An Experimental Study of Irregular Wave Forces on Multiple Quasi-ellipse Caissons

1. Dalian Jiucheng Municipal Design Co. Ltd., Dalian 116000, China

2. CCCC Water Transportation Consultants Co. Ltd., Beijing 100007, China

3. State Key Lab. of Coastal and Offshore Eng., Dalian University of Technology, Dalian 116024, China

An Experimental Study of Irregular Wave Forces on Multiple Quasi-ellipse Caissons

Xiaozhong Ren1＊, Peng Zhang2, Yuxiang Ma3and Yufan Meng1

1. Dalian Jiucheng Municipal Design Co. Ltd., Dalian 116000, China

2. CCCC Water Transportation Consultants Co. Ltd., Beijing 100007, China

3. State Key Lab. of Coastal and Offshore Eng., Dalian University of Technology, Dalian 116024, China

An experimental investigation of irregular wave forces on quasi-ellipse caisson structures is presented. Irregular waves were generated based on the Jonswap spectrum with two significant wave heights, and the spectrum peak periods range from 1.19 s to 1.81 s. Incident wave directions relative to the centre line of the multiple caissons are from 0° to 22.5°. The spacing between caissons ranges from 2 to 3 times that of the width of the caisson. The effects of these parameters on the wave forces of both the perforated and non-perforated caissons were compared and analyzed. It was found that the perforated caisson can reduce wave forces, especially in the transverse direction. Furthermore, the relative interval and incident wave direction have significant effects on the wave forces in the case of multiple caissons.

relative wave length; relative interval; incident wave direction; relative wave height; quasi-ellipse caisson; perforated quasi-ellipse caisson; irregular wave forces

1 Introduction

Gravity dolphin structures are widely used in harbour construction (Zhao, 2008; Hou, 2008). This kind of structure has many advantages including being able to support large loads, has strong structural integrity and durability, and has good resistance to freezing and earthquakes. Furthermore, it is relatively quick to construct and easy to ensure building quality as it involves minimum underwater works.

The quasi-ellipse caisson is a new type of gravity dolphin structure. It was first adopted for the construction of the gravity dolphin wharf of the Dalian ore terminal (phase Ⅱproject) (Bai and Hu, 2006). A caisson is normally made up of three parts, the front and rear parts are the semicircle sections and the middle part is a rectangular section. Compared with the conventional circular caisson, the quasi-ellipse caisson is considered better suited for the large-scale precast concrete construction because a wharf structure with a single row of quasi-ellipse caissons are lesslikely to suffer from uneven settlement in comparison with the use of two rows of circular caissons (Zhu and Ding, 2007; Dong, 2008). In a similar way as the perforated circular caisson (Neelamaniet al., 2000; Vijayalakshmiet al., 2007) and the perforated rectangular caisson (Liet al., 2002, 2003, 2005; Chenet al., 2003; Suhet al., 2006; Liuet al., 2006, 2007, 2008) that have long been investigated and used in practice, it is expected that the perforated quasi-ellipse caissons will also reduce the reflected waves in front of the caisson and the wave forces on the caisson.

At present, despite their successful use in practice, the hydrodynamic behaviour of the quasi-ellipse caisson is little known, especially in regards to the perforated quasi-ellipse caisson. The linear wave force on a quasi-ellipse caisson has recently been calculated using a two-dimensional source representation method by Renet al.(2009). Wanget al.(2011) have also successfully developed a 3D domain numerical model. But these calculations are limited to a single quasi-ellipse caisson without considering the multiple quasi-ellipse caissons and perforated quasi-ellipse caissons. The wave forces on the multiple quasi-ellipse caissons are expected to be very different from the wave forces on a single caisson as the adjacent caissons may interact strongly with each other in a complicated way. In order to get a better understanding of the characteristics of multiple quasi-ellipse caissons and provide necessary guidance for engineering design, the wave forces on the multiple quasi-ellipse caissons were studied in a scaled physical model. Both non-perforated and perforated quasi-ellipse caisson arrays were tested for a range of wave and caisson parameters. The relationships between the wave forces and wave parameters such as relative wave length, incident wave direction, and relative wave height are presented and discussed.

2 Experimental design

The experiment was carried out in the marine environment flume at the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, China. The wave flume was 50 m in length, 3.0 m in width and 1.0 m in height. The irregular wave-making system was equipped at one end of the flume and the wave energy dissipating devicewas at the other end. The modeled caisson array consisting of three caissons was put in the middle of the flume either perpendicular or at a certain angle to the wave direction, as shown in Fig. 1.

Fig. 1 Sketch of the experimental setup

The quasi-ellipse caisson and the perforated quasi-ellipse caisson used in the experiment are illustrated in Fig. 2. The front and rear parts of the caisson are semicircle sections with a diameter of 28.2 cm and the middle part of the caisson is a rectangular section with a length of 28.2 cm and a width of 17.8 cm. The height of the caisson is 47.2 cm. The perforated quasi-ellipse caisson has four square holes on either sidewalls of the rectangular section with the side length of the holes being 5 cm. The caisson in the middle which is instrumented to measure the wave forces is made of plexiglass while the other two, which are used to set up the multiple caisson arrays, are made of wood. The different relative intervals between the caissons is achieved by moving the side caissons toward or away from the centre caisson and the different incident wave directions are achieved by rotating the caisson array relative to the fixed point of the centre caisson. The wave forces on the caisson are measured by a load cell and the interval of the data acquisition is 0.02 s. The example photos of the experiments at different incident wave directions are shown in Fig. 3.

Fig. 2 Sketch of the quasi-ellipse caisson and the perforated quasi-ellipse caisson model

Fig. 3 Photos of the experiment

3 Test Conditions

The irregular waves with the Jonswap spectrum (Hasselmann,et al., 1973; Goda, 1999) were used for this model test. The incident wave directionsβare 0°, 11.25°, 22.5°, andβbeing defined is shown in Fig. 4. The significant wave heightH1/3has values of 10.0 cm and 11.07 cm, the spectrum peak periodsTpare 1.19 s, 1.30 s, 1.41 s, 1.53 s, 1.71 s, 1.81 s and the relative wave lengthkDvaries from 0.5 to 0.9. The two conditions of water depthdare 39.08 cm and 46.40 cm. The relative intervals, the ratio of the distance between the caisson centersLto the width of the caissonD, are 2.00, 2.68, and 3.00. Both quasi-ellipse caissons and the perforated quasi-ellipse caissons were tested under the same wave and water depth conditions.

4 Test Results and Discussions

4.1 The wave force on a single caisson

From the measure time series of the wave force using the load cell, significant wave force on the caisson was calculated and used for all subsequent comparison analysis. The magnitude of the positive wave force on the singlenon-perforated quasi-ellipse caisson withβ=0° is denoted byand its direction coincides with the positive X axis as indicated in Fig. 4. Similarly, the magnitude of the negative wave force on the single non-perforated quasi-ellipse caisson is denoted byand it is in the direction opposite to. The wave forces on the single caisson versus the relative wave length are shown in Fig. 5. It can be seen thatandare generally comparable in magnitudes withbeing somewhat smaller thanand both reach the maximum values atkD=0.783. The difference betweenand, which is likely due to the nonlinearity of the wave field around the structure, is mostly within 10% of thevalues over the range of thekDtested.

Fig. 4 Sketch of incident wave direction β and wave force

Fig. 5 The wave forces of the single caisson versus relative wave lengthkD(H1/3/d=0.216)

4.2 The time history of the measured wave and wave force

The sampling time length is 163.84 seconds. The time history of the measured wave and wave force during 80 seconds and 160 seconds are shown in Fig. 6.

The period of the transverse wave force is shorter than the period of the incident wave. The transverse wave force is related to the high-order frequency. The high-order frequency is an important factor for the transverse wave force.

Fig. 6 Time series of the irregular wave surface and wave forces on perforated multiple quasi-ellipse caissons (β=22.5o,H1/3/d=0.216,Tp=1.81s,L/D=2.00)

4.3 The influence coefficients of group caissons

With the incident waves acting on the multiple caissons, the components of the wave force on the middle caisson along theXaxis are expressed byandwhile the components along theYaxis are expressed byandas shown in Fig.4. In order to better understand the interactions among the multiple quasi-ellipse caissons, the influence coefficients for the group caissons are defined asandin theXdirection, andandin theYdirection, respectively.

4.3.1 The effect of the relative interval on the influence coefficients

The influence coefficients of the group caissons versus the relative wave length are shown in Fig. 7 with Fig. 6(a)～(c) corresponding toβ=0o, 11.25oand 22.5o, respectively. The solid symbols and solid lines represent the experimental results for the quasi-ellipse caisson, and the hollow symbols and dashed lines represent the corresponding perforated caissons. It can be seen that the relative interval has a significant effect on the influence coefficients, withanddecreasing with the increasing of the relative interval. This result is to be expected as that for the inline wave force, the interactions of multiple caissons become weakened as the relative interval increases, and as the wave reflection effects of other caissons on the middle caisson decreases with the increasing relative interval, so do the wave pressures. It is also noticed that this relationship is nonlinear as the interaction is strong for the relative interval of 2.00, but the values for the relative intervals of 2.68 and 3.00 are very close. In addition, increased gaps between caissons may result in a reduction in the wave runup in the front and at the rear of the middle caisson. Over the entire range of thekDand the relative interval tested, theandfor the perforated caissons are smaller than those of the non-perforated caissons as expected.

With regard to the transverse forces, forβ=0othe influence coefficientsandare relatively small and not affected much by the relative interval although there is some slight increasing with the increasing of thekD. For the cases concerning oblique incidence, the influence coefficients increase up to a certain value of the relative interval and then reduce at a higher relative interval, with the interaction effect being the strongest for a relative interval of 2.68. This is believed to be due to the wave reflection effect of the other caissons on the middle caisson which reaches the maximum at a certain relative interval.

Forβ＞0oandalso reduce with the increase of the relative wave length in a way similar to that forβ=0o. But the influence coefficientsandare seen to increase significantly with the increasing relative wave length with the maximum values whenL/Dattained 2.68. As the decrease of the relative wave length,kD, is equivalent to the increase in the wave period, T, the data indicate that for all cases tested, the influence coefficients of the group caissons inXdirectionandincrease withTincreasing while the influence coefficients of the group caissons inYdirectionanddecrease as the wave period increases.

The influence coefficients of the perforated quasi-ellipse caisson show similar behaviour withkDandL/Dbut with greatly reduced values. Compared with the quasi-ellipse caisson, the influence coefficients of the group caissons inXdirectionandare reduced by 5%, the influence coefficients of the group caissons inYdirectionandare significantly decreased about 30%, respectively. This clearly demonstrates that the perforated quasi-ellipse caisson has the effect of reducing the wave force on the caisson, especially for the transverse wave force. The perforated quasi-ellipse caisson also has some ability to reduce wave runup at the front and at the rear of the multiple caissons, but it is more effective in reducing wave runup between caissons and reducing the wave reflection effect of the lateral caissons on the middle caisson.

Fig. 7 The influence coefficients of group caissons versus relative wave length at the different incident angles

4.3.2 Incident wave direction effects

The influence coefficients of the group caissons versus the incident wave direction are displayed in Fig. 8 with solid symbols depicting the experimental results of the quasi-ellipse caisson and the hollow symbols for the corresponding perforated quasi-ellipse caisson.

Fig. 8 The influence coefficients of group caissons versus incident wave direction (L/D=2.68,H1/3/d=0.216)

As expected for all angles bothanddecrease monotonously with the increase of the kD. What is not so obvious is that for a given kD,increases at first, then decreases with the increasing incident wave direction. The reason is that the increase in the wave incident angle has two effects: it reduces the inline component of the wave pressure but at the same time it causes stronger interactions between the caissons. The first effect reduceswhile the second effect increases it. When the angle increases slightly from 0o, the second effect is stronger so thatincreases until a certain value of the incident wave direction is reached and after that, any further increase in the incident wave angle results in the first effect becoming the dominantand then decreasing. Curiously the same analysis doesn’t seem to apply toasshows a monotonous decreasing tendency with the increasing incident wave angle. This is perhaps due to the complex waves formed at the rear of the middle caisson due to the reflections from the other caissons and from the side wall, which lead to a much smaller interaction effect on the wave pressure on the middle caisson.

In theYdirectionandtend to increase with the increasing incident wave direction as expected as the effective relative interval will reduce with the increasing of the incident wave angle, and the wave reflection effect of the other caissons on the middle caisson will be greatly strengthened and the wave pressure on the sidewall will increase obviously. Thus, the transverse wave force increases sharply with the incident wave direction ranging from 0oto 22.5o, and the results of the incident wave direction at 11.25oare about three times that for the incident wave direction at 0o.

4.3.3 Relative wave height effect on the influence coefficients

The influence coefficients of the group caissons versus the relative interval are shown in Fig. 9 in which the solid symbols and solid lines represent the quasi-ellipse caisson and the hollow symbols and dashed lines represent the perforated quasi-ellipse caisson results.

It can be seen that the relative wave height has an important influence on the interactional effect of multiple caissons. The larger the relative wave height, the greater the influence coefficients are in both theXandYdirections. This once again confirms the role of wave nonlinearity. With an increase in wave height, the high-order wave forces become more and more important and the smaller the relative interval (stronger interactions), the stronger the effect of the relative wave height on the influence coefficients of the group caissons inXdirectionand

Fig. 9 The effect coefficients of the group caissons versus the relative interval at the different relative wave heights and wave angles

As for the effect of the relative intervalL/D, forβ=0o, the data also show that the effect of the relative wave height on the inline influence coefficientsandis generally stronger for both the quasi-ellipse caisson and the perforated quasi-ellipse caisson at a lowerL/Dand also indicate that beyond a certain value, further increasing in the gaps between the caissons has adecreasing effect on the influence coefficients. The behaviour of the influence coefficients for the force component in the Y direction is somewhat different. The greatest values ofandoccur at the relative interval of 2.68 and values at the relative interval of 2.00 and 3.00 are smaller. This shows that the nonlinearity effect has a directional dependency which varies with the relative intervalL/D. An obvious implication of these results is that with the engineering design of perforated or non-perforated multiple quasi-ellipse caissons, it is important to consider the nonlinear wave effect instead of using the linear wave theory. Similarly, this behaviour of influence coefficients is suitable for the cases regarding the oblique incidence.

Both the variations of the relative wave height and caisson perforation have effects on the influence coefficients of group caissons,and, with the perforation effects being more pronounced.

5 Conclusions

The irregular wave forces on the multiple quasi-ellipse caissons were experimentally investigated and some conclusions were drawn:

1) The influence coefficients of the group caissons are greatly affected by thekD:anddecrease with the increase of thekDwhileandshow the opposite trend.

2) The relative interval has a significant effect on the influence coefficients of the group caissons:andgenerally decrease with the increasing of the relative interval, whileandtend to increase with the relative interval up to a certain value and then reduce at a higher relative interval.

3) Compared with the non-perforated multiple quasi-ellipse caissons, the effects of the perforated group caissons in theXdirection are small,andare reduced by about 5%. However, the corresponding results in theYdirection are significant,andare decreased by about 30%.

4) The influence coefficients of the group caissons in theXdirection:increases at first, then decreases with the increasing of the incident wave direction;decreases as the incident wave direction increases. The influence coefficients of the group caissons in theYdirection:andtend to increase with the increasing of the incident wave direction.

5) The relative wave height has a notable enhancing effect on the influence coefficients of the group caissons and this effect reduces for the inline wave force with increasingL/D. The effect of the relative wave height on the influence coefficients, especially forand, is generally stronger for the perforated quasi-ellipse caissons than for the non-perforated caissons, which is mainly due to the result of the complicated nonlinear wave-wave interactions for perforation.

6) It is very important to consider using the nonlinear wave theory instead of the linear wave theory for the engineering design of perforated or non-perforated multiple quasi-ellipse caissons.

Bai Jingtao, Hu Jiashun (2006). Research on and design of new structure of elliptical caissoned pier.Journal of Port & Waterway Engineering, 395(11), 25-30.

Chen Xuefeng, Li Yucheng, Wang Yongxue, Dong Guohai, Bai Xue (2003). Numerical simulation of wave interaction with perforated caisson breakwaters.China Ocean Engineering,17(1), 33-43.

Dong Zhongya (2008). Computation method for floating stability of elliptical caissons.Journal of Port & Waterway Engineering, 411(1), 53-59.

Goda Y (1999). A comparative review on the functional forms of directional wave spectrum.Coastal Engineering,41(1), 1-20.

Hasselmann K, Bernett TP, Bocaws E, Carlson H, Cartwright DE, Enke K, Ewing JA, Gienapp H, Hasselmann DE, Kruseman P, Meerburg A, Müller P, Olbers DJ, Richter K, Sell W, Walden H, (1973). Measurement of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP).Erganzungsheft zur Deutsches Hydrographisches Zeitschrift Reihe A8,12, 7-95.

Hou Wei (2008).Dynamic analysis of gravity pier. Master Degree Thesis.Dalian University of Technology, Dalian. (in Chinese)

Li Yucheng, Liu Hongjie, Dong Guohai (2005). Reflection of oblique incident waves by perforated caissons with traverse wall.Journal of Hydrodynamics, Ser.B,17(3), 257-268.

Li Yucheng, Liu Hongjie, Sun Dapeng (2003). Analysis of wave forces induced by the interaction of oblique incident waves with partially-perforated caisson structures.Journal of Hydrodynamics, Ser.A,18(5), 553-563.

Li Yucheng, Liu Hongjie, Teng Bin, Sun Dapeng (2002). Reflection of oblique incident waves breakwaters with partially-perforated wall.China Ocean Engineering,16(3), 329-342.

Liu Yong, Li Yucheng, Teng Bin, Jiang Junjie (2006). Experimental and theoretical investigation of wave forces on a partially-perforated caisson breakwater with a rock-filled core.China Ocean Engineering,20(2), 179-198.

Liu Yong, Li Yucheng, Teng Bin, Jiang Junjie, Ma Baolian (2008). Total horizontal and vertical forces of irregular waves on partially perforated caisson breakwaters.Coastal Engineering,55(6), 537-552.

Liu Yong, Li Yucheng, Teng Bin (2007). Wave interaction with a perforated wall breakwater with a submerged horizontal porous plate.Ocean Engineering,34(17-18), 2364-2373.

Neelamani S, Koether G, Schuttrumpf H, Muttray M, Oumeraci H (2000). Wave forces on, and water-surface fluctuations around a vertical cylinder encircled by a perforated square caisson.Ocean Engineering,27(7), 775-800.

Ren Xiaozhong, Wang Yongxue, Wang Guoyu (2009). Theirregular wave loading on the quasi-ellipse caisson.Journal of Ship & Ocean Engineering,38(1), 85-89.

Suh KD, Park JK, Park WS (2006). Wave reflection from partially perforated-wall caisson breakwater.Ocean Engineering,33(2), 264-280.

Vijayalakshmi K, Neelamani S, Sundaravadivelu R, Murali K (2007). Wave runup on a concentric twin perforated circular cylinder.Ocean Engineering,34(2), 327-336.

Wang Yongxue, Ren Xiaozhong, Wang Guoyu (2011). Numerical simulation of nonlinear wave force on a quasi-ellipse caisson.Journal of Marine Science and Application,10(3), 265-271.

Zhao Shifeng (2008).Research on the key technologies in the construction of large open style offshore deep-water wharf. Master Degree Thesis, Dalian University of Technology.

Zhu Guochun, Ding Jianxin (2007). Design and application of ellipsoidal caisson’s suspended rudder.Journal of China Harbour Engineering,150(4), 61-62.

Author biographies

XiaozhongRenwas born in 1981. Dr. Ren graduated from Dalian University of Technology. He is an engineer at Dalian Jiucheng Municipal Design Co., Ltd. His research interests include wave interaction with structures and designing of port engineering.

Peng Zhangreceived his master’s degree from Dalian University of Technology. He is an engineer at CCCC Water Transportation Consultants Co., Ltd. His research interest is designing of port engineering.

YuxiangMa,PH.D, associate professor, a researcher at the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, his main research interestsinclude nonlinear water wave theory and wave-structure interaction.

YufanMengwas born in 1987. She graduated from DaLian Ocean University, with a bachelors degree, assistant engineer. She is working at Dalian Jiucheng Municipal Design Co. Ltd. Her research interests include designing of Ports and Channel Engineering.

1671-9433(2014)03-0265-09

Received date: 2013-12-09.

Accepted date: 2014-05-12.

Foundation item: Supported by the National Natural Science Foundation of China under Grant No. 51109032, and the National Natural Science Foundation of China under Grant No. 50921001.

＊Corresponding author Email: renxiaozhong2000@163.com

? Harbin Engineering University and Springer-Verlag Berlin Heidelberg 2014