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Bridge Scour and Stream Instability Countermeasures: Experience, Selection, and Design Guidance-Third Edition
Design Guideline 9 Grout-Filled Mattresses
Grout-filled mattresses (mats) are comprised of a double layer of strong synthetic fabric, typically woven nylon or polyester, sewn into a series of pillow-shaped compartments that are connected internally by ducts. The compartments are filled with a concrete grout that flows from compartment to compartment via the ducts. Mats are typically sewn together or otherwise connected (less commonly) by special zips, straps, or ties prior to filling.
When set, the grout forms a mat made up of a grid of interconnected blocks. Grout-filled mats are reinforced by cables laced through the mat (Figure 9.1) before the concrete is pumped into the fabric form, creating what is often called an articulating block mat (ABM). Flexibility and permeability are important functions for stream instability and bridge scour countermeasures. Therefore, systems that incorporate filter points or weep holes (allowing for pressure relief across the mat) combined with relatively small-diameter ducts (to allow breakage and articulation between the grout blocks) are the preferred products. This design guideline considers two applications of grout-filled mattresses: Application 1 - bank revetment and bed armor; and Application 2 - pier scour protection.
Grout-filled mat systems can range from very smooth, uniform surface conditions that approach cast-in-place concrete in terms of surface roughness, to extremely irregular surfaces exhibiting the roughness of moderate size rock riprap. Because this type of revetment is fairly specialized, comprehensive technical information on specific mat types and configurations is available from a number of manufacturers of this type of revetment. Mats are typically available in standard nominal thicknesses of 4, 6, and 8 in. (100, 150, and 200 mm). A few manufacturers produce mats up to 12 in. (300 mm) thick.
There is limited field experience with the use of grout-filled mat systems as a scour counter-measure for bridge piers. More frequently, these systems have been used for shoreline protection, protective covers for underwater pipelines, bridge abutment spill slopes, and channel armoring where the mat is placed across the entire channel width and keyed into bridge abutments or stream banks. The guidance for pier scour applications provided in this document has been developed primarily from NCHRP Report 593 (Lagasse et al. 2007).
The benefits of grout-filled mats are that the fabric installation can be completed quickly, without the need for dewatering. Because of the flexibility of the fabric prior to filling, laying out the forms and pumping them with concrete grout can be performed in areas where room for construction equipment is limited. Figure 9.2 shows the inspection of a completed installation at an abutment with limited clearance.
The geotextile comprising the fabric form must exhibit sufficient strength to resist the pressure of the grout during filling. Cords connect the upper layer of fabric to the lower layer at the center of each compartment. The cords are interwoven with the fabric in two sets of four cords each, one set for the upper layer and one set for the lower layer. Typical strength requirements call for each cord to have a minimum breaking strength of 160 lbs.
The grout-filled ducts should be no more than 10% of the maximum thickness of the block compartment so that flexibility and articulation can be achieved in the finished installation. Cables enter and exit each compartment through opposing grout ducts; alternatively, cable ducts may be provided for insertion of cables through each compartment. When cable ducts are used, the maximum allowable diameter should be limited to 1.0 in. (25 mm).
The geotextile comprising the fabric form should meet or exceed the values shown for the properties in Table 9.1 (Iowa Department of Transportation 2004).
Cables are installed between the two layers of fabric prior to filling with grout. The cables run through the individual compartments in a manner that provides for both lateral and longitudinal connection. The cables enter and exit the compartments through opposing grout ducts. Cables should be high tenacity, low elongation continuous filament polyester fibers, with a core contained within an outer jacket. The core should be between 65 to 75% of the total weight of the cable.
Cable splices are made with aluminum compression fittings such that a single fitting results in a splice strength of 80% of the breaking strength of the cable. Two fittings separated by a minimum of 6 in. (150 mm) should be used per splice. When the installation is completed, the cables and splices are completely encased by the concrete grout.
The concrete grout consists of a mixture of Portland cement, fine aggregate, water, admixtures, and fly ash (optional) to provide a pumpable slurry. The grout should have an air content of not less than 5% nor more than 8% of the volume of the grout, and should obtain a minimum 28-day compressive strength of 2,000 lb/in2 (13,750kPa). The mix should result in a dry unit weight of the cured concrete of no less than 130 lb/ft3 (2,080 kg/m3). Prior to installation, the grout should be tested for flowability using the flow cone method of ASTM D 6449, with an efflux time not less than 9 seconds nor more than 12 seconds using this method.
The Engineer may require adjustment of the mix proportions to achieve proper solids suspension and optimum flowability. After the mix has been designated, it may not be changed without approval of the Engineer. A recommended basic mix design consists of the following:
Cement: Cement shall be Portland Type I or Type II, at the rate of 10 sacks (940 pounds) per cubic yard.
Fly Ash: Fly ash may be substituted for cement for up to 25% by weight (mass) of cement.
Fine Aggregate: Fine aggregate 2100 pounds (surface dry weight) per cubic yard.
Water: 45 gallons (375 pounds) per cubic yard, or enough to provide a thick creamy consistency.
Air-entraining Admixtures: Air-entraining admixtures may be required to achieve the required air content.
Liquid Curing Compounds: Liquid curing compounds may be required to achieve the required strength and set time.
When installed, the grout-filled mat shall exhibit the nominal properties shown in Table 9.2.
Flexibility of the grout-filled mats is a major factor in the successful performance of these systems. The ability to adjust to differential settlement, frost heave, or other changes in the subgrade is desirable. For example, settlement around the perimeter of a grout-filled mat at a bridge pier is beneficial if scour occurs around the periphery of the mat. Some mat products are more rigid than others, and are therefore more prone to undermining and subsequent damage. Rigid systems are less suitable, in general, for use as bank protection or as a bridge scour countermeasure. Designers are encouraged to familiarize themselves with the flexibility and performance of various grout-filled mat materials and products for use in riverine environments.
Hydrodynamic forces of drag and lift both act to destabilize a grout-filled mattress. These destabilizing forces are resisted by the weight of the mat and the frictional resistance between the bottom of the grout-filled mat and the channel subgrade material. While the individual compartments may articulate within the mat and the mat remains structurally sound, the general design approach is to consider the mat as a rigid monolithic layer. This reflects the mode of failure observed at field installations, which is typically a sliding-type failure. In the following analysis, it is assumed that potential uplift force due to soil water pressure beneath the mat is negligible, or alternatively, that allowance for pressure relief has been made by installing weep holes or selecting a mat system manufactured with integral filter points between the individual compartments.
Grout-filled mat selection and sizing criteria are based on an analysis of sliding stability of the mat on the subgrade. In general, the sliding safety factor (SF) is a ratio of forces resisting sliding to forces causing sliding to occur. Figure 9.3 presents a schematic diagram of the forces acting to destabilize a grout-filled mat on a channel bank. The analysis methodology purposely omits any restraining forces due to cables or the additional stability afforded by mechanical anchoring devices for the sake of conservatism in design.
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 flow chart 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 various types of Articulating Concrete Block (ACB) installations. In this approach, the minimum allowable factor of safety for ACBs at bridge piers, for example, is 1.5. This base value is then multiplied by two factors, each equal to or greater than 1.0, to account for risk and uncertainty. Figure 9.4 shows the HCFCD flow chart method. The method is also considered appropriate for grout-filled mats, since the design method results in a calculated safety factor.
For grout-filled mats placed on channel beds or banks, the shear stress on the mattress is calculated as follows:
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:
The equation representing the ratio of stabilizing to destabilizing forces on a mat tending to slide is:
In Equation 9.3, both the lift and drag forces are assumed equal to the applied shear stress τdes. Note that for mats placed only on the channel bed, the side slope angle θ is zero, and Equation 9.3 reduces to:
In practice, the coefficient of static friction μ depends on the characteristics of the mat-subsoil interface, which is a function of the mat geometry, geotextile, soil type, and degree to which the mat can be seated into the subsoil to achieve intimate contact. Manufacturers typically supply the value of μ for use with their various products for different soil types. These design values may often be quoted as an equivalent friction angle δ, expressed in degrees. The relationship between μ and δ is:
Typical values of the friction angle δ for grout-filled mats range from 25° on non-cohesive soils to as great as 45° on cohesive silts and clays. However, for mats underlain by a filter fabric, a maximum friction angle of 32.5° on cohesive soils is suggested for design (Bowser-Morner Associates Inc., 1989).
Manufacturers should also supply the appropriate Manning's n resistance coefficient for each product. Grout-filled mat systems can range from very smooth, uniform surface conditions approaching cast in place concrete in terms of surface roughness, to extremely irregular surfaces exhibiting substantial projections into the flow, resulting in boundary roughness approaching that of moderately-sized rock riprap.
Fabric forms might be considered to serve as filters as well as forms (Sprague and Koutsourais 1992). Water in the grout mix will bleed through the fabric, producing a reduction in the water/cement ratio, which increases strength and durability. The cement film provides a bond between the concrete fill and the fabric, as well as a degree of protection against ultraviolet degradation. However, in view of the long-term performance that grout filled mats must provide, performance should not depend on the fabric form material, but instead upon the weight and durability of the (cured) concrete grout, its cabled connections, and its ability to articulate, combined with the effectiveness of the underlying filter.
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 that 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. 2001b) 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 from maximum scour which for this application is considered to be toe scour, contraction scour, and long-term degradation (Figure 9.6).
Recommended revetment termination at the top and toe of the bank slope are provided in Figures 9.5 and 9.6 for armored-bed and soft-bottom channel applications, respectively. Similar termination trenches are recommended for the upstream and downstream limits of the grout-filled mat revetment.
The following example illustrates the grout-filled mat design procedure using the method presented in Section 9.3.3. The example is presented in a series of steps that can be followed by the designer in order to select the appropriate thickness of the grout-filled mat based on a pre-selected target factor of safety. The primary criterion for product selection is that the computed factor of safety for the armor meets or exceeds the pre-selected target value. This problem is presented in English units only because grout-filled mattresses in the U.S. are manufactured and specified in units of inches and pounds.
A grout-filled mat system is proposed to arrest lateral migration on the outside of a bend. The channel banks are cohesive, and the grout-filled mat will be placed on a properly selected nonwoven geotextile. The channel dimensions and design hydraulic conditions are given in Table 9.3.
Step 1. Determine a target factor of safety for this project:
Use Figure 9.4 to compute a target factor of safety. For this example, a target factor of safety of 1.7 is selected as follows:
The target factor of safety for this project site is calculated as:
SFT = (SFB)(XC)(XM) = (1.3)(1.3)(1.0) = 1.7
Step 2. Calculate design shear stress
The maximum bed shear stress at the cross section is calculated using Equation 9.1:
τdes = Kb(γ)(y)(Sf)
First calculate Kb using Equation 9.2:
Since Rc/T = 750/120 = 6.25
Kb = 2.38 - 0.206(6.25) + 0.0073(6.25)2 = 1.38
so τdes = 1.38 (62.4 lb/ft3) (5.0 ft) (0.005 ft/ft) = 2.15 lb/ft2
Step 3. Determine the appropriate friction angle
Since the bank soil is cohesive and the grout-filled mat is to be placed on a geotextile filter, a friction angle of 32.5° is selected based on the discussion in Section 9.3.3. Using Equation 9.5, the coefficient of static friction μ is determined from the friction angle:
μ = tan(32.5°) = 0.64
Note: Alternatively, laboratory testing can be performed to determine a specific friction angle using the site-specific soil with the proposed geotextile and the specific fabric used in the manufacture of the mat.
Step 4. Calculate safety factors for various mat thicknesses
From Equation 9.3,
Assuming a unit weight for grout of 130 lb/ft3, and substituting the known quantities for the unit weight of water (62.4 lb/ft3), the side slope and bed slope angles (θ and α), and the design shear stress (τdes), the factor of safety equation for this application simplifies to:
Using nominal sizes of 4, 6, 8, and 12 in. (0.33, 0.5, 0.67, and 1.0 ft) for commercially-available grout-filled mats, the safety factors for this site-specific application are calculated as:
Step 5. Specify the grout-filled mat:
The calculated factor of safety for the 8-inch mat is larger than the site-specific target factor of safety of 1.7 for this project, therefore the 8-inch mat is specified. Material properties of the mat should be in accordance with the guidelines in Section 9.2 of this document. A filter should be provided beneath the grout-filled mat, designed in accordance with the procedures described in Design Guideline 16 of this document.
The hydraulic stability of grout-filled mats 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, "Counter-measures to Protect Bridge Piers from Scour" (Lagasse et al. 2007).
The issues involved in selecting a target factor of safety for designing grout-filled mats for pier scour protection are described in Section 9.3.2, and illustrated in flow chart fashion in Figure 9.4. 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.
It is important to note that the 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 (Lagasse et al. 2007), the section-average approach velocity V must be multiplied by factors that are a function of the shape of the pier and its location in the channel:
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:
The local shear stress at the base of the pier, τdes, is calculated using a rearranged form of Manning's equation:
Based on small-scale laboratory studies performed for NCHRP Project 24-07(2)(Lagasse et al. 2007), the optimum performance of grout-filled mats as a pier scour countermeasure was obtained when the mattresses were extended a distance of at least two times the pier width in all directions around the pier.
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. While there is no 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 (α) as given below (after Richardson and Davis 2001):
Grout-filled mats should be placed so that the long axis is parallel to the direction of flow. Where only local scour is present, the grout-filled mats may be placed horizontally such that the top of the mat is flush with the bed elevation; however, when other types of scour are present, the matsmust 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 depth which for this application is considered to be contraction scour and long-term degradation (Figure 9.7). The mats should not be laid on a slope steeper than 1V:2H (50%). In some cases, this criterion may result in mats being placed further than two pier widths away from the pier.
Tests conducted under NCHRP Project 24-07(2) confirmed that grout filled mattresses can be effective scour countermeasures for piers under clear-water conditions. However, when dune-type bed forms were present, the mattresses were subject to both undermining and uplift, even when they were toed down below the depth of the bed form troughs. Therefore, grout-filled mattresses are not recommended for use as pier scour countermeasures under live-bed conditions where dunes may be present (Lagasse et al. 2007).
A filter is typically required for grout-filled mats at bridge piers. The filter, whether geotextile or granular, should be extended fully beneath the grout-filled mat. When using a granular stone filter, the filter layer should have a minimum thickness of 4 times the d50 of the filter stone or 6 in., whichever is greater. The granular filter layer thickness should be increased by 50% when placing under water.
Manufacturer's assembly instructions should be followed. Fabric forms should be placed on the filter layer and arranged according to the contract drawings prior to field seaming. An excess of fabric should be included to allow for as much as a 10% contraction in size after filling of the fabric forms. The manufacturer should be consulted to determine the amount of contraction anticipated for site specific conditions.
Fabric forms should be positioned so that the direction of grout placement shown on the contract drawing is followed, with the preferred direction being from upstream to downstream. Filling must always be performed from the lowest elevation first to the uppermost elevation last. Prior to filling, the double layers of adjacent mats should be connected by sewing with a hand held sewing machine or zipping, depending on manufacturers instructions. Custom fitting of mattresses around corners or curves should be done in accordance with the manufacturer's recommendations.
Care must be taken during installation so as to avoid damage to thegeotextile or subgrade during the installation process. Preferably, the grout filled mat placement and filling should begin at the upstream section and proceed downstream. If a mat system is to be installed starting downstream and proceeding in the upstream direction, a contractor option is to construct a temporary toe trench at the front edge of the mat system to protect against flow which could otherwise undermine the system during flow events that may occur during construction. Only the amount of fabric forms that can be filled in a day should be laid into position. After being filled with grout, the mattresses should not be pulled or pushed in any direction.
Grout filled mattresses placed under water require close observation and increased quality control to ensure a continuous countermeasure system. A systematic process for placing and continuous monitoring to verify that the grout is flowing to achieve the desired thickness is important.
Excavation, grading, and placement of grout filled mattresses and filter under water require additional measures. For installations of a relatively small scale, diversion of the stream around the work area may be accomplished during the low flow season. For installations on larger rivers or in deeper water, the area can be temporarily enclosed by a cofferdam, which allows for construction dewatering if necessary. Alternatively, a silt curtain made of plastic sheeting may be suspended by buoys around the work area to minimize environmental degradation during construction. Once under water and in the correct positions, the individual fabric forms can be sewn together or otherwise connected by divers prior to filling with grout.
Depending on the depth and velocity of the water, sounding surveys using a sounding pole or sounding basket on a lead line, divers, sonar bottom profiles, and remote operated vehicles (ROV) can provide some information about the mat placement and toedown.
A particular design called "articulating block mat" (ABM), used by the Oregon Department of Transportation, has two features which make it distinctive among fabric formed concrete mats. First, the horizontal seams within the mat are continuous, allowing the blocks to bend downward by hinging along this seam line. Second, the individual blocks are connected internally by a series of flexible polyester cables which keep the individual blocks firmly connected while allowing them to bend (Figure 9.8). Typical individual block sizes are on the order of 2.25 ft2 to 4.0 ft2 and the mass is approximately 400 lb each.
The following recommendations reflect experience from the Oregon Department of Transportation (ODOT) and Arizona Department of Transportation (ADOT). Research reports from an ODOT installation of an articulating grout filled mat erosion control system on Salmon Creek in Oakridge, Oregon also provide experience and insight on the use of these mats (Scholl 1991; Hunt 1993).
Scholl (1991) and Hunt (1993) describe some of the installation features specified by ODOT on the Salmon Creek Bridge as well as typical design features. For example, the original ODOT design was modified by the manufacturer due to the limitations of the product. The fabric forms could not be terminated in a smooth fan shaped pattern as shown in the original ODOT design. Therefore, the mat was cut at the seams to best fit the original design. It was anticipated that this would make the system somewhat less effective than the original design because of a greater susceptibility to undermining of the edges. Figures 9.10 and 9.11 show the final installation of the articulating block mat at Salmon Creek Bridge.
Some problems and solutions identified in the construction process by ODOT are:
The importance of the filter component of grout-filled mat installation should not be underestimated. Geotextile filters are most commonly used with grout-filled mats, although granular filters may be used. When using a granular stone filter, the layer should have a minimum thickness of 4 times the d50 of the filter stone or 6 in., whichever is greater. The d50 size of the granular filter should be determined by using the procedure presented in Design Guideline 16 of this document. 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 Guideline 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, it is strongly recommended that only a geotextile filter be considered; furthermore, grout-filled mats are NOT recommended for use as an armor layer where dunes are expected.
Sand-filled geotextile containers made of nonwoven needle punched fabric are particularly effective for placement under water. The fabric for the geotextile containers should be selected in accordance with the filter design criteria presented in Design Guideline 16, and placed such that the geotextile containers overlap to cover the required area. Geotextile containers can be fabricated in a variety of dimensions and weights. Each geotextile container should be filled with sand only to about two-thirds of the container's total volume so that it remains flexible and "floppy." The geotextile containers can also serve to fill a pre-existing scour hole around a pier prior to placing the grout-filled mats, as shown in Figure 9.12. For more detail, see Lagasse et al. (2007).
An observed key point of failure for grout-filled mats at bridge piers during laboratory studies occurs at the interface where the mat meets the bridge pier. During NCHRP Project 24-07(2), securing the geotextile to the pier prevented the leaching of the bed material from around the pier. This procedure worked successfully in the laboratory, but there are constructability implications that must be considered when using this technique in the field, particularly when placing the mattress under water.
A grout seal between the mattress and the pier is recommended. A grout seal is not intended to provide a structural attachment between the mattress and the pier, but instead is a simple method for plugging gaps to prevent bed sediments from winnowing out between the mattress and the structure. In fact, structural attachment of the mattress 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.
Anchors are not typically used with grout-filled mat systems; however, the layout guidance presented in Section 9.4 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 (grout-filled mats are not recommended in live-bed environments where dune-type bedforms are anticipated). Where such toe down depth cannot be achieved, for example where bedrock is encountered at shallow depth, a grout-filled mat system with anchors along the front (upstream) and sides of the installation are 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 ft is recommended. The following example is provided:
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 the corners of the system, calculate required pullout resistance per 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 bedform troughs will simply undermine the anchors as well as the system in general.
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