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Analysis of spudcan–footprint interaction in a single soil with nonlinear FEM

Analysis of spudcan–footprint interaction in a single soil with nonlinear FEM Pet. Sci. (2015) 12:148–156 DOI 10.1007/s12182-014-0007-4 OR IGINAL PAPER Analysis of spudcan–footprint interaction in a single soil with nonlinear FEM • • Dong-Feng Mao Ming-Hui Zhang • • Yang Yu Meng-Lan Duan Jun Zhao Received: 27 January 2014 / Published online: 24 January 2015 The Author(s) 2015. This article is published with open access at Springerlink.com Abstract The footprints that remain on the seabed after footprints is becoming more common and inevitable. offshore jack-up platforms completed operations and moved According to van den Berg’s statistics (Van den Berg et al. out provide a significant risk for any future jack-up installation 2004), within Shell EP Europe alone roughly 1,200 footprint at that site. Detrimental horizontal and/or rotational loads will points had been registered in geotechnical and footprint be induced on the base cone of the jack-up platform leg datasets. In addition, there are approximately 80 new single (spudcan) in the preloading process where only vertical loads footprint points added to the existing datasets every year. are normally expected. However, there are no specific Thus, it can be seen that footprints are not rare and they pose a guidelines on design of spudcan re-installation very close to or serious and growing threat to operational safety of jack-up partially overlapping existing footprints. This paper presents a drilling platforms. Figure 1 shows when a leg is close to an rational design approach for assessing spudcan–footprint existing footprint, the non-uniform bearing load caused interaction and the failure process of foundation in a single by the footprint will make the spudcan slide into the foot- layer based on nonlinear finite element method. The rela- print in the jacking process, which was proven by Gaudin tionship between the distance between the spudcan and the et al. (2007), Leung et al. (2007). The sliding trend is affected footprint and the horizontal sliding force has been obtained. by the leg stiffness, connection between leg and hull, and in- Comparisons of simulation and experimental results show that place condition of other two legs, and the size of the trend is the model in this paper can deal well with the combined measured by the horizontal sliding force and overturning problems of sliding friction contact, fluid–solid coupling, and moment (McClelland et al. 1982; Hossain and Randolph convergence difficulty. The analytical results may be useful to 2007; Bouwmeester et al. 2009). If a slide occurs, the legs jack-up installation workovers close to existing footprints. will incline in different directions, so that the legs may become stuck in the platform and this would mean the plat- Keywords Jack-up  Existing footprint  Spudcan– form cannot be raised. The potential risk of slipping is a serious threat to the operational safety of platforms. footprint interaction  Numerical simulation  Nonlinearity Re-installing a spudcan very close to or partially over- lapping existing footprints is generally not recommended 1 Introduction in the guidelines (SNAME OC-7 panel. 2007; Hossain and Randolph 2008). In a situation where this is inevitable, the With an increase in frequency of operations, the situation that guidelines recommend the use of an identical jack-up installation of jack-up platforms on sites which contains old (same footing geometries and leg spacing) and locating it in exactly the same position as the previous unit, where possible. However, it is unlikely that two jack-up units D.-F. Mao (&)  M.-H. Zhang  Y. Yu  M.-L. Duan  J. Zhao have an identical design because the structures of most College of Mechanical and Transportation Engineering, China units are often custom-made and the deployments of units University of Petroleum, Beijing 102249, China are subject to availability. It is evident that existing e-mail: maodf@cup.edu.cn guidelines are not adequate for rig operators to install jack- up units in close proximity to existing footprints safely. Edited by Yan-Hua Sun 123 Pet. Sci. (2015) 12:148–156 149 Fig. 1 Schematic diagram of existing footprint problems New rig Resultant forces at the leg-hull connection 1ʹ Overstressing the braces Footprints HH ʹ Piled jacket platform V V ʹ Footprint Footprint issues involve soil elastoplasticity, material explanations for tests. This paper takes various factors and geometric nonlinearities, fluid–solid coupling, friction including failure process of foundation, nonlinearity, slid- contact during spudcan preloading, and difficult conver- ing friction contact, and fluid–solid coupling into account. gence of numerical solutions (Hanna and Meyerhof 1980; It discusses the finite element model of spudcan–footprint Kellezi and Stromann 2003; DeJong et al. 2004; Deng and interaction in spudcan re-installation near an existing Kong 2005; Leung et al. 2008). Previous research mainly footprint as well as handling relative parameters. With the focuses on the spudcan–footprint interaction through the model of the spudcan–footprint interaction, the changes of centrifuge model test. Murff et al. (1991), Hossain et al. horizontal sliding force on the spudcan at different offset (2005), Cassidy et al. (2004, 2009), Teh et al. (2010), Gan distances between the spudcan and the footprint were (2009), Gan et al. (2012), Kong et al. (2010, 2013), Xie analyzed with ABAQUS software. The finite element et al. (2012) conducted a series of drum centrifuge model model was validated by comparing the simulation result tests to investigate spudcan–footprint interaction and the with experimental results. effect of leg stiffness on spudcan–footprint interaction. With the centrifuge model tests, Stewart and his coworkers (Stewart 2005; Stewart and Finnie 2001) studied the effect 2 Analytical methods and computing model of bending rigidity of legs on spudcan–footprint interaction and the influence of the distance between the spudcan and During jacking, the deformation of the surrounding soil is the footprint on sliding. Dean and Serra (2004) discussed very large, which results in changes in pore pressure and the effect of equivalent stiffness of legs on spudcan–foot- then a reduction in the effective strength of the soil. To print interaction. Teh et al. (2006) reported a set of test analyze spudcan–footprint interaction, the coupling of results investigating the effects of sloping seabed (30 stress/fluid flow in soil should be considered. Undrained inclined to the horizontal) and footprint on loads developed total stress analysis is used in the computing model, i.e., the in jack-up legs. They found that the effect of the footprint total stress is the sum of effective stress and hydrostatic is much greater than that of the seabed slope. This indicates pressure. Thus, the equilibrium equation in the vertical that the footprint problem is more serious than a sloping direction is as follows (Houlsby and Martin 2003): seabed. Other researchers have tried to investigate the > dS 0 0 0 footprint problem with numerical simulation (Zhang et al. qg  c S ð1  n Þ ðz  zÞ ; z  z dr r z w w w dz ¼ ; 2011, 2014). Jardine et al. (2002) simplified a three- dz > 0 0 qg; z  z  z dimensional model to a plane strain one to deal with footprint issues. The current understanding of this topic is ð1Þ still insufficient, and only a small number of studies of the where r is the vertical stress, Pa; q is the soil dry density, footprint problem are available in the public domain. 3 3 kg/m ; c is the water gravity density, N/m ; S is the soil w r Although it is a great challenge to obtain a converged 0 0 saturation, %; z is the free water surface elevation, m; z numerical solution, a good numerical model and solution is w is the elevation of interface between dry soil and partially very important because it is able to achieve more accurate 0 0 saturated soil, m; and n is porosity, %; when z  z in estimation of carrying capacity of spudcans and better 123 150 Pet. Sci. (2015) 12:148–156 0 0 completely saturated, S ¼ 1, and when z  z  z ,in between the spudcan and the surrounding soil, and the spudcan surface is taken as the active surface and the soil partially saturated, S \1. The advantage of ABAQUS in soil engineering is that it surface as the passive surface (Zhuang et al. 2005). The principle for choosing an active or passive surface is that provides not only various elastic/plastic constitutive mod- els for soil but also coupled analysis of stress/fluid flow in the mesh of the passive surface should be finer, and if both mesh densities are similar to each other, the surface of the soil. In numerical computation, the finite element mesh is fixed on the soil skeleton, and fluid may flow through the softer material should be passive. The tangential contact obeys the Coulomb friction law, and the normal contact mesh and satisfy the fluid continuity equation. The Forchheimer equation (Zeng and Grigg 2006) is adopted to follows the hard touching mode, i.e., penetration is not allowed between the spudcan element and the soil element, describe nonlinear flow in soil (porous medium). Since less but they are allowed to separate (Zhuang et al. 2005). In relative parameters in calculation are needed, the Mohr– Coulomb constitutive model is used (Li 2004), i.e., the soil order to obtain the correct horizontal sliding force–dis- placement curve, the displacement control method is used is considered as a perfect elastic–plastic material, and obeys the noncorrelation flow rule. The Mohr–Cou- to load. A simplified spudcan, with its side friction ignored because of its relative smaller area, is adopted to reduce the lomb yield criterion is as follows: difficulty of convergence in calculation. The friction s þ r sin /  c cos / ¼ 0; ð2Þ coefficients for undrained clay and drained granular soil are where s ¼ðr  r Þ=2 is half of the difference of maxi- 1 3 0.2–0.3 and tan d, respectively, where d is the friction mum and minimum principal stresses, kPa; r ¼ðr þ m 1 angle between the spudcan and the soil. It must be pointed r Þ=2 is the average value of maximum and minimum 3 out that whether setting a reasonable degree of spudcan– principal stresses, kPa; c is cohesion, kPa; and / is the soil contact will lead to the calculation converging or not. internal friction angle, . Except for over-consolidated soil, Since the ultimate bearing capacity would be underesti- clay always shows little dilatancy, and thus the dilatancy mated if the initial geo-stress equilibrium were not consid- angle / = 0. Assume that the deformation modulus is ered in numerical simulation, this paper deals with the initial approximately proportional to the undrained shear strength, geo-stress equilibrium first and imports a stress file with an then E ¼ 500s (s is the undrained shear strength, kPa). u u ‘initial conditions’ method. This is instead of the ‘Geostatic’ A vertical plane containing the line connecting the way, a commonly used geo-stress equilibrium analysis spudcan and the footprint center is chosen and a finite method in general simulation involving in soil that is difficult element model is established, as shown in Fig. 2. The to deal with for such a complex problem as spudcan–soil diameter and depth of the footprint are D and d, respec- interaction with an existing footprint. In addition, because of tively. In order to reduce the boundary effect on accuracy serious soil deformation under a large spudcan penetration of the numerical simulation, the width and depth of the depth, in order to avoid huge warping and ensure accuracy of surrounding soil are taken as 15D and 7d, respectively. The calculation, ALE self-adaptive meshes are employed. offset distance between the spudcan and the footprint center is denoted as S. The 8-node plane strain and pore pressure element, CPE8PR, is used to simulate the soil 3 Spudcan–footprint interaction in clay element to avoid self-locking phenomena and to increase the computational accuracy in numerical simulation. The 3.1 Failure process of clay foundations active–passive surface contact algorithm is used to deal with the contact interaction and relative displacement Let S = 0.75D (D = 6m, d = 6 m). The mechanical characteristics of uniform soil such as clay are shown in Table 1. The gradual failure process of clay foundation occurs in three stages: elastic balance, plastic expansion, and com- Spundcan plete plastic damage (Fig. 3). Figure 3a shows that plastic damage first appears at the bottom edge of the footprint Footprint Contact surface Soil Fixed boundary Table 1 Material parameters of single-layer foundation Effective density Cohesion Internal friction q, kg/m C, kPa angle /, 8 15D 860 20 0 Fig. 2 Schematic diagram of the finite element model 7d Pet. Sci. (2015) 12:148–156 151 close to the spudcan. Figure 3b shows the expansion of the shown in Fig. 4. This indicates that the plastic zone soil foundation plastic zone from the bottom edge of the becomes larger with an increase in S and the failure pattern footprint toward the farther edge of the spudcan with load of soil around the spudcan gradually changes from asym- increasing. Figure 3c indicates that when the complete metric to symmetric. plastic damage of clay foundation appears, the plastic zones have expanded to form a continuous sliding surface. 3.3 Soil movement patterns at different S 3.2 Clay foundation yield at different S When the spudcan arrives at the designed depth, the soil displacement vectors under different S are shown in Changing only S while keeping other parameters constant, Fig. 5, from which we see that there is an obvious uplift the situations of clay foundation yield at different S are trend at the bottom of the footprint and the soil near the footprint clearly migrates toward the footprint. The bulge on the farther side surface of the clay foundation changes little with an increase in S. However, the apophysis on the footprint bottom increases significantly and the soil movement patterns on the closer side to the spudcan and below the spudcan change greatly. When S is small, part (a) (b) (c) of the soil below the spudcan moves to the footprint, while another part migrates downward with the spudcan. Fig. 3 Plastic zone of clay foundation in loading (part around the With the S increasing, the soil under the spudcan bottom footprint) (a) S = 1 (b) S = 2 (c) S = 3 (d) S = 4 (e) S = 5 (f) S = 6 (g) (h) S = 8 (i) S = 9 (j) S = 10 S = 7 Fig. 4 The complete plastic damage zone at different S (part around the footprint) (a) S = 1 (b) S = 2 (c) S = 3 (d) S = 4 (e) S = 5 (f) S = 6 (g) S = 7 (h) S = 8 (i) S = 9 (j) S = 10 Fig. 5 The displacement vector of clay at different S (part around the spudcan) 123 152 Pet. Sci. (2015) 12:148–156 basically migrates downward, while most of the soil on Table 2 Peak horizontal forces at different ‘S’ the closer side of the footprint moves into the footprint S,m S/D Peak horizontal force, MN and only a little moves downward with the spudcan edge. 1 0.166 0.264 This may provide a coping idea for jack-up re-installation 2 0.333 0.497 close to footprint (which will be discussed in a separate 3 0.498 0.593 paper). 4 0.664 0.698 3.4 Influence of S on horizontal slip force 5 0.834 0.653 6 1.000 0.561 The relation between the horizontal slipping force on the 7 1.166 0.504 spudcan and the spudcan vertical displacement, i.e., 8 1.333 0.443 depth at different S is displayed in Fig. 6. This shows 9 1.498 0.383 that at any S, with the depth increasing, the horizontal 10 1.664 0.326 force on the spudcan increases initially then decreases after it reaches a peak value. The peak values at dif- ferent S appear at a depth from 2.5 to 4.5 m, and the spudcan in future operations, m; S is the distance between maximum peak horizontal force is about 0.7 MN when the spudcan and the footprint center, m; and d is the depth S = 4 m. This indicates that the most potentially dan- of the footprint, m. gerous situation is when the spudcan partially overlaps In this paper, only the influence of the offset distance on the existing footprint. In order to investigate the overall the peak horizontal slip force on the spudcan is considered, relationship between the peak horizontal force on the as given in Table 2. The horizontal force on the spudcan spudcan and S, the peak horizontal forces are sorted at will be zero when S = 0 as the spudcan is located exactly different S in dimensionless form (Table 2). in the footprint. Using Matlab to fit the numerical simu- For the problem with a ‘footprint,’ the horizontal slip lation results, the peak horizontal force on the spudcan is force on the spudcan varies with soil strength, footprint obtained as follows: dimension, diameter of the spudcan, and the offset distance 1:3439 S S between the spudcan and the footprint center. Taking these H ¼ 4:1248   exp 1:9555 ; ð4Þ max D D f f factors into consideration, the expression of the peak hor- izontal force on the spudcan in dimensionless form can be The fitting curve of Eq. (4) and the numerical simulation summarized as results are shown in Fig. 7. This demonstrates that the D S d curvature tolerance of Eq. (4) is very small and it could H ¼ f ; ;  s D ; ð3Þ max u reliably represent the relationship between the peak hori- D D D f f f zontal sliding force on the spudcan and the offset distance where H is the peak horizontal force on the spudcan, max S. The peak horizontal force reaches a maximum value MN; S is the soil undrained shear strength; D is the u f diameter of the footprint, m; D is the diameter of the 1.0 0.9 Horizontal force, MN 0.8 –0.8 –0.7 –0.6 –0.5 –0.4 –0.3 –0.2 –0.1 0.0 0.7 –1 0.6 S = 1 m 0.5 –2 S = 2 m 0.4 S = 3 m S = 4 m –3 0.3 S = 5 m S = 6 m 0.2 –4 S = 7 m 0.1 S = 8 m S = 9 m –5 S = 10 m 0 0.5 1.0 1.5 2.0 S/D –6 Fig. 6 The horizontal force–depth diagram at different S Fig. 7 The fitted curve between the peak horizontal force and S Depth, m Peak horizontal force Pet. Sci. (2015) 12:148–156 153 1.0 horizontal force becomes almost zero, which means in this case that the influence of the existing footprint could be 0.9 ignored. 0.8 0.7 0.6 4 Verification of numerical simulation results 0.5 Based on the University of Western Australia centrifuge 0.4 model test (Table 3; Gan 2009), we built 2-dimensional 0.3 and 3-dimensional simulation models (Fig. 9) to conduct 0.2 finite element simulation. Results at different S (0.25D, 0.50D, 0.75D,1.0D) are shown in Figs. 10 and 11. Com- 0.1 parisons of results from the 2-dimensional or 3-dimen- sional simulation models and from the experiments 01 2 34 5 6 7 8 S/D indicate that the simulation results are in good agreement with experimental results, and the results from the Fig. 8 The whole relation between the peak horizontal force and S 3-dimensional model are a little closer to the test results than those from the 2-dimensional model. However, with when S/D = 0.6. The horizontal force increases quickly the 3-dimensional model, not only the computing time before it reaches the maximum value and then gradually needed is much longer, but also the calculation is much decreases. The rate of decrease is far less than the rate of more difficult to converge. Using the 2-dimensional model increase. In order to observe the successive change of the built in this paper would significantly reduce the necessary peak horizontal force, the horizontal force is calculated at computing time, and the simulation results are in good larger ‘S according to Eq. (4), and the whole relation agreement with experimental results, which shows that the between the peak horizontal sliding force and the offset 2-dimensional model built in this paper is feasible and distance is given in Fig. 8. When S/D C 5, the peak reliable. Table 3 List of major experimental parameters (after Gan 2009) Test No. Spudcan diameter Initial penetration Re-penetration Remarks Initial Re-penetration Size Soil strength profile Preload Penetration Radial R /D d f penetration D ,m ratio pressure depth distance s , kPa k, kPa/m kD /s um f um D ,m D /D q , kPa d ,m R ,m f f s 0 0 d OA1 6 6 1 25 5 1.20 460 5.84 0.0 0.00 Tests done in NUS OA2 6 6 1 28 5 1.07 460 5.61 1.5 0.25 OA3 6 6 1 28 5 1.07 460 5.30 3.0 0.50 OA4 6 6 1 28 5 1.07 460 5.19 4.5 0.75 OA5 6 6 1 28 5 1.07 460 5.19 6.0 1.00 OA6 6 6 1 30 5 1.00 460 4.70 9.0 1.50 Test No. Size R /D Depth ratio Re-penetration d f ratio D /D d /D f s s f Maximum horizontal load, H Maximum moment, M max max 2 3 d/D H ,MN h, degree H/s D d/D M ,MN e/D M/s D s max u s s max s u s OA1 1 0.00 0.97 1.02 0.11 0.54 0.06 0.98 0.31 0.005 0.03 OA2 1 0.25 0.94 0.75 0.41 2.76 0.20 0.78 1.81 0.033 0.14 OA3 1 0.50 0.88 0.84 0.49 2.32 0.23 0.44 1.91 0.047 0.15 OA4 1 0.75 0.87 0.52 0.72 4.29 0.34 0.10 2.29 0.109 0.18 OA5 1 1.00 0.86 0.78 0.63 2.69 0.30 0.27 2.13 0.047 0.17 OA6 1 1.50 0.78 0.88 0.30 1.15 0.14 0.44 0.45 0.007 0.03 Peak horizontal force 154 Pet. Sci. (2015) 12:148–156 with sliding friction contact, fluid–solid coupling, nonlinear elastic–plastic deformation, and convergence problems. Horizontal force, MN 0.0 0.1 0.2 0.3 0.4 0.5 0.5 0.7 0.8 –2 –4 –6 0.25D 0.50D –8 0.75D 1.00D –10 Fig. 9 3-dimensional finite element model (a) Experimental results Horizontal force, MN 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 5 Conclusions 1. In the initial loading stage, plastic damage first appears –2 at the bottom edge of the footprint close to the spud- can. Then the plastic zone expands with increasing load and finally it forms a continuous sliding surface. –4 2. With an increase in the distance between the spudcan and the footprint, the soil failure pattern gradually –6 changes from asymmetric to symmetric. 3. The soil migration patterns on the closer side of the 0.25D 0.50D footprint and below the spudcan change greatly at –8 0.75D different offset distances. With the distance increasing, 1.00D the soil on the spudcan bottom basically migrates –10 downward, while most of the soil on the closer side of (b) 2-dimensional simulation results the footprint moves into the footprint, and only a little moves downward with the spudcan edge. This means Horizontal force, MN 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ‘‘stomping’’ (repeated raising and lowering of the jack- up leg) may be a successful solution for the jack-up installation close to a footprint. –2 4. The peak horizontal sliding forces on spudcan at different offset distances modeled with Matlab to fit the numerical simulation results and the possible –4 dangerous ranges during re-installation have been obtained. The peak horizontal force reaches its max- –6 imum value when S/D = 0.6. When S/D C 5, the horizontal sliding force becomes almost zero, which –8 means in this case that the influence of the footprint 0.25D 0.50D could be ignored. 0.75D 5. The numerical simulation results show good agreement 1.00D –10 with experimental results, indicating clearly that the (c) 3- dimensional simulation results finite element model built in this paper can be used to solve the problems of spudcan–footprint interaction Fig. 10 Simulation and experimental results Depth, m Depth, m Depth, m Pet. Sci. (2015) 12:148–156 155 (a) The plastic zone in the loading of clay foundation (b) The displacement vector of clay foundation Fig. 11 2-dimensional and 3-dimensional numerical simulation results Acknowledgments This work is financially supported by the Hossain MS, Randolph MF. Investigating potential for punch-through National Natural Science Foundation of China (Grant No. 51379214) for spud foundations on layered clays. In: Proceedings of the and the National Science and Technology Major Project (Grant No. 17th ISOPE. Lisbon; 1–6 July 2007. pp. 1510–17. 2011ZX05027-005-001). Hossain MS, Randolph MF. 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Analysis of spudcan–footprint interaction in a single soil with nonlinear FEM

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Springer Journals
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Copyright © 2015 by The Author(s)
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Earth Sciences; Mineral Resources; Industrial Chemistry/Chemical Engineering; Industrial and Production Engineering; Energy Economics
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1672-5107
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10.1007/s12182-014-0007-4
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Abstract

Pet. Sci. (2015) 12:148–156 DOI 10.1007/s12182-014-0007-4 OR IGINAL PAPER Analysis of spudcan–footprint interaction in a single soil with nonlinear FEM • • Dong-Feng Mao Ming-Hui Zhang • • Yang Yu Meng-Lan Duan Jun Zhao Received: 27 January 2014 / Published online: 24 January 2015 The Author(s) 2015. This article is published with open access at Springerlink.com Abstract The footprints that remain on the seabed after footprints is becoming more common and inevitable. offshore jack-up platforms completed operations and moved According to van den Berg’s statistics (Van den Berg et al. out provide a significant risk for any future jack-up installation 2004), within Shell EP Europe alone roughly 1,200 footprint at that site. Detrimental horizontal and/or rotational loads will points had been registered in geotechnical and footprint be induced on the base cone of the jack-up platform leg datasets. In addition, there are approximately 80 new single (spudcan) in the preloading process where only vertical loads footprint points added to the existing datasets every year. are normally expected. However, there are no specific Thus, it can be seen that footprints are not rare and they pose a guidelines on design of spudcan re-installation very close to or serious and growing threat to operational safety of jack-up partially overlapping existing footprints. This paper presents a drilling platforms. Figure 1 shows when a leg is close to an rational design approach for assessing spudcan–footprint existing footprint, the non-uniform bearing load caused interaction and the failure process of foundation in a single by the footprint will make the spudcan slide into the foot- layer based on nonlinear finite element method. The rela- print in the jacking process, which was proven by Gaudin tionship between the distance between the spudcan and the et al. (2007), Leung et al. (2007). The sliding trend is affected footprint and the horizontal sliding force has been obtained. by the leg stiffness, connection between leg and hull, and in- Comparisons of simulation and experimental results show that place condition of other two legs, and the size of the trend is the model in this paper can deal well with the combined measured by the horizontal sliding force and overturning problems of sliding friction contact, fluid–solid coupling, and moment (McClelland et al. 1982; Hossain and Randolph convergence difficulty. The analytical results may be useful to 2007; Bouwmeester et al. 2009). If a slide occurs, the legs jack-up installation workovers close to existing footprints. will incline in different directions, so that the legs may become stuck in the platform and this would mean the plat- Keywords Jack-up  Existing footprint  Spudcan– form cannot be raised. The potential risk of slipping is a serious threat to the operational safety of platforms. footprint interaction  Numerical simulation  Nonlinearity Re-installing a spudcan very close to or partially over- lapping existing footprints is generally not recommended 1 Introduction in the guidelines (SNAME OC-7 panel. 2007; Hossain and Randolph 2008). In a situation where this is inevitable, the With an increase in frequency of operations, the situation that guidelines recommend the use of an identical jack-up installation of jack-up platforms on sites which contains old (same footing geometries and leg spacing) and locating it in exactly the same position as the previous unit, where possible. However, it is unlikely that two jack-up units D.-F. Mao (&)  M.-H. Zhang  Y. Yu  M.-L. Duan  J. Zhao have an identical design because the structures of most College of Mechanical and Transportation Engineering, China units are often custom-made and the deployments of units University of Petroleum, Beijing 102249, China are subject to availability. It is evident that existing e-mail: maodf@cup.edu.cn guidelines are not adequate for rig operators to install jack- up units in close proximity to existing footprints safely. Edited by Yan-Hua Sun 123 Pet. Sci. (2015) 12:148–156 149 Fig. 1 Schematic diagram of existing footprint problems New rig Resultant forces at the leg-hull connection 1ʹ Overstressing the braces Footprints HH ʹ Piled jacket platform V V ʹ Footprint Footprint issues involve soil elastoplasticity, material explanations for tests. This paper takes various factors and geometric nonlinearities, fluid–solid coupling, friction including failure process of foundation, nonlinearity, slid- contact during spudcan preloading, and difficult conver- ing friction contact, and fluid–solid coupling into account. gence of numerical solutions (Hanna and Meyerhof 1980; It discusses the finite element model of spudcan–footprint Kellezi and Stromann 2003; DeJong et al. 2004; Deng and interaction in spudcan re-installation near an existing Kong 2005; Leung et al. 2008). Previous research mainly footprint as well as handling relative parameters. With the focuses on the spudcan–footprint interaction through the model of the spudcan–footprint interaction, the changes of centrifuge model test. Murff et al. (1991), Hossain et al. horizontal sliding force on the spudcan at different offset (2005), Cassidy et al. (2004, 2009), Teh et al. (2010), Gan distances between the spudcan and the footprint were (2009), Gan et al. (2012), Kong et al. (2010, 2013), Xie analyzed with ABAQUS software. The finite element et al. (2012) conducted a series of drum centrifuge model model was validated by comparing the simulation result tests to investigate spudcan–footprint interaction and the with experimental results. effect of leg stiffness on spudcan–footprint interaction. With the centrifuge model tests, Stewart and his coworkers (Stewart 2005; Stewart and Finnie 2001) studied the effect 2 Analytical methods and computing model of bending rigidity of legs on spudcan–footprint interaction and the influence of the distance between the spudcan and During jacking, the deformation of the surrounding soil is the footprint on sliding. Dean and Serra (2004) discussed very large, which results in changes in pore pressure and the effect of equivalent stiffness of legs on spudcan–foot- then a reduction in the effective strength of the soil. To print interaction. Teh et al. (2006) reported a set of test analyze spudcan–footprint interaction, the coupling of results investigating the effects of sloping seabed (30 stress/fluid flow in soil should be considered. Undrained inclined to the horizontal) and footprint on loads developed total stress analysis is used in the computing model, i.e., the in jack-up legs. They found that the effect of the footprint total stress is the sum of effective stress and hydrostatic is much greater than that of the seabed slope. This indicates pressure. Thus, the equilibrium equation in the vertical that the footprint problem is more serious than a sloping direction is as follows (Houlsby and Martin 2003): seabed. Other researchers have tried to investigate the > dS 0 0 0 footprint problem with numerical simulation (Zhang et al. qg  c S ð1  n Þ ðz  zÞ ; z  z dr r z w w w dz ¼ ; 2011, 2014). Jardine et al. (2002) simplified a three- dz > 0 0 qg; z  z  z dimensional model to a plane strain one to deal with footprint issues. The current understanding of this topic is ð1Þ still insufficient, and only a small number of studies of the where r is the vertical stress, Pa; q is the soil dry density, footprint problem are available in the public domain. 3 3 kg/m ; c is the water gravity density, N/m ; S is the soil w r Although it is a great challenge to obtain a converged 0 0 saturation, %; z is the free water surface elevation, m; z numerical solution, a good numerical model and solution is w is the elevation of interface between dry soil and partially very important because it is able to achieve more accurate 0 0 saturated soil, m; and n is porosity, %; when z  z in estimation of carrying capacity of spudcans and better 123 150 Pet. Sci. (2015) 12:148–156 0 0 completely saturated, S ¼ 1, and when z  z  z ,in between the spudcan and the surrounding soil, and the spudcan surface is taken as the active surface and the soil partially saturated, S \1. The advantage of ABAQUS in soil engineering is that it surface as the passive surface (Zhuang et al. 2005). The principle for choosing an active or passive surface is that provides not only various elastic/plastic constitutive mod- els for soil but also coupled analysis of stress/fluid flow in the mesh of the passive surface should be finer, and if both mesh densities are similar to each other, the surface of the soil. In numerical computation, the finite element mesh is fixed on the soil skeleton, and fluid may flow through the softer material should be passive. The tangential contact obeys the Coulomb friction law, and the normal contact mesh and satisfy the fluid continuity equation. The Forchheimer equation (Zeng and Grigg 2006) is adopted to follows the hard touching mode, i.e., penetration is not allowed between the spudcan element and the soil element, describe nonlinear flow in soil (porous medium). Since less but they are allowed to separate (Zhuang et al. 2005). In relative parameters in calculation are needed, the Mohr– Coulomb constitutive model is used (Li 2004), i.e., the soil order to obtain the correct horizontal sliding force–dis- placement curve, the displacement control method is used is considered as a perfect elastic–plastic material, and obeys the noncorrelation flow rule. The Mohr–Cou- to load. A simplified spudcan, with its side friction ignored because of its relative smaller area, is adopted to reduce the lomb yield criterion is as follows: difficulty of convergence in calculation. The friction s þ r sin /  c cos / ¼ 0; ð2Þ coefficients for undrained clay and drained granular soil are where s ¼ðr  r Þ=2 is half of the difference of maxi- 1 3 0.2–0.3 and tan d, respectively, where d is the friction mum and minimum principal stresses, kPa; r ¼ðr þ m 1 angle between the spudcan and the soil. It must be pointed r Þ=2 is the average value of maximum and minimum 3 out that whether setting a reasonable degree of spudcan– principal stresses, kPa; c is cohesion, kPa; and / is the soil contact will lead to the calculation converging or not. internal friction angle, . Except for over-consolidated soil, Since the ultimate bearing capacity would be underesti- clay always shows little dilatancy, and thus the dilatancy mated if the initial geo-stress equilibrium were not consid- angle / = 0. Assume that the deformation modulus is ered in numerical simulation, this paper deals with the initial approximately proportional to the undrained shear strength, geo-stress equilibrium first and imports a stress file with an then E ¼ 500s (s is the undrained shear strength, kPa). u u ‘initial conditions’ method. This is instead of the ‘Geostatic’ A vertical plane containing the line connecting the way, a commonly used geo-stress equilibrium analysis spudcan and the footprint center is chosen and a finite method in general simulation involving in soil that is difficult element model is established, as shown in Fig. 2. The to deal with for such a complex problem as spudcan–soil diameter and depth of the footprint are D and d, respec- interaction with an existing footprint. In addition, because of tively. In order to reduce the boundary effect on accuracy serious soil deformation under a large spudcan penetration of the numerical simulation, the width and depth of the depth, in order to avoid huge warping and ensure accuracy of surrounding soil are taken as 15D and 7d, respectively. The calculation, ALE self-adaptive meshes are employed. offset distance between the spudcan and the footprint center is denoted as S. The 8-node plane strain and pore pressure element, CPE8PR, is used to simulate the soil 3 Spudcan–footprint interaction in clay element to avoid self-locking phenomena and to increase the computational accuracy in numerical simulation. The 3.1 Failure process of clay foundations active–passive surface contact algorithm is used to deal with the contact interaction and relative displacement Let S = 0.75D (D = 6m, d = 6 m). The mechanical characteristics of uniform soil such as clay are shown in Table 1. The gradual failure process of clay foundation occurs in three stages: elastic balance, plastic expansion, and com- Spundcan plete plastic damage (Fig. 3). Figure 3a shows that plastic damage first appears at the bottom edge of the footprint Footprint Contact surface Soil Fixed boundary Table 1 Material parameters of single-layer foundation Effective density Cohesion Internal friction q, kg/m C, kPa angle /, 8 15D 860 20 0 Fig. 2 Schematic diagram of the finite element model 7d Pet. Sci. (2015) 12:148–156 151 close to the spudcan. Figure 3b shows the expansion of the shown in Fig. 4. This indicates that the plastic zone soil foundation plastic zone from the bottom edge of the becomes larger with an increase in S and the failure pattern footprint toward the farther edge of the spudcan with load of soil around the spudcan gradually changes from asym- increasing. Figure 3c indicates that when the complete metric to symmetric. plastic damage of clay foundation appears, the plastic zones have expanded to form a continuous sliding surface. 3.3 Soil movement patterns at different S 3.2 Clay foundation yield at different S When the spudcan arrives at the designed depth, the soil displacement vectors under different S are shown in Changing only S while keeping other parameters constant, Fig. 5, from which we see that there is an obvious uplift the situations of clay foundation yield at different S are trend at the bottom of the footprint and the soil near the footprint clearly migrates toward the footprint. The bulge on the farther side surface of the clay foundation changes little with an increase in S. However, the apophysis on the footprint bottom increases significantly and the soil movement patterns on the closer side to the spudcan and below the spudcan change greatly. When S is small, part (a) (b) (c) of the soil below the spudcan moves to the footprint, while another part migrates downward with the spudcan. Fig. 3 Plastic zone of clay foundation in loading (part around the With the S increasing, the soil under the spudcan bottom footprint) (a) S = 1 (b) S = 2 (c) S = 3 (d) S = 4 (e) S = 5 (f) S = 6 (g) (h) S = 8 (i) S = 9 (j) S = 10 S = 7 Fig. 4 The complete plastic damage zone at different S (part around the footprint) (a) S = 1 (b) S = 2 (c) S = 3 (d) S = 4 (e) S = 5 (f) S = 6 (g) S = 7 (h) S = 8 (i) S = 9 (j) S = 10 Fig. 5 The displacement vector of clay at different S (part around the spudcan) 123 152 Pet. Sci. (2015) 12:148–156 basically migrates downward, while most of the soil on Table 2 Peak horizontal forces at different ‘S’ the closer side of the footprint moves into the footprint S,m S/D Peak horizontal force, MN and only a little moves downward with the spudcan edge. 1 0.166 0.264 This may provide a coping idea for jack-up re-installation 2 0.333 0.497 close to footprint (which will be discussed in a separate 3 0.498 0.593 paper). 4 0.664 0.698 3.4 Influence of S on horizontal slip force 5 0.834 0.653 6 1.000 0.561 The relation between the horizontal slipping force on the 7 1.166 0.504 spudcan and the spudcan vertical displacement, i.e., 8 1.333 0.443 depth at different S is displayed in Fig. 6. This shows 9 1.498 0.383 that at any S, with the depth increasing, the horizontal 10 1.664 0.326 force on the spudcan increases initially then decreases after it reaches a peak value. The peak values at dif- ferent S appear at a depth from 2.5 to 4.5 m, and the spudcan in future operations, m; S is the distance between maximum peak horizontal force is about 0.7 MN when the spudcan and the footprint center, m; and d is the depth S = 4 m. This indicates that the most potentially dan- of the footprint, m. gerous situation is when the spudcan partially overlaps In this paper, only the influence of the offset distance on the existing footprint. In order to investigate the overall the peak horizontal slip force on the spudcan is considered, relationship between the peak horizontal force on the as given in Table 2. The horizontal force on the spudcan spudcan and S, the peak horizontal forces are sorted at will be zero when S = 0 as the spudcan is located exactly different S in dimensionless form (Table 2). in the footprint. Using Matlab to fit the numerical simu- For the problem with a ‘footprint,’ the horizontal slip lation results, the peak horizontal force on the spudcan is force on the spudcan varies with soil strength, footprint obtained as follows: dimension, diameter of the spudcan, and the offset distance 1:3439 S S between the spudcan and the footprint center. Taking these H ¼ 4:1248   exp 1:9555 ; ð4Þ max D D f f factors into consideration, the expression of the peak hor- izontal force on the spudcan in dimensionless form can be The fitting curve of Eq. (4) and the numerical simulation summarized as results are shown in Fig. 7. This demonstrates that the D S d curvature tolerance of Eq. (4) is very small and it could H ¼ f ; ;  s D ; ð3Þ max u reliably represent the relationship between the peak hori- D D D f f f zontal sliding force on the spudcan and the offset distance where H is the peak horizontal force on the spudcan, max S. The peak horizontal force reaches a maximum value MN; S is the soil undrained shear strength; D is the u f diameter of the footprint, m; D is the diameter of the 1.0 0.9 Horizontal force, MN 0.8 –0.8 –0.7 –0.6 –0.5 –0.4 –0.3 –0.2 –0.1 0.0 0.7 –1 0.6 S = 1 m 0.5 –2 S = 2 m 0.4 S = 3 m S = 4 m –3 0.3 S = 5 m S = 6 m 0.2 –4 S = 7 m 0.1 S = 8 m S = 9 m –5 S = 10 m 0 0.5 1.0 1.5 2.0 S/D –6 Fig. 6 The horizontal force–depth diagram at different S Fig. 7 The fitted curve between the peak horizontal force and S Depth, m Peak horizontal force Pet. Sci. (2015) 12:148–156 153 1.0 horizontal force becomes almost zero, which means in this case that the influence of the existing footprint could be 0.9 ignored. 0.8 0.7 0.6 4 Verification of numerical simulation results 0.5 Based on the University of Western Australia centrifuge 0.4 model test (Table 3; Gan 2009), we built 2-dimensional 0.3 and 3-dimensional simulation models (Fig. 9) to conduct 0.2 finite element simulation. Results at different S (0.25D, 0.50D, 0.75D,1.0D) are shown in Figs. 10 and 11. Com- 0.1 parisons of results from the 2-dimensional or 3-dimen- sional simulation models and from the experiments 01 2 34 5 6 7 8 S/D indicate that the simulation results are in good agreement with experimental results, and the results from the Fig. 8 The whole relation between the peak horizontal force and S 3-dimensional model are a little closer to the test results than those from the 2-dimensional model. However, with when S/D = 0.6. The horizontal force increases quickly the 3-dimensional model, not only the computing time before it reaches the maximum value and then gradually needed is much longer, but also the calculation is much decreases. The rate of decrease is far less than the rate of more difficult to converge. Using the 2-dimensional model increase. In order to observe the successive change of the built in this paper would significantly reduce the necessary peak horizontal force, the horizontal force is calculated at computing time, and the simulation results are in good larger ‘S according to Eq. (4), and the whole relation agreement with experimental results, which shows that the between the peak horizontal sliding force and the offset 2-dimensional model built in this paper is feasible and distance is given in Fig. 8. When S/D C 5, the peak reliable. Table 3 List of major experimental parameters (after Gan 2009) Test No. Spudcan diameter Initial penetration Re-penetration Remarks Initial Re-penetration Size Soil strength profile Preload Penetration Radial R /D d f penetration D ,m ratio pressure depth distance s , kPa k, kPa/m kD /s um f um D ,m D /D q , kPa d ,m R ,m f f s 0 0 d OA1 6 6 1 25 5 1.20 460 5.84 0.0 0.00 Tests done in NUS OA2 6 6 1 28 5 1.07 460 5.61 1.5 0.25 OA3 6 6 1 28 5 1.07 460 5.30 3.0 0.50 OA4 6 6 1 28 5 1.07 460 5.19 4.5 0.75 OA5 6 6 1 28 5 1.07 460 5.19 6.0 1.00 OA6 6 6 1 30 5 1.00 460 4.70 9.0 1.50 Test No. Size R /D Depth ratio Re-penetration d f ratio D /D d /D f s s f Maximum horizontal load, H Maximum moment, M max max 2 3 d/D H ,MN h, degree H/s D d/D M ,MN e/D M/s D s max u s s max s u s OA1 1 0.00 0.97 1.02 0.11 0.54 0.06 0.98 0.31 0.005 0.03 OA2 1 0.25 0.94 0.75 0.41 2.76 0.20 0.78 1.81 0.033 0.14 OA3 1 0.50 0.88 0.84 0.49 2.32 0.23 0.44 1.91 0.047 0.15 OA4 1 0.75 0.87 0.52 0.72 4.29 0.34 0.10 2.29 0.109 0.18 OA5 1 1.00 0.86 0.78 0.63 2.69 0.30 0.27 2.13 0.047 0.17 OA6 1 1.50 0.78 0.88 0.30 1.15 0.14 0.44 0.45 0.007 0.03 Peak horizontal force 154 Pet. Sci. (2015) 12:148–156 with sliding friction contact, fluid–solid coupling, nonlinear elastic–plastic deformation, and convergence problems. Horizontal force, MN 0.0 0.1 0.2 0.3 0.4 0.5 0.5 0.7 0.8 –2 –4 –6 0.25D 0.50D –8 0.75D 1.00D –10 Fig. 9 3-dimensional finite element model (a) Experimental results Horizontal force, MN 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 5 Conclusions 1. In the initial loading stage, plastic damage first appears –2 at the bottom edge of the footprint close to the spud- can. Then the plastic zone expands with increasing load and finally it forms a continuous sliding surface. –4 2. With an increase in the distance between the spudcan and the footprint, the soil failure pattern gradually –6 changes from asymmetric to symmetric. 3. The soil migration patterns on the closer side of the 0.25D 0.50D footprint and below the spudcan change greatly at –8 0.75D different offset distances. With the distance increasing, 1.00D the soil on the spudcan bottom basically migrates –10 downward, while most of the soil on the closer side of (b) 2-dimensional simulation results the footprint moves into the footprint, and only a little moves downward with the spudcan edge. This means Horizontal force, MN 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 ‘‘stomping’’ (repeated raising and lowering of the jack- up leg) may be a successful solution for the jack-up installation close to a footprint. –2 4. The peak horizontal sliding forces on spudcan at different offset distances modeled with Matlab to fit the numerical simulation results and the possible –4 dangerous ranges during re-installation have been obtained. The peak horizontal force reaches its max- –6 imum value when S/D = 0.6. When S/D C 5, the horizontal sliding force becomes almost zero, which –8 means in this case that the influence of the footprint 0.25D 0.50D could be ignored. 0.75D 5. The numerical simulation results show good agreement 1.00D –10 with experimental results, indicating clearly that the (c) 3- dimensional simulation results finite element model built in this paper can be used to solve the problems of spudcan–footprint interaction Fig. 10 Simulation and experimental results Depth, m Depth, m Depth, m Pet. Sci. (2015) 12:148–156 155 (a) The plastic zone in the loading of clay foundation (b) The displacement vector of clay foundation Fig. 11 2-dimensional and 3-dimensional numerical simulation results Acknowledgments This work is financially supported by the Hossain MS, Randolph MF. Investigating potential for punch-through National Natural Science Foundation of China (Grant No. 51379214) for spud foundations on layered clays. In: Proceedings of the and the National Science and Technology Major Project (Grant No. 17th ISOPE. Lisbon; 1–6 July 2007. pp. 1510–17. 2011ZX05027-005-001). Hossain MS, Randolph MF. 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Published: Jan 24, 2015

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