1 Abtract Rubble Mound Breakwater Chritian Linde Olen Griffith Univerity, Faculty of Engineering and Information Technology, Gold Coat Campu. 1. Abtract The paper deal with the deign of a rubble mound breakwater. The deign i carried out according to the Coatal Engineering Manual, 2006, and contain deign of the height of the rubble mound breakwater, the tone ize in each layer and bearing capacity of the oil. 2. Introduction Deign of rubble mound breakwater i a very cplex matter. Thi i due to all the different parameter that affect the deign e.g. wave height, varying water depth, variation of tone ize, lope angle, damage level and o on. The deign i often baed on empirical expreion developed by everal experiment. In the follow, the deign i given and after that the height and tone ize are determined. Finally, the bearing capacity of the oil i determined.. Deign Condition In the following ection, the deign condition are decribed. The rubble mound breakwater mut fulfill the condition given in Table.1. Allowable overtopping, q: 0.4 m /ec/m Armor unit: rough quarry tone Armor and under layer material i quarry tone, γ a : 2.5 t/m Structure lope: 1:2 Shape: Symmetric Table.1: Deign condition for the rubble mound breakwater. The water depth, h, varie between 5.5m and at high water up to 7.2m. It i therefore neceary to determine the wave length, L, for both cae. The wave length i determined by iterating (.1), where T i the wave period. 2 gt 2π h L= tanh 2π L (.1) 1
Rubble Mound Breakwater The deign condition for the water are given in Table.2. Water depth, SWL: 5.5 m Beach lope: 1:20 Deign high water: 1.7 m H 2 m H 1/10 T m or T L o 2.5 m 8 ec 100 m L h=5.5 55.4 L h=7.2 62.2 Table.2: Deign condition for the water. The deign condition for the oil are given in Table., where it i aumed that it i not poible to have a failure or ettlement in the Limetone layer at the depth of 21.5m. 0 m Sand γ = 17 kn/m fine to medium looe φ = 0 c = 0 5.5 m Clay γ = 14 kn/m Soft φ = 0 Over-conolidated c = 50 kpa e o = 2.2 k = 10-5 cm/ a v = x10 - m 2 /kn C c = 0. 21.5 m Limetone Table.: Deign condition for the oil. Furthermore, a toe, to protect the armor layer, mut be contructed but the height i till unknown. The rubble mound breakwater i deigned with to under layer beneath the armor layer. Beneath thee layer there i a core. The top width of the rubble mound breakwater mut a leat be time the tone diameter of the armor tone. The breaking condition for ware are given by Hb 078. h = (.2) b 2
4 Deign of Rubble Mound Breakwater The minimal water depth for non breaking wave i determined to.2m uing H 1/10. Thi mean that the toe mut be lower than 2.m or ele the wave will break. The rubble mound breakwater i illutrated in Figure -1. All the relevant parameter for the figure are given in Table.1 to Table.. 1:20 DWL SWL Toe Armor UL1 UL2 Core 1:2 Sand Clay Figure -1: Illutration of rubble mound breakwater. Limetone 4. Deign of Rubble Mound Breakwater In the following chapter, the rubble mound breakwater i deigned. The deign i done according to Coatal Engineering Manual, 2006. Before the layer can be deigned, the elevation i determined. Finally, the toe i deigned. 4.1. Deign Elevation The deign elevation conit of contribution fr a wave run up on the lope, the wave it elf, the ettlement of the rubble mound and a freeboard which provide afety againt overtopping. In the following, thee parameter are determined. Freeboard The height of the freeboard i determined according to Owen (1980, 1982), Table VI-5-8 in Coatal Engineering Manual. The equation to determine the height i given by q Rc 1 = aexp b gh T H H γ r (.)
Rubble Mound Breakwater where g i the gravitational acceleration, 9.82m/ 2 i a coefficient that i 0.5-0.6, here 0.6 ince thi yield the bigget freeboard R c i the freeboard or height of elevation 2 = H m 0. 02 L = 62. 2m =, equation VI-5-2 a i a coefficient that i read to 0.01 (for traight mooth lope) b i a coefficient that i read to 22 (for traight mooth lope) γ r Note that the wave length for the depth of 7.2m i ued ince thi i the deign wave length. The height of the freeboard i then calculated to be 1.24m, which i illutrated in Figure 4-1. DWL Armor UL1 UL2 Core Figure 4-1: Illutration of freeboard, R c. Wave Run up Wave rum up i a phenenon caued by the breaking wave on a lope, cf. Figure 4-2. Figure 4-2: Wave run up and run down. [CEM, 2006] 4
4 Deign of Rubble Mound Breakwater The exceedance level i choen a 2% and for rack armored lope with irregular wave the run up can be calculated by equation VI-5-1 given by R H ui% ( ξ ) 15 ξ ( ) 1 C /C = B for. D/ B (.4) where D B C i coefficient which i 1.97, c.f. Table VI-5-5 i coefficient which i 1.17, c.f. Table VI-5-5 i coefficient which i 0.46, c.f. Table VI-5-5 The urf-imilarity parameter ξ i given by equation VI-5-2 tanα ξ = = 279. (.5) The wave run up i then determined according to (.4) R H ui% ( ) 1 / 0. 46 046. 117 279 15 279 197 117 1 R = 75. m ui% =.. for... /. =. (.6) The deign elevation con be determined according to R = h+ η + R+ deign ρtotal (.7) where ρ total i the total ettlement which here are et to 0.1m η i the wave etup and equal to 0 The deign elevation i determined to R = 72. + 124. + 75. + 01. = 12. m (.8) deign 5
Rubble Mound Breakwater 4.2. Deign of Layer The ma of the armor layer i determined according to Table VI-5-22. Thi i for irregular head on wave were the lope i between 1.5<cotα< and for non-overtopping. The damage level i choen to be between 0-5%. The equation i given by M 50 = K D ρ H ρ 1 cotα ρw (.9) where ρ i the ma denity of rock, 2.5t/m ρ w i the ma denity of water, 1t/m H i the wave height, here H K D i the tability coefficient read to 2.4 for non breaking wave The reult i given by M. 25. 24. 1 2 1 25. 2 t 50 = = 12 m (.10) It i now poible to determine the equivalent cubic length of the median rock D M 12. = 50 n50 08. m ρ = 25. = (.11) The width of the cret i determined by equation VI-5-116 given by W B= nkδ wa 1/ (.12) where n k Δ (mooth) i the number of tone ( i recmended a a minimum number) i the layer coefficient given in Table VI-5-51 and i 1.02 for quarrytone W i the primary armor unit weight, here equal to M 50 6
4 Deign of Rubble Mound Breakwater w a i the pecific weight of armor unit material The width i then calculated to 1/ 12. B = 102. = 24. m 25. (.1) The average thickne of the armor and underlayer (r) are determined by equation VI-5-117 given by (.14) where it i typical that n i 2 for all layer. W r = nkδ wa 1/ (.14) The placing denity, alo known a the number of armor unit per area, i given by equation VI-5-118 Na A 2 / P wa = nkδ 1 100 W (.15) Where A i the urface area and P i the cover layer average poroity given in Table VI-5-51 and i 8 for quarrytone (mooth). The thickne and the number of armor unit per area are then determined 1/ 12. r = 2102. = 16. m 2. 2/ N a 8 2. 5 = 2102. 1 = 45. tone / m 1 100 1. 2 2 (.16) (.17) The deign of the underlayer, the core, and the toe i done according to Figure VI-5-55 hown in Figure 4-. 7
Rubble Mound Breakwater Figure 4-: Deign of layer. [CEM, 2006] Uing Figure 4- and equation (.14) and (.15) the unit weight, layer thickne and amount of unit per area are determined and the reult are given in Table 4.1 where the volume of tone for unit length i calculated uing Figure 4-4 Layer Vol. of tone W D n50 r N a for unit length [t/m ] [m] [m] [tone/m 2 ] [m /m] Armor 1.2 0.8 1.6 4.5 98 UL 1 0.12 0.7 0.8 21 46 UL 2 0.006 0.14 0. 154 17 Toe 0.12 0.7 1.6 21 12 Core 0.00 0.11 - - 251 Table 4.1: dimenion for the rubble mound breakwater. The core volume of tone pr unit length i found by uing a poroity of 64% cf. Table VI- 5-51. The volume of all the tone for 1m of rubble mound breakwater i Vol total 1 98 46 17 12 251 424m / m m = + + + + = (.18) 8
5 Bearing Capacity 2,4 AL UL 1 DWL UL 2 7,2 SWL,9 20,74 Core 12, 2,4 8,86 9,17 Toe 1,6 Figure 4-4: Dimenion for the rubble mound breakwater. The total load of the rubble mound breakwater without buoyancy i given by W 424 m 25 kn 10600 kn m m m 1m = = (.19) The load acting on the eabed i affected of the buoyancy and i therefore lower than (.19) ugget. The wort cae i for SWL becaue thi give the mallet buoyancy force. It i aumed due to area conidering that 75% of the tructure i expoed for buoyancy and the load on the eabed i determined by Weabed 10kN / m = 10600 25% + 10600 75% = 580 kn m (.20) 1m 25kN / m 5. Bearing Capacity In the following, a tatic poible force ditribution i ued to determine the bearing capacity. When uing a tatic poible force ditribution the bearing capacity will be afe. Since there doe not exit a imple olution for the bearing capacity of a foundation on two layer oil (and and clay), it i aumed that the failure will occur in the clay. The force fr the rubble mound breakwater i ditributed trough the layer of and a hown in Figure 5-1. 9
Rubble Mound Breakwater Figure 5-1: Stre ditribution. The tre on the clay i then given by σ = 580kN / m clay 9kPa 55.m = 8. 86m 2 + 9. 17m+ 2 2 (.21) One tre band i introduced below the tre on the clay a illutrated in Figure 5-2. By uing imple tatic and auming a Mohr-Coulb failure function it i poible to determine the bearing capacity of the clay. Sand Effective area Clay Stre band Stre band Figure 5-2: Illutration of one tre band. Since the and give the ame force on both ide of the tre band it can be neglected. The Mohr-Coulb olution i illutrated in Figure 5- τ c u 4xc u σ Figure 5-: Mohr-Coulb circle for one tre band. 10
6 Structural Deign Summery A the two Mohr-Coulb circle ugget, the bearing capacity of the foundation i equal to 4 time c u and with a c u of 50kPa, cf. Table., the bearing capacity i 200kPa and the layer of clay will not fail ince the load calculated in (.21) i 9kPa. A more fine tatic olution can be made by uing a infinite number of tre band, but it i not neceary ince it only make the bearing capacity better. 6. Structural Deign Summery The main reult are ummarized in Table 6.1. The dimenion of the rubble mound breakwater i given in Figure 4-4. L h=5.5 55.4 L h=7.2 62.2 Freeboard 1.24m Exceedance level for run-up 2% Run up.75 Deign elevation 12.m M 50armor 1.2t/m M 50ul1 0.12t/m M 50ul2 0.006t/m M 50core 0.00t/m Cret width, B 2.4m r armor 1.6m r ul1 0.8m r ul2 0.m N a,armor 4.5tone/m 2 N a,ul1 21tone/m 2 N a,ul2 154tone/m 2 N a,toe 21tone/m 2 Weight reduced of buoyancy 580kN/m Table 6.1: Main reult. 7. Reference [CEM, 2006] Coatal Engineering Manual, 2006. 11