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ISFOG 2010


									Simplified numerical model for soil pile interaction behavior of single
offshore piles under cyclic lateral loading
Mohammad Mahdi Memarpour
Iran University of Science and Technology
Mehrdad Kimiaei
Centre for Offshore Foundation systems, University of Western Australia
Mohsenali Shayanfar
Iran University of Science and Technology

ABSTRACT: Fixed steel platforms are one of the most common structural systems currently used for oil
exploitation purposes. Many of these platforms need to be reassessed for various reasons such as damaged
members and installation of new equipment on deck. To assess platform conditions, ultimate capacity of these
structures must be calculated on which structural behavior of supported piles plays a significant role.
Offshore pile foundations are often subjected to lateral cyclic loads due to environmental forces applied to the
supported structure. Pile foundation analysis commonly include the use of a Beam on Nonlinear Winkler
Foundation (BNWF) model in which the soil reaction is related to lateral deflection through prescribed curves
however this model is very sensitive to the way one considers the p-y curves for the analysis.
This paper outlines a new robust BNWF model, considering nonlinear cyclic pile-soil interaction behavior,
based on the API recommended p-y cyclic curves. This model is developed using ABAQUS software and it
can be easily implemented in comprehensive models for ultimate strength analysis of fixed offshore platforms.
In addition to soil elasto-plastic behavior, this model is able to capture soil strength degradation, gapping
phenomenon and drag forces on offshore piles under cyclic loadings. In a series of numerical simulations,
results of this model are compared well with the existing models in cyclic behavior of offshore piles and
experimental test results as well.

   1 INTRODUCTION                                          approaches is the capability of performing the pile-
                                                           soil-interaction analysis in a fully coupled manner
Pile supported offshore and coastal structures in          However, these two methods are not commonly
marine soil deposits are subjected to large static         used in design offices mainly due to their
and cyclic lateral loads. Usually, the critical lateral    presumed excessive computational costs and their
forces on piles used in coastal structures are due to      complexity for common pile dynamic response
berthing and mooring forces, whereas in offshore           analysis. (El Naggar et al. 2005)
jacket platforms, piles are subjected to cyclic               Beam on Nonlinear Winkler Foundation
lateral loads due to waves. Nonlinear PSI (pile-soil       (BNWF) method is a simplified approach that can
interaction) is one of the main parameters which           account for nonlinear PSI and is commonly used in
can deeply affect the overall response of the              professional geotechnical engineering and research
supported structures.                                      practices as well. In the BNWF method, pile is
   FE (finite element) and BE (boundary element)           modeled as a series of discrete beam-column
methods are direct numerical approaches for                elements resting on a series of springs and
solving pile-soil interaction problems on which the        dashpots representing the stiffness and enrgy
soil, pile and pile-soil-interfaces are modeled all        dissipation through the soil layers (Kimiaei et al.
together in one integrated model. For example,             2004). Generally, BNWF models are efficient and
Trochanis et al. (1988) used finite element method         reasonably precise methods that can account for
(FEM) whereas Kaynia & Kausel (1982)                       various complicated conditions in a simple
implemented the boundary element method (BEM)              manner. For example, Novak et al. (1978) and El
for response analysis of piles. FEM and BEM both           Naggar & Bentley (2000) have used BNWF
treat the soil as a continuum medium and provide           models for piles subjected to lateral dynamic loads.
powerful tools for conducting soil-pile-structure             Some BNWF models use the p-y curves
interaction analyses. Main advantage of such               approach (unit load transfer curves) in which the
soil stiffness is represented using nonlinear p-y          Combining these three components, it has been
(soil resistance versus pile deflection) curves.        shown that seismic soil pile interaction
Boulanger et al. (1999) and Kimiaei et al. (2004)       (incorporating gap development and drag forces on
used BNWF models based on p-y curve approach            the piles) can be reasonably modelled (Boulanger
for seismic soil pile structure interaction problems.   et al 1999)
Nonlinear p-y, t-z and Q-z curves can be used in
BNWF models for showing nonlinear lateral, axial
and end bearing behavior of the pile in soil layers.
However results of such BNWF models is very
sensitive how these nonlinear p-y, t-z and Q-z
curves are implemented in the models.
   For lateral behavior of piles, different p-y (soil
lateral resistance versus pile lateral deflection)
curves have been proposed for soft (Matlock
1970), stiff clay (Reese and Welch 1975) and sand
(Cox et al. 1974, Reese et al. 1974) layers. These
curves are adopted by API (American Petroleum
Institute) for routine use in the design of
foundations for offshore platforms (API 2000).
   In this paper a new simplified and robust
BNWF model based on the Boulanger model, is
presented that can be used for cyclic response
analysis of laterally loaded piles. General finite
element analysis software, ABAQUS (SIMULIA,
2004) is used for development of this model.
Effects of drag forces and soil strength degradation
on cyclic response of piles are investigated in this
study.                                                  Figure 1. Characteristics of Nonlinear p-y Element: (a)
                                                        Components; (b) Behaviour of Components. (Boulanger et al.
                                                            Another BNWF model has been presented by
Boulanger et al. (1999) presented a BNWF model          Taciroglu et al. is similar to Boulanger model. In a
for pile soil interaction analysis which incorporates   general, it has three sections; (i) a drag element for
three main parts connected in series as it is shown     frictional contac, (ii) a gap element and (iii)
in Figure 1a. First part in this model is a gap         Elastoplastic p-y element for hysteretic response of
element which is a combination of drag and              the soil.
closure springs. These two springs are connected in         Drag element models the pile movement inside
parallel and together they model the soil behavior      the gap. Classically, this element behaves
in the gap region around the pile. Force-               independent of strain rate in a totally plastic and
displacement behavior of these springs is               one-dimensional manner. Characteristic of this
illustrated in Figure 1b. In the gap region, closure    element can be seen in Figure 2.
spring takes no load and the total soil resistance
will only be provided through the drag spring.
Reaching at the end of the gap region, parallel
combination of drag and closure springs represent
a rigid behaviour for the gap element (infinite total
    Second part in the Boulanger model is the near
field element or plastic spring. The plastic spring
has an initial range of rigid behavior between -
0.35Pult< P <0.35Pult (where Pult is ultimate lateral
soil capacity) and out of this range it shows a
plastic behavior (Figure 1b). Third part of this
model shows the soil behaviour in the far field. It
is modeled by an elastic spring (showing the soil       Figure 2. Drag element for modeling the friction between the
stiffness) in parallel combination with a dashpot       soil and the pile. (Taciroglu et al. 2003)
(showing energy dissipation through the system
under cyclic loadings)
   When the gap is open, the major role of the gap                In the present study user element (UEL) feature
element is to prevent any stress in the elastoplastic          of general finite element program, ABAQUS
spring. A gap element would not transmit any                   (SIMULIA, 2004), is used to incorporate CPSI
stress when the gap is open, and be rigid when the             approach into FE models for cyclic response
gap is closed. A smoother transition between                   analysis of offshore piles. The developed UEL is a
closed-gap and open-gap phases can be achieved                 robust single node element which can be switched
via a projection operator which maps a perfectly               between static or cyclic responses and all soil input
transmitted stress into a stress that is transmitted           parameters can also be easily changed by the user.
through a gap.
   Finally, elastoplastic element which includes a
linear spring and a frictional spring are connected
in series. Figure 3 indicates combination of the
elements and the element behavior.

                                                               Figure 4. Static and Cyclic p-y curves as per API
                                                               recommnedations (API RP 2A-2000)
Figure 3. Assembly detail of a pile-soil interaction element
(Taciroglu et al. 2003)
                                                                  In ABAQUS models using this CPSI user
                                                               element, pile and surrounding soil are subdivided
                                                               into a number of discrete layers. Pile and soil
   3 MODEL DESCRIPTION                                         layers will be represented by a node at the end of
                                                               each segment. The stiffness of each pile segment
Soil hysteretic behaviour under lateral cyclic                 is modeled using the standard stiffness matrix of
loading shows significant changes in soil strength             beam column elements. Single-node CPSI user
and stiffness (Matlock 1970). These sequential                 element, representing cyclic pile soil interaction,
degradations in soil characteristics can influence             will be attached to each node on the pile elements.
the pile responses in sequential loading cycles. For           Stiffness of the soil layer around the pile segment
laterally loaded offshore piles, API recommends                at each node will be updated based on total lateral
two different types of static and cyclic p-y curves            deflection of the pile. Stiffness matrices of the pile
which are both schematically shown in Figure 4. It             segments and surrounding soil layers are then
is seen that by increasing the pile lateral                    assembled,      through      ABAQUS         nonlinear
deflections, cyclic p-y curve incorporates a notable           procedures, to form the global structural stiffness
reduction in the soil strength.                                matrix of the system.
   The BNWF model developed in this study,
namely CPSI (Cyclic Pile Soil Interaction)
hereafter, is based on the concepts in the
Boulanger model (Boulanger 1999). Main                                                              1

advantage of CPSI model comparing with BNWF
models by Boulanger at al (1999) and Kimiaei at al                                             0.5

(2004) is the capability of this model for soil
strength degradation under cyclic loads. Using
CPSI model, during each iteration in nonlinear pile            -12   -10   -8   -6   -4   -2
                                                                                                         0   2   4   6     8          10   Y/Yc 12

response analysis, ultimate cyclic resistance of the
soil (Pult) will be updated based on the total lateral                                         -0.5
                                                                                                                         Boulanger model
                                                                                                                         Static API
deflection of the pile as per API recommendations.                                                                       Cyclic API

Typical soil hysteric curves for Boulanger and
CPSI models comparing with API static and cyclic
p-y curves are shown in Figure 5, 6 respectively.              Figure 5. Static and cyclic API p-y curves and Boulanger
                                                               model behavior
                                               1.2                                                ABAQUS software and CPSI user elements are
                                                                                               employed to model and analyze this pile under


                                                                                               described lateral cyclic loadings. This model
                                                                                               includes 70 nodes, 69 beam standard elements and
                                                                                               69 CPSI user elements.
                                                                                               Table 2. Dimensions of pile segments
-12      -10    -8   -6     -4            -2          0      2   4   6   8        10      12   Element size            Depth below sea bed
                                                                         CPSI model            0.5 m                   0.0 to -20 m
                                               -0.4                      Static API
                                                                         Cyclic API            1.0 m                   -20 to -35 m
                                                                                               2.0 m                   -35 to -55 m
                                                                                               5.0 m                   -55 to -80 m
 Figure 6. Static and cyclic API p-y curves and CPSI model

        4 CASE STUDY

 To investigate response of offshore piles under
 cyclic lateral loads, using features of this CPSI
 model, a steel pile from a sample 4- legged fixed
 platform in the Persian Gulf is studied here. This
 pile has circular cross section with 137cm outside
 diameter and 80m penetration below seabed.
 Detailed information about this pile is given in
 table 1.

 Table 1. Pile model main characteristics
      pile height                                     80 m
      External Diameter                               1371 mm
                                                      60 mm (0 to-7.5m)
                                                      65mm (-7.5 to -20m)
      Pile thickness
                                                      45mm (-20 to -28m)
                                                      30mm (-28 to -80m)
      Elasticity modulus                              2.1E5 MPa
      Density                                         7800 Kg/m3
      yielding point                                  3.6e5 KN/m2                              Figure 7. Pile and properties of the soil layers
      Total vertical load                             14 MN
      Total horizontal load                           2 MN                                        5 NUMERICAL RESULTS & DISCUSSION

    The soil profile in this field consisted of 3                                              Main objective of this part is to investigate the
 horizontal layers and the pile is loaded with a                                               effects of following input parameters on lateral
 content vertical load of 14 MN and 10 cycles of                                               cyclic response of offshore piles:
 sinusoidal lateral loads of 2 MN.
    At soil top layers, where there are higher pile                                                •    Drag force on piles in the gap region
 lateral deflections comparing with the other parts                                                •    Soil strength degradation
 of the pile, a fine mesh of pile segmentation is
 used. Moving down toward the pile tip along the                                                  Using CPSI model, with no soil strength
 pile shaft, the pile deflections and internal forces                                          degradation, pile response analysis is carried out
 will decrease rapidly and hence a coarse mesh can                                             for drag force of αPult (where α and Pult represen5t
 be used in this area. table 2 shows a summary of                                              drag coefficient and lateral capacity of the soil at
 the pile segmentations used in this study.                                                    each stage). Three different α coefficients are used
    Figure 7 shows general view of this pile, CPSI                                             in these sensitivity analyses: α = 0 % (no drag
 model, soil layers and physical properties of the                                             effect), α = 30 % (used by Boulanger et al. (1999))
 soil layers.                                                                                  and α = 50 % (used by Wallace et al. (2002)).
   Results of the peak pile deflections (lateral                                                                                             Pile Shear Force (MN)
displacement at seabed level), peak shear force and                                                                                                   0
peak bending moments along the first and the last                                                                  -3          -2            -1            0          1              2                                                            3

loading cycles, are presented in table 2.                                                                                                            -10

Table 2. Result of pile response analysis for different drag

                                                                                                                                                                                                              Pile Penetration below seabed (m)
 drag coefficient                   0%            30%            50%
            1 cyc.                  -0.378        -0.378         -0.378
 Disp.            th                                                                                                                                 -40
            10 cyc.                 -0.441        -0.439         -0.437                                                                Cycle 1
                                                                                                                                       Cycle 10
            difference              16.40%        16.10%         15.70%
            1st cyc.                -1.72         -1.72          -1.72
 Force      10th cyc.               -1.88         -1.87          -1.87                                                                               -60
            difference              9.30%         8.70%          8.70%
             st                                                                                                                                      -70
            1 cyc.                  19.5          19.5           19.5
 Moment     10th cyc.               21.3          21.2           21.2
 (MN.m)                                                                                                                                              -80
            difference              9.20%         8.70%          8.70%
                                                                                                                    Figure 9. Pile shear force for drag coefficient of 30% along
                                                                                                                   the pile shaft.
   It is seen that different drag coefficients, α, has
no important effect on any of the calculated pile                                                                                      Pile Bending Mom ent (MN.m )
responses either for the first or for the last loading                                                                        0
cycle. It is also observed that pile deflection, shear                                                                  -5         0             5         10    15             20                 25
force, and bending moment for all three different
cases (α = 0%, 30%, 50%) for the 10th cycle are                                                                              -10

about 16%, 9%, 9% respectively higher than the
results for the 1st loading cycle.                                                                                           -20

   Pile deflections, shear forces and bending

                                                                                                                                                                                         Pile penetration below seabed (m)
moments along the pile shaft for drag coefficient of                                                                         -30
30% at the first and the last loading cycles shown
in Figures 8-10.
                             Pile deflection (m )
                                                            0                                                                -50                                     Cycle 1
    -0.5     -0.4            -0.3          -0.2     -0.1         0                                           0.1                                                     Cycle 10

                                                           -10                                                               -60

                                                           -20                                                               -70
                                                                         Pile penetration below seabed (m)

                                                           -30                                                               -80

                                                                                                                   Figure 10. Pile bending moment for drag coefficient of 30%
                       Cycle 1                             -40                                                     along the pile shaft.
                       Cycle 10

                                                                                                                       In the second part of this study the effects of
                                                                                                                   soil strength degradation on overall response of
                                                           -60                                                     offshore piles under lateral cyclic loading is
                                                                                                                   assessed. Results of pile deflections, shear forces
                                                                                                                   and bending moments for the last loading cycle
                                                                                                                   (i.e. 10th cycle) along the pile shaft for drag
                                                                                                                   coefficient of 30% using CPSI model
                                                           -80                                                     (incorporating cyclic P-Y curve) and Boulanger
Figure 8. Pile deflection for drag coefficient of 30% along                                                        model (incorporating static P-Y curve) are shown
the pile shaft.                                                                                                    in figures 11-13, respectively. All these results
                                                                                                                   show that soil strength degradation (using CPSI
model) will lead to significant increase in the pile                                                                                                                 Pile Bending Moment (MN.m)
response values.                                                                                                                                            0
                                                                                                                                                    -10          0            10        20            30    40
                         Pile Deflection (m )
-1.2    -1        -0.8       -0.6         -0.4   -0.2           0       0.2


                                                                                                                                                                                                           Pile Penetration below seabed (m)

                                                                        Pile Penetration below seabed (m)


                                                        -50                                                                                                -60

                                                                                                                                                                                         CPSI model
                                                                                                                                                                                         Boulanger model
              CPSI model
              Boulanger model                           -70

                                                                                                                                                Figure 13. Pile bending moment for cyclic (CPSI) and static
                                                                                                                                                model (Boulanger) along the pile shaft (drag Coef. 30 %)
Figure 11. Pile deflection for cyclic (CPSI) and static model
(Boulanger) along the pile shaft (drag Coef. 30 %)
                                                                                                                                                Table 3. Result of pile response analysis for CPSI and
                           Pile Shear Force (MN)                                                                                                Boulanger models.
                                   0                                                                                                                                   CPSI        Boulanger Difference
  -4     -3        -2         -1      0      1          2           3                                                         4                                        model       model         (%)
                                    -10                                                                                                                                -0.967      -0.408        137
                                                                                                                                                Shear Force
                                    -20                                                                                                                                -2.94       -1.87         57.2
                                                                                                            Pile Penetration below seabed (m)

                                                                                                                                                Bending Moment
                                                                                                                                                                       33.8        21.2          59.4
                                    -30                                                                                                         (MN.m)

                                                                                                                                                     6 CONCLUSIONS
                                                                                                                                                A simplified and roboust BNWF model for cyclic
                                                                                                                                                pile soil interaction analysis of offshore piles was
                                    -60                                                                                                         introduced. This model was incorporated as a user
                                                    CPSI model
                                                                                                                                                element in ABAQUS software and it was used for
                                                                                                                                                series of response analysis of offshore piles under
                                                    Boulanger model
                                                                                                                                                lateral cyclic loads.
                                                                                                                                                   Effects of different drag coefficients and soil
                                                                                                                                                strength degradations on the pile response values
Figure 12. Pile shear force for CPSI and Boulanger model                                                                                        (peak pile deflections, peak shear forces & peak
along the pile shaft (drag Coef. 30%)                                                                                                           bending moments) were studied and it was
                                                                                                                                                concluded that:
   Peak deflections, shear forces and peak bending
moments for CPSI and Boulanger model are                                                                                                        •     Drag Coefficient has no important effect on
summarized in table 3. It is seen that peak pile                                                                                                      overall pile response results.
deflection, peak shear force and peak bending
moment for CPSI model are approximately 132%,                                                                                                   •     Incorporating soil strength degradation (using
57% and 59% higher than the results for Boulanger                                                                                                     CPSI model) will lead to significant increase in
model. CPSI model will also shift downward the                                                                                                        pile response values comparing with static P-Y
location of the critical section of the pile for shear                                                                                                curves (using Boulanger model)
forces and bending moments by about 4m.
   7 AKNOWLEDGMENTS                                                Mechanics Conference, 16-18 July 2003. University of
                                                                   Washington: Seattle.
                                                                Trochanis, A., Bielak, J., & Christiano, P. 1988. A
This work forms part of the activities of the Centre               threedimensional nonlinear study of piles leading to the
for Offshore Foundation Systems (COFS),                            development of a simplified model. Department of Civil
established under the Australian Research                          Engineering, Carnegie Institute of Technology. Report R-
Council’s Research Centres Program and now                         88–176.
                                                                Wallace, J. W., Fox, P. J., Stewart, J. P., Janoyan, K., Qiu, T.
supported by the State Government of Western                       & Lermitte, S. P. 2002. Cyclic large deflection testing of
Australia as a Centre of Excellence. The authors                   shaft bridges. Part II: Analytical studies. Report from
would like to thank IUST (Iran University of                       California Dept. of Transportation: Los Angeles.
Science and Technology) and COFS for their
financial & technical supports during this study.


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