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Bridge Scour and Stream Instability Countermeasures: Experience, Selection, and Design Guidance-Third Edition

Design Guideline 8 Articulating Concrete Block Systems

8.1 INTRODUCTION

Articulating concrete block systems (ACBs) provide a flexible alternative to riprap, gabions and rigid revetments. These systems consist of preformed units which either interlock, are held together by cables, or both to form a continuous blanket or block matrix (Figure 8.1). This design guideline considers two applications of ACB's: Application 1 - bank revetment and bed armor; and Application 2 - pier scour protection.

For over three decades, ACB systems have been used for streambank revetment or full channel armoring where the mat is placed across the entire channel cross section. For this reason, guidelines for these applications are well established (Harris County Flood Control District 2001). Guidance for the design of ACBs for protection against pier scour is derived from NCHRP Report 593, "Countermeasures for Protecting Bridge Piers from Scour" (Lagasse et al. 2007).

The term "articulating," as used in this document, implies the ability of individual blocks of the system to conform to changes in the subgrade while remaining interconnected by virtue of block interlock and/or additional system components such as cables, ropes, geotextiles, or geogrids. ACB systems include interlocking and non-interlocking block geometries; cabled and non-cabled systems; and vegetated and non-vegetated systems. Block systems are typically available in both open-cell and closed-cell varieties.

Manufacturers of ACBs have a responsibility to test their products and to develop design parameters based on the results from these tests. A standard performance test is given in ASTM D7277. Since ACBs vary in shape, size, and performance from one system to the next, each system will have unique design parameters. A procedure to develop hydraulic design criteria for ACBs given the appropriate hydraulic stability performance data for a particular block system is presented in this section.

Images of two types of interlocking block systems. In (a) the system is made up of two types of blocks, larger flat cylindrical blocks with three smaller evenly spaced cylindrical cut outs on the edge, and smaller regular flat triangular blocks with cylindrical shapes on the apexes. The cylindrical apexes of the smaller regular flat triangular blocks loosely fit into the cutouts of the larger flat cylindrical blocks, locking them together.  In (b) rectangular blocks with overlapping and interlocking edge sections are in staggered rows. The blocks are cabled together in one direction via two holes through their bases.
     (a)                                                                            (b)
Figure 8.1. Examples of (a) interlocking block system (courtesy American Excelsior) and (b) cabled block system (courtesy Armortec).

8.2 BACKGROUND

Beginning in 1983, a group of agencies of the federal government, led by the Federal Highway Administration (FHWA), initiated a multi-year research and testing program in an effort to determine, quantitatively, the performance and reliability of commercially available erosion protection treatments. The research was concluded in 1989, with the final two years of testing concentrated on the performance of ACBs. Full-scale testing methodologies and results for embankment overtopping conditions from the FHWA research are published in Clopper and Chen (1988) and Clopper (1989).

The tests provided both qualitative and quantitative insight into the hydraulic behavior and stability of these types of revetments. Failure mechanisms were identified and quantitatively described as a result of that research effort. Threshold hydraulic loadings were related to forces causing instability in order to better define selection, design, and installation guidelines. Concurrently with the FHWA tests, researchers in the United Kingdom were also evaluating similar erosion protection systems at full scale. Both groups of researchers agreed that an accurate, yet suitably conservative, definition of "failure" for ACBs can be described as the local loss of intimate contact between the revetment and the subgrade it protects. This loss of contact can result in the progressive growth of one or more of the following destabilizing processes:

  1. Ingress of flow beneath the armor layer, causing increased uplift pressure and separation of blocks from the subgrade.
  2. Loss of subgrade soil through gradual piping erosion and/or washout.
  3. 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).
  4. Loss of block or group of blocks from the revetment matrix, directly exposing the subgrade to the flow.

Therefore, selection, design, and installation considerations must be concerned primarily with maintaining intimate contact between the block system and the subgrade for the stress levels associated with the hydraulic conditions of the design event. It should be noted that a suitable filter layer beneath the blocks, and in some cases a drainage layer of granular or synthetic material, are considered to be an integral component(s) of the overall ACB system.

The individual blocks of an ACB armor layer must be dense and durable, and the matrix must be flexible and porous. ASTM International has published Standard D-6684 (2005) specifically for ACB systems. Concrete properties required by this standard include the following:

Average of 3 Units Individual Unit
• Minimum allowable compressive strength, lb/in2 4,000 3,500
• Maximum allowable water absorption, lb/ft3 , (%) 9.1 ( 7.0%) 11.7 ( 9.4%)
• Minimum allowable density in air, lb/ft3 130 125
• Freeze-thaw durability As specified by owner in accordance with ASTM C-67, C-666, or C-1262

ASTM Standard D-6684 also specifies minimum strength properties of geotextiles according to the severity of the conditions during installation. Harsh installation conditions (vehicular traffic, repeated lifting, realignment, and replacement of mattress sections, etc.) require stronger geotextiles.

8.3 APPLICATION 1: HYDRAULIC DESIGN PROCEDURE FOR ACB SYSTEMS FOR BANK REVETMENT OR BED ARMOR
8.3.1 Hydraulic Stability Design Procedure

The hydraulic stability of ACB systems is analyzed using a "discrete particle" approach. The design approach is similar to that introduced by Stevens and Simons (1971) as modified by Julien (1995) in the derivation of the "Factor of Safety" method for sizing rock riprap. In that method, a calculated factor of safety of 1.0 or greater indicates that the particles will be stable under the given hydraulic conditions and site geometry (e.g., side slope and bed slope). For ACBs, the Factor of Safety force balance has been recomputed considering the weight and geometry of the blocks, and the Shields relationship for estimating the particle's critical shear stress is replaced with actual test results (Clopper 1992).

Considerations are also incorporated into the design procedure to account for the additional forces generated on a block that protrudes above the surrounding matrix due to subgrade irregularities or imprecise placement. The analysis methodology purposely omits any restraining forces due to cables, because any possible benefit that cables might provide are reflected in the performance testing of the block. Cables may prevent blocks from being lost entirely, but they do not prevent a block system from failing through loss of intimate contact with the subgrade. Similarly, the additional stability afforded by vegetative root anchorage or mechanical anchoring devices, while recognized as potentially significant, is ignored in the stability analysis procedure for the sake of conservatism in block selection and design.

A drainage layer may be used in conjunction with an ACB system. A drainage layer lies between the blocks and the geotextile and/or granular filter. This layer allows "free" flow of water beneath the block system while still holding the filter material to the subsoil surface under the force of the block weight. This free flow of water can relieve sub-block pressure and has appeared to significantly increase the hydraulic stability of ACB systems based on full-scale performance testing conducted since the mid 1990s.

Drainage layers can be comprised of coarse, uniformly sized granular material, or can be synthetic mats that are specifically manufactured to permit flow within the plane of the mat. Granular drainage layers are typically comprised of 1- to 2-inch crushed rock in a layer 4 inches or more in thickness. The uniformity of the rock provides significant void space for flow of water. Synthetic drainage nets typically range in thickness from 0.25 to 0.75 inches and are manufactured using stiff nylon fibers or high density polyethylene (HDPE) material. The stiffness of the fibers supports the weight of the blocks, thus providing large hydraulic conductivity within the plane of the drainage net.

Many full-scale laboratory performance tests have been conducted with a drainage layer in place. When evaluating a block system, for which performance testing was conducted with a drainage layer, a drainage layer must also be used in the design. This recommendation is based on the improvement in the hydraulic stability of systems that have incorporated a drainage layer in the performance testing.

8.3.2 Selecting a Target Factor of Safety

The designer must determine what factor of safety should be used for a particular application. 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 Harris County Flood Control District, Texas (HCFCD 2001) has developed a simple flowchart approach that considers the type of application, uncertainty in the hydraulic and hydrologic models used to calculate design conditions, and consequences of failure to select an appropriate target factor of safety to use when designing an ACB installation. In this approach, the minimum allowable factor of safety is recommended based on the type of application (e.g., bank protection, bridge scour protection, dam overtopping, etc). This base value is then multiplied by two factors, each greater than 1.0, to account for risk and uncertainty. Figure 8.2 shows the Harris County flow chart method for determining the target factor of safety.

8.3.3 Design Method

Factor of Safety Method: The stability of a single block is a function of the applied hydraulic conditions (velocity and shear stress), the angle of the inclined surface on which it rests, and the weight and geometry of the block. Considering flow along a channel bank as shown in Figure 8.3, the forces acting on a concrete block are the lift force FL, the drag force FD, and the components of the submerged weight of the block, WS, both into and along the plane of the slope. Block stability is determined by evaluating the moments about the point O about which rotation can take place. The components of these forces are shown in Figure 8.3.

The safety factor (SF) for a single block in an ACB matrix is defined as the ratio of restraining moments to overturning moments:

Equation 8.1: Safety Factor, SF equals [l subscript 2 times W subscript s times a theta] divided by [ l subscript 1times W subscript s times the square root of (1 minus (a theta) squared) times cosine beta plus l subscript 3 times F subscript D times cosine delta plus l subscript 4 times F subscript L plus l subscript 3 times F subscript D, prime, times cosine theta plus l subscript 4 times F subscript L, prime]. Notation explained in text. (8.1)

Note that additional lift and drag forces F'L and F'D are included to account for protruding blocks that incur larger forces due to impact. The design implications regarding a protruding block are discussed in detail later in this section.

The moment arms l1, l2, l3, and l4 are determined from the block dimensions shown in Figure 8.4. In the general case, the pivot point of overturning will be at the downstream corner of the block; therefore, the distance from the center of the block to the corner should be used for both l2 and l4. Since the weight vector acts through the center of gravity, one half the block height should be used for l1. The drag force acts both on the top surface of the block (shear drag) and on the body of the block (form drag). Considering both elements of drag, eight-tenths the height of the block is considered a reasonable estimate of l3.

Flowchart for determining a target safety factor, SF subscript t.  Notes. The intent of this flow chart is to provide a systematic procedure for preselecting a target factor of safety (SFT) or an ACB system. No simple decision support system can encompass all significant factors that will be encountered in practice; therefore, this low chart should not replace prudent engineering judgment. SFB is a base factor of safety that considers the overall complexity of flow that the ACB system will be exposed to. SFB should reflect erosive flow characteristics that cannot be practically modeled, such as complex flow lines and turbulence. X subscript c is multiplier to incorporate conservatism when the consequence of failure is severe when compared to the cost of the ACB system. X subscript M is a multiplier to incorporate conservatism when the degree of uncertainty in the modeling approach is high, such as the use of a simple model applied to a complex system.	  Step 1. Determine Base safety factor, SF subscript B, based on application. Range 1.0 to 2. Guidance, Example Applications. Values: Channel bed or bank, 1.2 - 1.4. Bridge pier or abutment, 1.5 - 1.7. Overtopping spillway 1.8-2. Step 2: Determine multiplier based on consequence of failure X subscript c. Range 1.0 to 2 Guidance, Consequence of failure, Values; Low, 1.0 -1.2. Medium, 1.3 - 1.5. High, 1.6 - 1.8. Extreme or loss of life 1.9 - 2.0 Step 3. Determine Multiplier based on uncertainty of Hydraulic modeling, X subscript M. Range 1.0 to 2. Guidance, Type of Modeling Used, Values: Deterministic (e.g. HEC-RAS, RMA-2V), 1.0 -1.3. Empirical or Stochastic (e.g. Manning or Rational Equation), 1.4 - 1.7. Estimates, 1.8 - 2.0. Step 4. Calculate target Factor of Safety, SF Subscript T  Where target safety factor equals (base safety factor, SF subscript B) times (Multiplier based on consequence of failure, X subscript c) times (Multiplier based on Model uncertainty, X subscript M).
Figure 8.2. Selecting a target factor of safety (HCFCD 2001).

Schematic of a single block on channel side slope showing force diagrams from four planes, with factor of safety variables defined.  A. Channel cross section view. Forces on block resting on side slope: Force due to gravity, W subscript s. Theta, bank angle from horizontal. Force down the bank slope W subscript s times sine (theta subscript 1) times cosine (theta subscript zero). Force perpendicular to bank slope, W subscript s times a subscript theta. B. View normal to plane of channel bank. Theta zero, Channel bed slope. Block projection once in motion is part downstream and part down the bank slope at angle beta between block motion and the vertical. Drag force, F subscript D, is parallel to bed slope and is along streamline. Angle delta is angle between drag force and block motion. Angle theta is acute angle between vertical and a line perpendicular to bed slope. Force down the bank perpendicular to bed slope is w subscript s times sine theta times cosine theta zero. Section A-A' is through the block projection once in motion looking diagonally upslope and downstream. C. View of section A-A' along bank. Forces on Block: Lift force, F subscript L, perpendicular up, a distance l subscript 4 from the most downstream point of the block. W subscript s times a subscript theta perpendicular down a distance l subscript 2 from the most downstream point of the block. Force F subscript D times cosine delta acting a distance l subscript 3 from bank . Force W subscript s times the square root of [(1 minus a subscript theta) squared] times cosine beta acting distance l subscript 1 from the bank.  D. View Normal to section A-A'. Forces on Block: Component of force acting normal to A-A' "upslope", F subscript D times sine delta acting a distance l subscript 3 from bank . Component of force acting normal to A-A' "downslope", Force W subscript s times the square root of [(1 minus a subscript theta) squared] times sine beta acting distance l subscript 1 from the bank.
Figure 8.3. Single block on a channel side slope with factor of safety variables defined.

Schematic diagrams in plan and profile views of a block in flow with moment arms shown. In profile view with flow above the block moment arm l subscript 1 equals half the block height, l subscript 3 equal s 8 tenths of the block height. In plan view, with flow diagonal across the block, moment arms l subscript 2 and l subscript 4 are one half the diagonal distance across the block.
Figure 8.4. Schematic diagram of a block showing moment arms l1, l2, l3, and l4.

The shear stress on the block is calculated as follows:

Equation 8.2: Design shear stress, Tau subscript des, equals K subscript b, times gamma, times y, times S subscript f. (8.2)

where:

τdes = Design shear stress, lb/ft2
Kb = Bend coefficient (dimensionless)
γ = Unit weight of water, lb/ft3
y = Maximum depth of flow on revetment, ft
Sf = Slope of the energy grade line, ft/ft

The bend coefficient Kb is used to calculate the increased shear stress on the outside of a bend. This coefficient ranges from 1.05 to 2.0, depending on the severity of the bend. The bend coefficient is a function of the radius of curvature Rc divided by the top width of the channel T, as follows:

K subscript b equals 2 for 2 Rc/T
Equation 8.3: K subscript b equals 2.38 minus 0.206 times [(R subscript c) divided by T] plus 0.0073 times [(R subscript c) divided by T] squared  for 10 > Rc/T > 2 (8.3)
K subscript b equals 1.05 for Rc/T 10

Protruding Blocks: While some manufacturers developed design charts to aid in the design of ACB systems, those charts generally are based on the assumption of a "perfect" installation (i.e., no individual blocks protrude into the flow). In reality, some placement tolerance must be anticipated and the factor of safety equation modified to account for protruding blocks, illustrated in Figure 8.5. Because poor installation, or differential settlement over time, can cause blocks to exceed the design placement tolerance, the actual factor of safety can be greatly reduced and may lead to failure. Therefore, subgrade preparation and construction inspection become critical to successful performance of ACB systems. Blocks must not be placed directly on an irregular surface such as cobbles or rubble. A suitably smooth subgrade can often be achieved by removing the largest blocky materials and placing imported sand or road base material prior to placing the geotextile.

Sketch showing additional forces due to flowing water on a protruding ACB block. With upstream edge protruding into flow the vertical protrusion distance is delta z, the upwards Force through the center of the block due to lift is F subscript L, prime, the downstream force through the raised upstream top edge due to drag is F subscript D, prime.
Figure 8.5. Sketch showing additional lift and drag forces on a protruding block.

The additional drag force on the block created by the protrusion is calculated as follows:

Equation 8.4: Drag force due to protrusion equals one half times C times [delta Z times b times rho times (v subscript des) squared].   (8.4)

where:

F'D = Drag force due to protrusion, lb
C = Drag coefficient assumed equal to 1.0
Δz = Protrusion height, ft
b = Projected block width, ft

(Note: This width is typically taken as 2 times the moment arm L2 ; see Figure 8.4)
ρ = Mass density of water, slugs/ft3
Vdes = Design velocity, ft/s

For typical revetment applications, the design velocity Vdes is taken as the cross sectional average velocity. If a detailed hydraulic analysis has been performed, a more representative local velocity can be used for Vdes.

Lastly, the additional lift force due to the protrusion F'L is assumed equal to the drag force F'D. Both of these forces create additional destabilizing moments associated with a protruding block.

Dividing Equation 8.1 by l1WS and substituting terms yields the final form of the factor of safety equations as summarized in Table 8.1. The equations can be used with any consistent set of units; however, variables are indicated here in U.S. customary (English) units.

8.3.4 Layout Details for ACB Bank Revetment and Bed Armor

Longitudinal Extent: The 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 material. The minimum distances recommended are an upstream distance of 1.0 channel width and a downstream distance of 1.5 channel widths. The channel reach which experiences severe hydraulic forces is usually identified by site inspection, examination of aerial photography, hydraulic modeling, or a combination of these methods.

Many site-specific factors have an influence on the actual length of channel that should be protected. Factors that control local channel width (such as bridge abutments) may produce local areas of relatively high velocity and shear stress due to channel constriction, but may also create areas of ineffective flow further upstream and downstream in "shadow zone" areas of slack water. In straight reaches, field reconnaissance may reveal erosion scars on the channel banks that will assist in determining the protection length required.

In meandering reaches, since the natural progression of bank erosion is in the downstream direction, 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" (Lagasse et al. 2001) provides guidance for the assessment of lateral migration. The design engineer is encouraged to review this reference for proper implementation.

Vertical Extent. The vertical extent of the revetment should provide freeboard above the design water surface. A minimum freeboard of 1 to 2 ft should be used for unconstricted reaches and 2 to 3 ft for constricted reaches. If the flow is supercritical, the freeboard should be based on height above the energy grade line rather than the water surface. The revetment system should either cover the entire channel bottom or, in the case of unlined channel beds, extend below the bed far enough so that the revetment is not undermined by the maximum scour which for this application is considered to be toe scour, contraction scour, and long-term degradation (Figure 8.7).

Recommended revetment termination at the top and toe of the bank slope are provided in Figures 8.6 and 8.7 for armored-bed and soft-bottom channel applications, respectively. Similar termination trenches are recommended for the upstream and downstream limits of the ACB revetment.

Table 8.1. Factor of Safety Design Equations for ACB Systems.
Equation 8.5: Lift force, F subscript L, prime, equals drag force, F subscript D, prime, equals 0.5 times rho times b times delta Z times [ V subscript des ] squared. (8.5)
aθ = Projection of WS into plane of subgrade
b = Block width normal to flow (ft)
F'D, F'L = added drag and lift forces due to protruding block (lb)
lx = Block moment arms (ft)
γc = Concrete density, lb/ft3
γw = Density of water, lb/ft3
Vdes = Design velocity (ft/s)
W = Weight of block in air (lb)
WS = Submerged block weight (lb)
Δz = Height of block protrusion above ACB matrix (ft)
β = Angle between block motion and the vertical
δ = Angle between drag force and block motion
η0 = Stability number for a block on a horizontal surface
η1 = Stability number for a block on a sloped surface
θ = Angle between side slope projection of WS and the vertical
θ 0 = Channel bed slope (degrees)
θ 1 = Side slope of block installation (degrees)
ρ = Mass density of water (slugs/ft3)
τc = Critical shear stress for block on a horizontal surface (lb/ft2)
τdes = Design shear stress (lb/ft2)
SF = Calculated factor of safety
Equation 8.6: Stability number for a block on a horizontal surface, eta subscript zero equals (tau subscript des) divided by (tau subscript c) (8.6)
Equation 8.7: Angle between side slope projection of WS and the vertical, theta, equals arc tangent [tangent theta subscript 0 divided by tangent theta subscript 1]. (8.7)
Equation 8.8: Projection of WS into plane of subgrade, a subscript theta, equals square root of [ (cosine theta subscript 1 ) squared minus (sine theta subscript 0 ) squared ]. (8.8)
Equation 8.9: Angle between block motion and the vertical, beta, equals arctangent of [(cosine (theta subscript zero plus theta)) divided by [((l subscript 4 divided by l subscript three plus one) times the square root of ((1 minus a subscript theta) squared) divided by (eta subscript zero times (l subscript 2 divided by l subscript 1))} plus sine (theta subscript zero plus theta)] (8.9)
Equation 8.10: Angle between drag force and block motion, delta equals 90 degrees minus beta minus theta.  (8.10)
Equation 8.11: Stability number for a block on a sloped surface, Eta subscript 1 equals eta subscript 0 [(l subscript 4 divided by l subscript 3 ) plus sine (theta subscript 0 plus theta plus beta) divided by ((l subscript 4 divided by l subscript 3 ) plus 1)]. (8.11)
Equation 8.12: Submerged block weight, W subscript s, equals W times [(Gamma subscript c minus gamma subscript w) divided by gamma subscript c].   (8.12)
Equation 8.13: Safety Factor, SF equals [(l subscript 2 divided by l subscript 1) times a subscript theta] divided by [cosine beta times square root of ((1 minus a subscript theta) squared) plus eta subscript 1 times (l subscript 2 divided by l subscript 1) plus (l subscript 3 times F subscript D, prime times cosine delta plus l subscript 4 times F subscript L, prime) divided by (l subscript 1 times W subscript s)]. (8.13)

Note: The equations cannot be solved for θ1= 0 (i.e., division by 0 in Equation 8.7); therefore, a very small but non-zero side slope must be entered for the case of θ1= 0.

Sketch in cross section showing ACB bank and bed armor. At the top of slope the ACB mat turns down and is buried in a top termination trench. The minimum radius of curvature into the termination trench and at toe of slope is per block manufactures recommendations. Mat is level with the channel bottom. Underlying the entire armor is geotextile or granular bedding or both.
Figure 8.6. Recommended layout detail for bank and bed armor.

Sketch in cross section showing ACB bank armor. At the top of slope the ACB mat turns down and is buried in a top termination trench. The minimum radius of curvature into the termination trench is per block manufactures recommendations. Mat continues at bank slope to a toe down depth based on maximum scour depth. Underlying the entire armor is geotextile or granular bedding or both.
Figure 8.7. Recommended layout detail for bank revetment where no bed armor is required.

8.3.5 Filter Requirements

The importance of the filter component of an articulating concrete block installation should not be underestimated. Geotextile filters are most commonly used with ACBs, although coarse granular filters may be used where native soils are coarse and the particle size of the filter is large enough to prevent winnowing through the cells and joints of the ACB system. When using a granular stone filter, the layer should have a minimum thickness of 4 times the d50 of the filter stone or 6 inches, whichever is greater. The d50 size of the granular filter should be greater than one half the smallest dimension of the open cells of the system. When placing a granular filter under water, its thickness should be increased by 50%.

The filter must retain the coarser particles of the subgrade while remaining permeable enough to allow infiltration and exfiltration to occur freely. It is not necessary to retain all the particle sizes in the subgrade; in fact, it is beneficial to allow the smaller particles to pass through the filter, leaving a coarser substrate behind. Detailed aspects of filter design are presented in Design Guide 16 of this document.

Some situations call for a composite filter consisting of both a granular layer and a geotextile. The specific characteristics of the base soil determine the need for, and design considerations of the filter layer. In cases where dune-type bedforms may be present at the toe of a bank slope protected with an ACB system, it is strongly recommended that only a geotextile filter be considered.

8.3.6 ACB Design Example

The following example illustrates the ACB design procedure using the Factor of Safety equations presented in Table 8.1. The example is presented in a series of steps that can be followed by the designer in order to select the appropriate ACB system based on a pre-selected target factor of safety. The primary criterion for product selection is if the computed factor of safety for the ACB system meets or exceeds the pre-selected target value. The example assumes that hydraulic testing has been performed to quantify a critical shear stress for that particular system. This problem is presented in English units only because ACB systems in the U.S. are manufactured and specified in units of inches and pounds.

Problem Statement:

Meandering River has a history of channel instability, both vertically and laterally. A quantitative assessment of channel stability has been conducted using the multi-level analysis from Hydraulic Engineering Circular No. 20, "Stream Stability at Highway Structures" (Lagasse et al. 2001). A drop structure has been designed at the downstream end of a bendway reach to control bed elevation changes. However, there is concern that lateral channel migration will threaten the integrity of the drop structure. An ACB system is proposed to arrest lateral migration. Figure 8.8 presents a definition sketch for this example problem.

The design procedure assumes that appropriate assessment of hydraulic and geomorphic conditions has been made prior to the design process. The US Army Corps of Engineers' HEC-RAS model has been used to determine the design hydraulic conditions for the project reach. A velocity distribution across the cross section was calculated at River Mile 23.4 using HEC-RAS. Figure 8.9 presents the velocity distribution as determined using 9 flow subsections across the main channel. The velocity distribution indicates that the maximum velocity expected at the outside of the bend is 11.0 ft/s, which will be used as the design value in the factor of safety calculations. The corresponding depth at this location, which is the channel thalweg depth at the toe of the bank slope, is 8.4 feet.

Sketch in cross section and plan view showing ACB bank armor installation. Sketch (a) in plan view, shows armoring around the entire outside curvature of the bend. Upstream armoring extent is to approximately a channel width, 200 ft, above the bend point of curvature. Downstream extents appear to be approximately the same distance past the point of tangency. Sketch (b) in cross section shows maximum bank slope of 1 vertical to 2 horizontal. ACB at the top of slope provides two feet of freeboard, turns down, and is buried in a termination trench. Turn down is 3 bocks minimum with a minimum radius of 6 ft. Toe down of ACB at toe of slope is to maximum depth of scour. Underlying the entire armor is geotextile or granular bedding or both.
Figure 8.8. Definition sketch of example problem setting and ACB installation (not to scale).

Graphical sketch of a river cross section. Station along the x- axis and elevation along the y axis. Stream tube velocity values range from 3 feet per second through 11 feet per second, noted as design velocity, at the thalweg,
Figure 8.9. Velocity distribution at River Mile 23.4 from HEC-RAS model.

Table 8.2 presents pertinent results from the hydraulic model at the cross section (River Mile 23.4) that is exposed to the most severe hydraulic conditions.

Table 8.2. Design Conditions for River Mile 23.4.
Channel discharge Q (ft3/s) 6,444
Cross section average velocity Vave (ft/s) 8.1
Maximum velocity Vdes (ft/s) 11.0
Hydraulic radius R (ft) 4.3
Maximum depth y (ft) 8.4
Side slope, V:H 1V:2H
Bed slope So (ft/ft) 0.010
Slope of energy grade line Sf (ft/ft) 0.007
Channel top width T (ft) 200
Radius of curvature Rc (ft) 750
Step 1. Determine a target factor of safety for this project:

Use Figure 8.2 to compute a target factor of safety. For this example, a target factor of safety of 1.7 is selected as follows:

  • A base safety factor SFB of 1.3 is chosen because the river is sinuous and high velocities can be expected on the outside of bends.
  • The base safety factor is multiplied by a factor for the consequence of failure XC using a value of 1.3, since at this location the consequence of failure is ranked as "low" to "medium."
  • The uncertainty associated with the hydrology and hydraulic analysis is considered "low" for this site, based on available hydrologic and hydraulic data, and the recent study associated with the drop structure design. Therefore, the factor XM for hydrologic and hydraulic uncertainty is given a value of 1.0.

The target factor of safety for this project site is calculated as:

SFT = (SFB)(XC)(XM) = 1.7

Step 2. Calculate design shear stress

The maximum bed shear stress at the cross section is calculated using Equation 8.2:

τdes= Kb(γ)(y)(Sf)

First calculate Kb using Equation 8.3:

Since Rc/T = 750/200 = 3.75,

Kb = 2.38 - 0.206(3.75) + 0.0073(3.75)2 = 1.71

so τdes= 1.71 (62.4 lb/ft3) (8.4 ft) (0.007 ft/ft) = 6.3 lb/ft2

Step 3. Obtain ACB properties

Contact ACB manufacturers and/or review ACB catalogs and select several systems that are appropriate for the given application based on a preliminary assessment of the hydraulic conditions. At the same time obtain the block properties necessary for design. These properties generally include the moment arms in shown in Figure 8.4, the weight of the block, and the critical shear stress for the block on a horizontal surface.

For this example, two products from ACB Systems, Inc. are considered to be potential candidates based on guidance from the manufacturer. ACB Systems, Inc. suggests that the 106-OC or 108-OC systems would likely be appropriate for velocities in the range of 10 to 15 ft/s. The block properties provided by the manufacturer are shown in Table 8.4.

Table 8.4. Block Properties for ACB Example Problem.
Block Designation Block

Thickness

(in)
Block width

(in)
Block length

(in)
Weight in Air

(lb)
Moment arms (inches) τc

(at horizontal)

(lb/ft2)
l1 l2 l3 l4
106-OC 6.0(1) 15.5 17.25 99 3 11.6 4.8 11.6 19.2
108-OC 8.0 15.5 17.25 132 4 11.6 6.4 11.6 24.6

Notes: (1) Tested block

Step 4. Calculate the factor of safety parameters for each product

4a) Calculate the additional lift FL' and drag FD' on a protruding block using Equation 8.5 and assuming that the maximum allowable placement tolerance Δz is ½ inch:

Equation 8.5: Lift force, F subscript L, prime, equals drag force, F subscript D, prime, equals 0.5 times rho times b times delta Z times [ V subscript des ] squared.

Using the projected width of the block as 2 times the moment arm L2,

Block System Parameter: FL' and FD' (pounds)
106-OC block system 0.5 times (1.94 slugs per cubic foot) times ((2 times 11.6 inches) divided (12 inches per ft)) times (0.5 inches divided by 12 inches per foot) times (11 ft per second) squared equals 9.45 pounds.
108-OC block system 0.5 times (1.94 slugs per cubic foot) times ((2 times 11.6 inches) divided (12 inches per ft)) times (0.5 inches divided by 12 inches per foot) times (11 ft per second) squared equals 9.45 pounds.

4b) Calculate the stability number for a block on a horizontal surface using Equation 8.6:

eta subscript zero equals (tau subscript des) divided by (tau subscript c)
Block System Parameter: η0(dimensionless)
106-OC block system 6.3 pounds per cubic foot divided by 19.2 pounds per cubic foot equals 0.328
108-OC block system 6.3 pounds per cubic foot divided by 24.6 pounds per cubic foot equals 0.256

4c) Calculate angle θ using Equation 8.7:

theta, equals arc tangent [tangent theta subscript 0 divided by tangent theta subscript 1].

Note that the longitudinal channel slope is 0.01 ft/ft, therefore angle θ0 = 0.57o

The side slope of the channel bank is 1:2H, therefore angle θ1 = 26.6o

Block System Parameter: Angle θ (degrees)
106-OC block system arc tangent [tangent 0.57 degrees divided by tangent 26.6 degrees] equals 1.14 degrees.
108-OC block system arc tangent [tangent 0.57 degrees divided by tangent 26.6 degrees] equals 1.14 degrees.

4d) Calculate aθ using Equation 8.8:

a subscript theta, equals square root of [ (cosine theta subscript 1 ) squared minus (sine theta subscript 0 ) squared ].
Block System Parameter: aθ (dimensionless)
106-OC block system a subscript theta, equals square root of [(cosine 26.6) squared minus (sine 0.57)squared] equals 0.8943.
108-OC block system a subscript theta, equals square root of [(cosine 26.6) squared minus (sine 0.57)squared] equals 0.8943.

4e) Calculate angle β using Equation 8.9:

Angle between block motion and the vertical, beta, equals arctangent of [(cosine (theta subscript zero plus theta)) divided by [((l subscript 4 divided by l subscript three, plus one) times {the square root of ((1 minus a subscript theta) squared) divided by (eta subscript zero times (l subscript 2 divided by l subscript 1))} plus sine (theta subscript zero plus theta)]
Block System Parameter: Angle β (degrees)
106-OC block system Substituting into equation 8.9 the above example problem values for the 106-OC block system, the result is beta equals 39 degrees.
108-OC block system Substituting into equation 8.9 the above example problem values for the 108-OC block system, the result is beta equals 30 degrees.

4f) Calculate angle δ using Equation 8.10:

Angle between drag force and block motion, delta, equals 90 degrees minus beta minus theta.
Block System Parameter: Angle δ(degrees)
106-OC block system 90°- 39.0°- 1.14°= 49.86°
108-OC block system 90°- 30.0°- 1.14°= 58.86°

4g) Calculate the stability number η1on a sloped surface using Equation 8.11:

Stability number for a block on a sloped surface, Eta subscript 1 equals eta subscript 0 [(l subscript 4 divided by l subscript 3 ) plus sine (theta subscript 0 plus theta plus beta) divided by ((l subscript 4 divided by l subscript 3 ) plus 1)].
Block System Parameter: η1(dimensionless)
106-OC block system Substituting into equation 8.11 the above example problem values for the 106-OC block system, the result Stability number for this block equals 0.295.
108-OC block system Substituting into equation 8.11 the above example problem values for the 108-OC block system, the Stability number for this block equals 0.213.

4h) Calculate the submerged weight of each block using Equation 8.12, assuming the density of the concrete is 140 lb/ft3 and using the density of fresh water which is 62.4 lb/ft3:

Submerged block weight, W subscript s, equals W times [(Gamma subscript c minus gamma subscript w) divided by gamma subscript c].
Block System Parameter: Submerged block weight Ws (pounds)
106-OC block system 99 lbs times [(140 minus 62.4) divided by 140] = 54.9 lbs
108-OC block system 132 lbs times [(140 minus 62.4) divided by 140] = 73.2 lbs

4i) Calculate the factor of safety for each block using Equation 8.13:

Safety Factor, SF equals [(l subscript 2 divided by l subscript 1) times a subscript theta] divided by [cosine beta times square root of ((1 minus a subscript theta) squared) plus eta subscript 1 times (l subscript 2 divided by l subscript 1) plus (l subscript 3 times F subscript D, prime times cosine delta plus l subscript 4 times F subscript L, prime) divided by (l subscript 1 times W subscript s)].
Block System Parameter: Submerged block weight Ws (pounds)
106-OC block system Substituting into equation 8.13 the above example problem values for the 106-OC block system, the Safety factor for this block equals 1.48.
108-OC block system Substituting into equation 8.13 the above example problem values for the 108-OC block system, the Safety factor for this block equals 1.74.
Step 5. Select and specify appropriate block

Given the project-specific hydraulic conditions and geometry, the 6-inch thick block ("106-OC") does not meet the target safety factor of 1.7 required for this project. Therefore, the 8-inch thick block ("108-OC") is selected for use. The recommended concrete quality and related physical properties of the block are provided by ASTM International standard D-6684.

8.4 APPLICATION 2: DESIGN GUIDELINES FOR ACB SYSTEMS FOR PIER SCOUR
8.4.1 Hydraulic Stability Design Procedure

The hydraulic stability of articulating block systems at bridge piers can be assessed using the factor of safety method as previously discussed. However, uncertainties in the hydraulic conditions around bridge piers warrant increasing the factor of safety in lieu of a more rigorous hydraulic analysis. Experience and judgment are required when quantifying the factor of safety to be used for scour protection at an obstruction in the flow. In addition, when both contraction scour and pier scour are expected, design considerations for a pier mat become more complex. The following guidelines reflect guidance from NCHRP Report 593, "Countermeasures to Protect Bridge Piers from Scour" (Lagasse et al. 2007).

8.4.2 Selecting a Target Factor of Safety

The issues involved in selecting a target factor of safety for designing ACBs for pier scour protection are described in Section 8.3.2, and illustrated in flowchart fashion in Figure 8.2. Note that for bridge scour applications, the minimum recommended factor of safety is 1.5, as compared to a value of 1.2 for typical bank revetment and bed armor applications.

8.4.3 Design Method

Design conditions in the immediate vicinity of a bridge pier are more severe than the approach conditions upstream. Therefore, the local velocity and shear stress should be used in the design equations. As recommended in NCHRP Report 593, the section-average approach velocity Vavg must be multiplied by factors that are a function of the shape of the pier and its location in the channel:

Equation 8.14: Design velocity, V Subscript des, equals K subscript 1 times K subscript 2 times V subscript avg. Terms explained in the text. (8.14)

where:

Vdes = Design velocity for local conditions at the pier, ft/s
K1 = Shape factor equal to 1.5 for round-nose piers and 1.7 for square-edged piers
K2 = Velocity adjustment factor for location in the channel (ranges from 0.9 for pier near the bank in a straight reach to 1.7 for pier located in the main current of flow around a sharp bend)
Vavg = Section average approach velocity (Q/A) upstream of bridge, ft/s

If the velocity distribution is available from stream tube or flow distribution output from a 1-D model, or directly computed from a 2-D model, then only the pier shape coefficient should be used to determine the design velocity. The maximum velocity in the active channel Vmax is recommended since the channel could shift and the maximum velocity could impact any pier:

Equation 8.15: Design velocity, V subscript des equals (K subscript 1) times (V subscript max) (8.15)

The local shear stress at a pier should be calculated as:

Equation 8.16: Design shear stress for local conditions, Tau subscript des, equals [(n times V subscript des) divided by K subscript u] squared, times (Gamma subscript w) divided by ( y to the power one third) (8.16)

where:

τdes = Design shear stress for local conditions at pier, lb/ft2
n = Manning's "n" value for block system
Vdes = Design velocity as defined by Equation 8.14 or 8.15, ft/s
γw = Density of water, 62.4 lb/ft3 for fresh water
y = Depth of flow at pier, ft
Ku = 1.486 for English units, 1 for SI units

For pier scour applications, the angle θ0 (bed slope) should be taken as the typical channel bed slope in the vicinity of the pier for use in the Factor of Safety equations. If the ACB system is toed down at a slope away from the pier (see Section 8.4.4 regarding layout details), then the angle θ1 (side slope) should be taken as the lateral slope of the ACB system installation.

8.4.4 Layout Details for ACB Pier Scour Protection

Based on small-scale laboratory studies performed described in NCHRP Report 593, the optimum performance of ACBs as a pier scour countermeasure was obtained when the blocks were extended a distance of at least two times the pier width in all directions around the pier. Where only local scour is present, the ACB system may be placed horizontally such that the top of the blocks are flush with the bed elevation, with turndowns provided at the system periphery. However, when other processes or types of scour are present, the block system must be sloped away from the pier in all directions such that the depth of the system at its periphery is greater than the maximum scour which for this application is considered to be the depth of contraction scour and long-term degradation, or the depth of bedform troughs, whichever is greater (Figure 8.10). The blocks should not be laid on a slope steeper than 1V:2H (50%). In some cases, this limitation may result in blocks being placed further than two pier widths away from the pier.

Methods of predicting bedform geometry can be found in Karim (1999) and van Rijn (1984). An upper limit on crest-to-trough heightDis provided by Bennet (1997) as Δ < 0.4y where y is the depth of flow. This guidance suggests that the maximum depth of the bedform trough below ambient bed level is approximately 0.2 times the depth of flow.

Schematics in Profile and Plan view of ACB layout for pier scour countermeasure.  Schematic a) profile view: The upstream and downstream edge of the ACB layer is toed down to maximum scour depth or depth of bedform trough, whichever is greatest. Toe down slope is no greated than 1 Vertical to 2 Horizontal. With pier width-to-flow as "a" the extents are 2a upstream and downstream. Filter is underlying the armor from the pier to the periphery of the gabions. Schematic b) plan view: The gabion extent is a minimum of 2a in all directions from the pier.
Figure 8.10. ACB layout diagram for pier scour countermeasures.

In the case of wall piers or pile bents consisting of multiple columns where the axis of the structure is skewed to the flow direction, the lateral extent of the protection should be increased in proportion to the additional scour potential caused by the skew. Therefore, in the absence of definitive guidance for pier scour countermeasures, it is recommended that the extent of the armor layer should be multiplied by a factor Kα, which is a function of the width (a) and length (L) of the pier (or pile bents) and the skew angle (a as given below (after Richardson and Davis 2001):

Equation 8.17: K subscript alpha equals [(a times cosine alpha plus L times sine alpha) divided by a] to the power 0.65   (8.17)
8.4.5 Filter Requirements

A filter is typically required for articulating concrete block systems at bridge piers. The filter should be extended fully beneath the ACB system. When using a granular stone filter, the layer should have a minimum thickness of 4 times the d50 of the filter stone or 6 inches, whichever is greater. The d50 size of the granular filter should be greater than one half the smallest dimension of the open cells of the system. When placing a granular filter under water, its thickness should be increased by 50%. When placing a geotextile filter under water, the geotextile should be securely attached to the bottom of the pre-assembled ACB mat prior to lifting with 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. Detailed procedures for filter design are presented in Design Guide 16 of this document.

As with ACB bank revetment, in cases where dune-type bedforms may be present, it is strongly recommended that only a geotextile filter be considered for use at bridge piers.

8.4.6 Guidelines for Seal Around a Pier

An observed point of failure for articulating block systems at bridge piers occurs at the seal where the mat meets the bridge pier. During NCHRP Projects 24-07, securing the geotextile to the pier prevented the leaching of the bed material from around the pier (Parker et al. 1998). During flume studies at the University of Windsor (McCorquodale 1993) and for the NCHRP Project 24-07(2) study (Lagasse et al. 2007), the mat was grouted to the pier.

A grout seal is not intended to provide a structural attachment between the mat and the pier, but instead is a simple method for plugging gaps to prevent bed sediments from winnowing out from beneath the system. In fact, structural attachment of the mat to the pier is strongly discouraged. The transfer of moments from the mat to the pier may affect the structural stability of the pier, and the potential for increased loadings on the pier must be considered. When placing a grout seal under water, an anti-washout additive is required.

The State of Minnesota Department of Transportation (MnDOT) has installed a cabled ACB mat system for a pier at TH 32 over Clearwater River at Red Lake Falls, Minnesota. MnDOT suggested that the riverbed could be excavated around the piers to the top of the footing. The mat could be put directly on top of the footing and next to the pier with concrete placed underneath, on top of, or both, to provide a seal between mat and pier.

The State of Maine Department of Transportation (MDOT) has designed an articulating block system for a pier at Tukey's Bridge over Back Cove. MDOT recommended a design in which grout bags were placed on top of the mat at the pier location to provide the necessary seal.

8.5 ANCHORS

MnDOT also recommends the use of anchors when installing a cabled ACB mattress, although as discussed in Section 8.3, no additional stability is attributed to the cables themselves. MnDOT requires duckbill-type soil anchors placed 3 to 4 feet deep at the corners of the ACB mattresses, and at regular intervals of approximately 8 feet on center-to-center spacing throughout the area of the installation.

In reality, if uplift forces on a block system were great enough to create tension in the cables, then soil anchors could provide a restraining force that is transmitted to a group of blocks in the matrix. Using the same reasoning, anchors would be of no use in an uncabled system, unless there was a positive physical vertical interlock from block to block in the matrix. It should be noted that the stability analysis procedure presented in Section 8.3.1 is intended to ensure that uplift forces do not exceed the ACB system's capability, irrespective of cables.

The layout guidance presented in Section 8.4 indicates that the system should be toed down to a termination depth at least as deep as any expected contraction scour and long-term degradation, or bed form troughs, whichever is greater. Where such toe down depth cannot be achieved, for example where bedrock is encountered at shallow depth, a cabled system with anchors along the front (upstream) and sides of the installation is recommended. The spacing of the anchors should be determined based on a factor of safety of at least 5.0 for pullout resistance based on calculated drag on the exposed leading edge. Spacing between anchors of no more than 4 feet (1.3 m) is recommended. The following example is provided:

Given:

ρ = Mass density of water (slugs/ft3) 1.94
V = Approach velocity (ft/s) 10
Δz = Height of block system (ft) 0.5
b = Width of block installation (perpendicular to flow) (ft) 40

Step 1: Calculate total drag force Fd on leading edge of system:

Fd = 0.5ρV2(Δz)(b) = 0.5(1.94)(102)(0.5)(40) = 1,940 lbs

Step 2: Calculate required uplift restraint using 5.0 safety factor:

Frestraint = 5.0(1,940) = 9,700 lbs

Step 3: Counting anchors at corners of system, calculate required pullout resistance per anchor (rounded to the nearest 10 lb):

  1. Assume 11 anchors at 4 ft spacing: 9,700 lb/11 anchors = 880 lb/anchor
  2. Assume 21 anchors at 2 ft spacing: 9,700 lb/21 anchors = 460 lb/anchor

Anchors should never be used as a means to avoid toeing the system down to the full required extent where alluvial materials are present at depth. In this case, scour or bed form troughs will simply undermine the anchors as well as the system in general.

8.6 REFERENCES

ASTM International, 2005, "Standard D6684 - Specification for the Materials and Manufacture of Articulating Concrete Block Revetment Systems," West Conshohocken, PA.

ASTM International, 2008, "Standard D7277 - Standard Test Method for Performance Testing of Articulating Concrete Block (ACB) Revetment Systems for Hydraulic Stability in Open Channel Flow," West Conshohocken, PA.

Bennett, J.P., 1997, "Resistance, Sediment Transport, and Bedform Geometry Relationships in Sand-Bed Channels," in: Proceedings of the U.S. Geological Survey (USGS) Sediment Workshop, February 4-7.

Clopper, P.E. and Chen, Y., 1988, "Minimizing Embankment Damage During Overtopping Flow," FHWA-RD-88-181, Office of Engineering and Highway Operations R&D, McLean, VA.

Clopper, P.E., 1989, "Hydraulic Stability of Articulated Concrete Block Revetment Systems During Overtopping Flow," FHWA-RD-89-199, Office of Engineering and Highway Operations R&D, McLean, VA.

Clopper, P.E., 1992, "Protecting Embankment Dams with Concrete Block Systems," Hydro Review, Vol. X, No. 2, April.

Harris County Flood Control District, 2001, "Design Manual for Articulating Concrete Block Systems," prepared by Ayres Associates, Project No. 32-0366.00, Fort Collins, CO

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, 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., Schall, J.D., and Richardson, E.V., 2001, "Stream Stability at Highway Structures," Third Edition, Hydraulic Engineering Circular No. 20, FHWA-NHI-01-002, Washington, D.C.

McCorquodale, J.A., Moawad, A., and McCorquodale, A.C., 1993, "Cable-tied Concrete Block Erosion Protection," Hydraulic Engineering '93, San Francisco, CA, Proceedings (1993), pp. 1367-1362.

Parker, G., Toro-Escobar, C., and Voight, R.L., Jr., 1998, "Countermeasures to Protect Bridge Piers from Scour," User's Guide, Vol. 1, prepared for National Cooperative Highway Research Program, Transportation Research Board, National Research Council, NCHRP Project 24-7, St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN (revised 7/1/99).

Parker, G., Toro-Escobar, C., and Voight, Jr., R.L., 1998, "Countermeasures to Protect Bridge Piers from Scour," Final Report, Vol. 2, prepared for National Cooperative Highway Research Program, Transportation Research Board, National Research Council, NCHRP Project 24-7, St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN.

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, CO.

Transportation Research Board, 1999, "1998 Scanning Review of European Practice for Bridge Scour and Stream Instability Countermeasures," National Cooperative Highway Research Program, Research Results Digest Number 241, July, Washington, D.C.

van Rijn, L.C., 1984, "Sediment Transport, Part III: Bed Forms and Alluvial Roughness," Journal of Hydraulic Engineering, Vol. 110, No. 12, December.

Updated: 09/22/2011

FHWA
United States Department of Transportation - Federal Highway Administration