Penetration Characteristics of Mono-Column Composite Bucket Foundation for Offshore Wind Turbines

Abstract

To address the issue of seepage and soil plugging during the sinking of mono-column composite bucket foundations (MCCBFs), experiments were conducted on the installation of foundations under a variety of complex geological conditions. The effect of negative pressure sinking mode on the foundation’s seepage field was analyzed, the formation mechanism of soil plugging in sand was explained, and an efficient method for calculating the height of soil plugging was proposed in conjunction with these investigations. The findings demonstrate that the finite element method simulation of the soil’s seepage field is the most accurate, that the pumping volume of the foundation during sinking through is high, that the formation of the soil plug height is high, and that clear depressions can be seen on the foundation manifold’s exterior. The equation presented in this study makes it easier to forecast the height of a foundation plug and can offer direction for engineering design.

1. Introduction

Offshore wind power is an important source of renewable energy. Floating offshore wind represents a new frontier of renewable energy [1,2,3,4]. China already has the greatest installed offshore wind capacity in the world as of 2023, with a cumulative total of over 30.51 GW, which accounts for 49% of the world’s total, as the offshore wind sector there has continued to expand in size and cost in recent years. China, the UK, and Germany have been leading the development of installed offshore wind capacity over the previous three years, and this trend is projected to continue [5]. The most significant barrier to the development of offshore wind power remains the cost issue, as state subsidies for offshore wind power in China have been eliminated, and offshore wind power has now reached parity state [6,7].

Driven by the rapid development of offshore wind farms, bucket foundations have come to constitute a very promising form of foundation for offshore wind turbines [8]. In recent years, the suction bucket, a novel kind of foundation that is quicker to install and significantly lowers building costs, has gained popularity in the field of marine engineering both domestically and internationally [9,10]. Figure 1 illustrates the steel “mono-column + connection + bucket” overall structure of the mono-column composite bucket foundation (MCCBF) [11,12], which fully utilizes the benefits of the bucket and monopile foundation structure through the connection structure. Without the use of piling or buried rock construction, the foundation can be built entirely on land, transported by barge at sea, and promptly sunk on site to save time. This can significantly increase construction efficiency and lower the project’s overall cost.

The issue with the MCCBF stems from the design and development process. Particularly in light of the design and construction challenges posed by shallow rock base and hard sandwich geology, there is an urgent need to clarify the sinking process of the foundation. Self-weight sinking and suction sinking are the two main stages of a suction bucket’s sinking process, with suction sinking being the more difficult stage and changing the soil’s composition [13,14]. Sand allows for significant seepage, which alters the effective stress in the soil surrounding the bucket and has the effect of damping seepage. Additionally, it may result in the soil becoming looser and plugs forming in the bucket. Furthermore, too little of a negative pressure difference may lengthen the construction process and raise costs, while too high of a negative pressure may result in infiltration damage or plug failure, among other things. To encourage their industrial utilization, accurate analysis of seepage and soil plugs during the sinking of bucket foundations is crucial.

For the seepage during the penetration process, Zhang et al. [15] investigated the seepage characteristics during the sinking of the suction bucket, revealing the characteristics of the distribution of the super-pore water pressure around the bucket, and proposed a formula for computing the sinking resistance based on the effective stress and friction angle of the soil taking into consideration the seepage reduction effect. Through direct observation of the suction bucket installation using the PIV technique, Ragni et al. [16] provided information about the soil condition during penetration. Sandstone particles at the bucket’s end travel toward the bucket during penetration as bottom-up seepage reduces the relative density of the sand inside the bucket and raises its permeability. The sand soil plug inside the bucket saw a modest increase in permeability during the change in permeability under soil suction, according to Erbrich and Tjelta [17,18] and Houlsby et al. [19] centrifuge trials.

A group of centrifuge tests were performed to investigate the lateral bearing capacity of the suction bucket foundation with three aspect ratios. Force-controlled lateral static and cyclic tests were performed at a centrifuge acceleration of 50 g. Four soil conditions were considered in centrifuge tests with a combination of loose/dense and dry/saturated sand [20,21]. The development of the plug and the plug’s height are the primary factors impacting the sink penetration when the soil inside the foundation travels upwards during the construction of suction bucket penetration. To measure the suction force value, seepage action, and the amount of soil plug uplift, Kim et al. [14] used centrifugal model tests in the sand. They also indirectly assessed the impact of soil plug loosening through bending unit tests and static touch tests. They discovered that seepage action significantly affects soil plug uplift during the installation of suction bucket sinking penetration. In model tests on the sink penetration of suction foundations in the sand, Zhang et al. [22] discovered that soil plugs formed during suction penetration are caused by upward seepage from the sand in the bucket and that the height of the soil plugs increases roughly linearly with increasing depth of penetration. Guo et al. [23,24] discovered that the new intermittent pumping technique could successfully decrease soil uplift while not lengthening the installation time of caissons in soft clay seabed, and by further investigating the formation process of soil plugs, they discovered that the wall thickness of the foundation and the composition of the clay are the two primary factors in the formation of soil plugs.

The current research on the sinking process of the suction bucket at this stage mainly focuses on the homogeneous soil body, and there is a lack of analyses on the complex conditions such as layered soil and shallow cover layer. In actual engineering, most seabed conditions are complex soil conditions with uneven distribution, which have a great impact on the suction during the sinking process of the bucket foundation. Generally speaking, the problems in the installation process of the suction bucket mainly focus on seepage and soil plugging. To further analyze the seepage and soil clogging mechanisms of the MCCBF when sinking under difficult geological settings, In this research, small-scale testing is used to investigate soil plugging and seepage issues during the sinking of bucket foundations in complex geology, which encourages the use of buckets in the engineering territory.

2. Model Test in Sand

2.1. Test Model and Loading Device

The suction bucket model test was conducted in a dirt box that measured 2 m in length, 2 m in width, and 1.2 m in height. As illustrated in Figure 2, the model box’s bottom was fitted with an injection and drainage pipe as well as a 20 cm thick gravel filter layer that was used to separate the test soil from the filter layer by placing a geotextile on top of it.

Before each test, the test sand is uniformly loaded into the model soil box using the sand drop method. The height of the sand soil is 70 cm. After the sand drop, water is injected from the bottom of the soil box through the water injection pipe until the water surface is higher than the mud surface, which is 15 cm. The soil is static and maintained for 24 h after the water injection.

The equipment used for the MCCBF sinking test is primarily depicted in Figure 3. An inclinometer is positioned at the top of the foundation to track the inclination of the foundation as it sinks, and earth pressure gauges and pore pressure gauges are installed inside the top of the bucket and on the side walls to track changes in the pressure of the soil and water in the pore spaces. In addition to the valves used to connect with the compartments on top of the MCCBF, the top of the water and gas replacement bucket is also equipped with a valve that is intelligently connected to the vacuum pump and a valve that is connected to the atmosphere. The foundation can sink when the atmospheric valve is opened because of its weight, and it can sink by suction under steady pressure when the atmospheric valve is closed and the vacuum pump is turned on. To achieve the leveling of the foundation during the suction sinking process, several valves can be designed to control the flow rate of each chamber by varying the opening size of the valve.

The test model is a scaled-down version of the prototype installed in Yangjiang, Guangdong Province, and has dimensions of 60 cm in diameter by 17 cm in height and 2 mm for the manifold, the center column, and the outer wall. The superstructure is stiffened, and the mass of the foundation is 40 kg, as indicated in Figure 4 because the focus of this work is on the interactions between the cylinder soils rather than on how the superstructure deforms. It should be emphasized that due to the limitations of the test settings, the small-scale test cannot recreate the stressed state of the soil body. As a result, the goal of this paper’s research is to summarize and analyze the test phenomenon.

In this test, two different types of soil are employed. The first is Fujian standard sand, a type of sand that is frequently used by academics in China. The on-site sand conditions can be restored as much as possible because of the sand’s small particle size. The physical characteristics of the Fujian standard sand are listed in Figure 5 and

Table 1. Sand parameters.

Items	Value
Saturation density (g/cm3)	17.50
The angle of internal friction (°)	28.10
Compression modulus (MPa)	0.81
Permeability coefficient (cm/s) Average diameter (mm)	4.12 × 10−4 0.17
Nonuniformity coefficient Cu	1.57
Curvature coefficient Cc	0.96

uniformly.

Figure 5 shows the particle grading curve of Fujian standard sand, where d₆₀, d₅₀, d₃₀, and d₁₀ are used to represent the soil particle sizes corresponding to the vertical coordinates of 60%, 50%, 30%, and 10% on the particle size distribution curve. The nonuniformity coefficient C_u and the curvature coefficient C_c are commonly used in research to describe the grading situation, and their formulae are as follows:

$$C_u=\frac{d_{60}}{d_{10}}$$

(1)

$$C_c=\frac{{\left(d_{30}\right)}^2}{d_{60}{d}_{10}}$$

(2)

The other soil, Tianjin clay, was chosen.

Table 2. Clay parameters.

Items	Value
Saturation density (g/cm3)	18.53
Cohesive forces (kPa)	0.85
Compression modulus (MPa)	0.56
Permeability coefficient (cm/s)	5.99 × 10 −7

displays the results of indoor geotechnical tests used to determine the clay’s fundamental characteristics.

2.2. Test Procedure

Figure 6 depicts the steps involved in the MCCBF indoor sedimentation test procedure. They are as follows:

(1)

Locate the sensor number, after which it is buried in the soil body and placed on the sensor zero’s structure, and then open the data collector to begin recording the experimental results;

(2)

Place the MCCBF in the center of the test soil box directly above, attach the PU gas pipe from each foundation compartment’s valve to the replacement water and gas bucket, and open the atmospheric interface;

(3)

Close the atmospheric interface, connect the pull-wire displacement gauge to the top of the foundation, lower the MCCBF to the bottom of the cylinder to make contact with the mud surface, start the vacuum pump for pumping until all the gases inside the bucket are discharged, close the vacuum pump, and open the atmospheric interface;

(4)

Disengage the crane in case the structure sinks due to weight;

(5)

When the foundation stops producing vertical displacement, close the atmospheric interface, open the vacuum pump, apply suction sinking and suction pump starting pressure of 1.5 kPa. When the bucket sinks at a speed of less than 0.01 mm/s, the negative pressure is applied to raise the negative pressure by 0.5 kPa. Enter the next negative pressure interval of the sinking until the foundation stops sinking;

(6)

Release the water and gas replacement bucket pressure by opening the atmospheric interface, then close the valve on top of the foundation to complete the sinking.

3. Test Results

3.1. Test Result in Sand

The foundation into the dirt is shallow, the sinking resistance is low, the foundation sinking speed is even, sinking to 38.2 mm, and the sinking speed is significantly low. This is because the greater the depth of the sinking, the higher the level of soil stress and the greater the corresponding sinking resistance. Until the depth of 42.39 mm, the foundation is not self-gravity sinking. The foundation sinking speed in the suction sinking stage follows a similar trend to the self-weight sinking stage, both of which experience an initial spike and then a subsequent drop. The area between the dotted lines in the suction sinking stage of the Figure 7 represents the stages in which the vacuum pump’s negative pressure gradually increases. It can be seen that, until the vacuum pump’s negative pressure reaches a stable level, the sinking speed of the foundation suddenly increases after each increase in that pressure. Then, as the negative pressure continues to rise, the foundation sinks more slowly. The foundation is perceived to have finished sinking when it stops doing so, and the final depth of the foundation sinking in the sand is 159.7 mm.

Figure 8 depicts the compartment pressure measured on the sand’s surface as the MCCBF is sunk into it. Hydrostatic pressure is reduced by balancing the pore water pressure value before the sinking and installation to counteract its effects. With the foundation at the self-gravity sinking stage, the pore pressure in each compartment monitored during sinking is essentially the same, and the change in pore pressure value is comparatively constant within the relative depth of 0.24. When the pump starts, the foundation continues to sink. During the start-up phase, there are large fluctuations in the hole pressure, but once the foundation sinks to a relative depth of 0.7, the hole pressure growth enters a stable phase and increases gradually. Once the foundation sinks to its full depth, the maximum hole pressure in each compartment is 1.05 kPa.

The pore pressures in the side compartments and the center compartment are measured by pore manometers buried at various positions in the soil, as illustrated in Figure 9 when seepage occurs in the foundation. Sinking in sand considerably increases the amount of seepage in the soil. When suction subsidence happens, pore water moves from the outside of the cylinder to the interior, increasing the pore pressure that the pore manometer measures along the seepage path and increasing the head loss the closer it is to the seepage starting point.

The volumetric water between the foundation and the mud surface, which extrudes in the process of sinking the top of the bucket to the mud surface, and the water generated by seepage in the soil in the process of suction sinking make up the majority of drainage in the process of foundation sinking through. The MCCBF’s pumping volume curve for sinking in sand is shown in Figure 10. The pump’s flow rate is approximately 0.021 L/s throughout the sinking process, and the variability in the middle is primarily due to turning the valve on and off during leveling. No seepage drainage is produced during the self-weight sinking stage, and during the initial suction sinking stage, the foundation sinks and releases quickly with little seepage drainage. The foundation resistance increases and the penetration speed decreases when it sinks into the mud surface by about 135 mm. At this point, seepage in sand plays a role in reducing the resistance to sinking penetration, causing the foundation to continue to sink. At this point, the drainage volume of seepage water occupies a higher proportion, and the pump flow rate tends to be constant.

In the process of sinking and the completion of sinking, the state of the external soil body of the bucket is shown in Figure 11. In the whole process of sinking, the disturbance to the soil body is relatively small, and the inclination angle of the whole process is also within the control range. When foundation suction sinking is complete, the external soil corresponding to each compartment plate has a specific depression, the top cover of the bucket is higher than the soil’s surface by a specific height, and there is a specific amount of soil blockage. During the foundation suction sinking stage, the depression of the external soil corresponding to the compartment plate is more obvious.

3.2. Test Result in Clay Overlying the Sand Layer

Figure 12 shows the depth of the foundation into the mud by its weight is 23.03 mm, in the stage of suction sinking, the foundation’s average penetration velocity in the overlying clay is 0.155 mm per second, and the average penetration velocity in the sandy soil is 0.084 mm per second. The penetration velocity increases and then decreases in each stage of suction sinking. The foundation’s final depth of sinking in the clay layer above the sand layer is 165.54 mm.

Figure 13 depicts the observed compartment pressures during sinking under the sand over clay geological conditions. Since a portion of the gas is retained in the compartments during sinking, the foundation’s initial entry into the mud causes the gas to extrude, which increases pressure in the compartments. The consistency of the monitored compartment pressures during sinking is high. The change in pore pressures in Compartments 1 and 4 is more pronounced in the initial stage. The foundation is sinking beneath its weight at a relative depth between 0.0 and 0.13. If the relative depth is 0.28 or less, the pore pressure of each compartment is more stable, and there is a slow increase in pore pressure as the penetration depth increases during the stage of sinking under suction (Compartments 1 and 4 are still significantly affected by the gas in the bucket). The maximum pore pressure of each compartment is 7.39 kPa after sinking penetration, which is the excessive pore pressure exerted in the process of confirming the completion of foundation sinking. According to the curve, the maximum pore pressure needed in the process of sinking penetration is approximately 5.4 kPa. The pore pressure rises more quickly at the clay and sand interface.

Figure 14 depicts the drainage of the foundation during the subsidence phase when the foundation is in the sand layer overlying the clay layer. The total volume of drainage is essentially the same as the total volume of drainage of the foundation penetrating the soil layer throughout that phase, indicating that there is very little seepage during the process of sinking and penetrating the sand layer overlying the clay layer.

3.3. Test Result on Shallow Overburden

3.3.1. Sand Overlying Shallow Overburden

Figure 15 depicts the sinking and penetration curves during foundation installation in the shallow cover. Under its weight, the foundation dips to a depth of 35.31 mm, and at each stage of suction sinking, the penetration velocity rises and subsequently falls. The foundation sinks to an ultimate depth of 151.41 mm in the shallow cover.

Figure 16 depicts the monitored compartment pressures during sinking penetration under shallow overburden geological circumstances. The measured compartment pressures during sinking penetration exhibit great consistency and a moderately increasing trend with increasing penetration depth. In the relative depth range of 0.0 to 0.2, the foundation is in the self-gravity sinking stage. Each compartment’s pore pressure gradually grows during the sinking under the suction stage, reaching a maximum of 1.05 kPa after the sinking penetration is finished.

In Figure 17, the drainage of the foundation in the shallow overburden is depicted. During the self-weight sinking stage, no seepage drainage is produced, and during the initial suction sinking stage, the foundation sinks and releases more quickly and seepage drainage occupies a smaller percentage of the space. The foundation extrusion is lesser, the seepage in the sandy soil is stronger, the proportion of seepage water in the drainage volume increases, and the flow rate of the pump tends to remain constant when the foundation sinks into the mud surface by about 138 mm. At this point, the foundation penetration significantly slows down.

3.3.2. Clay Overlying Shallow Overburden

Figure 18 depicts the MCCBF’s sinking depth vs time curve in the shallow overburden atop clay. The foundation descends at a depth of 20.72 mm under its weight because the clay surface soil’s poor strength causes it to enter the mud rapidly, penetrating to 11.5 mm. After that, the penetration speed dramatically reduces. The foundation’s sinking penetration speed is more constant during the suction sinking stage, averaging 0.152 mm/s in the depth range of 20.7 to 160 mm, before drastically slowing down to reach the foundation’s final sinking depth of 167.9 mm.

Figure 19 displays the observed compartment pressures as the foundation sinks into the clay of the shallow overburden. Because the inclination of the direction of Compartment 1 is the most visible in the sinking process of the foundation, its pore pressure value is larger throughout the sinking process while that of the other compartments tends to remain constant. The pressure difference between the inside and outside of the cabin roof increases to 1–1.5 kPa at the beginning of the suction sinking stage. When the sinking penetration reaches a relative depth of 0.8, the cabin pressure increases to 2.5–4 kPa. At a relative depth of 0.8 or less, the cabin pressure continues to rise. By the time the sinking penetration is complete, the maximum pressure difference between all the compartments is monitored to be 7.3 kPa.

Figure 20 depicts the drainage of the foundation during the subsidence phase when the foundation is overlying a clay layer on top of a shallow overburden. The foundation compartment accounts for 97% of the total drainage, and the presence of less seepage water monitored later in the process at higher compartment pressures is less than the total volume of drainage from the foundation penetration into the soil layer during the subsidence phase.

4. Characterization of Foundation Penetration Seepage

The soil body and soil box are the same size. The outer edges of the bucket and the soil body are set as impermeable boundaries, and the shallow overburden is considered to be permeable given that the upper surface of the shallow overburden layer is typically the rock debris after weathering. This model is created using ABAQUS and can be seen in Figure 21. The bottom of the soil is fully fixed with horizontal constraints applied on the side, and contact pairs are used to simulate the relationship between the soil and the foundation [25]. The upper surface of the soil body in the cylinder is subjected to a super pore water pressure of 1 kPa, and the structure and soil body are adopted as C3D8P solid units. The models are established at four sinking states with relative depths of 0.4, 0.6, 0.8, and 1 to study the seepage field morphology when the foundation is sinking through to various depths, assuming that the state of steady state seepage is reached at each stage, and disregarding the tilting and leveling of the foundation.

It can be seen by extracting the pore water pressure at the inner and outer walls of the MCCBF side compartments, as well as at the inner wall of the middle compartment, that the ratio of the pore water pressure gradually decreases from one to zero, with the loss of the negative pressure being greater in the interior of the bucket, which reaches 0.703, along the bucket wall of the side compartments. The negative pressure loss of the MCCBF in the sand obtained by numerical simulation is compared with that in the numerical simulation, as shown in Figure 22, which demonstrates that the numerical simulation of the seepage field of the MCCBF in the test is based on the corresponding position cabin pressure measured in the test, and the ratio of it to the cabin pressure at the top of the capsule is taken as the pore water pressure ratio.

Figure 23 displays the distribution of pore water pressure in the seepage field within the soil when the relative depth of the foundation sinking penetration is one. Sand has a wider spread of pore water pressure, and the central soil body in the bucket is impacted by a wider range of negative pressure in the depth direction. The soil body in the bucket close to the bucket wall exhibits a more intense pore water pressure isopotential line, a greater hydraulic gradient, and a more pronounced negative pressure effect on the soil body. The influence on the soil outside the foundation is smaller when the foundation is on a shallow cover layer, and seepage water in sand primarily originates from the lower permeable layer. Pore water pressure isopotential lines are concentrated inside the cylinder. The pore pressure isopotential line is concentrated on the surface clay of the clay layer atop the sand layer, and there is no seepage in the sand, which is essentially consistent with the test results. The permeability coefficient of the clay is substantially lower than that of the sand.

See Figure 24 for a detailed analysis of the distribution of pore water pressure at the inner and outer walls of the bucket side compartment and the inner wall of the middle compartment in various depths of penetration. The seepage formed around the bucket penetration affects the effective stress of the soil body. The pore water pressure on the surface of the soil inside the foundation is one, and the pore water pressure on the surface of the soil outside is zero, with the vertical coordinate representing the relative depth of penetration and the horizontal coordinate representing the pore water pressure ratio. In sand, the pore water pressure decreases in the side compartments along the bucket wall in a manner akin to a straight line, and there is a nonlinear change at the bucket’s end that is further decreased as the depth of penetration increases. The pore water pressure gradually decreases at the end of the bucket due to the thin wall of the bucket, yet there is a progressive increase along the bucket wall downward on the outside of the side compartments. The pore water pressure varies throughout the inner wall of the middle compartment similarly to the side compartments, but with a smaller percentage reduction.

The rule of pore water pressure change along the cylinder wall in the shallow overburden sand layer is similar to that of pure sandy soil, but the pore pressure loss at the inner wall of the cylinder side compartment accounts for a higher percentage, and the pore pressure loss out of the cylinder wall of the middle compartment is also larger. The inner part of the foundation and the lower part of the foundation are primarily responsible for the seepage. The pore pressure loss is likewise concentrated in the overlying clay layer, particularly when the clay is overlying the sand layer, but there is no uniform seepage of water during the sinking test because the permeability coefficient in the clay layer is very low.

The pore water pressure at the bucket end of the foundation is essential for determining its resistance to sinking and penetration since it can be seen from the above figure that the pore pressure loss of the foundation exhibits an approximately linear variation from the soil surface to the bucket end.

Table 3. Summary of negative pressure losses.

Relative Penetration Depth	Sandy Soil			The Shallow Cover is Covered with Sand
	Outer End of Side Cabin	Inner End of Side Cabin	Mid-Cabin End	Outer End of Side Cabin	Inner End of Side Cabin	Mid-Cabin End
0.4	0.320	0.408	0.771	0.268	0.341	0.657
0.6	0.313	0.345	0.682	0.227	0.255	0.503
0.8	0.285	0.319	0.611	0.167	0.195	0.352
1.0	0.262	0.298	0.571	0.109	0.130	0.200

displays the extracted pore water pressure ratios for both the sand beneath the shallow overburden and the sand at the cylinder’s end. When the values at the side compartment ends were taken as the average of the compartments inside and outside the compartments, the relationship between the pore ratio and sinking penetration depth at the bucket side compartments and center compartment ends was fitted. The results of the fitting are as follows:

$$\begin{array}{l}{\alpha }_{OS}=0.416-0.14h^{\prime }\\ {\alpha }_{IS}=0.894-0.336h^{\prime }\\ {\alpha }_{OSR}=0.427-0.308h^{\prime }\\ {\alpha }_{ISR}=0.961-0.76h^{\prime }\end{array}$$

(3)

Among them, ${\alpha }_{OS}$ is the negative pressure loss at the end of the side tank in sandy soil, ${\alpha }_{IS}$ is the negative pressure loss at the end of the middle tank in the sand, ${\alpha }_{OSR}$ is the negative pressure loss at the end of the side tank in the sand covering the overlying layer, ${\alpha }_{ISR}$ is the negative pressure loss at the end of the middle tank in the sand covering the shallow cover, $h^{\prime }=h/H$ is based on the relative depth of penetration.

5. Soil Plug Analysis

In the sinking test study of MCCBF, the situation when foundation penetration is completed is shown in Figure 25. When the soil mass is pure sandy soil, an obvious soil plug phenomenon can be observed, and obvious sand subsidence can be seen on the outside of the foundation, and the subsidence is deeper at the location of the subdivision plate. When the sand layer is covered with clay, a certain height of the soil plug can also be observed, but the height of the soil plug is low. The soil plug effect is the most obvious in the shallow layer covered with sand, and the height of the soil plug is the highest, nearly twice that in the pure sand, while the soil plug in the shallow layer covered with clay is the smallest, and the top of the cylinder can sink to the surface of the cylinder top.

The soil plug height of Tank 7 and Tank 13 MCCBF under various geological conditions is calculated as shown in Figure 26. In the sandy soil covered by a shallow overlying layer, the soil plug height of Tank 13 foundation is significantly higher than that of Tank 7 foundation, while there is little difference between Tank 13 foundation and Tank 7 foundation in other geological conditions. The reason for this phenomenon is mainly the larger flow and higher velocity of Tank 13 foundation during penetration in the test. In the shallow permeable cover layer, the main reason for the formation of earth plug is the bottom–up seepage in the lower part of the soil mass, which is called the upwelling earth plug, and upwelling earth plug is mainly related to the seepage velocity of the soil mass at the bottom of the foundation.

Through the foundation penetration test, it can be considered that the soil plug height in the foundation is mainly composed of two parts: $h_{isp}$ is the initial soil plug generated by the foundation squeezing soil and $h_{ssp}$ is the suction plug generated during the suction penetration process:

$$h_{sp}=h_{isp}+h_{ssp}$$

(4)

The initial state of penetration of the MCCBF is that the bottom of the foundation just touches the mud surface and the cabin is filled with water, as shown in Figure 27a. At the completion stage of self-weight penetration, the foundation side wall and the subdivision plate are partially embedded in the soil, and part of the water inside the subdivision is replaced by the soil, as shown in Figure 27b. The consideration here is that under ideal conditions, the foundation subsidence has no inclination angle, the soil surface is relatively flat, and the sand gravel is evenly laid in the subdivision after entering the bucket. After foundation self-weight penetration, soil mass is extruded with the same volume as the subdivision plate and outer wall of the penetration cylinder, in which half of the soil mass in the outer wall can be considered to be extruded to the outside of the foundation and half into the subdivision, while the soil mass volume removed by the subdivision plate and the center column only remains in the subdivision, which forms an initial soil plug generated by soil extrusion. Its height can be calculated by Equation (5):

$$h_{isp}=\frac{1}{S_{up}}\left(\frac{1}{2}{V}_{\mathrm{wall}}+V_{\mathrm{panels}}+V_{\mathrm{column}}\right)$$

(5)

Subsequently, the water is pumped by the pump. In the process of suction sinking in the sand, the pore water outside the bucket flows into the bucket, and the sand gravel at the bottom and end of the bucket moves into the bucket, as shown in Figure 27c.

With the continuous occurrence of seepage, the sand on the outer wall of the cylinder gradually decreases, and when the penetration is completed, the soil outside the cylinder forms a depression near the wall, as shown in Figure 27d. For the external soil corresponding to the MCCBF subdivision plate, due to the seepage effect of the two tanks, the soil sag outside the subdivision plate becomes more obvious, as shown.

The suction soil plug $h_{ssp}$ in the sand is considered to be composed of two parts. One is formed by the movement of sand along the wall of the cylinder. Along the seepage channel at the side wall, sand rushes into the foundation to form the side wall soil plug $h_{sspo}$ which is also the main reason for the sand soil depression outside the foundation. Another type of earth plug, $h_{sspd}$, is thought to be formed by the upwelling of sand at the bottom caused by bottom-up water flow in the tank.

$$h_{ssp}=h_{sspo}+h_{sspd}$$

(6)

The formation of the side wall earth plug $h_{sspo}$ is mainly caused by the seepage carrying sand at the end, and it is believed that the amount of sand carrying is mainly proportional to the water head at the end of the cylinder:

$$h_{sspo}=\frac{A\pi D}{S_{\mathrm{top}}}(1-\alpha )P_s$$

(7)

Among them, A is a dimensionless coefficient and $\alpha$ is the head loss at the end of the cylinder. It can be calculated by the formula. $P_S$ is the difference of water head applied to the top of the cylinder during penetration; it is a function of penetration depth h. The unit is m. h_o is based on self-re-entry mud depth.

Upwelling plug $h_{sspd}$ is believed to be proportional to volume V_s of seepage pumping:

$$h_0\propto V_{sw}$$

(8)

In addition, seepage volume V_s can be

$$V_{sw}=v_{s}t$$

(9)

According to Darcy’s law, permeability velocity v_s is proportional to permeability coefficient k and the hydraulic gradient:

$$v_s=k\frac{dP}{dL}$$

(10)

Therefore, upwelling earth plug $h_{sspd}$ is

$$h_{sspd}=B{\displaystyle {\int }_{t_0}^t{v}_s}dt=B\frac{(1-\alpha )P_{s}k}{L}t$$

(11)

Among them, B is dimensionless coefficient, L is the length of the seepage path, k is the permeability coefficient of soil.

It should be noted that penetration head P_s here is a function of penetration depth h, and penetration depth h is a function of time t. The main reason for the consideration of the sample is that the flow rate of the pump is fixed, and with the gradual increase in the pressure difference in the foundation into the mud chamber, the penetration speed also increases first and then decreases. Therefore, this formula is derived on the assumption that the pump is always open during the installation process and the flow rate is certain (in the process of solving, the penetration path of pure sandy soil is taken as four times the penetration depth of 4 h, and the distance between the bottom of the cylinder and the shallow covering layer is taken as 200 h).

Based on the standard set of test soil plugs measured in sandy soil and sandy soil over shallow overlays, the coefficient is calculated as

A = 0.00159a
B = 1.176 × 10⁻⁶

(12)

For comparison of the calculated results of the fitting formula with the test results, see Figure 28. It can be seen that the fitted soil plug height is distributed around the measured height of the test, and the average error of all results is 14.68%, indicating that the fitting formula has a certain reliability.

In the clay overlying the shallow overlying layer, the formation of soil plugs is hardly observed, which is mainly due to the low permeability coefficient of the viscous soil, so the occurrence of seepage cannot be observed. At the same time, due to the high compressibility of the viscous soil, when the foundation penetration reaches the mud surface, the soil inside the foundation can be compressed under the action of the pressure difference at the top of the cylinder, so that the clay can be further compressed and consolidated.

6. Conclusions

In this chapter, the model test method is used to study the sinking and installation process of MCCBF in various geological conditions. The seepage characteristics of soil caused by suction subsidence are analyzed in combination with finite element software, the reasons for the formation of soil plugs are expounded, and the prediction formula of penetration resistance considering the influence of seepage is derived. The main conclusions are as follows:

(1)

The amount of water pumped when the foundation is immersed in sandy soil is higher than the volume of boiled water discharged during the foundation penetration process, and obvious seepage can be observed. However, in the clay and clay sand mixed geology, the volume of water extracted from foundation penetration is the same as that of water discharged during foundation penetration.

(2)

Soil plugs are formed in the process of penetration of MCCBF. After the completion of foundation penetration, the lower end of the foundation top cover is higher than the original mud surface and obvious depressions can be observed on the outside of the foundation side wall in the penetration of sandy soil and pure sandy soil on the shallow cover layer. Comparison of soil plug heights yields the following order: the sandy soil covered by a shallow cover layer > the pure sand and clay mixed layer > the clay covered by a shallow cover layer.

(3)

During sedimentation, the excess pore water pressure of the cylindrical foundation is mainly concentrated in the cylinder. In sand soil with strong permeability, the excess pore water outside the cylinder accounts for a relatively high proportion. However, when there is viscous soil with a low permeability coefficient in the surface soil, the pore pressure loss occurs in the cylinder.

This article analyzes the sinking and installation process of cylindrical foundation through a combination of experiments and finite element software, but there are also some problems that need to be solved. (1) The article takes the small-scale model test in the laboratory as the main research object, and cannot restore the stress level of the actual soil in the project. Therefore, the dilatation, shear contraction, and drainage characteristics of sand during the test loading process are different from those of the machine position in the project. There is a lack of quantitative analysis of the bearing and deformation characteristics of foundations under layered geology. If equipment allows, a centrifuge can be used for further research. (2) During the sinking process, it is difficult to control the pumping rate and air pressure in each cabin to be consistent, so the cylindrical foundation will tilt. In the future, it will be necessary to conduct further research on the leveling operation during the sinking process. (3) Due to the limitations of the test conditions, further analysis of the soil plugging situation in the overlying clay of the sand layer cannot be carried out, and the critical suction in the layered soil also needs to be studied.