Experimental Study on Static Pressure Sedimentation for a Thick-Walled Bucket Foundation in Sand

Abstract

As an emerging foundation structure for offshore wind turbines, bucket foundations with superior bearing capacities and efficient construction procedures have attracted significant attention in China. Thick-walled bucket foundations with concrete skirts can effectively reduce the cost and prevent the buckling problem of steel skirts during construction, transportation, and installation. However, great challenges are encountered during the sinking process, and the accurate calculation of sinking resistance is a critical process. Static-pressure tests of thin-walled and thick-walled models in sand were performed to measure the penetration resistance and soil pressure at the sidewalls and ends. The horizontal-soil-pressure coefficients of different models were calculated, and the end and skin-friction coefficients in the cone-penetration test method are recommended. The drag-reduction effects of the anti-drag ring and pressure-pull-out loading method were examined, and the drag-reduction effect was evident for the bucket foundation. The drag-reduction effect of the pressure-pull-out loading method is mainly reflected in the end zone.

1. Introduction

Offshore wind power is characterized by high wind speeds, low turbidity, less land occupancy, and a large installed capacity. The installed capacity of global offshore wind power is increasing each year, and China’s offshore wind power is rapidly developing. In 2020, China’s new offshore wind installed capacity accounted for 50% of the world’s capacity, and by 2020, the cumulative installed capacity accounted for 28% of the world’s capacity.

China is rich in offshore wind-energy resources. The potential installed capacity within a 5–50-m water depth is approximately 500 GW. By 2050, the installed capacity of offshore wind power in China will reach 150 GW [1,2]. At present, the basic structural forms of offshore foundations mainly include gravity, piles, tripods, jackets, and floating foundations, which are suitable for different water depths [3,4,5]. Bucket foundations (Figure 1) are a new type of foundation structure proposed by Tianjin University based on the characteristics of China’s offshore and soft-clay foundations [6,7]. They can provide good anti-overturning bearing capacity [8,9], have the advantages of high construction efficiency and low construction cost, and have been successfully applied in practical projects [10,11,12]. The sinking of a bucket foundation is divided into two processes: the weight penetration and negative penetration stages. The weight penetration depth greatly affects the critical negative pressure in the negative penetration stage, so it is important to accurately calculate the depth in the weight penetration stage.

Lian [13] performed a series of laboratory tests to study the mechanisms of the interactions between a model and saturated sand during static and negative-pressure sedimentations and evaluated and revised previous formulas for calculating the penetration resistance and required suction. Tran [14,15,16] studied the characteristics of bucket foundations when they subsided in sandy soil and layered soil, described the formation process of plugs, and revealed the influence of different levels of negative pressure on foundation penetration. Zhu [17] studied the penetration and pull-out resistance in silty soil using large-scale bucket-foundation-model tests. Houlsby [18] established the penetration-resistance formula in clay and verified it through on-site measurements. Cao [19] studied the static and negative penetrations of bucket foundations in clay through a centrifuge test and recommended the value of the friction coefficient based on undrained shear-strength side-resistance calculations. Lian [20], Liu [21,22], Chen [23], Andersen [24], and Doherty [25] studied the penetration resistance of bucket foundations in different soil properties and presented the values of coefficients based on a cone-penetration test (CPT). Usually, $k_p$ is 0.5 and $k_f$ is 0.03 for silty clay. For sand and silt, $k_p$ is 1.8 and $k_f$ is 0.003, respectively. In engineering, the formulas for calculating the penetration resistance of the American Petroleum Institute [26] and the DET Norske Veritas [27] are commonly used. Wei [28] studied the drag-reduction effect and mechanism of the pressure-pull-out loading method, which means pulling upward for a displacement and then pressing down again when the penetration resistance becomes large. Existing results show that seepage failure is more likely to occur in sand than in clay, and it cannot provide sufficient pressure for the penetration of the foundation.

With the increase in the water depth and the development of large-scale wind turbines, the weight and size of bucket foundations will be further enlarged. As a result, thin-walled steel skirts begin to buckle easily and become unstable in the onshore prefabrication process. Therefore, adopting thick-walled skirts is a direction for future development. To reduce the construction pressure of sinking, skirts and inner stiffeners are welded with 25 mm steel. The accurate calculation of penetration resistance is the key to the application of bucket foundations.

However, comparing the sinking process of thin-walled and thick-walled bucket foundations with existing test models of different scales of bucket foundations is difficult. Therefore, this study performed a full-size, local model test on thin-walled and thick-walled bucket foundations in sand during static-pressure sedimentation, measured the lateral and end soil pressure, and explored the applicability of existing resistance calculation formulas for bucket foundations. At the same time, the drag-reduction effect of the pressure-pull-out loading method for thin-walled and thick-walled test models was examined.

2. Model Tests

2.1. Model Design and Sensor-Acquisition System

The concept presented in this study aims to determine the penetration resistance of thick-walled and thin-walled bucket foundations. For this purpose, a more considerate scale of the test model, especially for the skirt thickness, should be taken into consideration. The diameter of a bucket foundation is usually large, i.e., 30–36 m, and the height is 10–12 m. If the scale is strictly modeled, as can be seen in

Table 1. Size comparison between the prototype and the test model.

Prototype Diameter (Height)/m	Prototype Skirt Thickness/m	Scale	Model Diameter (Height)/cm	Model Skirt Thickness/cm
30–10	0.025	1:30	100–33.3	0.083
30–10	0.3	1:30	100–33.3	1
30–10	0.025	1:20	150–50	0.125
30–10	0.3	1:20	150–50	1.5

, the thickness of the thin-walled bucket skirt is approximately 0.8 mm in the small-scale test, which may raise the possibilities of manufacturing difficulties and buckling failures under static-pressure test conditions.

However, the projection-area ratio of the skirt to the top cover is 0.33–0.28% for a thin-walled bucket foundation and 4–3.33% for a thick-walled bucket foundation. The compaction effect is weak, and the foundation inclination is strictly controlled under 3‰ (that is 0.17°) through the leveling system in the process of sinking, so as to avoid the change of penetration resistance caused by the incline. Therefore, this study takes the arc length corresponding to a central angle of 2° and approximates it as a line segment with a length of approximately 0.6 m for a bucket foundation with a diameter between 30 m and 36 m (Figure 2). Making such a simplification allows the bucket-skirt thickness to be consistent with the prototype, thus making clear the difference between thick-walled and thin-walled bucket foundations.

The height of the model was set to 1.7 m according to the test-site conditions. The thickness of the steel thin-walled model was 25 mm, denoted as BB25. The thicknesses of the thick-walled model were 30 and 40 cm, denoted as HB30 and HB40, respectively. An embedded soil-pressure sensor on the model was used at the bottom and along the upper side of the length to measure the soil pressure during the sinking process. The sensor of the thin-walled model adopts surface grooves, whereas the thick-walled model adopts an internally embedded pipeline.

The sensor and data-acquisition system are shown in Figure 3. The size of the soil-pressure gauge is 16 mm in diameter and 6 mm in height. The pore-pressure gauge is 18 mm in diameter and 14 mm in height. The connection mode of the sensor is full bridge. The data-acquisition system is a WKD3840 Dynamic and Static Signal Test System Host (made by Weekend Measurement and Control Equipment Technology Co., Ltd., Tianjin, China).

2.2. Equipment and Method

As shown in Figure 4, the test-loading system is composed of the steel structure of the reaction beam, mobile girder, mobile platform, and hydraulic cylinder. The mobile girder and platform move together to make the hydraulic cylinder reach any point in the test site. The maximum pressure of the hydraulic cylinder is 25 t, and the maximum tension is 20 t, which is used for the downward and upward pulling of the model. The rated stroke of the hydraulic cylinder is 1 m, and the depth of pressing can be increased to 2.2 m with the extension rod. The expansion rate can be adjusted from 0.1 mm/s to 20 mm/s.

The soil-pressure sensors are installed at heights of 10 and 40 cm from the bottom on both sides. The four-point sensors on both sides are denoted as Y-10, Y-40, J-10, and J-40. In the test, the distance between the side walls of the test site on which J-10 and J-40 are located is 0.8 m, which is the side near the wall. Y-10 and Y-40 are the distal wall sides, as shown in Figure 5.

To examine the drag-reduction effect of the anti-drag ring on the friction resistance in sand, this study adopted a comparative test of a single model, where only an anti-drag ring was installed on one side of the thin-walled (25 mm) and thick-walled (30 cm) models. The anti-drag ring was arranged at the midpoint of two sensors on one side. The sensors on one side of the drag-reduction ring are denoted as W-10 and W-40, and those on the other side are denoted as WO-10 and WO-40, as shown in Figure 6. Then, in the experimental study on the pressure-pull-out loading method, the two position sensors are referred to as M-10 and M-40.

In this paper, the drag-reduction strategy of the pressure-pull-out loading method under static pressure is preliminarily discussed. The pore-water-pressure sensor was arranged at the predetermined depth. An elevated view of the test is presented in Figure 7.

2.3. Sand

Natural marine sand of 4 m × 4 m × 2 m was maintained in the test site. The grading curve and particle composition of the sand are shown in Figure 8 and

Table 2. Composition of sand particles.

Particles (mm)	2–1	1–0.5	0.5–0.25	0.25–0.075	<0.075
Content (%)	3.1	20	53.3	22.4	1.2
Cumulative content (%)	100	96.9	76.9	23.6	1.2

, respectively. Based on the results of the composition of particles, the non-uniformity coefficient $C_u$ is 2.59, the curvature coefficient $C_c$ is 1.16, the average particle size $d_{50}$ is 0.369 mm, the effective particle size $d_{10}$ is 0.161 mm, and the relative compactness is 0.384. The soil parameters of the soil bed, such as saturated density, internal friction angle, cohesion, and compression modulus, were also tested, as shown in

Table 3. Soil parameters.

Saturated Density (g/cm3)	Specific Gravity	Relative Density	Void Ratio	Compression Modulus (MPa)	Cohesion (kPa)	Internal Friction Angle
1.89	2.69	0.63	0.665	20.06	0.3	31.9

. Notably, the internal friction angle was tested using the direct-shear method under unconsolidated conditions considering the sinking process, and the tested stress levels were 50, 100, 150, and 200 kPa, increasing sequentially. All of the sand sample tests were completed in the geotechnical laboratory. The relation of the cone resistance to the cone depth is shown in Figure 8.

Before the test, the model was lifted to the installation bridge, the model was connected with the lower flange of the hydraulic cylinder through the tension and pressure sensor, and the sensor was connected and checked individually. Then, the model was sunk at a constant speed through the pressure of the hydraulic cylinder, and the data was recorded. Finally, when the hydraulic cylinder reached the maximum stroke, the extension rod was replaced, and it was pressed down to the design depth.

3. Test Results

3.1. Sinking Resistance of the Thin-Walled and Thick-Walled Models

The sensor data for the models of soil pressure, tension, and displacement are shown in Figure 9 and Figure 10.

Figure 9 shows that the sinking resistance of the thick-walled models is much greater than that of the thin-walled model due to the increase in the model thickness. With the growth of the end area, the compaction effect on the soil before the penetration depth of 0.3 m became evident, such that the end soil pressure of the thick-walled model was greater than that of the thin-walled model. When the depth was between 0.3 m and 1 m, the end soil pressure of the thin-walled model was slightly greater than that of the thick-walled model. This result shows that the thickness of the model has little effect on the end pressure as the depth increases. As shown in Figure 9b, the end soil pressure of the three models increased approximately linearly after the depth of 0.3 m, without sudden growth.

The lateral soil-pressure readings for the three models are depicted in Figure 10. On the J-10 and J-40 sides, when the depth was less than 0.5 m, the soil pressure at J-10 of the thick-walled models was less than that of the thin-walled model. When the depth was larger than 0.5 m, the compaction effect should have made the soil pressure of the thick-walled models larger. The soil pressure of the thick-walled model at J-40 was greater than that of the thin-walled model, indicating that the soil pressure near the side wall of the test site increased with the growth of the model’s thickness. On the Y-10 and Y-40 sides, the soil pressure of the thin-walled model at Y-10 was greater than that of the thick-walled model, whereas the soil pressure at Y-40 was similar to that at J-40, and the soil pressure of the thick-walled model was higher. By comparing the data of J-10 and Y-10 with those of J-40 and Y-40, it can be concluded that the distance from the side wall of the test to the model had a certain influence on the lateral soil pressure in this research, and the lateral soil pressure was larger at a smaller distance.

3.2. Horizontal-Soil-Pressure Coefficient $K$

The variation of the horizontal-soil-pressure coefficient of the thin-walled and thick-walled models with depth can be calculated through the measured data in the experiment, as shown in Figure 11, Figure 12 and Figure 13. The horizontal-soil-pressure coefficient was calculated by taking the part that tends to be stable.

The horizontal-soil-pressure coefficient shows that the soil pressure at J-40 and Y-40 of the thick-walled model was greater than that at J-10 and Y-10, which indicates that, with the sinking of the model, the soil was gradually compacted, resulting in the increase in the lateral soil pressure at the same depth. However, the soil pressure at J-40 of the thin-walled model was greater than that at J-10, and the soil pressure at Y-40 was less than that at Y-10, which also indicates that the compaction effect of the near-wall side was more evident. There was no side-resistance-degradation phenomenon, and the far-wall side experienced the resistance-degradation phenomenon.

The results show that the compaction effect on the horizontal-soil-pressure coefficient of the near-wall side of the models is greater than that of the far-wall side, and the horizontal-soil-pressure coefficient of the thick-walled models was greater than that of the thin-walled model. The horizontal-soil-pressure coefficients at the near and far walls of the BB25 model were 1.86 and 0.93, respectively. The values of the HB30 model were 2.51 and 1.16, respectively. The values of the HB40 model were 3.54 and 2.14, respectively. Since the compaction effect in the penetration process of the large-diameter, wide-shallow bucket foundations was weak, the horizontal-soil-pressure coefficients at the far walls were adopted.

In previous studies, Andersen [29] suggested $K=1.1$ in the laboratory model tests. $K=1.1$ was adopted by Wang [30], and Chen [31] considered $K=1.2$ in the laboratory. Their recommended values for horizontal-soil-pressure coefficients based on small-scale tests of thin-walled bucket foundations were found to be much greater than those provided by the DNV, which suggests a $K$ value of 0.8 for the bucket foundation. Furthermore, little research has been done regarding the influence of increasing the skirt thickness. Based on the partial full-scale experiment designed in this paper, the horizontal-soil-pressure coefficients are recommended, and the calculated results are well-fitted with the experimental measurement and much closer to the DNV results, which were derived from the engineering experience. Also, the horizontal-soil-pressure coefficients for bucket foundations of different thicknesses were provided as references for future wind power projects.

3.3. CPT Coefficient Fitting

The penetration resistance is calculated using the following expression [26]:

$$Q_c=Q_s+Q_t={\int }_0^z{f}_s\left(z\right)A_{s}dz+q_u{A}_t,$$

(1)

where

$Q_c$—total penetration resistance; $Q_s$—skin-friction resistance; $Q_t$—end resistance; $f_s\left(z\right)$—unit skin friction; $A_s$—side area; $q_u$—unit-cone resistance; and $A_t$—tip area.

The skin-friction resistance per unit side area is calculated according to Equation (2), and the end resistance per unit tip area is considered in Equation (3) [27].

$$f_s\left(z\right)=k_f{q}_c\left(z\right),$$

(2)

$$q_u=k_p{q}_c\left(z\right),$$

(3)

where

$k_f$—skin-friction coefficient, 0.001–0.003; $k_p$—end coefficient, 0.3–0.6; and $q_c\left(z\right)$—cone resistance, kPa.

In Figure 14, the black line represents the thin-walled model, the red line represents the thick-walled model of 30 cm, the blue line represents the thick-walled model of 40 cm, and the other lines represent the resistance fitting with different $k_p$ and $k_f$ values. In Figure 14a, based on the CPT measurement results, Equation (3) is applied to calculate the fitting of unit-end resistance. It shows that the optimal $k_p$ values for BB25, HB30, and HB40 are 1.5, 1.4, and 1.4, respectively. In Figure 14b, the $Q_s$ calculation method in Equation (1) is applied to calculate the model friction resistance. It shows that the optimal $k_f$ values for BB25, HB30, and HB40 are 0.008, 0.012, and 0.016, respectively.

From the comparison between the thin- and thick-walled coefficients, it can be seen that the $k_p$ experiences no significant increase with the increasing skirt thickness, while the $k_f$ increases significantly. This can be explained by the fact that the growth of the skirt thickness compacts the surrounding soil and causes the lateral soil pressure to increase.

In Figure 15, the two black lines on the far right represent the 25 mm thin-walled model, the two red lines in the middle represent the 30 cm thick-walled model, and the two blue lines on the far left represent the 40 cm thick-walled model. Figure 15 verifies that the resistance-calculation results based on the above values are in good agreement with the measured data, indicating that the end and skin-friction coefficients are reasonable when calculating the penetration resistance of the thin-walled and thick-walled models in sand.

4. Drag Reduction Strategy

4.1. Anti-Drag Ring

To examine the drag-reduction effect of the anti-drag ring on the skin-friction resistance in sand, this study adopted a single-model comparison test, where only one side of the BB25 and HB30 models was fitted with an anti-drag ring, and the soil pressure was recorded during the test. The soil pressures on two sides, with and without an anti-drag ring, of the HB30 model are not significantly different, so the drag-reduction effect of the anti-drag ring for the thick-walled models was not clear under the test conditions. The results of the soil pressure on both sides of the BB25 model are shown in Figure 16.

In Figure 16, the left side shows a comparison of the data of the two sides of the soil pressure under the anti-drag ring. The anti-drag ring has little effect on the soil pressure at the lower side of the ring, and the change in soil pressure on both sides is similar. Meanwhile, on the right side, the anti-drag ring can reduce the soil pressure at its upper side, and the drag-reduction effect is clear.

4.2. Pressure-Pull-Out Loading Method

In Figure 17, Figure 18 and Figure 19, the recorded sensor values, including displacement, resistance, soil pressure, pore pressure, and lateral soil pressure, are presented.

As shown in Figure 17, the hydraulic cylinder was used to apply reciprocating loads in the test, and the BB25 model moved to reciprocate at depths of 0.9 and 0.95 m. In the first cycle, the resistance significantly decreased and slowly increased with the number of circles. This finding indicates that, for the 25 mm thin-walled model, the pressure-pull-out loading method had the most evident drag-reduction effect, and the effect decreased with the increase in the cycle period.

As shown in Figure 18, the soil pressure at the end significantly fluctuated, which cannot truly reflect the change of the end resistance. However, the pore water pressure reached the maximum when the model reached the depth for the first time. With the increase in the number of cycles, the pore pressure tended to be stable, and no noticeable pore-pressure accumulation was detected in the test.

From the variation trend of the horizontal soil pressure in Figure 19, it can be seen that the pressure-pull-out loading method mainly affects the soil pressure at M-10, which proves that the drag-reduction is mainly caused by the end resistance, and the soil pressure at the upper side hardly changes. To prove the drag-reduction effect of the pressure-pull-out loading method on different thickness models, tests with thicknesses of 16 mm, 25 mm, 30 mm, and 30 cm were performed, and the results are shown in Figure 20.

The pressure-pull-out loading method could diminish the penetration resistance, and the drag-reduction effect was gradually weakened with the growth of the model thickness. When the thickness was 30 cm, the penetration resistance almost did not decrease. The resistance of the 16 mm model slowly decreased with the increase in the number of cycles, and when the thicknesses were 25 and 30 mm, the resistance gradually increased with the rise in the number of cycles. Particularly, with a thickness of 30 cm, the penetration resistance even surged. The findings show that the pressure-pull-out loading method is not recommended for thick-walled bucket foundations under certain test conditions.

5. Conclusions

The weight-penetration depth greatly affects the critical negative pressure in the negative penetration stage, so it is very important to accurately calculate the depth in the weight-penetration stage. Accordingly, this study considers an arc length corresponding to a central angle of 2° and approximates it as a line segment with a length of approximately 0.6 m for the thick-walled bucket foundation with a diameter between 30 m and 36 m. The following conclusions can be made:

(1)

The resistance characteristics of the thin-walled model and two thick-walled models were compared through an experiment. The end pressure of the thick-walled models was different from that of the thin-walled model under the condition of the experimental depth, but there were no clear multiple increases. The horizontal-soil-pressure coefficient of the near-wall side was larger than that of the far-wall side for models because of the compaction effect. The horizontal-soil-pressure coefficients at the near-wall and far-wall sides were 1.86 and 0.93 for BB25, 2.51 and 1.16 for HB30, and 3.54 and 2.14 for HB40, respectively.

(2)

The suggested values of the end and skin-friction coefficients of the models under the test conditions were presented. The end coefficient of the thin-walled model was 1.5, and the skin-friction coefficient was 0.008. The end and skin-friction coefficients of the HB30 model were 1.4 and 0.012, respectively. The end and skin-friction coefficients of the HB40 model were 1.5 and 0.016, respectively.

(3)

The anti-drag ring can reduce the soil pressure at its upper side, and the drag-reduction effect was evident. However, the setting of the anti-drag ring will increase the end resistance, so attention should be paid to the practical engineering application.

(4)

The pressure-pull-out loading method can significantly reduce the end resistance of the thin-walled model, and the resistance will not continue to decrease with the increase in cycle times. For the thick-walled model, this strategy has no drag-reduction effect, and the resistance will grow with the increase in cycle times. The pressure-pull-out loading method is suitable for the thin-walled foundation, but it is not recommended for thick-walled foundations.

The on-site negative-penetration stage has a long duration and a large depth. Thus, the sinking process of thick-walled foundations under negative pressure and the pressure-pull-out loading method should be further studied.