Design of A Bionic Spudcan and Analysis of Penetration and Extraction Performances for Jack-up Platform

The mechanisms of soil−structure interaction have drawn much attention in the past years in the installation and operation of jack-up platform. A bionic spudcan produced by biomimetic of egg and snail shell is proposed, and the performance of the penetration and extraction are analyzed by numerical method. The geometric contour of egg and snail shell is measured, and its mathematical model is established respectively. According to the structure of existing spudcan of jack-up platform, three kinds of typical biomimetic spudcan are designed. Furthermore, numerical analysis models of biomimetic spudcan are established respectively to study the soil−structure interaction mechanism in the process of penetration and extraction, and contrastive analysis of resistance characteristics are carried out. To conclude, the results show that the biomimetic spudcan facilitates the platform installation, and it is also beneficial to the improvement of the bearing capacity of spudcan.


Introduction
In the offshore oil industry, most drilling operations in water depths up to 120 m are performed from self-elevating mobile jack-up units. However, with the advance of technology, the platform adapted to the water depth of 180 m has been developed. A typical jack-up platform has a buoyant triangular hull and three independent truss-work legs. The foundations of independent-leg jack-ups approximate large inverted cones, commonly known as 'spudcans'. Roughly circular in plan, spudcans typically have a shallow conical underside (in the order of 15° to 30° to horizontal) and can have a sharp protruding point (ISO, 2012).
Spudcan, a critical component of jack-up platform, interacts with seabed directly, and the design of a spudcan determines the penetration and extraction performance and standing stability of the platform. The seabed is known to consist of layers of soil with different shear strengths, when a jack-up is installed in stiff-over-soft clay seabed, and the spudcan punches through a layer of stiffer soil into softer soil. The spudcan temporarily loses vertical capacity, causing rapid uncontrolled penetration. It is likely to cause instability of the platform, such as 'punch-through' failure, spudcan scour, creep settlements and severe slope . When the storm comes, there is often too much extraction resistance. Therefore the jack-up cannot be removed from specific-site in time.
As a result, in the installation and operation of jack-up platform, the mechanism of soil-structure interaction has been highly concerned by academia and industry. At present, there are abundant theoretical research achievements on spudcans penetration and extraction (Zheng et al., 2016;Hu et al., 2014;Duan et al., 2010). The numerical calculation method is gradually applied to the analysis of soil-structure interaction (Nazem et al., 2009;Qiu et al., 2010).
The penetration and extraction processes of spudcan involve large deformations and contact problems. It is difficult to solve those problems with classical finite element method. A new Coupled Eulerian-Lagrangian (CEL) approach has been widely used to overcome the difficulties with regard to finite element method and large deformation analyses (Tho et al., 2012;Yi et al., 2012;Hamann et al., 2015;Zhang et al., 2013).
The bearing capacity of spudcan has been studied dur-ing the installation of independent-leg jack-up rigs in strong over weak layered seabed (Hu et al., 2018;Hossain et al., 2010). The problem of punch-through has been studied under the condition that spudcan penetrated layered soil (Hu et al., 2015;Yu et al., 2012). Li et al. (2013Li et al. ( , 2017 studied the bearing capacity of spudcan with lattice leg in penetration process as well as under the condition that spudcan embedded deeply. Based on the existing shape of spudcans, the influence of spudcan shape on the penetration performance has been studied (Hossain et al., 2017;Hu et al., 2016). The existing spudcans cannot effectively solve the safety problems such as 'punch-through' and time-consuming extraction of jack-up drilling platform. Therefore, it is necessary to design a type of spudcan to meet the need of safety operation of jack-up platform. The eggshell is a kind of rotation shells with multifocal surfaces of positive Gaussian curvature (Babich, 1993). It has the advantages of reasonable streamline and material distribution (Zhang et al., 2016). Bradfield (1951) found that the blunt end always appears first followed by the sharp end when a goose lays eggs,which has been attributed to the streamlined structure. This process is very similar to the extraction of jack-up's spudcans. Zhang et al. (2005) studied the microstructure characteristics of an eggshell and proposed biomimetic applications. Using the Cartesian coordinate system, Lebedv et al. created the egg shell shape function . With the aid of egg shell shape, Zhang et al. (2016Zhang et al. ( , 2017 proposed the design theory and method to utilize an egg shaped biomimetic pressure hull adapted to 1000 m depth. Snails are a type of shellfish, found mainly in water, and often act in the soil. Snail shape is a dextral structure, and consists of a helicoid, helical bend, body whorl and stylolite. The helicoid and helical bend structure has an outward expansion structure. Therefore, the interior space available to the snail is large, and it has a good rigid connection with the soil. Harary and Tal (2011) used a reverse scan technology to study the geometrical property of Spiral organism. Based on the snail shell structure,  deduced the 2D mathematical expression of snail shells, and provided a good reference for spudcan design.
As mentioned above, the egg shells have good streamline shape and reasonable material distribution. The snail shells have large spatial expansion structure and the ability to drill soil. All of these provide inspiration for the design of spudcans, which also ignited our research interest. Therefore, in order to overcome the limitations of the existing spudcan structure in the installation and operation of the jack-up platform, a bionic spudcan is proposed based on the excellent biological characteristics of egg shell and snail shell.
In this paper, the outer surface of egg shell and snail shell was scanned in the form of a point cloud and automatically transformed into a computer-aided design (CAD) model, and a mathematical model was established based on experimental data. After that, a bionic spudcan composed of egg shell and snail shell was designed according to the mathematical model. This determination considered the characteristics of egg shell and snail shell, as well as the required performance of the spudcans. Then, the penetrating and extraction performance of the proposed spudcan was analyzed by CEL method. Particularly, layered soil was selected to simulate the penetration process. Finally, the results were compared with the ordinary spudcans and some meaningful conclusions were drawn.

Experiments of egg shell and snail shell
2.1 Egg's contour shape testing As shown in Fig. 1, the geometry of typical eggshell consists of sharp end, blunt end, major axis and minor axis. The contour curve of the goose egg can be described by Eq.
where, L is the major axis, and B is the minor axis.
To obtain the value of n, ten goose eggs were selected, then, the value of the major axis and minor axis were measured (Fig. 2). The testing value and Pearson correlation coefficient (PCC) are shown in Table 1.
From Table 1, the following results can be obtained: the average value of the major axis of the eggshell is 79.03 mm, and minor axis is 53.95 mm. Here, egg shape factor is 0.6828 and PCC is 0.9913. Thus, the generatrix function of egg shape can be expressed by Eq. (2). (2)

Snail's contour shape testing
Unlike the eggshell, the contour equation of the snail shell has not been studied so far. As shown in Fig. 3, defining main geometric parameters of snail shell includes the length and height of snail layer. Considering the manufacturing difficulty, the spudcan is designed as axisymmetric body and contains features of snail shell. Selecting the contour shape of the top snail layer as a part of the lower part generatrix. To obtain the contour shape of snail, we selected ten snails and cleaned out the internal object. As shown in Fig. 4, the outer surface of each snail was measured through a three-dimensional optical scanner (Open Technologies Corporation: Single scanning range: 150 mm×115 mm×150 mm; scanner pixel: 200M; accuracy: 0.02 mm). Then, a 2-D plane graph of the shell (front view) was obtained. Data was extracted by the CAXA software, and imported to the ORIGIN software. Fig. 5 shows the test data curve and its fit curve.
On the basis of experiment data, the mathematical expression of this curve, given as Eq. (3), is first derived in ORIGIN software. PCC of curve reaches 0.9793, which indicates that the fit curve is very close to the trial curve.
To verify Eq. (3), the measurements of ten samples are performed. All PCC measurements are listed in Table 2 and the average value is 0.9929. Therefore, it can be concluded that the Eq. (3) can be used to express the snail's profile curve.
Length and height value of each shell layer are analyzed, since the size of each layer is different from one another. CAXA software was used to obtain length and height of each layer with the results shown in Table 3. As can be seen from Table 3, the ratio of length to height for each layer did not show significant variation. Ratio was found to be 1.41, 2.57 and 3.32 for the top layer to the third layer respectively.    As can be seen from the above discussion, the obtained mathematical model of snail shell is reliable, which indicates that the appearance configuration of egg shell and snail shell is to be expressed accurately. In the next step, the data obtained from the proceeding sections is used to combine the egg and snail shells to develop a biomimetic spudcan of jack-up platform.

Design of the biomimetic spudcan
At present, most jack-up drilling platforms are supported by three legs with each of the same structure spudcan. The existing typical spudcan structure is a combination of the upper and lower cone, and the apex angles of two cones are in the range of 120°-150°. It typically has a shallow and hard cone on the bottom of lower cone so as to reduce the sideslip risks of jack-up platform.
The structure of spudcan largely influences the process of soil-structure interaction. The upper and lower cones of spudcan have an effect on the process of extraction and penetration respectively. Accordingly, the characteristics of eggshell and snail shell mentioned above are taken into account to design three kinds of biomimetic spudcans in this paper. The structure of that is composed of traditional cone, eggshell and snail shell respectively. The typical structural forms are cone-snail shaped (the upper and lower parts of spudcan are cone and snail shell shaped respectively), egg-cone shaped (the upper and lower parts of spudcan are egg and cone shell shaped respectively) and egg-snail shaped (the upper and lower parts of spudcan are egg and snail shell shaped respectively). In order to facilitate the comparative analysis of the spudcan's performance with different structures, the maximum cross-section diameter D and total height H of the spudcan are selected as the main structural dimensions, and the same leg structure is adopted, which includes leg length L, diameter of leg d.
Due to the particularity of the contour shape of egg shell, that is, asymmetric on the minor axis, the natural process by which a goose lays eggs are taken into account. The process of laying eggs is the blunt end of egg leaving the mother's body first (Bradfield, 1951). As a result, in the design process of bionic spudcans, the blunt end of the egg is used as the design basis to create the upper cone of biomimetic spudcan. For the lower conical body of spudcan, it is designed as a snail shell with two layers. The ratio of the layer e is 1.42:2.57. As the cross-section of the spudcan has great influence on the resistance during the process of penetration and extraction, the maximum section must be guaranteed to be the same in the design. On the other hand, in order to compare with the ordinary spudcan, four kinds of spudcan models are established, as shown in Fig. 6, where D=6 m, H=2.81 m, L=30 m and d=1 m.
3.2 Numerical model and parameters selection of biomimetic spudcans As the 'punch-through' failure occurred mainly in the layered foundation, soil was set as a laminated structure in the penetration process simulation, with the upper layer as stiff soil, and lower layer as soft soil. In the extraction process simulation, soil adhesion was not taken into account; assume that the extraction process of spudcan was carried out with the help of high-pressure water jet (Gaudin et al., 2011). In this paper, the CEL method was used to simulate the process of penetration and extraction under undrained condition.
To reduce computing resources, only one-quarter model was created because of structure and boundary symmetry. As illustrated in Fig. 7, the numerical model for the penetration process (Fig. 7a) included spudcan, Euler area, stiff soil and soft soil. The numerical model for the extraction process (Fig. 7b) included spudcan, Euler area and soft soil, and the spudcan was buried in soft soil as well. To avoid boundary effects, the radius and height of soil were 6D and 10D, respectively (Hossain, 2008).
Soil area was defined as Euler elements, which has 223200 EC3D8R elements. In addition, the element size in the Euler area that spudcan may pass through was small, and the further the distance was from this area, the bigger the size was. The spudcans had 160000−180000 Lagrange elements with C3D4 elements mainly chosen to discrete spudcan models with some C3D6 and C3D8 elements. In order to simulate the flow of soil, an empty space was established above the spudcan. The symmetric boundary condition was defined on the plane of symmetry . The spudcan and leg were set as a rigid body and operated at constant rate v. Contact between soil and spudcan was enforced using a general contact which was based on a penalty contact method .
Soil parameters are selected based on the Hossian experiment (Hossain, 2008). In the penetration process, the effective unit weight and undrained shear strength of soft soil are 7.43 kN/m 3 and 11.0 kPa respectively, that of stiff soil are 8.03 kN/m 3 and 38.3 kPa respectively, the thickness of stiff soil is 5 m and the penetration rate is 0.5 m/s. In the extraction process, the effective unit weight and undrained shear strength of soft clay are 7 kN/m 3 and 12 kPa respectively, and the extraction rate is 0.3 m/s.
The numerical simulations were carried out under undrained condition. Undrained conditions were satisfied according to the criterion of Finnie (1993), with the non-dimensional velocity index, , exceeding 30, where v is the penetration rate, D the spudcan diameter and (2.6 m 2 /a) the consolidation coefficient (Hossain, 2008). Hence, Poisson ratio is set as 0.49 and elastic modulus is determined by the following expression.
α S u where, is elastic modulus factor, and selected according to Table 4 (Tang and Zhang, 2015), E is elastic modulus of clay, and is undrained shear strength.   84 GUO Sheng et al. China Ocean Eng., 2020, Vol. 34, No. 1, P. 80-88 4 Simulation and results analysis 4.1 Simulation of the penetration process 4.1.1 Penetration resistance analysis The calculation processes of the penetration are carried out in commercial package ABAQUS for four types of spudcans. As shown in Fig. 8, relationship between penetration resistance and depth can be obtained from simulation results. Fig. 8 shows that the penetration resistance increases dramatically in the initial phase, mainly due to the rapid increase of contact area between spudcan and soil. When the depth exceeds 4.8 m, the spudcan begins to enter the soft soil. The resistance however, does not decrease directly. In the case, resistance forces tend merely to become slower, but still rise. This is because the soil foundation experiences shear failure and result in soil plugging the bottom of spudcan. As a result, the plug enters the soft soil with the spudcan, which compacts the top of the soft soil and increases the resistance. The thickness of the soil plug is mainly affected by the diameter of the spudcan, the properties of the stiff soil layer and the pre-load.
It is also found that when the depth of the penetration is smaller than 8 m, the resistance of the lower snail-shaped spudcan is smaller than that of the lower cone-shaped spudcan. This makes it more favorable to penetrate spudcan in the initial phase of platform operation, and the legs can be penetrated into soil smoothly. On the other hand, since the lower cones of the two types of bionic spudcans are snailshaped, the resistance of the bionic spudcans at the initial phase is almost equal. When the depth exceeds 8 m, soil plug effect was gradually reduced, and the resistance starts to go down. In general, the resistance of biomimetic spudcan is significantly higher than that of ordinary spudcan at this time. This is conducive to the stability of the platform and largely reduces the probability of 'punch-through' failure.
The penetration resistance values of the four types of spudcans were, in descending order, egg-snail, egg-cone, cone-snail and ordinary shaped. It is shown that the upper egg shaped spudcans have higher load capacity than the upper cone shaped spudcans. The average penetration resistance value of egg-snail shaped spudcan is 33.6% higher than that of ordinary spudcan, which is calculated based on the resistance value after spudcan inserted 10 m into the soil.

Analysis of the formation and influence of soil plug
Soil flow has significant influence on penetrating operation, and the flow mechanism of soil has been studied deeply Hossain, 2008). As penetration depth increased, the spudcan entering into the soft soil layer, the soil no longer flows up, and it flows down due to effect of soil plug. Fig. 9 shows the final phase of the process of penetrating operation for the four models.
As shown in Fig. 9, two kinds of soil plugs are formed at the lower end of the spudcan. One is the inverted cone plug (Figs. 9a and 9b) produced by the lower conical spudcan, the other is the triangular strip (Figs. 9c and 9d) of soil produced by the lower snail spudcan. Whatever the plug, it will go into the soft soil with the spudcan. Thus, an inverted cone plug is formed by the lower cone shaped spudcan,  GUO Sheng et al. China Ocean Eng., 2020, Vol. 34, No. 1, P. 80-88 and the triangle strip shaped plug was formed by the lower snail shaped spudcan.
The following conclusions are obtained through the comprehensive analysis of the simulation results in Fig. 8 and Fig. 9. The influence of triangular strip plug on soil flow is more than that of inverted cone plug. At the final phase, stiff soil fills the cavity, and surrounds the spudcan. Among them, the upper egg-shaped spudcans have small soil overburden, and the soil flow of ordinary spudcan is larger, obviously. It shows that soil flow caused by biomimetic spudcan is the least in the four models.

Extraction resistance analysis
In the same way, we use ABAQUS to calculate the processes of the extraction. From simulation results, relationship between extraction resistance and depth can be obtained, as shown in Fig. 10.
As illustrated in Fig. 10, the extraction resistance increases rapidly due to the soil compression and topsoil overburden, reaching its maximum at the depth of 0.8 m in the initial phase. It can be observed that the ultimate extraction resistance of the biomimetic spudcan is smaller than that of the ordinary one. Subsequently, the extraction resistance is in a stable phase with some fluctuations. When the depth exceeds 7 m, the extraction resistance trends to decrease due to the decrease of overburden caused by soil backflow.
The following findings can also be directly observed from the Fig. 10. The order of resistance values of the four types of spudcans, from small to large, is egg-snail, egg-cone, cone-snail and ordinary shaped. The extraction resistance of two kinds of upper egg-shaped bionic spudcans is obviously smaller than that of two kinds of upper cone-shaped bionic spudcans. This can be attributed to the good streamline structure of the upper egg-shaped spudcan. This makes that the overburden flows back along the surface of egg shell-shaped spudcan in the process of extraction. Thus, the resistance of extraction spudcan is largely reduced.
The average extraction resistance value of the egg-snail shaped spudcan reduced by 36.6% than that of ordinary spudcan, which was calculated based on the resistance value after spudcan extracted 0.8 m. Moreover, the extraction resistance of the egg-snail shaped spudcan was smaller than that of the egg-cone shaped spudcan. It indicates that the special expansion structure of the bottom of bionic spudcan also has influence on extraction.

Analysis of the formation and influence of topsoil
The extraction operation of jack-up platform is not only affected by soil flow, but also affected by the topsoil. Fig. 11 shows the final phase of the extraction process, the shape of topsoil is found to be stable when the spudcan extracts out the soil.
Due to the different structure of the spudcans, the hump height of top soil caused by the soil deformation during the extraction process is not equal. The heights of humping soil are 7.35 m (Fig. 11a), 6.5 m (Fig. 11b), 7 m (Fig. 11c) and 6 m (Fig. 11d), respectively.
In addition, the humping soil is different in volume and section shape. It can be observed that the humping soil pro-  duced by the upper conical spudcans is half ellipsoidal shaped (Figs. 11a and 11c), and the humping soil produced by the upper egg-shaped spudcan is strip shaped (Figs. 11b  and 11d). The humping soil volume produced by the egg-snail shaped spudcan is the smallest, which helps to extract out spudcan easily.

Conclusions
Based on the current requirements and problems in the existing spudcans of jack-up platform, on account of the reasonable streamline shape of the egg shell and the good contact stiffness between the snail shell and the soil, a design method of egg-snail biomimetic spudcan was proposed. The resistance of the penetration and extraction was studied, the numerical analysis results showed that the egg-snail shaped spudcan was conducive to the operation of penetration and extraction. These results provide theoretical reference and application guidance for further research and development in academia and industry.
According to the biomimetic spudcan study conducted, the following specific conclusions can be drawn.
(1) In the initial phase of penetration operation, the resistance of the two kinds of lower-snail shaped spudcan is consistent, both of which are smaller than that of the lowercone shaped spudcan, making it easier to penetration spudcan. After entering the soft soil layer, the resistance of the biomimetic spudcans increases, among which the resistance of the egg-snail shaped spudcan is the largest. This is conducive to the stability of the platform and largely reduces the probability of 'punch-through' failure.
(2) In the extraction operation, the resistance of three kinds of biomimetic spudcans is smaller than that of ordinary spudcans, while the resistance of egg-snail shaped spudcan is the smallest. It shows that the operation performance of the egg-snail biomimetic spudcan is more prominent. According to the soil flow, the biomimetic spudcans is more favorable for the extraction. All these indicate that the bionic characteristics of egg-snail shell are more suitable for the practical application of spudcans.