a large increment of surcharge load is applied, there is
normally an obvious increase in the gradient of the settlement-time curve. In order to determine the
ultimate settlement under these conditions, data obtained from the final stage of loading should be
used (Asaoka, 1978).
Another possibility of assessing the degree of consolidation is based on pore water pressure
measurements (Chu and Yan, 2005). To estimate an average degree of consolidation, the pore
water distribution over the entire soil depth needs to be established. As a schematic illustration
serves Figure 23, where a combined fill surcharge and vacuum load is considered.
Figure 23: Pore water pressure distribution under combined surcharge and vacuum load
According to Figure 23, the average degree of consolidation can be calculated as
U avg = 1 −
∫ [u ( z ) − u ( z )]dz
∫ [u ( z ) − u ( z )]dz
t
s
0
s
(21)
where
us ( z ) = γ w z − s
(22)
and u0 (z) = initial pore water pressure at depth z; ut (z) = pore water pressure at depth z and at time
t; us (z) = suction line; γw = unit weight of water; s = suction applied.
According to (Chu and Yan, 2005), this method has the several advantages compared to the
method using settlement data:
• It relies on field pore pressure data, whereas using settlement data, the ultimate settlement has to
be predicted.
• The degree of consolidation can be calculated at any time during consolidation process.
• Although it is difficult to carry out, in multilayered soils the degree of consolidation can be
calculated for one particular layer.
However, the method using pore pressure data tends to underestimate, whereas the method using
settlement data tends to overestimate the degree of consolidation. Therefore, it is recommended to
use both methods when calculating the degree of consolidation.
These problems have also been observed by Hansbo (1997). The factors for the differences
might be as follows (Yan and Chu, 2005):
T. Stapelfeldt, Preloading and vertical drains. 21
• Measurements were conducted at specific points only.
• Involved uncertainties in the prediction of ultimate settlement, such as measurements of initial
settlements or affection of measurements by secondary compression.
• The excess pore pressure may be maintained at higher levels due to the compression and
rearrangement of the soil structure.
5 GROUND DEFORMATION CAUSED BY PRELOADING
Preloading by an embankment will not only cause settlement of the soft subsoil but also generally
outward lateral displacement. This lateral displacement is mainly caused by the shear stresses
induced by the embankment load, and if these shear stresses are big enough they will cause shear
failure within the subsoil (see Figure 24). By contrast, the vacuum pressure technique tends to
apply an isotropic consolidation pressure to the soft subsoil. The isotropic consolidation will induce
settlement and inward lateral displacement. This kind of inward deformation may cause some
surface cracks around the improvement area, but normally there is no possibility of general shear
failure (Chai et al., 2005).
Figure 24: Lateral deformation of subsoil (Chai et al., 2005)
Among others, Yan and Chu (2003) reported of lateral inward displacements caused by vacuum
loading. Figure 25 serves as an example where lateral displacements were measured by means of
inclinometer. It can be seen that the lateral displacements were greatest at the ground level and
reduced with depth. Yan and Chu (2003) also reported of cracks that developed near the preloaded
area. Both the inward and the outward lateral displacement can cause problems if there is any kind
of structure adjacent to the treated area.
T. Stapelfeldt, Preloading and vertical drains. 22
Figure 25: Example of lateral displacements (Yan and Chu, 2005)
There are different opinions regarding the rate of settlement induced by surcharge loading or
vacuum pressure. In order to solve this problem, Chai et al (2005) conducted several oedometer
tests on samples with different initial effective stresses and under one-way drainage conditions with
either surcharge or vacuum loading. They investigated three different scenarios: Samples near the
ground surface, samples from about the middle of a treated region (initial vertical effective stress
σ´vo = 40 kPa) and samples located deeper in the ground (initial vertical effective stress
σ´vo = 80 kPa). A maximum achievable vacuum pressure of about 80 kPa in the field was
considered in the tests for both vacuum and surcharge load.
The resulting settlement-time curves are shown in Figure 26 to Figure 28, respectively. It can be
seen from the Figures, that for low initial vertical effective stresses (0 and 40 kPa), the vacuum
pressure-induced settlement is less compared to the corresponding surcharge load. In case of an
initial vertical effective stress of 80 kPa, the settlements for both vacuum pressure and surcharge
load are approximately the same.
It was reported, that in case of low initial vertical effective stresses, when disassembling the
testing apparatus, the soil samples had separated from the confining ring. This indicates the inward
lateral displacement mentioned above.
Whether the magnitude of settlements resulting from vacuum pressure and corresponding
surcharge loading under oedometer conditions are the same depends on whether a k0 condition (no
horizontal strain) can be maintained (Chai et al., 2005). If there is any lateral displacement in the
sample when applying vacuum pressure under oedometer conditions, the only horizontal stress will
eventually be due to the vacuum pressure. Thus, if the vacuum pressure is larger than the required
stress to maintain a k0 condition, lateral displacement will occur and the vacuum pressure will
induce less settlement than the surcharge load. Otherwise, the vacuum pressure will induce the
same settlement as the corresponding surcharge load and no lateral deformation will occur.
T. Stapelfeldt, Preloading and vertical drains. 23
Figure 26: Settlement-time curves of samples near ground surface (Chai et al., 2005)
Figure 27: Settlement-time curves of samples from about the middle of a treated region (Chai et al., 2005)
Figure 28: Settlement-time curves from samples located deeper in the ground (Chai et al., 2005)
T. Stapelfeldt, Preloading and vertical drains. 24
From their observations, Chai et al., 2005 derived a stress ratio, k, which is defined as follows:
k=
∆σ VAC
∆σ VAC + ∆σ´V 0
(23)
If k ≤ k0, there will be no lateral displacement and vice versa. For the above mentioned laboratory
tests with low initial vertical effective stresses and an assumed value of k0 = 0,5, the stress ratio, k,
is higher than k0, hence there will be lateral displacement. In case of an initial vertical effective
stress of 80 kPa, the stress ratio, k, is equal to k0. Thus, the k0 condition was fulfilled, no lateral
displacement was observed and the resulting settlement induced by vacuum pressure was almost
the same than the settlement induced by surcharge loading. In Figure 29 the relationship between
the stress ratio and a settlement ratio Svac / Sl (Svac is the settlement induced by vacuum pressure and
Sl is the settlement induced by surcharge loading) is illustrated. It can be seen, that the settlement
ratio increases almost linearly with decreasing stress ratio. The minimum settlement ratio close to
the ground surface is about 0,81.
Figure 29: Stress ratio versus settlement ratio
T. Stapelfeldt, Preloading and vertical drains. 25
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