Geosynthetics 2015

February 15-18, Portland, Oregon

Comparison of GMSE and GRS Design Methodology

Mike Adams, Federal Highway Administration, USA, Mike.Adams@dot.gov Jennifer Nicks, Ph.D., P.E., Federal Highway Administration, USA, Jennifer.Nicks@dot.gov ABSTRACT Conventional design of geosynthetically reinforced mechanically stabilized earth (GMSE) walls on the National Highway System (NHS) follows the AASHTO LRFD Bridge Design Specifications. For internal stability, the Simplified Method is recommended; however, research conducted at the Turner-Fairbank Highway Research Center concludes that the Simplified Method does not predict resistance at the strength limit state. Findings also indicate that a closely-spaced (≤ 0.3 m) geosynthetic reinforced soil (GRS) wall with purely frictional connections would not satisfy typical GMSE design requirements for wall heights greater than 2 m, effectively precluding them from use on the NHS. This is contrary to the results of large-element GRS performance tests loaded to failure and the in-service performance of many GRS walls and abutments. This paper presents a design example to compare the design methods and provides recommendations for the design of generic, frictionally connected GRS walls and abutments. 1. INTRODUCTION 1.1 Technology Definitions Geosynthetically reinforced mechanically stabilized earth (GMSE) walls are a traditional form of MSE built with geosynthetic reinforcement in lieu of a metallic reinforcement. Geosynthetic Reinforced Soil (GRS) technology is defined by the Federal Highway Administration (FHWA) as closely-spaced layers of geosynthetic reinforcement and compacted granular fill material (Adams et al. 2011). The frequency of the reinforcement in GRS, less than or equal to 0.3m (12 in), results in a new composite material. This new GRS composite behaves differently from the more conventional, larger spaced geosynthetic Mechanically Stabilized Earth (GMSE) walls in which the reinforcement serves as independent tie-backs within the soil mass.

1.2 Evolution of Reinforced Soil in the US The history of reinforced soil can be traced back for thousands of years. From the Ziggurats in Iraq to the Great Wall of China, man had included locally available plant materials to strengthen the earth, realizing its benefits through observation, trial and error. After these early initial uses, the technology went into hiatus until the advent of man-made materials, leading to the modern design of reinforced soil. The modern era of Mechanically Stabilized Earth (MSE) began in the 1960s with the use of discrete steel strips. Shortly after in the 1970’s, the first recorded use of geosynthetics for wall construction in the United States was by the US Forest Service (Fig. 1). The performance of these early wrapped faced walls was impressive. During the late 1970s/early 1980s, in the rush to deploy the technology, practitioners and researchers developed a unified MSE design specification principally based on the behavior of reinforced soil walls built with discrete metallic reinforcement elements, within the framework of classical soil mechanics and cantilever wall systems. Throughout the past few decades, there has been several reiterations of the MSE design code developing into a mature technology; however, the division of reinforcement types into extensible (i.e. geosynthetic) and non-extensible (i.e. metallic) within the mainstream practice of MSE created limitations on the use of geosynthetics and their application. During the 1970s, others continued to explore the use of geosynthetics outside the context of MSE design specifications and framework, creating a separate distinct evolutionary path for geosynthetic reinforced soil technology (Fig. 1). The evolutionary path of GRS technology has led to a variety of applications based on the concept that closely spaced GRS behaves as a composite material different from that of a tieback.

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Figure 1. Evolution of Reinforced Soil

Through NCHRP 556 (Wu et al. 2006), the first design guidelines for GRS abutments, utilizing the benefits of close spaced GRS, was developed. This intermediate step in separating design methodology still used the Simplified Method to estimate geosynthetic strength at rupture, but limits on the spacing were implemented for bridge abutments. FHWA developed another design method for closely spaced GRS soil walls used for bridge support (Adams et al. 2011). This was the first step by the federal agency to differentiate between GRS and GMSE; the former acting as a new composite material and the later acting as a tie-back system. The FHWA GRS design method is based on over 40 years of research and evaluation of numerous in-service walls and abutments. The GRS design methodology differs in nine major aspects from current practice for GMSE outlined in AASHTO and GEC-11: (1) reinforcement spacing, (2) reinforcement length, (3) friction angle, (4) vertical capacity, (5) deformations, (6) reinforcement strength, (7) pullout, (8) connection requirements, and (9) limiting eccentricity. To understand the impact each of these has on the entire design process, a design example is performed. 2. DESIGN EXAMPLE 2.1 Background To illustrate the evolution of design, a comparison using the AASHTO (2012) versus the FHWA design method for the Founders/Meadows Bridge over U.S. Interstate 25 near Denver, CO is evaluated. The two-span structure is the first major bridge supported by spread footings directly bearing on GMSE abutments with modular block facing (Abu-Hejleh et al. 2003); the center pier is supported by a spread footing on rock. Each span is 34.5 m long, consisting of 20 prestressed box girders connected to a stub abutment. Approach slabs transition the roadway to the bridge. A cross-section of the 6 m tall GMSE abutment is shown in Fig. 2.

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Figure 2. Founders/Meadows Bridge Cross-Section (Abu-Hejleh et al. 2001) 2.2 GMSE Design The design of Founders/Meadows followed the 1996 AASHTO and CDOT bridge design specifications (Abu-Hejleh et al. 2000). A summary of the main design dimensions and parameters are shown in Table 1. The GMSE consisted of 157 kN/m polyethylene geogrids, mechanically connected to concrete facing blocks at 0.4 m vertical spacing. The reinforced backfill was well-graded silty sand, with a maximum dry unit weight of 22.1 kN/m

3. A default friction angle of 34 degrees

was used in the design; however, testing of the backfill with large-scale direct shear tests (0.3 m by 0.3 m box) indicated that the material had a friction angle of 48 degrees. In current AASHTO (2012) specifications, 34 degrees is still the default in lieu of testing; if directly measured, the friction angle is capped at 40 degrees in design using the Simplified Method for GMSE walls and abutments.

Table 1. Summary of Founders/Meadows GMSE Design.

Parameter Symbol Value Units

Reinforcement Spacing Sv 0.4 m Reinforcement Strength

1

Strength Reduction Factor2

Tf

RFglobal 157.3 5.82

kN/m -

Base Embedment Length B 8 m Base to Height Ratio B/H 1.3 - Setback Distance

3 a 1.35 m

Footing Width Footing Length Footing Embedment Depth

4

Footing Surcharge5

Live Load Surcharge6

Backfill Friction Angle7

b L d qt qLL φ

3.81 34.5 0.76 115 35 34

m m m kPa kPa deg

1MARV value for geogrid, according to ASTM D6637,

2Global reduction factor to account for long-term strength loss due

to creep, durability, installation damage, and uncertainty, 3Distance from the front edge of the footing to the back of the

wall face, 4Depth from base of footing to top of wall face,

5Dead load only from the bridge,

6Live load from the bridge

only, 7Default friction angle used in design

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The internal stability design for the wall was conducted by a GMSE wall vendor, whereas the external stability was conducted by the state agency. Details on the design are provided by Abu-Hejleh et al. (2000). 2.3 GRS Design If the Founders/Meadows bridge had been designed using the FHWA GRS guidelines (Adams et al. 2011), then how would the final product differ from the bridge we know today? The first difference would be in the reinforcement spacing. Founders/Meadows used a spacing of 0.4 m, whereas GRS design is capped at 0.3 m. The typical spacing used for in-service bridges, however, is 0.2 m. Assuming 0.2 m reinforcement spacing, the GRS design guidelines are followed below, step-by-step, with commentary as related to GMSE design for comparison. Since the original design was performed in Allowable Stress Design (ASD), ASD is used in the GRS design; however, LRFD guidelines are available (Adams et al. 2011) 2.3.1 Step 1: Establish Project Requirements The project requirements are outlined by Abu-Hejleh et al. (2000), and include the geometry of the bridge, the loading conditions, and the performance criteria. None of this would change by using the GRS design method. 2.3.2 Step 2: Perform a Site Evaluation The foundation soil properties are the same regardless of the design method. While test results were not found, the friction angle of the clay stone bedrock was assumed to equal 27 degrees with no cohesion (Abu-Hejleh et al. 2000). The retained earth behind the abutment wall was also assumed to be similar to the foundation material, with a friction angle of 27 degrees and no cohesion. As noted previously, a default friction angle of 34 degrees was used for the reinforced backfill. In GRS design, no limitation on friction angle is imposed, if testing according to proper standards. As such, the measured friction angle of 48 degrees is used. 2.3.3 Step 3: Evaluate Project Feasibility Overall, four foundation alternatives were considered by Colorado DOT, with the GMSE abutments proving viable for the site (Abu-Hejleh et al. 2000). The foundation materials were competent, consisting of bedrock, and the structure was a grade crossing; therefore, no additional scour or seismic considerations were needed. 2.3.4 Step 4: Determine Layout of GRS Abutment Regardless of design method, the elevation of the roadway and bridge would have remained the same. In this case, the top of the roadway is 8 m from the base of the wall. While the Founders/Meadows Bridge was supported directly on the foundation material, a Reinforced Soil Foundation (RSF) is recommended with GRS abutments (Adams et al. 2011). The RSF serves a similar purpose, to provide embedment, but it also helps spread the load and decrease the applied pressure to the foundation soil. The minimum depth of the RSF is 0.25 times the base embedment length of reinforcement; however, to help keep the design comparison level, a depth of 0.61 m was selected, the same as the embedment in the real bridge case. Assuming the same layout of the superstructure, girders 0.89 m deep and deck at 0.13 m thick (Fig. 2), the height from the base of the abutment (not including the RSF) to the bottom of the bridge beams is 6.4 m. Using concrete masonry units (CMUs) as facing, with a height of 0.2 m, a total of 32 courses are needed to form the GRS abutment. The length of the beams is independent of design method; however, the footing width, and thus the applied pressure can change. In GRS design, a minimum bearing width of 0.76 m is required; it is also recommended not to exceed a target bearing pressure of 190 kPa. To determine the bearing width, the dead and live loads are needed.

2.3.5 Step 5: Calculate Applicable Loads The design dead and live loads were back calculated from the given applied dead and live load pressures on the Founders/Meadows Bridge and the geometry of the footing. For 115 kPa of applied dead load pressure on a footing area of 131.5 m

2 (Table 1), the dead load is 15.1 MN; for 35 kPa of estimated live load pressure on the same footing area, the

live load is 4.6 MN. The total dead plus live load is therefore 19.7 MN. With GRS design, however, the box beams used can bear directly on the GRS abutments, without the need for a separate footing or stem wall. This reduces the applied dead load by approximately 5.9 MN. In addition, the total beam lengths can be reduced because the footing area can be designed smaller to support loads up to 190 kPa. As an initial estimate, the bearing area is designed as 2 m wide by 34.5 m in length, or 69 m

2. This reduces the length of

the superstructure length by approximately 1.8 m on each side, equating to approximately 0.9MN of additional dead load

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removed. Subtracting the dead load components removed as part of the GRS design, the total dead load is 8.3 MN. The live load doesn’t change, so the total dead and live load is 12.9 MN per abutment. For the estimated bearing area of 69 m

2, the applied pressure would be 187 kPa, within the target limit of 190kPa. This resulting bridge footprint on the GRS

abutments is considerably smaller than the actual size of the footing used. Note that the width of the beam seat plays a role in the base length of reinforcement. The reinforcement should extend the same amount in front of and behind the footing. If the footing is 2 m, and has the minimum setback of 0.2 m, then the base length of reinforcement should be about 2.4 m, which is greater than the minimum required of 1.8 m. The base to height ratio in this case is therefore 0.4. AASHTO (2012) suggests that the minimum length of reinforcement for abutments is at least 6.7 m, or as as required by internal and external stability requirements, which greatly increases the excavation required, and thus the cost. As the truncated base of the abutment is built, the reinforcement layers get progressively longer to follow the cut-slope of the excavation. Within the bearing bed reinforcement zone, located in the top 5 courses directly underneath the beam seat, secondary reinforcement spacing is 0.1 m, and is placed between the primary layers to limit lateral deformations at the top of the abutment wall. Another primary difference in the loads between GRS and GMSE design is the ability to use the measured friction angle of the backfill material. The design takes advantage of the strength properties of the quality backfill selected. The active earth pressure coefficients are 0.282 and 0.147 for 34 and 48 degree friction angles, respectively. Therefore, the lateral earth pressures are significantly reduced in GRS design. 2.3.6 Step 6: Conduct an External Stability Analysis A GRS abutment is a gravity structure; external stability is therefore evaluated for direct sliding, bearing capacity, and global stability failure modes. This does not change regardless of design code; however, current MSE design methods also include a check to limit eccentricity (AASHTO 2012). This check is to ensure tension failure does not occur whereby the reinforced soil mass lifts-up at the heel. This assumes that the reinforced soil mass has no resistance from the retained fill. Observations have shown that the flexible nature of GRS composites results in more uniform stress distribution that can resist large eccentric vertical and lateral loads in-service (Kost et al. 2014). Observations also show that the combination of vertical and lateral loads does not cause excessive deformation at the face of the GRS mass or other serviceability issues. Other attributes specific to the IBS eliminate overturning as a mode of failure, since the superstructure supported on the GRS abutments acts as a strut to resist overturning; furthermore, the integrated approach above its heel also helps resist overturning. 2.3.7 Step 7: Conduct an Internal Stability Analysis The internal stability analysis for GRS is the largest departure from GMSE design. AASHTO (2012) requires that reinforcement strength, connection strength, and reinforcement pullout be evaluated for internal stability. In GRS design (Adams et al. 2011), internal stability consists of verifying bearing resistance of the GRS abutment, ensuring deformations are within tolerable limits, without checks for reinforcement strength requirements; connection strength and reinforcement pullout.

2.3.7.1 Bearing Resistance A major contribution of the FHWA GRS design method is the ability to estimate vertical capacity. One method for determining capacity is empirically via a performance test, or mini-pier experiment (Adams et al. 2011). A mini-pier experiment is a large-scale, 1.4 m square base by 2 m tall, load test that provides information about the material strength properties of a particular GRS composite built with a unique combination of reinforcement, compacted fill, and facing elements (Adams et al. 2014). The procedure involves axially loading the GRS mass while measuring vertical and lateral deformations to obtain a stress-strain curve. This information can then be used to aid in the design process to predict performance of a full-scale GRS wall or abutment. The analytical method consists of a semi-empirical soil-geosynthetic capacity equation to estimate the vertical capacity of a particular GRS composite (Eq. 1).

p

Kanult

q

v

fd

s

S

TV

max6

7.0,

[1]

Where qult,an = nominal vertical capacity, Sv = reinforcement spacing, dmax = maximum aggregate size, Tf = ultimate reinforcement strength (MARV), and Kp = passive earth pressure coefficient. Note that this is the design form of the equation, with terms for the confining stress due to the facing and cohesion within the soil, removed for added

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conservatism (Adams et al. 2011). The expression has been validated against numerous large scale laboratory experiments and full-scale test walls with good agreement. A reinforcement strength of 70 kN/m spaced at 0.2 m is typically used for GRS abutments, so that was used as the starting point in the design. With a friction angle of 48 degrees and a maximum aggregate size of about 50.8 mm for the material, the bearing resistance from Eq. 1 is 1880 kPa. For the applied pressure of 187 kPa, this represents a factor of safety of 10. A factor of safety of at least 3.5 is needed in design (Adams et al. 2011a).

2.3.7.2 Deformations Another major contribution of the FHWA GRS design method is the ability to estimate deformations. Vertical and lateral deformations post-construction within the GRS abutment, excluding the effects of foundation settlement, can be estimated based on the results of a performance test, as previously described. Using the applicable stress-strain curve, the vertical strain at a given surcharge or bridge dead load can be found. Tolerable limits are set by the bridge engineer, but FHWA recommends limiting vertical strain to 0.5% of the height (Adams et al. 2011a). In the absence of testing, an alternative recommended by Nicks et al. 2013a is to limit applied pressures to 10% of the estimated bearing resistance (Eq. 1). In this case, the bearing pressure would be limited to 188 kPa, which meets the previous design requirements, so no iterations of footing size are needed. For the 6.4 m tall wall, at a surcharge of about 190 kPa, a maximum of 32 mm of settlement within the GRS abutment would be estimated (0.5% vertical strain). Lateral deformation is calculated based on the postulate of zero volume change within the GRS mass (Adams et al. 2002): the volume loss vertically due to settlement is equal to the volume gained laterally due to bulging. The corresponding expression to calculate the lateral deformation is given by Eq 2.

H

vD

volqb

LD

,2

[2]

Where DL = maximum lateral deformation, bq,vol = setback distance (0.2 m) plus the bearing width (2 m), Dv = maximum vertical deformation, and H = height of the abutment (6.4 m). In this case, assuming the maximum vertical deformation of 32 mm, the maximum lateral deformation would be 22 mm. Immediate settlement of the footing was measured at about 13 mm, with up to an additional 10 mm post-construction after a year (Abu-Hejleh et al. 2001); well within these tolerable limits. Similarly, measured lateral deformation after placement of the bridge was about 9 mm.

2.3.7.3 Required Reinforcement Strength In the GRS-IBS design method, reinforcement strength has two criteria: (1) the reinforcement strength required to prevent failure at a given working load (Eq. 3) must be less than the allowable reinforcement strength (Eq. 4) and (2) the reinforcement strength (Eq. 3) must be less than the strength at 2% strain as tested by ASTM 6637 for geogrids or 4595 for geotextiles. These criteria help ensure that the reinforcement meets both strength and service limit requirements.

vS

d

vS

h

reqT

max6

7.0

[3]

globalRF

fT

aT [4]

Where Treq = required reinforcement strength, σh = lateral earth pressure at the reinforcement layer, Sv = reinforcement spacing, dmax = maximum grain size, Ta = allowable long-term reinforcement strength, Tf = ultimate tensile strength, and RFglobal = global strength reduction factor of 3.5 (Adams et al. 2011). Eq. 3 is very similar to that presented in AASHTO (2012) to determine the maximum reinforcement load (Eq. 5), except it includes an empirically derived term in the denominator, based on comparisons to large-scale load tests (Adams et al. 2011).

vS

hT

max [5]

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The GRS design approach utilizes a single global strength reduction factor of 3.5 regardless of polymer type when the reinforcement spacing is small and quality backfill materials are used, which is a departure from GMSE design (Eq. 6). Therefore with a 70 kN/m polypropylene (PP) geotextile assumed in the design, the allowable long-term design strength of the geosynthetic is 20 kN/m.

DRF

CRRF

IDRF

fT

aT [6]

Where RFID, RFCR, and RFD are reduction factors for installation damage, creep, and durability. In addition, a factor of safety was also included in the AASHTO and CDOT 1996 guidelines (Abu-Hejleh et al. 2000). Guidance on how to determine these values is provided by Berg et al. (2009); however, most suppliers can provide this information. After calculating the lateral earth pressure, the maximum required reinforcement strength is found to equal approximately 7.7 kN/m (Eq. 1). This meets the strength requirements, and a PP geotextile can also be found that also meets that strength at 2%. According to the design loads, no bearing bed reinforcement would be needed; however, the minimum required is to a depth of 5 courses of block, or about 1 m.

2.3.7.4 Reinforcement Pullout Current GMSE guidance requires that internal stability with respect to the pullout mode of failure be satisfied (AASHTO 2012). This criterion is meant to ensure that the reinforcement is embedded a sufficient length beyond an assumed active failure wedge to prevent the reinforcement from pulling out of the reinforced backfill. Pullout of the reinforcement, however, is not a possible failure mode for composite closely-spaced reinforced soil systems, as in GRS. In fact, no pullout failure has been observed when compacted granular backfill is employed and external stability is satisfied.

2.3.7.5 Connection Requirements In the GRS design method, a full AASHTO connection is recommended whereby the reinforcement is sandwiched in between two facing blocks without any lips or pins. This type of reinforcement-facing connection is permitted in current GMSE design practice (AASHTO 2012); however, a check of the frictional connection strength between the facing element and the reinforcement is required. The connection strength must be greater than the maximum factored tension on the reinforcement due to the thrust against the face. This GMSE design requirement was first recommended by an industry-wide group; however, it was not based on theoretical calculations (Soong and Koerner 1997). Based on previous frictional connection testing at Turner-Fairbank Highway Research Center between hollow core CMU blocks and 70 kN/m PP geotextile, the interface friction angle is approximately 38 degrees, for a frictional coefficient of 0.78 (Nicks et al. 2013b). The ultimate connection strength under no additional applied normal load is 2.3 kN/m, and the maximum connection strength at the base of the wall, with the most applied normal load from the weight of the facing above, is approximately 15 kN/m. Without any reduction for long-term strength loss, the reinforcement loads calculated would exceed the connection strength if following GMSE design to a depth of 2 m below the top of the wall (Fig. 3). Using the default reduction factors from GEC-11 (Berg et al. 2009), the long-term connection strength never exceeds the connection load. With the purely frictional connection method successfully used on numerous in-service GRS walls and abutments constructed for more than 20 years, it is clear that the GMSE design for connection is flawed when reinforcement spacing is less than 0.3m. For closely spaced GRS, the thrust at the face is not equal to the internal lateral stress, as assumed in MSE wall design. Soong and Koerner (1997) and Wu (2007) conclude that the pressure at the face develops independently between each reinforcement layer and surcharge does not transfer to the face. Wu (2001) proposed that this distribution between closely spaced layers is based on the concept of bin pressure for frictionally connection segmental facing. The connection load assuming bin pressure is equal to about 0.1 kN/m, constant throughout the depth of the wall, which is well below the short- and long-term connection strength for the purely frictional connection. Because of the issues associated with the use of purely frictional connections in GMSE design (AASTHO 2012), positive connections are required between the blocks and geosynthetic. In the Founders/Meadows bridge project, the maximum lateral stress was estimated at 55.5 kPa, assuming a Ranking distribution and 34 degree friction angle, located at the base of the wall (Abu-Hejleh et al. 2000). Multiplying this by the reinforcement spacing (0.4 m), the maximum estimated connection load is 22.2 kN/m, meaning the long-term connection strength must be at least that value. This requires a high-strength material, explaining the large difference in reinforcement strength requirements between the design methods. Note that to reduce connection loads near the top of the wall, the footing was embedded. Once footing

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embedment was needed, approach slabs were then required to transition the bridge and approach (AASHTO 2012). This adds enormous costs and is not needed if using close reinforcement spacing and GRS design.

Figure 3. Estimated Connection Strength Requirements

2.3.8 Step 8-9: Implement Design Details and Finalize Material Quantities and Layout The last steps to GRS design are to finalize the layout for ease of construction, drainage, and other considerations that might affect the performance, serviceability, or efficiency of design (Adams et al. 2011). Design of other features, such as scour countermeasures, guardrails, and the GRS integrated approach behind the backwall is needed. Quantities should also be determined, and may impact the reinforcement schedule based on typical roll widths. 2.4 Design Example Summary After following the steps outlined above for GRS design, the final result can be evaluated and compared to the actual case history for Founders/Meadows (Fig. 4, Table 2). While the frequency of reinforcement is greater, the embedment lengths are smaller (i.e. reduced excavation), the footing width is almost cut in half, the bridge loads are increased, no embedment is required (i.e. no need for approach slabs, sleeper slabs, etc.), and the required strength of the reinforcement is reduced. Quantifying the difference in costs between the two design methodologies for this comparison is difficult; however, the volume of excavation, reinforced backfill, concrete for the superstructure are considerably less for GRS, as shown in Figs. 2 and 4. Additional savings is also offered considering the generic components GRS system.

Table 2. Comparison of Founders/Meadows GRS and GMSE Designs.

Parameter Symbol Units GRS GMSE

Reinforcement Spacing Sv m 0.2 0.4 Reinforcement Strength

1

Strength Reduction Factor2

Tf

RFglobal kN/m -

70 3.5

157.3 5.82

Base Embedment Length B m 2.4 8 Base to Height Ratio B/H - 0.4 1.3 Setback Distance

3 a m 0.2 1.35

Footing Width Footing Length Footing Embedment Depth

4

Footing Surcharge5

Live Load Surcharge6

Backfill Friction Angle7

b L d qt qLL

φ

m m m kPa kPa deg

2.0 34.5 0 120 67 48

3.81 34.5 0.76 115 35 34

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Figure 4. GRS Design of the Founders/Meadows Bridge (units are m) 3. CONCLUSIONS

To fully evaluate the design of GMSE and GRS designs, the entire process must be completed. Focus on one aspect of the design does not provide the entire picture. Through evaluation of the Founders/Meadows Bridge case history, it was found that considerable savings can be made by using GRS design (Adams et al. 2011) rather than using GMSE, in which reinforcement spacing can be proportionally changed the with reinforcement strength, thus making it more advantageous to design with larger spacing. As discussed above, the composite behavior achieved with close spacing supports the need to have a different method. A review of the differences in the design procedures is shown in Table 3.

Table 3. Comparison summary between GRS and GMSE design methods.

Parameter Symbol GRS (Adams et al. 2011)

GMSE (AASHTO 2012)

Reinforcement Spacing Sv ≤ 0.3 m ≤ 0.8 m Base Embedment Length Backfill Friction Angle Bearing Resistance Vertical Deformation Lateral Deformation Reinforcement Rupture

B

φ qult DV

DL

Treq

≥ 0.3H or 1.8 m ≥ 38 deg Empirically, or Eq. 1 Empirically, or 10% of Eq. 1 Eq. 2 Eq. 3 and Eq. 4

≥ 6.7 m ≤ 40 deg No method provided. No method provided. No method provided. Eq. 5 and Eq. 6

Reinforcement Pullout Connection Strength Limiting Eccentricity

- - -

No criterion. No criterion. No criterion.

Required. Required. Required.

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