Hydraulic stability of antifer block armour layers Physical model study

Transcription

1 Hydraulic stability of antifer block armour layers Physical model study Paulo Freitas Department of Civil Engineering, IST, Technical University of Lisbon Abstract The primary aim of the study is to experimentally investigate the stability performance of antifer block armour layers on a 1:1.5 slope, under the effect of irregular waves, for different placement methods. A literature review on the armour layer stability, as well as 2 different stability formulas for different armour units, is firstly presented. The rubble mound structure scaling requirements, scale effects in these models and the material used in rubble mound construction are discussed. The results demonstrate that the best performing placement method corresponds to the regular placement method. However, in this method, the reflected significant wave heights are higher than in the semi-irregular placement method. Key words: Rubble Mound Breakwater; Antifer Block; Hydraulic Stability; Placement Method; Damage Assessment. 1. INTRODUCTION Several evidences of the influence of placement method on the stability of antifer block armour layers are well known and studied. The problem of rubble mound breakwaters stability involves a large number of parameters. As a consequence, the studies of hydraulic armour layer are very complex due to the interaction between these parameters. This extended abstract is divided into six chapters. In the second chapter the armour layer stability is discussed, such as the stability formulas for different armour units. On the third chapter, the required theory to design and operate a scaled physical model of a rubble mound breakwater is presented, as well as the materials used in rubble mound construction. In chapter four the model construction is discussed together with the different placement methods. On the fifth chapter, the results and the values downscaled to the prototype are presented. The last chapter contains the conclusion remarks and suggestions for future work. 2. RUBBLE MOUND BREAKWATER Rubble mound breakwaters can be found along the coastline, to either protect the coastal area against wave action or create sheltered areas where vessels can navigate and berth safely. The wave energy in this type of structure is dissipated by absorption and part of it is reflected. A rubble mound breakwater is usually constituted by a core of quarry run and an under layer of random shaped and random-placed stones, protected with an armour layer of selected armour units Antifer block The antifer cube is a massive armour unit that was created as a result of laboratory research conducted for the breakwaters of Antifer Harbour in France. So, their first use was on the Antifer breakwaters and later they have been used in the repair works of the west breakwater of Sines harbour (Fig. 1). Fig. 1: Use of antifer blocks in repair works of the west breakwater in Sines harbour (Portugal) The blocks have a geometric shape close to a cube, but they present four grooves and a slightly tapered shape (Fig. 2) [1]. 1

2 Nowadays the most widely used equations in the design of some concrete armour units are the Hudson equation and Van der Meer equations Hudson equation Hudson formula can be described by equation (3) for concrete armour units [2]. Here the first term corresponds to the stability parameter and the second represents the slope angle and the K D factor. ( ) (3) Fig. 2: Geometrical characteristics of Antifer Cubes 2.2. Hydraulic stability The hydraulic stability of the armour layer on the front slope has been widely investigated for many years. To understand the breakwaters performance against wave action, it is necessary to describe some physical processes. Generally, the common failure mode of the armour layer is failure of singles units when the wave dislocating force is greater than the stabilizing force. The instability of these units is caused by wave forces, which tend to move the blocks once a critical value is exceeded. Those wave-generated forces are known as drag and lift forces that are withstood by the interlocking effect and/or block weight. where D n is the nominal diameter of the armour unit, K D is the Hudson stability parameter (-) and α is the slope angle ( ). The value of K D depends mainly on the type of armour layer adopted. However, this value also depends on the wave steepness, ratio of depth to wavelength, ratio of wave height to depth, thickness and porosity of cover layer, armour unit surface roughness, incident wave angle, shape of armour unit, slope of bottom seaward of structure, crest width, method of placing the breakwater materials, and damage level. In Table 1, suggested K D values are presented. This formula has, however, limitations: - the use of regular waves only; - no description of the damage level; - the use of non-overtopped and permeable structures only. ( ) ( ) (1) where ρ m is the density of armour units (kg/m 3 ), ρ w is the density of water (kg/m 3 ), D is the nominal diameter, g is the gravitational acceleration (m/s 2 ), v is the flow velocity (m/s), F D is the drag force, F L is the lift force and F G is the gravitational force. Assuming that the velocity of a wave on the slope is proportional to the celerity in shallow water, equation (1) can be shortened, and the stability parameter is obtained. ( ) (2) where H is the characteristic wave height, Δ is the relative densiy (-) and N s is the stability parameter. Armour unit Breaking wave Table 1: Suggested K D values K D Structure trunk Nonbreaking wave Tetrapod Modified cube Tetrapod Modified cube Antifer Cube cotg α 1.5 to H 5 H 1/3 Manual SPM 1975 [3] SPM 1984 [4] Rock Manual 2007 [2] 2

3 2.4. Van der Meer equations To overcome the limitations of Hudson formula, Van der Meer conducted an extended research on the stability of breakwater. For armour layers composed by cubes in a double layer on a 1:1.5 slope with 3 ξ m 6 (ξ m surf similarity parameter), based on nondepth-limited wave conditions, Van der Meer proposed the equations (4) and (5) [5]. ( ) (4) ( ) (5) where H s is the significant wave height, N od is the number of displaced units related to a width of one nominal diameter, for displacements higher than 2D n (-), N o,mov is the number of displaced units related to a width of one nominal diameter, for all type of displacements (-), s m is the mean wave steepness (-) and N z is the number of waves (-) Damage The damage in armour layers is related to the specific conditions and duration of a sea state. It can be characterized by counting the number of displaced units or measuring the eroded surface profile of the armour slope. The damage can be expressed in terms of a relative displacement D, which is defined as the ratio between the number of displaced units and the total number of units within a specific zone (usually the area between ± H s around Still Water Level is used) [4]. (6) The K D values suggested for Hudson formula are obtained for a level of damage smaller than 5%, measured between ± H s around Still Water Level. Broderick defined the damage (S) as the relation between the eroded surface profile and the square of the nominal stone diameter [6]. In Table 2, the damage levels associated to the structure damage classification are presented. Table 2: Damage level by N od and S for double layer armour Armour unit / Damage parameter Slope Initial damage Intermediate damage Failure Rock / S 1: Modified cube / N od Tetrapod/ N od 1:1.5 1: MODEL SET-UP Manual USACE, 2011 [6] USACE, 2011 [6] CIRIA et al., 2007 [2] USACE, 2011 [6] CIRIA et al., 2007 [2] This chapter presents the theory to design and operate scaled physical models of a rubble mound breakwater, as well as the materials used in the rubble mound construction Scaling requirements and scale effects Physical modelling is based on the idea that the model behaves in a similar way to the prototype that intends to represent. Thus, a validated physical model can be used to predict the prototype's behaviour under a specified set of conditions. However, there is a possibility that the physical model may not represent the prototype behaviour due to scale effects and laboratory effects [7]. Gravity forces predominate in free surface flows and thus most hydraulic models can be designed using the Froude criterion [8]. (8) (9) where N t is the time scale (-), N l is the length scale (-) and N M is the mass scale (-). In equation (9) it is assumed that relative density relationship is the same for model and prototype. where A e is the eroded area. (7) The linear geometric scaling of material diameters that follows from Froude scaling may lead to viscous forces, corresponding to small Reynolds numbers. 3

4 This means that the flow regime in the breakwater armour units of the model is laminar, instead of turbulent, to avoid viscous scale effects. However, this scale effect can be neglected if the Reynolds number is greater than 30000, obtained by equation (10) [7]. least, 3H s (3 18cm=54cm) to avoid breaking conditions before the structure. However, due to issues related with glasses safety, a value of 45cm was chosen [2] Materials used in the construction and structural parameters (10) Armour Layer where R e is the Reynolds number (-), υ is the kinematic coefficient of viscosity (m 2 /s) and H s,i is the incident significant wave height. The results obtained in this study were downscaled according to Froude similitude criterion using a length scale of 1: Facilities The experimental research was performed in the wave flume of the hydraulic and environment laboratory of Instituto Superior Técnico. After building the model, the placed antifer layers were tested for a peak wave period of 1.4s with different significant wave heights, i.e. 10cm, 12cm, 14cm, 16cm and 18cm. The channel has a length of 22m, a width of 0.7m and a height of 1m and has a system of wave generation with dynamic wave absorption (Fig. 3). In this work, the irregular waves were produced by the HR WaveMaker wave generation software, adjusted to JONSWAP spectral shape. The waves were measured with four probes and the data was recorded and analysed by HR Data Acquisition and Analysis software. One camera was used to capture video of every tests and take pictures before and after each test. About 600 antifer cubes were used in the construction of the breakwater armour layer. The antifer blocks are made available by LNEC (National Laboratory for Civil Engineering) (Fig. 4). The blocks are made of concrete, filled up with small spheres of metal and were painted to avoid friction scale effects and to observe more easily their eventual displacement. The proprieties and dimensions of the block are presented in Table 3 and Table 4. ρ c (kg/m 3 ) Table 3: Block proprieties of used antifer cubes D n15 D n50 D n85 M 15 M 50 M H Table 4: Block dimensions of used antifer cubes V (cm 3 ) A B C D r Fig. 4: Example of used antifer blocks The gradation D n85 /D n15 is and the gradation M 85 /M 15 is Fig. 3: Wave flume The duration for each test was defined for 2000 waves. The water depth in the flume should be, at Under Layer Graded rock was used in the construction of the breakwater under layer (granite stones) (Fig. 5). The standard Froude scaling method for the under layer is based on the relation between the armour layer weight ant the under layer weight. The typical value recommended to the weight ratio is around 10 [6].

5 The proprieties of the graded rock are presented in Table 5. ρ r (kg/m 3 ) Table 5: Graded rock proprieties of used stones D n15 D n50 D n85 M 15 M 50 M MODEL CONSTRUTION AND PLACEMENT METHODS Knowing the elevation of the crest and the slope, the model dimensions were drawn on the glass of the flume. The material of the core was placed in stages to allow the settlement of the core (Fig. 6). During the construction of the core, irrigations were made in order to facilitate the settlement. Fig. 5: Graded rock used in under layer The gradation D n85 /D n15 is and the gradation M 85 /M 15 is The nominal diameter of the rocks should be around 19.9g, however the value obtained after the sieve selection was smaller, corresponding to 14.6g Core Quarry run is used as core material. Generally the top weight pretended in rubble mound breakwaters core is 1000kg and the bottom weight is 1kg. The lowest value is recommended to avoid geotechnical instability [9]. Therefore, the material of the core was constructed using 5 types of gravel with different gradations. The proprieties of the quarry run are presented in Table 6. Fig. 6: Core of the model After placing the core, the graded rock of the under layer was placed one by one. Firstly, the first layer of under layer was placed and then the second layer (Fig. 7). ρ r (kg/m 3 ) D n15 Table 6: Quarry run proprieties D n50 D n85 M 15 M 50 M The gradation D n85 /D n15 is and the gradation M 85 /M 15 is The porosity of the core is around 30% Toe and superstructure Rectangular concrete blocks with an edge of 10cm has been applied in the construction of the breakwater toe protection, as well as in the superstructure. In this way, the instability of the armour layer induced by the possible movements of the toe is avoided. Fig. 7: Under layer of the model under construction After placing the core, the under layer and the concrete blocks of the toe in a stable way, the antifer blocks were placed one by one, for each test. In Fig. 8, the sketch of the breakwater cross section, as well as, material characteristics used in the model, are presented. 5

6 different for some placement methods, leading to different thickness of armour layer. Fig. 8: Breakwater cross section In this study 3 different placement methods of armour layer were analysed. Each placement method was designed to have porosity of around 50%. For values above 50% the stability may be insufficient and for values below occurs a paving action (consequently grater overtopping) [10]. Fig. 9: Configuration of the first layer of armour layer (regular pattern) The techniques of the placement are defined as row by row or layer by layer, see Fig. 10 and Fig. 11, respectively. The geometry of the placed antifer for each placement method, was calculated using the formulas described in Table 7 [9]. Table 7: Basic geometric design formulae and parameters for placed armour units First Second Third Fourth Fifth Sixth Based on the armour layer thickness (t), the Layer coefficient (K Δ ) was calculated Based on the dimensionless upslope distance (y=1,08), the dimensionless horizontal distance (x) was calculated The horizontal and upslope centre to centre distance between blocks was calculated The packing density coefficient (nº of blocks / nº of possible blocks) was calculated The numbers of antifer blocks per unit area was calculated The value of packing density coefficient was verified ( ) The value y=1.08, means that the spacing between blocks along the upslope does not exist. The configuration of the first layer of the armour layer is the same for all placement methods (Fig. 9). However, the horizontal centre to centre distance is Fig. 10: Row by Row Fig. 11: Layer by Layer The assessment of the damage was measured between ± H s around Still Water Level for each test. Classification of the movements of the armour units is required in the counting method. Such classification was based on the displacement of each block, measured in units of nominal diameter. In this work distances lower than 1D n were not considered as damage. 5. RESULTS In the reflection analysis, reflection coefficients for fast Fourier transform (NFFT) with 256, 512 and 1024 points obtained in the reflection routine were analysed and the incident significant wave heights were calculated. To check the accuracy of the results, the reflection coefficients were determined using the incident and reflected wave spectral energy in order to obtain the incident significant wave heights and compare the results Semi-irregular placement method For this experiment the antifer blocks of the first layer are placed by the regular pattern (Fig. 9). After every 4-5 rows of the first layer, the second layer is placed by dropping the blocks above the holes (Fig. 12). The 6

7 thickness of armour layer is defined as the nominal diameter plus the height of the antifer cube. In the Fig. 13, damage ratios for the displacements are presented, for 2 different references areas. Fig. 12: Semi-irregular placement method The properties of the armour layer and the wave series are presented in Table 8 and Table 9. The reflection coefficients and Reynolds number are presented in Table 10. Table 8: Layer properties for semi-irregular placement method x (-) 1.86 t measured 8.60 y (-) 1.08 P (%) 49.8 ΔX 8.06 K Δ (-) ΔY 4.67 ϕ (%) 49.8 t calculated 8.63 N c (blocks/m 2 ) H s,input Table 9: Wave series for semi-irregular placement method H m0,i T p (s) T m (s) s m (-) N s (-) Fig. 13: Damage for semi-irregular placement method The Hudson stability parameter was calculated for a damage of 5%, for the first wave series were the first displacements were observed. From this follows K D =2.1. This value is similar to the value found by Frens [11] (K D,Frens =2.3) Regular placement method 1 The antifer blocks are placed row by row (Fig. 10). The blocks in the first layer are placed with their grooves perpendicular to the slope (Fig. 14). The blocks of the second layer are placed diagonal for the first row directing to the left and for the second row to the right and so on (Fig. 15). Table 10: Reflection and Reynolds number for semi-irregular placement method H s,input Reflection R e (-) C r (-) NFFT (points) eq Analysing the video, is visible that in the first wave series, the blocks are displaced around SWL. In this placement method the effect of interlocking is low. Consequently the hydraulic stability is mostly guaranteed by the weight of the block. Fig. 14: Regular placement method 1 (ΔX=8.1cm) Fig. 15: Thickness of armour layer (t=h+d n) The properties of the armour layer and the wave series are presented in Table 11 and Table 12. The reflection coefficients and Reynolds number are presented in Table 13. 7

8 Table 11: Layer properties for regular placement method 1 x (-) 1.86 t measured 8.60 y (-) 1.08 P (%) 49.8 ΔX 8.06 K Δ (-) ΔY 4.67 ϕ (%) 49.8 t calculated 8.63 N c (blocks/m 2 ) Table 12: Wave series for regular placement method 1 H s,input H m0,i T p (s) T m (s) s m (-) N s (-) waves for the last test (N s =2.06) where the displacements observed was low, almost null. From this follows K D =5.8. This value when associated with the value found by Frens is almost equal, K D,Frens =6.4 [11] Regular placement method 2 The placement of the antifer blocks is similar to the regular placement method 1 (Fig. 17). However the packing density is lower, and the horizontal centre to centre distance is higher (Fig. 18). The antifer blocks are placed row by row (Fig. 10). The blocks in the first layer are placed with their grooves perpendicular to the slope (Fig. 17). The blocks of the second layer are placed diagonal for the first row directing to the left and for the second row to the right and so on (Fig. 18). Table 13: Reflection and Reynolds number for regular placement method 1 H s,input Reflection R e (-) C r (-) NFFT (points) eq waves The first blocks were displaced only in the last test for H m0,i =0.129m. In this test, the blocks were not replaced. As a result, the displacement occurs for a total of 2000 waves plus 1000 waves. In this placement method, the effect of interlocking is efficient, providing a high hydraulic stability. In Fig. 16, damage ratios for the displacements are presented for references area ±18cm. Fig. 17: Regular placement method 2 (ΔX=8.8cm) Fig. 18: Thickness of armour layer (t 1.85H, increase of 20% in the distance between blocks when compared with regular placement method 1) The properties of the armour layer and the wave series are presented in Table 14 and Table 15. The reflection coefficients and Reynolds number are presented in Table 16. Table 14: Layer properties for regular placement method 2 Fig. 16: Damage for regular placement method 1 The Hudson stability parameter was calculated for a damage of 0.8%. Therefore that value was determined x (-) 2.02 t measured 7.94 y (-) 1.08 P (%) 49.9 ΔX 8.75 K Δ (-) ΔY 4.67 ϕ (%) 45.9 t calculated 7.96 N c (blocks/m 2 )

9 H s,input Table 15: Wave series for regular placement method 2 H m0,i T p (s) T m (s) s m (-) N s (-) Table 16: Reflection and Reynolds number for regular placement method 2 H s,input Reflection R e (-) C r (-) NFFT (points) eq The first blocks were displaced in the third wave series for H m0,i =0.125m. In the last test (H m0,i =0.128m) the blocks were not displaced. Consequently, the reflection visualized in the basin was higher and therefore greater reflected significant wave height was obtained, around 5cm (wave breaking along the basin was higher). The effect of interlocking is efficient, but lower when compared with regular placement method 1. In Fig. 19, damage ratios for the displacements are presented, for 2 different references areas. The scaling of the design units and time series was adjusted using the equations (8) and (9) (Froude similitude criterion). A length scale of 1:60 has been applied for the breakwater model, and the unit sizes and design storm were determined for the prototype (see Table 17, Table 18, Table 19 and Table 20). Table 17: Armour Unit specifications for the prototype Antifer cubes D n,50 M 50 Prototype 2.50m 42.98ton Model 4.33cm 199g Table 18: Graded rock specifications for the under layer Grades Rock D n,50 M 50 Prototype 1.07m 3.15ton Model 1.78cm 14.60g Table 19: Quarry run specifications for the core Quarry Run D n,50 M 50 Prototype 0.41m kg Model 0.68cm 0.81g Table 20: Design Storm for the prototype (Semi-irregular placement method) Prototype H s,input H m0,i T p (s) T m (s) Analysing Table 9 and Table 20, the incident significant wave height of 0.139m and the peak period of 1.38s obtained in the model corresponds to a H m0,i =8.3m and a T p =10.7s in the prototype. 6. CONCLUDING REMARKS AND SUGGESTIONS FOR FUTURE WORK Fig. 19: Damage for regular placement method 2 The Hudson stability parameter was calculated for a damage of 0.6%. Therefore, that value was determined for N s =1.99, which is associated to the lowest displacements, almost null. From this follows K D =4.0. This value when compared with the value obtained by Frens is almost equal, K D,Frens =4.1 [11] Study values Froude-scaled for a prototype with a geometrical scale of 1:60 Among the various conclusions drawn from this study, the following ones deserve to be specially mentioned: In the semi-irregular placement method, the reflection coefficients are smaller than the coefficients obtained in regular placement methods. This value tends to decrease when increasing incident significant wave heights, since the damage and porosity are greater for higher H m0,i. 9

10 The regular placement methods are more stable and the reflection coefficients are higher. However in the regular placement method 2, the values of reflection coefficients are greater when compared with the regular placement method 1, due to the fact that the first layer is more exposed to wave breaking. The settlement of the core in the reference area for wave action in the regular placement method 2 was higher. In physical modelling, tests should be repeated in order to check the accuracy of the results. However in this study the tests have not been repeated. Nevertheless, the comparison between the Hudson stability coefficients, obtained in this work with the results found by Frens in 2007, allow to verify that the values are similar. For the semi-irregular placement method K D =2.1 is suggested for a damage of 5%, since in this placement method is easy to repair the armour layer by placing a new block in the revealed hole. For regular placement methods 1 and 2, the values K D =5.8 and K D =4.0 are suggested, respectively. These values were obtained for damage almost null, due to the fact that the armour layer cannot be repaired by filling up the holes, because the upper blocks tend to slide down (chain reaction). In conclusion, the regular placement method 1 appears to have the best stability performance. However this method, when compared with regular 2, has a bigger consumption of concrete on manufacturing of antifer blocks, due to the higher numbers of antifer blocks per unit area. There are some changes and studies that could be done to consolidate the trends here presented. Construct a model with armour layers composed by antifer cubes in a double layer on a 1:2 slope, for all placement methods tested in this study. Test the placement methods studied for different peak wave periods and reduce the number of waves to Use a small scale crawler crane and pressure clamp in the construction of the armour layer. Study other placement methods on a 1:1.5 and 1:2 slope, as the regular placement with smaller horizontal centre to centre distance. 7. BIBLIOGRAPHY [1] Pita, C., Memória Nº "Dimensionamento Hidráulico do Manto de Quebra-mares de Talude", LNEC, Lisboa, [2] CIRIA, CUR, CETMEF, "The Rock Manual. The use of Rock in hydraulic engineering", 2nd ed., Ch. 5, C683, CIRIA, London, [3] Coastal Engineering Research Center, "Shore Protection Manual", 2nd ed., Vol. 2, Ch. 7, U.S. Government Printing Office, Washington, DC, [4] Coastal Engineering Research Center, "Shore Protection Manual", 4th ed., Vol. 2, Ch. 7, U.S. Government Printing Office, Washington, DC, [5] Van der Meer, J.; Heydra, G., Journal of Coastal Engineering - "Rocking armour units: Number, location and impact velocity", Elsevier Science Publishers B. V., Amsterdam, [6] U. S. Army Corps of Enginners, "Coastal Engineering Manual", Part VI, Ch.5, Washington, DC, [7] Hughes, S., "Physical Models and Laboratory Techniques in Coastal Engineering", World Scientific, Singapore, [8] Quintela, A., "Hidráulica", 10ª ed., Fundação Calouste Gulbenkian, Lisboa, [9] CIRIA, CUR, CETMEF, "The Rock Manual. The use of Rock in hydraulic engineering", 2nd ed., Ch. 3, C683, CIRIA, London, [10] Maquet, J., Developments in Geotechnical Engineering, 37 - "Design and construction of mounds for breakwaters and coastal protection - Port of Antifer, France", P. Bruun, Ed., Elsevier Science Publishers B. V., Amsterdam, [11] Frens, A., "The impact of placement method on Antifer-block stability", Delft University of Technology, Delft,