design of reinforced piled earth structures under … · design of reinforced piled earth...

GeoAmericas 2016 3rd Pan-American Conference on Geosynthetics

DESIGN OF REINFORCED PILED EARTH STRUCTURES UNDER STATIC AND VARIABLE LOADS

C. Moormann, J. Lehn and J. Aschrafi, Institute for Geotechnical Engineering (IGS), University of Stuttgart, Germany

ABSTRACT The application of basal reinforced embankments on piled earth structures, is an approved method particularly in traffic route engineering. With this technique, static and variable loads are transferred through a soil layer with low bearing capacity e.g. soft clay, into deeper stiffer soil layers. The ”Recommendations for Design and Analysis of Earth Structures using Geosynthetic Reinforcements”, known as ´EBGEO´ from the German Society for Geotechnics e.V. (DGGT), provide recommendations on calculation, design, and execution of reinforced piled earth structures, similar to CUR 226 and BS 8006. All these recommendations are based on specific geometrical, mechanical and load related boundary conditions, which are not fully transferable to all geotechnical applications. Common design approaches are not able to provide a detailed prediction of the deformation behavior (bending/curvature) of the composite earth structure. That's why it is essential for deformation sensitive problems to apply more sophisticated numerical simulations or even large scale tests. For traffic route engineering the objective is often to minimize the height of the bearing layer and/or to enlarge the pile spacing of the basal reinforced piled embankment to a technical and economic optimum. For a reinforced bearing layer of reduced thickness it is essential, to predict the stability of the arching effect also due to cyclic loading as well as effects of settlement of the bearing layer in a reliable way. The paper will present the results of a comprehensive study on optimization of basal reinforced piled earth structures using a three dimensional numerical model. Based on this, the results of the FE-study on the load and deformation behavior is presented, giving special consideration to the investigation of the load distribution between the granular layer (arching effects), the geosynthetic reinforcement and the subsoil support. In this context, the results of a single layered reinforced structure is compared to a multi-layered ductile reinforced structure and discussed in detail. A proposal for an improved design approach will be formulated discussing the assumptions for the load distribution on the reinforcement as well as for the subsoil support.

1 Introduction Earth structures and embankments supported by piles and reinforced with geogrids (GR) have been successfully applied for many projects especially for road construction. The basic idea of the bearing-system is to take the GR into account to the load transfer. The arch model from Zaeske (2001) is often used as a basis for the theory of load transfer. Here, the load distribution is divided into three components (see Figure 1a). One part is carried directly by an arch effect of the granular layer into the supporting members (A), another part is carried through the membrane effect of the geosynthetic grid indirectly into the support members (B) and the remainder is transferred via the soft layer (C). The geosynthetic acts both as a membrane as well as a reinforcement of the soil in order to mitigate the punching shear in the bearing layer (Heerten et al., 2012). Hence, the supporting system has clear advantages over


unreinforced dams, e.g. there is practically no consolidation in the soft soil and the settlements are low (Alexiew, 2004)

Numerous studies have already been conducted on reinforced piled earth structures. Model tests have been carried out by Zaeske (2001), Heitz (2006), van Eekelen et al. (2012a/2012b), Blanc et al. (2013) and Okyay et al. (2014). Furthermore, different numerical investigations have already been performed (Zaeske 2001, Heitz 2006, Arwanitaki & Triantafyllidis 2006, Moormann & Aschrafi 2013, Girout et al. 2014, van der Peet 2014, van der Peet & van Eekelen 2014, Moormann & Aschrafi 2014).

The main objective of this research is the optimization of single-layer and multilayer reinforced piled earth structures under static and non-static actions. Especially multilayer reinforcements with more than two layers of geosynthetic grid are not yet considered in current design guidelines. Furthermore, the influence of variable loads on the arch stability is not understood sufficiently and current recommendations such as the ´EBGEO´ give only simplified geometric conditions for the design of reinforced piled earth structures. Besides, the design of piled embankments with the EBGEO (2011) is limited. For special requirements in geometry or load-bearing capacity, numerical simulations need to be incorporated into the design planning. However, as shown in Figure 1b, cyclic loads influence the behavior of reinforced systems. In order to acquire a better understanding of the load-bearing and the deformation behavior of piled reinforced earth structures, a parametric study with real dimensions was carried out to investigate the influence of the number of geosynthetic-layers, the type of load (static and quasi-static with low number of cycles), and the embankments height. 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 is limited to a comparatively low number of cycles because of the high computation time (every cycle is simulated) and the accumulation of incremental numerical errors (Niemunis, 2000). The other option would be an explicit calculation approach, whereby only plastic deformations are calculated due to cyclic loading bundles (Arwanitaki & Triantafyllidis, 2006).

Based on the model tests of van Eekelen et al. (2012), the load approach of the German EBGEO (2011) was already modified and questioned in terms of efficiency with regard to the dimensioning of the geogrid reinforcement (van Eekelen et al., 2013). It has been shown that the load distribution, for calculating the tensions and strains in the geosynthetic, is rather formed as an inverse triangular load in many cases and not as an expected triangular load distribution. Furthermore, a modified bedding approach was introduced, which also assumes bedding in the field of the soft layer. The underlying model experiments and simulations were carried out only with static actions; the application of the modified approach under cyclic loading has not yet been finally clarified in detail.


Figure 1: a) Load transfer of a reinforced piled embankment modified from Zaeske (2001): load part A: directly transferred load by arching; load part B: load transferred by GR; load part C: load carried by the soft soil b) Effects of cyclic loading in a reinforced system (Heitz, 2006)

2 Analytical design method of the German EBGEO (2011) The analytical calculation method of the German EBGEO is mainly based on the studies of Zaeske (2001) and Heitz (2006). The recommendation depends on the arrangement of the load-bearing members either in a rectangular grid or in a triangular grid (rotated 45°). A one or two-layer biaxial geogrid or a two-layer crosswise monoaxial geogrid is recommended when piles are used. In a two-layer reinforcement, a soil layer with a height of 15 to 30 cm should be applied between the geogrids. The analytical calculation method of the EBGEO is not valid for more than two geosynthetic layers.

The EBGEO defines a pile efficiency factor in the analytical calculation which describes the load transferred through the arching effect directly to the piles. According to the membrane effect in the GR it is assumed, that the main stress takes place in a reinforcement strip between the vertical point bearing elements, which enables a plane observation of the system. The load on the GR strip of width b is derived as a line load qz from the vertical stresses σz0, which were assumed to be constant, integrated over the influence area AL in the reinforcement plane. Finally, a triangular distributed line load qz with a maximum in the centre of the field is assumed (see Figure 2a). The supporting effect of the soft soil between the vertical bearing elements is taken into account by the approach of subgrade reaction under the reinforcement strips, however the subgrade reaction in the field outside of the reinforcement strips is not considered by the present calculation methods. The determination of the forces and deformations in the geogrids is based on a simplified formula for an elastic embedded rope. Zaeske (2001) created a nomogram to solve these differential equations in the case of infinite rigid and vertical support members. This nomogram was adopted in the EBGEO to determine the maximum GR strain (see Figure 2b).

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 2: a) Resulting action Fk on the reinforcement plane. b) Determination of the maximum strain εx and sag f of GR (EBGEO, 2010).

However, the design technique of the EBGEO is not directly applicable to non-static actions. There are geometric conditions, such as an h / (s-d) ratio of 2.0, which must be fulfilled under variable loads. At the present state of knowledge there is a stable arch under variable loads. If these conditions are not observed, reference is made to the arch reduction process by Heitz (2006). Depending on the geometry, the frequency and the stress an arch reduction factor κ is determined.

3 Numerical modeling of the parametric study The numerical simulations were calculated with the Finite-Element-Method (FEM). In order to take second order geometric effects (geometric nonlinearity) into account, the simulations were done with the application of an updated Lagrange-formulation. Thereby the geometry of the finite element mesh is updated during the stepwise incremental loading, which leads to more realistic geogrid forces.

3.1 Geometry For reasons of symmetry, a quarter of one pile was simulated in the three-dimensional numerical model (see Figure 3) and was simplified assumed to be fixed. The pile diameter is 0.9 m, the soft soil is 5 m high, the height of the bearing layer is 3 m (except in the investigations of the influence of the embankment height) and the pile center-to-center spacing is 2.5 m. The load-bearing system was simulated with a 1-layered and a 3-layered geogrid reinforcement. Ideal contact between the materials was assumed. Nevertheless, different settlements and relative displacements are possible in the numerical model (e.g. due to the elastoplastic material behavior of the subsoil). Especially between the soil and the geogrid, it is assumed that the compound behavior is high (interlocking of soil and grid).

sy

by,subst.

sy

sx

x

y

Lwy

sx

bx,subst.

Lwx

Fy,k

Fx,k

Fx,k

post-likesupport

sz0,k = const.

ALx

ALy

d

bx,subst.

qz,k

a) b)

6.0

5.55.0

4.5

4.03.5

3.02.52.01.51.0

0.5

0.00.00 0.05 0.10 0.15 0.20

max

[%]

ex

0.00.2

0.40.6

0.81.0

1.5 2.0 =

0.16

0.12

0.10

0.08

0.060.04

2.5

3.0

3.54.0

5.0

10.0

k Ls,k W´2

Jk

F / bk ers

Jk

[-]

f /LW


Figure 3: a) Basic geometry and symmetrical part for the numerical investigations; m is the average stress and c is the cyclic stress b) Numerical model with a deformed mesh (scale up factor 5)

3.2 Material parameters For the numerical studies with quasi-static cyclic loading, a hypoplastic constitutive law with intergranular strain has been used for the sand layer, which is described briefly below.

The hypoplastic material model describes the soil as a nonlinear and inelastic material. Furthermore, there is no distinction between elastic and plastic strains, whereby the yield surface, the flow rule and hardening laws are not applicable (EANG, 2014). Nevertheless, a distinction is made between loading, unloading, and reloading. Von Wolffersdorff developed the basic hypoplastic model for cohesionless soils (von Wolffersdorff, 1996). Niemunis & Herle (1997) added the intergranular strain to eliminate ratcheting under cyclic loading (unrealistic high accumulation of deformation). By intergranular strain the stiffness increases with changes in direction of the stress direction, whereby the "ratcheting effect" is avoided. Table 1 shows the used material parameters for the hypoplastic model with intergranular strain.

The concrete pile (E = 24 x 106 kN/m²) and the geogrid (with an isotropic axial stiffness and no bending stiffness) were modeled as linear-elastic elements. An elastoplastic constitutive model with a failure criterion by Mohr-Coulomb was used for the soft soil (E = 1000 kN/m², c’ = 20 kN/m², ’ = 20°).

h

5 m

1.25 m0.45 m

sc= 30 kN/m2

sm= 40 kN/m2

2.5 m

0.9 m

0.1 mGeogrid

Bearing layer

Soft soil

Bearing layer

Soft soil

Pile

a) Basic system sketch for the numerical model b) Numerical model

part for thenumericalsimulation


Table 1: Material parameters for the hypoplastic model for sand (Wichtmann, 2005)

φc hs n ed0 eco ei0 α β R mR mT βr χ

[°] [MPa] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-] [-]

31.2 591 0.5 0.577 0.874 1.005 0.12 1.0 10-4 2.9 1.45 0.20 6.0

3.3 Simulation process After generating the initial stress state of the clay (K0-Procedure) of the numerical simulation, the concrete pile was activated (wished in place). After that the base layer and GR were activated following by the quasi-static loading. Different authors, e.g. von Wolffersdorff and Schwab (2001), already showed the possibility to simulate low-frequency cyclic loads with a quasi-static loading. Hence, there is no need to define special boundary conditions and to simulate absorber for dynamic waves (only standard fixities: zmin fixed in all directions, x and y fixed horizontal). Examples of this type of cyclic loads are locks and pumped-storage power plants – two application fields of geogrid reinforced piled embankments.

Table 2: Simulation process

Phase Description

0 Generating the initial stress state (clay)

1 Installation of the pile (wished in place)

2 Activating of the base layer and the geosynthetic-reinforcement

3-X quasi-static load (40 kN/m² ± 30 kN/m²)

3.4 Results and discussion of the parametric study

3.4.1 Influence of single-layer and multilayer reinforcement under cyclic loading Below, the influence of multi-layer geogrid reinforcement under quasi-static loading will be investigated. A single layer is compared with a three-layer reinforced embankment (sand layer height of 3 m). To ensure comparability of the systems, the sum of the axial stiffness Jk of the geogrid (GR) is kept constant.

Figure 4 represents the geogrid force of the reinforced support layer after 1 and 25 load cycles. Figure 5 shows the geogrid force of a three-layer reinforcement. For better clarity, only the lower and the upper layer are shown. In the single-layer reinforcement, the maximum tension force is significantly higher due to the higher axial rigidity. The peak is due to the strong curvature (large strains) near the pile heads perimeter. Due to the shear stress, the tensile force in the geogrid is reduced to the center. After 25 cycles, the load tension in the geogrid increases slightly and the maximum shifts towards the pile.


Figure 4: Geogrid force F after 1 and 25 load cycles for a 1-layered reinforced embankment; Jk is the axial stiffness of the GR

Figure 5: Geogrid force F after 1 and 25 load cycles for a 3-layered reinforced embankment; Jk is the axial stiffness of each GR

In the three-layer reinforcement, the lower position is always on a similar course. In this case the maximum value drops after 25 load cycles. In the upper reinforcement layer, another tension force profile exists. The tension peak is not as expected. Due to the higher position of the top layer the curvature is reduced and the “stamping area” increased.

0.0 0.5 1.0 1.5 2.0 2.50

5

10

15

20

25

30

35

Tens

ion

forc

e F

in g

eogr

id [k

N/m

]

Distance xsfrom pile axis [m]

1-layered GRJk = 17700 kN/m

load cycle1 25

0.0 0.5 1.0 1.5 2.0 2.50

5

10

15

20

25

30

35 3-layered GRJk = 5900 kN/mper layer

1. load cycleupper GR lower GR

25. load cycleupper GR lower GR

Tens

ion

forc

e F

in g

eogr

id [k

N/m

]



The load transfer factor E for different numbers of load cycles is shown in Figure 6. The single layer and the multilayer reinforcement show no significant differences, so no recommendation for one or the other can be given. However, it cannot review the load bearing characteristics under a higher number of load cycles. Therefore, further numerical or experimental investigations are necessary.

Figure 6: Load transfer factor E of the 1-layered and the 3-layered reinforced embankment

3.4.2 Influence of the embankment height under cyclic loading The following is a study on the influences of the embankments height under quasi-static cyclic loading. The bearing layer is single reinforced. Heights of 1, 2 and 3 m were investigated. The ratio of the height of the embankment to the effective center distance of the piles (h / (s-d)) was at 1 m height 0.38, at 2 m 0.76 and 1.2 at 3 m.

Figure 7 shows the settlement results, at the top edge of the embankment, over the number of loading cycles. The three heights mentioned above were plotted. The settlement of the 1m embankment rises at the beginning and then flattens out. The really strong geogrid forces in Figure 10 after 25 or even only 5 loading cycles indicate an unstable arch in the 1 m embankment.

0 5 10 15 20 250.0

0.5

1.0

Load

tran

fer f

acto

r E [-

]

Number of load cycles N [-]

1-layered 3-layered


Figure 7: Settlement for a 1 m, 2 m and 3 m high embankment

Figure 8: Load transfer factor E for a 1 m, 2 m and 3 m high embankment

It should be mentioned that the serviceability of the 1 m layer cannot be guaranteed in the long term. Figure 9 illustrates the settlements at the surface and the deformation of the geogrid subject to the models width. Significant settlement differences can be recognized on the surface.

Figure 9: Settlement at the surface and the geogrid of the 1 m, 2 m and 3 m high embankment

0 5 10 15 20 250.0

0.5

1.0

Load

tran

sfer

fact

or E

[-]

Number of load cycles N

1 m 2 m 3 m

0.0 0.5 1.0 1.5 2.0 2.525

20

15

10

5

0

-5 Settlement after25 load cycles

h Surface GR1 m 2 m 3 m

Set

tlem

ent [

mm

]



Figure 10: Geogrid force of the 1 m, 2 m and the 3 m high embankment after 5 and 25 load cycles

The lowest settlements for 25 load cycles of the 1 m embankment can be explained on the one hand on the numerical simulation process and the other hand on the linear-elastic material behavior of the geogrid. After the activation of the support layer, the geogrid receives comparatively high tensile forces, creating a very weak arch in the sand layer and thus results in a pre-stressing of the GR. After activating of the bearing layer in the numerical model, the settlements are set to zero. The model with the 3 m high bearing layer has a low settlement. This behavior as well as the slight increase in geogrid forces and the relatively constant load transfer factor (see Figure 8) suggest a stable arch. The 2 m base course thickness shows until circa 10 load cycles a similar deformation behavior as the 3 m thick sand layer. Under further quasi-static cyclic loading the settlement increases significantly and then proceeds to the deformation behavior of the 1 m high bearing layer. The geogrid forces increase highly from 5 to 25 load cycles and the load transfer factor in the first 15 cycles decreases. This indicates an unstable arch under non-static loading.

4 Conclusion, optimization approaches and outlook Reducing the embankments height and increasing the distance between the piles of reinforced piled embankments may leads to a significant economic optimization. Especially under non static actions the structural behavior is not well known therefore, the geometric requirements of the recommendations and the simplified analytical calculation approaches may lead to an oversized system.

Below, the stress distribution over the single layered geogrid (see Figure 11), the resulting line load (see Figure 12) and the bedding stress (see Figure 14) are shown after 1 and 25 load cycles. To determine the line load, the tension acting on the load catchment area is integrated and distributed on the reinforcement strips. The stress distribution over the geogrid and the line load show a significant change after 25 load cycles. Figure 13 shows the different load figures from the British Standard BS8006, the german EBGEO and the modified load distribution from van Eekelen et

0.0 0.5 1.0 1.5 2.0 2.50

5

10

15

20 5th load cycle1 m 2 m 3 m

25th load cycle1 m 2 m 3 m

Tens

ion

forc

e F

in g

eogr

id [k

N/m

]



al. (2012a/2012b). That the modified load approach (inverse triangular distribution) conditionally does not apply by stress redistribution in quasi-static cyclic exposure in the studied geometry and the selected load scheme.

Figure 11: Stress distribution z on the geogrid reinforcement in a section between the piles after 1 and 25 load cycles

Figure 12: Calculated resulting line load q on a reinforcement strip between the piles considering the load influence area after 1 and 25 load cycles

Figure 13: Load figures of the loads on the GR (load components B and C): Load of the reinforcement strip between two load-bearing elements; basic approach of BS8006; basic approach of EBGEO; modified recommendation based on model tests from van Eekelen et al. (2012a/2012b)

0.0 0.5 1.00

100

200

300

Stre

ss

z abo

ve th

e G

R [k

N/m

]

Distance xs from the edge of the pile cap [m]

1st Load cycle 25th Load cycle

0.0 0.5 1.00

100

200

Line

load

q [k

N/m

]


1st Load cycle 25th Load cycle

Bs8006 EBGEO Modified loaddistribution

S


Figure 14: Stress distribution over the soft soil

The numerical investigations led to the following conclusions:

� The stability of the arch in the sand layer under non static actions depends on the compliance of the required minimum embankment height.

� According to the FE-study and the model tests by Heitz, a multi-layer reinforcement results in more stable soil arching under cyclic loading. The numerical simulation shows no significant influence of the number of layers of reinforcement. However, a system stiffening over the pile heads was recognized ("plate/beam-like" supporting).

� The modified load approach (inverse triangular load distribution by van Eekelen, 2012b) seems to be not applicable under cyclic loading.

One of the research focuses at the Institute for Geotechnical Engineering (IGS) at the University of Stuttgart are geogrid reinforced earth structures under cyclic and dynamic loads. The aim of current research projects is an improved and realistic numerical simulation of geosynthetics and its interaction with the soil under mainly non static actions. Furthermore experimental investigations 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:

� the behavior among higher number of load cycles; � 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 with regard to optimize the bearing

system.

0.0 0.5 1.00

100

200

300

bedd

ing

stre

ss

z [kN

/m]


1. Load cycle 25. Load cycle


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