ArmorFlex Design Manual ABRIDGED VERSION Design Manual for ArmorFlex Articulating Concrete Blocks

Transcription

1 Armorlex eign Manual ABRIGE VERSION 00 eign Manual for Armorlex Articulating Concrete Block

2 . INTROUCTION Thi document i an abridged verion of the full Armorlex eign Manual, available from Armortec. Thi manual wa developed pecifically to upplement the Armorlex eign Package and include only the upporting documentation for the deign equation ued by the oftware application. Subequent ection preent development of the deign equation, a deign example, and reference. Subject that have been omitted from thi manual, which are included in the full verion, include open channel hydraulic, laboratory teting, intallation, and other pecial topic. The uer i encouraged to contact Armortec for a full verion of the Armorlex eign Manual for dicuion of ubject beyond the cope of thi document.. ESIGN EQUATIONS AN EXAMPLE. Hydraulic Stability of the Armorlex Sytem ue to the mode of failure exhibited by articulating concrete block revetment ytem, the mot vulnerable component of an Armorlex revetment ytem i an individual block located at the toe of a channel ide lope. The approach ued to determine the tability of the block i imilar to the approach ued by Simon and Senturk for riprap izing (ref.6). The force acting on a block placed on the ide lope of a channel are hown in igure.. The following lit contain a decription of the major variable: = angle (in degree) of the channel bed = angle (in degree) of the ide lope = angle (in degree) between the weight vector and the reultant force vector in the plane of the ide lope = angle (in degree) between the drag vector and the reultant force vector in the plane of the ide lope = drag force acting on the block (lb) L = lift force acting on the block (lb),,, 4 = moment arm for repective force (ft) W = buoyant (ubmerged) weight of the block (lb) A can be een in igure., the moment of overturning will act along the reultant force, R, about the point O. Point O in thi cae i the downtream and downlope corner of the block. If the block i in equilibrium, the um of moment about point O along R mut equal zero. The ummation of the moment about O reult in: M W co W in co co (.) o 0 4 L The factor of afety, S, i the ratio of the reiting moment to the overturning moment. or the Armorlex block the factor of afety i: Armorflex eign Manual-Abridged Verion

3 igure.. orce diagram for an Armorlex block on a channel ide lope. Armorflex eign Manual-Abridged Verion

4 S M reiting (.) M overturning W co W inco co 4 L by dividing both the numerator and the denominator by W S : co S inco with being: ' (.) co W 4 L (.4) W or motion along R, the moment of the force perpendicular to R (igure.d) mut balance. Thi reult i: in W inin (.5) olving Equation.5 for in: in W in in (.6) from the definition of in igure. and baic geometric relation co co(90 ) in( ) (.7) in in(90 ) co( ) (.8) in co co in in (.9) ubtituting Equation.9 in Equation.6: in coco W in in in (.0) dividing both ide by in and rearranging term: co co in W in in in in (.) ubtituting tan for in/co and olving for tan: Armorflex eign Manual-Abridged Verion

5 tan W in co in (.) dividing both the numerator and denominator by : tan W co in in (.) for flow over a plane flat bed, where = 0 and = 0: W W for thi ituation Equation. become: (.4) S (.5) when the afety factor i unity (incipient condition at the threhold of motion) become, for other condition: O C (.6) where: O = maximum hear tre on channel (lb/ft ) C = critical hear tre of lining (lb/ft ) relating to : ' co W W W W (.7) for implification define the ratio M/N: M / N 4 L (.8) ubtituting Equation.7 and.8 into Equation.7 and reducing: M/N in( ) ' M/N (.9) Armorflex eign Manual-Abridged Verion 4

6 olving Equation.4 for W and ubtituting Equation.8: W M/N 4 L rearranging the term W from Equation. and ubtituting Equation.0: (.0) M/ N (.) W W ubtituting Equation. into Equation.: tan co M/N in in (.) Table. contain a ummary of the equation ued in the factor of afety procedure for the Armorlex block ytem. In order to olve for the factor of afety equation the following need to be known;,,, 4,,, C, and O. Table. contain value for the variable aociated with the different clae of Armorlex concrete block. ue to the difficulty of determining the lift force, L, it i et equal to the drag force,, a a conervative etimate; therefore, L. Armorflex eign Manual-Abridged Verion 5

7 Table. actor of Safety Equation. co S (.) inco ' tan co M/N in in (.4) M/N in( ) ' M/N (.5) O C (.6) M/ N 4 (.7). Stability Analyi for Projecting Block The previou ection aumed that the Armorlex block were placed to achieve a fluh, mooth urface with no projecting block. In reality, achieving uch an intallation require precie ubgrade preparation. The following ection decribe the theory that take into account the additional force that affect a projecting block. The factor of afety analyi for a projecting block i the ame a in the previou ection, with the addition of an extra drag force term,, which account for the impact of the flow againt the projecting face. The reulting equation i: Mreiting W co S (.8) M W inco co 'co ' overturning dividing the numerator and denominator by W : 4 L 4 L S inco co ' ' ' co W W (.9) Armorflex eign Manual-Abridged Verion 6

8 with the ame a in the previou ection: ' co W W (.0) ubtituting Equation.7 into Equation.8: S (.) inco co ' ' ' in( ) W W The additional drag force, ', caued by the projecting block i determined uing the impule-momentum principal. The drag force equation i: ' C A N V (.) where: = drag force (lb.) caued by projecting block = denity of water (lug/ft ) C = coefficient of drag A N = area of projecting face normal to the flow (ft ) V = flow velocity (ft/) or the cae of a projecting block, the area normal to the flow, A N, i equal to the area created by the projection. A drag coefficient, C, of 0.5 ha been found to adequately model a projecting block. Subtituting the area and the drag coefficient into Equation. the drag force become: ' 0.5( z)wv (.) where: z = height of projecting urface normal to the flow (ft) w = width of projecting urface normal to the flow (ft) The additional lift force due to the projecting block, L, i aumed equal to the additional drag force,, a a conervative etimate. Block placement preciion in laboratory teting i generally conidered to be in the range of +/- 0.5 inche. In practice, the deigner pecifie a project-pecific block placement tolerance, where a minimum value of 0.5 inche i recommended unle pecific circumtance allow for more preciion in block intallation. Table. contain a ummary of the equation ued to determine the factor of afety for a projecting Armorlex block. Armorflex eign Manual-Abridged Verion 7

9 {tc " " \l }Table. actor of Safety Equation for Projecting Block. co S (.4) ' ' inco ' in( ) W W co (.5) tan M/N in in ' 0.5zwV (.6) O C M/N in( ) ' M/N M/ N 4 (.7) (.8) (.9) In order to olve the factor of afety equation, the following need to be known;,,, 4,, z, w, V,,, C, and O. Table. contain the value for the variable aociated with the different clae of Armorlex concrete block. ata ued in the development of thi information were meaured or extrapolated from the teting program hown below. Tet are divided into two categorie: with and without the ue of a drainage layer. Becaue it i known that drainage layer increae block performance, block that have been teted with a drainage layer hould be deigned and contructed with a imilar drainage ytem. The block that are deigned from tet data that incorporated a drainage layer are all the opencell tapered block (-T).. Block teted without the ue of a drainage layer: Armorlex Cla 0-S (HWA R-88-8, November 988) Armorlex Cla 40-L (Ayre Aociate, Proj. No , July 000) Armorlex Cla 45-L (Ayre Aociate, Proj. No , July 000). Block teted with a drainage layer (ynthetic or granular) between the geotextile and the revetment: Armorlex Cla 40-T (Ayre Aociate, Proj. No , May 000) Armorflex eign Manual-Abridged Verion 8

10 Block Cla Submerged Weight (Lb) Table.. actor of Safety Equation Variable. & 4 (ft) (ft) (ft) 0 degree (pf) 0-S S S S L L L L L L L L T T T T NOTE: Moment arm and critical hear tree aume block orientation of the block with the long axi parallel to flow. Armorflex eign Manual-Abridged Verion 9

11 . eign Example Uing a given channel deign, ae the hydraulic tability of the Armorlex 45-L block auming a vertical projection of ½ inch, with unvegetated (e.g., newly intalled) condition. In a field application when conidering intallation variable, thi type of offet can occur. The following example will illutrate the potential intability caued by additional force affecting a projecting block. The previouly decribed theory will be utilized to determine the factor of afety. Given: 00-year deign dicharge: Q =500 ft / Channel lope: S 0 = 0.05 ft/ft Channel ide lope Z = H:V Channel bend radiu R c = 80 ft Bottom width b = 0 ft Required factor of afety:.50 Step etermine the normal depth, y, for a bottom width of 0 ft; aume n = 0.0: rom the nomograph of igure., for Bottom width b = 0 ft, y =.9 ft Step etermine velocity and bed hear tre (including bend correction): a. Velocity: V = Q/A = Q/y(b+Zy) = (500 ft /) / (6.8 ft ) =.78 ft/ b. Maximum hear tre: 0 = K b ys 0 rom igure., with R c /b = 80/0 = 8.0, determine K b =. 0 = (.) x (6.4 lb/ft ) x (.9ft) x (0.05 ft/ft) = 8.0 lb/ft Table. outline the procedure for determining the factor of afety for a block, which exhibit a pecified projection height. rom tep one and two above, y =.9 ft V =.78 ft/ 0 = 8.0 lb/ft Armorflex eign Manual-Abridged Verion 0

12 igure.. Nomographic olution of Manning' equation for trapezoidal channel. Armorflex eign Manual-Abridged Verion

13 igure.. actor for determining hear tre at channel bend. Step etermine the value for λ and θ from the channel geometry (igure.): Channel lope S = 0.05 ft/ft, o λ = tan - (0.05) =.86 degree Side lope Z = H:V, o θ = tan - (/Z) = 8.4 degree Step 4 etermine η uing the C value from Table. for cla 45-L block: η o c 8.0 lb/ft.7lb/ft 0.59 Step 5 etermine ratio M/N uing the fact that the drag force, i aumed equal to the lift force, L 4. M/ N Armorflex eign Manual-Abridged Verion

14 Step 6 etermine angle β β tan coλ tan M / N inθ inλ η co(.86) ft in(8.4) in(.86) 0.59.ft o Step 7 etermine η' η η 4 in(λ β) in( ) Step 8 etermine the additional drag force,, due to a projecting block: ' 0.5ρ zwv lug (0.5in) ft ft in ft in ft.6in.78 5.lb Step 9 Calculate the factor of afety for cla 45-L cloed-cell block: coθ S ' " ' inθ coβ η inλ β W W S in(8.4)co(44.66).ft 0.98ft. co (0.7ft)5.lb.ft5.lb 0.45 in (0.98ft)56.lb (0.98ft)56.lb.58 rom the factor of afety analyi, the Armorlex 45-L cla block exhibit a factor of afety greater than the deired.5 even with the aumption that block will have a ½-inch projection. Armorflex eign Manual-Abridged Verion

15 . REERENCES. Baker, R., 989. "Pre-cat Concrete Block for am Spillway." Water Power and am Contruction, Vol. 4, No. 7, July.. Clopper, P.E., 989. "Hydraulic Stability of Articulated Concrete Block Revetment Sytem uring Overtopping low." ederal Highway Adminitration Publication No. HWA-R-89-99, Wahington,.C.. Clopper, P.E., 99. "Protecting Embankment am with Concrete Block Sytem." Hydro Review, Vol. X, No., April. 4. Clopper, P.E. and Y.H. Chen, 988. "Minimizing Embankment amage uring Overtopping low." ederal Highway Adminitration Publication No. HWA-R-88-8, Wahington,.C. 5. Hewlett, H.W.M., Boorman, L.A., and Bramley, M.E., 987. "eign of Reinforced Gra Waterway." Report No. 6, Contruction Indutry Reearch and Information Aociation (CIRIA), 6 Storey' Gate, London, England SWP AU. 6. Simon,.B., and.y. Senturk, 976. Sediment Tranport Technology, Water Reource Publication. Armorflex eign Manual-Abridged Verion 4