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

julian.lehn@igs.uni-stuttgart.de2 Insititute for Geotechnical Engineering (IGS), University of Stuttgart, Pfaffenwaldring 35, 70569

Stuttgart, Germanychristian.moormann@igs.uni-stuttgart.de

3 Insititute for Geotechnical Engineering (IGS), University of Stuttgart, Pfaffenwaldring 35, 70569Stuttgart, Germany

johannes.aschrafi@igs.uni-stuttgart.de

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.

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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

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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

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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-

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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

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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.

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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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