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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 GuideAPPENDIX C. LRFD DESIGN PROCEDUREC.1 INTRODUCTIONAn AASHTO LRFD procedure is presented in this appendix to permit the designer a choice of design methodology formats for GRS–IBS.^{( 9 )} This procedure is primarily a fit to the ASD solutionbut does include some LRFD features. For example, checking the external stability of earth–retaining structures is well defined by AASHTO LRFD. For internal stability of GRS structures, however, LRFD is not well defined yet. Since there is not enough statistical information available to fully calibrate LRFD for internal stability, the LRFD method has been fit to ASD. This means that the designer will arrive at the same answer for internal stability whether using ASD or LRFD. In the future, once more performance tests and case studies have been evaluated, the resistance factors for both vertical capacity and reinforcement strength may change from those presented in this appendix. For LRFD, AASHTO defines the various load factors and load combinations that need to be considered in the design of bridge and transportation structures.^{(9)} Table 16 and table 17 reproduce these load combinations and load factors. Resistance factors for external stability are also given by AASHTO.^{( 9 )} For direct sliding, a resistance factor for shear resistance ( Φ_{r} ) is included. For sliding of soil on soil, Φ_{r}is equal to 1. For bearing capacity, the resistance factor ( Φ_{bc} ) is equal to 0.65. Finally, for global stability, the resistance factor is 0.65. Table 16. Typical load combinations and load factors.^{( 9 )}
Table 17. Load factors for permanent loads.^{( 9 )}
C.2 GRS–IBS DESIGN GUIDELINESThe following nine basic steps for the design of GRS–IBS are reproduced from section 4.4:
Once these steps are accomplished, the GRS–IBS can be constructed. The basic design guidelines are the same whether using ASD or LRFD. However, the detailed equations within step 6 and step 7 will differ between the two design methods. In this appendix, only the differences in step 6 and step 7 that result from conversion to the LRFD format are presented. Refer to C.2.1 Step 6–Conduct an External Stability Analysis The external stability of a GRS–IBS is evaluated by looking at the following potential external failure mechanisms:
C.2.1.1 Direct Sliding The total factored driving force for LRFD (F_{R}) is calculated in much the same way as in ASD (F_{n})except load factors are applied to each component of thrust force. Equation 70 modifies equation 13 to include the load factors γ_{EH MAX}, γ_{ES MAX}, and γ_{LS}, which are determined using table 16 and table 17.
The factored resisting force (R_{R}) is calculated using equation 71. This equation is the LRFD modification of equation 14 that includes a shear resistance factor ( Φ_{τ} ). For sliding, Φ_{τ} is equal to 1.0. ^{( 9 )}
Where W_{t,R} is determined using equation 72, which is equation 15 modified to include the appropriate load factors, Φ_{EV MIN}, Φ_{DC MIN} and Φ_{DC MIN}, from table 17.
For LRFD, the ratio of the factored resistance and the factored driving force must be greater than or equal to 1.0 (see equation 73). If not, consider lengthening the reinforcement at the base.
C.2.1.2 Bearing Capacity In this section, the ASD equations to evaluate bearing capacity have been modified to include the appropriate load and resistance factors of LRFD. Equation 74 is the LRFD version of equation 18.
Where ΣV_{R} is the total factored vertical load on the GRS abutment (see equation 75), B_{RSF} is the width of the RSF, and e_{B,R} is the eccentricity of the resulting force at the base of the wall (see equation 76).
Where γ_{EV MAX,} γ_{LS,} γ_{ES MAX} and γ_{DC MAX}, are load factors found from table 16 and table 17, W is the weight of the GRS abutment, W_{RSF} is the weight of the RSF, W_{face} is the weight of the facing elements, q_{t}is the roadway LL, q_{rb} is the road base DL, b_{rb,t} is the width of the traffic and road base surcharges over the GRS abutment, q_{b} is the bridge DL, b is the width of the bridge seat, q_{LL} is the bridge LL, ΣM_{D,R} is the total factoreddriving moment, ΣM_{R,R} is the total factored resisting moment, and ΣV_{R} is the total factored verticalload. The moments should be calculated about the bottom center of the RSF length for the specific layout of the GRS abutment. If e_{B,Rn} is negative, take e_{B,R} equal to zero for the term B_{RSF}–2e_{B,R}. The factored bearing capacity of the foundation (q_{R}) can be found using equation 77. Based on AASHTO, the resistance factor ( Φ_{bc}) is equal to 0.65.^{( 9 )}
Where c_{f} is the cohesion of the foundation soil, N_{c}, N_{γ}, and N_{q} are dimensionless bearing capacitycoefficients (see table 4 ), Φ_{f}is the unit weight of the foundation soil, B' is the effective foundation width (equal to B_{RSF}–2e_{B,R}), and D_{f} is the depth of the embedment. The ratio of the factored bearing resistance and the factored applied pressure must be greater than or equal to 1.0 (see equation 78). If not, increase the width of the GRS abutment and RSF (by increasing the length of the reinforcement layers), replace the foundation soil with a more competent soil, or add embedment depth.
C.2.1.3 Global Stability According to AASHTO, the Service I Load Combination should be used to evaluate global stability.^{( 9 )} For the Service I limit state, the load factor is 1.0 for permanent loads. When the geotechnical parameters are not well defined or the slope does contain or support a structural element, the shear resistance factor is 0.65. This corresponds to a factor of safety of 1.5. C.2.2 Step 7–Conduct Internal Stability Analysis C.2.2.1 Vertical Capacity It is recommended that the ultimate capacity be found empirically, if possible. A resistance factor for capacity ( Φ_{cap}) of 0.45 should be applied to the nominal vertical capacity (q_{n}) to account for uncertainty. This resistance factor value is based on fitting to the ASD method. C.2.2.1.1 Empirical Method: The factored applied pressure on the GRS abutment (V_{applied,f,emp}) is equal to the sum of the vertical pressures on the bridge bearing area multiplied by their respective load factors (see equation 79). The vertical pressures include the bridge DL (q_{b}) and LL (q_{LL}).
Where γ_{DC MAX} and γ_{LL} are load factors found from table 16 and table 17. The factored applied pressure must be less than or equal to the factored vertical capacity (see equation 80). The resistance factor ( Φ_{cap} ) is equal to 0.45.
C.2.2.1.2 Analytical Method: As an alternative, the load–carrying capacity of a GRS abutment can be evaluated using an analytical formula, referred to as the soil–geosynthetic composite capacity equation.^{( 11 )} The nominal ultimate load–carrying capacity (q_{n,an}) of a GRS wall constructed with a granular backfillcan be determined by the soil–geosynthetic composite capacity equation, shown in equation 81.^{( 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 determined using equation 26. The factored applied pressure on the GRS mass (V_{applied,f}) is equal to the sum of the vertical forces multiplied by their respective load factors (see equation 82). This includes the bridge DL (q_{b}) and LL (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.
Where γ_{DC MAX} and γ_{LL} are load factors found from table 16 and table 17. The factored applied pressure must be less than the factored ultimate capacity (see equation 83).The resistance factor ( Φ_{cap} ) is equal to 0.45.
C.2.2.2 Deformations The method to estimate both vertical and lateral deformations is not dependent on the design code chosen (ASD or LRFD). Therefore, refer to section 4.4.7.2 to estimate deformations. C.2.2.3 Required Reinforcement Strength The factored required reinforcement strength in the direction perpendicular to the wall face ( T_{req,f} )can be determined analytically by equation 84. The required factored reinforcement strength should be calculated at each layer of reinforcement to ensure adequate strength throughout the GRS abutment. For the serviceability check (comparing the required strength to the reinforcement strength at 2 percent strain), the unfactored required reinforcement strength should be used (see equation 85).
Where S_{v}is the reinforcement spacing, d_{max} is the maximum grain size of backfill, σ_{h,f}is the total factored lateral stress within the GRS abutment at a given depth and location (see equation 86), and σ_{h}is the total unfactored lateral stress within the GRS abutment at a given depth and location (equation 32).
Where σ_{h,W,f} is the factored lateral earth pressure using Rankine's active stress condition (see equation 87), σ_{h,bridge,f} is the factored lateral pressure due to the equivalent bridge load (see eqautaion 88), σ_{h,rb,f} is the factored lateral pressure due to the road base DL (see equation 89), and σ_{h,t,f} is the factored lateral pressure due to the roadway LL (see equation 90).
Where γ_{DC MAX}, γ_{ES MAX}, γ_{LS}, and γ_{LL} are load factors found from table 16 and table 17; q_{b}, q_{rb}, q_{t}, and q_{LL} are the bridge DL, road base DL, roadway LL and bridge LL, respectively; K_{ar} is the active earth pressure coefficient for the reinforced fill; and α_{b} and β_{b}are the angles shown in table 15, found using equation 91 and equation 92, respectively.
For abutments, a minimum wide width tensile strength (T_{f}) of 4,800 lb/ft is required.
AMENDED May 24, 2012 Since geosynthetic reinforcements of similar strength can have rather different load–deformation relationships depending on their material, it is important that the nominal (unfactored) 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 the unfactored T_{req}is greater than , either a different geosynthetic must be chosen or the ultimate strength must be increased.
C.3 DESIGN EXAMPLE (LRFD): BOWMAN ROAD BRIDGE, DEFIANCE COUNTY, OH
In this section, the equations formatted for the LRFD method in section C.2 are demonstrated. For additional details and discussion in support of these calculations, see the corresponding sections of the design example in the ASD format contained in C.3.6 Step 6–Conduct an External Stability Analysis C.3.6.1 Direct Sliding The driving forces on the GRS abutment are comprised of 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 94.
The lateral force due to the road base and traffic surcharges are calculated in equation 95 and equation 96.
The total factored driving force (F_{R}) is then calculated in equation 97. The load factors are determined using table 16 and table 17.
The factored resisting force (R_{R}) is calculated according to equation 71, where Φ_{T} is the resistance factor for shear resistance (equal to 1.0 for sliding).^{( 9 )} The total resisting weight (W_{t,R}) includes the weight of GRS plus the weight of bridge beam plus the weight of the road base over the GRS abutment, as shown in equation 72. Since the LLs are not permanent, they cannot be counted as a resisting force. The total resisting weight is calculated in equation 98.
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 factored resisting force is calculated in equation 99.
This resisting force (15,239 lb/ft) is greater than the driving force (14,068 lb/ft); therefore, direct sliding is not an issue. C.3.6.2 Bearing Capacity Before calculating the factored applied vertical bearing pressure, the factored eccentricity of the resulting force at the base of the wall must be calculated. 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 and are calculated in equation 100.
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 resisting moments are calculated in equation 101. The weight of the GRS abutment is also included as a resisting moment.
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 the LLs (bridge and roadway). The total vertical load is calculated in equation 102.
The eccentricity of the resulting force at the base of the RSF is then calculated in equation 103.
The vertical pressure is a result of the weight of the GRS mass, the bridge seat load, and the traffic surcharge and is calculated in equation 104.
The nominal bearing capacity is then calculated in equation 105. The degrees bearing capacity factors (N_{c} and N_{γ}) were found using table 4 for the foundation friction angle of 0.
Applying the resistance factor of 0.65 to the nominal bearing capacity, the factored bearing capacity (q_{R}) is equal to 13,481 psf. The factored bearing capacity is greater than the factored vertical pressure (7,862 psf), so bearing capacity is not an issue in this case. C.3.6.3 Global Stability Global and compound stability was checked using the software program ReSSA. Global stability is not a problem. C.3.7 Step 7–Conduct Internal Stability Analysis C.3.7.1 Vertical Capacity The ultimate capacity of a GRS abutment can be determined using two different methods: empirical or analytical. C.3.7.1.1 Empirical Method: The empirical method uses the results of a performance test on a GRS composite material identical (or very similar) to that used in the field. The ultimate vertical capacity is found by looking at the applicable stress–strain curve from the performance test for a vertical strain of 5 percent (see figure 32 ). The capacity (q_{n,emp}) is equal to 26 ksf. Note that the linear line extension shown in figure 32 is to project the capacity to 5 percent. The factored applied pressure on the GRS mass (V_{applied,f}) is found in equation 106:
The ratio of the factored vertical capacity (with a resistance factor of 0.45) to the factored applied pressure (V_{applied,f}) must be greater than or equal to 1, as shown in equation 107.
C.3.7.1.2 Analytical Method: Alternatively, the nominal capacity is found analytically for a granular backfill, where S_{v} is equal to 8 inches, d_{max} is equal to 0.5 inches, T_{f} is equal to 4,800 lb/ft, and Φ_{r} is equal to 48 degrees. Note that although the spacing under the bridge bearing area is 4 inches, 8 inches was chosen to be conservative in the calculation for the entire mass.
Where the coefficient of passive earth pressure for the reinforced fill (K_{pr}) is found in equation 109.
The factored applied pressure on the GRS mass (V_{applied,f}) is found in equation 110.
The ratio of the factored ultimate capacity (with a resistance factor of 0.45) to the factored applied pressure (V_{applied,f}) must be less than 1, as shown in equation 111.
C.3.7.2 Deformations C.3.7.2.1 Vertical Deformation: The vertical strain is estimated by using figure 33 for the total bridge load (q_{b}) of 2,600 lb/ft^{2}. The vertical strain is, therefore, about 0.3 percent–under the tolerable limit of 0.5 percent. Note that the road base surcharge is not included because it does not act over the same location. The vertical deformation is the product of the vertical strain and the height of the GRS mass and is calculated in equation 112.
C.3.7.2.2 Lateral Deformation: The lateral strain and deformation are found in equation 113 and equation 114.
C.3.7.3 Required Reinforcement Strength
The strength of the reinforcement used at Bowman Road Bridge is 4,800 lb/ft.
The factored lateral stress ( σ_{h,f} ) is a combination of the factored lateral stresses due to the road baseDL ( σ_{h,rb,f} ), the roadway LL ( σ_{h,t,f} ), the GRS reinforced soil ( σ_{h,W,f}), and an equivalent bridgeload ( σ_{h,bridge,f} ). 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 in table 18. An example calculation for the required reinforcement strength at a depth (z) of 5.3 ft (the eighth reinforcement layer from the top) is shown in equation 116. First, the lateral pressure must be found. Remember, the location of interest is directly under the centerline of the bridge load (where x = 0.5b =0.5(4ft) = 2 ft).
Where the lateral pressure is found using equation 117 through equation 120.
The values for α and β are found in equation 121 and 122.
The lateral earth pressure and required reinforcement strength should be found along the entire depth of the wall. The reinforcement spacing (S_{v}) for the required reinforcement strength calculation is 4 inches where secondary reinforcement layers are present and 8 inches where there are no secondary reinforcement layers. The depth at which secondary reinforcement layers are present is determined by applying the 8inch reinforcement spacing for the entire height of the GRS mass. The depth at which the required reinforcement spacing does not exceed the factored reinforcement capacity of 1,920 lb/ft is the depth above which 4–inch spacing is required ( see table 18 ). Table 18. Depth of bearing bed reinforcement calculations (LRFD).
Based on table 18, 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. There should, therefore, be no issues with reinforcement strength in the abutment. C.3.8 Step 8–Implement Design Details All design details were considered. Since it is a skewed bridge, a 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 (see figure 35 ).
