pre loading and vertical drains

8/6/2019 Pre Loading and Vertical Drains

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T. Stapelfeldt, Preloading and vertical drains. 1

Preloading and vertical drains

T. StapelfeldtHelsinki University of Technology

ABSTRACT: This report has been done at the Laboratory of Soil Mechanics and FoundationEngineering of Helsinki University of Technology as part of the licentiate seminar of geotechnicsand 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 andpotential damages to the structures.

In this report preloading techniques and the usage of vertical drains are described. It introducesinstallation methods of drains and possible influences of the drain efficiency. In addition, methodsfor assessing the effectiveness of soil improvement are described.

1 INTRODUCTIONIn 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. Thesesoft soil deposits have a low bearing capacity and exhibit large settlements when subjected toloading. It is therefore inevitable to treat soft soil deposits prior to construction activities in order toprevent differential settlements and subsequently potential damages to structures.

Different ground improvement techniques are available today. Every technique should lead toan increase of soil shear strength, a reduction of soil compressibility and a reduction of soilpermeability. The choice of ground improvement technique depends on geological formation of thesoil, soil characteristics, cost, availability of backfill material and experience in the past. Accordingto Bergado et al. (1996) they can be divided broadly into two categories. The first category includestechniques which require foreign materials and utilisation of reinforcements. They are based onstiffening columns either by the use of a granular fill (stone columns), by piling elements which arenot 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 bydewatering, i.e. preloading techniques often combined with vertical drains.

This report will focus on preloading techniques and utilisation of vertical drains. Preloading isthe application of surcharge load on the site prior to construction of the permanent structure, untilmost of the primary settlement has occurred. Since compressible soils are usually characterized byvery low permeability, the time needed for the desired consolidation can be very long, even withvery high surcharge load. Therefore, the application of preloading alone may not be feasible withtight construction schedules and hence, a system of vertical drains is often introduced to achieveaccelerated radial drainage and consolidation by reducing the length of the drainage paths.


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Although preloading and vertical drains are very close connected, in this work it is tried to treatthem separately. In chapter 2, the common methods of preloading are described. These methods areconventional 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, factorsinfluencing 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 fieldmeasurements. 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 TECHNIQUESPreloading generally refers to the process of compressing the soil under applied vertical stress priorto construction and placement of the final construction load. The two common preloadingtechniques are conventional preloading, e. g. by means of an embankment, and vacuum induced

preloading.

2.1Conventional preloadingThe simplest solution of preloading is a preload, e. g. by means of an embankment. When the loadis placed on the soft soil, it is initially carried by the pore water. When the soil is not verypermeable, which is normally the case, the water pressure will decrease gradually because the porewater is only able to flow away very slowly in vertical direction. In order not to create any stabilityproblems, 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, theexcess 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 belowthe stress increase caused by the temporary surcharge. By increasing the time of temporaryoverloading, 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 alwaysbe in an overconsolidated state and the secondary compression for overconsolidated soil is muchsmaller than that of normally consolidated soil. This will benefit greatly the subsequentgeotechnical design (Chu et al., 2004).


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SurchargeDesign load

Time

Final settlement for design load

Load

Settlement

Figure 2: Resulting settlement due to preloading

2.2Vacuum preloadingSometimes it is not feasible to place a fill embankment because the soft soil might be sometimes soweak that even a common 1.5 m embankment might already cause stability problems. Then it canbe 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 drainsand 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 maintainair 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 anincrease in effective stress in the soil, which in turn is leading to an accelerated consolidation.

Figure 3: Vacuum system (after Masse et al., 2001)


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The common advantages of vacuum preloading are that there is no extra fill material needed, theconstruction times are generally shorter and it requires no heavy machinery. Moreover, nochemical admixtures will penetrate into the ground and thus it is an environmental friendly groundimprovement method (Chai, 2005).

Further advantages of the method are that isotropic consolidation eliminates the risk of failureunder 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 airthroughout 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 areaAccording to Masse et al., (2001), unsuccessful attempts have been recorded in the past fortechnological reasons. However, a major obstacle to development of vacuum based consolidation isthe lack of understanding of its basic principles.

2.3Principles of preloadingFigure 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 conventionalsurcharge.

Atmospheric pressure is generally a not varying parameter in geotechnics. Since soil stresscalculations are normally based on effective stresses, atmospheric pressure can be disregarded incalculations. Considering atmospheric pressure, the effective stress state in initial conditions can bewritten as follows:

= - u = (Pa + h) (Pa + wh) (1)

where: = vertical effective stress, = total vertical stress, u = pore water pressure,Pa = atmospheric pressure, = unit weight of soil, w = unit weight of water and h = depth of soillayer.

In case of a conventional surcharge, the total stress will increase due to the additional load andthus, 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 ineffective stress is due to a reduction of pore water pressure, i. e. applying negative pressure.


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Figure 4: Vertical stress profiles: (a) initial in situ conditions, (b) conventional surcharge and (c) vacuum-

induced surcharge (after Elgamal and Adalier, 1996)

In terms of stress path distributions, the stress state can be described in triaxial space with meaneffective stress p and the deviator stress q, defined as:

31 =q (2)

( )31

23

1 +=p (3)

where 1 and 3 are the principal normal stresses.

In Figure 5 different stress paths are described. Starting from an in situ stress state at point A, thecurve ABC describes the case of conventional preloading. When the fill is placed, it follows curveAB with a possible failure if point B would cross the failure line Kf. Consolidation will take placefrom B to C in the area of h > 0 above the K0-line and hence, outward lateral deformation willoccur.

Line AD corresponds to oedometric consolidation. As for vacuum induced preloading, the stresspath follows the line AE. This is due to the fact that, during vacuum consolidation, the soil is underquasi isotropic conditions and thus the principal normal stresses are equal. It can be seen that theentire stress path is under the K0-line with the field of h < 0 and hence under horizontalcompression or inward lateral displacement respectively.


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longitudinal channel wick functioning as a drain, and a sleeve of paper of fibrous material as a filterprotecting the core.

3.2Types of verticalIn 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]Typicalspacing[m]

Maximumlength [m]

Sand drain Driven or vibratoryclosed-end mandrel(displacement type)

0,15 - 0,6 1 - 5 30

Sand drain Hollow stem continuous-flight auger (lowdisplacement)

0,3 - 0,5 2 - 5 35

Sand drain Jetted (non-displacement) 0,2 - 0,3 2 - 5 30Prefabricated

sand drains(sandwicks)

Driven or vibratory

closed-end mandrel;flight auger; rotary wash boring (displacement ornon-displacement)

0,06 - 0,15 1,2 - 4 30

Prefabricatedband-shapeddrains

Driven or vibratoryclosed-end mandrel(displacement or lowdisplacement)

0,05 - 0,1(equivalentdiameter)

1,2 - 3,5 60

Sand drains are basically boreholes filled with sand. As for the displacement type of sand drains, aclosed mandrel is driven or pushed into the ground with resulting displacement in both vertical andhorizontal directions. The installation causes therefore disturbances, especially in soft and sensitiveclays, which reduces the shear strength and horizontal permeability.

The low- or non-displacement installations are considered to have less disturbing effects on thesoil. 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 befound close to the construction site.

Drains might become discontinuous because of careless installation or horizontal soildisplacement during the consolidation process.

During filling bulking of the sand might appear which could lead to cavities and subsequently tocollapse due to flooding.

Construction problems and/or budgetary burdens might arise due to the large diameter of sanddrains.

The disturbance of the soil surrounding each drain caused by installation may reduce thepermeability, 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 displacementinstallation. Figure 7 shows a typical mandrel and the typical shape of a prefabricated drain. Thedimensions of the prefabricated drains are much smaller compared to sand drains (see Table 1) andsubsequently are the dimensions of the mandrel. Thus, the degree of soil disturbance caused by thesize of the mandrel during installations is lower.


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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 Figure8). Sometimes it might also be a piece of drain itself (Holtz et al., 1991). The purpose of the anchoris to prevent soil from entering the mandrel and plugging it during penetration. It also keeps thedrain at the desired depth as the mandrel is withdrawn.

Figure 8: Drain, mandrel and anchor plate (Cramer, undated)

3.3Drain properties3.3.1Equivalent diameter for band-shaped drainsThe conventional theory of consolidation with vertical drains assumes that the vertical drains arecircular in their cross-section. Since most of the prefabricated drains are rectangular in cross-section (band-shaped), the rectangular drain has to be converted into an equivalent cylindricalshape. That implies that the equivalent diameter has the same theoretical radial drainage capacity asthe band-shaped drain. Hansbo (1979) suggested that both band-shaped and circular drains lead topractically same degree of consolidation if their circumferences are equal. Hence, the equivalentdiameter (dw) of a band-shaped drain with width (a) and thickness (b) (see Figure 9) can beexpressed by:

)ba(d

w

+=

2(4)


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Figure 9: A typical cross-section of a band-shaped drain (Holtz et al., 1991)

3.3.2Discharge capacityThe purpose of using prefabricated vertical drains is to release the excess pore water pressure insoil 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 thedisturbance (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 andsubsequently decreases the discharge capacity due to a reduction of the cross-sectional areaavailable 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 foldingof 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, possiblydue to biological and chemical activities.

Hydraulic gradient: The measured discharge capacity varies with different hydraulic gradientsand is smaller when a higher hydraulic gradient is used. This might be due to the loss of flowenergy as a result of turbulent flow at a high hydraulic gradient.


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Figure 10: Folded drain

3.3.3Properties of the filterIn 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 thesame 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 befilled with soil and get clogged,

the filter needs to be strong enough to withstand high lateral pressure in order not to besqueezed 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)


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In order to meet the above mentioned requirements, there are basic filter design criteria that have tobe satisfied. Soil retention ability:The first criterion is that the Apparent Opening Size (AOS) has to be sufficiently small so that itcan prevent clay particles from penetrating through the filter into drain. On the other hand, the AOScannot be too small as the filter has to provide a sufficient permeability. A commonly used

criterion is the following (Chu et al., 2004):

859532 D)(O (5)

and

50501210 D)(O (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 atleast one order of magnitude higher than that of the soil. As the soil to be treated by prefabricatedvertical drains usually has a very low permeability, this requirement should be met in most cases(Chu et al., 2004).

Sfkk 10 (7)

where:kf is the permeability of the filter and kS is the permeability of the soil.

Mechanical properties of the filter and the corePrefabricated vertical drains should have adequate strength to sustain the tensile stresses subjectedto it during the installation process. Theses forces are mainly tensile, partly from the drains selfweight and partly from friction between the drain and the installation equipment. According toKremer et al. (1983), the maximum tensile force develops when the mandrel accelerates and at thestart 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 spliceddrain 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 minimumcurvature because of the orientation of the guides (cylinders). If vibratory equipment is used forinstallation, 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 asfollows:

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.


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The criteria of a tensile load of 0,5 kN and a strain = 2 % are based on estimates of the tensileforces and strains in the drain which may occur during the installation procedure. The maximumlongitudinal strain of = 10 % is required in order to limit the deformation of the drain duringinstallation. 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 bothwet 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). Theyinstrumented 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 draininstallation in a 25-30 m depth is about 20-25 s and additionally withdrawal is requiring another30 s. For safety reasons, the installation speed was slowed down. Figure 13 illustrates the tensionmeasured by the two strain gauges. The tension measured in strain gauge A increased graduallywith installation depth to about 800 N during 93 s. The drain anchored at about 24 m depth and themandrel was held stationary for about 163 s. Tension still increased until the mandrel waswithdrawn although the drain was free to roll off from the drum. A sharp increase in tension up to1000 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 constantuntil the end of monitoring. In contrast, the tension measured in strain gauge B was smallerthroughout the installation but began to increase even after cutting the drain.

A second test was carried out with normal installation speed. The measurements indicate thealmost 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.


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Figure 13: Location of strain gauges and measurement of forces during installation and withdrawal of

mandrel (after Karunaratne et al., 2003)

3.4Factors influencing the drain efficiency3.4.1Smear effectThe installation of vertical drains by means of a mandrel causes significant remoulding of thesubsoil, especially adjacent to the mandrel. Hence, a zone of smear will be developed with reducedpermeability and increased compressibility. In varved soils the finer and more impervious layerswill be dragged down and smeared over the more pervious layers (Barron, 1948). The smear zonecreates additional resistance which must be overcome by the excess water. This, in turn, will retardthe rate of consolidation.

The behaviour of permeability and compressibility within the smear zone is different than thebehaviour of the undisturbed soil, hence, the behaviour of soil stabilised with vertical drains cannot 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 twozones. The smear zone is the zone in the immediate vicinity of the drain and the other is theundisturbed zone (see Figure 14).

Figure 14: Smear effect (Hansbo 1994)


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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 designpurposes 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:

2

)65( ms

dd = (8)

where (dm) is the diameter of a circle with an area equal to the cross sectional area of the mandrelor the cross sectional area of the anchor at the tip, which ever is greater. At this diameter, thetheoretical 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) tobe 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 thedrain but the coefficient of vertical permeability remains almost unchanged.


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Figure 16: Horizontal permeability (left; a), vertical permeability (left; b) and ratio of (kh/ kv) (right) alongradial 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 zonethe value has an average of 1,15. Thus it is close to unity and the permeability of the smear zonecan 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 outusing a small mandrel in one half of the site and a large mandrel in the other half. The resultsindicated a faster settlement rate and a slightly higher compression in the small mandrel area. Thatwould verify that a smaller smear zone was developed in the vicinity of the smaller mandrel.

3.4.2Well resistanceThe relevant features for the design and performance of vertical drains are their hydraulic proper-ties: the discharge capacity of the cross-section and their filter permeability. If during the consoli-dation period the discharge capacity of the drain is reached, the overall consolidation process isretarded. In such cases, the drains exhibit a resistance to water flow into them which known as wellresistance. It can develop and increase as the deterioration of the drain filter may lead to asignificant reduction of the cross-section. Furthermore, fine soil particles may pass through thefilter and decrease the area available for flow. Finally, folding of the drain because of largesettlements may result in a reduced discharge capacity (Holtz et al., 1991). It is suggested that aslong as the working discharge capacity of a prefabricated vertical drain exceeds 100-150 m / 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 factorsmentioned 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 maximumdischarge length and permeability of the soil. If the drainage length is changing, the requireddischarge capacity may change significantly. The same occurs if the permeability is not determinedaccurately. In these cases some drains may not be able to meet the requirements anymore.


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3.6Theory of Vertical DrainsThe basic theory of radial consolidation around a vertical drain system is an extension of theclassical one-dimensional consolidation theory.

Barron (1948) studied the two extreme cases of free strain and equal strain and showed that theaverage 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 thatthe differential settlements occurring over this zone have no effect on the redistribution of stressesby arching of the fill load. The equal strain hypothesis on the other hand assumes that the loadapplied is rigid and equal vertical displacement in enforced at the surface, i.e. horizontal sectionsremain horizontal. The solution for the second case is considerably simpler (Barron 1948).

3.6.1Equal vertical strain hypothesis (Barron, 1948)Barron developed a solution of the horizontal consolidation under ideal conditions using anaxisymmetric 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. Darcys 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:

+

=

2

21

r

u

r

u

rc

t

uh

(11)

where u is the excess pore pressure at any point and at any time t, r is the radial distance of theconsidered point from the centre of the drained cylinder and ch is the horizontal coefficient ofconsolidation.

Under ideal conditions (no smear effect and no well resistance), the average degree of

consolidation for radial drainage is as follows:

=

h

h

TexpU

81 (12)

with


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e

h

h

D

tcT = (13)

and

2

2

2

2

4

13

1 n

n)nln(

n

n

= (14)

where De is the diameter of the equivalent soil cylinder, dw is the equivalent diameter of the drainand n (n = De / dw) is the spacing ratio.

3.6.2Approximate equal strain hypothesis (Hansbo, 1981)Hansbo (1981) derived an approximate solution for vertical drain based on the equal strainhypothesis to take both a zone of smear with a reduced permeability and well resistance intoconsideration.

By applying Darcys law, the rate of flow of internal pore water in the radial direction can beestimated. The total flow of water from slice, dz, to the drain, dQ1, is equal to the change of flow ofwater from the surrounding soil, dQ2, which is proportional to the change of volume of the soilmass (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

=F

TexpU r

r

81 (15)

where (in a simplified form)

w

h

w

h

rsq

k)zl(z,)sln(

k

k

s

nlnFF)n(FF

22750 +

+

=++= (16)

and F(n) is the drain spacing factor, Fs the smear effect, Fr the well resistance, kh is the horizontalpermeability, kw reduced permeability in the smear zone and s is given by s = rs / rw.

For smear effect only, the parameter is given by


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750,)sln(k

k

s

nlnF)n(FF

w

h

s

+

=+= (17)

In case of a perfect drain, the parameter reduces to

( ) 750,nln)n(FF == (18)

4 ESTIMATION OF THE DEGREE OF CONSOLIDATIONThe degree of consolidation is usually used as one of the criteria for assessing the effectiveness ofsoil improvement work using the fill surcharge or vacuum preloading method. It is also often usedas a design specification (Chu and Yan, 2005). The degree of consolidation is normally calculatedas the ratio of the current settlement to the ultimate settlement. However, for a soil improvementproject, the ultimate settlement is unknown and has to be predicted.

There are different methods available to estimate the ultimate settlement and the degree ofconsolidation. One of these methods is the Asaoka method:

The Asaoka method (Asaoka, 1978) is a method of settlement observation for one-dimensionalconsolidation in which earlier observations are used to predict the ultimate primary settlement. Ifnecessary, the in situ coefficient of consolidation can also be backcalculated after the analysis. Themain advantage of this method is its simplicity. In common settlement analysis conditions such asthe initial distribution of the excess pore pressure, the drain length, the final vertical strain of soilsand the coefficient of consolidation are considered to be given in advance of the analysis. It isknown that these estimations are quite uncertain. For the Asaoka method neither determination ofsoil properties nor measuring of the field pore pressure behaviour is needed.

Asaoka showed that one-dimensional consolidation settlements at certain time intervals couldbe described as a first order approximation:

110nS += nS (19)

where S1, S2, , Sn are settlements observations. Sn denotes the settlement at time tn. The timeinterval 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 of0 and 1 are given by the intercept of the fitted straight linewith the Sn - axis and the slope. The ultimate primary settlement can be calculated with theexpression:

1

0

1

=

ultS (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 Figure21): 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 0 and 1 and the intercepting point with the 45-line to determine the ultimateprimary settlement.


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Figure 21: Asaoka method

Besides one-dimensional consolidation, the Asaoka method assumes a constant load andhomogeneous soil. If these assumptions are not fulfilled observational data may have an initial orfinal 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 givelow 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 ofconsolidation. The Asaoka method is also strongly dependent on the used time interval.


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In case of staged construction and when a large increment of surcharge load is applied, there isnormally an obvious increase in the gradient of the settlement-time curve. In order to determine theultimate settlement under these conditions, data obtained from the final stage of loading should beused (Asaoka, 1978).

Another possibility of assessing the degree of consolidation is based on pore water pressuremeasurements (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 illustrationserves 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

[ ]

[ ]

= dz)z(u)z(u

dz)z(u)z(u

Us

st

avg

0

1 (21)

where

sz)z(uws

= (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; w = 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 usingsettlement data tends to overestimate the degree of consolidation. Therefore, it is recommended touse both methods when calculating the degree of consolidation.

These problems have also been observed by Hansbo (1997). The factors for the differencesmight be as follows (Yan and Chu, 2005):


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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 PRELOADINGPreloading by an embankment will not only cause settlement of the soft subsoil but also generallyoutward lateral displacement. This lateral displacement is mainly caused by the shear stressesinduced by the embankment load, and if these shear stresses are big enough they will cause shearfailure within the subsoil (see Figure 24). By contrast, the vacuum pressure technique tends toapply an isotropic consolidation pressure to the soft subsoil. The isotropic consolidation will inducesettlement and inward lateral displacement. This kind of inward deformation may cause somesurface cracks around the improvement area, but normally there is no possibility of general shearfailure (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 vacuumloading. Figure 25 serves as an example where lateral displacements were measured by means ofinclinometer. It can be seen that the lateral displacements were greatest at the ground level andreduced with depth. Yan and Chu (2003) also reported of cracks that developed near the preloadedarea. Both the inward and the outward lateral displacement can cause problems if there is any kindof structure adjacent to the treated area.


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Figure 25: Example of lateral displacements (Yan and Chu, 2005)

There are different opinions regarding the rate of settlement induced by surcharge loading orvacuum pressure. In order to solve this problem, Chai et al (2005) conducted several oedometertests on samples with different initial effective stresses and under one-way drainage conditions witheither surcharge or vacuum loading. They investigated three different scenarios: Samples near theground surface, samples from about the middle of a treated region (initial vertical effective stressvo = 40 kPa) and samples located deeper in the ground (initial vertical effective stressvo = 80 kPa). A maximum achievable vacuum pressure of about 80 kPa in the field wasconsidered 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 beseen from the Figures, that for low initial vertical effective stresses (0 and 40 kPa), the vacuumpressure-induced settlement is less compared to the corresponding surcharge load. In case of aninitial vertical effective stress of 80 kPa, the settlements for both vacuum pressure and surchargeload are approximately the same.

It was reported, that in case of low initial vertical effective stresses, when disassembling thetesting apparatus, the soil samples had separated from the confining ring. This indicates the inwardlateral displacement mentioned above.

Whether the magnitude of settlements resulting from vacuum pressure and correspondingsurcharge loading under oedometer conditions are the same depends on whether a k0 condition (nohorizontal strain) can be maintained (Chai et al., 2005). If there is any lateral displacement in thesample when applying vacuum pressure under oedometer conditions, the only horizontal stress willeventually be due to the vacuum pressure. Thus, if the vacuum pressure is larger than the requiredstress 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 thesame settlement as the corresponding surcharge load and no lateral deformation will occur.


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From their observations, Chai et al., 2005 derived a stress ratio, k, which is defined as follows:

0VVAC

VAC

k

+= (23)

If k k0, there will be no lateral displacement and vice versa. For the above mentioned laboratorytests 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 almostthe 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 settlementratio 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


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6 REFERENCESAsaoka, A. 1978. Observational Procedure of Settlement Prediction. Soils and Foundations, Vol.

18, No. 4, Dec. 1978. Japanese Society of Soil Mechanics and Foundation Engineering. pp. 87-101.

Barron, R. A. 1948. Consolidation of fine-grained soils by drain wells. Transactions ASCE,

Vol. 113, paper 2346, pp. 718-724.Bergado, D. T., Anderson, L. R., Miura, N., Balasubramaniam, A. S. 1996. Soft ground

improvement in lowland and other environments. New York: ASCE Press.Bergado, D. T., Manivannan, R., Balasubramaniam, A. S. 1996. Proposed criteria for discharge

capacity of prefabricated vertical drains. Geotextiles and Geomembranes 14 (1996), 481-505.Chai, J.-C., Carter, J. P., Hayashi, S. 2005. Ground Deformation induced by Vacuum

Consolidation. Journal of geotechnical and geoenvironmental engineering, Vol. 131, No. 12,Dec. 2005, 1552-1561.

Chai, J.-C., Hayashi, S., Carter, J. P. 2005. Characteristics of vacuum consolidation.Proceedings ofthe 16th International Conference on Soil Mechanics and Geotechnical Engineering. Osaka12. - 16.09.2005. Rotterdam, Millpress.

Chu, J., Bo, M. W., Choa, V. 2004. Practical considerations for using vertical drains in soilimprovement projects. Geotextiles and Geomembranes 22 (2004) 101-117.

Chu, J., Yan, S. W. 2005. Estimation of Degree of Consolidation for Vacuum Preloading Projects.International Journal of Geomechanics, Vol. 5, June 1, 2005, 158-165.Cramer, J. M. Undated. Vertical wick drains consolidate tail minings. Company report.

www.nilex.com.Elgamal, A. W., Adalier, K. 1996. Soil Stabilization by Ambient Pore Pressure and Geomembrane

Containment. Geosynthetics International, Vol. 3, No. 4.Hansbo, S. 1979. Consolidation of clay by band-shaped prefabricated drains. Ground Engineering,

July, Vol. 12, No.5.Hansbo, S. 1981. Consolidation of fine-grained soils by prefabricated drains. Proceedings, 10th

International Conference on Soil Mechanics and Foundation Engineering, Vol. 3, Stockholm.Hansbo, S. 1994.Foundation Engineering. Amsterdam. Elsevier Science B. V.Hansbo, S. 1997. Practical aspects of vertical drain design. Proceedings, 14th International

Conference on Soil Mechanics and Foundation Engineering, Vol. 3, Hamburg.Holtz, R. D., et al. 1991. Prefabricated Vertical Drains: Design and Performance, CIRIA ground

engineering report: ground improvement. Oxford: Butterworth Heinemann Ltd.Indraratna, B., Balasubramaniam, A. S., Sivaneswaran, N. 1997. Analysis of settlement and lateral

deformation of soft clay foundation beneath two full-scale embankments. Int. Journal forNumerical and Analytical Methods in Geomechanics, Vol. 21, 599-618.

Indraratna, B., Redana, I. W. 1998. Laboratory determination of smear zone due to vertical draininstallation. Journal of geotechnical and geoenvironmental engineering, Vol. 124, No.2, Feb.1998, 180-184.

Indraratna, B., Rujikiatkamjorn, C., Sathananthan, I., 2005. Radial consolidation of clay usingcompressibility indices and varying horizontal permeability. Canadian Geotechnical Journal,Vol. 42, No. 5, Oct. 2005, 1330-1341

Jamiolkowski, M., Lancellota, R. and Wolski, W. 1983. Precompression and speeding upconsolidation. Proceedings, Eighth European Conference on Soil Mechanics and FoundationEngineering, Vol. 3. Helsinki.

Karunaratne, G. P., Chew, S. H., Leong, K. W., Wong, W. K., Lim, L. H., Yeo, K. S., Hee, A. M.2003. Installation stress in prefabricated vertical drains. Journal of geotechnical andgeoenvironmental engineering, Vol. 129, No. 9, September 2003, 858-860.

Kremer, R. H. J., Oostveen, J. P., van Weele, A. F., De Jager, W. F: J., Meyvogel, I. J. 1983. Thequality of vertical drainage.Proceedings, Eighth European Conference on Soil Mechanics andFoundation Engineering, Vol. 2. Helsinki.

Masse, F., et al. 2001. Vacuum consolidation: A review of 12 years of successful development.http://www.menard-soltraitement.com.


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Tan, S-A., Chew, S-H. 1996. Comparison of the Hyperbolic and Asaoka Observational Method ofMonitoring Consolidation with Vertical Drains. Soils and Foundations, Vol. 36, No. 3, Sept.1996. Japanese Geotechnical Society. pp. 31-42.

Yan, S. W., Chu, J. 2003. Soil improvement for a road using the vacuum preloading method.Ground Improvement(2003) 7, No. 4, 165172.

Yan, S. W., Chu, J. 2005. Soil improvement for a storage yard using the combined vacuum and fill

preloading method. Canadian Geotechnical Journal, Vol. 42, 2005, 1094-1104.Yeung, A. T. 1997. Design curves for prefabricated vertical drains. Journal of geotechnical and

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pre loading and vertical drains

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