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doi: 10.1016/j.proeng.2016.06.055
Numerical Investigations on the Load Distribution over the
Geogrid of a Basal Reinforced Piled Embankment
under Cyclic Loading
Julian Lehn1, Christian Moormann1, and Johannes Aschrafi1
1 Insititute for Geotechnical Engineering (IGS), University of
Stuttgart, Pfaffenwaldring 35, 70569Stuttgart, Germany
[email protected] Insititute for Geotechnical
Engineering (IGS), University of Stuttgart, Pfaffenwaldring 35,
70569
Stuttgart, [email protected]
3 Insititute for Geotechnical Engineering (IGS), University of
Stuttgart, Pfaffenwaldring 35, 70569Stuttgart, Germany
[email protected]
Abstract
The application of basal reinforced piled embankments and earth
structures is an approvedmethod particularly in traffic route
engineering as technique for transferring static and vari-able
loads on soil layers with low bearing capacity (e.g. soft clay)
into deeper stiffer soillayers. Amongst others like CUR 226 and BS
8006 the EBGEO (Recommendations for Designand Analysis of Earth
Structures using Geosynthetics Reinforcements) of the German
Societyfor Geotechnics e.V. (DGGT) provides recommendations on
calculation, design and executionof reinforced piled earth
structures. These recommendations are based on specific
geometri-cal, mechanical and load related boundary conditions,
which are not fully transferable to allgeotechnical applications.
For traffic route engineering the objective is often to minimize
theheight of the bearing layer of the reinforced earth structure to
a technical optimum. For areinforced base layer it becomes
essential, to predict the stability of the arch also due to
cyclicloading as well as effects of surface deformation of the
bearing layer in a reliable way.The paper presents the results of a
three dimensional numerical simulation of a
single-layeredreinforced piled embankment under quasi-static cyclic
loading and compares the stress distri-bution over the geogrid to
current analytical methods.
Keywords: Reinforced piled earth structures, cyclic loads,
geotextile reinforcement, numerical simula-
tion
Procedia Engineering
Volume 143, 2016, Pages 435–444
Advances in Transportation Geotechnics 3 . The 3rdInternational
Conference on Transportation Geotechnics
(ICTG 2016)
Selection and peer-review under responsibility of the Scientific
Programme Committee of ICTG 2016c© The Authors. Published by
Elsevier B.V.
435
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1 Introduction
Earth structures and embankments supported by piles and
reinforced with geogrids (GR) havebeen successfully applied for
many projects especially for road construction. The
geosyntheticacts both as a membrane as well as a reinforcement of
the soil in order to mitigate the punchingshear in the bearing
layer [10]. Hence, the supporting system has clear advantages over
unre-inforced dams, e.g. there is practically no consolidation in
the soft soil and the settlements arelow [1]. The arch model from
[32] is often used as a basis for the theory of load transfer.
Here,the load distribution is divided into three components (see
Figure 1 a). One part is carrieddirectly by an arching effect of
the granular layer into the supporting members (A), anotherpart is
carried through the membrane effect of the geosynthetic grid
indirectly into the supportmembers (B) and the remainder is
transfered via the soft layer (C).
Numerous studies have already been conducted on reinforced piled
earth structures. Modeltests have been carried out by [32] to [17].
Furthermore different numerical investigations havealready been
performed e.g. by [32], [11] and [3] to [14].
The aim of this research is a verification of current load
approaches for which which therequired geosynthetic reinforcement
is to be designed. Especially the influence of cyclic loadson the
arch stability is not understood sufficiently and current
recommendations so as theEBGEO (2011) [7] give only simplified
geometric conditions for the design of reinforced piledearth
structures. Besides, the design of piled embankments with the EBGEO
is limited. Forspecial requirements in geometry or load-bearing
capacity numerical simulations need to beincorporated into the
design planning. However, as shown in Figure 1 b), cyclic loads
have arelevant influence on reinforced systems. In order to get a
better understanding of the load-bearing and the deformation
behavior of piled reinforced earth structures a parametric
studywith real dimensions was carried out to investigate the
influence of cyclic loading. Therefore,the non-static actions will
be simulated as a quasi-static load, since the bearing and
deformation(elastic and plastic) behavior can be observed for each
cycle. But this implicit calculation islimited to a comparatively
low number of cycles because of the high computation time
(everycycle is simulated) and the accumulation of incremental
numerical errors [15]. The other optionwould be an explicit
calculation approach, whereby only plastic deformations are
calculateddue to package of cycles [3].
Based on the model tests of van Eekelen [24], the load approach
of the German EBGEO(2011) was already modified and questioned in
terms of efficiency with regard to the dimen-sioning of the geogrid
reinforcement [26]. It has been shown that the load distribution,
forcalculating the tensions and strains in the geosynthetic, is
rather formed as an inverse triangu-lar load in many cases and not
as an triangular load distribution assumed so far. Furthermore,a
modified bedding approach was introduced, which also assumes
bedding in the field of thesoft layer. The underlying model
experiments and simulations were carried out only with
staticactions; the application of the modified approach under
cyclic loading has not yet been finallyclarified in detail. The
vertical stress distribution of a numerical simulation of a
single-layerreinforced piled earth structures under static and
non-static action will be compared with theapproach of EBGEO and
the modified approach of [26].
The simulation of cyclic loads is important for many
geotechnical constructions, particularlyfor traffic route
engineering like piled embankments to predict the deformations and
potentialappearing of excess pore water pressure which has a big
influence on the load capacity of thestructure. Nevertheless, the
simulation of highly non-linear soil behavior under cyclic load
isstill a particular challenge. Especially the simulation of a
realistic behavior under a high numberof cycles is still a central
question of many research projects.
Numerical Investigations of a Piled Embankment under Cyclic
Loading Lehn et al.
436
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cyclic loads
grain rearrangement
entire system: arching area: (above GR) (below GR)
compaction effects GR hindered formationof shear bands
stiffening effectof the GR
sand layerpushed in soft soil
subgrade effectget lost
strain increase and higher sag in the GR
surface settlement
stress due topunching shear
stiffer areasattract stresses
h
mineral bearing layerarching
Load
A A
Load components A and B + C
C
BB B
CC
Soft soil
a) b)
Figure 1: a) Load transfer of a reinforced piled embankment
(modified from [32]): load partA: directly transferred load by
arching; load part B: load transferred by GR; load part C:
loadcarried by the soft soil; b) Effects of cyclic loading in a
reinforced system [11]
2 Numerical Modeling
2.1 Numerical Approaches for the Simulation of Cyclic
Loading
There are basically two types of numerical approaches for the
simulation of cyclic loads. Theimplicit approach on the one hand
and the explicit on the other hand. It is important tomention, that
the terminology refers only to the calculation of the accumulation
of the soildeformations under cyclic loads and should not be
confused with the well-known term for theintegration type in
numerical simulations. The implicit approach calculates every cycle
andthe total deformation behavior (elastic and plastic strains). In
comparison to this approach,explicit models calculate only the
accumulated plastic deformations under a given number ofcycles
(package of cycles).
There are different explicit approaches for the numerical
simulation of plastic strain accu-mulation, e.g. [8] to [16]. The
high-cycle accumulation model for sand (HCA model) from [27]allows
numerical simulations up to two million cycles [29] and has already
successfully appliedin different projects ([3], [27] and [20] to
[31]). As mentioned before, despite the advantage ofsimulating a
high number of load cycles with explicit accumulation models, the
cyclic loadingwas simulated implicitly to see the change of the
arching effect and the load distribution overthe GR under the
non-static action from load cycle to load cycle.
2.2 Numerical Modeling of Geogrids
For the numerical simulation of reinforced earth structures a
suitable formulation for the geosyn-thetics, an advanced frictional
contact algorithm and sophisticated constitutive modeling
areimportant predictions for a realistic approach. In FE-codes
geogrid layers are usually modeledwith beam- (2D-model) or shell-
respectively membrane-elements (3D-model) with no
bending-stiffness.
In practice, many geosynthetic reinforcement applications are
loaded perpendicularly totheir plane (e.g. traffic route
engineering). Due to this loading type, in combination with thelow
bending stiffness of the geosynthetic-reinforcement, the
reinforcement is loaded mainly by
Numerical Investigations of a Piled Embankment under Cyclic
Loading Lehn et al.
437
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second order geometric effects (geometric nonlinearity).
Therefore the geometry of the meshhas to be updated during the
stepwise incremental loading. As the geotextile is no
longerhorizontal, tensile strains in the geotextile develop due to
vertical loading. The presently usedFE-programs provide often a
calculation procedure for that purpose, which is based on anupdated
Lagrange formulation.
3 Numerical Simulation
3.1 Description and Geometry of the Numerical Model
The three dimensional numerical simulation of a single-layered
reinforced piled embankmentunder quasi-static cyclic loading was
done with the finite element method (FEM) using thesoftware Plaxis
3D 2013.01. The numerical model consist of around 50 000 10-noded
tetrahedralelements. Figure 2 shows the three cross sections used
for the following visualization of the archby showing the direction
of the principle stresses and the geometry and the discretization
ofthe three-dimensional numerical model. For reasons of symmetry, a
quarter of one pile wouldbe enough and would save a lot of
computation time. Although, six piles were modeled to showdifferent
cross sections and though the different shapes of the arch and
their stability underthe quasi-static cyclic loading. The pile area
is 0.8m× 0.8m, the thickness of the soft soil is 1m, the height of
the bearing layer is 2.5m and the distance from pile axis to pile
axis is 2.5mwhich leads to a ratio of the height of the embankment
to the effective center distance of 0.95.The geogrid-reinforcement
was placed directly on the pile and above the soft soil to
preventpunching failure in the sand layer between the pile and the
GR, according to the simulationsof reinforced piled embankments
under static loading ([21], [22]). Furthermore, an interfacebetween
pile cap and GR was added to simulate a more realistic behavior as
otherwise therewould be nearly no slip. An interface between pile
and subsoil and between GR and soil (sandand soft soil) was added
as well. The vertical interface was extended 0.15 m into the
bearinglayer.
Figure 2: a) three cross sections for the analysis of the shape
of the arch and its stability underthe quasi-static cyclic loading;
b) geometry of the 3D model
Numerical Investigations of a Piled Embankment under Cyclic
Loading Lehn et al.
438
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3.2 Material Parameters
For the numerical studies with quasi-static cyclic loading the
Hardening Soil model with smallstrain stiffness (HS small) has been
used for the bearing layer [4]. The HS small model showshysteresis
in cyclic loading, but the implemented version does not generate
accumulated strains[6]. Nevertheless, different authors already
used the material model for dynamic and cyclicloading of
geosynthetic reinforced earth structures and showed a good
agreement to measure-ments, e. g. [12]. The concrete pile was
modeled linear-elastic, as well as the geogrid (with anisotropic
axial stiffness of 1 500 kN/m and no bending stiffness). An
elastoplastic constitutivemodel with a failure criterion by
Mohr-Coulomb was used for the soft soil. Table 3.2 shows
thematerial parameters used in the numerical simulation.
Unit Pile (LE) Soft soil (MC) Bearing layer(HS small)
InterfaceGR-Pile(MC)
γunsat kN/m3 25 18 19 15
γsat kN/m3 - 20 20.6 15
E(50) kN/m2 25 · 106 1 · 103 60 · 103 25 · 106
Eoed kN/m2 - - 60 · 103 25 · 106
Eur kN/m2 - - 180 · 103 -
m - - - 0.3880 -
ν(ur) - 0.0 0.2 0.2 0.0
c kN/m2 - 5 1 1
ϕ ◦ - 10 40.5 10
ψ ◦ - 0 10.5 0
pref kN/m2 - - 100 -
Knc0 - - - 0.35 -
Rinter - 1.0 0.6 0.9 1.0
γ0.7 kN/m3 - - 0.1 · 10−3 -
Gref0 kN/m2 - - 120 · 103 -
Table 1: Soil material sets used in the numerical
simulations
3.3 Simulation Process
After generating the initial stress state of the clay
(K0-Procedure), the concrete pile was ac-tivated (wished in place).
After that the base layer and GR were activated following by
thequasi-static loading. Different authors, e. g. [30], already
showed the possibility to simulatelow-frequency cyclic loads with a
quasi-static loading. Hence, there is no need to define
specialboundary conditions and to simulate absorber for dynamic
waves (only standard fixities: zminfixed in all directions, x and y
fixed horizontal). Examples of this type of cyclic loads are
locksand pumped-storage power plants - two application fields of
geogrid reinforced piled embank-
Numerical Investigations of a Piled Embankment under Cyclic
Loading Lehn et al.
439
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ments. A quasi-static load of 40 kN/m2 ± 30 kN/m2, which means
an alternating load from 10kN/m2 to 70 kN/m2 was applied.
3.4 Numerical Results
Figure 3 shows the vertical stress distribution over the
geosynthetic reinforcement which willdetermine the strain and the
geogrid force in the analytical approaches (i. e. the stress
distribu-tion in the pile area is not shown). Figure 3 a) shows the
geometry of the numerical model andthe analyzed area, Figure 3 b)
and c) shows the analytical approaches of van Eekelen
(inversetriangle over the GR strip) and of the EBGEO (triangle over
the GR strip) and Figure 3 d), e)and f) the distribution of the
numerical calculation for a static surface load of 70 kN/m2,
after50 load cycles and after 70 load cycles. The stress
distribution of the numerical simulation isdifferent to the load
distribution of the EBGEO and fits better to the inverse triangle.
Thegeneral course of the vertical stress distribution remain the
same during cycle loading, thoughthere are some slight quantitative
changes and the course at the stress curve near the pile capgets
smoother.
Figure 3: Vertical stress distribution over the geogrid
reinforcement (stress above the pile isnot shown)
Following [2], the height i. e. the shape of the arch is
interpreted by the vertical stressdistribution in the embankment.
The highest vertical stress describes the outer line of the archand
the lowest vertical stress the inner line. Table 3.4 shows the
height of the outer and theinner line of the arch in the middle of
cross section 1 (GR strip) for the static surface load of70 kN/m2,
after 20, after 50 and after 70 load cycles. The results show a
redistribution at thebeginning of the quasi-static loading. After
around 50 load cycles a stable arch is set up.
Figure 4 shows the principle stress direction for the three
cross sections (see Figure 2 a)for the static surface load and for
the non-static loading after 50 load cycles and after 70
loadcycles. Due to the direction of the principle stresses, the
arching effect can be visualized. As the
Numerical Investigations of a Piled Embankment under Cyclic
Loading Lehn et al.
440
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static surface loadof 70 kN/m2
after 20 cycles after 50 cycles after 70 cycles
height of the outerline of the arch
1.20 m 2.05 m 2.31 m 2.31 m
height of the innerline of the arch
0.46 m 0.17 m 0.17 m 0.17 m
Table 2: Height of the arch in middle of cross section 1: GR
strip in meter starting from thepile head
figures implies, there is no significant difference in the
arches due to the cyclic loading. Figures4 d) to f) shows that
there is also an arching effect in the cross section 2 which
confirms theassumption of the Concentric Arches model of [23].
4 Conclusion and Outlook
Reducing the embankments height and increasing the distance
between the piles of reinforcedpiled embankments lead to a
significant economic optimization. Especially under non
staticactions the structural behavior is not well known, so that
the geometric requirements of therecommendations and the simplified
analytical calculation approaches may lead to an
oversizedsystem.
The numerical investigations led to the following
conclusions:
• The shape of the arch in the sand layer changes under the non
static action, but can beevaluated as stable for the investigated
load, number of load cycles and geometry withthe constitutive law
applied.
• The modified load approach (inverse triangular load
distribution) and the basic idea ofthe three dimensional Concentric
Arches model of [23] seems to be more realistic as theapproach of
the EBGEO under static as well as under cyclic loading.
One of the research focuses at the Institute for Geotechnical
Engineering (IGS) at the Universityof Stuttgart are geogrid
reinforced earth structures under cyclic and dynamic loads. The
aimof current research projects is an improved and realistic
numerical simulation of geotextilesand its interaction with the
soil under mainly non static actions. Furthermore
experimentalinvestigations with different research partners are
planned for the future.
As an outlook and target for additional investigations on piled
reinforced embankment,following points should be mentioned:
• a verification of the numerical model against experimental
data will be carried out;• the behavior among higher number of load
cycles with explicit accumulation models (e. g.
HCA model) and with cyclic and dynamic model and field
tests;
• creep strain in geogrid and time-dependent reduction of
strength (creep rupture);• further specific investigations of the
influence of multilayer reinforcement under cyclic and
dynamic action;
• further studies on reduced sand layer thickness under mainly
non-static action for opti-mizing the bearing system.
Numerical Investigations of a Piled Embankment under Cyclic
Loading Lehn et al.
441
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Figure 4: Principle stress direction (not the same scale) in
cross section 1 (over the geogridstrip): a) under static surface
load of 70 kN/m2, b) after 50 load cycles and c) after 70
loadcycles; in cross section 2 (square): d) under static surface
load of 70 kN/m2, e) after 50 loadcycles and f) after 70 load
cycles; in cross section 3 (diagonal): g) under static surface load
of70 kN/m2, h) after 50 load cycles and i) after 70 load cycles
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