Rajagopal KARPURAPU. Department of Civil ...... Bathurst, R.J., Simac, M.R., and Berg, R.R., Review of the NCMA Segmental Retaining. Wall Design Manual ...
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md Geotechnics 17 (1995) 219-299 0 1995 Elsevier Science Limited in Great Britain. A11 rights reserved 0266-352X/95/39.50
ELSEVIER
BEHAVIOUR
OF GEOSYNTHETIC
REINFORCED
SOIL RETAINING
WALLS
USING THE FINITE ELEMENT METHOD Rajagopal KARPURAPU Department
of Civil Engineering,
Department
of Civil Engineering,
Indian Institute of Technology, Madras, India 600036 Richard J. BATHURST Royal Military College of Canada, Kingston, Ontario, Canada
K7K 5LO
ABSTRACT The Paper describes finite element models that are used 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 (geosynthetic) 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 analyses 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 standard 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 simulate 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 completed 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 techniques. 279
280 The most common
methods
based on limit-equilibrium
of analysis for geosynthetic
methods
reinforced
limited in their ability to predict stresses, forces and boundary and offer no information more, current methods not distinguish
Composite
on deformations
(i.e. excessively finite element
my but cannot provide within component a discrete
facing treatments
materials.
approach
methods
is adopted
soil retaining
analyses of reinforced
structures
within a test facility 2.4m wide x 6m
were 3m high and were constructed
sheeting
arrangement.
at the test facility boundaries
simulations,
0.7m wide and one central instrumented
A complete
discussion
One physical test was an incremental directly behind
central instrumented
and Benjamin
[16] and Bathurst comprising
during placement
the panel [4, 211. Once backfill operations
row of panels the external supports were removed
assumed
simulating
ported externally
four rows of panels
and compaction were completed
in the weak direction
panel construction
Both walls were reinforced and extending
construction
of soil behind
a
and moved to the next row of panels. Layers
the stacked panels to providevertical
for the duration of fill placement.
ment was complete.
The different
a full-height
in
wall test
[4] .
compressibility
to the facing system. In the second physical test the panel units were bolted together three columns
shear-
wall section
of edge effects in the RMC retaining
supported
of soft foam rubber were placed between
plywood/
frictional
plane strain condition
panel wall structure
each 0.75m high that were individually
of reduced
sec-
the contained
by using a composite
The combination
and a decoupled
facility can be found in the Papers by Bathurst
located
with three col-
sand was used as the backfill. Friction between
in a physical model that was close to the idealized
numerical
such as load
PROGRAM
soil and the vertical sidewalls of the test facility were minimized
resulted
soil structures
in order to explore mechanisms
of two outer sections
tion 1 m wide. A dense granular
ing resistance
and
(e.g. [9-U]). In the current investigation,
walls were constructed
long x 4m high. The completed
Plexiglass/polyethylene
econo-
acting between
layers and soil fill.
EXPERIMENTAL
umns of panels composed
Further-
in this Paper can-
and have been proven to
to isolate mechanisms
To date, most finite element
reinforcement
Two reinforced
components.
(e.g. [S-S]) h ave the advantage of computational
methods
the detail that is required
finite element between
at working load levels
safe) [3-41.
have been based on discrete finite element transfer
reactions
and strains in the structure
walls built with different
are
offer simplicity they are
of design and analysis for the types of wails described
between
be conservative
soil wall structures
(e.g. [l-3]). While these methods
to create
[22]. These panels units were sup-
The supports were removed once fill placewith four layers of a biaxial geogrid oriented
3m into the backfill.
techniques different
and wall facing type can be anticipated
to result in
wall response.
panel wall
qualitatively
and quantitatively
construction
means that outward wall deformations
The use of incremental
are developed
as construction
proceeds
281
from base to wall crest. Hence, tensile loads in the reinforcement construction
are generated during the
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 panel structure that is braced externally for the duration of construction prevents mobilization of the reinforcement In addition,
tensile capacity until the full height of fill is placed and the props removed.
the monolithic
panel construction
and pinned
toe connection
results in
constrained wall deformations. Despite obvious differences in wall construction it is interesting 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 behaviour of the backfill soil, polymeric reinforcement, tween components
wall facing units, and the interfaces be-
[9-111.
displacement Dotentiometer surcharae
T
E
load ring D
3m
*-_$(-
f-i
reinfircement
Layer 2
-
1 ,,_,___.~p 0.5m T
I Din
load cell
FIGURE 1
Cross-section view of incremental panel wall test
282 of sheet polymeric reinforcement
The properties
on the rate of loading, duration [13] have explicitly included
under tensile load are strongly dependent
of load application
and temperature
time as a parameter
[24,25]. Matsui and San
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 model
granular
the time dependency
soils), then isochronous
of geosynthetic
stiffness data can be used directly to
reinforcement
in soil retaining
wall structures
[9-111. The strength
and stiffness properties
ear elastic models,
no-tension
of granular soils have been modelled
models, and more rigorous elastic-plastic
The major disadvantagewith
advanced
mulated
containing
in terms of functions
determined perbolic
using routine laboratory
constitutive
plasticity features
models for soils is that the models are for-
parameters
whose numerical
values cannot be easily
tests. In the current investigation
a modified form of hy-
model was developed
of granular
more, these parameters to hyperbolic
constitutive
and was shown to capture
soil behaviour
with a minimum
can be estimated
from routine
models of the type originally proposed
eter that is required
to accurately
large-scale
walls constructed
retaining
simulate
laboratory
strength,
and
Further-
testing. The modification
by Duncan et al. [28] is a dilatancy param-
laboratory
shear test data and the behaviour
with the same granular
of
soil. Pullout tests performed
and soil materials
onstrate
of soil in contact with the reinforcement
This soil dilatancy is responsible
stiffness,
number of parameters.
geogrid reinforcement that dilatancy
using simple lin-
models [5-15,26,27J.
on
similar to those used in the current study clearly democcurs during shear transfer.
in part for the bond capacity that can develop in the anchorage
zone [29]. The interfaces
between
lated using stick-slip clude normal pressure earlier investigations candidate
various components
acting at the interface have been obtained
reinforcement
simulation
special nonlinear
have been simuparameters
strength properties
with and
structures.
ELEMENT
SIMULATION
in this Paper was performed
(GEOFEM)
developed
by the authors
[30]. The package contains a general purpose constitutive
in-
in these
from direct shear and pullout tests performed
work reported
and ancillary utilities
College of Canada
[9-151. The interface
as in the reinforced
FINITE
The numerical
soil structures
models where independent
and backfill soils tested over the same range of normal pressures
at the same soil densities
program
in reinforced
type models and hyperbolic
models developed
using a finite element at the Royal Military
program that includes some
for analysis of soil-polymeric
reinforcement
interaction. The finite element
mesh used for the numerical
is made up of quadrilateral elements,
and triangular
and nodal link elements
simulations
continuum
to represent
elements,
components
is shown in Figure 2. The mesh interface
of the reinforced
elements,
uniaxial
soil wall. Figure
283
anel-soil interface temporary external props during construction
I
3m
1 OSm
T FIGURE 2
Finite element mesh for full-height panel wall test
3 shows mesh details at the reinforcement-panel
each element at these junctions.
connections
and the nodes associated with
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 automatic mesh generation utility that is part of the GEOPEM suite of programs. The finite element 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 downward 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 Equation 1: r
1
BE D B, dv +
{du)i
BE oj B, dV I
V
I
= { P,
[BIT {U } j
]i V
(1)
284
L zero thickness Element 2 3 4 5 6 7 6 9 10 FIGURE 3
Type
Nodes 9-l -3-l l-6-2-7-10 11-3-5-13-7-4-8-12 16-14-9-11-15-10 20-18-11-13-19-12 26-14-16-28-21-15-22-27 17-29-2816-23-22 17-29-23 18-30-29-17-24-23 30-18-20-32-24-19-25-31 11-17
quadrilateral quadrilateral interface interface quadrilateral interface uniaxial bar interface quadrilateral nodal link
Details of finite element mesh at panel-geosynthetic connections
Here, BL and BN are linear and non-linear et al. [31], D is the constitutive
strain-displacement
matrix, and i is the current
relations
to the stresses at the previous load step (i-l) for the first iteration iterations
within a load step, oj corresponds
The load vector in GEOFEM and the internal forces computed on the right hand side of Equation
to the stresses
is formulated
oj corresponds
at a load step. For subsequent
at the previous iteration.
as the difference
from the element
as discussed by Bathe
load step number.
between
the external
stresses in the previous iteration
1. This formulation
ensures that any out-of-balance
is carried forward during the analysis thus satisfying the equilibrium
loads
as shown force
of the total system at all
stages of analysis. The pin connection gular element
units in the incremental mined
from physical
units in the numerical was determined
at the base of the panels was modelled
using a six-noded
as shown in Figure 4. The stiff foam layers separating wall were modelled tests. This arrangement simulation.
using solid elements
inverted trian-
the individual facing panel with a bulk modulus deter-
allowed for independent
movement
of panel
The stiffness of the facing panel in bending and compression
from physical testing prior to construction.
285
stiffneSSpin +f--
pin +--
a)
full-height panel wall FIGURE 4
The incremental
b)
incremental panel wall
Finite element models for wall facing panels
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 simulated 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-balance force norm Nf, defined in terms of out-of-balance
forces Sfi and the applied forces fi
(Equation 2) was less than 0.5%.
N, =
1
Sfi 6f,
5
fi fi
J
(2)
N
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 Young’s modulus Et and tangent bulk modulus Kt. Modulus values are related 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. Poisson’s ratio v at any stage of analysis was computed using the tangent Et and Kr values and was allowed to vary
286 between 0 and 0.495. When the magnitude of Poisson’s ratio exceeds these limits, the magnitude 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 simulations 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,and 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 dilation 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 analysis 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 Eldridge [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-plastic problems in geomechanics such as simple shear, direct shear and bearing capacity of footings. Figure 5 shows some typical results from the simulation of a simple shear test using properties for the sand used in the RMC walls that has a peak friction angle $ of 53” and a dilation angle ‘II,of 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:
287
v
25 shear strain (%,)
a) normalized stress-strain behaviour modified model
p
original model
-‘M
25 shear strain (%)
b) volumetric behaviour 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 volumetric strain curve dsY/dy predicted by the current model is very close to tan+ the conventional hyperbolic model predictsvolumetric ume change during plastic deformation.
In contrast,
compression before yield and zerovol-
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 hyperbolic 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
288 TABLE 1 Hyperbolic parameters for RMC Soil Parameter
Value
K, m
950
%
Parameter
Value
Parameter
Value
n
0.5
C
0
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. Values 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 developed from isochronous load-strain-time
layers is modelled using a nonlinear equation 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 experiments. 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 Jt = a de
+ BE=
(4)
= A + ABE
An excellent curve-fitwas obtained by usingvalues of 60 and -126 for constants A and B respectively as shown in Figure 8b. Compressive forces are not allowed to develop within the reinforcement
elements
as the geosynthetic
reinforcement
layers behave as fabric sheets.
289
0
5.0
2.5 horizontal
a) normalized
stress versus displacement
10.0
7.5
displacement
(mm)
response
2.6 E g E
1.5
g 1.0 S S Ef- 0.5. e 3 .g 0.6
-
test data
---
FEM
2 -0.5 2.5
5.0
b) vertical displacement
versus horizontal
0
horizontal
FEM simulation
FIGURE 6
7.5
displacement
(mm)
displacement
of direct shear test data
0
--15 4 0
test data FEM 100
200
300
400
500
600
plate pressure (kPa) FIGURE 7
Comparison of experimental and predicted pressure-settlement behaviour in plate bearing test
10.0
290
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 fness values, one in the tangential
stif-
(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 backfill 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 reinforcement 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 granular 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 failure plane through the reinforced soil zone at the end of each test. The collapse surcharge pressures for the full-height and incremental wall tests were 80kPa and 70kPa respectively. Incipient 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 fullheight 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. between initial soil failure and reinforcement
The period
rupture was about 250 hours during which large
291
30
6 6.25 kN/m r
20
/
Q e .L t” v) IO
0
0
200
100
400
600
600
l(
2i /
-
test data
or
-y-
~~~+Ztion
IO
0
0
0.10
strain E (mm/mm)
a) constant load (creep) test data FIGURE 8
0.05
time ( hrs )
b) curve-fit for 100 hour isochronous test data
100 hour isochronous load-strain behaviour of geosynthetic reinforcement TABLE 2
Properties of interface elements
initial shear stiffness initial normal stiffness residual shear stiffness residual normal stiffness friction angle
panel/soil interface
soillgeosynthetic
1000 kN/m3 lo6 kN/m3 10 kN/m3 100 kN/m3 2o”
lo6 kN/m3 lo6 kN/m3 10 kN/m3 100 kN/m3 5.9
interface
creep deformations were measured. The peak strains were observed to occur within the reinforced 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 numerical analyses with q=O“ predicted much greater panel displacements and larger reinforcement strains. In some cases the over-prediction was a factor of two greater than measured values as demonstrated
in Figures 10 and 11.
geosynthetic 100
F L E
rupture ~4
end of construction
80
0
400
FIGURE 9
Figure
800 elapsed time (hours)
Panel displacements
10 shows measured
wall during surcharge
during RMC full-height
and predicted
displacements
wall failed between
to those observed
that the finite element placements
and predicted
using*=
reinforcement.
by the numerical Measured
simulations
panel wall
are very close
it is important
in accurate
to note
predictions
of dis-
pressure).
facing profiles are shown in Figure 11. The
at two stages during the final (maximum)
to conditions
Displacements
and predicted
strain magnitude
are reported
corresponding
and the full-height
15”. In addition,
of each to the val-
results show that
collapse pressures
in this study resulted
lateral displacement
panel displacements
charge load increment synthetic
adopted
The predicted
at working load levels (e.g. at 20-40 kPa surcharge
Measured measured
approach
The finite element
60kPa and 75 kPa pressure
in the physical experiments
at the mid-height
in the figure correspond
of surcharge.
failed at slightly greater than 80kPa pressure.
1600 panel wall test
lateral displacements
steps. The measured
ues at the end of each lOOhour increment the incremental
1200
sur-
at soil failure and incipient rupture of geo-
corresponding
to soil failure are accurately
predicted
using W= 15 ‘. reinforcement
tensile strains are illustrated
and trend in strain distribution
in Figure 12. The peak
profiles along the length of the reinforcement
layers in the rigid and flexible facing systems are captured
by the numerical
ple, the elevated strain levels recorded
for the relatively rigid facing test are
evident
in the numerical
results.
at the connections
Similarly, the peak strain levels occurring
forced soil zone are close to the observed strains at the panel connections
results. For examwithin the rein-
internal failure zone. The predicted
agreed within f 1% strain of the measured
reinforcement
values in excess of
200
-
measured
) ---
0
FEM
I
7
20
40 surcharge
60
80
100
(kPa)
a) incremental panel wall FIGURE 10
0
20
40
60
80
100
surcharge (kPa) b) full-height panel wall
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 Experimentally
can be identified.
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 assumption that the reinforced soil zone can be divided into active and resistant zone based on classical 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
294
r
soil failure
3.0
prior to geosynthetic rupture
soil failure
3.0-
I, ,L
~=15” /
2.5
70 kPa surcharge
0,
I 0
I 50
I
---
FEM
---
FEM
-
measured
-
measured
100
150
I 1 I I I , 100 150 200 2 I
panel displacement a)
incremental
Measured
of the wall facing performed elements surcharge
b) and predicted through
is developed
full-height
(mm)
panel wall
the entire loading range. The data illusfor a significant
and distribution
soil zone can be expected is captured
portion
of the
of vertical pressures
to be influenced
to the wall facing. Figure 15 shows that this effect is pronounced in physical experiments
io
at the base of the wall and hence the facing
capacity of the trial walls. The magnitude
The trend observed
2
panel displacements
with a rigid footing are responsible
ing at the base of the reinforced
200
panel displacement
satisfactorily
load shedding
in combination
50
(mm)
panel wall
FIGURE 11
trates that significant
0
at large surcharge
in the numerical
act-
by load shedding pressures.
simulations.
CONCLUSIONS This Paper presents
details of discrete type finite element
forced soil walls together ous components
with the material models employed
in these structures.
The modified
modelling
for geosynthetic
to simulate the behaviour
form of hyperbolic
reinof vari-
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
performance
of geosynthetic
reinforced
simulate all significant
soil walls at both working load and collapse conditions.
features The Paper
295
Layer 4
incremental
wall Layer 3
-
0
0.5
full-height
1.0
panel wall
1.5
2.0
2.5
3.0
8full-height
panel wall
Layer 2
‘;i 5 .5 s” UY 01 0
1
0.5
1.0
1.5
2.0
2.5
3.0
3full-height
T 5 .E S *
2.J I0, 0
panel wall Layer 1
\ \
incremental wall cfull-height panel wall
\ I’. \ ~_---\--,___
FIGURE 12
0.5
-
I
measured FEM
---
__ 1.0
Strain in geosynthetic
1.5
reinforcement
2.0
2.5
1 3.0
layers at incipient collapse
296 observed failure surface in test
v
------------
OV 0
0.5
layer 1
1 .o
1.5
2.0
distance from toe (m) ----
distance from toe (m)
M
a) incremental panel wall FIGURE 13 further demonstrates ing the approach
here is that the strength
Predicted and measured Internal failure surfaces
in this investigation. and stiffness
from the results of independent finite
element
b) full-height panel wall
that construction-induced
adopted
modelling
FEM observed failure surface in test
differences
in behaviour
An important
conclusion
properties
routine laboratory
of the composite
of component
materials
can be simulated
us-
of the work described can be determined
tests and then successfully
implemented
in
structure.
ACKNOWLEDGEMENTS
Financial
support for the work reported
Program (ARP) program tional Defence,
here was provided
and by the Chief of Construction
through the Academic
and Properties,
Research
Department
of Na-
Canada. REFERENCES
1.
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Walls, &&r
2.
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297
OS_ I b 0 10 20
1 I I 30 40 50 60 70 surcharge (kPa)
a) incremental
0
10
20
b) propped FIGURE 14
i 80
Rh-cm
I f%
panel wall
30 40 50 60 surcharge (kPa)
70
80
I R”
panel wall
Predicted
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reactions at pinned toe restraint
75-
-------------
50- ’
end of construction
--
25-
0 0
I 1
I 2
I 3
measured FEM
I 4
distance from toe (m) FIGURE 15
Distribution of earth pressures at base of backfill (incremental panel wall)
i
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version
received
3 March
1994; accepted
