Model Tests on the Penetration Resistance of Bucket Foundations for Offshore Wind Turbines in Sand

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, mainly owing to their efficient construction. However, the penetration resistance of the suction penetration of a bucket foundation, when calculated inaccurately, may lead to installation failure of the foundation. In this study, model tests were performed on the suction penetration of a mono-bucket mono-compartment foundation and a mono-bucket multi-compartment foundation in saturated fine marine sand, aiming to compare their penetration resistances and critical suctions, and the development of a soil plug in the two models was analyzed. The results will provide a design reference for the penetration construction of bucket foundations for offshore wind turbines.


Introduction
The foundations for offshore wind turbines include mono-piles, jacket piles, bucket foundations, and floating foundations [1][2][3][4]. Among them, bucket foundations have been used extensively in wind farms worldwide owing to their apparent advantages, such as convenient installation, low construction cost, and high recyclability. In 1994, Europipe 16/11-E offshore platform was successfully installed using a bucket foundation for the first time on a jacket platform in Norway [5]. In 2002, the first 3 MW wind turbine prototype with a bucket foundation, 12 m in diameter and 6 m in height, was erected in the test field of the Frederikshavn wind farm in Denmark [6]. Three years later, another 6 MW wind turbine prototype with a bucket foundation was mounted again in Denmark [7]. In the same year, in Germany, a 6 MW offshore wind turbine was designed with a suction bucket foundation [7,8]. The whole structure was made of steel and designed with bulkheads at the top of the head cover, making it possible to increase weight through filling. The bucket wall at the bottom was used for suction penetration. In 2010, researchers at Tianjin University [9][10][11][12][13] developed a novel foundation for offshore wind turbines, i.e., the large-scale composite bucket foundation based on the traditional bucket foundations. Next, the test prototype was prepared, and construction completed in the sea area near Qidong, Jiangsu Province, followed by one-step installation. By 2019, the composite bucket foundation was successfully applied to the 3.3 MW and 6.45 MW offshore wind turbines of the Jiangsu Dafeng offshore wind farm [14]. Figure 1 shows the transportation of the CBF. Suction penetration is an important process during the installation of a bucket foundation, and it is driven by the difference pressure inside and outside the bucket [16,17]. The water and air in the bucket are pumped out using a vacuum pump to reduce the internal pressure to negative, thus creating a pressure difference between the inside and outside. When the pressure difference exceeds the penetration resistance, the foundation is slowly pressed into the sand. After installation, the penetration position of the foundation must meet predetermined requirements, such as its bearing capacity should reach the design value [18,19]. In the penetration process, soil plug and seepage failure are the main causes of installation failure. When the suction during construction is too large, the bucket experiences soil plug, or even seepage failure, inside; when it is insufficient, the foundation fails to penetrate [20,21]. For this reason, reasonable control of suction application has always been a core issue in this field, and the accurate prediction of penetration resistance is critical for the success of bucket foundations. In marine sand, the critical suction is the maximum suction during construction, beyond which it is susceptible to seepage failure. Existing studies mainly focus on the critical suction of the mono-compartment bucket foundation [22][23][24][25][26], but rarely pay attention to that of the multi-compartment bucket foundation. In fact, due to the use of inner skirt plates and bulkheads in the bucket, the seepage field of sand during penetration is different in the case of the multi-compartment bucket foundation, and the position where sand experiences initial seepage failure is also unclear. Thus, based on the research on the penetration of the composite bucket foundation [27][28][29][30][31], this study further compared the penetration resistance of the mono-compartment bucket foundation and the multi-compartment bucket foundation in sand. In addition, a formula was proposed for calculating the maximum critical suction of the multi-compartment bucket foundation during penetration into sand, thus offering some reference for practical engineering.

Test Model and Test Procedures
The test used two models, i.e., mono-compartment bucket foundation (Model 1) and multicompartment bucket foundation (Model 2). They are wide-shallow foundations, with the aspect ratio of 0.4, and their dimensions are listed in Table 1. The scale of the test model to the prototype is 1: 100. Suction penetration is an important process during the installation of a bucket foundation, and it is driven by the difference pressure inside and outside the bucket [15,16]. The water and air in the bucket are pumped out using a vacuum pump to reduce the internal pressure to negative, thus creating a pressure difference between the inside and outside. When the pressure difference exceeds the penetration resistance, the foundation is slowly pressed into the sand. After installation, the penetration position of the foundation must meet predetermined requirements, such as its bearing capacity should reach the design value [17,18]. In the penetration process, soil plug and seepage failure are the main causes of installation failure. When the suction during construction is too large, the bucket experiences soil plug, or even seepage failure, inside; when it is insufficient, the foundation fails to penetrate [19,20]. For this reason, reasonable control of suction application has always been a core issue in this field, and the accurate prediction of penetration resistance is critical for the success of bucket foundations. In marine sand, the critical suction is the maximum suction during construction, beyond which it is susceptible to seepage failure. Existing studies mainly focus on the critical suction of the mono-compartment bucket foundation [21][22][23][24][25], but rarely pay attention to that of the multi-compartment bucket foundation. In fact, due to the use of inner skirt plates and bulkheads in the bucket, the seepage field of sand during penetration is different in the case of the multi-compartment bucket foundation, and the position where sand experiences initial seepage failure is also unclear. Thus, based on the research on the penetration of the composite bucket foundation [26][27][28][29][30], this study further compared the penetration resistance of the mono-compartment bucket foundation and the multi-compartment bucket foundation in sand. In addition, a formula was proposed for calculating the maximum critical suction of the multi-compartment bucket foundation during penetration into sand, thus offering some reference for practical engineering.

Test Model and Test Procedures
The test used two models, i.e., mono-compartment bucket foundation (Model 1) and multicompartment bucket foundation (Model 2). They are wide-shallow foundations, with the aspect ratio of 0.4, and their dimensions are listed in Table 1. The scale of the test model to the prototype is 1:100.
The test models used a steel bucket wall and a plexiglass lid connected to flanges to guarantee the sealing performance of foundations in the penetration process. In the case of the mono-compartment bucket foundation, the top lid is cut with two openings, one used for connecting to the vacuum pump and the other for connecting to the negative-pressure sensor, as shown in Figure 2a. The multi-compartment bucket foundation is divided into seven compartments by inner skirt plates and bulkheads, as shown in Figure 2c. The lid of each compartment also has two connection holes, one used for connecting to the vacuum pump and the other for connecting to the negative-pressure sensor. In the picture, t and t 1 refer to the thickness of the bucket skirt and the bulkhead, t 2 refers to the thickness of the top lid of the model, D so and D mo refer to width of the side compartments and the central compartment respectively. The suction of each compartment can be independently controlled to level the foundation. The test models used a steel bucket wall and a plexiglass lid connected to flanges to guarantee the sealing performance of foundations in the penetration process. In the case of the monocompartment bucket foundation, the top lid is cut with two openings, one used for connecting to the vacuum pump and the other for connecting to the negative-pressure sensor, as shown in Figure 2a. The multi-compartment bucket foundation is divided into seven compartments by inner skirt plates and bulkheads, as shown in Figure 2c. The lid of each compartment also has two connection holes, one used for connecting to the vacuum pump and the other for connecting to the negative-pressure sensor. In the picture, t and t1 refer to the thickness of the bucket skirt and the bulkhead, t2 refers to the thickness of the top lid of the model, Dso and Dmo refer to width of the side compartments and the central compartment respectively. The suction of each compartment can be independently controlled to level the foundation.   Figure 3 shows the sand penetration test system, whose pumping system provides suction for the multi-compartment bucket foundation and guarantees the stability of negative pressure applied in each stage.  Figure 3 shows the sand penetration test system, whose pumping system provides suction for the multi-compartment bucket foundation and guarantees the stability of negative pressure applied in each stage.

Sand Preparation
The sand used in this test was collected from the Bohai Bay, Tianjin. Figure 4 shows the particle size distribution curve of sand obtained using the laboratory soil test, and Table 2 lists the physical and mechanical parameters of the sand. The sand had a coefficient of non-uniformity of Cu = 2.9. According to the sand classification criteria, the content of the grains with a diameter of greater than 0.25 mm did not exceed 50% of total weight, and the content of grains with a diameter greater than 0.075 mm exceeded 85%. Fine sand was used in this test and, after the completion of the test under each working condition, the sand was vibrated to guarantee the same density.

Test Process and Test Conditions
The penetration of the mono-compartment/multi-compartment bucket foundation comprises two stages. In the first stage, the vent holes on the head cover were opened, and the model penetrated stably under self-weight. In the second stage, the vacuum pump and the water-air displacements were loaded in steps, i.e., stepwise penetration: first, the valve between the foundation and the waterair displacements were closed, and the air in the water-air displacement was pumped out using a vacuum pump, so that the suction pressure of the water-air displacement would reach the preset

Sand Preparation
The sand used in this test was collected from the Bohai Bay, Tianjin. Figure 4 shows the particle size distribution curve of sand obtained using the laboratory soil test, and Table 2 lists the physical and mechanical parameters of the sand. The sand had a coefficient of non-uniformity of C u = 2.9. According to the sand classification criteria, the content of the grains with a diameter of greater than 0.25 mm did not exceed 50% of total weight, and the content of grains with a diameter greater than 0.075 mm exceeded 85%. Fine sand was used in this test and, after the completion of the test under each working condition, the sand was vibrated to guarantee the same density.

Sand Preparation
The sand used in this test was collected from the Bohai Bay, Tianjin. Figure 4 shows the particle size distribution curve of sand obtained using the laboratory soil test, and Table 2 lists the physical and mechanical parameters of the sand. The sand had a coefficient of non-uniformity of Cu = 2.9. According to the sand classification criteria, the content of the grains with a diameter of greater than 0.25 mm did not exceed 50% of total weight, and the content of grains with a diameter greater than 0.075 mm exceeded 85%. Fine sand was used in this test and, after the completion of the test under each working condition, the sand was vibrated to guarantee the same density.

Test Process and Test Conditions
The penetration of the mono-compartment/multi-compartment bucket foundation comprises two stages. In the first stage, the vent holes on the head cover were opened, and the model penetrated stably under self-weight. In the second stage, the vacuum pump and the water-air displacements were loaded in steps, i.e., stepwise penetration: first, the valve between the foundation and the waterair displacements were closed, and the air in the water-air displacement was pumped out using a vacuum pump, so that the suction pressure of the water-air displacement would reach the preset

Test Process and Test Conditions
The penetration of the mono-compartment/multi-compartment bucket foundation comprises two stages. In the first stage, the vent holes on the head cover were opened, and the model penetrated stably under self-weight. In the second stage, the vacuum pump and the water-air displacements were loaded in steps, i.e., stepwise penetration: first, the valve between the foundation and the water-air displacements were closed, and the air in the water-air displacement was pumped out using a vacuum pump, so that the suction pressure of the water-air displacement would reach the preset level. After that, the valve of the water-air displacement connected to the model was gradually opened to slowly form a steady negative pressure inside the foundation. When the model began to penetrate stably under a stable suction, the pipeline regulation valve was closed, after which the suction soon disappeared. Following that, the above steps were repeated to apply stable suction for the next stage until the model penetrated in place. The test adopted three-step negative pressure loading and six-step negative pressure loading, and ultimately penetrated to a depth equal to the bucket height. In the test process, the angle of inclination of the foundation was controlled to a maximum of 0.17 • which can be monitored by the inclinometer, and this angle is used in the industrial project. Figure 5 shows the layout of the sensors in the test, and Table 3 lists the test conditions of this study. level. After that, the valve of the water-air displacement connected to the model was gradually opened to slowly form a steady negative pressure inside the foundation. When the model began to penetrate stably under a stable suction, the pipeline regulation valve was closed, after which the suction soon disappeared. Following that, the above steps were repeated to apply stable suction for the next stage until the model penetrated in place. The test adopted three-step negative pressure loading and six-step negative pressure loading, and ultimately penetrated to a depth equal to the bucket height. In the test process, the angle of inclination of the foundation was controlled to a maximum of 0.17° which can be monitored by the inclinometer, and this angle is used in the industrial project. Figure 5 shows the layout of the sensors in the test, and Table 3

Effect of the Mode of Suction Application on Penetration Resistance
Figures 6 and 7 show the variation curves of suction and displacement with time in the penetration process of the mono-compartment bucket foundation. The water level on the saturated sand was low. In foundation penetration, there was air in the bucket, so pumping out the air would create a negative pressure inside. In that case, suction was the pressure difference inside and outside the bucket, and the sum of the suction and foundation self-weight was the driving force required by foundation penetration. Regarding the relationship curve between the displacement and time, the xcoordinate denotes the time of suction penetration, while the y-coordinate denotes the penetration displacement of the foundation. The curve only illustrates the suction penetration process. Given that the foundation penetrated to 15 mm under self-weight, suction penetration had an initial displacement of 15 mm. As shown in Figures 8 and 9, PS1-1 and PS1-2 adopted three-step and sixstep loading, respectively, and penetration suction increased stepwise. The suction of each step was maintained at a relatively stable state until the displacement of the foundation would no longer increase. After that, suction was increased to carry on foundation penetration. Ultimately, the  Table 3. Contents of penetration test in sand.

Test Number
Foundation Type Multi-compartment bucket foundation PS2-2

Effect of the Mode of Suction Application on Penetration Resistance
Figures 6 and 7 show the variation curves of suction and displacement with time in the penetration process of the mono-compartment bucket foundation. The water level on the saturated sand was low. In foundation penetration, there was air in the bucket, so pumping out the air would create a negative pressure inside. In that case, suction was the pressure difference inside and outside the bucket, and the sum of the suction and foundation self-weight was the driving force required by foundation penetration. Regarding the relationship curve between the displacement and time, the x-coordinate denotes the time of suction penetration, while the y-coordinate denotes the penetration displacement of the foundation. The curve only illustrates the suction penetration process. Given that the foundation penetrated to 15 mm under self-weight, suction penetration had an initial displacement of 15 mm. As shown in Figures 8 and 9, PS1-1 and PS1-2 adopted three-step and six-step loading, respectively, and penetration suction increased stepwise. The suction of each step was maintained at a relatively stable state until the displacement of the foundation would no longer increase. After that, suction was increased to carry on foundation penetration. Ultimately, the foundation penetrated to approximately −110 mm, and the final suction required by penetration was uniformly approximately −2.5 kPa.  As indicated by a comparison between the mono-compartment and multi-compartment bucket foundations in terms of their penetration processes, the penetration methods uniformly adopted stepwise loading, with small penetration suction in each case. Ultimately, they had the same penetration depth, with the same soil plug height of 10 mm, as shown in Figure 10. In the end, neither of them could fully penetrate into the soil. In the case of the mono-compartment bucket foundation   Figure 9b contain the self-weight penetration process of the foundation. With increasing suction applied to a foundation, the penetration depth of the foundation increased as well. Ultimately the foundation penetrated to approximately −110 mm, in which case the internal pressure of the compartment was roughly −4 kPa.
As indicated by a comparison between the mono-compartment and multi-compartment bucket foundations in terms of their penetration processes, the penetration methods uniformly adopted stepwise loading, with small penetration suction in each case. Ultimately, they had the same penetration depth, with the same soil plug height of 10 mm, as shown in Figure 10. In the end, neither of them could fully penetrate into the soil. In the case of the mono-compartment bucket foundation the soil plug heights were consistent, and the soil plug heights in the middle and on the sides of the bucket were almost the same. In the case of the multi-compartment bucket foundation, the side compartments and the central compartment had different soil plug heights. The side compartments underwent more serious soil plug and had a larger soil plug height than that of the central compartment, probably because of the two reasons. First, the side compartments had a smaller cross-sectional area and soil dilatancy is more obvious. Second, under the action of penetration suction, the sand at the bottom of the bucket wall had a larger hydraulic gradient, and the sand would flow across the bucket wall into the bucket. As indicated by a comparison between the mono-compartment and multi-compartment bucket foundations in terms of their penetration processes, the penetration methods uniformly adopted stepwise loading, with small penetration suction in each case. Ultimately, they had the same penetration depth, with the same soil plug height of 10 mm, as shown in Figure 10. In the end, neither of them could fully penetrate into the soil. In the case of the mono-compartment bucket foundation the soil plug heights were consistent, and the soil plug heights in the middle and on the sides of the bucket were almost the same. In the case of the multi-compartment bucket foundation, the side compartments and the central compartment had different soil plug heights. The side compartments underwent more serious soil plug and had a larger soil plug height than that of the central compartment, probably because of the two reasons. First, the side compartments had a smaller crosssectional area and soil dilatancy is more obvious. Second, under the action of penetration suction, the sand at the bottom of the bucket wall had a larger hydraulic gradient, and the sand would flow across the bucket wall into the bucket.

Effects of Inner Skirt Plates and Bulkheads on Penetration Resistance
The penetration resistance of the mono-compartment and multi-compartment bucket foundations were compared under the same texture condition to analyze the effects of inner skirt plates and bulkheads on the penetration resistance of foundations. To prevent analysis results from being affected by the foundation dimensions, analysis variables were nondimensionalized. Figure 11 compares the relationship curves between the penetration depth and applied suction for the mono-compartment and multi-compartment bucket foundations, where the transverse axis

Effects of Inner Skirt Plates and Bulkheads on Penetration Resistance
The penetration resistance of the mono-compartment and multi-compartment bucket foundations were compared under the same texture condition to analyze the effects of inner skirt plates and bulkheads on the penetration resistance of foundations. To prevent analysis results from being affected by the foundation dimensions, analysis variables were nondimensionalized. Figure 11 compares the relationship curves between the penetration depth and applied suction for the mono-compartment and multi-compartment bucket foundations, where the transverse axis denotes dimensionless suction, and the longitudinal axis denotes dimensionless penetration depth. In Figure 11, h is the penetration depth of the foundation, D is the inner diameter of the bucket, D 0 is the outer diameter, D = (D i + D o )/2; γ is the effective unit weight of sand, and s is the penetration suction is denoted by s. Apparently, the penetration suction of the mono-compartment bucket foundation was smaller than that of the mono-bucket multi-compartment foundation. denotes dimensionless suction, and the longitudinal axis denotes dimensionless penetration depth. In Figure 11, h is the penetration depth of the foundation, D is the inner diameter of the bucket, D0 is the outer diameter, ; γ ′ is the effective unit weight of sand, and s is the penetration suction is denoted by s. Apparently, the penetration suction of the mono-compartment bucket foundation was smaller than that of the mono-bucket multi-compartment foundation. The penetration resistance of a foundation is the sum of the penetration suction and the selfweight of the foundation. In this study, the penetration resistances of the mono-compartment and multi-compartment bucket foundations were calculated and nondimensionalized, thus acquiring the penetration resistance differences between the two foundations at different penetration depths, as shown in Figure 12. Figure 12a shows the penetration resistances of PS1-1 and PS2-1 and their penetration resistance difference; Figure 12b shows the penetration resistances of PS1-2 and PS2-2 and their penetration resistance difference. In Figure 12, the transverse axis denotes the dimensionless penetration resistance (where cross A is the cross-sectional area of the bucket foundation), while the longitudinal axis denotes the ratio of the penetration depth to the foundation diameter.
As shown in Figure 12, the penetration resistance of the mono-compartment bucket foundation was less than that of the multi-compartment bucket foundation. In the initial stage of suction penetration, the penetration resistance difference between the two foundations was small-with increasing penetration depth, it increased as well. The reason for this was that, in the initial stage of foundation penetration, the penetration depth was small, and the side frictions of the inner skirt plates and bulkheads were low, resulting in a small penetration resistance difference between the two foundations. However, with increasing penetration depth, the side frictions of the inner skirt plates and bulkheads gradually increased as well, further enlarging the penetration resistance difference.  The penetration resistance of a foundation is the sum of the penetration suction and the self-weight of the foundation. In this study, the penetration resistances of the mono-compartment and multi-compartment bucket foundations were calculated and nondimensionalized, thus acquiring the penetration resistance differences between the two foundations at different penetration depths, as shown in Figure 12. Figure 12a shows the penetration resistances of PS1-1 and PS2-1 and their penetration resistance difference; Figure 12b shows the penetration resistances of PS1-2 and PS2-2 and their penetration resistance difference. In Figure 12, the transverse axis denotes the dimensionless penetration resistance (where A cross is the cross-sectional area of the bucket foundation), while the longitudinal axis denotes the ratio of the penetration depth to the foundation diameter. The penetration resistance of a foundation is the sum of the penetration suction and the selfweight of the foundation. In this study, the penetration resistances of the mono-compartment and multi-compartment bucket foundations were calculated and nondimensionalized, thus acquiring the penetration resistance differences between the two foundations at different penetration depths, as shown in Figure 12. Figure 12a shows the penetration resistances of PS1-1 and PS2-1 and their penetration resistance difference; Figure 12b shows the penetration resistances of PS1-2 and PS2-2 and their penetration resistance difference. In Figure 12, the transverse axis denotes the dimensionless penetration resistance (where cross A is the cross-sectional area of the bucket foundation), while the longitudinal axis denotes the ratio of the penetration depth to the foundation diameter.
As shown in Figure 12, the penetration resistance of the mono-compartment bucket foundation was less than that of the multi-compartment bucket foundation. In the initial stage of suction penetration, the penetration resistance difference between the two foundations was small-with increasing penetration depth, it increased as well. The reason for this was that, in the initial stage of foundation penetration, the penetration depth was small, and the side frictions of the inner skirt plates and bulkheads were low, resulting in a small penetration resistance difference between the two foundations. However, with increasing penetration depth, the side frictions of the inner skirt plates and bulkheads gradually increased as well, further enlarging the penetration resistance difference.  As shown in Figure 12, the penetration resistance of the mono-compartment bucket foundation was less than that of the multi-compartment bucket foundation. In the initial stage of suction penetration, the penetration resistance difference between the two foundations was small-with increasing penetration depth, it increased as well. The reason for this was that, in the initial stage of foundation penetration, the penetration depth was small, and the side frictions of the inner skirt plates and bulkheads were low, resulting in a small penetration resistance difference between the two foundations. However, with increasing penetration depth, the side frictions of the inner skirt plates and bulkheads gradually increased as well, further enlarging the penetration resistance difference.

Verification of the Critical Suction in the Penetration Process of the Mono-Compartment Bucket Foundation
At present, there are already some mature models for calculating the critical suction in the penetration process of the traditional mono-compartment bucket foundation. Thus, the first step is to deduce a model for calculating the critical suction of the mono-compartment bucket foundation and then compare it with the existing calculation models [26].
The relationship between the hydraulic gradient i, suction s, and seepage path l can be expressed as follows: When hydraulic gradient i reaches the following critical gradient, sand experiences seepage failure, in which case the critical suction s rcit is represented by the following formula.
The site experiencing seepage failure first was the mud surface on the inner side of bucket wall, i.e., the hydraulic outlet adjoining the bucket wall. The above formula was used to deduce the dimensionless relationship between the seepage path and penetration depth, as shown in Figure 13. Next, the seepage path obtained can be substituted into Formula (3) to acquire the relationship between the critical suction and penetration depth, as shown in Figure 14.
At present, there are already some mature models for calculating the critical suction in the penetration process of the traditional mono-compartment bucket foundation. Thus, the first step is to deduce a model for calculating the critical suction of the mono-compartment bucket foundation and then compare it with the existing calculation models [27].
The relationship between the hydraulic gradient i, suction s, and seepage path l can be expressed as follows: When hydraulic gradient i reaches the following critical gradient, sand experiences seepage failure, in which case the critical suction rcit s is represented by the following formula.
The site experiencing seepage failure first was the mud surface on the inner side of bucket wall, i.e., the hydraulic outlet adjoining the bucket wall. The above formula was used to deduce the dimensionless relationship between the seepage path and penetration depth, as shown in Figure 13. Next, the seepage path obtained can be substituted into Formula (3) to acquire the relationship between the critical suction and penetration depth, as shown in Figure 14.
This study mainly focused on the wide-shallow bucket foundations; therefore, the range of h/D was confined to 0-0.4 in this study. The results of the seepage path and critical suction calculated in this study were compared to the values calculated by Randolph and Feld's formulas [26,27]. As shown in Figure 13, the seepage paths obtained by the three methods were very close. In Figure 14, the critical suction calculated in this study fitted well with the value calculated by Randolph's formula [26].

Critical Suction in the Penetration Process of the Multi-Compartment Bucket Foundation
The seepage path and critical suction for the multi-compartment bucket foundation were calculated by the same method as used for the mono-compartment bucket foundation. Due to the use of inner skirt plates and bulkheads, the multi-compartment bucket foundation had three hydraulic outlets, i.e., G, F, and H, as shown in Figure 15. Each of the above three outlets was in turn taken as the point experiencing seepage failure first to calculate the seepage path and critical suction, as shown in Figures 15 and 16. The result indicates that the hydraulic outlet G had the shortest seepage path and the smallest critical suction. As a result, with increasing penetration suction, point G would be This study mainly focused on the wide-shallow bucket foundations; therefore, the range of h/D was confined to 0-0.4 in this study. The results of the seepage path and critical suction calculated in this study were compared to the values calculated by Randolph and Feld's formulas [25,26]. As shown in Figure 13, the seepage paths obtained by the three methods were very close. In Figure 14, the critical suction calculated in this study fitted well with the value calculated by Randolph's formula [25].

Critical Suction in the Penetration Process of the Multi-Compartment Bucket Foundation
The seepage path and critical suction for the multi-compartment bucket foundation were calculated by the same method as used for the mono-compartment bucket foundation. Due to the use of inner skirt plates and bulkheads, the multi-compartment bucket foundation had three hydraulic outlets, i.e., G, F, and H, as shown in Figure 15. Each of the above three outlets was in turn taken as the point experiencing seepage failure first to calculate the seepage path and critical suction, as shown in Figures 15 and 16. The result indicates that the hydraulic outlet G had the shortest seepage path and the smallest critical suction. As a result, with increasing penetration suction, point G would be most susceptible to seepage failure; therefore, the critical suction at hydraulic outlet G should be adopted as the control criterion on the maximum suction for mono-bucket multi-compartment foundation. Through curve fitting based on these points, the dimensionless functional relationship between the critical suction and penetration depth was obtained, as shown by Equation (4): The seepage path and critical suction for the multi-compartment bucket foundation were calculated by the same method as used for the mono-compartment bucket foundation. Due to the use of inner skirt plates and bulkheads, the multi-compartment bucket foundation had three hydraulic outlets, i.e., G, F, and H, as shown in Figure 15. Each of the above three outlets was in turn taken as the point experiencing seepage failure first to calculate the seepage path and critical suction, as shown in Figures 15 and 16. The result indicates that the hydraulic outlet G had the shortest seepage path and the smallest critical suction. As a result, with increasing penetration suction, point G would be most susceptible to seepage failure; therefore, the critical suction at hydraulic outlet G should be adopted as the control criterion on the maximum suction for mono-bucket multi-compartment foundation. Through curve fitting based on these points, the dimensionless functional relationship between the critical suction and penetration depth was obtained, as shown by Equation (4): The critical suction calculated by the formula and the suction actually applied in the test was compared, as shown in Figure 17. Clearly, the suction actually applied in the test was always less than the critical suction, except in the initial stage of PS2-2 (where it was greater than the critical suction due to improper suction control). No seepage failure occurred in the test process, and this result was consistent with our observation.    The critical suction calculated by the formula and the suction actually applied in the test was compared, as shown in Figure 17. Clearly, the suction actually applied in the test was always less than the critical suction, except in the initial stage of PS2-2 (where it was greater than the critical suction due to improper suction control). No seepage failure occurred in the test process, and this result was consistent with our observation.

Conclusions
In conclusion, a model test was designed and successfully applied to the suction penetration of a mono-compartment bucket foundation and a multi-compartment bucket foundation in sand to investigate the effects of inner skirt plates and bulkheads on the penetration resistance of the multicompartment bucket foundation. The test results indicate that the penetration resistance of the monocompartment bucket foundation was clearly less than that of the mono-bucket multi-compartment foundation. In the initial stage of the suction penetration, the penetration resistance difference between the two foundations was small. Later, the increase in the penetration depth increased the penetration resistance difference.
In the penetration process, both of them experienced soil plug. Specifically, the monocompartment bucket foundation exhibited consistent soil plug heights. The multi-compartment bucket foundation had different soil plug heights on the side compartments and the central compartment.
The side compartments underwent more serious soil plug and had a larger soil plug height than that of the central compartment. In addition, in the course of foundation penetration, the soil surface on the inner side of the bucket wall was the hydraulic outlet most susceptible to seepage failure, or the site experiencing seepage failure first. Taking this as the criterion for judging the occurrence of sand seepage failure, the critical suction in the penetration process of the multi-compartment bucket foundation was analyzed.

Conclusions
In conclusion, a model test was designed and successfully applied to the suction penetration of a mono-compartment bucket foundation and a multi-compartment bucket foundation in sand to investigate the effects of inner skirt plates and bulkheads on the penetration resistance of the multi-compartment bucket foundation. The test results indicate that the penetration resistance of the mono-compartment bucket foundation was clearly less than that of the mono-bucket multi-compartment foundation. In the initial stage of the suction penetration, the penetration resistance difference between the two foundations was small. Later, the increase in the penetration depth increased the penetration resistance difference.
In the penetration process, both of them experienced soil plug. Specifically, the mono-compartment bucket foundation exhibited consistent soil plug heights. The multi-compartment bucket foundation had different soil plug heights on the side compartments and the central compartment.
The side compartments underwent more serious soil plug and had a larger soil plug height than that of the central compartment. In addition, in the course of foundation penetration, the soil surface on the inner side of the bucket wall was the hydraulic outlet most susceptible to seepage failure, or the site experiencing seepage failure first. Taking this as the criterion for judging the occurrence of sand seepage failure, the critical suction in the penetration process of the multi-compartment bucket foundation was analyzed.