influence of stone column installation on settlement reduction
TRANSCRIPT
Computers and Geotechnics 59 (2014) 87–97
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Computers and Geotechnics
journal homepage: www.elsevier .com/locate /compgeo
Influence of stone column installation on settlement reduction
http://dx.doi.org/10.1016/j.compgeo.2014.03.0030266-352X/� 2014 Elsevier Ltd. All rights reserved.
⇑ Corresponding author. Address: Group of Geotechnical Engineering, Depart-ment of Ground Engineering and Materials Science, University of Cantabria, Avda.de Los Castros, s/n, 39005 Santander, Spain. Tel.: +34 942 201813; fax: +34 942201821.
E-mail addresses: [email protected] (J. Castro), [email protected](M. Karstunen), [email protected] (N. Sivasithamparam).
Jorge Castro a,⇑, Minna Karstunen b,c, Nallathamby Sivasithamparam d,e
a Department of Ground Engineering and Materials Science, University of Cantabria, Santander, Spainb Department of Civil and Environmental Engineering, Chalmers University of Technology, Gothenburg, Swedenc School of Engineering, Aalto University, Espoo, Finlandd Computational Geomechanics Division, Norwegian Geotechnical Institute, Oslo, Norwaye Plaxis B.V., Delft, The Netherlands
a r t i c l e i n f o a b s t r a c t
Article history:Received 2 August 2013Received in revised form 20 December 2013Accepted 2 March 2014
Keywords:Stone columnsInstallationSettlement reductionNumerical modellingAnisotropyDestructuration
The paper presents numerical simulations investigating the settlement reduction caused by stonecolumns in a natural soft clay. The focus is on the influence of the soft soil alteration caused by columninstallation. A uniform mesh of end-bearing columns under a distributed load was considered. Therefore,the columns were modelled using the ‘‘unit cell’’ concept, i.e. only one column and the corresponding sur-rounding soil in axial symmetry. The properties of the soft clay correspond to Bothkennar clay, which ismodelled using S-CLAY1 and S-CLAY1S, which are Cam clay type models that account for anisotropy anddestructuration. The Modified Cam clay model is also used for comparison. Column installation wasmodelled independently to avoid mesh distortions, and soft soil alteration was directly considered inthe initial input values. The results show that the changes in the stress field, such as the increase of radialstresses and mean stresses and the loss of overconsolidation, are beneficial for high loads and closelyspaced columns but, on the contrary, may be negative for low loads, widely spaced columns and overcon-solidated soils. Moreover, whilst the rotation of the soil fabric reduces the settlement, in contrast the soildestructuration during column installation reduces the improvement.
� 2014 Elsevier Ltd. All rights reserved.
1. Introduction
Stone columns are one of the most common ground improve-ment techniques to improve soft soil deposits. They reduce thetotal and the differential settlements, accelerate consolidation,improve the bearing capacity and the slope stability and reducethe liquefaction potential. The improvement is achieved throughthe inclusion of gravel or crushed stone, which has a higher stiff-ness, strength and permeability than the natural soft soil. In addi-tion, column installation also modifies the properties of thesurrounding soil. However, design of stone columns does not usu-ally consider those installation effects and is usually based on theirperformance as rigid inclusions [1–3]. In this paper, the term‘installation effects’ refers to the changes in the state of soil dueto column installation. Some authors [4] account for certainchanges in the stress state due to installation by assuming a higher
value of the coefficient of earth pressure at rest than that for thenatural soil. The paper discusses the influence of the installationeffects on the settlement reduction, which is nowadays one ofthe major concerns in an accurate design of stone columns [5].
Stone columns are installed using a deep vibrator, either electricor hydraulic, similar to those used for vibrocompaction or vibroflo-tation. However, the alteration caused by the vibrator is com-pletely different in each ground improvement technique becauseof the different soil characteristics. In vibrocompaction, the vibra-tor is used in granular soils, and the vibration compacts the sur-rounding soil. The soil densification is the most important effectof vibrocompaction, and has been mainly analysed using field mea-surements [6,7], as it is difficult to model the process numerically[8]. In contrast, stone columns are typically used in soft cohesivesoils, as these cannot be compacted. The density of clay increasesonly after consolidation by the application of monotonic, long-term loads. Therefore, the installation effects of stone columnsare not usually considered and the main effect is assumed to bethe cavity expansion induced by the vibrating poker. There is alsoa range of soils that fall in between the two extremes discussedabove, in which densification is still possible, but additional gran-ular material is needed to ensure an effective improvement, e.g. to
Nomenclature
A areaar area replacement ratio: ar ¼ Ac=Ala, b constants of the hyperbolic fits for the installation
effects/absolute and relative effectiveness of destructur-ation in S-CLAY1S
c cohesioncu undrained shear strengthE Young’s modulusEm oedometric (constrained) modulus:
Em ¼ ½Eð1� mÞ�=½ð1þ mÞð1� 2mÞ�e void ratio (state parameter)H embankment heightKNC
0 coefficient of lateral earth pressure at rest in normallyconsolidated conditions
K0 coefficient of lateral earth pressure at restKi coefficient of lateral earth pressure after column instal-
lationL column length and thickness of the soft soil layerM slope of the critical state lineN column spacing ratio: N ¼ rl=rc
n improvement factorpa applied vertical pressurep0 effective mean stressp0m preconsolidation pressure (state parameter)p0mi intrinsic preconsolidation pressure (state parameter):
p0mi ¼ p0m=ð1þ vÞq deviatoric stressr distance from column axisrl, rc radius of the unit cell, of the columnsz settlementsz0 settlement without columnsa inclination of the yield surface (state parameter)
b settlement reduction factor/relative effectiveness ofrotational hardening in S-CLAY1
b� ratio of the settlement with and without installationeffects
v amount of bonding in S-CLAY1S (state parameter)c unit weighte straing stress ratio: g = q/p0
h Lode’s anglej slope of swelling line from e� ln p0 diagramk slope of post yield compression line from e� ln p0
diagramki slope of intrinsic post yield compression line from
e� ln p0 diagraml absolute effectiveness of rotational hardening in
S-CLAY1m Poisson’s ratior0 effective stress/ friction anglew dilatancy angleOCR overconsolidation ratioPOP pre-overburden pressure
Subscripts/superscripts0 initialCS at critical stated, v deviatoric, volumetrice, c, s, l embankment, column, soil, elementary cellp plasticr, z, h cylindrical coordinatesunsat, sat unsaturated, saturated
88 J. Castro et al. / Computers and Geotechnics 59 (2014) 87–97
avoid liquefaction [9]. In this paper only a purely cohesive soft soilis considered.
Experimental studies have shown some of the effects of columninstallation, e.g. the increase of pore pressures and horizontalstresses, and the remoulding of the surrounding soil has been mea-sured in the field [10–14]. There have also been attempts to inves-tigate these effects through physical modelling of the process bymeans of centrifuge testing [15,16], but the soils used are reconsti-tuted and hence not fully representative of natural clays.
Modelling the problem theoretically is complex, and althoughthe cavity expansion is a well-studied problem (e.g. [17,18]), thereare few numerical analyses of the installation effects of stone col-umns [19,20]. The authors have recently studied this numericallyusing advance soil models to reproduce the behaviour of naturalstructured soft soils [21].
Beyond the changes in the state of soil due to column installa-tion, the knowledge of the influence that those changes have on thesoil improvement is very limited. Schweiger [22] found that, ifthose changes are considered, the settlement of a circular footingwas reduced but only for high load levels. The improvement iscaused by the increase of mean stress in the clay, which enablesthe soil to carry more load and in turn provides a better lateral sup-port for the columns. Column installation was modelled imposing avolumetric strain field, which is similar to input post-installationvalues of the soil density and the lateral earth pressure. However,this approach needs of approximate estimations of the volumechange. Later, Kirsch [19] simulated the settlement reductioncaused by installation effects of a group of floating columns in asandy silt. He distinguished between individual installation effects,which were modelled applying a small cavity expansion (2–8%),
and a global installation effect in an enhanced zone around thegroup of columns with a higher stiffness (around twice the initialone). Those installation effects give a further reduction of the set-tlement of 40% and 5–25%, respectively. In the work above, theinstallation effects were somehow back-calculated from fieldmeasurements.
To clarify the influence that the changes in the state of soil due tocolumn installation have on the settlement reduction caused by thecolumns on soft cohesive soils, the authors carried out numericalsimulations using two advanced constitutive models, namely S-CLAY1 [23] and S-CLAY1S [24], which have been especially devel-oped to represent natural structured soft soils, a common type ofsoils to be treated with stone columns. The Modified Cam clay mod-el (MCC) [25] has also been used for comparison. The paper presentsthe ‘‘unit cell’’ models used to study several column spacings andembankment heights, in which a curve fitting of the initial stressesand state variables is used to account for the installation effects. Thesettlement reduction achieved for the different cases is analysed.The comparison of the settlement improvement with and withoutinstallation effects demonstrates the influence of the changes inthe stresses and soil structure, both fabric and interparticle bond-ing. The main positive and negative changes in the soil state dueto column installation are highlighted. Depending on the analysedcase, the effects of column installation either improve or reducethe settlement reduction of the stone column foundation.
2. Numerical model
The finite element code Plaxis v9 [26] was used to develop anumerical model of a reference problem that could help to
p'
q
p'mi p'm
1α
M1Natural
yield surface
Intrinsicyield surface
CSL
CSL
Fig. 2. Yield surfaces of the S-CLAY1S model [24].
J. Castro et al. / Computers and Geotechnics 59 (2014) 87–97 89
understand the influence of the changes in the state of soil due tocolumn installation. A uniform mesh of end-bearing columns un-der a distributed load was considered. Therefore, the columns weremodelled using the ‘‘unit cell’’ concept, i.e. only one column andthe corresponding surrounding soil in axial symmetry (Fig. 1). Asall the columns are simultaneously loaded, they will respond invirtually the same fashion, which justifies symmetry conditions.The inner boundary of the ‘‘unit cell’’ is the axis of symmetry anda smooth contact is assumed at the bottom. Consequently, rigid,frictionless and shear free boundaries are used except in the upperboundary, where the embankment is located.
In order to consider a realistic situation, properties of Bothken-nar clay were used for the soft soil. Stone columns have been ap-plied in Bothkennar clay [11,27] and similar Carse clays [5]. TheBothkennar soft clay test site has been the subject of a numberof comprehensive studies [28]. The soil at Bothkennar consists ofa firm to stiff silty clay crust about 1.0 m thick, which is underlainby about 19 m of soft clay. However, in the simulations the col-umns were assumed to reach a rigid layer at 10 m depth to avoidvery long or floating columns. The ground water level is 1.0 m be-low the ground surface. Typically to a structured soil the in situwater content is close to the liquid limit.
The behaviour of Bothkennar clay was modelled using the ad-vanced constitutive models S-CLAY1 and S-CLAY1S. MCC was alsoused for comparison purposes. S-CLAY1 is a Cam clay type of modelwith an inclined yield surface to model inherent anisotropy, and arotational component of hardening to model the development orerasure of fabric anisotropy during plastic straining. The stateparameter a defines the inclination of the yield surface in a p0–qdiagram (Fig. 2). The scalar value of a is defined in a simplified tri-axial stress space and is useful for common cross-anisotropic soils,but its vector definition {ai} is necessary for more general cases as
Embankment
Upper crust
Bothkennar
clay
Stone column
(rc=0.4 m)
Rollerboundaries
5 m
1 m
9 m
Fig. 1. Example of the numerical model and the finite element mesh (N = 5).
those present in this paper. The soil constants l and b are part ofthe rotational hardening law. l controls the rate at which the incli-nation of the yield surface tends towards its current target value,which depends on the current stress path. b defines the relativeeffectiveness of plastic shear (deviatoric) and volumetric strainsin changing the anisotropy. The initial inclination of the yieldsurface (a0) may be directly correlated with K0 for a normally con-solidated state, and similarly a theoretical link exists between b va-lue and normally consolidated K0. A test involving significantrotation of the yield surface, e.g. isotropic consolidation or un-drained shearing in triaxial extension, could be used to calibratel, but in practice empirical correlations with k are used [23].
The S-CLAY1S model accounts, additionally, for interparticlebonding and degradation of bonds, using an intrinsic yield surfaceand a hardening law describing destructuration as a function ofplastic straining. The bonding parameter, v, relates the sizes ofthe natural and intrinsic yield surfaces (v ¼ p0m=p0mi � 1) (Fig. 2). Itmay be related to the sensitivity of the soil, v = St � 1. Parametersa and b relate to the third additional hardening law used in themodel, which describes the degradation of bonding with plasticstraining. Parameter a controls the absolute rate of destructurationand parameter b defines the relative effectiveness of plastic shear(deviatoric) and volumetric strains [24]. For this constitutive mod-el the slope of the post yield compression line, k, corresponds to anintrinsic value, ki, which can be obtained from oedometer tests onreconstituted samples. In contrast, for S-CLAY1, the value for k isdetermined from oedometer tests on intact soil samples.
The models have been implemented as User-defined soil mod-els in Plaxis. An implementation that uses an automatic substep-ping in combination with a modified Newton–Raphsonintegration scheme [29] has been used instead of previous versionof Euler backward scheme used in Castro and Karstunen [21].
The values for S-CLAY1S model parameters (soil constants) forBothkennar clay are listed in Table 1 and are the same as those pre-viously used by the authors in their study of the changes in thestate of soil due to column installation [21]. S-CLAY1S model is for-mulated to be a hierarchical model, which reduces to S-CLAY1 byassuming a = 0 and v0 = 0, and using the apparent value of k. It fur-ther reduces to MCC model by additionally assuming l = 0 anda0 = 0. Note that the initial state variables correspond to in situ soilproperties before column installation. As explained in a later sec-tion, they are altered to account for column installation (post-installation values).
An embankment of 5 m, with the common properties listed inTable 2, was used to represent the distributed load. The heightand stiffness of the embankment allow for a full arching of theload, which can be considered as rigid. That was expected before-hand but also confirmed by the results. Therefore, the most impor-tant property of the embankment is the applied vertical pressure
Table 1S-CLAY1S parameters for Bothkennar clay.
Basic parameters Anisotropy Bonding
Depth (m) c (kN/m3) e0 OCR POP(kPa) K0 j m0 k M a0 l b v0 ki a b
0–1 18.0 1.1 – 30 1.35 0.02 0.2 0.48 1.4 0.539 30 0.94 5 0.18 11 0.21–10 16.5 2 1.5 – 0.544 0.02 0.2 0.48 1.4 0.539 30 0.94 5 0.18 11 0.2
Table 2Embankment and stone column parameters.
cunsat (kN/m3) csat (kN/m3) c (kPa) / (�) w (�) m (–) E (MPa)
Embankment 22 22 10 35 0 0.3 40Stone column 16 19 0.1 42 12 0.2 35
90 J. Castro et al. / Computers and Geotechnics 59 (2014) 87–97
(pa ¼ c0eH), where c0e is the effective unit weight of the embank-ment and H is its height. pa is usually normalised by the initial ver-tical stresses (
Pc0sz) (e.g. [2]). c0s is the effective unit weight of each
layer of natural soil and z is the thickness of each layer over thedepth considered. As a reference, its value at the mean depth is 2.5.
Crushed stone (gravel) is used for column backfill and commonproperties were chosen for the numerical model (Table 2). TheYoung’s modulus of the column (Ec = 35 MPa) was chosen basedon a common modular ratio of around Ec/Es = 60. A linear elastic-perfectly plastic soil model using the Mohr–Coulomb yield crite-rion was considered to be representative enough to reproducethe interaction between the embankment and the column.
Column spacing is usually defined by the area replacement ra-tio, ar (area of the column, Ac, divided by the area of the unit cell,Al) or in terms of the radius or diameter ratio, N = rl/rc = 1/
par.
Three different values, namely N = 2, 3 and 5, were used as repre-sentative of the common range. The column diameter was 0.8 mbut it does not have an especial significance as most of the resultscan be scaled for other column diameters. An example of the finiteelement mesh is shown in Fig. 1. Mesh sensitivity analyses wereperformed to confirm the accuracy of the mesh, i.e. the use of a fi-ner mesh gave slightly higher settlements but the differences werenegligible.
-100
-80
-60
-40
-20
0
ent,
s z0 (c
m)
3. Reference case without installation effects
The first step to study the influence of column installation onthe soil improvement, especially on the settlement reduction, isto analyse the case without considering any changes in the stateof the soil due to column installation. This reference case is alsoused as a benchmark to evaluate the performance of the advancedconstitutive models in a boundary value problem for soft soil.
After generation of the initial stresses, without considering anyinstallation effects for this reference case, the column was wishedin place and the embankment was built. The results assuming theembankment construction in drained conditions were nearly thesame as those of an undrained loading followed by a consolidationphase (Table 3). Therefore, in the following, drained loading wasused to save computation time. The consolidation analysis was
Table 3Comparison between drained (D) and consolidation (C) loading. Reference casewithout installation effects (H = 5 m).
Settlement (cm) N = 2 N = 3 N = 5
C D C D C D
MCC 38.1 37.6 88.1 88.0 129.6 130.2S-CLAY1 50.1 50.3 101.5 101.2 137.4 140.6S-CLAY1S 42.2 41.8 78.5 77.7 102.2 103.7
fully coupled, following Biot’s theory [30]. Terzaghi’s principle todivide total stresses into effective stresses and pore pressuresand Darcy’s law for the water flow were used. Soil grains were as-sumed as incompressible and a very high bulk modulus of thewater was considered. Consolidation was computed using a fullyimplicit integration scheme [26]. For the consolidation analyses,the lateral and bottom boundaries were assumed as impervious.Only the soft soil was assumed as undrained, while the embank-ment and the column were assumed as fully drained. The horizon-tal and vertical hydraulic conductivities of Bothkennar clay wereassumed as 1.4 and 0.7 � 10�9 m/s, respectively [28]. Twice thosevalues were used for the upper crust.
The settlement of the soft soil under the embankment load isplotted in Fig. 3. This process corresponds to one dimensional com-pression. The small change of gradient of the settlement curvewhen the embankment height is around 1.4 m is caused by theslight overconsolidation of the soft soil (OCR = 1.5). MCC predictsslightly less settlement than S-CLAY1 because it overpredicts thehorizontal stresses in a K0-stress path. Consequently, the meanstress, p0, is slightly higher, and so is the apparent bulk stiffnessof the soil. In this case, K0 = 0.59 for MCC, whist with S-CLAY1 typemodels realistic K0-stress paths are predicted through inclusion ofsoil anisotropy, in this case K0 = 0.43, which is the normally consol-idated (NC) value (KNC
0 = 1 � sin/). In the S-CLAY1 type models, theyield surface is rotated to give the desired (realistic) K0 value. Inone dimensional compression, the incremental strain ratio isdeddev¼ 2
3, and, if the elastic strains are neglected, using the associatedflow rule,
depd
depv¼ 2ðg�aÞ
M2�g2, the correct stress path is obtained asgK0 ¼ 3 1�K0
1þ2K0.
-180
-160
-140
-120
0 1 2 3 4 5
MCCS-CLAY1S-CLAY1S
Embankment height, H (m)
Settl
em
Fig. 3. Reference settlement without columns.
0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5
MCCSCLAY1SCLAY1S
N=5
N=3
N=2
Embankment height, H (m)
Settl
emen
t red
uctio
n fa
ctor
, β
Fig. 6. Settlement reduction without installation effects.
J. Castro et al. / Computers and Geotechnics 59 (2014) 87–97 91
When the embankment load becomes more significant, S-CLAY1S model predicts considerably less settlement, which is morerealistic because the slope of the virgin compression line for MCCand S-CLAY1 (k = 0.48) is constant, and was adjusted for lowerstress levels when destructuration is important. For higher stresslevels, that apparent k value is too high. On the contrary, in theS-CLAY1S model, the apparent slope of the virgin compression linereduces with loading due to destructuration (Fig. 4).
When the soil is improved with columns, the settlement is re-duced and closer column spacings reduce predicted settlement(Fig. 5). Differences between soil models follow similar trends asfor the case without columns. The improvement is usually evalu-ated using the settlement reduction factor (Fig. 6), defined as theratio between the final settlement with and without improvement,b ¼ sz=sz0, or its inverse the improvement factor, n. For very lowloads, b is constant and the same for the different soil models be-cause the soil is overconsolidated and behaves elastically in bothimproved and unimproved cases. For slightly higher loads, the soilyields when it is not improved but stays overconsolidated for theimproved case. Therefore, there is a minimum value for anembankment height of around 1 m. If the columns are closelyspaced, they support more load and plastic strains in the improvedsoil appear later. That is why for N = 2 the minimum in b is for ahigher embankment load than for higher column spacings, because
0.4
0.8
1.2
1.6
2.0
100020 50 100 300 600
MCCS-CLAY1S-CLAY1S
Vertical effective stress, σ'v (kPa)
Void
ratio
, e
Fig. 4. One dimensional compression of the soil.
-140
-120
-100
-80
-60
-40
-20
0
0 1 2 3 4 5
MCCSCLAY1SCLAY1S
N=5N=3
N=2
Embankment height, H (m)
Settl
emen
t, s z (c
m)
Fig. 5. Settlement with columns without installation effects.
the soil improved with N = 2 needs a higher load to reach thepreconsolidation pressure. Once the soil is normally consolidated,the settlement reduction factor increases with the load level be-cause of the column yielding. In general, MCC predicts the bestimprovement because it overpredicts horizontal stresses and then,the column is better confined. On the contrary, S-CLAY1S predictsthe worst improvement because the interaction between soil andcolumn causes further soil destructuration.
4. Installation effects
Changes in the state of soil due to column installation werestudied by the authors in a previous paper [21], which forms thebasis for the present analysis. Column installation was modellednumerically as an expansion of a cylindrical cavity and the changeson the surrounding soil were revealed. The installation process ofonly one column was analysed, hence no interaction effects be-tween the installations of several columns were considered. Fur-thermore, the vibratory action of the probe was not modelledbecause it is expected to have only a small influence on this typeof soft soils.
Now, the aim is to study how the effects of installation of stonecolumn influence the settlement reduction. Modelling the loadingprocess directly after column installation is not convenient be-cause the mesh is very distorted and boundary conditions maynot be appropriate. Therefore, it was considered appropriate tomodel the loading process independently. The changes in the statevariables of Bothkennar clay after column installation were studiedand curve fitted. Those post-installation values were input as ini-tial values in the unit cell model (Fig. 1). Numerical implementa-tion of this procedure for initializing the stresses and statevariables was required.
The embankment was assumed to be raised after full dissipa-tion of the excess pore pressures generated during column con-struction, which is the desired situation and seems to be true inmost cases [13,14]. Besides, the upper crust was considered notto be affected by column installation for the sake of simplicity.
4.1. Stress field
Horizontal stresses increase after column installation and,therefore, the changes in the stress field are usually consideredthrough an increase in the lateral earth pressure coefficient, K0.For example, Priebe [4] already assumed in his method a value ofK0 = 1, which is higher than the initial value at rest for most soils.Kirsch [19] presented field measurements of K0 and showed that
92 J. Castro et al. / Computers and Geotechnics 59 (2014) 87–97
after column installation values between 1 and 1.7 times the initialone have been measured, depending on the distance to the column.Elshazly et al. [31,32] have numerically back-calculated, from fieldmeasurements of load–displacement curves, values of K0 between0.7 and 2.5, with average values around 1.3.
0
0.5
1.0
1.5
2.0
1 2 5 10 20
σ'r /σ'z0σ'θ /σ'z0σ'z/σ'z0
Zone 2
Hyper. fita/(r/rc)+b
Zone 3: Expandedintrinsic yield surface
Zone 1:Elastic
(c) SCLAY1S
Distance to column axis, r / rc
Nor
mal
ised
effe
ctiv
e st
ress
, σ'/ σ
' z 0
0
0.5
1.0
1.5
2.0
1 2 5 10 20
σ'r /σ'z 0σ'θ /σ'z 0σ'z /σ'z 0
Zone 2
Hyper. fita/(r/rc)+b
Zone 3: Expandedyield surface
Zone 1:Elastic
(a) MCC
Distance to column axis, r / rc
Nor
mal
ised
effe
ctiv
e st
ress
, σ'/ σ
' z 0
0
0.5
1.0
1.5
2.0
1 2 5 10 20
σ'r /σ'z0σ'θ /σ'z0σ'z /σ'z0
Zone 2
Hyper. fita/(r/rc)+b
Zone 1:Elastic
Zone 3: Expandedyield surface
(b) SCLAY1
Distance to column axis, r / rc
Nor
mal
ised
effe
ctiv
e st
ress
, σ'/ σ
' z 0
Fig. 7. Effective stresses after column installation and full consolidation.
Assuming an increase of the K0 value is a useful approach forcolumn design but it is just a simplification of the changes in thestress field during column installation. Fig. 7 shows the resultsfor the three soil models considered. The distance to the columnaxis is in logarithmic scale to amplify the zone of interest nearthe column. The vertical, radial and hoop (circumferential) stressesmay be still considered as the principal stresses as the shear stres-ses are negligible. The stress changes are different at differentdepths but they are directly proportional to the undrained shearstrength, cu, and therefore, also to the depth and the initial verticalstress in this case, because the OCR value is constant apart from theupper crust.
In the analyses performed, the yield surface is circular in thedeviatoric plane (Drucker–Prager). The analytical derivation of cu
for the MCC can be found, for example, in Potts and Zdravkovic[33]. Following a similar procedure, the value of cu for the S-CLAY1model is:
cu
r0z0¼ OCR
Mffiffiffi3p cos h
1þ 2KNC0
31þ M � aCSð Þ2
M2 � a2CS
" #jk�1
� 1þ B2� � 1þ 2KOC
0
� �1þ 2KNC
0
� �OCR 1þ B2
� �24
35
jk
ð1Þ
where
B ¼3 1� KNC
0
� �= 1þ 2KNC
0
� �� a0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
M2 � a20
qaCS ¼
ffiffi3p
M6 cos h is the scalar anisotropy parameter at critical state and h is
the Lode’s angle (h = �30� in triaxial compression and h = 0� in planestrain conditions). In this case, failure is reached for conditions sim-ilar to plane strain during the expansion of the cavity. Therefore, cu
is defined for plane strain conditions (e.g. [17]). The cu values for theMCC (a = 0) are different and, although the differences are verysmall in this case (0.538 and 0:545r0z0 for MCC and S-CLAY1, respec-tively), the results (Fig. 7) have been normalised by the initial ver-tical stress to avoid ambiguity on the value of cu.
As expected, radial stresses increase near the column, but verti-cal and hoop stresses also change (Fig. 7). Vertical stresses increasein the part nearest to the column, with the exception of S-CLAY1S,for which vertical stress decreases because of destructuration.Interestingly, the hoop stresses are quite different to radial stres-ses. Three different zones may be distinguished: (1) an elasticone (beyond 11.5–13.5 column radii depending on the soil model)where soil behaviour is always elastic and hoop stresses decrease,(2) an area that is plastic during undrained expansion of the cavity
0
1
2
√3
0 2 4 6 8
pp'
End of undrainedcavity expansion
End ofconsolidation
MCC
Zone 2
Zone 3a
Zone 3 Notes:Total stress values do not includeambient pore pressure.cu in plane strain conditions
CSL
K0
p / cu , p' / cu
q / c
u
Fig. 8. Stress paths.
1.6
1.7
1.8
1.9
2.0
0 1 2 3 4 5
MCCS-CLAY1S-CLAY1S
Hyperbolic fite=e0-a/(r/rc-b)
e0=2.0OCR0=1.5χ0=5
rc=0.4 m
Distance to column axis, r / rc
Void
ratio
, e
Fig. 9. Hyperbolic fit of the void ratio after column installation and consolidation.
J. Castro et al. / Computers and Geotechnics 59 (2014) 87–97 93
but is not after consolidation, where vertical stresses change onlyslightly and (3) points that are on the yield surface also afterconsolidation (closer than 4.5–6 column radii), where the initialyield surface is expanded. To clarify that, the stress paths of pointsin the different zones are plotted in Fig. 8 for the MCC as an exam-ple. In Zone 3, there are points where the yield surface is signifi-cantly expanded (Zone 3a).
The input of those post-installation stresses require curvefitting, ensuring that equilibrium is fulfilled:
@r0r@rþ r0r � r0h
r¼ 0 ð2Þ
neglecting shear stresses to avoid unnecessary complexity.For normal column spacings, the soil between the columns will
be in Zone 3. Therefore, for the sake of simplicity, it is reasonable toassume the vertical and hoop stresses constant. For the radialstress, the following hyperbolic curve gives the best fit obeyingEq. (2):
r0rr0z0¼ a
r=rcþ b ð3Þ
where a and b are the fitting parameters. The value of those fittingparameters and the fitted curves are shown in Table 4a and Fig. 7,respectively.
4.2. Void ratio and Overconsolidation
Column installation not only alters the stress field but also thevalues for the state parameters of the soil, such as the void ratio(Fig. 9). The void ratio decreases just near the column, less than4.5–6 column radii (Zone 3). However, the densification is
Table 4Curve fitting of initial stresses and state parameters.
Fit
a b r2
(a) Void ratio: e ¼ 2� ar=rc�b
MCC 0.0491 0.774 0.998S-CLAY1 0.0615 0.741 0.996S-CLAY1S 0.0838 0.796 0.988
(b) Radial stress: r0rr0z0¼ a
r=rcþ b
MCC 0.595 1.270 0.996S-CLAY1 1.210 0.828 1.000S-CLAY1S 0.597 0.784 0.965
r0z=r0z0 r0h=r0z0
N = 2 N = 3 N = 5
(c) Vertical and hoop stresses: constant (average values)MCC 1.394 1.297 1.232 1.270S-CLAY1 1.086 1.062 1.100 0.828S-CLAY1S 0.755 0.845 0.992 0.784
Fit
a b
(d) Anisotropy: ai ¼ aðr=rcÞ þ bar �0.095 1.46ah 0.000 0.77az 0.095 0.77
Fit
a r2
(e) Destructuration v=v0 ¼ að1� 1r=rcÞ
S-CLAY1S 1.13 0.975
r: Pearson’s correlation coefficient.
especially important in the area closer than 2 column radii (Zone3a). Weber et al. [16] measured a similar value of 2.5 column radiifor the densification area. They fitted the data points of porosityand density using a hyperbolic function; a similar function maybe here proposed to fit the void ratio:
e ¼ e0 �a
r=rc � bð4Þ
where a and b are the fitting parameters. The parameter b must belower than 1 because the void ratio cannot be negative. The value ofthose fitting parameters and the fitted curves are shown in Table 4aand Fig. 9.
The results for MCC and S-CLAY1 are quite similar, but soildestructuration due to column installation causes a greater densi-fication of the soil. The value of the void ratio is directly related tothe changes in the mean effective stresses and the mobilized soilstiffness. The mean effective stresses, p0, and the size of the yieldsurface, given by p0m, are plotted in Fig. 10. The different zones pre-viously distinguished are also visible here: (1) far from the column,the mean effective stresses does not change, (2) the mean effectivestress increases but without expanding the yield surface becausethe overconsolidation ratio is OCR = 1.5, (3) the current stress point
0
0.5
1.0
1.5
2.0
2.5
3.0
1 2 5 10 20 30
MCCS-CLAY1S-CLAY1S
Zone 123
3a
p'mi
p'm
p'
p'm
OCR0=1.5χ0=5
Distance to column axis, r / rc
Nor
mal
ised
effe
ctiv
e m
ean
pres
sure
, p'/ p
' 0
Fig. 10. Size of the yield surface and effective mean stresses after columninstallation and consolidation.
0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5 6 7 8 9 10
Hyperbolic fitNumerical analysis
rc=0.4 m
Distance to column axis, r / rc
Bond
ing
para
met
er, χ
/ χ 0
Fig. 12. Bonding parameter after column installation and consolidation.
94 J. Castro et al. / Computers and Geotechnics 59 (2014) 87–97
is on the yield surface and (3a) the yield surface is notably ex-panded through strain hardening, p0m increases (Fig. 8). Note thatthe extension of these zones is slightly different depending onthe soil model. The current mean effective stress, p0, does not nec-essarily coincide with p0m when the point is on the yield surface(Fig. 10) because p0m is the mean effective stress at the apex ofthe yield surface (Fig. 2) [23]. The relative expansion of the yieldsurface is similar for MCC and S-CLAY1, which explains the similarresults for the void ratio. For S-CLAY1S, the intrinsic yield surface,p0mi, is significantly expanded in Zone 3a. The densification or thestrain hardening is only important in Zone 3a, i.e. for closely spacedcolumns.
4.3. Anisotropy
The advanced soil models S-CLAY1 and S-CLAY1S are used toreproduce the changes in soil fabric due to column installation.The inclination of the yield surface changes, as shown in Fig. 11,where the components of the fabric tensor, {ai}, are plotted. Thetwo anisotropic models predict almost identical changes in anisot-ropy. To study the influence that those changes have on the settle-ment reduction, they are input as initial values after their fitting.By definition of the fabric tensor [23], the fitting of those compo-nents must fulfilled that
13ðar þ ah þ azÞ ¼ 1 ð5Þ
For the sake of simplicity, it seems sensible to keep ah constantand decrease az the same amount that ar increases. For commoncolumn spacings, a straight line gives the best fit, ai ¼ aðr=rcÞ þ b.The value of the fitting parameters a and b and the fitted straightlines are shown in Table 4d and Fig. 11, respectively.
4.4. Destructuration
S-CLAY1S model reproduces the destructuration caused by col-umn installation (Fig. 12). The changes in the bonding parameter,v, which controls the size of the intrinsic yield surface (Fig. 10),p0m ¼ p0mið1þ vÞ, are fitted using the following hyperbolic curve
v=v0 ¼ a 1� 1r=rc
� �ð6Þ
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
0 1 2 3 4 5 6 7 8 9 10
Linear fitNumerical results
αθ
αr
αz
αz0=1.36
αr0=αθ0=0.82
rc=0.4 m
Distance to column axis, r / rc
Incl
inat
ion
of th
e yi
eld
surfa
ce, α
i
Fig. 11. Components of the fabric tensor after column installation andconsolidation.
The fitting curve accounts for full remoulding in the soil-columncontact and should not be used for high column spacings to avoidvalues of the bonding parameter higher than the initial one.
5. Soil improvement with installation effects
After the evaluation of the changes in the stresses and the stateparameters due to column installation and applying curve fitting,the soil improvement caused by the columns is analysed usingthe unit cell model (Fig. 1). The fitting curves are used to inputthe initial values of the surrounding soil that account for the effectsof installation. For the column, c and K0 are adjusted to give thesame vertical and radial stresses as those of the soil at their inter-face to ensure equilibrium. After that initialization of the stressesand state variables, a so-called ‘‘nil-step’’, i.e. a calculation stepwithout any changes, is simulated to verify equilibrium and thecorrectness of the initial values. Then, the embankment is intro-duced in only one calculation phase, as its construction is simu-lated in drained conditions. The analysis of the results focuses onthe settlement reduction factor, b, and the influence of the soilmodel (Fig. 13).
To help to evaluate the influence of the changes in the state ofsoil due to column installation, a new parameter is introduced,b*, which is the ratio between the settlement considering thosechanges and the settlement without them (Fig. 14).
Interestingly, if the changes in the soil state due to columninstallation are considered, the settlement is not always reduced.A positive effect (b* < 1) is achieved for closely spaced columnsand high embankment loads. Although no interaction effects wereconsidered by the installation of several columns, the stress incre-ment and other effects of installation are more evident near thecolumns (Zone 3a). The increment of radial stresses leads to a bet-ter lateral confinement of the columns and the increment of thepreconsolidation pressure (p0m) causes a strain hardening of thesoil. Therefore, the settlement is reduced for closely spaced col-umns as expected. The effect of the embankment load was not soclearly foreseen, yet Schweiger [22] already found numericallythat, if the effects of column installation are considered, the settle-ment was reduced only for high load levels. For low embankmentloads, the soil is overconsolidated; the remoulding effect of the col-umn installation erases the soil overconsolidation and, conse-quently, has a negative effect on the settlement reduction. Theremay be even no improvement (b > 1) for low loads. The soil consid-ered in this analysis (Bothkennar clay) is only slightly overconsol-idated (OCR = 1.5). In highly overconsolidated stiffer soils (OCR > 2),this remoulding effect may have a more negative influence on thesettlement reduction. That has already been detected in the field;
0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5
With install.W/o install.(a) MCC
N=5
N=3
N=2
Embankment height, H (m)
Settl
emen
t red
uctio
n fa
ctor
, β
0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4 5
With install.W/o install.(b) S-CLAY1
N=5
N=3
N=2
Embankment height, H (m)
Settl
emen
t red
uctio
n fa
ctor
, β
0
0.2
0.4
0.6
0.8
1.0
1.2
0 1 2 3 4 5
With install.W/o install.
(c) S-CLAY1S
N=5
N=3
N=2
Embankment height, H (m)
Settl
emen
t red
uctio
n fa
ctor
, β
Fig. 13. Settlement reduction with installation effects.
0
0.5
1.0
1.5
2.0
0 1 2 3 4 5
MCCS-CLAY1S-CLAY1S
- Negative effect
+ Positive effect
(a) N=2
Embankment height, H (m)
Influ
ence
of i
nsta
llatio
n ef
fect
s, β
*
0
0.5
1.0
1.5
2.0
0 1 2 3 4 5
MCCS-CLAY1S-CLAY1S
- Negative effect
+ Positive effect
(b) N=3
Embankment height, H (m)
Influ
ence
of i
nsta
llatio
n ef
fect
s, β
*
0
0.5
1.0
1.5
2.0
0 1 2 3 4 5
MCCS-CLAY1S-CLAY1S
- Negative effect
+ Positive effect
(c) N=5
Embankment height, H (m)
Influ
ence
of i
nsta
llatio
n ef
fect
s, β
*
Fig. 14. Ratio of the settlement with and without installation effects: (a) N = 2; (b)N = 3; and (c) N = 5.
J. Castro et al. / Computers and Geotechnics 59 (2014) 87–97 95
for example, Serridge and Sarsby [27] alert on the negative effect ofcolumn installation in the upper crust, which is clearlyoverconsolidated.
The S-CLAY1 model predicts a more positive effect of the col-umn installation in the settlement reduction than MCC because itaccounts for the soil anisotropy (Fig. 14). On one hand, the radialstresses after column installation and consolidation are predicted
to be higher for S-CLAY1 than MCC (Fig. 7) and on the other hand,the changes in the soil anisotropy during installation (Fig. 15) havea positive effect in reducing the settlement because energy is dis-sipated in the evolution of anisotropy. To help to visualize thechanges in the soil fabric, Fig. 16 shows the (az–ah, ar–ah) vectorin arbitrary points. This vector changes from horizontal directionfor an initial vertical cross anisotropy towards a nearly verticalone for radial cross anisotropy after column installation and con-
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
1.4
1.5
0 1 2 3 4 5 6 7 8 9 10
After load.After install.
S-CLAY1N=55m depth
αθ
αr
αz
αz0=1.36
αr0=αθ0=0.82
rc=0.4 m
Distance to column axis, r / rc
Incl
inat
ion
of th
e yi
eld
surfa
ce, α
i
Fig. 15. Change in the components of the fabric tensor after embankment loading.
0.5(a)
αr-αθ
αz-αθ
(b)
0 1 2 3 4 5 6 7 8 9 10
S-CLAY1N=55m depth
(c)
Distance to column axis, r / rc
Fig. 16. Visualization of the soil fabric: (a) before column installation; (b) aftercolumn installation and consolidation; and (c) after embankment loading.
96 J. Castro et al. / Computers and Geotechnics 59 (2014) 87–97
solidation. Fellenius and Samson [34] already measured in the fieldthis type of soil fabric rotation caused by pile driving. Hansbo [35]proposed based on field experience that in the ‘‘smear zone’’around a vertical drain, the horizontal permeability is proportionalto the vertical one in the intact soil, which may be justified by thesoil fabric rotation. The one dimensional compression caused bythe embankment load rotates again the fabric vector towards thehorizontal direction. Its length is equal to a0 = 0.539 for the initialsituation, and this changes only slightly.
When the soil sensitivity is included (S-CLAY1S), the changes inthe soil state due to column installation are less positive than forthe S-CLAY1 model (Fig. 14). The destructuration of the soil duringcolumn installation, considered as the decrease of v (the amount ofbonding), is on its own positive because the soil sensitivity prior tothe embankment load is lower and therefore, the destructuration
during the loading process is less important. However, the soildestructuration during column installation causes also a decreaseof the preconsolidation pressure, p0m, and reduces the increase ofthe radial stresses (Figs. 7c and Fig. 10). Therefore, the overall effectof soil destructuration is negative.
Fig. 14 demonstrates that including the changes in the soil statedue to column installation is not always positive, it depends oneach case and is difficult to quantify, as it is a function of columnspacing, OCR and soil sensitivity.
6. Conclusions
Numerical simulations using advanced soil models were per-formed to study the influence of stone column installation inreducing the settlement of a natural soft clay. For low loads andlarge column spacings, special care should be paid to columninstallation because it has a negative effect on the settlementreduction, especially in overconsolidated soils, which are clearlydamaged by column installation.
Soil fabric plays a crucial role on the influence of the installationeffects on the soil improvement. Soil anisotropy has a positive ef-fect because of the rotation of the soil fabric and the increase ofthe radial stresses.
As a summary, the following changes in the state of the soil dueto column installation have a positive influence on the settlementreduction:
(a) increase of the radial stresses, which laterally confined thecolumn;
(b) strain hardening of the soil, i.e. increase of the preconsolida-tion pressure, which increases the soil stiffness, related tothis effect is the reduction of the void ratio;
(c) change of the soil anisotropy, from cross (horizontal) anisot-ropy to vertical and again to horizontal after embankmentloading;
and the following have a negative influence:
(d) decrease of the OCR, which increases the soil plastic strains;(e) soil destructuration, which leads to lower stress increments,
specially radial ones, and diminishes the improvement, and(f) excess pore pressures, which have been assumed as fully
dissipated in this paper but, if still present when theembankment is going to be elevated, cause some soil consol-idation and reduce the effective stresses.
Acknowledgements
The research was carried out as part of a Marie Curie Industry-Academia Partnerships and Pathways project on ‘‘ModellingInstallation Effects in Geotechnical Engineering (GEO-INSTALL)’’(PIAP-GA-2009-230638).
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