A numerical study on the use of geofoam to increase the external stability of reinforced soil walls

The magnitudes and distributions of earth pressure behind the reinforced zone in the wall models with and without the geofoam panel are compared to quantify the reductions in lateral ear

A numerical study on the use of geofoam to increase the external stability of reinforced soil walls

K Hatami1 and A F Witthoeft2

1Assistant Professor, School of Civil Engineering and Environmental Science, University of Oklahoma,

202 W Boyd St, Room 334, Norman, OK 73019, USA, Telephone: +1 405 325 2674; Telefax: +1 405

325 4217, E-mail: kianoosh@ou.edu

2Undergraduate Research Assistant, School of Civil Engineering and Environmental Science, University

of Oklahoma, Norman, OK 73019, USA, Telephone: +1 765 494 6246; Telefax: +1 765 494 0395,

E-mail: awitthoeft@purdue.edu

Received 2 January 2008, revised 2 June 2008, accepted 17 June 2008

ABSTRACT: The potential benefit of placing a panel of compressible (i.e expanded polystyrene)

geofoam behind the reinforced zone of mechanically stabilized earth (MSE) walls is investigated

using a numerical modeling approach A panel of geofoam is placed immediately behind the

reinforced zone during the construction phase of an idealized plane-strain reinforced soil segmental

wall model The analysis procedure includes the modeling of soil compaction The magnitudes and

distributions of earth pressure behind the reinforced zone in the wall models with and without the

geofoam panel are compared to quantify the reductions in lateral earth pressure, resultant lateral

force and overturning moment expected due to the placement of the geofoam material Predicted

magnitudes of facing lateral deformation and reinforcement strains are also compared among cases

studied in order to evaluate the effect of geofoam on wall serviceability It is shown that placing

geofoam behind the reinforced zone can reduce the maximum lateral earth pressure behind this

zone by as much as 50% depending on the geofoam thickness and stiffness values The magnitudes

of total lateral earth force (i.e the resultant force of the lateral earth pressure distribution) behind

the reinforced mass and overturning moment about the wall toe are shown to decrease by 31% and

26%, respectively These findings point to a significant potential for using geofoam to reduce the

lateral earth pressure demand on MSE walls (i.e as opposed to rigid retaining walls examined

previously) and thereby increase their serviceability and their factors of safety against external

instability

KEYWORDS: Geosynthetics, Geofoam, MSE retaining walls, Reinforced soil

REFERENCE: Hatami, K & Witthoeft, A (2008) A numerical study on the use of geofoam to increase

the external stability of reinforced soil walls Geosynthetics International, 15, No 6, 452–470

[doi: 10.1680/gein.2008.15.6.452]

1 INTRODUCTION

1.1 Previous work regarding geofoam applications

Expanded polystyrene (EPS) foam, commonly known as

geofoam, has gained widespread popularity as a

construc-tion material in a variety of geotechnical and

transporta-tion engineering applicatransporta-tions in recent years Example

applications include construction of lightweight

embank-ments and paveembank-ments (Duskov 2000; Jutkofsky et al

2000; Horvath 2004a, 2004b; Stark et al 2004), static and

seismic earth pressure reduction behind rigid retaining

walls (Horvath 1991a, 1991b; Inglis et al 1996; Aytekin

1997; Reeves and Filz 2000; Stark et al 2004; Zarnani et

al 2005; Bathurst et al 2007a, 2007b; Zarnani and

Bathurst 2007, 2008), and functions such as drainage,

thermal insulation and attenuation of noise and vibration

(Horvath 2005; Koerner 2005) The use of low-stiffness (i.e compressible) geoinclusions to allow controlled yield-ing of the backfill and hence reduce lateral earth pressures against rigid retaining walls has been reported in the literature as early as the mid-1980s (McGown et al 1987; Partos and Kazaniwsky 1987)

McGown et al (1987, 1988) and Horvath (1991a, 1991b) examined the idea of using reinforcement layers in combination with a compressible layer (or geofoam) behind

a rigid wall to achieve a greater reduction of earth pressure behind the wall compared with the case of using geofoam alone Horvath (1991a) investigated the influence of rein-forcement tensile modulus and geofoam thickness on the reduction of lateral earth pressure behind an idealized 3 m-high rigid wall using a finite element approach His results indicated that a 0.05 m-thick geofoam panel compressed by

about 0.005 m could reduce the lateral earth pressure

behind a rigid wall retaining an unreinforced backfill to the

values corresponding to an active state Using a 0.6 m-thick

geofoam panel would result in significantly lower lateral

earth pressure magnitudes behind the rigid wall compared

with the 0.05 m case Horvath (1991a) found that using

very extensible reinforcement (i.e nonwoven geotextiles)

would not result in any additional reduction in lateral earth

pressure behind the wall compared with using geofoam

alone On the contrary, using stiff reinforcement (i.e steel)

combined with geofoam panels would reduce the lateral

earth pressure behind the wall to negligible values Horvath

(1991b) examined the extent of reduction in lateral earth

pressure behind rigid walls for the case where the wall was

subjected to surcharge loading on its backfill His analysis

indicated that the structural demand on rigid walls

sub-jected to backfill surcharge loading could be reduced

significantly by using geofoam behind the wall, offering a

cost-effective design approach in such loading situations

The additional effect of backfill reinforcement on

reducing lateral earth pressure behind a rigid wall has also

been investigated in several other studies (e.g Tsukamoto

et al 2002; Abu-Hejleh et al 2003; Horvath 2003;

Hazarika and Okuzono 2004; Horvath 2004b, 2005) In all

these studies the geofoam has been placed (or modeled in

the analysis) between the backfill and a rigid retaining

wall However, to the best of the present authors’

know-ledge, no studies have addressed the potential use of

geofoam behind the reinforced zone of mechanically

stabilized earth (MSE) walls to reduce lateral earth

pressures behind the reinforced mass Such an application

is distinct from the configurations investigated in the

previous studies The horizontal earth force and

over-turning moment resulting from the magnitude and

distri-bution of lateral earth pressure behind the reinforced zone

in MSE walls are important design parameters for their

external stability analysis (e.g Elias et al 2001; AASHTO

2002; NCMA 2002) In this paper it is shown that the

assumption of active state lateral earth pressure

magni-tudes behind the reinforced mass of MSE walls could be

inaccurate and unsafe (see Section 1.2) This inaccuracy is

attributed primarily to the compaction-induced increase in

lateral earth pressures, which could approach (or even

exceed) magnitudes corresponding to the at-rest

condi-tions, as demonstrated in several past studies on rigid

retaining walls (e.g Duncan et al 1991, Filz and Duncan

1996) Placement of geofoam panels behind the reinforced

zone could help ensure that reduced lateral earth pressure

magnitudes will develop behind the reinforced mass, as

assumed in the current design guidelines

1.2 Lateral earth pressure magnitudes behind

reinforced zone of MSE walls

External stability analyses of MSE walls in the current

limit-equilibrium design approaches are based on the

assumption that an active state is developed over the entire

wall height behind the reinforced zone (e.g Elias et al

2001; NCMA 2002) This assumption is made to reduce

the conservatism in the design of MSE walls due to the

overall satisfactory performance of these structures (e.g

Koerner 2005) This approach is based on the postulation that MSE walls are flexible structures and hence can undergo sufficient deformations during their construction that would result in fully active conditions in their back-fills There is a wealth of experimental evidence that supports the notion of developing an active state within the reinforced zone behind the facing of MSE walls at the end of construction For instance, measured reinforcement strains in several instrumented MSE walls in the field and full-scale test walls in the laboratory reported by several past studies have indicated that maximum reinforcement strains at the end of construction are typically in the range 1–2% in MSE walls with select backfills, depending on the wall height and reinforcement properties (e.g Allen and Bathurst 2002) In addition, typical magnitudes reported for the frictional efficiency of the interface between high-quality backfill and geogrid reinforcement (e.g Holtz et al 1997; Koerner 2005), in addition to observations in recent full-scale prototype studies on MSE walls (Hatami and Bathurst 2005, 2006), have indicated that slippage of reinforcement within the backfill is unlikely, and therefore the strains in the geogrid reinforce-ment and in the backfill soil are compatible As a result, strains on the order of 1–2% are expected to develop in the backfill, which are sufficient to develop active states within the reinforced zone and especially behind the wall facing These strain magnitudes are also compatible with observations made by Allen et al (2003) and Miyata and Bathurst (2007) on the response of several instrumented MSE walls in the field, where satisfactory performance was observed in the walls with granular and cohesive (i.e

strain was less than 3% and 4%, respectively (Huang et al 2007)

In contrast to the availability of the experimental evidence on the response of soil within the reinforced mass, no measured data are available on the distributions

of lateral earth pressure behind the reinforced zone of MSE walls Therefore, in this study, this information was extracted from a numerical model that was validated against measured data on several response parameters from a series of well-instrumented full-scale test walls simultaneously (Hatami and Bathurst 2005, 2006) The RMC walls have also been used to validate a numerical model by Guler et al (2007) The test walls were carefully constructed in a controlled laboratory environment at the Royal Military College of Canada (RMC) Figure 1 shows

an example numerical grid for the RMC test walls investigated in this study Each of these walls was constructed with a modular block facing, and was different from the other walls in its reinforcement design (i.e reinforcement tensile modulus and vertical spacing), as listed in Table 1 Details of wall construction, instrumenta-tion and monitoring program have been reported in several previous studies (e.g Bathurst et al 2000, 2001, 2006; Hatami and Bathurst 2005, 2006) The data used to calibrate and validate the numerical model for the MSE walls included wall facing deformations, axial strain distributions over the length of all reinforcement layers, reinforcement connection loads, independent horizontal

and vertical components of facing toe reactions, and

vertical earth pressure distributions at the foundation level

Horizontal earth pressures behind the reinforced mass

were not measured in any of the test walls However,

Figure 2 shows the lateral earth pressure distributions for

six of the RMC test walls as predicted using the validated

numerical model Note that y and H (on the vertical axis)

refer to the vertical distance from the bottom of the wall

and the total wall height, respectively All earth pressure

results (both vertical and lateral) are normalized with

the total wall height, H These conventions are followed throughout the paper The results shown in Figure 2a depict predicted distributions for Walls 1–3, in which a lightweight vibrating plate compactor was used to compact the backfill during construction (Hatami and Bathurst 2005) Walls 5–7 (Figure 2b) were constructed using a jumping jack that exerted a greater compaction effort on

Reinforcement

0.6 m

2.52 m

5.95 m Stiff facing toe

Location where earth pressure distributions in Figure 2 and horizontal displacements in Figure 3 are reported

Interfaces

Modular blocks

Location of geofoam panel in proposed configuration

Figure 1 Typical numerical model for RMC test walls used to determine earth pressure distributions and horizontal

displacements shown in Figures 2 and 3

Table 1 Reinforcement properties and configurations in RMC test walls examined in this study (data from Hatami and Bathurst 2006)

Material type

Number of layers

Aperture dimensions (mm 3 mm)

Tensile modulus properties (Equation 4)

Note: Wall 4 was constructed using a different facing and construction technique, and therefore it was not included in this study.

the backfill (Hatami and Bathurst 2006) The undulatory

characteristics observed in the results shown in Figure 2

are attributed to the unloading–reloading model used for

the soil subjected to a transitory uniform pressure applied

at each soil lift during construction (Section 3.1.2)

None-theless, the following observations can be made from the

results shown in Figure 2

show a satisfactory agreement with the theoretical

weight and depth in the backfill, respectively

Walls 1–3, which were constructed using a lighter

top of the wall and approach an at-rest condition (K0) toward the bottom of the backfill Predicted

lateral earth pressure distributions for Walls 5–7, which were constructed using a jumping jack, indicate increased magnitudes comparable to (or exceeding) the at-rest conditions over the entire backfill depth This is attributed to greater locked-in stresses in the soil behind the reinforced mass when subjected to a more significant compaction effort compared with Walls 1–3 The predicted lateral earth pressure magnitudes in Walls 5–7 tend to exceed the at-rest value at the bottom of the backfill This tendency is common in all wall models in the vicinity of the rigid foundation, with the values for Walls 5–7 greater than those in Walls 1–3

coeffi-cient behind the reinforced mass verify the

reinforced zone as described in item 2 above An additional interesting observation is that significant

0.50 0.25

Earth pressure,σ γh/ sH

1.0

0.75 0.50

Earth pressure,σ γh/ sH

(b)

Lateral earth pressure Coefficient,K ⫽ σ σh / v

Normalized lateral Earth pressure,σ γh/ sH

Normalized vertical

0 0 0.2 0.4 0.6 0.8

1.0

Wall 1 Wall 2 Wall 3

0 0 0.2 0.4 0.6 0.8

1.0

Wall 1 Wall 2 Wall 3

0 0 0.2 0.4 0.6 0.8

1.0

Wall 1 Wall 2 Wall 3

(a)

0 0 0.2 0.4 0.6 0.8

1.0

Wall 5 Wall 6 Wall 7

0 0 0.2 0.4 0.6 0.8

1.0

Wall 5 Wall 6 Wall 7

0 0 0.2 0.4 0.6 0.8

1.0

Wall 5 Wall 6 Wall 7

Lateral earth pressure Coefficient,K ⫽ σ σh / v

Normalized lateral Earth pressure,σ γh/ sH

Normalized vertical

Figure 2 Earth pressure results behind reinforced zone of selected RMC test walls with modular facing as predicted using a validated numerical model: (a) walls compacted using lightweight vibrating plate; (b): walls compacted using higher-energy jumping jack

K values could develop at the top of the walls subjected to significant compaction effort (e.g Walls 5–7 in Figure 2b) Also, the K values near the

reinforced zone (i.e when reinforcement tensile modulus is greater) The K values near the backfill

measured in the field walls that have been used as a basis for adopting approaches such as the coherent gravity method for the design of MSE walls (e.g

Elias et al 2001) However, results shown in Figure 2b indicate that lateral earth pressure magnitudes behind the reinforced mass of well-compacted walls

in the field could be significantly greater than the values suggested in the current design guidelines, based on the assumption of active state over the entire backfill depth As a result, the assumption of

behind the reinforced zone may not be safe in the external stability analysis of MSE walls Develop-ment of compaction-induced, excess lateral earth pressures in MSE walls has been reported previously (e.g Ingold 1983)

Figure 3 shows horizontal displacement of the backfill

behind the reinforced zone for the same test walls as

predicted using the validated numerical model The

magnitudes of the predicted displacements are normalized

with respect to the wall height The results shown in

Figure 3 indicate that predicted horizontal displacements

behind the reinforced mass are slightly smaller in walls

compacted with greater compaction effort than those

compacted using a lighter compactor This observation is consistent with the expectation that a better-compacted soil will be stiffer and exhibit a reduced lateral deforma-tion behavior At the same time, results shown in Figure

3 indicate that the magnitudes of normalized lateral displacement of the backfill behind the reinforced zone

in all walls examined are significantly smaller than those required for the soil to develop a fully active state For instance, magnitudes of lateral displacement needed for a dense cohesionless backfill material (e.g sand backfill used in RMC test walls) to fully develop an active state

displacement of the backfill and H is the height of the wall (e.g Bowles 1996; Das 2004) It should be noted

that other studies (e.g Sherif et al 1982) have reported the influence of factors such as the angle of internal friction of the backfill material on the amount of deformation required to reach an active state Displace-ment results for all RMC test walls shown in Figure 3

with the predicted magnitudes of lateral earth pressure behind their reinforced mass (Figure 2), which for the most part are greater than active lateral earth pressure magnitudes

The results shown in Figures 2 and 3 indicate that reducing at-rest (i.e K0) lateral earth pressures to active (i.e Ka) levels requires greater soil deformations than the magnitudes expected to occur behind the reinforced zone

of typical segmental retaining walls in the field Placing a geofoam panel behind the reinforced mass is investigated

in the present study as a possible method to achieve the

0.0010 0.0005

0.0010 0.0005

0 0 0.2 0.4 0.6 0.8 1.0

Wall 1 Wall 2 Wall 3

0 0 0.2 0.4 0.6 0.8 1.0

Wall 5 Wall 6 Wall 7

Normalized lateral displacement, ∆ /H

Minimum displacement required for acti

Minimum displacement required for acti

Figure 3 Horizontal displacement of soil behind reinforced zone for selected RMC test walls with modular facing as predicted using a validated numerical model: (a) walls compacted using lightweight vibrating plate; (b) walls compacted using higher-energy jumping jack Note: minimum displacement required for active state in the soil is indicated

reduced (i.e active state) lateral earth pressure magnitudes

desired behind the reinforced zone

1.3 Present study

The primary objective of this paper is to examine the

influence of placing a panel of geofoam between the

reinforced and retained zones of a typical MSE wall on

the magnitude and distribution of lateral earth pressure

behind the reinforced zone at the end of construction It is

postulated that controlled yielding of the retained soil

against the compressible inclusion (i.e geofoam panel)

behind the reinforced zone can help reduce the

construc-tion-induced stresses behind the reinforced mass over the

entire height of the wall In this study, a numerical

modeling approach is adopted to examine the influences

of geofoam compressibility, geofoam panel thickness, and

reinforcement tensile modulus on the amount of reduction

in facing out-of-alignment and lateral earth pressure

behind the reinforced zone The same numerical model

that was validated against a series of RMC test wall

results (Hatami and Bathurst 2005, 2006) was modified to

include a geofoam panel behind the reinforced zone In

addition, capabilities of the numerical model to simulate

controlled yielding of a backfill against a moving/flexible

boundary (e.g backfill/geofoam interface) were validated

against measured data, as described in Section 2

The program Fast Lagrangian Analysis of Continua

(FLAC; Itasca 2005) was used to carry out the numerical

simulations FLAC is suitable for modeling problems that

involve large deformation and plastic behavior In

addi-tion, complex user-defined constitutive models for

compo-nent materials can be programmed and included in the

analysis, as needed

2 MODEL DEVELOPMENT AND

VALIDATION

2.1 Model tests used for validation of the numerical

model

A series of instrumented model-scale tests was conducted

at the University of Strathclyde in order to investigate the

reduction of lateral earth pressure in a soil mass due to

lateral displacement (i.e controlled yielding) of a vertical

boundary (McGown et al 1987, 1988) Soil was placed to

a height of 1 m inside a test tank 1.17 m high by 1.92 m

long by 0.45 m wide The soil mass was constructed on a

rigid foundation and was enclosed within three vertical

faces using rigid glass wall panels The remaining vertical

face of the soil mass was supported by a set of 20 plates,

0.05 m high by 0.45 m wide, which were able to move

independent of each other The plates were coated with

against vertical displacement Horizontal displacement of

the plates in different tests was resisted by springs that

had different stiffness magnitudes The soil used for the

model tests was Leighton Buzzard sand The backfill

a sand-raining technique A friction angle value of 49.68

was reported, based on the results of direct shear testing conducted on samples prepared to the same dry density

2.2 Numerical modeling of controlled yielding tests 2.2.1 Numerical model

Physical tests at the University of Strathclyde were used to validate the numerical model developed in this study Selected results reported in the same study by McGown et

al (1987) were also used to validate an FEM model by Karpurapu and Bathurst (1992) Figure 4 illustrates the plane-strain numerical model simulating a representative physical test setup Dimensions of the numerical grid (1.00 m high 3 1.92 m long) are consistent with the dimensions of the retained soil as reported by McGown et

al (1987, 1988) Except as mentioned below, an aspect ratio of 1H:1V was used for the zones throughout the numerical model A fixed boundary condition in the horizontal direction was applied at the numerical grid-points on the backfill far-end boundary to simulate a smooth rigid vertical panel A fixed boundary condition in both horizontal and vertical directions was used at the bottom boundary to simulate a rigid foundation A thin (i.e aspect ratio of 5H:1V ) soil layer was used across the entire base of the retained soil mass to simulate an interface between the soil and the rigid foundation The authors and colleagues have successfully used such an approach to simulate the backfill/foundation interface in their previous studies to analyze the response of reinforced soil-retaining walls subjected to static and dynamic load-ing conditions (e.g Bathurst and Hatami 1998; Hatami and Bathurst 2000)

2.2.2 Soil The retained soil (including the thin soil simulating the backfill/foundation interface) was modeled as a homoge-neous, isotropic, nonlinear elastic-plastic material with Mohr–Coulomb failure criterion and dilation angle (non-associated flow rule) Nonlinear elastic behavior of the soil material was simulated using the hyperbolic Young’s modulus formulation proposed by Duncan et al (1980) and the hyperbolic bulk modulus formulation described by Boscardin et al (1990) The hyperbolic model has been

Vertical boundary fixed

in horizontal direction Retained

soil

Fixed boundary

Spring–plate system

B⫽ 1.92 m

Thin soil interface layer

Figure 4 FLAC numerical grid used for validation of controlled yielding numerical model against test data reported by McGown et al (1987)

used in previous studies to simulate reinforced soil wall

behavior with a satisfactory level of accuracy (e.g Ling

2003; Hatami and Bathurst 2005, 2006) and it has been

shown to yield accuracy comparable to that of more

complex models such as single-bounding models (Ling

2003) The model walls were constructed using the

material properties listed in Table 2 The soil properties

used in this study were based on the values reported by

Boscardin et al (1990) for a well-graded sand compacted

to 95% standard Proctor density The friction angle and

density values used in this study were the same as those

reported by McGown et al (1987, 1988) and Karpurapu

1 kPa) was assumed to account for the apparent cohesion

invariably present due to moisture (i.e suction) in the

backfill soil The notion of apparent cohesion in soils due

to a small amount of moisture has been reported in

previous reinforced soil wall studies (Cazzuffi et al 1993;

Rowe and Skinner 2001; Hatami and Bathurst 2005,

2006) The model was constructed in 0.05 m lifts, and was

allowed to reach equilibrium after placement of each soil

layer

2.2.3 Spring–plate system The system of springs and independently movable plates was modeled as a column (i.e stack) of independent linear elastic zones separated from each other through interfaces that were rigidly supported in the vertical direction (Figure 4) All gridpoints (one at each corner for a total of four)

of these zones were fixed in the vertical direction to simulate the horizontal rails on which the plates were mounted (providing vertical support) In addition, the two gridpoints at the left of each zone were fixed in the horizontal direction (as shown in Figure 4) to simulate the mounting plate, which prevented global lateral (i.e rigid body) translation of the facing system All five different test cases reported by McGown et al (1987), including a rigid boundary case (i.e the vertical boundary was fixed

in horizontal direction) and four cases with different spring stiffness values for the linear elastic spring–plate system, were simultaneously modeled in the present study Each of the 20 springs in the stack of springs used in the model tests (Section 2.1) was simulated using one elastic zone with material properties as listed in Table 3 The qualifying terms used in Table 3 to describe the stiffness

of the springs are as reported by McGown et al (1987), who also reported nominal spring constants for the differ-ent springs they used in their model tests However, the actual spring constants, determined based on the measured lateral stresses and lateral displacements reported by McGown et al (1987), differed from the nominal values Therefore the Young’s modulus values for the elastic column used in the numerical model (Table 3) were calculated using the actual (i.e back-calculated) spring constants and accounting for the width of the column of linear elastic zones In order to simulate independent horizontal springs, the Poisson’s ratio values for all zones

zone in the elastic column was isolated from the neighbor-ing zones usneighbor-ing free-slidneighbor-ing interfaces so as to deform independently Rigid facing plates were simulated by attaching one structural node to each of the gridpoints of

Table 2 Soil properties for model verification

Note: The friction angle value at the soil/foundation interface was

assumed to be the same as the soil internal friction angle value.

Table 3 Elastic zone properties simulating the spring–plate system for model verification

Very soft springs

Soft springs Medium stiff

springs

Stiff springs

Spring–plate system

Soil/plate interface

a These values correspond to a zone size of 0.05 m by 0.05 m and equivalent spring constants back-calculated from the soil pressure and boundary displacements reported by McGown et al (1987).

the elastic column (for a total of 40 structural nodes) and

constraining the two structural nodes representing each

plate to move together The interface strength and stiffness

values reported in Table 3 were determined by matching

the lateral earth pressure distribution results obtained for

the case of rigid vertical boundary with the measured

values reported by McGown et al (1987) The same

interface properties were subsequently (and consistently)

used for all other cases that included spring–plate systems

(i.e compliant boundary) as listed in Table 3 Two of the

compliant boundary systems, i.e the ‘soft’ and ‘stiff ’

spring cases, were also simulated in a verification study

reported by Karpurapu and Bathurst (1992)

2.3 Results

Figures 5a and 5b show normalized measured and

spring–plate vertical boundary The predicated horizontal

soil Figure 5a shows the results for the soft spring and

stiff spring cases, together with the corresponding

simu-lated results reported by Karpurapu and Bathurst (1992)

Figure 5b shows the results for the additional cases of

rigid spring, very soft spring, and medium spring, which

are plotted in a separate graph for clarity It can be

observed that all predicted results show satisfactory

agree-ment with the measured data with respect to both

magnitudes and distributions of earth pressures for all five

cases reported by McGown et al (1987)

Figures 5c and 5d show values of measured and

normalized with respect to its height H, for all four

flexible boundary cases reported by McGown et al

(1987) The results shown in Figures 5c and 5d are also

presented in two sections for clarity Figure 5c shows

measured and predicted results for stiff and soft spring

cases, together with the predicted distributions reported by

Karpurapu and Bathurst (1992) for comparison Figure 5d

shows results for the additional verification cases

simu-lated in this study It can be observed that predicted values

from the present study are in satisfactory agreement with

the corresponding measured values for all the cases

reported by McGown et al (1987)

3 RESPONSE OF FIELD-SCALE

SEGMENTAL WALLS WITH GEOFOAM

PROTECTION BEHIND REINFORCED

ZONE

3.1 Numerical model and material properties

3.1.1 Numerical model

Following the verification of the numerical approach, as

described in Section 2, a field-scale segmental retaining

wall model was developed to carry out the primary

analyses of this study Figure 6 shows a typical

plane-strain numerical model of a 6 m-high segmental wall used

in this study The control case (i.e with zero geofoam

thickness) model shown in Figure 6 was developed using

FLAC models that were validated against extensive meas-ured performance results from a series of well-instrumen-ted 3.6 m-high prototype walls teswell-instrumen-ted in a controlled laboratory environment (Hatami and Bathurst 2005, 2006; Hatami et al 2005; Bathurst and Hatami 2006) A backfill width-to-height ratio of 2 to 1 was adopted to represent a sufficiently wide backfill This was done to ensure that potential failure planes in the backfill would not be intercepted by the far-end boundary A fixed boundary condition in the horizontal direction was assumed at the numerical gridpoints on the backfill far-end boundary to allow for free settlement of soil along that boundary A rigid foundation beneath the backfill soil was simulated using linear elastic continuum zones fixed in the vertical and horizontal directions An interface was placed across the entire rigid foundation to allow for its interaction with the backfill soil and the bottom facing block (Hatami and Bathurst 2005, 2006) Description of the interface model

is given in the FLAC manual (Itasca 2005), and the interface properties are given in Table 4

The wall facing was modeled as a column of concrete blocks 0.15 m high 3 0.30 m wide, using linear elastic continuum zones with the batter angle equal to 38 The bulk and shear modulus values of the facing blocks were

Interfaces were used to allow for the interaction of backfill soil with the segmental facing, and for the interaction between the individual blocks Interface properties used in the wall models are listed in Table 4

3.1.2 Soil The soil constitutive model described in Section 2.2.2 was used to simulate the backfill material for the 6 m wall cases with material properties as given in Table 5 The soil model represented a good-quality granular soil (e.g well-graded sand) with material properties as reported by Huang et al (2007) The wall models were constructed in 0.15 m backfill lifts The facing blocks, soil, reinforce-ment elereinforce-ments and geofoam panel (in models with geofoam) were constructed in layers, and the model was allowed to reach equilibrium following the placement of each layer After placement of each backfill lift, compac-tion was simulated by applicacompac-tion of an 8 kPa vertical load across the top of each soil lift It has been observed in previous studies (Hatami and Bathurst 2005) that an equivalent static vertical load may be used to approximate the effects of compaction on lateral earth pressure in the backfill and on wall facing deformation with reasonable accuracy

3.1.3 Geofoam

An elasticized geofoam material model was used in this study Elasticized geofoam is produced by mechanical or thermal treatment of EPS, which results in the reduction

of its Young’s modulus value but increases the range of strains for which the EPS maintains a linear response to compressive stresses (e.g Horvath 1995) Both elasticized and non-elasticized EPS have been shown to exhibit linear elastic response to compressive loading over the range of

elasticized geofoam and , 0.5% for stiff non-elasticized

geofoam: Horvath 1995; Athanasopoulos et al 1999)

Therefore all geofoam types were modeled as linear

elastic materials The density of the geofoam was assumed

reported in the literature (e.g Negussey and Jahanandish 1993; Horvath 1995; Koerner 2005) The geofoam control

0 0.2 0.4 0.6 0.8 1.0

0

McGownet al.(1987), stiff McGownet al.(1987), soft Karpurapu and Bathurst (1992), stiff Karpurapu and Bathurst (1992), soft FLAC, stiff

FLAC, soft

0 0.2 0.4 0.6 0.8 1.0

McGownet al.(1987), medium McGownet al.(1987), very soft FLAC, medium

FLAC, very soft

Normalized lateral earth pressure,σ γh/ sH

Normalized lateral displacement,∆ H/ (%)

0 0.2 0.4 0.6 0.8 1.0

0

McGownet al.(1987), stiff McGownet al.(1987), soft Karpurapu and Bathurst (1992), stiff Karpurapu and Bathurst (1992), soft FLAC, stiff

FLAC, soft

0.20 0.15

0.10 0.05

0 0.2 0.4 0.6 0.8 1.0

McGownet al.(1987), rigid McGownet al.(1987), medium McGownet al.(1987), very soft FLAC, medium

FLAC, very soft FLAC, rigid

0.50 0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10

Figure 5 (a, b) Measured and predicted lateral stress distributions at end of construction; (c, d) wall lateral displacements at end of construction

mechanical response curve reported by Horvath (1995) A

according to the regression equation suggested by Horvath

(1995),

not account for the dependence of geofoam Poisson’s ratio value on confining pressure as reported in earlier studies (e.g Negussey and Jahanandish 1993; Preber et al 1994; Horvath 1995) The effective Poisson’s ratio value for the range of confining pressure values applicable to model walls examined in this study is approximately zero (Preber

et al 1994) Furthermore, it was observed that the

0–0.1 did not result in significant variation in predicted

Vertical boundary fixed in horizontal direction

Retained zone

Rigid foundation

Segmental facing with 3° batter

L⫽ 3.9 m

B⫽ 12.0 m

Reinforced zone

Geofoam panel

Reinforcement layers at 0.6 m spacing (layer number increases upward from layer 1 at 0.3 m

Figure 6 Typical FLAC numerical grid for 6 m-high segmental wall simulations

Table 4 Interface properties for 6 m-high segmental wall

models

Block/block interface

Soil/block interface

Soil/foundation interface and block/foundation interface

Table 5 Soil properties for 6 m-high segmental wall models

a The range of permissible values.