Synthesis and Evaluation of The Service Limit State of Engineered Fills for Bridge Support

CHAPTER 5.
NUMERICAL AND CONSTITUTIVE MODELS FOR COMPACTED FILL AND REINFORCED SOIL FOR BRIDGE SUPPORTS

5.1 Modeling of Compacted Soils

Various constitutive models have been utilized to model compacted soils, such as the linear elastic model, elastic-plastic Mohr-Coulomb model, hyperbolic stress-strain models, modified Cam Clay model, elastic-plastic viscoplastic models, extended two-invariant geologic cap model, and generalized plasticity models. (See references 121, 72, 122–128, 74, 129–135, 70, and 136.) An excellent review of the capabilities and shortcomings of different soil constitutive models can be found in Lade’s publication, “Overview of Constitutive Models for Soils.”⁽¹³⁷⁾ The soils can be any type: plastic or non-plastic, open-graded or well-graded, and coarse-grained or fine-grained, if appropriate models with appropriate input parameters are used.

Assignment of reasonable values for parameters used in soil constitutive models greatly influences the success and accuracy of any numerical analysis. For simple soil constitutive models, material parameters are often readily available from routine laboratory tests; however, that is not always the case for advanced constitutive models and precise identification of parameter values imposes a significant challenge. The effect of constitutive models on simulated responses of GRS structures has been investigated. Hatami and Bathurst compared the results of finite difference analyses (using FLAC2D™) for GRS SRWs with measured results from physical tests.⁽⁷¹⁾ They modeled compacted fill soil using the hyperbolic stress-strain model proposed by Duncan et al. combined with a Mohr-Coulomb failure criterion and the simple linear elastic-plastic Mohr-Coulomb model.⁽¹³⁸⁾ The simple elastic-plastic soil model was shown to be sufficient for predicting wall deformation, footing reaction response, and peak strain values in reinforcement layers for strains of less than 1.5 percent if appropriate values for the constant elastic modulus and Poisson’s ratio for the sand backfill soil are used. However, it is problematic to select a suitable single-value elastic modulus given the stress level dependency of granular soils. Different trends in the distribution of strains were observed when the nonlinear and linear elastic–plastic soil models were used, with the former giving a better fit to the measured data.

Huang et al. employed three well-known constitutive soil models in finite difference analyses (using FLAC2D™) of two instrumented reinforced soil segmental walls reported by Hatami and Bathurst.^(139,71,118) These models (in order of increasing complexity) are the linear elastic-plastic Mohr-Coulomb model, the Duncan-Chang hyperbolic model with a modification by Boscardin et al., and Lade’s single hardening constitutive model for frictional soils. (See references 138 and 140–143.) The modified Duncan-Chang model accounts for plane strain condition in addition to the triaxial condition considered in the original version of the model.^(138,71) Lade’s model considers a single yield surface and can capture both work-hardening and softening for frictional geomaterials.^(141–143) Major advantages of such a model lies in the fact that the effects of stress-dependent stiffness, shear dilatancy, and strain softening on soil mechanical behavior are accounted for. Moreover, the effects of plane strain conditions are explicitly accounted for within this model, and no empirical adjustment, as done for the modified Duncan-Chang model, is required to increase elastic modulus values from triaxial test results. On the downside, several model parameters lack physical meaning, and thus application of this model demands significant expertise in interpreting available test results, calibration of model parameters using element test results, and assignment of correct values for the model parameters. Predictions from analyses using the considered soil constitutive models were within measurement accuracy for the end-of-construction and surcharge load levels corresponding to working stress conditions. The elastic-plastic Mohr-Coulomb model was reported to be best suited for the analysis of reinforced soil walls that are at incipient collapse than for the working stress conditions. The modified Duncan-Chang model with plane strain boundary condition was reported to be a better candidate considering an optimal balance between prediction accuracy and availability of parameters from conventional triaxial compression tests.

Helwany et al. used a cap plasticity model to represent soil constitutive behavior in plane strain FEAs (using finite element (FE) code DYNA3D, an older version of LS-DYNA) of full-scale GRS bridge abutment testing.^(70,144) Drucker and Prager yield criterion is used in association with a strain hardening elliptic cap model.^(145,146) Such a model is capable of accounting for the effects of stress history, loading path, and intermediate principal stress on mechanical behavior of soil.⁽¹⁴⁷⁾ However, a two-invariant based model, such as the one used by Helwany et al. cannot capture dilatancy and anisotropy (stress-induced and fabric).⁽⁷⁰⁾ Recently, Wu et al. conducted two-dimensional numerical analyses using PLAXIS to simulate laboratory-scale GSGC tests that aimed to investigate the performance of GRS masses with different reinforcing conditions.⁽⁷⁴⁾ In the numerical analyses, the compacted soil was modeled using a hardening soil model, the reinforcement was modeled as a linear elastic material with an ultimate T_f, and sequential placement of reinforcements and compaction-induced stresses were considered. The FE results were in good agreement with laboratory test results. The FEAs demonstrated that the presence of geosynthetic reinforcement had a tendency to suppress dilation of the surrounding soil, which was potentially due to increased confinement provided by the embedded reinforcement layers and, thus, reduced the angle of dilation of the soil mass. Soil dilation is an important mechanism that controls the efficiency of load transfer from the reinforcement to the soil during shear deformations in reinforced soil structures.⁽¹⁴⁸⁾ The dilation behavior offers a new explanation of the reinforcing mechanism, and the angle of dilation provides a quantitative measure of the degree of reinforcing effect of a GRS mass.

In summary, past research studies have shown that various constitutive behaviors of compacted fill play an important role in the response of structures founded on engineered fills, which may manifest at different strain levels. For example, the strain-softening behavior may be important for pullout conditions but negligible for working conditions and SLS conditions with small allowable strains. The effect of strain hardening and dilation at SLS conditions may or may not be significant and warrants additional investigation. Although constitutive models that are capable of producing nonlinear stress-strain behaviors have shown to be more advantageous, simple linear elastic-plastic models may be sufficient for predicting the deformation of engineered fills and strains in reinforcement layers for working conditions and SLS conditions if appropriate model parameters are used.

5.2 Modeling Reinforced Soil as a Single Composite Material

In early numerical analyses of reinforced soils, the reinforcement and its surrounding soil are modeled as a single composite material.^(149–151) In this approach, it is assumed that: (1) the friction between reinforcements and compacted soil is large enough so that there is no relative displacement between the two materials, and (2) the strain of compacted soil in the horizontal direction is equal to that of the reinforcements. The assumptions behind this approach, however, may not be valid for SLS, where slippage between reinforcement and soil may not be negligible.⁽¹¹⁸⁾ In recent numerical analyses, the reinforcement and surrounding compacted soil are hence modeled separately.

5.3 Modeling of Reinforcements

Geosynthetic or metallic reinforcements are often modeled as a linear elastic material. (See references 72, 74, 121, 123, 124, 127, 128, 131, 132, and 152–155.) This treatment is considered sufficient as the stress and strain levels in working condition are generally low. In FE models, reinforcements are often modeled as slender objects (e.g., cable element) with a normal stiffness but with no bending stiffness.⁽¹²⁴⁾ This simplification is generally valid.⁽¹⁵⁶⁾

The nonlinear stress-strain behavior of geosynthetic reinforcement has been considered. Ling et al. modeled the geosynthetic reinforcement as a nonlinear material, having developed a hyperbolic load-strain relationship.^(157,158) Using their FEM model, Ling et al. simulated the construction response of a GRS retaining wall with a concrete-block facing.⁽¹⁵⁷⁾ Comparisons between measured and predicted behavior were presented for the wall deformation, vertical and lateral stresses, and strains in the geogrid layers. Satisfactory agreement between the measured and predicted results was observed. Under the working condition, however, the strains in the geogrid layers were small (less than 1 percent); hence, the geogrid essentially behaved as a linear elastic material. Fakharian and Attar simulated the well-instrumented Founders/Meadows segmental GRS bridge abutment near Denver, CO, where the geosynthetic reinforcement was modeled using elastic-plastic cable elements in FLAC 2D.⁽¹³⁴⁾ Satisfactory agreement was observed between the simulated and recorded facing displacement, vertical earth pressures, and geogrid strains. They observed that the maximum horizontal displacement of the facing due to deck load for the bridge abutment occurred at an elevation equivalent to 60 percent of the height of the front face of the abutment. They also observed that the geogrid experienced small strains (less than 1 percent) under the working condition.

For some cases, time-dependent behaviors of reinforcements could be important. For example, secondary settlement behavior has recently been observed in experimental studies on foundations supported by GRS.^(21,27) Hence, it is important that time-dependent behaviors (e.g., creep) of geosynthetic reinforcements are accounted for in the modeling of GRS. For example, Sharma et al. modeled the reduction of linear elastic stiffness values with time based on the results of creep tests.⁽¹⁵⁹⁾ Lopes et al. simulated the load-strain-time response of an instrumented sloped reinforced wall by using a viscoelastic creep model.⁽¹⁶⁰⁾ Karpurapu and Bathurst modeled both the nonlinear load–strain and time-dependent responses of a polymeric geogrid using a parabolic load–strain model fitted to the results of creep tests.⁽¹²⁹⁾ The geosynthetic reinforcements were recently modeled using an elastic-viscoplastic bounding surface model to investigate the long-term performance of GRS structures.^(135,161) Kongkitkul et al. presented an elastic-viscoplastic model that describes rate-dependent load-strain behavior of polymer geosynthetic materials.⁽¹⁶²⁾ The constitutive model is comprised of three components: a hypo-elastic component, a nonlinear inviscid component, and a nonlinear viscous component. Omission of one or more nonlinear components in this model yields the nonlinear elastic-plastic or hypo-elastic models, which are rather common in literature.

In summary, past research has shown that for reinforced soils, it is reasonable to model the reinforcements as linear elastic materials under working conditions because the strains developed in the reinforcements are generally small. The effect of nonlinear and time-dependent stress-strain behaviors of reinforcements, particularly geosynthetic reinforcements, on engineered fills at SLS and long term conditions is relatively unknown and warrants additional research.

5.4 Modeling of Soil-Reinforcement Interactions

Several research studies have investigated soil-reinforcement interactions using analytical and numerical methods. (See references 153 and 163–170.) Palmeira provides a comprehensive summary of different experiments and theoretical models used to evaluate soil-geosynthetics interactions under different loading and boundary conditions.⁽¹⁷¹⁾ Common numerical analyses (mostly using FE or finite difference scheme) of GRS structures and foundations on reinforced soil usually idealize geogrid layers as equivalent planar reinforcement layers with frictional characteristics. The geometric shape of the geogrid layer, particularly the presence or absence of transverse reinforcement, and bending stiffness are often ignored. Although these simplifications may not be valid under pullout loading conditions, they are generally valid under working conditions and, likely, SLS conditions.^(172,173)

The basic differences between metal and geosynthetic reinforcement are their stiffness, structures, and the interactions occurring at the reinforcement-soil interfaces.⁽¹¹⁵⁾ Metal reinforcement is usually in the form of straps or mats, whereas geosynthetic reinforcement is usually in the form of grids or planar sheets. The planar structure and flexibility of geosynthetics enable the shear forces inside the soil mass to be transferred to geosynthetic reinforcement more uniformly and without interruptions. Metal reinforcements usually have smooth surfaces; whereas most geosynthetics have fabric-like surfaces (geotextiles) or grid structures (geogrids), which produce better soil-reinforcement bonding. Consequently, slippage occurs at the interface between soil and metal reinforcement, but in GRSs, the slippage surfaces were observed to occur inside the soil mass next to the reinforcement.⁽¹⁷⁴⁾ Many of the modeling techniques for soil-geosynthetic interactions are also applicable to the interaction between soil and metallic reinforcements after adjustments to model parameters accounting for the aforementioned differences.

In most of the earlier FEM simulations of GRS, the soil-reinforcement interface behavior was modeled by using interface elements, such as joint elements of zero or non-zero thickness and node compatibility spring elements. (See references 129, 131, 133, and 175–186.) In this approach, the interface elements were formulated as a stiff spring in each of the shear and normal directions until slip occurred, at which point deformation could occur along the interface according to a Mohr-Coulomb failure criterion. (See references 72, 122, 128, and 135.) This approach also enables the specification of a decreased interface friction compared to the friction of the soil to model residual friction at the soil-reinforcement interface.^(127,130) However, this approach involves assumption of horizontal and vertical stiffness values for the interface elements that are difficult to determine experimentally.⁽¹²¹⁾ In 3D FEAs of a square footing bearing on reinforced sand, Kurian et al. employed 3D interface elements with zero thickness and with shear stiffness following a hyperbolic relation.^(152,187) Penalty-type interface elements that allow sliding, friction, and separation facilitate modeling of interfaces between any two dissimilar materials have also been used in FE modeling of GRS structures and foundations bearing on reinforced soil.^(70,134) More recently, the soil-reinforcement interface behavior has been modeled using contact algorisms without assuming the contact stiffness values.⁽¹²¹⁾

5.5 Numerical Modeling of Structures Supported by Engineered Soils

Most numerical models discussed previously were utilized to conduct parametric studies to investigate the effect of various parameters such as geometry and arrangement of reinforcement and soil properties on the response of structures supported by engineered soils. Few of these models have been validated against large-scale physical tests, and they are discussed in this section.

Karpurapu and Bathurst modeled the behavior of two carefully constructed and monitored large-scale GRS retaining walls (9.84 ft (3 m) high).⁽¹²⁹⁾ The walls were constructed using a dense sand fill and layers of geosynthetic reinforcement attached to two different facing treatments: an incremental panel wall versus a full height panel wall. The model walls were taken to collapse using a series of uniform surcharge loads applied at the sand fill surface. To model the GRS retaining wall, a modified form of hyperbolic stress-strain model was used to model the backfill soil. A nonlinear equation developed from isochronous load-strain-time test data was used to model the reinforcement, and the soil-reinforcement interface was modeled using joint elements of zero thickness.⁽¹³⁸⁾ To investigate the effect of soil dilation on GRS wall performance, two sets of numerical analyses were performed: one set with a soil dilation angle of 0 degrees and the other using a value of 15 degrees based on laboratory direct shear test results. The numerical analyses with no dilation were shown to have predicted much greater panel displacements and larger reinforcement strains. In some cases, the over-prediction was greater than measured values even at working load conditions by a factor of 2; whereas the numerical analyses with 15-degree soil dilation accurately predicted panel displacements and reinforcement strains. The results of their numerical study indicate that it is possible to accurately simulate all significant performance features of GRS walls at both working load and collapse conditions, and it is important to properly model facing treatment and consider soil dilation in the behaviors of GRS walls even at working load conditions.

Holtz and Lee developed FLAC2D™ models to simulate six case histories, including the WSDOT geotextile wall (41.34 ft (12.6 m) high) in Seattle, WA, and five of the test walls (20.01 ft (6.1 m) high) constructed at the FHWA reinforced soil project site in Algonquin, IL.^(120,188) The reinforcements for these walls included woven and nonwoven geotextiles, geogrids, steel strips, and steel bar mats. In these models, the compacted soil was modeled using a nonlinear elastic-plastic Mohr-Coulomb model with a hyperbolic stress-strain relationship, and the reinforcements were modeled as linear elastic materials with tensile and compressive strength. It was assumed that no slippage occurred between the soil and geosynthetic reinforcements, and interface elements were used to model the interaction between different materials or the discontinuities between the same materials, such as interfaces between backfill soil and structural facing and interfaces between structural facing units. Construction consequence of the walls was modeled by applying a uniform vertical stress equivalent to the overburden stress from each lift to the entire surface of each new soil layer before solving the model to equilibrium. Results of this study confirmed that the developed models were able to provide reasonable working strain information of GRS walls. ⁽¹²⁰⁾ However, accurate material properties were the key to a successful performance modeling of GRS walls.

Hatami and Bathurst conducted numerical modeling of four full-scale reinforced-soil SRWs (11.81 ft (3.6 m) high) using FLAC2D™.⁽¹¹⁸⁾ The reinforcements for these walls included PP geogrid, PET geogrid, and WWM. In their model, the compacted soil was modeled using a nonlinear elastic-plastic model with a Mohr-Coulomb failure criterion and a dilation angle.⁽¹⁸⁹⁾ Compaction-induced stresses in the segmental walls were modeled by applying a transient uniform vertical pressure to the backfill surface at each stage during the simulation of wall construction. The effect of compaction on the reduction of fill Poisson’s ratio was modeled by adjusting soil model parameters from triaxial and plane strain tests to ensure reasonably low values of Poisson’s ratio. These modeling techniques were shown to have greatly improved the match between measured and predicted features. Results of this study showed that it is important to include compaction effects in the simulations in order to accurately model the construction and surcharge loading response of the reinforced soil walls. Comparison of predicted and measured results also suggested that the assumption of a perfect bond between the reinforcement and the soil may not be valid. In a follow up study, Hatami and Bathurst investigated the influence of backfill material type on the performance of soil-reinforced walls under working stress condition.⁽¹⁹⁰⁾ It was concluded that the addition of a small amount of cohesive strength can significantly reduce wall lateral displacements in case of negligible relative displacement between reinforcement and backfill soil.

Helwany et al. conducted a numerical study on the effects of backfill on the performance of GRS retaining walls.⁽⁷³⁾ In their numerical model, the backfill soil was modeled using the modified hyperbolic model, and the reinforcement was modeled as linear elastic.⁽¹³⁸⁾ Their numerical model was validated by comparing the results with the measurements from a well-instrumented large-scale laboratory test conducted on a GRS retaining wall (9.84 ft (3 m) high) under well-controlled test conditions.⁽¹⁹¹⁾ The validated model was then utilized to conduct a parametric study on the effects of backfill on the performance of GRS retaining walls. It was shown that the stiffness of the geosynthetic reinforcement had a considerable effect of the behavior of the GRS retaining wall when the stiffness and shear strength of the backfill were relatively low.

Ling et al. simulated the performance of a full-scale instrumented GRS retaining wall (16.40 ft (5 m) high) using an FEM model.⁽¹⁵⁸⁾ The retaining wall was backfilled with a volcanic ash clay reinforced with a woven-nonwoven geotextile, and details of the test conditions were provided by Murata et al.⁽¹⁹²⁾ In the FEM model, the backfill soil was modeled as a Hookean material, the geotextile was modeled as having a hyperbolic stress-strain relationship, and no slippage was allowed at the soil-reinforcement interface. Compaction stresses induced during construction were not accounted for in the model. Results of their study indicated that the FEM model was able to capture the overall behavior of the retaining wall. The results showed that the GRS retaining wall performed as an integrated system, with the facing, geosynthetic and backfill soil interacting with each other to facilitate stress transfer and thus minimized deformation. It was also shown that stiffness values of the facing and reinforcements played equally important roles in the performance of GRS walls.

In a follow-up study, Ling et al. simulated another full-scale instrumented GRS retaining wall (19.68 ft (6 m) high) using an improved FEM model.⁽¹⁵⁷⁾ The retaining wall was backfilled with a silty sand reinforced with a UX geogrid. Details of the test conditions were provided.^(193,194) In the improved FEM model, the backfilled soil was modeled using a nonlinear hyperbolic model, the geogrid was modeled as a having a hyperbolic stress-strain relationship, and the interface behaviors were modeled using interface elements allowing slippage.⁽¹³⁸⁾ The results indicate that the FEM model predictions matched the measured results in terms of wall deformation, vertical and lateral stress, and strains in the geogrid layers.

Rowe and Skinner modeled the performance of a full-scale GRS retaining wall (26.25 ft (8 m) high) constructed on a layered soil foundation.⁽¹²²⁾ The foundation consisted of a 2.62-ft (0.8-m) hard crust underlain by 9.68 ft (2.95 m) of soft loam (sandy/silty) and then 4.26 ft (1.3 m) of stiff clay. Below the clay was 5.74 ft (1.75 m) of fine sand underlain by a layer of clayey/fine sand extending to a depth below 32.80 ft (10 m). The wall was constructed with 16 segmented concrete facing blocks, a sandy backfill material with 30 percent fines, and 11 layers of geogrid reinforcement 19.68 ft (6 m) long. In the FEM model, the backfill and foundation soils were modeled using an elastic-plastic model with a Mohr-Coulomb failure criterion, the geogrid was modeled as linear elastic, and the soil-reinforcement interface was modeled using interface elements. Compaction stresses induced during construction were not accounted for in the model. It was observed that the predicted behavior compared reasonably well with the observed behavior of the full-scale wall. The numerical results indicate that for the case of a GRS wall constructed on a yielding foundation, the stiffness and strength of the foundation can have a significant effect on the wall’s behavior. A highly compressible and weak foundation layer can significantly increase the deformations at the wall’s face and base and the strains in the reinforcement layers. It is interesting to note that trial analyses (with and without considering dilation) performed during this study did not exhibit any significant effects of dilation on analyses results except for a small difference in the vertical stress at the toe of the wall.

Helwany et al. simulated the behavior of full-scale GRS bridge abutment (15.25 ft (4.65 m) high) using LS-DYNA (formerly known as DYNA3D).⁽⁷⁰⁾ The backfill soil was simulated utilizing an extended two-invariant geologic cap model, and the geosynthetic reinforcement was modeled as an isotropic elastic-plastic material. The FEAs show that the performance of a GRS abutment, resulting from complex interaction among the various components, subjected to a service load or a limiting failure load can be simulated in a reasonably accurate manner. This numerical investigation also showed that the performance of GRS bridge abutments is greatly affected by the soil placement conditions (signified by the friction angle of the compacted soil), reinforcement stiffness, and reinforcement spacing.

The numerical studies presented show that numerical models can realistically model the mechanical behavior of soil-geosynthetic composite and capture the performance features of GRS walls, such as the wall deformation, vertical and lateral stress, and strains in the geogrid layers, at both working load and collapse conditions. These studies have highlighted the importance of properly modeling complex constitutive behaviors of compacted fill and foundation soil (e.g., soil dilatancy and softening at large displacement), stress-strain relationship of reinforcements, and sequential construction and compaction-induced stresses. However, no numerical studies have been conducted to investigate the SLS of structures supported by engineered soil.

5.6 Numerical Modeling of Long-Term Behavior of GRS Structures

Although past studies have produced reasonable solutions, particularly when the material model parameters were calibrated to fit model-scale test results, to understand short-term (immediately after load placement) load-settlement behavior of shallow foundations bearing on GRS, few of these studies could account for time-dependent secondary deformation (settlement) behavior of foundations under service load. Such secondary settlement behavior has recently been observed in experimental studies, and it is important that such deformation is accounted for in calculation of total foundation settlement.^(21,27) Moreover, it is also important to understand the stress distribution profile below the footing on reinforced ground. Such understanding will further facilitate economic design by restricting fill placement only down to the zone of influence below the foundation. Several numerical studies on long-term behavior of GRS structures are summarized in this section.

Helwany and Wu developed a numerical model for analyzing long-term performance of GRS structures.⁽¹⁹⁵⁾ In their model, compacted soil was modeled using an anisotropic extension of the Cam-clay model, which is capable of describing the effects of stress anisotropy, stress reorientation, and creep of normally consolidated and lightly overconsolidated clays. A generalized geosynthetic creep model developed by Helwany and Wu was used to simulate time-dependent behavior of the geosynthetic reinforcement.⁽¹⁹⁵⁾ It was assumed that slippage did not occur at the soil-geosynthetic interface under service loads, which was generally valid for extensible geosynthetic reinforcement. This investigation clearly demonstrates that the time-dependent deformation behavior of the confining soil played an important role in the long-term creep behavior of GRS structures. Hence, a rational design of GRS structures must account for the long-term soil-geosynthetic interaction.

Liu and Won and Liu et al. modeled the long-term behavior of GRS retaining walls with different backfill soils.^(186,135) According to Liu and Won, the backfill soil was assumed to be time independent and modeled using a generalized plasticity model for sand, the reinforcement was modeled using the elastic-plastic viscoplastic bounding surface model for geosynthetics, and the soil-reinforcement interface was modeled using interface elements. (See references 186, 136, 161, and 196.) According to Liu et al., the backfill soil was modeled as time dependent using an elastic-plastic viscoplastic model obeying Drucker-Prager yield criterion and Singh-Mitchell creep model but with nonlinear elastic properties.⁽¹³⁵⁾ The reinforcement and soil-reinforcement interface were modeled in the same way as Liu and Won.⁽¹⁸⁶⁾ In both studies, the numerical models were validated using the experimental results of a long-term PT on sand-geosynthetic composite reported in Helwany and Wu and Helwany.^(197,198)

Liu and Won and Liu et al. demonstrated that the load distribution in backfill soil and reinforcement depended on their time-dependent properties, which determine the long-term performance of GRS walls.^(186,135) It was shown that large soil creep can lead to a significant increase in both wall displacement and reinforcement load. Conversely, if soil creep is smaller than reinforcement creep, reinforcement load would decrease due to load relaxation, but the soil stress could increase significantly. This indicates that backfill soil must have adequate strength to compensate the long-term reduction of load carried by reinforcement due to load relaxation. The results of these studies indicate that in the design of GRS structures, it is necessary to take into account the relative creep rate of reinforcement and backfill soil, especially if backfill soil with high cohesive fines contents is used.

Past numerical studies have shown that the creep deformation of a GRS wall is a result of soil-geosynthetic interaction. The creep rate of the geosynthetic reinforcement may accelerate or decrease depending on the relative creep rate between the backfill and geosynthetic reinforcement.⁽¹⁹⁹⁾ For a GRS structure with a well-compacted granular backfill, the time-dependent deformation is small and the rate of deformation of the soil-geosynthetic composite typically decreases rapidly with time.⁽¹⁹⁹⁾ Hence, creep deformation of geosynthetic reinforcement in a GRS structure may or may not be a design issue, depending on the soil-geosynthetic interaction. It should be noted that no numerical studies have been conducted to investigate the long-term deformation of GRS walls supported by reinforced soil.

5.7 Similarities and Differences Between Pier and Abutment Foundation Deformation Models

In common transportation engineering practice, deep foundations are frequently used to support lateral and vertical loads at pier and abutment locations for bridges. However, recent research shows that spread footings, if analyzed and designed adequately, can be an economic option for bridge support.⁽²⁰⁰⁾ Although shallow foundations may provide a viable alternative in terms of their capacity to support structural load, their use is often restricted to avoid excessive settlement at bridge foundation locations. Nonetheless, settlement calculations and the serviceability limit state criteria set to check the calculated settlement are often overly conservative in terms of actual load-settlement response of shallow spread footings bearing on compacted, reinforced or unreinforced engineered fills and the tolerable movement criteria used to design them. While similar foundation-soil load transfer mechanisms can be expected, for a given bearing stratum (i.e., engineered fills with or without embedded reinforcement layers) at both pier and abutment locations, the load-deformation behavior is expected to vary at these locations. The major difference would arise from the 3D (close or similar to a triaxial condition) stress state existing below square, rectangular, and circular spread footings when compared to a confined plane strain condition (i.e., strain in the out-of-the plane direction is zero) strain existing at the abutment locations.

Dimensions of shallow foundation affect bearing capacity and load-displacement behavior on granular soil.⁽²⁰¹⁾ Fakher and Jones point out that the foundation dimension effects should be studied in order to critically judge the behavior of foundations on reinforced soil and that the role of reinforcement in enhancing foundation performance might be misjudged without the consideration of such effect.⁽²⁰²⁾ Based on results of FE simulations, Chen and Abu-Farsakh show that foundation dimension effects became negligible when reinforcement depth ratio (i.e., ratio of total reinforcement depth to foundation width) and reinforcement ratio (E_RA_r/E_sA_s; where A_r and A_s are area of reinforcement and reinforced soil per unit width, respectively) remains constant.⁽¹⁵⁴⁾ Such a conclusion is valid for design for ULS (e.g., bearing capacity of foundation) with a specified relative settlement (i.e., ratio of settlement and characteristic width of a foundation) criterion. However, for serviceability limit state design based on absolute values of foundation settlement, dimensions of shallow foundations are expected to play a major role in SLS.

Apart from the difference in bearing capacity failure mechanism under the above stated conditions, an additional difference is expected to arise from state-dependent strength behavior of compacted granular fill material and placement conditions; a reflection of this would be through different degrees of dilation for the same compacted density.^(70,203) Such differences in strength-deformation behavior are likely to change the load-deformation behavior of shallow foundations at pier bents and the compacted fill at abutment locations. Another key difference might arise from the load eccentricity caused by the combined loading and the ratio of lateral to vertical loading. Load eccentricity may have a larger impact on lateral and vertical movements of spread footings below bridge piers when compared to its effect in controlling movements at abutment support locations.