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Experimental investigation of current-induced local scour around composite bucket foundation in silty sand
Ocean Engineering 117 (2016) 311–320
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Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Experimental investigation of current-induced local scour around composite bucket foundation in silty sand Tongshun Yu a,b,n, Jijian Lian b, Zhongqiang Shi b,c, Hongzhen Wang b a
College of Engineering, Ocean University of China, Qingdao 266100, China State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China c China Harbour Engineering Company Ltd., Beijing 100027, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 8 September 2015 Received in revised form 29 December 2015 Accepted 20 March 2016
In recent years, local scour has received attention because it may have a negative effect on coastal structures. Because of the large-scale arc transition and other special constructs, flow patterns around composite bucket foundation are complicated, and the local scour around composite bucket foundation has rarely been reported in the literature. In the present study, a detailed laboratory testing program on model with diameters of 150 cm and 75 cm embedded in silty sand was conducted in a flume. The scouring process and equilibrium scour hole geometry under steady and bidirectional current were investigated in detail. A procedure was suggested to predict the ultimate scour depth based on the observed variation of the scour depth over a limited time period. The equilibrium scour depth under a bidirectional current was approximately 16% less than that under a steady current, and there were two spoon-shaped scour holes in the steady current scour, whereas four saddle-shaped scour holes were discovered in bidirectional current scour. Based on these results, a functional relationship was suggested between the scour depth and other parameters, such as the diameter of the foundation, Shields parameter and median diameter of the soil bed. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Local scour Composite bucket foundation Current Maximum scour depth
1. Introduction Mono-pile, gravity-base, tripod, jacket structure and suction caisson foundations are widely applied in the development of offshore wind power (Byrne and Houlsby, 2003). Mono-pile structures are the most widely used in offshore wind structures and gravity foundation is the second most common. However, the strict requirements for construction equipment and technologies restrict the wide application of mono-pile structures in China. Gravity foundation structures require more than 5000 t of concrete for the effective transmission of wind turbine loads, and the construction cost of the jacket foundation structure is high. A new offshore foundation, the wide-shallow composite bucket foundation, is shown in Fig. 1 and was proposed by Lian et al. (2011, 2012) and Ding et al. (2013) due to the advantages of reduced construction cost and shortened construction period compared to conventional foundations. The composite bucket foundation usually has a large diameter (generally larger than 20 m, especially for wind turbines with more than 3 WM power in China) and an n Corresponding author at: College of Engineering, Ocean University of China, Qingdao 266100, China. E-mail address: [email protected] (T. Yu).
http://dx.doi.org/10.1016/j.oceaneng.2016.03.045 0029-8018/& 2016 Elsevier Ltd. All rights reserved.
aspect ratio (the skirt length to the foundation diameter) of less than 0.5 (Liu et al., 2014). The foundation takes full advantage of the high tensile capacity of steel strands and the high compressive capacity of concrete so that the problem of transferring the large moment and horizontal loads from the tower to the foundation can be solved by designing the pre-stressing arc transition structure. However, because of the large-scale arc transition and other special constructs, as shown in Fig. 1, the flow pattern around the composite bucket foundation under the action of current is complicated, which is illustrated schematically in Fig. 2. It is inaccurate to estimate the scouring depth using empirical formulas based on other types of foundations, such as pile foundations. Local scour of sediments around ocean structures has been studied extensively because it has been identified as one of the key factors that cause structure failure or undesired deposition in coastal and offshore engineering. To investigate scour when designing waterway, coastal and offshore structures, numerical analysis (Lu et al., 2005; Zhao and Cheng, 2010b) and experimental study (Sumer and Fredsøe, 2000; Pagliara and Kurdistani, 2013) are the two main methods for the determination of the scour depth. Usually, a numerical hydrodynamic model is proposed in numerical analysis, whereas in experimental study, test flumes and measurements are designed. Kim et al. (2014) built a hydrodynamic model with an adaptive multilevel structure Cartesian
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composite bucket foundation due to the lack of laboratory observations. There is no published literature on the local scour around composite bucket foundation. The present study investigates the flow and scour around composite bucket foundation via laboratory tests. The main objectives of this study were to investigate: (1) the mechanism of scour around a composite bucket foundation subject to a steady and bidirectional current; (2) the difference between the scour characteristics under a steady and bidirectional current; and (3) the relationship between the maximum scour depth and other dimensionless parameters. The arrangement of this paper is as follows. In Section 2, the test setup, the approach used for the tests and the test procedure are presented. The results of the scour test for a composite bucket foundation under steady and bidirectional current are presented in Section 3. A comparison of the results under a steady and bidirectional current and discussions are given in Section 3, and the conclusions of the paper are given in Section 4.
Fig. 1. Photograph of a composite bucket foundation.
z
Vortex shedding
x
Hammed water
2. Test setup and measurements 2.1. Dimensional analysis
Boundary layer U
Horseshoe vortex
Contraction of streamlines
y
Fig. 2. Sketch of the flow around a composite bucket foundation.
grid to analyze the local scour around cylinders in a side-by-side or tandem arrangement. Dixen et al. (2013) described the results of scour around a half-buried sphere exposed to a steady current by combined numerical and experimental investigation. Because of the scaling effect, laboratory tests tend to overestimate scour depth measurements (Lee and Sturm, 2008b). Despite the effect of scaling, laboratory tests are still widely used as the main method for investigating local scour mechanisms (Lee and Mizutani, 2008a; Zhao et al. 2012). There are also some empirical formulae that are used to predict the maximum scour depth for various coastal structures at the prototype size. Matutano et al. (2013) summarized the most important formulations developed for predicting the maximum scour depth of mono-pile foundations under different flow conditions (steady current only, waves only, or steady current and waves). Amini et al. (2012) provided a reasonable formula to predict the scour depth at pile groups under steady flows. With these methods, several researchers have assessed the scour depth around traditional coastal structures, including vertical circular cylinders (Zhao et al., 2010a; Roulund et al., 2005), submarine pipelines (Lu et al., 2005), bridge piers with different shapes (Khosronejad et al., 2012), rubble mound breakwaters (Sumer and Fredsøe, 2000), and new types of structures (Pagliara and Palermo, 2008; Pagliara and Kurdistani, 2013; Zhang et al.2009). Most of the studies of the local scour around marine structures have focused on scour due to waves (Sumer and Fredsoe, 2001), currents (Rambabu et al., 2003; Zhao et al., 2010a) or combined waves and currents (Qi and Gao, 2014; Cheng et al., 2014). Myrhaug et al. (2009) derived the scour depth below pipelines and around single vertical piles for combined waves plus currents. Most previous studies placed an emphasis on the scour around various traditional and new types of coastal structures, but few studies have examined the flow and effect of scour around
The local scour around a composite bucket foundation under the current involves a complex interaction among current, foundation and its neighboring soil. There are many variables that play relevant role on the scour around a composite bucket foundation, such as the foundation, sand-bed and fluid properties. The foundation properties can be characterized by its diameter ( B ). The sand-bed properties can be summarized by median diameters of soil ( d50 ), sediment grain density ( ρs ), coefficient of permeability ( ks ), shear modulus of soil skeleton ( G ), and degree of saturation ( Sr ). The fluid physical properties can be characterized by water density ( ρw ) and kinematic viscosity of water ( ν ). The current flow can be characterized by water depth (h), velocity of the current (u), and representative near-bed velocity of the current flow ( Uc ). The gravitational acceleration ( g ) is included among the variables. Based on the aforementioned analysis, the equilibrium scour depth ( hb ) can be described by the following functional relationship:
hb = f (B, d50, ρs , ks, G, Sr , ρw , ν, h, u, Uc , g , ⋯)
(1)
Vortex formation is the most important mechanism of scour in front of the composite bucket foundation, and some parameters can be ignored in Eq. (1). Applying the Buckingham π theorem to these dimensional parameters, the scour for the composite bucket foundation is dependent on the following non-dimensional parameters:
⎞ ⎛h B d f ⎜ b , , 50 , Re , Fr , θ ⎟ = 0 ⎠ ⎝ h h h
(2)
where Re is the Reynolds number, Fr is the Froude number and θ is the Shields parameter. In the above equation, the Reynolds number can be ignored because the seabed acts as a rough wall with scour occurring (Lee and Mizutani, 2008a). These parameters are discussed in Section 3.3.4. 2.2. Test setup The laboratory scour experiments around composite bucket foundation under current were conducted in the water flume at the State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, China. The water flume was 35 m in length, 7 m in width and 1.6 m in height. A movable sand basin of
Weight pecentage of less than a certion size/%
T. Yu et al. / Ocean Engineering 117 (2016) 311–320
100 90 80 70 60 50 40 30 20 10 0 10
1
0.1
0.01
313
1E-3
Patical size/mm Fig. 3. Sediment grading curve. Fig. 5. Photograph of the experimental setup for the flume test.
50 ——Logarithmic law y=0 ∇
40
Height/cm
9 m in length and the same width as the water flume with a median sand diameter of d50 ¼0.12 mm (as seen in Fig. 3) and specific gravity s ¼ 2.65 was built in the middle of the water flume. The angle of repose of the sand was ϕs = 41° . The sediment recess was from 10 cm to 40 cm deep, and sediment of 40 cm deep was located at the center position. Water was recirculated into the flume by two pumps with a 1.27 m3/s capacity, which were controlled by a regular signal generator. Boards for flow-adjusting were fixed at the bottom of the water flume to minimize the turbulence characteristics of the inlet flow in the test, and the desired incident smooth flow was generated behind the boards. The model with a diameter of 150 cm or 75 cm (as seen in Fig. 4) was placed 17.5 m from the pump and seated on the bottom of the water flume. An ADV produced by Nortek AS mounted on an instrument carriage was used to measure the scour hole profiles and flow characteristics. The discharge from the flume was controlled with a flow control valve. A photograph of the experimental arrangement is shown in Fig. 5.
30 20 10
2.3. Undisturbed flows and test conditions Before the scour tests were conducted, the undisturbed velocity profiles above the sandy bed at the location where the model was installed later on (set as y¼ 0), were measured. The velocity profiles were measured using ADV. The mean velocity profiles were obtained by averaging the recorded velocity samples. Fig. 6 shows the measured velocity profiles at the location of the model when water depth was 0.5 m and depth averaged velocity was 0.2952 m/ s. The measured velocity profiles are correlated to the logarithmic law of the velocity profile (Zhao et al., 2010a).
u (z ) =
uf z ln (30 ) k ks
(3)
0
0
10
20 30 Velocity/cm/s
Fig. 6. Undisturbed mean velocity profile in the vertical direction at y¼ 0.
where z is the vertical distance from the seabed, uf is the friction velocity, ks is the Nikurase roughness and k ( =0.41) is the von Kármán constant. The origin of the vertical coordinate z was defined at the mean bed level if ripples exist. The uf and ks in Eq. (3) are obtained by the least square method based on the measured
Unit:cm
150cm 75cm
(a) Photograph of the models
40
(b) Dimension of model with a diameter of 150 cm
Fig. 4. Models of the composite bucket foundation.
T. Yu et al. / Ocean Engineering 117 (2016) 311–320
3
Table 1 Experimental conditions (s is the steady flow condition and b is the bidirectional flow condition in the experiments; * is the maximum Shields parameter in bidirectional flow condition).
Run 1s 150 Run 2b 150 Run 3s 75 Run 4b 75 Run Run Run Run Run
5s 6s 7s 8s 9s
75 75 75 75 75
Period/min Water depth/ cm
Skin friction shields parameter
Shields parameter
29.52 29.52/ 25.04 20.87 20.87/ 17.71 25 25 25 15 35
– 167.03
50 50
0.078 0.078*
0.525 0.525*
– 118.11
25 25
0.045 0.045*
0.17 0.17*
– – – – –
15 20 25 25 25
0.073 0.068 0.065 0.023 0.127
0.253 0.261 0.286 0.079 0.491
1
τb ρ (s − 1) gd50
Flow
5
composite bucket foundation 6 7
(4)
where τb = ρu2f is the bed shear stress in the horizontal direction, s = ρs /ρ is the specific gravity of the sediment grain. τb in Eq. (4) is the total shear stress which includes the effects of skin friction and the shear stress due to the bed forms such as sand ripples. For sediment transport purpose, the skin friction is responsible for bed load transport and entrainment of sand from the bed. The bed shear stress and the Shields parameter are calculated from the depth averaged velocity based on logarithmic velocity distribution. According to logarithmic profile of velocity, the bed shear stress 2 due to skin friction is τbs = ρCDs U¯ , where CDs = {k /[ln (h/z0s ) − 1]}2,
where the non-dimensional grain size D* is defined as D* = [g (s − 1) /v 2]1/3 d50 with v being the kinematic viscosity of water. The critical Shields parameter for sand size d50 ¼0.12 mm is estimated to be 0.068 based on Eq. (5). Table 1 provides a summary of the experimental conditions. The experiment was conducted under steady and bidirectional current, ranging from 15 cm to 50 cm in water depth and from 15 cm/s to 35 cm/s in velocity. In the experiment, two models with diameters of 150 cm and 75 cm were selected, and the diameter of the prototype composite bucket foundation was 30 m. The length scales between the model and prototype were 1:20 and 1:40 in accordance with the principles of Froude similarity, and the corresponding time scales were 1:4.47 and 1:6.32, respectively. Therefore, the periods for bi-directional flow were 167.03 min in run 2 and 118.11 min in run 4, with a prototype period of 12.4 h. During the bidirectional current of run 2, the maximum velocity of the flood tide was 29.52 cm/s, and the maximum velocity of the ebb tide was 25.04 cm/s. For run 4, 20.87 cm/s and 17.71 cm/s were the maximum velocity of flood tide and ebb tide. Experiment
was at 0 relative to flow direction
Point
was at 45o relative to flow direction
Point
was at 90o relative to flow direction
Point
was at 135o relative to flow direction
Point
was at 180o relative to flow direction
Point
was at 225o relative to flow direction
Point
was at 270o relative to flow direction
Point
was at 315o relative to flow direction Fig. 7. Location of the monitoring points.
170
Unit: cm
35
36 The second profile
(5)
o
Point
Y
The first profile
z0s = d50/12. Due to the existence of sand ripples, the roughness determined from velocity measurements are much larger than the skin friction roughness. This leads to a total Shields parameter larger than the skin friction Shields parameter. The sediment transport occurs if the skin friction Shields parameter exceeds the critical Shields parameter. One of the widely used empirical formulae for calculating the critical Shields parameter is
0.30 θcr = + 0.055 ⎡⎣ 1 − exp ( − 0.020D* ) ⎤⎦ 1 + 1.2D*
X
8
velocities. It can be seen that the velocity distributions in the vertical direction follow logarithmic distribution in the whole water depth. The Shields parameter θ is the non-dimensional bed shear stress, which is defined by
θ=
Y
85
Maximum velocity of flow/cm/s
4
75
Diameter of model/ cm
2
X
75
Test
Unit: cm
1
composite bucket foundation
170
314
Flow
70 Fig. 8. Location of the monitoring profiles.
run 2 was the comparative trial of run 1. Similarly, experiment run 4 was the comparative trial of run 3. The flow set was as follows: the flow direction of the flood tide in experiment runs 2 and 4 was the same as the flow direction of the steady current, the maximum velocity of the flood tide which was larger than the velocity of the ebb tide in the bidirectional current was the same as the velocity of the corresponding steady current. Taking the model with a diameter of 150 cm as an example, the time variation of the scour depth at regular time intervals of one
T. Yu et al. / Ocean Engineering 117 (2016) 311–320
1
Unit: cm
80
315
0
Fl ow
80
model
360
200
X
Scour depth/cm
-1
Y
-2 (0°) (45°) (90°) (135°) (180°) (225°) (270°) (315°)
-3 -4 -5
360 -6 Fig. 9. Locations of the topography measuring points.
0
4
8
12
16
20
24
28
32
36
Time/h hour was monitored at eight monitoring points, which were numbered as shown in Fig. 7 around composite bucket foundation model. The points were located along the circumference in a symmetric arrangement, and the distance between the monitoring points and model edge was 10 cm. The naming rule was as follows: point ① was at 0° with the direction of flow, and point ② was at 45° with the direction of flow. Similarly point ⑧ was at 315°. The process of scour eventually reached a state of equilibrium with time if the time variation of the scour depth of the eight monitoring points at regular time intervals of one hour was less than 0.3 cm. The time variation of the scour depth was also monitored by two rows of monitoring points in a direction perpendicular to the flow, as shown in Fig. 8, around the composite bucket foundation model. Two profiles were located on both sides of the model in a symmetric arrangement, and the distance between profiles and the circle center of the model was 85 cm. There were 35 monitoring points on each profile, and the distance between neighboring monitoring points in the same profile was 5 cm. The scour pattern was determined based on the scour depth of the measurements points within the scope of 360 cm 360 cm, as shown in Fig. 9, around the model with a diameter of 150 cm. The scour depth of each point was recorded by the ADV one by one. To obtain the scour pattern in detail, while reducing the time required for reading data, points at a distance interval of 10 cm at the edge of the scour area were selected for the scour depth record, and the points of serious scour around the model were placed at a distance interval of 5 cm. There were approximately two thousand and five hundred measuring points in the area, and twelve hours are required to complete the scour depth record. The topography of the ultimate basin was obtained by TECPLOT. The distances of the monitoring points, profiles and locations of the topography measuring points were halved during the experiment using the model with a diameter of 75 cm. For the experiment runs using the model with a diameter of 75 cm, the time for recording the scour depth of each point was approximately ten hours. 2.4. Test procedure For each test run, the bed conditions were thoroughly checked before the experiment was performed, and the sand bed was 5 mm below the water surface. Given that the scour depth around the structure did not generally exceed 20 cm for this small-scale laboratory test, it was determined that the initial bed conditions might affect the final results. Therefore, to minimize the error caused by the initial bed profile, the sand bed was repeatedly
Fig. 10. Scour depth as a function of t recorded at eight monitoring points for experimental run 1.
leveled until the measured bed profile was within a tolerance range of 5 mm based on the ideal conditions. After setting the initial sand bed, water was allowed to rise along the flume until the required still water level was reached, and water was added sufficiently slowly to reduce air entrainment inside the seabed and prevent disturbances of the initial bed conditions. The flow depth was monitored throughout the experiment run against graduated scales attached to the flume wall. In general, testing was continued for two or three uninterrupted days, and an experiment was terminated when no scouring was observed for at least two successive hours. The scour depth of each point shown in Fig. 8 was recorded by ADV one by one. After the recording was complete, the water in the scour hole was drained by siphoning. Then, the detailed geometry of the scour hole was photographed.
3. Results and discussion To investigate the scouring process and the equilibrium scour hole geometry for composite bucket foundation under steady and bidirectional current, experiment runs 1–4 using models with diameters of 150 cm and 75 cm were tested. The results presented in Sections 3.1 and 3.2 are for the model with a diameter of 150 cm. In addition, experiment runs 5–9 used the model with a diameter of 75 cm, and the effects of the depth and flow velocity on the ultimate scour depth were investigated. 3.1. Results of the steady current 3.1.1. Time-development of the steady current-induced scour depth Fig. 10 shows the time variation of the scour depth at eight monitoring points for experimental run 1 (the larger the absolute value of the scour depth in the curve, the more serious the scour). The scouring process commenced from the back of the model, and at monitoring points No. ③–⑦, the time variation of the scour depth which was less than 2 cm, was small during the scour process. The scour depths of monitoring points No. ①, ② and ⑧ downstream of the model were much bigger than the other locations. No scouring was observed from the 34th to 36th hour, so the equilibrium scour time was 34 h. Considerable oscillations of the scour depth with time were observed, and the oscillations were caused by the migration of the sand ripples in the flume. Fig. 11 shows the time variation of the scour depth on the first and second profiles for experimental run 1. As scour progressed,
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a)
b)
2 0
3
1h 8h 15h 22h 29h 36h 38h
2
-4 -6 1h 8h 15h 22h 29h 36h 38h
-8 -10 -12 -14 -90
-60
-30
0
30
60
90
Coordinate of the first profile/cm
Scour depth/cm
Scour depth/cm
-2
1 0 -1 -2 -3 -90
-60
-30
0
30
60
90
Coordinate of the second profile/cm
Fig. 11. Time variation of the scour depth of the first and second profiles for experimental run 1.
Fig. 12. Photograph and topography of the equilibrium scour hole for experimental run 1.
the number of scoured points on the first profile increased, and the scour depth also increased. There were two scour holes on the first profile. The scour depth of the larger hole was 12.4 cm, and the two scour holes ran through the entire profile. The time variation of the scour depth on the second profile showed that no obvious scour occurred on the second profile during the scour process, and even sediments were observed to build up at some points of the second profile. 3.1.2. Equilibrium scour hole profiles in steady current scour The scour depth of points shown in Fig. 9 was recorded by ADV one by one when the equilibrium state was reached in run 1, and the topography was drawn by TECPLOT. Fig. 12 shows a photograph and the topography of the equilibrium scour hole for experimental run 1. A scour pit downstream of the model was recognizable, and there were two scour holes symmetrically along the flow direction downstream of the model. The first profile crossed the two holes. There were obvious sand ripples approximately perpendicular to the flow direction around the model, and the heights of these ripples were smaller than 1.5 cm. A ridgeshape sand dune, which aligned in the middle of the flow direction, was formed in the wake of the foundation, and the peak of the sand ridge was formed at a location where the mean flow reversed. Although there were sand ripples around the scour pit, the bed in the scour pit was always smooth, especially at the bottom of the pit. When a crest of a sand ripple reached the front edge of the scour pit, it collapsed and slid into the bottom of the scour pit. At the bottom of the scour pit (approximately 17 cm from the model), the vortex shedding picked up the sediment particles into suspension. The scour of sediment at the bottom of the scour hole increased the slope angle of the scour pit. Morphologically, the
two “wide” and “fat” scour holes which were deep in the front and swallow in the back were spoon-shaped, and the maximum scour depth was 15 cm for run 1. The bed slopes downstream of the sand pit were smaller than the angle of repose of the sediment, and the slopes at the upstream edge of the sand pit were almost same as the angle of repose. No scour pit was observed upstream or at the sides of the foundation, which was different from the scour pit of the pile foundation (Zhao et al., 2010a). Zhao et al. (2010a) predicted that the initiation of the scour around a vertical cylinder was a combination of the horseshoe vortex and the vortex shedding. The scour in front of the cylinder was due to the horseshoe vortex and that behind the cylinder was due to the vortex shedding. In the present investigation, because of the ring beams and foundation plate between the arc transition and the bucket buried in the silty sand, the effect of the horseshoe vortex on the suspension of sediment particles in front of the foundation was relatively small, and no scour was discovered upstream of the model. The initiation of the scour around the composite bucket foundation was due to vortex shedding, and the peculiar structural features in steady current scour prevented scour upstream of the foundation. Morphologically, in the investigation of the vertical circular cylinder foundation (Zhao et al., 2010a), the location of the maximum depth of the scour pit was close to the foundation, whereas the location was farther from the composite bucket foundation. Based on the two differences between the cylinder foundation and the composite bucket foundation, the structural features could keep the deepest pit away from the model and enhance the safety of the composite bucket foundation in currentinduced scour.
317
profile led to the slightly asymmetric scour hole.
2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
(0°) (45°) (90°) (135°) (180°) (225°) (270°) (315°)
0
4
8
12 16 Time/h
20
24
28
Fig. 13. Scour depth as a function of t recorded at eight monitoring points for experimental run 2.
3.2. Results of the bidirectional current 3.2.1. Time-development of the bidirectional current-induced scour depth Fig. 13 shows the time variation of the scour depth at the eight monitoring points for experimental run 2. At the beginning of the scour period, the scour depth of each point oscillated around the original level. The scour depths at monitoring points No. ①, ② and ⑧, which were much larger than the other location as in the run 1, increased at a faster rate after 6 h of testing, and the time variation of the scour depth at other monitoring points was less than 2.5 cm during the test. After approximately 25 h, the scour depth of each monitoring point stabilized, so the equilibrium scour time was 25 h. Oscillation was as obvious as in experiment run 1 during the time variation of the scour depth at eight points. The scour depths at the monitoring points downstream of the model in the flood tide were much larger than the scour depths at the points downstream in the ebb tide. The time variation of the scour depth of the first profile and the second profile at the two sides of the model for experimental run 2 is presented in Fig. 14. The same phenomena as in experiment run 1 were observed, where the number of scoured points on the profiles increased, and the scour depth increased as the scour process progressed. There were two scour holes on the first profile, of which the scour depth of the bigger hole was 10.4 cm, and the two scour holes ran through the entire profile. Fig. 14 shows that only one obvious scour hole with a scour depth of 6.02 cm ran through the second profile. The slightly asymmetric initial bed
a)
3.2.2. Equilibrium scour hole profiles in bidirectional current scour After experiment run 2 was terminated, the water in the scour hole was drained by siphoning, and the scoured topography was photographed. Fig. 15 shows the photograph and topography by TECPLOT of the equilibrium scour hole for experimental run 2. Sand ripples around the model were observed in the photograph. Four scour holes were approximately symmetrically located along the flow direction and two larger holes, which ran through the first profile, were located at the downstream of the foundation in the flood tide, whereas two smaller holes were at the downstream of the model in the ebb tide. The location of the maximum scour depth in the bidirectional current scour experiment depended on whether the flood tide or ebb tide had a bigger velocity. For the sand pits, the bed slopes of the profiles far from the model were smaller than the angle of repose of the sediment, and the ones closer to the model were similar to the angle of repose. The four “wide” and “fat” scour holes, which were low in the middle and high at the two ends, were saddle-shaped, but they were shorter and much closer to the model than the ones in the steady current experiment. The maximum scour depth was 13 cm for the experiment run conducted in bidirectional current with a maximum velocity of 29.52 cm/s. The scour depths at the sides of the model were small and were less than the scour depth downstream and upstream of the model. The deepest pit was far from the model, similarly to experimental run 1, and the structural features enhanced the safety of the composite bucket foundation in bidirectional current-induced scour. It was stated that scour depth was larger in steady flows than in bi-directional flows, but Figs. 10 and 13 appeared to show deeper scour in some monitoring points for bi-directional flow. That was because scour holes were farther from the model in steady flows. In tidal flows, the monitoring points were much closer to the location of the maximum depth of the scour pit. Under the precondition the maximum depth of the scour hole in unidirectional flows was about 15% larger than that in bi-directional flows, but the scour depths in some monitoring points were larger in bi-directional flow. 3.3. Discussion 3.3.1. Comparison between the steady current scour and bidirectional current scour Fig. 16 presents a comparison of the contour plot of the equilibrium scour holes under different flow conditions taking the model with a diameter of 150 cm as an example. The ultimate scour depths under steady and bidirectional current were 15 cm and 13 cm, respectively. According to experiment runs 3 and 4, the
b)
2
2 1
0
0 Scour depth/cm
-2 -4 1h 6h 11h 16h 21h 26h 27h
-6 -8 -10 -12 -90
-60
-30
0
30
Coordinate of the first profile/cm
60
90
Scour depth/cm
Scour depth/cm
T. Yu et al. / Ocean Engineering 117 (2016) 311–320
-1 -2 1h 6h 11h 16h 21h 26h 27h
-3 -4 -5 -6 -7 -90
-60
-30
0
30
60
Coordinate of the second profile/cm
Fig. 14. Time variation of the scour depth of the first and second profiles for experimental run 2.
90
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Fig. 15. Photograph and topography of the equilibrium scour hole for experimental run 2.
maximum depths of the equilibrium scour hole under steady and bidirectional current were 8 cm and 6.5 cm, respectively. Diverse observations were made in the comparison between the steady current scour and bidirectional current scour, such as: (a) the maximum equilibrium scour depth under bidirectional current was approximately 16% less than that under steady current; (b) there were four scour holes upstream and downstream of the model in the experiment run with bidirectional current scour because of the two-way flow in the experiment, whereas only two scour holes were observed in steady current scour; and (c) the range of equilibrium scour holes that were spoon-shaped was larger than the saddle-shaped scour holes in bidirectional current scour. 3.3.2. Effect of depth on the scour hole The results of the ultimate scour depth versus water depth for the models are shown in Fig. 17. The maximum equilibrium scour depths of these three experiment runs with water depths of 15 cm, 20 cm and 25 cm were 8.75 cm, 9.4 cm and 9.8 cm, respectively. The variation in the scour depth was due to the change in flow depth. From this topography, it was clear that for a model of a particular diameter, the scour depth increased slightly with increased water depth. 3.3.3. Effect of flow velocity on the scour hole The results of the ultimate scour depth versus velocity of flow for the models are shown in Fig. 18. The maximum scour depths induced by steady current with velocities of 15 cm, 25 cm and
35 cm were 1.2 cm, 9.8 cm and 20.1 cm, respectively. The scour depth varied appreciably with current velocity. From this topography, it was clear that for a composite bucket foundation of a particular diameter, the scour depth increased with increased flow velocity. The topography of experiment run 9 showed that the slight asymmetry of the initial bed profile resulted in asymmetrical scour holes under a current with a larger flow velocity. 3.3.4. Relationship between the maximum scour depth and the other dimensionless parameters The scour depth under steady current was related to various parameters based on Eq. (2). The small influence of water depth and large influence of current speed suggested that the Froude number was not the governing parameter, so the Froude number could be ignored as Reynolds number. Grouping all of the parameters, the ultimate scour depth is expressed in terms of a combined dimensionless parameter that includes the Shields parameter and the non-dimensional numbers relating the soil properties and the diameter of the composite bucket foundation.
hb /h = a 0 (B/h)a1 θ a2 (d50/h)a3
(6)
To conduct correlation analysis, after taking the logarithm
ln (hb /h) = ln a 0 + a1 ln (B/h) + a2 ln θ + a3 ln (d50/h)
(7)
Based on the nine experiment runs, the coefficients were obtained through multiple regression analysis:
a 0 = 15.60, a1 = −0.796, a2 = 1.484, a3 = 1.796
Fig. 16. Contour plot of the equilibrium scour hole for experiments conducted in steady and bidirectional current around the model with a diameter of 150 cm.
(8)
T. Yu et al. / Ocean Engineering 117 (2016) 311–320
319
Fig. 17. Topography by TECPLOT of the equilibrium scour hole under different water depths and constant velocity.
Fig. 18. Topography by TECPLOT of the equilibrium scour hole under different velocities and the same water depth.
tested under suitable simulated conditions.
and the following correlation was obtained:
hb /h =
15.6 (B/h)−0.796θ1.484 (d
50
/h)1.796
(9)
The coefficient of correlation was 0.965. Hence, the above equation can be used for the prediction of the ultimate scour depth for the range of 40000 < Re < 200000, 0.09 < Fr < 0.23, and d50 = 0.12 mm . Based on the present experimental data, an equation relating ultimate scour depth to the related parameters was suggested. Due to the complex nature of physicochemical forces involved in studies conducted in silty sand sediments, a simple empirical analysis is not adequate to obtain predictions for scour depths. At best, the results from this study are applicable to a similar type of sediment
4. Conclusions Scour around a composite bucket foundation was investigated by performing laboratory tests. The scouring process, time variation of the scour depth, equilibrium scour hole geometry, and the effect of the water depth and flow velocity on the maximum scour depth were analyzed. The results can be summarized as follows: 1. There are two spoon-shaped scour holes at the back of the composite bucket foundation in steady current-induced scour, whereas the scour depth in front of the model is small. For the
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composite bucket foundation embedded in silty sand under bidirectional current, the scour depth around the model varies around the original level at the beginning of the scour period, and four saddle-shaped scour holes are formed on both sides of the model at the equilibrium state. 2. Comparison between the steady current scour and bidirectional current scour showed that maximum equilibrium scour depth under bidirectional current is approximately 16% less than that under steady current, and the scour holes under bidirectional current are shorter and much closer to the model than the ones in steady current experiment. 3. Compared with the pile foundation, the scour around the composite bucket foundation is due to the effects of vortex shedding in the wake of the model (excluding the horseshoe vortex), and the structural features of the composite bucket foundation can improve the safety in current-induced scour. 4. The normalized equilibrium scour depth increases slightly with increasing water depth, and increases significantly with the increasing flow velocity. A general relationship for the scour depth around the composite bucket foundation in terms of the combined Shields number and non-dimensional parameters relating the soil properties and the width of the composite bucket foundation has been suggested. Preliminary study of the mechanism of scour around the composite bucket foundation is presented in this paper. However, to summarize the empirical formula to predict the maximum scour depth around composite bucket foundation, more tests with various water depths, velocities, diameters of foundation and soil properties are needed.
Acknowledgments This work was financially supported by the Funds for Creative Research Groups of China (Grant No. 51321065), the Fundamental Research Funds for the Central Universities (Grant No. 201513002) and the National Natural Science Foundation of China (Grant No. 51509230). Support from the funding agency is sincerely acknowledged.
References Amini, A., Melville, B.W., Ali, T.M., Ghazali, A.H., 2012. Clear-water local scour around pile groups in shallow-water flow. J. Hydraul. Eng. 138 (2), 177–185.
Byrne, B.W., Houlsby, G.T., 2003. Foundations for offshore wind turbines. Philos. Trans. R. Soc. A 361 (1813), 2909–2930. Cheng, L., Yeow, K., Zang, Z.P., Li, F.J., 2014. 3D scour below pipelines under waves and combined waves and currents. Coast. Eng. 83, 137–149. Ding, H.Y., Lian, J.J., Li, A.D., Zhang, P.Y., 2013. One-step-installation of offshore wind turbine on large-scale bucket-top-bearing bucket foundation. Trans. Tianjin Univ. 19 (3), 188–194. Dixen, M., Sumer, B.M., Fredsøe, J., 2013. Numerical and experimental investigation of flow and scour around a half-buried sphere. Coast. Eng. 73, 84–105. Khosronejad, A., Kang, S., Sotiropoulos, F., 2012. Experimental and computational investigation of local scour around bridge piers. Adv. Water Resour. 37, 73–85. Kim, H.S., Nabi, M., Kimura, I., Shimizu, Y., 2014. Numerical investigation of local scour at two adjacent cylinders. Adv. Water Resour. 70, 131–147. Lee, K.H., Mizutani, N., 2008a. Experimental study on scour occurring at a vertical impermeable submerged breakwater. Appl. Ocean. Res. 30 (2), 92–99. Lee, S.O., Sturm, T., 2008b. Scaling issues for laboratory modeling of bridge pier scour. In: Proceedings of 4th International Conference on Scour and Erosion, 5– 7 Nov., Tokyo, Japan, pp. 111–115. Lian, J.J., Ding, H.Y., Zhang, P.Y., Yu, R., 2012. Design of large-scale prestressing bucket foundation for offshore wind turbines. Trans. Tianjin Univ. 18 (2), 79–84. Lian, J.J., Sun, L.Q., Zhang, J.F., Wang, H.J., 2011. Bearing capacity and technical advantages of composite bucket foundation of offshore wind turbines. Trans. Tianjin Univ. 17 (2), 132–137. Liu, M.M., Yang, M., Wang, H.J., 2014. Bearing behavior of wide-shallow bucket foundation for offshore wind turbines in drained silty sand. Ocean Eng. 82 (15), 169–179. Lu, L., Li, Y.C., Qin, J.M., 2005. Numerical simulation of the equilibrium profile of local scour around submarine pipelines based on renormalized group turbulence model. Ocean Eng. 32 (17–18), 2007–2019. Matutano, C., Negro, V., López-Gutiérrez, J.S., Esteban, M.D., 2013. Scour prediction and scour protections in offshore wind farms. Renew. Energy 57, 358–365. Myrhaug, D., Ong, M.C., Føien, H., Gjengedal, C., Leira, B.J., 2009. Scour below pipelines and around vertical piles due to second-order random waves plus a current. Ocean Eng. 36 (8), 605–616. Pagliara, S., Kurdistani, S.M., 2013. Scour downstream of cross-vane structures. J. Hydro-Environ. Res. 7 (4), 236–242. Pagliara, S., Palermo, M., 2008. Scour control downstream of block ramps. J. Hydraul. Eng. 134 (9), 1376–1382. Qi, W.G., Gao, F.P., 2014. Equilibrium scour depth at offshore monopile foundation in combined waves and current. Sci. China Technol. Sci. 57 (5), 1030–1039. Rambabu, M., Narasimha Rao, S., Sundar, V., 2003. Current-induced scour around a vertical pile in cohesive soil. Ocean Eng. 30 (7), 893–920. Roulund, A., Sumer, B.M., Fredsøe, J., Michelsen, J., 2005. Numerical and experimental investigation of flow and scour around a circular pile. J. Fluid Mech. 534, 351–401. Sumer, B.M., Fredsøe, J., 2000. Experimental study of 2D scour and its protection at a rubble-mound breakwater. Coast. Eng. 40 (1), 59–87. Sumer, B.M., Fredsoe, J., 2001. Wave scour around a large vertical circular cylinder. J. Waterway, Port, Coastal Ocean Eng. 127 (3), 125–134. Zhang, H., Nakagawa, H., Kawaike, K., Baba, Y., 2009. Experiment and simulation of turbulent flow in local scour around a spur dyke. Int. J. Sediment Res. 24 (1), 33–45. Zhao, M., Cheng, L., Zang, Z.P., 2010a. Experimental and numerical investigation of local scour around a submerged vertical circular cylinder in steady currents. Coast. Eng. 57 (8), 709–721. Zhao, M., Cheng, L., 2010b. Numerical investigation of local scour below a vibrating pipeline under steady currents. Coast. Eng. 57 (4), 397–406. Zhao, M., Zhu, X.S., Cheng, L., Teng, B., 2012. Experimental study of local scour around subsea caissons in steady currents. Coast. Eng. 60, 30–40.
Contents lists available at ScienceDirect
Ocean Engineering journal homepage: www.elsevier.com/locate/oceaneng
Experimental investigation of current-induced local scour around composite bucket foundation in silty sand Tongshun Yu a,b,n, Jijian Lian b, Zhongqiang Shi b,c, Hongzhen Wang b a
College of Engineering, Ocean University of China, Qingdao 266100, China State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China c China Harbour Engineering Company Ltd., Beijing 100027, China b
art ic l e i nf o
a b s t r a c t
Article history: Received 8 September 2015 Received in revised form 29 December 2015 Accepted 20 March 2016
In recent years, local scour has received attention because it may have a negative effect on coastal structures. Because of the large-scale arc transition and other special constructs, flow patterns around composite bucket foundation are complicated, and the local scour around composite bucket foundation has rarely been reported in the literature. In the present study, a detailed laboratory testing program on model with diameters of 150 cm and 75 cm embedded in silty sand was conducted in a flume. The scouring process and equilibrium scour hole geometry under steady and bidirectional current were investigated in detail. A procedure was suggested to predict the ultimate scour depth based on the observed variation of the scour depth over a limited time period. The equilibrium scour depth under a bidirectional current was approximately 16% less than that under a steady current, and there were two spoon-shaped scour holes in the steady current scour, whereas four saddle-shaped scour holes were discovered in bidirectional current scour. Based on these results, a functional relationship was suggested between the scour depth and other parameters, such as the diameter of the foundation, Shields parameter and median diameter of the soil bed. & 2016 Elsevier Ltd. All rights reserved.
Keywords: Local scour Composite bucket foundation Current Maximum scour depth
1. Introduction Mono-pile, gravity-base, tripod, jacket structure and suction caisson foundations are widely applied in the development of offshore wind power (Byrne and Houlsby, 2003). Mono-pile structures are the most widely used in offshore wind structures and gravity foundation is the second most common. However, the strict requirements for construction equipment and technologies restrict the wide application of mono-pile structures in China. Gravity foundation structures require more than 5000 t of concrete for the effective transmission of wind turbine loads, and the construction cost of the jacket foundation structure is high. A new offshore foundation, the wide-shallow composite bucket foundation, is shown in Fig. 1 and was proposed by Lian et al. (2011, 2012) and Ding et al. (2013) due to the advantages of reduced construction cost and shortened construction period compared to conventional foundations. The composite bucket foundation usually has a large diameter (generally larger than 20 m, especially for wind turbines with more than 3 WM power in China) and an n Corresponding author at: College of Engineering, Ocean University of China, Qingdao 266100, China. E-mail address: [email protected] (T. Yu).
http://dx.doi.org/10.1016/j.oceaneng.2016.03.045 0029-8018/& 2016 Elsevier Ltd. All rights reserved.
aspect ratio (the skirt length to the foundation diameter) of less than 0.5 (Liu et al., 2014). The foundation takes full advantage of the high tensile capacity of steel strands and the high compressive capacity of concrete so that the problem of transferring the large moment and horizontal loads from the tower to the foundation can be solved by designing the pre-stressing arc transition structure. However, because of the large-scale arc transition and other special constructs, as shown in Fig. 1, the flow pattern around the composite bucket foundation under the action of current is complicated, which is illustrated schematically in Fig. 2. It is inaccurate to estimate the scouring depth using empirical formulas based on other types of foundations, such as pile foundations. Local scour of sediments around ocean structures has been studied extensively because it has been identified as one of the key factors that cause structure failure or undesired deposition in coastal and offshore engineering. To investigate scour when designing waterway, coastal and offshore structures, numerical analysis (Lu et al., 2005; Zhao and Cheng, 2010b) and experimental study (Sumer and Fredsøe, 2000; Pagliara and Kurdistani, 2013) are the two main methods for the determination of the scour depth. Usually, a numerical hydrodynamic model is proposed in numerical analysis, whereas in experimental study, test flumes and measurements are designed. Kim et al. (2014) built a hydrodynamic model with an adaptive multilevel structure Cartesian
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composite bucket foundation due to the lack of laboratory observations. There is no published literature on the local scour around composite bucket foundation. The present study investigates the flow and scour around composite bucket foundation via laboratory tests. The main objectives of this study were to investigate: (1) the mechanism of scour around a composite bucket foundation subject to a steady and bidirectional current; (2) the difference between the scour characteristics under a steady and bidirectional current; and (3) the relationship between the maximum scour depth and other dimensionless parameters. The arrangement of this paper is as follows. In Section 2, the test setup, the approach used for the tests and the test procedure are presented. The results of the scour test for a composite bucket foundation under steady and bidirectional current are presented in Section 3. A comparison of the results under a steady and bidirectional current and discussions are given in Section 3, and the conclusions of the paper are given in Section 4.
Fig. 1. Photograph of a composite bucket foundation.
z
Vortex shedding
x
Hammed water
2. Test setup and measurements 2.1. Dimensional analysis
Boundary layer U
Horseshoe vortex
Contraction of streamlines
y
Fig. 2. Sketch of the flow around a composite bucket foundation.
grid to analyze the local scour around cylinders in a side-by-side or tandem arrangement. Dixen et al. (2013) described the results of scour around a half-buried sphere exposed to a steady current by combined numerical and experimental investigation. Because of the scaling effect, laboratory tests tend to overestimate scour depth measurements (Lee and Sturm, 2008b). Despite the effect of scaling, laboratory tests are still widely used as the main method for investigating local scour mechanisms (Lee and Mizutani, 2008a; Zhao et al. 2012). There are also some empirical formulae that are used to predict the maximum scour depth for various coastal structures at the prototype size. Matutano et al. (2013) summarized the most important formulations developed for predicting the maximum scour depth of mono-pile foundations under different flow conditions (steady current only, waves only, or steady current and waves). Amini et al. (2012) provided a reasonable formula to predict the scour depth at pile groups under steady flows. With these methods, several researchers have assessed the scour depth around traditional coastal structures, including vertical circular cylinders (Zhao et al., 2010a; Roulund et al., 2005), submarine pipelines (Lu et al., 2005), bridge piers with different shapes (Khosronejad et al., 2012), rubble mound breakwaters (Sumer and Fredsøe, 2000), and new types of structures (Pagliara and Palermo, 2008; Pagliara and Kurdistani, 2013; Zhang et al.2009). Most of the studies of the local scour around marine structures have focused on scour due to waves (Sumer and Fredsoe, 2001), currents (Rambabu et al., 2003; Zhao et al., 2010a) or combined waves and currents (Qi and Gao, 2014; Cheng et al., 2014). Myrhaug et al. (2009) derived the scour depth below pipelines and around single vertical piles for combined waves plus currents. Most previous studies placed an emphasis on the scour around various traditional and new types of coastal structures, but few studies have examined the flow and effect of scour around
The local scour around a composite bucket foundation under the current involves a complex interaction among current, foundation and its neighboring soil. There are many variables that play relevant role on the scour around a composite bucket foundation, such as the foundation, sand-bed and fluid properties. The foundation properties can be characterized by its diameter ( B ). The sand-bed properties can be summarized by median diameters of soil ( d50 ), sediment grain density ( ρs ), coefficient of permeability ( ks ), shear modulus of soil skeleton ( G ), and degree of saturation ( Sr ). The fluid physical properties can be characterized by water density ( ρw ) and kinematic viscosity of water ( ν ). The current flow can be characterized by water depth (h), velocity of the current (u), and representative near-bed velocity of the current flow ( Uc ). The gravitational acceleration ( g ) is included among the variables. Based on the aforementioned analysis, the equilibrium scour depth ( hb ) can be described by the following functional relationship:
hb = f (B, d50, ρs , ks, G, Sr , ρw , ν, h, u, Uc , g , ⋯)
(1)
Vortex formation is the most important mechanism of scour in front of the composite bucket foundation, and some parameters can be ignored in Eq. (1). Applying the Buckingham π theorem to these dimensional parameters, the scour for the composite bucket foundation is dependent on the following non-dimensional parameters:
⎞ ⎛h B d f ⎜ b , , 50 , Re , Fr , θ ⎟ = 0 ⎠ ⎝ h h h
(2)
where Re is the Reynolds number, Fr is the Froude number and θ is the Shields parameter. In the above equation, the Reynolds number can be ignored because the seabed acts as a rough wall with scour occurring (Lee and Mizutani, 2008a). These parameters are discussed in Section 3.3.4. 2.2. Test setup The laboratory scour experiments around composite bucket foundation under current were conducted in the water flume at the State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, China. The water flume was 35 m in length, 7 m in width and 1.6 m in height. A movable sand basin of
Weight pecentage of less than a certion size/%
T. Yu et al. / Ocean Engineering 117 (2016) 311–320
100 90 80 70 60 50 40 30 20 10 0 10
1
0.1
0.01
313
1E-3
Patical size/mm Fig. 3. Sediment grading curve. Fig. 5. Photograph of the experimental setup for the flume test.
50 ——Logarithmic law y=0 ∇
40
Height/cm
9 m in length and the same width as the water flume with a median sand diameter of d50 ¼0.12 mm (as seen in Fig. 3) and specific gravity s ¼ 2.65 was built in the middle of the water flume. The angle of repose of the sand was ϕs = 41° . The sediment recess was from 10 cm to 40 cm deep, and sediment of 40 cm deep was located at the center position. Water was recirculated into the flume by two pumps with a 1.27 m3/s capacity, which were controlled by a regular signal generator. Boards for flow-adjusting were fixed at the bottom of the water flume to minimize the turbulence characteristics of the inlet flow in the test, and the desired incident smooth flow was generated behind the boards. The model with a diameter of 150 cm or 75 cm (as seen in Fig. 4) was placed 17.5 m from the pump and seated on the bottom of the water flume. An ADV produced by Nortek AS mounted on an instrument carriage was used to measure the scour hole profiles and flow characteristics. The discharge from the flume was controlled with a flow control valve. A photograph of the experimental arrangement is shown in Fig. 5.
30 20 10
2.3. Undisturbed flows and test conditions Before the scour tests were conducted, the undisturbed velocity profiles above the sandy bed at the location where the model was installed later on (set as y¼ 0), were measured. The velocity profiles were measured using ADV. The mean velocity profiles were obtained by averaging the recorded velocity samples. Fig. 6 shows the measured velocity profiles at the location of the model when water depth was 0.5 m and depth averaged velocity was 0.2952 m/ s. The measured velocity profiles are correlated to the logarithmic law of the velocity profile (Zhao et al., 2010a).
u (z ) =
uf z ln (30 ) k ks
(3)
0
0
10
20 30 Velocity/cm/s
Fig. 6. Undisturbed mean velocity profile in the vertical direction at y¼ 0.
where z is the vertical distance from the seabed, uf is the friction velocity, ks is the Nikurase roughness and k ( =0.41) is the von Kármán constant. The origin of the vertical coordinate z was defined at the mean bed level if ripples exist. The uf and ks in Eq. (3) are obtained by the least square method based on the measured
Unit:cm
150cm 75cm
(a) Photograph of the models
40
(b) Dimension of model with a diameter of 150 cm
Fig. 4. Models of the composite bucket foundation.
T. Yu et al. / Ocean Engineering 117 (2016) 311–320
3
Table 1 Experimental conditions (s is the steady flow condition and b is the bidirectional flow condition in the experiments; * is the maximum Shields parameter in bidirectional flow condition).
Run 1s 150 Run 2b 150 Run 3s 75 Run 4b 75 Run Run Run Run Run
5s 6s 7s 8s 9s
75 75 75 75 75
Period/min Water depth/ cm
Skin friction shields parameter
Shields parameter
29.52 29.52/ 25.04 20.87 20.87/ 17.71 25 25 25 15 35
– 167.03
50 50
0.078 0.078*
0.525 0.525*
– 118.11
25 25
0.045 0.045*
0.17 0.17*
– – – – –
15 20 25 25 25
0.073 0.068 0.065 0.023 0.127
0.253 0.261 0.286 0.079 0.491
1
τb ρ (s − 1) gd50
Flow
5
composite bucket foundation 6 7
(4)
where τb = ρu2f is the bed shear stress in the horizontal direction, s = ρs /ρ is the specific gravity of the sediment grain. τb in Eq. (4) is the total shear stress which includes the effects of skin friction and the shear stress due to the bed forms such as sand ripples. For sediment transport purpose, the skin friction is responsible for bed load transport and entrainment of sand from the bed. The bed shear stress and the Shields parameter are calculated from the depth averaged velocity based on logarithmic velocity distribution. According to logarithmic profile of velocity, the bed shear stress 2 due to skin friction is τbs = ρCDs U¯ , where CDs = {k /[ln (h/z0s ) − 1]}2,
where the non-dimensional grain size D* is defined as D* = [g (s − 1) /v 2]1/3 d50 with v being the kinematic viscosity of water. The critical Shields parameter for sand size d50 ¼0.12 mm is estimated to be 0.068 based on Eq. (5). Table 1 provides a summary of the experimental conditions. The experiment was conducted under steady and bidirectional current, ranging from 15 cm to 50 cm in water depth and from 15 cm/s to 35 cm/s in velocity. In the experiment, two models with diameters of 150 cm and 75 cm were selected, and the diameter of the prototype composite bucket foundation was 30 m. The length scales between the model and prototype were 1:20 and 1:40 in accordance with the principles of Froude similarity, and the corresponding time scales were 1:4.47 and 1:6.32, respectively. Therefore, the periods for bi-directional flow were 167.03 min in run 2 and 118.11 min in run 4, with a prototype period of 12.4 h. During the bidirectional current of run 2, the maximum velocity of the flood tide was 29.52 cm/s, and the maximum velocity of the ebb tide was 25.04 cm/s. For run 4, 20.87 cm/s and 17.71 cm/s were the maximum velocity of flood tide and ebb tide. Experiment
was at 0 relative to flow direction
Point
was at 45o relative to flow direction
Point
was at 90o relative to flow direction
Point
was at 135o relative to flow direction
Point
was at 180o relative to flow direction
Point
was at 225o relative to flow direction
Point
was at 270o relative to flow direction
Point
was at 315o relative to flow direction Fig. 7. Location of the monitoring points.
170
Unit: cm
35
36 The second profile
(5)
o
Point
Y
The first profile
z0s = d50/12. Due to the existence of sand ripples, the roughness determined from velocity measurements are much larger than the skin friction roughness. This leads to a total Shields parameter larger than the skin friction Shields parameter. The sediment transport occurs if the skin friction Shields parameter exceeds the critical Shields parameter. One of the widely used empirical formulae for calculating the critical Shields parameter is
0.30 θcr = + 0.055 ⎡⎣ 1 − exp ( − 0.020D* ) ⎤⎦ 1 + 1.2D*
X
8
velocities. It can be seen that the velocity distributions in the vertical direction follow logarithmic distribution in the whole water depth. The Shields parameter θ is the non-dimensional bed shear stress, which is defined by
θ=
Y
85
Maximum velocity of flow/cm/s
4
75
Diameter of model/ cm
2
X
75
Test
Unit: cm
1
composite bucket foundation
170
314
Flow
70 Fig. 8. Location of the monitoring profiles.
run 2 was the comparative trial of run 1. Similarly, experiment run 4 was the comparative trial of run 3. The flow set was as follows: the flow direction of the flood tide in experiment runs 2 and 4 was the same as the flow direction of the steady current, the maximum velocity of the flood tide which was larger than the velocity of the ebb tide in the bidirectional current was the same as the velocity of the corresponding steady current. Taking the model with a diameter of 150 cm as an example, the time variation of the scour depth at regular time intervals of one
T. Yu et al. / Ocean Engineering 117 (2016) 311–320
1
Unit: cm
80
315
0
Fl ow
80
model
360
200
X
Scour depth/cm
-1
Y
-2 (0°) (45°) (90°) (135°) (180°) (225°) (270°) (315°)
-3 -4 -5
360 -6 Fig. 9. Locations of the topography measuring points.
0
4
8
12
16
20
24
28
32
36
Time/h hour was monitored at eight monitoring points, which were numbered as shown in Fig. 7 around composite bucket foundation model. The points were located along the circumference in a symmetric arrangement, and the distance between the monitoring points and model edge was 10 cm. The naming rule was as follows: point ① was at 0° with the direction of flow, and point ② was at 45° with the direction of flow. Similarly point ⑧ was at 315°. The process of scour eventually reached a state of equilibrium with time if the time variation of the scour depth of the eight monitoring points at regular time intervals of one hour was less than 0.3 cm. The time variation of the scour depth was also monitored by two rows of monitoring points in a direction perpendicular to the flow, as shown in Fig. 8, around the composite bucket foundation model. Two profiles were located on both sides of the model in a symmetric arrangement, and the distance between profiles and the circle center of the model was 85 cm. There were 35 monitoring points on each profile, and the distance between neighboring monitoring points in the same profile was 5 cm. The scour pattern was determined based on the scour depth of the measurements points within the scope of 360 cm 360 cm, as shown in Fig. 9, around the model with a diameter of 150 cm. The scour depth of each point was recorded by the ADV one by one. To obtain the scour pattern in detail, while reducing the time required for reading data, points at a distance interval of 10 cm at the edge of the scour area were selected for the scour depth record, and the points of serious scour around the model were placed at a distance interval of 5 cm. There were approximately two thousand and five hundred measuring points in the area, and twelve hours are required to complete the scour depth record. The topography of the ultimate basin was obtained by TECPLOT. The distances of the monitoring points, profiles and locations of the topography measuring points were halved during the experiment using the model with a diameter of 75 cm. For the experiment runs using the model with a diameter of 75 cm, the time for recording the scour depth of each point was approximately ten hours. 2.4. Test procedure For each test run, the bed conditions were thoroughly checked before the experiment was performed, and the sand bed was 5 mm below the water surface. Given that the scour depth around the structure did not generally exceed 20 cm for this small-scale laboratory test, it was determined that the initial bed conditions might affect the final results. Therefore, to minimize the error caused by the initial bed profile, the sand bed was repeatedly
Fig. 10. Scour depth as a function of t recorded at eight monitoring points for experimental run 1.
leveled until the measured bed profile was within a tolerance range of 5 mm based on the ideal conditions. After setting the initial sand bed, water was allowed to rise along the flume until the required still water level was reached, and water was added sufficiently slowly to reduce air entrainment inside the seabed and prevent disturbances of the initial bed conditions. The flow depth was monitored throughout the experiment run against graduated scales attached to the flume wall. In general, testing was continued for two or three uninterrupted days, and an experiment was terminated when no scouring was observed for at least two successive hours. The scour depth of each point shown in Fig. 8 was recorded by ADV one by one. After the recording was complete, the water in the scour hole was drained by siphoning. Then, the detailed geometry of the scour hole was photographed.
3. Results and discussion To investigate the scouring process and the equilibrium scour hole geometry for composite bucket foundation under steady and bidirectional current, experiment runs 1–4 using models with diameters of 150 cm and 75 cm were tested. The results presented in Sections 3.1 and 3.2 are for the model with a diameter of 150 cm. In addition, experiment runs 5–9 used the model with a diameter of 75 cm, and the effects of the depth and flow velocity on the ultimate scour depth were investigated. 3.1. Results of the steady current 3.1.1. Time-development of the steady current-induced scour depth Fig. 10 shows the time variation of the scour depth at eight monitoring points for experimental run 1 (the larger the absolute value of the scour depth in the curve, the more serious the scour). The scouring process commenced from the back of the model, and at monitoring points No. ③–⑦, the time variation of the scour depth which was less than 2 cm, was small during the scour process. The scour depths of monitoring points No. ①, ② and ⑧ downstream of the model were much bigger than the other locations. No scouring was observed from the 34th to 36th hour, so the equilibrium scour time was 34 h. Considerable oscillations of the scour depth with time were observed, and the oscillations were caused by the migration of the sand ripples in the flume. Fig. 11 shows the time variation of the scour depth on the first and second profiles for experimental run 1. As scour progressed,
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b)
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Scour depth/cm
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1 0 -1 -2 -3 -90
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30
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Fig. 11. Time variation of the scour depth of the first and second profiles for experimental run 1.
Fig. 12. Photograph and topography of the equilibrium scour hole for experimental run 1.
the number of scoured points on the first profile increased, and the scour depth also increased. There were two scour holes on the first profile. The scour depth of the larger hole was 12.4 cm, and the two scour holes ran through the entire profile. The time variation of the scour depth on the second profile showed that no obvious scour occurred on the second profile during the scour process, and even sediments were observed to build up at some points of the second profile. 3.1.2. Equilibrium scour hole profiles in steady current scour The scour depth of points shown in Fig. 9 was recorded by ADV one by one when the equilibrium state was reached in run 1, and the topography was drawn by TECPLOT. Fig. 12 shows a photograph and the topography of the equilibrium scour hole for experimental run 1. A scour pit downstream of the model was recognizable, and there were two scour holes symmetrically along the flow direction downstream of the model. The first profile crossed the two holes. There were obvious sand ripples approximately perpendicular to the flow direction around the model, and the heights of these ripples were smaller than 1.5 cm. A ridgeshape sand dune, which aligned in the middle of the flow direction, was formed in the wake of the foundation, and the peak of the sand ridge was formed at a location where the mean flow reversed. Although there were sand ripples around the scour pit, the bed in the scour pit was always smooth, especially at the bottom of the pit. When a crest of a sand ripple reached the front edge of the scour pit, it collapsed and slid into the bottom of the scour pit. At the bottom of the scour pit (approximately 17 cm from the model), the vortex shedding picked up the sediment particles into suspension. The scour of sediment at the bottom of the scour hole increased the slope angle of the scour pit. Morphologically, the
two “wide” and “fat” scour holes which were deep in the front and swallow in the back were spoon-shaped, and the maximum scour depth was 15 cm for run 1. The bed slopes downstream of the sand pit were smaller than the angle of repose of the sediment, and the slopes at the upstream edge of the sand pit were almost same as the angle of repose. No scour pit was observed upstream or at the sides of the foundation, which was different from the scour pit of the pile foundation (Zhao et al., 2010a). Zhao et al. (2010a) predicted that the initiation of the scour around a vertical cylinder was a combination of the horseshoe vortex and the vortex shedding. The scour in front of the cylinder was due to the horseshoe vortex and that behind the cylinder was due to the vortex shedding. In the present investigation, because of the ring beams and foundation plate between the arc transition and the bucket buried in the silty sand, the effect of the horseshoe vortex on the suspension of sediment particles in front of the foundation was relatively small, and no scour was discovered upstream of the model. The initiation of the scour around the composite bucket foundation was due to vortex shedding, and the peculiar structural features in steady current scour prevented scour upstream of the foundation. Morphologically, in the investigation of the vertical circular cylinder foundation (Zhao et al., 2010a), the location of the maximum depth of the scour pit was close to the foundation, whereas the location was farther from the composite bucket foundation. Based on the two differences between the cylinder foundation and the composite bucket foundation, the structural features could keep the deepest pit away from the model and enhance the safety of the composite bucket foundation in currentinduced scour.
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profile led to the slightly asymmetric scour hole.
2 1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10
(0°) (45°) (90°) (135°) (180°) (225°) (270°) (315°)
0
4
8
12 16 Time/h
20
24
28
Fig. 13. Scour depth as a function of t recorded at eight monitoring points for experimental run 2.
3.2. Results of the bidirectional current 3.2.1. Time-development of the bidirectional current-induced scour depth Fig. 13 shows the time variation of the scour depth at the eight monitoring points for experimental run 2. At the beginning of the scour period, the scour depth of each point oscillated around the original level. The scour depths at monitoring points No. ①, ② and ⑧, which were much larger than the other location as in the run 1, increased at a faster rate after 6 h of testing, and the time variation of the scour depth at other monitoring points was less than 2.5 cm during the test. After approximately 25 h, the scour depth of each monitoring point stabilized, so the equilibrium scour time was 25 h. Oscillation was as obvious as in experiment run 1 during the time variation of the scour depth at eight points. The scour depths at the monitoring points downstream of the model in the flood tide were much larger than the scour depths at the points downstream in the ebb tide. The time variation of the scour depth of the first profile and the second profile at the two sides of the model for experimental run 2 is presented in Fig. 14. The same phenomena as in experiment run 1 were observed, where the number of scoured points on the profiles increased, and the scour depth increased as the scour process progressed. There were two scour holes on the first profile, of which the scour depth of the bigger hole was 10.4 cm, and the two scour holes ran through the entire profile. Fig. 14 shows that only one obvious scour hole with a scour depth of 6.02 cm ran through the second profile. The slightly asymmetric initial bed
a)
3.2.2. Equilibrium scour hole profiles in bidirectional current scour After experiment run 2 was terminated, the water in the scour hole was drained by siphoning, and the scoured topography was photographed. Fig. 15 shows the photograph and topography by TECPLOT of the equilibrium scour hole for experimental run 2. Sand ripples around the model were observed in the photograph. Four scour holes were approximately symmetrically located along the flow direction and two larger holes, which ran through the first profile, were located at the downstream of the foundation in the flood tide, whereas two smaller holes were at the downstream of the model in the ebb tide. The location of the maximum scour depth in the bidirectional current scour experiment depended on whether the flood tide or ebb tide had a bigger velocity. For the sand pits, the bed slopes of the profiles far from the model were smaller than the angle of repose of the sediment, and the ones closer to the model were similar to the angle of repose. The four “wide” and “fat” scour holes, which were low in the middle and high at the two ends, were saddle-shaped, but they were shorter and much closer to the model than the ones in the steady current experiment. The maximum scour depth was 13 cm for the experiment run conducted in bidirectional current with a maximum velocity of 29.52 cm/s. The scour depths at the sides of the model were small and were less than the scour depth downstream and upstream of the model. The deepest pit was far from the model, similarly to experimental run 1, and the structural features enhanced the safety of the composite bucket foundation in bidirectional current-induced scour. It was stated that scour depth was larger in steady flows than in bi-directional flows, but Figs. 10 and 13 appeared to show deeper scour in some monitoring points for bi-directional flow. That was because scour holes were farther from the model in steady flows. In tidal flows, the monitoring points were much closer to the location of the maximum depth of the scour pit. Under the precondition the maximum depth of the scour hole in unidirectional flows was about 15% larger than that in bi-directional flows, but the scour depths in some monitoring points were larger in bi-directional flow. 3.3. Discussion 3.3.1. Comparison between the steady current scour and bidirectional current scour Fig. 16 presents a comparison of the contour plot of the equilibrium scour holes under different flow conditions taking the model with a diameter of 150 cm as an example. The ultimate scour depths under steady and bidirectional current were 15 cm and 13 cm, respectively. According to experiment runs 3 and 4, the
b)
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Fig. 14. Time variation of the scour depth of the first and second profiles for experimental run 2.
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Fig. 15. Photograph and topography of the equilibrium scour hole for experimental run 2.
maximum depths of the equilibrium scour hole under steady and bidirectional current were 8 cm and 6.5 cm, respectively. Diverse observations were made in the comparison between the steady current scour and bidirectional current scour, such as: (a) the maximum equilibrium scour depth under bidirectional current was approximately 16% less than that under steady current; (b) there were four scour holes upstream and downstream of the model in the experiment run with bidirectional current scour because of the two-way flow in the experiment, whereas only two scour holes were observed in steady current scour; and (c) the range of equilibrium scour holes that were spoon-shaped was larger than the saddle-shaped scour holes in bidirectional current scour. 3.3.2. Effect of depth on the scour hole The results of the ultimate scour depth versus water depth for the models are shown in Fig. 17. The maximum equilibrium scour depths of these three experiment runs with water depths of 15 cm, 20 cm and 25 cm were 8.75 cm, 9.4 cm and 9.8 cm, respectively. The variation in the scour depth was due to the change in flow depth. From this topography, it was clear that for a model of a particular diameter, the scour depth increased slightly with increased water depth. 3.3.3. Effect of flow velocity on the scour hole The results of the ultimate scour depth versus velocity of flow for the models are shown in Fig. 18. The maximum scour depths induced by steady current with velocities of 15 cm, 25 cm and
35 cm were 1.2 cm, 9.8 cm and 20.1 cm, respectively. The scour depth varied appreciably with current velocity. From this topography, it was clear that for a composite bucket foundation of a particular diameter, the scour depth increased with increased flow velocity. The topography of experiment run 9 showed that the slight asymmetry of the initial bed profile resulted in asymmetrical scour holes under a current with a larger flow velocity. 3.3.4. Relationship between the maximum scour depth and the other dimensionless parameters The scour depth under steady current was related to various parameters based on Eq. (2). The small influence of water depth and large influence of current speed suggested that the Froude number was not the governing parameter, so the Froude number could be ignored as Reynolds number. Grouping all of the parameters, the ultimate scour depth is expressed in terms of a combined dimensionless parameter that includes the Shields parameter and the non-dimensional numbers relating the soil properties and the diameter of the composite bucket foundation.
hb /h = a 0 (B/h)a1 θ a2 (d50/h)a3
(6)
To conduct correlation analysis, after taking the logarithm
ln (hb /h) = ln a 0 + a1 ln (B/h) + a2 ln θ + a3 ln (d50/h)
(7)
Based on the nine experiment runs, the coefficients were obtained through multiple regression analysis:
a 0 = 15.60, a1 = −0.796, a2 = 1.484, a3 = 1.796
Fig. 16. Contour plot of the equilibrium scour hole for experiments conducted in steady and bidirectional current around the model with a diameter of 150 cm.
(8)
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Fig. 17. Topography by TECPLOT of the equilibrium scour hole under different water depths and constant velocity.
Fig. 18. Topography by TECPLOT of the equilibrium scour hole under different velocities and the same water depth.
tested under suitable simulated conditions.
and the following correlation was obtained:
hb /h =
15.6 (B/h)−0.796θ1.484 (d
50
/h)1.796
(9)
The coefficient of correlation was 0.965. Hence, the above equation can be used for the prediction of the ultimate scour depth for the range of 40000 < Re < 200000, 0.09 < Fr < 0.23, and d50 = 0.12 mm . Based on the present experimental data, an equation relating ultimate scour depth to the related parameters was suggested. Due to the complex nature of physicochemical forces involved in studies conducted in silty sand sediments, a simple empirical analysis is not adequate to obtain predictions for scour depths. At best, the results from this study are applicable to a similar type of sediment
4. Conclusions Scour around a composite bucket foundation was investigated by performing laboratory tests. The scouring process, time variation of the scour depth, equilibrium scour hole geometry, and the effect of the water depth and flow velocity on the maximum scour depth were analyzed. The results can be summarized as follows: 1. There are two spoon-shaped scour holes at the back of the composite bucket foundation in steady current-induced scour, whereas the scour depth in front of the model is small. For the
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composite bucket foundation embedded in silty sand under bidirectional current, the scour depth around the model varies around the original level at the beginning of the scour period, and four saddle-shaped scour holes are formed on both sides of the model at the equilibrium state. 2. Comparison between the steady current scour and bidirectional current scour showed that maximum equilibrium scour depth under bidirectional current is approximately 16% less than that under steady current, and the scour holes under bidirectional current are shorter and much closer to the model than the ones in steady current experiment. 3. Compared with the pile foundation, the scour around the composite bucket foundation is due to the effects of vortex shedding in the wake of the model (excluding the horseshoe vortex), and the structural features of the composite bucket foundation can improve the safety in current-induced scour. 4. The normalized equilibrium scour depth increases slightly with increasing water depth, and increases significantly with the increasing flow velocity. A general relationship for the scour depth around the composite bucket foundation in terms of the combined Shields number and non-dimensional parameters relating the soil properties and the width of the composite bucket foundation has been suggested. Preliminary study of the mechanism of scour around the composite bucket foundation is presented in this paper. However, to summarize the empirical formula to predict the maximum scour depth around composite bucket foundation, more tests with various water depths, velocities, diameters of foundation and soil properties are needed.
Acknowledgments This work was financially supported by the Funds for Creative Research Groups of China (Grant No. 51321065), the Fundamental Research Funds for the Central Universities (Grant No. 201513002) and the National Natural Science Foundation of China (Grant No. 51509230). Support from the funding agency is sincerely acknowledged.
References Amini, A., Melville, B.W., Ali, T.M., Ghazali, A.H., 2012. Clear-water local scour around pile groups in shallow-water flow. J. Hydraul. Eng. 138 (2), 177–185.
Byrne, B.W., Houlsby, G.T., 2003. Foundations for offshore wind turbines. Philos. Trans. R. Soc. A 361 (1813), 2909–2930. Cheng, L., Yeow, K., Zang, Z.P., Li, F.J., 2014. 3D scour below pipelines under waves and combined waves and currents. Coast. Eng. 83, 137–149. Ding, H.Y., Lian, J.J., Li, A.D., Zhang, P.Y., 2013. One-step-installation of offshore wind turbine on large-scale bucket-top-bearing bucket foundation. Trans. Tianjin Univ. 19 (3), 188–194. Dixen, M., Sumer, B.M., Fredsøe, J., 2013. Numerical and experimental investigation of flow and scour around a half-buried sphere. Coast. Eng. 73, 84–105. Khosronejad, A., Kang, S., Sotiropoulos, F., 2012. Experimental and computational investigation of local scour around bridge piers. Adv. Water Resour. 37, 73–85. Kim, H.S., Nabi, M., Kimura, I., Shimizu, Y., 2014. Numerical investigation of local scour at two adjacent cylinders. Adv. Water Resour. 70, 131–147. Lee, K.H., Mizutani, N., 2008a. Experimental study on scour occurring at a vertical impermeable submerged breakwater. Appl. Ocean. Res. 30 (2), 92–99. Lee, S.O., Sturm, T., 2008b. Scaling issues for laboratory modeling of bridge pier scour. In: Proceedings of 4th International Conference on Scour and Erosion, 5– 7 Nov., Tokyo, Japan, pp. 111–115. Lian, J.J., Ding, H.Y., Zhang, P.Y., Yu, R., 2012. Design of large-scale prestressing bucket foundation for offshore wind turbines. Trans. Tianjin Univ. 18 (2), 79–84. Lian, J.J., Sun, L.Q., Zhang, J.F., Wang, H.J., 2011. Bearing capacity and technical advantages of composite bucket foundation of offshore wind turbines. Trans. Tianjin Univ. 17 (2), 132–137. Liu, M.M., Yang, M., Wang, H.J., 2014. Bearing behavior of wide-shallow bucket foundation for offshore wind turbines in drained silty sand. Ocean Eng. 82 (15), 169–179. Lu, L., Li, Y.C., Qin, J.M., 2005. Numerical simulation of the equilibrium profile of local scour around submarine pipelines based on renormalized group turbulence model. Ocean Eng. 32 (17–18), 2007–2019. Matutano, C., Negro, V., López-Gutiérrez, J.S., Esteban, M.D., 2013. Scour prediction and scour protections in offshore wind farms. Renew. Energy 57, 358–365. Myrhaug, D., Ong, M.C., Føien, H., Gjengedal, C., Leira, B.J., 2009. Scour below pipelines and around vertical piles due to second-order random waves plus a current. Ocean Eng. 36 (8), 605–616. Pagliara, S., Kurdistani, S.M., 2013. Scour downstream of cross-vane structures. J. Hydro-Environ. Res. 7 (4), 236–242. Pagliara, S., Palermo, M., 2008. Scour control downstream of block ramps. J. Hydraul. Eng. 134 (9), 1376–1382. Qi, W.G., Gao, F.P., 2014. Equilibrium scour depth at offshore monopile foundation in combined waves and current. Sci. China Technol. Sci. 57 (5), 1030–1039. Rambabu, M., Narasimha Rao, S., Sundar, V., 2003. Current-induced scour around a vertical pile in cohesive soil. Ocean Eng. 30 (7), 893–920. Roulund, A., Sumer, B.M., Fredsøe, J., Michelsen, J., 2005. Numerical and experimental investigation of flow and scour around a circular pile. J. Fluid Mech. 534, 351–401. Sumer, B.M., Fredsøe, J., 2000. Experimental study of 2D scour and its protection at a rubble-mound breakwater. Coast. Eng. 40 (1), 59–87. Sumer, B.M., Fredsoe, J., 2001. Wave scour around a large vertical circular cylinder. J. Waterway, Port, Coastal Ocean Eng. 127 (3), 125–134. Zhang, H., Nakagawa, H., Kawaike, K., Baba, Y., 2009. Experiment and simulation of turbulent flow in local scour around a spur dyke. Int. J. Sediment Res. 24 (1), 33–45. Zhao, M., Cheng, L., Zang, Z.P., 2010a. Experimental and numerical investigation of local scour around a submerged vertical circular cylinder in steady currents. Coast. Eng. 57 (8), 709–721. Zhao, M., Cheng, L., 2010b. Numerical investigation of local scour below a vibrating pipeline under steady currents. Coast. Eng. 57 (4), 397–406. Zhao, M., Zhu, X.S., Cheng, L., Teng, B., 2012. Experimental study of local scour around subsea caissons in steady currents. Coast. Eng. 60, 30–40.