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Federal Highway Administration > Publications > Research > Infrastructure > Structures > Geosynthetic Reinforced Soil Integrated Bridge System Interim Implementation Guide 
Publication Number: FHWAHRT11026
Date: January 2011 
Geosynthetic Reinforced Soil Integrated Bridge System Interim Implementation GuideCHAPTER 4. DESIGN METHODOLOGY FOR GRS–IBS
4.1 OVERVIEW OF GRS–IBS DESIGN METHODDuring the past 30 years, GRS technology has been used to build walls, shallow foundations, culverts, bridge abutments, and rock fall barriers. The technology also has been used to stabilize slopes and repair roadways. This chapter focuses on the GRS design method used for GRS–IBS including an abutment and wing walls. While GRS technology can provide solutions in a variety of applications and under certain extreme conditions, the design method described in this manual provides a recipe for design of GRS–IBS with limitations on abutment heights, bridge spans, and design loads. The design methods described in this chapter are appropriate for GRS structures (an abutment and wing walls) with a vertical or near vertical face and at a height that does not exceed 30 ft. Although the majority of bridges built with GRS–IBS have spans of less than 100 ft, spans of up to 140 ft have been constructed. While larger spans are possible, the bearing stress on the GRS abutment is limited to 4,000 lb/ft^{2}. The demands of longer spans on GRS–IBS are not fully understood at this time, and it is recommended that engineers limit bridge spans to approximately 140 ft until further research has been completed. GRS–IBS abutment capacities are dependent on a combination of the strength of the fill material and the strength of the reinforcement when built in accordance with the two rules of GRS construction: (1) good compaction (95 percent of maximum dry unit weight, according to AASHTO T99) of high–quality granular fill and (2) closely spaced layers of reinforcement (12 inches or less). It is recommended that design or allowable bearing pressure be limited to 4,000 lb/ft^{2}. For design pressures larger than 4,000 lb/ft^{2}, the performance criteria must be checked against the applicable stress–strain curve resulting from a performance test (discussed later in this chapter and in appendix B). The performance criteria for GRS–IBS consist of a tolerable vertical strain of 0.5 percent and lateral strain of 1 percent. A significant amount of research and practical experience has shown that GRS–IBS designed and constructed within the limits defined in this manual will produce safe, durable systems. The design process starts with establishing the project requirements from which the preliminary geometry of GRS–IBS is determined. Once the geometry is defined, it is then evaluated against external and internal modes of failure. An iterative process is used to assess the geometry and make adjustments as necessary to facilitate construction and assure long–term performance. Economy should also be a consideration when evaluating each design alternative (e.g., deeper embedment versus larger footing). A general and identifying feature of the GRS–IBS design is a mass built with alternating layers of compacted granular fill material and closely spaced reinforcement (less than or equal to 12 inches). In nearly all of the GRS masses built in the United States as full–scale experiments or as in–service structures, however, the design has been based on an 8–inch layered system. There are other features and principles common to a GRS mass. Most GRS walls have been built with dry–stacked concrete facing blocks and are flexible (in terms of global bending stiffness). A GRS abutment is a type of gravity structure. Therefore, external stability should be evaluated for the direct sliding, bearing capacity, global stability, and overturning failure modes limiting this type of construction. However, because a GRS mass is relatively ductile and free of tensile strength, overturning about the toe, in a strict sense, is not a possible response to earth pressures at the back of the mass or loading on its top. Other attributes of GRS–IBS also tend to preclude overturning as a mode of failure. GRS–IBS consists of two abutments supporting an integrated superstructure that would function as a strut to resist overturning, and each GRS mass has a reinforced integration zone above its heel, also resisting the overturning mode of failure. Consequently, while direct sliding, bearing capacity, and global stability are evaluated in conventional ways, overturning is sometimes addressed by inspection and comparison to observations of past performance. Observations of past performance show that the flexible, internally stabilized soil mass of GRS IBS construction, in combination with an RSF, results in more uniform stress distribution, resisting any applied vertical and lateral loads. Observations also show that, in addition to lack of overturning, the combination of vertical and lateral loads, as limited by analysis of direct sliding, bearing capacity, and global stability, does not cause excessive deformation at the face of the GRS mass or other undesirable performance. While this combination of unique features and behavior eliminates the need to analyze overturning as a failure mode for completed GRS–IBS, the engineer may choose to analyze for overturning during an intermediate phase of construction with consideration for the time needed for an overturning mechanism to develop and the concurrent level of loading or for project configurations different from those described herein. For example, overturning may still be a viable failure mode for abutment wing walls constructed with GRS technology if they retain soil other than reinforced soil from the abutment or opposite wing wall (i.e., if they retain natural soil). GRS is inherently internally stable because of the interaction between the soil and the reinforcement layers. The strength and stiffness of a GRS mass depends on the unique combination of compacted soil and reinforcement. The vertical capacity of the GRS abutment can be determined either empirically or analytically. Empirically, the capacity is found using a stress–strain curve specific to the combination of the reinforcement type and granular fill material. If the designer uses a combination of the materials previously tested, then the appropriate stress–strain curve can be used for design. If the designer decides to change the materials from those already tested, then a performance test can be performed to obtain an applicable stress–strain curve for the empirical method. Guidelines on how to conduct a performance test are given in appendix B. Alternatively, the designer can predict the ultimate vertical capacity of the GRS abutment by using an analytical equation. The equation is a function of reinforcement spacing, soil strength, and soil grain size. Note that the analytical method does not predict vertical deformation. A performance test is needed to adequately predict the deformation behavior of the GRS abutment. This design method is based on the results of many full–scale experiments and verified using case history performance data collected on several in–service GRS structures more than 20 years old. The design of GRS–IBS is based on the following assumptions:
As described in greater detail in subsequent sections of this manual, GRS–IBS design and construction processes follow from these basic assumptions and principles.
4.2 BASIC DESIGN STEPS FOR GRS–IBSThere are nine basic steps in the design of GRS–IBS (see figure 9). Note that the design philosophy illustrated in this section is Allowable Stress Design (ASD). It is FHWA policy that design for all Federal–aid funded projects be conducted using the AASHTO Load and Resistance Factor Design (LRFD) methodology. Guidelines to design GRS–IBS in an LRFD format are presented in appendix C. The LRFD format presented was normalized to produce the same results as the ASD method and does not represent a statistically based calibration that would be consistent with other AASHTO LRFD methods. After sufficient data is produced and collected as a result of this technology deployment and other efforts, a thorough statistical analysis will be performed to produce LRFD specifications for the design of GRS–IBS.
Figure 9. Chart. Steps for GRS–IBS design.
4.3 GRS–IBS DESIGN GUIDELINES4.3.1 Step 1–Establish Project Requirements The following parameters must be defined:
4.3.2 Step 2–Perform a Site Evaluation To properly assess conditions at the site, a site visit must be conducted. During this visit, the following must be performed by the agency and/or its designer:
4.3.3 Step 3–Evaluate Project Feasibility The feasibility of the project should be evaluated in terms of cost, logistics, technical requirements, and performance objectives. In particular, in the case of abutments for bridges constructed over water, the potential for scour, sedimentation, and/or channel instability must be evaluated in accordance with the policy and procedures of both FHWA and AASHTO. It is necessary to determine the potential for scour at all bridges constructed over water. If the abutment will be impacted by scour, additional design requirements are necessary (see chapter 6). These additional design requirements can be determined and implemented through a hydraulic and scour analysis of the site. Once the scour potential is determined, a countermeasure can be designed to protect the abutment against failure during a flood due to the scour that will occur at the toe of the abutment. A designed countermeasure will also protect the abutment from lateral channel migration that could undermine the foundation. 4.3.4 Step 4–Determine Layout of GRS–IBS The layout of GRS–IBS is ultimately based on site conditions (e.g., desired road alignment, right of way, geotechnical issues, and hydraulic considerations). A survey should be conducted to determine the location of the GRS abutment and the layout. The layout of the abutment face wall needs to coincide with the wing walls because the system is built from the bottom up one course at a time. Both walls are built at the same time. Use the following steps to design the abutment:
4.3.5 Step 5–Calculate Applicable Loads The applicable external pressures and loads (permanent and transient) on the reinforced zone of the GRS abutment should be calculated. The most common pressures (which may be resolved into forces) on GRS–IBS for stability computations are depicted in figure 14.
The applicable pressures on a GRS abutment are as follows:
4.3.5.1 Lateral Pressures and Stresses The lateral earth pressure can be calculated according to classical soil mechanics for active earth pressure. The active earth pressure coefficient (K_{a}) is calculated according to equation 1.
Where Φ is the friction angle of interest (for example, substitute Φ_{b} when calculating K_{ab} for the retained soil). The lateral stress distribution due to the weight of the GRS fill ( σ_{h,W}) is found using Rankine's active stress condition, shown in equation 2.
Where γ_{r} is the unit weight of the reinforced fill, z is the depth from the top of the wall, and K_{ar} is the coefficient of active earth pressure (equation 1) using the friction angle of the reinforced fill (Φ_{r}). The lateral stress distributions due to the equivalent roadway LL surcharge (Σ_{h,t}) and structural backfill of the integrated approach ( Σ _{h,rb}) are found according to equation 3 and equation 4, respectively.
Where q_{t} is the equivalent roadway LL surcharge, q_{rb} is the surcharge due to structural backfill (road base), and K_{ab} is the coefficient of active earth pressure (equation 1) using the friction angle of the retained backfill (Φ_{b}). Note that equation 3 and equation 4 assume that the loading is continuous across the retained soil. Where the loads are not continuous across the GRS abutment or retained soil, the lateral pressure is based on Boussinesq theory for load distribution through a soil mass for an area transmitting a uniform stress a distance x from the edge of the load (see figure 15 ).^{(8)} The actual pressure using this theory depends on the location of interest. For required reinforcement strength calculations, the location of interest is directly underneath the beam seat centerline (e.g., x = b_{q}/2 for the bridge DL).
The lateral pressure due to surcharge loading (Σ_{h,q}) is calculated according to equation 5.
Where q is the surcharge pressure (e.g., q_{b} for the bridge surcharge), K_{a} is the coefficient of activeearth pressure (equation 1), and α and β are the angles shown in figure 15 , found using equation 6 and equation 7, respectively. Note that α and β must be input in radians in equation 5.
The lateral pressure in the GRS abutment due to the superstructure DL and LL will have a trend similar to that shown in figure 16 , where the stress is highest at the top of the GRS abutment and lowest at the base. Note that the bearing bed reinforcement underneath the beam seat helps to mitigate the increased vertical (and thus lateral) pressures in this location. In fact, the bearing bed reinforcement is recommended in the design of GRS abutments for this reason.
Note that other load distributions are available besides Boussinesq. For example Westergaard is more applicable to a GRS mass than Boussinesq. However, it gives lower stresses than Boussinesq, and therefore, using Boussinesq will provide a more conservative estimate of stresses. 4.3.5.2 Dead Loads 4.3.5.2.1 Bridge: In a GRS–IBS design with adjacent concrete box beams, the bridge superstructure bears directly upon the GRS abutment. For superstructures with spread girders, a footing (which bears directly upon the GRS abutment) is necessary to ensure even load distribution on the GRS abutment. The equivalent DL design pressure on the abutment seat includes the dead loads due to the bridge beams, asphalt, overlay, guardrail, and any other applicable permanent loads related to the superstructure. 4.3.5.2.2 Road Base: Behind the bridge beams, road base is wrapped in geotextile (called the integrated approach). The wrapped face controls lateral load from the road base on the beam or abutment sill. 4.3.5.3 Live Loads There are two applications of LL that affect the design of GRS–IBS: LL on the approach pavement and LL on the superstructure. Both of these live loads are defined by AASHTO and should be appropriately quantified by the design engineer.^{( 9 )} 4.3.5.3.1 LL on the Approach Pavement: An LL surcharge (q_{t}) is used to account for the vehicular load on the approach pavement leading up to the superstructure. This load consists of a uniform height (h_{eq}) of earth that produces an equivalent lateral effect on the abutment as the application of the vehicular LL specified for the superstructure. The equivalent height of earth is dependent on the abutment height and the orientation of the abutment with respect to the roadway (e.g., perpendicular). This load is used for both internal and external stability analyses. 4.3.5.3.2 LL on the Superstructure: The vehicular LL used for designing GRS–IBS is determined by applying the HL–93 LL model to the superstructure. This model consists of appropriately locating a design truck or design tandem in combination with a design lane load in each design lane of the bridge to create the maximum force effect at each abutment. The vehicular portion of the LL model is amplified for dynamic load allowance (impact). The governing LL is distributed to the abutment by multiplying by the number of design lanes and dividing by the bridge seat bearing area. This equivalent distributed LL pressure on the abutment seat (q_{LL}) can be determined using equation 8.
Where N_{lanes} is the number of design lanes on the bridge, b is the bridge seat bearing width (see figure 14), B_{b} is the width of the bridge, and (LL+IM)_{total} is the governing abutment reaction for the HL–93 LL model for one lane. If the bridge seat bearing width is unknown and needs sizing, the LL from the superstructure should be quantified as a reaction (Q_{LL}) rather than a pressure (see equation 9).
4.3.5.4 Design Pressure Adding LL on the superstructure and bridge DL per abutment will give the total load that the bridge seat must support. Dividing this total load by the area of the bridge seat will give the bearing pressure. For abutment applications, the bearing pressure should be targeted to around 4,000 lbs/ft^{2}. If this is exceeded, the width of the bridge seat should be increased. Although higher design pressures have been successfully applied to in–service GRS–IBS, this is not encouraged.^{(1)} 4.3.6 Step 6–Conduct an External Stability Analysis The external stability of GRS–IBS is evaluated by looking at the following potential external failure mechanisms:
4.3.6.1 Direct Sliding The GRS abutment must resist translation, or direct sliding. The LL on the approach pavement (q_{t})is assumed to act only over the retained backfill and not the reinforced soil mass. While the contribution of q_{t} (and q_{LL}) is ignored for both a wall and an abutment, the bridge load (q_{b}) has a stabilization effect against direct sliding when considering an abutment. Since the road base extends over the GRS abutment and the retained backfill, it acts to both stabilize and drive direct sliding. Contributions to both the driving force and to the resisting force from the road base must be taken into account because it is a permanent load. The thrust forces behind the GRS abutment from the retained backfill (F_{b}), the road base (F_{rb}), and the roadway LL surcharge (F_{t}) are calculated using equation 10, equation 11, and equation 12.
Where γ_{b}is the unit weight of the retained backfill, K_{ab} is the active earth pressure coefficient for the retained backfill (equation 1), H is the height of the wall including the clear space distance, q_{rb} is the road base DL, and q_{t} is the roadway LL. The total driving force (F_{n}) is calculated by summing each thrust force previously calculated, as shown in equation 13.
The resisting force (R_{n}) is calculated according to equation 14.
Where W_{t} is the total resisting weight (calculated in equation 15), μ is the friction factor between the wall base and the foundation (taken as tan Φ_{crit}), and Φ_{crit} is the critical friction angle. Since the RSF is encapsulated with geotextile, sliding at the base of the GRS abutment will occur between soil and the geotextile reinforcement. The critical friction angle will therefore be the interface friction angle between the soil and reinforcement. The interface friction angle should be determined with an interface direct shear test for the particular combination of geosynthetic and reinforced fill material (ASTM D5321). If this information is not available for geotextiles and geogrids, assume that the friction factor is equal to ^{2}/_{3} times the tangent of the reinforced granularfill friction angle (μ = ^{2}/_{3}tan(Φ_{r})).
Where W is the weight of the GRS abutment (calculated in equation 16), q_{b} is the bridge DL, b is the width of the bridge load (measured along the direction of the roadway), q_{rb} is the road base DL, and b_{rb,t} is the width over the GRS abutment where the road base DL acts (see figure 14 ). The LL on the approach pavement and the superstructure are not included as resisting forces because they are transient loads.
Where γ_{r} is the unit weight of the reinforced fill, H is the height of the GRS abutment including the clear space distance, and B is the base width of the GRS abutment not including the wall facing. Direct sliding should also be checked at the interface between the RSF and the foundation soils. The factor of safety against direct sliding (FS_{slide}) is computed according to equation 17. The factor of safety must be greater than or equal to 1.5. If not, consider lengthening the reinforcement at the base.
4.3.6.2 Bearing Capacity To prevent bearing failure, the vertical pressure at the base of the RSF must not exceed the allowable bearing capacity of the underlying soil foundation. The vertical pressure is a result of the weight of the GRS abutment, the weight of the RSF, the bridge seat load, the LL on the superstructure, and the LL on the approach pavement. The pressure at the base (σ_{v,base,n}) is calculated according to a Meyerhof–type distribution, shown in equation 18.^{(10)}
Where ΣV is the total vertical load on the GRS abutment (calculated in equation 19), B_{RSF} is the width of the RSF, and e_{B,n} is the eccentricity of the resulting force at the base of the wall (calculated in equation 20).
Where W is the weight of the GRS abutment (equation 16), W_{RSF} is the weight of the RSF, W_{face} is the weight of the facing elements, q_{t}is the roadway LL, b_{rb,t} is the width of the traffic and road base load over the GRS abutment, q_{rb} is the road base surcharge, q_{b} is the bridge DL, b is the width of the bridge seat, and q_{LL} is the LL on the superstructure.
Where ΣM_{D} is the total driving moment, ΣM_{R} is the total resisting moment, and ΣV is the total vertical load (equation 19). The moments should be calculated about the bottom and center of the RSF for the specific layout of the GRS abutment. If e_{B,n} is negative, take e_{B,n} equal to zero for the term B_{RSF}–2e_{B,n}. The bearing capacity of the foundation (q_{n}) can be found using equation 21.^{( 9 )}
Where c_{f} is the coehsion of the foundation soil, N_{c}, N_{γ}, and N_{q} are dimensionless bearing capacity coefficients as shown in table 4 , γ_{f} is the unit weight of the foundation soil, B' is the effective foundation width (equal to B_{RSF}–2e_{B,n}), and D_{f} is the depth of embedment. The friction angle in table 4 should be taken as the foundation's friction angle ( φ_{f}). If groundwater is present, modifications to equation 21 may be necessary and are provided by AASHTO.^{( 9 )} Table 4. Bearing capacity factors.^{( 9 )}
The factor of safety against bearing failure (FS_{bearing}) is computed according to equation 22. The factor of safety must be greater than or equal to 2.5. If not, increase the width of the GRS abutment and RSF (by increasing the length of the reinforcements), replace the foundation soil with a more competent soil, or add embedment depth.
Beyond bearing capacity, consolidation settlement should be evaluated to ensure excessive deformations will not occur over the life of the bridge. Design considerations such as excavation and the RSF reduce the pressure on the foundation soil. Nevertheless, settlement of the foundation soil should be assessed as with any other spread footing according to FHWA guidance.^{( 7 )} Determining the criterion for tolerable foundation settlement is left up to the engineer. A stress history analysis should be conducted to ascertain settlement and stability prediction. Answers to the following questions will provide insight on the stress history for an efficient design:
4.3.6.3 Global Stability Global stability is evaluated according to classical slope stability theory using either rotational or wedge analysis. To facilitate the global stability check, it is prudent to collect accurate soil property information. Standard slope stability computer programs can then be used to assess the global and compound stability of a GRS structure. The factor of safety for global stability should equal at least 1.5.
4.3.7 Step 7–Conduct Internal Stability Analysis
The internal stability analysis will vary slightly depending on the whether ASD or LRFD is the chosen design method. ASD is presented in this chapter. For guidance on LRFD, refer to appendix 4.3.7.1 Ultimate Capacity The ultimate vertical capacity of a GRS abutment is found either empirically or analytically. It is recommended that the ultimate capacity be found empirically if possible. A performance test should be conducted to determine the ultimate capacity if the reinforced fill is different from those used in the performance tests reported in this guide (see appendix A). Testing will provide the most accurate results for the design. If a performance test cannot be performed, the analytical method can be used to determine the ultimate capacity. 4.3.7.1.1 Empirical Method: Empirically, the results of an applicable performance test using the same geosynthetic reinforcement and compacted granular backfill as planned for the site should be used. The ultimate vertical capacity in this case is defined as the stress at which the performance test mass strains 5 percent vertically. The ultimate vertical capacity is found in figure 20. For this performance test, the nominal capacity (q_{ult,emp}) is equal to 26 ksf for a vertical strain of 5 percent.
Note that figure 20 represents the load–settlement performance of a GRS structure with reinforcement spaced at 8 inches, well–compacted AASHTO No. 89 fill material (having a friction angle of 48 degrees and no cohesion), and 4,800 lb/ft woven PP geosynthetic reinforcement. Other materials have also been tested and are shown in the synthesis report.^{( 1 )} If the materials used are outside the recommendations provided in chapter 3, then a performance test must be performed to obtain the applicable stress–strain curve similar to figure 20. Guidance on setting up a performance experiment is given in appendix B. The total allowable pressure on the GRS abutment (V_{allow, emp}) is the ultimate capacity (q_{ult,emp}) divided by a factor of safety for capacity (FS_{capacity}) of 3.5, as shown in equation 23.
The applied vertical stress (V_{applied}), which is equal to the unfactored sum of the vertical pressures on the bridge bearing area, must be less than V_{allow,emp} (see equation 24). This includes the DL from the bridge (q_{b}) and the LL on the superstructure (q_{LL}). The DL due to the road base (q_{rb}) and the LL due to the approach pavement (q_{t}) are located behind the bearing area and are therefore not included in vertical capacity calculations related to the bridge superstructure.
4.3.7.1.2 Analytical Method: As an alternative, the load–carrying capacity of a GRS wall and abutment can also be evaluated using an analytical formula called the soil–geosynthetic composite capacity.^{( 11 )} The analytical formula was originally developed for GRS walls, but it is applicable to GRS abutments as well. Note that the analytical method assumes that the backfill satisfies the criteria outlined in chapter 3. The ultimate load–carrying capacity (q_{ult,an}) of a GRS wall constructed with a granular backfill can be determined by the soil–geosynthetic composite capacity equation shown in equation 25.^{( 11 )}
Where S_{v} is the reinforcement spacing, d_{max} is the maximum grain size of the reinforced backfill, T_{f} is the ultimate strength of the reinforcement, and K_{pr} is the coefficient of passive earth pressure for the reinforced fill (calculated in equation 26).
Where Φ_{r} is the friction angle of the reinforced backfill. The friction angle should be determined from a large–scale direct shear device (ASTM D3080). The total allowable pressure on the GRS abutment (V_{allow,an}) is the ultimate capacity found analytically (q_{ult,an}) divided by a factor of safety for capacity (FS_{capacity}) of 3.5 (see equation 27).
The applied vertical stress (V_{applied}), which is equal to the unfactored sum of the vertical pressures on the bridge bearing area, must be less than V_{allow,an}(see equation 28). This includes the DL from the bridge (q_{b}) and the equivalent LL on the bridge (q_{LL}). The DL due to the road base (q_{rb}) and the LL due to the approach pavement (q_{t}) are located behind the bearing area and are therefore not included in capacity calculations related to the bridge superstructure.
4.3.7.2 Deformations The approach for determining vertical deformation involves empirically finding the strain from an applicable performance test curve. If the materials used are within the specifications given in chapter 3, then the curve shown in figure 20 can be used. Otherwise, a performance test must be conducted (see appendix B). The lateral strain is then determined analytically assuming the theory of zero volume change.^{( 12 )} 4.3.7.2.1 Vertical: The vertical strain of the GRS abutment is found from the intersection of the applied vertical stress due to the DL (q_{b}) and the performance test design envelope for vertical strain (see figure 20 ). The vertical strain should be limited to 0.5 percent unless the engineer decides to permit additional deformation. The vertical deformation, or settlement, of the GRS abutment is the vertical strain multiplied by the height of the wall or abutment. Because the GRS abutment is built with a granular fill, the majority of settlement within the GRS abutment will occur immediately after the placement of DL (q_{b}) and before the bridge is opened to traffic. The settlement of the underlying foundation soils is determined separately using classic soil mechanics theory for immediate (elastic) and consolidation settlement. Factors such as excavation and the RSF should be taken into account, as the removal of overburden relieves stress on the foundation soil. Settlement of the foundation soil can be calculated using the FHWA Soils and Foundations Reference Manual.^{( 7 )} 4.3.7.2.2 Lateral: In response to a vertical load, the composite behavior of a properly constructed GRS mass is such that both the reinforcement and soil strain laterally together. This fact can be used to predict both the maximum lateral reinforcement strain and the maximum face deformation at a given load. The method conservatively assumes a zero volume change in the GRS abutment, which represents a worst–case scenario. The maximum lateral displacement of the abutment face wall can be estimated using equation 29.^{( 12 )} The lateral strain ( ε_{L}) is then found using equation 30 and should be limited to 1 percent.
Where b_{q,vol}is the width of the load along the top of the wall (including the setback), D_{v} is the verticalsettlement in the GRS abutment, H is the wall height including the clear space distance, and ε_{V}is the vertical strain at the top of the wall. Note that equation 29 and equation 30 come from the assumptions of a triangular lateral deformation and a uniform vertical deformation (see figure 21 ). This assumption is based on observed deformation behavior of GRS. Also note that the location of the maximum lateral deformation depends on the loading and fill conditions, but the volume gained will still equal the volume lost. The maximum deformation of a GRS abutment often occurs in the top third of the abutment/wall.^{( 11–13 )}
4.3.7.3 Required Reinforcement Strength The required reinforcement strength in the direction perpendicular to the wall face (T_{req}) can be determined analytically by equation 31.^{( 11 )} The required reinforcement strength should be calculated at each layer of reinforcement to ensure adequate strength throughout the GRS abutment.
Where S_{v}is the reinforcement spacing, d_{max} is the maximum grain size of backfill, and σ_{h} is the total lateral stress within the GRS abutment at a given depth and location (calculated in equation 32).
Where σ_{h,W}is the lateral earth pressure using Rankine's active stress condition (equation 2), σ_{h,bridge,eq} is the lateral pressure due to the equivalent bridge load (calculated in equation 33), σ_{h,rb} is the lateral pressure due to the road base (calculated in equation 34), and σ_{h,t} is the lateral pressure due to the roadway LL (calculated in equation 35). To simplify calculations, the approach LL and road base DL are extended across the abutment. The vertical components of these loads are then subtracted from the bridge DL and LL, giving an equivalent bridge load. The lateral stress due to the equivalent bridge load is then calculated according to Boussinesq theory. The location of interest to determine the maximum lateral pressure is directly underneath the centerline of the bridge bearing width.
Where q_{b}, q_{rb}, q_{t}, and q_{LL} are the bridge DL, road base DL, roadway LL, and bridge LL surcharges,respectively, and α_{b}and β_{b}are the angles shown in figure 15, found using equation 36 and equation 37, respectively.
The required reinforcement strength (T_{req}) must satisfy two criteria: (1) it must be less than the allowable reinforcement strength (T_{allow}), and (2) it must be less than the strength at 2 percent reinforcement strain () in the direction perpendicular to the abutment wall face. In design, a minimum value of the ultimate reinforcement strength (T_{allow}) is needed to ensure adequate ductility and satisfactory long–term performance. In addition, it is prudent to specify the resistance required at the working load () to ensure satisfactory performance under the in–service condition. For abutments, a minimum ultimate tensile strength (T_{f}) of 4,800 lb/ft is required. The allowablereinforcement strength (T_{allow}) is found by applying a factor of safety for reinforcement strength (FS_{reinf}) of 3.5 to the ultimate strength (see equation 38). The required reinforcement strength (T_{req}) must be less than T_{allow}.
Since geosynthetic reinforcements of similar strength can have rather different load–deformation relationships depending on the manufacturing process and the polymer used, it is important that T_{req} be less than the strength at 2 percent reinforcement strain. The strength of the reinforcement at 2 percent () is often given by the geosynthetic manufacturer. If T_{req}is greater than , a different geosynthetic must be chosen, the ultimate strength must be increased, or the reinforcement spacing must be decreased. While the strength of the reinforcement can theoretically vary along the height of the GRS abutment, it is recommended that only one strength of reinforcement be used throughout the entire abutment. This simplifies the construction process and avoids placement errors for the reinforcement. 4.3.7.3.1 Depth of Bearing Bed Reinforcement: The required reinforcement strength (T_{req}) is found at each 8–inch primary spacing layer. If T_{req} is greater than the allowable reinforcement strength (T_{allow}) or the strength at 2 percent strain (), then the reinforcement spacing must be reduced to 4 inches to the depth at which T_{req} is less than T_{allow} or .This depth is termed the bearing reinforcement bed. The minimum required depth is five courses of block. To check that 4–inch spacing for the bearing reinforcement bed is adequate, calculate the required reinforcement strength again for this new spacing in the top layers to ensure that T_{req} is less than T_{allow} and for all layers throughout the GRS abutment. 4.3.8 Step 8–Implement Design Detailsfigure 22 and figure 23 are typical cross sections of a GRS wall (or wing wall) and an abutment face wall and illustrate design details that will be discussed in this section.
In the case of an abutment, finalize the design layout for ease of construction, drainage, and other considerations that might affect the performance, serviceability, or efficiency of design. The following are some GRS design implications and related details for consideration:
4.3.9 Step 9–Finalize Material Quantities and LayoutTo develop the reinforcement schedule, choose a reinforcement length that makes use of the entire roll of the reinforcement material. Reinforcement material is usually 12– to 18–ft wide. For example, the width of a PP geosynthetic roll is 12 ft, and the base of a GRS wall is 6 ft including the width of the wall face. The roll can be cut in half by a chainsaw, and a 6–ft–wide roll can be used to build the base of the wall. The remaining 6–ft–wide rolls can be used for secondary or intermediate layers of reinforcement in the walls. Draw the layout to scale to avoid errors in the calculation of quantities. Add 10 percent to the estimate of all materials. When using CMU, use the exact dimensions of 7^{5}/_{8} inches by 7^{5}/_{8} inches by 15^{5}/_{8} inches and buy both corner and face blocks. Building GRS abutments vertically without a batter eliminates the need to trim blocks. This will make it more difficult to hide lateral movement and may give an illusion of instability when the structure is, in fact, stable. Use only high–quality, well–graded gravel, as specified in chapter 3. 4.4 DESIGN EXAMPLE: BOWMAN ROAD BRIDGE , DEFIANCE COUNTY , OHConstruction of Bowman Road Bridge was completed in October 2005 by a Defiance County, OH,construction crew. This project represents the initial deployment of GRS–IBS. The structure was chosen for a design example because it demonstrates many of the variables that can be accommodated by GRS–IBS technology and illustrates the versatility of the construction method. 4.4.1 Step 1–Establish Project Requirements GRS–IBS was used for the Bowman Road Bridge project. The project included an abutment and a wing wall on each side of the bridge. A top view of the proposed project is shown in figure 26. figure 27 is an aerial view of the site with the proposed bridge superimposed.
Figure 26. Illustration. Top view of Bowman Road Bridge showing the bridge, abutments, and wing walls.
Figure 27. Illustration. Aerial view of the existing site with the planned Bowman Road Bridge superimposed. Schematics of the proposed abutments are shown in figure 28 and figure 29 . The project requirements are as follows:
Figure 28. Illustration. Schematic of the west abutment for Bowman Road Bridge.
Figure 29. Illustration. Schematic of the east abutment for Bowman Road Bridge.
4.4.2 Step 2–Site Evaluation The previous bridge at the site was replaced because it was functionally obsolete and structurally deficient. The previous bridge did not experience any problems related to settlement or excessive deformations due to the site conditions. However, a sheet pile wall was installed to protect the stone wall abutments from erosion. The site evaluation determined that the existing sheet piling should remain in place to support the stream bank. This eliminated the need for wing walls on one side adjacent to the old bridge. The replacement structure required realignment to meet current road design standards for roadway safety because the location had been prone to accidents. The new Bowman Road Bridge crosses Powell Creek. The proposed location of the new abutments adjacent to the old bridge was not expected to cause any problems with the stream flow. A hydraulic analysis confirmed that the existing bridge did not have any appreciable potential scour. Therefore, an RSF with appropriate scour countermeasures (in this case, riprap) was used. A subsurface evaluation was conducted by performing standard penetration tests (SPTs) near the site. The physical characteristics of the soil were determined through index tests taken on split spoon samples. The foundation soil at the site was an overconsolidated clay (with intermediate layers of sandy silt and gravels) with N–values greater than 50 blows per ft at the elevation of the bottom of the abutment (determined from figure 28 and figure 29). Local experts indicated the clay had historically been preloaded with a nearly 1–mi–thick sheet of ice. The clay in this region is also known to be fat and sticky when wet. The bearing capacity of the stiff clay had not been a problem in past projects in the area. The N–value of the foundation soil can be correlated into an undrained shear strength using published guidance.^{( 8 )} For blow counts greater than 30 blows per ft, the unconfined compressive strength is greater than 8,000 lb/ft^{2}. The undrained shear strength is therefore estimated as at least 4,000 lb/ft^{2}. The design properties for the foundation soil are shown in table 5 .The retained backfill is composed of the same material as the foundation soil. Table 5. Foundation and retained backfill soil properties.
The road base was a granular fill material that was brought to the site. For the Bowman Road Bridge project, the properties of the road base are given in table 6. Table 6. Road base soil properties.
The reinforced fill for the GRS abutment was a select granular fill (AASHTO No. 89 stone). Testing was performed on this fill to determine the c and Φproperties. The properties of this fill are provided in table 7. Table 7. Reinforced fill properties.
4.4.3 Step 3–Evaluate Project Feasibility As mentioned in step 2, scour was not a significant concern for this bridge. The project was therefore considered feasible for this site. Scour protection was added as a precaution. The riprap was sized for 8.8–10.2 ft/s to create a scour protection apron adjacent to and in front of the abutment face and wing walls. Prior to placement, a 5– to 8–ft–wide strip of geotextile reinforcement between the face of the RSF and the riprap was pinned under the first course of facing blocks to secure it in place. The purpose of the geotextile reinforcement was to create a barrier to mitigate loss of soil beneath the riprap.
4.4.4 Step 4–Determine Layout of GRS–IBS
Figure 30. Illustration. Reinforcement schedule and RSF dimensions for Bowman Road Bridge.
4.4.5 Step 5–Calculate Loads The applicable surcharges and loads associated with the structure were a combination of vertical and lateral components. The vertical components include the surcharges due to the DL (superstructure and road base from the integrated approach) and the LL (superstructure and roadway), along with the weight of the GRS abutment. The lateral earth pressure due to the retained backfill, shown in table 8, were also considered. Lateral loads resulting from the DL and LL were calculated separately during the external and internal stability calculations performed in step 6 and step 7. Table 8. Loads and surcharges for Bowman Road Bridge.
Note that the weight of the GRS abutment was calculated with B equal to the shortest reinforcement layer not including the width of the wall face. This is a conservative assumption to simplify hand calculations. Several software programs are available that can account for the varying shape due to different reinforcement lengths along the height of the abutment. The weight of the facing blocks (W_{face}) is the weight of an individual CMU block (42 lb) divided by the length of theblock (15.625 inches), multiplied by the total number of blocks in a single column (24 in this case).
4.4.6 Step 6–Conduct an External Stability Analysis 4.4.6.1 Direct Sliding The driving forces on the GRS abutment include the lateral forces due to the retained backfill, the road base, and the traffic surcharge. The force due to the backfill is calculated in equation 39.
The lateral force due to the road base and traffic surcharges are calculated in equation 40 and equation 41, respectively.
The total driving force (F_{n}) is then calculated in equation 42.
The resisting force (R_{n}) is calculated according to equation 14. The total resisting weight (W_{t}) includes the weight of GRS plus the weight of the bridge beam plus the weight of the road base over the GRS abutment. Since the live loads are not permanent, they cannot be counted as a resisting force. Total resisting weight (W_{t}) is calculated in equation 43.
The friction force (μ) is equal to tan Φ_{crit}. The interface friction angle between the reinforced fill and the geotextile was measured at 39 degrees by conducting an interface direct shear test. The resisting force (R_{n}) calculation is shown in equation 44.
The factor of safety against direct sliding (FS_{slide}) is calculated in equation 45 to make sure it is greater than 1.5.
4.4.6.2 Bearing Capacity Before calculating the applied vertical bearing pressure, the eccentricity of the resulting force at the base of the wall must first be calculated using equation 20. The moments are calculated around the center of the base of the RSF. The driving moments (calculated as a counterclockwise moment) include the lateral force due to the retained backfill, the road base DL, and the roadway LL. The calculation is shown in equation 46.
The resisting moments (calculated as a clockwise moment) include the vertical force due to the bridge and road base DLs and the bridge and roadway LLs. The weight of the GRS abutment is also included as a resisting moment. This calculation is shown in equation 47.
The total vertical load is equal to the sum of the weight of the GRS abutment, the weight of the RSF, and the load due to the DLs (bridge and road base) and LLs (bridge and roadway). This calculation is shown in equation 48.
Thus, the eccentricity of the resulting force at the base of the RSF is calculated in equation 49.
The applied vertical pressure is then calculated in equation 50.
The bearing capacity is calculated in equation 51. The bearing capacity factors N_{c}, N_{γ}, and N_{q} were found using table 4 for the foundation friction angle of 0 degrees.
The factor of safety against bearing capacity failure is calculated in equation 52 to make sure it is greater than 2.5.
4.4.6.3 Global Stability Global and compound stability was checked using the software program ReSSA. Figure 31 is a screenshot of the global stability failure mode. The factor of safety was found to equal 6.6, much greater than the minimum requirement of 1.5. Global and compound stability were satisfied.
Figure 31. Screenshot. ReSSA results for global stability for Bowman Road Bridge.
4.4.7 Step 7–Conduct Internal Stability Analysis 4.4.7.1 Ultimate Capacity The ultimate capacity of a GRS abutment can be determined using two different methods: empirical or analytical. 4.4.6.1.1 Empirical Method: The empirical method uses the load test results of a performance test on a GRS composite material identical (or very similar) to that used in the field. The ultimate capacity is found empirically as the stress at 5 percent vertical strain from the stress–strain curve shown in figure 32. For this curve, the ultimate capacity (q_{ult,emp}) is 26 ksf.
Figure 32. Graph. Stress–strain curve for Bowman Road Bridge showing ultimate capacity. The total allowable pressure on the GRS abutment (V_{allow,emp}) is the ultimate capacity (q_{ult}) divided by a factor of safety for capacity (FS_{capacity}) of 3.5, as shown in equation 53.
The applied vertical stress (V_{applied}), which is equal to the unfactored sum of the vertical pressures on the bridge bearing area, must be less than V_{allow,emp}. This includes the DL from the bridge (q_{b}) and the LL due to the notional HL–93 load model (q_{LL}), as shown in equation 54.
4.4.7.1.2 Analytical Method: Alternatively, the ultimate capacity can be found analytically for a granular backfill. S_{v} is equal to 8 inches, d_{max} is equal to 0.5 inches,T_{f} is equal to 4800 lb/ft, and Φ_{r} is equal to 48 degrees ( see table 7 ). Although the spacing under the bridge bearing area was 4 inches, 8 inches was chosen in equation 55 to be conservative.
The passive earth pressure for the reinforced fill was determined with equation 56.
The total allowable pressure on the GRS abutment (V_{allow,an}) is the ultimate capacity (q_{ult,an}) divided by a factor of safety for capacity (FS_{capacity}) of 3.5, as shown in equation 57.
The applied vertical stress (V_{applied}), which is equal to the unfactored sum of the vertical pressures on the bridge bearing area, must be less than V_{allow}. This includes the DL from the bridge (q_{b}) and the LL due to trucks (q_{LL}). Applied vertical stress is calculated in equation 58.
4.4.7.2 Deformations 4.4.7.2.1 Vertical: The vertical strain is estimated by using figure 32 , as illustrated in figure 33 for the bridge DL (q_{b}) of 2,600 psf. The vertical strain is therefore about 0.3 percent–under the tolerable limit of 0.5 percent. The road base surcharge is not included since it does not act over the same location.
Figure 33. Graph. Vertical strain for Bowman Road Bridge. The vertical deformation is the product of the vertical strain and the height of the GRS abutment (including the clear space distance), as shown in equation 59.
4.4.7.2.2 Lateral: The lateral strain and deformation are found in equation 60 and equation 61.
4.4.7.3 Required Reinforcement Strength The strength of the reinforcement used at Bowman Road Bridge was 4,800 lb/ft. Applying a factor of safety of 3.5, the allowable reinforcement strength is 1,371 lb/ft. According to the manufacturer, is equal to 1,370 lb/ft. The maximum required reinforcement strength is found as a function of depth, as shown in equation 62.
The lateral stress (σ_{h}) is a combination of the lateral stresses due to the road base DL (σ_{h,rb}), the roadway LL (σ_{h,t}), the GRS reinforced soil (σ_{h,W}), and an equivalent bridge load (σ_{h,bridge,eq}). To simplify calculations, the roadway LL and road base DL can be extended across the abutment. The vertical components of these loads are then subtracted from the bridge DL and LL, giving an equivalent bridge load. The lateral stresses due to the equivalent bridge load are then calculated according to Boussinesq theory. The lateral stress is calculated for each depth of interest (each layer of reinforcement). All lateral stresses are calculated and shown in table 9. Table 9. Depth of bearing bed reinforcement calculations.
An example calculation for the required reinforcement strength at a depth (z) of 5.3 ft, or the eighth reinforcement layer from the top (see figure 34 ), is presented here. First, the lateral pressure is found in equation 63. Remember, the location of interest is directly under the centerline of the bridge load (where x = 0.5b =0.5(4ft) = 2 ft).
The calculation of each aspect of the lateral pressure is shown in equation 64 through equation 67.
The values for α and β are found in equation 68 and equation 69.
Figure 34. Illustration. Lateral pressure due to the bridge load. Based on table 9, the required reinforcement strength does not exceed the allowable strength or the strength at 2 percent at any reinforcement layer. Therefore, no bearing bed reinforcement is needed; however, the minimum requirement is that the bearing bed reinforcement should extend through five courses of blocks. In actuality, six courses of block were chosen to extend the bearing reinforcement bed in this case (to a depth of 4 ft below the top of the wall). This was chosen to be conservative since this was the first bridge built with GRS technology. Applying 4–inch spacing to the top six courses of blocks and 8–inch spacing for the remaining height of the wall, the required reinforcement strength was found (see table 10 ). The maximum required reinforcement is 716 lb/ft, which is less than the factored reinforcement strength of 1,371 lb/ft and the reinforcement strength at 2 percent. There should, therefore, be no issues with reinforcement strength in the abutment. Table 10. Required reinforcement along height of wall.
4.4.8 Step 8–Implement Design Details All design details were considered. Since it was a skewed bridge, the bearing area of 3 ft was maintained along the length of the face wall. The bearing bed reinforcement schedule was also maintained across the abutment face due to the superelevation, as shown in figure 35.
Figure 35. Illustration. Secondary reinforcement for superelevation at Bowman Road Bridge.
4.4.9 Step 9–Finalize Material Quantities and Layout The amount of reinforcement necessary is based on the reinforcement schedule. Reinforcement material came in 12– to 18–ft–wide rolls. The number of facing blocks was determined from the height and length of the abutment and wing walls. The amount of backfill required was determined in a similar fashion. Once final quantities are established, it is a good rule of thumb to order at least 10 percent more to account for unforeseen conditions.
