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Effects of long-term cyclic horizontal loading on bucket foundations in saturated loose sand
Applied Ocean Research 91 (2019) 101910
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Effects of long-term cyclic horizontal loading on bucket foundations in saturated loose sand
T
Ssenyondo Vicenta, Sung-Ryul Kimb, , Le Chi Hungc,d ⁎
a
Department of Civil Engineering, Dong-A University, Hadan2-dong, Saha-gu, Busan, South Korea Department of Civil and Environmental Engineering, Seoul National University, 1 Gwanak-ro, Gwanakgu, Seoul, South Korea c School of Physics, National University of Ireland, Galway, Ireland d Department of Civil Engineering, National University of Ireland, Galway, Ireland b
ARTICLE INFO
ABSTRACT
Keywords: Bucket foundation One-way cyclic horizontal load Accumulated rotation Unloading stiffness Pore water pressure Saturated loose sand
A 1-g model experimental study was conducted to investigate the accumulated rotations and unloading stiffness of bucket foundations in saturated loose sand. One-way horizontal cyclic loading was applied to model bucket foundations with embedment ratios 0.5 and 1.0. Up to 104 cycles of loading were applied at a frequency of 0.2 Hz varying load amplitudes. The accumulated rotation of the bucket foundations increased with the number of cycles and the load amplitudes. Empirical equations were proposed to describe the accumulated rotation of the foundations. The unloading stiffness of foundations increased with the number of cycles but decreased with an increase in load amplitude. The initial unloading stiffness of L/D = 1.0 (L is skirt length; D is foundation diameter) was approximately twice that of L/D = 0.5. Excess pore water pressure difference of 50% was observed between L/D = 0.5 and 1.0. The suction and static capacity of the bucket increased with increase of bucket embedment ratio with a difference of 69.5% and 73.6% respectively between L/D = 0.5 and 1.0.
1. Introduction A bucket foundation is made of steel structures, and takes the form of an inverted bucket with a uniform diameter (D) and length (L). The top cover is called the lid, whereas the vertical side is called the skirt. The weight of the superstructure is transferred to the foundation through a steel tower that is centrally fixed at the top of the bucket-lid. Stiffeners are added to increase the rigidity of the bucket-lid (Ibsen et al. [1]). Fig. 1a presents the composite features of the bucket foundation. Fig. 1b shows the bucket models used in this study. Bucket foundations were initially meant for use in oil and gas explorations. However, their use has been extended to the offshore wind industry in recent years. These foundations are applicable in clay and sand grounds, and can be modified from monopods to tripods depending on the depth of water at the site of installation. These foundations have been found convenient for use in shallow (30 m) and intermediate water depth (30 m–60 m). According to estimates, an offshore wind turbine can be subjected to more than 107 load cycles during this period. The long-term actions of cyclic loads from wind and waves significantly affect the design life of bucket foundations. The accumulated rotations of the wind turbine structure cause ground deformations, which shorten the fatigue life of
⁎
the structure (Bhattacharya [2]). Subsequent changes in soil–structure interaction cause variations in the unloading stiffness of the foundation. Previous studies on monopiles and bucket foundations revealed that the behavior of a foundation under cyclic loading is affected by different factors, e.g. the cyclic load characteristics, density of soil and foundation embedment depth, thus affects the stability of the wind turbine structure [3–9]. Nielsen et al. [10] conducted cyclic loading of bucket model (D = 500 mm, L/D = 0.5) under 1-g conditions, and deduced that there was a high dependence of foundation response on the frequency of loading. Barari and Ibsen [11] performed 1-g experimental model tests on buckets with (D = 300 mm, L/D = 1.0) in saturated dense fine silica sand. They illustrated that bucket stiffness increased with number of load cycles, and one way loading induced full mobilization of soil resistance to horizontal loading. Similar observations and conclusions were drawn in the work of LeBlanc [6] for monopiles and Zhu et al. [13] for bucket foundations in dry loose sand conducted at 1-g experimental tests. They additionally observed that the number of cycles had no significant effect on the unloading stiffness of the foundation, although the stiffness appeared to decrease with the increasing maximum cyclic load. Furthermore, studies for bucket foundations in saturated dense to very dense sands found that cyclic loading of the bucket at frequencies between 0.025
Corresponding author. E-mail address: [email protected] (S.-R. Kim).
https://doi.org/10.1016/j.apor.2019.101910 Received 20 February 2019; Received in revised form 19 June 2019; Accepted 3 August 2019 Available online 17 August 2019 0141-1187/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic of model bucket foundations. (a) Composition of a bucket foundation (b) Bucket foundation models.
and 0.2 induce partially drained conditions [14], and the accumulated rotation and stiffness of the bucket increased with the increasing number of cycles [15]. This paper presents a 1-g model experimental test study with the aim of investigating the effect of long-term cyclic horizontal loading of bucket foundations in saturated loose sand for the design of offshore wind turbine at the Saemangeum offshore windfarm in the Yellow Sea of Korea. The main difference between this study and previous studies is that, this study investigated bucket foundations in saturated loose sand to reflect the stress-dependent behaviour of the prototype soil. Thus the equations describing accumulated rotation and unloading stiffness of the bucket are different from those proposed by previous studies conducted for clay ground, dry and dense sands. Testing with the loose model ground is supported by findings in the studies of LeBlanc et al. [6], Altaee and Fellenius [24], Cerato and Lutenegger [25]. A series of static load tests was carried out followed by one-way cyclic horizontal load tests on bucket foundations with embedment ratios L/D = 0.5 and 1.0. Test results give an insight into the behavior of bucket foundations and provide baseline knowledge that is useful at the preliminary design stage of bucket foundations for offshore wind turbine structures.
2. Model tests 2.1. Set up of the cyclic load test equipment Figs. 2 and 3 show the schematic of the cyclic load test equipment used in the study. The equipment developed in this study is similar to the rig employed by LeBlanc et al. [6] and Zhu et al. [13] for dry loose sand. However, the differences between the test equipment developed from this study and those reported in previously works [6,13] are the test equipment developed in this study enables to perform the test with both saturated or dry sand under load and displacement controlled. The developed equipment can apply stable loading of more than 10,000 load cycles. It consisted of a horizontal steel frame (spanning along the tops of two vertical rigid steel supports), three pulleys, steel loading wires with a diameter of 1 mm and masses of M1 and M2, a pivoted steel frame, a driving motor (capable of producing load frequencies ranging between 0.01 and 1 Hz), and a rotational load lever. The soil container had an internal diameter D = 600 mm and depth h = 450 mm. Prototype simulation was carried out using two bucket models with embedment ratios, L/D = 0.5 and 1.0. The equipment was instrumented with a load cell, two linear variable differential transformers (LVDTs) and a pore water pressure transducer (PPT). Data logging and interpretation were carried out with the aid of a National Instrument (NI cDAQ-9188) Data logger and LabVIEW 2012 program. The working principle of the cyclic load test equipment can be described as follows;
Fig. 2. Schematic of the cyclic load test equipment. 2
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Fig. 3. Experimental set up of the model test equipment.
buckets, where Lm and Lp refer to the length of the model and prototype buckets, respectively. The scale ratio of 1:100 has been successfully applied in the studies of Zhu et al. [13] and Hung et al. [17] during physical modelling of prototype bucket foundations for offshore wind turbines. Application of this scaling ratio resulted into a very thin skirt thickness of 0.03 mm, which was practically difficult to fabricate. For this reason, a skirt thickness of t = 1 mm was considered. To prevent deformation between the tower of the bucket and the top-lid, the toplid was fabricated to have a thickness 5 mm. This takes into account the extra rigidity offered by stiffeners usually fabricated on the lid of typical prototype bucket foundation. Two holes were perforated through the bucket lid to facilitate drainage and air ventilation during bucket installation. A third hole was provided to allow for installation of the pore water pressure transducer (abbreviated as PPT in Fig. 2). Table 1 presents a summary of the geometrical properties of the bucket models and tower weight. The test program focused on investigating the accumulated rotation, unloading stiffness and the development of pore water pressure inside the bucket foundations subjected to long-term one-way cyclic horizontal loads of varying magnitudes. The program considered a total of eight tests, including two horizontal static load tests and six cyclic load tests. The load amplitude was varied at different values of cyclic load ratio Rc. A one-way loading condition was considered because it served as the dominant loading condition for offshore wind turbines and induces greater accumulated rotations compared to two-way loading (Haiderali et al. [18]) In the centrifuge study (a = 200 g) on the cyclic performance of caissons in sand, Cox et al. [15] applied a tower displacement rate of 0.05 mm/s, which is equivalent to 10 mm/s on prototype scale. A similar displacement rate for the prototype bucket was assumed in this study, and tower displacement rate of 0.3 mm/s applied during static testing. This displacement rate was obtained by applying the scaling law for velocity V = 1/ n1 /2 (Wood [16]), where n = 100 and the coefficient α = 0.5 for sand. Horizontal forces on bucket foundations tend to induce tensile loads on one side of the bucket and compressive loads on the other. Therefore, the bucket tends to show a pullout behaviour on one side. Though the bucket pullout behaviour is outside the scope of this study, the lessons learnt from such studies indicate that in dense sand, fully drained and undrained conditions may be considered at loading rates of 0.001 mm/s and 1000 mm/s respectively (Thieken et al. [19]). However, as pointed out by Foglia et al. [20] and Hung et al. [17], the offshore environment is dominantly featured by partially drained conditions. Accordingly, a loading rate of 0.3 mm/s was adopted for all experimental tests to induce the partially drained condition. In the current study, more than 10,000 cycles (N) of loading were applied to each load condition to simulate the long-term effect under
Table 1 Bucket dimensions and tower weight.
Skirt Length, L Diameter, D Skirt thickness, t Tower weight, W Lid thickness, tL
Prototype
Model
15 m/7.5 m 15 m 33 mm 10 MN Reinforced
150 mm (L/D = 1.0)/75 mm (L/D = 0.5) 150 mm 1 mm 10 N 5 mm
Initially, the balance condition of the equipment was set by making mass M2 equal the mass of the lever beam and its contents (i.e., driving motor, rotational lever and mass M1). At balance, the pivoted steel frame had to be laid in a perfectly horizontal position (i.e., lying at an angle of 90° with the vertical). A driving motor set to operate at a frequency of 0.2 Hz caused the rotation of M1, which in turn, caused the vertical oscillation of the lever beam and its contents. This way, a varying sinusoidal load was set up in the loading wire 1 attached to the tower of the bucket, causing the horizontal displacement of the bucket. Four LVDTs with the model CDP-10M and CDP-100M (Tokyo Sokki company, Shinagawa-ku, Tokyo, Japan) were used to monitor the horizontal displacements of the bucket, from which bucket rotations were computed. The accuracy of the CDP-10M and CDP-100 mm LVDTs were 0.0005 mm and 0.001 mm, respectively. The applied loads were monitored by a load cell model SBAS-10L load cell (CAS company, Seoul, Korea) with an accuracy of ± 0.001 kg. This load cell was connected to one end of loading wire 1. Prior to carrying out the test, the preliminary calibration of the load cell was carried out by fixing one end of the steel wire. The positions of the load cell and wire length were maintained in each test. A pore water pressure transducer with model P306AVS-01 (SSK company, Seoul, Korea) was used to monitor pore water pressure developments inside the bucket. 2.2. Bucket models and test program A steel prototype bucket foundation with Young’s modulus E = 210 GPa supporting a 5 MW wind turbine structure was considered. The prototype bucket had an outer diameter D = 15 m and skirt thickness t = 33 mm with L/D = 0.5 and 1, as suggested in the work of Foglia et al. [14] for a standard 5 MW prototype bucket foundation for an offshore wind turbine. Two bucket models made of aluminium with Young’s modulus E = 70 GPa and skirt thickness t = 1 mm were fabricated for use in the study. Scaling laws proposed by Wood [16] were applied to model bucket foundations. The bucket models were designed to have embedment ratios, L/D = 0.5 and 1.0 (L = 75 mm and 150 mm) in this study. A length scale ratio (n = Lm/Lp) of 1:100 was used to dimension model 3
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Table 2 Magnitudes of applied cyclic loads.
Table 3 Soil properties for model ground.
Loading
L/D = 0.5
L/D = 1.0
No. of tests
Description
Value
Static load, H0 (N) Cyclic load ratio, Rc (N)
3.94 0.20; 0.40; 0.56
12.90 0.30; 0.54; 0.72
2 6
Specific gravity, Gs Maximum void ratio, emax Minimum void ratio, emin Relative density, Dr Mean grain size, D50 (mm) Coefficient of uniformity, Cu Coefficient of curvature, Cc Permeability, k (m/s)
2.65 0.93 0.43 29% 0.11 2.89 1.07 2.51 × 10−4
one-way cyclic loading, as one-way cyclic loading is critical in offshore wind turbine [6]. This number of cycles is considered sufficient to capture the relevant features of the long-term cyclic response of the bucket foundation [14]. A loading frequency of 0.2 Hz was applied in this study [10]. The applied cyclic loading conditions are summarized in Table 2. 2.3. Model ground preparation Prior to model ground preparation, monotonic triaxial compression tests were carried out on a series of saturated cylindrical sand specimens to determine the steady state line for silica sand. The specimens had initial relative densities between 38 and 68%. The entire testing process including specimen preparation and testing procedures was carried out following the requirements of ASTM D7181-11 [21]. Fine silica sand was used for experimental studies because it exhibited similar particle sizes with sand at the Saemangeum site (prototype site). The void ratio and effective mean stress of the specimens at steady state, were evaluated and used to locate the position of the steady state line shown in Fig. 4. Li and Wang [22] noted that in cohesionless soils, a steady state line is obtained by plotting void ratios and normalized mean effective stresses in the e-(p’/pa)α space, where pa = atmospheric pressure (100 kPa), and the exponent α ranges between 0.6 and 0.8. This approach was adopted, and a straight line was found to best fit experimental data for α = 0.8. Previous studies found out that the model and prototype soils will exhibit a similar behaviour if their stress state positions lie equi-distant (void ratio difference, Δe) from the steady state line [23–25]. The insitu state of stress in the prototype soil was calculated considering a soil element at a depth of 15 m below sea bed (i.e. 0.15 m in model scale). This point corresponds to the foot of the bucket foundation with L/ D = 1.0 and skirt length of 15 m. It can be seen from Fig. 4 that the stress states at a soil depth of 0.15 m in the model will replicate those in the prototype soil at a depth
of 15 m. The corresponding relative densities of the model and prototype soils were 29 and 40%, respectively. Based on this finding, loose sand with relative density Dr = 29% was adopted as model soil for all experimental tests. Table 3 presents the soil properties of the model ground and Figs. 5 and 6 show the soil grain size distribution curve and unit weights of the
Fig. 4. Steady state line for silica sand.
Fig. 6. Unit weight of saturated sand.
Fig. 5. Grain size distribution curve of the model ground.
4
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model ground, respectively. The model ground was reconstituted by water pluviation (Kim et al. [26]). The method is known to give homogeneous grounds with loose relative densities of approximately 28%–30% and also provide initially saturated samples (Vaid and Negussey [27]). Before the start of the test, fine silica sand was fully saturated in a box for a period exceeding 48 h. The soil container was then filled with water to a height of 420 mm. A test sieve (ASTM No. 40) was stacked on to the soil container, ensuring that the mesh is fully submerged in water. Bits of saturated sand were placed and washed on the sieve, causing the sand particles to disperse and drop in water at a uniform velocity, hence forming the homogeneous loose ground. The process was repeated until the required ground depth of 300 mm was achieved. The relative density of the ground was 29%, thus, it had a loose classification (McCarthy [28]). Sand was kept saturated throughout the entire testing process and washing of the sand was evenly distributed on the mesh sieve. This process of soil preparation was adopted identically for all tests. Prior to bucket installation, the threaded tower was attached to the bucket, and drainage holes on the bucket lid were opened. The bucket was connected to the center of a circular guide beam. The guide beam was then adjusted to the central position of the soil container. It was ensured that horizontal movements of the guide beam are prevented. The bucket was then carefully positioned to touch the ground surface and self-penetration was allowed to take place for 10 min. When no further bucket penetration was observed, ballast weights were incrementally added on the bucket lid to continue the penetration. Penetration was completed when the bucket lid reached the model ground surface. For bucket installation in clay, a penetration velocity of 0.5 mm/s was deemed sufficient to prevent large interior overpressures that would break the seal formed between the bucket walls and the soil (Guo et al. [29]). The average penetration velocity was 0.05 mm/s for both L/D = 0.5 and 1.0. Compared to clay, model sand had a higher coefficient of permeability and therefore, this penetration velocity was satisfactory. Therefore, during bucket installation, pore pressure buildups and soil disturbances around the skirt were significantly minimized.
Fig. 7. Determination of the horizontal static failure loads of the bucket foundations.
and final sections of the curve. The load corresponding to the point of intersection of the two tangents is taken to be the static failure load of the foundation. In addition, this method was recommended by Samtani and Nowatzki [36] for use in determining the static ultimate (failure) load of drilled shafts. The static failure loads of the foundations were found to be 3.94 and 12.9 N for L/D = 0.5 and 1.0, respectively. The higher static capacity for L/D = 1.0 can be attributed to the higher passive resistance mobilized by the soil mass in the direction of bucket rotation. Meanwhile, a larger soil mass was confined by L/D = 1.0 compared with L/D = 0.5. Thus, during bucket rotation, a higher suction was developed in L/D = 1.0 than L/D = 0.5, as shown in Fig. 8. A suction pressure difference of 73.6% was observed between L/D = 0.5 and 1.0.
3. Results and discussions
3.2. Cyclic accumulated rotation of the bucket foundation
3.1. Horizontal static failure load of the bucket foundation
Cyclic load conditions of the test were obtained by using the relation Rc = Hc/H0, where Rc and Hc refer to the cyclic load ratio and cyclic
It can be perceived from previous studies that offshore wind turbines are subjected to higher magnitudes of horizontal forces than vertical forces. Therefore, accurate determination of the horizontal static capacity of foundations for these structures is a key factor in choosing realistic cyclic loading conditions, under which experimental testing is to be conducted. The static failure load (H0) was used to estimate the load amplitude Hc to be applied in the cyclic load test. The horizontal load was applied through a 1 mm diameter steel wire connected to the tower of the bucket. The loading point height was assigned at h = 380 mm from the ground surface to consider an eccentricity, e of circa 2.5 (e = M/ HD = hH/HD = h/D = 380/150 = 2.53), where M = moment and H = horizontal lateral load, D = diameter of suction bucket foundation. This e = 2.5 was adopted from previous studies (i.e. [14,30,31]). Fig. 7 shows the response of the bucket foundations to the applied load. Both curves showed a relatively linear behavior at low values of applied load. After a certain load was exceeded, the curves exhibited a nonlinear behavior. A similar observation has been reported by Zhang et al. [32]. The static failure load of the bucket increased with increase of bucket embedment ratio with a difference of 69.5% between L/ D = 0.5 and 1.0. Static failure loads were estimated using the tangent intersection method [33–35]. This method involves drawing tangents at the initial
Fig. 8. Suction development during static loading. 5
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Fig. 11. Definitions of rotation angles for the first and Nth cycles of loading, and unloading stiffness k.
Fig. 9. Example on horizontal bucket displacement during cyclic loading.
[14]). The cyclic angular rotation of the bucket can be generally evaluated in terms of (N ) , where Δ (N ) = N 0 [6,13,14]. Here, 0 and N refer 0 to the maximum rotation angles corresponding to the initial and Nth cycles of loading, respectively, as shown in Fig. 13. The long-term cyclic behavior of the bucket foundations can be described in Eq. (1) N
0 0
=Tb × N ×
(1)
where and parameters are the factors reflecting the effect of number of cycle N and L/D ratios, respectively. Tb is suggested to consider cyclic load ratios Rc. Experimental data (i.e., values of 0 and N ) were substituted into the normalized expression on the left side of Eq. (1), after which the values of , , and Tb were determined. The results are expressed graphically, as shown in Fig. 13. Solid lines were obtained by substituting experimental data into the left side of Eq. (1), in which the dashed lines (trend lines) represented the right side of the equation. With a large number of cycles, the accumulated rotation of the bucket foundations appeared to increase linearly with the number of cycles, as shown by the dashed lines. In the long-term, the curves appeared to almost converge, indicating the uniform behavior of the bucket foundation, irrespective of the variation in the amplitude of loading. Further, experimental data matched well with Eq. (1). Therefore, Eq. (1) can properly describe the accumulated rotation of the bucket foundation at a large number of cycles. The parameters , , and Tb were obtained by performing a least square regression analysis of experimental data as described in the following steps.
Fig. 10. Example on determination of the applied cyclic load amplitude.
load amplitude, respectively. Bucket displacements were observed to increase with the increasing number of cycles, as illustrated from the data of L/D = 1.0, Rc = 0.72 in Fig. 9. Hc was calculated as the difference in loads corresponding to the maximum and minimum points of the curve in Fig. 10, and was uniformly maintained throughout the tests. As illustrated by the example in Fig. 11, the bucket continued to rotate as the number of cycles increased. For each load magnitude, the first cycle of loading caused a large rotation of the foundation. A similar observation for loose dry sand has been reported in the study of Zhu et al. [39]. In order to understand the effect of long-term cyclic loading, several cyclic load tests were carried out varying load amplitudes. Fig. 12 illustrates the response of the bucket to the increasing number of cycles. As can be seen, the accumulated rotations of the bucket foundations (L/ D = 0.5 and 1.0) increased with the number of cycles irrespective of the load amplitude. The accumulated rotations also increased as the load amplitude increased. The same observations have been reported for loose dry sand (Zhu et al. [13]) and dense saturated sand (Foglia et al.
(a) An arbitrary value was assigned to each of the parameters on the right side of Eq. (1), and ( N 0 )/ 0 was evaluated considering each load amplitude. (b) A least square regression analysis was performed to define the values of, , and Tb. At this step, there was a slight variation in the values of and obtained from each of the load amplitude. Average values of and were obtained. (c) Average values of and for all load magnitudes were substituted into the right side of Eq. (1), and a least square regression was again performed to obtain values of Tb corresponding to each load amplitude. 6
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Fig. 12. Response of the bucket to increases in the cyclic load amplitude for L/D = 0.5 and 1.0.
Fig. 13. Prediction of long term cyclic accumulated rotation of the bucket using the proposed equation.
The average values of the exponent were found to be 0.085 and 0.23 for L/D = 0.5 and 1.0, respectively, whereas the average values of were 0.72 for L/D = 0.5 and 0.93 for L/D = 1.0. The value of the exponent = 0.23 obtained in this study for L/D = 1.0 is comparable to = 0.184 for dense saturated sand reported by Foglia et al. [14] for the same embedment ratio, and slightly lower than = 0.39 for dry loose sand reported by Zhu et al. [13]. It is likely that the value of the exponent is significantly affected by the bucket embedment depth and the saturation condition of sand. Fig. 14 shows the variation of Tb with Rc. As can be seen, Tb increased with the increasing values of cyclic load ratio Rc. A line of best fit drawn through the data points and extrapolated to meet the horizontal axis gave a threshold value of Rc = 0.13, below which accumulated rotations of the bucket foundation would be negligible. The threshold value of Rc = 0.13 obtained in this study is comparable to the value of Rc = 0.18 for saturated dense sand in the study of Foglia et al. [14], although smaller than the value of Rc = 0.23 for loose dry sand in the study of Zhu et al. [13]. Tb is empirically defined in Eq. (2) as
Tb = 0.7687Rc
0.096
(2)
Fig. 14. Definition of the cyclic parameter Tb.
As shown in Fig. 14, Tb values obtained in this study were compared with previously reported values for bucket foundations in loose dry sand (Zhu et al. [13]) and dense saturated sand (Foglia et al. [14]), using 1-g model tests. In the present study, Tb values for saturated loose sand were higher than those for loose dry sand, but smaller than those for dense saturated sand. Generally, loose sand results in lower Tb 7
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Fig. 15. Variation of unloading stiffness of the bucket with number of cycles.
values compared with dense saturated sand, as observed by LeBlanc et al. [6].
then performed to obtain new values of k 0 and Ak . Step 2, Ak value was adjusted to get a best trend line fitting experimental data. A least squares regression analysis was again performed to get the corresponding k 0 values. The above procedure was repeated for each load magnitude to obtain trend lines shown in Fig. 15. The constant value of Ak was found to be 0.0089 and 0.009 for L/D = 0.5 and 1.0, respectively. This revealed that the rate of increase of unloading stiffness was slightly higher in L/ D = 1.0 compared to L/D = 0.5. However, for simplicity of Eq. (3), Ak was rounded off to 0.01 for both L/D = 0.5 and 1.0. k 0 for both foundations was found to decrease with the increase of load magnitude (Fig. 16). The decrease of the initial unloading stiffness with increasing cyclic load magnitude was estimated by using the functions k 0 = 0.0347Rc 0.704 and k 0 = 0.0678Rc 0.617 , for L/D = 0.5 and 1.0 respectively. It can be seen from Fig. 16 that the initial unloading stiffness increased with increase in bucket embedment depth with a difference of 45% between L/D = 0.5 and 1.0. The initial unloading stiffness of the bucket foundation in saturated loose sand can be generally estimated by using Eq. (4) as following:
3.3. Unloading stiffness of bucket foundations The continuous rotation (tilting) of the wind turbine structure causes deformation of the soil surrounding the foundation. As soil structure characteristics change, a gap may be created between the foundation and the surrounding soil, resulting in a significant reduction in the stiffness of the wind turbine structure. Dynamic amplifications may occur, which increase vibration amplitudes of the structure [2,7]. Owing to the increased bending and deflection of the structure, the natural frequency of the wind turbine structure may fall within or close to the forcing frequencies of the wind, waves and rotor, hence damaging the fatigue life of the entire structure and its components. Therefore, to assess unloading stiffness is necessary. In this study, the unloading stiffness k of the bucket foundation was estimated to be equivalent to the slope of the dashed line as previously illustrated in Fig. 11. This approach was adopted from the study of Kelly et al. [40]. Fig. 15 shows the relationship among unloading stiffness, cyclic load magnitudes Rc, number of cycles N, and L/D ratios. The unloading stiffness of the foundations appeared to increase with the number of cycles, a behavior that contradicted the previously observed bucket foundations in dry loose sand (Zhu et al. [13]), but similar to monopiles in dry loose and medium-dense sand (LeBlanc et al. [6]). The initial decrease in the unloading stiffness, which was observed within the first 50 cycles of loading, can be attributed to the displacement and rearrangement of the soil particles and bedding of the footing into the soil. It was generally observed that, the unloading stiffness of the foundations decreased with the increasing cyclic load amplitude. An empirical equation was proposed to describe the relationship among unloading stiffness, cyclic load ratio Rc and number of load cycles N. The equation, which has a form similar to that proposed by Leblanc et al. [6], is suggested as follows:
kN = k 0 + Ak ln(N )
k 0 = 0.0678 ×
L D
0.9663
× Rc
0.6605
where k 0, L/D and Rc are as previously described.
(3)
where kN is the unloading stiffness of the bucket foundation at any number of cycles N, k 0 is the initial unloading stiffness and Ak is a constant value. Eq. (3) has been successfully applied in previous studies of [12,17] to estimate the evolution of unloading stiffness of bucket foundations in sand and clay grounds. Parametric values of Eq. (3) were obtained by performing a least squares regression analysis of experimental data using Microsoft excel computer program as following procedure: Step 1, the number of cycles N was input into Eq. (3), with arbitrary values assigned to k 0 and Ak . A least squares regression analysis was
Fig. 16. Initial unloading stiffness at different load magnitudes. 8
(4)
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Fig. 17. Effect of number of cycles and amplitude of loading on excess pore water pressure under bucket lid.
3.4. Pore water pressure development inside the bucket
development of positive excess pore pressures in L/D = 0.5 was attributed to the small volume of the soil trapped inside the bucket and higher rate of seepage from outside to inside of the bucket. On the other hand, the bucket with L/D = 1.0 contained a larger volume of soil due to the longer skirt length. The deep embedment and thus longer seepage length slowed down the degradation of suction inside the bucket. Fig. 19 illustrates the variation of bucket displacement and pore water pressure with the number of cycles for the case Rc = 0.4 (for L/ D = 0.5) and Rc = 0.54 (for L/D = 1). The figure captured the phase variation of displacement and pore water pressure for N = 5006–5006 cycles. This is because at a higher number of cycles, soil characteristics are likely to change significantly. So it was necessary to observe the phase variation between bucket displacement and pore water pressure. The displacement and pore water development for other cases showed a similar trend, thus they are not presented here. It can be seen from Fig. 19 that even at a higher number of cycles, the excess pore water pressure and bucket displacement varied sinusoidally with the number of cycles. The rate at which the excess pore water pressure generated was slower compared to that at which bucket displacement occurred. The phase difference was approximately 90 degrees. This phenomenon is crucial for the stability of the wind turbine structure because, if the rate at which positive excess pore water pressures develop inside the bucket is higher than that at which bucket displacement occurs, there is a high possibility that the accumulating excess pore water pressures may rise to higher values which may affect the stability of the windturbine structure. The curves show a continuous trend of rise and fall of excess pore water pressure because the ground permeability, loading rate, and cyclic load frequency applied were sufficient to permit the occurrence of partially drained conditions [10,19,41]. Due to long term cycling, the
During cyclic loading, excess pore water pressure buildup inside the bucket was monitored. The pore water pressure transducer (abbreviated as PPT in Fig. 2), was positioned under the bucket lid. Fig. 17 shows the variation of excess pore water pressure with the number of cycles. The curves were obtained by average filtering of raw data from experimental test. It can be observed that applying a horizontal force initially induced suction pressure inside the bucket. Positive excess pore water pressures were generated when the bucket restored to its original position. This push- pull mechanism of the bucket resulted into the sinusoidal variation of excess pore water pressures over an increasing number of cycles. The positive excess pore water pressure increased with the increase of load magnitude and number of cycles for L/D = 0.5 and 1.0. In the long-term, the positive excess pore water pressure generated inside the bucket with L/D = 0.5 was higher compared to that developed in L/D = 1.0. For example, at N = 10,000 cycles, excess pore water pressure values of 0.6 and 0.3 kPa were reached for Rc = 0.56 (L/D = 0.5), and Rc = 0.54 (L/D = 1.0) respectively. In this example, the positive excess pore water pressure in L/ D = 0.5 was approximately twice that in L/D = 1.0, despite Rc values being approximately equal. Fig. 17 was magnified to closely observe the development of excess pore water pressure for the first 20 cycles of loading (Fig. 18) and at higher number of cycles (N = 5000–5006) (Fig. 19). It can be seen that the magnitude of suction induced at the onset of cycling was larger compared to that induced by succeeding cycling for both L/D = 0.5 and L/D = 1.0. The suction pressure inside the bucket dissipated within N < 100 cycles in L/D = 0.5, and N < 1000 cycles in L/D = 1.0. The faster
Fig. 18. Development of excess pore water pressure under bucket lid for the first 20 cycles. 9
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Fig. 19. Displacement and pore water pressure variations with number of cycles.
Fig. 20. Variation of excess pore water pressure under bucket lid with bucket rotation.
soil particles rearranged into a dense state. This reduced the growth of excess pore water pressures at large number of cycles. Fig. 20 shows the variation of excess pore water pressure with bucket rotation. The abscissa presents rotation angles at peak points of load-rotation curves. During analysis, approximately same total number of load cycles was considered for L/D = 0.5 and 1.0. It can be seen from Fig. 20 that, by increasing the cyclic load amplitude, higher values of excess pore water pressures can be reached. It was observed that the first cycle of loading caused large rotation of the bucket. The suction pressure that developed inside the bucket at the onset of cyclic loading increased with increase of load amplitude in L/D = 0.5 and 1.0.
have no effect on the finite element results. The size of the mesh was gradually increased from 0.01 near the bucket to 0.05 m at the boundary of the model. The non-linear stress–strain behaviour of soil was simulated using the Mohr Coulomb failure criterion. The buoyant unit weight of the model ground was estimated from experimental data, while other input parameters for loose sand were taken from EAU [38] as shown in Table 4. The calculation of Young’s modulus of sand is presented in Eq. (5).
3.5. Validation of experimental test data
where at is the reference stress of 100 kPa and m is the mean principle stress of soil. Fig. 22 shows the load-rotation curves from finite element analysis and experimental test. The horizontal load on the bucket increased with bucket displacement similarly with the findings of the experimental test. Experimental curves matched well with finite element simulated curves. Thus experimental test results were reliable. The equations proposed in this study have some limitations, such as loading condition (one-way cyclic loading), number of load cycles (N = 104) and low L/D ratios (i.e., L/D ≤ 1). In addition, fine loose sand has been considered, but the type and relative density of sand may vary from one locality to another. One-way cyclic loading condition has been considered to be the dominant loading condition, yet in practice, two-way cyclic loading also imposes significant serviceability constraints. Such limitations should be addressed by further investigations, and the empirical equations presented in this study might be applied for preliminary design.
Es = k ×
In this study, numerical simulation was performed using ABAQUS software version 6.12 [37] to confirm the reliability of experimental test data. Previous studies conducted 1-g experimental tests on bucket foundations in dry loose and dense saturated sand. Equations were proposed to evaluate accumulated rotations and unloading stiffness of the bucket. However, the studies did not perform numerical simulation to confirm the reliability of experimental test data. The current study performed 3D finite element analysis applying steady state conditions to the model. Fig. 21 shows the soil model and finite element mesh applied during numerical simulation. Only half of the model was simulated because of symmetry. The bottom boundaries were restrained against displacement and rotation in the x, y and z directions. Similarly, for lateral boundaries, displacements and rotations in the x and y directions were set to zero. The bottom and lateral boundaries of the model were remotely set to distances of 2.5D below the tip and outer face of the bucket. The boundary extents of the model were found to 10
at
×
m at
(5)
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Fig. 21. Typical finite element model and mesh.
(1) The static capacity of the bucket increased with increase of bucket embedment ratio with a difference of 69.5% between L/D = 0.5 and 1.0. At static capacities, suction pressure difference of 73.6% was observed between L/D = 0.5 and 1.0 (2) The accumulated rotations of the bucket increased with the increasing number of cycles and load amplitude. Based on results, equations were suggested to evaluate the accumulated rotations of the bucket in saturated loose sand. The equations take into account the embedment ratio of the bucket, cyclic load amplitude and number of cycles. The proposed equation properly described the accumulated rotation of the model bucket foundations in saturated loose sand. (3) The unloading stiffness of the bucket foundations increased with the increasing number of cycles, but decreased with the increase of the load amplitude. An empirical equation was proposed to evaluate the unloading stiffness of the model bucket in saturated loose sand. The equation was obtained after performing a least squares linear regression analysis of experimental test data. The initial unloading stiffness of the bucket increased with embedment ratio with a difference of 45% between L/D = 0.5 and 1.0. (4) During cyclic loading, the rate of bucket displacement was higher than that at which excess pore water pressures were generated. The phase difference between the two was approximately /2 rads (90°). The excess pore water pressure generated increased with the number of cycles and load amplitude. (5) The excess pore water pressure increased at a slow rate for N > 10,000 cycles. Excess pore water pressures were higher in L/ D = 0.5 compared to L/D = 1.0. At N = 10,000 cycles, the study revealed an excess pore water pressure difference of 50% between Rc = 0.56 (L/D = 0.5), and Rc = 0.54 (L/D = 1.0) respectively.
Table 4 Soil parameters for FE simulation. Description
Value 3
Buoyant unit weight, γ’ (kN/m ) Oedometric stiffness parameter, κ Oedometric stiffness parameter, λ Poisson’s ratio, ν Internal friction angle, ϕ’ Dilation angle, ψ Cohesion, c’ (kPa)
7.46 200 0.7 0.3 30° 1° 0.1
Fig. 22. Comparison of load-rotation curves between experiment and numerical analysis.
Acknowledgements
4. Conclusion
This research was supported by the Development of Life-cycle Engineering Technique and Construction method for Global competitiveness upgrade of Cable bridges (16SCIP-B119960) from the Smart Civil Infrastructure Research Program funded by the Ministry of Land, Infrastructure and Transport (MOLIT) of the Korean government and the Korea Agency for Infrastructure Technology Advancement (KAIA) and by the Basic Science Research Program funded by the Ministry of Education, South Korea (NRF-2017R1D1A1B03033738).
This research investigated the effects of the long-term cyclic loading of bucket foundations in saturated loose sand by conducting a series of 1-g experimental tests. A total of eight tests (two static and six horizontal cyclic load tests) were performed on bucket foundations with embedment ratios L/D = 0.5 and 1.0. The excess pore water pressure development inside the bucket, accumulated rotations, unloading stiffness of the model bucket foundations were examined. Cyclic horizontal loading was applied under one-way loading condition at a frequency of 0.2 Hz. The following conclusions can be drawn: 11
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References
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Contents lists available at ScienceDirect
Applied Ocean Research journal homepage: www.elsevier.com/locate/apor
Effects of long-term cyclic horizontal loading on bucket foundations in saturated loose sand
T
Ssenyondo Vicenta, Sung-Ryul Kimb, , Le Chi Hungc,d ⁎
a
Department of Civil Engineering, Dong-A University, Hadan2-dong, Saha-gu, Busan, South Korea Department of Civil and Environmental Engineering, Seoul National University, 1 Gwanak-ro, Gwanakgu, Seoul, South Korea c School of Physics, National University of Ireland, Galway, Ireland d Department of Civil Engineering, National University of Ireland, Galway, Ireland b
ARTICLE INFO
ABSTRACT
Keywords: Bucket foundation One-way cyclic horizontal load Accumulated rotation Unloading stiffness Pore water pressure Saturated loose sand
A 1-g model experimental study was conducted to investigate the accumulated rotations and unloading stiffness of bucket foundations in saturated loose sand. One-way horizontal cyclic loading was applied to model bucket foundations with embedment ratios 0.5 and 1.0. Up to 104 cycles of loading were applied at a frequency of 0.2 Hz varying load amplitudes. The accumulated rotation of the bucket foundations increased with the number of cycles and the load amplitudes. Empirical equations were proposed to describe the accumulated rotation of the foundations. The unloading stiffness of foundations increased with the number of cycles but decreased with an increase in load amplitude. The initial unloading stiffness of L/D = 1.0 (L is skirt length; D is foundation diameter) was approximately twice that of L/D = 0.5. Excess pore water pressure difference of 50% was observed between L/D = 0.5 and 1.0. The suction and static capacity of the bucket increased with increase of bucket embedment ratio with a difference of 69.5% and 73.6% respectively between L/D = 0.5 and 1.0.
1. Introduction A bucket foundation is made of steel structures, and takes the form of an inverted bucket with a uniform diameter (D) and length (L). The top cover is called the lid, whereas the vertical side is called the skirt. The weight of the superstructure is transferred to the foundation through a steel tower that is centrally fixed at the top of the bucket-lid. Stiffeners are added to increase the rigidity of the bucket-lid (Ibsen et al. [1]). Fig. 1a presents the composite features of the bucket foundation. Fig. 1b shows the bucket models used in this study. Bucket foundations were initially meant for use in oil and gas explorations. However, their use has been extended to the offshore wind industry in recent years. These foundations are applicable in clay and sand grounds, and can be modified from monopods to tripods depending on the depth of water at the site of installation. These foundations have been found convenient for use in shallow (30 m) and intermediate water depth (30 m–60 m). According to estimates, an offshore wind turbine can be subjected to more than 107 load cycles during this period. The long-term actions of cyclic loads from wind and waves significantly affect the design life of bucket foundations. The accumulated rotations of the wind turbine structure cause ground deformations, which shorten the fatigue life of
⁎
the structure (Bhattacharya [2]). Subsequent changes in soil–structure interaction cause variations in the unloading stiffness of the foundation. Previous studies on monopiles and bucket foundations revealed that the behavior of a foundation under cyclic loading is affected by different factors, e.g. the cyclic load characteristics, density of soil and foundation embedment depth, thus affects the stability of the wind turbine structure [3–9]. Nielsen et al. [10] conducted cyclic loading of bucket model (D = 500 mm, L/D = 0.5) under 1-g conditions, and deduced that there was a high dependence of foundation response on the frequency of loading. Barari and Ibsen [11] performed 1-g experimental model tests on buckets with (D = 300 mm, L/D = 1.0) in saturated dense fine silica sand. They illustrated that bucket stiffness increased with number of load cycles, and one way loading induced full mobilization of soil resistance to horizontal loading. Similar observations and conclusions were drawn in the work of LeBlanc [6] for monopiles and Zhu et al. [13] for bucket foundations in dry loose sand conducted at 1-g experimental tests. They additionally observed that the number of cycles had no significant effect on the unloading stiffness of the foundation, although the stiffness appeared to decrease with the increasing maximum cyclic load. Furthermore, studies for bucket foundations in saturated dense to very dense sands found that cyclic loading of the bucket at frequencies between 0.025
Corresponding author. E-mail address: [email protected] (S.-R. Kim).
https://doi.org/10.1016/j.apor.2019.101910 Received 20 February 2019; Received in revised form 19 June 2019; Accepted 3 August 2019 Available online 17 August 2019 0141-1187/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Schematic of model bucket foundations. (a) Composition of a bucket foundation (b) Bucket foundation models.
and 0.2 induce partially drained conditions [14], and the accumulated rotation and stiffness of the bucket increased with the increasing number of cycles [15]. This paper presents a 1-g model experimental test study with the aim of investigating the effect of long-term cyclic horizontal loading of bucket foundations in saturated loose sand for the design of offshore wind turbine at the Saemangeum offshore windfarm in the Yellow Sea of Korea. The main difference between this study and previous studies is that, this study investigated bucket foundations in saturated loose sand to reflect the stress-dependent behaviour of the prototype soil. Thus the equations describing accumulated rotation and unloading stiffness of the bucket are different from those proposed by previous studies conducted for clay ground, dry and dense sands. Testing with the loose model ground is supported by findings in the studies of LeBlanc et al. [6], Altaee and Fellenius [24], Cerato and Lutenegger [25]. A series of static load tests was carried out followed by one-way cyclic horizontal load tests on bucket foundations with embedment ratios L/D = 0.5 and 1.0. Test results give an insight into the behavior of bucket foundations and provide baseline knowledge that is useful at the preliminary design stage of bucket foundations for offshore wind turbine structures.
2. Model tests 2.1. Set up of the cyclic load test equipment Figs. 2 and 3 show the schematic of the cyclic load test equipment used in the study. The equipment developed in this study is similar to the rig employed by LeBlanc et al. [6] and Zhu et al. [13] for dry loose sand. However, the differences between the test equipment developed from this study and those reported in previously works [6,13] are the test equipment developed in this study enables to perform the test with both saturated or dry sand under load and displacement controlled. The developed equipment can apply stable loading of more than 10,000 load cycles. It consisted of a horizontal steel frame (spanning along the tops of two vertical rigid steel supports), three pulleys, steel loading wires with a diameter of 1 mm and masses of M1 and M2, a pivoted steel frame, a driving motor (capable of producing load frequencies ranging between 0.01 and 1 Hz), and a rotational load lever. The soil container had an internal diameter D = 600 mm and depth h = 450 mm. Prototype simulation was carried out using two bucket models with embedment ratios, L/D = 0.5 and 1.0. The equipment was instrumented with a load cell, two linear variable differential transformers (LVDTs) and a pore water pressure transducer (PPT). Data logging and interpretation were carried out with the aid of a National Instrument (NI cDAQ-9188) Data logger and LabVIEW 2012 program. The working principle of the cyclic load test equipment can be described as follows;
Fig. 2. Schematic of the cyclic load test equipment. 2
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Fig. 3. Experimental set up of the model test equipment.
buckets, where Lm and Lp refer to the length of the model and prototype buckets, respectively. The scale ratio of 1:100 has been successfully applied in the studies of Zhu et al. [13] and Hung et al. [17] during physical modelling of prototype bucket foundations for offshore wind turbines. Application of this scaling ratio resulted into a very thin skirt thickness of 0.03 mm, which was practically difficult to fabricate. For this reason, a skirt thickness of t = 1 mm was considered. To prevent deformation between the tower of the bucket and the top-lid, the toplid was fabricated to have a thickness 5 mm. This takes into account the extra rigidity offered by stiffeners usually fabricated on the lid of typical prototype bucket foundation. Two holes were perforated through the bucket lid to facilitate drainage and air ventilation during bucket installation. A third hole was provided to allow for installation of the pore water pressure transducer (abbreviated as PPT in Fig. 2). Table 1 presents a summary of the geometrical properties of the bucket models and tower weight. The test program focused on investigating the accumulated rotation, unloading stiffness and the development of pore water pressure inside the bucket foundations subjected to long-term one-way cyclic horizontal loads of varying magnitudes. The program considered a total of eight tests, including two horizontal static load tests and six cyclic load tests. The load amplitude was varied at different values of cyclic load ratio Rc. A one-way loading condition was considered because it served as the dominant loading condition for offshore wind turbines and induces greater accumulated rotations compared to two-way loading (Haiderali et al. [18]) In the centrifuge study (a = 200 g) on the cyclic performance of caissons in sand, Cox et al. [15] applied a tower displacement rate of 0.05 mm/s, which is equivalent to 10 mm/s on prototype scale. A similar displacement rate for the prototype bucket was assumed in this study, and tower displacement rate of 0.3 mm/s applied during static testing. This displacement rate was obtained by applying the scaling law for velocity V = 1/ n1 /2 (Wood [16]), where n = 100 and the coefficient α = 0.5 for sand. Horizontal forces on bucket foundations tend to induce tensile loads on one side of the bucket and compressive loads on the other. Therefore, the bucket tends to show a pullout behaviour on one side. Though the bucket pullout behaviour is outside the scope of this study, the lessons learnt from such studies indicate that in dense sand, fully drained and undrained conditions may be considered at loading rates of 0.001 mm/s and 1000 mm/s respectively (Thieken et al. [19]). However, as pointed out by Foglia et al. [20] and Hung et al. [17], the offshore environment is dominantly featured by partially drained conditions. Accordingly, a loading rate of 0.3 mm/s was adopted for all experimental tests to induce the partially drained condition. In the current study, more than 10,000 cycles (N) of loading were applied to each load condition to simulate the long-term effect under
Table 1 Bucket dimensions and tower weight.
Skirt Length, L Diameter, D Skirt thickness, t Tower weight, W Lid thickness, tL
Prototype
Model
15 m/7.5 m 15 m 33 mm 10 MN Reinforced
150 mm (L/D = 1.0)/75 mm (L/D = 0.5) 150 mm 1 mm 10 N 5 mm
Initially, the balance condition of the equipment was set by making mass M2 equal the mass of the lever beam and its contents (i.e., driving motor, rotational lever and mass M1). At balance, the pivoted steel frame had to be laid in a perfectly horizontal position (i.e., lying at an angle of 90° with the vertical). A driving motor set to operate at a frequency of 0.2 Hz caused the rotation of M1, which in turn, caused the vertical oscillation of the lever beam and its contents. This way, a varying sinusoidal load was set up in the loading wire 1 attached to the tower of the bucket, causing the horizontal displacement of the bucket. Four LVDTs with the model CDP-10M and CDP-100M (Tokyo Sokki company, Shinagawa-ku, Tokyo, Japan) were used to monitor the horizontal displacements of the bucket, from which bucket rotations were computed. The accuracy of the CDP-10M and CDP-100 mm LVDTs were 0.0005 mm and 0.001 mm, respectively. The applied loads were monitored by a load cell model SBAS-10L load cell (CAS company, Seoul, Korea) with an accuracy of ± 0.001 kg. This load cell was connected to one end of loading wire 1. Prior to carrying out the test, the preliminary calibration of the load cell was carried out by fixing one end of the steel wire. The positions of the load cell and wire length were maintained in each test. A pore water pressure transducer with model P306AVS-01 (SSK company, Seoul, Korea) was used to monitor pore water pressure developments inside the bucket. 2.2. Bucket models and test program A steel prototype bucket foundation with Young’s modulus E = 210 GPa supporting a 5 MW wind turbine structure was considered. The prototype bucket had an outer diameter D = 15 m and skirt thickness t = 33 mm with L/D = 0.5 and 1, as suggested in the work of Foglia et al. [14] for a standard 5 MW prototype bucket foundation for an offshore wind turbine. Two bucket models made of aluminium with Young’s modulus E = 70 GPa and skirt thickness t = 1 mm were fabricated for use in the study. Scaling laws proposed by Wood [16] were applied to model bucket foundations. The bucket models were designed to have embedment ratios, L/D = 0.5 and 1.0 (L = 75 mm and 150 mm) in this study. A length scale ratio (n = Lm/Lp) of 1:100 was used to dimension model 3
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Table 2 Magnitudes of applied cyclic loads.
Table 3 Soil properties for model ground.
Loading
L/D = 0.5
L/D = 1.0
No. of tests
Description
Value
Static load, H0 (N) Cyclic load ratio, Rc (N)
3.94 0.20; 0.40; 0.56
12.90 0.30; 0.54; 0.72
2 6
Specific gravity, Gs Maximum void ratio, emax Minimum void ratio, emin Relative density, Dr Mean grain size, D50 (mm) Coefficient of uniformity, Cu Coefficient of curvature, Cc Permeability, k (m/s)
2.65 0.93 0.43 29% 0.11 2.89 1.07 2.51 × 10−4
one-way cyclic loading, as one-way cyclic loading is critical in offshore wind turbine [6]. This number of cycles is considered sufficient to capture the relevant features of the long-term cyclic response of the bucket foundation [14]. A loading frequency of 0.2 Hz was applied in this study [10]. The applied cyclic loading conditions are summarized in Table 2. 2.3. Model ground preparation Prior to model ground preparation, monotonic triaxial compression tests were carried out on a series of saturated cylindrical sand specimens to determine the steady state line for silica sand. The specimens had initial relative densities between 38 and 68%. The entire testing process including specimen preparation and testing procedures was carried out following the requirements of ASTM D7181-11 [21]. Fine silica sand was used for experimental studies because it exhibited similar particle sizes with sand at the Saemangeum site (prototype site). The void ratio and effective mean stress of the specimens at steady state, were evaluated and used to locate the position of the steady state line shown in Fig. 4. Li and Wang [22] noted that in cohesionless soils, a steady state line is obtained by plotting void ratios and normalized mean effective stresses in the e-(p’/pa)α space, where pa = atmospheric pressure (100 kPa), and the exponent α ranges between 0.6 and 0.8. This approach was adopted, and a straight line was found to best fit experimental data for α = 0.8. Previous studies found out that the model and prototype soils will exhibit a similar behaviour if their stress state positions lie equi-distant (void ratio difference, Δe) from the steady state line [23–25]. The insitu state of stress in the prototype soil was calculated considering a soil element at a depth of 15 m below sea bed (i.e. 0.15 m in model scale). This point corresponds to the foot of the bucket foundation with L/ D = 1.0 and skirt length of 15 m. It can be seen from Fig. 4 that the stress states at a soil depth of 0.15 m in the model will replicate those in the prototype soil at a depth
of 15 m. The corresponding relative densities of the model and prototype soils were 29 and 40%, respectively. Based on this finding, loose sand with relative density Dr = 29% was adopted as model soil for all experimental tests. Table 3 presents the soil properties of the model ground and Figs. 5 and 6 show the soil grain size distribution curve and unit weights of the
Fig. 4. Steady state line for silica sand.
Fig. 6. Unit weight of saturated sand.
Fig. 5. Grain size distribution curve of the model ground.
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model ground, respectively. The model ground was reconstituted by water pluviation (Kim et al. [26]). The method is known to give homogeneous grounds with loose relative densities of approximately 28%–30% and also provide initially saturated samples (Vaid and Negussey [27]). Before the start of the test, fine silica sand was fully saturated in a box for a period exceeding 48 h. The soil container was then filled with water to a height of 420 mm. A test sieve (ASTM No. 40) was stacked on to the soil container, ensuring that the mesh is fully submerged in water. Bits of saturated sand were placed and washed on the sieve, causing the sand particles to disperse and drop in water at a uniform velocity, hence forming the homogeneous loose ground. The process was repeated until the required ground depth of 300 mm was achieved. The relative density of the ground was 29%, thus, it had a loose classification (McCarthy [28]). Sand was kept saturated throughout the entire testing process and washing of the sand was evenly distributed on the mesh sieve. This process of soil preparation was adopted identically for all tests. Prior to bucket installation, the threaded tower was attached to the bucket, and drainage holes on the bucket lid were opened. The bucket was connected to the center of a circular guide beam. The guide beam was then adjusted to the central position of the soil container. It was ensured that horizontal movements of the guide beam are prevented. The bucket was then carefully positioned to touch the ground surface and self-penetration was allowed to take place for 10 min. When no further bucket penetration was observed, ballast weights were incrementally added on the bucket lid to continue the penetration. Penetration was completed when the bucket lid reached the model ground surface. For bucket installation in clay, a penetration velocity of 0.5 mm/s was deemed sufficient to prevent large interior overpressures that would break the seal formed between the bucket walls and the soil (Guo et al. [29]). The average penetration velocity was 0.05 mm/s for both L/D = 0.5 and 1.0. Compared to clay, model sand had a higher coefficient of permeability and therefore, this penetration velocity was satisfactory. Therefore, during bucket installation, pore pressure buildups and soil disturbances around the skirt were significantly minimized.
Fig. 7. Determination of the horizontal static failure loads of the bucket foundations.
and final sections of the curve. The load corresponding to the point of intersection of the two tangents is taken to be the static failure load of the foundation. In addition, this method was recommended by Samtani and Nowatzki [36] for use in determining the static ultimate (failure) load of drilled shafts. The static failure loads of the foundations were found to be 3.94 and 12.9 N for L/D = 0.5 and 1.0, respectively. The higher static capacity for L/D = 1.0 can be attributed to the higher passive resistance mobilized by the soil mass in the direction of bucket rotation. Meanwhile, a larger soil mass was confined by L/D = 1.0 compared with L/D = 0.5. Thus, during bucket rotation, a higher suction was developed in L/D = 1.0 than L/D = 0.5, as shown in Fig. 8. A suction pressure difference of 73.6% was observed between L/D = 0.5 and 1.0.
3. Results and discussions
3.2. Cyclic accumulated rotation of the bucket foundation
3.1. Horizontal static failure load of the bucket foundation
Cyclic load conditions of the test were obtained by using the relation Rc = Hc/H0, where Rc and Hc refer to the cyclic load ratio and cyclic
It can be perceived from previous studies that offshore wind turbines are subjected to higher magnitudes of horizontal forces than vertical forces. Therefore, accurate determination of the horizontal static capacity of foundations for these structures is a key factor in choosing realistic cyclic loading conditions, under which experimental testing is to be conducted. The static failure load (H0) was used to estimate the load amplitude Hc to be applied in the cyclic load test. The horizontal load was applied through a 1 mm diameter steel wire connected to the tower of the bucket. The loading point height was assigned at h = 380 mm from the ground surface to consider an eccentricity, e of circa 2.5 (e = M/ HD = hH/HD = h/D = 380/150 = 2.53), where M = moment and H = horizontal lateral load, D = diameter of suction bucket foundation. This e = 2.5 was adopted from previous studies (i.e. [14,30,31]). Fig. 7 shows the response of the bucket foundations to the applied load. Both curves showed a relatively linear behavior at low values of applied load. After a certain load was exceeded, the curves exhibited a nonlinear behavior. A similar observation has been reported by Zhang et al. [32]. The static failure load of the bucket increased with increase of bucket embedment ratio with a difference of 69.5% between L/ D = 0.5 and 1.0. Static failure loads were estimated using the tangent intersection method [33–35]. This method involves drawing tangents at the initial
Fig. 8. Suction development during static loading. 5
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Fig. 11. Definitions of rotation angles for the first and Nth cycles of loading, and unloading stiffness k.
Fig. 9. Example on horizontal bucket displacement during cyclic loading.
[14]). The cyclic angular rotation of the bucket can be generally evaluated in terms of (N ) , where Δ (N ) = N 0 [6,13,14]. Here, 0 and N refer 0 to the maximum rotation angles corresponding to the initial and Nth cycles of loading, respectively, as shown in Fig. 13. The long-term cyclic behavior of the bucket foundations can be described in Eq. (1) N
0 0
=Tb × N ×
(1)
where and parameters are the factors reflecting the effect of number of cycle N and L/D ratios, respectively. Tb is suggested to consider cyclic load ratios Rc. Experimental data (i.e., values of 0 and N ) were substituted into the normalized expression on the left side of Eq. (1), after which the values of , , and Tb were determined. The results are expressed graphically, as shown in Fig. 13. Solid lines were obtained by substituting experimental data into the left side of Eq. (1), in which the dashed lines (trend lines) represented the right side of the equation. With a large number of cycles, the accumulated rotation of the bucket foundations appeared to increase linearly with the number of cycles, as shown by the dashed lines. In the long-term, the curves appeared to almost converge, indicating the uniform behavior of the bucket foundation, irrespective of the variation in the amplitude of loading. Further, experimental data matched well with Eq. (1). Therefore, Eq. (1) can properly describe the accumulated rotation of the bucket foundation at a large number of cycles. The parameters , , and Tb were obtained by performing a least square regression analysis of experimental data as described in the following steps.
Fig. 10. Example on determination of the applied cyclic load amplitude.
load amplitude, respectively. Bucket displacements were observed to increase with the increasing number of cycles, as illustrated from the data of L/D = 1.0, Rc = 0.72 in Fig. 9. Hc was calculated as the difference in loads corresponding to the maximum and minimum points of the curve in Fig. 10, and was uniformly maintained throughout the tests. As illustrated by the example in Fig. 11, the bucket continued to rotate as the number of cycles increased. For each load magnitude, the first cycle of loading caused a large rotation of the foundation. A similar observation for loose dry sand has been reported in the study of Zhu et al. [39]. In order to understand the effect of long-term cyclic loading, several cyclic load tests were carried out varying load amplitudes. Fig. 12 illustrates the response of the bucket to the increasing number of cycles. As can be seen, the accumulated rotations of the bucket foundations (L/ D = 0.5 and 1.0) increased with the number of cycles irrespective of the load amplitude. The accumulated rotations also increased as the load amplitude increased. The same observations have been reported for loose dry sand (Zhu et al. [13]) and dense saturated sand (Foglia et al.
(a) An arbitrary value was assigned to each of the parameters on the right side of Eq. (1), and ( N 0 )/ 0 was evaluated considering each load amplitude. (b) A least square regression analysis was performed to define the values of, , and Tb. At this step, there was a slight variation in the values of and obtained from each of the load amplitude. Average values of and were obtained. (c) Average values of and for all load magnitudes were substituted into the right side of Eq. (1), and a least square regression was again performed to obtain values of Tb corresponding to each load amplitude. 6
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Fig. 12. Response of the bucket to increases in the cyclic load amplitude for L/D = 0.5 and 1.0.
Fig. 13. Prediction of long term cyclic accumulated rotation of the bucket using the proposed equation.
The average values of the exponent were found to be 0.085 and 0.23 for L/D = 0.5 and 1.0, respectively, whereas the average values of were 0.72 for L/D = 0.5 and 0.93 for L/D = 1.0. The value of the exponent = 0.23 obtained in this study for L/D = 1.0 is comparable to = 0.184 for dense saturated sand reported by Foglia et al. [14] for the same embedment ratio, and slightly lower than = 0.39 for dry loose sand reported by Zhu et al. [13]. It is likely that the value of the exponent is significantly affected by the bucket embedment depth and the saturation condition of sand. Fig. 14 shows the variation of Tb with Rc. As can be seen, Tb increased with the increasing values of cyclic load ratio Rc. A line of best fit drawn through the data points and extrapolated to meet the horizontal axis gave a threshold value of Rc = 0.13, below which accumulated rotations of the bucket foundation would be negligible. The threshold value of Rc = 0.13 obtained in this study is comparable to the value of Rc = 0.18 for saturated dense sand in the study of Foglia et al. [14], although smaller than the value of Rc = 0.23 for loose dry sand in the study of Zhu et al. [13]. Tb is empirically defined in Eq. (2) as
Tb = 0.7687Rc
0.096
(2)
Fig. 14. Definition of the cyclic parameter Tb.
As shown in Fig. 14, Tb values obtained in this study were compared with previously reported values for bucket foundations in loose dry sand (Zhu et al. [13]) and dense saturated sand (Foglia et al. [14]), using 1-g model tests. In the present study, Tb values for saturated loose sand were higher than those for loose dry sand, but smaller than those for dense saturated sand. Generally, loose sand results in lower Tb 7
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Fig. 15. Variation of unloading stiffness of the bucket with number of cycles.
values compared with dense saturated sand, as observed by LeBlanc et al. [6].
then performed to obtain new values of k 0 and Ak . Step 2, Ak value was adjusted to get a best trend line fitting experimental data. A least squares regression analysis was again performed to get the corresponding k 0 values. The above procedure was repeated for each load magnitude to obtain trend lines shown in Fig. 15. The constant value of Ak was found to be 0.0089 and 0.009 for L/D = 0.5 and 1.0, respectively. This revealed that the rate of increase of unloading stiffness was slightly higher in L/ D = 1.0 compared to L/D = 0.5. However, for simplicity of Eq. (3), Ak was rounded off to 0.01 for both L/D = 0.5 and 1.0. k 0 for both foundations was found to decrease with the increase of load magnitude (Fig. 16). The decrease of the initial unloading stiffness with increasing cyclic load magnitude was estimated by using the functions k 0 = 0.0347Rc 0.704 and k 0 = 0.0678Rc 0.617 , for L/D = 0.5 and 1.0 respectively. It can be seen from Fig. 16 that the initial unloading stiffness increased with increase in bucket embedment depth with a difference of 45% between L/D = 0.5 and 1.0. The initial unloading stiffness of the bucket foundation in saturated loose sand can be generally estimated by using Eq. (4) as following:
3.3. Unloading stiffness of bucket foundations The continuous rotation (tilting) of the wind turbine structure causes deformation of the soil surrounding the foundation. As soil structure characteristics change, a gap may be created between the foundation and the surrounding soil, resulting in a significant reduction in the stiffness of the wind turbine structure. Dynamic amplifications may occur, which increase vibration amplitudes of the structure [2,7]. Owing to the increased bending and deflection of the structure, the natural frequency of the wind turbine structure may fall within or close to the forcing frequencies of the wind, waves and rotor, hence damaging the fatigue life of the entire structure and its components. Therefore, to assess unloading stiffness is necessary. In this study, the unloading stiffness k of the bucket foundation was estimated to be equivalent to the slope of the dashed line as previously illustrated in Fig. 11. This approach was adopted from the study of Kelly et al. [40]. Fig. 15 shows the relationship among unloading stiffness, cyclic load magnitudes Rc, number of cycles N, and L/D ratios. The unloading stiffness of the foundations appeared to increase with the number of cycles, a behavior that contradicted the previously observed bucket foundations in dry loose sand (Zhu et al. [13]), but similar to monopiles in dry loose and medium-dense sand (LeBlanc et al. [6]). The initial decrease in the unloading stiffness, which was observed within the first 50 cycles of loading, can be attributed to the displacement and rearrangement of the soil particles and bedding of the footing into the soil. It was generally observed that, the unloading stiffness of the foundations decreased with the increasing cyclic load amplitude. An empirical equation was proposed to describe the relationship among unloading stiffness, cyclic load ratio Rc and number of load cycles N. The equation, which has a form similar to that proposed by Leblanc et al. [6], is suggested as follows:
kN = k 0 + Ak ln(N )
k 0 = 0.0678 ×
L D
0.9663
× Rc
0.6605
where k 0, L/D and Rc are as previously described.
(3)
where kN is the unloading stiffness of the bucket foundation at any number of cycles N, k 0 is the initial unloading stiffness and Ak is a constant value. Eq. (3) has been successfully applied in previous studies of [12,17] to estimate the evolution of unloading stiffness of bucket foundations in sand and clay grounds. Parametric values of Eq. (3) were obtained by performing a least squares regression analysis of experimental data using Microsoft excel computer program as following procedure: Step 1, the number of cycles N was input into Eq. (3), with arbitrary values assigned to k 0 and Ak . A least squares regression analysis was
Fig. 16. Initial unloading stiffness at different load magnitudes. 8
(4)
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Fig. 17. Effect of number of cycles and amplitude of loading on excess pore water pressure under bucket lid.
3.4. Pore water pressure development inside the bucket
development of positive excess pore pressures in L/D = 0.5 was attributed to the small volume of the soil trapped inside the bucket and higher rate of seepage from outside to inside of the bucket. On the other hand, the bucket with L/D = 1.0 contained a larger volume of soil due to the longer skirt length. The deep embedment and thus longer seepage length slowed down the degradation of suction inside the bucket. Fig. 19 illustrates the variation of bucket displacement and pore water pressure with the number of cycles for the case Rc = 0.4 (for L/ D = 0.5) and Rc = 0.54 (for L/D = 1). The figure captured the phase variation of displacement and pore water pressure for N = 5006–5006 cycles. This is because at a higher number of cycles, soil characteristics are likely to change significantly. So it was necessary to observe the phase variation between bucket displacement and pore water pressure. The displacement and pore water development for other cases showed a similar trend, thus they are not presented here. It can be seen from Fig. 19 that even at a higher number of cycles, the excess pore water pressure and bucket displacement varied sinusoidally with the number of cycles. The rate at which the excess pore water pressure generated was slower compared to that at which bucket displacement occurred. The phase difference was approximately 90 degrees. This phenomenon is crucial for the stability of the wind turbine structure because, if the rate at which positive excess pore water pressures develop inside the bucket is higher than that at which bucket displacement occurs, there is a high possibility that the accumulating excess pore water pressures may rise to higher values which may affect the stability of the windturbine structure. The curves show a continuous trend of rise and fall of excess pore water pressure because the ground permeability, loading rate, and cyclic load frequency applied were sufficient to permit the occurrence of partially drained conditions [10,19,41]. Due to long term cycling, the
During cyclic loading, excess pore water pressure buildup inside the bucket was monitored. The pore water pressure transducer (abbreviated as PPT in Fig. 2), was positioned under the bucket lid. Fig. 17 shows the variation of excess pore water pressure with the number of cycles. The curves were obtained by average filtering of raw data from experimental test. It can be observed that applying a horizontal force initially induced suction pressure inside the bucket. Positive excess pore water pressures were generated when the bucket restored to its original position. This push- pull mechanism of the bucket resulted into the sinusoidal variation of excess pore water pressures over an increasing number of cycles. The positive excess pore water pressure increased with the increase of load magnitude and number of cycles for L/D = 0.5 and 1.0. In the long-term, the positive excess pore water pressure generated inside the bucket with L/D = 0.5 was higher compared to that developed in L/D = 1.0. For example, at N = 10,000 cycles, excess pore water pressure values of 0.6 and 0.3 kPa were reached for Rc = 0.56 (L/D = 0.5), and Rc = 0.54 (L/D = 1.0) respectively. In this example, the positive excess pore water pressure in L/ D = 0.5 was approximately twice that in L/D = 1.0, despite Rc values being approximately equal. Fig. 17 was magnified to closely observe the development of excess pore water pressure for the first 20 cycles of loading (Fig. 18) and at higher number of cycles (N = 5000–5006) (Fig. 19). It can be seen that the magnitude of suction induced at the onset of cycling was larger compared to that induced by succeeding cycling for both L/D = 0.5 and L/D = 1.0. The suction pressure inside the bucket dissipated within N < 100 cycles in L/D = 0.5, and N < 1000 cycles in L/D = 1.0. The faster
Fig. 18. Development of excess pore water pressure under bucket lid for the first 20 cycles. 9
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Fig. 19. Displacement and pore water pressure variations with number of cycles.
Fig. 20. Variation of excess pore water pressure under bucket lid with bucket rotation.
soil particles rearranged into a dense state. This reduced the growth of excess pore water pressures at large number of cycles. Fig. 20 shows the variation of excess pore water pressure with bucket rotation. The abscissa presents rotation angles at peak points of load-rotation curves. During analysis, approximately same total number of load cycles was considered for L/D = 0.5 and 1.0. It can be seen from Fig. 20 that, by increasing the cyclic load amplitude, higher values of excess pore water pressures can be reached. It was observed that the first cycle of loading caused large rotation of the bucket. The suction pressure that developed inside the bucket at the onset of cyclic loading increased with increase of load amplitude in L/D = 0.5 and 1.0.
have no effect on the finite element results. The size of the mesh was gradually increased from 0.01 near the bucket to 0.05 m at the boundary of the model. The non-linear stress–strain behaviour of soil was simulated using the Mohr Coulomb failure criterion. The buoyant unit weight of the model ground was estimated from experimental data, while other input parameters for loose sand were taken from EAU [38] as shown in Table 4. The calculation of Young’s modulus of sand is presented in Eq. (5).
3.5. Validation of experimental test data
where at is the reference stress of 100 kPa and m is the mean principle stress of soil. Fig. 22 shows the load-rotation curves from finite element analysis and experimental test. The horizontal load on the bucket increased with bucket displacement similarly with the findings of the experimental test. Experimental curves matched well with finite element simulated curves. Thus experimental test results were reliable. The equations proposed in this study have some limitations, such as loading condition (one-way cyclic loading), number of load cycles (N = 104) and low L/D ratios (i.e., L/D ≤ 1). In addition, fine loose sand has been considered, but the type and relative density of sand may vary from one locality to another. One-way cyclic loading condition has been considered to be the dominant loading condition, yet in practice, two-way cyclic loading also imposes significant serviceability constraints. Such limitations should be addressed by further investigations, and the empirical equations presented in this study might be applied for preliminary design.
Es = k ×
In this study, numerical simulation was performed using ABAQUS software version 6.12 [37] to confirm the reliability of experimental test data. Previous studies conducted 1-g experimental tests on bucket foundations in dry loose and dense saturated sand. Equations were proposed to evaluate accumulated rotations and unloading stiffness of the bucket. However, the studies did not perform numerical simulation to confirm the reliability of experimental test data. The current study performed 3D finite element analysis applying steady state conditions to the model. Fig. 21 shows the soil model and finite element mesh applied during numerical simulation. Only half of the model was simulated because of symmetry. The bottom boundaries were restrained against displacement and rotation in the x, y and z directions. Similarly, for lateral boundaries, displacements and rotations in the x and y directions were set to zero. The bottom and lateral boundaries of the model were remotely set to distances of 2.5D below the tip and outer face of the bucket. The boundary extents of the model were found to 10
at
×
m at
(5)
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Fig. 21. Typical finite element model and mesh.
(1) The static capacity of the bucket increased with increase of bucket embedment ratio with a difference of 69.5% between L/D = 0.5 and 1.0. At static capacities, suction pressure difference of 73.6% was observed between L/D = 0.5 and 1.0 (2) The accumulated rotations of the bucket increased with the increasing number of cycles and load amplitude. Based on results, equations were suggested to evaluate the accumulated rotations of the bucket in saturated loose sand. The equations take into account the embedment ratio of the bucket, cyclic load amplitude and number of cycles. The proposed equation properly described the accumulated rotation of the model bucket foundations in saturated loose sand. (3) The unloading stiffness of the bucket foundations increased with the increasing number of cycles, but decreased with the increase of the load amplitude. An empirical equation was proposed to evaluate the unloading stiffness of the model bucket in saturated loose sand. The equation was obtained after performing a least squares linear regression analysis of experimental test data. The initial unloading stiffness of the bucket increased with embedment ratio with a difference of 45% between L/D = 0.5 and 1.0. (4) During cyclic loading, the rate of bucket displacement was higher than that at which excess pore water pressures were generated. The phase difference between the two was approximately /2 rads (90°). The excess pore water pressure generated increased with the number of cycles and load amplitude. (5) The excess pore water pressure increased at a slow rate for N > 10,000 cycles. Excess pore water pressures were higher in L/ D = 0.5 compared to L/D = 1.0. At N = 10,000 cycles, the study revealed an excess pore water pressure difference of 50% between Rc = 0.56 (L/D = 0.5), and Rc = 0.54 (L/D = 1.0) respectively.
Table 4 Soil parameters for FE simulation. Description
Value 3
Buoyant unit weight, γ’ (kN/m ) Oedometric stiffness parameter, κ Oedometric stiffness parameter, λ Poisson’s ratio, ν Internal friction angle, ϕ’ Dilation angle, ψ Cohesion, c’ (kPa)
7.46 200 0.7 0.3 30° 1° 0.1
Fig. 22. Comparison of load-rotation curves between experiment and numerical analysis.
Acknowledgements
4. Conclusion
This research was supported by the Development of Life-cycle Engineering Technique and Construction method for Global competitiveness upgrade of Cable bridges (16SCIP-B119960) from the Smart Civil Infrastructure Research Program funded by the Ministry of Land, Infrastructure and Transport (MOLIT) of the Korean government and the Korea Agency for Infrastructure Technology Advancement (KAIA) and by the Basic Science Research Program funded by the Ministry of Education, South Korea (NRF-2017R1D1A1B03033738).
This research investigated the effects of the long-term cyclic loading of bucket foundations in saturated loose sand by conducting a series of 1-g experimental tests. A total of eight tests (two static and six horizontal cyclic load tests) were performed on bucket foundations with embedment ratios L/D = 0.5 and 1.0. The excess pore water pressure development inside the bucket, accumulated rotations, unloading stiffness of the model bucket foundations were examined. Cyclic horizontal loading was applied under one-way loading condition at a frequency of 0.2 Hz. The following conclusions can be drawn: 11
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References
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