Computers and Geotechnics 56 (2014) 133–147 Contents lists available at ScienceDirect Computers and Geotechnics journal homepage: www.elsevier.com/locate/compgeo Post-installation pore-pressure changes around spudcan and long-term spudcan behaviour in soft clay Jiang Tao Yi a,⇑, Ben Zhao a, Yu Ping Li a, Yu Yang a, Fook Hou Lee a, Siang Huat Goh a, Xi Ying Zhang b, Jer-Fang Wu b a b Department of Civil & Environmental Engineering, National University of Singapore, Block E1A, #07-03, No. Engineering Drive 2, Singapore 117576, Singapore American Bureau of Shipping, ABS Plaza, 16855 Northchase Drive, Houston, TX 77060, USA a r t i c l e i n f o Article history: Received August 2013 Received in revised form November 2013 Accepted 28 November 2013 Available online 22 December 2013 Keywords: Eulerian analysis Coupled-flow Lagrangian analysis Spudcan footing Generation and dissipation of excess pore-pressure Long-term bearing resistance Rotational fixity a b s t r a c t This paper presents a dual-stage Eulerian–Lagrangian analysis for modelling the entire process of spudcan installation in soft clay, followed by consolidation and working load operation. The analysis consists of three components, namely undrained effective stress Eulerian analysis of spudcan installation, mesh-to-mesh variable mapping and coupled-flow Lagrangian analysis for the post-installation spudcan working behaviour. The results show good agreement with centrifuge model data but also highlight the importance of replicating the hysteretic behaviour of the soil. The findings also show that while a wished-in-place approach was able to model the long-term bearing response of the spudcan, rotational stiffness was over-estimated. This is due to the fact that, while the wished-in-place analysis was able to model the hardening of the soil ahead of the spudcan, it was unable to model the softening of back-flowed soil behind spudcan. The latter influences the spudcan fixity significantly, but not bearing response. Although the analyses were conducted using ABAQUS, they can, in principle, be conducted using other codes. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Spudcans are widely used as footings for offshore jack-up rigs. Spudcan installation in soft clay is essentially an undrained deep penetration event involving soil flow and excess pore pressure generation [1]. As the subsequent operational period of jack-up rig can be as long as years [2], dissipation of the excess pore pressure will alter the state of the soil, and thus the working behaviour of the spudcan, which includes bearing capacity and rotational fixity. Hence, the long-term spudcan behaviour is likely to be significantly affected by post-installation changes in pore pressure. The working behaviour of spudcan foundations is often analyzed by wishing the spudcan into place with the surrounding soil having an assumed stress state and strength distribution [3–6]. This is due to the fact that spudcan installation is a deep penetration problem which can only be addressed by large-deformation approaches such as Eulerian or Arbitrary Lagrangian–Eulerian (ALE) analysis [7,8]. As most large-deformation spudcan analyses to date [7–12] are based on total stress approaches, effective stress ⇑ Corresponding author. Address: Centre for Protective Technology, National University of Singapore, No. 12 Kent Ridge Road, Singapore 119223, Singapore. Tel.: +65 65164566; fax: +65 67761002. E-mail addresses: ceeyj@nus.edu.sg (J.T. Yi), ceezhaoben@nus.edu.sg (B. Zhao), ceelyp@nus.edu.sg (Y.P. Li), yang.yu@nus.edu.sg (Y. Yang), ceeleefh@nus.edu.sg (F.H. Lee), ceegsh@nus.edu.sg (S.H. Goh), xyzhang@eagle.org (X.Y. Zhang), jwu@ eagle.org (J.-F. Wu). 0266-352X/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compgeo.2013.11.007 and excess pore pressure cannot be computed and post-installation, pore pressure dissipation cannot be analyzed. More recently, an undrained, effective stress Eulerian approach for analyzing spudcan installation in clay was proposed by Yi et al. [1], who postulated that if a coupled-flow Lagrangian analysis can be dovetailed with such an effective stress Eulerian analysis, it may be well suited to solving the post-installation, working behaviour of spudcan foundations. This paper realizes the above postulation by presenting a method of conducting such a dual-stage Eulerian–Lagrangian analysis. The analysis consists of three components, namely undrained effective stress Eulerian analysis of spudcan installation, mesh-to-mesh variable mapping and coupled-flow Lagrangian analysis for the post-installation spudcan working behaviour. As the undrained effective stress Eulerian analysis has been reported previously [1], this paper focuses on the mesh-to-mesh mapping and coupled-flow Lagrangian analysis. Two examples are presented to illustrate the effect of consolidation on the bearing capacity and rotational fixity of a spudcan. The analytical results are benchmarked against centrifuge model data and compared with results of wished-in-place analyses. 2. Solution mapping from Eulerian to Lagrangian analyses As the undrained effective stress analysis for spudcan installation has been reported by Yi et al. [1], only a brief outline will be presented herein. Essentially, the effective stress computation is 134 J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 achieved by appropriately adding the bulk modulus of water to an effective stress constitutive model within the user subroutine VUMAT of ABAQUS/Explicit where the Eulerian calculation can be conducted. This allows the near-incompressibility of the soil as a whole to be reflected in the total stress–strain matrix, and the effective stress and pore pressure to be separately computed within VUMAT. In the present study, this effective stress computation technique is used in the first, or Eulerian, stage of the analysis. The second stage of the analysis involves coupled-flow Lagrangian computation. As the effective stress Eulerian analysis has to be solved in ABAQUS/Explicit [1] while the coupled-flow Lagrangian analysis has to be conducted in ABAQUS/Standard [13], the results of the effective stress Eulerian analysis have to be ported over as input to the Lagrangian analysis to perform the dual-stage Eulerian–Lagrangian analysis. There are also some other differences between the first and second stages. In the Eulerian computation, pore pressure is treated as an integration point variable [1]; in the Lagrangian computation, it is regarded as a nodal degree-offreedom [13]. In addition, the Eulerian analysis requires a very fine mesh around the spudcan to maintain computational stability and reduce high-frequency noise. For the coupled-flow Lagrangian analysis, such a fine mesh is often unnecessary, and may, in fact, destabilize the computation due to excessive element distortion in regions that undergo large deformation. This can occur, for instance, in the backflow region behind the spudcan, where the soil may undergo large deformation during consolidation. All these differences mean that a robust solution mapping process is needed to transfer the solution variables, viz. stresses, pore pressure and void ratio, from the Eulerian analysis to the Lagrangian analysis. Since ABAQUS’ built-in mapping algorithm for advection of element variables in ALE and Eulerian analyses not support Eulerian-toLagrangian mapping, a solution mapping algorithm has to be developed outside ABAQUS’ environment. 2.1. Interpolation methods Four interpolation methods were examined for solution mapping, namely the nearest-neighbour interpolation (N–n) method, inverse-distance weighted (IDW) method, Delaunay triangulation with linear interpolation (DTL) and natural neighbour interpolation (NNI). In the nearest-neighbour interpolation method, the value of the nearest point in the Eulerian mesh, hereafter termed ‘‘reference field’’, is assigned to prescribed point of the Lagrangian mesh, hereafter termed ‘‘destination field’’. Since the nearest neighbour interpolation only considers the nearest neighbour point, it tends to yield discontinuous, piecewise-constant interpolated data. In the inverse-distance weighted (IDW) method, the interpolated value is calculated by distance-weighted averaging the values of the reference field in the neighbourhood of the interpolated location. The interpolated value f(X) is given by f ðXÞ ¼ k X xi ðXÞui ð1Þ i¼1 where k is the number of original data points in the neighbourhood, ui the reference field value of the ith original data point and xi a weighting function. A common basis for assigning the weighting function is the inverse power of distance d between the interpolated location and original data point. This leads to xi ¼ dÀP = k X ÀP d ð2Þ i¼1 Fig. 1. Voronoi diagram and Delaunay triangulation. where p is inverse-distance index. A typical range of p is 2–4 and a value of 3.5 is adopted in this study; this is also the recommended value in Hu and Randolph [14]. In Delaunay triangulation with linear interpolation (DTL), the reference field is first decomposed into a collection of Delaunay triangles or ‘‘tiles’’. As shown in Fig. 1, for the two dimensional (2D) space (i.e. plane), Delaunay triangles are constructed in such a way that the circle circumscribing any triangle does not contain Fig. 2. Natural neighbour coordinate [16]. 135 J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 2.8 1.5 LRP 0.5 40° 0.9 1.7 6m Spudcan dimensions (a) A B (b) Fig. 3. 3D Eulerian FEM model (a) undeformed and (b) deformed. any other data point. The original data points of reference field correspond to the vertices of Delaunay triangles. The tile enclosing the interpolated location is then identified, the value of the destination field at this location interpolated from the values of the three vertices of the tile using the shape functions of a three-noded triangular element. For three-dimensional (3D) interpolations, the triangles are replaced by tetrahedrons. The natural neighbour interpolation (NNI) [15] is related to the Voronoi cell of a node, which is an enclosed area around the node where all points are closer to this node than any other node, Fig. 2a shows. As Fig. illustrates, the Voronoi cell is the geometric dual of Delaunay triangles. The natural neighbours of a node are those nodes whose Voronoi cells have common boundaries with it. In Fig. 2a and b, the nodes P1–P6 represent the original data points 136 J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 Table Cam-clay properties of kaolin clay (with reference to Goh [26]). Unit weight (c) Coefficient of permeability Slope of critical state line (M) Isotropic swelling index (j) Isotropic compression index (k) Effective Poisson’s ratio (m0 ) Specific of soil at critical state at a mean effective stress of kPa (C) Coefficient of earth pressure at rest (K0) 16 kN/m3 2.0 Â 10À8 m/s 0.9 0.053 0.244 0.33 3.221 where k is the number of natural neighbours. Ledoux and Gold [16] noted that the natural neighbour interpolation can produce a smoother and more continuous interpolating surface, compared to the other methods, particularly for irregularly distributed data. The natural neighbour interpolation scheme is similar, in principle, to the second-order advection method implemented in the Eulerian analysis of ABAQUS, which is also based on area/volume-weighted averaging [13]. 0.6 2.2. Evaluation of different mapping algorithms (a) Reference field (b) Destination field Fig. 4. Mesh configuration in 3D-to-2D solution mapping. in the reference field. When an node X from the destination field is introduced, the Voronoi cells are re-defined by the new boundaries ‘ab’ to ‘fa’’, between X and P1–P6, as shown in Fig 2b. The natural neighbour coordinates of X with respect to its ith neighbours /i(X) are defined as the ratios of their respective overlapping areas to the total area of the Voronoi cell of X, e.g. the natural neighbour coordinate of X with respect to P1 is given by /1 ðXÞ ¼ AreaðagbÞ Areaðabcdef Þ k X i¼1 /i ðXÞui Mean absolute error MAE ¼ ð3Þ Mean relative error MRE ¼ The interpolated value f(X) at X is then determined using f ðXÞ ¼ To evaluate the performance of these mapping techniques, an undrained effective-stress Eulerian analysis was first conducted using the 3D finite element model of a spudcan with a diameter of m, continuously penetrated to a depth of 16.5 m in normally consolidated soft clay, Fig. 3. The clay was modelled using the modified Cam-Clay model, with properties shown in Table 1. The stress, pore pressure and void ratio results were used as the reference fields for spatial interpolation. The interpolation algorithms were coded using MATLAB outside of ABAQUS environment. The spudcan installation problem is 2D axisymmetric but as Eulerian analysis can only be conducted for 3D models [1], the reference field so generated is also 3D. On the other hand, Lagrangian consolidation analysis can be conducted using either 2D axisymmetric or 3D mesh. For this reason, the performance of the interpolation techniques was assessed for both 3D-to-2D-axisymmetric mapping and 3D-to-3D mapping. For the former, the interpolation was only done within a radial plane of original 3D reference field. For the latter, interpolation was carried out throughout the whole model. Fig. 4a and b shows the reference and destination fields for 3D-to-2D-axisymmetric mapping and Figs. 5–7 show the total pore pressure (u), void ratio (e) and radial effective stress ðr0rr Þ interpolated using the four methods in 3D-to-2D-axisymmetric mapping. The N–n interpolation produced jagged interpolated contours with evident discontinuities. The IDW algorithm produces smoother contours, but fine discontinuities are still discernible, for example at the 250 kPa and 300 kPa contours near the bottom boundary (Fig. 5b), where the mesh is coarser. On the other hand, the DTL and NNI methods (Fig. 5c and d) produced interpolated fields which are significantly smoother. Both are visually so close to the original that the reference and its corresponding interpolated fields cannot be readily distinguished. To further quantify their interpolation accuracy, two set of nodes, labelled A and B, were chosen in the original reference field. As Fig. 4a shows, set A consists of 41 nodes in the fine mesh region and set B consists of 35 nodes in the coarse mesh region. The values of the reference field at these locations represent the reference values. For each node, an interpolated value is then computed using the values of the surrounding nodes and then compared with its reference value. The absolute difference between the interpolated and reference value is then taken to be the interpolation error at that node. Table shows four statistical measures of the interpolation errors of the two node sets, which are ð4Þ n 1X jy À y0i j n i¼1 i n 1X yi À yi n i¼1 yi Root mean square error RSME ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Xn ðy À y0i Þ2 i¼1 i n ð5Þ ð6Þ ð7Þ 137 -5 -5 -10 -10 Depth (m) Depth (m) J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 -15 -20 -20 -25 -25 10 15 20 25 30 15 20 (a) N-n (b) IDW -5 -5 -10 -10 -15 -20 -25 -25 10 15 20 25 30 10 15 20 Radial distance (m) Radial distance (m) 25 30 25 30 -15 -20 10 Radial distance (m) Radial distance (m) Depth (m) Depth (m) -15 Unit: kPa (d) NNI (c) DTL Fig. 5. Pore pressure (u) field before and after mapping (denoted by dash and solid line respectively). Pn ðyi À y0i Þ2 Coefficient of determination R2 ¼ À Pi¼1 n 2 i¼1 ðyi À yÞ ð8Þ where n is the number of data, yi and y0i the reference and interpo the mean of the reference data. As lated value of the ith point, and y can be seen from Table 2, the MAE, MRE and RSME show much greater differences between the four interpolation methods than the R2-value, indicating that they are more discriminating. Generally, the interpolation errors are more significant in the dense mesh area than coarse mesh region. For node set A, the NNI method consistently returns the smallest error. For node set B, the DTL algorithm performs slightly better in pore pressure and radial effective stress interpolation while the NNI algorithm gives the lowest error for the void ratio. This may be attributed to the fact that the reference fields change more rapidly in the dense mesh zone than in the coarse mesh zone, as illustrated in Figs. 5–7. The DTL method assumes that field values vary linearly within each Delaunay triangle. It is thus more suited to capturing the gradual changes in coarse mesh zone than the rapid changes in the dense mesh zone. Overall, the NNI algorithm appears to be effective for both dense and coarse mesh zones. A similar exercise was also conducted for the 3D-to-3D interpolation, using 131 nodes from the dense mesh area (those enclosed within box ‘‘A’’ in Fig 3b) and 68 nodes from the coarse mesh zone (those enclosed within box ‘‘B’’ in Fig 3b). As shown in Table 3, the trend remains the same, with the NNI method returning the lowest error in the fine mesh zone as well as the void ratio field in the coarse mesh zone, and the DTL method returning the lowest error for the pore pressure and radial effective stress fields in the coarse mesh zone. Tables and show that interpolation errors are much larger in the dense mesh area where rapid changes in field values occur. Hence, the interpolation technique should be able to minimise the interpolation errors in this area. For this reason, the NNI method was chosen as the interpolation technique for the examples below. 3. Example 1: long-term spudcan bearing response 3.1. Finite element model The first example involves the installation, unloading, longterm consolidation and reloading of a spudcan footing. Spudcan installation was conducted using undrained effective stress Eulerian analysis with the mesh shown in Fig. 3a. The soil domain was discretized into eight-noded Eulerian brick elements, whose constitutive behaviour was represented using the modified Cam-Clay (MCC) with parameters as shown in Table 1. The spudcan was modelled as a rigid Lagrangian body as its deformation is expected to be much smaller than that of the soil. Spudcan–soil interaction J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 -5 -5 -10 -10 Depth (m) Depth (m) 138 -15 -15 -20 -20 -25 -25 10 15 20 25 30 10 -5 -5 -10 -10 Depth (m) Depth (m) -15 -20 -25 -25 10 15 25 30 25 30 -15 -20 20 (b) IDW (a) N-n 15 Radial distance (m) Radial distance (m) 20 25 30 Radial distance (m) (c) DTL 10 15 20 Radial distance (m) (d) NNI Fig. 6. Void ratio (e) field before and after mapping (denoted by dash and solid line respectively). was modelled using the Eulerian–Lagrangian contact algorithm which is an extension of ABAQUS’ general contact formulation [13]. The Eulerian–Lagrangian contact is based on an enhanced immersed boundary method which can automatically compute and track the interface between the Eulerian soil domain and Lagrangian spudcan body. The intrusion of Lagrangian body can push material out of the Eulerian elements so that no overlap exists between the Lagrangian body and the material in the Eulerian domain. Friction was not considered in the analysis as the contact friction model in ABAQUS/Explicit only deals with total, not effective, stress. Hossain et al. [10] found that, for the deeply penetrated spudcan, spudcan–soil friction does not appear to affect the critical cavity depth and bearing capacity factor significantly. The spudcan was penetrated down to a depth of 16.5 m or 1.4 D below mudline, Fig. 3b. The boundary of the deformed mesh was then extracted from one radial section of Eulerian model and used to define the initial geometry of the axi-symmetric Lagrangian model in Fig. 8. Four-noded bilinear Lagrangian elements with displacement and pore-pressure degrees-of-freedom were used for the consolidation analysis. As noted by Yi et al. [17], the first-order element appears to be numerically more stable than the higher-order element in solving problems with relatively large deformation since it is less susceptible to element gross distortion. Zhou et al. [5] similarly used four-noded quadrilateral elements to model the extraction of spudcan. Zhang et al. [4] and Templeton [3] also made use of first order hexahedral elements to study the bearing capacity and rotational fixity of spudcan. The soil in the Lagrangian analysis was modelled using ABAQUS’ built-in modified Cam-clay (MCC) model with the same property set (Table 1). The spudcan deformation was again idealised as a rigid body. The Lagrangian consolidation analysis was conducted in three stages. The first stage was a dummy stage with a very short duration of 15 min, to re-establish stress equilibrium after solution mapping. When solution variables were mapped from Eulerian to Lagrangian mesh via spatial interpolation, some amount of stress and pore pressure errors are inevitably introduced, thereby resulting in some out-of-balance forces within the Lagrangian mesh. Allowing these out-of-balance forces to equilibrate helps to reduce subsequent errors and enhance computational stability. The second stage modelled the consolidation process after removal of the spudcan preload; the latter being modelled by a 25% reduction in axial loading from the penetration load while drainage was permitted at the top soil surface. In reality, the jack-up rig can be stationed at a location for several years [2], during which it can be subjected to highly variable loading conditions. In order to study the effects of consolidation, a 5-year duration was prescribed for 139 -5 -5 -10 -10 Depth (m) Depth (m) J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 -15 -15 -20 -20 -25 -25 10 15 20 25 30 Radial distance (m) 10 -5 -5 -10 -10 -15 -20 -25 -25 10 15 25 30 25 30 -15 -20 20 (b) IDW Depth (m) Depth (m) (a) N-n 15 Radial distance (m) 20 25 30 10 15 20 Radial distance (m) Radial distance (m) (c) DTL (d) NNI Unit: kPa Fig. 7. Radial effective stress ðr0rr Þ field before and after mapping (denoted by dash and solid line respectively). Table Errors for 3D-to-2D-axisymmetric interpolation (bolded rows indicated method with the lowest error measures). Node Set A Node Set B MRE RMS R2 MAE MRE RMS R2 Pore pressure (u) N–n 2.08271 IDW 0.406655 DTL 0.231915 NNI 0.195575 0.010724 0.003142 0.00175 0.001435 2.87226 0.563119 0.360609 0.304029 0.999594 0.999984 0.999994 0.999995 4.84838 0.157122 0.034877 0.046095 0.036576 0.000811 0.000306 0.000368 4.94263 0.279095 0.058252 0.072612 0.996871 0.99999 0.999999 Void ratio (e) N–n IDW DTL NNI 0.007172 0.001691 0.001861 0.001396 0.02127 0.004817 0.006236 0.004558 0.992725 0.999627 0.999375 0.999666 0.008059 0.000214 0.000183 0.000166 0.005976 0.000151 0.000128 0.000117 0.009376 0.000356 0.000294 0.000261 0.994209 0.999992 0.999994 0.999995 0.083553 0.028144 0.033611 0.026629 2.4647 0.583571 0.760426 0.568555 0.991721 0.999536 0.999212 0.999559 2.19265 0.074686 0.0286 0.031549 0.042576 0.001183 0.000819 0.001022 2.33084 0.136855 0.048252 0.060596 0.996834 0.999989 0.999999 0.999998 MAE 0.011601 0.002759 0.003196 0.00238 Radial effective stress ðr0rr Þ N–n 1.65614 IDW 0.330463 DTL 0.416427 NNI 0.312598 this stage and the only loading on the spudcan being the dead and working live load from the jack-up in the form of a static axial load. This does not detract from the aim of this paper which is to present a method of analyzing long-term behaviour of spudcan. The intro- duction of a ‘‘quiet’’ consolidation period of years also allows the effect of consolidation to be fully manifested. In the third stage, the spudcan was re-loaded to evaluate its post-consolidation load– displacement response. To accommodate the large soil deformation 140 J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 Table Errors for 3D-to-3D interpolation (bolded rows indicated method with the lowest error measures). Node Set A Node Set B MRE RMS R MAE MRE RMS R2 Pore pressure (u) N–n 0.970657 IDW 0.419122 DTL 0.27009 NNI 0.225656 0.006046 0.003006 0.001929 0.001434 2.08464 0.864296 0.697078 0.548816 0.999795 0.999965 0.999977 0.999986 4.57649 0.113872 0.012068 0.015546 0.038485 0.000836 0.0001 0.000126 4.59007 0.204039 0.015569 0.018718 0.996057 0.999992 1 Void ratio (e) N–n IDW DTL NNI 0.005597 0.001853 0.001731 0.001357 0.023588 0.00833 0.009506 0.006761 0.989814 0.99873 0.998346 0.999163 0.00855 0.000341 0.000213 0.000182 0.006255 0.000244 0.000147 0.000125 0.010087 0.000558 0.000364 0.000311 0.993617 0.99998 0.999992 0.999994 0.044691 0.019304 0.016622 0.016097 1.95791 0.745146 0.586582 0.509379 0.992668 0.998938 0.999342 0.999504 2.19691 0.056393 0.009898 0.014205 0.039828 0.000999 0.000205 0.000194 2.20731 0.094036 0.011648 0.018353 0.996087 0.999993 1 MAE 0.008843 0.002892 0.002736 0.002143 Radial effective stress ðr0rr Þ N–n 0.927565 IDW 0.362816 DTL 0.262365 NNI 0.270513 Figs. 11 and 12 plot the short- and long-term contours of mean effective stress (p0 ) and undrained shear strength (su) (i.e. those before and after years consolidation). The undrained shear strength su is inferred from Wroth’s [18] relationship su ¼ Fig. 8. Lagrangian FEM model for 2D-axisymmetric coupled flow calculation. anticipated in the spudcan re-loading stage, the nonlinear geometry option of ABAQUS/Standard was activated in the Lagrangian analysis. This feature involves transferring the state of the model at the end of one step to the next step as its initial state. Also, since conventional infinitesimal strain measures might not be appropriate given the large deformations and distortions, logarithmic strains were adopted. 3.2. Analysis results Fig. 9a–d shows the pore pressure at different times during consolidation. As shown in Fig. 9d, after about 180 days of consolidation, pore pressure is fairly close to hydrostatic. This is also reflected in the plots of excess pore pressure normalised by the in situ effective vertical stress, hereafter termed excess pore pressure ratio [1], Fig. 10a–d. As Fig. 10a shows, just after spudcan installation, very significant excess pore pressure is present down to a depth of about 1.5 times the radius below the spudcan tip. Much of this excess pore pressure dissipated within about months after installation. The actual time required for consolidation will depend upon the modulus of the soil and its coefficient of permeability. However, the properties used herein are fairly representative of medium plasticity clay. Hence the duration is not entirely unrealistic for such soils.  K M Ri p 2 ð9Þ where Ri is the isotropic overconsolidation ratio and K = (k À j)/k. Both sets of contours reflect a similar pattern, with the largest increase beneath the spudcan base, and a zone of weak, back-flowed soil behind the spudcan. The increase in undrained shear strength is also reflected in the ‘‘strength improvement ratio’’, defined as the ratio of the long-term, post-consolidation undrained shear to the in situ shear strength [19], shown in Fig. 13a–d. The long-term strength improvement ratio contour is similar in shape to the short-term excess pore pressure contour (Fig. 10a). This is not surprising since the dissipation of excess pore pressure translates into mean effective stress, and therefore strength increase. Both the undrained shear strength (Fig 12) and strength improvement ratio plots (Fig. 13) indicate the formation of a hardened soil plug beneath the spudcan and a zone of weak soil behind the spudcan. Within the hardened soil plug, soil strength increases by as much as 80% (Fig. 13d). At a depth of about R below the spudcan tip, the strength improvement ratio is approximately 1.5. Fig. 14 shows the computed load-settlement curve (‘‘FEM (dual stage)’’ in the graph) of the spudcan from installation through removal of preload, consolidation to reloading. The penetration depth in the graph corresponds to the distance from the spudcan conical tip to the mudline. As can be seen, the reloading response differs significantly from the initial loading response. The postconsolidation spudcan foundation behaves as if it had been preloaded to a much higher level. The Lagrangian analysis could not continue beyond Point F as excessive mesh distortion caused the computation to terminate. This is not surprising since the total settlement from Point B to Point F is approximately m, which is quite large for a Lagrangian computation. At the turning Point E, the reloading settlement is approximately 1.6 m, which is more than 10% of the spudcan diameter. In subsequent discussion, Point E will be considered as the point at which failure was initiated. Comparison of the bearing pressure at Point E with the pre-consolidation penetration resistance, that is Point B, indicates a significant increase in resistance of about 58%. Yi et al.’s [1] results indicated that the bearing capacity factor during installation is about 12.5. Applying the same bearing capacity factor to the 141 -5 -5 -10 -10 Depth (m) Depth (m) J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 -15 -20 -20 -25 -25 10 15 20 25 30 15 20 (a) (b) -5 -5 -10 -10 -15 -20 -25 -25 10 15 20 25 30 25 30 -15 -20 10 Radial distance (m) Radial distance (m) Depth (m) Depth (m) -15 10 15 20 Radial distance (m) Radial distance (m) (c) (d) 25 30 Unit: kPa Fig. 9. Total pore pressure contours (a) at the beginning of consolidation, (b) after 35 days consolidation, (c) after 90 days consolidation, (d) after 180 days consolidation. post-consolidation bearing capacity obtained from Point E would lead to an equivalent strength increase of about 58%, which is the strength increase at the spudcan axis at a depth of 0.7R beneath the tip (Fig. 13d). Using the strength increase at a depth of R beneath the tip with the same bearing factor would lead to a bearing capacity increase of about 50%, which is slightly conservative. This suggests that one may be able to estimate the post-consolidation bearing capacity of the spudcan by using the post-consolidation strength of the soil at a depth of R below the tip. 3.3. Comparison with centrifuge results The computed result in Fig. 14 was compared with the load-settlement curve measured in a centrifuge spudcan model in normally consolidated kaolin under 100-g model gravity. The modelling equipment as well as preparation and test procedures have been reported by Li et al. [20] and will not be repeated herein. The centrifuge test modelled the same sequence of events as those simulated in the numerical analysis. The trends indicated by the centrifuge and numerical results are similar throughout the entire sequence of events. The centrifuge measurements show a slightly lower penetration resistance during installation than the computed resistance. The computed and measured consolidation set- tlements agree remarkably well. On the other hand, during reloading, the centrifuge data indicate a stiffer response than the numerical results. The preceding overestimate of penetration resistance during installation occurs probably because the analysis does not consider the effect of strength degradation as soil flows around the spudcan, which was similarly noted by Hossain et al. [10]. The observed discrepancy during reloading, on the other hand, is likely related to the occurrence of partial consolidation in the experiment at the beginning of the reloading stage. In the centrifuge experiment, a closed-loop servo-control hydraulic loading system was employed to actuate the spudcan model. A load control mode was adopted during consolidation stage to maintain a working load level on the spudcan, which was subsequently switched to displacement mode at the beginning of the reloading stage. Due to the change of control mode and the enhanced soil stiffness after consolidation, some time was required for the servo-control hydraulic loading system to build up the needed hydraulic pressure to achieve the target penetration rate (i.e. the undrained rate). As a consequence, some partial consolidation might have occurred before the undrained target penetration rate was attained. The resulting partial consolidation would lead to a stiffer soil response than the numerical prediction. J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 0.5 0.5 Depth, d/R Depth, d/R 142 -0.5 -1 -1 -1.5 -1.5 0.5 1.5 2.5 1.5 (a) (b) 0.5 0.5 -0.5 -1 -1.5 -1.5 1.5 2.5 2.5 2.5 -0.5 -1 0.5 Radial distance, r/R 0.5 Radial distance, r/R Depth, d/R Depth, d/R -0.5 0.5 1.5 Radial distance, r/R Radial distance, r/R (c) (d) -5 -5 -10 -10 Depth (m) Depth (m) Fig. 10. Excess pore pressure ratio contours (a) at the beginning of consolidation, (b) after 35 days consolidation, (c) after 90 days consolidation, (d) after 180 days consolidation. Horizontal and vertical co-ordinates are normalised by the spudcan radius. -15 -15 -20 -20 -25 -25 10 15 20 25 30 10 15 20 Radial distance (m) Radial distance (m) (a) (b) 25 30 Unit: kPa Fig. 11. Contours of mean effective stress p0 (a) at the beginning of consolidation (short-term) (b) after years consolidation (long-term). 143 -5 -5 -10 -10 Depth (m) Depth (m) J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 -15 -15 -20 -20 -25 -25 10 15 20 25 30 10 15 20 Radial distance (m) Radial distance (m) (a) (b) 25 30 Unit: kPa 0.5 0.5 Depth, d/R Depth, d/R Fig. 12. Contours of undrained shear strength su (a) at the beginning of consolidation (short-term) (b) after years consolidation (long-term). -0.5 -1 -1 -1.5 -1.5 0.5 1.5 2.5 1.5 (a) (b) 0.5 0.5 -0.5 -1 -1.5 -1.5 1.5 2.5 2.5 2.5 -0.5 -1 0.5 Radial distance, r/R 0.5 Radial distance, r/R Depth, d/R Depth, d/R -0.5 0.5 1.5 Radial distance, r/R Radial distance, r/R (c) (d) Fig. 13. Strength improvement ratio contours (a) after 90 days consolidation, (b) after 180 days consolidation, (c) after year consolidation (d) after years consolidation. 144 J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 Spudcan Penetration Resistance F (MN) 0A 10 20 30 40 50 60 70 Penetration Depth d (m) FEM(dual-stage) Centifuge FEM(wished-in-place) 10 15 B C D E 20 F 25 -5 -5 -10 -10 Depth (m) Depth (m) Fig. 14. Load–displacement response of spudcan. Installation stage AB was analyzed using Eulerian approach. Stages BC (unloading), CD (consolidation) and DEF (reloading) were analyzed using Lagrangian approach. -15 -15 -20 -20 -25 -25 10 15 20 25 30 10 15 20 Radial distance (m) Radial distance (m) (a) (b) 25 30 Unit: kPa Fig. 15. Contours of undrained sheart strength su (a) at the beginning of consolidation (short-term) and (b) after years consolidation (long-term) from wished-in-place analysis. 3.4. Comparison with wished-in-place response In this section, comparison is made with the response of a wishedin-placed spudcan. Following the approach of Templeton [3] the spudcan was wished into place just above the target depth. A Lagrangian finite element analysis was then conducted in which the spudcan penetrated further by a small amount; the rationale of this being to impose the correct stress state on the soil below the spudcan. The finite element model for the wish-in-place analysis was similar to the preceding Lagrangian model for the coupled-flow analyses (Fig. 8) except that the soil domain was assumed to be undeformed. The spudcan was wished into a depth of 15.3 m and then further penetrated to the target depth of 16.5 m. The removal of preloading, consolidation and reloading were then simulated using the stages described above. As shown in Fig. 14, the long-term bearing response from the wished-in-place analysis is in close agreement with that of the dual-stage Eulerian–Lagrangian analysis. This is not surprising considering the close similarity in the long-term strength distributions beneath the spudcan obtained from the two analyses, as shown in Figs. 12b and 15b. Whilst the short-term strength distribution from the wished-in-place analysis (Fig. 15a) differs from that of the dual-stage Eulerian–Lagrangian analysis (Fig. 12a) in areas below and above spudcan due largely to the absence of the soil backflow mechanism in the former, their long-term strength distributions (Figs. 12b and 15b) are quite similar and of close magnitude in most areas except in the soft zone above the spudcan. In particular, as both analyses modelled the same consolidation period, with the spudcan subjected to an identical working load, the strength improvement beneath the spudcan observed in the dual-stage Eulerian–Lagrangian analysis was closely reproduced in the wished-inplace analysis. This explains the close agreement in their long-term bearing responses, which are mainly controlled by the hardened soil beneath the spudcan. 4. Example 2: short- and long-term spudcan fixity 4.1. Finite element model As the analysis of spudcan fixity is a three-dimensional problem, 3D-to-3D solution mapping has to be employed. As Fig. 16 show, semi-cylindrical meshes were used for both Eulerian J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 145 4.2. Analysis results Fig. 17a and b shows the bending moment M against angle of rotation h for both cases. The bending moment was taken to be the product of the horizontal force and the distance from the loading point to the load reference point (LRP) [21]. The LRP is defined at the lowest central point on the spudcan at which its maximum diameter is attained, as shown in Fig. 3a. The height of the applied horizontal load with respect to LRP is 25 m. Following SNAME [22], the rotational fixity (kr) is the ratio of the bending moment (M) to the angle of rotation (h). The gradient of a straight line joining the two ends of moment–angle loop gives the secant rotational fixity. As can be seen from calculation results (denoted by ‘‘FEM(dualstage)’’ in Fig. 17), the secant fixity for the ‘‘full-dissipation’’ case is just over twice that of the ‘‘no-dissipation’’ case, indicating that rotation fixity is also significantly enhanced by the consolidation process. 4.3. Comparison with centrifuge results (a) (b) Fig. 16. 3D FEM model for (a) Eulerian and (b) Lagrangian analysis. and Lagrangian analyses. As before, the spudcan was penetrated to a depth of 16.5 m and the deformed boundary was extracted to construct the Lagrangian mesh. Soil domain in the Lagrangian model was discretized into eight-noded hexahedral elements with displacement and pore-pressure degrees-of-freedom. 3D-to-3D mapping was conducted using the NNI method. The constitutive model and properties used were same as the previous example. The spudcan was then rocked by applying forward and backward horizontal displacement to the top of the spudcan shaft. Two cases were studied herein. For both cases, an equilibration stage with a short duration of 15 was first modelled in Lagrangian analysis to allow the soil and spudcan to re-establish equilibrium after solution mapping. The two cases differ in the second stage of Lagrangian analysis. For the short-term or ‘‘no dissipation’’ case, consolidation was not modelled after partial removal of the spudcan preload. For the long-term or ‘‘full dissipation’’ case, a consolidation period of years was prescribed. In the third stage, the spudcan in both cases was rocked by one cycle with a maximum angular amplitude of 0.4°. The computed results are also compared with data from centrifuge model tests. The conditions of the model tests and model preparation procedures are the same as those described earlier. The experimental apparatus to apply combined loading onto the model spudcan has been described by Yang et al. [23] and will not be repeated herein. Two centrifuge experiments were carried out corresponding to the ‘‘no-dissipation’’ and ‘‘full-dissipation’’ scenarios. As Fig. 17a shows, for the ‘‘no-dissipation’’ case, the trend and secant fixity of the computed and measured results are in general agreement. However, the computed result shows much less hysteresis in the loop than the measured results. This reflects one of the weaknesses of the Cam Clay model in dealing with cyclic loading. The partial removal of the preload brings the soil around spudcan into an elastic regime and Cam Clay is unable produce significant hysteresis below the yield surface. For the ‘‘full-dissipation’’ case, the measured secant fixity is slightly larger than the corresponding computed value. The measured hysteresis loop for the ‘‘full-dissipation’’ case is much smaller than the measured loop of the ‘‘no-dissipation’’ case. Subjectively, the agreement between the computed and measured loops also appears to be much better. Hence, one effect of the consolidation process is to reduce the hysteretic damping of the spudcan footing, giving a more ‘‘elastic’’ response. The measured post-consolidation secant fixity is about 2.3 times that of the pre-consolidation fixity. This is also reasonably close to computed value. 4.4. Comparison with wished-in-place spudcan fixity Comparison is also made with the computed response of wished-in-place spudcans. The procedure of simulating the wished-in-place is the same as that described above and the mesh used is similar to that shown in Fig. 16b. As Fig. 17a shows, for the ‘‘no-dissipation’’ case, the secant fixity computed by the wishedin-place analysis is about 70% higher than that computed by the Eulerian–Lagrangian analysis as well as the measured fixity. For the ‘‘full-dissipation’’ case, the wished-in-place analysis also over-estimates the secant fixity, albeit by a smaller margin of about 25%. As Fig. 12 shows, as the spudcan penetrates into the ground, the backflow soil is remoulded and is left in a softened state, in the short-term, and to a lesser extent, in the long-term. In contrast, although the wished-in-place analysis is able to replicate the increase in strength of the soil ahead of the spudcan, it is unable to model the softening of the soil behind the spudcan, Fig. 15. Since the rotational fixity depends on the strength of the soil all around, rather than just underneath, the spudcan, the soft- 146 J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 FEM(dual-stage) Centrifuge FEM(wished-in-place) kr=1864 MNm/rad kr=1768 MNm/rad kr=3139 MNm/rad Bending Moment M (MNm) 25 20 15 kr 10 -0.008 -0.006 -0.004 -0.002 0.002 0.004 0.006 0.008 Angle of rotation θ (radian) -5 -10 FEM(dual-stage) Centrifuge -15 FEM(wished-in-place) -20 -25 (a)“no–dissipation” case FEM(dual-stage) Centrifuge FEM(wished-in-place) kr=3891 MNm/rad kr=4117 MNm/rad kr=4792 MNm/rad Bending Moment M (MNm) 40 30 kr 20 10 -0.008 -0.006 -0.004 -0.002 0.002 0.004 0.006 0.008 Angle of rotation θ (radian) -10 -20 FEM (dual-stage) Centrifuge FEM(wished-in-place) -30 -40 (b) “full dissipation” case Fig. 17. Calculated and measured bending-moment–rotational-angle curves. ened backflow soil imposes a significant reduction on the rotational fixity, which cannot be modelled by the wished-in-place analysis. 5. Conclusions The foregoing results and discussion demonstrate the feasibility of conducting effective stress finite element modelling of the entire process of spudcan installation, consolidation and long-term operating behaviour, by using a dual-stage Eulerian–Lagrangian analysis. Comparison with centrifuge model data demonstrates the generally good agreement in trend but also highlights the shortcoming of the modified Cam-Clay model which cannot well replicate the hysteretic behaviour of the soil. The results also show that while a wished-in-place approach is able to model the longterm bearing response of the spudcan, rotational stiffness is substantially over-estimated. This is due to the fact that, while the wished-in-place analysis is able to model the hardening of the soil ahead of the spudcan, it is unable to model the softening of backflowed soil behind spudcan. The latter influences the rotational stiffness significantly, but not bearing response. Whilst both the Eulerian and Lagrangian stages in this study were conducted using ABAQUS, one can in principle use different software for the Eulerian and Lagrangian stages. Another advantage of this dual-stage Eulerian–Lagrangian approach is its required computational resource and time are virtually no more than the sum of two separate Eulerian and Lagrangian analyses, as no other user intervention except the one time solution mapping is needed. For instance, on a conventional desktop PC with 16 GB RAM and an i7 processor, Example took approximately 14 h in total to complete the (i) 3D Eulerian analysis, (ii) the 3Dto-2D mapping and (iii) the subsequent 2D consolidation analysis. Finally, application of the proposed dual-stage approach is not limited only to spudcan foundation problems. It is, in fact, suited for solving a wide range of offshore foundation problems involving rapid and large-scale undrained soil flow during installation followed by much longer embedment periods where changes in the geotechnical capacity with time may occur due to consolidation. An example is the offshore torpedo anchor. Its installation is undertaken by releasing it from a height of about 30–150 m above the seabed, with the free fall under gravity causing it to penetrate swiftly and deeply into the ground (possibly up to times its J.T. Yi et al. / Computers and Geotechnics 56 (2014) 133–147 length) [24]. As highlighted by Kay [25], the anchor capacity development with time after installation is one of main challenges for a robust torpedo pile geotechnical design. The development of the above dual-stage method may play a useful role for studying such a problem. Acknowledgments The authors acknowledge the research funding provided by the Agency for Science Technology and Research and the Maritime and Port Authority of Singapore through the Centre for Offshore Research and Engineering under the Offshore Technology Research Programme (Project No. 0821350042). References [1] Yi JT, Lee FH, Goh SH, Zhang XY, Wu J-F. Eulerian finite element analysis of excess pore pressure generated by spudcan installation into soft clay. Comput Geotech 2012;42:157–70. [2] Purwana OA. Centrifuge model study on spudcan extraction in soft clay. PhD Thesis, National University of Singapore; 2006. [3] Templeton JS. Spudcan fixity in clay, further results from a study for IADC. In: Proceedings of the 12th international conference, the jack-up platform, design construction and operation. London, England; 2009. [4] Zhang Y, Bienen B, Cassidy M, Gourvenec S. Undrained bearing capacity of deeply buried flat circular footings under general loading. J Geotech Geoenviron Eng 2012;138(3):385–97. [5] Zhou XX, Chow YK, Leung CF. Numerical modelling of extraction of spudcans. Geotechnique 2009;59(1):29–39. [6] Zhang Y, Bienen B, Cassidy MJ, Gourvenec S. The undrained bearing capacity of a spudcan foundation under combined loading in soft clay. Marine Struct 2011;24:459–77. [7] Hossain MS, Hu Y, Randolph MF, White DJ. Limiting cavity depth for spudcan foundations penetrating clay. Geotechnique 2005;55(9):679–90. [8] Tho K, Leung C, Chow Y, Swaddiwudhipong S. Eulerian finite-element technique for analysis of jack-up spudcan penetration. Int J Geomech 2012;12(1):64–73. [9] Hossain MS, Randolph MF. Deep-penetrating spudcan foundations on layered clays: numerical analysis. Geotechnique 2010;60(3):171–84. [10] Hossain MS, Randolph MF, Hu Y, White DJ. Cavity stability and bearing capacity of spudcan foundations on clay. 2006 Offshore technology conference (OTC ‘06). Houston, Texas, USA. OTC 177702006. 147 [11] Kellezi L, Stromann H. FEM analysis of jack-up spudcan penetration for multilayered critical soil conditions. In: Newson TA, editor. BGA International conference on foundations: innovations, observations, design and practice. Dundee, Scotland: Thomas Telford; 2003. p. 411–20. [12] Mehryar Z, Hu YX. Critical depth of spudcan foundation in layered soils. In: Proceedings of the fourteenth international offshore and polar engineering conference. Toulon, France; 2004. p. 647–53. [13] ABAQUS. ABAQUS analysis user’s manual. Version 6.12. Dassault Systèmes Simulia Corp., Providence, RI, USA; 2012. [14] Hu Y, Randolph MF. A practical numerical approach for large deformation problems in soil. Int J Numer Anal Meth Geomech 1998;22(5):327–50. [15] Sibson R. A brief description of natural neighbour interpolation. In: Barnett V, editor. Interpreting multivariate data. New York, USA: John Wiley; 1981. p. 21–36. [16] Ledoux H, Gold C. An efficient natural neighbour Interpolation algorithm for geoscientific modelling. In: Fisher Peter F, editor. Developments in spatial data handling: 11th international symposium on spatial data handling. Springer; 2004. p. 97–108. [17] Yi JT, Goh SH, Lee FH, Randolph MF. A numerical study of cone penetration in fine-grained soils allowing for consolidation effects. Geotechnique 2012;62(8):707–19. [18] Wroth CP. Interpretation of in situ soil tests. Geotechnique 1984;34(4):449–89. [19] Yi JT, Goh SH, Lee FH. Effect of sand compaction pile installation on strength of soft clay. Geotechnique 2013;63(12):1029–41. [20] Li YP, Lee FH, Goh SH, Yi JT, Zhang XY. Centrifuge study of the effects of lattice leg on penetration resistance and bearing behavior of spudcan foundations in NC clay. In: The 31st International Conference on Ocean, Offshore and Arctic Engineering (OMAE2012). July 1–6, Rio de Janeiro, Brazil; 2012. [21] Martin CM, Houlsby GT. Combined loading of spudcan foundations on clay: numerical modelling. Geotechnique 2001;51(8):687–99. [22] SNAME. Guidelines for site specific assessment of mobile jack-up units. New Jersey: Society of Naval Architects and Marine Engineers; Research Bulletin 5– 5A; 2008. [23] Yang Y, Lee FH, Goh SH, Wu J-F, Zhang XY. Pore pressure generation and dissipation effects on spudcan fixity in normally consolidated clay. In: The 32nd international conference on ocean, offshore and arctic engineering (OMAE2013), June 9–14, 2013, Nantes, France; 2013. [24] Hossain MS, Kim Y, Wang D. Physical and numerical modeling of installation and pull-out of dynamically penetrating anchors in clay and silt. In: The 32nd international conference on ocean, offshore and arctic engineering (OMAE2013), June 9–14, 2013, Nantes, France; 2013. [25] Kay S. Torpedo piles-VH capacity in clay using resistance envelope equations. In: The 32nd international conference on ocean, offshore and arctic engineering (OMAE2013), June 9–14, 2013, Nantes, France; 2013. [26] Goh TL. Stabilisation of an excavation by an embedded improved soillayer. PhD Thesis, National University of Singapore; 2003. [...]... Zhou XX, Chow YK, Leung CF Numerical modelling of extraction of spudcans Geotechnique 2009;59(1):29–39 [6] Zhang Y, Bienen B, Cassidy MJ, Gourvenec S The undrained bearing capacity of a spudcan foundation under combined loading in soft clay Marine Struct 2011;24:459–77 [7] Hossain MS, Hu Y, Randolph MF, White DJ Limiting cavity depth for spudcan foundations penetrating clay Geotechnique 2005;55(9):679–90... the spudcan and a zone of weak soil behind the spudcan Within the hardened soil plug, soil strength increases by as much as 80% (Fig 13d) At a depth of about R below the spudcan tip, the strength improvement ratio is approximately 1.5 Fig 14 shows the computed load-settlement curve (‘‘FEM (dual stage)’’ in the graph) of the spudcan from installation through removal of preload, consolidation to reloading... experiment at the beginning of the reloading stage In the centrifuge experiment, a closed-loop servo-control hydraulic loading system was employed to actuate the spudcan model A load control mode was adopted during consolidation stage to maintain a working load level on the spudcan, which was subsequently switched to displacement mode at the beginning of the reloading stage Due to the change of control... For this reason, the NNI method was chosen as the interpolation technique for the examples below 3 Example 1: long-term spudcan bearing response 3.1 Finite element model The first example involves the installation, unloading, longterm consolidation and reloading of a spudcan footing Spudcan installation was conducted using undrained effective stress Eulerian analysis with the mesh shown in Fig 3a The... the only loading on the spudcan being the dead and working live load from the jack-up in the form of a static axial load This does not detract from the aim of this paper which is to present a method of analyzing long-term behaviour of spudcan The intro- duction of a ‘‘quiet’’ consolidation period of 5 years also allows the effect of consolidation to be fully manifested In the third stage, the spudcan. .. Computers and Geotechnics 56 (2014) 133–147 Spudcan Penetration Resistance F (MN) 0 0A 10 20 30 40 50 60 70 Penetration Depth d (m) 5 FEM(dual-stage) Centifuge FEM(wished-in-place) 10 15 B C D E 20 F 25 Fig 14 Load–displacement response of spudcan Installation stage AB was analyzed using Eulerian approach Stages BC (unloading), CD (consolidation) and DEF (reloading) were analyzed using Lagrangian approach... is made with the response of a wishedin-placed spudcan Following the approach of Templeton [3] the spudcan was wished into place just above the target depth A Lagrangian finite element analysis was then conducted in which the spudcan penetrated further by a small amount; the rationale of this being to impose the correct stress state on the soil below the spudcan The finite element model for the wish-in-place... through removal of preload, consolidation to reloading The penetration depth in the graph corresponds to the distance from the spudcan conical tip to the mudline As can be seen, the reloading response differs significantly from the initial loading response The postconsolidation spudcan foundation behaves as if it had been preloaded to a much higher level The Lagrangian analysis could not continue beyond... Centrifuge study of the effects of lattice leg on penetration resistance and bearing behavior of spudcan foundations in NC clay In: The 31st International Conference on Ocean, Offshore and Arctic Engineering (OMAE2012) July 1–6, Rio de Janeiro, Brazil; 2012 [21] Martin CM, Houlsby GT Combined loading of spudcan foundations on clay: numerical modelling Geotechnique 2001;51(8):687–99 [22] SNAME Guidelines... four-noded quadrilateral elements to model the extraction of spudcan Zhang et al [4] and Templeton [3] also made use of first order hexahedral elements to study the bearing capacity and rotational fixity of spudcan The soil in the Lagrangian analysis was modelled using ABAQUS’ built-in modified Cam-clay (MCC) model with the same property set (Table 1) The spudcan deformation was again idealised as a rigid body . 1: long-term spudcan bearing response 3.1. Finite element model The first example involves the installation, unloading, long- term consolidation and reloading of a spudcan footing. Spudcan installation. bearing capacity of a spudcan foundation under combined loading in soft clay. Marine Struct 2011;24:459–77 . [7] Hossain MS, Hu Y, Randolph MF, White DJ. Limiting cavity depth for spudcan foundations. that, for the deeply penetrated spudcan, spudcan soil friction does not appear to affect the critical cavity depth and bearing capacity factor significantly. The spudcan was penetrated down to