"Challenges Faced in 3-D Finite Element Modelling of Stone Column Construction"

CHALLENGES FACED IN 3-D FINITE ELEMENT MODELLING
OF STONE COLUMN CONSTRUCTION
B.A. McCABE1
, M.M. KILLEEN1
& D. EGAN2
1
Dept. of Civil Engineering, National University of Ireland, Galway, Ireland
2
Keller Ground Engineering, Coventry, U.K.
Abstract
In all areas of geotechnical engineering involving an ‘installation’ and corresponding ground
displacement, the changes to the stress regime taking place tend to be poorly understood.
The installation of Vibro Replacement stone columns in soft clays and silts is no different,
and there is a shortage of high quality experimental data and proven mathematical approaches
to inform the stone column designer of the implications of the installation process. In this
paper, some conclusions are drawn regarding current analytical and numerical capability to
model stone column installation.
Keywords: analytical modelling, cavity expansion, installation, numerical modelling, Vibro
Replacement stone columns
1. Introduction
Vibro Replacement is a technique used to improve the bearing capacity and settlement
performance of a wide variety of soil types. In recent years, its application to marginal
ground conditions in Ireland, such as soft clays and silts and loose fills, has grown. McCabe
et al. (2007) and McNeill (2007) provide an explanation of the Vibro Replacement technique,
illustrate suitable soil types and design concepts, as well as providing some Irish case
histories.
The stress changes that construction of groups of columns impose on the surrounding ground
cannot be readily quantified, and there is a dearth of high quality field measurements that
might help to validate any mathematical prediction approach used. The importance of
construction effects to ground improvement design has been acknowledged with the advent
of a new Marie Curie Research Training Network called GEO-INSTALL from April 2009,
following on from the current AMGISS (Advanced Modelling of Ground Improvement in
Soft Soils) network. The AMGISS project has concentrated primarily on developing
constitutive models to reflect common soft soil characteristics such as anisotropy,
destructuration and bonding, whereas the new GEO-INSTALL network will focus on the
numerical issues associated with large strain modelling of displacement piles and stone
column installation.
In this paper, some lessons learned from undrained cavity expansion theory are presented.
The ability of 3-D finite element analysis to model the column construction process is
assessed based upon a comparison with cavity expansion theory. Possible methods of
building in an installation effect before the loading phases of numerical analyses are
suggested.
B.A. McCabe, M.M. Killeen & D. Egan - 1 -
Remedy Geotechnics Ltd
Technical Paper R12
www.remedygeotechnics.com

2. Installation Process
Well-constructed stone columns may be formed in soft silts and clays by inserting a bottom
feed depth vibrator poker into the ground (typical range of diameters 430-800mm). The poker
penetrates under the action of its own vibrations, assisted with the pull-down facility of the
rig if necessary. The vibrations are predominantly horizontal, and tend to densify materials
having in excess of 90% granular (sand and/or gravel) content. However clays, silts and
mixed ground conditions are not immediately densified by the vibrations; the improvement
comes from filling the hole formed by the poker with inert crushed stone or gravel and
compacting in stages from the base of the hole upwards. The performance of the stone
column depends largely on the lateral resistance of the soil around it. The poker acts as an
investigating tool in this respect and will match the quantity of stone supplied to the
consistency of the soil layer encountered. When using a standard 430mm diameter poker, the
final stone column diameter is typically 500-600mm.
There are two different approaches that may be adopted to construct stone columns. The
stone may be tipped in controlled amounts from the ground surface and compacted in layers
through repeated penetration and withdrawal of the poker; this system is referred to as ‘Top
Feed’. Alternatively, the stone may be fed from a hopper through a delivery tube along the
side of the poker. This ‘Bottom Feed’ method is preferred when hole collapse is likely, such
as when there is a high water table in granular soils and in weak clay soils. A schematic of
the Bottom Feed process is shown in Figure 1. More detailed information is given by
Sondermann and Wehr (2004) and others.
Figure 1 – Bottom Feed Vibro Replacement (courtesy of Keller Ground Engineering)
Technical Paper R12

3. Lessons from Cavity Expansion Theory
Yu (2000) illustrates that, with the exception of a zone at the top of a pile affected by the
ground surface, the soil displacement due to a single pile installation may be modelled by
analytical cavity expansion theories. Much of the soil is displaced predominantly in the radial
direction, so cylindrical cavity expansion (CCE) theory is most appropriate. Measurements of
the radial movement of the soil near a pile mid-depth taken from the field tests of Cooke and
Price (1978) and the model tests of Randolph et al. (1979) show good agreement with
theoretical solutions. Spherical cavity expansion applies locally where ground displacement
is affected by the pile tip.
The effect on the ground of constructing a stone column in fine soil may be estimated from
the undrained CCE formulation of Gibson and Anderson (1961). Since the poker expands a
hole from an initial diameter of zero to the poker diameter (430mm) and subsequently to the
diameter of the compacted column, the expansion is effectively infinite. On this basis, Egan
et al. (2008) suggest that modelling stone columns using CCE requires the additional
assumption that the equivalent cavity expansion pressure reaches its limit value (plim) during
installation, quantified in Gibson and Anderson (1961) by:
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎥
⎦
⎤
⎢
⎣
⎡
+
++=
)1(2
log10lim
υu
eu
c
E
cpp (1)
where p0 is the initial lateral total stress, cu is the undrained shear strength, E is Young’s
modulus and ν is Poisson’s ratio.
From a finite element (FE) modelling perspective, it is of interest to examine the
development of cavity pressure as a function of lateral expansion. The soil parameters used
for the prediction are shown in Table 1 and pertain to the Carse clay at Bothkennar, Scotland
(Nash et al., 1992). CCE predictions are plotted in Figure 2; the cavity pressure p is
normalised by plim and the current cavity radius a is normalised by the starting radius a0. The
curve shown in Figure 2 corresponds to mid-depth along a 5m long column; the curve in
normalized form is relatively insensitive to the depth (small changes to p0/plim, i.e. at a=a0)
and to the initial value of a0. It can be seen that considerable expansion is required to
approach the limit pressure; ≈0.15ao expansion is required to reach 0.8plim and ≈0.4ao
expansion is required to reach 0.9plim. On this basis, it would appear that FE models would
need to incorporate considerable lateral expansion to capture undrained installation
adequately.
Table 1 – Bothkennar parameters used in CCE model
Undrained shear strength, cu 14 + 2.3z (z=depth in m)
Young's modulus, E 3050 + 1447z (z=depth in m)
Earth pressure coefficient, Ko 0.5
Technical Paper R12

0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
Normalised Expansion (a/a0)
NormalisedCavityPressure(p/plim)
Figure 2 – Variation of cavity pressure with radius (undrained CCE)
The lateral variations of radial horizontal stress (based on Gibson and Anderson, 1961) and
pore water pressure (Randolph et al., 1979) predicted by CCE when p=plim are plotted in
Figure 3 and pertain to column mid-depth. The Randolph et al. (1979) expression for excess
pore water pressure in the plastic zone is given by:
⎟
⎠
⎞
⎜
⎝
⎛
=Δ
a
R
cu u ln2 (2)
where R is the radial extent of the plastic zone. In Figure 3, r is the radial distance from the
centre of the column. There is some field evidence that maximum excess pore pressures
measured in the ground around a stone column during installation conform to eqn. (2) (i.e.
Castro 2007, Egan et al. 2008). This, in addition to similar evidence for driven piles, gives
some credence to the use of CCE predictions to appraise the performance of FE analysis.
4. Finite Element Analysis
Few researchers have attempted to capture the effects of column construction in numerical
modelling by a CCE type approach. Guetif et al (2007) model installation in PLAXIS 2-D by
defining a cylinder of ‘dummy material’ about the axis of symmetry with purely elastic
properties and a nominal Young’s Modulus (E=20kPa). The dummy material is then
expanded from an initial diameter of 0.5m to a final diameter of 1.1m, before the properties
of the ‘dummy material’ are converted to those of stone.
The use of PLAXIS 3-D Foundation is preferable when modelling pad and strip foundations,
where the 3-D nature of a problem needs to be captured. However, it is known that PLAXIS
3-D has greater limitations than PLAXIS 2-D in terms of modelling larger strains. With this
Technical Paper R12

in mind, a simple PLAXIS 3-D model of a 5m long 600mm diameter stone column was
developed, supporting a 1m × 1m square footing (modelled as a floor in PLAXIS). Various
degrees of lateral expansion were applied to the column (a/a0 = 1.03, 1.06, 1.1, 1.33, 1.67)
and the radial total stress and pore pressure variation with radius was noted. The stone was
modelled as a Mohr Coulomb (MC) material while the more advanced Hardening Soil (HS)
model was used to represent the Bothkennar soft clay. In the latter case, the parameters used
are as consistent as possible with those deployed in the CCE model. All parameters are listed
in Table 2 and some of the Bothkennar parameters are taken from Kamrat-Pietraszewska et al
(2008). Undrained installation (without consolidation) was considered for the purposes of this
paper.
0
20
40
60
80
100
120
140
160
0 10 20 30 40 5
Normalised radial distance from borehole centre, r/a
Radial&tangentialtotalstressandpore
pressure(kPa)
0
Pore pressure
σθ: Tangential stress
σr: Radial stress
Figure 3 – Undrained CCE predictions for radial total stresses and pore pressures
Figure 4 – Mesh used for PLAXIS 3-D finite element analysis
Technical Paper R12

Table 2 – Parameters used to model Bothkennar soil profile in PLAXIS 3-D
HS Parameters Crust Carse Clay MC Parameters Stone
Depth (m) 0-1 1-20 Depth (m) 0-5
γ (kN/m3
) 19.0 16.5 γ (kN/m3
) 19.0
E 1.37 2.00 E 72000
POP (kPa) 30 - ν 0.2
OCR - 1.5 c' (kPa) 0.1
K0 0.7 0.5 φ (°) 45
Κ 0.02 0.02 ψ (°) 15
ν' 0.2 0.2
Λ 0.3 0.3
M 1.51 1.51
Only the data for a/a0 = 1.03, 1.10 and 1.33 lateral expansions are presented in Figure 5 for
brevity, where they are compared with cavity expansion values. The theoretical curve for
Figure 5(a) is based upon Randolph et al (1979). The variation of the radial stress with radial
distance from the centre of the stone column is adapted from Gibson & Anderson (1961) in
Figure 5(b). There are two theoretical curves shown in Figure 5(b), one representing the
radial stress assuming p=plim (i.e. what field conditions would suggest occurs) and the other
representing the radial stress due to the specified lateral expansion. It is observed that as the
lateral expansion increases, the PLAXIS data tends towards the plim curve as expected. The
general trend of how the radial total stress increase varies with radius r is captured quite well.
However, the PLAXIS 3-D radial total stress and excess pore pressure predictions are
irregular and do not vary smoothly, especially for a<r<2a. In fact at certain r/a values,
PLAXIS 3-D returns several different values of pore pressure and radial stress, indicating
major problems in handling the lateral expansion. It was found that these anomalies still
arose regardless of the mesh density chosen; further work is needed to decipher whether these
problems are due to a violation of small strain theory, the magnitude of the strains imposed in
relation to the size of the elements or other effects. It is of concern that anomalies arise even
for the smallest expansion (a/a0 = 1.03) and worsen as the extent of lateral expansion
increases. Clearly the scatter at the level of expansion needed to reach plim would be
unacceptable. In addition, the radial extent of the anomalies is such that there is no prospect
of modelling installation effects in groups of columns that are at typical field spacings (i.e.
1.2-2.3m). This work demonstrates that even with a relatively sophisticated soil model,
PLAXIS 3-D is currently incapable of capturing the installation effects properly. Although
measurements were not in purely fine materials, Elshazly et al. (2007) and Kirsch (2008)
show that successful modelling of load tests on column-reinforced ground requires the
inclusion of a post-installation improvement to the lateral earth pressure coefficient, K.
This paper has concentrated solely on undrained expansion; as the post-consolidation stresses
will not be correctly modelled if PLAXIS 3-D returns poor undrained cavity expansion
predictions. Further work could be focussed on PLAXIS 2-D with large undrained
expansions followed by a consolidation phase to estimate the permanent changes to K values
in the ground. Until a more suitable approach is developed, an approximate approach would
Technical Paper R12

be to initiate the model with an increased K (higher than K0 up to a maximum value of
perhaps Kp =1 in the undrained case) in the vicinity of the columns.
a/a0 = 1.03
-50
0
50
100
150
200
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Normalised radial distance (r/a)
Excesspwp(kPa)
PLAXIS 3-D
Randolph et al (1979)
a/a0 = 1.03
-50
0
50
100
150
200
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Changeinradialtotalstress(kPa)
PLAXIS 3-D
CCE
CCE (plim)
a/a0 = 1.1
-50
0
50
100
150
200
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Excesspwp(kPa)
PLAXIS 3-D
a/a0 = 1.1
-50
0
50
100
150
200
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
PLAXIS 3-D
CCE
CCE (plim)
a/a0 = 1.33
-50
0
50
100
150
200
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Excesspwp(kPa)
PLAXIS 3-D
a/a0 = 1.33
-50
0
50
100
150
200
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
PLAXIS 3-D
CCE
CCE (plim)
Figure 5(a) - Excess pore pressure (pwp)
versus normalised radial
distance for various lateral
expansions
Figure 5(b) - Total radial stress versus
normalised distance for
various lateral expansions
Technical Paper R12

5. Conclusion
This paper has illustrated that large cavity expansions need to be included in a numerical
analysis if the process of stone column installation is to be captured at a fundamental level. It
appears that the small strain or other limitations inherent in PLAXIS 3-D FE formulation
restricts its use for modelling the installation process. Further development work needs to be
carried out to provide PLAXIS 3-D with the capability of modelling larger strains. It should
also be borne in mind that PLAXIS 3-D is a quasi 3-D package in that meshing in the vertical
direction is basic as shown in Figure 4. In the interim, ‘work-arounds’ are possible that will
give more realistic predictions of column behaviour, one of which is to increase the post-
installation K above K0 to a maximum of Kp=1.
References
• Castro, J. (2007) Pore pressures during stone column installation, Proceedings of the 17th
European Young Geotechnical Engineers Conference, Ancona, Italy
• Cooke, R.W. and Price, G. (1978) Strains and displacements around friction piles,
Building Research Station CP 28/78, October.
• Egan, D., Scott, W. and McCabe, B.A. (2008) Installation effects of vibro replacement
stone columns in soft clay, 2nd
International Workshop on the Geotechnics of Soft Soils,
Focus on Ground Improvement, Glasgow, pp. 23-29.
• Elshazly, H, Hafez, D. and Mossaad, M. (2006) Back calculating vibro installation stresses
in stone-column-reinforced soils, ICE Ground Improvement, Vol. 10, No. 2, pp 47-53
• Gibson, R.E. and Anderson, W.F. (1961) In-situ measurement of soil properties with the
pressuremeter, Civil Engineering Public Works Review, Vol. 56, pp. 615-618
• Guetif, Z., Bouassida, M. and Debats, J.M. (2007) Improved soft clay characteristics due
to stone column installation, Computers and Geotechnics, Vol. 34(2), pp. 104-111
• Kamrat-Pietraszewska, D., Krenn, H., Sivasithamparam, N. and Karstunen, M. The
influence of anisotropy and destructuration on a circular footing, Proceedings of the 2nd
BGA International Conference on Foundations, Dundee, pp. 1527-1536
• Kirsch, F. (2008) Evaluation of ground improvement by groups of vibro stone columns
using field measurements and numerical analysis, 2nd
International Workshop on the
Geotechnics of Soft Soils, Focus on Ground Improvement, Glasgow, pp. 241-248
• McCabe, B.A., McNeill, J.A. and Black, J.A. (2007) Ground improvement using the vibro
stone column technique, Transactions of the Institution of Engineers of Ireland, 2007-08
• McNeill, J.A. (2007) Improvement of soft ground by Vibro stone columns, Proceedings of
the Engineers Ireland Soft Ground Engineering Conference, Feb 2007.
• Nash, D.F.T., Powell, J.J.M. and Lloyd, I.M. (1992) Initial investigations of the soft clay
test site at Bothkennar, Geotechnique, Vol. 42, No. 2, pp. 163-181
• Randolph, M.F., Carter, J.P. and Wroth, C.P. (1979) Driven piles in clay – the effects of
installation and subsequent consolidation, Geotechnique, Vol. 29, No. 4, pp. 361-393
• Sondermann, W. and Wehr, W. (2004) Deep vibro techniques, ground improvement, 2nd
Ed, pp. 57-92, Spon Press
• Yu, H.S. (2000) Cavity Expansion Methods in Geomechanics, Kluwer Academic
Publishers
Technical Paper R12

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