karpurapu & bathurst c&g v17 n3 1995

5/21/2018 Karpurapu & Bathurst C&G v17 n3 1995

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ELSEVIER

Computers md Geotechnics 17 (1995) 219-299

0 1995 Elsevier Science Limited

Printed in Great Britain. A11 rights reserved

0266-352X/95/39.50

BEHAVIOUR OF GEOSYNTHETIC REINFORCED SOIL RETAINING WALLS

USING THE FINITE ELEMENT METHOD

Rajagopal KARPURAPU

Department of Civil Engineering, Indian Institute of Technology, Madras, India 600036

Richard J. BATHURST

Department of Civil Engineering, Royal Military College of Canada, Kingston, Ontario,

Canada K7K 5LO

ABSTRACT

The Paper describes finite element models that are use to simulate the behaviour of two

carefully constructed and monitored large-scale geosynthetic reinforced soil retaining walls.

The walls were constructed using a dense sand fill and layers of extensible polymeric (geosyn-

thetic) reinforcement attached to two very different facing treatments. The model walls were

taken to collapse using a series of uniform surcharge loads applied at the sand fill surface. The

Paper demonstrates that correct modelling of the dilatant behaviour of the sand

soil

is required

to give accurate predictions of wall performance. A modified form of hyperbolic constitutive

model that includes a dilation parameter is adopted to model the behaviour of the granular

soil. Mechanical properties of the constituent components of the large-scale physical models

are established using standard laboratory tests including constant load tests on the polymeric

reinforcement from which isochronous load-strain-time data is developed. The results of anal-

yses show that the finite element model, constitutive models and implementation reported in

this study can accurately predict all important features of wall performance.

INTRODUCTION

The challenge in numerical simulation of geosynthetic reinforced soil wall performance is

to quantitatively predict all features of these composite structures using only the results of stan-

dard laboratory testing carried out on component materials. The challenge is compounded by

the problem of verification due to a general lack of high quality physical data that allows the

accuracy of finite element models to be tested against a wide range of measured response. This

Paper provides details of the finite element techniques and constitutive models used to simu-

late the measured response of two carefully constructed and monitored full-scale geosynthetic

reinforced soil walls constructed at the Royal Military College of Canada (RMC). The com-

pleted physical models were nominally identical in final appearance and function but differed

significantly in facing treatment and construction sequence. Hence, results of these physical

models provide a useful database against which to test the accuracy of numerical simulation

techniques for candidate wall structures that may be built using a variety of construction tech-

niques.

279


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The most common methods of analysis for geosynthetic reinforced soil wall structures are

based on limit-equilibrium methods (e.g. [l-3]). While these methods offer simplicity they are

limited in their ability to predict stresses, forces and boundary reactions at working load levels

and offer no information on deformations and strains in the structure components. Further-

more, current methods of design and analysis for the types of wails described in this Paper can-

not distinguish between walls built with different facing treatments and have been proven to

be conservative (i.e. excessively safe) [3-41.

Composite finite element methods (e.g. [S-S]) h

ave the advantage of computational econo-

my but cannot provide the detail that is required to isolate mechanisms acting between and

within component materials. To date, most finite element analyses of reinforced soil structures

have been based on discrete finite element methods (e.g. [9-U]). In the current investigation,

a discrete finite element approach is adopted in order to explore mechanisms such as load

transfer between reinforcement layers and soil fill.

EXPERIMENTAL PROGRAM

Two reinforced soil retaining walls were constructed within a test facility 2.4m wide x 6m

long x 4m high. The completed structures were 3m high and were constructed with three col-

umns of panels composed of two outer sections 0.7m wide and one central instrumented sec-

tion 1 m wide. A dense granular sand was used as the backfill. Friction between the contained

soil and the vertical sidewalls of the test f cility were minimized by using a composite plywood/

Plexiglass/polyethylene sheeting arrangement. The combination of reduced frictional shear-

ing resistance at the test facility boundaries and a decoupled central instrumented wall section

resulted in a physical model that was close to the idealized plane strain condition assumed in

numerical simulations, A complete discussion of edge effects in the RMC retaining wall test

facility can be found in the Papers by Bathurst and Benjamin [16] and Bathurst [4]

.

One physical test was an incremental panel wall structure comprising four rows of panels

each 0.75m high that were individually supported during placement and compaction of soil

located directly behind the panel [4, 211. Once backfill operations were completed behind a

row of panels the external supports were removed and moved to the next row of panels. Layers

of soft foam rubber were placed between the stacked panels to providevertical compressibility

to the facing system. In the second physical test the panel units were bolted together to create

three columns simulating a full-height panel construction [22]. These panels units were sup-

ported externally for the duration of fill placement. The supports were removed once fill place-

ment was complete. Both walls were reinforced with four layers of a biaxial geogrid oriented

in the weak direction and extending 3m into the backfill.

The different construction techniques and wall facing type can be anticipated to result in

qualitatively and quantitatively different wall response. The use of incremental panel wall

construction means that outward wall deformations are developed as construction proceeds


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from base to wall crest. Hence, tensile loads in the reinforcement are generated during the

construction phase. In addition, vertical deformation of the facing column is permissible due

to the compressibility of the joint material between panel rows. In contrast, the full-height pan-

el structure that is braced externally for the duration of construction prevents mobilization of

the reinforcement tensile capacity until the full height of fill is placed and the props removed.

In addition, the monolithic panel construction and pinned toe connection results in

constrained wall deformations. Despite obvious differences in wall construction it is interest-

ing to note that current limit equilibrium-based analysis methods cannot distinguish between

the generic forms of construction just described.

Following construction, the walls were subjected to a series of surcharge pressure incre-

ments by inflating air bags which were confined between the backfill soil and top of the test

facility. Each pressure increment was maintained at a constant magnitude for at least 100 hours

to measure time-dependent deformations in the wall structures.

A schematic of the wall and the instrumentation that was used as part of the monitoring pro-

gram are shown in Figure 1. Approximately 300 electronic instruments were installed in each

wall [23].

CONSTITUTIVE MODELS FOR COMPONENT MATERIAU

A number of different constitutive models are required to represent the mechanical beha-

viour of the backfill soil, polymeric reinforcement, wall facing units, and the interfaces be-

tween components [9-111.

displacement

Dotentiometer

surcharae

T

oad

3m

0.5m

T

E

ring -

D

load

cell

f-i

-_ (- -

reinfircement Layer 2

1

,,_,___.~p

I Din

FIGURE 1

Cross-section view of incremental panel wall test


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The properties of sheet polymeric reinforcement under tensile load are strongly dependent

on the rate of loading, duration of load application and temperature [24,25]. Matsui and San

[13] have explicitly included time as a parameter in a model that can simulate the reinforce-

ment stiffness as a function of both strain and time. If the creep effects of soil are not significant

(e.g. dense well-graded granular soils), then isochronous stiffness data can be used directly to

model the time dependency of geosynthetic reinforcement in soil retaining wall structures

[9-111.

The strength and stiffness properties of granular soils have been modelled using simple lin-

ear elastic models, no-tension models, and more rigorous elastic-plastic models [5-15,26,27J.

The major disadvantagewith advanced constitutive models for soils is that the models are for-

mulated in terms of functions containing parameters whose numerical values cannot be easily

determined using routine laboratory tests. In the current investigation a modified form of hy-

perbolic constitutive model was developed and was shown to capture stiffness, strength, and

plasticity features of granular soil behaviour with a minimum number of parameters. Further-

more, these parameters can be estimated from routine laboratory testing. The modification

to hyperbolic models of the type originally proposed by Duncan et al. [28] is a dilatancy param-

eter that is required to accurately simulate laboratory shear test data and the behaviour of

large-scale retaining walls constructed with the same granular soil. Pullout tests performed on

geogrid reinforcement and soil materials similar to those used in the current study clearly dem-

onstrate that dilatancy of soil in contact with the reinforcement occurs during shear transfer.

This soil dilatancy is responsible in part for the bond capacity that can develop in the anchorage

zone [29].

The interfaces between various components in reinforced soil structures have been simu-

lated using stick-slip type models and hyperbolic models where independent parameters in-

clude normal pressure acting at the interface [9-151. The interface strength properties in these

earlier investigations have been obtained from direct shear and pullout tests performed with

candidate reinforcement and backfill soils tested over the same range of normal pressures and

at the same soil densities as in the reinforced structures.

FINITE ELEMENT SIMULATION

The numerical simulation work reported in this Paper was performed using a finite element

program and ancillary utilities (GEOFEM) developed by the authors at the Royal Military

College of Canada [30]. The package contains a general purpose program that includes some

special nonlinear constitutive models developed for analysis of soil-polymeric reinforcement

interaction.

The finite element mesh used for the numerical simulations is shown in Figure 2. The mesh

is made up of quadrilateral and triangular continuum elements, interface elements, uniaxial

elements, and nodal link elements to represent components of the reinforced soil wall. Figure


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temporary external props

during construction

anel-soil interface

I

3m

1

OSm

FIGURE 2

Finite element mesh for full-height panel wall test

3 shows mesh details at the reinforcement-panel connections and the nodes associated with

each element at these junctions. This arrangement of elements was adopted after testing sev-

eral trial meshes for numerical accuracy and was also found to be efficient for use with an auto-

matic mesh generation utility that is part of the GEOPEM suite of programs. The finite ele-

ment mesh for each wall consists of approximately 1700 nodal points, 650 elements, and 3300

degrees of freedom.

The solution scheme employed in the computer code updates the stiffness matrix at every

iteration. Large deformation effects are accounted for in numerical simulations by using the

linearised updated Lagrangian method. In this method, the coordinates of nodes are updated

by adding the corresponding displacements of nodes at every load step. Without this scheme

it is not possible to model important effects such as the additional tensile resistance due to the

membrane action of the reinforcement as it deforms to a concave shape immediately behind

the full-height panel wall columns. This effect in physical models is the result of relative down-

ward movement of the soil immediately behind full-height retaining wall facing units.

The stiffness matrix is modified by the nonlinear stress correction terms as shown in Equa-

tion 1:

r 1

BE D B,

dv +

I

BE oj B, dV

I

{du)i =

{

P,

] i -

[BIT {U }

j

1)

V

V


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L zero thickness

Element

2

3

4

5

6

7

6

9

10

Type

Nodes

quadrilateral

9-l -3-l l-6-2-7-10

quadrilateral 11-3-5-13-7-4-8-12

interface 16-14-9-11-15-10

interface 20-18-11-13-19-12

quadrilateral 26-14-16-28-21-15-22-27

interface 17-29-28- 16-23-22

uniaxial bar

17 29 23

interface 18-30-29-17-24-23

quadrilateral 30-18-20-32-24-19-25-31

nodal link 11-17

FIGURE 3

Details of finite element mesh at panel-geosynthetic connections

Here,

BL

and

BN

are linear and non-linear strain-displacement relations as discussed by Bathe

et al. [31], D is the constitutive matrix, and i is the current load step number. oj corresponds

to the stresses at the previous load step (i-l) for the first iteration at a load step. For subsequent

iterations within a load step, oj corresponds to the stresses at the previous iteration.

The load vector in GEOFEM is formulated as the difference between the external loads

and the internal forces computed from the element stresses in the previous iteration as shown

on the right hand side of Equation 1. This formulation ensures that any out-of-balance force

is carried forward during the analysis thus satisfying the equilibrium of the total system at all

stages of analysis.

The pin connection at the base of the panels was modelled using a six-noded inverted trian-

gular element as shown in Figure 4. The stiff foam layers separating the individual facing panel

units in the incremental wall were modelled using solid elements with a bulk modulus deter-

mined from physical tests. This arrangement allowed for independent movement of panel

units in the numerical simulation. The stiffness of the facing panel in bending and compression

was determined from physical testing prior to construction.


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pin +-- stiffneSSpinf--

a) full-height panel wall b) incremental panel wall

FIGURE 4 Finite element models for wall facing panels

The incremental construction technique was simulated by placing rows of elements in se-

quence and gradually turning on gravity-induced body forces over several load steps (typically

ten for each layer and K, = 0.5). The external props used during wall construction were simu-

lated using springs with a linear axial stiffness value determined from measured prop forces

and wall displacements recorded during construction. The surcharge pressure on the wall was

applied in increments of 0.25 kPa per load step. The solution was iterated until the out-of-bal-

ance force norm Nf, defined in terms of out-of-balance forces Sfi and the applied forces fi

(Equation 2) was less than 0.5%.

J

Sfi 6f,

N, =

5 fi fi

(2)

Eight-noded quadrilateral elements were used to model the backfill soil in the wall. The

stiffness matrix and other element matrices corresponding to the soil were computed using

nine-point numerical integration rule. This numerical analysis satisfies the kinematic

constraints required to accurately model the plastic flow as described by Nagtegaal et al. [32].

A modified form of hyperbolic stress-strain model was employed in the current investigation

to model the stiffness behaviour of the backfill soil. The constitutive matrix D is formulated

in terms of tangent Youngs modulus Et and tangent bulk modulus Kt. Modulus values are re-

lated to the confining pressure as in the hyperbolic model originally proposed by Duncan et

al. [28]. These values are applicable only under monotonically increasing load conditions. In

the current study the friction angle of the soil was assumed to be constant. Poissons ratio v at

any stage of analysis was computed using the tangent Et and Kr values and was allowed to vary


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between 0 and 0.495. When the magnitude of Poissons ratio exceeds these limits, the magni-

tude of Kr is adjusted according to the value of I$ and the limiting value of v.

The hyperbolic model is simple to use and has the advantage that model parameters can

be easily determined

from

standard laboratory test data. This model has been used extensively

for the analysis of many soil structures as reported by Duncan et al. [28]. However, this model

can only be used for monotonically increasing load conditions as it is not applicable for simula-

tions involving unload-reload conditions.

Soil dilation is an important mechanism that controls the strength of soil and the efficiency

of load transfer from the reinforcement to the soil during shear deformations in reinforced soil

structures [29]. Conventional hyperbolic models lack the ability to simulate the dilation beha-

viour of granular soils. This deficiency in the original model can be overcome by using it in

conjunction with classical plasticity models.

Elastic-perfectly plastic models which are based on associated flow rules predict excessive

dilation of soil and hence it is common to employ a plastic potential function defined in terms

of a dilation angle II, nd use a non-associated flow rule to compute the plastic strains of soils.

Zienkiewicz et al. [36] have suggested a suitable form for the plastic potential function by using

dilation angle I in place of the friction angle I$ in the Mohr-Coulomb yield function. The same

yield and potential functions have been employed in the current investigation. The stress state

at any stage is computed by correcting the stresses along the flow direction defined by the dila-

tion angle in the potential function.

The constitutive matrix D which relates the incremental stresses and strains is formulated

using the current values of Et and Kr.

The incremental stresses are added to the total stresses

from the previous step to update the current stress state. If the updated stress state does not

satisfy the yield criterion, the excess stresses are released along the flow direction using the

dilation angle W_ This technique is similar to the initial stress methods. However, in our

method, the stiffness matrix is continually updated as the stress state changes during the analy-

sis rather than remaining constant as in initial stress methods. The advantage with this ap-

proach is that the stiffness matrix remains symmetric leading to significant savings in storage

space and computational effort.

The results from this model compare well with similar results reported by Byrne and El-

dridge [33] which were obtained using another form of dilatant hyperbolic model. The current

hyperbolic model has been observed to give accurate predictions of many classical elastic-plas-

tic problems in geomechanics such as simple shear, direct shear and bearing capacity of foot-

ings. Figure 5 shows some typical results from the simulation of a simple shear test using prop-

erties for the sand used in the RMC walls that has a peak friction angle $ of 53 and a dilation

angle II, f 1_5[17].The ultimate ratio of shear stress t to normal stress u, in simple shear can

can be expressed using the well-known relationship given in Equation 3 [ 181:


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v

25

shear strain ( ,)

a) normalized stress-strain behaviour

p

-M

25

shear strain ( )

b) volumetric behaviour

modified model

original model

FIGURE 5 Simple shear behaviour using modified hyperbolic model

wh), =

sin Cp cos$

1 - sin+ sinr$

The modified hyperbolic model gives failure stress ratios of 0.972 for 9 = 15 and 0.798

for q = O,

which are in agreement with Equation 3. With zero dilation, peak strengths are

18% lower than those predicted by the hyperbolic model with $I = 15. The slope of the volu-

metric strain curve dsY/dy predicted by the current model is very close to tan+ In contrast,

the conventional hyperbolic model predictsvolumetric compression

beforeyield

and zerovol-

ume change during plastic deformation. If the dilation angle I) is set to zero in the current hy-

perbolic model it degenerates to the original non-dilatant hyperbolic model.

The results of standard triaxial compression tests [19] carried out at densities lower than

those achieved in the as-built structures were used as a starting point for the estimation of hy-

perbolic soil parameters in the current FEM simulations of RMC walls. These parameters

were adjusted based on the results of direct shear tests from two different laboratories carried

out on sand specimens prepared at representative densities [17,34]. Plate bearing tests were

carried out at the surface of the sand backfill after the full-height propped panel wall test was

completed and these results were used as a further independent check on the accuracy of the

estimated parameters. Comparisons between experimental and FEM-predicted behaviour


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TABLE 1

Hyperbolic parameters for RMC Soil

Parameter Value

Parameter

Value

Parameter

Value

K,

950

n

0.5

C

0

m 0.65

Rf

0.75

A+

O0

250

@0

53O

21

W

from direct shear tests and a conventional plate bearing test are shown in Figures 6 and 7. Val-

ues of hyperbolic parameters used in the simulations are summarized in Table 1.

Reinforcement

The reinforcement layers were modelled using three-noded uniaxial elements. These ele-

ments represent a linear strain variation along their length. This order of strain variation is

compatible with that in the surrounding interface and soil elements.

The constitutive behaviour of reinforcement layers is modelled using a nonlinear equation

developed from isochronous load-strain-time test data. The isochronous load-strain data is in-

terpreted from constant load creep test results according to the method reported by McGown

et al. [24]. The creep load tests were performed by subjecting virgin reinforcement samples

to a constant tensile load for an extended period of time. The results of constant load (creep)

tests are shown in Figure 8a. The isochronous curve in Figure 8b for any elapsed time is

constructed from corresponding load and strain values as illustrated in the figures.

In this investigation, the lOOhour isochronous curve was used in the simulations since the

surcharge pressure increments were applied in roughly 100 hour time steps in the physical ex-

periments. The results of in-isolation tests [24,25] have shown that under staged loading the

polymeric materials exhibit a cumulative load-deformation response at the end of any incre-

ment of load that is equivalent to the deformation recorded as if the final load had been applied

in a single step.

In the numerical model, the load P in the reinforcement layer and the tangent stiffness Jr

are related to the strain E in the geosynthetic as shown in Equations 4 and 5.

P = As + BE=

(4)

J

t

= a = A + ABE

de

An excellent curve-fitwas obtained by usingvalues of 60 and -126 for constants and B respec-

tively as shown in Figure 8b. Compressive forces are not allowed to develop within the rein-

forcement elements as the geosynthetic reinforcement layers behave as fabric sheets.


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0

2.5

5.0 7.5

10.0

horizontal displacement (mm)

a) normalized stress versus displacement response

2.6

E

g 1.5

E

g

S

1.0

S

Ef- 0.5.

-

test data

e

---

FEM

.g 0.6

2

-0.5

0

2.5

5.0 7.5

10.0

horizontal displacement (mm)

b) vertical displacement versus horizontal displacement

FIGURE 6

FEM simulation of direct shear test data

0

- test data

--- FEM

15

4

0

100 200

300

400

500 600

plate pressure (kPa)

FIGURE 7

Comparison of experimental and predicted

pressure-settlement behaviour in plate bearing test


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Interface models

The interfaces between the reinforcement layers and soil and those between wall panels

and soil were modelled using six-noded joint elements of zero thickness. These elements have

linear shear strain variation along their length. The six noded joint elements were developed

by extending the four node joint element formulation reported by Ghaboussi et al. [35].

The

global stiffness matrix of these elements is formulated in terms of two independent stif-

fness values, one in the tangential (shear) direction and the other in the normal direction.

When the normal stress on the interface is compressive, perfect bond is assumed in the normal

direction and when the normal stress becomes tensile, the normal stiffness is assigned a small

value to allow debonding at the interface.

The shear strength and stiffness behaviour of interfaces between the wall panels and back-

fill soil were determined using data from direct shear tests carried out on physical models of

the sand/wall panel interface [ 161. The shear stiffness of interfaces between the soil and rein-

forcement was modelled using stick-slip type formulation in which perfect bond was assumed

when the shear stress is less than the shear strength defined by the Mohr-Coulomb model.

When the shear stress exceeds the shear strength, the shear stiffness was reduced to a small

residual value to allow for relative movement between the reinforcement and soil. Based on

the experimental observation that the interface friction angle between well-compacted granu-

lar soil and most types of geogrids is higher than that of the soil alone and that failure occurs

within the soil [29], it was decided to use greater shear strength values for the interface than

those for the soil alone. The properties used for all interface elements are reported in Table

RESULTS AND DISCUSSION

Selected experimental results

The physical models were monitored until collapse due to surcharging or until incipient

collapse was suspected [4,17,20-221. Both structures revealed a well-developed internal fail-

ure plane through the reinforced soil zone at the end of each test. The collapse surcharge pres-

sures for the full-height and incremental wall tests were 80kPa and 70kPa respectively. Incipi-

ent collapse was manifest as accelerated lateral panel displacements (e.g. Figure 9) and

elevated reinforcement strains indicating load transfer from soil to reinforcement. In the full-

height panel wall test the uppermost reinforcement layer ruptured at the panel connection.

The strains within the reinforcement layers revealed a saddle-shaped distribution with a peak

at the panel connections and another peak at about the location of the internal soil failure

plane.

The incremental panel wall failed in two distinct steps identified as initial shear failure of

the soil in the reinforced soil zone followed by load transfer to the reinforcement. The period

between initial soil failure and reinforcement rupture was about 250 hours during which large


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30

20

Q

e

.L

t

v)

IO

0

/

6.25 kN/m

0

200 400 600 600 l(

100

time ( hrs )

a) constant load (creep) test data

6

r

2i /

- test data

or -y- ~~~+Ztion

IO 0

0.05 0.10

0

strain E (mm/mm)

b) curve-fit for 100 hour

isochronous test data

FIGURE 8 100 hour isochronous load-strain behaviour of geosynthetic

reinforcement

TABLE 2

Properties of interface elements

panel/soil interface soillgeosynthetic interface

initial shear stiffness 1000 kN/m3

lo6 kN/m3

initial normal stiffness lo6 kN/m3 lo6 kN/m3

residual shear stiffness 10 kN/m3

10 kN/m3

residual normal stiffness 100 kN/m3 100 kN/m3

friction angle

2o

5.9

creep deformations were measured. The peak strains were observed to occur within the rein-

forced soil mass rather than at the connections as recorded in the full-height panel wall. The

distribution of reinforcement strains at incipient collapse in both tests are compared with pre-

dicted values later in the Paper (see Figure 12).

Numerics

One set of numerical analyses was performed with a soil dilation angle v=O and the other

using a value of v,= 15 based on laboratory direct shear test results described earlier. The nu-

merical analyses with q=O predicted much greater panel displacements and larger reinforce-

ment strains. In some cases the over-prediction was a factor of two greater than measured val-

ues as demonstrated in Figures 10 and 11.


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end of

construction

F 80

L

E

geosynthetic rupture ~4

400 800

1200 1600

elapsed time (hours)

FIGURE 9 Panel displacements during RMC full-height panel wall test

Figure 10 shows measured and predicted lateral displacements at the mid-height of each

wall during surcharge steps. The measured displacements in the figure correspond to the val-

ues at the end of each lOOhour increment of surcharge. The finite element results show that

the incremental wall failed between 60kPa and 75 kPa pressure and the full-height panel wall

failed at slightly greater than 80kPa pressure. The predicted collapse pressures are very close

to those observed in the physical experiments using*= 15. In addition, it is important to note

that the finite element approach adopted in this study resulted in accurate predictions of dis-

placements at working load levels (e.g. at 20-40 kPa surcharge pressure).

Measured and predicted lateral displacement facing profiles are shown in Figure 11. The

measured panel displacements are reported at two stages during the final (maximum) sur-

charge load increment corresponding to conditions at soil failure and incipient rupture of geo-

synthetic reinforcement. Displacements corresponding to soil failure are accurately predicted

by the numerical simulations using W= 15 .

Measured and predicted reinforcement tensile strains are illustrated in Figure 12. The peak

strain magnitude and trend in strain distribution profiles along the length of the reinforcement

layers in the rigid and flexible facing systems are captured by the numerical results. For exam-

ple, the elevated strain levels recorded at the connections for the relatively rigid facing test are

evident in the numerical results. Similarly, the peak strain levels occurring within the rein-

forced soil zone are close to the observed internal failure zone. The predicted reinforcement

strains at the panel connections agreed within f 1% strain of the measured values in excess of


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- measured

) --- FEM

I

0 20 40

60 80 100

surcharge (kPa)

a) incremental panel wall

7

0 20

40 60 80 100

surcharge (kPa)

b) full-height panel wall

FIGURE 10

Lateral panel displacements at the end of surcharge increments

1% strain at all surcharge levels. The 1% strain threshold is considered by the authors to be

the minimum value for which significant strains in the reinforcement can be identified.

Experimentally observed and numerically predicted failure surfaces (planes) in both walls

were found to closely match the failure surfaces given by Rankine theory using the peak friction

angle of the backfill soil (Figure 13). The failure surfaces in the numerical models are inferred

from either the location of peak reinforcement strains or from the shear strain contours as

shown in Figures 13a and 13b. This finding gives confidence to the widely used design assump-

tion that the reinforced soil zone can be divided into active and resistant zone based on classi-

cal earth pressure theory [l-2].

Figure 14 shows measured and predicted forces developed at the base of the wall facing

units. The comparison is reasonably good indicating that the interface elements in the vicinity


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soil failure

3.0

2.5

r

rior to

geosynthetic

rupture

70 kPa surcharge

--- FEM

- measured

0, I I I I 1 I I I ,

0 50 100 150 200 2

panel displacement (mm)


I

soil failure

3.0-

I, ,L ~=15

/

---

FEM

- measured

0 50 100 150 200 2

panel displacement (mm)


io

FIGURE 11 Measured and predicted panel displacements

of the wall facing performed satisfactorily through the entire loading range. The data illus-

trates that significant load shedding is developed at the base of the wall and hence the facing

elements in combination with a rigid footing are responsible for a significant portion of the

surcharge capacity of the trial walls. The magnitude and distribution of vertical pressures act-

ing at the base of the reinforced soil zone can be expected to be influenced by load shedding

to the wall facing. Figure 15 shows that this effect is pronounced at large surcharge pressures.

The trend observed in physical experiments is captured in the numerical simulations.

CONCLUSIONS

This Paper presents details of discrete type finite element modelling for geosynthetic rein-

forced soil walls together with the material models employed to simulate the behaviour of vari-

ous components in these structures. The modified form of hyperbolic model used by the au-

thors is shown to account for soil shear strength increase due to dilation. The results presented

in the Paper show that it is possible to accurately simulate all significant performance features

of geosynthetic reinforced soil walls at both working load and collapse conditions. The Paper


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Layer 4

incremental wall

Layer 3

- full-height

panel wall

0 0.5

1.0 1.5

2.0

2.5 3.0

8-

full-height panel wall Layer 2

;i

5

.5

s

UY

01 1

0 0 5

1.0

1.5 2.0

2.5 3.0

3-

T

2.J

full-height panel wall

5 Layer 1

.E

\

S

- \

incremental wall

* I-

cfull-height panel wall

I.

I

- measured

\ \

~_---\--,___ __

--- FEM

0, 1

0 0.5

1.0

1.5 2.0

2.5 3.0

FIGURE 12 Strain in geosynthetic reinforcement layers at incipient collapse


18/21

296

observed failure

surface in test

distance from toe (m)


v

layer 1------------

OV

0 0.5 1 o 1.5 2.0


---- FEM

M observed failure

surface in test


FIGURE 13 Predicted and measured Internal failure surfaces

further demonstrates that construction-induced differences in behaviour can be simulated us-

ing the approach adopted in this investigation. An important conclusion of the work described

here is that the strength and stiffness properties of component materials can be determined

from the results of independent routine laboratory tests and then successfully implemented in

finite element modelling of the composite structure.

ACKNOWLEDGEMENTS

Financial support for the work reported here was provided through the Academic Research

Program (ARP) program and by the Chief of Construction and Properties, Department of Na-

tional Defence, Canada.

1.

2.

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19/21

297

OS_

I b 1 I I i

1 20 30 40 50 60 70 80 Rh-cm

surcharge (kPa)

I


f

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surcharge (kPa)

I

R

b) propped panel wall

FIGURE 14 Predicted and measured reactions at pinned toe restraint

75-

-------------

0-

end of construction - measured

--5- FEM

0

I I I

I

1 2 3 4


i

FIGURE 15 Distribution of earth pressures at base of backfill

(incremental panel wall)


20/21

298

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Received 22 June 1993; revised version received 3 March 1994; accepted

30 March 1994

karpurapu & bathurst c&g v17 n3 1995

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