Theoretical and experimental investigation of a vertical wall response to wave impact

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Theoretical and experimental investigation of a vertical wall response to wave impact
  Ocean Engineering 29 (2002) 769–782 Theoretical and experimental investigation of avertical wall response to wave impact A.K. Tanrikulu, M.S. Kırkgo¨z  * , C. Du¨ndar Civil Engineering Department, Cukurova University, 01330 Adana, Turkey Received 20 December 2000; accepted 15 March 2001 Abstract The laboratory and field experiments so far have shown that when a wave breaks directlyon a vertical faced coastal structure, the resulting impact pressures may become very severein magnitude and short in duration. Some experimental evidence in the literature suggests thatthe structural response to the extremely high magnitude impact forces is only limited. Thisstudy is mainly concerned with the comparison of the theoretical and experimental results of a vertical wall response under the wave impact loading. In the dynamic analysis of the wallthe classical elastic plate theory is used and the numerical results for the dynamic values of the transverse displacement are obtained by employing the method of finite elements. In thetheoretical analyses the experimental pressure histories are used and the theoretical walldeflection histories are compared with the experimental results. The computational and experi-mental deflection histories exhibit similar patterns. The theoretical maximum wall deflectionsare mostly found to be slightly smaller than the experimental values.  ©  2002 Elsevier ScienceLtd. All rights reserved. 1. Introduction When a wave breaks directly on a vertical faced coastal structure, impact pressuresare produced which can be extremely high in magnitude and short in duration. Inrecent years, using very sensitive measuring devices, the history and spatial distri-bution of impact pressures from breaking waves on plane walls have been measuredboth in model (Mogridge and Jamieson, 1980; Kırkgo¨z, 1982; Chan and Merville,1988; Witte, 1988; Kırkgo¨z, 1991; Kırkgo¨z, 1992; Kırkgo¨z, 1995) and prototype * Corresponding author 0029-8018/02/$ - see front matter  ©  2002 Elsevier Science Ltd. All rights reserved.PII: S0029-8018(01)00052-X  770  A.K. Tanrikulu et al. / Ocean Engineering 29 (2002) 769–782 Nomenclature a  Width of the plate b  Height of the plate  D  Bending rigidity of the plate d  1  Still-water depth in the channel d  w  Still-water depth at breaking point  E   Modulus of elasticity F   Impact force on the unit width of the wall  H  0  Deep water wave height  H  1  Wave height in the channel h  Plate thickness  L 0  Deep water wavelength  p  Impact pressure T   wave period t   Time w  Plate de fl ection  x ,  y ,  z  Space coordinates n  Poisson ’ s ratio  r  Density of the steel platetests (Blackmore and Hewson, 1984; Partenscky, 1987). The impact pressures col-lected from these experiments show extreme variations even when all the waves ina particular test are identical.From the experimental results so far it has been observed that the dynamic forceresulting from a perfect impact on a vertical faced coastal structure, such as com-posite-type breakwaters, may become considerable although the occurrence of theperfect impact is infrequent. Some investigators (Carr, 1954) have pointed out thatthe rarely occurring extreme wave impact pressures and the resulting forces of veryshort duration are unlikely to be of serious consequence in designing a structureagainst sliding and overturning.The investigation of the dynamic behaviour of the vertical walls under the waveimpact load does not seem to have received much attention. Using the experimentalresults of K ı rkgo ¨ z (1982), the theoretical analysis of the response characteristics of a vertical caisson plate of composite breakwater exposed to wave impact was givenby K ı rkgo ¨ z and Mengi (1986), and a simpli fi ed procedure for the design of suchplates was proposed. The proposed design procedure was extended by K ı rkgo ¨ z andMengi (1987) for the dynamic analysis of caisson plates of different aspect ratios.Laboratory experiments were carried out by K ı rkgo ¨ z (1990) to measure the impactpressures and resulting de fl ections from breaking oscillatory waves on a vertical wallwith 1/10 foreshore slope. The results showed that the high magnitude impact forceswith very short durations have only minor and local in fl uence on the wall de fl ection  771  A.K. Tanrikulu et al. / Ocean Engineering 29 (2002) 769  –  782 histories, on the contrary, low impact forces which last longer produce relativelygreater wall de fl ections. In this study, the experimental results for the vertical wallde fl ection histories under wave impact loading obtained by K ı rkgo ¨ z (1990) are com-pared with the theoretical results. 2. Experiments Experiments are performed in a laboratory channel of 100 m long, 2 m wide, and1.25 m deep, equipped with a paddle-type wave generator. At the end of the channela 10 mm-thick vertical steel wall was installed on a beach having slope of 1/10. Fig.1 shows the arrangement of the test structure in the channel. As may be seen fromthe  fi gure, the steel wall was horizontally strengthened with a U-shaped beam, belowwhich the wall plate has dimensions of 2.00 × 0.57 m. The two ends of the beam andthe lower end of the plate are assumed to be simply supported, while the verticaledges of the plate are free.For measuring the impact pressure histories ten pressure transducers were mountedon the centre line of the wall at 30 mm intervals, the lowest transducer was 37 mmabove the bottom of the wall. For measuring the de fl ection histories of the wall adisplacement transducer was used that is  fi xed to the point 40 mm to the left of centre line and 187 mm above the lower edge. A detailed description of the experi-mental set-up is given by K ı rkgo ¨ z (1990).The regular oscillatory waves used in the experiments have the following proper-ties: wave period  T  = 2 s, wave height in deep water and in the channel  H  0 = 0.277 mand  H  1 = 0.259 m, still-water depth in the channel and at the wall  d  1 = 0.610 m and d  w = 0.160 m, deep water wave steepness  H  0  /   L 0 = 0.044, and total number of wavestested  N  = 90. At every wave impact the pressures and de fl ections from the transducers Fig. 1. Test structure in the channel.  772  A.K. Tanrikulu et al. / Ocean Engineering 29 (2002) 769  –  782 were recorded simultaneously with 25  µ s sampling rate for a duration of 102.4 ms.An example output from the ten pressure transducers and a displacement transduceris given in Fig. 2. 3. Theoretical analysis The dynamic behaviour of the steel vertical wall under the wave impact given inFig. 1 is formulated using the theory of elastic plates (Timoshenko, 1959). The plate Fig. 2. An example output showing the simultaneous histories of impact pressures and de fl ection atmeasuring points.  773  A.K. Tanrikulu et al. / Ocean Engineering 29 (2002) 769  –  782 is referred to a Cartesian coordinate system (  x ,  y ,  z ) in which the (  x ,  y ) plane coincideswith the mid-plane of the plate and the srcin is located at the bottom left corner(Fig. 3).  z  is in the direction of impact pressure  p (  x ,  y ,  t  ) in which  t   is time. Thedistributions of pressure in space and time determined experimentally are describedin the previous section.The dynamic equation governing the transverse displacement,  w , of the plate in  z  direction due to bending is  D  4 w   r hw ¨    r h 3 12  2 w ¨     p  (1)where  D =  Eh 3  /12(1  n 2 ) is the bending rigidity of the plate,  4 =  2 (  2 ) the biharmonicoperator,   2 =∂ 2  /  ∂  x 2 +∂ 2  /  ∂  y 2 Laplace ’ s operator,  h  the thickness of the plate,  E   themodulus of elasticity,  n  Poisson ’ s ratio, and dots designate the differentiation withrespect to time. The boundary conditions of the plate are given below. Vertical ends:  ∂ 2 w ∂  x 2   x  0, a  0 and at beam ends: ( w )  x  0, a  0 (2)  Horizontal ends: ( w )  y  0  0,   ∂ 2 w ∂  y 2   y  0, b  0 and at beam ends: ( w )  y  b  0 (3)in which  a  and  b  are the width and height of the plate respectively.We assume that the motion of the plate starts from the rest, then the initial con-ditions for the plate are Fig. 3. Finite element network for the test wall.
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