Estudio experimental del empuje sobre estructuras de ... · first stage of research, samples...

Estudio experimental del empuje sobre estructuras de contenciónen suelos reforzados con geomallas

Lissette Ruiz-Tagle*1, Felipe Villalobos**

Experimental study of the lateral earth pressure on retainingstructures in soils reinforced with geogrids

* Constructora Lancuyen Ltda., Concepción. CHILE** Universidad Católica de la Santísima Concepción. CHILE

Resumen

Este artículo presenta un estudio experimental de la variación de las tensiones de empuje sobre una pared que soporta un suelo reforzado con geomallas.

Para ello se utilizó un equipo diseñado y construido especialmente para ejecutar ensayos de empuje bajo condiciones de deformación plana. Se describe

el equipo de ensayo y los instrumentos de medición, así como el suelo y la preparación de las muestras de arena y la geomalla utilizada. En la primera

etapa de la investigación se ensayan muestras sin reforzar y se comparan los resultados con aquellos provenientes de las teorías clásicas de empuje.

Posteriormente se presentan los resultados de ensayos de empuje en suelo reforzado con una, dos, tres y cuatro geomallas. Se concluye que la incorporación

de geomallas como refuerzo en el suelo disminuye el empuje ejercido por el suelo sobre la estructura de contención. Esta disminución del empuje es de

aproximadamente un 25% cuando se usa una geomalla, un 50% con dos o tres geomallas y de un 75% con cuatro geomallas para los espaciamientos,

sobrecargas e incremento de desplazamientos usados. Resultó posible identificar que la distribución de la tensión de empuje con la profundidad no sólo

no sigue la variación triangular sino que se desarrollan arcos de tensiones en el suelo entre las geomallas.

Palabras Clave: Deformación plana, empuje activo, empuje en reposo, geomallas, arcos de tensión

Abstract

This article presents an experimental study on the variation with depth of the stresses due to lateral earth pressure on a wall retaining a soil reinforced with

geogrids. To this end, an apparatus was designed and constructed especially tailored for performing lateral earth pressure tests under plain strain conditions.

The experimental apparatus and the measurement instruments as well as the soil and the sample preparation and the geogrids used, are described. In a

first stage of research, samples without reinforcing are tested and the results are compared with those from classic earth pressure theories. Subsequently,

results from lateral earth pressure tests in soils reinforced with one, two, three and four geogrids are presented. It is concluded that the inclusion of geogrids

as soil reinforcement reduces the earth pressure on the retaining structure. This lateral earth pressure reduction is approximately of 25% when one geogrid

is used, 50% with two or three geogrids and 75% with four geogrids for the spacing, surcharges and displacement increments used. It was possible to identify

that the lateral earth pressure distribution with depth not only does not follow a triangular variation, but it develops stress arching in the soil and between

the geogrids.

Keywords: Plain strain, active earth pressure, at rest pressure, geogrids, and stress arching

Revista Ingeniería de Construcción Vol. 26 No3, Diciembre de 2011 www.ricuc.cl 299

1 Autor de correspondencia / Corresponding author:E-mail: [email protected]

1. Introducción 1. Introduction

Fecha de recepción: 19/ 05/ 2011Fecha de aceptación: 22/ 06/ 2011PAG. 299 - 320

Suelos reforzados con geomallas/Soils reinforced with geogrids

Nowadays the wide use of geosyntheticmaterials is practically unavoidable in construction works,mainly in road and drain works, among many otherapplications (Jones 1996; Müller-Rochholz 2008).

300 Revista Ingeniería de Construcción Vol. 26 No3, Diciembre de 2011 www.ricuc.cl

Lissette Ruiz-Tagle, Felipe Villalobos

Among these geosynthetic materials, the use of geogridsas a reinforcement element on retaining structures hasincreasingly been used for the replacement of traditionalwalls, for example any type of reinforced concrete wall(gravitational or cantilever). The selection of geogridsreinforcement is justified not only as the fastest constructiveand better finishing choice, but most relevant becauseit offers better static and seismic responses. Severe damageshave been observed in the access embankments andabutments of bridges located within the area affected bythe earthquake of moment magnitude 8.8 in February27th 2010 hitting Chile, from Valparaíso to Arauco(Verdugo et al., 2010; Hube et al., 2010). However, majordamages have practically not been reported in geogridsreinforced road embankments, abutments and walls; thefew cases known so far presented completely minordistresses likely to be restored. Las Ballenas bridges inthe Penco-Talcahuano Interportuaria motorway; Bonillaroundabout in Concepcion; north entrance to Chiguayanteand Temuco; rail road crossway in San Francisco deMostazal and Costanera Norte in Santiago are examplesof a better performance during the strong earthquake inFebruary 27th 2010. Tatsuoka et al. (1998) reported thatduring Kobe earthquake in 1995, retaining structures inrailroads embankments reinforced with geogrids werelater employed and they received minor repairing works.That was not the case for traditional retaining structures(gravitational walls, cantilever walls and reinforcedbattered walls), which required significant repairing worksdue to severe damages.

In order to design retaining structures reinforcedwith geogrids, traditional theories of lateral earth pressuresare generally used by assuming a uniform stress distributionon the retaining walls (Jones 1996; EBGEO 2009). In thecase of surcharges, for example a footing resting on thewall upper zone; it is considered that lateral earth pressureis constantly distributed with depth. And in the case oflateral earth pressure behind the wall, it is assumed thatit exerts a linear horizontal stress varying with depth, inaccordance with Rankine or Coulomb theories; bothdeveloped during XIX and XVIII centuries, respectively.The study of a static case is a relevant issue, since theseismic earth pressure can be derived from a pseudo-static case, as occurring in the well known seismic earthpressure theory by Mononobe and Okabe.

301Revista Ingeniería de Construcción Vol. 26 No3, Diciembre de 2011 www.ricuc.cl


Pachomow et al. (2007) present a database withtheir own data and with data from other authors,where experimental results (laboratory and in situ)as well as numerical results are shown. However, it isnot clear or systematic to note the effect of overburdenand wall displacement variations, neither the spacingeffect between geogrids.

Therefore, this article studies such effects, notthoroughly explained yet, with the purpose of determiningthe lateral earth pressure variation over the retaining wallheight. The wall is retaining a granular soil, initiallywithout geogrids and subsequently employing geogridsas soil reinforcement. The employed physical modelcorresponds to a sandy soil sample vertically loaded andexposed to lateral displacement by means of asophisticated test apparatus. Obtained results arecompared, when possible with uniform distributionsproposed by the classical theories of active or at restearth pressures.

Test EquipmentThe test apparatus designed and built by Ruiken

et al. (2010 a,b) at the University of RWTH Aachen, isa steel structure anchored to a foundation slab as depictedin Figure 1. The central zone allows the elaboration ofa sample of 1 m long per 1 m high and 0.45 wide. Suchsoil sample is able to exert lateral earth pressureindependently on two mobile side walls (block movementindicated by arrows in Figure 2a). The sample may alsobe loaded on its upper zone, where a constant surchargecan be placed by means of a compressed air cushion.The sample front facing shown in Figure 1 and 2a aremade of a thick glass and the opposite one located behindis made of steel; both facings are fixed, thus their motionis restricted. In this way, it is possible to reproduce plainstrain conditions, which enable the simulation of retainingstructures of a great length extent. The glass facing ismade of a crystal plate of 106 mm thickness and has anultimate deformation of 0.1 mm under 50 kPa surchargeloads (Hamm, 2008). The equipment walls deformationswill be analyzed further on. Retractile walls have a latexsurface which reaches an angle of friction of soil-latexinterface of approximately 2.6° by using silicone greaseof average viscosity. For the case of crystal wall frictionangle of the interface glass-soil is about 7.5°.


Figura 1. Vista frontal del equipo de ensayo con muestra preparada con 4 geomallasFigure 1. Front view of test apparatus including a sample prepared with 4 geogrids

Figura 2. Esquema del equipo experimental: a) vista frontal y b) vista superiorFigure 2. Experimental equipment sketch a) front view b) upper view


colchón de presión con aire comprimido para sobrecarga barra por donde desliza el bloquesliding platecompressed air cushion for surcharge – block

muestra de suelosoil sample

línea de 20 celdas decarga independientesline of 20 independentloading cells

manubrio paramover bloquecontrol lever tohandle the block

celdas decargaloadingplate

dial

suelosoil

celda decargaloading cell celdas de

cargaloadingcellsdial


Tabla 1. Instrumentación digital de los ensayosTable 1. Digital tests instrumentation


Data AcquisitionTable 1 summarizes the instruments employed

to measure loads and deformations. Loads were measuredby means of load cells type S. A pair of load cells installedin both mobile blocks, reacting inside the structuralframework of test equipment, was employed to measurethe resulting lateral earth pressure on each wall. It isworth mentioning that in order to develop the activeearth pressure test, the mobile block supporting the wallwith the soil behind was increasingly and manuallydisplaced by means of a control lever (see arrows andcontrol lever in Figure 2). In such a way it is possible tocontrol and simulate the development of soil lateral earthpressure on the wall. Another pair of load cells wasinstalled to measure the total strength taken by geogrids(Figure 5). Details concerning geogrids will be explainedlater on.

Normal horizontal earth pressure distributionsover the retaining wall were determined by means ofdeformations measured by 20 strain gauges, each oneinstalled at 50 mm depth (called loading cells inFigure 2). Strain gauges attached to the wall, measurethe deformation as long as they are deformed and; bymeans of their own calibration they allow the calculationof the applied stress, that is to say horizontal earth pressure.

InstrumentoInstrument

Celdas de cargaLoad cells

Celdas de cargaLoad cells

Strain gauges

Fabricante y modeloManufacturer and model

HBM-RSCM tensión y compresiónHBM-RSCM tension and compression

HBM-RSCM tensión y compresiónHBM-RSCM tension and compression

HBM 1-2441-6/120

Rango de mediciónMeasure Rank? Range

0 a 20 kN0 to 20 kN

0 a 20 kN0 to 2 kN

0 hasta 2% de deformación0 up to 2% deformation

Montaje y funciónAssembling and functions

Están instaladas entre los bloques móviles y el marcoestructural de reacción, miden la fuerza sobre las paredesen contacto con el sueloInstalled between mobile blocks and inside reactionstructural block; measure the load on the walls in contactwith the soil.

Se encuentran fijadas en los sujetadores de la geomallay por lo tanto miden la fuerza que toma la geomallaAttached to geogrid fasteners and therefore they measurestress exerted by geogrid.

Están colocados a lo largo de la pared cada 50 mm paradeterminar la distribución vertical de deformacioneshorizontales y así el empujeInstalled alongside the wall, every 50 mm, in order todetermine vertical distribution of horizontal deformationsand, therefore, soil pressure.


Figura 3. Disposición de los diales a) sobre la cara frontal de cristal y b) sobre la cara trasera de acero (dimensiones en mm)Figure 3. Dials arrangement a) over crystal front facing and b) over back steel facing (dimensions in mm)


Fixed walls deformationsAs previously indicated, the front glass facing

of 106 mm has an ultimate deformation of 0.1mm undera surcharge of 50 kPa, according to Hamm (2008). Fromnow on the distribution of horizontal earth deformationis shown, not only on the crystal facing, but also on thesteel facing located at the opposite side. At differentsurcharge and undercharge levels, deformation wasmeasured at several points by means of analog andelectronic dials (Figure 3). Above was executed with thepurpose of determining the influence of surcharge on thesystem deformation during a lateral earth pressure test,thus confirming the presence of plain strain conditions.From the measured results, it was determined that theglass facing deformations are higher than those in thesteel facing. Furthermore, horizontal deformations of theglass facing, although reaching a value higher than 0.1mm and, achieving an ultimate value of almost 0.25mmnext to the base (dial 5) for a surcharge of 50 kPa, it isstill restricted to no more than 0.24%. Therefore it isconcluded that the testing equipment is adequate to studydeformation conditions due to lateral earth pressure underplain strain conditions.

a) b)


Figura 4. Deformación horizontal de las dos paredes móviles laterales durante el llenado y bajo sobrecargaFigure 4. Horizontal deformations on two mobile side walls during filling process and under surcharge condition


Mobile walls deformationsThe horizontal deformation of side mobile walls,

where lateral earth pressure takes place, is a subject ofeven most relevant to assess. For measuring purposes,dials placed at three points alongside the two mobilewalls were used. Figure 4 shows the results ofmeasurements of horizontal deformations during the tankfilling and later under the application of different surchargelevels on the sample. It can be observed that from theapplication of a 20 kPa surcharge, horizontal deformationsincrease at great extent and an ultimate value is obtainedfor = 50 kPa. There is a difference in the horizontaldeformation measured for the two walls. The first showsa deformation not exceeding 0.15 mm and the otherreaches values of 0.8mm. Such wall deformations shouldbe taken into consideration for a further lateral earthpressure test, since they correspond to an initial conditionof at rest pressure.

/Stages/dials arrangement

height of sample h, Surcharge

Def

orm

ació

n ho

rizo

ntal

u, m

mH

oriz

onta

l def

orm

atio

n

upper

center

lower

/Stages /dials arrangement

height of sample h, Surcharge upper

center

lower

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orm

ació

n ho

rizo

ntal

u, m

mH

oriz

onta

l def

orm

atio

n


Figura 5. Barra que sujeta las tiras de la geomalla conectada a una celda de carga, strain gauges en la geomallaFigure 5. Bar supporting the geogrids straps connected to a load cell, strain gauges in the geogrids


2. Tested materials

GeogridsDue to an agreement with the manufacturer, it

is not possible to disclose the brand or the commercialname of geogrids. However, it is possible to indicate theirmain properties. According to the manufacturer the testedgeogrid resists a tensile strength per linear meter, at least,of 30 kN/m. The relation between the tensile load anddeformation of geogrids can be considered as linear fromzero up to a tensile strength 15 kN/m, corresponding toa 5% deformation. As far as stiffness terms EA areconcerned (Modulus of Young and Area A), derivativevalues obtained from limit strength of 2% reach adeformation of 600 kN/m; however, average values of700 kN/m have been measured during tensile load testsof large width. The value measured directly from tensiletests of large width is considered more appropriate thanthat value provided by the manufacturer. The testedgeogrid has white, plain and monolithical polypropylenestraps, which are pre-stretched and welded at the nodes.Mesh woven size is 32.5mm x 32.5mm. Strap thicknessis 0.9mm and junctions are 1.4mm.

Geogrids are connected at the mobile side endsto a bar specially designed to support each geogrids’strap, as indicated in Figure 5. This bar is connected toa load cell, which enables to measure the total or resultingload taken by the geogrids inside the soil.

Loading cell

supporting bar

geogrids


Figura 6. Posición de los strain gauges en la geomalla superior para el caso de ensayo con dos geomallas (geomalla inferior sin strain gauges)Figure 6. Strain gauges arrangement in the upper geogrid, for the case of two-geogrids test (lower geogrids without strain gauges)

Tabla 2. Propiedades geotécnicas de la arena de MarienbergTable 2. Geotechnical Properties of Marienberg’s sand


On the other side, geogrids were implementedwith strain gauges to measure deformations (Figure 5).Figure 6 presents an upper side view of geogrids showingthe central layout for such deformation sensors, and othersinstalled in an area next to the edge.

Granular soilThe soil under study is a sandy material extracted

from Marienberg town in Germany. The sand has agrading distribution ranging from sieves DIN N°5 to N°230(4 mm to 0.063 mm)

By means of drained triaxial tests, it wasconcluded that this sand has a maximum angle of internalfrictional angle of 40°and cohesion of 0 kPa for lateralearth pressure conditions summarized in Table 2.

Lado pared de vidrio/Crystal facing

Propiedad/Property

Peso específico/Specific weight Gs

Índice de vacíos máximo/Maximum void ratio emax

Índice de vacíos mínimo/Minimum void ratio emin

Porosidad máxima/Maximum Porosity nmax, %

Porosidad mínima/Minimum porosity nmin, %

Peso unitario seco /Unit dry weight d, kN/m3

Porosidad/Porosity n, %

Índice de vacíos/Void ratio e

Densidad relativa/Relative Density RD, %

Valor/Value

2.65

0.842

0.482

45.70

32.50

17.24

33.6

0.506

93.3

Lado pared de acero/Steel facing


Figura 7. Dispositivo cónico movible de control de riego de arena, esquema en c) no está a escala

Figure 7. Mobile conic device to control sand pluviation; sketch on c) is not drawn to full scale


The sand samples were prepared by using apluviation technique. The sand is placed inside a funneland it descends by gravity throughout a tube of 1.5 mmlong and 45 mm internal diameter. It is possible to reducethe tube diameter by means of several plates with smallerdiameters; the one used for the elaboration of twelvesamples was of 13mm. Above with the purpose of reducingonce again the section where sand grains descend, thusincreasing grains fall energy (Vaid and Negussey 1984).At the tube outlet, sand grains face a mobile conic deviceand they are pluviated in a radial way. The cone diameterat the very outlet area is 17 mm width, which turns intoan outlet ring of 14 mm (Figure 7). The whole pluviationsystem moves covering the whole sample area, thusmaintaining a constant rate at the grains falling sectionand also at the drop height, from the conical pluviationoutlet up to the surface of the sample.

The maximum dry unit weights were of 17.2kN/m3 app. (Table 2). The preparation of an unreinforcedsample, for a relative density of 93%, took almost 6 hours;and duration increased when more geogrids wereincluded.

a) b) c)



Test schedules and proceduresIn a first stage tests were conducted on

unreinforced geogrids samples; subsequently a geogridwas implemented in the center; two, three and up to fourgeogrids were uniformly spaced with depth. Loadingconditions considered the sequential application ofsurcharge increments without displacing mobile walls.Subsequently, displacement increments of mobile walls,ranging from 0.1 mm to 10 mm were applied, thusallowing the determination of active earth pressure andits variation with depth, for a constant surcharge of 50kPa. For tests in soils reinforced with geogrids, the mobilewalls were displaced until the resulting active earthpressure was balanced by the resulting load taken by thegeogrids.

Results from tests without geogridsFigure 8a presents the horizontal earth pressure

distribution measured by means of the vertical layoutincluding 20 strain gauges, placed in the center of amobile wall, and spaced every 50 mm. Experimentaldata correspond to the horizontal earth pressuredistribution for six surcharge states . The increase oflateral earth pressure under surcharge becomes clear.There is a major increase of lateral earth pressure in theupper wall side with a value higher at 75 mm depth.Besides, lines are included which correspond to theoreticaldistributions of at rest pressure h0 and active earthpressure ha. The determination of those lines considersthe expressions by Jaky and Rankine for at rest pressurek0 and active earth pressure ka coefficients, respectively;by using the internal friction angle of soil = 40 º andthe soil unit weight = 17.24 kN/m3 for the calculationof h0 and ha.

(1)

(2)

h0 = k z + k where k0 = 1- sen

ha = ka z + k where ka = 1- sen1+ sen


(3)


Triangular linear theoretical distributions withdepth approximate to values measured from the centralzone from 0.175 m and 0.825 m, without or with lowsurcharge. Furthermore, when experimental values tendto follow a linear distribution, the values are between thelines of at rest and active cases. In effect, for data in Figure8a, the active case should not be valid since the wall wasnot displaced. However, the lateral earth pressures arereduced for at rest case and approximate to active case,since walls are deformed. This is caused by the at restpressure and due to surcharge, as it was shown inFigure 4. As observed in Figure 9a small deformations(displacement ux = 0.2 mm) are enough to develop activeearth pressure. Going back to the case of only surchargevariation, without walls displacements, ux = 0 is presentedin Figure 8b, which corresponds to a distribution withlateral earth pressure coefficient K with depth, expressedas:

Where h is directly determined from tests.Once again theoretical values k0 y ka are only to beconsidered as the range where measurement determinedvalues are contained for the central wall zones, since inthe upper zone data move away from theoretical values,mainly because of surcharge effect. The lower zonepresents a boundary effect because the wall base is indirect contact with the sand sample base. A simulationcase is established for a very stiff foundation soil, forexample rock or cemented soil. That is why loadtransference or horizontal earth pressure takes placestowards the base as a vertical earth pressure effect. Thisis also known as stress arching effect. It was not possibleto measure such vertical load transferred from the bottomsoil to the equipment base.

K


Figura 8. Suelo sin refuerzo; variación con la profundidad de a) la tensión de empuje horizontal y b) del coeficiente de empuje lateral,para el caso con ux = 0 y variable

Figure 8. Unreinforced soil; variation with depth a) horizontal earth pressure stress and b) lateral earth pressure coefficient,for the case of ux = 0 and variable


The lateral earth pressure variation with depthfor different displacement levels of mobile wall arepresented in Figure 9a. The wall horizontal displacementrequired to develop the active earth pressure is proportionalto the wall height and to the soil stiffness. According toSowers (1979) the minimum displacement required forthe case of dense granular soils is 0.0005H, where H iswall height. Being H = 1 m, displacement ux = 0.5 mm.

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 5 10 15 20 25 30

Tensión de empuje horizontalHorizontal earth pressure stress h, kPa/m

Prof

undi

dad/

dept

hh

, m

0

10

20

30

40

50

kPa/m

u x = 0desplazamientoaplicadoapplied displacement

σha = 3,8 kPa/m

σ= 0 kPa/m

σ

σ h0 = 6,2 kPa/m σ ha = 14,6 kPa/m σ h0 = 24 kPa/m

= 50 kPa/m

ha = 10,9 kPa/m h0 = 17,9 kPa/m

σ

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

Coeficiente de empuje lateralLateral earth pressure coefficient

K

Prof

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dad/

dept

hz,

m

0

10

20

30

40

50

σkPa/m

u x = 0desplazamientoaplicadoapplieddisplacement

ka = 0,217

σ

k0 = 0,36

0 0,1 0,2 0,3 0,4 0,5 0,6


Figura 9. Suelo sin refuerzo; variación con la profundidad a) de la tensión de empuje horizontal y b) del coeficiente de empuje lateral,para el caso de = 50 kPa/m y ux variable

Figure 9. Unreinforced soil; variation with depth a) horizontal earth pressure stress and b) lateral earth pressure coefficient,for the case of = 50 kPa/m and ux variable


By observing both graphs in Figure 9, it is noticeable thatactive earth pressure is developed in the center zone forthe case ux = 0.2 mm. Such difference of 0.3 mm maybe produced, as already mentioned, because the wallundergoes initial deformations due to at rest pressure andsurcharge. For the cases with ux > 1 mm, the active earthpressure theory is no longer valid because lateral earthpressure values are considerably reduced because of therelaxation or decrease of horizontal earth pressure stress.

0 5 10 15 20 25 30

Tensión de empuje horizontalHorizontal earth pressure stress

σh, kPa/m

Prof

undi

dad/

dept

hz,

m

00,10,20,516810

u x , mm

σ= 50 kPa

σha = 14,6 kPa/m σh0 = 24 kPa/m

σha = 10,9 kPa/m σh0 = 17,9 kPa/m

0

0,2

0,4

0,6

0,8

1

0 0,1 0,2 0,3 0,4 0,5 0,6

Coeficiente de empuje lateralLateral earth pressure coefficient K

Prof

undi

dad/

dept

hz,

m

00,10,20,516810

u x , mm

ka = 0,217 k0 = 0,36

σ= 50 KPa



Test Results with geogridsLateral earth pressure test results are now

presented for the cases of one, two, three and fourgeogrids. The Figure 10a presents the lateral earth pressureexerted by a soil reinforced with two geogrids on thefixed wall, i.e., without applying wall displacement, butvarying the surcharge from 0 to 50 kPa/m. The geogridsare placed at 0.3 m and 0.7 m depth, respectively. At restpressure and active earth pressure theoretical curves havebeen included in the graph, the same as in the case ofunreinforced soil case. It can be observed that for thecase without surcharge, theoretical curves are able toapproximately represent experimental data only up to0.5 m, which is the most reduced section for the case ofunreinforced soil presented in Figure 8a. From 0.5 to 1m, theoretical earth pressures overestimate the measuredlateral earth pressures. It means that geogrid is takingsome portion of at rest pressure. Subsequently, whensurcharge is applied the same effect takes place, i.e., thelateral earth pressure measured from the wall withreinforced soil is lower than the one measured from thewall with unreinforced soil.

Figure 10b presents the upper geogriddeformation, which is stretched due to the increase oflateral earth pressure due to surcharge. The geogrid isfixed only at one end while the other is free. Because ofthis difference of boundary conditions at their ends,deformation distribution is not symmetrical. Geogridfixation by means of a cross bar connected to a load cellis presented in Figure 5 and the arrangement of straingauges in the geogrid is presented in Figure 6. Thesestrain gauges enable the measurement of deformationeffect at the center and alongside the geogrids. It mustbe noted that geogrid is most deformed in the zone whereit is fixed contrarily to the end where the geogrid is notfixed. A discharge of 50 to 0 kPa/m is includedsubsequently a recharge from 0 to 50 kPa/m is applied.Although unloading reduces deformation, the latter doesnot return to values close to zero. However, duringreloading deformation does return to values close to thatfor 50 kPa previously applied. It means that during initialload, plastic deformations take place and, during unloadingand reloading cycles, deformations are of elastic orrecoverable type.


Figure 10. Suelo con dos geomallas de refuerzo; a) variación con la profundidad de la tensión de empuje horizontal yb) deformación de la geomalla superior en el plano horizontal para el caso de variable y ux = 0

Figure 10. Soil reinforced with two geogrids a) variation with depth for horizontal earth pressure stress andb) upper geogrid deformation on a horizontal plane for the case variable and ux = 0


After completing the earth pressure tests due tosurcharge, the wall was successively displace in order toapply different states of active earth pressure. The resultsfrom active earth pressure under a constant surcharge of50 kPa/m and incremental displacements on one wallare presented in Figure 11a. The active earth pressureline has been also superimposed here for comparison.The theoretical line is only valid for the first 0.2 m,for a displacement of 0.2 mm. For displacementshigher than 1 mm, a considerable active earth pressureincrease takes places in the upper zone.

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

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1

0 5 10 15 20 25 30

Tensión de empuje horizontalHorizontal earth pressure stress σh, kPa/m

Prof

undi

dad/

dept

hz,

m

0

10

20

30

40

50

σ kPa/m

σha = 3,8 kPa/m σh0 = 6,2 kPa/m

σ= 0 kPa/m

σha = 14,6 kPa/m σh0 = 24 kPa/m

σ= 50 kPa/m

u x = 0desplazamientoaplicadoapplied displacement

σha = 10,9 kPa/m σh0 = 17,9 kPa/m

σ

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Posición de losstrain gauges/strain gauges arrangement , m

Def

orm

ació

n de

la g

eom

alla

geog

rid d

efor

mat

ion

ε ,%

01020304050050

σ kPa/mu x = 0desplazamientoaplicadoApplieddisplacement

0,14%

descarga/discharge recarga/recharge

σ



However, the contrary occurs from 0.2 m and lower,since lateral earth pressure successively decreases withux, even reaching negative earth pressure values. Suchnegative values indicate that a passive earth pressurewould be taking place because of geogrids tensile stress.

Figure 11b presents the results from uppergeogrid deformation due to displacements sequencesapplied on the wall, causing active earth pressure. Thoseresults are the continuation of deformations measuredfor the surcharge increase case. Once again it is observedthat deformation increases in the zone where geogrid isfixed. This increase becomes quite considerable in thefixed end, however, quite slight in the free end, showinga irregular deformation variation between both ends.

A third loading state was analyzed by means ofdisplacement applications on the other wall, located at theopposite side to the wall already tested. Figure 11c presentsdeformation results from the same geogrid, which aresuperimposed to previously measured deformations. Atthis time it is observed that geogrid at the free end is alsodeformed, although a deformation in the fixed end alsotakes place, accumulating a deformation value of 0.64%.This value is more than twice the deformation measuredin the remaining 90% of the geogrid. The 0.64% value ofdeformation 64% corresponds to the load taken by thegeogrid which is approximately 2 kN. By observing Figure13, it is noticeable that this load practically correspondsto the half of the active earth pressure developed for a2mm displacement, in the case of two geogrids.

0

0,1

0,2

0,3

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0,6

0,7

0,8

0,9

1

-5 0 5 10 15 20 25 30


Altu

ra d

el m

uro/

wal

l hei

ght

z, m

0

0,1

0,2

0,5

1

2

3

5

u x , mm

σ= 50 kPa

σha = 14,6 kPa/m

u x

σha = 10,9 kPa/m


Figura 11. Suelo con dos geomallas de refuerzo; a) variación con la profundidad de la tensión de empuje horizontal, b) yc) deformación de la geomalla superior en el plano horizontal para el caso de = 50 kPa/m y ux variable en ambas paredes

Figure 11. Soil reinforced with two geogrids a) variation with depth for horizontal earth pressure stress b) andc) upper geogrid deformation on the horizontal plane for the case = 50 kPa/m and ux variable in both walls


The series of tests concluded with the inclusionof three and four geogrids as reinforcement under thesame initial surcharge conditions. Subsequently,displacements were applied to the wall with fixedgeogrids and later on the wall with loose geogrids.The results on lateral earth pressure over walls withfixed and free geogrids are similar and, the cases withfree geogrids are presented below.

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Posición de los strain gauges/strain gauges arrangement , m

Def

orm

ació

n de

la g

eom

alla

/Geo

grid

def

orm

atio

n e,

%

00,10,20,30,40,5124510

u x , mm

ux de pared opuesta/opposite w

all

sobrecargasurcharge

u x = 0

u x

σ = 50 kPa

0,14%

0,36

%

0,14%

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

Posición de los strain gauges/strain gauges arrangement , m

Def

orm

ació

n de

la g

eom

alla

/Geo

grid

def

orm

atio

nε ,

% 0,00,10,20,30,40,50,81,01,41,8

u x , mm

sobrecargasurchargeu x = 0

σ = 50 kPa

u x

0,14%0,36%



Figure 12 presents the case of a soil reinforced with threegeogrids applying successive displacements on the freegeogrids wall. There is no evidence of similarity betweenthe theoretical linear distribution of active earth pressure,which in fact acquires a contrary trend, i.e., lateral earthpressure decreases with wall height. There is a slightincrease of lateral earth pressure under the geogrids,which is also noticeable in the case of two and fourgeogrids. Generally, it is possible to detect the presenceof a stress arching between geogrids. It reflects the geogridsability to absorb some or great lateral earth pressureportion, which is well evidenced in Figure 12b, with fourgeogrids. This stress arching effect transfers maximumstresses to the wall between geogrids and minimum stressjust where the geogrids are. That is why the lateral earthpressure on the wall is reduced as long as the number ofgeogrids increases. Although this arching mechanism hasalready been observed by Pachomov et al. (2007) inlaboratory tests with walls 3m height, it has not been soclear and systematically observed because of fewinstrumentation was available and greater reinforcementspacings.

To analyze the effect of geogrids quantity onthe lateral earth pressure, expressed as the resulting lateralearth pressure strength as a function of the walldisplacement, the graph presented in Figure 13 has beenmade. Such resultant loads of lateral earth pressure weremeasured by loading cells behind mobile walls. Theresultant load values of lateral earth pressure measuredby loading cells are well correlated with the resultantload of lateral earth pressure obtained from integrationalong the wall height for the measured curves h. InFigure 13 it can be noticed that active earth pressure isreduced in approximately 25% when one geogrid is used,50% with two geogrids and 75% with four geogrids.Similar results are obtained when two and three geogridsare used. This demonstrates that the use of geogrids, assoil reinforcement behind retaining structures, is a goodchoice to reduce lateral earth pressure.

In Figure 13 curves do not begin from a zerodisplacement, because as explained earlier, deformationsare developed in mobile walls during the initial surchargestage, which results in a difference for initial values. Sinceslight displacements take place (up to 0.3 mm) on thewall during surcharge stage, the geogrid is activatedbefore displacement phase (Figure 4). That has aconstructive implication to be considered in the designof retaining structures. In other words, controlled initialdeformations and slight wall deformations should beallowed during construction to reduce or to avoid theinitial at rest pressure.


Figura 12. Variación de la tensión de empuje horizontal con la altura para suelo reforzado con a) tres yb) cuatro geomallas para el caso de = 50 kPa/m y ux variable

Figure 12. Variation of horizontal earth pressure stress versus height for a soil reinforced with a) three andb) four geogrids for the case of = 50 kPa/m and ux variable


0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 5 10 15 20 25 30

Tensión de empuje horizontalHorizontal earth pressure stress

σh, kPa/m

Altu

ra d

el m

uro/

wal

l hei

ght

z, m

0,0

0,1

0,2

0,3

0,4

0,5

0,8

1,0

u x , mm

σ= 50 kPa

u x

σha = 10,9 kPa/m

σha = 14,6 kPa/m

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

0 5 10 15 20 25 30


Altu

ra d

el m

uro

/wal

l hei

ght

z, m

0,0

0,1

0,2

0,3

0,4

0,5

0,8

1,0

u x , mm

σ= 50 kPa

u x

σha = 10,9 kPa/m

σha = 14,6 kPa/m


Figure 13. Variación de la fuerza de empuje versus el desplazamiento horizontal del muro para los casossin y con varias geomallas de refuerzo

Figure 13. Lateral earth pressure strength variation versus wall horizontal displacement for caseswith and without several reinforcement geogrids


3. Conclusions

This article has presented and analyzed asophisticated experimental apparatus, which enables thestudy of lateral earth pressure under plain strain conditions.Results obtained from a series of tests on a smooth wallretaining soil with and without geogrid reinforcements,are initially interpreted according to at rest pressure andactive earth pressure theories. It is shown that there is aclear decrease of horizontal earth pressure when geogridsare used. Furthermore, the use of geogrids favors thereduction of lateral earth pressure between geogrids.Themechanism that enables such decrease is associated tothe development of stress arching. Such stress archingenables the reduction of lateral earth pressure wheregeogrids are located and increases lateral earth pressurebetween geogrids to a maximum value. The load takenby geogrids acts in opposite direction to that of the lateralearth pressure, thus partially absorbing soil horizontalstress against the wall. Distance between geogrids is afactor controlling the development of stress arching. Thelower the distance between geogrids, the greater definedthe formation of stress arching.

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8 9 10 11Desplazamiento horizontal/horizontal displacement u x , mm

Empu

je a

ctiv

o/ac

tive

eart

h pr

essu

re, k

N/m

no reforzado/Unreinforced1 geomalla/1 geogrid2 geomallas/2 geogrids3 geomallas/3 geogrids4 geomallas/4 geogrids

σ = 50 kP a


5. Referencias / References


EBGEO (2009), Empfehlungen für den Entwurf und die Berechnung von Erdkörpern mit Bewehrungen aus Geokunststoffen.Deutsche Gesellschaft für Geotechnik

Hamm C. (2008), Untersuchungen zum Entwurf eines Versuchsstandes zur Durchführung von biaxialen Druckversuchen mitgeogitterbewehrtem Boden. Diplomarbeit der Universität RWTH-Aachen

Hube M., Santa María H. and Villalobos F. (2010), Preliminary analysis of the seismic response of bridges during the Chilean27 February 2010 earthquake. Obras y Proyectos 8, 48-57

Jones C.J.F.P. (1996), Earth reinforcement and soil structures. Thomas TelfordMüller-Rochholz J. (2008), Geokunststoffe im Erd- und Verkehrswegebau. Werner VerlagPachomow D., Vollmert L. and Herold A. (2007), Der Ansatz des horizontalen Erddrucks auf die Front von KBE-Kronstruktionen.

J. Geotechnik Sonderheft, 129-136Ruiken A., Ziegler M., Vollmert L. and Duzic I. (2010a), Recent findings about the confining effect of geogrids from large scale

laboratory testing. 9th International Conference on Geosynthetics, Guarujá, BrazilRuiken A., Ziegler M., Ehrenberg H. and Höhny S. (2010b), Determination of the soil confining effect of geogrids. XIVth Danube-

European Conference on Geotechnical Engineering, Bratislava, Slowak RepublicSowers G.F. (1979), Introductory Soil Mechanics and Foundations: Geotechnical Engineering. MacMillan, New YorkTatsuoka F., Koseki J., Tateyama M., Munuf Y. and Horii K. (1998), Seismic stability against high seismic loads of geosynthetic-

reinforced soil retaining structures. Proceedings Sixth International Conference on Geosynthetics 1, 103-142, Atlanta, USAVaid Y.P. y Negussey D. (1984), Relative density of pluviated sand samples. Soils and Foundations 24, Nº2, 101-105Verdugo R., Villalobos F., Yasuda S., Konagai K., Sugano T., Okamura M., Tobita T. and Torres A. (2010), Description and analysis

of geotechnical aspects associated to the large 2010 Chile earthquake. Obras y Proyectos 8, 25-36

Deformation alongside the geogrid varies foreach loading phase, as well as the and whit that theabsorption or not of load, thus reaching a maximum nextto the wall, which indicates the lateral earth pressureproportion taken by the geogrid.

Horizontal earth pressure is reduced in 25%,50% and 75% depending on the use of one, two, threeor four geogrids, respectively.

Furthermore it was observed that geogrid absorbsloads before beginning wall displacement, i.e. duringsurcharge application stage.

Further research is required to study the effectof less rigid soil foundation than filling soil behind thewall and, to study the effect on wall stiffness.

4. Acknowledgements

The first author is thankful for the scholarshipgranted by the DAAD and also to the Universidad Católicade la Santisima Concepcion for the funds that allowedthe execution of laboratory tests for the current research,under the project framework “Investigation of the Stress-Strain-Behavior of Geogrid Reinforced Soil”. The firstauthor also wishes to specially thank Dipl.-Ing. AxelRuiken and the staff in the Geotechnics in ConstructionLaboratory in the RWTH-Aachen University.

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