Geosynthetics 2015 February 15-18, Portland, Oregon

Analytic Approach for Design of Reinforced Soil Bridge Pier on

Reinforced Soil Pads over Weaker Soils

V.K. Tyagi, Hi-Tech Geosynthtics Pvt. Ltd, India, vipkolon@yahoo.com

ABSTRACT Application of geosynthetic reinforced structures (GRS) in the construction of bridge piers and abutments over reinforced

foundation pads (RSF) has been demonstrated in several full-scale case histories. Further, the behavior of RSF

supporting GSF constructed over weak cohesive frictional fills has been demonstrated by conducting full scale load tests.

In these applications, the behavior of GRS and RSF have been comprehensively investigated through field monitoring

which has indicated that these systems satisfy the serviceability requirements prescribed by international codes. However,

the only analyses approaches to evaluate these systems involve numerical and physical modeling. To address this issue,

this paper presents analytic method based on limit equilibrium principles to help design theses systems.

1. INTRODUCTION

The effect of replacing existing low frictional fill soil by higher frictional fill is taken into consideration using enhanced bearing capacity coefficients in the bearing capacity analysis (Giroud and Noiray 1981). The German code on geosynthetic structures (EBGEO) recommends that if particular stringent demands are made on the deformation behavior of structure subjected to heavy loads and empirical data of past projects is very less, then Geotechnical Category – 3 (GC-3) case is applicable. These results should be verified by proper instrumented modeling and it is also important that results are checked with numerical analysis for plausibility. As per table 3.2, page 37 of EBGEO (2011), any bridge abutment/pier structure having height > 2m will come in GC-3 category. Limit equilibrium analysis of reinforced pad is appropriate for ultimate limit analysis for evaluating bearing capacity failure, external stability like sliding, overturning, pullout failure, global stability and strength of reinforcement. Yet it is unable to predict the serviceability state properly at functional stresses which is very important for GC-3 structures. The analytical method adopted by EBGEO applies to sheet reinforcements like geogrid or geotextile and not to three dimensional geosynthetics like geocells. Thus it becomes difficult to formulate mathematical forms in case of heterogeneous medium comprising of multiple geosynthetics. However empirical results obtained from physical and numerical modeling on multiple geosynthetics can be converted into graphs and tables and formulae can also be developed using regression methods in case of greater correlations. Guido et al. (1985) performed a series of laboratory model tests on rectangular and square footing. They indicated that bearing capacity ratio (BCR) at a settlement of 0.1B increases rapidly with increasing strip length up to a length of about 0.7B after which it remains relatively constant. Omar et al. (1993) conducted laboratory tests for the ultimate bearing capacity of strip and square foundations on sand reinforced with geogrid layers. From this experiment, they have drawn conclusions that for development of maximum bearing capacity, the effective depth of reinforcement is 2B for strip footings and 1.4B for square footings. Further they have observed that maximum width of reinforcement layers for optimum mobilization of maximum bearing capacity ratio is 8B for strip footings and 4.5B for square footings. Dash et al. (2001) have presented the laboratory test results of strip footings on geocell reinforced sand beds with additional planar reinforcement. Shin et al. (2000) have done laboratory test to determine the bearing capacity of strip footing supported by sand reinforced with multiple layers of geogrid of one type. The results show that the ratio of the critical depth of reinforcement below the footing w.r.t the width of footing is about 2. For a given reinforcements depth ratio, the BCR w.r.t ultimate load increases with the embedment ratio of the foundation. Dash et al. (2001) presented the results from laboratory model tests on a strip footing supported by sand reinforced with a geocell mattress. The parameters varied in the testing program include pattern of geocell formation, pocket size, height and width of geocell mattress, depth of the top of geocell mattress, tensile stiffness of the geogrids used to fabricate geocell and the relative density of sand. With the provisions of geocell reinforcement, failure is not observed even at a settlement equal to 50% of the footing width and a load as high as 8 times the ultimate bearing capacity of the unreinforced sand. The performance improvement is significant up to a geocell height equal to 2 times the width of the footing. Beyond that height, the improvement is marginal. The optimum width of the geocell layer is around 4 times the footing width at which stage the geocell would intercept all the potential rupture planes formed in the foundation soil. Aigen Zhao (1998) has presented the failure criterion for a reinforced soil composite.

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Figure 1. Cross-section elevation of GRS pier and RSF pad system

The failure criterion of anisotropic reinforced soil presented here is due to inclusion of geosynthetic reinforcement with preferred direction. The slip line method in relation with the derived failure criterion can be used for calculating the failure loads of geosynthetic reinforced soil structures. The inclusion of geosynthetic reinforcement enlarges the plastic failure region in a reinforced soil structure and significantly increases the load bearing capacity. Lopes and Ladeira (1996) have studied the interaction between well-graded gravelly sand and a uniaxial geogrid. The influence of the confinement pressure, soil density and displacement rate on the pull out resistance of the geogrid is discussed by analyzing the results of the pull out tests. The increase in the pull out resistance when the confinement stress increases, yet it is not in proportion to the increase in the normal stress because there is reduction in the adherence factor. Sawicki (1999) has proposed a simple model of the elasto-plastic soil reinforced with the visco-elastic geosynthetics. Two modes of reinforced soil behavior are considered within the framework of mechanics of composite materials. The first mode corresponds to the elastic soil (E-V mode) and the second one to plastic soil (P-V mode). During the E-V mode, the initial stress in reinforcement decreases, causing the regrouping of micro stresses in the soil down to the stage when a yield condition in the soil is reached. Then the P-V mode begins during which the stress in reinforcement remains constant but the macro strains increase due to creep. A method of estimating the initial stresses in rheological soil has been presented. Patra et al. (2005) have performed laboratory tests to determine the ultimate bearing capacity of embedded strip foundation on geogrid reinforced sand. The results have been compared with the bearing capacity theory developed by Huang and Menq (1997). Based on these tests, it was concluded that for the same soil, geogrid and configuration, the ultimate bearing capacity increases with increase in embedment ratio, Df/B. The theoretical relationship for ultimate bearing capacity developed by Huang and Menq (1997) provides somewhat conservative predictions. A prototype full-scale instrumented bridge pier resting over RSF pad was constructed as shown in Fig. 1 and load tested for demonstrating the feasibility of constructing a GRS bridge pier with discrete panels and RSF pad over weaker soils for evaluating the performance of the pier and foundation pad under various loading conditions, including pre-straining/pre-loading . The pier and foundation pad was instrumented to monitor load intensity, lateral deformation and vertical settlement. In this paper, more stress will be laid over the functionality of RSF pad. A numerical simulation was also performed using commercial software – ABAQUS (2012) for comparing the instrumented results with the numerical ones. The basic purpose of this whole exercise was to establish reliability and validity of limit equilibrium methods employed to design these reinforced structures. RSF pads have been analytically designed in detail in EBGEO (German Geotechnical Society 2011) using limit equilibrium method in accordance with DIN 1054, DIN 4017 and DIN 4019. The bearing capacity of RSF pad is evaluated in accordance with DIN 1054 and DIN 4017 and the settlement in accordance with DIN 4019. Limit equilibrium analysis is based on the assumption that the stability of RSF pads can be analyzed using the same failure model as for conventional foundations. This theory is supported by observation on small-scale tests (ZTV E-StB, ZTV SoB-StB). 2. DESIGN PHILOSOPHY

The focus of this study is to advance the state of practice of reinforced soil technology by correlating pilot scale

experimentation, numerical methods with limit equilibrium methods for constructing reinforced foundation pads which are

not normally used in conventional construction of bridge pier and abutment bearing heavy loads. The objective was to

develop empirical methods for design of reinforced pads using composite system of geosynthetics that are able to sustain

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superstructure load on piers within tolerable limits of strength and serviceability during construction phase and after

construction.

2.1 Numerical Modeling Approach

Numerical analysis of the overall structure was performed by analyzing the GRS and RSF pad as an integral structure for

simulating the overall behavior. Geogrids in numerical simulation requires some specific considerations for geometrical

and constitutive modeling taking into account geometric non-linearity and anisotropic behavior of geogrids. The

construction of reinforced foundation pad and geosynthetic reinforced pier is modeled stepwise, in order to simulate the

real construction process. The geogrids follow linear elastic constitutive behavior, while the soil layers are modeled with

more advanced soil models like Hardening Soil (HS) or Hardening Soil with small stiffness (HS –Small). For numerical

simulation of realistic behavior of reinforced soil structures, a suitable formulation for geogrids, an advanced frictional

contact algorithm and sophisticated constitutive modeling of the material are essential. In general FEM softwares, geogrid

layers are usually modeled with 2D-beam model or 3D shell or membrane elements with zero bending stiffness. The

geogrid reinforcement is primary loaded perpendicularly by second order geometric effects (geometric nonlinearity) as

bending stiffness are practically nil. As geogrid is no longer horizontal after load application, tensile strains in geogrid

develop due to vertical loading. Thus geometry of the mesh needs to be uploaded during the stepwise incremental

loading. Thus finite element (FE) analysis with updated Langrage procedure has to be done where stiffness matrix is

updated due to the new geometrical positions of the deformed elements. This FE procedure was adopted as case studies

with 2D FE-models have shown that ignoring of nonlinear effect leads to underestimation of geogrid strains by 20-30%

(Heitz 2006). In most FE analysis geogrids have been treated as flexible elastic elements that represent a grid like

structure. Geogrids have an axial tensional stiffness but almost nil bending stiffness i.e. they can only sustain tensile

forces, but no compression and bending. However in 2D-analysis simulation an elastic material behavior with axial

stiffness EA can not address the anisotropic behavior of biaxial geogrids. In 3D-simulation, the biaxial-anisotropic

(orthotropic) behavior of geogrid can be addressed by use of different axial rigidities e.g. EA1 and EA2. Thus a 3-D shell

element can be used to account for orthotropic behavior. An elastic-plastic constitutive model is often assumed for

interface elements. To distinguish between elastic and plastic material behavior, failure criteria by Mohr-Coulomb is used.

For static loads, single layer reinforced system are often considered to be more effective than multilayered reinforcement.

However, for dynamic loads, multilayered systems are assumed to be more sustainable (Arwanitaki & Triantafyllidis 2006).

In case of analytical methods as derived in EBGEO (2010), validity of membrane theory is assumed and calculated

membrane force is distributed to the geogrid layers according to their characteristic axial rigidity. The results obtained from

analytical methods adopted by EBGEO are on conservative side by 20-25% as non-linear effect is ignored which is

considered in FEM analysis. Thus for layers greater than two layers should be verified by numerical analysis. In case of

loading with eccentricity also, stress distribution due to non-linearity should be cross- verified by numerical methods. In

simple situations, a multiplication factor can be used to get correct values from analytical analysis.

2.2 Analytic Approach Analysis of GRS was in accordance with BS 8006 (2012) for internal and external stability and was then verified by

EBGEO. The results were almost comparable. These results were also verified by commercial software MSEW (3.0)

based on FHWA-NHI-00-043 (2001) along with seismic stability check. The results for external stability under sliding are

more conservative in BS-8006 under load combination B. As analytical methods are limited in considering the complexity

of interaction mechanism, non-linear behavior and prediction of deformations, numerical methods & full scale modeling

can be successfully used to establish correlation factors with analytical formulae. Then analytical methods can be

successfully used in similar situation for superior prediction of behavior of reinforced structure and cost-optimization.

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Figure 2. Prestraining of GSF pier and RSF pad system

3. CONSTRUCTION METHODOLOGY

The pier was supported on reinforced cement concrete (RCC) spread footing as shown in Fig. 2. The size of the footing

could not be beyond a certain limit as there was excessive increase in overall settlement beyond acceptable serviceability

limit. Thus it was decided to adopt reinforced soil pad below RCC footing for reduction of load intensity by providing large

area along with enhancement of bearing capacity as well as reduction in differential and total settlement. The height of the

pier was 5.0 m. The cross-section size of pier was 4m x 4m. The dimensions of RCC spread footing were kept as 5m x 5m

x 1.2m. The cross-section area of (RSF) was kept as 11m x 11m. The depth of the RSF was kept as 1.2m. After

excavation of area for foundation, a fabric separator (Woven Geotextile) was laid along the base and walls of the pit. Basic

function of this fabric separator was to maintain structural integrity of RSF pad. After the excavation of soil, the base of the

pit was compacted. The pit was refilled with granular sub base material ( = 35º, = 20kN/m3) along with layers of

geogrids and geocell as shown in Figure 1. The fill was compacted in 200 mm lifts to achieve 95% proctor density with

three layers of geogrid and one layer of geocell placed 200 mm apart. RSF pad was instrumented with strain gauges,

pressure cells and inclinometers for evaluating the performance of the RSP pad in detail. The GRS pier were constructed

using high strength polyester geogrids and discrete 3D-panels along with corner column junctions. The construction of

GRS pier is not being discussed here in detail as that is not the subject of the paper and its construction is very already

well documented. The GRS pier was pre-strained using hydraulic jacks and a specifically designed reaction system. The

jacks and concrete pads were bolted together with vertical steel rods. After completion of RSF and RCC footing, four

concrete reaction bottom pads were poured over RCC footing. The dimensions of the base pads were 2.50m x 2.50m x

0.3m thick. Four sections of special steel rods of 40 mm were anchored into each pad. Each pad was separated with

thermocol to maintain its independence. Load was measured with load cells and calculated from hydraulic jack pressure.

Load was maintained with an electrical hydraulic pump and strain box indicator connected to load cell. The experiment

ensured that the load is evenly applied over entire area of pier. A pressure transducer was connected to hydraulic line to

monitor jack pressure. The pier was loaded by squeezing the reinforced soil between concrete pads. Displacements were

measured with linear variable displacement transducers (LVDTs), linear potentiometers and mechanical/digital dial

gauges. Vertical settlements were measured from top pads. Lateral displacement was measured along the height of pier

walls. Strain gauges were of high elongation foil types. They were first glued on a heat set non woven fabric piece and

then glued over the geogrids. They were placed @ 0.2m interval in both directions on each layer.

4. NUMERICAL MODELING

The analytical methods proposed by several international codes have been developed based on theoretical and

experimental investigations. Thus these methods may not be completely applicable to all geosynthetic applications due to

variation in geometrical, mechanical, geosynthetic configuration and load. Fig. 3 represents the typical layout of

geosynthetics considered for increase of bearing capacity along with decrease in differential and total settlement.

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Figure 3. Increase in BCR (Bearing Capacity Ratio) by using geosynthetics

Thus it becomes imperative to use numerical modeling for observing the behavior of structure at working stress

conditions, inspecting the complex interaction between geogrids, soil and other rigid structures. It may also help in techno-

commercial optimization of the structure. It is also used as a tool for cross-verification of deformation of overall system

which is significant for such type of high loading structures. The geogrid material model adopted in this case was based on

the test data obtained from physical modeling of the structure which was cross-verified by user-defined model so that it

can be used in future projects without any physical simulation of structure. Geogrid material behavior was considered to

be anisotropic and non-linear, using the parameters listed in Table 1.

Table 1. Finite element material properties

The material model is assumed to be phenomenological as it is presumed to capture the mechanical response of yarns in

both warp and weft directions. It also accounts for non-linearity during the analysis step since it is intended to be finite-

strain approach. It is valid for structural directions not orthogonal to each other with deformation. This model defines the

local geogrid stress as a function of change in angle between the fibers (shear strain) and the normal strains along the

yarn directions. It also allows for the computation of local geogrid stress based on test data or user-defined model. The

geogrid material model defined in test data also assumes that the response along the warp and weft are independent of

each other and that the shear response is independent of the direct response along the yarns of geogrid. This model also

includes separate loading and unloading responses. It is also able to exhibit non-linear elastic behavior, damaged elastic

behavior and elastic-plastic type behavior with permanent deformation upon complete unloading. It is also able to deform

elastically to large tensile and shear strains and can have properties depending on temperatures and other variables.

Polyester (PET) geogrids were used for the project. PE geogrid consists of bundles of high tenacity PET yarns (1000 to

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1500 Deniers) woven at junctions to create a grid like structure. It is further coated with Poly Vinyl Chloride (PVE) material

for durability. The non-linear behavior of geogrids arises from the nonlinear response of individual yarns, the exchange of

crimp between the backfill and the geogrid as they are stretched and the contact and the friction between the yarns in

cross and in same direction. There is also passive resistance offered by transverse portion of grid. In general, geogrid

exhibits a significant stiffness only along the yarn directions under tension. The tensile response in warp and weft

directions may be coupled due to crimp exchange between backfill and geogrid and junctions between them. Under in-

plane shear deformation, the yarns in the warp and weft directions rotate with respect to each other. The resistance

increases with shear deformation as lateral passive resistance is formed between the backfill and yarns in each direction.

There is almost negligible stiffness in bending and in-plane compression. The behavior of geogrids is modeled

phenomenological in ABAQUS/Explicit to capture the non-linear anisotropic behavior. The planar kinematic states of

geogrid is described in terms of nominal direct strains in the geogrid plane and the angle between the warp and weft

direction. The engineering nominal shear strain, 12, is defined as the change in angle, 12, between the two yarn directions

going from referenced to deformed configuration. The nominal strains along the yarn directions n1 and n2 in the deformed

configuration are computed from respective yarn stretch values, 1 and 2. The fabric nominal stress, T, is converted to

the Cauchy stress, , and the subsequent internal forces arising from the fabric deformation are computed. The output of

geogrid nominal strains, geogrid nominal stresses, and the regular Cauchy stresses can be obtained. The relationship

between the Cauchy stress, , and the nominal stress, T, is:

𝐽𝜎 = 𝜆1 𝑇11 𝒏𝟏 𝒏𝟏 + 𝜆2 𝑇22 𝒏𝟐 𝒏𝟐 + 𝑇𝟏𝟐 csc(𝜓12) (𝒏𝟏𝒏𝟐 + 𝒏𝟐𝒏𝟏) − 𝑇12 cot(𝜓12) (𝒏𝟏 𝒏𝟏 + 𝒏𝟐 𝒏𝟐) [1]

where J is the volumetric Jacobian. The non-linear behavior of geocell arises from the nonlinear response, the exchange

of crimp between the backfill and the geogrid as they are stretched and the contact and the friction between the geocell

wall in cross and in same direction. There is also passive resistance offered by transverse portion of geocell. In general,

geocell exhibits a significant stiffness only along the longitudinal directions under tension. The tensile response in

perpendicular directions may be coupled due to crimp exchange between backfill and geocell and junctions between

them. The behavior of geocell is modeled phenomenological in ABAQUS/Explicit to capture the non-linear anisotropic

behavior. The planar kinematic states of geocell is described in terms of nominal direct strains in the geocell plane and the

angle between the perpendicular directions. The shape of geocell was modeled with a rhomboidal shape as assumed in

earlier experiment (Leschinsky and Ling 2012). Geocell and the infill material has also been modeled separately. Frictional

interface between the geocell and infill material has been modeled separately. Analytical model for estimating compaction

induced horizontal stress in the geocell reinforced base and for considering accumulated residual strain in geocell and

induced additional confining stress to the fill material has been deployed as provided by Yang (2010).

Finite element adopted for geogrid, geocell and soil is 4-node, doubly curved, general purpose, fully integrated finite-

membrane-strain shell element (S4 of Aqabus). As element stiffness is fully integrated, no spurious membrane or bending

zero energy mode exist and no membrane or bending mode hourglass stabilization is used. This element assumes that

the transverse shear force or strain (since the transverse shear treatment is based on the initial elastic modulus of the

material) is constant over the element. The Concrete in spread footing was considered as linear elastic with high stiffness

exhibiting non-yielding behavior. It was modeled with hexahedral 8-noded elements with reduced integration (C3D8R).

The double hardening model like hardening soil with small strain (HSsmall) is being used for modeling of soil. This is

basically an elastic-plastic hyperbolic model with Mohr-Coulomb failure criterion. The reason for using this model is due to

the importance accorded to small-strain stiffness under heavy loading. Ignoring small-strain stiffness in geotechnical

analysis may potentially lead to overestimation of foundation settlements and thus consequently underestimating stresses.

Accurate prediction of stresses is essential for design of geogrid reinforcement and over prediction of settlements may

result in uneconomical ground improvement. It is also recommended for serviceability Limit State analyses as it generally

predicts soil behavior and field measurements more precisely than basic linear-elasticity methods. It also accounts for

stress history which is crucial for flexible footing under heavy loading. Constitutive models available in Abaqus library do

not include double hardening models like HSsmall model. Thus we implemented this model in Abaqus with user subroutines

UMAT and VUMAT written in Python language on similar coding developed by Arslan and Sture (2008).

The behavior of a RSF pad sitting on the sub grade depends on many factors including the reinforcement type,

reinforcement spacing, reinforcement stiffness, footing embedment depth, reinforcement-soil interaction coefficient and

footing width. The effect of all these factors needs to be incorporated into a rational design method for RSF pad. In order

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to include the effect of different soil properties in the design method, additional finite element analyses were conducted

using friction angles of = 35º, 40º, 45º and 50º and varying elastic modulus of geocell (500 to 2000 MPa), soil (10 to 25

MPa) and axial stiffness of geogrids (3500 to 5000 kN/m). Based on the database generated by FE parametric study, a

multi-regression statistical analysis was conducted to develop a simple Bearing Capacity Ratio (BCR) and settlement ratio

(SR) model for use by geotechnical engineers in design of RCF pad with various alternatives. The full model described in

Eq. 2 that includes the effects of all variables and their interactions was first analyzed.

BCR = β0 + β1*X1 + β2*X2 + β3*X3 + β4*X4 + β5*X5 + β6X6 + β7X1*X2 + β8*X1X3 + β9*X1X4 + β10*X1X5 +

β11*X1X6 + β12*X2X3 + β13*X2X4 + β14*X2X5 + β15*X2X6 + β16*X3X4 + β17*X3X5 + β18*X3X6 +

β19*X4X5 + β20*X4X6 + β21*X5X6 [2]

where, BCR is the ultimate bearing capacity ratio of the reinforced soil (at s/B = 10%), X1 is the spacing ratio between

reinforcement layers (h/B), X2 is the average normalized stiffness of reinforcement (Jav / (Esav*Dav)], X3 is the footing

embedment ratio (d/B), X4 is the footing width ratio (B/4 m), X5 is the normalized friction angle of soil (/35), and X6 is the

normalized elastic modulus of soil (E/17.5 MPa). A stepwise variable selection procedure was then performed on the

general model shown in Eq. 2 5 to remove insignificant variables from the general model. The statistical variable selection

procedure showed that no interaction between these variables is significant and that reinforcement spacing, average

reinforcement stiffness, footing embedment, and footing width are the statistically significant variables for the BCR at the

95% confidence level. The multiple regression analysis was then conducted on the reduced model, and the results yielded

the model shown in Equation 3:

BCR = 3.6823 - 0.45851*X1 + 0.08947*X2 - 0.27817*X3 - 0.3945*X4 - 1.6964*X5 + 0.4276*X6 (R2 = 0.95) [3]

The relative importance of each independent variable on the BCR was assessed by comparing t values. Index |t| is a t-

statistical parameter, which is used for evaluating the statistical significance of design parameters; the higher the value is,

the more significant is the parameter. The results of t value comparison show that the spacing between reinforcement ratio

(|t| =17.85) has the most significant effect on the increase of bearing capacity among all variables. The stiffness of

reinforcement (|t| =5.85) has the weakest effect on the increase of bearing capacity among all variables. It is worth noting

that there is a tradeoff between increasing reinforcement stiffness and reducing reinforcement spacing. However, based

on the results of this study, it is advisable to decrease spacing increasing stiffness as far as reinforcement spacing is kept

within acceptable design range [i.e., 200 mm ≤ h ≤ 400 mm] and provided that it is cost-effective. Use of one layer of

geocell lowers the failure wedge, enhances bearing capacity and reduces differential and total settlement. The BCR

regression model in Eq. 3 was verified by comparing the results of the regression model with the results of finite element

analysis determined for 100 new reinforced cases of different configurations. The results of the comparison are presented

in Fig. 4. The absolute errors range from 0.14% to 2.25%, which suggests that the BCR values predicted by the

regression model in Eq. 3 have good correlation. Settlement reduction ratio (SRR) was obtained by interlinking it to

stiffness ratio and then to applied load and BCR in similar manner as evaluated in EBGEO (2011).

𝑆𝑅𝑅 =𝑆1

𝑆2=

𝐸2

𝐸1= 𝐵𝐶𝑅 − (

𝑈𝐿𝑇𝐼𝑀𝐴𝑇𝐸 𝐿𝑂𝐴𝐷

𝑈𝐵𝐶1) [4]

where S1 and S2 are settlement values of unreinforced soil and reinforced soil respectively; E1 and E2 are equivalent

stiffness of unreinforced soil and reinforced soil respectively; BCR being the bearing capacity ratio due to ground

improvement; ultimate load is the uniformly load applied to the RSF pad and UBC1 is the ultimate bearing capacity of

unreinforced ground. The SRR regression model in Eq. 4 was verified by comparing the results of the regression model

with the results of finite element analysis determined for 100 new reinforced cases of different configurations. The results

of the comparison are presented in Fig. 4. The load v/s settlement characteristics for pilot test have been plotted in Fig. 5

along with FEM results on unreinforced soil and reinforced soil. Good correlation exist between instrumented and FEM

results.

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Figure 4. Comparison of BCR and SCR obtained from regression model and FE analysis

Figure 5. Load v/s settlement characteristics

5. DISCUSSIONS

In this paper, the parameters that effect performance of RSF pad were extensively studied using the instrumented

monitoring approach, FEM approach and limit equilibrium approach advocated by various international codes. The results

obtained from these approaches were used to obtain empirical expressions for BCR and SRR using regression models.

There was strong correlations between results obtained through regression model and FEM. The instrumentations results

also correlated well with FEM results thus validating the constitutive modeling of soil, geocell and geogrid and interface

modeling between them. These findings are expected to provide useful guidelines for geotechnical engineers in selecting

appropriate values of design parameters as there was 25 to 30% under prediction of strength by limit equilibrium methods

under failure conditions. No clear picture is provided by limit equilibrium methods during stresses at working loads which is

very important for realistic prediction of behavior of structure. However, it should be pointed out that the finding from this

study are only valid for square RSF pad using geogrids and geocell. Suitable modifications can be done to account for

change in geometry in the footing which is not a very difficult task. The various variable parameters such as optimum

depth of the first reinforcement layer (u) and the effective length of the reinforcement (le), type of soils, and type of

reinforcement can be considered for wider span of research. The results of model tests conducted by Abu-Farsakh et al.

(2007a) on different type of soils clearly demonstrated this dependency. This point has also been mentioned and

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discussed in detail by Yetimoglu (1994) and Abu-Farsakh et al. (2007b). Therefore, more studies on the influence of soil

type and footing type, which were not covered in this FEM study, are highly desired in developing a rational and reliable

design methodology for RSF pads. The FEM analyses were validated using full-scale instrumented modeling tests and

then used to analyze full-scale square RSF pad over existing soil. The results also showed that the BCR decreases with

the increase in footing width. This is in agreement with other research studies (Das et al., 1994; and Elvidge and

Raymond, 2001). However, full-scale field tests are no longer required as numerical modeling and regression modeling is

showing high correlations. Thus FEM modeling for GC-3 type structures and regression model or limit equilibrium methods

with suitable correction factors can be used for GC-1 and GC-2 type structures.

6. CONCLUSIONS

Based on the results of finite element, full-scale modeling and regression analyses of a RSF pad, following conclusions

can be drawn:

1) Smaller spacing of reinforcement (200mm to 300mm) using high frictional fill loads to superior compaction of

reinforced fill and is the main factor for good performance. This envisaged reinforced system is having superior

seismic resistance.

2) Durability of geosynthetics is not considered to be a problem as they are closed spaced and adequate encapsulated.

3) The inclusion of reinforcement layers reduces the magnitude of vertical stress through redistribution of the load

applied on the footing onto a wider range, thus helping reduce the overall settlement of the soil below RSF pad.

4) A regression model was developed for BCR and SRR of RSF pad based on the results of FE analysis. The

verification showed that the model can be used to estimate BCR and SRR with good accuracy.

5) The BCR of the RSF pad decreases and SRR of RSF pad increases with the increase in reinforcement spacing.

6) The BCR of the RSF pad increases and SRR decreases with the increase in the reinforcement stiffness. The

stiffness-related increase is more remarkable at normalized reinforcement stiffness of less than 0.5.

7) The increase in footing embedment depth and/or footing width improves the ultimate bearing capacity of the

unreinforced soil more than that of the reinforced soil, resulting in a decrease in the BCR and an increase in the SRR.

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