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Design of a Geosynthetic Reinforced Segmental Retaining Wall In a Tiered Arrangement – Use of Numerical Modeling as a Design Aid

C. Yoo Sungkyunkwan University, Dept. of Civil and Environmental Engineering, Suwon, Korea csyoo@skku.edu

ABSTRACT: This paper presents a case history illustrating the use of finite-element procedure as a design aid for construction of a 12-m high geosynthetic-reinforced segmental retaining wall (SRW) in a tiered con-figuration on a yielding foundation containing a layer of relative soft soil deposit. On account of the concerns raised by the owner with regard to the adequacy of the original design in terms of the reinforcement distribu-tion, a verified finite-element model was employed to examine the effect of foundation yielding on the wall behavior and to find an optimum reinforcement distribution. The finite-element analysis provided relevant information on the mechanical behavior of the wall that was otherwise difficult to obtain from the limit-equilibrium based current design approaches. Practical implications of the findings obtained from this study are highlighted in this paper along with the role of numerical modeling in the design of geosynthetic-reinforced retaining walls.

1 INTRODUCTION

Geosynthetic-reinforced segmental retaining wall systems have become increasingly popular in Korea since its first appearance in the early 1990’s. Several benefits of the SRW systems include sound performance, aes-thetics, cost and expediency of construction. The mortarless construction and small size of modular facing blocks provide great freedom in constructing walls with complex geometry under unfavorable site conditions. Although many geosynthetic reinforced soil walls have been safely constructed and are performing well to date, there are many areas that need in-depth studies in order to better understand the mechanical behavior of SRW systems under more aggressive and harsh environments.

There are many situations where reinforced soil walls are constructed in a tiered configuration for a variety of reasons such as aesthetics, stability, and construction constraints, etc. Such a tiered configuration, however, tends to give design and construction engineers unnecessarily high confidence in terms of wall performance, especially for walls with an intermediate to large offset distance (D), as defined in Figure 1, i.e., D = 0.3 to 1.0 times lower tier height. A numerical investigation by Yoo and Kim (2002), however, revealed that for cases with such a range of offset distance, the interaction between the upper and the lower tiers is not insignificant, and that the equivalent surcharge approaches adopted in the current design approaches (Collins 1997, Elias and Christopher 1997) may yield unconservative results in some cases. In-depth studies are, therefore, re-quired to improve the current design approaches for SRWs in a tiered configuration.

A case history is presented in this paper concerning the use of finite-element (FE) procedure as a design aid for construction of a 12-m-high two-level tiered SRW. During early phases of construction, adequacy of the initial design was questioned due primarily to a possibility of foundation yielding that had not been consid-ered in the original design. On account of the limitations of the current limit-equilibrium based design ap-proaches that do not explicitly address the effect of foundation yielding, a calibrated FE model was employed to examine the effect of foundation yielding on the wall behavior and to find an optimum reinforcement dis-tribution. This paper describes the original design, the finite-element model used, the results of a parametric study on the effect of reinforcement distribution, and finally, practical implications for design.

2 REVIEW OF DESIGN METHODS FOR TIERED GR-SRW

The NCMA and the FHWA design guidelines adopt different assumptions regarding the wall behavior. Fundamental principles of each design approach are discussed under the subsequent subheadings.

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2.1 NCMA design approach The NCMA design approach (Collin 1997) basically replaces the upper tier with an equivalent surcharge of

which its magnitude is determined according to the offset distance D (Fig. 1). External and internal stability calculations for the lower tier are performed assuming the lower tier being a single wall under the equivalent surcharge. The upper tier is designed as if it were a single wall without taking into consideration of the possi-ble interaction between the upper and the lower tiers. As for a single wall, the local stability calculations for the connection failure, local overturning, and internal sliding are required to be checked for both tiers. Details of the design procedure are available elsewhere (Collin 1997).

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DH 2

q

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α

qeq = f (D)

H1

L1

L1

H1

Figure 1. Equivalent surcharge model (NCMA)

2.2 FHWA design approach The FHWA design guideline (Elias and Christopher 1997) requires determining the lower and the upper reinforcement length L1 and L2, respectively, that satisfy external stability requirements based on the offset distance D together with the lower and upper tier height, H1 and H2 , respectively, as follows:

• ( )φ−⟩ 90tan1HD ⇒ No interaction. Each tier is independently designed.

• ( )21201 HHD +≤ ⇒ Design for a single wall with a height of H = H1+H2.

• ( )21201 HHD +⟩ ⇒ For lower tier: 11 6.0 HL ≥ For upper tier: 22 7.0 HL ≥

H1

H2

D

σf

φγH2ζj

γi

ζ1

ζ2

σi

γH2

φς tan1 D= ⎟⎠⎞

⎜⎝⎛ +=

245tan2

φς oD

212

1 Hjf γ

ςςςς

σ−

−=

⎟⎠⎞

⎜⎝⎛ −≤

245tan1

φoHD

( )φ−> o90tan1HD 0=iσ

2Hi γσ =

( )φφ−≤<⎟

⎠⎞

⎜⎝⎛ − oo 90tan

245tan 11 HDH

σj

where: ,

245 φ

+o

Figure 2. Calculation model for vertical stress increase due to upper tier (FHWA)

φ = internal friction angleγ = unit weight of select fill

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For internal stability calculations, additional vertical stresses at depths due to the upper tier are computed based on the criteria given in Figure 2. The location of the potential failure surface required for the pullout capacity calculation is selected based on the offset distance D (Elias and Christopher 1997). Note, however, that these criteria are geometrically derived and empirical in nature. As for the NCMA approach, no provi-sion is made to take into account the possible interaction between the upper and the lower tiers when design-ing the upper tier. The connection failure should also be checked for both tiers as part of the internal stability calculations based on the procedure for a single wall (Elias and Christopher 1997).

3 FIELD WALL

3.1 Wall design and construction The wall under consideration was to be built at a land

development site in Korea (Fig. 3). The 10-m-high SRW with a two-tier wall arrangement was to retain a portion of fill to be used for a parking lot at the site. Modular blocks of 520 × 460 mm in plan and 200 mm in height were to be used to form the wall facing with no set-back. As seen in Figure 3 illustrating a typical design section of the original design, two types of high density polyeth-ylene geogrids, 6T and 10T having an index strength of 60 and 100 kN/m, respectively, were used as primary re-inforcements. In the original design, 5.3 and 3.8-m long geogrid layers, respectively, for the lower and the upper tiers were arranged at 0.6~0.8-m vertical spacing.

Decomposed granite soil classified as SP-SM available at the site was to be used as select fill. No shear strength tests results were reported. In the original design an in-ternal friction angle of φ=30° was assumed both for the backfill and for the retained soil. Construction specifica-tion required that the backfill material be compacted to a minimum of 95% of standard Proctor. A 300 mm-thick drainage layer was to be created immediately behind the wall facing using crushed gravels.

3.2 Site condition

The wall was initially designed with an assumption that the wall be situated on a non-yielding foundation. During initial construction phases, however, the contractor noticed some evidence of the presence of a soft soil layer at the foundation level. The contractor, however, did not take an immediate remedial action to miti-gate possible problems that could arise from the foundation yielding until unusually large settlements at the foundation level were noticed upon completion of the first 0.6-m-high wall. A number of borings around the wall periphery revealed a 3.0 to 4.0-m-thick alluvial sandy clay deposit with the SPT blow counts (N) less than 20, followed by a slightly weathered granite rock stratum. Concerns were therefore raised with regard to the effect of the soft soil layer on the wall behavior that had not been taken into consideration in the original design, prompting this investigation. 3.3 Limit equilibrium-based stability analysis of original design

Limit equilibrium-based stability analyses were conducted to check for the adequacy of the original design in meeting the minimum requirements specified by the NCMA and the FHWA design approaches. In the sta-bility analyses, an internal friction angle of 30º together with a unit weight of 19 kN/m3 was used for the select fill as used in the original design. The shear strength parameters for the compressible foundation soil were es-

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PG 6T H=0.2 L=5280

PG 10T H=0.8 L=5280

PG 10T H=1.4 L=5280

PG 10T H=2.0 L=5280

PG 6T H=2.6 L=5280

PG 6T H=3.2 L=5280

PG 6T H=4.0 L=5280

PG 6T H=4.8 L=5280

PG 6T H=0.2 L=3780

PG 6T H=1.0 L=3780

PG 6T H=1.6 L=3780

PG 6T H=2.4 L=3780

PG 6T H=3.2 L=3780

PG 6T H=4.0 L=3780

PG 6T H=4.8 L=3780

5000

500

5100

400

2500

q=13.0 kPa

q=100.0kPa

150

150

Figure 3. Geometry of field wall

unit: mm

176

timated based on local experience and the average STP blow counts N value of 15 as c’=30 kPa and o31=φ . For the internal friction angle, the relationship by Peck et al. (1974) given as Eq. (1) was used.

( ) ( )[ ]2601601 00054.03.01.27(deg) NN −+=φ (1) where (N1) 60=value of N60 (N corrected for field conditions) corrected to a standard values of kPa100'

0 =σ . Vendor provided allowable long-term design strengths (Ta) of the reinforcements were used as 27 kN/m and 45 kN/m for 6T and 10T, respectively. In addition to the stability analysis based on the current design ap-proaches, compound slope stability analyses were also performed using MSEW (Leshchinsky 1999) as sug-gested in the current design approaches.

Table 1 summarizes the results of the external and internal stability calculations. As seen in Table 1, the design did not satisfy the external stability requirement for the base sliding, specified by both design ap-proaches, due largely to the incompetent foundation. In addition, the design did not satisfy the internal stabil-ity requirement for the tensile overstress mode of failure according to the FHWA design approach, showing the minimum factor of safety value being much smaller than the required minimum of 1.0. Note that the fac-tors of safety against pullout failure are not shown since they are much greater than the required minimum. Although the design satisfied internal stability requirement for the tensile overstress specified by the NCMA design approach, the minimum factor of safety was only marginal. The results of the stability analyses based on the two design approaches clearly suggested that the wall was not adequately designed to meet the re-quirement for the internal stability, even without accounting for the incompetent foundation condition. The global stability analysis yielded the factor of safety close to being 1.0, implying potential for instability prob-lems arising from the incompetent foundation.

Table 1. Results of external and internal stability calculations for field cases

NCMA FHWA

External Internal External Internal

FSbsl FSot Ti,max (kN/m) (FSto)min FSbsl FSot Ti,max(kN/m) (FSto)min

1.07 2.14 24 1.13 1.24 2.10 38 0.71 Note) 1) FSbsl = factor of safety against base sliding 2) FSot = factor of safety against overturning

3) FSto = factor of safety against tensile overstress 4) Ti,max = maximum reinforcement load in lower tier

4 MITIGATION

On account of the site constraints, no foundation improvement technique could be implemented, and there-fore an attempt was made to modify the original design instead, recognizing the foundation condition. A FE procedure was adopted as a design aid with the aim of finding an optimum reinforcement distribution on ac-count of the fact that the current design approaches do not explicitly account for the effect of foundation yielding in design calculations.

4.1 Finite-element analysis

A commercial finite-element code

ABAQUS (Hibbitt, Karlsson, and Sorensen 2002) was used for analysis. ABAQUS was used in this study to take advantage of its ro-bustness in numerical solution strategy for soil nonlinearity. In the finite-element modeling, the wall components were carefully modeled including the foundation. The wall facing, the backfill soil, and the foundation were discre-tized using 8-node plane strain elements (CPE8R) with reduced integration, while the reinforcement was modeled using 3-node truss elements (T3D2).

A refined mesh (Fig. 4), consisting of over Figure 4. Finite-element mesh

177

5800 nodes and elements, respectively, was adopted to fully account for the construction procedure and to minimize the effect of mesh dependency on the results of finite-element analyses. The lateral and bottom boundaries were placed at locations with sufficiently distance. The interface behavior between the wall fac-ing and the backfill soil was modeled using a layer of interface elements (Desai et al. 1984) with appropriate mechanical properties. No interface was introduced between the soil and the reinforcements assuming no slip between the backfill and the reinforcements. This is justified since pullout tests on many soils show that slip occurs in the soil and not at the interface of the geogrids, unless the confining stress is extremely small.

In the analysis, the backfill and the foundation soil were assumed to follow the modified version of hyper-bolic stress-strain and bulk modulus model proposed by Duncan et al. (1980) while the wall facing block and the reinforcement were assumed to behave in a linear elastic manner. In addition, for the interface elements between the wall facing block and the backfill soil, a relatively low shear modulus but with a high bulk modulus was assigned to permit relative movement between the two media. The constitutive laws for the soil and the interface were implemented to ABAQUS with the help of built-in “User Subroutine” capability. In the hyperbolic model, the stress increments (dσ) are related to the strain increments (dε) based on the tangen-tial Young’s modulus Et and/or unloading-reloading modulus Eur, and bulk modulus B which are computed us-ing the Mohr-Coulomb soil strength parameters of c’ and φ’ in conjunction with the hyperbolic model parame-ters including stiffness modulus number for primary loading K, stiffness modulus number for unloading-reloading Kur, bulk modulus number Kb, stiffness modulus exponent n, bulk modulus exponent m, and failure ratio Rf. Considering the free draining characteristic of typical decomposed granite soils in Korea, a fully drained condition was assumed. Table 2 summarizes the input parameters for various wall components. It should be noted that the hyperbolic parameters for the backfill and the foundation soil were the “best-estimate” parameters based on local experience as well as the database provided by Duncan et al. (1980). On account of the discrete nature of the modular block facing, the Young’s modulus of the facing block was re-duced to 1/10 of that of concrete, giving a wall flexural stiffness of (EI)w=20 MN-m2/m. The detailed con-struction sequence was carefully simulated by adding layers of soil and reinforcement at designated steps. The finite-element modeling approach adopted in this study was calibrated against available instrumentation data for a full-scale tiered SRW. Details of the model verification are available elsewhere (Yoo 2003).

Table 2. Material properties used in finite element analyses Material c (kPa) φ (°) K Kur n Rf Kb M Es (MPa)

Backfill 0 30 300 350 0.5 0.8 175 0.2 - yielding 20 31 400 450 0.5 0.8 175 0.2 - foundation

non-yielding 100 40 1000 1500 0.7 0.9 800 0.2 - facing block - - - - - - - - 2,000

Note: For all materials, unit weight γ=18 kN/m3 and poisson’s ratio ν=0.3.

4.3 Parametric study

Using the finite-element model, a parametric study was conducted on a wide range of conditions having different reinforcement distributions. Also varied was the reinforcement stiffness. The original design was selected as a baseline condition. The reinforcement density in terms of vertical spacing was not considered as a variable since preliminary analyses indicated that the effect of reinforcement spacing was insignificant.

LL var.

UL constant

LL var.

UL var.

LL constant

UL var.

(a) Scheme A (b) Scheme B (c) Scheme CLL=lower reinforcement legnth UL=upper reinforcement legnth

Figure 5. Reinforcement distributions considered

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A series of analysis was conducted by varying either the lower or the upper reinforcement length at a time while keeping the other tier’s reinforcement length constant (Scheme A and B). For each scheme, a uniform reinforcement length was assumed in each tier. An additional set of cases in which the reinforcement lengths in both tiers were uniformly increased was also analyzed (Scheme C). In addition to the reinforcement legnth, two levels of reinforcement stiffness were considered, i.e., J=1000 kN/m and 2000 kN/m. Schematic views of the schemes considered are shown in Figure 5. 5 RESULTS AND DISCUSSION

5.1 Effect of foundation yielding The effect of foundation yielding on the mechanical behavior of the baseline condition was examined in

terms of wall deformation, reinforcement load, and stress state for two extreme cases in terms of the founda-tion rigidity, i.e. yielding and non-yielding foundations. Note that the relevant properties for each case are given in Table 2.

-100 0 100 200 300 400Lateral Wall Deformation (mm)

0

2

4

6

8

10

Wal

l Hei

ght f

rom

Bas

e (m

)

non-yielding foundationyielding foundation

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foundation level

0 10 20 30 40Reinforcement Tensile Load (kN/m)

0

2

4

6

8

10

Wal

l Hei

ght f

rom

Bas

e (m

)

non-yielding foundationyielding foundation

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foundation level

FHWA

(a) wall deformation (b) tensile load Figure 6. Effect of foundation yielding on wall behavior

(a) non-yielding foundation (b) yielding foundation

Figure 7. Stress ratio distribution

Figures 6 and 7 illustrate calculated lateral wall deformations, maximum reinforcement loads, and distribu-

tions of the shear stress ratio (ratio of mobilized shear stress to shear strength). Also shown are the calculated reinforcement tensile loads according to the FHWA design approach. As seen in these figures, the effect of foundation yielding was to increase the wall deformation as well as the reinforcement tensile loads in the lower tier. In fact, the foundation yielding caused an over 200% increase in the maximum lateral wall defor-mation at the top of the lower tier with a significant increase in the associated reinforcement tensile loads in the lower tier as great as 20 kN/m in the lower-most reinforcement layer. The interaction between the both

179

tiers also accompanied increases in the wall deformation as well as the reinforcement loads for the upper tier, especially at the base level. This trend is the result of the interaction between the lower and the upper tiers, and is not addressed in the current design assumptions. Although the reinforcement loads from the FE proce-dure fell below those computed based on the FHWA approach, the significant increases in the reinforcement loads arising from the foundation yielding observed in the FE results implied that the foundation yielding needed to be correctly accounted for in order to avoid any potential internal stability problems. The distribu-tions of the shear stress ratio shown in Figure 7, with the zones having a ratio greater than 90% being indi-cated, suggested that a global shear failure was likely for the yielding foundation case.

The results presented above strongly suggested that the original design might not be adequate to assure both the internal and the external stability of the wall for the yielding foundation scenario. An optimum rein-forcement layout was therefore sought for the worst-case scenario of yielding foundation with the aid of the finite-element procedure. 5.2 Effect of reinforcement distribution

The variation of maximum lateral wall deformation and stress ratio distribution are shown in Figure 8 for

different schemes in increasing the reinforcement length. As expected, increasing the reinforcement length, either the lower (LL) or the upper reinforcement length (UL), caused a decrease in the maximum wall defor-mation in all schemes but with different rates. Of importance trend was that the maximum lateral wall defor-mation was significantly reduced when keeping LL/H<0.6 in Schemes A and C, suggesting that LL/H=0.6 was a minimum critical length required to avoid excessive lateral wall deformation. Such a trend was not as evident in Scheme B in which UL/H varied, although the rate of decrease in max,hδ with UL/H decreased somewhat when UL/H>0.7.

0.4 0.5 0.6 0.7 0.8LL/H

150

200

250

300

350

400

Max

. Lat

. Wal

l Def

orm

atio

n δ h

,max

(mm

)

0.4 0.5 0.6 0.7 0.8UL/H

0.4 0.5 0.6 0.7 0.8RL/H

150

200

250

300

350

400Scheme A Scheme B Scheme C

LL var.

UL var.

LL constant

UL var.

LL var.

UL constant

UL/H=0.4J=1000 kN/m

LL/H=0.5J=1000 kN/m

RL=LL=ULJ=1000 kN/m

Figure 8. Variation of max,hδ with reinforcement distribution

Figure 9. Variation of stress state with reinforcement distribution

(a) LL/H=0.6, UL/H=0.8 (b) LL/H=0.8, UL/H=0.6 (c) LL/H=0.7, UL/H=0.7J=1000 kN/m J=1000 kN/m J=1000 kN/m

Figure 9 presents stress ratio distributions for cases having the same average reinforcement length

TL/H=0.7 but with different combinations of LL/H and UL/H. Note that TL is an average reinforcement length in both tiers, i.e., TL=(LL+UL)/2. One important trend shown in this figure was that the stress states within the reinforced soil block and the retained soil varied with the reinforcement distribution although TL/H

180

was the same. In fact, the case with a uniform length in both tiers, i.e., LL/H=UL/H=0.7, yielded the most fa-vorable stress state, i.e., least extent of zones of 9.0≥SL . Such information cannot be obtained from conven-tional limit-equilibrium based design/analysis tools, thus illustrating advantages of employing numerical mod-eling techniques in the design of reinforced soil walls with complex geometry. 5.3 Effect of reinforcement length

Figures 10 and 11 illustrate the variations of maximum lateral wall deformation max,hδ and maximum rein-

forcement strain maxε with LL/H and UL/H for two levels of stiffness, J=1000 and 2000 kN/m. As expected,

max,hδ and maxε decreased with increasing either of the reinforcement length to wall height ratios (LL/H, UL/H) but with different rates depending on the reinforcement stiffness. For example, the results for J=2000 kN/m showed narrow ranges of variation in max,hδ with UL/H than for J=1000 kN/m. Of interest trend shown in Figure 10 is that for a given TL/H, any combination of LL/H and UL/H yielded practically the same

max,hδ least within the range of the reinforcement lengths considered, as illustrated in Figure 10(c). Further-more, as seen in Figure 11, the maximum tensile strain in the lower tier reinforcement appeared to be mainly influenced by the upper tier reinforcement length and remained practically the same regardless of LL/H for a given UL/H, suggesting that the variation in max,hδ with LL/H for a given UL/H in fact represented the lateral deformation at the back of reinforcement soil block (external deformation). Such a trend was due in part to the fact that the range of reinforcement lengths considered (LL/H=0.6~0.8) was close to the critical LL/H. Further inspection of Figure 11 revealed that for a given TL/H, the maximum reinforcement strain maxε could be minimized when adopting longer reinforcement in the upper tier than in the lower tier. This trend is largely due to the fact that longer the upper tier reinforcement reduces the upper tier-induced surcharge load through stress redistribution. In view of reducing reinforcement loads, it is therefore desirable to arrange longer rein-forcement in the lower tier than in the upper tier for a given TL/H.

0.4 0.5 0.6 0.7 0.8UL/H

160

180

200

220

240

260

Max

. Lat

. Wal

l Def

orm

atio

n δ h

,max

(mm

)

LL

UL

LL/H0.60.70.8 J=1000 kN/m

0.4 0.5 0.6 0.7 0.8UL/H

100

120

140

160

180

200

Max

. Lat

. Wal

l Def

orm

atio

n δ h

,max

(mm

)

LL

UL

LL/H0.60.70.8 J=2000 kN/m

0.4 0.5 0.6 0.7 0.8TL/H

1.2

1.6

2.0

2.4

2.8

δ h,m

ax/H

(%) LL

UL

J (kN/m)10002000

Figure 10. Variation of max,hδ with reinforcement length

0.4 0.5 0.6 0.7 0.8UL/H

1.8

2.0

2.2

2.4

2.6

Max

imum

Ten

sile

Stra

in (%

)

LL

UL

LL/H0.60.70.8

J=1000 kN/m

0.4 0.5 0.6 0.7 0.8UL/H

1.0

1.2

1.4

1.6

1.8

Max

imum

Ten

sile

Stra

in (%

)

LL

UL

LL/H0.60.70.8

J=2000 kN/m

0.4 0.5 0.6 0.7 0.8TL/H

0.8

1.2

1.6

2.0

2.4

2.8

Max

imum

Ten

sile

Stra

in (%

)

LL

UL

J(kN/m)10002000

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������������������LL/H=0.8, UL/H=0.4

LL/H=0.6, UL/H=0.6

Figure 11. Variation of maxε with reinforcement length

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5.4 Optimum reinforcement distribution The results of the parametric study provided insights into the effect of reinforcement distribution on the

wall behavior in a quantitative manner. Based on these results, an optimum reinforcement distribution was se-lected based on a lateral wall deformation limit at service condition with due consideration of the tensile strains in the reinforcement layers. Considering relatively flexible site constraints in terms of the lateral wall deformation, it seemed reasonable to set the maximum allowable lateral wall deformation at 1.0~1.5%H. Ac-cording to the results of the parametric study, the above criterion could be met when geogrid reinforcements having J=2000 kN/m be placed with an average length of TL/H=0.7. Among the several possible reinforcement distributions for TL/H=0.7, a reinforcement distribution of LL/H=0.6 and UL/H=0.8 was recommended since such a distribution could minimize the reinforcement loads in the lower tier compared to other combinations.

The selected design was checked for its appropriateness based on the limit equilibrium-based current de-sign approaches. A global stability analysis was also carried out using the Bishop’s simplified method. The stability analysis based on the FHWA design approach yielded a minimum factor of safety against tensile overstress 1.2 with other factors of safety being much greater than the minimum required minimum values. The factor of safety against global failure also increased to 1.3, satisfying the required minimum of 1.3. These results confirmed that the suggested design satisfied the minimum requirements specified in the current design assumptions. 6 SUMMARY AND CONCLUSIONS

This paper presents a case history concerning the use of finite-element procedure in the design of a geosyn-thetic-reinforced segmental retaining wall in a tiered configuration on an unfavorable foundation condition. On account of the limitations in the current design approaches in dealing with foundation yielding, a verified finite-element model was used as a design aid in selecting an optimum reinforcement distribution that could assure short and long-term stability under possible foundation yielding.

The results revealed that the foundation yielding could significantly increase the wall deformation and the associated reinforcement loads. Furthermore, for a given average reinforcement length TL/H, any combina-tion of LL/H and UL/H yielded practically the same max,hδ at least within the range of the reinforcement lengths considered as long as 6.0/ ≥HLL . The maximum strain in the lower reinforcement appeared to be mainly influenced by the upper tier reinforcement length and remained practically the same regardless of the reinforcement length in the lower tier for a given UL/H. Further inspection of the results also indicated that for a given TL/H, it would be a bit more beneficial to employ longer reinforcement in the upper tier in view of reducing reinforcement loads in the lower tier. Based on the results of the parametric study, it was recom-mended that geogrid reinforcements having J=2000 kN/m be placed with combination of LL/H=0.6 and UL/H=0.8.

It is shown that despite the limitations of the soil models and analytical procedures, the finite-element pro-cedure can be effectively used in a non-routine design. Potential use of a verified finite-element procedure for designing geosynthetic-reinforced segmental retaining walls under complex boundary conditions was demon-strated.

REFERENCES

Bathurst, R.J., “Instrumentation of Geogrid-Reinforced Soil Walls”, Transportation Research Record, No. 1277, Soils, Geology, and Foundations, Modern Geotechnical Methods: Instrumentation and Vibratory Hammers, pp. 109-116(1990).

Chou, N. N. S. & Wu, J. T. H., “Investigating performance of geosynthetics reinforced soil walls”, Rep. No. CDOT-UCD-R-93-21, Colorado Dept. of Transportation. (1993).

Collin, J.G. & Berg, R.R., “Permanent geogrid reinforced soil retaining walls – US experience”, Proc. Recent Case Histories of Permanent Geosynthetic-Reinforced Soil Retaining Walls, Tatusoka and Leshchinsky (eds), pp. 61-68(1994).

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Collin, J., Design Manual for Segmental Retaining Walls, 2nd Ed. National Concrete Masonry Assosiation (NCMA), Virginia, USA. (1997)

Davis, E.H., “Theories of plasticity and the failure of soil masses”, Soil mechanics: Selected topics, I. K. Lee, ed., Butterworth’s, London, U.K., pp. 341-380(1968).

Desai, C.S., Zaman, M.M., Lightner, J.G., and Siriwardane, H.J., “Thin-layer elements interfaces and joints”, Int. J. for Num. Anal. Mech. in Geomech., Vol. 8, pp. 19~43(1984)

Duncan, J. M., Bryne, P., Wong, K. S. and Marbry, P., “Strength, Stress-Strain and Bulk Modulus Parameters for Finite Element Analyses of Stresses and Movements in Soil Masses,” Geotechnical Engineering Re-search Report No. UCB/GT/80-01, University of California, Berkeley. (1980)

Elias, V. & Christopher, B.R., “Mechanically Stabilized Earth Walls and Reinforced Soil Slopes, Design and Construction Guidelines”. FHWA Demonstration Project 82, FHWA, Washington, DC, FHWA-SA-96-071(1997).

Hibbitt, Karlsson, and Sorensen, Inc., ABAQUS users manual, Version 6.3, Providence, R.I. (2002). Juran, I. & Christopher, B., “Laboratory Model Study on Geosynthetic Reinforced Soil Retaining Walls”,

Journal of Geotechnical Engineering, ASCE, Vol. 115, NO. 7, pp. 905-926(1989). Kapurapu, R. & Bathurst, R.J., “Behavior of Geosynthetic Reinforced Soil Retaining Walls Using the Finite

Element Analysis”, Computers and Geotechnics, Vol. 17, pp. 179-299(1995). Leshchinsky, D., Putting Technology to Work: MSEW and ReSlope for Reinforced Soil-Structure Design.

Geotechnical Fabrics Report, Vol. 18, 34-39(1999). Park, B.Y., Personal communication (2000). Peck, R. B., Hanson, W. E., and Thornburn, T. H., Foundation Engineering, 2nd ed., Willey, New York (1974). Rowe, R.K. & Ho, S.K., “Continuous Panel Reinforced Soil Walls on Rigid Foundations”, Journal of Geo-

technical and Geoenvironmental Engineering, ASCE, Vol. 123, No. 10, pp. 912-920(1997). Simac, M.R., Christopher, B. R. & Bonczkiewicz, C., “Instrumented field performance of a 6 m geogrid soil

wall”, Proc. 5th Int. Conf. On Geotextiles, Geomembranes and Related Products”, Den Hoedt (ed.), pp. 53-59(1990).

Yoo. C. S., & Lee, K. M., “Investigation on Behavior of Reinforced Segmental Retaining Walls”, Journal of Korean Geotechnical Society, KGS, Vol. 15, NO. 1, pp. 53~62(1999).

Yoo. C. S., & Kim, J. S., “Behavior of Soil-Reinforced Retaining Walls in Tiered Arrangement”, Journal of Korean Geotechnical Society, KGS, Vol. 18, NO. 3, pp. 61~72(2002).

Yoo, C. S., “Measured and Predicted Behavior of a Geosynthetics-Reinforced Segmental Retaining Walls, In-ternal Report, Sungkyunkwan University (2003).