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, [email protected]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. 312
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Geosynthetics 2015 February 15-18, Portland, Oregon
Analytic Approach for Design of Reinforced Soil Bridge Pier on
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.
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: