An information series from the nationa authority on concrete masonry technoogy ACB REVETMENT DESIGN FACTOR OF SAFETY METHOD TEK -A Articuating Concrete Bocks (ACBs) () INTRODUCTION This TEK is intended to hep designers understand the ACB design methodoogy and the different variabes infuencing the design and safety factor seection. Articuating concrete bock (ACB) systems provide erosion protection to soi exposed to the hydrauic forces of moving water. ACB systems are a matrix of individua concrete bocks paced cosey together to form an erosion-resistant overay with specific hydrauic performance characteristics. Because it is composed of individua units, the ACB system can conform to minor changes in the subgrade without oss of intimate contact. Systems may be connected through geometric interock and/or other components such as cabes. Systems with openings in the bocks can typicay be vegetated to provide a "green" channe and faciitate infitration/exfitration of channe moisture. Figure iustrates a variety of ACB systems, but is not a-incusive of avaiabe systems. ACB units are concrete bock produced in accordance with Standard Specification for Materias and Manufacture of Articuating Concrete Bock (ACB) Revetment Systems, ASTM D 6684 (ref. ). Units must conform to minimum compressive strength, absorption and geometric specifications tested in accordance with Standard Test Methods for Samping and Testing Concrete Masonry Units and Reated Units, ASTM C 4 (ref. ). This TEK addresses the structura stabiity of ACB revetment systems as a function of site-specific hydrauic conditions and unit characteristics. This TEK does not address geotextie fiter and/ or subgrade fiter design, minimum instaation guideines critica to the proper performance of ACB revetments, or minimum upstream or downstream toe treatments. These topics are covered in design manuas such as references 5 and 6. FACTOR OF SAFETY METHOD Simiar to many rip rap sizing methods, the Factor of Safety method quantifies hydrauic stabiity of ACB systems using a discrete partice approach (see ref. 7). The design method invoves baancing the driving and resisting forces, incuding gravity, drag and ift as iustrated in Figure. In typica channe and spiway appications, faiure due to siding (sipping) of the ACB revetment aong the bed is remote. The revetment system is more apt to fai as a resut of overturning about the downstream edge of the ACB unit, or downstream corner point when the ACB unit is ocated on the side sope of a steep channe. For cases where the revetment is paced on steep side sopes (H:V or steeper), the design shoud evauate the potentia for sip shear faiures aong geosynthetic-acb unit interfaces induced by hydrauic and gravitationa forces (i.e., potentia sope instabiity). Figure Exampes of Proprietary ACB Systems (pan view). These are not incusive of a avaiabe configurations. No endorsement or recommendation is intended. Reated TEK: -9B, -3 Keywords: ACBs, articuating concrete bock, design, factor of safety, erosion contro, revetment NCMA TEK -A
Fow F 4 D 3 of faiure. These uncertainties are accounted for in the design by incorporating them into the target safety factor. As discussed beow, there are mutipe facets of the safety factor methodoogy that are considered as they reate to externa and interna design factors. Pivot point of rotation Overturning Forces & F = Drag & ift forces D & = Additiona drag & ift force from bock protuding above ACB matrix W = Gravity force parae to sope S Figure Moment Baance on an ACB at Incipient Faiure (ref. 6) Fow Z D S Externa Factors. Compexity of the hydrauic system and uncertainty of the input hydrauics. A hydrauic systems are not of the same Restraining Forces compexity. Modeing the fow characteristics F of a stream bank or channe is much different R = Inter-bock restraint W S= Gravity force norma to sope than the design of scour protection around bridge piers. If the fow is reativey uniform and predictabe, then the designer may seect a ower vaue for the target safety factor. As the compexity of the system increases, so too shoud the sophistication of the mode used to determine the hydrauic parameters. Utiizing a simpistic mode in a compex environment may warrant an increase in the target safety factor (i.e., greater than.5). Conversey, if a compex mode is used to anayze a simpistic design scenario, then a ower target safety factor may be adequate (i.e., ess than.5).. Consequence of faiure. As with the compexity of the hydrauic system, the overa consequence of faiure needs to be understood. Faiure that resuts in oss of ife is much different from a faiure resuting in soi erosion aong a stream bank in which no oss of ife or property is imminent. Increasing the target safety factor is one way of potentiay offsetting environmenta conditions that are considered high risk. W F R Figure 3 Schematic of Protruding Bock (ref. 6) Fundamenta principes of open channe fow and rigid body mechanics are used aong with hydrauic test resuts suppied by manufacturers. The size and weight of the ACB units, as we as performance data from fu-scae aboratory testing, are considered in evauating the ratio of resisting to overturning moments (the force baance approach). This ratio defines the factor of safety against upift. The design procedure accounts for additiona forces appied to the unit when protrusions above the matrix occur, such as subgrade irreguarities or due to improper pacement (see Figure 3). Faiure is defined as oss of intimate contact between the ACB unit and subgrade. The effects of cabes or rods, vegetative root anchorage or mechanica anchorage devices are conservativey ignored. Target Factor of Safety There are severa factors that need to be understood and considered when evauating the appropriate target safety factor for design purposes. These can be categorized into two groups; externa and interna factors. The externa group consists of factors such as the compexity of the hydrauic system, the uncertainty of the input hydrauics, and the overa consequence Interna Factors. Extrapoation of Test Data. In order to use the safety factor methodoogy, the critica shear stress of the unit aong a horizonta surface must be understood and quantified. An equation is used for the extrapoation of test resuts from a steeper bed sope to a horizonta sope. A second extrapoation takes pace from the tested units to thicker, untested units. In both processes, it is assumed that the intra-bock restraint is the same for a thicknesses of the units. Under this assumption, the extrapoation equations ony consider the weight and thickness of the units. This moment baance approach (obtained from the geometry of the unit) negects any intra-bock restraint. This assumption can be very conservative given the fact that thicker units have much more intra-bock friction than thinner units given the shape of the bocks. As iustrated in Figure 4, the bottom haf of an ACB unit is essentiay a rectange of concrete with adjacent units resting against six surrounding units (because the units are paced in a running bond pattern, there are six adjacent units, rather than four). As the unit increases in thickness, so too does the intra-bock friction. Currenty, the safety factor methodoogy does not account for this variabe, which ony increases the conservatism of this design approach for such conditions. NCMA TEK -A
. Performance Vaues. Hydrauic testing on different footprint or casses of bocks and tapers for a variety of dam overtopping and spiway appications has been performed by system manufacturers. In many of these tests, the testing faciity was unabe to fai the system under a 4 ft (. m) and 5 ft (.5 m) overtopping scenario. Nevertheess, the resuting shear stresses obtained from the tests are used within the safety factor methodoogy as a threshod, or faiure, shear stress. This issue is compounded when extrapoating to thicker units. Without being abe to reach a threshod condition in the testing fume, icensors and manufacturers extrapoate shear stress vaue from a stabe vaue. A arge degree of conservatism in the performance vaues of the units is the resut of not being abe to fai these systems under aboratory conditions. 3. Interaction between Veocity and Shear Stress. In fume testing of the units (see Fig. 5), two of the most important resuts obtained are: a stabe shear stress; and, veocity at a downstream point under the highest fow conditions. Consider for exampe testing resuts whereby the highest boundary shear stress and veocity obtained was. b/ft (,63 Pa) and 6. ft/s (7.96 m/s), respectivey. In the safety factor methodoogy one utiizes a shear stress of. b/ft (,63 Pa) regardess of the expected design veocity for every design utiizing this particuar unit (provided that the design veocity is ess than or equa to the tested veocity). Common hydrauic sense woud state that if the veocity was ony ft/s (3.66 m/s) for a given appication, then the system coud withstand a much arger shear stress than. b/ft (,63 Pa). Therefore, an additiona degree of conservatism is present when the design veocity is ess than the tested veocity and the design utiizes the maximum shear stress generated during the higher veocity event. 4. Aowabe shear stress in a vegetated state. A of the testing on existing ACB systems has taken pace in a non-vegetated state. In contrast, many ACB appications for overtopping and spiway appications seek a fina system that is fuy vegetated. A series of hydrauic tests conducted by the U.S. Army Corp of Engineers investigated the performance of identica ACB systems in both vegetated and non-vegetated conditions (ref. 4). The end resut was an increase in the aowabe shear stress of 4% when vegetated. Taking into consideration a of the points addressed above, what is the proper target safety factor required for a dam overtopping or spiway appication? It is safe to state that 4 in. (4 mm) Revetment cabe 9 in. (9 mm) Revetment cabe the methodoogy used for ACB design is fu of conservative assumptions. From the fact that tapered ACB systems have not reached their threshod condition in the testing fume to the fact that vegetation increases the aowabe shear stress, it is apparent that the resuting safety factor can be conservative by 5%. Therefore, a target safety factor of.3.5 is adequate for appications in which the design hydrauics and site geometry are ceary understood, such as dam overtopping or spiway appications. Utimatey, the externa factors and overa design of the project wi need to be evauated and decided on by the engineer of record. It may aso be appropriate for an individua experienced in ACB design to offer an opinion on how these factors shoud be incorporated into an overa target safety factor. Hydrauic Considerations The main hydrauic variabe in ACB stabiity design is the tota hydrauic oad (or bed shear stress) created by a varying discharge within a fixed geometric cross-section. The ratio of designed average cross-sectiona bed shear to the ACB's critica shear vaue (obtained from testing) is used, in part, for practica anaysis and evauation of ACB stabiity. The cross-section averaged bed shear stress, τ o, can be cacuated for design using a simpe equation (ref. 3): τ o = γ R S f τ o is appied over the channe boundary, regardess of channe ining. Shear stress is a function of the hydrauic radius and the sope of the energy ine (for the simpest case the bed sope), both defined by channe geometry and fow conditions. The cross-section averaged bed shear stress is suitabe for uniform fow conditions such as those found in ong straight reaches of open channes with uniform cross section. It may be determined using simpified mode approaches, such as the Manning equation or the HEC-RAS mode (ref. ). For cases invoving bends, confuences, constrictions and fow obstructions, more sophisticated hydrauic modeing is generay appropriate, such as a two-dimensiona mode which can evauate time-dependent fow conditions or compex geometry (ref. ). Design veocity is often determined using the Manning Equation for steady uniform fow as foows (ref. 3): Q = (.486/n) A R /3 S / f [inch-pound] Q = (/n) A R /3 / S f [metric] An iterative process is used to determine the fow depth, y o, because both the area and hydrauic radius are functions of y o. Cross-sectiona averaged veocity of fow is then defined as V = Q/A. As noted previousy, compex hydrauic systems require sophisticated modeing to determine averaged veocity. The cross-sectiona averaged bed shear stress and cross sectiona averaged veocity shoud be determined by a design professiona famiiar with hydrauic design practices. Figure 4 Comparison of the Potentia Intra-Bock Friction Between 4.5 in. (4 mm) and 9. in. (9 mm) ACB Units. (ref. 6) NCMA TEK -A 3
ACB Revetment Considerations Historicay, manufacturers of ACB systems pubished performance data from fu-scae tests performed in accordance with Federa Highway Administration guideines (ref. 8). Two reativey new ASTM standards have been deveoped based on the FHWA method: Standard Guide for Anaysis and Interpretation of Test Data for Articuating Concrete Bock (ACB) Revetment Systems in Open Channe Fow, ASTM D776 (ref. 3) and Standard Test Method for Performance Testing of Articuating Concrete Bock (ACB) Revetment Systems for Hydrauic Stabiity in Open Channe Fow, ASTM D777 (ref. 4), that eventuay wi repace the FHWA test method. This data provides the critica shear stress, τ c, and is based on specific fow conditions and ACB system characteristics. The manufacturer shoud specify whether the critica shear stress is for a unit on a horizonta surface or on an incined surface. Vaues for a unit on a horizonta surface are commony specified. It is important that the designer consider the fu-scae test configuration and hydrauic conditions used to derive the critica shear stress on a horizonta surface. Testing invoves the construction of a fu-scae test embankment that is subsequenty exposed to hydrauic oad unti faiure defined as the oca oss of intimate contact between the ACB unit and the subgrade it protects. A schematic of a typica fume is iustrated in Figure 5. ACB system stabiity is evauated by summing the driving and resisting moments about the toe of an individua ACB unit. The inter-bock restraint, F R, is ignored, as is any contribution from cabes, anchorages and vegetation (see Figure ). ACB pacement or subgrade irreguarities can resut in one unit protruding above the ACB matrix, as shown in Figure 3. The protrusion height, ΔZ, is a function of instaation practice and bock-to-bock interface, and is often assumed to be / 4 to / in. (6 to 3 mm). However, the designer must consider sitespecific conditions and adjust ΔZ as required. The ift force,, resuting from the protrusion is conservativey assumed equa to the drag force, D. The estabished design methodoogy assumed that the fow was parae to the bock and cacuated the drag forces using the bock width perpendicuar to the fow, b (see equation for D in Tabe and Figure 6b). However, in the fied not a ACB appications have the fow aigned with the sides of the bock. To account for that uncertainty, it is recommended that the diagona distance of the bock,, be used instead of b in the drag force cacuations (see Figure 6b). It is recommended that the designer anayze the project conditions and determine the appropriate dimension for determining the drag forces, D, and safety factors on each project. Exampes of non-parae fow conditions are open channes and evees where the fow aignment is uncertain during the ife of the project. The factor of safety against oss of intimate contact is considered to be a function of design bed shear stress, critica shear stress, channe geometry and ACB unit geometry and weight. Figure iustrates unit moment arms based on unit geometry. The safety factor for a singe ACB unit is determined from the ratio of restraining moments to overturning moments. Considering the submerged unit weight,, unit moment arms and drag and ift forces, the safety factor, SF is defined as (ref. 6): SF = a θ a θ cosβ + 3 cosδ + 4 F + 3 cosδ + 4 F Dividing by and substituting terms, the equation for SF resoves to that presented in Tabe. Tabe aso outines the cacuations necessary for determining factor of safety. DESIGN EXAMPE A trapezoida channe section with 3H:V side sopes (Z = 3, θ = 8.4 o ) and a base width b of 5 ft (4.6 m) requires stabiization. The -year design discharge is 45 ft 3 /s (.7 m 3 /s), and the channe sope S o is.3 ft/ft (.3 m/m) (θ =.7 o ). The channe has a uniform bed and no fow obstructions (i.e. confuences, bends or changes in geometry). Manning s n is specified as.35. Based on design conditions, the energy grade ine S f is assumed equa to the channe sope S o. Step Determine fow depth and cross-sectiona averaged veocity: Q =.486/n A R /3 S f / A = by o + Zy o, cross-sectiona fow area P = b + (y o +(Zy o ) ) /, wetted perimeter Inet diffuser (straightens and smooths incoming fow) Point gauge and veocity probe Testing fume 9 ft (7.4 m) ong x ft (3.4 m) high x 4 ft (. m) wide Video Camera Fow meter Carriage Revetment Soi Embankment Headbox 36 in. (.9 m) pipe Embankment test section Taibox Figure 5 aboratory Fume Schematic 4 NCMA TEK -A
Tabe Design Equations for ACB Systems (ref. 6) SF = ( / )a θ a θ cosβ + η / δ + β + θ = 9 o or π / radians where: β = arctan a ( 4 / 3 + ) θ η / ( ( ) + 3 cosδ + 4 F ' ) cos( θ + θ) Note: The equations cannot be soved for θ = (i.e., division by ); therefore, a negigibe side sope must be entered for the case of θ =. ( ) + sin( θ + θ) θ = arctan sinθ cosθ sinθ cosθ = arctan tanθ tanθ η = τ des / τ c ( ) 4 / 3 + η = 4 / 3 + sin θ + θ + β η a θ = cos θ sin θ F ' = F ' D =.5 ΔZ b u ρv des = C S C R = A/P, hydrauic radius By iteration, the fow depth y o is determined to be. ft (.6 m). V = Q/A = 45 ft 3 /s /44.73 ft =. ft/s (3. m/s) Step Cacuate design shear stress: τ des = γ R S f = (6.4 b/ft 3 )(.58 ft)(.3 ft/ft) =.96 psf (.4 kpa) Step 3 Seect target factor of safety: Based on the anaysis of the project conditions, such as type of appication, ow consequence of faiure and the empirica hydrauic mode, the designer has recommended a target factor of safety, SF T, for the project of.34. Step 4 Seect potentia ACB product and obtain geomorphic and critica shear stress data: The proposed ACB manufacturer specifies a critica shear stress, τ c, for the unit on a horizonta surface of 3 psf (.4 kpa) for a maximum veocity of ft/s (6. m/s), submerged unit weight of 38 b (7. kg) and dimensions of 5 (w) x 8 () x 5 (h) in. (38 x 457 x 7 mm). Step 5 Cacuate factor of safety against incipient unit movement: Given; W s = 35 b (6 kg) b u =.5 ft (46 mm) τ c = 3 psf (.4 kpa) η o =.96/3 =.987 and determining the foowing geometricay (see Figure 6); = 5// =.8 ft (63 mm) = 4 = 8 + 5 * =.976 ft (97 mm) 3 =.8(5)/ =.333 ft ( mm) and assuming (see discussion); ΔZ =.47 ft (3 mm) the foowing are cacuated using the equations in Tabe : = D =.5(ΔZ) b ρ V =.5(.47 ft)( x.976 ft)(.94 sugs/ft 3 )(. ft/s) = 8.5 b NCMA TEK -A 5
Top of bank B W sin cos S a W S B' Bed of channe (a) Channe cross-section b b and and 4 and 4 a a Fow Fow Fow aigned with the bock Fow not aigned with the bock (b) Pan view of unit Fow direction 4 F C A 3 FD cos Fow direction A' Bock projection once in motion W S Vertica Horizonta sin cos sin cos Channe bank at toe of sope - a sin cos (d) Section A - A' 8 3= / (bock height) Bank aong A - A' a C' -a sin (c) Section - ', view norma to pane of channe bank Bank norma to A - A' = / (e) Section C - C' (fow direction norma to page) (bock height) Figure 6 ACB Unit Design Variabes 6 NCMA TEK -A
For this open channe appication the fow is not considered to aign with the bock, so b = a θ =.948 θ = 5.6 β = 9.4 η =.8 δ = 65.4 SF =.43 Because the cacuated factor of safety exceeds the target, the proposed ACB system is stabe against oss of intimate contact. An ACB Design Spreadsheet (ref. 5) that makes these cacuations much easier is avaiabe free on request via the NCMA web site at: http://www.ncma.org/resources/design/ Pages/ACB_Design.aspx. NOTATIONS: A = cross-sectiona fow area, ft (m ) a q = projection of W s into subgrade beneath bock (Tabe ) b = width of channe base, ft (mm) b u = width of ACB unit in the direction of fow, ft (mm) = drag force, b (kn) D = additiona drag forces, b (kn) F = ift force, b (kn) = additiona ift forces, b (kn) (Tabe ) F R = inter-bock restraint, b (kn) x = bock moment arms, ft (mm) n = Manning s roughness coefficient Q = design discharge, ft 3 /s (m 3 /s) R = hydrauic radius (A/wetted perimeter), ft (m) S C = specific gravity of concrete (assume.) S f = energy grade ine, ft/ft (m/m) S o = bed sope, ft/ft (m/m) SF = cacuated factor of safety (Tabe ) SF T = target factor of safety V = cross-sectiona averaged fow veocity, ft/s (m/s) W = weight of bock, b (kg) W s = submerged weight of bock, b (kg) (Tabe ) W s = gravity force parae to sope, b (kn) W s = gravity force norma to sope, b (kn) y o = fow depth, ft (m) Z = horizonta to vertica ratio of channe side sope β = ange of bock projection from downward direction, once in motion, degrees or radians γ = unit weight of water, 6.4 pcf (, kg/m 3 ) ΔZ = height of bock protrusion above ACB matrix, ft (mm) δ = ange between drag force and bock motion, degrees or radians η o = stabiity number for a horizonta surface (Tabe ) η = stabiity number for a soped surface (Tabe ) θ = ange between side sope projection of WS and the vertica, degrees or radians (Tabe ) θ = channe bed sope, degrees or radians θ = channe side sope, degrees or radians ρ = mass density of water,.94 sugs/ft 3 (, kg/m 3 ) τ c = critica shear stress for bock on a horizonta surface, b/ft (kpa) τ des = design shear stress, b/ft (kpa) τ o = cross-section averaged bed shear stress, b/ft (kpa) NCMA TEK -A 7
REFERENCES. Standard Specification for Materias and Manufacture of Articuating Concrete Bock (ACB) Revetment Systems, ASTM D 6684-4(). ASTM Internationa,.. Standard Test Methods for Samping and Testing Concrete Masonry Units and Reated Units, ASTM C 4-9. ASTM Internationa,. 3. Standard Guide for Anaysis and Interpretation of Test Data for Articuating Concrete Bock (ACB) Revetment Systems in Open Channe Fow, ASTM D776-8. ASTM Internationa,. 4. Standard Test Method for Performance Testing of Articuating Concrete Bock (ACB) Revetment Systems for Hydrauic Stabiity in Open Channe Fow, ASTM D777-8. ASTM Internationa, 5. Design Manua for Articuating Concrete Bock Systems. Harris County Food Contro District, Houston, Texas,. 6. Design Manua for Articuating Concrete Bock, TR A. Nationa Concrete Masonry Association,. 7. Bridge Scour and Stream Instabiity Countermeasures: Experience, Seection, and Design Guidance 3rd Edition. Federa Highway Administration Hydrauic Engineering Circuar No. 3. 8. Copper, P. E. and Y. Chen. Minimizing Embankment Damage During Overtopping Fow, Technica Report FHWA RD-88-8. Federa Highway Administration, 988. 9. Copper, P. E. Hydrauic Stabiity of Articuated Concrete Bock Revetment Systems During Overtopping Fow, Technica Report FHWA RD-89-99. Federa Highway Administration, 989.. RMA Version 4.5. United States Army Corps of Engineers. USACE Waterways Experiment Station, 8.. HEC-RAS Version 4.. United States Army Corps of Engineers. USACE Hydroogic Engineering Center,.. Articuated Concrete Bock for Erosion Contro, TEK -9B. Nationa Concrete Masonry Association, Herndon, Virginia,. 3. Morris, H. M. and J. Wiggert. Appied Hydrauics in Engineering, Second Edition, James Wiey & Sons, 97. 4. ipscomb, C.M, C.I. Thornton, S.R. Abt, and J. R. eech. Performance of Articuated Concrete Bocks in Vegetated and Un- Vegetated Conditions. Proceedings of the Internationa Erosion Contro Association 3nd Annua Conference and Exposition, as Vegas, NV, February 5-8,. 5. Articuating Concrete Bock (ACB) Design Spreadsheet, TRAS. Nationa Concrete Masonry Association, Herndon, Virginia,. NCMA and the companies disseminating this technica information discaim any and a responsibiity and iabiity for the accuracy and the appication of the information contained in this pubication. NATIONA CONCRETE MASONRY ASSOCIATION 375 Sunrise Vaey Drive, Herndon, Virginia 7 www.ncma.org To order a compete TEK Manua or TEK Index, contact NCMA Pubications (73) 73-9 8 NCMA TEK -A