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 NGM 2016 Reykjavik
Proceedings of the 17th Nordic Geotechnical Meeting
Challenges in Nordic Geotechnic 25th – 28th of May

Analysis of inclined piles in settling soil

F. Resare
ELU Konsult, Sweden, fredrik.resare@elu.se

A.B. Lundberg, G. Axelsson

ELU Konsult, Sweden

ABSTRACT
The use of raked, or batter, piles is an efficient way to handle horizontal forces in constructions.
However, if the soil around the pile settles the structural capacity of each pile is reduced because
of induced bending moments in the pile. There is currently no validated method in Sweden to
analyse horizontal loading from settling soil. In the current paper a non-linear 3D finite element
model is validated against a field test from the scientific literature, and the results are compared
to three different beam-spring models. These models consist of a state-of-practice model where a
subsoil reaction formulation is used, a model where the soil is considered as a distributed load,
and a model with a wedge type of failure. Furthermore, a parametric study is conducted for
drained soil conditions where the weight and friction angle of the material are varied. The
standard soil reaction model yields an induced bending moment almost three times larger than the
one obtained from the field test and the two other calculation methods. The latter beam-spring
models should therefore be considered in practical design.

Keywords: Raked piles, batter piles, inclined piles, settling soil, soil structure interaction.

(e.g. changes in pore pressure and creep)

1 INTRODUCTION occur over longer timescales, which prohibits
field verification of the model before the
Simplified beam-spring models are construction is finished. This is a frequent
frequently used in design for simulation of occurring problem in geotechnical design.
axially and laterally loaded piles, (Erbrich et This paper discusses numerical
al, 2010). Such models should contain the simulation of a simplified beam-spring model
main mechanisms controlling the soil- for a laterally loaded included pile in settling
structural system, and the validity of the soil for drained soil conditions, which is
models should be carried out with assumed to be suitable for the long-term
experimental or numerical methods. conditions of the soil. The structural design,
Experimental methods include full-scale and simplified model ground conditions,
field models, which naturally contains numerical model and proposed new models
empirical evidence of the validity of the of the particular case are discussed.
model. The latter is the standard method of
verification, and should accompanied with a 2 PILE DESIGN CONSIDERATIONS
suitable simplified analytical model leads to a
robust design methodology, which could The Northern Scandinavian ground
however be relatively conservative. conditions are characterized by soft soils
The use of such simplified models such as clay and peat, placed on a layer of till
outside normal experience, poses the deposited on hard rock, (Johannessen &
questions about how well the real field case Bjerrum, 1969). A commonly used method to
is modelled. Model simplifications comprise transfer loads for overlying structures to the
material, geometry and boundary conditions. hard rock is to use relatively slender piles
Any of the factors may not be realistically that are installed by driving the pile base into
models, which could lead an overtly safe of the till layer or drilling the pile base into the
unsafe design. Some mechanical mechanisms rock. These end-bearing piles are in most
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 Modelling, analysis and design - Piles

cases dynamically tested to control the experiments. Because of the relatively

geotechnical bearing capacity, i.e. the complicated processes governing the soil
capacity of the end-bearing rock or till behaviour, including soil settlement,
beneath the pile. consolidation and creep, field experiments
This particular piling method results in are the most reliable method of assessment.
very high utilization of the structural capacity In the scientific literature, field experiments
of the pile. In many cases this factor limits have only been covered in Takahasi (1985).
the allowable load on the pile. Design Laboratory models are also discussed in
calculations for these piles are normally Takahasi (1985) along with both numerical
carried out by calculating the buckling load and analytical calculation models. Laboratory
and structural strength, following the experiments are also discussed in Kohno et
procedure described by Bernander & Svensk, al, 2010 and Rao et al, 1994. Numerical
1970. This calculation method has proven to studies include boundary element models in
the robust and has resulted in a safe design. Poulos, 2006, where the significance of the
Such end-bearing piles carry a relatively horizontal load on the piles are discussed in
high load: in the case of a concrete-filled 140 detail, but where a relatively simplified
mm steel tubular pile with a wall thickness of model in adapted to the pile-soil interaction.
8 mm, the allowable load can exceed 1.2 The field, laboratory and numerical
MN, which makes the foundation system models mentioned above all detail the
very efficient by using a small amount of resulting bending moments for inclined piles,
steel and concrete. But the small diameter of and a beam-spring model for inclined piles is
these piles results in a limited lateral pile proposed in Takahasi et al, 1985 and Kohno
bearing capacity; especially since the top et al, 2010. No comparison between a full
layer of the soil frequently consist of very range of soil parameter (friction angle and
soft clay. Inclined piles are instead preferred effective weight) has however been carried
as a structural solution, where an inclination out, since this required a large number of
of 4:1 to the vertical axis is typically used as simulations, which was outside the scope of
a maximum inclination. Pile groups subjected these scientific works. In the current paper a
to high levels of horizontal load, e.g. a bridge numerical model is therefore adapted to an
abutment, therefore normally include a large inclined pile, and different beam-spring
number of inclined piles. models are compared to the simulations.

2.1 Alternatives for modelling and design of

3 CURRENT BEAM-SPRING
realistic pile-soil mechanism CALCULATION MODEL
Current design methods for the structural
strength of piles in settling soil consist of a The calculation model used in Sweden today
simplified beam-spring model, outlined in (Svahn and Alén, 2006) is based on the
Svan & Alén, 2006 (and Reese et al, 1974, equation for a beam on an elastic foundation.
for vertical piles), or a full 3D-FEM-model. The force distribution in the beam on an
The beam-spring model results in limited elastic foundation can be described as a
calculation time and is frequently used in fourth-order differential equation, Equation
design. 3D-FEM models have not been of 1, by dividing the beam in infinitely small
extended practical use for the current types of elements.
slender piles, although frequently used for
lateral loading of larger offshore piles, e.g. (1)
Erbrich et al, 2010.
The simplified beam-spring models are Where EI is the bending stiffness of the pile,
obviously a simplification of the soil N is the normal force along the pile axis, D is
conditions around the pile, and result from an the width of the pile, ky is the soil reaction
idealisation in 2D of the soil. The real soil- transversal to the pile, yg is the ground
pile deformation mechanism in 3D can be settlement, and yi is the i-th differential of the
assessed in laboratory, field and numerical horizontal position along the pile axis x.
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 Analysis of inclined piles in settling soil

Equation 1 can be simplified to Equation 2

given that the normal force can be assumed
to be constant along the pile, which a suitable
assumption for an end-bearing piles. The
interesting part of the pile is situated at the
pile head where the effective stress is
relatively low, which makes this assumption
relatively correct.

(2)

In the current calculation model the position

of the soil is a function of the depth to
replicate the displacement of the soil. The
relative movement of the soil is illustrated in Figure 2 Illustration of the division of the
Figure 1. settlement into a transversal and a longitudinal
component.
This beam-spring model has been used
to calculate the bending moment resulting
from the settlement and soil conditions in the
field experiments in Takahashi, 1985. The
field experiment consisted of soil settlement
resulting from deposition of fill on soft clay
made for a road structure. Measurements
were carried out on instrumented pipe piles
driven in inclined pairs along the road. The
calculated bending moment, according to
Svahn and Alén, 2006, along the pile
Figure 1 Illustration of the difference in compared to the measured bending moment
displacement between the settling soil and the
can be seen in Figure 3. This Figure also
pile causing lateral earth pressure.
shows that the bending moment is larger
close to the top of the pile. In the rest of this
3.1 Description of the Swedish standard article only the maximum value of the
bending moment will be referred to, however
In the current calculation model the subgrade the distribution of the bending moment is
reaction, ky, is set according to empirical relatively similar for all cases, i.e. at the top
values recommended by Reese et al. (1974). part of the pile. It should also be noted that
The settlement is adapted as a relative the different between the measured and
movement between the soil and the pile. The calculated values of the bending moments
settlement is divided into a transversal and a seems to be related through a scale factor,
longitudinal component, see Figure 2. From signifying the extra moment resulting from
this the transversal part is applied as the the idealization of the 3D pile-soil interaction
movement of the soil and the differential to a 2D beam-spring model.
equation can be solved. There are also some limitations present
in the 2D analytical beam-spring model, e.g.
only one type of soil can be used for the
entire length of the pile. Another limitation is
that the settlement profile is fixed and does
not always represent the actual settlement,
since this has to be simplified to an analytical
function, e.g. an exponential function.

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 Modelling, analysis and design - Piles

displacement of the pile is equal or limited to

the soil displacement, which is more suitable
than a load resulting only from the friction
angle and effective stress in the traditional
earth pressure approach in the current
calculation model. The formulation of this
behaviour is summarized in Equation (3).
This discretization assumes that the soil goes
to failure and therefor becomes a load
hanging on the top part of the pile.

(3)

where γ is the weight of the soil and θ is the

inclination of the pile relative to the vertical
Figure 3 Comparison between the bending axis.
moment as calculated with the current method
(Svahn and Alén, 2006) and the bending moment 4.2 Wedge failure approach
as measured in the full scale experiment by Based on a failure mode described by Reese
Takahasi (1985). et al. (1974) the top part of the soil is
considered to have a cone like plastic failure
4 ALTERNATIVE BEAM-SPRING which is also observed in the 3D finite
MODELS element model, discussed below. Similar to
the distributed load approach the soil is
The comparison between the measured and divided into a distributed load along the top
calculated bending moments in Figure 3 of the pile, and a subsequent subsoil reaction
displays that the current model (Svahn and along the deeper parts of the pile. The load is
Alén, 2006) clearly overestimates the suggested to grow with the weight of the
measured bending moment. This beam-spring cone shown in Figure 4. Furthermore it is
model is therefore compared to two different assumed that only the transversal part of the
calculation models, described below. The weight will act lateral to the pile causing
common principle of the two models is that bending moment (and not the load resulting
the pressure against the pile is reduced, from increased shaft friction), thus only this
which means that the force does not exceed part of the weight is to be taken into account.
the weight of the soil above it. This is a The total load acting on the pile can therefore
suitable principle to avoid stress distribution be described as Equation 4.
resulting which no natural base that result
from the simplification of the model.
(4)
4.1 Distributed load approach
The distributed load approach is originally
discussed in Takahashi, 1985. The model
results in a division between the top part of
the pile and the following lower part along
the principle in Randolph, 2014, to represent
the real soil response resulting for the
different boundary conditions. The soil is
therefore divided into two parts; a distributed
load part, and a subgrade reaction. The load
is applied as a function of the pile width and
is limited to the subgrade reaction of the soil Figure 4 Illustration of the wedge failure and
so that no load will be applied if the parameters used for Equation 4.

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 Analysis of inclined piles in settling soil

5 3D FEM MODEL The soil was modelled as 3D solid elements

(C3D8 and C3D4 type of elements, (Hibbitt,
In order to assess the real behaviour of the Karlsson, & Sorensen. (2001)) and the pile
soil, either laboratory models (Kohno et al, was modelled as shell elements (S4 type of
2010), numerical models (Poulos, 2006), or elements, Hibbitt, Karlsson, & Sorensen.
field models (Takahashi, 1985) are possible (2001)) in order to save computational time
approaches. In the current scientific work a during the simulation. As settlement per
3D finite element model was used to validate definition is pore water dissipation, drained
the different 2D-models. The advantage of a parameters were used for the clay.
numerical model is that parameter studies are To simulate the settlement a stress-free
possible, and the behaviour of the real case strain level was induced in the soil body
can be studies for different configuration causing the desired settlement profile. The
without the limitations of a laboratory or field settlement in the soil was modelled using
model, (Randolph, 2014). The current orthotropic temperature dependency hence
analysis was performed in a 3D FEM shrinking the soil in the vertical direction to
software (Hibbitt, Karlsson, & Sorensen. represent the settlement profile from the
(2001)). The computer model was first experiment. This resulted in a controlled
validated against the field study in Takahashi, deformation, in which the load against the
1985. Subsequently a parametric study was pile was controlled by the effective stress
carried out to compare the behaviour of the level in the soil. The excess pore pressure
3D-FEM model to the different and 2D was consequently not included in the model,
beam-spring formulations. but since most of the bending moments occur
close to the pile head (according to Figure 3),
5.1 Geometry, boundary conditions and FE this should have a relatively small influence
discretization on the calculation results, possibly resulting
Figure 5 represents the geometry of the in an overestimation of the bending moments
model, consisting of the pile and the in pile compared to the short-term process, in
surrounding soil. A symmetry plane along the which less settlements occur and the
pile axis has been used to save computational beginning of consolidation. The pile's top
time. The boundary conditions were set so was restrained to move in the horizontal
that no displacement perpendicular to the direction to represent the pinned condition
surface will occur except for the top surface from the study. Interaction between the pile
which was free to move, and the plane of and the surrounding soil was modelled using
symmetry where symmetrical conditions penalty type interface. For the normal
were applied. behaviour a small pretension was applied
between the soil and the pile by changing the
clearance when contact pressure is zero and
for the tangential behaviour a friction
coefficient of 0.385 was assumed (Helwany,
2007). This is a suitable estimate following
standard values of the interface friction angle,
(Randolph, 2014). The behaviour of the steel
is assumed to be linear elastic and a Young's
modulus of 200 GPa was assumed along with
a Poisson's ratio of 0.3.

5.2 Validation of field measurements

The numerical model was calibrated against
the field measurements presented in
Figure 5 Basic geometry used for the finite Takahashi, 1985. The field measurements
element model. consisted on settlement in a clay soil covered
by fill material. The soil was modelled

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 Modelling, analysis and design - Piles

according to the guidelines presented in Table 1 Studied cases.

3
Trafikverket (2011a), which are normally weight (kg/m ) 500 1200 2000
used in practical design. The elastic Friction (deg)
properties of the soil were assumed to be angle
linear and isotropic with a Young's modulus 25 X X X
35 X X Unable
calculated as 250·cu for the clay and 50 MPa
to finish
for the fill material in the embankment. The 45 X X X
plastic behaviour was modelled using Mohr-
Coulomb plasticity with a friction angle of 45
degrees for the embankment. As settlement in 6 RESULTS
this case per definition occurs due to the
6.1 Validation of the numerical model
dissipation of water drained parameters were
used for the clay body, and an alternating The numerical model was initially validated
value for the clay to estimate the impact of against the measurements presented in
this value (since no drained parameters were Takahashi, 1985. The maximum bending
presented in Takahashi, 1985). The friction moment at each settlement level was
angle of the clay however had very low effect calculated, following the distribution shown
on the results. Furthermore a Poisson's ratio in Figure 3. The maximum bending moments
of 0.3 was assumed for the soil body. typically occurred close to the surface at the
same vertical level, showing relatively small
5.3 Parametric study change during the soil settlement process,
In order to compare the different 2D beam- (Takahashi, 1985). Figure 6 shows the
spring formulations, (Svahn and Alén, 2006), bending moment against the ground surface
Reese et al, 1974 and Takahashi, 1985), a settlement in the numerical model and the
parametric study comparing the 3D FEM field measurements. It can be observed that
numerical model to different 2D beam-spring the results are very close to the measured
model was conducted. The settlement profile values and it is assumed that the model
in the 3D-model was predefined, so that the replicate the field test relatively well. From
settlement increased linearly over the entire the results it can also be observed that a
depth. A similar settlement profile was used wedge like failure mode occurs as shown in
in the beam-spring model. The density of the Figure 7 indicating that a different failure
soil was set to 0.5, 1.2, and 2 t/m3 and the mechanism occurs in the first few meters
friction angle was set to 25, 35, and 45 than in the rest of the pile.
degrees for a total of 9 combinations, shown
in Table 1. The Young's modulus of the soil
was set to 50 MPa for the entire depth and a
cohesion of 2 kPa was used to prevent
numerical problems close to the surface. This
results in a simplification of the soil
parameters, since the modulus tends to
increase with the friction angle, but this was
not considered in the model. A total
settlement of 25 cm was induced and the
maximum bending moments were calculated
in the 3D-FEM model and the beam spring
models, following the distribution of bending
moment shown in Figure 3.The coefficient of
subgrade reaction was chosen as 7 MN/m3
increasing linearly with the depth and limited Figure 6 Maximum bending moment plotted
to 49MN/m3 for all 2D cases (Trafikverket, against the settlement of ground surface.
2011b).

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 Analysis of inclined piles in settling soil

6.3 Results using the distributed load

approach according to Takahashi, 1985
Figure 9 shows the bending moment
calculated according to the distributed
loading approach, (Takahashi, 1985),
compared to the ground surface settlement
calculated with the 3D-FEM model. It can be
seen that the proposed model gives a
maximum bending moment close to the one
obtained in the 3D model.

Figure 7 Plastic zones in the completed finite

element solution indicating a different failure
mode in the top of the pile.

As the 3D finite element model is assumed to

replicate the results from the field tests, the
validated numerical 3D-FEM model was then
adapted for comparison to the different 2D
discretization approaches with the field
measurements in Takahashi, 1985.
Figure 9 Maximum bending moment plotted
6.2 Beam-spring model according to Svahn
against the settlement of ground surface using the
& Alén, 2006 distributed load approach.
Figure 8 shows the bending moment
calculated according to Svahn and Alén,
2006, compared to the simulation by the 3D- 6.4 Results using the wedge failure approach
FEM model. It can be seen that the proposed according to Reese, 1974
model gives a maximum bending moment far Figure 10 shows the bending moment
greater than that obtained in the 3D model. calculated with the wedge approach
according to Reese et al, compared to the
ground surface settlement calculated with the
3D-FEM model. It can be seen that this
model gives a maximum bending moment
close to the one obtained in the 3D model.

Figure 8 Maximum bending moment plotted

against the settlement of ground surface using
PKR101.

Figure 10 Maximum bending moment plotted

against the settlement of ground surface using the
wedge failure approach.

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 Modelling, analysis and design - Piles

7 DISCUSSION

6.5 Results from the parametric study Ground settlement, including soil creep,
After assessing the different between the occur over extended time periods, and many
beam-spring approaches compared to the factors such as ground water level and
field measurement in Takahashi, 1985, a presence of organic soil influence the
parametric study was carried out. The soil settlement profile and settlement rate. A
friction angle and the weight of the soil were relatively simplified soil deformation model
varied according to Table 1. The results are has been adapted to the inclined pile in
shown in Figure 11. The abscissa shows the settling to simulate the drained soil
effective weight of the soil and the ordinate conditions in the current paper. The vertical
the friction angle. It was first be observed strain profile was imposed on the soil
that the proposed beam-spring models (Svahn according to the field test case, and a Mohr-
and Alén, 2006, Takahashi, 1985 and Reese Coulomb yield model was included in the
et al, 1974) results in different bending model to simulate the plastic behaviour
moments depending on the friction angle and during settlement. The results are in line with
the weight of the soil. Moreover, it is also the wedge yield theory discussed in literature,
noticeable that the distributed load model is e.g. Randolph 2014, Reese 1974, Takahashi
independent of the friction angle but gives a 1985. It appears from the results that the
maximum bending moment closer to the one main response of the soil can be separated
obtained in the 3D models in comparison to into a surface field mechanism, and a deeper
the wedge failure method. All three ways of earth pressure mechanism, following the
calculating the reaction of the pile give standard theory of beam-spring models for
results on the safe side, however by using horizontal offshore piles, (Randolph, 2014).
Svahn and Alén, 2006, the calculations A numerical parametric study of the variation
results in a bending moment of over 3 times of the soil weight and friction angle confirms
the value obtained from the 3D-FEM the importance of the geometry of the soil on
simulation. the inclined pile, in which the bending
moments did not change very much when
these factors were varied. The mechanism
with the least necessary resistance before
yield controls the position of transformation
between the top and deep yield type through
the wedge mechanism in the soil. Because of
the relatively large displacement in the top
soil layer at yield, more advanced soil models
incorporating small-strain behaviour would
probably have limited impact on the
simulation. However, a soil model including
viscoelastic behaviour such as creep would
probably improve the numerical model.

8 CONCLUSIONS
Figure 11 Maximum bending moment in pile
divided with the maximum bending moment for a
Analysis of imposed vertical deformation
friction angle of 35 degrees and a weight of 1.2 (simulating ground settlement) shows that a
t/m3 plotted against the weight of the soil. wedge-type yield mechanism occurs in the
top part of the soil. This mechanism is not
correctly simulated by the current calculation
model (Svahn and Alén, 2006), in which an
earth-pressure formulation is adapted along
the whole pile depth. The alternative beam-

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 Analysis of inclined piles in settling soil

spring models that differentiate between the Fellenius, B. H. (1972). Down-drag on piles in clay
top layer and bottom layer with either a due to negative skin friction. Canadian Geotechnical
Journal, 9(4), 323-337.
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distributed load depending on the width of Abaqus application.
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