A Flume Study on Regular Wave Transformation and Bed Scouring near a Rectangular Submerged Obstacle upon a Fluidized Bed ABSTRACT 1.

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1 A Flume Study on Regular Wave Transformation and Bed Scouring near a Rectangular Submerged Obstacle upon a Fluidized Bed Shiaw-Yih Tzang Shan-Hwei Ou Yun-Che Yang 3 Yung-Lung Chen ABSTRACT Experiments with a wave flume set-up have been conducted to investigate effects of wave-induced foundation soil s fluidization on the interactions between non-breaking regular waves and a submerged impermeable rectangular obstacle. The results demonstrate that wave heights would be reduced by maximum as 5% near the obstacle over the test fine sandy bed after the occurrence of soil fluidization. The derived wave reflection ratios are found to be less than.3 and are less dependent on the resulting fluidization events or the thickness of fluidized layers than relative water depth and resonance events. In the three phases of the resonant fluidization tests, wave reflections ratios have become more distinctly different. In case of fluidization response, especially with occurrence of resonance mechanism, sediment suspensions would become more rigorous on the upstream than on the downstream sides of the obstacle. On both sides of the obstacle, bed elevations are more greatly reduced than those of an unfluidized bed after wave generation in each test of the three test series. But the scour ranges are found to have particularly converged to a pattern of half scour hole in shallower water depths.. INTRODUCTION Previous experimental measurements on plane beds had shown typical pore pressure responses of fluidized fine sandy beds induced by monochromatic waves (Tzang & Ou, 6). Based on magnitude of pore pressure build-up and occurrence of resonance mechanism during wave loading, they have defined three soil responses including one unfluidized (UF) and two fluidized responses, i.e. the resonantly fluidized (RF) and non-resonantly fluidized (NRF). In addition, significant sediment suspensions at near above beds were typically found upon a fluidized bed (Tzang et al., 8). They pointed out that a fluidized bed is likely to be more compliable and deformed to wave motions than a solid (or unfluidized) bed as being reported by other researchers, e.g. Sawicki & Swidzinski (989). In the case of installing a coastal structure, wave-structure interactions would become more complicated or even cause severe failure events once the foundation bed soils are fluidized or liquefied (e.g. de Groot et al., 6). From experimental investigations, Sumer et al. (999) and Teh et al. (3) had confirmed that sphere and cube-shaped bodies could sink into wave-liquefied bed soils. Kudella et al. (6) found from foundation soil under a caisson breakwater that pore pressure build-ups are closely related to residual soil deformation, which are caused by caisson motions induced by both pulsating and breaking waves. In field, liquefaction has also been pointed out to be one of the wave-induced failure causes of the coastal structures National Taiwan Ocean University, Keelung, Taiwan, R.O.C. Tajen University, Pingtung, Taiwan, R.O.C. 3 National Cheng Kung University, Tainan, Taiwan, R.O.C. sytzang@mail.ntou.edu.tw (Shiaw-Yih Tzang) B-35

2 (e.g. Chaney & Fang, 99). Not until recently, wave-induced momentary liquefaction has been successfully measured around a coastal structure (Mory et al., 7). Since increasing demand on installing submerged breakwaters for an optional coastal protection measure worldwide (e.g. Mendez, et al. ) and locally (e.g. Hsu, et al., ; Tsai, et al., 6), above findings might have critical impacts on the applications of submerged breakwaters. So far, most studies have been dedicated to exploring the wave transformation and wave impacts on the structures particularly over an impermeable or rigid beds rather on a failed bed. Thus in this study, it is particularly aimed at investigating with experimental set-ups the associated wave transformation and bed scouring induced by regular waves in the vicinity of a impervious submerged obstacle during the occurrence of a fluidized response.. EXPERIMENTAL SETUPS As shown in Fig., the experiments were conducted in a wave flume (37m(L) x m (W) x.m (H)) with an indented soil trench (3m(L) x m (W) x.5m (H)) filled with a fine sand (d5=.73 mm) at a constant water depth of 5 cm. The particle size distribution curve is shown in Fig. and the associated soil properties are listed in Table. Six locally produced capacity wave gauges (ARC, WHL-5) were installed above the soil trench with one above the obstacle, another one behind it, and three at locations of 5cm, cm and 5 cm upstream of the obstacle. Bed morphology was recorded by employing an infrared optical altimeter (MT. E.P.I.-) with a motion speed of mm/sec and an accuracy of. mm as shown in Fig. 3(a). The calibration tests have illustrated that the output voltages were linearly increased with depth in both clear and turbid water. The near-bed suspended sediment concentrations (SSC) in the water column were measured by four optical probes (Delft Hydraulics, FOSLIM) at a height of cm and were located 5 cm and cm from the obstacle on both upstream and downstream sides. Accordingly, six pore pressure transducers (Kyowa, BP-5 GRS) were installed in three vertical sections at two depths, i.e. 5 cm and 3 cm below bed surface. The three sections include one in the central point of the obstacle and the other two with a span of 5 cm to both upstream and downstream sides of the obstacle. The bed responses are classified with the records of pore pressure. Fig. 3(b) shows that the test submerged obstacle (S.O.) was made of transparent acrylic box with a height of cm and a thickness of 5 cm with the same width of the wave flume. The box was filled with concrete blocks so that the total weight of the obstacle was 3 kg to simulate a prototype with a unit weight of.6 t/m from a model scale of /7. Wave conditions of three test series have assigned wave periods of. s,.5 s, and. s or corresponding relative water depths of.69,.5, and.83, respectively. Each series consists of at least 9 tests and the generated wave heights are listed in Table for further analysis. Each test series stands for conducting waves from on a freshly deposited soil to on pre-loaded one with consolidation periods of about 3 to hours between two consecutive tests. Detailed information on the test soil bed preparation, test procedures, data acquisition/process and calibrations for pore pressure transducers and SSC probes can be referred to Tzang & Ou (6) and Tzang, et al. (8). B-36

3 Table Summary of soil properties of the test fine sand Soils d 5 (mm) ρ s (g/cm 3 G (N/m ) n k (m 3 s/kg) ν ) Shear modulus Porosity Permeability Poisson s ratio Sand Table Summary of design test conditions and typical results Test h (cm) H (cm) T (s) Response d f (cm) K r A UF. A RF.3 A UF.53 A UF.6 A UF. A RF 8.9.7*.8**.63 A NRF 8..9 A NRF 6.. A NRF.9.7 A UF.9 A UF.8 B UF.85 B UF.9 B UF. B RF 3.7.7*.6**. B NRF B NRF.5.9 B NRF.. B NRF B NRF..8 B UF.87 B UF.8 C UF.3 C UF.8 C UF.37 C RF *.69**.7 C NRF C NRF C NRF C NRF.. C UF.8 Note: UF: unfluidized RF: resonantly fluidized NRF: non-resonantly fluidized; d f : thickness of fluidized soil-layer *: pre-fluidized phase **: transient phase B-37

4 .3 Fig. Set-ups of experimental wave flume (unit: m) d 5 =.73 mm 8 Weight percentage (%) Particle size (mm) Fig. Particle distribution curve of the test fine sand (a) (b) Fig3. Photos of the instrument of (a) infrared altimetry and (b) model submerged obstacle B-38

5 3. Wave Decay 3. Wave Transformation upon a fluidized bed Fig. displays the typical simultaneous measurements of surface waves and pore pressures (d=-5 cm) at a location 5 cm upstream of the S.O. for three different soil responses from Test B. The soil responses can be clearly identified from the pore pressure records. It is seen in Fig. (a) that over an unfluidized bed, even with relatively small pore pressure build-ups, overloading waves have changed insignificantly. However over a fluidized bed the waves have decayed significantly after pore pressures building up to maximum values as seen in Fig. (b) and (c), respectively. For example, the wave heights have started to decay from about 5 cm to about.5 cm in the RF response of Fig. (b) and from about 5 cm to about 3 cm in the NRF response of Test (c). The decay ratio shall be further quantified later. The events of wave decay during a fluidized response have not only occurred in the above-mentioned one location but also along the propagation. From simultaneous measurements of waves and pore pressures during the RF response of Test B, as shown in Fig. 5, similar wave-decay pattern could be noticed to have occurred at the locations above the S.O. and at 5 cm downstream of the S.O. It is also seen that the pore pressures at the three locations from a deeper depth of 3 cm have started to build up almost simultaneously and attained to similar maximum values with slightly different oscillation amplitudes. Accordingly, waves at the three locations have almost simultaneously started to decay to similarly steady heights at close times. From both Fig. and Fig. 5, we simply find the close relationships between the fluidization response and wave decay in addition to commonly acknowledged wave transformations resulting from wave-s.o. interactions. By applying the zero-up-crossing scheme, temporal variations of amplitudes of surface wavesηand build-up of the mean pore pressures P at a depth of 3 cm, hereafter called excess pore pressure, can be derived for typical soil responses. Fig. 6 displays the results in each test for three typical soil responses at the location of 5 cm upstream of the S.O. from the three test series. In this figure, the normalized wave amplitudes are expressed asη/ηmax and normalized excess pore pressure are expressed as P/ Ps where Ps stand for the theoretical static soil stress as the upper limit for pore-pressure records. According to the listed soil properties in Table, the value of Ps at a depth of 3 cm is about 5 N/m in present study. It is clearly seen in the three test series of Fig. 6 that for continuous wave loading with different periods, wave amplitudes change insignificantly over an unfluidized bed (with relatively small P) but decay significantly after the occurrences of fluidized responses (with relatively large P). By taking as the decay ratio the normalized wave amplitudeη/ηmax from tests of fluidized response after the occurrence times of initiation of excess pore pressure tie, the decay ratios for the shown fluidized tests are found to range from.8 to.5. Meanwhile, excess pore pressures increase rapidly to maximum values and then reduced gradually through the remaining wave loadings. In particular, the decreasing values of decay ratio quite distinctly proceed with the development of thickness of fluidized bed soil layer in terms of increasing excess pore pressure. On the other hand, the values of decay ratio in the B-39

6 post-fluidization phase in fluidized tests are found to increase slightly with the gradually decreasing excess pore pressure. This has further confirmed the critical role played by bed fluidization on the wave decay. Even with wave decay, it can still be reasonably expected that wave reflection on upstream side the S.O. might also be influenced to different degrees by characteristic soil responses. This shall be illustrated in the following chapter. 3. Wave Reflection By applying the scheme for calculating wave reflection ratios Kr based on spectrum analysis (Mansard & Funke, 98) to records of the three consecutive wave gauges upstream of the S.O., the calculations for all the listed tests in each test series are shown in Fig. 7. The processed records are extracted from the relatively steady stage for representing the wave patterns. The values listed above symbol in Fig. 7 stand for the derived incident wave height while the values of the thickness of fluidized soil layer are also listed near the symbols of the fluidized tests (in grid-shadowed region). For the three resonantly fluidized tests, i.e. Test A-6, Test B-, and Test C-, reflection ratios are particularly calculated from the data in the pre-fluidized, transient (resonance) and later post-fluidized phases, respectively. The results in Fig. 7 illustrate that the reflection ratios are not clearly dependent on the soil responses in the UF and NRF tests while greatly significant differences are noted in the different phases in RF tests. The variation trends of the reflection ratio with soil responses are similar between Test Series A and C, which are quite different from those of Test Series B. For example in the UF tests before the RF test of Test Series A & C, reflection ratios seem to decrease with larger incident waves. In NRF tests, reflection ratios seem to be similar to each other and not dependent on the magnitudes of incident wave nor on the thickness of fluidized soil layer df. But generally in three test series, the values of reflection ratio in NRF tests with smaller df become similar to those in the UF tests. From the three RF tests, it is observed that the reflection ratios in the pre-fluidized and transient phases become more similar for increasing values of df and shallower water depths. The reflection ratios in the post-fluidized phase become larger than those in transient phase only in Test A-6 and even larger in Test C-. However, the reflection ratio in the post-fluidized phase of Test B- becomes very small possibly due to more significant wave decay. So far, the underlying mechanism for interpreting differences in reflection behavior of the three RF tests is yet to be explored. B-

7 B-3 d = -5 cm B-3 η (cm) P (N/m ) (a) UF η (cm) - B- P (N/m ) 6 8 d = -5 cm B- - - (b) RF η (cm) - B-5 P (N/m ) 6 8 d = -5 cm B (c) NRF Fig. Synchronous records of measured waves and pore pressures in a depth of 5 cm at 5 cm upstream of the S.O. for typical soil responses of (a) UF, (b) RF and (c) NRF (Test Series B) η (cm) η (cm) η (cm) P (N/m ) P (N/m ) P (N/m ) d = -3 cm (a) 5 cm upstream (b) midpoint d = -3 cm 5 d = -3 cm (c) 5 cm downstream Fig5. Synchronous records of wave and pore pressure in a depth of 3 cm along wave propagation in a RF test at locations of (a) 5 cm upstream, (b) midpoint, and (c) 5 cm downstream of the S.O. (Test B-) B-

8 η / η max η / η max η / η max =9.7 =. =6. =7.6 =. =. A-5 A-6 A-7 B-3 B- B-5 C-3 C- C (a) wave amplitude P / Ps P / Ps P / Ps d = -3 cm =9.7 d = -3 cm =. d = -3 cm =6. =7.6 A-5 A-6 A-7 B-3 B- B-5 C-3 C- C-5 =. = (b) excess pore pressure Fig6. Synchronous derivations of normalized (a) wave amplitude and (b) excess pore pressure for three typical soil responses of Test Series A, B and C B-

9 .5 K r..3.. H i =.8. Post-fluidized phase Transient phase** **.7.5* Pre-fluidized phase*.9 3. d f = [8.9] [8.] [6.] [.9] (a) Test Series A K r..3.. H i =.9 Pre-fluidized phase* 3.8 Post-fluidized phase.6 d f = [3.7] [8.] [.5] [.] [6.6] [.] 3.* ** Transient phase** (b)test Series B K r..3.. H i =. Transient phase** 3.. Pre-fluidized phase*. 3.7**.* Post-fluidized phase d f = [5.9] [9.8] [6.9] [5.6] [.] (c) Test Series C.6.5 Fig7. Calculated wave reflection ratios for each test of Test Series (a) A, (b) B, and (c) C B-3

10 . SCOURING DISTRIBUTION As reported by Tzang, et al. (8), significant suspended sediment suspensions (SSC) are always found over a fluidized sandy bed. This also suggests that under continuous wave loading, potentially larger sediment transport rate could result in more significant bed form changes. Typical measurements of the SSC of the three characteristic soil responses at locations 5 cm upstream and downstream of the S.O. from Test B are demonstrated in Fig. 8. It is immediately seen that the values of SSC are much larger in fluidized tests (Test B- & B-5) than in the unfluidized test (Test B-3). In the two fluidized tests, values of maximum SSC, SCCmax, are much larger in the RF test than in the NRF test. In addition in the three soil responses, the values of SCCmax are much larger on the upstream side than on the downstream side while there are certain time lags for the occurrence times of SSC at the downstream location. For example, the values of SCCmax are.5 g/l, 3. g/l and 8. g/l at the upstream location of Test B-3, Test B-, and Test B-5, respectively. The corresponding values at the downstream location are about g/l,. g/l, and.8 g/l. As a result, measurements of the evolving bed form along the central line on upstream and downstream sides of the S.O. with tests of the three test series are displayed in Fig. 9. It is noted in this figure that in the three test series the original beds are not perfectly horizontal but the differences are less than cm. Under repeated wave loadings, bed elevations particularly in the vicinity of the submerged obstacle are found to gradually drop to maximum values of about 3 cm. In general, the drop rates are more spectacular in the fluidized tests and on the downstream side. In particular, the drop rates are seen to be largest in the RF tests than in the NRF tests implying that the occurrence of resonance could have more influences on changes of the bed form. This is also in agreement with the measurements of SSC for different soil responses on both sides of the S.O. That is, even more active sediment suspensions over a fluidized bed upstream, the transported sediments could be partially caught on the upstream side of the S.O. resulting in smaller drop of the bed elevation while the carried away of sediments over the beds downstream resulting in larger drop. However, the extension of the bed scouring decreases in shallower water depths. As shown in Fig. 9, the bed scouring has converged to a bed form with half scour hole within 5 to cm on both side of the S.O. in Test Series C with longest period or shallowest relative water depth. B-

11 SSC (g/l) B-3 5 cm upstream B- SSC (g/l) (a) UF 3-3 B-3 5 cm downstream B- SSC (g/l) SSC (g/l) SSC (g/l) cm upstream B-5 5 cm upstream (b) RF SSC (g/l) cm downstream B-5 5 cm downstream (c) NRF Fig8. Synchronous records of wave-induced SSC at locations 5 cm both upstream and downstream for typical soil responses of (a) UF, (b) RF, and (c) NRF of Test Series B B-5

12 seabed elevation (cm) - submerged obstacle downstream upstream original A- A-5 A-6 A-7 A-8 final seabed elevation (cm) distance (cm) - original B- B-3 B- B-5 B-6 final downstream (a) Test Series A submerged obstacle upstream seabed elevation (cm) distance (cm) (b) Test Series B - downstream submerged obstacle upstream original C- C-3 C- C-5 C-6 final distance (cm) (c) Test Series C Fig9. Evolutions of bed elevation in the vicinity of the S.O. after each test of Test Series (a) A, (b) B, and (c) C 5. CONCLUDING REMARKS Wave transformations and bed scouring due to interactions of surface waves and a submerged obstacle over a fluidized sandy bed have been investigated with a flume setup. The water depths are fixed at 5 cm and wave periods are assigned with. s,.5 s, and. s with different incident wave heights for three test series. During each experimental test, surface waves, pore pressures and suspended sediment concentrations are synchronously measured. After each test, bed elevations along wave propagation on both upstream and downstream sides are surveyed. The results have shown that waves have significantly decayed immediately after the beds being fluidized, especially with B-6

13 the occurrence of resonance mechanism. The wave decay can be seen to be closely dependent on the development of excess pore pressure. In present study, the decay ratio could have become as small as.5. On the other hand, wave reflections from the submerged obstacle are found to be less dependent on bed soil s responses or the thickness of fluidized soil layer. Moreover, wave-induced bed soil s fluidization would result in more significant sediment suspension and bed scour. The bed scour are noted to have converged to zones in the vicinity of the S.O. and even to form a half scour hole near both sides of the obstacle for shallower wave conditions. Though effects of bed soil s responses on wave transformation and bed scouring are confirmed, still several unsolved results on wave reflection need to be clarified with more experimental measurements. ACKNOWLEDGMENTS The study is financially supported by the National Science Council, Republic of China, under project number of NSC 93-6-E-9-6. REFERENCES [] Chaney, R.C., and Fang, H.Y., 99. Liquefaction in the Coastal Environment: An Analysis of Case Histories. Mar. Geotech., pp [] de Groot, M.B., Kudella, M., Meijers, P., and Oumeraci, H., 6. Liquefaction Phenomena Underneath Marine Gravity Structures Subjected to Wave Loads. J. Waterw., Port, Coastal, and Ocean Engineering Div., ASCE 3(), pp [3] Hsu, T.W., Hsieh, C.M., and Hwang, R.,. Using RANS to Simulate Vortex Generation and Dissipation Around Submerged Breakwaters. Coastal Engineering 5, pp [] Kudella, M., Oumeraci, H., de Groot, M.B., and Meijers, P., 6. Large-scale Experiments on Pore Pressure Generation Underneath a Caisson Breakwater. J. Waterw., Port, Coastal, and Ocean Engineering Div., ASCE 3(), pp [5] Mansard, E. P. D., and Funke, E. R., 98. The measurement of incident and reflected spectra using a least squares method. Proc. 7th Int. Conf. on Coastal Eng., Sydney, ASCE, pp [6] Mendez, J.F., Losada, I.J., and Losada, M.A.,. Wave-induced Mean Magnitudes in Permeable Submerged Breakwaters. J. Waterw., Port, Coastal, and Ocean Engineering Div., ASCE 7(), pp [7] Mory, M., Michallet H., Bonjean, D., Piedra-Cueva, I., Barnoud, J.M., Foray, P., Abadie, S., and Breul, P., 7. A Field Study of Momentary Liquefaction Caused by Waves Around a Coastal Structures. J. Waterw., Port, Coastal, and Ocean Engineering Div., ASCE 33(), pp [8] Sawicki, A., and Swindzinski, W., 989. Pore Pressure Generation, Dissipation and Resolidification in Saturated Subsoil. Soils Found., 9(), pp [9] Sumer, B.M., Fredsøe, J, Christensen, S., and Lind, M. T., 999. Sinking/floatation of Pipelines and Other Objects in Liquefied Soil under B-7

14 Waves. Coastal Engineering 38, pp [] Teh, T.C., Palmer, A.C., and Damgaard, J., 3. Experimental Study of Marine Pipelines on Unstable and Liquefied Seabed. Coastal Engineering 5, pp. -7. [] Tsai, C.P., Chen, H.B., and Lee, F.C., 6. Wave Transformation over Submerged Permeable Breakwater on Porous Bottom. Ocean Engineering 33, pp [] Tzang, S.-Y., Ou, S.-H., 6. Laboratory Flume Studies on Monochromatic Wave-fine Sandy Bed Interactions: Part : Soil fluidization. Coastal Engineering 53, pp [3] Tzang, S.-Y., Ou, S.-H. and Hsu, T.-W., 8. Laboratory Flume Studies on Monochromatic Wave-fine Sandy Bed Interactions: Part : Sediment suspensions. Coastal Engineering, DOI:.6/j.coastaleng B-8

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