Articulated Concrete Block Design. By Bryan N. Scholl; Christopher I. Thornton, Ph.D., P.E.; and Barrie King, E.I.T.

Transcription

1 Articulated Concrete Block Design By Bryan N. Scholl; Christopher I. Thornton, Ph.D., P.E.; and Barrie King, E.I.T. AUGUST 2010

2 Professional Development Series Articulated Concrete Block Design By Bryan N. Scholl; Christopher I. Thornton, Ph.D., P.E.; and Barrie King, E.I.T. Sediment transport in streams and rivers is inevitable as the stream or river transport capacity rises and falls with the streamflow. If the transport capacity in a location exceeds the sediment supply, erosion will occur. Streambank erosion must be controlled in critical areas (e.g. near bridge crossings for safety as well as economic reasons. The same is true of bridge piers where general and local scour during a flood event may temporarily or permanently lower the streambed level by several feet, potentially endangering the structure. Articulated concrete block systems (ACBs are an effective countermeasure if properly designed and installed. This article will cover ACB design including the safety factor analysis and overturning moment design approach outlined in Hydraulic Engineering Circular No. 23: Bridge Scour and Stream Instability Countermeasures: Experience, Selection, and Design Guidance-Third Edition, Volume 2 (HEC-23. ACBs provide a flexible option to other erosion countermeasures such as riprap, soil cement, grout-filled mattresses, etc. As they are not intended for slope stabilization, slope stability must be ascertained prior to considering an ACB system. ACB systems are composed of preformed concrete blocks that are interconnected through a combination of form and/or cables. The blocks are able to articulate to some degree along their adjoining faces, allowing the system to conform to changes in the subgrade while maintaining the protective cover. Open-cell forms of ACB are also available that allow vegetation to be established, improving stability and aesthetic appeal. A few generic examples of potential ACB shapes are presented in Figure 1. Regardless of the manufacturer specifics, failure of an ACB system is Figure 1. Examples of ACB units and systems (TEK 11-12, 2002 Instructions The Professional Development Series is a unique opportunity to earn continuing education credit by reading specially focused, sponsored articles in CE News. If you read the following article, display your understanding of the stated learning objectives, and follow the simple instructions, you can fulfill a portion of your continuing education requirements at no cost to you. This article also is available online at After reading the learning objectives below, read the Professional Development Series article, complete the quiz and mail or fax your answers to the Professional Development Series sponsor for grading. Submittal instructions are provided on the Reporting Form on page 7. If you answer at least 80 percent of the questions correctly, you will receive a certificate of completion from the sponsor within 90 days and will be awarded 1.0 professional development hour (equivalent to 0.1 continuing education unit in most states. Or, go to continuing-education.html to take the quiz online; quiz answers will be graded automatically and, if you answer at least 80 percent of the questions correctly, you can immediately download a certificate of completion. Note: It is the responsibility of the licensee to determine if this method of continuing education meets his or her governing board(s of registration s requirements. Learning Objectives After reading this article you should understand: Design applications of articulated concrete blocks (ACB s. Acceptable factor of safety values with respect to application. ACB design procedure for hydraulic velocity and bed shear. The industry s definition of failure for ACB Systems. Scour countermeasure design. Professional Development Series Sponsor CONTECH Construction Products Inc. 2 PDH Professional Development Advertising Section CONTECH Construction Products Inc.

3 always defined as the local loss of intimate contact between the revetment and the subgrade it protects. Extensive testing and field monitoring has shown loss of contact can result in one or more of the following: ingress of flow beneath the armor layer, causing increased uplift pressure and separation of blocks from the subgrade; loss of subgrade soil through gradual piping erosion and/ or washout; enhanced potential for rapid saturation and liquefaction of subgrade soils, causing shallow slip geotechnical failure (especially in fine-grained, low-cohesive soils on steep slopes; and loss of block or group of blocks from the revetment matrix, directly exposing the subgrade to flow. The importance of maintaining intimate contact with the subgrade cannot be overstated, and a suitable filter and/or drainage layer are considered essential to the proper design of an ACB system. A detailed discussion of filter design is beyond the scope of this article but may be found in Design Guide 16 of HEC-23. If dune-type bedforms may occur at the protected slope s toe, it is strongly recommended that only a geotextile filter be considered. When evaluating a potential ACB system for which performance testing utilized a drainage layer, a drainage layer must also be used in the design. ACB system design uses a discrete particle approach Table 1. Base factor of safety, SF B Example Application SF B Channel bed or bank Bridge pier or abutment Overtopping spillway Table 2. Consequence of failure multiplier, X C Consequence of failure Low Medium High Extreme or loss of life X C similar to that introduced by Stevens and Simons (1971 and modified by Julien (1995 in the Factor of Safety derivation method for sizing riprap. For ACBs, the force balance has been recomputed using the weight and geometry of the concrete blocks and test results are used in place of the Shield s relationship. Also, additional lift and drag forces generated by block protrusion above the surrounding matrix level are considered. Figure 2 presents additional lift and drag forces created by block protrusion, F' L and F' D respectively. The recommended design procedure for ACBs is the factor of safety method. Step 1 is to determine the minimum acceptable target factor of safety from site-specific details using Tables 1 through 3 and the relationship: SF T = SF B X C X M Eq. 1 where SF T = target factor of safety, SF B = base factor of safety, X C = multiplier based on consequence of failure, and X M = multiplier based on hydraulic model uncertainty. According to HEC-23, typically, a minimum allowable factor of safety of 1.2 is used for revetment (bank protection when the project hydraulic conditions are well known and the installation can be conducted under well-controlled conditions. Higher factors of safety are typically used for protection at bridge piers, abutments, and at channel bends due to the complexity in computing hydraulic conditions at these locations. The proposed design is then evaluated using a moment balance approach to follow. The factor of safety is then iteratively evaluated against the minimum acceptable value until an acceptable design is determined. Once the target factor of safety has been determined (Step 1, design steps are as follows: 2 calculate design shear stress, 3 obtain ACB properties, 4 calculate the factor of safety parameters for each product, and 5 calculate the factor of safety for potential blocks and choose the appropriate product based on the target factor of safety. Design shear stress τ des is calculated using Equation 2: τ des = K b γ y S f Eq. 2 where τ des = design shear stress (lb/ft 2, K b = bend coefficient (dimensionless, γ = unit weight of water (lb/ft 3, Figure 2. Additional lift and drag created by block protrusion (Lagasse, 2009 Table 3. Multiplier base on hydraulic model, X M Hydraulic model Deterministic (e.g. HEC-RAS, RMA-2V Empirical or stochastic (e.g. Manning s or Rational Equation Estimates X M Professional Development Advertising Section CONTECH Construction Products Inc. PDH 3

4 Articulated Concrete Block Design y = maximum depth of flow on revetment (ft, and S f = slope of the energy grade line (ft/ft. The bend coefficient is used to calculate the increased shear stress on the outside of a bend. K b is a function of the ratio of the radius of curvature R c and the top width of the channel, T: K b = 2.0 for 2 R c /T R ( c R ( c K b = for 10 > R c /T > 2 T T K b = 1.05 for R c /T 10 Eq. 3 Figures 3 through 6 present schematics of a single ACB on a side slope with variables defined for the factor of safety analysis. Required block properties that must be obtained are presented in Figure 5 and Figure 6. In the general case, the pivot point O will be located at the downstream, downslope corner of the block. The safety factor S F of a single block in the ACB matrix that must be evaluated against the previously calculated target factor of safety SF T is the ratio of restraining moments to overturning moments, ( 2 / 1 a θ SF = Eq. 4 cosβ (1 a θ 2 + η 1 ( 2 / F' D cosδ + 4 F' L 1 W S Variable definitions and calculation methods are presented in Table 4. These equations may be used with English or SI units provided consistency is maintained. Once a block has been selected, the longitudinal and vertical extent of the installation must be determined. Longitudinally, revetment armor should be continuous for a distance which extends both upstream and downstream of the region which experiences hydraulic forces severe enough to cause dislodging and/or transport of bed or bank Table 4. Factor of safety design equations F' L = F' D = 0.5ρb( z(v des 2 Eq. 5 η 0 = τ des /τ C Eq. 9 θ = arctan(tanθ 0 /tanθ 1 Eq. 6 δ = 90 β θ ( + 1 ( + sin(θ + θ 0 η 0 ( 2 / 1 cos(θ 0 + θ β = arctan Eq a θ ( 4 3 a q = projection of W S into subgrade plane b = block width normal to flow (ft (typically accepted as 2 times 1 2 F' D = F' L = added drag/lift from block protrusion (lb, x = block moment arm (ft γ c = block concrete density (lb/ft 3 γ w = density of water (lb/ft 3 V des = design velocity (ft/s W = weight of block in air (lb W s = submerged block weight (lb Eq. 8 Dz = block protrusion height above matrix (ft (value will have to be assumed based on block placement tolerance b = angle between block motion and vertical (degrees a θ = (cosθ 1 2 (sinθ 0 2 Eq. 10 ( 4 / 3 + sin(θ 0 + θ+ β η 1 = η 0 Eq. 11 ( ( 4 / W S = W γ C γ ( W γ C d = angle between drag force and block motion (degrees h 0 = stability number of a block on horizontal surface (dimensionless h 1 = stability number of a block on sloped surface (dimensionless q = angle between side slope projection of W S and vertical (degrees q 0 = channel bed slope (degrees q 1 = side slope of block installation (degrees r = mass density of water 1.94 (slugs/ft 3 t c = critical shear stress for block on a horizontal surface (lb/ft 2 t des = design shear stress (lb/ft 2 Eq. 12 Note: q 1 = 0 for the equations cannot be solved; a very small, non-zero side slope must be used when q 1 = 0. 4 PDH Professional Development Advertising Section CONTECH Construction Products Inc.

5 material. The minimum distances recommended are an upstream distance of 1.0 channel width and a downstream distance of 1.5 channel widths.... In meandering reaches, the present limit of erosion may not necessarily define the ultimate downstream limit. FHWA s Hydraulic Engineering Circular No. 20, Stream Stability at Highway Structures, provides guidance for the assessment of lateral migration. Vertically, freeboard above the design water surface must be provided. If the reach is unconstricted, a minimum Figure 3. Channel cross section freeboard is 1 to 2 feet; if constricted, the minimum is 2 to 3 feet. For supercritical flow, freeboard is measured from the energy grade line, not the water surface. The system must cover the entire channel bottom. Or, if the channel bed is unlined, it must extend below the bed level to the extent that it will not be undermined by maximum scour caused by toe scour, contraction scour, and long-term degradation in combination. The recommended extent of vertical installation is presented in Figures 7 and 8. Safety factor calculation methods are similar for revetment or pier scour applications with two notable exceptions: design velocity V des and design shear stress τ des determination. For typical revetment applications, a cross sectional average velocity is generally acceptable if a detailed hydraulic analysis has not been performed. Flow conditions near bridge piers are more severe; however, and require that local velocity and shear stress values be determined. If a Figure 6. View normal to section A-A (shown in Figure 4 Figure 4. Top view of block on side slope Figure 7. Recommended revetment installation for bank and bed armor Figure 5. Section A-A (shown in Figure 4 Figure 8. Recommended revetment installation without bed armor Professional Development Advertising Section CONTECH Construction Products Inc. PDH 5

6 Articulated Concrete Block Design stream velocity distribution is unavailable, the recommended method is provided in NCHRP Report 593: V des = K 1 K 2 V avg Eq. 13 where V des = design velocity for conditions at the pier (ft/s, K 1 = pier shape factor equaling 1.5 for round-nose piers and 1.7 for square-edge piers, K 2 = velocity adjustment factor for pier location in the channel ranging from 0.9 near the bank in a straight reach to 1.7 when the pier is located in the main current of flow around a sharp bend, and V avg = average approach velocity upstream of the bridge (ft/s. If the velocity distribution is available, the maximum velocity in the active channel V max should be used and V des = K 1 V max Eq. 14 The design shear stress at the pier is then calculated using, ( 2 nv des γ W K y 1/3 u τ des = Eq. 15 where τ des = design shear stress for local pier conditions (lb/ft 2, n = Manning s n value for the block system, V des = design velocity determined by Equation 13 or 14 (ft/s, γ w = unit weight of water (62.4 lb/ft 3 for fresh water, y = depth of flow at pier (ft, and K u = for English units, 1.0 for SI. It has been shown that optimum performance of ACBs in pier scour protection is obtained when the blocks are extended at least twice the pier width in all directions from the pier. Recommended pier installation is presented in Figure 9. If only local scour is expected, the system may Figure 9. Recommended pier installation extents be installed horizontally, flush with the streambed providing turndowns at the periphery. If other processes or types of scour are expected, the system must be sloped away from the pier in all directions, terminating at the periphery below the streambed at a depth greater than the maximum expected scour or bedform troughs, whichever is greater. Blocks should not be placed on a slope greater than 2H:1V (50 percent, even if this results in blocks being placed greater than two pier widths from the pier. Assistance in predicting bedform geometry may be found in Karim (1999, van Rijn (1984, and Bennett (1997, who provided an upper limit of crest-to-trough height, Δ, as Δ < 0.4y where y is the depth of flow. This would suggest the maximum bedform trough depth below ambient level is approximately 0.2 times the depth of flow. Wall piers or pile bents consisting of multiple columns may be skewed to the direction of flow and the ACB protection must be extended to protect against the additional scour potential. In the absence of definitive guidance, the system should be extended by a factor Kα a function of pier width (a, length (L and skew angle (α, ( 0.65 acosα + Lsinα K α = Eq. 16 a A filter is typically required for bridge pier applications of ACBs and should extend beneath the complete extent of the system. The geotextile should be securely attached to the bottom of the pre-assembled ACB mat prior to lifting with a crane and spreader bar. In shallow water where velocities are low, the geotextile may be placed under water and held in place temporarily with weights until the blocks are placed. As in the case of revetment installations, if dune-type bedforms may be present, it is strongly recommended that only a geotextile filter be considered. An observed failure point at ACB bridge pier installations is the seal where the mat meets the pier. Securing the geotextile to the pier aids in preventing bed material loss around the pier. Structural attachment of the mat to the pier is strongly discouraged; moment transfer from the mat to the pier may affect the structural stability of the pier. When properly designed, an ACB system can provide an excellent design alternative when considering the level of protection afforded for the installed cost. Bryan N. Scholl, is a research assistant for Colorado State University. He can be contacted at bnscholl@engr.colostate. edu. Christopher I. Thornton, Ph.D., P.E., is director of the Hydraulics Laboratory and Engineering Research Center at Colorado State University. He can be contacted at thornton@engr. colostate.edu. Barrie King, E.I.T., is the supervisor of engineering for CONTECH Construction Product s Armortec product line. He can be contacted at kingb@contech-cpi.com. 6 PDH Professional Development Advertising Section CONTECH Construction Products Inc.

7 REFERENCES Bennett, J.P., 1997, Resistance, Sediment Transport, and Bedform Geometry Relationships in Sand-Bed Channels, in: Proceedings of U.S. Geological Survey Sediment Workshops, Feb Dunlap, S., 2001, Design Manual for Articulating Concrete Block Systems, Harris County Flood Control District, Houston, Texas. Julien, P.Y., 1995, Erosion and Sedimentation, Cambridge University Press, Cambridge, UK. Karim, F., 1999, Bed-Form Geometry in Sand-Bed Flows, Journal of Hydraulic Engineering, vol. 125, No.12, December. Lagasse, P.F., Schall, J.D., and Richardson, E.V., 2001, Stream Stability at Highway Structures, Third Edition, Hydraulic Engineering Circular No. 20, FHWA NHI , Washington, D.C. Lagasse, et al., 2007, Countermeasures to Protect Bridge Piers from Scour, NCHRP Report 593, Transportation Research Board, National Academies of Science, Washington, D.C. Lagasse, P.F., Clopper, P.E., Pagán-Ortiz, J.E., Zevenbergen, L.W., Arneson, L.A., Schall, J.D., and Girard, L.G., 2009, Bridge Scour and Stream Instability Countermeasures: Experience, Selection and Design Guidance, Volume 2, Third Edition, Hydraulic Engineering Circular No. 23, FHWA NHI , Washington, D.C. ( Stevens, M.A., and Simons, D.B., 1971, Stability Analysis for Coarse Granular Material on Slopes, in: River Mechanics, Shen, H.E. (ed., Water Resources Publications, Fort Collins, Colo. van Rijn, L.C., 1984, Sediment Transport, Part III: Bed Forms and Alluvial Roughness, Journal of Hydraulic Engineering, vol. 110, No. 12, December. Articulating Concrete Block Revetment Design Factor of Safety Method, TEK National Concrete Masonry Association, Herndon, Virginia, Professional Development Series Sponsor: 9025 Centre Pointe Dr., Suite 400, West Chester, OH Phone: Fax: Web: CE News Professional Development Series Reporting Form Article Title: Articulated Concrete Block Design Publication Date: August 2010 Sponsors: CONTECH Construction Products Inc. Valid for credit until: August 2012 Instructions: Select one answer for each quiz question and clearly circle the appropriate letter. Provide all of the requested contact information. Fax this Reporting Form to (You do not need to send the Quiz; only this Reporting Form is necessary to be submitted. Or, go to to take the quiz online. 1 a b c d 6 a b c d 2 a b c d 7 a b c d 3 a b c d 8 a b c d 4 a b c d 9 a b c d 5 a b c d 10 a b c d Required contact information Last Name: First Name: Middle Initial: Title: Firm Name: Address: City: State: Zip: Telephone: Fax: Certification of ethical completion: I certify that I read the article, understood the learning objectives, and completed the quiz questions to the best of my ability. Additionally, the contact information provided above is true and accurate. Signature: Date: Professional Development Advertising Section CONTECH Construction Products Inc. PDH 7

8 Quiz instructions On the Professional Development Series Reporting Form, circle the correct answer for each of the following questions. Or, go to www. cenews.com/continuing-education.html to take the quiz online; quiz answers will be graded automatically and, if you answer at least 80 percent of the questions correctly, you can immediately download a certificate of completion. 1. ACBs provide a flexible erosion countermeasure alternative to which of the following? a soil cement c riprap b grout-filled mattresses d all of the above 2. Which of the following is the failure criterion for ACB systems? a block protrusion greater than 0.25 inch b average soil loss greater than 0.5 inch c local loss of intimate contact between the revetment and the subgrade d visible deformation of the ACB system surface 3. Which of the following is most correct? a a drainage layer is required for ACB installation b a suitable filter and/or drainage layer are essential c a drainage layer is required if used during performance testing d b and c 4. What is the most likely Target Factor of Safety, SF T, for a bridge pier installation on a metropolitan interstate highway using HEC-RAS to determine flow velocity? a 1.2 c 3.2 b 2.2 d For an outside bend bank revetment installation, where the radius of curvature is 920 feet, top width is 218 feet, maximum flow depth is 9.1 feet, bed slope is ft/ ft and energy grade line is ft/ft, determine the design shear stress. a 4.2 psf c 7.9 psf b 6.5 psf d 9.3 psf 6. A square ACB with a surface area of 2 ft 2 is installed with flow perpendicular at 8.9 ft/s and protrudes 0.6 inches above the surrounding matrix. What is the added drag force? a 5.4 lb c 64.5 lb b 7.7 lb d lb 7. Provided the ACB in the above figure, t des = 6.3 lb/ft 2, t c = 24.6 lb/ft 2, Δz = 0.5 inch, S 0 = 0.01 ft/ft, side slope of 2H:1V, V des = 11.0 ft/s, and concrete density of 140 lb/ft 3, calculate the factor of safety, SF. a 1.48 c 1.74 b 2.15 d Which statement best describes what freeboard should be maintained for an ACB revetment system? a a minimum freeboard of 1 to 2 feet is acceptable for an unconstricted reach b freeboard should never be less than 3 feet c a minimum freeboard of 2 to 3 feet is acceptable for a constricted reach d both a and c 9. What is one of the major calculation differences when designing an ACB system for a bridge pier application versus a revetment? a bed-form influences b design velocity c angle between block motion and vertical calculation d added drag force determination 10. For a bridge pier application, what installation width results in optimum performance of ACBs? a at least 1 pier width c at least 2 pier widths b at least 1.5 pier widths d at least 3 pier widths 8 PDH Professional Development Advertising Section CONTECH Construction Products Inc.