Study on Seepage Characteristics of Composite Bucket Foundation Under Eccentric Load

Under the effect of eccentric loads, when the suction pressure of the composite bucket foundation is leveled, the seepage failure is very easy to occur. The seepage failure occurrence causes the foundation to settle unevenly and impairs the bearing performance. This study uses ABAQUS finite element software to establish a composite bucket foundation model for finite element analysis. The model simulates the seepage of the foundation penetrating process under eccentric load to reveal the induced seepage characteristics of the bucket foundation. The most vulnerable position of seepage failure under the eccentric loading is elucidated. Critical suction formulas for different offset eccentric moment strategies are derived and compared with existing literature formulas. Then the derived formula is supplemented and corrected according to the pressure difference between adjacent cabins. Conclusions can be drawn: (1) Under eccentric loads, the critical suction decreases about 7%–10%. (2) The pressure difference between adjacent cabins impacts significantly on the seepage field, and the critical suction, at most, can be reduced by 17.56%. (3) the offset strategies have little effect on the seepage field. Efficient and appropriate strategies can be selected to meet the requirement of leveling in engineering project.


Introduction
As a clean, environmentally friendly, and renewable energy source, offshore wind energy resources have attracted increasing attention. At the same time, many technical challenges still constrain their development: the foundation of a wind turbine is subjected to large eccentric loads, the terrain of the sea bed is complex, the requirements for corrosion protection are strict, and the power transmission is difficult. Therefore, a composite bucket foundation (CBF), which is suitable for poor foundation conditions and has a strong bearing capability and short construction period at sea, with broad development prospects came into being (Ding et al., 2017a(Ding et al., , 2017b(Ding et al., , 2015Zhang et al., 2017). Fig. 1 shows an example of the application of CBF in practical engineering.
As a new structural form, CBF has a bulkhead structure that makes the foundation significantly different from the previous related foundation. The setting of the inner part of the cabin can improve the stability of the foundation towing and realize the precise leveling of the installation process.
The arrangement of the bulkhead enhances the dynamic bearing capacity of the wide-shallow composite bucket foundation and improves the rigidity of the bucket foundation. The one-step installation of the CBF can save 30%− 50% of the cost. CBFs are subject to environmental loads such as wind, waves, and currents during the penetration stage and may also be subject to external loads such as ship collisions. Wind, waves, and currents generate horizontal driving forces, which act on the tower of wind turbine and generate eccentric loads (see Fig. 2). When the foundation is installed and sunk, the sum of the buoyancy of the cylinder and the difference between the internal and external pressure is higher than the penetration resistance to sinking smoothly (Fu et al., 2020;Guo et al., 2012;Wang et al., 2019;Li et al., 2015). The sinking process under negative pressure causes a seepage resistance reduction effect, but it is also necessary to pay attention to controlling the suction to prevent seepage failure.
At present, there are few studies on the critical suction of CBF under eccentric loads which can be analyzed by re-ferring to the related literature when the foundation has no eccentricity. Regarding the bucket foundation, many critical suction calculation formulas have been derived. Feld (2001) used SEEP for numerical simulations and proposed a formula for calculating the critical suction of a mono-bucket foundation with penetration depth. Houlsby and Byrne (2005) used an average hydraulic gradient at the same depth to measure the seepage failure, and considered different permeability coefficients of the inner and outer soil to expand the critical suction formula further. By comparing previous studies, Senders and Randolph (2009) found that when the depth is large or small, the calculation methods differ significantly, but most of them can agree well. Ibsen and Thilsted (2010) used the FLAC3D finite difference software to calculate the seepage path of the maximum hydraulic gradient at the top outlet, and improved the formula for calculating the critical suction.
The study of the critical suction potential requires the analysis of the underlying negative pressure penetration process. Erbrich and Tjelta (1999) simulated the settlement of a CBF in the sand with a finite element method and obtained that the negative pressure can reduce the side friction and tip resistance of the cylinder. Jostad (2002, 2004) used a numerical model to study the change in shear strength of the soil around the outer wall of the foundation when the suction anchor sinks under negative pressure as the pore pressure dissipates. Zhang et al. (2004) studied the characteristics of the seepage field during the penetration of the mono-bucket foundation in the Yellow River Delta. Tran and Randolph (2008) investigated the variation of soil pore pressure during the suction penetration process of bucket foundations by centrifugal tests and numerical simulations. The study revealed the relationship between pore pressure development and negative pressure sinking at critical negative pressure. Andersen et al. (2008) proposed a method for calculating the penetration resistance and the required negative pressure of a bucket foundation sinking into the dense sand. Romp (2013) discussed the influence of layered soil (that is, the different permeability coefficients of the upper and lower layers) on the sinking of the suction foundation. The upper layer of clay limits the seepage path of pore water when suctioning negative pressure. Mehravar et al. (2017) used FLAC3D software to establish a model of sinking bucket foundation, and analyzed the effects of seepage, foundation size, and cylinder wall thickness on the penetration resistance. The results are compared with the centrifuge test to adequately estimate the negative pressure required when the foundation sinks to different depths. Zhang et al. (2016) studied the pore water pressure at the outer wall of the bucket foundation during sinking through real-time monitoring.
Based on above studies, this paper uses the finite element software ABAQUS to further analyze the seepage characteristics of CBF under eccentric loads, and derive the formula for calculating the critical suction about the pressure difference between adjacent cabins.

Finite element modeling
There are twelve bulkheads inside the CBF, which divide the cylinder into seven honeycomb cabins. Based on the CBF in actual engineering, this paper uses the finite element analysis software ABAQUS to establish a three-dimensional finite element model of the bottom cylinder of the CBF. The prototype of the finite element simulation in this paper is a 6.45 MW CBF in a sea area in Jiangsu Province, China, with a scale of 1:35. In the model, solid elements (C3D8R) were used to simulate the soil model, and the steel cylinders are modeled as shell elements (S4R). The diameter D of the steel cylinder is 1 m, and the height H is 0.28 m; the diameter of the soil model is 6D, and the height is 10H. The CBF consists of a center cabin and six side cabins. The side length of the center cabin is D/4, and the bulkheads are steel plates with a thickness of 1.5 mm. In order to facilitate the distinction, the side cabins are numbered 1−6 (Fig. 3). The soil and the top of the cylinder are fixed with end constraint and set as impervious boundary conditions. The interaction between the foundation and the soil is set as surface-to-surface contact, and the penalty function algorithm is selected for the tangential behavior. The friction between the cylinder and the soil is controlled by setting the friction coefficient, and the friction coeffi-  cient is set to 0.3. Different pore pressure values are set on the inside and the outside of the cylinder to simulate the vacuum suction during the sinking installation process. During the installation process, the horizontal force on the upper structure will produce an overturning moment. The eccentric moment simplifies the force mode and transfers it to the cylinder, which is equivalent to applying a certain amount of vertical downward eccentric force on the side cabin. Changing the side cabins' pressure to make the structure bear a moment opposite to the overturning direction can offset the eccentric load. The pore pressure on the soil surface inside the cylinder is negative, and the pore pressure on the soil outside the cylinder is 0. So the negative pressure difference produces a sinking suction. Then, different negative pressures are applied to different side cabins, which will produce different magnitudes of suction and offset the moment induced by the eccentric load. To offset the eccentric moment, three methods are generally used: reducing the negative pressure in a single cabin, reducing the negative pressure between two adjacent cabins, and reducing the negative pressure among three adjacent cabins. Fig. 4 shows the finite element model. The cylinder is a shell element, and the material is steel with an elastic modulus of 210 GPa, the poisson ratio of 0.3, and the yield strength of 345 MPa. The soil molded in this paper is homogeneous sand. Table 1 lists the main characteristics.

Working condition
This study analyzes two different positions of eccentric loads and their corresponding offset strategies (Fig. 5). In Position 1, the eccentric load is located on the top of the bulkhead of the two side cabins. At this time, the negative pressure of the side cabins 1 and 2 is reduced. This case corresponds to the two-cabins offset strategy (TwCOS). In Position 2 the eccentric load is directly above a single side cabin. At this time, two offset strategies can be adopted. One is to reduce the negative pressure of the side cabins 1, 2, and 6 while those of the remaining cabins keep unchanged, that is, the three-cabins offset strategy (ThCOS). The other strategy is to reduce the negative pressure of one side cabin only and keep those of the other cabins unchanged to achieve leveling and sinking, that is, the single-cabin offset strategy (SCOS). The side cabins that reduce negative pressure are defined as offset cabins, while the others are non-offset cabins.   Given the three offset strategies of the above two eccentric positions, the seepage characteristics of each strategy with different depths and different eccentric moments are analyzed. According to the different penetration depth l, the following five operating conditions are selected for analysis: l/D=0.12, 0.16, 0.20, 0.24, and 0.28 (where l/D is the ratio of the penetration depth to the diameter of the steel cylinder). The eccentric moment can be offset by the force generated by the pressure difference between the offset cabins and the non-offset cabins, so that the structure can be in a force balance. After determining the negative pressure value of each cabin at different depths during normal sinking, the negative pressure value of the offset cabin can be calculated from the magnitude of the eccentric moment. The upper limit of critical negative pressure controls the inabil- ity and causes seepage failure of the soil, and the lower limit must overcome the penetrating resistance to make sure it sinks. When the same moments are applied, the SCOS generates the maximum pressure difference. The maximum pressure difference occurs when the negative pressure in the offset cabin is zero, and the critical negative pressure is reached in the non-offset cabins. Based on the critical suction formula in Feld (2001), the eccentric moment that can be offset is 96.8 N·m. Since the formula does not consider the effects of bulkheads and eccentric loads, this value should be appropriately reduced. Therefore, this study takes 80 N·m as the upper limit of the applied moment. According to the applied eccentric moment M, the following working conditions are selected: M=10, 50, and 80 N·m. Therefore, the negative pressure of the offset cabin at each depth can be determined, as shown in Table 3. 3 Analysis of seepage characteristics 3.1 Analysis of variations in pore pressure (negative pressure) Take the penetration depth of 16 cm and the eccentric moment of 50 N·m as an example. Fig. 6 is a schematic diagram of the selected MON cross section. Figs. 7a−7d give the pore pressure distribution diagrams at the relative depth l/D=0.16 at the MON cross section in the case of non-eccentricity, SCOS, ThCOS, and TwCOS, respectively.  These figures highlight that the negative pressure variation rate of the center cabin in the CBF is smaller than that of the side cabins, and the negative pressure contour line distributes in an arc shape. Under the eccentric condition, the changes in negative pressure in non-offset cabins and center cabin are similar to those under non-eccentric conditions, while the negative pressure changes in offset cabins differ. Owing to the sidewall effect, the seepage occurs mostly at the bulkhead and the cylinder wall. Therefore, the negative pressure and differential pressure of the side cabin along with the depth of the sidewall under the non-eccentric condition and SCOS are analyzed. From the soil surface to a depth of 5L, points at a depth of 0.01L were selected to study the curve. P i is the absolute value of the negative pressure at each point, while P is the negative pressure on the soil surface in the non-offset cabin (3 000 Pa for this example). ΔP i is the negative pressure difference between two adjacent points; L i is the depth of each point; L is the penetration depth of the cylinder (16 cm). Fig. 8 is a schematic diagram of the research position along the CBF's section, which includes the center axis (CA), the center cabin sidewall (CCSW), the side cabin inner wall (SCIW), the side cabin cylinder wall-in (SCCW-in), and the side cabin cylinder wall-out (SCCW-out).   9 shows the changes in the negative pressure and pressure difference along with the depth of the CA, CCSW, SCIW, SCCW-in and SCCW-out under non-eccentric conditions. From Fig. 9a, the existence of several distortion points in the figure reflects the sidewall effect on the seepage, the negative pressure changes from sharp to gentle, and the position of the CA, whose curve changes smoothly, has little effect because it is far away from the cylinder wall. At each position, the distortion, with almost no lag, occurs at the relative depth of about 1, which is consistent with the positions of the bottoms of the cylinder and the bulkheads. The negative pressure at the anterior stage of the distortion varies greatly. At the CA, the CCSW and the SCIW, the change of negative pressure at the front section is small. Fig. 9b shows the pressure difference at the position of the bulkhead and the cylinder wall. The negative pressure at the bottom of the cylinder wall has the largest change and the maximum seepage. The relative pressure difference inside the cylinder wall decreases from the maximum value of 0.079 to 0.0044, i.e., it corresponds to a decrease of 94%; the outside difference of the cylinder wall varies from −0.0283 to 0.0041, i.e., about 115%. The negative sign indicates that the seepage direction changes. When the depth is about 1, the sign of the SCCW-out curve changes and the seepage direction is opposite. This behavior shows that the soil outside the cylinder first seeps inward along the cylinder wall, and then seeps into the soil outside the cylinder at a depth below the cylinder. The pressure difference at the position of the cylinder wall first increases and then decreases, while the pressure difference at the position of the internal skirt changes in the opposite direction. The pressure difference of the CCSW first increases and then decreases, consistently with the changes in the cylinder wall, while that of the SCIW decreases and then increases. This trend highlights the presence of a seepage into the cabin and a seepage into the center cabin at this position, both of which inhibit each other to some extent. The sign is positive, indicating that the inward seepage from the outside of the cylinder is still the dominant one. Fig. 10 shows the seepage direction under non-eccentricity, where the arrows indicate the seepage direction.
In the same way, the changes of negative pressure under eccentric working conditions are studied, and the SCOS is used as an example to illustrate the different changes of the offset cabin and the non-offset cabin. Fig. 11 highlights that the change in the negative pressure of the non-offset cabin is more consistent with the noneccentric working condition, while that in the negative pressure of the offset cabin is different. The negative pressure varies little because the offset cabin exerts a small negative pressure. The negative pressure at the bottom of the cylinder wall decreases, while the overall trend of the curve does not vary significantly. The change in pressure difference is analyzed in detail (Fig. 12). The pressure difference between the offset cabin and the CCSW is greater than that of the non-offset cabin, while the pressure difference at the SCCW-in and the SCCW-out is smaller. The sign of the pressure difference at the SCIW is negative at a relative depth of 0.81 to 1.06, indicating that the seepage direction has been changed because the amount of the seepage to the outside of the cylinder is smaller than that inside the cylinder. Similarly, the same situation occurs at the SCIW of the offset cabin (1.09−1.16). With the pressure difference, the outward seepage of the offset cabin is mainly to the center cabin and other side cabins (non-offset cabins). At this time, the outward seepage is dominant, as Fig. 13 shows for the direction of the seepage.
The data related to the key nodes show that the negative pressure changes drastically, and the pressure difference gradually increases within the penetration depth. The influence range of the sidewall effect is basically at a relative depth of about 1, but the actual situation may be lagged   slightly. The non-offset cabin under the eccentric condition is similar to that of the non-eccentric condition. The pressure difference in the cylinder wall has the widest gap, indicating the largest influence of the cylinder wall on the seepage. The comparison results show that the negative pressure at the sidewalls of non-offset cabins is smaller than that without eccentricity, suggesting that the negative pressure is reduced considerably about 3%, due to the seepage between the adjacent cabins. The pressure difference of the offset cabin at the CCSW increases significantly, highlighting the greater impact of the seepage between the adjacent cabins on the internal skirt.

Seepage velocity analysis
In order to study the influence of the offset moment on different cabins, a penetration depth of 0.16 m and eccentric moment of 50 N·m were selected as examples to analyze the diverse seepage velocity of different cabins with the offset strategies of the above. Fig. 14, Fig. 15, and Fig. 16 show the percolation velocity diagrams for SCOS, TwCOS, and ThCOS, respectively. The maximum velocity of about 2.3×10 −6 m/s appears at the bottom of the cylinder wall of the non-offset cabin. The velocity distribution of the three strategies is different. The comparison shows that the velocity at the bottom of the cylinder of the ThCOS is higher than that of the SCOS and TwCOS, while it is almost the same as that of the non-offset. The velocity distribution of the center cabin is uneven, with a relatively high velocity near the offset cabin. The maximum values of the SCOS, ThCOS, and TwCOS are of 1.477×10 −6 , 1.501×10 −6 , and 1.602×10 −6 m/s, respectively. Then, the bottom velocity of the cylinder wall of each cabin (only the side cabins 1, 2, 3, and 4 are selected from the symmetry) is further extracted, and the results are listed in Table 4.
From Table 4, the highest velocity belongs to the non-    offset cabins that are farther away from the offset cabins, while the velocity is the smallest for those farthest away from the non-offset cabins. These data highlight that the seepage at the bottom of the adjacent cabins has the most significant impact on the non-offset and offset cabins.

Calculation of critical suction
4.1 Most unfavorable position for seepage failure By comparing and analyzing the hydraulic gradient changes of the soil surface at different positions, the most unfavorable position of the seepage failure of the three offset strategies under non-eccentric and eccentric conditions can be found.
For non-eccentricity conditions, two paths from the center axis of the center cabin to one of the side cabin cylinder walls are selected for analysis.
According to Fig. 17, the hydraulic gradient along the path of bulkhead a is slightly larger than that of the path b along the middle of the cabin. Also, the seepage of the side cabin is more significant than that of the center cabin because of the presence of the bulkhead and internal skirt which leads to an increase in seepage. The side cabins are closer to the soil outside the cylinder than the center cabin, so its seepage path is shorter. The figure shows that the most unfavorable position of seepage failure under non-eccentric conditions appears at the intersection of the side cabin's bulkhead and the cylinder wall.
Since the seepage in the center cabin is smaller than that in the side cabins and the largest seepage occurs in the bulkhead of the cabin, only the seepage of the bulkhead of the side cabins under eccentric conditions is studied. Also, the negative pressure of the offset cabin is lower than that of the non-offset cabin, and the seepage of the offset cabin is lower than that of the non-offset cabin. The maximum seepage occurs at the bulkhead of the non-offset cabin. By taking the position of the bulkhead of the non-offset cabin as the control condition, the research path is selected according to the symmetry. Four paths of a, b, c, and d for Tw-COS, three paths of a, b, and c for ThCOS, and five paths of a, b, c, d, and e for SCOS are investigated. The paths close to the different cabins on both sides of the bulkhead are taken since the two non-offset cabins have a common bulkhead.
By considering that the seepage failure, such as soil flow and piping, which occurs mostly at the seepage outlet, the outlet hydraulic gradient i of the soil at the outlet depth of 0.002D is i=Δh/0.002D (where Δh is the head loss). Fig. 18 gives the calculated hydraulic gradient i under each path. In the figure, the abscissa is the distance from this position to the center of the cylinder. The position of the offset cabin is marked with a circle.
From the figure, the hydraulic gradient gradually increases outward from the center of the cylinder. The maximum values all appear at the cylinder walls of the non-offset cabin of the path a and are 1.047 for SCOS, 1.0095 for ThCOS, and 1.0145 for TwCOS, respectively.
In summary, the most unfavorable position of seepage failure occurs in the non-offset cabin adjacent to the offset cabin, specifically at the intersection of the bulkhead and cylinder wall. According to Fig. 19, it generates at the position A because of a pressure differential between the cabin and outside. Therefore, the seepages from the outside of the cylinder and the adjacent cabin occur at the same time, and the seepage at the sidewall is the largest. Moreover, at the intersection A of the cylinder wall of the non-offset cabin which is adjacent to the offset cabin and the bulkhead, is the most unfavorable position for seepage failure.

Calculation of seepage path
During the penetration stage, the increase in suction leads to seepage failure at the soil surface, the point A in Fig. 19 first. Then this point is used as the calculation con-   trol point. The hydraulic gradient of the soil on the upper surface of the inside of the cylinder wall is i, and the seepage path satisfies the following equation: where L is the length of the permeation path, S is the value of the applied negative pressure, and is the bulk density of water. Fig. 20 shows the change of relative seepage path L/l with relative depth l/D under non-eccentricity (NE), SCOS, ThCOS, and TwCOS. The seepage path is smaller under eccentric conditions. Also, the higher the depth is, the smaller the difference in the seepage path is compared with the noneccentric working condition. This behavior is due to the pressure difference between the offset cabin and the outside of the cabin that leads to an increase in the loss of water head in the soil near the bulkhead and an increase in the hydraulic gradient of the seepage outlet. Under eccentric conditions, the ThCOS's seepage path is the largest, while for the SCOS it is the smallest. In fact, under the same eccentric moment condition, the pressure difference between the adjacent cabins of the SCOS is the largest. So it is necessary to pay attention to preventing seepage failure when the adjacent cabins' pressure difference occurs during leveling.
By fitting the relative seepage path L/l and the relative depth l/D, the following equations can be obtained.

Derivation of the critical suction formula
During the penetration stage of the bucket foundation, high suction pressure will cause seepage damage to the surrounding soil, which will cause uneven settlement of the cylinder and adversely affect the bearing capacity of the bucket foundation. Therefore, further analysis should be done on the magnitude of the maximum suction that can cause seepage failure of the soil. The negative pressure at the critical state of seepage failure of the soil at the seepage outlet is defined by the critical suction S cri . According to the principle of effective stress and Darcy's law, when the seepage force produces an upward seepage force so that no effective stress is transmitted among the soil particles in the cylinder, the soil reaches a critical failure state and the applied negative pressure is equal to the critical suction. When the effective stress is zero, the seepage force equals the soil bulk density, that is: That is:   CHEN Qing-shan et al. China Ocean Eng., 2021, Vol. 35, No. 1, P. 123-134 γ w γ ′ where i cri is the critical hydraulic gradient of the outlet, is the bulk density of water. is the floating bulk density, given by: where G s is the specific gravity of soil particles; e is the void ratio of soil. By substituting Eq. (8) into Eq. (7), the critical hydraulic gradient is obtained as: The critical suction calculation formula can be obtained from Eq. (1): Feld (2001) used the calculation results of the finite element software SEEP to obtain the equation for the critical suction of mono bucket foundation: In order to verify the reliability of the finite element, we use the finite element software ABAQUS to calculate the critical suction formula for the mono bucket foundation without bulkhead: and (16). It indicates that the result calculated by ABAQUS is more consistent with the result obtained by SEEP in Feld (2001), which proves the reliability and correctness of the ABAQUS result. The results of critical suc-tion under the eccentric conditions presented in this paper are smaller than those in the case without bulkheads and internal skirt in Feld (2001). These results prove that the bulkheads increase the seepage effect of the structure, and reduce the critical suction. Further, the influence of the eccentric moment on the critical suction is analyzed by comparing Eqs. (11)−(14) (Fig. 22). The figure highlights that the critical suction is smaller than that without eccentricity. Also, the critical suction of SCOS is the smallest. The critical suction reductions under eccentric conditions are 10.8% for SCOS, 7.5% for ThCOS, and 7.6% for TwCOS, indicating that the effect of the pressure difference between adjacent cabins on seepage cannot be ignored.

Influence of different eccentric moments on seepage
By taking the SCOS as an example, Fig. 23 shows the change of the relative seepage path with the relative penetration depth under different eccentric moments. The larger the eccentric moment is, the smaller the relative seepage diameter can be because the eccentric moment causes a more considerable pressure difference between the adjacent cabins. Therefore, the critical suction formula should be modified with the pressure difference between adjacent cabins as a variable to accommodate different eccentricity conditions.
Take the penetration depth of 0.16 m as an example and define L 0 as the length of the seepage path without eccentricity at this depth; L i is the length of the seepage path with different eccentric moments, P 0 is the negative pressure of 132 CHEN Qing-shan et al. China Ocean Eng., 2021, Vol. 35, No. 1, P. 123-134 the non-offset cabin, and ΔP i is the pressure difference between the offset and non-offset cabins. Table 5 lists the different eccentric conditions.  0  10  3000  265  25  3000  662  40  3000  1059  50  3000  1324  60  3000  1588  70  3000  1853  80 3000 2118 Fig. 24 shows the relative relationship between the eccentric seepage path L and the pressure difference P i . Based on this, the adimensional equation can be fitted: where L 0 is the length of the permeation path without eccentricity, and P 0 is the negative pressure of the non-offset cabin. By combining the calculation Eq. (11) and Eq. (17) of the seepage path under the non-eccentric condition, the calculation formula of critical suction of a single cabin offset is obtained: Similarly, Eqs. (19) and (20) for the change in the critical suction of the ThCOS and TwCOS with the pressure difference can be fitted in Fig. 25. ThCOS: TwCOS: By integrating the expressions of each offset strategy, this paper gives the final critical suction formulas for the number of offset cabins, the pressure difference between the offset cabin and the non-offset cabin, and the penetration depth, as in Eq. (21).
where n is the number of offset cabins, and n ranges from 1 to 5. From the SCOS's Eq. (18), when the negative pressure of the offset cabin is zero, the pressure difference reaches the maximum. That is, the maximum eccentric moment can be offset. At this time, the critical suction decreases by 17.56% compared with the non-eccentric working condition, which cannot be ignored. In engineering projects, attention should be paid to the adjustment of the pressure difference between the adjacent cabins of the CBF to avoid it being excessively larger and causing seepage failure. Also, from Eq. (21), the selection of the offset strategy barely affects the critical suction, and the difference can be controlled within 5%. Therefore, a multi-cabin offset strategy can be selected according to actual needs when levelling the foundation and efficient and smooth penetrating installation can be achieved.

Conclusions
In this paper, a composite bucket foundation model is established based on ABAQUS finite element software. The seepage characteristics of the foundation under eccentricity, non-eccentricity, different offset eccentric moment strate- gies, and different eccentric moments are studied. The calculation formula of critical suction is deduced. The main conclusions are as follows: (1) Under eccentric conditions, the main part of the cabin seepage is from the outside to the inside, but for the internal skirt in the offset cabin, a section of the opposite direction appears at the bottom of the outer wall. At this time, the seepage between adjacent cabins dominates, and the seepage from the offset cabin to the other cabins is the dominant one.
(2) The hydraulic gradient of seepage on the soil surface for each side cabin is calculated. The most unfavorable position of seepage failure under eccentric working conditions is obtained, specifically in the side of the non-offset cabin where the bulkhead of the offset and non-offset cabins intersect with the cylinder wall.
(3) Based on the equations in literature, this paper derives a critical suction formula for the load cases with and without eccentricity. The comparison of the results suggests that the non-eccentric formula is more in line with existing literature. The critical suction calculated by the eccentric formula has been reduced, by 10.8% for SCOS, 7.5% for ThCOS and 7.6% for TwCOS, respectively.
(4) The pressure difference between adjacent cabins leads to an increase in the hydraulic gradient of the soil surface, where the seepage failure is more likely to occur. The critical suction shows the maximum decrease of 17.56% compared with the case without eccentricity. Therefore, in the actual project, the influence of the pressure difference between the adjacent cabins on the seepage should be accounted for.
(5) This study takes the eccentric moment as the control variable and integrates various offset strategies to support the calculation of the critical suction formula. The calculated formula of the critical suction S cri as a function of the number n of offset tanks, the relative pressure difference P i /P 0 , and the relative penetration depth l/D are given.