dynamic nonlinear behavior of fixed offshore jacket piles

INTERNATIONAL JOURNAL OF CIVIL AND STRUCTURAL ENGINEERING Volume 2, No 1, 2011

© Copyright 2011 All rights reserved Integrated Publishing services Research article ISSN 0976 – 4399

Received on July 2011 published on September2011 260

Dynamic nonlinear behavior of fixed offshore jacket piles Mohamad Ahangar 1 , Khosro Bargi 2 , Hesam Sharifian 1 , Morteza Safarnezhad 1

1 Ph.D. student, Department of Civil Engineering, College of Engineering, University of Tehran

2 Professor, Department of Civil Engineering, College of Engineering, University of Tehran

[email protected]

ABSTRACT

The response of pile supported fixed offshore jackets is very sensitive under earthquake loadings. These structures shall be able to undergo the seismic loadings without any failure. To reach this purposes the dynamic analysis should be considered because of some factors like soil nonlinearity, energy dissipation, nonlinear behavior of foundations, discontinuity condition at pile soil interfaces and etc. the noticeable part of dynamic response of fixed offshore jackets is nonlinear behavior of piles. In this paper, innovative and newest approaches in nonlinear analysis together with ABAQUS modeling to be used to extract the useful conclusions related to dynamic nonlinear response of fixed offshore jackets.

Keywords: Pile, nonlinear dynamic response, interaction, seismic behavior

1. Introduction

The recent development of offshore industries (in particular the exploration and production of oil and gas) leads to growing demand for realistic predictions of offshore platforms behavior. Earthquake design of offshore platforms in seismic active areas is one of the most important parts in offshore platforms design. Evaluation of the pilesoilstructure interaction due to earthquake induced ground accelerations is an important step in seismic design of both the structure and piles. ‘Dynamic response will be defined as those characteristics of the structural system that can not be attributed to notime varying or static response. Inertial, damping and kinematics effects developed by loadings that have significant variations in time will be include in dynamic response. Dynamic response of offshore platforms due to earthquake excitations (and all cyclic loadings) would be inherently on nonlinear behavior because of the following reasons:

1 Nonlinear behavior of the soil at a wide range of shear strain (Soil behavior would be linear only at very small shear strains of approximately less than 4 10 %).

2 PileSoil interaction, which is affected by different nonlinear behavior of interface elements (Gapping and Cavein effect) for different type of the soils (clay and sand).

3 The seismic loading rates, which potentially could cause significant stresses and nonlinear material behavior of piles and superstructure.

Dynamic response of piles in offshore platforms is a function of the characteristics of the loading, dynamic pilesoil interaction behavior and dynamic characteristics of the piles structural system. In recent years the interaction problem during earthquake loadings has received considerable attention and studies indicate the nature of ground motion input and the

Dynamic nonlinear behavior of fixed offshore jacket piles Mohamad Ahangar, Khosro Bargi, Hesam Sharifian, Morteza Safarnezhad

International Journal of Civil and Structural Engineering 261 Volume 2 Issue 1 2011

mechanism of pile soil interaction play an important role in determination of platform design loads.

The earliest systematic theoretical studies of dynamic soil pile interaction are due to Parmelee et al (1964), Tajimi (1966), Penzien (1970) and Novak (1974). Parmelee (1964) and Penzien (1970) employed a nonlinear discrete model and a static theory to describe e the dynamic elastic stress and displacements of fields. Tajimi (1966) used a linear viscoelastic stratum of the KelvinVoigt type to model the soil and in his analysis of the horizontal response he neglected the vertical component of the soil motion. Novak (1974) assumed linearity and an elastic soil layer composed of independent infinitesimally thin horizontal layers extending to infinity.

Recently investigators have begun to develop numerical methods in which all the soil, pile, superstructure and soilpilesuperstructure interfaces are modeled simultaneously together. Yegian and Wright (1973), Angelides and Rosset (1980), Randolph (1981), Faruque and Dessail (1982), Trochanis et al. (1988) and Wu(1997) used finite Element Method (FEM) whereas Sanches (1982), Kaynia and Kausel (1982) and Sen et al (1985) implemented Boundary Element Method (BEM) for dynamic response analysis of piles. In both FEM and BFM the soil is treated as a continuum media. Discritization of a three dimensional continuum media and generation for a multitude of degrees of freedom in FEM and deriving of complex Green functions for complicated media in BEM, make both of these methods impractical for seismic response analysis of offshore platforms.

The finite and boundary element methods potentially provides the most powerful tools for conducting Seismic SoilPileStructure Interaction (SSPSI) analyses, but they have not yet been fully realized as a practical accepted method mainly due to their presumed excessive computational costs and their complexity for common pile dynamic response analysis. The main advantage of such approaches is the capability of performing the SSPSI analysis of pile in a fully coupled manner, without resorting to independent calculations of site or superstructure response.

The Beam on Nonlinear Winkler Foundation (ABAQUS) method is a dimplified approach that can account for nonlinear SoilPileStructure Interaction (SPSI) and has proven useful in professional engineering and research practices. Trochanis (1991) showed that the response of laterally loaded piles predicted using a ABAQUS formulation agreed well with static load test data and nonlinear three dimensional FEM. Boulanger et al (1999) showed that the results of seismic response of piles using ABAQUS modeling agreed well with centrifuge experimental tests.

ABAQUS models are the most versatile, economical and popular methods that can account for various complicated conditions in a simple manner. Basic components criteria in a ABAQUS models for dynamic response analysis of offshore piles are adopted in this paper. In ABAQUS method the pile is modeled as a series of a discrete beamcolumn members resting on a series of springs and dashpots indicating the nonlinear dynamic behavior of soils. In seismic loadings, "free field" ground motion time histories are usually computed in a separate site response analysis and then applied to soilpile spring supports in ABAQUS models. A singular disadvantage of a ABAQUS mode is the two dimensional simplification of the soilpile contact, which ignores the radial ad threedimensional components of interaction.



2. Model Description

All above studies indicate that when a pile is subjected to highlevel lateral loading, the soil nonlinearity and relative movement at the pilesoil interface will strongly affect the pile behavior. Any model to be used for dynamic response analysis of piles should allow for variation of soil properties with depth. Nonlinear soil behavior, nonlinear behavior of pile soil interfaces, energy dissipation through radiation and hysteretic damping and soil strength degradation due to cyclic loads. During earthquake excitation all the components of a ABAQUS mode (representing the pile and surrounding soils) will be subjected to free field ground motions.

Figure 1 shows the general view of an ABAQUS model and its main components in dynamic nonlinear response analysis of offshore platforms. It is clear that for nonlinear dynamic response analysis of piles based on ABAQUS assumptions, each model should contain the following items:

1 Pile modeling 2 Soil stiffness and Damping modeling 3 PileSoil interface modeling 4 Free field excitations

3. Pile Modeling

The pile and surrounding soil layers are subdivided into a couple of discrete segments with pile nodes corresponding to soil nodes at the same elevation. Stiffness matrix of beam column elements are used to model to the structural stiffness matrix of each pile segment. These structural stiffness matrices of the pile segments will be assembled to build the global structural stiffness matrix of the whole pile.

4. Soil Model

In ABAQUS hypothesis there are two different methods of solid modeling as follows: 1 hyperbolic stressstrain approach 2 PY curves approach

4.1 PileSoil Interface

One of the main sources in nonlinear dynamic response of piles is the relative movement of the soil and pile at interfaces. It is clear that each ABAQUS model shall include particular pilesoil interface elements to account for such relative movements. Behavior of these interface elements in compression and tension are quite different and therefore the pilesoil interface elements together with springs, dashpots and masses (if any) are usually modeled separately on each side of the pile. According to different behavior of cohesive and cohesion less soils, there should be different type of interface elements. When the tensile stress is detected in soil springs, these interface elements should detach pile nodes from the soil nodes and it means that a gap will be created between pile and the soil. These gaps in cohesive soils (clay) will not be filled with the soils again and it means that there would be a gap development (permanent displacement of soil nodes) during earthquake excitations in clay soils (Matlock 1978, Nogami 1992).



Figure 1: General View of ABAQUS models for nonlinear dynamic response analysis of offshore platforms

There would be cavein behavior in cohesion less soils (sand) resulting in backfilling of sand particles around the pile. It means that any developed gap in sand will be simultaneously filled with backfilled soil again and no permanent gaps will be developed. (ElNaggar 2000). Considering different soil behavior in compression and tension (gapping in clay layers and cavein in sand layers), the soil reactions and the pile oil interface elements will be modeled separately on both side of the piles. General views of soil reaction versus pile deflections for cohesive and cohesionless soils (indicating gapping and cave in behaviors) are shown in figs. 2 and 3 respectively



Figure 2: Typical Soil reactionPile deflection Behavior for cohesive soils (Gapping) soils (Cavein)

Figure 3: Typical soil reactionPile deflection Behavior for cohesionless

4.2 Free Field Excitations

Earthquake induced loading on buried structures can be separated into two basic loading conditions of kinematic and inertial. These ABAQUS models (including pile, springs, dashpots and pilesoil interface elements) only deal with inertial loadings due to earthquake excitations. Kinematic loadings are an important part in dynamic response of piles due to seismic excitations in ABAQUS hypothesis. In these kinematic loadings, dynamic ground



motions of the soil layers in free field due to earthquake excitations at bed rock should be determined.

Results of such free field calculation (acceleration or displacement time histories at different soil layers) will be used as the input excitation at support nodes of the ABAQUS models. In such type of calculations, the free field motions are uncoupled from the pile ABAQUS models. In seismic loadings because of the different wave polarities in the near field and far filed, uncoupling the nonlinear pilesoil interaction in near field from the free field responses would be a reasonable approximation.

Fen et al (1991) performed and extensive parametric study using an equivalent linear approach to develop dimensionless graphs for pile head deflections versus the free field response. Markis and Gazetas (1992) applied free field accelerations to a one dimensional ABAQUS model. Bentley (2000) performed a full three dimensional transient nonlinear dynamic analysis (3 D wave propagation) and compared the results with equivalent linear 1D methods.

In dynamic response analysis of piles, free field motions may be calculated by any desired wave propagation method such as equivalent linear (used in SHAKE91 software) or nonlinear procedures. SHAKE (Schanbel et al 1972) is still commonly used after 30 years of its release and it is a reference computer program in geotechnical earthquake engineering. In SHAKE it is assumed that the cyclic soil behavior can be simulated using an equivalent linear model representing the soil stress strain response based on KelvinVoigt model. Wang (1998) used SHAKE for free field motion analysis and showed an acceptable agreement between calculated results and the recorded results in centrifuge tests.

5. Summary and Conclusion

Dynamic soil reaction and pile head response to harmonic loads for both the PY and hyperbolic approaches in ABAQUS models were compared by ElNaggar and Bentley (2000). A pile with the outside diameter of d = 0.5 m , length of l=15 m and an elastic modulus ( ) E p equal to 35 GPa was used (as shown in Fig. 4). A parabolic soil profile with the ratio of

1000 E E p s = / at the pile base was assumed. The undrained shear strength of the clay was assumed to be 25 kPa.

Figure 4: The model used by ElNaggar and Bentley (2000) for comparing PY curve and hyperbolic approaches

Figure 5 shows the displacement time history of the pile head for a harmonic load with single amplitude equal to 10 kN at a frequency of 2 Hz applied at the pile head. Fig 6 shows the



calculated dynamic soil reaction (at 1.0 m depth) for a harmonic displacement of a single amplitude equal to 0.03 d (0.015 m) at a frequency of 2 Hz applied at the pile head.

Figure 5: Pile head response due to harmonic load with single amplitude equal to 10 kN at a frequency of 2 Hz.

Figure 6: Calculated Dynamic soil reaction at 1.0 m depth for harmonic displacement with single amplitude equal to 0.03d at a frequency of 2 Hz.

In Figures 5, 6 it is seen that hyperbolic and PY curve models show very similar responses at the pile head displacement and soil reactions respectively and both stabilize after approximately five cycles. ElNaggar and Bentley (2000) also showed that dynamic soil reactions are in general larger than the static reactions because of the contribution from damping. Employing the same definition used for static PY curves, dynamic PY curves (which are frequency depended) can be established to relate the pile deflections to the corresponding dynamic soil reactions at any depth below the ground surface. These dynamic PY curves can be implemented in equivalent static analyses, which are now used in earthquake analysis of offshore platforms.

Several implementations of Dynamic PY methods (different configuration of nonlinear springs and dashpots in Parallel and Series Radiation Damping) together with free field effects were compared with Centrifuge model tests (performed at University of California, Davis) by Wang et al. (1998).

Centrifuge tests were performed on samples of normally consolidated San Francisco Bay Mud (density of about 1700 kg/m 3 ) with a crust of dense sand (density of about 2100 kg/m 3 ) on the surface of clay. The water table was at the ground surface. General configuration,



dimension and instrumentations of this model are shown in Fig. 7. A scale factor N = 50 was used in this model and so all dimensions shown in Fig. 7 should be factored by a scale factor of 50 in prototype units. More explanations about centrifuge modeling tests and scaling laws could be referred to Kutter (1992). In prototype terms, this model represents a superstructure mass of 1.44 ton and pile head mass of 1.12 ton supported by a 317 mm diameter steel pipe having a wall thickness of 10 mm. Santa Cruz during the 1989 Loma Prieta Earthquake was used to excite the base of the centrifuge mode.

Figure 7: Configuration of Centrifuge model test (Wang et al 1998)

Table – 1 shows the conditions and methods in two different numerical cases used by Wang et al (1998) for simulation of the centrifuge model test results. All ABAQUS modeling and nonlinear analysis carried out using DRAIN2D (Dynamic Response Analysis of Inelastic 2D structures, version 1.10Prakash & Powell 1993). Dynamic motions of the free field (which are used as the input excitations of the supports in ABAQUS model) carried out using SHAKE (Schnabel et al, 1972) which uses the equivalent linear procedure for nonlinear soil behavior

Table 1: Input information for numerical cases

Damping Model

Damping Coefficient PY Curves Generation PY Strength

Case A Parallel 4 s B v ρ Piecewise (Matlock) Linear . 1 ult x P

Case B Series 4 s B v ρ Piecewise (Matlock) Linear . 1 ult x P

Recorded and calculated spectral accelerations for above cases are shown in Figs. 8 a, b respectively. In Fig. 8a it is seen that only the peak acceleration for superstructure is predicted well by the results of CASE A meanwhile the peak acceleration for the pile head and frequency content for both locations (superstructure and pile head) are not well predicted. In Fig. 8 b it is seen that the peak acceleration for the pile head and frequency content for both locations (superstructure and pile head) are well predicted and only the peak acceleration for superstructure is predicted dynamic response of the pile at pile head and superstructure responses) is seen in CASE B which series radiation damping is used. Comparing the response spectra for Cases A and B (in Figs. 8 a, b) it is concluded that



parallel radiation damping acted to restrict the lateral movement of the pile head and therefore resulted in a stiffer system (higher frequency content) than for the series radiation damping.

Figure 8a: Acceleration response spectra (Calculated in Case A)

Figure 8b: Acceleration response spectra (Calculated in Case B)

The highest peak moment in CASE a is about 29% more that CASE B meanwhile the location of the highest peak moment in CASE A (close to ground surface) is quite different that CASE B (about 2 m below ground surface). It should be noted that peak moment at the ground surface depends primarily on the superstructure acceleration and coincidence of the natural period of the system and predominant period of the shaking. Parallel radiation damping is likely to produce a stiffer system than series radiation damping and it allows forces to bypass the hysteretic system through a parallel dashpot. Therefore parallel radiation damping results in a more rapid reduction in bending moments with depth than is calculated using series radiation damping.

6. References

1. Matlok, H. (1970), “Correlations for design of laterally loaded piles in soft clay”. Proceeding of the 2 nd Offshore Technology Conference, Huston, Tex., 1, pp 577588.

2. ElNaggar, M. H. and Bentley, K. J. (2000), “Dynamic analysis for laterally loaded piles and dynamic py curves”, Canadian Geotechnical Journal, 37, pp 11661183.



3. Kutter B. L., (1992), “Dynamic centrifuge modeling of geotechnical structures”, Transp. Res. Rec. 1336, Transportation Research Board, Washington, D.C., pp 2430.

4. Markis, M., Gazetas, G., (1992), “Dynamic pile soil pile interaction”. Part II, Lateral ans seismic response. Earthquake Engineering and Structural Dynamics, 21, pp 145 162.

5. Kaynia, A. and Kausel, E. (1982), “Dynamic Stiffness and Seismic Response of Pile Groups,” Rpt. R8203, Massachusetts Inst. of Technology, Cambridge.

6. Gazetas, G. and Doprby, R. (1984) “Horizontal response of piles in layered soils”. Journal of Geotechnical Engineering, ASEC, 110(1), pp 2040.

7. Fen, K., Gazetas, G., Kaynia, A., Kausel, E., and Ahmed, S. (1991), “Kinematic response of singl piles and pile groups”, Journal of Geotech. Eng., ASCE 117(12), 18601879.

8. ElNaggar, M. H. and Novak, M. (1996), “Nonlinear Analysis for dynamic lateral pile rssponse”. Journal of Soil Dynamics and Earthquake Engineering, 14(4), pp 233244.

9. Bentley, K. J. and EiNaggar, M. H. (2000), “Numerical analysis of kinematic response of single piles”, Canadian Geotechnical Journal, 37, pp 13681382.

10. Angelides, D. C. and Roesset, J. M., (1980), “Nonlinear dynamic stiffness of piles”, Research report R 8013, Dept. of Civil Engineering, MIT, Cambridge, Massachusetts.

11. ElNaggar, M. H. and Novak, M. (1995), “Nonlinear lateral interaction in pile dynamics”, Journal of Soil Dynamics and Earthquake Engineering, 14(3), pp 141157.

12. ElNaggar, M. H. and Novak, M. (1994), “Nonlinear model for dynamic axial pile response”. Journal of Geotechnical Engineering, ASCE, 120 (2), pp 308329.

13. American Petroleum institute. (2000), “Recommended practice for planning, designing and constructing fixed offshore platforms”. API Recommended Practice 2A (RP2A). 21 st ed. American Petroleum Institute, Washington, D. C., pp 4755.

14. Parmele, R. A., Penzien, J., Scheffey, C. F., Seed, H. B. and Thiers, G. R. (1964), “Seismic effects on structures supported on piles extending through deep sensitive clays”, Inst. Eng. Res., University of California, Berkeley, Rep. SEM 642.

15. Kagawa, T., and Kraft, L. (1980), “Seismic PY Responses of Flexible Piles”, J. Geotech. Eng., ASCE, 106(8), pp 899918.

dynamic nonlinear behavior of fixed offshore jacket piles

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