simulation of soil plug effects in open steel pipe piles considering
TRANSCRIPT
40th Annual Conference on Deep Foundations, Oakland, California, USA, 2015
Simulation of Soil Plug Effects in Open Steel Pipe Piles Considering the Complex Soil-Structure-Interaction During Installation Christian Moormann, Johannes Labenski, Johannes Aschrafi Published in: Proceedings of the 40
th Annual Conference on Deep Foundations, Oakland, California,
USA, 2015.
SIMULATION OF SOIL PLUG EFFECTS IN OPEN STEEL PIPE PILES
CONSIDERING THE COMPLEX SOIL-STRUCTURE-INTERACTION DURING
INSTALLATION
Christian Moormann, Institute for Geotechnical Engineering (IGS), University of Stuttgart, Germany,
PH (0049) 711 685-62437; Fax (0049) 711 685-62439; email: [email protected]
Johannes Labenski, Institute for Geotechnical Engineering (IGS), University of Stuttgart, Germany,
PH (0049) 711 685-63779; Fax (0049) 711 685-62439; email: [email protected]
Johannes Aschrafi, Institute for Geotechnical Engineering (IGS), University of Stuttgart, Germany,
PH (0049) 711 685-65552; Fax (0049) 711 685-62439; email: [email protected]
ABSTRACT
Open steel pipe piles are used for various applications in costal engineering, port structures and
increasingly important for offshore structures. During the installation of open steel pipe piles the
formation of a plug has an influence on the installation process of the pile and also on the final bearing
capacity. The formation of the plug depends on different factors, e.g. the pile diameter and the installation
method. This paper starts with a structured overview about analytical methods (API, EAP-EAU, UWA-05,
HKU-12, Modified API) to calculate the axial bearing capacity of open steel pipe piles. The numerical
simulation of the installation process of open steel pipe piles has to fulfill high demands, i.e. to accurately
represent the penetration of the pile inside the soil, the formation of the plug and also the stresses and
strains during the installation. A numerical back analysis of a comprehensive field test, using the Coupled
Eulerian-Lagrangian (CEL) method and a hypoplastic constitutive model for sand, reveals the stresses and
displacements of the soil and of the piles. The analysis provides a comprehensive understanding of soil-
pile interaction.
Keywords: steel pipe piles, plug, bearing capacity, soil-pile-interaction, Coupled Eulerian-Lagrangian method
INTRODRUCTION
The particular difficulty in the numerical simulation of plug formation, is that the effect of plugging inside
open ended steel pipe piles has not been fully investigated. In scientific papers different approaches are
documented to explain this phenomenon. Some are based on in-situ tests and others are based on
numerical simulations. One of the challenges is to determine the end bearing capacity and shaft friction of
the steel pipe pile. Different approaches have been developed over the years to determine them e.g. from
Randolph et. al. (1991, 1994) and Paik et. al. (2003). Recent approaches are the ICP-05 Method (Jardine
2005), the UWA-05 Method (Lehane 2005) and the HKU-12 Method (Yu & Yang 2012a). A comparison
of some methods can be found in Schneider et al. (2010). A plug inside an open steel pipe pile can be
visualized as a spatial bracing of soil between the inner surfaces of the pile, cf. Lüking (2010).. However
according to Lüking & Kempfert (2012) this bracing only exists for the height in the end of the pile equal
to twice its diameter.
To identify a plug inside a pile, there are different measurable parameters. One parameter is the
development of stresses around the pile during and after its installation. Henke (2013) measured the in-
and outside horizontal stresses at the pile tip during the installation. The results showed higher stresses on
the inside compared to the outside. To validate his measurements he performed a numerical back-analysis
of the measured installation process and got matching results.
A further measurable parameter is the so called Incremental Filling Ratio (IFR) introduced by Brucy et al.
(1991). It is defined as follows
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Fig. 1. Description of a soil plug: a) no plugging effect, b) partially plugged, c) fully plugged.
IFR�= �h�L� [1]
where h = the height of the soil column inside the pipe pile (cf. Fig. 1), L = the embedded length of the
pile inside the soil (cf. Fig. 1) and � = incremental value, i.e. for every x meters of driving the
corresponding values have to be determined and the respective IFR has to be calculated.
Three different situations come to rise.: IFR equal zero, IFR equal one and IFR less than one. An IFR with
the value zero means, that the pile is closed, i.e. there is no soil inside the pile and �h is always zero. In
this case there are high radial stresses around the pile tip. An IFR with the value of one, means that the soil
inside the pile is not moving downwards, i.e. there is no plug and �h equals �L. In this case the horizontal
stresses around the pile tip do not differ significantly from the initial stress state. An IFR with a value less
than one means that there is a partial plugging inside the open steel pile. There are higher radial stresses
than with an open steel pile, but lower radial stresses than with a closed steel pile.
In real applications, for example in the installation of offshore piles, it can be hard to determine the IFR as
the height of the plug as well as the penetration depth of the pile need to be continuously monitored. For
this reason Paik et al. (2003) introduced the so called Plug Length Ratio (PLR) . It is defined similar to
the IFR except that the PLR is not an incremental value and is only once measured at the end of the
installation process.
PLR�=� h L� [2]
The formation of the plug depends among other things on the installation method. From field tests and
numerical simulations it is know that the soil around a vibratory-driven pile tends not to build a bracing.
Whereas a jacked pile builds a bracing inside the pile, cf. Henke (2009). An impact-driven pile tends to
build a bracing, even though not to the same extent as a jacked pile.
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ANALYTICAL APPROACHES
API
The API (2007) suggests a formula to calculate the ultimate axial bearing capacity. The approach does not
specifically distinguish between a plugged or unplugged pile. The values used to calculate the capacity of
the pile are based on experience for a conservative design.
To determine the axial bearing capacity of open steel pipe piles the API suggests the following formula
Qtot
= Qb+ Q
s=�q
b Ab+� �s�As�j [3]
Where Qtot = total axial bearing capacity, Qb = end bearing, Qs = shaft resistance, qb = unit end bearing
capacity (cf. Fig. 1), Ab = D2 �/4, �s = unit shaft friction (cf. Fig. 1), As = corresponding side surface area
of the pile and j = the different soil layers.
In cohesionless soils, the API proposes the following formula for the unit shaft friction at a given depth z
and the unit end bearing capacity
�s�=�� �v0' (z) ���max [4]
qb= Nq�v0
' (z) ��qmax
[5]
Where � = dimensionless shaft friction factor, �'v0 = �sub • z, �sub = submerged unit weight of the soil, z =
depth below ground level, �max�= maximum unit shaft friction, Nq = dimensionless bearing capacity factor
and qmax = maximum unit end bearing.
The values of � and q are limited due to the fact, that the shaft friction and end bearing for long piles do
not increase linearly with the overburden pressure. The missing values can be determined according to
Table 6.4.3-1 of the API. So as to activate the full capacity of the pile, a local pile displacement after the
installation is needed. Therefore the API introduces the t-z and Q-z curves (cf. Fig. 2) for frictional and
end bearing resistance respectively.
Modified API
The method by Gudavalli et al. (2013) suggests improved design values for the API. By analyzing 1355
test piles (406mm < d < 914mm) Gudavalli et al. obtained an improved equation for the end bearing factor
which is valid for driven piles installed into dense to very dense sand with a range of PLR from 0.76 to
0.91.
Nq�=�12.3 PLR-8.4 [6]
Gudavalli et al. suggests the following formula to estimate the value of �
��= �3.5�-�3.2 PLR� e-0.023 L [7]
which is valid only for a 0.76 < PLR < 0.91 and 10m < L < 30m. If no PLR could be measured during the
pile driving process, it can be estimated as follows
PLR�= �d1.4� 0.19
[8]
where 0.378 m < d < 0.876 m.
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Fig. 2: a) t-z curve for sand to determine the activated frictional resistance. b) Q-z curve to determine the activated end bearing resistance.
Harmonization of EA Piling and EAU
Lüking & Becker (2015) propose a method for the axial bearing capacity based on the calculation methods
for open steel pipe piles of EA-Pfähle (2012) and EAU (2012). Both, EA-Pfähle, Recommendation on
Piling, and EAU, Recommendations on waterfront structures, harbours and waterways, are elaborated by
the German Geotechnical Society and widely-used in Germany and partly Europe.
The method distinguishes between three cases: fully plugged (D � 0.5m), no plugging effect (D � 1.5m)
and partially plugged (0.5m < D < 1.5m). The total axial bearing capacity for a fully plugged open steel
pipe pile reads
Qtot,case1
(s)�= �b,plug
qb,plug
Aplug+ qb,an
Aan+� �s �s,j As,jj [9]
where s = settlement of the pile after installation, �plug = 2.52 e-1.85 D [-] with D in [m], qb,plug =
characteristic value of the bearing resistance of the plug [kPa] (cf. Fig. 1), Aplug = value of the area of the
plug [m2], qb,an = characteristic value of the bearing resistance of the annulus [kPa] (cf. Fig. 1), Aan = area
of the annulus [m2], �s = 1.53 e-1.85 D [-] with D in [m], �s,j = characteristic value of the shaft friction on the
outside, for the layer of soil j [kPa] and As,j = area of the outer shaft in the layer j [m2].
In the case of no plugging effect, the proposed formula reads
Qtot,case2
s� = qb,an
Aan�+� � ��s �s,j As,jj �+� � �is,j Ais,jj [10]
where �is,j = characteristic value of the shaft friction on the inside for the layer of soil j [kPa] (cf. Fig. 1)
and Ais,j = area of the inner shaft area in the layer j minus the top 0.2 L of the pile [m2].
For a partially plugged pile both previous methods are combined
Qtot
s��= Qtot,case1
s��+� Qtot,case2
s� [11]
where � and ���calculation factors considering the pile diameter D according to Fig. 3.
a) b)
536
Fig 3. Calculation factors and �according to Lüking & Becker (2015).
The values needed to use [6] and [7] are presented in Table 1. There are two values for each parameter.
The lower bound describes the 10% quantile, whereas the upper bound describes the 50% quantile. It has
to be noted that the approach is actually limited to a cone resistance qc � 25 MPa.
ssg*�mm �=�0.05 � ��s �s,j�ssg*� As,jj �MPa ���10 mm [12]
where ssg* = settlement of the pile after installation, at which the friction starts to be mobilized.
Table 1. Design parameters for cohesionless soil according to Lüking & Becker (2015)
qc Settlement s qb,an qb,plug �s �is
[MPa] [mm] [kPa] [kPa] [kPa] [kPa]
Case 1 Case 2
7.5 ssg* 15 – 25 15 – 20 5 – 10
0.035 D 3900 – 7500 1200 – 3300
0.100 D 7500 – 9000 2250 – 4000 25 – 35 20 – 30 10 – 15
15 ssg* 35 – 50 30 – 45 10 – 20
0.035 D 7900 – 11500 2100 – 4000
0.100 D 15000 – 18000 4000 – 6250 50 – 70 40 – 60 20 – 30
25 ssg* 40 – 70 35 – 60 15 – 25
0.035 D 10300 – 16300 2500 – 4750
0.100 D 20000 – 25000 4750 – 7250 60 – 90 50 – 80 22 – 40
The settlement of the pile is needed to activate the frictional and bearing resistance. After a settlement of
0.1 D it is assumed, that the resistance of the pile is fully activated.
UWA-05
The UWA-05 method by Lehane et al. (2005) is a CPT based method. The axial capacity of the pile is
divided into the base capacity qb and the shaft friction �f. The base capacity is the end bearing resistance at
a pile base movement of 10% of the pile diameter and is, according to Xu et al. (2005), again divided into
the bearing resistance of the annulus qb,an and the plug qb,plug.
The total axial capacity of open steel pipe piles according to the UWA-05 method can be calculated as
follows
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Qtot�=�Q
b�+�Q
s�= q
b
�
4 D2�+ �D � �f dz� [13]
Xu et al. (2005) states the following equations
qb = q
b,an Ar + q
b,plug �1�-�Ar� [14]
where qb,an = 0.6 qc,avg, qb,plug = (0.6 – 0.45 FFR) qc,avg, Ar = 1 – (d/D)2 (cf. Fig. 1) and qc,avg = averaged CPT
cone resistance according to Schmertmann (1978).
FFR is a value to describe the grade of plugging, similar to the PLR and IFR presented above. The FFR is
an empirical value defined by the following function:
FFR = min �1, �d 1.5� �0.2� �with d in [m] [15]
The base capacity for the general case states
qb�= �0.15�+�0.45 Ar,p� qc,avg
[16]
where Ar,p = 1 – FFR (d/D)2.
In the case of large diameter piles (FFR = 1, Ar,p = Ar) the base capacity states
qb�= 0.15�+�0.45 Ar� qc,avg
[17]
The unit shaft friction of the open steel pipe pile depends on the radial stresses around the shaft and can be
calculated for the general case by the following formula
�f�= �0.03 qc �Ar,s�0.3 �max �L-z
D,2�-0.5
+ 4 G �rD� � tan �cv [18]
Where �f = unit shaft friction, qc = CPT tip stress at the depth of interest, Ar,s = 1 – IFR (d/D)2, z = depth
below ground level, G = shear modulus, �r = radial displacement of the shear equals to 0.02mm for a
slightly rusty steel surface in sand (cf. Jardine 2005) and �cv = constant volume interface friction angle
which depends on the median grain size of the sand.
If IFR could not be measured during the pile installation, it can be estimated by
IFRmean� min �1, �d 1.5� �0.2� with d in [m] [19]
The shear modulus G can be calculated by
G�=�185 qc �qc
pa
� ��'v0p
a� -0.5�
-0.75
[20]
Where pa = 100 [kPa].
For the case of large diameter piles, [15] simplifies to the following
�f�= 0.03 qc Ar
0.3 �max �h
D,2�0.5
tan �cv [21]
538
HKU-12
The HKU-12 method proposed by Yu and Yang (2012a) is a CPT based method, similar to the UWA-05
method. The axial capacity is divided into the base capacity and the shaft friction. The base capacity is
then again split into the bearing resistance of the annulus and the plug.
The HKU-12 method is also using equation [13] to determine the total end bearing Qb. The base capacity
qb,an and the capacity of the plug qb,plug can be calculated as follows
qb,an
= �1.063-0.045 �L D� �� qc,avg
��0.46 qc,avg
[22]
qb, plug
= 1.063 qc,avg
e-1.933 PLR [23]
where qc,avg = averaged CPT cone resistance according to Yu and Yang (2012a).
According to Yu and Yang (2012b), the capacity of the shaft can be determined according to the following
equations.
Qs= � D�L tan �cv � ��rc
' + ��'r� d�1
0 [24]
where cv = friction angle as proposed in the UWA-05 Method and ��������������describing an observed
soil horizon around the pile relative to the total pile length in the soil L.
The stationary radial effective stress is defined as
�'rc�=�0.03 �0.3 �L D� �-0.5 �1-��-0.5
qc ��0.021 �0.3�q
c [25]
where ��= 1 – PLR (d/D)2 > 0.
The increase in radial effective stress during static loading can be calculated as follows
��'r�=�4G �r �D2�-�PLR d2�-0.5
[26]
If no PLR value could be measured, the following equation can be used
PLR�= min�1, d0.15� [27]
CASE STUDY
To examine the quality of the above presented design methods, a case study is carried out. An open steel
pipe pile with an outer diameter D of 0.76m and a thickness of 36mm is driven 38.7m into the soil. The
original test was carried out under the name of EURIPIDES and is described by Kolk et al. (2005). The
CPT profile of the soil indicates that the sustainable layer of soil starts 22m below ground level. The
average CPT cone resistance is 5 MPa between the ground level and a depth of 22m. Between 22 and 50m
below ground level the CPT cone resistance was in the order of 40 to 80 MPa. Therefore the weak layer of
soil was not considered for the determination of the different total bearing capacities.
In Fig. 4 the measured resistance-settlement curve is shown. Also the total bearing resistances calculated
by the different design methods are marked at a settlement of 0.1 D. The measured total resistance of the
pile reads 12.5 MN. The API and the approach by Lüking & Becker (EAP EAU) are similar, both with a
maximum resistance of 4 - 5 MN. However the API underestimates the real resistance which may be due
to the fact that the unit end bearing and unit shaft friction are limited by a maximum value.
539
Fig. 4. a) CPT profile of the test site. b) Resistance-settlement curve of the test pile and with the calculated resistances. c) Dimensions of the open test pipe pile.
The underestimation by the German approach can be owed to the lack of design parameters for soils with
a CPT cone resistance > 25 MPa. The modified API approach shows a resistance of 8.5 MN which is
closer than the original API, but still substantial underestimates the reality. The reason here could be that
the pile of the case study does not fit well with the test piles of the modified API’s approach. The result of
the UWA-05 and HKU-12 method accurately correspond with the measurement.
It is evident that none of the presented methods could correctly estimate the measured total axial bearing
capacity, except for the two CPT based method. These methods are all based on empirical relationships,
but to estimate the axial bearing capacity the complex soil-structure interaction around the pile needs to be
analyzed. To do so, sophisticated numerical simulations need to be utilized, so as to understand the
development of stresses and strains during the installation of open ended pipe piles.
NUMERICAL SIMULATION
The numerical simulation of the steel pipe pile installation into soil, has to deal with large deformations. A
standard Lagrangian finite element simulation would fail because of the high extent of mesh distortion. To
overcome this problem a special numerical method, the so called Coupled Eulerian-Lagrangian (CEL)
method, is used. Qiu et al. (2009) and Henke (2013) already showed the potential of the CEL method for
geotechnical applications undergoing large deformations. To simulate the behaviour of the soil a
hypoplastic constitutive law is used. The numerical simulation of the installation of a steel pipe pile was
carried out using the software ABAQUS/Explicit.
Numerical method
The CEL method attempts to capture the advantages of both, the Lagrangian and Eulerian method. For
geotechnical problems, a Lagrangian mesh is used to discretize structures; while an Eulerian mesh is used
to discretize the subsoil. During the numerical analysis the Eulerian material is tracked as it flows through
the mesh by computing its Eulerian Volume Fraction (EVF). Each Eulerian material is designated a
percentage, which represents the portion of that element filled with a material. If an Eulerian element is
L = 40 m
D = 0.76 m
a) b) c)
540
completely filled with material, its EVF is 1. If there is no material in the element, its EVF is 0 (cf.
Dassault Systèmes 2014). The interface between structure and subsoil can be represented using the
boundary of the Lagrangian domain. On the other hand, the Eulerian mesh, which represents the soil that
may experience large deformations, has no problems regarding mesh and element distortions. The
interested reader is referred to Benson (1992), Benson (1995) and Benson (2000) for a detailed derivation.
Contact between the Eulerian and Lagrangian domain is utilized using the general contact algorithm inside
ABABQUS, which is based on a penalty contact method described by Benson and Okazawa (2004). The
Lagrangian elements can move through the Eulerian mesh without resistance until they encounter an
Eulerian element filled with material. Seed points are created on the Lagrangian element edges and faces
while anchor points are created on the Eulerian material surface. The penalty method approximates hard
pressure-over closure behavior, which allows small penetration of the Eulerian material into the
Lagrangian domain. The formula for the penalty contact reads
Fp�=�kp dp [28]
where Fp = contact force that is enforced between the seeds and anchor points, kp = penalty stiffness which
depends on the Lagrangian material on one side and on the Eulerian material on the other side and
dp = penetration distance.
Constitutive model
The hypoplastic constitutive model from von Wolffersdorff (1996), with the small-strain extension by
Niemunis and Herle (1997) is used to simulate the behavior of the soil. This constitutive model is able to
adequately represent the nonlinear and anelastic behavior of granular materials. The hypoplasticity
possesses of a rate dependent formulation. It is consistent with mechanical soil properties, e.g.
contractibility, dilatancy and the change of stiffness due to the actual stress state, the void ratio and cyclic
loading. The ABAQUS implementation was done using a user subroutine provided by Gudehus et al.
(2008).
The hypoplastic constitutive parameters for Karlsruher Sand used in this paper are listed in Table 2.
Table 2. Hypoplastic parameters of Karlsruher Sand by Herle (1997)
�c hs n ed0 eco ei0 � � R mR mT �r
[°] [MPa] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-]
30 5800 0.28 0.53 0.84 1.00 0.13 1.05 10-4 5.0 2.0 0.50 6.0
Numerical model
The geometry of the numerical model is based on the geometry of the case study. The model with its
dimensions and discretization is shown in Fig 5. The numerical model consists of one layer of void and
two layers of soil. The first soil layer with a thickness of 22m is loosely packed, the second, a 38m layer
densely packed. The pile is jacked in with a constant velocity of 0.5 m/s.
The parallelization of the given simulation has been tested at the bwUniCluster, in Karlsruhe, Germany.
The bwUniCluster owns 512 calculation nodes with 64GB ram per node. Each node consists of two Octa-
Core Intel Xeon E5-2670 CPUs. Compared to a workstation containing a Quad-Core Intel Xeon E3-1240,
a 32-fold speedup could be achieved on the cluster utilizing 64 cores.
541
Fig. 5. Numerical model showing the initial vertical stress and the discretization around the pile.
Results
Figure 6 shows the results of the numerical simulation. First of all the simulation shows the formation of a
plug inside the open steel pipe pile, i.e. the soil inside the pile is pushed down with the pile.
As stated at the beginning of this paper, the stresses at the inside of a pile are much higher compared to the
outside, if a plug occurs. In Fig 6a and 6b this effect can be seen. Especially the vertical stress on the
inside of the pile is high while on the outside the soil is barely effected. Also the horizontal stress is
significantly higher on the inside compared to the outside. Moreover the stress tends to concentrate at the
tip of the pile.
2 m
30 m30 m
22 m
38 m
(e =0.65)0
(e =0.57)0
open steelpipe pile:
0.76 mt = 36 mm�
L= 45m
542
To see whether the soil is compacted or loosened it is necessary to investigate the distribution of the void
ratio around the pile. This distribution is presented in Fig. 6c. The soil inside the pile is going to be
compacted. The highest grade of compaction can be found at the tip of the pile. At the outside of the pile
the soil is compacted along the shaft. But in direct contact the soil is also loosened at the shaft. This
phenomenon can also be observed below the compaction zone at the tip of the pile.
Fig. 6. a) Vertical stress [kPa] distribution around the pile tip. b) Horizontal stress [kPa] distri-bution around the pile tip. c) Void ratio e [-] distribution around the pile tip.
CONCLUSIONS
In this paper a comprehensive summary about state of the art methods to determine the total axial bearing
capacity of open steel pipe piles has been presented.
In a case study the reliability of these methods has been shown and compared with a field test. It could be
seen that all of the analytical methods either underestimate or overestimate the real bearing capacity of the
pile.
To investigate the bearing behavior of open steel pipe piles and thus to be able to investigate the design
methods one needs to understand the complex soil-structure interaction during the installation of the pile.
Therefor numerical simulations need to be utilized. The numerical simulation presented here demonstrates
the development of stresses and strains, in a plausible manner, of the soil around the pile due to the
installation process. The results of the simulation match with the definitions of a plug stated in this paper.
OUTLOOK
In further research a focus will be put on the numerical simulation of the installation process of open steel
pipe piles. The change of state variables around the pile will be compared for different installation
methods to draw conclusions about the axial and lateral bearing capacity.
To validate the numerical model and investigate the axial and lateral bearing behavior of driven and
vibrated piles with large diameters a comprehensive field test will be utilized. This field test, known as the
VIBRO project, was recently carried out in North Germany (cf. Herwig & Gattermann 2015).
a) b) c)
543
ACKNOWLEDGEMENTS
This work was partially performed on the computational resource bwUniCluster funded by the Ministry of
Science, Research and the Arts Baden-Württemberg and the Universities of the State of Baden-
Württemberg, Germany, within the framework program bwHPC.
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