Compaction processes in a tilled sandy soil · 2007-07-31 · Compaction processes in a tilled sandy soil Lesturgez, G. 1, 2; C. Hartmann 1; D. Tessier 2 and R. Poss 1 Keyword: sandy

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Session 4 “Physical properties of tropical sandy soils”

Compaction processes in a tilled sandy soil

Lesturgez, G. 1, 2; C. Hartmann 1; D. Tessier 2 and R. Poss 1

Keyword: sandy soil, oedometer, compaction, hydrocollapse, rearrangement

Abstract

Sandy soils are often considered as structurally inert because of their massive structure and the absenceof shrink-swell properties. Frequent and severe compaction observed in agricultural fields raises the questionof the processes and factors that control soil compaction and its reversibility. In the sandy upland soils ofNortheast Thailand, subsoil compaction (20-40 cm) is a common feature that impairs root development andtherefore is responsible for low crop production. The objective of this study was to determine the processesand factors that control soil compaction in order to improve soil management practices. Oedometer tests wereconducted on aggregate beds. An initial loose layer was prepared and was subsequently submitted toa compression pressure. Two parameters were controlled: (i) the mechanical compression pressure, and(ii) the water content. A first series of experiments was carried out on aggregate beds (i) under dry conditions,(ii) under wet conditions, and (iii) by wetting dry samples under constant compression pressures. A secondseries of experiments dealt with the application of compression-relaxation pressures to understand their roleon soil particle re-arrangement and to characterize soil elasticity.

Wet and dry compression curves appeared as envelopes delimiting the subsidence range. Results showedthat soil structure collapsed almost entirely under low pressure and the phenomenon started at very low watercontent. The subsequent compression-relaxation curves showed the absence of soil elasticity.

We used theses results as a framework to understand sandy soil behaviour in the field. The results canexplain why sandy soils are easily and inevitably compactable even under reduced traffic load. Because oflow soil elasticity and the close contact between the soil particles after compaction, we suggest that a smallbulk density increase can result in a high increase in penetration resistance, even in wet conditions. Weconclude that alternative and adapted techniques such as slotting or biological drilling are options to managethe sandy soils in order to preserve or even improve their physical properties.

1 IRD, UR176 SOLUTIONS, Land DevelopmentDepartment, Office of Science for Land Development,Phaholyothin Road, Chatuchak, Bangkok 10900, Thailand,[email protected]

2 INRA, Unité de Science du Sol, Centre de Recherche deVersailles-Grignon, Route de St-Cyr, 78026 Versailles,France.

Introduction

Soil compaction in agricultural systems isa worldwide concern and has received considerableattention over the past decades (Soane and vanOuwerkerk, 1994; Hamza and Anderson, 2005). Soilcompaction is defined as: “the process by which soilgrains are rearranged to decrease void space and bringthem into closer contact with one another, therebyincreasing the bulk density” (Soil Science Society ofAmerica, 1996). The vast majority of soil compactionin modern agriculture is often attributed to heavy

machinery and traffic load (Flowers and Lal, 1998).However other processes can be involved and soilcompaction may occur without traffic load on soilsurface. For example, the formation of a dense subsoillayer known as “fragipan” is interpreted by soilcollapse under its own weight. This process occurswhen a metastable arrangement of particles is wettedunder a constant confining pressure (weight of the toplayer in the case of natural collapse) (Assallay et al.,1997; 1998).

Sandy soils are often considered as structurallyinert because of their weak structure and the absenceof shrink-swell properties but frequent and severecompaction observed in agricultural fields raisesthe question of the processes and factors that controlsoil compaction and its reversibility. In the sandyupland soils of Northeast Thailand, subsoil compaction(20-40 cm) is a common feature that impairs root

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development and therefore is responsible for low cropproduction (Bruand et al., 2004). Comparisonsbetween forest and adjacent cultivated area haveproved that the compact layer commonly observed inagricultural fields was induced by intensive agricultureof the last decades (Lesturgez, 2005). Sandy soils ofthe region have developed mainly from light texturedaeolian material (Boonsener, 1991) well known for itsproblematic characteristics for engineering works(Udomchoke, 1991; Kohgo et al., 2000). On the otherhand, deep ploughing and subsoiling have always beeninefficient in overcoming this compaction inagricultural systems since soil re-compacts after thefirst heavy rain. This suggest that collapsibility is a keyfactor not only in deep profiles but also in thesuperficial and tilled layers (Hartmann et al., 1999;Hartmann et al., 2002).

Compaction of aggregates beds in a dry state,hydrocollapse (also known as hydroconsolidation)and load-upload cycles under the same pressure(traffic load conditions), can be involved in theformation or the reformation of a compact layer. Theobjective of the study was to investigate the processesof soil compaction in a tilled sandy soil subjected tonon-flooding rains and evaluate their respectivecontribution to total soil compaction. Experimentsfocussed on uniaxial compactability, hydrocollapse andrearrangement under traffic load.

Material and methods

Soil characteristics and sampling

The samples were collected in a sugarcane fieldlocated in Ban Phai District, 40-km from Khon KaenCity, Northeast Thailand (16°08′N, 102°44′E). Thechoice of the site was based on a previous investigationthat highlighted the presence of a compact layerlocated at 20-40 cm depth that was representative ofthe general situation of subsoil compaction (Lesturgez,2005). The soil has a sandy texture with no or veryweak structure. It belongs to the Nam Phong soil series(Imsamut and Boonsompoppan, 1999) and wasclassified as a loamy, siliceous, isohyperthermic ArenicHaplustalf (Soil Survey Staff, 1998) or Arenic Acrisol(FAO, 1998). Three undisturbed samples werecollected from the vertical face of a pit, respectively inthe topsoil (0-15 cm), in the compact subsoil (15-25 cm)and underneath the compact layer (40-50cm). Selectedchemical and physical characteristics of the samplesare presented in Table1. Mineralogical characteristicsof the studied soil were investigated using X-raydiffraction. When the sand and silt fractions were

exclusively constituted of quartz, the clay fractionincluded kaolinite, traces of illite and a significantproportion of small quartz particles. The three sampleswere identical in their mineralogy and the particle sizedistribution of the sand fraction. They differed onlyin their clay content (from 70gkg -1 in the topsoil to136 g kg-1 in the deepest layer). A last sample (puresand material) was prepared from the topsoil horizonby sieving the >50 µm material from the whole soilafter dispersion in sodium hexametaphosphate.

Sample preparation

The samples were manually crumbled in thelaboratory in order to produce small aggregates similarto tillage-induced aggregates. The aggregates werepoured into a ring 50mm in diameter , and 18mm inheight placed on a porous plate using a small funnelfixed 5-cm above the middle of the ring. The ring wasoverfilled, then the surface was carefully levelled off,and the assemblage thoroughly cleaned with a smallbrush. The assemblage was then installed in theoedometer and the top cap gently positioned.Preliminary tests had shown that the preparation of theaggregate beds using this method allowed theformation of a metastable arrangement of aggregateswith a bulk density similar to that of the topsoil afterploughing.

Design of the oedometer apparatus

The oedometer test is classically used forconsolidation and compression studies of fine-grainedsoil samples, such as clays and silts, since it recreatesthe conditions of volume change with zero lateral strain(i.e. one-dimensional compression). The oedometerapparatus used (Figure 1) allows the application ofan axial load that ranges from 0 to 1,500 kPa. Weapplied a range of 29 pressure steps (2, 5, 10, 15, 20,25, 30, 35, 40, 45, 50, 60, 70, 80, 90, 100, 150, 200,300, 400, 500, 600, 700, 800, 900, 1,000, 1,100, 1,300and 1,500 kPa), with 5 minutes interval between eachstep (minimum duration to reach equilibrium). Thechange in volume of the samples was recordedcontinuously by measuring the vertical displacement ofthe rigid top platen used to apply the load. The designof the apparatus allows the injection of water on the topof the sample. Drainage was free through the porousplate located below the sample. The volume of waterinjected into and drained from the samples can also berecorded. Bulk density and average water content werederived from these measurements. The backgroundnoise of the oedometer originating from internaldeformation (porous plates) and elasticity of the

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membrane was estimated during preliminary tests onuncompressible Plexiglas cylinders and results werecorrected accordingly.

We used the following experiment to characterizethe compaction in dry and wet conditions:

(a) To characterize the behaviour in dry conditions,an air-dried aggregate bed of the control and thethree horizons was prepared with five replicates.The series of pressure steps was applied and thechanges in bulk density recorded.

(b) To characterize the behaviour in a wet state, anidentical set of aggregate beds was prepared.The beds were saturated by injecting waterunder no load until drainage began at the bottomof the samples. The series of pressure steps wasthen applied while the samples were keptsaturated in a free draining state. The changes inbulk density were continuously recorded.

Hydroconsolidation tests

Hydroconsolidation is characterised by anabrupt change in bulk density of samples loaded attheir in situ water content and then flooded.Hydroconsolidation under a constant load Pw wasstudied in a three-stage test:

(a) Air-dried samples (5 repetitions for each depth)were loaded step by step to a constant load Pw

of 2, 100, 500 and 1,500kPa.

(b) While the axial load Pw was maintained on thesample, water was injected at 50mm 3min -1

through the porous plate located on the top ofthe sample until drainage started at the bottomof the porous plate.

(c) The load was then increased step by step on thewet samples from Pw to 1,500kPa. Watercontinued to be added freely at no pressure tokeep the sample wet until the end of the test.

Compression-relaxation tests

The purpose of this test was to characterisesubsequent compaction (i.e. rearrangement processes)under a series of identical axial loads in wet conditions.The test consisted of a series of compressions/relaxations applied on wet samples:

(a) Five samples of each horizon were saturated andthen loaded step by step to create stresses PR of100, 500 and 1,500kPa. Water was added freelyat no pressure to keep the samples wetthroughout the test.

(b) A series of 70 cycles of compression (PR) andrelaxation (0 kPa) was applied on the wetsamples. Bulk density was continuouslyrecorded.

Results

Figure 2 presents the compaction curves usingthe classical compaction approach. Both dry and wetbulk density measurements are presented as a functionof axial load. For the pure sand, compaction due toaxial load was very low over the range of pressures andthere was no significant difference between dry andwet curve (Figure 2-a). Compaction was low andhighly heterogeneous between replicates for the threesoil samples up to 25kPa. There was no significantdifference between the dry and wet samples in thisrange of pressures (Figure 2-b, c, d). Bulk densityincreased sharply above 25kPa and became morehomogeneous. Beyond 100 kPa, the bulk densityincreased with depth for any given load all soil samples(Figure 2-b, c, d). At 1,500kPa the dry bulk densitiesreached 1.60, 1.63 and 1.69 Mg.m-3 for the 0-15, 15-25and 40-50cm depths, respectively .

Figure 3 presents the results of the hydro-consolidation test on the pure sand material. Thecompaction either in the dry or wet state was almostinsignificant and there was no significant differencebetween the dry curve and the wet curve at anypressure. Therefore, the collapse was insignificant.

Figure 1. Oedometer apparatus

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sometimes significantly lower than that of the wetcurve (P <0.05). However, the difference was no moresignificant when the loads were increased afterhydrocollapse had occurred. As the dry and wetcompaction curves tend to get closer at high pressure,we can assume that for very high loads, no morecollapse will occur.

Figure 5 presents the changes in bulk densitywith increasing water content at constant load(Pw= 1,500 kPa) for the three soil horizons. Tworeplicates are presented for each depth as a means tohighlight heterogeneity. In agreement with the

Figure 2. Air-dried ( ) and wet ( ) compaction curves for (a) sand fraction, (b) 0-15 cm,(c) 25-35 cm, and (d) 40-50 cm. Average and standard deviation (n = 5)

Figure 3. Hydrocollapse curves for pure sand material

compaction in wet conditions, the lowest collapse wasrecorded for the 0-15cm depth sample, and theintensity of collapse increased with depth. Collapsealways occurred in a range of gravimetric soil moisturebetween 5 and 15%.

Figure 6 presents the compression-relaxationcurves. The bulk density increased by at least 0.1T .m-3

at PR=1,500kPa from the initial compaction to theend of rearrangement cycles. The soil samplespresented significant elasticity. The material recovereda significant proportion of the porosity when the axialpressure was relaxed but some of the deformation is

Figure 4 presents the resultsof the hydroconsolidation testtogether with the results of thecompaction test for the 25-35cmdepth layer. Collapse resulting fromwater injection (represented on thechart as white arrows), alwaysresulted in a final bulk densitybetween the dry and the wetcompaction values. The increase inbulk density as a result ofhydrocollapse was quite similarover the range 50 <Pw <1,500kPa,even though the largest bulkdensity change was recorded for anaxial load of 100kPa. The bulkdensity after hydrocollapse was

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non-reversible and the bulk density increased for eachcycle. The deformation intensity decreased as thenumber of cycles increased. The rearrangementintensity increased with depth. Similar results wereobtain at PR=100 and 500kPa (data not shown).

Discussion

Compaction of the pure sand

For the pure sand, the sensitivity to compaction,in dry and in wet conditions as well, was very small

locking between the grains (Lesturgez, 2005).

Compaction of soil samples

In contrast, the compaction curves recorded withthe soil samples in wet condition proved that the samesandy material mixed together with clay and silt washighly compactable. In dry conditions compactionstarted at around 25kPa and increased with increasingpressure until 1,500kPa. In the case of aggregate beds,collapse was in part the consequence of thedeformation of the aggregates (Faure, 1976). Thisprocess was not active in the pure sand material understudy because aggregates were absent. Dry compactionmay in part result from the deformation of clayparticles. However, the contribution of this processmust be limited, given the low clay content of thematerial (Table 1) and the high proportion of quartzgrains within the clay fraction (Bruand et al., 2004).The major contributing factor associated withcompaction was probably due to lubrication, theplanar-shaped clay minerals helping the sand grainsslip against each other.

Hydrocollapse

When water is injected in the samples,hydrocollapse proved to be a phenomenon that

Figure 4. Hydrocollapse curves for 23-35 cm soil sample

Table 1. Selected physical and chemical properties of the soil at the study site

Particle size distribution (g kg-1)BD (Mg m-3)

mesh equivalent diameter in µmpH

<2 2-20 20-50 50-200 200-500500- 1,000-

Mean SD1,000 2,000

10-15 cm 70 81 122 614 100 11 2 6.1 3.2 1.61 0.1325-35 cm 86 87 122 601 94 8 2 5.6 3.0 1.75 0.0440-50 cm 136 88 115 565 86 8 2 4.6 3.9 1.67 0.02

CEC is cation-exchange capacity measured in cobalt-hexamine, BD is dry bulk density measured in the field using cylinders and SDis standard deviation (n = 5).

CEC(cmolc kg-1)

Figure 5. Bulk density versus depth during collapse atPw = 1,500 kPa

and can be considered as beingindependent of the applied pressure(Figure 4). The sand grains did notreorganize under pressure, evenwhen wet. This result suggests thatthe lubricant effect of the water wasineffective in the case of thismaterial. Two factors can explainthis unusual behaviour. Firstly, thebulk density was already 1.46T m -3

at the beginning of the experiment,probably because the size of thesand grains was distributed overa large range (Table 1). Secondly,most sand grains had a jagged shapeaccording to them aeolian origin,that probably resulted in inter-

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developed fully under constant pressure and at anygiven pressure (Figure 3). Indeed, whatever the initialpressure, the final bulk density was almost identical tothe bulk density obtained by compaction in wetconditions. This result, consistent with the observationsof Assallay et al. (1998) on loess materials, has a directapplication in predicting the collapse. Maximumcollapse under any load can indeed be estimated by thedifference between the dry and wet compaction curvesunder the considered load. Maximum hydrocollapsewas recorded for Pw=200kPa, close to the value of100kPa observed by Assouline et al. (1997) onaggregate beds. It has been shown in aeolian depositsthat collapse needed a small amount of clay to develop(Rogers et al., 1994), and that collapse intensityincreased with clay content up to 25% clay (Assallayet al., 1998). The same increase in hydrocollapse withclay content was observed in this experiment, but therange of clay content covered by the three samples wasnot sufficient to determine a maximum value. Theincrease in water content with clay content forhydrocollapse to develop (Figure 5) suggests that theprocess is related to the hydration of the clay minerals.Faure (1976) mentioned the importance of the clayfraction in compaction of sandy soil and introduced thenotion of water potential and clay hydration. In thethree horizons hydrocollapse started between 3 and7% of gravimetric water content. This low watercontent proves that the phenomenon becomes active inany horizon as soon as it gets wet. The samplespresented a mechanical behaviour similar to metastabledeposits (Assallay et al., 1997). These properties,usually associated with loess and loess-like deposits(Jefferson et al., 2003), are therefore not confined tosilty materials and develop also in sandy soils.

Compression-relaxation cycles

The mathematical description of soil com-paction is based on relationships between bulk densityand applied stress (Assouline, 2002). This approachassumes that after a sample has been consolidatedunder a pressure P1, the consolidation would resumeonly for a pressure P2 >P1 (Guérif, 1982). This theoryis not applicable to the results of this study as a seriesof successive stresses under the same axial loadresulted in a substantial increase in bulk density(Figure 6). The relaxation between successive stressesallowed the internal friction between sand grains todecrease and therefore permitted the network of forcesto reorganise during the next axial load, leading toincreased bulk density. The asymptotic shape of thecurve showed the development of the soil structuretowards the highest possible bulk density. The

rearrangement test in a wet state is probably the mostrepresentative test to simulate vehicle traffic load as itmodels as series of confined uniaxial stresses under thesame pressure.

Contribution of the different processes to total soilcompaction

The contribution of dry compaction,hydrocollapse and compression-relaxation cycles tobulk density increase was estimated from our results ata load of 1,500kPa. The last series, namely “field” isthe bulk density measured in the field using cylinders(Figure 7). The effect of the three processes on bulkdensity increased with clay content. However, thecontribution of the three processes to bulk densityincrease remained similar in relative value whateverthe clay content. Dry compaction represented around50% of total compaction, when hydrocollapse andrearrangement ranged between 20 and 30%. In thefield dry compaction and hydrocollapse under lowpressure (weight of the upper soil horizons) are the firsttwo processes to develop after tillage. The many tillageoperations usual in the region induce through asuccession of traffic loads, rearranges the fabric toproduce the usual massive aspect of the soil with highbulk density. The close lay out of grains, with smallparticles filling the voids left between bigger ones, hasbeen described by Bruand et al. (2004) as the mainfactor of high resistance to penetration of the compactlayer. Finally, as soil sensitivity to compactionincreases with clay content and clay content increaseswith depth, the most sensitive horizons are the deepest.As a consequence the deeper the soil tillage, the higheris the risk of compaction and the final density. The bulkdensity is highest in the 20-40cm layer probablybecause this layer supports the wheels of the tractorsduring ploughing (at least three times a year). Surfaceaxial load due to vehicle traffic may also be transmittedto subsoil horizons through the massive and often dry

Figure 6. Bulk density during compression-relaxationcycles (0-1,500kPa)

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topsoil, increasing bulk density through rearrangementprocesses. In the field the highest bulk density valueswere recorded in the 20-40 cm (Figure 7) depthinterval despite the higher sensitivity to compaction ofthe lower horizon (Figure 2). Two kinds of tillageoperations are to distinguish: frequent tillage of the0-20 cm interval depth and some punctual deep tillageoperations with the objective to break the compactlayer. As the soil is highly collapsible and sensitive torearrangement, the density of the post-tilled layer reachinevitably high values as a function of time. Thefrequency of tillage in the topsoil (0-20cm) does notallow high density as in the 20-40cm interval depth asthe structure return frequently to the tilled state.However, the 20-40cm interval depth benefits as it hasthe enough time to accumulate the combine effect ofthe traffic load. As for the lower layers (>40 cm depth),tillage operation have never change organisation of thestructure and if aggregates beds from this layer arehighly sensitive, the actual weakly developed structureis stable. It has been shown that tilled layers are muchmore sensitive to compaction than massively structured

or already compacted subsoil (Schäfer-Landefeld et al.,2004). Porosity of this layer is mainly constituted ofbiopores which are usually stable because they developin a stable structure (Dexter, 1987; Bruand et al.,1996). These results suggest that the deeper the soil istilled, the higher is the risk in obtaining high bulkdensities. Deep tillage is therefore not an option torehabilitate compact subsoils due to the instability ofthe resulting structure. However, alternative techniquessuch as slotting (Hartmann et al., 1999) or biologicaldrilling (Lesturgez et al., 2004) have proved to beefficient is such unstable soils. These techniques ensurethe development of pathway for the roots through thecompact layer and preserve the massive and stablestructure surrounding them.

Conclusions

The compaction of the sandy material studiedunder uniaxial load was trivial, even in wet conditions.The same material was highly sensitive to compactionwhen mixed with silt and clay. The sensitivity tocompaction increased with increasing clay content.Compaction in the dry state, hydrocollapse (collapseunder increasing water content at constant pressure)and rearrangement under a series of successive loadswere more pronounced when clay content increased.However, the contribution of each phenomenon to finalbulk density was approximately constant whatever theclay content. Most part of soil compaction (around50%) was due to dry compaction. Hydrocollapseexplained about half of the remaining compaction.Hydrocollapse was responsible for sharp increases inbulk density as a result of small increases in watercontent (gravimetric water content between 3 and 7%),even under low pressure. The rearrangement undersuccessive loads explained 20 to 30% of the final bulkdensity, even though the bulk density was alreadyhigher than 1.65Mgm -3 after dry compaction andhydrocollapse. As clay content increased with depth,the deeper horizons were the most sensitive tocompaction. The highest bulk densities were howevermeasured in the 20-40cm layer in the field. The directtraffic load resulting from the many ploughings a yearusual in the region is probably a part of the explanationbut the structural effect of deep ploughing (whichchanged the massive structure of the layer intoa metastable organisation of aggregates very sensitiveto densification) is probably the main factor. Deeptillage is therefore not an option to rehabilitate compactsubsoils due to the instability of the resulting structureand alternative techniques conserving part of the initialstability are recommended.

Figure 7. Dry compaction, hydroconsolidation andrearrangement (compression-relaxation cycles for eachdepth at Pw = 1,500 kPa

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Acknowledgments

This work was part of a project funded by theInstitute of Research for Development (IRD), theDepartment of Technical and Economic Co-operation(DTEC) and the Land Development Department(LDD) under the approval of the National ResearchCouncil of Thailand (NRCT). The authors gratefullyacknowledge Andrew Noble (IWMI) and Ary Bruand(University of Orléans) for their helpful comments onthese data.

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Physical reorganization of sand due to the motion of a solid intruder

Kolb, E.1; E. Clément1; S. Douady2 and S. Courrech du Pont2

Keywords: model granular media, reorganizations of grains, force chains

Abstract

The sandy soil can be considered as an example of fragile matter from a physical point of view; ourapproaches are to identify the most simple elementary mechanisms responsible for the instability and thereorganization of the sandy structure and thus to characterize the physical parameters involved in theweakness of this type of soil. We thus use a very simple model of granular soil without any biological orchemical influences. The ability of an intruder to move in such a model granular media is a test of theresistance to reorganisation of a granular soil.

1 ESPCI/UPMC, PMMH (Laboratoire de Physiqueet Mécanique des Milieux Hétérogènes), Equipe Granulaires,10 rue Vauquelin, 75231 Paris Cédex 05 France, [email protected]

2 ENS, LPS, 24 rue Lhomond, 75 005 Paris, France

Introduction

Sandy soils are very unstable or evolvingmaterials, whose properties are not well known,making it thus difficult to manage for agriculturalpurposes. Due to the low content of clay, the cohesionbetween grains of the soil is low and the sandy soil canbe particularly sensitive to any external perturbation,whatever the origins are: climatic (intense rain,capillary rise) or anthropogenic (ploughing, mechanicalvibrations) for example. In this work, we areconsidering the sandy soil as an example of fragilematter from a physical point of view; our approachesare to identify the most simple elementary mechanismsresponsible for the instability and the reorganization ofthe sandy structure and thus to characterize thephysical parameters involved in the weakness of thistype of soil. We thus use a very simple model ofgranular soil without any biological or chemicalinfluences. This approach aims to test the part of thephysical influence in the instability of real soils.

In a first section, we will describe how wereduce the problem to model physical experiments andmention the characteristic features of dry granularmedia. In the second section we will describe in moredetails a particular experiment for testing the instabilityof a granular media. In particular the resistance toreorganisation of a granular medium is characterisedby the ability of an intruder to move in it. The strength

needed to displace it and the size of the reorganisationaround critically depends on the original packing ofgrains and could give information on the ability ofa worm or a root to penetrate this type of medium.

I – Model granular media for experiments

Granular matter we use in physics arecollections of grains of controlled dispersity, simpleform and known grain density (Fontainebleau sandmade of rounded grains of 300 µm of diameters,monodisperse glass beads or metallic ball-bearingbeads…). Their diameters are always larger than themicrometer, so that the thermal agitation does not playany role in the motion of the grains. Moreover, wechoose large diameters (of the order of 100 µm toseveral millimetric sizes) to minimize for example dragforces produced by the interstitial fluid (generally airin the porosity of the granular network) so that theinteractions are mediated through the direct contactsbetween grains. In the case of non-cohesive grains,these interactions are limited to collisions and contactforces, according to the duration of contact betweengrains.

Despite these drastic simplifications which seemto be very naive from a practical point of view, thevariety of phenomena observed with model granularmedia is very rich and still complex. We will describebelow the main features of a granular structure whichcould play a role in a real sandy soil.

The heterogeneity of forces

In granular materials, force is rarely transmitteduniformly, but rather preferentially along a network

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forming force chains. The network of contact forcescan be observed by photoelastic measurements (Figure 1)(Behringer). It appears to be very heterogeneous,forming chains along which the forces are particularlyintense encompassing regions bearing relatively smallloads. Then the description of the transmission offorces inside a granular medium is quite a greatchallenge where the inhomogeneity of the materialleads to unexpected behaviours.

The spatial distribution of forces is large, withfluctuations of the order of the mean force. Accordingto (Radjai et al., 1997) the network of contact forcescan be divided into 2 parts: the large network for forceslarger than the mean force bears most of the load witha stress tensor and angular distribution of contactdirections which is suited to oppose externalconstraints. On the other hand, the small force network(forces smaller than the mean force) shows isotropiccontact direction and a weak anisotropy of the stresstensor with the major principal axis oriented in sucha way that it opposes the buckling of large force chains(Clément, 1999).

These chains play an important role in many ofthe properties of the granular material, such as thetransmission of sound and the fragility of the packingalong particular directions (Cates et al., 1998).Generally the mesh size of the large force network isof the order of 10 grains, which is also the typical sizeof a shear band.

The history dependence

The protocol of preparation is particularlyimportant for granular materials and determines the

subsequent mechanical properties. For examplepreparing a dry sand pile by using a point source (sandfalling from a funnel) or a pluviation technique (sandfalling from a grid) leads to the same macroscopic pilewith a repose angle (angle between the slope of the pileand the horizontal) which is around 30° for both piles(Figure 2). However the measured pressure profiles onthe bottom below the sand piles are rather different.When the sand pile is built from a point source, thereis a dip of pressure below the apex of the pile, whilethere is a maximum of pressure when the pile isprepared by pluviation (Vanel et al., 1999). This drasticdifference in the pressure profiles can not be inferredfrom macroscopic properties like the angle of reposeand therefore the internal coefficient of friction is notsufficient for describing the mechanical properties ofa sand pile. Some microscopic parameters have to betaken into account.

The importance of preparation can act onpacking fraction but also on finer parameters like thedirections of contacts between grains and theorientations of the force network (De Gennes et al.,1999). The evolving nature of the mechanicalproperties of a granular medium can be illustrated bythe following experiment (Figure 3) where somephotoelastic discs are placed into a shear box. Initiallybefore applying the shear the medium is isotropic(there is no anisotropy in the orientations of contactdirections) and the response to a point force on top ofthe box is maximal along the direction of the force(applying a point force is a way to test the mechanicalproperties). However if the box is submitted to an

Figure 1. Force distribution network as observed ina photoelastic system with birefringent discs placed inbetween circular polarizers (Behringer)

Figure 2. Dimensionless normal stress profiles P/ρρρρρgHversus dimensionless radial distance r/R beneath conicalpiles of sand of height H and radius R. The preparationtechniques are illustrated by the corresponding photos onthe right side (top: point source; bottom: pluviation)(Vanel et al., 1999)

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initial preshear some new force chains are createdalong direction 1 which tend to oppose the shear. Anew “texture” is formed and the mechanical propertieshave changed, as it can be observed on the shift of theresponse to a point force (Atman et al., 2005).

The fragility

Granular materials as other particulate materialsare examples of fragile matter. For non-cohesive grainsthere is a lack of resistance of contact forces to anyextension. The internal structure (the contact and forcenetworks) can evolve and adapts itself to support theapplied load as we have seen before. Then theincremental response can be elastic only to“compatible” loads. Incompatible loads like the oneproduced for example by a change of compressionaxis, even if small, will cause finite, plasticreorganizations: irreversible rearrangements will beproduced in the structure (Cates et al., 1998).

The different scales

The approach used at a macroscopic scale in soilmechanics is usually based on standard compressionexperiments like triaxial tests, from which constitutiverelations between stresses, deformations and directionsof deformations are obtained. In this approach, the soilcan be considered as an effective continuum mediumbut the constitutive elasto-plastic relations betweenstresses and strains inferred from these tests are mostlynon-linear, piece-wise, anisotropic and cruciallydepend on the history of the loading/unloading cycles(Clément, 1999).

The problem of granular materials is that thereis no clear separation between microscopic andmacroscopic scales, from the size of the micrometricasperities in the surface area of contact of grains tothe mesoscopic scale of force chains and till the

macroscopic size of the bulk material of soil. Thereforemany scales are involved in the resulting mechanicalproperties and microscopic rearrangements can havea drastic effect on macroscopic properties. This is thereason why we perform the following experiment.

II – Experiment on reorganizations in a granularmedium due to a solid intrusion

In this part we describe in more detailsa conceptually simple experiment (Kolb et al., 2004).It consists in testing the local resistance of a granularmaterial by moving an intruder in it. From a practicalpoint of view it bears similarities with standardpenetrometry tests currently used in soil mechanics.

However we want to focus here on themicroscopic perturbation introduced by themeasurement itself, which is a consequence of thefragile nature of granular material. The network ofcontacts between grains is not permanent and theperturbation induced by the motion of an intruder(which can be a rough model for the growth of a rootor the progression of a worm) can open or close somecontacts and produce some irreversible rearrangementsthat change the nature of the granular structure itselfand thus of the complementary porous matrix, whataffects its mechanical properties at a larger scale.Therefore we want to characterize the rearrangementsinduced by the displacement of the intruder and therange of the effect of perturbation inside the granularmaterial. Thus we apply a local and cyclic perturbationinside the granular packing for both detectingthe displacements of grains in the vicinity ofthe perturbation and characterizing the evolutionof the structure by investigating the irreversibledisplacements after a given number of cycles ofperturbation.

Experimental setup

For this purpose we use a 2 dimensional (2D)granular media. That means the motions of grains canonly occur inside a plane, there is no influence of thethird dimension. Once again it is an oversimplificationof a real sandy soil but it gives some hints on themicro-reorganizations of granular material because the2D geometry allows to directly follow the motion ofeach grain by simply using a camera above the setup.More precisely the grains are not beads but smallmetallic hollow cylinders whose form is adapted tothe 2D geometry: the axis of the cylinders areperpendicular to the plane of motion (see Figure 4right part) The cylinders have two different outerdiameters d1 = 4 mm and d2 = 5 mm. Mixing 2 types

Figure 3. Importance of the microscopic scale on themechanical propertiesLeft: schematic of the shear box.Middle: Visualisation of contact forces between grains byuse of photoelastic grains.Right: Mean response to a point force applied along thedirection of the arrow. The intensity of the mean stressgrows when it is darker (Atman et al. 2005).

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of grains leads to a disordered granular media byavoiding crystallization, i.e. regular stacking of thegrains. This is done in purpose for obtaining genericresults. The inner diameters of the cylinders are alsodifferent, which allows a proper determination of thetype of grains for further image analysis.

Around 4,000 such grains in an equal proportionin mass of the two types of cylinders are piled up ontoan inclinable plane (Figure 4 left part). All cylindershave a 3-mm height and lye on this plane (a lowfrictional glass plate allowing a backward illumination)without rocking. The lateral and bottom walls are madeof Plexiglas and delimits a rectangular frame of L =26.8 cm (54 d2) width and an adjustable height oftypically H = 34.4 cm (70 d2). The 2D packing fractionc defined as the ratio of the surface of grains to thetotal surface they occupy is then c = 0.749 ±0.004.

For the experiment the bottom plane is tilted atan angle ø (see Figure 4 inset of the right part) suchas to control the confinement pressure inside thegranular material by an effective gravity field gsin øwhere g is the gravity acceleration. A value of ø = 33°is chosen for being larger than the static Coulombangle of friction between the grains and the glass platewhich is around θ = 20° (µgrain/glass = tan θ is the staticfriction coefficient between grains and glass).Therefore the grains spontaneously move downward ifthey have the possibility to find a place below.

The intruder is a big grain of diameter d2 locatedin the median part of the container at a 21.2 cm (i.e.42 d2) depth from the upper free surface. The intruderis attached to a rigid arm in Plexiglas (reinforced bymetallic parts) moved by a translation stage anda stepping motor driven by a computer. The armmotion takes place along the median axis Y of thecontainer and is parallel to the plane. In this report we

use an intruder displacement value U0 of a fraction ofa grain diameter (U0 = 1.25 mm ≈ d2 /3) giving a typicalstrain less than 10-2, far above the elastic limit but alsofar below the usual fully developed plasticity domainwhere shear bands appear. The intruder is moving upthen down to its first position and then again up anddown and so on with always the same amplitudeof displacement U0, thus performing cycles ofdisplacements in a quasi-static way. The up and downmotions along the Y-axis are separated by rest periodsduring which pictures with a high resolution CCDcamera (1280*1024 pixels2) are taken. The imageframe is centered slightly above the intruder and coversa zone of area 39 d2*31 d2 (see Figure 4 right part).

In the following, we use the notation i for theindex corresponding to the ith image just before the ith

displacement of the intruder (upward or downward)and n for the cycle number with n = int[{i+1}/2] whereint is the integer part. For each image i, the center ofeach grain is determined with precision using thecomputation of the correlation on grey-levels betweenan image of the packing and two reference imagescorresponding to both grain types (d1 and d2). Note thatthe inner diameter of the cylindrical hole, which isdifferent for each grain type (small or big), helpscrucially for the proper determination of the centre andof the grain type. Hence, we obtain, for each image, thelocations of more than a thousand grains with aresolution down to 0.05 pixels. The displacement ofeach single grain is then calculated by the differencebetween its position in image i and in image j. Thismethod allows a precision of less than 10 µm (d2 /600)for the displacements. Thus we obtain 2 types ofinformations:

� the displacement field in response to an upwardor downward intruder motion (also called theresponse function) by comparing images i andi+1.

� the irreversible displacement field by comparingimages i and i+2. (Between images i and i+2the intruder has accomplished a cycle ofdisplacement but some grains don’t come backto their first positions; they have undergoneirreversible displacements).

Experimental results

Displacement fields as a response to the motion of theintruder

The displacements fields have been computedfor 16 independent realizations prepared in the same

Figure 4. Left: Experimental setup. Right: typicalframe of observation of the piling. The intruder is belowthe black point (inset: sketch of the experimental setupviewed from the side)

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way. We plot in Figure 5 the displacement of grainsinduced by an upward motion of the intruder(the figure presents the response obtained in the caseof the second upward motion of the intruder, forexample). We observe that the amplitudes ofdisplacements are very small and that there is someredirection effect towards the lateral walls, but the mostimportant point is that the grains that move are notobligatory close to the intruder and that theperturbation due to the solid intruder has a long rangeeffect. The second point is that the displacement fieldis very sensitive to the particular organization of grainsand probably linked to the force network of eachconfiguration.

We can extract from these results a meanbehaviour by averaging over the 16 realizations insidelittle binning cells of size 1.2 d2*1.2 d2 regularly locatedin the Cartesian coordinates (O, X, Y) reference frame.

This gives the mean displacement field presented inFigure 6. We clearly notice that the granular motion isnot localized in the vicinity of the intruder and that thissmall perturbation of only one third of a grain diameterindeed produces a far field effect. Furthermore, thepresence of two displacement rolls is observed near theintruder. They are located symmetrically on each sideof the intruder but turn in opposite directions. Besidesthis near field effect, the main response principallyoccurs above the intruder with displacement vectorsthat tend to align along the radial directions from theintruder.

The typical decay of the response with the radialdistance r from the intruder is analysed. After severalcycles the response to an upward perturbation exhibitsa 1/ra dependence where a is close to 1, what can bemodelled by the following relation (eq.1):

(eq.1)

This relation is valid in the upper part above theintruder for a distance larger than 7 d2 (far enough fromthe rolls). The function f (θ) of the polar angle θ(defined in Figure 4) has a typical bell shape with itsmaximum value for θ = 0 corresponding to thedirection of the intruder motion. The dimensionlessparameter bi gives the amplitude of the response for theith intruder motion.

Evolution of the response with the number of cycles:reversibility/irreversibility

We followed the evolution of the response (viathe parameter bi ) with the number of cycles or

Figure 5. Displacements fields observed for the secondupward motion of the intruder (i = 3 or n = 2) for twoindependent realizations a and b. The point correspondsto the location of the intruder. All displacements havebeen magnified by a factor of 50 and the scales are givenin pixels. The intruder is initially located in X = 0, Y = 0before its upward motion

Figure 6. Mean upward displacement field for thesecond upward motion of the intruder (i = 3 or n = 2). Alldisplacements have been magnified by a factor of 70. Thecoordinates are expressed in unity of a big grainsize d2

ui ≈ bi U0 d2 f (θ)

er↑→ →

r

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grains inside a specific surface and the so called“tapping one’’ consisting in tapping the walls of theinclined container just before beginning theexperiment. Note that the initial mean packing fractionis c = 0.750 ±0.002 for tapping preparation so thatthere is no significant change of ø compared with thefirst preparation described before (called the normalone).

However the effects on the subsequent responseobserved by mean of the displacement field arequite visible as it can be observed on Figure 7 withgrey-levels corresponding to different amplitudes ofdisplacements. We clearly observe that the response isenhanced and more directive in the direction of gravityfor the tapping preparation. In both cases, changes inmean packing fraction along the experiments are lessthan 1/1,000 and they certainly would not explain suchdifferences in the evolution process. It is then naturalto look for the influence of local configurationparameters such as the evolution of contact directiondistribution or other texture parameters at the level ofthe grains. This analysis reveals that a difference couldbe observed between the 2 types of preparation only ifwe compare the mean coordination number (the meannumber of contacts per grain), which is a microscopicparameter at the level of the contact size.

Conclusion

We experimentally determine the reorganisationfield due to a small localised cyclic displacementapplied to a packing of hard grains under gravitymodelling the physical parameters that could beinvolved in a sandy soil. We surprisingly find that thedisplacement fields in response to the small localperturbation are quite long range in the direction of theperturbation and quite evolving. We also propose herenew results on the effect of a slight difference in thepreparation procedure: We compare the evolution ofthe response function along the cycling procedure andwe show that the initial configurations prepared eitherby random mixing of grains at constant surface orunder a weak tapping have a clearly different responseeven though the mean packing fraction obtained inthese two cases are extremely close. Not only the firstresponse but also the further evolution during thecycling procedure is different, showing that there isstill a memory effect of the initial preparation aftermany cycles. With this experiment we want toemphasize the role of microscopic rearrangements inthe stability of a granular packing.

Figure 7. Mean upward displacement field for normal(above) and tapping (below) preparations for the9th cycle. The grey-level code corresponds to differentamplitude of displacements given in pixels. 33 pixelscorrespond to the diameter of a big grain d2

equivalently with i: the parameter bi decreasesprogressively with i and then saturates to a constantvalue after about 60 displacements, i.e. 30 cycles. Eachcycle of motion of the intruder produces someirreversible displacements of grains, and then thestructure of the material changes and the followingresponse to the next motion of the intruder is different.Note that in spite of these irreversible displacementsmainly downward in the direction of gravity, there isno detectable increase of the mean packing fraction(averaged over the 16 experiments) with the number ofcycles n: it stays constant with a relative error of 0.1%.But after n ≈ 30 cycles, both mean responses forupward and downward motions of the intruder arealmost identical: a quasi-stationary regime or “limitcycle’’ is obtained and the packing seems to be morestable with regard to the perturbation.

Dependence on preparation

We now compare 2 modes of preparation: theoriginal one obtained by random initial mixing of

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References

Atman A.P.F.; Brunet P.; Geng J.; Reydellet G.; Claudin P.;Behringer R.P.; Clément E. 2005. From the stressresponse function (back) to the sand pile«dip». The European Physical Journal E-Soft Matter,17, nº1, 93-100.

Behringer R.P. http://www.phy.duke.edu/research/ltb/ltbgroup.html

Cates M.E.; Wittmer J.P.; Bouchaud J.-P.; Claudin. P. 1998.Jamming, Force Chains, and Fragile Matter. PhysicalReview Letters, 81, 1841-1844.

Clément E. 1999. Rheology of granular media. CurrentOpinion in Colloid & Interface Science, 4, 294-299.

De Gennes P.G. 1999. Granular Matter: a tentative view.Reviews of Modern Physics, Vol. 71, Nº2, Centenary1999.

Jaeger H.; Nagel S.; Behringer R.P. 1996. The physics ofgranular materials. Physics Today, April 1996.

Kolb. E; Cviklinski J.; Lanuza J.; Claudin P.; Clément E.2004. Reorganization of a dense granular assembly:the unjamming response function. Physical Review E,69, 0313061-0313065.

Radjai F.; Wolf D.E.; Jean M.; Moreau J.J. 1997. Bimodalcharacter of stress transmission in Granular Packings.Physical Review Letters, 80, 61-64.

Vanel L.; Howell D.; Clark D.; Behringer R.P.; Clément E.1999. Memories in sand: Experimental tests ofconstruction history on stress distributions undersandpiles. Physical Review E, 60, 5040-5043.

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