-
Comparison of different models for analysing foundations on jet
grout columns
F. Tschuchnigg, H. F. Schweiger Computational Geotechnics Group,
Institute for Soil Mechanics and Foundation Engineering, Graz
University of Technology, Graz, Austria
Keywords: embedded beam, finite element, 3D model, ground
improvement, jet grout column
ABSTRACT: If ground conditions are such that the load from
structures such as high rise buildings cannot be supported by
shallow foundations several options exist. An economical
alternative to a classical pile or piled raft foundation could be
the use of jet grouted columns. In general a large number of jet
grouted columns has to be constructed resulting in a problem which
is difficult to analyse and numerical methods are increasingly
utilised to calculate the performance of such foundations. As a
two-dimensional representation of pile groups is usually not
sufficient 3D modelling is required, leading to very large models
if all piles are discretized with volume elements. An attractive
method to reduce the complexity of such models is the use of a
so-called embedded pile concept where piles are not explicitly
modelled with continuum finite elements but replaced by a special
formulation which can take into account the behaviour of a pile
penetrating a finite element in any orientation. The paper compares
the results obtained for a raft supported by jet grouted columns
with three different models: a 2D plane strain model, a full 3D
model with volume discretisation of the columns and one model with
the embedded pile formulation. Finally application of the embedded
pile concept to a practical problem is presented.
1 Introduction In general one has several possibilities to model
a foundation supported by jet grout columns. The easiest and
fastest way is to define a 2D plane strain model in which,
depending on the geometry, either the diameter or the stiffness of
the jet grouted columns has to be adapted to plane strain
conditions. Such a model is convenient for principle studies as
variations of inclinations or lengths of the jet grout columns, but
due to the geometrical restrictions calculated settlements are not
very reliable. Hence in most cases a 3D model is necessary to
assess the settlement behaviour of such structures. In a 3D model,
when using Plaxis 3D Foundation (Brinkgreve and Swolfs, 2007), one
has two alternatives to model jet grout columns. The first option
to model such foundations is the standard finite element approach,
which means the piles are modelled with volume elements and the
interaction of the pile and the surrounding soil is described with
interface elements. The roughness of the interaction
(soil-structure) is defined with a strength reduction factor Rinter
and this factor determines the interface strength with respect to
the soil strength. The problem with this approach is that for a
large number of jet grouted columns this leads to computationally
demanding models which may be beyond the capabilities of the code
or simply take to long to analyse from a practical point of view.
The alternative way to define piles or columns in a 3D model is the
embedded pile approach. An embedded pile consists of a beam element
which can be placed in arbitrary direction in the subsoil, embedded
interface elements to model the interaction of the structure and
the surrounding soil and embedded non-linear spring elements at the
pile base to describe the base resistance. When assigning the
embedded pile additional nodes are automatically generated inside
the existing finite elements and the pile-soil interaction
behaviour is linked to the relative displacements between the pile
nodes and the existing soil nodes (Sadek and Shahrour, 2004). The
connection between the soil and pile nodes is achieved with
embedded interface elements. A diameter d, the unit weight and the
stiffness E is assigned to the embedded beam element, although
geometrically it remains a line element. The diameter d in the
material data set determines an elastic zone in the soil around the
beam, i.e. plastic soil behaviour is excluded (Engin, 2006) with
the argument, that in reality the column has a finite thickness d.
Maximum skin friction and base resistance is assigned to the
special interface elements and therefore the bearing capacity of
the pile or column is an input to the analysis and not a
result.
-
2 Comparison of different models This chapter presents the
comparison of different models for analysing foundations on jet
grout columns. Figure 1 shows the geometry of the example. The soil
profile consists of six layers and is modelled with the Hardening
Soil model, a double hardening model available in the Plaxis model
library. The parameters are given in Table 1. A pre-overburden
pressure (POP) of 600kN/m2 is applied to all soil layers except the
gravel layer to generate the pre-consolidation pressure. The K0
value in all pre-consolidated layers is set to K0=0.7. The
foundation slab is defined as a linear elastic material and the
properties are shown in Table 2. The properties of the jet grout
piles are discussed in the next sections. Drained conditions are
assumed for all analyses.
Figure 1. Geometry of the example
Table 1. Soil model properties
Soil layer unsat sat E50,ref Eoed,ref Eur,ref Cref [kN/m3]
[kN/m3] [kN/m2] [kN/m2] [kN/m2] [kN/m2] [ ] [ ]
Gravel 21.0 21.5 40000 40000 120000 0.1 35.0 5.0
Sandy silt 1 20.0 20.0 15000 15000 45000 20.0 27.5 0.0
Fine to medium dense sand 1 20.0 21.0 20000 20000 60000 5.0 32.5
2.5
Sandy silt 2 20.0 20.0 15000 15000 45000 30.0 27.5 0.0
Fine to medium dense sand 2 20.0 21.0 20000 20000 60000 5.0 32.5
2.5
Stiff base layer 20.0 20.0 30000 30000 90000 30.0 27.5 0.0
Soil layer Type ur pref m K0nc Rf Rinter POP [ - ] [kN/m2] [ - ]
[ - ] [ - ] [ - ] [kN/m2]
Gravel Drained 0.2 100 0.00 0.426 0.9 1.0 0
Sandy silt 1 Drained 0.2 100 0.60 0.538 0.9 1.0 600
Fine to medium dense sand 1 Drained 0.2 100 0.50 0.462 0.9 1.0
600
Sandy silt 2 Drained 0.2 100 0.60 0.538 0.9 1.0 600
Fine to medium dense sand 2 Drained 0.2 100 0.50 0.462 0.9 1.0
600
Stiff base layer Drained 0.2 100 0.60 0.538 0.9 1.0 600
-
Table 2. Properties for foundation slab
Type unsat sat Eref Rinter [kN/m3] [kN/m3] [ - ] [kN/m2] [ -
]
Concrete Drained 25.0 25.0 0.15 28000000 1.0
2.1 2D model This section shows the results of a 2D plane strain
model for the example in Figure 1. Two different configurations are
studied. In the first one (Figure 2(a)) all jet grout columns are
vertical and in the second one the outer piles are inclined (Figure
2(b)). The diameter d has been taken as the true diameter and the
stiffnesses of the piles are converted into equivalent stiffnesses
according to their spacings (Table 3). The Mohr-Coulomb model is
used to describe the behaviour of the jet grouted columns. The
interaction between jet grouted columns and the subsoil can be
assumed as very rough hence no interface elements are defined
between columns and soil. The contour plots of maximum vertical
displacements for these two models are presented in Figure 3(a) and
3(b). The value of maximum settlements (uy,max) for the model with
vertical piles is 71.5mm and for the model where the outer piles
are inclined uy,max is 68mm.
Figure 2. 2D models
Table 3. Properties of the jet grout piles for the 2D model
jet grout pile Diameter Spacing Type unsat sat Eref cref [m] [m]
[kN/m3] [kN/m3] [ - ] [kN/m2] [kN/m2] [ ]
JGP 1 0.8 2.0 Drained 21.5 21.5 0.15 5000000 1350 32.5
JGP 2 0.8 1.0 Drained 21.5 21.5 0.15 2500000 675 32.5
all piles vertical outer piles inclined
(a) (b)
-
Figure 3. Contour plot of vertical displacements for 2D
models
2.2 3D model with standard finite element approach For this
calculation the 2D model (Figure 2) is extended to a 3D strip model
as shown in Figure 4(a). The jet grout columns are discretized
(Figure 4(b)) and described with Mohr-Coulomb material behaviour
(Table 4). Again no interfaces are defined between the structure
and the column. The soil profile and parameters are the same as for
the 2D model. With this approach just one calculation with vertical
piles is presented, due to the fact that it is not possible to
define inclined volume piles in Plaxis 3D Foundation. The maximum
value of settlements uy,max is 70mm, a contour plot of vertical
displacements is presented in Figure 5.
Figure 4. 3D model with discretized piles
Table 4. Properties of the discretized jet grout piles for the
3D model
Jet grout pile Diameter Type unsat sat Eref cref [m] [kN/m3]
[kN/m3] [ - ] [kN/m2] [kN/m2] [ ]
JGP 0.8 Drained 21.5 21.5 0.15 10000000 2700 32.5
(a) (b)
0 mm
36 mm
72 mm
all piles vertical outer piles inclined
(a) (b)
-
Figure 5. Contour plot of vertical displacements with
discretized piles
2.3 3D model with embedded piles With this concept it is
possible to model piles in arbitrary direction in the soil hence
the two models as considered for the plane strain case are
presented (Figure 6). The outer piles have an inclination of 1 to
5. The diameter of the embedded piles shown in Figure 6(a) and (b)
are not the real diameters of the jet grout columns as defined in
the input. What is printed here is just the beam element in the
middle of the embedded pile but the elastic region around the
embedded pile, which is equal to the real diameter, is not shown.
As mentioned previously the bearing capacity of the embedded piles
is an input and in this example defined by a linear skin friction
distribution and a base resistance. The input parameters for the
embedded piles are given in Table 5. The maximum settlement when
all piles are vertical is 73.5mm (Figure 7(a)) and for inclined
outer piles uy,max decreases to 69.5mm (Figure 7(b)). The purpose
of this example was to compare different modelling approaches for
working load conditions and therefore limiting values for skin
friction and base resistance have been chosen such that they are
well beyond mobilized values for the loads considered.
Figure 6. Foundation with piles for the embedded pile models
(a) (b)
-
Table 5. Embedded pile properties
Eref d top,max bot,max Fmax [kN/m3] [kN/m2] [m] [kN/m] [kN/m]
[kN]
Jet grout column soil+1.0 10000000 0,8 0.0 502.0 600
Figure 7. Vertical displacements for the embedded pile
models
2.4 Conclusion Results, both from plane strain and embedded pile
analysis show that the inclination of the outer piles leads to a
reduction of vertical displacements of roughly 4mm which
corresponds to about 5%. This is due to the fact, that the inclined
piles and the vertical piles next to these can mobilize more skin
friction. Both 2D models are in good agreement with the embedded
pile calculations. The difference of maximum vertical displacements
is less then 3%. The difference between the model with the embedded
pile concept and the model with volume piles is roughly 5%. The
reason therefore is probably an overestimation of the tip
resistance in the standard finite element approach (Engin et al.,
2007).
3 Application of the embedded pile concept In this section the
application of the embedded pile concept for a practical foundation
problem is presented. The design calculation based on the bearing
capacity of individual piles required about 3000 jet grouted piles
and therefore even with the embedded pile option a simplification
of the FE-model was necessary. In the model two areas are
distinguished, namely ones which are not sensible for the
superstructure and in which the load is not very high and ones
where the loads are very high and the superstructure is very
sensitive to (differential) settlements. The former are modelled as
homogenized blocks, meaning that the zones of the sub-soil in which
the jet grout columns are installed are defined with smeared
properties. For the latter the embedded pile concept is applied.
The final model for the application of the embedded pile approach
is shown in Figure 8(a). The dimensions of the model are
500/50/400m and it consists of roughly 48000, 15noded wedge
elements. In Figure 8(b) a top view of the structural elements
without the subsoil is presented. The sensitive section consists of
615 embedded piles with different lengths, inclinations and
spacings. The soil profile is the same as in the example before,
but the soil properties have been slightly modified. The
pre-consolidation pressure in this case is increased to 800kN/m2.
The foundation slabs are discretized and defined as linear elastic
material. Because of the dimensions of the model and computational
limitations it is not possible to model the slabs with all details
and therefore some geometric simplifications have been required.
The properties of the embedded piles are shown in Table 6. The
capacity is defined by a constant skin friction distribution and a
base resistance. The constant distribution of the skin friction is
probably not realistic, but in working load conditions the skin
friction is not fully mobilized hence the distribution plays a
minor role. One of the most important information of this
calculation is the global settlement behaviour of the construction
because the complete structure is modelled, including all areas
with significant different load intensities. In Figure
0 mm
37 mm
74 mm (b) (a)
-
9(a) the vertical displacements of the structural elements are
presented. The maximum settlements are in the region where the jet
grout columns are modelled in detail with the embedded pile option
and a value of 63mm for uy,max is obtained. The subway tunnel, in
the left part of the model experiences settlements in the range of
10mm. The difference in load bearing behaviour of the jet grouted
columns can also be evaluated. As an example Figure 9(b) shows the
distribution of the axial force for an inclined pile in the outer
row where the maximum settlements are obtained. The continuous
decrease of the axial force confirms that the inclined piles
mobilize significant skin friction. On the contrary piles within a
group, with small spacings, are not able to mobilize the same
degree of skin friction and therefore they are transferring the
load via the base resistance into the soil.
Figure 8. Model with embedded piles in sensitive areas
Table 6. Embedded pile properties
Eref d top,max bot,max Fmax [kN/m3] [kN/m2] [m] [kN/m] [kN/m]
[kN]
Jet grout column soil+1.0 10000000 0,8 251.0 251.0 1000
Figure 9. Contour plot of vertical displacements (a) and axial
force in an inclined jet grouted column (b)
(a) (b)
(a) (b)
-
4 Discussion and conclusions A comparison of different models
for analysing a foundation supported by jet grout columns and the
application of the embedded pile option to a practical problem has
been presented. The results from the comparison of different models
show that all models give the same order of magnitude for
deformations. Altogether the maximum difference in vertical
settlements for all different modelling assumptions is less than 5%
and as a consequence of minor importance. The application of the
embedded piles concept emphasized the benefit of this approach.
With this concept it is possible to model a high number of piles or
columns because no discretisation of the piles is necessary and
very large computational models can be avoided. In the application
example of this paper even the embedded pile concept reached its
limitations and therefore two types of modelling have been
combined. The areas which are not sensitive for the superstructure
have been modelled with smeared properties and in sensible zones
every single pile is modelled as an embedded pile. The outcome is
the global settlement behaviour of the entire structure. However
detailed information in the section with embedded piles, for
example relative displacements and mobilization of the skin
friction is obtained. Another benefit is that the influence of
different spacings, pile lengths and diameters can be evaluated
with reasonable effort in these sensitive areas. Concerning the
distribution of the skin friction along an embedded pile, it is
obvious that the mobilization of the skin friction is influenced by
the distribution in the failure state, which is an input. In
working load conditions this predefined distribution of the skin
friction does not change the results significantly but for ultimate
limit state analysis assumptions for the distribution of the
limiting skin friction, base resistance, elastic region around the
pile and mesh coarseness may have a significant influence on the
result.
References Brinkgreve R.B.J., Swolfs W.M. 2007. Plaxis 3D
Foundation, Finite element code for soil and rock analyses. Users
manual, the
Netherlands.
Engin H.K., Septanika E.G., Brinkgreve R.B.J. 2007. Improved
embedded beam elements for the modelling of piles. Proc. 10th Int.
Conf. on numerical models in geomechanics NUMOG X, Rhodos (Greece),
475-480.
Engin H.K. 2006. A report on embedded piles. Plaxis internal
report.
Sadek M., Shahrour I. 2004. A three dimensional embedded beam
element for reinforced geomaterials. Int. J.f.Numerical and
Analytical Methods in Geomechanics, 931-946.
/ColorImageDict > /JPEG2000ColorACSImageDict >
/JPEG2000ColorImageDict > /AntiAliasGrayImages false
/CropGrayImages true /GrayImageMinResolution 300
/GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true
/GrayImageDownsampleType /Bicubic /GrayImageResolution 300
/GrayImageDepth -1 /GrayImageMinDownsampleDepth 2
/GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true
/GrayImageFilter /DCTEncode /AutoFilterGrayImages true
/GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict >
/GrayImageDict > /JPEG2000GrayACSImageDict >
/JPEG2000GrayImageDict > /AntiAliasMonoImages false
/CropMonoImages true /MonoImageMinResolution 1200
/MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true
/MonoImageDownsampleType /Bicubic /MonoImageResolution 1200
/MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000
/EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode
/MonoImageDict > /AllowPSXObjects false /CheckCompliance [ /None
] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false
/PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000
0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true
/PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ]
/PDFXOutputIntentProfile () /PDFXOutputConditionIdentifier ()
/PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped
/False
/Description > /Namespace [ (Adobe) (Common) (1.0) ]
/OtherNamespaces [ > /FormElements false /GenerateStructure true
/IncludeBookmarks false /IncludeHyperlinks false
/IncludeInteractive false /IncludeLayers false /IncludeProfiles
true /MultimediaHandling /UseObjectSettings /Namespace [ (Adobe)
(CreativeSuite) (2.0) ] /PDFXOutputIntentProfileSelector /NA
/PreserveEditing true /UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /LeaveUntagged /UseDocumentBleed false
>> ]>> setdistillerparams> setpagedevice