2010_Effect-of-the-concrete-density-on-the-stability - Xbloc

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Damage (Nod)Damage (Nod)Damage (Nod)51,40Design value1,201,00 a = 2102 kg/m 3 a = 2465 kg/m 3 a = 2915 kg/m 30,800,600,400,200,000,00 1,00 2,00 3,00 4,00 5,00 6,00Stability Number (Ns)Figure 4 Comparison damage development <strong>of</strong> armour units with 2102, 2465 and 2915 kg/m 3 , slope cot α =1.331,40Design value1,201,00 a = 2102 kg/m 3 a = 2465 kg/m 3 a = 2915 kg/m 30,800,600,400,200,000,00 1,00 2,00 3,00 4,00 5,00 6,00Stability Number (Ns)Figure 5 Comparison damage development <strong>of</strong> armour units with 2102, 2465 and 2915 kg/m 3 , slope cot α = 1.51,40Design value1,201,00 a = 2102 kg/m 3 a = 2465 kg/m 3 a = 2915 kg/m 30,800,600,400,200,000,00 1,00 2,00 3,00 4,00 5,00 6,00Stability Number (Ns)Figure 6 Comparison damage development <strong>of</strong> armour units with 2102, 2465 and 2915 kg/m 3 , slope cot α = 2

6From <strong>the</strong> model tests it can be concluded that <strong>the</strong> influence <strong>of</strong> <strong>the</strong> specific weight is not correctlydescribed by <strong>the</strong> stability number (H s /ΔD n ). It is found that <strong>the</strong> stability number underestimates <strong>the</strong>positive effect <strong>of</strong> increasing specific weight on a slope <strong>of</strong> 1:1.5 and steeper. For a slope <strong>of</strong> 1:2 <strong>the</strong>stability number tends to overestimate <strong>the</strong> effect <strong>of</strong> <strong>the</strong> heavy <strong>concrete</strong> mass, where as <strong>the</strong> effect <strong>of</strong><strong>concrete</strong> mass is correctly described by <strong>the</strong> stability number for <strong>the</strong> standard and light <strong>concrete</strong>elements. The assumed dominance <strong>of</strong> lift and drag forces stabilized by <strong>the</strong> submerged weight on which<strong>the</strong> stability number is based, does not hold for steep slopes <strong>of</strong> rock and Dolos and in general, Xbloc .O<strong>the</strong>r forces have significant influence on <strong>the</strong> stability.When assessing <strong>the</strong> forces on a single armour unit due to oscillation flow over and through <strong>the</strong>armour several forces can be identified. It is generally known that due to <strong>the</strong> oscillating flow over <strong>the</strong>slope <strong>the</strong>re is lift force, drag force and inertia force acting on <strong>the</strong> armour unit. The forces vary inmagnitude and direction with time and depends on structural parameters and <strong>the</strong> type <strong>of</strong> breaking. Ingeneral, <strong>the</strong> flow forces becomes more drag and lift dominated for flatter slopes but for steep slopes <strong>the</strong>inertia force becomes more and more dominating (HELGASON AND BURCHARTH, 2005).Stabilizing forces can be accounted to three mechanisms; armour unit weight, friction andinterlocking. All types <strong>of</strong> elements have a partial contribution <strong>of</strong> weight, interlocking and friction to <strong>the</strong>stability. The contribution <strong>of</strong> each mechanism to <strong>the</strong> total stability depends amongst o<strong>the</strong>rs on <strong>the</strong>armour units shape, placement (contact points) and slope angle. The stabilizing gravitation forcereduces with increasing slope angle as function <strong>of</strong> cosα.Interlocking and friction are a function <strong>of</strong> <strong>the</strong> (submerged) weight <strong>of</strong> <strong>the</strong> elements. The frictionforce depends on <strong>the</strong> normal force between <strong>the</strong> elements and <strong>the</strong> contact surface area. In <strong>the</strong> case <strong>of</strong>interlocking <strong>the</strong> amount <strong>of</strong> weight <strong>of</strong> <strong>the</strong> surrounding block which rest on top <strong>of</strong> <strong>the</strong> element is <strong>of</strong>importance Interlocking and friction increases with increasing slope angle due to <strong>the</strong> increasingcomponent <strong>of</strong> <strong>the</strong> gravitational force parallel to <strong>the</strong> slope. The contribution <strong>of</strong> each mechanism canhowever not be defined precisely.From <strong>the</strong> performed model tests with Xbloc as well as <strong>the</strong> results <strong>of</strong> HELGASON AND BURCHARTH(2005) on rock and Scholtz and Zwamborn (1982) on Dolos it can be concluded that <strong>the</strong> influence <strong>of</strong><strong>the</strong> relative <strong>density</strong> on <strong>the</strong> hydraulic stability is not linear as <strong>the</strong> stability number indicates. This nonlinearitycan be addressed to <strong>the</strong> contribution <strong>of</strong> interlocking and friction to <strong>the</strong> stability. In addition, <strong>the</strong>contribution <strong>of</strong> interlocking and friction to <strong>the</strong> influence differs for different slope angles and is<strong>the</strong>refore a function <strong>of</strong> <strong>the</strong> slope angle.To determine <strong>the</strong> function <strong>of</strong> x in equation (1) as a power <strong>of</strong> <strong>the</strong> relative <strong>density</strong> (∆) <strong>the</strong> method <strong>of</strong>ZWAMBORN (1978) is used as presented in Fig.2. First <strong>the</strong> stability numbers (H s /∆D n ) are determinedfor start <strong>of</strong> damage (N od =0.05), intermediate damage (N od =0.1) and failure (N od =0.55) from <strong>the</strong>3 3damage curves. The stability numbers were used to plot <strong>the</strong> relative <strong>density</strong> against ( Dn/ H )cot ina log-log graph for each slope angle. The graphs are presented in Fig. 7. The function term3 3xf (( D / H )cot )K has been fitted through <strong>the</strong> data point. The following values <strong>of</strong> x are found:ncotα = 1.33 Start <strong>of</strong> damage x = 8.8 Moderate damage x = 6.1 Failure x = 6.3cotα = 1.5 Start <strong>of</strong> damage x = 3.0 Moderate damage x = 3.9 Failure x =4.65cotα = 2.0 Start <strong>of</strong> damage x = 1.8 Moderate damage x = 1.7 Failure x = 1.9

7Figure 7 Relative rock volume ((D n/H s) 3 cotα) vs relative <strong>density</strong> for Nod = 0.05, 0.1 and 0.55; slope cotα =1.33, cotα = 1.5 and cotα = 2 (left to right).The influence <strong>of</strong> <strong>the</strong> relative <strong>density</strong> and slope angle for Xbloc armour units can be described by:HsbaD (3)nIn which a and b are functions <strong>of</strong> <strong>the</strong> slope angle. The hydraulic stability <strong>of</strong> Xbloc armour units can<strong>the</strong>refore be described as a function <strong>of</strong> <strong>the</strong> slope angle and relative <strong>density</strong> by:H K fg( ) ( , ) with: f( , ) f( ) (4)DnNo solution for <strong>the</strong> function f(α) and g(α) are presented in this paper as <strong>the</strong> range <strong>of</strong> tested parameters islimited. Fur<strong>the</strong>r research is required to validate <strong>the</strong> relation presented (4). It is also suggested toinvestigate <strong>the</strong> influence <strong>of</strong> <strong>the</strong> relative <strong>density</strong> for various types <strong>of</strong> armour units.ConclusionsIt is concluded from <strong>the</strong> model tests that <strong>the</strong> influence <strong>of</strong> <strong>the</strong> specific weight on <strong>the</strong> hydraulic stability <strong>of</strong>Xbloc armour layers is not correctly described by <strong>the</strong> stability number (N s ). The assumed dominance <strong>of</strong>lift and drag forces stabilised by <strong>the</strong> submerged weight on which <strong>the</strong> stability number is based, does nothold because o<strong>the</strong>r forces have significant influence <strong>the</strong> stability. With an increasing slope angle, <strong>the</strong>inertia, friction and interlocking force become more dominant. For Xbloc interlocking is <strong>the</strong> dominantstability mechanism. Although interlocking is <strong>the</strong> most characterising stabilisation mechanism <strong>the</strong>re is apartial contribution <strong>of</strong> gravity and friction to <strong>the</strong> stability as well. The amount <strong>of</strong> contribution <strong>of</strong> eachmechanism to <strong>the</strong> total stability depends on <strong>the</strong> armour units shape, placement (contact points) andslope angle. All stability mechanisms (gravity, friction and interlocking) depend on <strong>the</strong> weight <strong>of</strong> <strong>the</strong>element and are a function <strong>of</strong> <strong>the</strong> slope. Therefore <strong>the</strong> influence <strong>of</strong> <strong>the</strong> specific weight is always afunction <strong>of</strong> <strong>the</strong> slope angle and depends on <strong>the</strong> type <strong>of</strong> element. However, <strong>the</strong> contribution <strong>of</strong> eachmechanism can however not be defined precisely.The influence <strong>of</strong> <strong>the</strong> specific weight in relation to stability number can be concluded from <strong>the</strong> modeltest:

Damage number Nod [-]8 The stability number underestimates <strong>the</strong> effect <strong>of</strong> <strong>the</strong> specific weight for single layerinterlocking armour units for a slope <strong>of</strong> 2:3 and steeper. The underestimation increases forsteeper slope angles. The expected start <strong>of</strong> damage (H s ≥ 120% H d ) and failure (H s ≥ 150% H d ),with H d is <strong>the</strong> design wave height, is underestimated for heavy <strong>concrete</strong> elements andoverestimates for <strong>the</strong> light <strong>concrete</strong> elements.For a slope <strong>of</strong> 1:2 <strong>the</strong> stability number tends to overestimate <strong>the</strong> effect <strong>of</strong> <strong>the</strong> heavy <strong>concrete</strong>element, where as <strong>the</strong> normal and light <strong>concrete</strong> element are in close resemblance with eacho<strong>the</strong>r and <strong>the</strong> expected start <strong>of</strong> damage (H s ≥ 120% H d ) and failure (H s ≥ 150% H d ) .The power <strong>of</strong> one <strong>of</strong> <strong>the</strong> relative <strong>density</strong> () value in <strong>the</strong> stability formula determines <strong>the</strong> influence <strong>of</strong><strong>the</strong> relative <strong>density</strong> on <strong>the</strong> stability and is a function <strong>of</strong> <strong>the</strong> slope angle. The hydraulic stability <strong>of</strong> Xblocarmour units can <strong>the</strong>refore be described as a function <strong>of</strong> <strong>the</strong> slope angle and relative <strong>density</strong> by relation(4). When <strong>the</strong> relation is fitted to <strong>the</strong> test results <strong>the</strong> spread in <strong>the</strong> test damage curves is reducedsignificantly, see Fig.8.1.400.551.201.000.8080% conf. bandDamage progression0.600.400.200.000.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80Stability number (H s /D n aΔ b )Figure 8 Damage curves with modified stability nr. (4)DiscussionIn order to describe <strong>the</strong> stability <strong>of</strong> complex shaped armour units <strong>the</strong> stability should be expressedas <strong>the</strong> sum <strong>of</strong> each mechanisms. It is believed to be necessary to focus on quantification <strong>of</strong> <strong>the</strong>mechanism to <strong>the</strong> total stability in relation to armour unit type. Each type <strong>of</strong> unit will have a differentcontribution <strong>of</strong> weight, friction and interlocking to <strong>the</strong> total stability and all are a function <strong>of</strong> armourunit shape, placement and slope angle.ACKNOWLEDGMENTSThis research was performed under supervision <strong>of</strong> <strong>the</strong> faculty <strong>of</strong> Civil Engineering at DelftUniversity <strong>of</strong> Technology and supported by Delta Marine Consultants. Delta Marine Consultants is atrademark <strong>of</strong> BAM Infraconsult bv.

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